Finite Group Databasebeta

← #33259001

Subgroups — #33259001

Order 18688.

2404 conjugacy classes of subgroups.

The subgroup lattice has 1668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989186C211yesmaximal, characteristic, complemented
2C2×#17989177C211yesmaximal, characteristic, complemented
3#22618305C211yesmaximal, characteristic, complemented
4#22618299C211yesmaximal, characteristic, complemented
5#22618264C211yesmaximal, characteristic, complemented
6#22618235C211yesmaximal, characteristic, complemented
7#22616097C211yesmaximal, characteristic, complemented
8#22616086C211yesmaximal, characteristic, complemented
9#22616075C211yesmaximal, characteristic, complemented
10#22616064C211yesmaximal, characteristic, complemented
11#22615082C211yesmaximal, characteristic, complemented
12#22615067C211yesmaximal, characteristic, complemented
13#22615052C211yesmaximal, characteristic, complemented
14#22615037C211yesmaximal, characteristic, complemented
15#22614891C211yesmaximal, characteristic, complemented
16#22614857C211yesmaximal, characteristic, complemented
17#22614823C211yesmaximal, characteristic, complemented
18#22614637C211yesmaximal, characteristic, complemented
19#22614607C211yesmaximal, characteristic, complemented
20#22614263C211yesmaximal, characteristic, complemented
21#22614064C211yesmaximal, characteristic, complemented
22#22613940C211yesmaximal, characteristic, complemented
23#22613901C211yesmaximal, characteristic, complemented
24#22613480C211yesmaximal, characteristic, complemented
25#22613465C211yesmaximal, characteristic, complemented
26#22612599C211yesmaximal, characteristic, complemented
27#22612588C211yesmaximal, characteristic, complemented
28#22612437C211yesmaximal, characteristic, complemented
29C2×#17988476C211yesmaximal, characteristic, complemented
30C4×#14556551C211yesmaximal, characteristic, complemented
31C73×#2549C211yesmaximal, characteristic, complemented
32#17989186—28no—
33#17989177—28no—
34C2×#14556586C2211yescharacteristic
35C2×#14556586C2211yescharacteristic
36C2×#14556586C2211yescharacteristic, complemented
37C2×#14556586C2211yescharacteristic, complemented
38C2×#14556582C2211yescharacteristic, complemented
39C2×#14556582C2211yescharacteristic, complemented
40C2×#14556580C2211yescharacteristic
41C2×#14556580C2211yescharacteristic
42C2×#14556580C2211yescharacteristic
43C2×#14556576C2211yescharacteristic
44C2×#14556576C2211yescharacteristic
45C2×#14556576C2211yescharacteristic, complemented
46C2×#14556576C2211yescharacteristic, complemented
47C2×#14556575C2211yescharacteristic
48C2×#14556575C2211yescharacteristic
49C2×#14556575C2211yescharacteristic
50C2×#14556567C2211yescharacteristic, complemented
51C2×#14556567C2211yescharacteristic, complemented
52C2×#14556566C2211yescharacteristic
53C2×#14556566C2211yescharacteristic
54C2×#14556566C2211yescharacteristic
55C2×#14556565C2211yescharacteristic
56C2×#14556565C2211yescharacteristic
57C2×#14556565C2211yescharacteristic
58C2×#14556561C2211yescharacteristic
59C2×#14556561C2211yescharacteristic
60C2×#14556561C2211yescharacteristic
61C2×#14556553C2211yescharacteristic, complemented
62C2×C4×C22⋊D73C2211yescharacteristic
63C2×#14556551C2211yescharacteristic
64C2×#14556551C2211yescharacteristic
65C2×#14556551C2211yescharacteristic
66C2×#14556551C2211yescharacteristic
67C22×#11924007C2211yescharacteristic
68C22×#11924005C2211yescharacteristic
69C22×#11924005C2211yescharacteristic
70C22×#11924005C2211yescharacteristic
71C22×C4×Dic73C2211yescharacteristic
72C2×C42×D73C2211yescharacteristic, complemented
73#17988526C2211yescharacteristic, complemented
74#17988526C2211yescharacteristic, complemented
75#17988524C2211yescharacteristic
76#17988524C2211yescharacteristic
77#17988519C2211yescharacteristic, complemented
78#17988519C2211yescharacteristic, complemented
79#17988514C2211yescharacteristic, complemented
80#17988514C2211yescharacteristic, complemented
81#17988513C2211yescharacteristic
82#17988513C2211yescharacteristic, complemented
83#17988509C2211yescharacteristic
84#17988509C2211yescharacteristic
85#17988509C2211yescharacteristic
86#17988509C2211yescharacteristic, complemented
87#17988505C2211yescharacteristic
88#17988505C2211yescharacteristic, complemented
89#17988504C2211yescharacteristic
90#17988504C2211yescharacteristic
91#17988504C2211yescharacteristic
92#17988504C2211yescharacteristic
93#17988504C2211yescharacteristic
94#17988504C2211yescharacteristic, complemented
95#17988498C2211yescharacteristic
96#17988498C2211yescharacteristic, complemented
97#17988497C2211yescharacteristic
98#17988497C2211yescharacteristic
99#17988497C2211yescharacteristic
100#17988497C2211yescharacteristic, complemented
101#17988494C2211yescharacteristic, complemented
102#17988489C2211yescharacteristic
103#17988489C2211yescharacteristic
104#17988489C2211yescharacteristic
105#17988489C2211yescharacteristic
106#17988488C2211yescharacteristic
107#17988488C2211yescharacteristic
108#17988488C2211yescharacteristic
109#17988488C2211yescharacteristic
110#17988488C2211yescharacteristic, complemented
111#17988486C2211yescharacteristic, complemented
112#17988483C2211yescharacteristic, complemented
113#17988483C2211yescharacteristic, complemented
114#17988483C2211yescharacteristic, complemented
115#17988479C2211yescharacteristic
116#17988479C2211yescharacteristic
117#17988479C2211yescharacteristic
118#17988479C2211yescharacteristic, complemented
119#17988479C2211yescharacteristic, complemented
120#17988479C2211yescharacteristic, complemented
121#17988477C2211yescharacteristic
122#17988477C2211yescharacteristic
123#17988477C2211yescharacteristic
124#17988477C2211yescharacteristic
125#17988477C2211yescharacteristic, complemented
126#17988477C2211yescharacteristic, complemented
127#17988476C2211yescharacteristic
128#17988476C2211yescharacteristic
129#17988476C2211yescharacteristic
130#17988476C2211yescharacteristic
131#17988476C2211yescharacteristic
132#17988476C2211yescharacteristic
133#17988476C2211yescharacteristic
134#17988476C2211yescharacteristic
135#17988476C2211yescharacteristic
136#17988476C2211yescharacteristic
137#17988476C2211yescharacteristic, complemented
138#17988476C2211yescharacteristic, complemented
139#17988476C2211yescharacteristic, complemented
140#17988476C2211yescharacteristic, complemented
141#17988470C2211yescharacteristic, complemented
142#17988470C2211yescharacteristic, complemented
143#17988466C2211yescharacteristic
144#17988466C2211yescharacteristic
145#17988465C2211yescharacteristic
146#17988465C2211yescharacteristic
147#17988465C2211yescharacteristic
148#17988465C2211yescharacteristic
149#17988465C2211yescharacteristic
150#17988465C2211yescharacteristic, complemented
151#17988465C2211yescharacteristic, complemented
152#17988465C2211yescharacteristic, complemented
153#17988464C2211yescharacteristic
154#17988464C2211yescharacteristic
155#17988458C2211yescharacteristic, complemented
156#17988458C2211yescharacteristic, complemented
157#17988452C2211yescharacteristic, complemented
158#17988448C2211yescharacteristic
159#17988444C2211yescharacteristic, complemented
160#17988442C2211yescharacteristic
161C4⋊C4×Dic73C2211yescharacteristic, complemented
162C4×#11924007C2211yescharacteristic, complemented
163#17988438C2211yescharacteristic, complemented
164#17988438C2211yescharacteristic, complemented
165C22⋊C4×Dic73C2211yescharacteristic
166C22⋊C4×Dic73C2211yescharacteristic
167C4×#11924005C2211yescharacteristic, complemented
168#17988434C2211yescharacteristic, complemented
169#17988434C2211yescharacteristic, complemented
170#17988434C2211yescharacteristic, complemented
171#17988434C2211yescharacteristic, complemented
172C2×#14556498C2211yescharacteristic
173C42×Dic73C2211yescharacteristic, complemented
174C2×C22⋊Q8×C73C2211yescharacteristic
175C2×C22⋊Q8×C73C2211yescharacteristic
176#398×C73C2211yescharacteristic, complemented
177#398×C73C2211yescharacteristic, complemented
178#395×C73C2211yescharacteristic, complemented
179#395×C73C2211yescharacteristic, complemented
180#391×C73C2211yescharacteristic, complemented
181#391×C73C2211yescharacteristic, complemented
182#389×C73C2211yescharacteristic, complemented
183#389×C73C2211yescharacteristic, complemented
184#385×C73C2211yescharacteristic
185#385×C73C2211yescharacteristic
186#380×C73C2211yescharacteristic
187C4×C22⋊C4×C73C2211yescharacteristic
188C2×#95×C73C2211yescharacteristic
189C24×D73C2311yescharacteristic
190C22×D292C2311yescharacteristic
191C22×D292C2311yescharacteristic
192C22×D292C2311yescharacteristic
193C22×D292C2311yescharacteristic
194C22×D292C2311yescharacteristic
195C22×D292C2311yescharacteristic
196C22×D292C2311yescharacteristic
197C22×D292C2311yescharacteristic
198C22×D292C2311yescharacteristic
199C22×C22⋊D73C2311yescharacteristic
200C22×C22⋊D73C2311yescharacteristic
201C22×C22⋊D73C2311yescharacteristic
202C23×Dic73C2311yescharacteristic
203C23×Dic73C2311yescharacteristic
204C23×Dic73C2311yescharacteristic
205C22×C4×D73C2311yescharacteristic
206C22×C4×D73C2311yescharacteristic
207C22×C4×D73C2311yescharacteristic
208C22×C4×D73C2311yescharacteristic
209C22×C4×D73C2311yescharacteristic
210#14556586—24no—
211#14556586—24no—
212#14556586—24no—
213#14556586—24no—
214#14556582—24no—
215#14556582—24no—
216#14556580—24no—
217#14556580—24no—
218#14556580—42no—
219#14556576—24no—
220#14556576—24no—
221#14556576—24no—
222#14556576—24no—
223#14556575—24no—
224#14556575—24no—
225#14556575—24no—
226#14556567—24no—
227#14556567—24no—
228#14556566—24no—
229#14556566—24no—
230#14556566—42no—
231#14556565—24no—
232#14556565—24no—
233#14556565—24no—
234#14556561—24no—
235#14556561—24no—
236#14556561—24no—
237#14556553—42no—
238C4×C22⋊D73—24no—
239#14556551—24no—
240#14556551—24no—
241#14556551—24no—
242#14556551D418yescomplemented
243C2×C4⋊Dic73C2311yescharacteristic
244C2×C4⋊Dic73C2311yescharacteristic
245C2×C4⋊Dic73C2311yescharacteristic
246C2×C4⋊Dic73C2311yescharacteristic
247C2×C4⋊Dic73C2311yescharacteristic
248C2×C4⋊Dic73C2311yescharacteristic
249C2×C4⋊Dic73C2311yescharacteristic
250C2×C4⋊Dic73C2311yescharacteristic
251C2×C4⋊Dic73C2311yescharacteristic
252C2×#11924007—24no—
253C2×#11924007C2311yescharacteristic
254C2×#11924007C2311yescharacteristic
255C2×#11924007C2311yescharacteristic
256C2×#11924007C2311yescharacteristic
257C2×#11924007C2311yescharacteristic
258C2×#11924007C2311yescharacteristic
259C2×#11924007C2311yescharacteristic
260C2×#11924007C2311yescharacteristic
261C2×#11924007C2311yescharacteristic
262C2×C22⋊Dic73C2311yescharacteristic
263C2×#11924005—24no—
264C2×#11924005—24no—
265C2×#11924005—42no—
266C2×#11924005C2311yescharacteristic
267C2×#11924005C2311yescharacteristic
268C2×#11924005C2311yescharacteristic
269C2×#11924005C2311yescharacteristic
270C2×#11924005C2311yescharacteristic
271C2×#11924005C2311yescharacteristic
272C2×#11924005C2311yescharacteristic
273C2×#11924005C2311yescharacteristic
274C2×#11924005C2311yescharacteristic
275C2×#11924005C2311yescharacteristic
276C2×#11924005C2311yescharacteristic
277C2×#11924005C2311yescharacteristic
278C2×#11924005C2311yescharacteristic
279C2×#11924005C2311yescharacteristic
280C2×#11924005C2311yescharacteristic
281C2×#11924005C2311yescharacteristic
282C2×#11924005C2311yescharacteristic
283C2×#11924005C2311yescharacteristic
284C2×#11924005C2311yescharacteristic
285C2×#11924005C2311yescharacteristic
286C2×#11924005C2311yescharacteristic
287C2×#11924005C2311yescharacteristic
288C2×#11924005C2311yescharacteristic
289C2×#11924005C2311yescharacteristic
290C2×#11924005C2311yescharacteristic
291C2×#11924005C2311yescharacteristic
292C2×#11924005C2311yescharacteristic
293C2×#11924005C2311yescharacteristic
294C2×#11924005C2311yescharacteristic
295C2×#11924005C2311yescharacteristic
296C2×#11924005C2311yescharacteristic
297C2×#11924005C2311yescharacteristic
298C2×#11924005C2311yescharacteristic
299C2×#11924005C2311yescharacteristic
300C2×#11924005C2311yescharacteristic
301C2×#11924005C2311yescharacteristic
302C2×#11924005C2311yescharacteristic
303C2×#11924005C2311yescharacteristic
304C2×#11924005C2311yescharacteristic
305C2×#11924005C2311yescharacteristic
306C2×#11924005C2311yescharacteristic
307C2×#11924005C2311yescharacteristic
308C2×#11924005C2311yescharacteristic
309C2×#11924005C2311yescharacteristic
310C2×#11924005C2311yescharacteristic
311C2×#11924005C2311yescharacteristic
312C2×#11924005C2311yescharacteristic
313C2×C4×Dic73—42no—
314C2×C4×Dic73C2311yescharacteristic
315C2×C4×Dic73C2311yescharacteristic
316C2×C4×Dic73C2311yescharacteristic
317C2×C4×Dic73C2311yescharacteristic
318C2×C4×Dic73C2311yescharacteristic
319C2×C4×Dic73C2311yescharacteristic
320C2×C4×Dic73C2311yescharacteristic
321C2×C4×Dic73C2311yescharacteristic
322C2×C4×Dic73C2311yescharacteristic
323C2×C4×Dic73C2311yescharacteristic
324C2×C4×Dic73C2311yescharacteristic
325C2×C4×Dic73C2311yescharacteristic
326C2×C4×Dic73C2311yescharacteristic
327C42×D73—42no—
328#14556498C2311yescharacteristic
329#14556498C2311yescharacteristic
330#14556498C2311yescharacteristic
331#14556498C2311yescharacteristic
332#14556498C2311yescharacteristic
333#14556498C2311yescharacteristic
334#14556498C2311yescharacteristic
335#14556498C2311yescharacteristic
336#14556498C2311yescharacteristic
337#14556498C2311yescharacteristic
338#14556498C2311yescharacteristic
339#14556498C2311yescharacteristic
340#14556498C2311yescharacteristic
341#14556498C2311yescharacteristic
342#14556498C2311yescharacteristic
343#14556498C2311yescharacteristic
344#14556498C2311yescharacteristic
345#14556498C2311yescharacteristic
346#14556498C2311yescharacteristic
347#14556498C2311yescharacteristic
348C22×Q8×C73C2311yescharacteristic
349C22×Q8×C73C2311yescharacteristic
350C23×C4×C73C2311yescharacteristic
351C23×C4×C73C2311yescharacteristic
352C23×C4×C73C2311yescharacteristic
353C22⋊Q8×C73—24no—
354C22⋊Q8×C73—24no—
355C2×C4⋊C4×C73C2311yescharacteristic
356C2×C4⋊C4×C73C2311yescharacteristic
357C2×C4⋊C4×C73C2311yescharacteristic
358C2×C4⋊C4×C73C2311yescharacteristic
359C2×C4⋊C4×C73C2311yescharacteristic
360C2×C4⋊C4×C73C2311yescharacteristic
361C2×C4⋊C4×C73C2311yescharacteristic
362C2×C4⋊C4×C73C2311yescharacteristic
363C2×C4⋊C4×C73C2311yescharacteristic
364C2×C4⋊C4×C73C2311yescharacteristic
365C2×C4⋊C4×C73C2311yescharacteristic
366C2×C4⋊C4×C73C2311yescharacteristic
367C2×C22⋊C4×C73C2311yescharacteristic
368C2×C22⋊C4×C73C2311yescharacteristic
369C2×C22⋊C4×C73C2311yescharacteristic
370C2×C22⋊C4×C73C2311yescharacteristic
371C2×C42×C73C2311yescharacteristic
372C2×C42×C73C2311yescharacteristic
373#95×C73C2311yescharacteristic
374#95×C73C2311yescharacteristic
375#95×C73C2311yescharacteristic
376#95×C73C2311yescharacteristic
377#95×C73C2311yescharacteristic
378#95×C73C2311yescharacteristic
379#95×C73C2311yescharacteristic
380#95×C73C2311yescharacteristic
381#95×C73C2311yescharacteristic
382#95×C73C2311yescharacteristic
383#95×C73C2311yescharacteristic
384#95×C73C2311yescharacteristic
385C23×D73—22no—
386C23×D73—22no—
387C23×D73—22no—
388C23×D73—41no—
389C23×D73—41no—
390C23×D73—41no—
391C23×D73—41no—
392C23×D73C2411yescharacteristic
393C23×D73C2411yescharacteristic
394C23×D73C2411yescharacteristic
395C23×D73C2411yescharacteristic
396C23×D73C2411yescharacteristic
397C2×D292—22no—
398C2×D292—22no—
399C2×D292—22no—
400C2×D292—22no—
401C2×D292—22no—
402C2×D292—22no—
403C2×D292—22no—
404C2×D292—22no—
405C2×D292—22no—
406C2×D292—41no—
407C2×D292—41no—
408C2×D292—41no—
409C2×D292—41no—
410C2×D292—41no—
411C2×D292—41no—
412C2×D292—41no—
413C2×D292—41no—
414C2×D292—41no—
415C2×D292—41no—
416C2×D292—41no—
417C2×D292—41no—
418C2×D292—41no—
419C2×D292—41no—
420C2×D292—41no—
421C2×D292—41no—
422C2×D292—41no—
423C2×D292—41no—
424C2×C22⋊D73—22no—
425C2×C22⋊D73—22no—
426C2×C22⋊D73—22no—
427C2×C22⋊D73—22no—
428C2×C22⋊D73—22no—
429C2×C22⋊D73—22no—
430C2×C22⋊D73—22no—
431C2×C22⋊D73—22no—
432C2×C22⋊D73C2×D414yes—
433C22×Dic73—22no—
434C22×Dic73—22no—
435C22×Dic73—22no—
436C22×Dic73—22no—
437C22×Dic73—22no—
438C22×Dic73—41no—
439C22×Dic73—41no—
440C22×Dic73—41no—
441C22×Dic73C2×D414yes—
442C22×Dic73C2411yescharacteristic
443C22×Dic73C2411yescharacteristic
444C22×Dic73C2411yescharacteristic
445C22×Dic73C2411yescharacteristic
446C22×Dic73C2411yescharacteristic
447C22×Dic73C2411yescharacteristic
448C22×Dic73C2411yescharacteristic
449C22×Dic73C2411yescharacteristic
450C22×Dic73C2411yescharacteristic
451C22×Dic73C2411yescharacteristic
452C22×Dic73C2411yescharacteristic
453C2×C4×D73—22no—
454C2×C4×D73—22no—
455C2×C4×D73—22no—
456C2×C4×D73—22no—
457C2×C4×D73—22no—
458C2×C4×D73—41no—
459C2×C4×D73—41no—
460C2×C4×D73—41no—
461C2×C4×D73—41no—
462C2×C4×D73—41no—
463C2×C4×D73—41no—
464C2×C4×D73—41no—
465C2×C4×D73—41no—
466C2×C4×D73—41no—
467C2×C4×D73C2×D414yes—
468C4⋊Dic73—22no—
469C4⋊Dic73—22no—
470C4⋊Dic73—22no—
471C4⋊Dic73—22no—
472C4⋊Dic73—22no—
473C4⋊Dic73—22no—
474C4⋊Dic73—22no—
475C4⋊Dic73—22no—
476C4⋊Dic73—22no—
477#11924007—22no—
478#11924007—22no—
479#11924007—22no—
480#11924007—22no—
481#11924007—22no—
482#11924007—22no—
483#11924007—22no—
484#11924007—22no—
485#11924007C2×D414yes—
486C22⋊Dic73—22no—
487#11924005—22no—
488#11924005—22no—
489#11924005—22no—
490#11924005—22no—
491#11924005—22no—
492#11924005—22no—
493#11924005—22no—
494#11924005—22no—
495#11924005—22no—
496#11924005—22no—
497#11924005—22no—
498#11924005—22no—
499#11924005—22no—
500#11924005—22no—
501#11924005—22no—
502#11924005—22no—
503#11924005—22no—
504#11924005—22no—
505#11924005—22no—
506#11924005—22no—
507#11924005—22no—
508#11924005—22no—
509#11924005—22no—
510#11924005—22no—
511#11924005—22no—
512#11924005—22no—
513#11924005—22no—
514#11924005—22no—
515#11924005—22no—
516#11924005—22no—
517#11924005—22no—
518#11924005—22no—
519#11924005—22no—
520#11924005—22no—
521#11924005—41no—
522#11924005—41no—
523#11924005—41no—
524#11924005—41no—
525#11924005—41no—
526#11924005—41no—
527#11924005—41no—
528#11924005—41no—
529#11924005—41no—
530#11924005—41no—
531#11924005—41no—
532#11924005—41no—
533#11924005C2×D414yes—
534C4×Dic73—22no—
535C4×Dic73—22no—
536C4×Dic73—22no—
537C4×Dic73—22no—
538C4×Dic73—22no—
539C4×Dic73—22no—
540C4×Dic73—22no—
541C4×Dic73—41no—
542C4×Dic73—41no—
543C4×Dic73—41no—
544C4×Dic73—41no—
545C4×Dic73—41no—
546C4×Dic73C2×D414yes—
547C24×C73C2411yescharacteristic
548C2×Q8×C73—22no—
549C2×Q8×C73—22no—
550C2×Q8×C73—41no—
551C2×Q8×C73—41no—
552C2×Q8×C73—41no—
553C2×Q8×C73—41no—
554C22×C4×C73—22no—
555C22×C4×C73—22no—
556C22×C4×C73—41no—
557C22×C4×C73—41no—
558C22×C4×C73—41no—
559C22×C4×C73—41no—
560C22×C4×C73—41no—
561C22×C4×C73—41no—
562C22×C4×C73#4114yes—
563C22×C4×C73C2411yescharacteristic
564C22×C4×C73C2411yescharacteristic
565C22×C4×C73C2411yescharacteristic
566C22×C4×C73C2411yescharacteristic
567C22×C4×C73C2411yescharacteristic
568C22×C4×C73C2411yescharacteristic
569C22×C4×C73C2411yescharacteristic
570C22×C4×C73C2411yescharacteristic
571C22×C4×C73C2411yescharacteristic
572C22×C4×C73C2411yescharacteristic
573C22×C4×C73C2411yescharacteristic
574C22×C4×C73C2411yescharacteristic
575C22×C4×C73C2411yescharacteristic
576C22×C4×C73C2411yescharacteristic
577C4⋊C4×C73—22no—
578C4⋊C4×C73—22no—
579C4⋊C4×C73—22no—
580C4⋊C4×C73—22no—
581C4⋊C4×C73—22no—
582C4⋊C4×C73—22no—
583C4⋊C4×C73—41no—
584C4⋊C4×C73—41no—
585C4⋊C4×C73—41no—
586C4⋊C4×C73—41no—
587C4⋊C4×C73—41no—
588C4⋊C4×C73—41no—
589C22⋊C4×C73—22no—
590C22⋊C4×C73—22no—
591C22⋊C4×C73C2×D414yes—
592C22⋊C4×C73#4114yes—
593C42×C73—41no—
594C42×C73—41no—
595C23×C73—21no—
596C23×C73—21no—
597C23×C73—21no—
598C23×C73—21no—
599C23×C73C22×D412yes—
600C23×C73C2×#4112yes—
601C23×C73C2×#4112yes—
602C23×C73C2511yescharacteristic
603C22×D73—21no—
604C22×D73—21no—
605C22×D73—21no—
606C22×D73—21no—
607C22×D73—21no—
608C22×D73—21no—
609C22×D73—21no—
610C22×D73—21no—
611C22×D73—21no—
612C22×D73—21no—
613C22×D73—21no—
614C22×D73—21no—
615C22×D73—21no—
616C22×D73—21no—
617C22×D73—21no—
618C22×D73—21no—
619C22×D73—21no—
620C22×D73—21no—
621C22×D73—21no—
622C22×D73—21no—
623C22×D73—21no—
624C22×D73—21no—
625C22×D73—21no—
626C22×D73—21no—
627C22×D73—21no—
628C22×D73—21no—
629C22×D73—21no—
630C22×D73—21no—
631C22×D73—21no—
632C22×D73—21no—
633C22×D73—21no—
634C22×D73—21no—
635C22×D73—21no—
636C22×D73—21no—
637C22×D73—44no—
638C22×D73—44no—
639C22×D73—44no—
640C22×D73—82no—
641C22×D73—82no—
642C22×D73—82no—
643C22×D73—82no—
644C22×D73C22×D412yes—
645Q8×C73—82no—
646Q8×C73—82no—
647C2×C4×C73—21no—
648C2×C4×C73—21no—
649C2×C4×C73—21no—
650C2×C4×C73—21no—
651C2×C4×C73—21no—
652C2×C4×C73—21no—
653C2×C4×C73—21no—
654C2×C4×C73—21no—
655C2×C4×C73—21no—
656C2×C4×C73—21no—
657C2×C4×C73—21no—
658C2×C4×C73—21no—
659C2×C4×C73—21no—
660C2×C4×C73—21no—
661C2×C4×C73—21no—
662C2×C4×C73—21no—
663C2×C4×C73—21no—
664C2×C4×C73—21no—
665C2×C4×C73—21no—
666C2×C4×C73—21no—
667C2×C4×C73—21no—
668C2×C4×C73—21no—
669C2×C4×C73—21no—
670C2×C4×C73—21no—
671C2×C4×C73—21no—
672C2×C4×C73—21no—
673C2×C4×C73—21no—
674C2×C4×C73—21no—
675C2×C4×C73—21no—
676C2×C4×C73—21no—
677C2×C4×C73—21no—
678C2×C4×C73—21no—
679C2×C4×C73—21no—
680C2×C4×C73—21no—
681C2×C4×C73—21no—
682C2×C4×C73—21no—
683C2×C4×C73—44no—
684C2×C4×C73—82no—
685C2×C4×C73—82no—
686C2×C4×C73C22×D412yes—
687C2×C4×C73C22×D412yes—
688C2×C4×C73C2×#4112yes—
689C2×C4×C73C2×#4112yes—
690C2×C4×C73C2×#4112yes—
691C2×C4×C73C2×#4112yes—
692C22⋊D73—28no—
693C22⋊D73—44no—
694C22⋊D73—44no—
695C2×Dic73—21no—
696C2×Dic73—21no—
697C2×Dic73—21no—
698C2×Dic73—21no—
699C2×Dic73—21no—
700C2×Dic73—21no—
701C2×Dic73—21no—
702C2×Dic73—21no—
703C2×Dic73—21no—
704C2×Dic73—21no—
705C2×Dic73—21no—
706C2×Dic73—21no—
707C2×Dic73—21no—
708C2×Dic73—21no—
709C2×Dic73—21no—
710C2×Dic73—21no—
711C2×Dic73—21no—
712C2×Dic73—21no—
713C2×Dic73—21no—
714C2×Dic73—21no—
715C2×Dic73—21no—
716C2×Dic73—21no—
717C2×Dic73—21no—
718C2×Dic73—21no—
719C2×Dic73—21no—
720C2×Dic73—21no—
721C2×Dic73—21no—
722C2×Dic73—21no—
723C2×Dic73—21no—
724C2×Dic73—44no—
725C2×Dic73—44no—
726C2×Dic73—44no—
727C2×Dic73C22×D412yes—
728C2×Dic73C22×D412yes—
729C2×Dic73C22×D412yes—
730C2×Dic73H(5,𝔽2)12yes—
731D292—44no—
732D292—82no—
733D292—82no—
734D292—82no—
735D292—82no—
736D292—82no—
737D292—82no—
738D292—82no—
739D292—82no—
740C4×D73—44no—
741C4×D73—44no—
742C4×D73—44no—
743C4×D73—82no—
744C4×D73—82no—
745C22×C73—22no—
746C22×C73—22no—
747C22×C73—22no—
748C22×C73—22no—
749C22×C73—22no—
750C22×C73—22no—
751C22×C73#53214yes—
752C22×C73C23×D411yescharacteristic
753C22×C73C22×#4111yescharacteristic
754C22×C73C22×#4111yescharacteristic
755C22×C73C2×H(5,𝔽2)11yescharacteristic
756C22×C73#58511yescharacteristic
757C22×C73#58511yescharacteristic
758C22×C73#58511yescharacteristic
759C2×D73—22no—
760C2×D73—22no—
761C2×D73—22no—
762C2×D73—41no—
763C2×D73—41no—
764C2×D73—41no—
765C2×D73—41no—
766C2×D73—41no—
767C2×D73—41no—
768C2×D73—41no—
769C2×D73—41no—
770C2×D73—41no—
771C2×D73—41no—
772C2×D73—41no—
773C2×D73—41no—
774C2×D73—41no—
775C2×D73—41no—
776C2×D73—41no—
777C2×D73—41no—
778C2×D73—41no—
779C2×D73—41no—
780C2×D73—41no—
781C2×D73—41no—
782C2×D73—41no—
783C2×D73—41no—
784C2×D73—41no—
785C2×D73—41no—
786C2×D73—41no—
787C2×D73—41no—
788C2×D73—41no—
789C2×D73—41no—
790C2×D73—41no—
791C2×D73—41no—
792C2×D73—41no—
793C2×D73—41no—
794C2×D73—88no—
795C4×C73—22no—
796C4×C73—22no—
797C4×C73—22no—
798C4×C73—22no—
799C4×C73—22no—
800C4×C73—22no—
801C4×C73—41no—
802C4×C73—41no—
803C4×C73—41no—
804C4×C73—41no—
805C4×C73—41no—
806C4×C73—41no—
807C4×C73—41no—
808C4×C73—41no—
809Dic73—22no—
810Dic73—22no—
811Dic73—22no—
812Dic73—22no—
813Dic73—41no—
814Dic73—41no—
815Dic73—41no—
816Dic73—41no—
817Dic73—41no—
818Dic73—41no—
819Dic73—41no—
820#35009—731nomaximal, Sylow
821C2×C73—24no—
822C2×C73C2×#53211yescharacteristic
823C2×C73#345511yescharacteristic
824C2×C73#345911yescharacteristic
825C2×C73#349611yescharacteristic
826C2×C73#350011yescharacteristic
827C2×C73#351311yescharacteristic
828C2×C73#352111yescharacteristic
829D73—42no—
830D73—81no—
831D73—81no—
832D73—81no—
833D73—81no—
834C2×#539—731no—
835C2×#538—731no—
836#2861—731no—
837#2860—731no—
838#2854—731no—
839#2850—731no—
840#2664—731no—
841#2663—731no—
842#2662—731no—
843#2661—731no—
844#2560—731no—
845#2559—731no—
846#2558—731no—
847#2557—731no—
848#2549D7311yescharacteristic, complemented
849#2543—731no—
850#2539—731no—
851#2534—731no—
852#2521—731no—
853#2519—731no—
854#2488—731no—
855#2472—731no—
856#2464—731no—
857#2461—731no—
858#2425—731no—
859#2424—731no—
860#2322—731no—
861#2321—731no—
862C4×#121—731no—
863C2×#388—731no—
864C42×D4—731no—
865C73#3500911yescharacteristic, complemented, Sylow
866#539—1468no—
867#538—1468no—
868C2×#126—731no—
869C2×#126—731no—
870C2×#126—731no—
871C2×#126—731no—
872C2×#125—731no—
873C2×#125—731no—
874C2×#124—731no—
875C2×#124—731no—
876C2×#124—731no—
877C2×#123—731no—
878C2×#123—731no—
879C2×#123—731no—
880C2×#123—731no—
881C2×#123—731no—
882C2×#123—731no—
883C2×#123—731no—
884C2×C22⋊Q8—731no—
885C2×C22⋊Q8—731no—
886C2×C22⋊Q8C2×D7311yescharacteristic
887C2×C22⋊Q8C2×D7311yescharacteristic
888C2×#121—731no—
889C2×#121—731no—
890C2×#121—731no—
891C2×#121—731no—
892C2×#121—731no—
893C2×#121—731no—
894C2×#120—731no—
895C2×#120—731no—
896C2×#120—731no—
897C2×C4×D4—731no—
898C2×C4×D4—731no—
899C2×C4×D4—731no—
900C2×C4×D4—731no—
901C2×C4×D4—731no—
902C2×C4×D4—731no—
903C22×C4⋊C4—731no—
904C22×C22⋊C4—731no—
905C22×C22⋊C4—731no—
906C22×C22⋊C4—731no—
907C22×C42—731no—
908C22×C42—731no—
909#400—731no—
910#400—731no—
911#399—731no—
912#399—731no—
913#398—731no—
914#398—731no—
915#398C2×D7311yescharacteristic, complemented
916#398C2×D7311yescharacteristic, complemented
917#397—731no—
918#397—731no—
919#397—731no—
920#397—731no—
921#396—731no—
922#396—731no—
923#396—731no—
924#396—731no—
925#395C2×D7311yescharacteristic, complemented
926#395C2×D7311yescharacteristic, complemented
927#394—731no—
928#394—731no—
929#394—731no—
930#394—731no—
931#394—731no—
932#394—731no—
933#394—731no—
934#394—731no—
935#393—731no—
936#393—731no—
937#392—731no—
938#392—731no—
939#392—731no—
940#392—731no—
941#391—731no—
942#391C2×D7311yescharacteristic, complemented
943#391C2×D7311yescharacteristic, complemented
944#390—731no—
945#390—731no—
946#390—731no—
947#390—731no—
948#390—731no—
949#390—731no—
950#390—731no—
951#390—731no—
952#390—731no—
953#389—731no—
954#389—731no—
955#389—731no—
956#389—731no—
957#389C2×D7311yescharacteristic, complemented
958#389C2×D7311yescharacteristic, complemented
959#388—731no—
960#388—731no—
961#388—731no—
962#388—731no—
963#388—731no—
964#388—731no—
965#388—731no—
966#388—731no—
967#388—731no—
968#388—731no—
969#388—731no—
970#388—731no—
971#388—731no—
972#388—731no—
973#388—731no—
974#388—731no—
975#388—731no—
976#388—731no—
977#388—731no—
978#388—731no—
979#388—731no—
980#388—731no—
981#388—731no—
982#388—731no—
983#388—731no—
984#388—731no—
985#387—731no—
986#387—731no—
987#386—731no—
988#386—731no—
989#386—731no—
990#386—731no—
991#386—731no—
992#386—731no—
993#386—731no—
994#386—731no—
995#386—731no—
996#386—731no—
997#386—731no—
998#386—731no—
999#385—731no—
1000#385—731no—
1001#385C2×D7311yescharacteristic
1002#385C2×D7311yescharacteristic
1003#382—731no—
1004#381—731no—
1005#380—731no—
1006#380C2×D7311yescharacteristic
1007#379—731no—
1008C4×C4⋊C4—731no—
1009C4×C4⋊C4—731no—
1010C4×C4⋊C4—731no—
1011C4×C4⋊C4—731no—
1012C4×C22⋊C4—731no—
1013C4×C22⋊C4—731no—
1014C4×C22⋊C4—731no—
1015C4×C22⋊C4—731no—
1016C4×C22⋊C4—731no—
1017C4×C22⋊C4—731no—
1018C4×C22⋊C4—731no—
1019C4×C22⋊C4C2×D7311yescharacteristic
1020C2×#95—731no—
1021C2×#95C2×D7311yescharacteristic
1022C43—731no—
1023C25—731no—
1024C22×Q8C22×D7311yescharacteristic
1025C22×Q8C22×D7311yescharacteristic
1026C22×D4—731no—
1027C22×D4—731no—
1028C22×D4—731no—
1029C22×D4—731no—
1030C22×D4—731no—
1031C22×D4—731no—
1032C22×D4—731no—
1033C22×D4—731no—
1034C22×D4—731no—
1035C22×D4—731no—
1036C22×D4—731no—
1037C22×D4—731no—
1038C23×C4—731no—
1039C23×C4—731no—
1040C23×C4—731no—
1041C23×C4—731no—
1042C23×C4—731no—
1043C23×C4—731no—
1044C23×C4—731no—
1045C23×C4—731no—
1046C23×C4C22×D7311yescharacteristic
1047C23×C4C22×D7311yescharacteristic
1048C23×C4C22×D7311yescharacteristic
1049#126—1464no—
1050#126—1464no—
1051#126—1464no—
1052#126—1464no—
1053#125—1464no—
1054#125—1464no—
1055#124—2922no—
1056#124—1464no—
1057#124—1464no—
1058#123—1464no—
1059#123—1464no—
1060#123—1464no—
1061#123—1464no—
1062#123—1464no—
1063#123—1464no—
1064#123—1464no—
1065C22⋊Q8—24no—
1066C22⋊Q8—24no—
1067C22⋊Q8—1464no—
1068C22⋊Q8—1464no—
1069#121—2922no—
1070#121—1464no—
1071#121—1464no—
1072#121—1464no—
1073#121—1464no—
1074#121—1464no—
1075#120—1464no—
1076#120—1464no—
1077#120—1464no—
1078C4×D4—2922no—
1079C4×D4—738no—
1080C4×D4—1464no—
1081C4×D4—1464no—
1082C4×D4—1464no—
1083C4×D4—1464no—
1084C2×C4⋊C4—731no—
1085C2×C4⋊C4—731no—
1086C2×C4⋊C4—731no—
1087C2×C4⋊C4—731no—
1088C2×C4⋊C4—731no—
1089C2×C4⋊C4—731no—
1090C2×C4⋊C4—731no—
1091C2×C4⋊C4—731no—
1092C2×C4⋊C4—731no—
1093C2×C4⋊C4—731no—
1094C2×C4⋊C4—731no—
1095C2×C4⋊C4—731no—
1096C2×C4⋊C4—731no—
1097C2×C4⋊C4—731no—
1098C2×C4⋊C4—731no—
1099C2×C4⋊C4—731no—
1100C2×C4⋊C4—731no—
1101C2×C4⋊C4—731no—
1102C2×C4⋊C4—1464no—
1103C2×C4⋊C4C22×D7311yescharacteristic
1104C2×C4⋊C4C22×D7311yescharacteristic
1105C2×C4⋊C4C22×D7311yescharacteristic
1106C2×C4⋊C4C22×D7311yescharacteristic
1107C2×C4⋊C4C22×D7311yescharacteristic
1108C2×C4⋊C4C22×D7311yescharacteristic
1109C2×C4⋊C4C22×D7311yescharacteristic
1110C2×C4⋊C4C22×D7311yescharacteristic
1111C2×C4⋊C4C22×D7311yescharacteristic
1112C2×C4⋊C4C22×D7311yescharacteristic
1113C2×C4⋊C4C22×D7311yescharacteristic
1114C2×C4⋊C4C22×D7311yescharacteristic
1115C2×C22⋊C4—2922no—
1116C2×C22⋊C4—731no—
1117C2×C22⋊C4—731no—
1118C2×C22⋊C4—731no—
1119C2×C22⋊C4—731no—
1120C2×C22⋊C4—731no—
1121C2×C22⋊C4—731no—
1122C2×C22⋊C4—731no—
1123C2×C22⋊C4—731no—
1124C2×C22⋊C4—731no—
1125C2×C22⋊C4—731no—
1126C2×C22⋊C4—731no—
1127C2×C22⋊C4—731no—
1128C2×C22⋊C4—731no—
1129C2×C22⋊C4—731no—
1130C2×C22⋊C4—731no—
1131C2×C22⋊C4—731no—
1132C2×C22⋊C4—731no—
1133C2×C22⋊C4—731no—
1134C2×C22⋊C4—731no—
1135C2×C22⋊C4—731no—
1136C2×C22⋊C4—731no—
1137C2×C22⋊C4—731no—
1138C2×C22⋊C4—731no—
1139C2×C22⋊C4—731no—
1140C2×C22⋊C4—731no—
1141C2×C22⋊C4—731no—
1142C2×C22⋊C4—731no—
1143C2×C22⋊C4—731no—
1144C2×C22⋊C4—731no—
1145C2×C22⋊C4—731no—
1146C2×C22⋊C4—731no—
1147C2×C22⋊C4—731no—
1148C2×C22⋊C4—731no—
1149C2×C22⋊C4—731no—
1150C2×C22⋊C4—731no—
1151C2×C22⋊C4—731no—
1152C2×C22⋊C4—731no—
1153C2×C22⋊C4—731no—
1154C2×C22⋊C4—731no—
1155C2×C22⋊C4—731no—
1156C2×C22⋊C4—731no—
1157C2×C22⋊C4—731no—
1158C2×C22⋊C4—731no—
1159C2×C22⋊C4—731no—
1160C2×C22⋊C4—731no—
1161C2×C22⋊C4—731no—
1162C2×C22⋊C4—731no—
1163C2×C22⋊C4—731no—
1164C2×C22⋊C4—1464no—
1165C2×C22⋊C4—1464no—
1166C2×C22⋊C4C22×D7311yescharacteristic
1167C2×C22⋊C4C22×D7311yescharacteristic
1168C2×C22⋊C4C22×D7311yescharacteristic
1169C2×C22⋊C4C22×D7311yescharacteristic
1170C2×C42—2922no—
1171C2×C42—2922no—
1172C2×C42—731no—
1173C2×C42—731no—
1174C2×C42—731no—
1175C2×C42—731no—
1176C2×C42—731no—
1177C2×C42—731no—
1178C2×C42—731no—
1179C2×C42—731no—
1180C2×C42—731no—
1181C2×C42—731no—
1182C2×C42—731no—
1183C2×C42—731no—
1184C2×C42—731no—
1185C2×C42C22×D7311yescharacteristic
1186C2×C42C22×D7311yescharacteristic
1187#95—731no—
1188#95—731no—
1189#95—731no—
1190#95—731no—
1191#95—731no—
1192#95—731no—
1193#95—731no—
1194#95—731no—
1195#95—731no—
1196#95—731no—
1197#95—731no—
1198#95—731no—
1199#95—731no—
1200#95—731no—
1201#95—731no—
1202#95—731no—
1203#95—731no—
1204#95—731no—
1205#95—731no—
1206#95—731no—
1207#95C22×D7311yescharacteristic
1208#95C22×D7311yescharacteristic
1209#95C22×D7311yescharacteristic
1210#95C22×D7311yescharacteristic
1211#95C22×D7311yescharacteristic
1212#95C22×D7311yescharacteristic
1213#95C22×D7311yescharacteristic
1214#95C22×D7311yescharacteristic
1215#95C22×D7311yescharacteristic
1216#95C22×D7311yescharacteristic
1217#95C22×D7311yescharacteristic
1218#95C22×D7311yescharacteristic
1219C24—2921no—
1220C24—2921no—
1221C24—2921no—
1222C24—2921no—
1223C24—731no—
1224C24—731no—
1225C24—731no—
1226C24—731no—
1227C24—731no—
1228C24—1462no—
1229C24—1462no—
1230C24—1462no—
1231C24C23×D7311yescharacteristic
1232C2×Q8—22no—
1233C2×Q8—22no—
1234C2×Q8—41no—
1235C2×Q8—41no—
1236C2×Q8—41no—
1237C2×Q8—41no—
1238C2×D4—2921no—
1239C2×D4—2921no—
1240C2×D4—2921no—
1241C2×D4—2921no—
1242C2×D4—2921no—
1243C2×D4—2921no—
1244C2×D4—2921no—
1245C2×D4—2921no—
1246C2×D4—2921no—
1247C2×D4—2921no—
1248C2×D4—2921no—
1249C2×D4—2921no—
1250C2×D4—2921no—
1251C2×D4—2921no—
1252C2×D4—2921no—
1253C2×D4—2921no—
1254C2×D4—2921no—
1255C2×D4—2921no—
1256C2×D4—734no—
1257C2×D4—1462no—
1258C2×D4—1462no—
1259C2×D4—1462no—
1260C2×D4—1462no—
1261C2×D4—1462no—
1262C2×D4—1462no—
1263C2×D4—1462no—
1264C2×D4—1462no—
1265C2×D4—1462no—
1266C2×D4—1462no—
1267C2×D4—1462no—
1268C2×D4—1462no—
1269C2×D4—1462no—
1270C2×D4—1462no—
1271C2×D4—1462no—
1272C2×D4—1462no—
1273C2×D4—1462no—
1274C22×C4—22no—
1275C22×C4—22no—
1276C22×C4—41no—
1277C22×C4—41no—
1278C22×C4—41no—
1279C22×C4—41no—
1280C22×C4—41no—
1281C22×C4—41no—
1282C22×C4—2921no—
1283C22×C4—2921no—
1284C22×C4—2921no—
1285C22×C4—2921no—
1286C22×C4—2921no—
1287C22×C4—2921no—
1288C22×C4—2921no—
1289C22×C4—2921no—
1290C22×C4—2921no—
1291C22×C4—2921no—
1292C22×C4—2921no—
1293C22×C4—2921no—
1294C22×C4—734no—
1295C22×C4—734no—
1296C22×C4—731no—
1297C22×C4—731no—
1298C22×C4—731no—
1299C22×C4—731no—
1300C22×C4—731no—
1301C22×C4—731no—
1302C22×C4—731no—
1303C22×C4—731no—
1304C22×C4—731no—
1305C22×C4—731no—
1306C22×C4—731no—
1307C22×C4—1462no—
1308C22×C4—1462no—
1309C22×C4—1462no—
1310C22×C4—1462no—
1311C22×C4—1462no—
1312C22×C4—1462no—
1313C22×C4—1462no—
1314C22×C4—1462no—
1315C22×C4—1462no—
1316C22×C4—1462no—
1317C22×C4#1192402914yes—
1318C22×C4C23×D7311yescharacteristic
1319C22×C4C23×D7311yescharacteristic
1320C22×C4C23×D7311yescharacteristic
1321C22×C4C23×D7311yescharacteristic
1322C22×C4C23×D7311yescharacteristic
1323C22×C4C23×D7311yescharacteristic
1324C22×C4C23×D7311yescharacteristic
1325C22×C4C23×D7311yescharacteristic
1326C22×C4C23×D7311yescharacteristic
1327C22×C4C23×D7311yescharacteristic
1328C22×C4C23×D7311yescharacteristic
1329C22×C4C23×D7311yescharacteristic
1330C22×C4C23×D7311yescharacteristic
1331C22×C4C23×D7311yescharacteristic
1332C4⋊C4—22no—
1333C4⋊C4—22no—
1334C4⋊C4—22no—
1335C4⋊C4—22no—
1336C4⋊C4—22no—
1337C4⋊C4—22no—
1338C4⋊C4—41no—
1339C4⋊C4—41no—
1340C4⋊C4—41no—
1341C4⋊C4—41no—
1342C4⋊C4—41no—
1343C4⋊C4—41no—
1344C4⋊C4—734no—
1345C4⋊C4—1462no—
1346C4⋊C4—1462no—
1347C4⋊C4—1462no—
1348C4⋊C4—1462no—
1349C4⋊C4—1462no—
1350C4⋊C4—1462no—
1351C4⋊C4—1462no—
1352C4⋊C4—1462no—
1353C4⋊C4—1462no—
1354C4⋊C4—1462no—
1355C4⋊C4—1462no—
1356C4⋊C4—1462no—
1357C4⋊C4—1462no—
1358C4⋊C4—1462no—
1359C4⋊C4—1462no—
1360C4⋊C4—1462no—
1361C4⋊C4—1462no—
1362C22⋊C4—22no—
1363C22⋊C4—22no—
1364C22⋊C4—2921no—
1365C22⋊C4—2921no—
1366C22⋊C4—2921no—
1367C22⋊C4—2921no—
1368C22⋊C4—2921no—
1369C22⋊C4—2921no—
1370C22⋊C4—2921no—
1371C22⋊C4—2921no—
1372C22⋊C4—2921no—
1373C22⋊C4—2921no—
1374C22⋊C4—2921no—
1375C22⋊C4—2921no—
1376C22⋊C4—734no—
1377C22⋊C4—1462no—
1378C22⋊C4—1462no—
1379C22⋊C4—1462no—
1380C22⋊C4—1462no—
1381C22⋊C4—1462no—
1382C22⋊C4—1462no—
1383C22⋊C4—1462no—
1384C22⋊C4—1462no—
1385C22⋊C4—1462no—
1386C22⋊C4—1462no—
1387C22⋊C4—1462no—
1388C22⋊C4—1462no—
1389C22⋊C4—1462no—
1390C22⋊C4—1462no—
1391C22⋊C4—1462no—
1392C22⋊C4—1462no—
1393C22⋊C4—1462no—
1394C22⋊C4—1462no—
1395C22⋊C4—1462no—
1396C22⋊C4—1462no—
1397C22⋊C4—1462no—
1398C22⋊C4—1462no—
1399C22⋊C4—1462no—
1400C22⋊C4—1462no—
1401C22⋊C4—1462no—
1402C22⋊C4—1462no—
1403C22⋊C4—1462no—
1404C22⋊C4—1462no—
1405C22⋊C4—1462no—
1406C22⋊C4—1462no—
1407C22⋊C4—1462no—
1408C22⋊C4—1462no—
1409C22⋊C4—1462no—
1410C22⋊C4—1462no—
1411C22⋊C4—1462no—
1412C22⋊C4D4×D7314yes—
1413C22⋊C4#1192402914yes—
1414C42—41no—
1415C42—41no—
1416C42—2921no—
1417C42—2921no—
1418C42—2921no—
1419C42—2921no—
1420C42—2921no—
1421C42—734no—
1422C42—1462no—
1423C42—1462no—
1424C42—1462no—
1425C42—1462no—
1426C42—1462no—
1427C42—1462no—
1428C42—1462no—
1429C23—21no—
1430C23—21no—
1431C23—21no—
1432C23—21no—
1433C23—2924no—
1434C23—2924no—
1435C23—2924no—
1436C23—5842no—
1437C23—5842no—
1438C23—5842no—
1439C23—5842no—
1440C23—732no—
1441C23—1461no—
1442C23—1461no—
1443C23—1461no—
1444C23—1461no—
1445C23—1461no—
1446C23—1461no—
1447C23—1461no—
1448C23—1461no—
1449C23—1461no—
1450C23—1461no—
1451C23—1461no—
1452C23—1461no—
1453C23—1461no—
1454C23—1461no—
1455C23—1461no—
1456C23—1461no—
1457C23—1461no—
1458C23—1461no—
1459C23—1461no—
1460C23—1461no—
1461C23—1461no—
1462C23—1461no—
1463C23—1461no—
1464C23—1461no—
1465C23—1461no—
1466C23—1461no—
1467C23—1461no—
1468C23—1461no—
1469C23—1461no—
1470C23—1461no—
1471C23—1461no—
1472C23—1461no—
1473C23—1461no—
1474C23—1461no—
1475C23C2×D4×D7312yes—
1476C23C2×#1192402912yes—
1477C23C2×#1192402912yes—
1478C23C24×D7311yescharacteristic
1479Q8—82no—
1480Q8—82no—
1481D4—2924no—
1482D4—2924no—
1483D4—2924no—
1484D4—5842no—
1485D4—5842no—
1486D4—5842no—
1487D4—5842no—
1488D4—5842no—
1489D4—5842no—
1490D4—5842no—
1491D4—5842no—
1492D4—1468no—
1493C2×C4—21no—
1494C2×C4—21no—
1495C2×C4—21no—
1496C2×C4—21no—
1497C2×C4—21no—
1498C2×C4—21no—
1499C2×C4—21no—
1500C2×C4—21no—
1501C2×C4—21no—
1502C2×C4—21no—
1503C2×C4—21no—
1504C2×C4—21no—
1505C2×C4—21no—
1506C2×C4—21no—
1507C2×C4—21no—
1508C2×C4—21no—
1509C2×C4—21no—
1510C2×C4—21no—
1511C2×C4—21no—
1512C2×C4—21no—
1513C2×C4—21no—
1514C2×C4—21no—
1515C2×C4—21no—
1516C2×C4—21no—
1517C2×C4—21no—
1518C2×C4—21no—
1519C2×C4—21no—
1520C2×C4—21no—
1521C2×C4—21no—
1522C2×C4—21no—
1523C2×C4—21no—
1524C2×C4—21no—
1525C2×C4—21no—
1526C2×C4—21no—
1527C2×C4—21no—
1528C2×C4—21no—
1529C2×C4—44no—
1530C2×C4—82no—
1531C2×C4—82no—
1532C2×C4—2924no—
1533C2×C4—2924no—
1534C2×C4—2924no—
1535C2×C4—2924no—
1536C2×C4—2924no—
1537C2×C4—2924no—
1538C2×C4—5842no—
1539C2×C4—5842no—
1540C2×C4—732no—
1541C2×C4—732no—
1542C2×C4—732no—
1543C2×C4—732no—
1544C2×C4—1461no—
1545C2×C4—1461no—
1546C2×C4—1461no—
1547C2×C4—1461no—
1548C2×C4—1461no—
1549C2×C4—1461no—
1550C2×C4—1461no—
1551C2×C4—1461no—
1552C2×C4—1461no—
1553C2×C4—1461no—
1554C2×C4—1461no—
1555C2×C4—1461no—
1556C2×C4—1461no—
1557C2×C4—1461no—
1558C2×C4—1461no—
1559C2×C4—1461no—
1560C2×C4—1461no—
1561C2×C4—1461no—
1562C2×C4—1461no—
1563C2×C4—1461no—
1564C2×C4—1461no—
1565C2×C4—1461no—
1566C2×C4—1461no—
1567C2×C4—1461no—
1568C2×C4—1461no—
1569C2×C4—1461no—
1570C2×C4—1461no—
1571C2×C4—1461no—
1572C2×C4—1461no—
1573C2×C4C2×D4×D7312yes—
1574C2×C4C2×D4×D7312yes—
1575C2×C4C2×#1192402912yes—
1576C2×C4C2×#1192402912yes—
1577C2×C4C2×#1192402912yes—
1578C2×C4C2×#1192402912yes—
1579C22—22no—
1580C22—22no—
1581C22—22no—
1582C22—22no—
1583C22—22no—
1584C22—22no—
1585C22—2921no—
1586C22—2921no—
1587C22—2921no—
1588C22—2921no—
1589C22—2921no—
1590C22—2921no—
1591C22—2921no—
1592C22—2921no—
1593C22—2921no—
1594C22—2921no—
1595C22—2921no—
1596C22—2921no—
1597C22—2921no—
1598C22—2921no—
1599C22—2921no—
1600C22—2921no—
1601C22—2921no—
1602C22—2921no—
1603C22—2921no—
1604C22—2921no—
1605C22—2921no—
1606C22—2921no—
1607C22—2921no—
1608C22—2921no—
1609C22—2921no—
1610C22—2921no—
1611C22—2921no—
1612C22—2921no—
1613C22—2921no—
1614C22—2921no—
1615C22—2921no—
1616C22—2921no—
1617C22—5848no—
1618C22—1462no—
1619C22—1462no—
1620C22—1462no—
1621C22#1798913814yes—
1622C22C22×D4×D7311yescharacteristic
1623C22C22×#1192402911yescharacteristic
1624C22C22×#1192402911yescharacteristic
1625C22H(5,𝔽2)×D7311yescharacteristic
1626C22#1798942211yescharacteristic
1627C22#1798942311yescharacteristic
1628C22#1798942311yescharacteristic
1629C4—22no—
1630C4—22no—
1631C4—22no—
1632C4—22no—
1633C4—22no—
1634C4—22no—
1635C4—41no—
1636C4—41no—
1637C4—41no—
1638C4—41no—
1639C4—41no—
1640C4—41no—
1641C4—41no—
1642C4—41no—
1643C4—2921no—
1644C4—2921no—
1645C4—2921no—
1646C4—2921no—
1647C4—2921no—
1648C4—2921no—
1649C4—2921no—
1650C4—1462no—
1651C4—1462no—
1652C4—1462no—
1653C4—1462no—
1654C2—24no—
1655C2—2922no—
1656C2—5841no—
1657C2—5841no—
1658C2—5841no—
1659C2—5841no—
1660C2C2×#1798913811yescharacteristic
1661C2#2262332311yescharacteristic
1662C2#2262334311yescharacteristic
1663C2#2262369111yescharacteristic
1664C2#2262371711yescharacteristic
1665C2#2262387411yescharacteristic
1666C2#2262400211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D73
commutator, socle, cosocleC23×C73C25
FittingC73×#2549C2
hypercenter#2549D73
hypocenterC73#35009
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #2549

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#17989186C2semidirect
2. C2×#17989177C2semidirect
3. #22618305C2semidirect
4. #22618299C2semidirect
5. #22618264C2semidirect
6. #22618235C2semidirect
7. #22616097C2semidirect
8. #22616086C2semidirect
9. #22616075C2semidirect
10. #22616064C2semidirect
11. #22615082C2semidirect
12. #22615067C2semidirect
13. #22615052C2semidirect
14. #22615037C2semidirect
15. #22614891C2semidirect
16. #22614857C2semidirect
17. #22614823C2semidirect
18. #22614637C2semidirect
19. #22614607C2semidirect
20. #22614263C2semidirect
21. #22614064C2semidirect
22. #22613940C2semidirect
23. #22613901C2semidirect
24. #22613480C2semidirect
25. #22613465C2semidirect
26. #22612599C2semidirect
27. #22612588C2semidirect
28. #22612437C2semidirect
29. C2×#17988476C2semidirect
30. C4×#14556551C2semidirect
31. C73×#2549C2semidirect
36. C2×#14556586C22semidirect
37. C2×#14556586C22semidirect
38. C2×#14556582C22semidirect
39. C2×#14556582C22semidirect
45. C2×#14556576C22semidirect
46. C2×#14556576C22semidirect
50. C2×#14556567C22semidirect
51. C2×#14556567C22semidirect
61. C2×#14556553C22semidirect
72. C2×C42×D73C22semidirect
73. #17988526C22semidirect
74. #17988526C22semidirect
77. #17988519C22semidirect
78. #17988519C22semidirect
79. #17988514C22semidirect
80. #17988514C22semidirect
82. #17988513C22semidirect
86. #17988509C22semidirect
88. #17988505C22semidirect
94. #17988504C22semidirect
96. #17988498C22semidirect
100. #17988497C22semidirect
101. #17988494C22semidirect
110. #17988488C22semidirect
111. #17988486C22semidirect
112. #17988483C22semidirect
113. #17988483C22semidirect
114. #17988483C22semidirect
118. #17988479C22semidirect
119. #17988479C22semidirect
120. #17988479C22semidirect
125. #17988477C22semidirect
126. #17988477C22semidirect
137. #17988476C22semidirect
138. #17988476C22semidirect
139. #17988476C22semidirect
140. #17988476C22semidirect
141. #17988470C22semidirect
142. #17988470C22semidirect
150. #17988465C22semidirect
151. #17988465C22semidirect
152. #17988465C22semidirect
155. #17988458C22semidirect
156. #17988458C22semidirect
157. #17988452C22semidirect
159. #17988444C22semidirect
161. C4⋊C4×Dic73C22semidirect
162. C4×#11924007C22semidirect
163. #17988438C22semidirect
164. #17988438C22semidirect
167. C4×#11924005C22semidirect
168. #17988434C22semidirect
169. #17988434C22semidirect
170. #17988434C22semidirect
171. #17988434C22semidirect
173. C42×Dic73C22semidirect
176. #398×C73C22semidirect
177. #398×C73C22semidirect
178. #395×C73C22semidirect
179. #395×C73C22semidirect
180. #391×C73C22semidirect
181. #391×C73C22semidirect
182. #389×C73C22semidirect
183. #389×C73C22semidirect
242. #14556551D4semidirect
848. #2549D73semidirect
865. C73#35009semidirect
915. #398C2×D73semidirect
916. #398C2×D73semidirect
925. #395C2×D73semidirect
926. #395C2×D73semidirect
942. #391C2×D73semidirect
943. #391C2×D73semidirect
957. #389C2×D73semidirect
958. #389C2×D73semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#179891862
C2×#179891772
#226183052
#226182992
#226182642
#226182352
#226160972
#226160862
#226160752
#226160642
#226150822
#226150672
#226150522
#226150372
#226148912
#226148572
#226148232
#226146372
#226146072
#226142632
#226140642
#226139402
#226139012
#226134802
#226134652
#226125992
#226125882
#226124372
C2×#179884762
C4×#145565512
C73×#25492
#3500973