Finite Group Databasebeta

← #33292930

Subgroups — #33292930

Order 18688.

2406 conjugacy classes of subgroups.

The subgroup lattice has 1628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989176C211yesmaximal, characteristic
2C2×C22⋊Q8×D73C211yesmaximal, characteristic, complemented
3#22618226C211yesmaximal, characteristic, complemented
4#22618224C211yesmaximal, characteristic, complemented
5#22616532C211yesmaximal, characteristic, complemented
6#22616531C211yesmaximal, characteristic, complemented
7#22616530C211yesmaximal, characteristic, complemented
8#22616529C211yesmaximal, characteristic, complemented
9#22616504C211yesmaximal, characteristic, complemented
10#22616502C211yesmaximal, characteristic, complemented
11#22616499C211yesmaximal, characteristic, complemented
12#22616281C211yesmaximal, characteristic, complemented
13#22616279C211yesmaximal, characteristic, complemented
14#22616278C211yesmaximal, characteristic, complemented
15#22616276C211yesmaximal, characteristic, complemented
16#22616275C211yesmaximal, characteristic, complemented
17#22616273C211yesmaximal, characteristic, complemented
18#22616272C211yesmaximal, characteristic, complemented
19#22616267C211yesmaximal, characteristic, complemented
20#22615705C211yesmaximal, characteristic, complemented
21#22615705C211yesmaximal, characteristic, complemented
22#22615407C211yesmaximal, characteristic, complemented
23#22615309C211yesmaximal, characteristic, complemented
24#22615282C211yesmaximal, characteristic, complemented
25#22615279C211yesmaximal, characteristic, complemented
26#22614420C211yesmaximal, characteristic, complemented
27#22614404C211yesmaximal, characteristic, complemented
28#22613294C211yesmaximal, characteristic, complemented
29#22613291C211yesmaximal, characteristic, complemented
30#22612525C211yesmaximal, characteristic, complemented
31C73×#2698C211yesmaximal, characteristic, complemented
32C22×Q8×D73C2211yescharacteristic
33C23×C4×D73C2211yescharacteristic
34#17989176—28no—
35C2×#14556586C2211yescharacteristic
36C2×#14556579C2211yescharacteristic
37C2×#14556577C2211yescharacteristic
38C2×#14556576C2211yescharacteristic
39C2×#14556576C2211yescharacteristic
40C2×#14556576C2211yescharacteristic
41C2×#14556575C2211yescharacteristic
42C2×#14556574C2211yescharacteristic
43C2×#14556573C2211yescharacteristic
44C2×#14556571C2211yescharacteristic
45C2×#14556571C2211yescharacteristic, complemented
46C2×#14556570C2211yescharacteristic
47C2×#14556569C2211yescharacteristic
48C2×#14556569C2211yescharacteristic
49C2×#14556569C2211yescharacteristic
50C2×#14556569C2211yescharacteristic, complemented
51C2×#14556569C2211yescharacteristic, complemented
52C2×#14556568C2211yescharacteristic
53C2×#14556568C2211yescharacteristic
54C2×#14556567C2211yescharacteristic
55C2×#14556567C2211yescharacteristic, complemented
56C22⋊Q8×D73—28no—
57C2×#14556566C2211yescharacteristic
58C2×#14556566C2211yescharacteristic
59C2×#14556564C2211yescharacteristic
60C2×#14556561C2211yescharacteristic
61C2×#14556561C2211yescharacteristic
62C2×C4×D292C2211yescharacteristic
63C2×#14556553C2211yescharacteristic
64C2×C4⋊C4×D73C2211yescharacteristic
65C2×C4⋊C4×D73C2211yescharacteristic
66C2×C4⋊C4×D73C2211yescharacteristic
67C2×C22⋊C4×D73C2211yescharacteristic
68C2×C22⋊C4×D73C2211yescharacteristic
69#17988525C2211yescharacteristic, complemented
70#17988521C2211yescharacteristic, complemented
71#17988521C2211yescharacteristic, complemented
72#17988520C2211yescharacteristic, complemented
73#17988520C2211yescharacteristic, complemented
74#17988519C2211yescharacteristic, complemented
75#17988519C2211yescharacteristic, complemented
76#17988518C2211yescharacteristic, complemented
77#17988517C2211yescharacteristic, complemented
78#17988516C2211yescharacteristic
79#17988516C2211yescharacteristic
80#17988516C2211yescharacteristic, complemented
81#17988516C2211yescharacteristic, complemented
82#17988516C2211yescharacteristic, complemented
83#17988516C2211yescharacteristic, complemented
84#17988515C2211yescharacteristic
85#17988515C2211yescharacteristic
86#17988514C2211yescharacteristic
87#17988514C2211yescharacteristic
88#17988511C2211yescharacteristic, complemented
89#17988509C2211yescharacteristic, complemented
90#17988509C2211yescharacteristic, complemented
91#17988509C2211yescharacteristic, complemented
92#17988508C2211yescharacteristic, complemented
93#17988508C2211yescharacteristic, complemented
94#17988508C2211yescharacteristic, complemented
95#17988507C2211yescharacteristic, complemented
96#17988507C2211yescharacteristic, complemented
97#17988505C2211yescharacteristic
98#17988505C2211yescharacteristic
99#17988505C2211yescharacteristic, complemented
100#17988504C2211yescharacteristic
101#17988504C2211yescharacteristic
102#17988504C2211yescharacteristic, complemented
103#17988503C2211yescharacteristic
104#17988503C2211yescharacteristic
105#17988502C2211yescharacteristic
106#17988502C2211yescharacteristic
107#17988500C2211yescharacteristic, complemented
108#17988500C2211yescharacteristic, complemented
109#17988500C2211yescharacteristic, complemented
110#17988498C2211yescharacteristic, complemented
111#17988493C2211yescharacteristic, complemented
112#17988491C2211yescharacteristic, complemented
113#17988491C2211yescharacteristic, complemented
114#17988491C2211yescharacteristic, complemented
115#17988491C2211yescharacteristic, complemented
116#17988489C2211yescharacteristic, complemented
117#17988488C2211yescharacteristic, complemented
118#17988485C2211yescharacteristic, complemented
119#17988482C2211yescharacteristic, complemented
120#17988482C2211yescharacteristic, complemented
121#17988481C2211yescharacteristic
122#17988480C2211yescharacteristic
123#17988479C2211yescharacteristic
124#17988479C2211yescharacteristic, complemented
125#17988479C2211yescharacteristic, complemented
126#17988478C2211yescharacteristic
127#17988477C2211yescharacteristic
128#17988476C2211yescharacteristic
129#17988476C2211yescharacteristic, complemented
130#17988476C2211yescharacteristic, complemented
131#17988475C2211yescharacteristic
132#17988474C2211yescharacteristic, complemented
133#17988471C2211yescharacteristic, complemented
134#17988470C2211yescharacteristic, complemented
135#17988466C2211yescharacteristic
136#17988465C2211yescharacteristic
137#17988465C2211yescharacteristic
138#17988465C2211yescharacteristic
139#17988465C2211yescharacteristic
140#17988465C2211yescharacteristic
141#17988465C2211yescharacteristic
142#17988465C2211yescharacteristic
143#17988465C2211yescharacteristic
144#17988465C2211yescharacteristic
145#17988465C2211yescharacteristic
146#17988464C2211yescharacteristic
147#17988461C2211yescharacteristic
148#17988461C2211yescharacteristic
149#17988461C2211yescharacteristic
150#17988461C2211yescharacteristic
151#17988461C2211yescharacteristic
152#17988461C2211yescharacteristic
153#17988461C2211yescharacteristic, complemented
154#17988461C2211yescharacteristic, complemented
155#17988459C2211yescharacteristic
156#17988458C2211yescharacteristic
157#17988458C2211yescharacteristic
158#17988458C2211yescharacteristic
159#17988458C2211yescharacteristic
160#17988458C2211yescharacteristic, complemented
161#17988458C2211yescharacteristic, complemented
162#17988456C2211yescharacteristic, complemented
163#17988456C2211yescharacteristic, complemented
164#17988452C2211yescharacteristic, complemented
165#17988449C2211yescharacteristic
166#17988449C2211yescharacteristic
167#17988448C2211yescharacteristic
168#17988446C2211yescharacteristic
169#17988444C2211yescharacteristic
170#17988442C2211yescharacteristic
171#17988442C2211yescharacteristic
172C4×#11924005C2211yescharacteristic
173#17988434C2211yescharacteristic
174C2×#126×C73C2211yescharacteristic
175C2×C22⋊Q8×C73C2211yescharacteristic
176#400×C73C2211yescharacteristic, complemented
177#398×C73C2211yescharacteristic, complemented
178#398×C73C2211yescharacteristic, complemented
179#397×C73C2211yescharacteristic
180#397×C73C2211yescharacteristic
181#395×C73C2211yescharacteristic, complemented
182#391×C73C2211yescharacteristic, complemented
183#389×C73C2211yescharacteristic, complemented
184#388×C73C2211yescharacteristic
185#387×C73C2211yescharacteristic, complemented
186#385×C73C2211yescharacteristic
187#382×C73C2211yescharacteristic, complemented
188#381×C73C2211yescharacteristic
189C24×D73C2311yescharacteristic
190C22×Dic146C2311yescharacteristic
191C22×Dic146C2311yescharacteristic
192C22×Dic146C2311yescharacteristic
193C22×Dic146C2311yescharacteristic
194C2×Q8×D73—24no—
195C2×Q8×D73—42no—
196C2×Q8×D73—42no—
197C22×D292C2311yescharacteristic
198C22×D292C2311yescharacteristic
199C22×D292C2311yescharacteristic
200C22×D292C2311yescharacteristic
201C22×D292C2311yescharacteristic
202C22×C22⋊D73C2311yescharacteristic
203C22×C22⋊D73C2311yescharacteristic
204C23×Dic73C2311yescharacteristic
205C22×C4×D73—24no—
206C22×C4×D73—42no—
207C22×C4×D73—42no—
208C22×C4×D73C2311yescharacteristic
209C22×C4×D73C2311yescharacteristic
210C22×C4×D73C2311yescharacteristic
211C22×C4×D73C2311yescharacteristic
212C22×C4×D73C2311yescharacteristic
213C22×C4×D73C2311yescharacteristic
214C22×C4×D73C2311yescharacteristic
215C22×C4×D73C2311yescharacteristic
216C22×C4×D73C2311yescharacteristic
217C22×C4×D73C2311yescharacteristic
218#14556586—24no—
219#14556579—24no—
220#14556577—24no—
221#14556576—24no—
222#14556576—42no—
223#14556576—42no—
224#14556575—42no—
225#14556574—42no—
226#14556573—24no—
227#14556571—24no—
228#14556571—42no—
229#14556570—24no—
230#14556569—24no—
231#14556569—24no—
232#14556569—24no—
233#14556569—42no—
234#14556569—42no—
235#14556568—24no—
236#14556568—24no—
237#14556567—24no—
238#14556567—42no—
239#14556566—24no—
240#14556566—24no—
241#14556564—24no—
242#14556561—24no—
243#14556561—24no—
244C4×D292—24no—
245#14556553—24no—
246C2×C4⋊Dic73C2311yescharacteristic
247C2×C4⋊Dic73C2311yescharacteristic
248C2×C4⋊Dic73C2311yescharacteristic
249C2×C4⋊Dic73C2311yescharacteristic
250C2×C4⋊Dic73C2311yescharacteristic
251C2×C4⋊Dic73C2311yescharacteristic
252C2×C4⋊Dic73C2311yescharacteristic
253C2×C4⋊Dic73C2311yescharacteristic
254C2×C4⋊Dic73C2311yescharacteristic
255C2×#11924007C2311yescharacteristic
256C2×#11924007C2311yescharacteristic
257C2×#11924007C2311yescharacteristic
258C2×#11924007C2311yescharacteristic
259C2×#11924007C2311yescharacteristic
260C2×#11924007C2311yescharacteristic
261C2×#11924007C2311yescharacteristic
262C2×#11924007C2311yescharacteristic
263C2×#11924007C2311yescharacteristic
264C2×#11924007C2311yescharacteristic
265C2×#11924007C2311yescharacteristic
266C2×#11924007C2311yescharacteristic
267C2×#11924007C2311yescharacteristic
268C2×#11924007C2311yescharacteristic
269C2×#11924007C2311yescharacteristic
270C2×#11924007C2311yescharacteristic
271C2×#11924007C2311yescharacteristic
272C2×#11924007C2311yescharacteristic
273C4⋊C4×D73—24no—
274C4⋊C4×D73—24no—
275C4⋊C4×D73—24no—
276C2×C22⋊Dic73C2311yescharacteristic
277C2×C22⋊Dic73C2311yescharacteristic
278C2×C22⋊Dic73C2311yescharacteristic
279C2×C22⋊Dic73C2311yescharacteristic
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×#11924005C2311yescharacteristic
314C2×#11924005C2311yescharacteristic
315C2×#11924005C2311yescharacteristic
316C22⋊C4×D73—24no—
317C22⋊C4×D73D418yes—
318C2×C4×Dic73C2311yescharacteristic
319C2×C4×Dic73C2311yescharacteristic
320C2×C4×Dic73C2311yescharacteristic
321C2×C4×Dic73C2311yescharacteristic
322#14556498C2311yescharacteristic
323#14556498C2311yescharacteristic
324#14556498C2311yescharacteristic
325#14556498C2311yescharacteristic
326#14556498C2311yescharacteristic
327#14556498C2311yescharacteristic
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
349C23×C4×C73C2311yescharacteristic
350#126×C73—24no—
351C22⋊Q8×C73—24no—
352C2×C4⋊C4×C73C2311yescharacteristic
353C2×C4⋊C4×C73C2311yescharacteristic
354C2×C4⋊C4×C73C2311yescharacteristic
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×C22⋊C4×C73C2311yescharacteristic
364C2×C22⋊C4×C73C2311yescharacteristic
365C2×C22⋊C4×C73C2311yescharacteristic
366C2×C22⋊C4×C73C2311yescharacteristic
367C2×C22⋊C4×C73C2311yescharacteristic
368C2×C22⋊C4×C73C2311yescharacteristic
369C2×C42×C73C2311yescharacteristic
370C2×C42×C73C2311yescharacteristic
371#95×C73C2311yescharacteristic
372#95×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—41no—
388C23×D73—41no—
389C23×D73—41no—
390C23×D73—41no—
391C23×D73C2×D414yes—
392C23×D73C2411yescharacteristic
393C23×D73C2411yescharacteristic
394C23×D73C2411yescharacteristic
395C23×D73C2411yescharacteristic
396C2×Dic146—22no—
397C2×Dic146—22no—
398C2×Dic146—22no—
399C2×Dic146—22no—
400C2×Dic146—22no—
401C2×Dic146—22no—
402C2×Dic146—22no—
403C2×Dic146—41no—
404C2×Dic146—41no—
405C2×Dic146—41no—
406C2×Dic146—41no—
407C2×Dic146—41no—
408Q8×D73—416no—
409C2×D292—22no—
410C2×D292—22no—
411C2×D292—22no—
412C2×D292—22no—
413C2×D292—22no—
414C2×D292—22no—
415C2×D292—22no—
416C2×D292—22no—
417C2×D292—22no—
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—41no—
427C2×C22⋊D73—41no—
428C2×C22⋊D73—41no—
429C2×C22⋊D73—41no—
430C22×Dic73—22no—
431C22×Dic73—22no—
432C22×Dic73—41no—
433C22×Dic73C2411yescharacteristic
434C22×Dic73C2411yescharacteristic
435C22×Dic73C2411yescharacteristic
436C22×Dic73C2411yescharacteristic
437C22×Dic73C2411yescharacteristic
438C22×Dic73C2411yescharacteristic
439C22×Dic73C2411yescharacteristic
440C22×Dic73C2411yescharacteristic
441C22×Dic73C2411yescharacteristic
442C22×Dic73C2411yescharacteristic
443C22×Dic73C2411yescharacteristic
444C22×Dic73C2411yescharacteristic
445C2×C4×D73—22no—
446C2×C4×D73—22no—
447C2×C4×D73—22no—
448C2×C4×D73—22no—
449C2×C4×D73—22no—
450C2×C4×D73—22no—
451C2×C4×D73—22no—
452C2×C4×D73—22no—
453C2×C4×D73—22no—
454C2×C4×D73—22no—
455C2×C4×D73—22no—
456C2×C4×D73—22no—
457C2×C4×D73—416no—
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×D73—41no—
468C2×C4×D73—41no—
469C2×C4×D73—41no—
470C2×C4×D73—41no—
471C2×C4×D73—41no—
472C2×C4×D73—41no—
473C2×C4×D73—41no—
474C2×C4×D73C2×D414yes—
475C2×C4×D73C2×D414yes—
476C4⋊Dic73—22no—
477C4⋊Dic73—22no—
478C4⋊Dic73—22no—
479C4⋊Dic73—22no—
480C4⋊Dic73—22no—
481C4⋊Dic73—41no—
482C4⋊Dic73—41no—
483C4⋊Dic73—41no—
484C4⋊Dic73—41no—
485#11924007—22no—
486#11924007—22no—
487#11924007—22no—
488#11924007—22no—
489#11924007—22no—
490#11924007—22no—
491#11924007—22no—
492#11924007—22no—
493#11924007—22no—
494#11924007—22no—
495#11924007—41no—
496#11924007—41no—
497#11924007—41no—
498#11924007—41no—
499#11924007—41no—
500#11924007—41no—
501#11924007—41no—
502#11924007—41no—
503C22⋊Dic73—22no—
504C22⋊Dic73—41no—
505C22⋊Dic73—41no—
506C22⋊Dic73C2×D414yes—
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—22no—
522#11924005—22no—
523#11924005—22no—
524#11924005—22no—
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#11924005—41no—
534#11924005—41no—
535#11924005—41no—
536#11924005—41no—
537#11924005—41no—
538#11924005—41no—
539#11924005—41no—
540#11924005—41no—
541#11924005C2×D414yes—
542#11924005C2×D414yes—
543C4×Dic73—22no—
544C4×Dic73—41no—
545C4×Dic73—41no—
546C4×Dic73—41no—
547C24×C73C2411yescharacteristic
548C2×Q8×C73—22no—
549C2×Q8×C73—22no—
550C2×Q8×C73—41no—
551C22×C4×C73—22no—
552C22×C4×C73—22no—
553C22×C4×C73—41no—
554C22×C4×C73C2411yescharacteristic
555C22×C4×C73C2411yescharacteristic
556C22×C4×C73C2411yescharacteristic
557C22×C4×C73C2411yescharacteristic
558C22×C4×C73C2411yescharacteristic
559C22×C4×C73C2411yescharacteristic
560C22×C4×C73C2411yescharacteristic
561C22×C4×C73C2411yescharacteristic
562C22×C4×C73C2411yescharacteristic
563C22×C4×C73C2411yescharacteristic
564C22×C4×C73C2411yescharacteristic
565C22×C4×C73C2411yescharacteristic
566C22×C4×C73C2411yescharacteristic
567C22×C4×C73C2411yescharacteristic
568C4⋊C4×C73—22no—
569C4⋊C4×C73—22no—
570C4⋊C4×C73—22no—
571C4⋊C4×C73—22no—
572C4⋊C4×C73—22no—
573C4⋊C4×C73—22no—
574C4⋊C4×C73—22no—
575C4⋊C4×C73—41no—
576C4⋊C4×C73—41no—
577C4⋊C4×C73—41no—
578C4⋊C4×C73—41no—
579C22⋊C4×C73—22no—
580C22⋊C4×C73—22no—
581C22⋊C4×C73—22no—
582C22⋊C4×C73—41no—
583C22⋊C4×C73—41no—
584C22⋊C4×C73C2×D414yes—
585C42×C73—22no—
586C42×C73—41no—
587C23×C73—21no—
588C23×C73—21no—
589C23×C73—21no—
590C23×C73—21no—
591C23×C73—21no—
592C23×C73—21no—
593C23×C73C22×D412yes—
594C23×C73C2511yescharacteristic
595C22×D73—21no—
596C22×D73—21no—
597C22×D73—21no—
598C22×D73—21no—
599C22×D73—21no—
600C22×D73—21no—
601C22×D73—21no—
602C22×D73—21no—
603C22×D73—21no—
604C22×D73—21no—
605C22×D73—28no—
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—44no—
621C22×D73—44no—
622C22×D73—44no—
623C22×D73—44no—
624C22×D73—44no—
625C22×D73—44no—
626C22×D73C22×D412yes—
627C22×D73C22×D412yes—
628C22×D732−1+412yes—
629C22×D732−1+412yes—
630Q8×C73—44no—
631C2×C4×C73—21no—
632C2×C4×C73—21no—
633C2×C4×C73—21no—
634C2×C4×C73—21no—
635C2×C4×C73—21no—
636C2×C4×C73—21no—
637C2×C4×C73—21no—
638C2×C4×C73—21no—
639C2×C4×C73—21no—
640C2×C4×C73—21no—
641C2×C4×C73—21no—
642C2×C4×C73—21no—
643C2×C4×C73—21no—
644C2×C4×C73—21no—
645C2×C4×C73—21no—
646C2×C4×C73—21no—
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—44no—
671C2×C4×C73C22×D412yes—
672C2×C4×C73C22×D412yes—
673C2×C4×C73H(5,𝔽2)12yes—
674C22⋊D73—82no—
675C22⋊D73—82no—
676C2×Dic73—21no—
677C2×Dic73—21no—
678C2×Dic73—21no—
679C2×Dic73—21no—
680C2×Dic73—21no—
681C2×Dic73—21no—
682C2×Dic73—21no—
683C2×Dic73—21no—
684C2×Dic73—21no—
685C2×Dic73—21no—
686C2×Dic73—21no—
687C2×Dic73—21no—
688C2×Dic73—21no—
689C2×Dic73—21no—
690C2×Dic73—21no—
691C2×Dic73—21no—
692C2×Dic73—21no—
693C2×Dic73—21no—
694C2×Dic73—21no—
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—44no—
710C2×Dic73C22×D412yes—
711C2×Dic73C22×D412yes—
712C2×Dic73H(5,𝔽2)12yes—
713D292—44no—
714D292—44no—
715D292—82no—
716D292—82no—
717D292—82no—
718C4×D73—28no—
719C4×D73—44no—
720C4×D73—44no—
721C4×D73—44no—
722C4×D73—44no—
723C4×D73—44no—
724C4×D73—44no—
725C4×D73—44no—
726C4×D73—82no—
727C4×D73—82no—
728Dic146—44no—
729Dic146—44no—
730Dic146—44no—
731Dic146—82no—
732C22×C73—22no—
733C22×C73—22no—
734C22×C73—22no—
735C22×C73—41no—
736C22×C73—41no—
737C22×C73—41no—
738C22×C73—41no—
739C22×C73C23×D411yescharacteristic
740C22×C73C2×H(5,𝔽2)11yescharacteristic
741C22×C73C2×H(5,𝔽2)11yescharacteristic
742C22×C73C2×2−1+411yescharacteristic
743C22×C73C2×2−1+411yescharacteristic
744C22×C73#58511yescharacteristic
745C22×C73#58511yescharacteristic
746C2×D73—22no—
747C2×D73—22no—
748C2×D73—22no—
749C2×D73—22no—
750C2×D73—22no—
751C2×D73—22no—
752C2×D73—22no—
753C2×D73—22no—
754C2×D73—22no—
755C2×D73—416no—
756C2×D73—41no—
757C2×D73—41no—
758C2×D73—41no—
759C2×D73—41no—
760C2×D73—41no—
761C2×D73—41no—
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#53614yes—
775C4×C73—22no—
776C4×C73—22no—
777C4×C73—22no—
778C4×C73—41no—
779C4×C73—41no—
780C4×C73—41no—
781C4×C73—41no—
782C4×C73—41no—
783C4×C73—41no—
784C4×C73—41no—
785C4×C73—41no—
786C4×C73—41no—
787C4×C73—41no—
788C4×C73—41no—
789Dic73—22no—
790Dic73—22no—
791Dic73—22no—
792Dic73—41no—
793Dic73—41no—
794Dic73—41no—
795Dic73—41no—
796Dic73—41no—
797Dic73—41no—
798Dic73—41no—
799Dic73—41no—
800Dic73—41no—
801#36716—731nomaximal, Sylow
802C2×C73—42no—
803C2×C73C2×#53611yescharacteristic
804C2×C73#348411yescharacteristic
805C2×C73#348511yescharacteristic
806C2×C73#354111yescharacteristic
807C2×C73#354111yescharacteristic
808C2×C73#354111yescharacteristic
809C2×C73#354111yescharacteristic
810D73—24no—
811D73—42no—
812D73—81no—
813D73—81no—
814C2×#538—731no—
815C22×C22⋊Q8—731no—
816#2849—731no—
817#2849—731no—
818#2700—731no—
819#2700—731no—
820#2700—731no—
821#2700—731no—
822#2698—731no—
823#2698—731no—
824#2698—731no—
825#2698D7311yescharacteristic, complemented
826#2681—731no—
827#2681—731no—
828#2681—731no—
829#2681—731no—
830#2680—731no—
831#2680—731no—
832#2680—731no—
833#2680—731no—
834#2622—731no—
835#2622—731no—
836#2591—731no—
837#2583—731no—
838#2579—731no—
839#2579—731no—
840#2504—731no—
841#2502—731no—
842#2409—731no—
843#2409—731no—
844#2312—731no—
845C73#3671611yescharacteristic, complemented, Sylow
846C23×Q8—731no—
847C24×C4—731no—
848#538—1468no—
849C2×#126—731no—
850C2×#126C2×D7311yescharacteristic
851C2×#124—731no—
852C2×#124—731no—
853C2×#123—731no—
854C2×#123—731no—
855C2×#123—731no—
856C2×#123—731no—
857C2×#123—731no—
858C2×#123—731no—
859C2×C22⋊Q8—731no—
860C2×C22⋊Q8—731no—
861C2×C22⋊Q8—731no—
862C2×C22⋊Q8—731no—
863C2×C22⋊Q8—731no—
864C2×C22⋊Q8—731no—
865C2×C22⋊Q8—731no—
866C2×C22⋊Q8—731no—
867C2×C22⋊Q8—731no—
868C2×C22⋊Q8—731no—
869C2×C22⋊Q8—731no—
870C2×C22⋊Q8—731no—
871C2×C22⋊Q8—1468no—
872C2×C22⋊Q8C2×D7311yescharacteristic
873C2×#121—731no—
874C2×#121—731no—
875C2×#121—731no—
876C2×#120—731no—
877C2×#120—731no—
878C2×C4×D4—731no—
879C2×C4×D4—731no—
880C22×C4⋊C4—731no—
881C22×C4⋊C4—731no—
882C22×C4⋊C4—731no—
883C22×C22⋊C4—731no—
884C22×C22⋊C4—731no—
885#400—731no—
886#400C2×D7311yescharacteristic, complemented
887#398—731no—
888#398—731no—
889#398—731no—
890#398—731no—
891#398—731no—
892#398—731no—
893#398—731no—
894#398—731no—
895#398C2×D7311yescharacteristic, complemented
896#398C2×D7311yescharacteristic, complemented
897#397—731no—
898#397—731no—
899#397—731no—
900#397—731no—
901#397—731no—
902#397—731no—
903#397—731no—
904#397—731no—
905#397—731no—
906#397—731no—
907#397C2×D7311yescharacteristic
908#397C2×D7311yescharacteristic
909#396—731no—
910#396—731no—
911#396—731no—
912#396—731no—
913#395—731no—
914#395—731no—
915#395—731no—
916#395—731no—
917#395—731no—
918#395C2×D7311yescharacteristic, complemented
919#394—731no—
920#394—731no—
921#394—731no—
922#394—731no—
923#394—731no—
924#394—731no—
925#394—731no—
926#394—731no—
927#394—731no—
928#394—731no—
929#393—731no—
930#393—731no—
931#393—731no—
932#393—731no—
933#391—731no—
934#391—731no—
935#391—731no—
936#391—731no—
937#391—731no—
938#391C2×D7311yescharacteristic, complemented
939#390—731no—
940#390—731no—
941#389—731no—
942#389—731no—
943#389—731no—
944#389C2×D7311yescharacteristic, complemented
945#388—731no—
946#388—731no—
947#388—731no—
948#388—731no—
949#388—731no—
950#388—731no—
951#388—731no—
952#388—731no—
953#388—731no—
954#388—731no—
955#388—731no—
956#388C2×D7311yescharacteristic
957#387—731no—
958#387—731no—
959#387—731no—
960#387C2×D7311yescharacteristic, complemented
961#386—731no—
962#386—731no—
963#386—731no—
964#386—731no—
965#386—731no—
966#386—731no—
967#386—731no—
968#386—731no—
969#386—731no—
970#386—731no—
971#386—731no—
972#386—731no—
973#385—731no—
974#385—731no—
975#385—731no—
976#385—731no—
977#385—731no—
978#385—731no—
979#385—731no—
980#385—731no—
981#385—731no—
982#385—731no—
983#385—731no—
984#385—731no—
985#385—731no—
986#385—731no—
987#385—731no—
988#385C2×D7311yescharacteristic
989#384—731no—
990#384—731no—
991#382—731no—
992#382C2×D7311yescharacteristic, complemented
993#381—731no—
994#381—731no—
995#381—731no—
996#381C2×D7311yescharacteristic
997#380—731no—
998#380—731no—
999#379—731no—
1000#379—731no—
1001C4×C22⋊C4—731no—
1002C4×C22⋊C4—731no—
1003C25—731no—
1004C22×Q8—2922no—
1005C22×Q8—2922no—
1006C22×Q8—731no—
1007C22×Q8—731no—
1008C22×Q8—731no—
1009C22×Q8—731no—
1010C22×Q8—1464no—
1011C22×Q8C22×D7311yescharacteristic
1012C22×D4—731no—
1013C22×D4—731no—
1014C22×D4—731no—
1015C22×D4—731no—
1016C22×D4—731no—
1017C22×D4—731no—
1018C22×D4—731no—
1019C23×C4—2922no—
1020C23×C4—2922no—
1021C23×C4—731no—
1022C23×C4—731no—
1023C23×C4—731no—
1024C23×C4—731no—
1025C23×C4—731no—
1026C23×C4—731no—
1027C23×C4—731no—
1028C23×C4—731no—
1029C23×C4—731no—
1030C23×C4—731no—
1031C23×C4—731no—
1032C23×C4—1464no—
1033C23×C4C22×D7311yescharacteristic
1034#126—24no—
1035#126—1464no—
1036#124—1464no—
1037#124—1464no—
1038#123—2922no—
1039#123—2922no—
1040#123—2922no—
1041#123—2922no—
1042#123—1464no—
1043#123—1464no—
1044C22⋊Q8—24no—
1045C22⋊Q8—2922no—
1046C22⋊Q8—2922no—
1047C22⋊Q8—2922no—
1048C22⋊Q8—2922no—
1049C22⋊Q8—1464no—
1050C22⋊Q8—1464no—
1051C22⋊Q8—1464no—
1052C22⋊Q8—1464no—
1053C22⋊Q8—1464no—
1054C22⋊Q8—1464no—
1055C22⋊Q8—1464no—
1056C22⋊Q8—1464no—
1057#121—1464no—
1058#121—1464no—
1059#121—1464no—
1060#120—1464no—
1061#120—1464no—
1062C4×D4—1464no—
1063C4×D4—1464no—
1064C2×C4⋊C4—731no—
1065C2×C4⋊C4—731no—
1066C2×C4⋊C4—731no—
1067C2×C4⋊C4—731no—
1068C2×C4⋊C4—731no—
1069C2×C4⋊C4—731no—
1070C2×C4⋊C4—731no—
1071C2×C4⋊C4—731no—
1072C2×C4⋊C4—731no—
1073C2×C4⋊C4—731no—
1074C2×C4⋊C4—731no—
1075C2×C4⋊C4—731no—
1076C2×C4⋊C4—731no—
1077C2×C4⋊C4—731no—
1078C2×C4⋊C4—731no—
1079C2×C4⋊C4—731no—
1080C2×C4⋊C4—731no—
1081C2×C4⋊C4—731no—
1082C2×C4⋊C4—731no—
1083C2×C4⋊C4—731no—
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—1464no—
1092C2×C4⋊C4—1464no—
1093C2×C4⋊C4—1464no—
1094C2×C4⋊C4C22×D7311yescharacteristic
1095C2×C4⋊C4C22×D7311yescharacteristic
1096C2×C4⋊C4C22×D7311yescharacteristic
1097C2×C4⋊C4C22×D7311yescharacteristic
1098C2×C4⋊C4C22×D7311yescharacteristic
1099C2×C4⋊C4C22×D7311yescharacteristic
1100C2×C4⋊C4C22×D7311yescharacteristic
1101C2×C4⋊C4C22×D7311yescharacteristic
1102C2×C4⋊C4C22×D7311yescharacteristic
1103C2×C4⋊C4C22×D7311yescharacteristic
1104C2×C4⋊C4C22×D7311yescharacteristic
1105C2×C22⋊C4—731no—
1106C2×C22⋊C4—731no—
1107C2×C22⋊C4—731no—
1108C2×C22⋊C4—731no—
1109C2×C22⋊C4—731no—
1110C2×C22⋊C4—731no—
1111C2×C22⋊C4—731no—
1112C2×C22⋊C4—731no—
1113C2×C22⋊C4—731no—
1114C2×C22⋊C4—731no—
1115C2×C22⋊C4—731no—
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—738no—
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—1464no—
1147C2×C22⋊C4C22×D7311yescharacteristic
1148C2×C22⋊C4C22×D7311yescharacteristic
1149C2×C22⋊C4C22×D7311yescharacteristic
1150C2×C22⋊C4C22×D7311yescharacteristic
1151C2×C22⋊C4C22×D7311yescharacteristic
1152C2×C22⋊C4C22×D7311yescharacteristic
1153C2×C42—731no—
1154C2×C42—731no—
1155C2×C42—731no—
1156C2×C42—731no—
1157C2×C42C22×D7311yescharacteristic
1158C2×C42C22×D7311yescharacteristic
1159#95—731no—
1160#95—731no—
1161#95—731no—
1162#95—731no—
1163#95—731no—
1164#95—731no—
1165#95—731no—
1166#95—731no—
1167#95—731no—
1168#95—731no—
1169#95—731no—
1170#95—731no—
1171#95—731no—
1172#95—731no—
1173#95—731no—
1174#95—731no—
1175#95—731no—
1176#95—731no—
1177#95—731no—
1178#95—731no—
1179#95—731no—
1180#95—731no—
1181#95—731no—
1182#95—731no—
1183#95—731no—
1184#95—731no—
1185#95C22×D7311yescharacteristic
1186#95C22×D7311yescharacteristic
1187#95C22×D7311yescharacteristic
1188#95C22×D7311yescharacteristic
1189#95C22×D7311yescharacteristic
1190#95C22×D7311yescharacteristic
1191#95C22×D7311yescharacteristic
1192#95C22×D7311yescharacteristic
1193#95C22×D7311yescharacteristic
1194#95C22×D7311yescharacteristic
1195#95C22×D7311yescharacteristic
1196#95C22×D7311yescharacteristic
1197#95C22×D7311yescharacteristic
1198#95C22×D7311yescharacteristic
1199C24—2921no—
1200C24—2921no—
1201C24—2921no—
1202C24—2921no—
1203C24—734no—
1204C24—731no—
1205C24—731no—
1206C24—731no—
1207C24—731no—
1208C24—1462no—
1209C24—1462no—
1210C24C23×D7311yescharacteristic
1211C2×Q8—22no—
1212C2×Q8—22no—
1213C2×Q8—41no—
1214C2×Q8—2921no—
1215C2×Q8—2921no—
1216C2×Q8—2921no—
1217C2×Q8—2921no—
1218C2×Q8—2921no—
1219C2×Q8—29216no—
1220C2×Q8—1462no—
1221C2×Q8—1462no—
1222C2×Q8—1462no—
1223C2×Q8—1462no—
1224C2×Q8—1462no—
1225C2×Q8—1462no—
1226C2×Q8—1462no—
1227C2×D4—2921no—
1228C2×D4—2921no—
1229C2×D4—2921no—
1230C2×D4—2921no—
1231C2×D4—2921no—
1232C2×D4—2921no—
1233C2×D4—2921no—
1234C2×D4—2921no—
1235C2×D4—2921no—
1236C2×D4—2921no—
1237C2×D4—1462no—
1238C2×D4—1462no—
1239C2×D4—1462no—
1240C2×D4—1462no—
1241C2×D4—1462no—
1242C2×D4—1462no—
1243C2×D4—1462no—
1244C2×D4—1462no—
1245C2×D4—1462no—
1246C2×D4—1462no—
1247C2×D4—1462no—
1248C22×C4—22no—
1249C22×C4—22no—
1250C22×C4—41no—
1251C22×C4—2921no—
1252C22×C4—2921no—
1253C22×C4—2921no—
1254C22×C4—2921no—
1255C22×C4—2921no—
1256C22×C4—2921no—
1257C22×C4—2921no—
1258C22×C4—2921no—
1259C22×C4—2921no—
1260C22×C4—2921no—
1261C22×C4—2921no—
1262C22×C4—2921no—
1263C22×C4—2921no—
1264C22×C4—2921no—
1265C22×C4—2921no—
1266C22×C4—2921no—
1267C22×C4—29216no—
1268C22×C4—2921no—
1269C22×C4—734no—
1270C22×C4—734no—
1271C22×C4—731no—
1272C22×C4—731no—
1273C22×C4—731no—
1274C22×C4—731no—
1275C22×C4—731no—
1276C22×C4—731no—
1277C22×C4—731no—
1278C22×C4—731no—
1279C22×C4—731no—
1280C22×C4—731no—
1281C22×C4—731no—
1282C22×C4—731no—
1283C22×C4—1462no—
1284C22×C4—1462no—
1285C22×C4—1462no—
1286C22×C4—1462no—
1287C22×C4—1462no—
1288C22×C4—1462no—
1289C22×C4—1462no—
1290C22×C4—1462no—
1291C22×C4—1462no—
1292C22×C4—1462no—
1293C22×C4—1462no—
1294C22×C4—1462no—
1295C22×C4—1462no—
1296C22×C4—1462no—
1297C22×C4C23×D7311yescharacteristic
1298C22×C4C23×D7311yescharacteristic
1299C22×C4C23×D7311yescharacteristic
1300C22×C4C23×D7311yescharacteristic
1301C22×C4C23×D7311yescharacteristic
1302C22×C4C23×D7311yescharacteristic
1303C22×C4C23×D7311yescharacteristic
1304C22×C4C23×D7311yescharacteristic
1305C22×C4C23×D7311yescharacteristic
1306C22×C4C23×D7311yescharacteristic
1307C22×C4C23×D7311yescharacteristic
1308C22×C4C23×D7311yescharacteristic
1309C22×C4C23×D7311yescharacteristic
1310C22×C4C23×D7311yescharacteristic
1311C4⋊C4—22no—
1312C4⋊C4—22no—
1313C4⋊C4—22no—
1314C4⋊C4—22no—
1315C4⋊C4—22no—
1316C4⋊C4—22no—
1317C4⋊C4—22no—
1318C4⋊C4—41no—
1319C4⋊C4—41no—
1320C4⋊C4—41no—
1321C4⋊C4—41no—
1322C4⋊C4—2921no—
1323C4⋊C4—2921no—
1324C4⋊C4—2921no—
1325C4⋊C4—2921no—
1326C4⋊C4—2921no—
1327C4⋊C4—2921no—
1328C4⋊C4—2921no—
1329C4⋊C4—2921no—
1330C4⋊C4—2921no—
1331C4⋊C4—2921no—
1332C4⋊C4—2921no—
1333C4⋊C4—2921no—
1334C4⋊C4—1462no—
1335C4⋊C4—1462no—
1336C4⋊C4—1462no—
1337C4⋊C4—1462no—
1338C4⋊C4—1462no—
1339C4⋊C4—1462no—
1340C4⋊C4—1462no—
1341C4⋊C4—1462no—
1342C4⋊C4—1462no—
1343C4⋊C4—1462no—
1344C4⋊C4—1462no—
1345C4⋊C4—1462no—
1346C4⋊C4—1462no—
1347C4⋊C4—1462no—
1348C4⋊C4—1462no—
1349C22⋊C4—22no—
1350C22⋊C4—22no—
1351C22⋊C4—22no—
1352C22⋊C4—41no—
1353C22⋊C4—41no—
1354C22⋊C4—2921no—
1355C22⋊C4—2921no—
1356C22⋊C4—2921no—
1357C22⋊C4—2921no—
1358C22⋊C4—2921no—
1359C22⋊C4—2921no—
1360C22⋊C4—2921no—
1361C22⋊C4—2921no—
1362C22⋊C4—2921no—
1363C22⋊C4—2921no—
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—734no—
1373C22⋊C4—734no—
1374C22⋊C4—734no—
1375C22⋊C4—1462no—
1376C22⋊C4—1462no—
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⋊C4D4×D7314yes—
1395C42—22no—
1396C42—41no—
1397C42—2921no—
1398C42—2921no—
1399C42—2921no—
1400C42—1462no—
1401C23—21no—
1402C23—21no—
1403C23—21no—
1404C23—21no—
1405C23—21no—
1406C23—21no—
1407C23—2924no—
1408C23—2924no—
1409C23—2924no—
1410C23—2924no—
1411C23—2924no—
1412C23—2924no—
1413C23—732no—
1414C23—732no—
1415C23—732no—
1416C23—732no—
1417C23—1468no—
1418C23—1461no—
1419C23—1461no—
1420C23—1461no—
1421C23—1461no—
1422C23—1461no—
1423C23—1461no—
1424C23—1461no—
1425C23—1461no—
1426C23—1461no—
1427C23—1461no—
1428C23—1461no—
1429C23—1461no—
1430C23—1461no—
1431C23—1461no—
1432C23—1461no—
1433C23—1461no—
1434C23—1461no—
1435C23—1461no—
1436C23—1461no—
1437C23—1461no—
1438C23—1461no—
1439C23—1461no—
1440C23—1461no—
1441C23—1461no—
1442C23C2×D4×D7312yes—
1443C23C24×D7311yescharacteristic
1444Q8—44no—
1445Q8—2924no—
1446Q8—2924no—
1447Q8—2924no—
1448Q8—5842no—
1449D4—2924no—
1450D4—2924no—
1451D4—5842no—
1452D4—5842no—
1453D4—5842no—
1454D4—5842no—
1455D4—5842no—
1456C2×C4—21no—
1457C2×C4—21no—
1458C2×C4—21no—
1459C2×C4—21no—
1460C2×C4—21no—
1461C2×C4—21no—
1462C2×C4—21no—
1463C2×C4—21no—
1464C2×C4—21no—
1465C2×C4—21no—
1466C2×C4—21no—
1467C2×C4—21no—
1468C2×C4—21no—
1469C2×C4—21no—
1470C2×C4—21no—
1471C2×C4—21no—
1472C2×C4—21no—
1473C2×C4—21no—
1474C2×C4—21no—
1475C2×C4—21no—
1476C2×C4—21no—
1477C2×C4—21no—
1478C2×C4—21no—
1479C2×C4—21no—
1480C2×C4—21no—
1481C2×C4—21no—
1482C2×C4—21no—
1483C2×C4—21no—
1484C2×C4—21no—
1485C2×C4—21no—
1486C2×C4—21no—
1487C2×C4—21no—
1488C2×C4—21no—
1489C2×C4—21no—
1490C2×C4—21no—
1491C2×C4—21no—
1492C2×C4—21no—
1493C2×C4—21no—
1494C2×C4—21no—
1495C2×C4—44no—
1496C2×C4—2924no—
1497C2×C4—2924no—
1498C2×C4—2924no—
1499C2×C4—2924no—
1500C2×C4—2924no—
1501C2×C4—2924no—
1502C2×C4—2924no—
1503C2×C4—2924no—
1504C2×C4—5842no—
1505C2×C4—5842no—
1506C2×C4—732no—
1507C2×C4—732no—
1508C2×C4—732no—
1509C2×C4—1468no—
1510C2×C4—1461no—
1511C2×C4—1461no—
1512C2×C4—1461no—
1513C2×C4—1461no—
1514C2×C4—1461no—
1515C2×C4—1461no—
1516C2×C4—1461no—
1517C2×C4—1461no—
1518C2×C4—1461no—
1519C2×C4—1461no—
1520C2×C4—1461no—
1521C2×C4—1461no—
1522C2×C4—1461no—
1523C2×C4—1461no—
1524C2×C4—1461no—
1525C2×C4—1461no—
1526C2×C4—1461no—
1527C2×C4—1461no—
1528C2×C4—1461no—
1529C2×C4—1461no—
1530C2×C4—1461no—
1531C2×C4—1461no—
1532C2×C4—1461no—
1533C2×C4—1461no—
1534C2×C4—1461no—
1535C2×C4—1461no—
1536C2×C4—1461no—
1537C2×C4—1461no—
1538C2×C4—1461no—
1539C2×C4—1461no—
1540C2×C4—1461no—
1541C2×C4—1461no—
1542C2×C4—1461no—
1543C2×C4C2×D4×D7312yes—
1544C2×C4C2×D4×D7312yes—
1545C2×C4#1455663712yes—
1546C22—22no—
1547C22—22no—
1548C22—22no—
1549C22—41no—
1550C22—41no—
1551C22—41no—
1552C22—41no—
1553C22—29216no—
1554C22—2921no—
1555C22—2921no—
1556C22—2921no—
1557C22—2921no—
1558C22—2921no—
1559C22—2921no—
1560C22—2921no—
1561C22—2921no—
1562C22—2921no—
1563C22—2921no—
1564C22—2921no—
1565C22—2921no—
1566C22—2921no—
1567C22—2921no—
1568C22—2921no—
1569C22—2921no—
1570C22—2921no—
1571C22—2921no—
1572C22—734no—
1573C22—1462no—
1574C22—1462no—
1575C22—1462no—
1576C22—1462no—
1577C22—1462no—
1578C22—1462no—
1579C22—1462no—
1580C22—1462no—
1581C22—1462no—
1582C22C22×D4×D7311yescharacteristic
1583C22H(5,𝔽2)×D7311yescharacteristic
1584C22C2×#1455663711yescharacteristic
1585C222−1+4×D7311yescharacteristic
1586C222−1+4×D7311yescharacteristic
1587C22#1798942311yescharacteristic
1588C22#1798942411yescharacteristic
1589C4—22no—
1590C4—22no—
1591C4—22no—
1592C4—41no—
1593C4—41no—
1594C4—41no—
1595C4—41no—
1596C4—41no—
1597C4—41no—
1598C4—41no—
1599C4—41no—
1600C4—41no—
1601C4—41no—
1602C4—41no—
1603C4—2921no—
1604C4—2921no—
1605C4—2921no—
1606C4—2921no—
1607C4—2921no—
1608C4—2921no—
1609C4—2921no—
1610C4—2921no—
1611C4—2921no—
1612C4—1462no—
1613C4—1462no—
1614C4—1462no—
1615C2—42no—
1616C2—2922no—
1617C2—5841no—
1618C2—5841no—
1619C2—1464no—
1620C2#536×D7311yescharacteristic
1621C2#2262356111yescharacteristic
1622C2#2262357011yescharacteristic
1623C2#2262421511yescharacteristic
1624C2#2262422111yescharacteristic
1625C2#2262422711yescharacteristic
1626C2#2262423011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D73
commutator, socle, cosocleC23×C73C25
FittingC73×#2698C2
prime radicalC2×#17989176C2
hypercenter#2698D73
hypocenterC73#36716
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #2698

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊Q8×D73C2semidirect
3. #22618226C2semidirect
4. #22618224C2semidirect
5. #22616532C2semidirect
6. #22616531C2semidirect
7. #22616530C2semidirect
8. #22616529C2semidirect
9. #22616504C2semidirect
10. #22616502C2semidirect
11. #22616499C2semidirect
12. #22616281C2semidirect
13. #22616279C2semidirect
14. #22616278C2semidirect
15. #22616276C2semidirect
16. #22616275C2semidirect
17. #22616273C2semidirect
18. #22616272C2semidirect
19. #22616267C2semidirect
20. #22615705C2semidirect
21. #22615705C2semidirect
22. #22615407C2semidirect
23. #22615309C2semidirect
24. #22615282C2semidirect
25. #22615279C2semidirect
26. #22614420C2semidirect
27. #22614404C2semidirect
28. #22613294C2semidirect
29. #22613291C2semidirect
30. #22612525C2semidirect
31. C73×#2698C2semidirect
45. C2×#14556571C22semidirect
50. C2×#14556569C22semidirect
51. C2×#14556569C22semidirect
55. C2×#14556567C22semidirect
69. #17988525C22semidirect
70. #17988521C22semidirect
71. #17988521C22semidirect
72. #17988520C22semidirect
73. #17988520C22semidirect
74. #17988519C22semidirect
75. #17988519C22semidirect
76. #17988518C22semidirect
77. #17988517C22semidirect
80. #17988516C22semidirect
81. #17988516C22semidirect
82. #17988516C22semidirect
83. #17988516C22semidirect
88. #17988511C22semidirect
89. #17988509C22semidirect
90. #17988509C22semidirect
91. #17988509C22semidirect
92. #17988508C22semidirect
93. #17988508C22semidirect
94. #17988508C22semidirect
95. #17988507C22semidirect
96. #17988507C22semidirect
99. #17988505C22semidirect
102. #17988504C22semidirect
107. #17988500C22semidirect
108. #17988500C22semidirect
109. #17988500C22semidirect
110. #17988498C22semidirect
111. #17988493C22semidirect
112. #17988491C22semidirect
113. #17988491C22semidirect
114. #17988491C22semidirect
115. #17988491C22semidirect
116. #17988489C22semidirect
117. #17988488C22semidirect
118. #17988485C22semidirect
119. #17988482C22semidirect
120. #17988482C22semidirect
124. #17988479C22semidirect
125. #17988479C22semidirect
129. #17988476C22semidirect
130. #17988476C22semidirect
132. #17988474C22semidirect
133. #17988471C22semidirect
134. #17988470C22semidirect
153. #17988461C22semidirect
154. #17988461C22semidirect
160. #17988458C22semidirect
161. #17988458C22semidirect
162. #17988456C22semidirect
163. #17988456C22semidirect
164. #17988452C22semidirect
176. #400×C73C22semidirect
177. #398×C73C22semidirect
178. #398×C73C22semidirect
181. #395×C73C22semidirect
182. #391×C73C22semidirect
183. #389×C73C22semidirect
185. #387×C73C22semidirect
187. #382×C73C22semidirect
825. #2698D73semidirect
845. C73#36716semidirect
886. #400C2×D73semidirect
895. #398C2×D73semidirect
896. #398C2×D73semidirect
918. #395C2×D73semidirect
938. #391C2×D73semidirect
944. #389C2×D73semidirect
960. #387C2×D73semidirect
992. #382C2×D73semidirect

Maximal subgroups

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

subgroupindex
C2×#179891762
C2×C22⋊Q8×D732
#226182262
#226182242
#226165322
#226165312
#226165302
#226165292
#226165042
#226165022
#226164992
#226162812
#226162792
#226162782
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