Finite Group Databasebeta

← #33300183

Subgroups — #33300183

Order 18688.

1886 conjugacy classes of subgroups.

The subgroup lattice has 1584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22618258C211yesmaximal, characteristic, complemented
2#22618255C211yesmaximal, characteristic, complemented
3#22617871C211yesmaximal, characteristic, complemented
4#22617860C211yesmaximal, characteristic, complemented
5#22617824C211yesmaximal, characteristic, complemented
6#22617824C211yesmaximal, characteristic, complemented
7#22617536C211yesmaximal, characteristic, complemented
8#22617468C211yesmaximal, characteristic, complemented
9#22617323C211yesmaximal, characteristic, complemented
10#22617259C211yesmaximal, characteristic, complemented
11#22617206C211yesmaximal, characteristic, complemented
12#22617206C211yesmaximal, characteristic, complemented
13#22617042C211yesmaximal, characteristic, complemented
14#22616694C211yesmaximal, characteristic, complemented
15#22616636C211yesmaximal, characteristic, complemented
16#22616578C211yesmaximal, characteristic, complemented
17#22616518C211yesmaximal, characteristic, complemented
18#22615705C211yesmaximal, characteristic, complemented
19#22615670C211yesmaximal, characteristic, complemented
20#22614858C211yesmaximal, characteristic, complemented
21#22614819C211yesmaximal, characteristic, complemented
22#22613650C211yesmaximal, characteristic, complemented
23#22613477C211yesmaximal, characteristic, complemented
24#22613474C211yesmaximal, characteristic, complemented
25#22613415C211yesmaximal, characteristic, complemented
26#22613394C211yesmaximal, characteristic, complemented
27#22613373C211yesmaximal, characteristic, complemented
28#22612630C211yesmaximal, characteristic, complemented
29#22612560C211yesmaximal, characteristic, complemented
30#388×D73C211yesmaximal, characteristic, complemented
31C73×#2740C211yesmaximal, characteristic, complemented
32C2×#14556581C2211yescharacteristic, complemented
33C2×#14556576C2211yescharacteristic
34C2×#14556576C2211yescharacteristic
35C2×#14556573C2211yescharacteristic
36C2×#14556573C2211yescharacteristic
37C2×#14556566C2211yescharacteristic
38C2×#14556565C2211yescharacteristic, complemented
39C2×#14556564C2211yescharacteristic
40C2×#14556564C2211yescharacteristic
41C2×#14556564C2211yescharacteristic
42C2×#14556561C2211yescharacteristic
43C2×#14556561C2211yescharacteristic
44C2×#14556559C2211yescharacteristic
45C2×C4×D292C2211yescharacteristic
46C2×#14556553C2211yescharacteristic
47C2×C4×C22⋊D73C2211yescharacteristic
48C2×C4⋊C4×D73C2211yescharacteristic
49C2×C22⋊C4×D73C2211yescharacteristic
50C2×C22⋊C4×D73C2211yescharacteristic
51C2×C22⋊C4×D73C2211yescharacteristic
52C2×C42×D73C2211yescharacteristic
53#17988529C2211yescharacteristic, complemented
54#17988526C2211yescharacteristic, complemented
55#17988526C2211yescharacteristic, complemented
56#17988522C2211yescharacteristic
57#17988522C2211yescharacteristic
58#17988521C2211yescharacteristic, complemented
59#17988519C2211yescharacteristic, complemented
60#17988517C2211yescharacteristic, complemented
61#17988516C2211yescharacteristic
62#17988516C2211yescharacteristic
63#17988516C2211yescharacteristic, complemented
64#17988515C2211yescharacteristic
65#17988515C2211yescharacteristic
66#17988514C2211yescharacteristic
67#17988514C2211yescharacteristic, complemented
68#17988513C2211yescharacteristic, complemented
69#17988511C2211yescharacteristic
70#17988511C2211yescharacteristic, complemented
71#17988511C2211yescharacteristic, complemented
72#17988510C2211yescharacteristic
73#17988510C2211yescharacteristic
74#17988505C2211yescharacteristic
75#17988505C2211yescharacteristic
76#17988504C2211yescharacteristic
77#17988504C2211yescharacteristic
78#17988504C2211yescharacteristic
79#17988503C2211yescharacteristic
80#17988503C2211yescharacteristic
81#17988503C2211yescharacteristic
82#17988503C2211yescharacteristic
83#17988502C2211yescharacteristic
84#17988502C2211yescharacteristic
85#17988502C2211yescharacteristic
86#17988502C2211yescharacteristic, complemented
87#17988502C2211yescharacteristic, complemented
88#17988502C2211yescharacteristic, complemented
89#17988501C2211yescharacteristic
90#17988497C2211yescharacteristic
91#17988496C2211yescharacteristic
92#17988496C2211yescharacteristic
93#17988495C2211yescharacteristic
94#17988495C2211yescharacteristic
95#17988488C2211yescharacteristic
96#17988488C2211yescharacteristic
97#17988488C2211yescharacteristic, complemented
98#17988487C2211yescharacteristic
99#17988487C2211yescharacteristic
100#17988487C2211yescharacteristic, complemented
101#17988487C2211yescharacteristic, complemented
102#17988484C2211yescharacteristic, complemented
103#17988483C2211yescharacteristic, complemented
104#17988482C2211yescharacteristic, complemented
105#17988482C2211yescharacteristic, complemented
106#17988482C2211yescharacteristic, complemented
107#17988482C2211yescharacteristic, complemented
108#17988481C2211yescharacteristic
109#17988481C2211yescharacteristic, complemented
110#17988480C2211yescharacteristic
111#17988479C2211yescharacteristic
112#17988479C2211yescharacteristic
113#17988479C2211yescharacteristic
114#17988479C2211yescharacteristic, complemented
115#17988479C2211yescharacteristic, complemented
116#17988478C2211yescharacteristic
117#17988478C2211yescharacteristic
118#17988478C2211yescharacteristic, complemented
119#17988478C2211yescharacteristic, complemented
120#17988478C2211yescharacteristic, complemented
121#17988477C2211yescharacteristic
122#17988477C2211yescharacteristic, complemented
123#17988476C2211yescharacteristic
124#17988476C2211yescharacteristic, complemented
125#17988476C2211yescharacteristic, complemented
126#17988475C2211yescharacteristic
127#17988475C2211yescharacteristic
128#17988475C2211yescharacteristic
129#17988475C2211yescharacteristic, complemented
130#17988475C2211yescharacteristic, complemented
131#17988475C2211yescharacteristic, complemented
132#17988474C2211yescharacteristic, complemented
133#17988474C2211yescharacteristic, complemented
134#17988473C2211yescharacteristic, complemented
135#17988471C2211yescharacteristic, complemented
136#17988470C2211yescharacteristic, complemented
137#17988469C2211yescharacteristic, complemented
138#17988468C2211yescharacteristic, complemented
139#17988466C2211yescharacteristic
140#17988465C2211yescharacteristic
141#17988465C2211yescharacteristic
142#17988465C2211yescharacteristic
143#17988465C2211yescharacteristic
144#17988465C2211yescharacteristic
145#17988465C2211yescharacteristic, complemented
146#17988465C2211yescharacteristic, complemented
147#17988463C2211yescharacteristic
148#17988463C2211yescharacteristic
149#17988463C2211yescharacteristic
150#17988463C2211yescharacteristic, complemented
151#17988461C2211yescharacteristic
152#17988461C2211yescharacteristic
153#17988461C2211yescharacteristic, complemented
154#17988461C2211yescharacteristic, complemented
155#17988458C2211yescharacteristic
156#17988458C2211yescharacteristic
157#17988458C2211yescharacteristic, complemented
158#17988454C2211yescharacteristic, complemented
159#17988451C2211yescharacteristic, complemented
160#17988451C2211yescharacteristic, complemented
161#17988449C2211yescharacteristic
162#17988449C2211yescharacteristic, complemented
163#17988447C2211yescharacteristic, complemented
164#17988446C2211yescharacteristic
165#17988446C2211yescharacteristic
166#17988444C2211yescharacteristic
167#17988444C2211yescharacteristic, complemented
168#17988442C2211yescharacteristic
169#17988434C2211yescharacteristic
170#95×D73C2211yescharacteristic
171#95×D73C2211yescharacteristic
172#399×C73C2211yescharacteristic
173#398×C73C2211yescharacteristic, complemented
174#397×C73C2211yescharacteristic
175#397×C73C2211yescharacteristic
176#396×C73C2211yescharacteristic, complemented
177#394×C73C2211yescharacteristic
178#390×C73C2211yescharacteristic
179#388×C73C2211yescharacteristic
180#388×C73C2211yescharacteristic, complemented
181#387×C73C2211yescharacteristic, complemented
182#387×C73C2211yescharacteristic, complemented
183#387×C73C2211yescharacteristic, complemented
184#386×C73C2211yescharacteristic
185#381×C73C2211yescharacteristic, complemented
186#380×C73C2211yescharacteristic, complemented
187C24×D73C2311yescharacteristic
188C22×D292C2311yescharacteristic
189C22×D292C2311yescharacteristic
190C22×D292C2311yescharacteristic
191C22×D292C2311yescharacteristic
192C22×D292C2311yescharacteristic
193C22×C22⋊D73C2311yescharacteristic
194C22×C22⋊D73C2311yescharacteristic
195C22×C22⋊D73C2311yescharacteristic
196C22×C22⋊D73C2311yescharacteristic
197C22×C22⋊D73C2311yescharacteristic
198C22×C22⋊D73C2311yescharacteristic
199C22×C4×D73C2311yescharacteristic
200C22×C4×D73C2311yescharacteristic
201C22×C4×D73C2311yescharacteristic
202C22×C4×D73C2311yescharacteristic
203C22×C4×D73C2311yescharacteristic
204C22×C4×D73C2311yescharacteristic
205C22×C4×D73C2311yescharacteristic
206C22×C4×D73C2311yescharacteristic
207#14556581—42no—
208#14556576—42no—
209#14556576—42no—
210#14556573—42no—
211#14556573—42no—
212#14556566—24no—
213#14556565—42no—
214#14556564—42no—
215#14556564—42no—
216#14556564—42no—
217#14556561—42no—
218#14556561—42no—
219#14556559—42no—
220C4×D292—42no—
221#14556553—42no—
222C4×C22⋊D73—24no—
223C2×C4⋊Dic73C2311yescharacteristic
224C2×C4⋊Dic73C2311yescharacteristic
225C2×C4⋊Dic73C2311yescharacteristic
226C2×C4⋊Dic73C2311yescharacteristic
227C2×C4⋊Dic73C2311yescharacteristic
228C2×C4⋊Dic73C2311yescharacteristic
229C2×#11924007C2311yescharacteristic
230C2×#11924007C2311yescharacteristic
231C2×#11924007C2311yescharacteristic
232C2×#11924007C2311yescharacteristic
233C2×#11924007C2311yescharacteristic
234C2×#11924007C2311yescharacteristic
235C2×#11924007C2311yescharacteristic
236C2×#11924007C2311yescharacteristic
237C2×#11924007C2311yescharacteristic
238C2×#11924007C2311yescharacteristic
239C2×#11924007C2311yescharacteristic
240C2×#11924007C2311yescharacteristic
241C2×#11924007C2311yescharacteristic
242C2×#11924007C2311yescharacteristic
243C2×#11924007C2311yescharacteristic
244C2×#11924007C2311yescharacteristic
245C4⋊C4×D73—42no—
246C2×C22⋊Dic73C2311yescharacteristic
247C2×C22⋊Dic73C2311yescharacteristic
248C2×C22⋊Dic73C2311yescharacteristic
249C2×C22⋊Dic73C2311yescharacteristic
250C2×C22⋊Dic73C2311yescharacteristic
251C2×C22⋊Dic73C2311yescharacteristic
252C2×C22⋊Dic73C2311yescharacteristic
253C2×C22⋊Dic73C2311yescharacteristic
254C2×C22⋊Dic73C2311yescharacteristic
255C2×#11924005C2311yescharacteristic
256C2×#11924005C2311yescharacteristic
257C2×#11924005C2311yescharacteristic
258C2×#11924005C2311yescharacteristic
259C2×#11924005C2311yescharacteristic
260C2×#11924005C2311yescharacteristic
261C2×#11924005C2311yescharacteristic
262C2×#11924005C2311yescharacteristic
263C2×#11924005C2311yescharacteristic
264C2×#11924005C2311yescharacteristic
265C2×#11924005C2311yescharacteristic
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
289C22⋊C4×D73—24no—
290C22⋊C4×D73—42no—
291C22⋊C4×D73—42no—
292C2×C4×Dic73C2311yescharacteristic
293C2×C4×Dic73C2311yescharacteristic
294C2×C4×Dic73C2311yescharacteristic
295C2×C4×Dic73C2311yescharacteristic
296C2×C4×Dic73C2311yescharacteristic
297C2×C4×Dic73C2311yescharacteristic
298C2×C4×Dic73C2311yescharacteristic
299C42×D73—42no—
300#14556498C2311yescharacteristic
301#14556498C2311yescharacteristic
302#14556498C2311yescharacteristic
303#14556498C2311yescharacteristic
304#14556498C2311yescharacteristic
305#14556498C2311yescharacteristic
306#14556498C2311yescharacteristic
307#14556498C2311yescharacteristic
308#14556498C2311yescharacteristic
309#14556498C2311yescharacteristic
310#14556498C2311yescharacteristic
311#14556498C2311yescharacteristic
312#14556498C2311yescharacteristic
313#14556498C2311yescharacteristic
314#14556498C2311yescharacteristic
315#14556498C2311yescharacteristic
316#14556498C2311yescharacteristic
317#14556498C2311yescharacteristic
318#14556498C2311yescharacteristic
319#14556498C2311yescharacteristic
320#14556498C2311yescharacteristic
321#14556498C2311yescharacteristic
322#14556498C2311yescharacteristic
323#14556498C2311yescharacteristic
324#14556498C2311yescharacteristic
325#14556498C2311yescharacteristic
326#14556498C2311yescharacteristic
327#14556498C2311yescharacteristic
328C22×D4×C73C2311yescharacteristic
329C23×C4×C73C2311yescharacteristic
330C2×C4⋊C4×C73C2311yescharacteristic
331C2×C4⋊C4×C73C2311yescharacteristic
332C2×C4⋊C4×C73C2311yescharacteristic
333C2×C4⋊C4×C73C2311yescharacteristic
334C2×C4⋊C4×C73C2311yescharacteristic
335C2×C4⋊C4×C73C2311yescharacteristic
336C2×C4⋊C4×C73C2311yescharacteristic
337C2×C4⋊C4×C73C2311yescharacteristic
338C2×C22⋊C4×C73C2311yescharacteristic
339C2×C22⋊C4×C73C2311yescharacteristic
340C2×C22⋊C4×C73C2311yescharacteristic
341C2×C22⋊C4×C73C2311yescharacteristic
342C2×C22⋊C4×C73C2311yescharacteristic
343C2×C22⋊C4×C73C2311yescharacteristic
344C2×C22⋊C4×C73C2311yescharacteristic
345C2×C22⋊C4×C73C2311yescharacteristic
346C2×C22⋊C4×C73C2311yescharacteristic
347C2×C22⋊C4×C73C2311yescharacteristic
348C2×C22⋊C4×C73C2311yescharacteristic
349C2×C42×C73C2311yescharacteristic
350C2×C42×C73C2311yescharacteristic
351#95×C73C2311yescharacteristic
352#95×C73C2311yescharacteristic
353#95×C73C2311yescharacteristic
354#95×C73C2311yescharacteristic
355#95×C73C2311yescharacteristic
356#95×C73C2311yescharacteristic
357#95×C73C2311yescharacteristic
358#95×C73C2311yescharacteristic
359#95×C73C2311yescharacteristic
360#95×C73C2311yescharacteristic
361#95×C73C2311yescharacteristic
362#95×C73C2311yescharacteristic
363C23×D73—22no—
364C23×D73—22no—
365C23×D73—22no—
366C23×D73—41no—
367C23×D73—41no—
368C23×D73—41no—
369C23×D73—41no—
370C23×D73C2411yescharacteristic
371C23×D73C2411yescharacteristic
372C23×D73C2411yescharacteristic
373C23×D73C2411yescharacteristic
374C2×D292—22no—
375C2×D292—22no—
376C2×D292—22no—
377C2×D292—22no—
378C2×D292—22no—
379C2×D292—22no—
380C2×D292—22no—
381C2×D292—41no—
382C2×D292—41no—
383C2×D292—41no—
384C2×D292—41no—
385C2×D292—41no—
386C2×D292—41no—
387C2×D292—41no—
388C2×D292—41no—
389C2×C22⋊D73—22no—
390C2×C22⋊D73—22no—
391C2×C22⋊D73—22no—
392C2×C22⋊D73—22no—
393C2×C22⋊D73—41no—
394C2×C22⋊D73—41no—
395C2×C22⋊D73—41no—
396C2×C22⋊D73—41no—
397C2×C22⋊D73—41no—
398C2×C22⋊D73—41no—
399C2×C22⋊D73—41no—
400C2×C22⋊D73—41no—
401C2×C22⋊D73—41no—
402C2×C22⋊D73—41no—
403C2×C22⋊D73—41no—
404C2×C22⋊D73—41no—
405C2×C22⋊D73—41no—
406C2×C22⋊D73—41no—
407C22×Dic73C2411yescharacteristic
408C22×Dic73C2411yescharacteristic
409C22×Dic73C2411yescharacteristic
410C22×Dic73C2411yescharacteristic
411C22×Dic73C2411yescharacteristic
412C22×Dic73C2411yescharacteristic
413C22×Dic73C2411yescharacteristic
414C22×Dic73C2411yescharacteristic
415C22×Dic73C2411yescharacteristic
416C22×Dic73C2411yescharacteristic
417C22×Dic73C2411yescharacteristic
418C22×Dic73C2411yescharacteristic
419C2×C4×D73—22no—
420C2×C4×D73—22no—
421C2×C4×D73—22no—
422C2×C4×D73—22no—
423C2×C4×D73—22no—
424C2×C4×D73—22no—
425C2×C4×D73—22no—
426C2×C4×D73—22no—
427C2×C4×D73—41no—
428C2×C4×D73—41no—
429C2×C4×D73—41no—
430C2×C4×D73—41no—
431C2×C4×D73—41no—
432C2×C4×D73—41no—
433C2×C4×D73—41no—
434C2×C4×D73—41no—
435C2×C4×D73—41no—
436C2×C4×D73—41no—
437C2×C4×D73—41no—
438C2×C4×D73—41no—
439C2×C4×D73—41no—
440C2×C4×D73—41no—
441C2×C4×D73—41no—
442C2×C4×D73#4114yes—
443C4⋊Dic73—22no—
444C4⋊Dic73—41no—
445C4⋊Dic73—41no—
446C4⋊Dic73—41no—
447C4⋊Dic73—41no—
448C4⋊Dic73—41no—
449#11924007—22no—
450#11924007—22no—
451#11924007—22no—
452#11924007—22no—
453#11924007—41no—
454#11924007—41no—
455#11924007—41no—
456#11924007—41no—
457#11924007—41no—
458#11924007—41no—
459#11924007—41no—
460#11924007—41no—
461#11924007—41no—
462#11924007—41no—
463#11924007—41no—
464#11924007—41no—
465C22⋊Dic73—22no—
466C22⋊Dic73—22no—
467C22⋊Dic73—22no—
468C22⋊Dic73—41no—
469C22⋊Dic73—41no—
470C22⋊Dic73—41no—
471C22⋊Dic73—41no—
472C22⋊Dic73—41no—
473C22⋊Dic73—41no—
474#11924005—22no—
475#11924005—22no—
476#11924005—22no—
477#11924005—22no—
478#11924005—22no—
479#11924005—22no—
480#11924005—22no—
481#11924005—22no—
482#11924005—22no—
483#11924005—22no—
484#11924005—22no—
485#11924005—41no—
486#11924005—41no—
487#11924005—41no—
488#11924005—41no—
489#11924005—41no—
490#11924005—41no—
491#11924005—41no—
492#11924005—41no—
493#11924005—41no—
494#11924005—41no—
495#11924005—41no—
496#11924005—41no—
497#11924005—41no—
498#11924005—41no—
499#11924005—41no—
500#11924005—41no—
501#11924005—41no—
502#11924005—41no—
503#11924005—41no—
504#11924005—41no—
505#11924005—41no—
506#11924005—41no—
507#11924005—41no—
508C4×Dic73—22no—
509C4×Dic73—41no—
510C4×Dic73—41no—
511C4×Dic73—41no—
512C4×Dic73—41no—
513C4×Dic73—41no—
514C4×Dic73—41no—
515C24×C73C2411yescharacteristic
516C24×C73C2411yescharacteristic
517C2×D4×C73—41no—
518C2×D4×C73—41no—
519C2×D4×C73—41no—
520C22×C4×C73—22no—
521C22×C4×C73—41no—
522C22×C4×C73—41no—
523C22×C4×C73C2411yescharacteristic
524C22×C4×C73C2411yescharacteristic
525C22×C4×C73C2411yescharacteristic
526C22×C4×C73C2411yescharacteristic
527C22×C4×C73C2411yescharacteristic
528C22×C4×C73C2411yescharacteristic
529C22×C4×C73C2411yescharacteristic
530C22×C4×C73C2411yescharacteristic
531C22×C4×C73C2411yescharacteristic
532C22×C4×C73C2411yescharacteristic
533C22×C4×C73C2411yescharacteristic
534C22×C4×C73C2411yescharacteristic
535C22×C4×C73C2411yescharacteristic
536C4⋊C4×C73—22no—
537C4⋊C4×C73—41no—
538C4⋊C4×C73—41no—
539C4⋊C4×C73—41no—
540C4⋊C4×C73—41no—
541C4⋊C4×C73—41no—
542C4⋊C4×C73—41no—
543C4⋊C4×C73—41no—
544C22⋊C4×C73—22no—
545C22⋊C4×C73—41no—
546C22⋊C4×C73—41no—
547C22⋊C4×C73—41no—
548C22⋊C4×C73—41no—
549C22⋊C4×C73—41no—
550C22⋊C4×C73—41no—
551C22⋊C4×C73—41no—
552C22⋊C4×C73—41no—
553C22⋊C4×C73—41no—
554C22⋊C4×C73—41no—
555C42×C73—41no—
556C42×C73—41no—
557C23×C73—21no—
558C23×C73—21no—
559C23×C73—21no—
560C23×C73—21no—
561C23×C73—21no—
562C23×C73—21no—
563C23×C73—21no—
564C23×C73—21no—
565C23×C73—21no—
566C23×C73—21no—
567C23×C73—21no—
568C23×C73—21no—
569C23×C73—21no—
570C23×C73—21no—
571C23×C73C2511yescharacteristic
572C22×D73—21no—
573C22×D73—21no—
574C22×D73—21no—
575C22×D73—21no—
576C22×D73—21no—
577C22×D73—21no—
578C22×D73—21no—
579C22×D73—21no—
580C22×D73—21no—
581C22×D73—21no—
582C22×D73—21no—
583C22×D73—21no—
584C22×D73—21no—
585C22×D73—21no—
586C22×D73—21no—
587C22×D73—21no—
588C22×D73—21no—
589C22×D73—21no—
590C22×D73—21no—
591C22×D73—21no—
592C22×D73—21no—
593C22×D73—21no—
594C22×D73—21no—
595C22×D73—21no—
596C22×D73—21no—
597C22×D73—44no—
598C22×D73—44no—
599C22×D73—44no—
600C22×D73—82no—
601C22×D73—82no—
602C22×D73—82no—
603C22×D73—82no—
604C22×D73C2×#4112yes—
605C22×D73H(5,𝔽2)12yes—
606C22×D73H(5,𝔽2)12yes—
607D4×C73—82no—
608C2×C4×C73—21no—
609C2×C4×C73—21no—
610C2×C4×C73—21no—
611C2×C4×C73—21no—
612C2×C4×C73—21no—
613C2×C4×C73—21no—
614C2×C4×C73—21no—
615C2×C4×C73—21no—
616C2×C4×C73—21no—
617C2×C4×C73—21no—
618C2×C4×C73—21no—
619C2×C4×C73—21no—
620C2×C4×C73—21no—
621C2×C4×C73—21no—
622C2×C4×C73—21no—
623C2×C4×C73—21no—
624C2×C4×C73—21no—
625C2×C4×C73—21no—
626C2×C4×C73—21no—
627C2×C4×C73—21no—
628C2×C4×C73—21no—
629C2×C4×C73—21no—
630C2×C4×C73—21no—
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—82no—
647C2×C4×C73C2×#4112yes—
648C22⋊D73—44no—
649C22⋊D73—82no—
650C22⋊D73—82no—
651C22⋊D73—82no—
652C22⋊D73—82no—
653C22⋊D73—82no—
654C2×Dic73—21no—
655C2×Dic73—21no—
656C2×Dic73—21no—
657C2×Dic73—21no—
658C2×Dic73—21no—
659C2×Dic73—21no—
660C2×Dic73—21no—
661C2×Dic73—21no—
662C2×Dic73—21no—
663C2×Dic73—21no—
664C2×Dic73—21no—
665C2×Dic73—21no—
666C2×Dic73—21no—
667C2×Dic73—21no—
668C2×Dic73—21no—
669C2×Dic73—21no—
670C2×Dic73—21no—
671C2×Dic73—21no—
672C2×Dic73—21no—
673C2×Dic73—21no—
674C2×Dic73—21no—
675C2×Dic73—21no—
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×Dic73C2×#4112yes—
689C2×Dic73H(5,𝔽2)12yes—
690D292—44no—
691D292—44no—
692D292—82no—
693D292—82no—
694D292—82no—
695C4×D73—44no—
696C4×D73—44no—
697C4×D73—44no—
698C4×D73—44no—
699C4×D73—82no—
700C4×D73—82no—
701C4×D73—82no—
702C4×D73—82no—
703C22×C73—41no—
704C22×C73—41no—
705C22×C73—41no—
706C22×C73—41no—
707C22×C73—41no—
708C22×C73—41no—
709C22×C73—41no—
710C22×C73—41no—
711C22×C73—41no—
712C22×C73—41no—
713C22×C73—41no—
714C22×C73—41no—
715C22×C73—41no—
716C22×C73—41no—
717C22×C73C22×#4111yescharacteristic
718C22×C73C2×H(5,𝔽2)11yescharacteristic
719C22×C73C2×H(5,𝔽2)11yescharacteristic
720C22×C73C2×H(5,𝔽2)11yescharacteristic
721C22×C73#58511yescharacteristic
722C22×C73#58511yescharacteristic
723C22×C73#58511yescharacteristic
724C2×D73—22no—
725C2×D73—22no—
726C2×D73—22no—
727C2×D73—22no—
728C2×D73—22no—
729C2×D73—22no—
730C2×D73—41no—
731C2×D73—41no—
732C2×D73—41no—
733C2×D73—41no—
734C2×D73—41no—
735C2×D73—41no—
736C2×D73—41no—
737C2×D73—41no—
738C2×D73—41no—
739C2×D73—41no—
740C2×D73—41no—
741C2×D73—41no—
742C2×D73—41no—
743C2×D73—41no—
744C2×D73—41no—
745C2×D73—41no—
746C2×D73—41no—
747C2×D73—41no—
748C2×D73—41no—
749C2×D73—41no—
750C2×D73—41no—
751C2×D73—88no—
752C2×D73#54014yes—
753C4×C73—22no—
754C4×C73—41no—
755C4×C73—41no—
756C4×C73—41no—
757C4×C73—41no—
758C4×C73—41no—
759C4×C73—41no—
760C4×C73—41no—
761C4×C73—41no—
762C4×C73—41no—
763C4×C73—41no—
764C4×C73—41no—
765C4×C73—41no—
766Dic73—22no—
767Dic73—22no—
768Dic73—41no—
769Dic73—41no—
770Dic73—41no—
771Dic73—41no—
772Dic73—41no—
773Dic73—41no—
774Dic73—41no—
775Dic73—41no—
776Dic73—41no—
777Dic73—41no—
778#36987—731nomaximal, Sylow
779C2×C73—81no—
780C2×C73—81no—
781C2×C73C2×#54011yescharacteristic
782C2×C73#349311yescharacteristic
783C2×C73#350511yescharacteristic
784C2×C73#353311yescharacteristic
785C2×C73#353411yescharacteristic
786C2×C73#355811yescharacteristic
787C2×C73#356011yescharacteristic
788D73—24no—
789D73—81no—
790D73—81no—
791D73—81no—
792#2854—731no—
793#2853—731no—
794#2803—731no—
795#2803—731no—
796#2800—731no—
797#2800—731no—
798#2777—731no—
799#2773—731no—
800#2761—731no—
801#2756—731no—
802#2753—731no—
803#2753—731no—
804#2741—731no—
805#2740D7311yescharacteristic, complemented
806#2711—731no—
807#2707—731no—
808#2703—731no—
809#2699—731no—
810#2622—731no—
811#2617—731no—
812#2539—731no—
813#2534—731no—
814#2442—731no—
815#2425—731no—
816#2424—731no—
817#2419—731no—
818#2418—731no—
819#2416—731no—
820#2325—731no—
821#2318—731no—
822C2×#388—731no—
823C73#3698711yescharacteristic, complemented, Sylow
824C2×#125—731no—
825C2×#123—731no—
826C2×#123—731no—
827C2×#123—731no—
828C2×#123—731no—
829C2×#121—731no—
830C2×#121—731no—
831C2×#121—731no—
832C2×#121—731no—
833C2×#121—731no—
834C2×#120—731no—
835C2×#120—731no—
836C2×#120—731no—
837C2×C4×D4—731no—
838C2×C4×D4—731no—
839C2×C4×D4—731no—
840C22×C4⋊C4—731no—
841C22×C22⋊C4—731no—
842C22×C22⋊C4—731no—
843C22×C22⋊C4—731no—
844C22×C42—731no—
845#400—731no—
846#400—731no—
847#400—731no—
848#399—731no—
849#399—731no—
850#399C2×D7311yescharacteristic
851#398—731no—
852#398—731no—
853#398—731no—
854#398C2×D7311yescharacteristic, complemented
855#397—731no—
856#397—731no—
857#397—731no—
858#397—731no—
859#397—731no—
860#397—731no—
861#397—731no—
862#397—731no—
863#397C2×D7311yescharacteristic
864#397C2×D7311yescharacteristic
865#396—731no—
866#396—731no—
867#396—731no—
868#396—731no—
869#396—731no—
870#396C2×D7311yescharacteristic, complemented
871#394—731no—
872#394—731no—
873#394—731no—
874#394—731no—
875#394—731no—
876#394—731no—
877#394—731no—
878#394—731no—
879#394—731no—
880#394—731no—
881#394—731no—
882#394—731no—
883#394—731no—
884#394—731no—
885#394—731no—
886#394—731no—
887#394C2×D7311yescharacteristic
888#392—731no—
889#392—731no—
890#392—731no—
891#392—731no—
892#392—731no—
893#390—731no—
894#390—731no—
895#390—731no—
896#390—731no—
897#390—731no—
898#390—731no—
899#390—731no—
900#390C2×D7311yescharacteristic
901#389—731no—
902#389—731no—
903#389—731no—
904#389—731no—
905#389—731no—
906#389—731no—
907#388—731no—
908#388—731no—
909#388—731no—
910#388—731no—
911#388—731no—
912#388—731no—
913#388—731no—
914#388—731no—
915#388—731no—
916#388—731no—
917#388—731no—
918#388—731no—
919#388—731no—
920#388—731no—
921#388—731no—
922#388—731no—
923#388—731no—
924#388—731no—
925#388—731no—
926#388—731no—
927#388—731no—
928#388—731no—
929#388—731no—
930#388—731no—
931#388C2×D7311yescharacteristic
932#388C2×D7311yescharacteristic, complemented
933#387—731no—
934#387—731no—
935#387—731no—
936#387—731no—
937#387—731no—
938#387—731no—
939#387—731no—
940#387C2×D7311yescharacteristic, complemented
941#387C2×D7311yescharacteristic, complemented
942#387C2×D7311yescharacteristic, complemented
943#386—731no—
944#386—731no—
945#386—731no—
946#386—731no—
947#386—731no—
948#386—731no—
949#386—731no—
950#386—731no—
951#386—731no—
952#386—731no—
953#386—731no—
954#386—731no—
955#386C2×D7311yescharacteristic
956#385—731no—
957#385—731no—
958#385—731no—
959#385—731no—
960#385—731no—
961#385—731no—
962#385—731no—
963#383—731no—
964#382—731no—
965#382—731no—
966#381—731no—
967#381—731no—
968#381C2×D7311yescharacteristic, complemented
969#380—731no—
970#380—731no—
971#380—731no—
972#380—731no—
973#380—731no—
974#380C2×D7311yescharacteristic, complemented
975#379—731no—
976C4×C22⋊C4—731no—
977C2×#95—731no—
978C2×#95—731no—
979C25—731no—
980C22×D4—731no—
981C22×D4—731no—
982C22×D4—731no—
983C22×D4—731no—
984C22×D4—731no—
985C22×D4—731no—
986C22×D4—731no—
987C22×D4—731no—
988C22×D4—731no—
989C22×D4—731no—
990C22×D4—731no—
991C22×D4C22×D7311yescharacteristic
992C23×C4—731no—
993C23×C4—731no—
994C23×C4—731no—
995C23×C4—731no—
996C23×C4—731no—
997C23×C4—731no—
998C23×C4—731no—
999C23×C4—731no—
1000C23×C4C22×D7311yescharacteristic
1001#125—2922no—
1002#123—2922no—
1003#123—2922no—
1004#123—2922no—
1005#123—2922no—
1006#121—2922no—
1007#121—2922no—
1008#121—2922no—
1009#121—2922no—
1010#121—1464no—
1011#120—2922no—
1012#120—2922no—
1013#120—2922no—
1014C4×D4—2922no—
1015C4×D4—2922no—
1016C4×D4—1464no—
1017C2×C4⋊C4—2922no—
1018C2×C4⋊C4—731no—
1019C2×C4⋊C4—731no—
1020C2×C4⋊C4—731no—
1021C2×C4⋊C4—731no—
1022C2×C4⋊C4—731no—
1023C2×C4⋊C4—731no—
1024C2×C4⋊C4—731no—
1025C2×C4⋊C4—731no—
1026C2×C4⋊C4—731no—
1027C2×C4⋊C4—731no—
1028C2×C4⋊C4—731no—
1029C2×C4⋊C4—731no—
1030C2×C4⋊C4—731no—
1031C2×C4⋊C4—731no—
1032C2×C4⋊C4—731no—
1033C2×C4⋊C4—731no—
1034C2×C4⋊C4—731no—
1035C2×C4⋊C4—731no—
1036C2×C4⋊C4—731no—
1037C2×C4⋊C4—731no—
1038C2×C4⋊C4—731no—
1039C2×C4⋊C4—731no—
1040C2×C4⋊C4C22×D7311yescharacteristic
1041C2×C4⋊C4C22×D7311yescharacteristic
1042C2×C4⋊C4C22×D7311yescharacteristic
1043C2×C4⋊C4C22×D7311yescharacteristic
1044C2×C4⋊C4C22×D7311yescharacteristic
1045C2×C4⋊C4C22×D7311yescharacteristic
1046C2×C4⋊C4C22×D7311yescharacteristic
1047C2×C4⋊C4C22×D7311yescharacteristic
1048C2×C22⋊C4—2922no—
1049C2×C22⋊C4—2922no—
1050C2×C22⋊C4—731no—
1051C2×C22⋊C4—731no—
1052C2×C22⋊C4—731no—
1053C2×C22⋊C4—731no—
1054C2×C22⋊C4—731no—
1055C2×C22⋊C4—731no—
1056C2×C22⋊C4—731no—
1057C2×C22⋊C4—731no—
1058C2×C22⋊C4—731no—
1059C2×C22⋊C4—731no—
1060C2×C22⋊C4—731no—
1061C2×C22⋊C4—731no—
1062C2×C22⋊C4—731no—
1063C2×C22⋊C4—731no—
1064C2×C22⋊C4—731no—
1065C2×C22⋊C4—731no—
1066C2×C22⋊C4—731no—
1067C2×C22⋊C4—731no—
1068C2×C22⋊C4—731no—
1069C2×C22⋊C4—731no—
1070C2×C22⋊C4—731no—
1071C2×C22⋊C4—731no—
1072C2×C22⋊C4—731no—
1073C2×C22⋊C4—731no—
1074C2×C22⋊C4—731no—
1075C2×C22⋊C4—731no—
1076C2×C22⋊C4—731no—
1077C2×C22⋊C4—731no—
1078C2×C22⋊C4—731no—
1079C2×C22⋊C4—731no—
1080C2×C22⋊C4—731no—
1081C2×C22⋊C4—731no—
1082C2×C22⋊C4—731no—
1083C2×C22⋊C4—731no—
1084C2×C22⋊C4—731no—
1085C2×C22⋊C4—731no—
1086C2×C22⋊C4—731no—
1087C2×C22⋊C4—731no—
1088C2×C22⋊C4—731no—
1089C2×C22⋊C4—731no—
1090C2×C22⋊C4—731no—
1091C2×C22⋊C4—731no—
1092C2×C22⋊C4—731no—
1093C2×C22⋊C4—1464no—
1094C2×C22⋊C4C22×D7311yescharacteristic
1095C2×C22⋊C4C22×D7311yescharacteristic
1096C2×C22⋊C4C22×D7311yescharacteristic
1097C2×C22⋊C4C22×D7311yescharacteristic
1098C2×C22⋊C4C22×D7311yescharacteristic
1099C2×C22⋊C4C22×D7311yescharacteristic
1100C2×C22⋊C4C22×D7311yescharacteristic
1101C2×C22⋊C4C22×D7311yescharacteristic
1102C2×C22⋊C4C22×D7311yescharacteristic
1103C2×C22⋊C4C22×D7311yescharacteristic
1104C2×C22⋊C4C22×D7311yescharacteristic
1105C2×C42—2922no—
1106C2×C42—731no—
1107C2×C42—731no—
1108C2×C42—731no—
1109C2×C42—731no—
1110C2×C42—731no—
1111C2×C42—731no—
1112C2×C42—731no—
1113C2×C42C22×D7311yescharacteristic
1114C2×C42C22×D7311yescharacteristic
1115#95—731no—
1116#95—731no—
1117#95—731no—
1118#95—731no—
1119#95—731no—
1120#95—731no—
1121#95—731no—
1122#95—731no—
1123#95—731no—
1124#95—731no—
1125#95—731no—
1126#95—731no—
1127#95—731no—
1128#95—731no—
1129#95—731no—
1130#95—731no—
1131#95—731no—
1132#95—731no—
1133#95—731no—
1134#95—731no—
1135#95—731no—
1136#95—731no—
1137#95—731no—
1138#95—731no—
1139#95—731no—
1140#95—731no—
1141#95—731no—
1142#95—731no—
1143#95C22×D7311yescharacteristic
1144#95C22×D7311yescharacteristic
1145#95C22×D7311yescharacteristic
1146#95C22×D7311yescharacteristic
1147#95C22×D7311yescharacteristic
1148#95C22×D7311yescharacteristic
1149#95C22×D7311yescharacteristic
1150#95C22×D7311yescharacteristic
1151#95C22×D7311yescharacteristic
1152#95C22×D7311yescharacteristic
1153#95C22×D7311yescharacteristic
1154#95C22×D7311yescharacteristic
1155C24—2921no—
1156C24—2921no—
1157C24—2921no—
1158C24—2921no—
1159C24—731no—
1160C24—731no—
1161C24—731no—
1162C24—731no—
1163C24—1462no—
1164C24—1462no—
1165C24—1462no—
1166C24C23×D7311yescharacteristic
1167C24C23×D7311yescharacteristic
1168C2×D4—41no—
1169C2×D4—41no—
1170C2×D4—41no—
1171C2×D4—2921no—
1172C2×D4—2921no—
1173C2×D4—2921no—
1174C2×D4—2921no—
1175C2×D4—2921no—
1176C2×D4—2921no—
1177C2×D4—2921no—
1178C2×D4—2921no—
1179C2×D4—2921no—
1180C2×D4—2921no—
1181C2×D4—2921no—
1182C2×D4—2921no—
1183C2×D4—2921no—
1184C2×D4—2921no—
1185C2×D4—2921no—
1186C2×D4—2921no—
1187C2×D4—2921no—
1188C2×D4—2921no—
1189C2×D4—2921no—
1190C2×D4—2921no—
1191C2×D4—2921no—
1192C2×D4—2921no—
1193C2×D4—1462no—
1194C2×D4—1462no—
1195C2×D4—1462no—
1196C2×D4—1462no—
1197C2×D4—1462no—
1198C2×D4—1462no—
1199C2×D4—1462no—
1200C2×D4—1462no—
1201C2×D4—1462no—
1202C2×D4—1462no—
1203C2×D4—1462no—
1204C22×C4—22no—
1205C22×C4—41no—
1206C22×C4—41no—
1207C22×C4—2921no—
1208C22×C4—2921no—
1209C22×C4—2921no—
1210C22×C4—2921no—
1211C22×C4—2921no—
1212C22×C4—2921no—
1213C22×C4—2921no—
1214C22×C4—2921no—
1215C22×C4—2921no—
1216C22×C4—2921no—
1217C22×C4—2921no—
1218C22×C4—2921no—
1219C22×C4—2921no—
1220C22×C4—2921no—
1221C22×C4—2921no—
1222C22×C4—734no—
1223C22×C4—731no—
1224C22×C4—731no—
1225C22×C4—731no—
1226C22×C4—731no—
1227C22×C4—731no—
1228C22×C4—731no—
1229C22×C4—731no—
1230C22×C4—731no—
1231C22×C4—731no—
1232C22×C4—731no—
1233C22×C4—731no—
1234C22×C4—731no—
1235C22×C4—1462no—
1236C22×C4—1462no—
1237C22×C4—1462no—
1238C22×C4—1462no—
1239C22×C4—1462no—
1240C22×C4—1462no—
1241C22×C4—1462no—
1242C22×C4—1462no—
1243C22×C4C23×D7311yescharacteristic
1244C22×C4C23×D7311yescharacteristic
1245C22×C4C23×D7311yescharacteristic
1246C22×C4C23×D7311yescharacteristic
1247C22×C4C23×D7311yescharacteristic
1248C22×C4C23×D7311yescharacteristic
1249C22×C4C23×D7311yescharacteristic
1250C22×C4C23×D7311yescharacteristic
1251C22×C4C23×D7311yescharacteristic
1252C22×C4C23×D7311yescharacteristic
1253C22×C4C23×D7311yescharacteristic
1254C22×C4C23×D7311yescharacteristic
1255C22×C4C23×D7311yescharacteristic
1256C4⋊C4—22no—
1257C4⋊C4—41no—
1258C4⋊C4—41no—
1259C4⋊C4—41no—
1260C4⋊C4—41no—
1261C4⋊C4—41no—
1262C4⋊C4—41no—
1263C4⋊C4—41no—
1264C4⋊C4—2921no—
1265C4⋊C4—2921no—
1266C4⋊C4—2921no—
1267C4⋊C4—2921no—
1268C4⋊C4—2921no—
1269C4⋊C4—2921no—
1270C4⋊C4—2921no—
1271C4⋊C4—2921no—
1272C4⋊C4—2921no—
1273C4⋊C4—2921no—
1274C4⋊C4—2921no—
1275C4⋊C4—2921no—
1276C4⋊C4—2921no—
1277C4⋊C4—2921no—
1278C4⋊C4—2921no—
1279C4⋊C4—2921no—
1280C4⋊C4—2921no—
1281C4⋊C4—1462no—
1282C4⋊C4—1462no—
1283C4⋊C4—1462no—
1284C4⋊C4—1462no—
1285C4⋊C4—1462no—
1286C22⋊C4—22no—
1287C22⋊C4—41no—
1288C22⋊C4—41no—
1289C22⋊C4—41no—
1290C22⋊C4—41no—
1291C22⋊C4—41no—
1292C22⋊C4—41no—
1293C22⋊C4—41no—
1294C22⋊C4—41no—
1295C22⋊C4—41no—
1296C22⋊C4—41no—
1297C22⋊C4—2921no—
1298C22⋊C4—2921no—
1299C22⋊C4—2921no—
1300C22⋊C4—2921no—
1301C22⋊C4—2921no—
1302C22⋊C4—2921no—
1303C22⋊C4—2921no—
1304C22⋊C4—2921no—
1305C22⋊C4—2921no—
1306C22⋊C4—2921no—
1307C22⋊C4—2921no—
1308C22⋊C4—2921no—
1309C22⋊C4—2921no—
1310C22⋊C4—2921no—
1311C22⋊C4—2921no—
1312C22⋊C4—2921no—
1313C22⋊C4—2921no—
1314C22⋊C4—2921no—
1315C22⋊C4—2921no—
1316C22⋊C4—2921no—
1317C22⋊C4—2921no—
1318C22⋊C4—2921no—
1319C22⋊C4—2921no—
1320C22⋊C4—2921no—
1321C22⋊C4—2921no—
1322C22⋊C4—2921no—
1323C22⋊C4—2921no—
1324C22⋊C4—2921no—
1325C22⋊C4—2921no—
1326C22⋊C4—1462no—
1327C22⋊C4—1462no—
1328C22⋊C4—1462no—
1329C22⋊C4—1462no—
1330C22⋊C4—1462no—
1331C22⋊C4—1462no—
1332C22⋊C4—1462no—
1333C22⋊C4—1462no—
1334C22⋊C4—1462no—
1335C22⋊C4—1462no—
1336C22⋊C4—1462no—
1337C22⋊C4—1462no—
1338C22⋊C4—1462no—
1339C22⋊C4—1462no—
1340C42—41no—
1341C42—41no—
1342C42—2921no—
1343C42—2921no—
1344C42—2921no—
1345C42—2921no—
1346C42—2921no—
1347C42—2921no—
1348C42—1462no—
1349C23—21no—
1350C23—21no—
1351C23—21no—
1352C23—21no—
1353C23—21no—
1354C23—21no—
1355C23—21no—
1356C23—21no—
1357C23—21no—
1358C23—21no—
1359C23—21no—
1360C23—21no—
1361C23—21no—
1362C23—21no—
1363C23—2924no—
1364C23—2924no—
1365C23—2924no—
1366C23—5842no—
1367C23—5842no—
1368C23—5842no—
1369C23—5842no—
1370C23—732no—
1371C23—732no—
1372C23—732no—
1373C23—1461no—
1374C23—1461no—
1375C23—1461no—
1376C23—1461no—
1377C23—1461no—
1378C23—1461no—
1379C23—1461no—
1380C23—1461no—
1381C23—1461no—
1382C23—1461no—
1383C23—1461no—
1384C23—1461no—
1385C23—1461no—
1386C23—1461no—
1387C23—1461no—
1388C23—1461no—
1389C23—1461no—
1390C23—1461no—
1391C23—1461no—
1392C23—1461no—
1393C23—1461no—
1394C23—1461no—
1395C23—1461no—
1396C23—1461no—
1397C23—1461no—
1398C23C24×D7311yescharacteristic
1399D4—82no—
1400D4—2924no—
1401D4—2924no—
1402D4—2924no—
1403D4—5842no—
1404D4—5842no—
1405D4—5842no—
1406D4—5842no—
1407D4—5842no—
1408D4—5842no—
1409D4—5842no—
1410D4—5842no—
1411C2×C4—21no—
1412C2×C4—21no—
1413C2×C4—21no—
1414C2×C4—21no—
1415C2×C4—21no—
1416C2×C4—21no—
1417C2×C4—21no—
1418C2×C4—21no—
1419C2×C4—21no—
1420C2×C4—21no—
1421C2×C4—21no—
1422C2×C4—21no—
1423C2×C4—21no—
1424C2×C4—21no—
1425C2×C4—21no—
1426C2×C4—21no—
1427C2×C4—21no—
1428C2×C4—21no—
1429C2×C4—21no—
1430C2×C4—21no—
1431C2×C4—21no—
1432C2×C4—21no—
1433C2×C4—21no—
1434C2×C4—21no—
1435C2×C4—21no—
1436C2×C4—21no—
1437C2×C4—21no—
1438C2×C4—21no—
1439C2×C4—21no—
1440C2×C4—21no—
1441C2×C4—21no—
1442C2×C4—21no—
1443C2×C4—21no—
1444C2×C4—21no—
1445C2×C4—21no—
1446C2×C4—21no—
1447C2×C4—21no—
1448C2×C4—21no—
1449C2×C4—82no—
1450C2×C4—2924no—
1451C2×C4—2924no—
1452C2×C4—2924no—
1453C2×C4—2924no—
1454C2×C4—5842no—
1455C2×C4—5842no—
1456C2×C4—5842no—
1457C2×C4—5842no—
1458C2×C4—732no—
1459C2×C4—732no—
1460C2×C4—1461no—
1461C2×C4—1461no—
1462C2×C4—1461no—
1463C2×C4—1461no—
1464C2×C4—1461no—
1465C2×C4—1461no—
1466C2×C4—1461no—
1467C2×C4—1461no—
1468C2×C4—1461no—
1469C2×C4—1461no—
1470C2×C4—1461no—
1471C2×C4—1461no—
1472C2×C4—1461no—
1473C2×C4—1461no—
1474C2×C4—1461no—
1475C2×C4—1461no—
1476C2×C4—1461no—
1477C2×C4—1461no—
1478C2×C4—1461no—
1479C2×C4—1461no—
1480C2×C4—1461no—
1481C2×C4—1461no—
1482C2×C4—1461no—
1483C2×C4—1461no—
1484C2×C4—1461no—
1485C2×C4—1461no—
1486C2×C4—1461no—
1487C2×C4—1461no—
1488C2×C4—1461no—
1489C2×C4—1461no—
1490C2×C4—1461no—
1491C2×C4—1461no—
1492C2×C4—1461no—
1493C2×C4—1461no—
1494C2×C4#41×D7312yes—
1495C22—41no—
1496C22—41no—
1497C22—41no—
1498C22—41no—
1499C22—41no—
1500C22—41no—
1501C22—41no—
1502C22—41no—
1503C22—41no—
1504C22—41no—
1505C22—41no—
1506C22—41no—
1507C22—41no—
1508C22—41no—
1509C22—2921no—
1510C22—2921no—
1511C22—2921no—
1512C22—2921no—
1513C22—2921no—
1514C22—2921no—
1515C22—2921no—
1516C22—2921no—
1517C22—2921no—
1518C22—2921no—
1519C22—2921no—
1520C22—2921no—
1521C22—2921no—
1522C22—2921no—
1523C22—2921no—
1524C22—2921no—
1525C22—2921no—
1526C22—2921no—
1527C22—2921no—
1528C22—2921no—
1529C22—2921no—
1530C22—5848no—
1531C22—734no—
1532C22—1462no—
1533C22—1462no—
1534C22—1462no—
1535C22—1462no—
1536C22—1462no—
1537C22—1462no—
1538C22C2×#41×D7311yescharacteristic
1539C22H(5,𝔽2)×D7311yescharacteristic
1540C22H(5,𝔽2)×D7311yescharacteristic
1541C22H(5,𝔽2)×D7311yescharacteristic
1542C22#1798942311yescharacteristic
1543C22#1798942311yescharacteristic
1544C22#1798942411yescharacteristic
1545C4—22no—
1546C4—41no—
1547C4—41no—
1548C4—41no—
1549C4—41no—
1550C4—41no—
1551C4—41no—
1552C4—41no—
1553C4—41no—
1554C4—41no—
1555C4—41no—
1556C4—41no—
1557C4—41no—
1558C4—2921no—
1559C4—2921no—
1560C4—2921no—
1561C4—2921no—
1562C4—2921no—
1563C4—2921no—
1564C4—2921no—
1565C4—2921no—
1566C4—2921no—
1567C4—2921no—
1568C4—1462no—
1569C4—1462no—
1570C2—81no—
1571C2—81no—
1572C2—5841no—
1573C2—5841no—
1574C2—5841no—
1575C2—1464no—
1576C2#540×D7311yescharacteristic
1577C2#2262364511yescharacteristic
1578C2#2262376211yescharacteristic
1579C2#2262410611yescharacteristic
1580C2#2262411411yescharacteristic
1581C2#2262445311yescharacteristic
1582C2#2262447811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D73
commutator, socle, cosocleC23×C73C25
FittingC73×#2740C2
hypercenter#2740D73
hypocenterC73#36987
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #2740

Complements

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

NH ≅ G/Ntype
1. #22618258C2semidirect
2. #22618255C2semidirect
3. #22617871C2semidirect
4. #22617860C2semidirect
5. #22617824C2semidirect
6. #22617824C2semidirect
7. #22617536C2semidirect
8. #22617468C2semidirect
9. #22617323C2semidirect
10. #22617259C2semidirect
11. #22617206C2semidirect
12. #22617206C2semidirect
13. #22617042C2semidirect
14. #22616694C2semidirect
15. #22616636C2semidirect
16. #22616578C2semidirect
17. #22616518C2semidirect
18. #22615705C2semidirect
19. #22615670C2semidirect
20. #22614858C2semidirect
21. #22614819C2semidirect
22. #22613650C2semidirect
23. #22613477C2semidirect
24. #22613474C2semidirect
25. #22613415C2semidirect
26. #22613394C2semidirect
27. #22613373C2semidirect
28. #22612630C2semidirect
29. #22612560C2semidirect
30. #388×D73C2semidirect
31. C73×#2740C2semidirect
32. C2×#14556581C22semidirect
38. C2×#14556565C22semidirect
53. #17988529C22semidirect
54. #17988526C22semidirect
55. #17988526C22semidirect
58. #17988521C22semidirect
59. #17988519C22semidirect
60. #17988517C22semidirect
63. #17988516C22semidirect
67. #17988514C22semidirect
68. #17988513C22semidirect
70. #17988511C22semidirect
71. #17988511C22semidirect
86. #17988502C22semidirect
87. #17988502C22semidirect
88. #17988502C22semidirect
97. #17988488C22semidirect
100. #17988487C22semidirect
101. #17988487C22semidirect
102. #17988484C22semidirect
103. #17988483C22semidirect
104. #17988482C22semidirect
105. #17988482C22semidirect
106. #17988482C22semidirect
107. #17988482C22semidirect
109. #17988481C22semidirect
114. #17988479C22semidirect
115. #17988479C22semidirect
118. #17988478C22semidirect
119. #17988478C22semidirect
120. #17988478C22semidirect
122. #17988477C22semidirect
124. #17988476C22semidirect
125. #17988476C22semidirect
129. #17988475C22semidirect
130. #17988475C22semidirect
131. #17988475C22semidirect
132. #17988474C22semidirect
133. #17988474C22semidirect
134. #17988473C22semidirect
135. #17988471C22semidirect
136. #17988470C22semidirect
137. #17988469C22semidirect
138. #17988468C22semidirect
145. #17988465C22semidirect
146. #17988465C22semidirect
150. #17988463C22semidirect
153. #17988461C22semidirect
154. #17988461C22semidirect
157. #17988458C22semidirect
158. #17988454C22semidirect
159. #17988451C22semidirect
160. #17988451C22semidirect
162. #17988449C22semidirect
163. #17988447C22semidirect
167. #17988444C22semidirect
173. #398×C73C22semidirect
176. #396×C73C22semidirect
180. #388×C73C22semidirect
181. #387×C73C22semidirect
182. #387×C73C22semidirect
183. #387×C73C22semidirect
185. #381×C73C22semidirect
186. #380×C73C22semidirect
805. #2740D73semidirect
823. C73#36987semidirect
854. #398C2×D73semidirect
870. #396C2×D73semidirect
932. #388C2×D73semidirect
940. #387C2×D73semidirect
941. #387C2×D73semidirect
942. #387C2×D73semidirect
968. #381C2×D73semidirect
974. #380C2×D73semidirect

Maximal subgroups

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

subgroupindex
#226182582
#226182552
#226178712
#226178602
#226178242
#226175362
#226174682
#226173232
#226172592
#226172062
#226170422
#226166942
#226166362
#226165782
#226165182
#226157052
#226156702
#226148582
#226148192
#226136502
#226134772
#226134742
#226134152
#226133942
#226133732
#226126302
#226125602
#388×D732
C73×#27402
#3698773