Finite Group Databasebeta

← #33300092

Subgroups — #33300092

Order 18688.

1410 conjugacy classes of subgroups.

The subgroup lattice has 1290 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22618267C211yesmaximal, characteristic, complemented
2#22618256C211yesmaximal, characteristic
3#22617484C211yesmaximal, characteristic, complemented
4#22617481C211yesmaximal, characteristic, complemented
5#22617366C211yesmaximal, characteristic, complemented
6#22617346C211yesmaximal, characteristic, complemented
7#22617336C211yesmaximal, characteristic, complemented
8#22617299C211yesmaximal, characteristic, complemented
9#22617289C211yesmaximal, characteristic, complemented
10#22617280C211yesmaximal, characteristic, complemented
11#22617188C211yesmaximal, characteristic
12#22617165C211yesmaximal, characteristic
13#22617098C211yesmaximal, characteristic, complemented
14#22617064C211yesmaximal, characteristic
15#22617018C211yesmaximal, characteristic, complemented
16#22617006C211yesmaximal, characteristic, complemented
17#22616992C211yesmaximal, characteristic
18#22616100C211yesmaximal, characteristic, complemented
19#22616080C211yesmaximal, characteristic
20#22615460C211yesmaximal, characteristic, complemented
21#22615373C211yesmaximal, characteristic, complemented
22#22615368C211yesmaximal, characteristic, complemented
23#22615248C211yesmaximal, characteristic, complemented
24#22614811C211yesmaximal, characteristic, complemented
25#22614789C211yesmaximal, characteristic, complemented
26#22614728C211yesmaximal, characteristic, complemented
27#22614724C211yesmaximal, characteristic, complemented
28#22612714C211yesmaximal, characteristic
29#22612681C211yesmaximal, characteristic, complemented
30#22612322C211yesmaximal, characteristic, complemented
31C73×#2764C211yesmaximal, characteristic, complemented
32C2×#14556575C2211yescharacteristic
33C2×#14556568C2211yescharacteristic
34C22×C4×Dic73C2211yescharacteristic
35C73⋊#401C2211yescharacteristic
36C73⋊#401C2211yescharacteristic
37#17988529C2211yescharacteristic
38#17988529C2211yescharacteristic
39#17988529C2211yescharacteristic
40#17988529C2211yescharacteristic
41#17988528C2211yescharacteristic
42#17988528C2211yescharacteristic
43#17988528C2211yescharacteristic
44#17988528C2211yescharacteristic
45#17988528C2211yescharacteristic
46#17988528C2211yescharacteristic
47#17988528C2211yescharacteristic
48#17988527C2211yescharacteristic
49#17988527C2211yescharacteristic
50#17988527C2211yescharacteristic
51#17988526C2211yescharacteristic
52#17988525C2211yescharacteristic
53#17988522C2211yescharacteristic
54#17988522C2211yescharacteristic
55#17988521C2211yescharacteristic
56#17988521C2211yescharacteristic
57#17988518C2211yescharacteristic
58#17988516C2211yescharacteristic
59#17988516C2211yescharacteristic
60#17988516C2211yescharacteristic
61#17988515C2211yescharacteristic
62#17988514C2211yescharacteristic
63#17988513C2211yescharacteristic
64#17988510C2211yescharacteristic
65#17988510C2211yescharacteristic
66#17988508C2211yescharacteristic
67#17988508C2211yescharacteristic
68#17988507C2211yescharacteristic
69#17988506C2211yescharacteristic
70#17988506C2211yescharacteristic
71#17988503C2211yescharacteristic
72#17988502C2211yescharacteristic
73#17988500C2211yescharacteristic
74#17988500C2211yescharacteristic
75#17988499C2211yescharacteristic
76#17988498C2211yescharacteristic
77#17988494C2211yescharacteristic
78#17988493C2211yescharacteristic
79#17988492C2211yescharacteristic
80#17988491C2211yescharacteristic
81#17988491C2211yescharacteristic
82#17988491C2211yescharacteristic
83#17988491C2211yescharacteristic
84#17988491C2211yescharacteristic
85#17988487C2211yescharacteristic
86#17988486C2211yescharacteristic
87#17988485C2211yescharacteristic
88#17988484C2211yescharacteristic
89#17988484C2211yescharacteristic
90#17988482C2211yescharacteristic
91#17988482C2211yescharacteristic
92#17988482C2211yescharacteristic
93#17988480C2211yescharacteristic
94#17988480C2211yescharacteristic
95#17988479C2211yescharacteristic
96#17988479C2211yescharacteristic
97#17988478C2211yescharacteristic
98#17988477C2211yescharacteristic
99#17988477C2211yescharacteristic
100#17988477C2211yescharacteristic
101#17988476C2211yescharacteristic
102#17988476C2211yescharacteristic
103#17988476C2211yescharacteristic
104#17988476C2211yescharacteristic
105#17988476C2211yescharacteristic
106#17988476C2211yescharacteristic
107#17988475C2211yescharacteristic
108#17988475C2211yescharacteristic
109#17988474C2211yescharacteristic
110#17988474C2211yescharacteristic
111#17988474C2211yescharacteristic
112#17988474C2211yescharacteristic
113#17988474C2211yescharacteristic
114#17988473C2211yescharacteristic
115#17988473C2211yescharacteristic
116#17988473C2211yescharacteristic
117#17988473C2211yescharacteristic
118#17988472C2211yescharacteristic
119#17988472C2211yescharacteristic
120#17988472C2211yescharacteristic
121#17988472C2211yescharacteristic
122#17988471C2211yescharacteristic
123#17988471C2211yescharacteristic
124#17988471C2211yescharacteristic
125#17988470C2211yescharacteristic
126#17988470C2211yescharacteristic
127#17988470C2211yescharacteristic
128#17988470C2211yescharacteristic
129#17988469C2211yescharacteristic
130#17988469C2211yescharacteristic
131#17988469C2211yescharacteristic
132#17988469C2211yescharacteristic
133#17988469C2211yescharacteristic
134#17988468C2211yescharacteristic
135#17988468C2211yescharacteristic
136#17988468C2211yescharacteristic
137#17988468C2211yescharacteristic
138#17988468C2211yescharacteristic
139#17988466C2211yescharacteristic
140#17988464C2211yescharacteristic
141#17988463C2211yescharacteristic
142#17988461C2211yescharacteristic
143#17988461C2211yescharacteristic
144#17988460C2211yescharacteristic
145#17988459C2211yescharacteristic
146#17988458C2211yescharacteristic
147#17988454C2211yescharacteristic
148#17988454C2211yescharacteristic
149#17988454C2211yescharacteristic
150#17988452C2211yescharacteristic
151#17988451C2211yescharacteristic
152#17988451C2211yescharacteristic
153#17988450C2211yescharacteristic
154#17988449C2211yescharacteristic
155#17988448C2211yescharacteristic
156#17988448C2211yescharacteristic
157#17988448C2211yescharacteristic
158#17988446C2211yescharacteristic
159#17988445C2211yescharacteristic
160#17988445C2211yescharacteristic
161#17988445C2211yescharacteristic
162C4⋊C4×Dic73C2211yescharacteristic
163C4⋊C4×Dic73C2211yescharacteristic
164C4×#11924007C2211yescharacteristic
165#17988438C2211yescharacteristic
166#17988438C2211yescharacteristic
167C22⋊C4×Dic73C2211yescharacteristic
168C22⋊C4×Dic73C2211yescharacteristic
169C4×#11924005C2211yescharacteristic
170#17988432C2211yescharacteristic
171#17988432C2211yescharacteristic
172#400×C73C2211yescharacteristic
173#400×C73C2211yescharacteristic
174#398×C73C2211yescharacteristic
175#398×C73C2211yescharacteristic
176#397×C73C2211yescharacteristic
177#393×C73C2211yescharacteristic
178#391×C73C2211yescharacteristic
179#391×C73C2211yescharacteristic
180#388×C73C2211yescharacteristic
181#388×C73C2211yescharacteristic
182#385×C73C2211yescharacteristic
183#385×C73C2211yescharacteristic
184#383×C73C2211yescharacteristic
185#383×C73C2211yescharacteristic
186#381×C73C2211yescharacteristic
187C22×Dic146C2311yescharacteristic
188C22×Dic146C2311yescharacteristic
189C22×C22⋊D73C2311yescharacteristic
190C23×Dic73C2311yescharacteristic
191C23×Dic73C2311yescharacteristic
192C22×C4×D73C2311yescharacteristic
193#14556575—24no—
194#14556568—24no—
195C2×C4⋊Dic73C2311yescharacteristic
196C2×C4⋊Dic73C2311yescharacteristic
197C2×C4⋊Dic73C2311yescharacteristic
198C2×C4⋊Dic73C2311yescharacteristic
199C2×C4⋊Dic73C2311yescharacteristic
200C2×C4⋊Dic73C2311yescharacteristic
201C2×C4⋊Dic73C2311yescharacteristic
202C2×C4⋊Dic73C2311yescharacteristic
203C2×#11924007C2311yescharacteristic
204C2×#11924007C2311yescharacteristic
205C2×#11924007C2311yescharacteristic
206C2×#11924007C2311yescharacteristic
207C2×#11924007C2311yescharacteristic
208C2×#11924007C2311yescharacteristic
209C2×#11924007C2311yescharacteristic
210C2×#11924007C2311yescharacteristic
211C2×#11924007C2311yescharacteristic
212C2×#11924007C2311yescharacteristic
213C2×#11924007C2311yescharacteristic
214C2×#11924007C2311yescharacteristic
215C2×#11924007C2311yescharacteristic
216C2×#11924007C2311yescharacteristic
217C2×#11924007C2311yescharacteristic
218C2×#11924007C2311yescharacteristic
219C2×#11924007C2311yescharacteristic
220C2×#11924007C2311yescharacteristic
221C2×#11924007C2311yescharacteristic
222C2×#11924007C2311yescharacteristic
223C2×#11924007C2311yescharacteristic
224C2×C22⋊Dic73C2311yescharacteristic
225C2×C22⋊Dic73C2311yescharacteristic
226C2×C22⋊Dic73C2311yescharacteristic
227C2×C22⋊Dic73C2311yescharacteristic
228C2×C22⋊Dic73C2311yescharacteristic
229C2×#11924005C2311yescharacteristic
230C2×#11924005C2311yescharacteristic
231C2×#11924005C2311yescharacteristic
232C2×#11924005C2311yescharacteristic
233C2×#11924005C2311yescharacteristic
234C2×#11924005C2311yescharacteristic
235C2×#11924005C2311yescharacteristic
236C2×#11924005C2311yescharacteristic
237C2×#11924005C2311yescharacteristic
238C2×#11924005C2311yescharacteristic
239C2×#11924005C2311yescharacteristic
240C2×#11924005C2311yescharacteristic
241C2×#11924005C2311yescharacteristic
242C2×C4×Dic73—24no—
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×C4×Dic73C2311yescharacteristic
253C2×C4×Dic73C2311yescharacteristic
254C2×C4×Dic73C2311yescharacteristic
255C2×C4×Dic73C2311yescharacteristic
256#14556498C2311yescharacteristic
257#14556498C2311yescharacteristic
258#14556498C2311yescharacteristic
259#14556498C2311yescharacteristic
260#14556498C2311yescharacteristic
261#14556498C2311yescharacteristic
262#14556498C2311yescharacteristic
263#14556498C2311yescharacteristic
264#14556498C2311yescharacteristic
265#14556498C2311yescharacteristic
266#14556498C2311yescharacteristic
267#14556498C2311yescharacteristic
268#14556498C2311yescharacteristic
269#14556498C2311yescharacteristic
270#14556498C2311yescharacteristic
271#14556498C2311yescharacteristic
272#14556498C2311yescharacteristic
273#14556498C2311yescharacteristic
274#14556498C2311yescharacteristic
275#14556498C2311yescharacteristic
276#14556498C2311yescharacteristic
277#14556498C2311yescharacteristic
278#14556498C2311yescharacteristic
279#14556498C2311yescharacteristic
280#14556498C2311yescharacteristic
281#14556498C2311yescharacteristic
282#14556498C2311yescharacteristic
283#14556498C2311yescharacteristic
284#14556498C2311yescharacteristic
285#14556498C2311yescharacteristic
286#14556498C2311yescharacteristic
287#14556498C2311yescharacteristic
288#14556498C2311yescharacteristic
289#14556498C2311yescharacteristic
290#14556498C2311yescharacteristic
291#14556498C2311yescharacteristic
292#14556498C2311yescharacteristic
293#14556498C2311yescharacteristic
294#14556498C2311yescharacteristic
295#14556498C2311yescharacteristic
296#14556498C2311yescharacteristic
297#14556498C2311yescharacteristic
298#14556498C2311yescharacteristic
299#14556498C2311yescharacteristic
300#14556498C2311yescharacteristic
301#14556498C2311yescharacteristic
302#14556498C2311yescharacteristic
303#14556498C2311yescharacteristic
304#14556498C2311yescharacteristic
305#14556498C2311yescharacteristic
306#14556498C2311yescharacteristic
307#14556498C2311yescharacteristic
308#14556498C2311yescharacteristic
309#14556498C2311yescharacteristic
310C22×Q8×C73C2311yescharacteristic
311C23×C4×C73C2311yescharacteristic
312C2×C4⋊C4×C73C2311yescharacteristic
313C2×C4⋊C4×C73C2311yescharacteristic
314C2×C4⋊C4×C73C2311yescharacteristic
315C2×C4⋊C4×C73C2311yescharacteristic
316C2×C4⋊C4×C73C2311yescharacteristic
317C2×C4⋊C4×C73C2311yescharacteristic
318C2×C4⋊C4×C73C2311yescharacteristic
319C2×C22⋊C4×C73C2311yescharacteristic
320C2×C22⋊C4×C73C2311yescharacteristic
321C2×C22⋊C4×C73C2311yescharacteristic
322C2×C22⋊C4×C73C2311yescharacteristic
323C2×C22⋊C4×C73C2311yescharacteristic
324C2×C22⋊C4×C73C2311yescharacteristic
325C2×C42×C73C2311yescharacteristic
326C2×C42×C73C2311yescharacteristic
327#95×C73C2311yescharacteristic
328#95×C73C2311yescharacteristic
329#95×C73C2311yescharacteristic
330#95×C73C2311yescharacteristic
331#95×C73C2311yescharacteristic
332#95×C73C2311yescharacteristic
333#95×C73C2311yescharacteristic
334#95×C73C2311yescharacteristic
335#95×C73C2311yescharacteristic
336#95×C73C2311yescharacteristic
337#95×C73C2311yescharacteristic
338#95×C73C2311yescharacteristic
339#95×C73C2311yescharacteristic
340#95×C73C2311yescharacteristic
341#95×C73C2311yescharacteristic
342#95×C73C2311yescharacteristic
343#95×C73C2311yescharacteristic
344#95×C73C2311yescharacteristic
345C23×D73C2411yescharacteristic
346C2×Dic146—22no—
347C2×Dic146—41no—
348C2×Dic146—41no—
349C2×Dic146—41no—
350C2×Dic146—41no—
351C2×Dic146—41no—
352C2×C22⋊D73—22no—
353C2×C22⋊D73—41no—
354C2×C22⋊D73—41no—
355C22×Dic73—22no—
356C22×Dic73—22no—
357C22×Dic73—41no—
358C22×Dic73—41no—
359C22×Dic73—41no—
360C22×Dic73#4114yes—
361C22×Dic73C2411yescharacteristic
362C22×Dic73C2411yescharacteristic
363C22×Dic73C2411yescharacteristic
364C22×Dic73C2411yescharacteristic
365C22×Dic73C2411yescharacteristic
366C22×Dic73C2411yescharacteristic
367C22×Dic73C2411yescharacteristic
368C22×Dic73C2411yescharacteristic
369C22×Dic73C2411yescharacteristic
370C22×Dic73C2411yescharacteristic
371C22×Dic73C2411yescharacteristic
372C22×Dic73C2411yescharacteristic
373C22×Dic73C2411yescharacteristic
374C22×Dic73C2411yescharacteristic
375C22×Dic73C2411yescharacteristic
376C2×C4×D73—41no—
377C2×C4×D73—41no—
378C2×C4×D73—41no—
379C4⋊Dic73—22no—
380C4⋊Dic73—22no—
381C4⋊Dic73—22no—
382C4⋊Dic73—41no—
383C4⋊Dic73—41no—
384C4⋊Dic73—41no—
385C4⋊Dic73—41no—
386C4⋊Dic73—41no—
387#11924007—22no—
388#11924007—22no—
389#11924007—22no—
390#11924007—22no—
391#11924007—22no—
392#11924007—41no—
393#11924007—41no—
394#11924007—41no—
395#11924007—41no—
396#11924007—41no—
397#11924007—41no—
398#11924007—41no—
399#11924007—41no—
400#11924007—41no—
401#11924007—41no—
402#11924007—41no—
403#11924007—41no—
404#11924007—41no—
405#11924007—41no—
406#11924007—41no—
407#11924007—41no—
408C22⋊Dic73—22no—
409C22⋊Dic73—41no—
410C22⋊Dic73—41no—
411C22⋊Dic73—41no—
412C22⋊Dic73—41no—
413#11924005—22no—
414#11924005—22no—
415#11924005—22no—
416#11924005—41no—
417#11924005—41no—
418#11924005—41no—
419#11924005—41no—
420#11924005—41no—
421#11924005—41no—
422#11924005—41no—
423#11924005—41no—
424#11924005—41no—
425#11924005—41no—
426C4×Dic73—22no—
427C4×Dic73—22no—
428C4×Dic73—22no—
429C4×Dic73—22no—
430C4×Dic73—41no—
431C4×Dic73—41no—
432C4×Dic73—41no—
433C4×Dic73—41no—
434C4×Dic73—41no—
435C4×Dic73—41no—
436C4×Dic73—41no—
437C4×Dic73—41no—
438C4×Dic73—41no—
439C24×C73C2411yescharacteristic
440C2×Q8×C73—41no—
441C2×Q8×C73—41no—
442C2×Q8×C73—41no—
443C22×C4×C73—22no—
444C22×C4×C73—41no—
445C22×C4×C73—41no—
446C22×C4×C73C2411yescharacteristic
447C22×C4×C73C2411yescharacteristic
448C22×C4×C73C2411yescharacteristic
449C22×C4×C73C2411yescharacteristic
450C22×C4×C73C2411yescharacteristic
451C22×C4×C73C2411yescharacteristic
452C22×C4×C73C2411yescharacteristic
453C22×C4×C73C2411yescharacteristic
454C22×C4×C73C2411yescharacteristic
455C22×C4×C73C2411yescharacteristic
456C22×C4×C73C2411yescharacteristic
457C22×C4×C73C2411yescharacteristic
458C22×C4×C73C2411yescharacteristic
459C22×C4×C73C2411yescharacteristic
460C4⋊C4×C73—41no—
461C4⋊C4×C73—41no—
462C4⋊C4×C73—41no—
463C4⋊C4×C73—41no—
464C4⋊C4×C73—41no—
465C4⋊C4×C73—41no—
466C4⋊C4×C73—41no—
467C22⋊C4×C73—22no—
468C22⋊C4×C73—22no—
469C22⋊C4×C73—41no—
470C22⋊C4×C73—41no—
471C22⋊C4×C73—41no—
472C22⋊C4×C73—41no—
473C42×C73—41no—
474C42×C73—41no—
475C23×C73—21no—
476C23×C73—21no—
477C23×C73—21no—
478C23×C73—21no—
479C23×C73—21no—
480C23×C73—21no—
481C23×C73C2×#4112yes—
482C23×C73C2511yescharacteristic
483C22×D73—21no—
484C22×D73—21no—
485C22×D73—21no—
486C22×D73—21no—
487C22×D73—21no—
488C22×D73—21no—
489C22×D73—21no—
490Q8×C73—82no—
491C2×C4×C73—21no—
492C2×C4×C73—21no—
493C2×C4×C73—21no—
494C2×C4×C73—21no—
495C2×C4×C73—21no—
496C2×C4×C73—21no—
497C2×C4×C73—21no—
498C2×C4×C73—21no—
499C2×C4×C73—21no—
500C2×C4×C73—21no—
501C2×C4×C73—21no—
502C2×C4×C73—21no—
503C2×C4×C73—21no—
504C2×C4×C73—21no—
505C2×C4×C73—21no—
506C2×C4×C73—21no—
507C2×C4×C73—21no—
508C2×C4×C73—21no—
509C2×C4×C73—21no—
510C2×C4×C73—21no—
511C2×C4×C73—21no—
512C2×C4×C73—21no—
513C2×C4×C73—21no—
514C2×C4×C73—21no—
515C2×C4×C73—21no—
516C2×C4×C73—21no—
517C2×C4×C73—21no—
518C2×C4×C73—21no—
519C2×C4×C73—21no—
520C2×C4×C73—21no—
521C2×C4×C73—21no—
522C2×C4×C73—21no—
523C2×C4×C73—21no—
524C2×C4×C73—21no—
525C2×C4×C73—21no—
526C2×C4×C73—21no—
527C2×C4×C73—21no—
528C2×C4×C73—21no—
529C2×C4×C73—21no—
530C2×C4×C73—21no—
531C2×C4×C73—21no—
532C2×C4×C73—21no—
533C2×C4×C73—44no—
534C22⋊D73—82no—
535C2×Dic73—21no—
536C2×Dic73—21no—
537C2×Dic73—21no—
538C2×Dic73—21no—
539C2×Dic73—21no—
540C2×Dic73—21no—
541C2×Dic73—21no—
542C2×Dic73—21no—
543C2×Dic73—21no—
544C2×Dic73—21no—
545C2×Dic73—21no—
546C2×Dic73—21no—
547C2×Dic73—21no—
548C2×Dic73—21no—
549C2×Dic73—21no—
550C2×Dic73—21no—
551C2×Dic73—21no—
552C2×Dic73—21no—
553C2×Dic73—21no—
554C2×Dic73—21no—
555C2×Dic73—21no—
556C2×Dic73—21no—
557C2×Dic73—21no—
558C2×Dic73—21no—
559C2×Dic73—21no—
560C2×Dic73—21no—
561C2×Dic73—21no—
562C2×Dic73—21no—
563C2×Dic73—21no—
564C2×Dic73—21no—
565C2×Dic73—21no—
566C2×Dic73—21no—
567C2×Dic73—21no—
568C2×Dic73—21no—
569C2×Dic73—21no—
570C2×Dic73—21no—
571C2×Dic73—21no—
572C2×Dic73—21no—
573C2×Dic73—21no—
574C2×Dic73—21no—
575C2×Dic73—21no—
576C2×Dic73—21no—
577C2×Dic73—44no—
578C2×Dic73—44no—
579C2×Dic73C2×#4112yes—
580C2×Dic73C2×#4112yes—
581C2×Dic732−1+412yes—
582C4×D73—82no—
583Dic146—82no—
584Dic146—82no—
585C22×C73—22no—
586C22×C73—22no—
587C22×C73—22no—
588C22×C73—41no—
589C22×C73—41no—
590C22×C73—41no—
591C22×C73—41no—
592C22×C73C22×#4111yescharacteristic
593C22×C73C2×2−1+411yescharacteristic
594C22×C73#58511yescharacteristic
595C22×C73#58511yescharacteristic
596C22×C73#58511yescharacteristic
597C22×C73#58511yescharacteristic
598C22×C73#58511yescharacteristic
599C2×D73—41no—
600C2×D73—41no—
601C2×D73—41no—
602C2×D73—41no—
603C2×D73—41no—
604C2×D73—41no—
605C2×D73—41no—
606C4×C73—41no—
607C4×C73—41no—
608C4×C73—41no—
609C4×C73—41no—
610C4×C73—41no—
611C4×C73—41no—
612C4×C73—41no—
613C4×C73—41no—
614C4×C73—41no—
615C4×C73—41no—
616C4×C73—41no—
617C4×C73—41no—
618C4×C73—41no—
619C4×C73—41no—
620Dic73—22no—
621Dic73—22no—
622Dic73—22no—
623Dic73—41no—
624Dic73—41no—
625Dic73—41no—
626Dic73—41no—
627Dic73—41no—
628Dic73—41no—
629Dic73—41no—
630Dic73—41no—
631Dic73—41no—
632Dic73—41no—
633Dic73—41no—
634Dic73—41no—
635#36984—731nomaximal, Sylow
636C2×C73—42no—
637C2×C73#345511yescharacteristic
638C2×C73#349111yescharacteristic
639C2×C73#349511yescharacteristic
640C2×C73#355711yescharacteristic
641C2×C73#356511yescharacteristic
642C2×C73#356611yescharacteristic
643C2×C73#356811yescharacteristic
644D73—81no—
645#2855—731no—
646#2853—731no—
647#2774—731no—
648#2773—731no—
649#2765—731no—
650#2764D7311yescharacteristic, complemented
651#2763—731no—
652#2762—731no—
653#2759—731no—
654#2758—731no—
655#2758—731no—
656#2751—731no—
657#2750—731no—
658#2745—731no—
659#2743—731no—
660#2739—731no—
661#2738—731no—
662#2737—731no—
663#2665—731no—
664#2663—731no—
665#2596—731no—
666#2588—731no—
667#2588—731no—
668#2577—731no—
669#2533—731no—
670#2532—731no—
671#2528—731no—
672#2527—731no—
673#2335—731no—
674#2332—731no—
675#2283—731no—
676C73#3698411yescharacteristic, complemented, Sylow
677C2×#123—731no—
678C2×C22⋊Q8—731no—
679C22×C42—731no—
680#401—731no—
681#401—731no—
682#400—731no—
683#400—731no—
684#400—731no—
685#400—731no—
686#400—731no—
687#400—731no—
688#400—731no—
689#400—731no—
690#400—731no—
691#400—731no—
692#400—731no—
693#400—731no—
694#400—731no—
695#400—731no—
696#400—731no—
697#400—731no—
698#400C2×D7311yescharacteristic
699#400C2×D7311yescharacteristic
700#399—731no—
701#399—731no—
702#398—731no—
703#398—731no—
704#398—731no—
705#398C2×D7311yescharacteristic
706#398C2×D7311yescharacteristic
707#397—731no—
708#397—731no—
709#397—731no—
710#397—731no—
711#397—731no—
712#397—731no—
713#397C2×D7311yescharacteristic
714#396—731no—
715#396—731no—
716#395—731no—
717#395—731no—
718#395—731no—
719#395—731no—
720#395—731no—
721#394—731no—
722#394—731no—
723#393—731no—
724#393—731no—
725#393—731no—
726#393—731no—
727#393C2×D7311yescharacteristic
728#391—731no—
729#391—731no—
730#391—731no—
731#391—731no—
732#391—731no—
733#391—731no—
734#391—731no—
735#391—731no—
736#391C2×D7311yescharacteristic
737#391C2×D7311yescharacteristic
738#390—731no—
739#389—731no—
740#389—731no—
741#389—731no—
742#389—731no—
743#389—731no—
744#389—731no—
745#389—731no—
746#388—731no—
747#388—731no—
748#388—731no—
749#388—731no—
750#388—731no—
751#388—731no—
752#388—731no—
753#388—731no—
754#388—731no—
755#388—731no—
756#388—731no—
757#388—731no—
758#388—731no—
759#388—731no—
760#388—731no—
761#388—731no—
762#388C2×D7311yescharacteristic
763#388C2×D7311yescharacteristic
764#387—731no—
765#387—731no—
766#387—731no—
767#387—731no—
768#387—731no—
769#387—731no—
770#387—731no—
771#387—731no—
772#387—731no—
773#387—731no—
774#387—731no—
775#387—731no—
776#387—731no—
777#387—731no—
778#387—731no—
779#387—731no—
780#387—731no—
781#387—731no—
782#387—731no—
783#387—731no—
784#387—731no—
785#387—731no—
786#387—731no—
787#387—731no—
788#387—731no—
789#387—731no—
790#387—731no—
791#387—731no—
792#387—731no—
793#387—731no—
794#386—731no—
795#386—731no—
796#386—731no—
797#385—731no—
798#385—731no—
799#385—731no—
800#385—731no—
801#385—731no—
802#385C2×D7311yescharacteristic
803#385C2×D7311yescharacteristic
804#383—731no—
805#383—731no—
806#383—731no—
807#383C2×D7311yescharacteristic
808#383C2×D7311yescharacteristic
809#382—731no—
810#382—731no—
811#382—731no—
812#381—731no—
813#381—731no—
814#381—731no—
815#381—731no—
816#381—731no—
817#381C2×D7311yescharacteristic
818#380—731no—
819#380—731no—
820#380—731no—
821#380—731no—
822C4×C4⋊C4—731no—
823C4×C4⋊C4—731no—
824C4×C4⋊C4—731no—
825C4×C4⋊C4—731no—
826C4×C4⋊C4—731no—
827C4×C22⋊C4—731no—
828C4×C22⋊C4—731no—
829C4×C22⋊C4—731no—
830#376—731no—
831#376—731no—
832C22×Q8—731no—
833C22×Q8—731no—
834C22×Q8C22×D7311yescharacteristic
835C22×D4—731no—
836C23×C4—731no—
837C23×C4—731no—
838C23×C4—731no—
839C23×C4C22×D7311yescharacteristic
840#123—1464no—
841C22⋊Q8—1464no—
842C2×C4⋊C4—731no—
843C2×C4⋊C4—731no—
844C2×C4⋊C4—731no—
845C2×C4⋊C4—731no—
846C2×C4⋊C4—731no—
847C2×C4⋊C4—731no—
848C2×C4⋊C4—731no—
849C2×C4⋊C4—731no—
850C2×C4⋊C4—731no—
851C2×C4⋊C4—731no—
852C2×C4⋊C4—731no—
853C2×C4⋊C4—731no—
854C2×C4⋊C4—731no—
855C2×C4⋊C4—731no—
856C2×C4⋊C4—731no—
857C2×C4⋊C4—731no—
858C2×C4⋊C4—731no—
859C2×C4⋊C4—731no—
860C2×C4⋊C4—731no—
861C2×C4⋊C4—731no—
862C2×C4⋊C4—731no—
863C2×C4⋊C4—731no—
864C2×C4⋊C4—731no—
865C2×C4⋊C4—731no—
866C2×C4⋊C4—731no—
867C2×C4⋊C4—731no—
868C2×C4⋊C4—731no—
869C2×C4⋊C4—731no—
870C2×C4⋊C4—731no—
871C2×C4⋊C4C22×D7311yescharacteristic
872C2×C4⋊C4C22×D7311yescharacteristic
873C2×C4⋊C4C22×D7311yescharacteristic
874C2×C4⋊C4C22×D7311yescharacteristic
875C2×C4⋊C4C22×D7311yescharacteristic
876C2×C4⋊C4C22×D7311yescharacteristic
877C2×C4⋊C4C22×D7311yescharacteristic
878C2×C22⋊C4—731no—
879C2×C22⋊C4—731no—
880C2×C22⋊C4—731no—
881C2×C22⋊C4—731no—
882C2×C22⋊C4—731no—
883C2×C22⋊C4—731no—
884C2×C22⋊C4—731no—
885C2×C22⋊C4—731no—
886C2×C22⋊C4—731no—
887C2×C22⋊C4—731no—
888C2×C22⋊C4—731no—
889C2×C22⋊C4—731no—
890C2×C22⋊C4—731no—
891C2×C22⋊C4—731no—
892C2×C22⋊C4—731no—
893C2×C22⋊C4—731no—
894C2×C22⋊C4—731no—
895C2×C22⋊C4—731no—
896C2×C22⋊C4C22×D7311yescharacteristic
897C2×C22⋊C4C22×D7311yescharacteristic
898C2×C22⋊C4C22×D7311yescharacteristic
899C2×C22⋊C4C22×D7311yescharacteristic
900C2×C22⋊C4C22×D7311yescharacteristic
901C2×C22⋊C4C22×D7311yescharacteristic
902C2×C42—731no—
903C2×C42—731no—
904C2×C42—731no—
905C2×C42—731no—
906C2×C42—731no—
907C2×C42—731no—
908C2×C42—731no—
909C2×C42—731no—
910C2×C42—731no—
911C2×C42—731no—
912C2×C42—731no—
913C2×C42—731no—
914C2×C42—731no—
915C2×C42—1464no—
916C2×C42C22×D7311yescharacteristic
917C2×C42C22×D7311yescharacteristic
918#95—731no—
919#95—731no—
920#95—731no—
921#95—731no—
922#95—731no—
923#95—731no—
924#95—731no—
925#95—731no—
926#95—731no—
927#95—731no—
928#95—731no—
929#95—731no—
930#95—731no—
931#95—731no—
932#95—731no—
933#95—731no—
934#95—731no—
935#95—731no—
936#95—731no—
937#95—731no—
938#95—731no—
939#95—731no—
940#95—731no—
941#95—731no—
942#95—731no—
943#95—731no—
944#95—731no—
945#95—731no—
946#95—731no—
947#95—731no—
948#95—731no—
949#95—731no—
950#95—731no—
951#95—731no—
952#95—731no—
953#95—731no—
954#95—731no—
955#95—731no—
956#95—731no—
957#95—731no—
958#95—731no—
959#95—731no—
960#95—731no—
961#95—731no—
962#95—731no—
963#95—731no—
964#95—731no—
965#95—731no—
966#95—731no—
967#95—731no—
968#95—731no—
969#95—731no—
970#95—731no—
971#95—731no—
972#95C22×D7311yescharacteristic
973#95C22×D7311yescharacteristic
974#95C22×D7311yescharacteristic
975#95C22×D7311yescharacteristic
976#95C22×D7311yescharacteristic
977#95C22×D7311yescharacteristic
978#95C22×D7311yescharacteristic
979#95C22×D7311yescharacteristic
980#95C22×D7311yescharacteristic
981#95C22×D7311yescharacteristic
982#95C22×D7311yescharacteristic
983#95C22×D7311yescharacteristic
984#95C22×D7311yescharacteristic
985#95C22×D7311yescharacteristic
986#95C22×D7311yescharacteristic
987#95C22×D7311yescharacteristic
988#95C22×D7311yescharacteristic
989#95C22×D7311yescharacteristic
990C24—731no—
991C24C23×D7311yescharacteristic
992C2×Q8—41no—
993C2×Q8—41no—
994C2×Q8—41no—
995C2×Q8—2921no—
996C2×Q8—2921no—
997C2×Q8—2921no—
998C2×Q8—2921no—
999C2×Q8—2921no—
1000C2×Q8—1462no—
1001C2×D4—2921no—
1002C2×D4—2921no—
1003C2×D4—1462no—
1004C22×C4—22no—
1005C22×C4—41no—
1006C22×C4—41no—
1007C22×C4—2921no—
1008C22×C4—2921no—
1009C22×C4—2921no—
1010C22×C4—2921no—
1011C22×C4—2921no—
1012C22×C4—2921no—
1013C22×C4—734no—
1014C22×C4—731no—
1015C22×C4—731no—
1016C22×C4—731no—
1017C22×C4—731no—
1018C22×C4—731no—
1019C22×C4—731no—
1020C22×C4—731no—
1021C22×C4—731no—
1022C22×C4—731no—
1023C22×C4—731no—
1024C22×C4—731no—
1025C22×C4—731no—
1026C22×C4—731no—
1027C22×C4—731no—
1028C22×C4—731no—
1029C22×C4—1462no—
1030C22×C4—1462no—
1031C22×C4C23×D7311yescharacteristic
1032C22×C4C23×D7311yescharacteristic
1033C22×C4C23×D7311yescharacteristic
1034C22×C4C23×D7311yescharacteristic
1035C22×C4C23×D7311yescharacteristic
1036C22×C4C23×D7311yescharacteristic
1037C22×C4C23×D7311yescharacteristic
1038C22×C4C23×D7311yescharacteristic
1039C22×C4C23×D7311yescharacteristic
1040C22×C4C23×D7311yescharacteristic
1041C22×C4C23×D7311yescharacteristic
1042C22×C4C23×D7311yescharacteristic
1043C22×C4C23×D7311yescharacteristic
1044C22×C4C23×D7311yescharacteristic
1045C4⋊C4—41no—
1046C4⋊C4—41no—
1047C4⋊C4—41no—
1048C4⋊C4—41no—
1049C4⋊C4—41no—
1050C4⋊C4—41no—
1051C4⋊C4—41no—
1052C4⋊C4—2921no—
1053C4⋊C4—2921no—
1054C4⋊C4—2921no—
1055C4⋊C4—2921no—
1056C4⋊C4—2921no—
1057C4⋊C4—2921no—
1058C4⋊C4—2921no—
1059C4⋊C4—2921no—
1060C4⋊C4—2921no—
1061C4⋊C4—2921no—
1062C4⋊C4—2921no—
1063C4⋊C4—2921no—
1064C4⋊C4—2921no—
1065C4⋊C4—2921no—
1066C4⋊C4—2921no—
1067C4⋊C4—2921no—
1068C4⋊C4—2921no—
1069C4⋊C4—2921no—
1070C4⋊C4—2921no—
1071C4⋊C4—2921no—
1072C4⋊C4—2921no—
1073C4⋊C4—1462no—
1074C4⋊C4—1462no—
1075C4⋊C4—1462no—
1076C4⋊C4—1462no—
1077C4⋊C4—1462no—
1078C4⋊C4—1462no—
1079C4⋊C4—1462no—
1080C4⋊C4—1462no—
1081C22⋊C4—22no—
1082C22⋊C4—22no—
1083C22⋊C4—41no—
1084C22⋊C4—41no—
1085C22⋊C4—41no—
1086C22⋊C4—41no—
1087C22⋊C4—2921no—
1088C22⋊C4—2921no—
1089C22⋊C4—2921no—
1090C22⋊C4—2921no—
1091C22⋊C4—2921no—
1092C22⋊C4—2921no—
1093C22⋊C4—2921no—
1094C22⋊C4—2921no—
1095C22⋊C4—2921no—
1096C22⋊C4—2921no—
1097C22⋊C4—2921no—
1098C22⋊C4—2921no—
1099C22⋊C4—2921no—
1100C22⋊C4—2921no—
1101C22⋊C4—1462no—
1102C22⋊C4—1462no—
1103C22⋊C4—1462no—
1104C22⋊C4—1462no—
1105C42—41no—
1106C42—41no—
1107C42—2921no—
1108C42—2921no—
1109C42—2921no—
1110C42—2921no—
1111C42—2921no—
1112C42—2921no—
1113C42—2921no—
1114C42—2921no—
1115C42—2921no—
1116C42—1462no—
1117C42—1462no—
1118C42—1462no—
1119C42—1462no—
1120C23—21no—
1121C23—21no—
1122C23—21no—
1123C23—21no—
1124C23—21no—
1125C23—21no—
1126C23—1461no—
1127C23—1461no—
1128C23—1461no—
1129C23—1461no—
1130C23—1461no—
1131C23—1461no—
1132C23—1461no—
1133C23#41×D7312yes—
1134C23C24×D7311yescharacteristic
1135Q8—82no—
1136Q8—5842no—
1137Q8—5842no—
1138D4—5842no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—44no—
1182C2×C4—2924no—
1183C2×C4—2924no—
1184C2×C4—5842no—
1185C2×C4—732no—
1186C2×C4—732no—
1187C2×C4—732no—
1188C2×C4—1461no—
1189C2×C4—1461no—
1190C2×C4—1461no—
1191C2×C4—1461no—
1192C2×C4—1461no—
1193C2×C4—1461no—
1194C2×C4—1461no—
1195C2×C4—1461no—
1196C2×C4—1461no—
1197C2×C4—1461no—
1198C2×C4—1461no—
1199C2×C4—1461no—
1200C2×C4—1461no—
1201C2×C4—1461no—
1202C2×C4—1461no—
1203C2×C4—1461no—
1204C2×C4—1461no—
1205C2×C4—1461no—
1206C2×C4—1461no—
1207C2×C4—1461no—
1208C2×C4—1461no—
1209C2×C4—1461no—
1210C2×C4—1461no—
1211C2×C4—1461no—
1212C2×C4—1461no—
1213C2×C4—1461no—
1214C2×C4—1461no—
1215C2×C4—1461no—
1216C2×C4—1461no—
1217C2×C4—1461no—
1218C2×C4—1461no—
1219C2×C4—1461no—
1220C2×C4—1461no—
1221C2×C4—1461no—
1222C2×C4—1461no—
1223C2×C4—1461no—
1224C2×C4—1461no—
1225C2×C4—1461no—
1226C2×C4—1461no—
1227C2×C4—1461no—
1228C2×C4—1461no—
1229C2×C4—1461no—
1230C22—22no—
1231C22—22no—
1232C22—22no—
1233C22—41no—
1234C22—41no—
1235C22—41no—
1236C22—41no—
1237C22—2921no—
1238C22—2921no—
1239C22—2921no—
1240C22—2921no—
1241C22—2921no—
1242C22—2921no—
1243C22—2921no—
1244C22C2×#41×D7311yescharacteristic
1245C222−1+4×D7311yescharacteristic
1246C22#1798942211yescharacteristic
1247C22#1798942211yescharacteristic
1248C22#1798942311yescharacteristic
1249C22#1798942311yescharacteristic
1250C22#1798942411yescharacteristic
1251C4—41no—
1252C4—41no—
1253C4—41no—
1254C4—41no—
1255C4—41no—
1256C4—41no—
1257C4—41no—
1258C4—41no—
1259C4—41no—
1260C4—41no—
1261C4—41no—
1262C4—41no—
1263C4—41no—
1264C4—41no—
1265C4—2921no—
1266C4—2921no—
1267C4—2921no—
1268C4—2921no—
1269C4—2921no—
1270C4—2921no—
1271C4—2921no—
1272C4—2921no—
1273C4—2921no—
1274C4—2921no—
1275C4—2921no—
1276C4—2921no—
1277C4—1462no—
1278C4—1462no—
1279C4—1462no—
1280C2—42no—
1281C2—5841no—
1282C2#2262331311yescharacteristic
1283C2#2262362611yescharacteristic
1284C2#2262367411yescharacteristic
1285C2#2262442911yescharacteristic
1286C2#2262457311yescharacteristic
1287C2#2262459211yescharacteristic
1288C2#2262462311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D73
commutator, socle, cosocleC23×C73C25
FittingC73×#2764C2
prime radicalC22×C22⋊D73C23
hypercenter#2764D73
hypocenterC73#36984
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #2764

Complements

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

NH ≅ G/Ntype
1. #22618267C2semidirect
3. #22617484C2semidirect
4. #22617481C2semidirect
5. #22617366C2semidirect
6. #22617346C2semidirect
7. #22617336C2semidirect
8. #22617299C2semidirect
9. #22617289C2semidirect
10. #22617280C2semidirect
13. #22617098C2semidirect
15. #22617018C2semidirect
16. #22617006C2semidirect
18. #22616100C2semidirect
20. #22615460C2semidirect
21. #22615373C2semidirect
22. #22615368C2semidirect
23. #22615248C2semidirect
24. #22614811C2semidirect
25. #22614789C2semidirect
26. #22614728C2semidirect
27. #22614724C2semidirect
29. #22612681C2semidirect
30. #22612322C2semidirect
31. C73×#2764C2semidirect
650. #2764D73semidirect
676. C73#36984semidirect

Maximal subgroups

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

subgroupindex
#226182672
#226182562
#226174842
#226174812
#226173662
#226173462
#226173362
#226172992
#226172892
#226172802
#226171882
#226171652
#226170982
#226170642
#226170182
#226170062
#226169922
#226161002
#226160802
#226154602
#226153732
#226153682
#226152482
#226148112
#226147892
#226147282
#226147242
#226127142
#226126812
#226123222
C73×#27642
#3698473