Finite Group Databasebeta

← #33056040

Subgroups — #33056040

Order 18688.

648 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619974C211yesmaximal, characteristic
2#22618954C211yesmaximal, characteristic, complemented
3#22608793C211yesmaximal, characteristic, complemented
4#22608786C211yesmaximal, characteristic, complemented
5#22608765C211yesmaximal, characteristic, complemented
6#22608758C211yesmaximal, characteristic, complemented
7#22608753C211yesmaximal, characteristic, complemented
8#22608741C211yesmaximal, characteristic, complemented
9C8×#11924015C211yesmaximal, characteristic, complemented
10C8×#11924013C211yesmaximal, characteristic, complemented
11#22608722C211yesmaximal, characteristic, complemented
12#22608355C211yesmaximal, characteristic, complemented
13#22608339C211yesmaximal, characteristic, complemented
14#22608231C211yesmaximal, characteristic, complemented
15C73×#2993C211yesmaximal, characteristic, complemented
16C2×C4×D292C2211yescharacteristic
17#17988920C411yescharacteristic
18#17988903C411yescharacteristic
19#17988884C411yescharacteristic
20#17988884C411yescharacteristic
21#17988799C411yescharacteristic
22#17988799C411yescharacteristic
23#17988737C411yescharacteristic
24#17988720C411yescharacteristic
25C4×#11924015C2211yescharacteristic
26C4×#11924015C2211yescharacteristic
27C4×#11924013C2211yescharacteristic
28C4×#11924013C2211yescharacteristic
29C8×D292C2211yescharacteristic
30C8×D292C2211yescharacteristic
31C8×D292C2211yescharacteristic
32C8×D292C2211yescharacteristic
33#17988652—21no—
34#17988652—21no—
35#17988640C2211yescharacteristic
36#17988640C2211yescharacteristic
37#17988640C2211yescharacteristic
38C22⋊C8×D73—21no—
39C22⋊C8×D73—21no—
40#17988339C2211yescharacteristic, complemented
41#17988339C2211yescharacteristic, complemented
42#17988337C2211yescharacteristic, complemented
43#17988337C2211yescharacteristic, complemented
44Q8⋊#10596831C2211yescharacteristic, complemented
45Q8⋊#10596831C2211yescharacteristic, complemented
46D4⋊#10596831C2211yescharacteristic, complemented
47D4⋊#10596831C2211yescharacteristic, complemented
48#17988314C2211yescharacteristic
49#17988314C2211yescharacteristic
50#17988314C2211yescharacteristic
51#17988314C2211yescharacteristic
52#17988309C2211yescharacteristic, complemented
53#17988309C2211yescharacteristic, complemented
54#17988308C2211yescharacteristic, complemented
55C8×#10596831C2211yescharacteristic, complemented
56#529×C73C2211yescharacteristic
57#446×C73C2211yescharacteristic, complemented
58C8×Q8×C73C2211yescharacteristic, complemented
59#436×C73—21no—
60#436×C73C2211yescharacteristic, complemented
61#435×C73—21no—
62C8×D4×C73C2211yescharacteristic, complemented
63#433×C73—21no—
64#431×C73C2211yescharacteristic
65#424×C73—21no—
66#423×C73C2211yescharacteristic
67C22×D292C2×C411yescharacteristic
68C22×C4×D73—21no—
69C2×#11924015C2×C411yescharacteristic
70C2×#11924015C2×C411yescharacteristic
71C2×#11924013C2×C411yescharacteristic
72C2×#11924013C2×C411yescharacteristic
73C2×C8×D73—21no—
74C2×C8×D73—21no—
75C2×C8×D73—21no—
76C2×C8×D73—21no—
77C4×D292—21no—
78C4×D292—21no—
79C4×D292C2×C411yescharacteristic
80C4×D292C2×C411yescharacteristic
81C4×D292C2311yescharacteristic
82C4×D292C2311yescharacteristic
83C2×C4⋊Dic73C2×C411yescharacteristic
84C2×#11924005—21no—
85#14556524C2×C411yescharacteristic
86#14556524C2×C411yescharacteristic
87#14556522C2×C411yescharacteristic
88#14556522C2×C411yescharacteristic
89C4⋊#10596831—21no—
90C4⋊#10596831C2×C411yescharacteristic
91C4⋊#10596831C2×C411yescharacteristic
92C4⋊#10596831C2311yescharacteristic
93C4⋊#10596831C2311yescharacteristic
94#14556515C2×C411yescharacteristic
95#14556515C2×C411yescharacteristic
96#14556512C2×C411yescharacteristic
97#14556512C2×C411yescharacteristic
98#14556511C2×C411yescharacteristic
99#14556511C2×C411yescharacteristic
100#14556511C2×C411yescharacteristic
101#14556511C2×C411yescharacteristic
102C22⋊#10596831—21no—
103C22⋊#10596831—21no—
104C22⋊#10596831C2×C411yescharacteristic
105C22⋊#10596831C2×C411yescharacteristic
106#14556503—21no—
107#14556503—21no—
108#14556503—21no—
109#14556503—21no—
110C4×#10596831—21no—
111C4×#10596831C2311yescharacteristic
112C4×#10596831C2311yescharacteristic
113C4×#10596831C2311yescharacteristic
114C4×#10596831C2311yescharacteristic
115C2×M16×C73—21no—
116C2×M16×C73—21no—
117C22×C8×C73—21no—
118#126×C73—21no—
119#125×C73C2×C411yescharacteristic
120#124×C73C2×C411yescharacteristic
121#123×C73—21no—
122C22⋊Q8×C73C2×C411yescharacteristic
123#121×C73C2×C411yescharacteristic
124C4×Q8×C73C2311yescharacteristic
125C4×D4×C73—21no—
126C4×D4×C73C2311yescharacteristic
127#117×C73—21no—
128C2×C42×C73C2311yescharacteristic
129C4⋊C8×C73—21no—
130C4⋊C8×C73—21no—
131C4⋊C8×C73—21no—
132C4⋊C8×C73D411yescharacteristic
133C4⋊C8×C73D411yescharacteristic
134C4⋊C8×C73C2311yescharacteristic
135C4⋊C8×C73C2311yescharacteristic
136C22⋊C8×C73—21no—
137C22⋊C8×C73—21no—
138C22⋊C8×C73D411yescharacteristic
139C22⋊C8×C73D411yescharacteristic
140#97×C73—21no—
141C4×C8×C73—21no—
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144C23×D73—21no—
145C2×D292—21no—
146C2×D292—22no—
147C2×D292—22no—
148C2×D292C22×C411yescharacteristic
149C2×D292C22×C411yescharacteristic
150C22×Dic73—21no—
151C2×C4×D73—21no—
152C2×C4×D73—21no—
153C2×C4×D73—21no—
154C2×C4×D73—21no—
155C2×C4×D73—81no—
156C2×C4×D73—81no—
157#11924015—22no—
158#11924015—22no—
159#11924013—22no—
160#11924013—22no—
161C2×#10596831—21no—
162C2×#10596831—21no—
163C2×#10596831—21no—
164C2×#10596831—21no—
165C2×#10596831C22×C411yescharacteristic
166C2×#10596831C22×C411yescharacteristic
167C2×#10596831C22×C411yescharacteristic
168C2×#10596831C22×C411yescharacteristic
169C8×D73—81no—
170C8×D73—81no—
171C8×D73—81no—
172C8×D73—81no—
173C4⋊Dic73—21no—
174C4⋊Dic73C22×C411yescharacteristic
175C4⋊Dic73C22×C411yescharacteristic
176#11924005—21no—
177#11924005—21no—
178#11924005—21no—
179#11924005—21no—
180C2×Q8×C73C22×C411yescharacteristic
181C2×D4×C73—21no—
182C2×D4×C73C22×C411yescharacteristic
183C22×C4×C73—21no—
184C22×C4×C73C22×C411yescharacteristic
185C22×C4×C73C2×D411yescharacteristic
186C22×C4×C73#4111yescharacteristic
187M16×C73—81no—
188M16×C73—81no—
189C2×C8×C73—21no—
190C2×C8×C73—21no—
191C2×C8×C73—81no—
192C2×C8×C73C2×D411yescharacteristic
193C2×C8×C73C2×D411yescharacteristic
194C2×C8×C73C2×D411yescharacteristic
195C2×C8×C73C2×D411yescharacteristic
196C4⋊C4×C73—21no—
197C4⋊C4×C73—21no—
198C4⋊C4×C73—21no—
199C4⋊C4×C73—21no—
200C4⋊C4×C73C22×C411yescharacteristic
201C4⋊C4×C73C22×C411yescharacteristic
202C22⋊C4×C73—21no—
203C22⋊C4×C73—21no—
204C22⋊C4×C73—21no—
205C22⋊C4×C73—21no—
206C22⋊C4×C73—21no—
207C42×C73—21no—
208C42×C73C22×C411yescharacteristic
209C42×C73C2×D411yescharacteristic
210C42×C73#4111yescharacteristic
211C42×C73C2411yescharacteristic
212C23×C73—21no—
213C23×C73C4×D411yescharacteristic
214C22×D73—21no—
215C22×D73—21no—
216C22×D73—24no—
217C22×D73—81no—
218C22×D73—81no—
219Q8×C73—21no—
220Q8×C73—21no—
221D4×C73—21no—
222D4×C73—21no—
223D4×C73—81no—
224C2×C4×C73—21no—
225C2×C4×C73—21no—
226C2×C4×C73—21no—
227C2×C4×C73—21no—
228C2×C4×C73—21no—
229C2×C4×C73—21no—
230C2×C4×C73—21no—
231C2×C4×C73—41no—
232C2×C4×C73—41no—
233C2×C4×C73—41no—
234C2×C4×C73C4×D411yescharacteristic
235C2×C4×C73C4×D411yescharacteristic
236C2×C4×C73C4×D411yescharacteristic
237C2×C4×C73C23×C411yescharacteristic
238C2×C4×C73C22×D411yescharacteristic
239C2×C4×C73C2×#4111yescharacteristic
240C2×Dic73—21no—
241C2×Dic73—21no—
242C2×Dic73—81no—
243D292—24no—
244D292—21no—
245D292—21no—
246D292#13112yes—
247D292#13112yes—
248C4×D73—41no—
249C4×D73—41no—
250C4×D73—41no—
251C4×D73—41no—
252C4×D73—81no—
253C4×D73—81no—
254C8×C73—21no—
255C8×C73—21no—
256C8×C73—21no—
257C8×C73—21no—
258C8×C73—41no—
259C8×C73—41no—
260#10596831—21no—
261#10596831—21no—
262#10596831—21no—
263#10596831—21no—
264#10596831—41no—
265#10596831—41no—
266#10596831—41no—
267#10596831—41no—
268C22×C73—21no—
269C22×C73—21no—
270C22×C73—21no—
271C22×C73—41no—
272C22×C73—41no—
273C22×C73—41no—
274C22×C73C2×C4×D411yescharacteristic
275C2×D73—22no—
276C2×D73—22no—
277C2×D73—41no—
278C2×D73—41no—
279C2×D73—41no—
280C2×D73—41no—
281C2×D73—84no—
282C4×C73—21no—
283C4×C73—21no—
284C4×C73—21no—
285C4×C73—21no—
286C4×C73—41no—
287C4×C73—41no—
288C4×C73—41no—
289C4×C73C2×#13111yescharacteristic
290C4×C73C2×#13111yescharacteristic
291C4×C73#57611yescharacteristic
292C4×C73#57711yescharacteristic
293Dic73—41no—
294Dic73—41no—
295#17918—731nomaximal, Sylow
296C2×C73—41no—
297C2×C73—81no—
298C2×C73#292911yescharacteristic
299C2×C73#294611yescharacteristic
300C2×C73#295711yescharacteristic
301D73—42no—
302D73—42no—
303#3105—731no—
304#2993D7311yescharacteristic, complemented
305#2972—731no—
306#1586—731no—
307#1585—731no—
308#1582—731no—
309#1581—731no—
310#1580—731no—
311SD16⋊C8—731no—
312C8×SD16—731no—
313C8×D8—731no—
314#1574—731no—
315#1486—731no—
316#1482—731no—
317#1454—731no—
318C73#1791811yescharacteristic, complemented, Sylow
319#529C2×D7311yescharacteristic
320C2×C4×D4—731no—
321#484—731no—
322#481—731no—
323#478—731no—
324#478—731no—
325#463—731no—
326#463—731no—
327#450—731no—
328#447—731no—
329#446C2×D7311yescharacteristic, complemented
330C8×Q8C2×D7311yescharacteristic, complemented
331C4×SD16—731no—
332C4×SD16—731no—
333C4×D8—731no—
334C4×D8—731no—
335#436—21no—
336#436C2×D7311yescharacteristic, complemented
337#435—21no—
338C8×D4—731no—
339C8×D4—731no—
340C8×D4—731no—
341C8×D4—731no—
342C8×D4—1461no—
343C8×D4—1461no—
344C8×D4C2×D7311yescharacteristic, complemented
345#433—21no—
346#431—731no—
347#431—731no—
348#431—731no—
349#431C2×D7311yescharacteristic
350#424—21no—
351#423C2×D7311yescharacteristic
352C2×C22⋊C8—1461no—
353C2×C22⋊C8—1461no—
354#335—731no—
355#335—731no—
356#334—731no—
357#334—731no—
358Q8⋊C8—731no—
359Q8⋊C8—731no—
360D4⋊C8—731no—
361D4⋊C8—731no—
362D4⋊C8—731no—
363D4⋊C8—731no—
364D4⋊C8—731no—
365D4⋊C8—731no—
366#322—731no—
367#322—731no—
368#322—731no—
369C82—731no—
370C22×D4—731no—
371C23×C4—1461no—
372C2×SD16—731no—
373C2×SD16—731no—
374C2×D8—731no—
375C2×D8—731no—
376C2×M16—21no—
377C2×M16—21no—
378C22×C8—21no—
379C22×C8—1461no—
380C22×C8—1461no—
381C22×C8—1461no—
382C22×C8—1461no—
383#126—21no—
384#125C4×D7311yescharacteristic
385#124C4×D7311yescharacteristic
386#123—21no—
387C22⋊Q8C4×D7311yescharacteristic
388#121C4×D7311yescharacteristic
389C4×Q8C22×D7311yescharacteristic
390C4×D4—21no—
391C4×D4—731no—
392C4×D4—731no—
393C4×D4—731no—
394C4×D4—731no—
395C4×D4—1461no—
396C4×D4—1461no—
397C4×D4C22×D7311yescharacteristic
398#117—21no—
399C2×C4⋊C4—731no—
400C2×C22⋊C4—1461no—
401C2×C42C22×D7311yescharacteristic
402#107—731no—
403#107—731no—
404#106—731no—
405#106—731no—
406C4⋊C8—21no—
407C4⋊C8—21no—
408C4⋊C8—21no—
409C4⋊C8—731no—
410C4⋊C8—731no—
411C4⋊C8—731no—
412C4⋊C8—731no—
413C4⋊C8—1461no—
414C4⋊C8C22⋊D7311yescharacteristic
415C4⋊C8C22⋊D7311yescharacteristic
416C4⋊C8C22×D7311yescharacteristic
417C4⋊C8C22×D7311yescharacteristic
418#103—731no—
419#103—731no—
420#102—731no—
421#102—731no—
422#102—731no—
423#102—731no—
424#102—731no—
425#102—731no—
426C22⋊C8—21no—
427C22⋊C8—21no—
428C22⋊C8—731no—
429C22⋊C8—731no—
430C22⋊C8—1461no—
431C22⋊C8—1461no—
432C22⋊C8—1461no—
433C22⋊C8—1461no—
434C22⋊C8—1461no—
435C22⋊C8—1461no—
436C22⋊C8C22⋊D7311yescharacteristic
437C22⋊C8C22⋊D7311yescharacteristic
438#97—21no—
439C4×C8—21no—
440C4×C8—731no—
441C4×C8—731no—
442C4×C8—731no—
443C4×C8—731no—
444C4×C8—1461no—
445C4×C8C22×D7311yescharacteristic
446C4×C8C22×D7311yescharacteristic
447C24—1461no—
448C2×Q8C2×C4×D7311yescharacteristic
449C2×D4—21no—
450C2×D4—731no—
451C2×D4—731no—
452C2×D4—1462no—
453C2×D4—1462no—
454C2×D4—1461no—
455C2×D4C2×C4×D7311yescharacteristic
456C22×C4—21no—
457C22×C4—5841no—
458C22×C4—5841no—
459C22×C4—1461no—
460C22×C4—1461no—
461C22×C4—1461no—
462C22×C4—1461no—
463C22×C4—1461no—
464C22×C4C2×C4×D7311yescharacteristic
465C22×C4C2×C22⋊D7311yescharacteristic
466C22×C4#1192402811yescharacteristic
467SD16—1462no—
468SD16—1462no—
469D8—1462no—
470D8—1462no—
471M16—81no—
472M16—81no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—81no—
476C2×C8—5841no—
477C2×C8—5841no—
478C2×C8—5841no—
479C2×C8—5841no—
480C2×C8—731no—
481C2×C8—731no—
482C2×C8—731no—
483C2×C8—731no—
484C2×C8—1461no—
485C2×C8—1461no—
486C2×C8—1461no—
487C2×C8—1461no—
488C2×C8C2×C22⋊D7311yescharacteristic
489C2×C8C2×C22⋊D7311yescharacteristic
490C2×C8C2×C22⋊D7311yescharacteristic
491C2×C8C2×C22⋊D7311yescharacteristic
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—731no—
497C4⋊C4—731no—
498C4⋊C4—1461no—
499C4⋊C4C2×C4×D7311yescharacteristic
500C4⋊C4C2×C4×D7311yescharacteristic
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—21no—
506C22⋊C4—1461no—
507C22⋊C4—1461no—
508C22⋊C4—1461no—
509C22⋊C4—1461no—
510C42—21no—
511C42C2×C4×D7311yescharacteristic
512C42C2×C22⋊D7311yescharacteristic
513C42#1192402811yescharacteristic
514C42C23×D7311yescharacteristic
515C23—21no—
516C23—5841no—
517C23—5841no—
518C23—1464no—
519C23—1461no—
520C23—1461no—
521C23C4×C22⋊D7311yescharacteristic
522Q8—21no—
523Q8—21no—
524D4—21no—
525D4—21no—
526D4—81no—
527D4—732no—
528D4—732no—
529D4—1464no—
530D4—1461no—
531D4—1461no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—2921no—
543C2×C4—2921no—
544C2×C4—2921no—
545C2×C4—2921no—
546C2×C4—5841no—
547C2×C4—5841no—
548C2×C4—5841no—
549C2×C4—1461no—
550C2×C4—1461no—
551C2×C4C4×C22⋊D7311yescharacteristic
552C2×C4C4×C22⋊D7311yescharacteristic
553C2×C4C4×C22⋊D7311yescharacteristic
554C2×C4C22×C4×D7311yescharacteristic
555C2×C4C22×C22⋊D7311yescharacteristic
556C2×C4C2×#1192402811yescharacteristic
557C8—21no—
558C8—21no—
559C8—21no—
560C8—21no—
561C8—41no—
562C8—41no—
563C8—2921no—
564C8—2921no—
565C8—2921no—
566C8—2921no—
567C8—1461no—
568C8—1461no—
569C8—1461no—
570C8—1461no—
571C22—21no—
572C22—21no—
573C22—21no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—2921no—
578C22—2921no—
579C22—2921no—
580C22—2921no—
581C22—5844no—
582C22—1462no—
583C22—1462no—
584C22C2×C4×C22⋊D7311yescharacteristic
585C4—21no—
586C4—21no—
587C4—21no—
588C4—21no—
589C4—41no—
590C4—41no—
591C4—41no—
592C4—2921no—
593C4—2921no—
594C4#131×D7311yescharacteristic
595C4#131×D7311yescharacteristic
596C4#1798939011yescharacteristic
597C4#1798939511yescharacteristic
598C2—41no—
599C2—81no—
600C2—2922no—
601C2—2922no—
602C2#2261862311yescharacteristic
603C2#2261875911yescharacteristic
604C2#2261884611yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#2993C2
socleC22×C73C2×C4×D4
prime radical#17988720C4
cosocleC42×C73C24
hypercenter#2993D73
hypocenterC73#17918
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2993

Complements

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

NH ≅ G/Ntype
2. #22618954C2semidirect
3. #22608793C2semidirect
4. #22608786C2semidirect
5. #22608765C2semidirect
6. #22608758C2semidirect
7. #22608753C2semidirect
8. #22608741C2semidirect
9. C8×#11924015C2semidirect
10. C8×#11924013C2semidirect
11. #22608722C2semidirect
12. #22608355C2semidirect
13. #22608339C2semidirect
14. #22608231C2semidirect
15. C73×#2993C2semidirect
40. #17988339C22semidirect
41. #17988339C22semidirect
42. #17988337C22semidirect
43. #17988337C22semidirect
44. Q8⋊#10596831C22semidirect
45. Q8⋊#10596831C22semidirect
46. D4⋊#10596831C22semidirect
47. D4⋊#10596831C22semidirect
52. #17988309C22semidirect
53. #17988309C22semidirect
54. #17988308C22semidirect
55. C8×#10596831C22semidirect
57. #446×C73C22semidirect
58. C8×Q8×C73C22semidirect
60. #436×C73C22semidirect
62. C8×D4×C73C22semidirect
304. #2993D73semidirect
318. C73#17918semidirect
329. #446C2×D73semidirect
330. C8×Q8C2×D73semidirect
336. #436C2×D73semidirect
344. C8×D4C2×D73semidirect

Maximal subgroups

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

subgroupindex
#226199742
#226189542
#226087932
#226087862
#226087652
#226087582
#226087532
#226087412
C8×#119240152
C8×#119240132
#226087222
#226083552
#226083392
#226082312
C73×#29932
#1791873