Finite Group Databasebeta

← #33057834

Subgroups — #33057834

Order 18688.

656 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22620527C211yesmaximal, characteristic
2#22618677C211yesmaximal, characteristic, complemented
3#22608843C211yesmaximal, characteristic, complemented
4#22608821C211yesmaximal, characteristic, complemented
5#22608809C211yesmaximal, characteristic, complemented
6#22608793C211yesmaximal, characteristic, complemented
7#22608765C211yesmaximal, characteristic, complemented
8#22608760C211yesmaximal, characteristic, complemented
9#22608741C211yesmaximal, characteristic, complemented
10C8×#11924013C211yesmaximal, characteristic, complemented
11#22608684C211yesmaximal, characteristic, complemented
12#22608347C211yesmaximal, characteristic, complemented
13#22608344C211yesmaximal, characteristic, complemented
14#22608234C211yesmaximal, characteristic, complemented
15C73×#2969C211yesmaximal, characteristic, complemented
16C2×#14556599—21no—
17#17989137C2211yescharacteristic
18#17988997C411yescharacteristic
19#17988977C411yescharacteristic
20#17988953C411yescharacteristic
21#17988946C411yescharacteristic
22#17988838C411yescharacteristic
23#17988838C411yescharacteristic
24#17988835C411yescharacteristic
25#17988835C411yescharacteristic
26C4×#11924015C2211yescharacteristic
27C4×#11924015C2211yescharacteristic
28C4×#11924013C2211yescharacteristic
29C4×#11924013C2211yescharacteristic
30#17988666C2211yescharacteristic
31#17988666C2211yescharacteristic
32#17988660—21no—
33#17988660—21no—
34C8×D292C2211yescharacteristic
35C8×D292C2211yescharacteristic
36C2×C4⋊#10596831C2211yescharacteristic
37#17988555—21no—
38C4×#11924012C2211yescharacteristic
39C4×#11924012C2211yescharacteristic
40#17988339C2211yescharacteristic
41#17988339C2211yescharacteristic
42#17988337C2211yescharacteristic
43#17988337C2211yescharacteristic
44Q8⋊#10596831C2211yescharacteristic
45Q8⋊#10596831C2211yescharacteristic
46D4⋊#10596831C2211yescharacteristic
47D4⋊#10596831C2211yescharacteristic
48#17988314C2211yescharacteristic
49#17988314C2211yescharacteristic
50#17988314C2211yescharacteristic
51#17988314C2211yescharacteristic
52#17988309C2211yescharacteristic
53#17988309C2211yescharacteristic
54#17988308C2211yescharacteristic
55C8×#10596831C2211yescharacteristic
56#529×C73C2211yescharacteristic
57#446×C73C2211yescharacteristic
58C8×Q8×C73C2211yescharacteristic
59#436×C73—21no—
60#436×C73C2211yescharacteristic
61#435×C73—21no—
62C8×D4×C73C2211yescharacteristic
63#433×C73—21no—
64#431×C73C2211yescharacteristic
65#405×C73—21no—
66C4×M16×C73C2211yescharacteristic
67C2×#11924028—21no—
68C2×#11924015C2×C411yescharacteristic
69C2×#11924015C2×C411yescharacteristic
70C2×#11924013C2×C411yescharacteristic
71C2×#11924013C2×C411yescharacteristic
72#14556599—44no—
73C2×#11924012—21no—
74C2×#11924012C2×C411yescharacteristic
75C2×#11924012C2×C411yescharacteristic
76C2×#11924011—21no—
77C2×#11924011—21no—
78C22×#10596831—21no—
79C2×C8×D73—21no—
80C2×C8×D73—21no—
81#14556591C2×C411yescharacteristic
82#14556588C2×C411yescharacteristic
83#14556579—21no—
84#14556565—21no—
85#14556565C2×C411yescharacteristic
86#14556565C2×C411yescharacteristic
87C4×D292—21no—
88C4×D292C2311yescharacteristic
89C4×D292C2311yescharacteristic
90#14556524C2×C411yescharacteristic
91#14556524C2×C411yescharacteristic
92#14556522C2×C411yescharacteristic
93#14556522C2×C411yescharacteristic
94C4⋊#10596831—21no—
95C4⋊#10596831C2311yescharacteristic
96C4⋊#10596831C2311yescharacteristic
97#14556515C2×C411yescharacteristic
98#14556515C2×C411yescharacteristic
99#14556512C2×C411yescharacteristic
100#14556512C2×C411yescharacteristic
101#14556511C2×C411yescharacteristic
102#14556511C2×C411yescharacteristic
103#14556511C2×C411yescharacteristic
104#14556511C2×C411yescharacteristic
105#14556503—21no—
106#14556503—21no—
107#14556503—21no—
108#14556503—21no—
109#14556502—21no—
110#14556502C2×C411yescharacteristic
111#14556502C2×C411yescharacteristic
112C4×#10596831C2311yescharacteristic
113C4×#10596831C2311yescharacteristic
114C4×#10596831C2311yescharacteristic
115C4×#10596831C2311yescharacteristic
116C2×M16×C73—21no—
117C2×M16×C73D411yescharacteristic
118C2×M16×C73D411yescharacteristic
119C22×C8×C73—21no—
120#126×C73—21no—
121#125×C73C2×C411yescharacteristic
122#124×C73C2×C411yescharacteristic
123#123×C73—21no—
124C22⋊Q8×C73C2×C411yescharacteristic
125#121×C73C2×C411yescharacteristic
126C4×Q8×C73C2311yescharacteristic
127C4×D4×C73—21no—
128C4×D4×C73C2311yescharacteristic
129#117×C73—21no—
130C2×C42×C73C2311yescharacteristic
131C4⋊C8×C73—21no—
132C4⋊C8×C73—21no—
133C4⋊C8×C73C2311yescharacteristic
134C4⋊C8×C73C2311yescharacteristic
135C22⋊C8×C73—21no—
136C22⋊C8×C73—21no—
137C22⋊C8×C73—21no—
138#97×C73—21no—
139#97×C73D411yescharacteristic
140#97×C73D411yescharacteristic
141C4×C8×C73—21no—
142C4×C8×C73—21no—
143C4×C8×C73C2311yescharacteristic
144C4×C8×C73C2311yescharacteristic
145#11924028—42no—
146#11924028—42no—
147C2×Dic146—21no—
148C2×D292—21no—
149C2×D292—21no—
150C2×D292C22×C411yescharacteristic
151C2×D292C22×C411yescharacteristic
152C2×C22⋊D73—21no—
153C2×C22⋊D73—21no—
154C2×C4×D73—21no—
155C2×C4×D73—21no—
156#11924015—22no—
157#11924015—41no—
158#11924013—22no—
159#11924013—41no—
160#11924012—22no—
161#11924012—41no—
162#11924012—42no—
163#11924011—42no—
164#11924011—42no—
165C2×#10596831—21no—
166C2×#10596831—21no—
167C2×#10596831—21no—
168C2×#10596831—21no—
169C2×#10596831—42no—
170C2×#10596831C22×C411yescharacteristic
171C2×#10596831C22×C411yescharacteristic
172C2×#10596831C22×C411yescharacteristic
173C2×#10596831C22×C411yescharacteristic
174C8×D73—42no—
175C8×D73—42no—
176C4⋊Dic73—21no—
177C4⋊Dic73C22×C411yescharacteristic
178C4⋊Dic73C22×C411yescharacteristic
179#11924005—21no—
180#11924005—21no—
181#11924005—21no—
182#11924005—21no—
183C2×Q8×C73C22×C411yescharacteristic
184C2×D4×C73—21no—
185C2×D4×C73C22×C411yescharacteristic
186C22×C4×C73—21no—
187C22×C4×C73C22×C411yescharacteristic
188C22×C4×C73C2×D411yescharacteristic
189C22×C4×C73#4111yescharacteristic
190M16×C73—22no—
191M16×C73—41no—
192M16×C73—42no—
193C2×C8×C73—21no—
194C2×C8×C73—21no—
195C2×C8×C73—42no—
196C2×C8×C73C2×D411yescharacteristic
197C2×C8×C73C2×D411yescharacteristic
198C2×C8×C73C2×D411yescharacteristic
199C2×C8×C73C2×D411yescharacteristic
200C4⋊C4×C73—21no—
201C4⋊C4×C73—21no—
202C4⋊C4×C73—21no—
203C4⋊C4×C73—21no—
204C4⋊C4×C73C22×C411yescharacteristic
205C4⋊C4×C73C22×C411yescharacteristic
206C22⋊C4×C73—21no—
207C22⋊C4×C73—21no—
208C22⋊C4×C73—21no—
209C22⋊C4×C73—21no—
210C22⋊C4×C73—21no—
211C42×C73—21no—
212C42×C73C22×C411yescharacteristic
213C42×C73C2×D411yescharacteristic
214C42×C73#4111yescharacteristic
215C42×C73C2411yescharacteristic
216C23×C73—21no—
217C23×C73C4×D411yescharacteristic
218C22×D73—21no—
219C22×D73—21no—
220Q8×C73—21no—
221Q8×C73—21no—
222D4×C73—21no—
223D4×C73—21no—
224D4×C73—81no—
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—21no—
232C2×C4×C73—41no—
233C2×C4×C73—41no—
234C2×C4×C73—41no—
235C2×C4×C73C4×D411yescharacteristic
236C2×C4×C73C4×D411yescharacteristic
237C2×C4×C73C4×D411yescharacteristic
238C2×C4×C73C23×C411yescharacteristic
239C2×C4×C73C22×D411yescharacteristic
240C2×C4×C73C2×#4111yescharacteristic
241C22⋊D73—42no—
242C22⋊D73—42no—
243C2×Dic73—21no—
244C2×Dic73—21no—
245D292—21no—
246D292—21no—
247D292—21no—
248D292—21no—
249D292—42no—
250D292—81no—
251C4×D73—41no—
252C4×D73—41no—
253C4×D73—41no—
254C4×D73—41no—
255Dic146—42no—
256C8×C73—21no—
257C8×C73—21no—
258C8×C73—21no—
259C8×C73—41no—
260C8×C73—41no—
261C8×C73AGL(1,ℤ/8)12yes—
262#10596831—22no—
263#10596831—21no—
264#10596831—21no—
265#10596831—21no—
266#10596831—41no—
267#10596831—41no—
268#10596831—41no—
269#10596831#13112yescomplemented
270C22×C73—21no—
271C22×C73—21no—
272C22×C73—21no—
273C22×C73—41no—
274C22×C73—41no—
275C22×C73—41no—
276C22×C73C2×C4×D411yescharacteristic
277C2×D73—41no—
278C2×D73—41no—
279C2×D73—41no—
280C2×D73—41no—
281C2×D73—41no—
282C2×D73—41no—
283C4×C73—21no—
284C4×C73—21no—
285C4×C73—21no—
286C4×C73—21no—
287C4×C73—41no—
288C4×C73—41no—
289C4×C73—41no—
290C4×C73C2×#13111yescharacteristic
291C4×C73#56811yescharacteristic
292C4×C73C2×AGL(1,ℤ/8)11yescharacteristic
293C4×C73#57511yescharacteristic
294Dic73—41no—
295Dic73—41no—
296#18076—731nomaximal, Sylow
297C2×C73—41no—
298C2×C73—81no—
299C2×C73#293511yescharacteristic
300C2×C73C4×AGL(1,ℤ/8)11yescharacteristic
301C2×C73#295611yescharacteristic
302D73—81no—
303D73—81no—
304#3171—731no—
305#2969D7311yescharacteristic, complemented
306#2935—731no—
307#1594—731no—
308#1590—731no—
309#1588—731no—
310#1586—731no—
311#1582—731no—
312#1581—731no—
313SD16⋊C8—731no—
314C8×D8—731no—
315#1565—731no—
316#1484—731no—
317#1483—731no—
318#1455—731no—
319C73#1807611yescharacteristic, complemented, Sylow
320C2×#131—1461no—
321#532—731no—
322#529C2×D7311yescharacteristic
323#501—731no—
324#496—731no—
325#490—731no—
326#489—731no—
327#469—731no—
328#469—731no—
329#468—731no—
330#468—731no—
331#446C2×D7311yescharacteristic
332C8×Q8C2×D7311yescharacteristic
333C4×SD16—731no—
334C4×SD16—731no—
335C4×D8—731no—
336C4×D8—731no—
337#436—21no—
338#436—731no—
339#436—731no—
340#436C2×D7311yescharacteristic
341#435—21no—
342#435—1461no—
343#435—1461no—
344C8×D4—731no—
345C8×D4—731no—
346C8×D4C2×D7311yescharacteristic
347#433—21no—
348#431C2×D7311yescharacteristic
349C2×C4⋊C8—731no—
350#408—1461no—
351#405—21no—
352C4×M16—731no—
353C4×M16—731no—
354C4×M16C2×D7311yescharacteristic
355#335—731no—
356#335—731no—
357#334—731no—
358#334—731no—
359Q8⋊C8—731no—
360Q8⋊C8—731no—
361D4⋊C8—731no—
362D4⋊C8—731no—
363D4⋊C8—731no—
364D4⋊C8—731no—
365D4⋊C8—731no—
366D4⋊C8—731no—
367#322—731no—
368#322—731no—
369#322—731no—
370C82—731no—
371C2×#41—1461no—
372C2×SD16—731no—
373C2×SD16—731no—
374C2×D8—731no—
375C2×D8—731no—
376#131—2924no—
377C2×M16—21no—
378C2×M16—731no—
379C2×M16—731no—
380C2×M16—1461no—
381C2×M16—1461no—
382C2×M16—1461no—
383C2×M16C22⋊D7311yescharacteristic
384C2×M16C22⋊D7311yescharacteristic
385C22×C8—21no—
386C22×C8—1461no—
387C22×C8—1461no—
388C22×C8—1461no—
389C4⋊Q8—731no—
390#127—731no—
391#126—21no—
392#125C4×D7311yescharacteristic
393#124—1461no—
394#124C4×D7311yescharacteristic
395#123—21no—
396C22⋊Q8C4×D7311yescharacteristic
397#121—731no—
398#121—731no—
399#121—1461no—
400#121C4×D7311yescharacteristic
401C4×Q8C22×D7311yescharacteristic
402C4×D4—21no—
403C4×D4—731no—
404C4×D4—731no—
405C4×D4—1461no—
406C4×D4C22×D7311yescharacteristic
407#117—21no—
408C2×C42C22×D7311yescharacteristic
409#107—731no—
410#107—731no—
411#106—731no—
412#106—731no—
413C4⋊C8—21no—
414C4⋊C8—21no—
415C4⋊C8—731no—
416C4⋊C8—731no—
417C4⋊C8—1461no—
418C4⋊C8C22×D7311yescharacteristic
419C4⋊C8C22×D7311yescharacteristic
420#103—731no—
421#103—731no—
422#102—731no—
423#102—731no—
424#102—731no—
425#102—731no—
426#102—731no—
427#102—731no—
428C22⋊C8—21no—
429C22⋊C8—21no—
430C22⋊C8—21no—
431C22⋊C8—1461no—
432C22⋊C8—1461no—
433C22⋊C8—1461no—
434C22⋊C8—1461no—
435#97—21no—
436#97—731no—
437#97—731no—
438#97—1461no—
439#97C22⋊D7311yescharacteristic
440#97C22⋊D7311yescharacteristic
441C4×C8—21no—
442C4×C8—21no—
443C4×C8—731no—
444C4×C8—731no—
445C4×C8—731no—
446C4×C8—731no—
447C4×C8C22×D7311yescharacteristic
448C4×C8C22×D7311yescharacteristic
449#41—2922no—
450#41—2922no—
451C2×Q8—1461no—
452C2×Q8C2×C4×D7311yescharacteristic
453C2×D4—21no—
454C2×D4—731no—
455C2×D4—731no—
456C2×D4—1461no—
457C2×D4—1461no—
458C2×D4—1461no—
459C2×D4—1461no—
460C2×D4C2×C4×D7311yescharacteristic
461C22×C4—21no—
462C22×C4—1461no—
463C22×C4—1461no—
464C22×C4C2×C4×D7311yescharacteristic
465C22×C4C2×C22⋊D7311yescharacteristic
466C22×C4#1192402811yescharacteristic
467SD16—2921no—
468SD16—1462no—
469D8—2921no—
470D8—1462no—
471M16—22no—
472M16—41no—
473M16—42no—
474M16—2922no—
475M16—2922no—
476M16—2922no—
477M16—2921no—
478M16—1462no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—42no—
482C2×C8—2922no—
483C2×C8—2922no—
484C2×C8—2922no—
485C2×C8—731no—
486C2×C8—731no—
487C2×C8—731no—
488C2×C8—731no—
489C2×C8—1461no—
490C2×C8—1461no—
491C2×C8—1461no—
492C2×C8—1461no—
493C2×C8C2×C22⋊D7311yescharacteristic
494C2×C8C2×C22⋊D7311yescharacteristic
495C2×C8C2×C22⋊D7311yescharacteristic
496C2×C8C2×C22⋊D7311yescharacteristic
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—731no—
502C4⋊C4—731no—
503C4⋊C4—1461no—
504C4⋊C4C2×C4×D7311yescharacteristic
505C4⋊C4C2×C4×D7311yescharacteristic
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—21no—
509C22⋊C4—21no—
510C22⋊C4—21no—
511C22⋊C4—1461no—
512C22⋊C4—1461no—
513C22⋊C4—1461no—
514C22⋊C4—1461no—
515C42—21no—
516C42C2×C4×D7311yescharacteristic
517C42C2×C22⋊D7311yescharacteristic
518C42#1192402811yescharacteristic
519C42C23×D7311yescharacteristic
520C23—21no—
521C23—1461no—
522C23—1461no—
523C23C4×C22⋊D7311yescharacteristic
524Q8—21no—
525Q8—21no—
526Q8—2922no—
527D4—21no—
528D4—21no—
529D4—81no—
530D4—2922no—
531D4—2922no—
532D4—2922no—
533D4—5841no—
534D4—1461no—
535D4—1461no—
536D4—1461no—
537D4—1461no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—2921no—
549C2×C4—2921no—
550C2×C4—2921no—
551C2×C4—2921no—
552C2×C4—1461no—
553C2×C4—1461no—
554C2×C4C4×C22⋊D7311yescharacteristic
555C2×C4C4×C22⋊D7311yescharacteristic
556C2×C4C4×C22⋊D7311yescharacteristic
557C2×C4C22×C4×D7311yescharacteristic
558C2×C4C22×C22⋊D7311yescharacteristic
559C2×C4C2×#1192402811yescharacteristic
560C8—21no—
561C8—21no—
562C8—21no—
563C8—41no—
564C8—41no—
565C8—2921no—
566C8—2921no—
567C8—2921no—
568C8—732no—
569C8—1462no—
570C8—1461no—
571C8—1461no—
572C8—1461no—
573C8#1455661612yes—
574C22—21no—
575C22—21no—
576C22—21no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—2921no—
581C22—2921no—
582C22—2921no—
583C22—2921no—
584C22—2921no—
585C22—2921no—
586C22C2×C4×C22⋊D7311yescharacteristic
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—41no—
592C4—41no—
593C4—41no—
594C4—2921no—
595C4—2921no—
596C4#131×D7311yescharacteristic
597C4#1798935211yescharacteristic
598C4C2×#1455661611yescharacteristic
599C4#1798938511yescharacteristic
600C2—41no—
601C2—81no—
602C2—5841no—
603C2—5841no—
604C2#2261867311yescharacteristic
605C2C4×#1455661611yescharacteristic
606C2#2261883811yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#2969C2
socleC22×C73C2×C4×D4
prime radical#22620527C2
cosocleC42×C73C24
hypercenter#2969D73
hypocenterC73#18076
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ #2969

Complements

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

NH ≅ G/Ntype
2. #22618677C2semidirect
3. #22608843C2semidirect
4. #22608821C2semidirect
5. #22608809C2semidirect
6. #22608793C2semidirect
7. #22608765C2semidirect
8. #22608760C2semidirect
9. #22608741C2semidirect
10. C8×#11924013C2semidirect
11. #22608684C2semidirect
12. #22608347C2semidirect
13. #22608344C2semidirect
14. #22608234C2semidirect
15. C73×#2969C2semidirect
269. #10596831#131semidirect
305. #2969D73semidirect
319. C73#18076semidirect

Maximal subgroups

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

subgroupindex
#226205272
#226186772
#226088432
#226088212
#226088092
#226087932
#226087652
#226087602
#226087412
C8×#119240132
#226086842
#226083472
#226083442
#226082342
C73×#29692
#1807673