Finite Group Databasebeta

← #33057838

Subgroups — #33057838

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#22620520C211yesmaximal, characteristic
2#22618935C211yesmaximal, characteristic, complemented
3#22608843C211yesmaximal, characteristic, complemented
4#22608819C211yesmaximal, characteristic, complemented
5#22608807C211yesmaximal, characteristic, complemented
6#22608795C211yesmaximal, characteristic, complemented
7#22608767C211yesmaximal, characteristic, complemented
8#22608758C211yesmaximal, characteristic, complemented
9#22608743C211yesmaximal, characteristic, complemented
10C8×#11924013C211yesmaximal, characteristic, complemented
11#22608681C211yesmaximal, characteristic, complemented
12#22608348C211yesmaximal, characteristic, complemented
13#22608342C211yesmaximal, characteristic, complemented
14#22608234C211yesmaximal, characteristic, complemented
15C73×#2935C211yesmaximal, characteristic, complemented
16#17989121C2211yescharacteristic
17#17988993C411yescharacteristic
18#17988974C411yescharacteristic
19#17988951C411yescharacteristic
20#17988949C411yescharacteristic
21#17988838C411yescharacteristic
22#17988838C411yescharacteristic
23#17988831C411yescharacteristic
24#17988831C411yescharacteristic
25#17988717C2211yescharacteristic
26C8×Dic146C2211yescharacteristic
27C4×#11924016C2211yescharacteristic
28C4×#11924016C2211yescharacteristic
29C4×#11924013C2211yescharacteristic
30C4×#11924013C2211yescharacteristic
31#17988666C2211yescharacteristic
32#17988663—21no—
33#17988656—21no—
34C8×D292C2211yescharacteristic
35#17988649—21no—
36#17988640C2211yescharacteristic
37#17988544—21no—
38C4×#11924012C2211yescharacteristic
39C4×#11924012C2211yescharacteristic
40#17988339C2211yescharacteristic
41#17988339C2211yescharacteristic
42#17988337C2211yescharacteristic
43#17988337C2211yescharacteristic
44#17988317C2211yescharacteristic
45#17988317C2211yescharacteristic
46D4⋊#10596831C2211yescharacteristic
47D4⋊#10596831C2211yescharacteristic
48D4⋊#10596831C2211yescharacteristic
49D4⋊#10596831C2211yescharacteristic
50#17988314C2211yescharacteristic
51#17988314C2211yescharacteristic
52#17988309C2211yescharacteristic
53#17988309C2211yescharacteristic
54#17988308C2211yescharacteristic
55C8×#10596831C2211yescharacteristic
56C2×#131×C73—21no—
57#532×C73C2211yescharacteristic
58#436×C73C2211yescharacteristic
59#436×C73C2211yescharacteristic
60#435×C73—21no—
61#435×C73—21no—
62C8×D4×C73C2211yescharacteristic
63C8×D4×C73C2211yescharacteristic
64C2×C4⋊C8×C73C2211yescharacteristic
65#408×C73—21no—
66C4×M16×C73C2211yescharacteristic
67C2×#11924016C2×C411yescharacteristic
68C2×#11924016C2×C411yescharacteristic
69C2×#11924013C2×C411yescharacteristic
70C2×#11924013C2×C411yescharacteristic
71C2×#11924012—21no—
72C2×#11924012C2×C411yescharacteristic
73C2×#11924012C2×C411yescharacteristic
74C2×#11924011—21no—
75C2×C8×D73—21no—
76#14556585—21no—
77#14556583C2×C411yescharacteristic
78#14556579C2×C411yescharacteristic
79#14556574—21no—
80#14556570C2×C411yescharacteristic
81#14556565C2×C411yescharacteristic
82C4×Dic146C2311yescharacteristic
83C4×D292C2311yescharacteristic
84C4×C22⋊D73—21no—
85#14556548—21no—
86#14556524C2×C411yescharacteristic
87#14556524C2×C411yescharacteristic
88#14556522C2×C411yescharacteristic
89#14556522C2×C411yescharacteristic
90C4⋊#10596831C2311yescharacteristic
91C4⋊#10596831C2311yescharacteristic
92#14556520—21no—
93#14556520—21no—
94#14556514C2×C411yescharacteristic
95#14556514C2×C411yescharacteristic
96#14556512C2×C411yescharacteristic
97#14556512C2×C411yescharacteristic
98#14556512C2×C411yescharacteristic
99#14556512C2×C411yescharacteristic
100#14556511C2×C411yescharacteristic
101#14556511C2×C411yescharacteristic
102C22⋊#10596831—21no—
103#14556503—21no—
104#14556503—21no—
105#14556502—21no—
106#14556502C2×C411yescharacteristic
107#14556502C2×C411yescharacteristic
108#14556501—21no—
109C4×#10596831—21no—
110C4×#10596831C2311yescharacteristic
111C4×#10596831C2311yescharacteristic
112C4×#10596831C2311yescharacteristic
113C4×#10596831C2311yescharacteristic
114C8×Dic73—21no—
115C2×#41×C73—21no—
116#131×C73—44no—
117C2×M16×C73—21no—
118C2×M16×C73—21no—
119C2×M16×C73D411yescharacteristic
120C2×M16×C73D411yescharacteristic
121C22×C8×C73—21no—
122C22×C8×C73—21no—
123C22×C8×C73—21no—
124C4⋊Q8×C73C2×C411yescharacteristic
125#127×C73C2×C411yescharacteristic
126#124×C73—21no—
127#121×C73—21no—
128#121×C73C2×C411yescharacteristic
129#121×C73C2×C411yescharacteristic
130C4×D4×C73—21no—
131C4×D4×C73C2311yescharacteristic
132C4×D4×C73C2311yescharacteristic
133C2×C42×C73C2311yescharacteristic
134C4⋊C8×C73—21no—
135C4⋊C8×C73C2311yescharacteristic
136C4⋊C8×C73C2311yescharacteristic
137C22⋊C8×C73—21no—
138C22⋊C8×C73—21no—
139C22⋊C8×C73—21no—
140C22⋊C8×C73—21no—
141#97×C73D411yescharacteristic
142#97×C73D411yescharacteristic
143C4×C8×C73C2311yescharacteristic
144C4×C8×C73C2311yescharacteristic
145C2×Dic146C22×C411yescharacteristic
146C2×D292C22×C411yescharacteristic
147C2×C22⋊D73—21no—
148C2×C4×D73—21no—
149#11924016—22no—
150#11924016—41no—
151#11924013—22no—
152#11924013—41no—
153#11924012—22no—
154#11924012—41no—
155#11924012—42no—
156#11924011—42no—
157C2×#10596831—21no—
158C2×#10596831—21no—
159C2×#10596831—21no—
160C2×#10596831—21no—
161C2×#10596831C22×C411yescharacteristic
162C2×#10596831C22×C411yescharacteristic
163C2×#10596831C22×C411yescharacteristic
164C2×#10596831C22×C411yescharacteristic
165C8×D73—42no—
166C4⋊Dic73C22×C411yescharacteristic
167C4⋊Dic73C22×C411yescharacteristic
168#11924007—21no—
169#11924007—21no—
170#11924007—21no—
171#11924007—21no—
172C22⋊Dic73—21no—
173#11924005—21no—
174#11924005—21no—
175#11924005—21no—
176#11924005—21no—
177C4×Dic73—21no—
178#41×C73—42no—
179#41×C73—42no—
180C2×Q8×C73—21no—
181C2×D4×C73—21no—
182C2×D4×C73—21no—
183C2×D4×C73—21no—
184C2×D4×C73—21no—
185C2×D4×C73C22×C411yescharacteristic
186C2×D4×C73C22×C411yescharacteristic
187C22×C4×C73—21no—
188C22×C4×C73—21no—
189C22×C4×C73C22×C411yescharacteristic
190C22×C4×C73C2×D411yescharacteristic
191C22×C4×C73#4111yescharacteristic
192M16×C73—22no—
193M16×C73—41no—
194M16×C73—42no—
195M16×C73—42no—
196C2×C8×C73—21no—
197C2×C8×C73—21no—
198C2×C8×C73—42no—
199C2×C8×C73—42no—
200C2×C8×C73—42no—
201C2×C8×C73C2×D411yescharacteristic
202C2×C8×C73C2×D411yescharacteristic
203C2×C8×C73C2×D411yescharacteristic
204C2×C8×C73C2×D411yescharacteristic
205C4⋊C4×C73—21no—
206C4⋊C4×C73C22×C411yescharacteristic
207C4⋊C4×C73C22×C411yescharacteristic
208C22⋊C4×C73—21no—
209C22⋊C4×C73—21no—
210C22⋊C4×C73—21no—
211C22⋊C4×C73—21no—
212C42×C73C22×C411yescharacteristic
213C42×C73C2×D411yescharacteristic
214C42×C73#4111yescharacteristic
215C42×C73C2411yescharacteristic
216C23×C73—21no—
217C23×C73—21no—
218C23×C73C4×D411yescharacteristic
219C22×D73—21no—
220Q8×C73—42no—
221D4×C73—21no—
222D4×C73—21no—
223D4×C73—21no—
224D4×C73—21no—
225D4×C73—42no—
226D4×C73—42no—
227D4×C73—42no—
228D4×C73—81no—
229C2×C4×C73—21no—
230C2×C4×C73—21no—
231C2×C4×C73—21no—
232C2×C4×C73—21no—
233C2×C4×C73—21no—
234C2×C4×C73—21no—
235C2×C4×C73—41no—
236C2×C4×C73—41no—
237C2×C4×C73—41no—
238C2×C4×C73—41no—
239C2×C4×C73—41no—
240C2×C4×C73C4×D411yescharacteristic
241C2×C4×C73C4×D411yescharacteristic
242C2×C4×C73C4×D411yescharacteristic
243C2×C4×C73C23×C411yescharacteristic
244C2×C4×C73C22×D411yescharacteristic
245C2×C4×C73C2×#4111yescharacteristic
246C22⋊D73—81no—
247C2×Dic73—21no—
248C2×Dic73—21no—
249C2×Dic73—21no—
250D292—21no—
251D292—21no—
252C4×D73—41no—
253C4×D73—41no—
254Dic146—21no—
255Dic146—21no—
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×C73—41no—
277C22×C73—41no—
278C22×C73—41no—
279C22×C73C2×C4×D411yescharacteristic
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×C73C2×#13111yescharacteristic
290C4×C73#56811yescharacteristic
291C4×C73C2×AGL(1,ℤ/8)11yescharacteristic
292C4×C73#57511yescharacteristic
293Dic73—41no—
294Dic73—41no—
295Dic73—41no—
296#18076—731nomaximal, Sylow
297C2×C73—41no—
298C2×C73—81no—
299C2×C73—81no—
300C2×C73#293511yescharacteristic
301C2×C73C4×AGL(1,ℤ/8)11yescharacteristic
302C2×C73#295611yescharacteristic
303D73—81no—
304#3171—731no—
305#2969—731no—
306#2935D7311yescharacteristic, complemented
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—21no—
321#532C2×D7311yescharacteristic
322#529—731no—
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#446—731no—
332C8×Q8—731no—
333C4×SD16—731no—
334C4×SD16—731no—
335C4×D8—731no—
336C4×D8—731no—
337#436—731no—
338#436—1461no—
339#436C2×D7311yescharacteristic
340#436C2×D7311yescharacteristic
341#435—21no—
342#435—21no—
343#435—1461no—
344C8×D4—731no—
345C8×D4C2×D7311yescharacteristic
346C8×D4C2×D7311yescharacteristic
347#433—1461no—
348#431—731no—
349C2×C4⋊C8C2×D7311yescharacteristic
350#408—21no—
351#405—1461no—
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—21no—
372C2×SD16—731no—
373C2×SD16—731no—
374C2×D8—731no—
375C2×D8—731no—
376#131—44no—
377C2×M16—21no—
378C2×M16—21no—
379C2×M16—731no—
380C2×M16—731no—
381C2×M16—1461no—
382C2×M16—1461no—
383C2×M16C22⋊D7311yescharacteristic
384C2×M16C22⋊D7311yescharacteristic
385C22×C8—21no—
386C22×C8—21no—
387C22×C8—21no—
388C22×C8—1461no—
389C4⋊Q8C4×D7311yescharacteristic
390#127C4×D7311yescharacteristic
391#126—1461no—
392#125—731no—
393#124—21no—
394#124—731no—
395#123—1461no—
396C22⋊Q8—731no—
397#121—21no—
398#121—731no—
399#121C4×D7311yescharacteristic
400#121C4×D7311yescharacteristic
401C4×Q8—731no—
402C4×D4—21no—
403C4×D4—731no—
404C4×D4—1461no—
405C4×D4C22×D7311yescharacteristic
406C4×D4C22×D7311yescharacteristic
407#117—1461no—
408C2×C42C22×D7311yescharacteristic
409#107—731no—
410#107—731no—
411#106—731no—
412#106—731no—
413C4⋊C8—21no—
414C4⋊C8—731no—
415C4⋊C8—731no—
416C4⋊C8—1461no—
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—21no—
432C22⋊C8—1461no—
433C22⋊C8—1461no—
434C22⋊C8—1461no—
435#97—731no—
436#97—731no—
437#97—1461no—
438#97—1461no—
439#97C22⋊D7311yescharacteristic
440#97C22⋊D7311yescharacteristic
441C4×C8—731no—
442C4×C8—731no—
443C4×C8—731no—
444C4×C8—731no—
445C4×C8—1461no—
446C4×C8—1461no—
447C4×C8C22×D7311yescharacteristic
448C4×C8C22×D7311yescharacteristic
449#41—42no—
450#41—42no—
451C2×Q8—21no—
452C2×Q8—731no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—731no—
458C2×D4—1461no—
459C2×D4C2×C4×D7311yescharacteristic
460C2×D4C2×C4×D7311yescharacteristic
461C22×C4—21no—
462C22×C4—21no—
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—42no—
475M16—2922no—
476M16—2922no—
477M16—2921no—
478M16—1462no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—42no—
482C2×C8—42no—
483C2×C8—42no—
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—731no—
499C4⋊C4—731no—
500C4⋊C4—1461no—
501C4⋊C4—1461no—
502C4⋊C4—1461no—
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—1461no—
511C22⋊C4—1461no—
512C22⋊C4—1461no—
513C22⋊C4—1461no—
514C22⋊C4—1461no—
515C42—1461no—
516C42C2×C4×D7311yescharacteristic
517C42C2×C22⋊D7311yescharacteristic
518C42#1192402811yescharacteristic
519C42C23×D7311yescharacteristic
520C23—21no—
521C23—21no—
522C23—1461no—
523C23C4×C22⋊D7311yescharacteristic
524Q8—42no—
525Q8—1461no—
526Q8—1461no—
527D4—21no—
528D4—21no—
529D4—21no—
530D4—21no—
531D4—42no—
532D4—42no—
533D4—42no—
534D4—81no—
535D4—5841no—
536D4—1461no—
537D4—1461no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—2921no—
550C2×C4—2921no—
551C2×C4—1461no—
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#1455661712yes—
574C22—21no—
575C22—21no—
576C22—21no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—2921no—
584C22—2921no—
585C22—2921no—
586C22C2×C4×C22⋊D7311yescharacteristic
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—41no—
592C4—41no—
593C4—2921no—
594C4—2921no—
595C4—2921no—
596C4#131×D7311yescharacteristic
597C4#1798935211yescharacteristic
598C4C2×#1455661711yescharacteristic
599C4#1798938511yescharacteristic
600C2—41no—
601C2—81no—
602C2—81no—
603C2—5841no—
604C2#2261867311yescharacteristic
605C2C4×#1455661711yescharacteristic
606C2#2261883811yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#2935C2
socleC22×C73C2×C4×D4
prime radical#22620520C2
cosocleC42×C73C24
hypercenter#2935D73
hypocenterC73#18076
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ #2935

Complements

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

NH ≅ G/Ntype
2. #22618935C2semidirect
3. #22608843C2semidirect
4. #22608819C2semidirect
5. #22608807C2semidirect
6. #22608795C2semidirect
7. #22608767C2semidirect
8. #22608758C2semidirect
9. #22608743C2semidirect
10. C8×#11924013C2semidirect
11. #22608681C2semidirect
12. #22608348C2semidirect
13. #22608342C2semidirect
14. #22608234C2semidirect
15. C73×#2935C2semidirect
269. #10596831#131semidirect
306. #2935D73semidirect
319. C73#18076semidirect

Maximal subgroups

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

subgroupindex
#226205202
#226189352
#226088432
#226088192
#226088072
#226087952
#226087672
#226087582
#226087432
C8×#119240132
#226086812
#226083482
#226083422
#226082342
C73×#29352
#1807673