Finite Group Databasebeta

← #11887163

Subgroups — #11887163

Order 1152.

1138 conjugacy classes of subgroups.

The subgroup lattice has 623 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596188C211yesmaximal, characteristic
2#10593958C211yesmaximal, characteristic, complemented
3C3×#5075C211yesmaximal, characteristic, complemented
4C3×#5070C211yesmaximal, characteristic, complemented
5#10591467C212yesmaximal, complemented
6#10591465C212yesmaximal, complemented
7#10591419C212yesmaximal, complemented
8#10591416C212yesmaximal, complemented
9C4×#3717C211yesmaximal, characteristic, complemented
10#10590327C211yesmaximal, characteristic, complemented
11#10590300C211yesmaximal, characteristic, complemented
12#81577—31nomaximal
13#80395—31nomaximal
14C2×D4×C3⋊D3—21no—
15C2×D4×C3⋊D3C2212yes—
16C32×#127C2211yescharacteristic
17#64147—21no—
18#64147C2212yes—
19#64146—22no—
20C4×C4⋊(C3⋊D3)C2211yescharacteristic
21C4×C4⋊(C3⋊D3)C2211yescharacteristic
22C2×C3×#214C2212yescomplemented
23C3×#869C2211yescharacteristic, complemented
24C3×C4×Dic6C2211yescharacteristic, complemented
25#63900C2212yescomplemented
26#63894—21no—
27#63888—22no—
28#63871C2212yescomplemented
29#63869—21no—
30C2×#3717C2211yescharacteristic
31C2×#3710C2212yescomplemented
32C3×#832C2212yescomplemented
33C3×#832C2212yescomplemented
34C3×#832C2212yescomplemented
35C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
36C3×C4×C3⋊C8C2211yescharacteristic, complemented
37#63573C2212yescomplemented
38#63573C2211yescharacteristic, complemented
39#63566C2211yescharacteristic, complemented
40#63564C2212yes—
41#63564C2211yescharacteristic
42#63557C2212yescomplemented
43#5730—31no—
44#5717—31no—
45#5717—31no—
46#5717—61no—
47#5579—31no—
48C3×#486—31no—
49C3×#460—31no—
50#5171—32no—
51#5169—32no—
52#5084—31no—
53#5075D311yescharacteristic, complemented
54#5070D311yescharacteristic, complemented
55C4×#215—31no—
56#4842—31no—
57#4834—31no—
58#4778—32no—
59#4777—32no—
60#4777—32no—
61#4776—32no—
62D3×#102—32no—
63D3×#102—32no—
64C4×#204—31no—
65C8×D12—31no—
66C23×C3⋊D3—22no—
67C2×C32×D4—21no—
68C2×C32×D4—21no—
69C2×C32×D4C2312yes—
70C2×#638—22no—
71C2×#638—22no—
72D4×C3⋊D3—24no—
73D4×C3⋊D3—42no—
74D4×C3⋊D3—44no—
75C2×C4⋊(C3⋊D3)D411yescharacteristic
76C2×C4⋊(C3⋊D3)C2311yescharacteristic
77C2×C4×C3⋊D3—21no—
78C2×C4×C3⋊D3C2312yes—
79C2×C3×Dic6—21no—
80C2×C3×Dic6C2311yescharacteristic
81C2×#624—22no—
82C32×C42C2311yescharacteristic
83#3757—22no—
84#3752—21no—
85#3752D412yes—
86C4⋊(C3⋊Dic3)D411yescharacteristic
87C4⋊(C3⋊Dic3)C2311yescharacteristic
88C3×#214—42no—
89C3×C4⋊Dic3—21no—
90C3×C4⋊Dic3C2312yes—
91C3×C4⋊Dic3C2311yescharacteristic
92C3×Dic3⋊C4—21no—
93C3×C4×Dic3—21no—
94C2×C3×C3⋊C8C2312yes—
95C2×C3×C3⋊C8C2311yescharacteristic
96C2×C3×C3⋊C8C2311yescharacteristic
97#3724—22no—
98Dic3⋊Dic3—22no—
99#3722—22no—
100#3717—22no—
101#3710—42no—
102#3295—91noSylow
103C2×D3×D4—32no—
104C2×D3×D4—32no—
105C2×D3×D4—62no—
106C2×D3×D4—61no—
107C2×D3×D4—61no—
108C2×D3×D4—62no—
109C2×C3×SD16—32no—
110C3×C4⋊Q8—31no—
111C3×#127—21no—
112C3×#127C2×D311yescharacteristic
113C3×#127C2×D311yescharacteristic
114C3×C4×Q8—31no—
115#946—32no—
116#946—62no—
117C2×#215—31no—
118#938—32no—
119#938—32no—
120#938—62no—
121#938—61no—
122#938—61no—
123#938—62no—
124#937—62no—
125#937—62no—
126#937—64no—
127C2×#214C2×D312yescomplemented
128C2×#204—31no—
129C2×D3×C8—32no—
130C2×D3×C8—32no—
131#897—32no—
132#896—62no—
133#893—61no—
134D3×C4⋊C4—32no—
135D3×C4⋊C4—32no—
136#890—61no—
137C4×D12—31no—
138C4×D12—31no—
139C4×D12—31no—
140C4×D12—31no—
141C4×D12—61no—
142C4×D12—61no—
143C4×D12—61no—
144#870—61no—
145#869C2×D311yescharacteristic, complemented
146C4×Dic6C2×D311yescharacteristic, complemented
147C3×C4⋊C8—31no—
148C3×#102—32no—
149C3×#102—32no—
150C3×#102—32no—
151C3×C4×C8—31no—
152#835—31no—
153#832C2×D312yescomplemented
154#832C2×D312yescomplemented
155#832C2×D312yescomplemented
156#821—32no—
157#821—31no—
158(C2×D3)⋊C8—32no—
159(C2×D3)⋊C8—32no—
160#817—32no—
161#817—31no—
162#816—31no—
163#809—31no—
164#809—32no—
165#808—31no—
166#808—32no—
167C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
168C4×C3⋊C8C2×D311yescharacteristic, complemented
169C23×C32—22no—
170C22×C3⋊D3—21no—
171C22×C3⋊D3—44no—
172C22×C3⋊D3—44no—
173C22×C3⋊D3—82no—
174C22×C3⋊D3C2×D412yes—
175C32×D4—22no—
176C32×D4—22no—
177C32×D4—42no—
178C32×D4—81no—
179C2×C32×C4C2×D411yescharacteristic
180C2×C32×C4C2×D411yescharacteristic
181C2×C32×C4C2411yescharacteristic
182#638—44no—
183#638—44no—
184C2×C3⋊Dic3—21no—
185C2×C3⋊Dic3C2×D412yes—
186C4⋊(C3⋊D3)—21no—
187C4⋊(C3⋊D3)SD1614yescomplemented
188C4⋊(C3⋊D3)#4112yes—
189C4×C3⋊D3—22no—
190C4×C3⋊D3—22no—
191C4×C3⋊D3—42no—
192C2×C3×Dic3—21no—
193C2×C3×Dic3—22no—
194C2×C3×Dic3—21no—
195C3×Dic6—21no—
196C3×Dic6—21no—
197C3×Dic6—81no—
198#624—82no—
199C3×C3⋊C8—21no—
200C3×C3⋊C8—21no—
201C3×C3⋊C8—22no—
202#554—91no—
203D42—91no—
204#486—31no—
205#481—92no—
206#476—91no—
207#465—92no—
208#460—31no—
209#450—92no—
210C4×SD16—91no—
211C8×D4—91no—
212C2×#102—92no—
213C23×D3—62no—
214C23×D3—62no—
215C23×D3—64no—
216C2×C3×Q8—31no—
217C2×C3×Q8—61no—
218C2×C3×D4—22no—
219C2×C3×D4—22no—
220C2×C3×D4—21no—
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—22no—
225C2×C3×D4C22×D312yes—
226C2×C3×D4C22×D312yes—
227C2×#67—62no—
228C2×#67—62no—
229C2×#67—62no—
230C2×#67—62no—
231C2×#67—64no—
232C2×#67—64no—
233D3×D4—64no—
234D3×D4—64no—
235D3×D4—124no—
236D3×D4—122no—
237D3×D4—122no—
238D3×D4—124no—
239D3×D4—124no—
240D3×D4—124no—
241D3×D4—128no—
242C2×D12—31no—
243C2×D12—31no—
244C2×D12—31no—
245C2×D12—31no—
246C2×D12—61no—
247C2×D12—61no—
248C2×C4×D3—32no—
249C2×C4×D3—32no—
250C2×C4×D3—62no—
251C2×C4×D3—62no—
252C2×C4×D3—61no—
253C2×C4×D3—61no—
254C2×C4×D3—62no—
255C2×C4×D3—62no—
256C2×Dic6—21no—
257C2×Dic6C22×D311yescharacteristic
258C3×SD16—122no—
259C2×C3×C8—31no—
260C2×C3×C8—31no—
261C2×C3×C8—32no—
262C3×C4⋊C4—31no—
263C3×C4⋊C4—32no—
264C3×C4⋊C4—61no—
265C3×C4⋊C4—61no—
266C3×C42—21no—
267C3×C42—61no—
268C3×C42C22×D311yescharacteristic
269C3×C42C22×D311yescharacteristic
270#217—62no—
271#217—62no—
272#217—64no—
273#215—62no—
274#214—42no—
275(C2×D3)⋊C4—32no—
276(C2×D3)⋊C4—32no—
277(C2×D3)⋊C4—62no—
278(C2×D3)⋊C4—62no—
279(C2×D3)⋊C4—62no—
280(C2×D3)⋊C4—62no—
281(C2×D3)⋊C4—61no—
282(C2×D3)⋊C4—61no—
283C4⋊Dic3—21no—
284C4⋊Dic3—31no—
285C4⋊Dic3—31no—
286C4⋊Dic3—31no—
287C4⋊Dic3—31no—
288C4⋊Dic3—61no—
289C4⋊Dic3—61no—
290C4⋊Dic3—62no—
291C4⋊Dic3C22×D311yescharacteristic
292C4⋊Dic3C22×D312yes—
293Dic3⋊C4—21no—
294Dic3⋊C4—62no—
295Dic3⋊C4—62no—
296Dic3⋊C4—62no—
297C4×Dic3—21no—
298C2×C3⋊C8C22×D311yescharacteristic
299C2×C3⋊C8C22×D311yescharacteristic
300C2×C3⋊C8C22×D312yes—
301#204—62no—
302D3×C8—122no—
303D3×C8—122no—
304C22×C32—42no—
305C22×C32—42no—
306C22×C32—42no—
307C22×C32C22×D411yescharacteristic
308C2×C3⋊D3—22no—
309C2×C3⋊D3—22no—
310C2×C3⋊D3—22no—
311C2×C3⋊D3—41no—
312C2×C3⋊D3—41no—
313C2×C3⋊D3—88no—
314C2×C3⋊D3C2×SD1614yes—
315C32×C4—21no—
316C32×C4C2×SD1612yes—
317C32×C4C2×#4111yescharacteristic
318C32×C4H(5,𝔽2)11yescharacteristic
319C3⋊Dic3—22no—
320C3⋊Dic3—41no—
321C3×Dic3—41no—
322C3×Dic3—41no—
323C3×Dic3—42no—
324C22×D4—92no—
325C22×D4—181no—
326C2×SD16—32no—
327C2×SD16—91no—
328C22×C8—92no—
329C4⋊Q8—31no—
330#127D3211yescharacteristic
331#125—181no—
332C22⋊Q8—92no—
333C22⋊Q8—182no—
334#121—92no—
335#121—181no—
336#120—182no—
337C4×Q8—31no—
338C4×D4—91no—
339C4×D4—91no—
340C4×D4—181no—
341C2×C4⋊C4—92no—
342#106—91no—
343#106—92no—
344C4⋊C8—31no—
345#103—91no—
346#102—32no—
347#102—32no—
348#102—32no—
349#102—91no—
350#102—92no—
351C22⋊C8—92no—
352C4×C8—31no—
353C23×C3—24no—
354C23×C3—22no—
355C23×C3—22no—
356C22×D3—32no—
357C22×D3—32no—
358C22×D3—62no—
359C22×D3—62no—
360C22×D3—61no—
361C22×D3—61no—
362C22×D3—124no—
363C22×D3—124no—
364C22×D3—124no—
365C22×D3—124no—
366C22×D3—128no—
367C22×D3—128no—
368C22×D3—242no—
369C22×D3—242no—
370C22×D3—244no—
371C3×Q8—61no—
372C3×Q8—61no—
373C3×Q8—241no—
374C3×D4—22no—
375C3×D4—22no—
376C3×D4—22no—
377C3×D4—22no—
378C3×D4—42no—
379C3×D4—42no—
380C3×D4—44no—
381C3×D4—42no—
382C3×D4—42no—
383C3×D4—81no—
384C3×D4—81no—
385C3×D4—82no—
386C2×C3×C4—21no—
387C2×C3×C4—21no—
388C2×C3×C4—21no—
389C2×C3×C4—61no—
390C2×C3×C4—61no—
391C2×C3×C4—62no—
392C2×C3×C4D3×D411yescharacteristic
393C2×C3×C4D3×D411yescharacteristic
394C2×C3×C4D3×D411yescharacteristic
395C2×C3×C4D3×D411yescharacteristic
396C2×C3×C4C23×D311yescharacteristic
397C2×C3×C4C23×D311yescharacteristic
398#67—124no—
399#67—124no—
400#67—124no—
401#67—124no—
402#67—128no—
403#67—128no—
404C2×Dic3—21no—
405C2×Dic3—21no—
406C2×Dic3—22no—
407C2×Dic3—32no—
408C2×Dic3—32no—
409C2×Dic3—62no—
410C2×Dic3—62no—
411C2×Dic3—61no—
412C2×Dic3—61no—
413D12—34no—
414D12—34no—
415D12—32no—
416D12—32no—
417D12—64no—
418D12—62no—
419D12—62no—
420D12—61no—
421D12—61no—
422C4×D3—62no—
423C4×D3—62no—
424C4×D3—62no—
425C4×D3—62no—
426C4×D3—122no—
427C4×D3—122no—
428C4×D3—124no—
429C4×D3—122no—
430C4×D3—122no—
431C4×D3—242no—
432C4×D3—242no—
433Dic6—21no—
434Dic6—21no—
435Dic6—81no—
436C3×C8—61no—
437C3×C8—61no—
438C3×C8—62no—
439C3⋊C8—22no—
440C3⋊C8—21no—
441C3⋊C8—21no—
442C2×C32—82no—
443C2×C32#54611yescharacteristic
444C2×C32C22×SD1611yescharacteristic
445C2×C32#57611yescharacteristic
446C3⋊D3—24no—
447C3⋊D3—42no—
448C24—182no—
449C2×Q8—31no—
450C2×Q8—61no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—91no—
454C2×D4—91no—
455C2×D4—182no—
456C2×D4—184no—
457C2×D4—182no—
458C2×D4—362no—
459C2×D4—364no—
460C2×D4C2×D3212yes—
461C22×C4—92no—
462C22×C4—182no—
463C22×C4—181no—
464SD16—122no—
465SD16—182no—
466C2×C8—31no—
467C2×C8—31no—
468C2×C8—32no—
469C2×C8—362no—
470C4⋊C4—31no—
471C4⋊C4—32no—
472C4⋊C4—61no—
473C4⋊C4—61no—
474C4⋊C4—91no—
475C4⋊C4—91no—
476C4⋊C4—182no—
477C4⋊C4—182no—
478C22⋊C4—92no—
479C22⋊C4—182no—
480C22⋊C4—182no—
481C22⋊C4—181no—
482C42—61no—
483C42C2×D3211yescharacteristic
484C22×C3—21no—
485C22×C3—44no—
486C22×C3—44no—
487C22×C3—44no—
488C22×C3—42no—
489C22×C3—42no—
490C22×C3—42no—
491C22×C3—42no—
492C22×C3—42no—
493C22×C3—42no—
494C22×C3C2×D3×D411yescharacteristic
495C22×C3C2×D3×D411yescharacteristic
496C2×D3—34no—
497C2×D3—34no—
498C2×D3—64no—
499C2×D3—62no—
500C2×D3—62no—
501C2×D3—62no—
502C2×D3—62no—
503C2×D3—64no—
504C2×D3—62no—
505C2×D3—62no—
506C2×D3—122no—
507C2×D3—122no—
508C2×D3—122no—
509C2×D3—122no—
510C2×D3—121no—
511C2×D3—121no—
512C2×D3—121no—
513C2×D3—121no—
514C2×D3—248no—
515C2×D3—248no—
516C2×D3—2416no—
517C3×C4—21no—
518C3×C4—21no—
519C3×C4—21no—
520C3×C4—21no—
521C3×C4—22no—
522C3×C4—41no—
523C3×C4—121no—
524C3×C4—121no—
525C3×C4—122no—
526C3×C4D3×SD1612yes—
527C3×C4D3×SD1612yes—
528C3×C4#100411yescharacteristic
529C3×C4D3×#4111yescharacteristic
530C3×C4D3×#4111yescharacteristic
531C3×C4#100911yescharacteristic
532Dic3—42no—
533Dic3—41no—
534Dic3—41no—
535Dic3—62no—
536Dic3—62no—
537Dic3—122no—
538Dic3—122no—
539Dic3—121no—
540Dic3—121no—
541C32#329511yescharacteristic, complemented, Sylow
542C23—22no—
543C23—92no—
544C23—181no—
545C23—364no—
546C23—364no—
547C23—722no—
548Q8—61no—
549Q8—61no—
550Q8—241no—
551D4—22no—
552D4—22no—
553D4—42no—
554D4—81no—
555D4—92no—
556D4—94no—
557D4—181no—
558D4—364no—
559D4—364no—
560C2×C4—61no—
561C2×C4—61no—
562C2×C4—62no—
563C2×C4—92no—
564C2×C4—182no—
565C2×C4—182no—
566C2×C4—181no—
567C2×C4—362no—
568C2×C4—722no—
569C2×C4#381111yescharacteristic
570C2×C4#381111yescharacteristic
571C2×C4C22×D3211yescharacteristic
572C8—61no—
573C8—61no—
574C8—62no—
575C2×C3—21no—
576C2×C3—21no—
577C2×C3—21no—
578C2×C3—84no—
579C2×C3—82no—
580C2×C3—82no—
581C2×C3#561211yescharacteristic
582C2×C3#567611yescharacteristic
583C2×C3#575711yescharacteristic
584C2×C3C2×D3×SD1611yescharacteristic
585C2×C3C2×D3×SD1611yescharacteristic
586C2×C3#577411yescharacteristic
587D3—64no—
588D3—64no—
589D3—124no—
590D3—124no—
591D3—122no—
592D3—122no—
593C22—42no—
594C22—42no—
595C22—42no—
596C22—94no—
597C22—182no—
598C22—182no—
599C22—182no—
600C22—361no—
601C22—361no—
602C22—728no—
603C22C2×#381111yescharacteristic
604C4—21no—
605C4—121no—
606C4—122no—
607C4—121no—
608C4—182no—
609C4—361no—
610C4#6393012yes—
611C4#6431211yescharacteristic
612C4#6431411yescharacteristic
613C3—21no—
614C3#8039511yescharacteristic, complemented
615C3#8157711yescharacteristic, complemented
616C2—82no—
617C2—184no—
618C2—362no—
619C2#1059510211yescharacteristic
620C2C2×#6393011yescharacteristic
621C2#1059524311yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#127C22
socleC22×C32C22×D4
prime radical#10596188C2
hypercenter#127D32
hypocenterC32#3295
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
2. #10593958C2semidirect
3. C3×#5075C2semidirect
4. C3×#5070C2semidirect
5. #10591467C2semidirect
6. #10591465C2semidirect
7. #10591419C2semidirect
8. #10591416C2semidirect
9. C4×#3717C2semidirect
10. #10590327C2semidirect
11. #10590300C2semidirect
22. C2×C3×#214C22semidirect
23. C3×#869C22semidirect
24. C3×C4×Dic6C22semidirect
25. #63900C22semidirect
28. #63871C22semidirect
31. C2×#3710C22semidirect
32. C3×#832C22semidirect
33. C3×#832C22semidirect
34. C3×#832C22semidirect
35. C3×C4⋊(C3⋊C8)C22semidirect
36. C3×C4×C3⋊C8C22semidirect
37. #63573C22semidirect
38. #63573C22semidirect
39. #63566C22semidirect
42. #63557C22semidirect
53. #5075D3semidirect
54. #5070D3semidirect
127. C2×#214C2×D3semidirect
145. #869C2×D3semidirect
146. C4×Dic6C2×D3semidirect
153. #832C2×D3semidirect
154. #832C2×D3semidirect
155. #832C2×D3semidirect
167. C4⋊(C3⋊C8)C2×D3semidirect
168. C4×C3⋊C8C2×D3semidirect
187. C4⋊(C3⋊D3)SD16semidirect
541. C32#3295semidirect
614. C3#80395semidirect
615. C3#81577semidirect

Maximal subgroups

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

subgroupindex
#105961882
#105939582
C3×#50752
C3×#50702
#105914672
#105914652
#105914192
#105914162
C4×#37172
#105903272
#105903002
#815773
#803953