Finite Group Databasebeta

← #11868805

Subgroups — #11868805

Order 1152.

886 conjugacy classes of subgroups.

The subgroup lattice has 593 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#3799C211yesmaximal, characteristic
2D3×#869C211yesmaximal, characteristic, complemented
3#10592545C211yesmaximal, characteristic, complemented
4C3×#4851C211yesmaximal, characteristic, complemented
5C3×#4837C211yesmaximal, characteristic, complemented
6#10590804C212yesmaximal, complemented
7#10590759C212yesmaximal, complemented
8#10590681C212yesmaximal, complemented
9#10590671C212yesmaximal
10#10590313C211yesmaximal, characteristic, complemented
11#10590301C211yesmaximal, characteristic, complemented
12#81012—31nomaximal
13#79060—31nomaximal
14C2×#3799C2211yescharacteristic
15C2×D3×Dic6—21no—
16C4×C4⋊(C3⋊D3)C2211yescharacteristic
17#64078C2211yescharacteristic
18C2×C3×ΓL(1,𝔽25)C2212yes—
19C3×C42×D3C2211yescharacteristic
20C3×#869C2211yescharacteristic
21C3×C4×Dic6C2211yescharacteristic
22#63918—21no—
23#63918C2212yes—
24#63904—21no—
25C4×#626—21no—
26#63894C2211yescharacteristic
27D3×C4⋊Dic3—21no—
28D3×C4⋊Dic3C2212yes—
29C4×#624—21no—
30#63866—21no—
31Dic3×Dic6C2211yescharacteristic
32#63841C2211yescharacteristic
33#63836—21no—
34C32×C4⋊C8C2211yescharacteristic
35#63648C2212yes—
36#63645C2212yes—
37C3×#817C2212yes—
38C3×#816C2212yes—
39C3×Dic3⋊C8C2212yes—
40C3×C4⋊(C3⋊C8)C2211yescharacteristic
41#63575C2212yes—
42#63573C2212yes—
43#63566C2212yes—
44#63564C2212yes—
45D3×C4⋊Q8—31no—
46C4×#239—31no—
47C4×#235—31no—
48C2×#869—31no—
49C3×#475—31no—
50C3×#423—31no—
51#5133—32no—
52#5121—32no—
53#5087—31no—
54#5020—31no—
55#4870—32no—
56#4861—32no—
57#4851—31no—
58#4851D311yescharacteristic, complemented
59#4850—32no—
60#4846—31no—
61#4846—31no—
62#4846—31no—
63#4846—61no—
64#4842—32no—
65#4837D311yescharacteristic, complemented
66#4803—32no—
67#4793—32no—
68C2×C4⋊(C3⋊D3)C2311yescharacteristic
69C2×C4×C3⋊D3—21no—
70C2×#634—21no—
71C2×C3×C4×D3D411yescharacteristic
72C2×C3×C4×D3D411yescharacteristic
73C2×C3×C4×D3C2311yescharacteristic
74C2×C3×Dic6—21no—
75C2×C3×Dic6C2311yescharacteristic
76C2×#627—22no—
77C2×#626—21no—
78C2×#624—21no—
79C2×#624—21no—
80C2×D3×Dic3—22no—
81#3799—22no—
82#3799Q814yescomplemented
83D3×Dic6—44no—
84C2×C32×C8C2312yes—
85C32×C42C2311yescharacteristic
86#3752—21no—
87C4⋊(C3⋊Dic3)—21no—
88C4⋊(C3⋊Dic3)C2312yes—
89C4⋊(C3⋊Dic3)C2311yescharacteristic
90C3×C4⋊Dic3—21no—
91C3×C4⋊Dic3C2312yes—
92C3×C4⋊Dic3C2311yescharacteristic
93C3×Dic3⋊C4—21no—
94C3×C4×Dic3—21no—
95C3×C4×Dic3D411yescharacteristic
96C3×C4×Dic3D411yescharacteristic
97C3×C4×Dic3C2311yescharacteristic
98C2×C3×C3⋊C8C2312yes—
99C3×ΓL(1,𝔽25)—24no—
100Dic3⋊Dic3—21no—
101Dic3⋊Dic3—22no—
102Dic3⋊Dic3—22no—
103#3722—21no—
104(C2×D3)⋊Dic3—21no—
105Dic32—21no—
106Dic32—21no—
107#3079—91noSylow
108C2×#239—31no—
109C2×D3×Q8—61no—
110C2×#235—31no—
111C22×Dic6—61no—
112C2×C3×M16—32no—
113C3×C4⋊Q8—31no—
114C3×C4×Q8—31no—
115C2×C3×C42—31no—
116Q8×Dic3—31no—
117#944—61no—
118C4×#67—61no—
119C4×#67—61no—
120#926—31no—
121C2×C4⋊Dic3—32no—
122C2×C4⋊Dic3—61no—
123C2×ΓL(1,𝔽25)C2×D312yes—
124#893—31no—
125#893—61no—
126#892—31no—
127#892—61no—
128D3×C4⋊C4—32no—
129D3×C4⋊C4—61no—
130#888—32no—
131#888—61no—
132C4×D12—31no—
133C4×D12—31no—
134C4×D12—31no—
135C4×D12—61no—
136C4×D12—61no—
137#872—61no—
138C42×D3—61no—
139C42×D3—61no—
140C42×D3C2×D311yescharacteristic
141#869—31no—
142#869—31no—
143#869—32no—
144#869—61no—
145#869—61no—
146#869—61no—
147#869C2×D311yescharacteristic
148C4×Dic6—31no—
149C4×Dic6C2×D311yescharacteristic
150C3×#106—32no—
151C3×C4⋊C8—21no—
152C3×C4⋊C8—32no—
153C3×C4⋊C8—31no—
154C3×C4⋊C8C2×D311yescharacteristic
155C3×C4⋊C8C2×D311yescharacteristic
156C3×#103—32no—
157#835—32no—
158#821—32no—
159#821—32no—
160#821—32no—
161#821—62no—
162#818—32no—
163#818—32no—
164#818—32no—
165#818—62no—
166#817—32no—
167#817C2×D312yes—
168#816—32no—
169#816C2×D312yes—
170Dic3⋊C8C2×D312yes—
171#809—32no—
172#808—32no—
173#807—32no—
174C4⋊(C3⋊C8)C2×D311yescharacteristic
175C22×C3⋊D3—21no—
176C22×C3×D3C2×D411yescharacteristic
177C2×C32×C4C2×D411yescharacteristic
178C2×C32×C4C2×D411yescharacteristic
179C2×C32×C4C2411yescharacteristic
180C2×C3⋊Dic3—21no—
181C2×C3⋊Dic3—22no—
182C4⋊(C3⋊D3)—21no—
183C4⋊(C3⋊D3)C2×Q812yescomplemented
184C4×C3⋊D3—42no—
185#634—42no—
186C2×C3×Dic3—21no—
187C2×C3×Dic3—21no—
188C2×C3×Dic3—22no—
189C2×C3×Dic3C2×D411yescharacteristic
190C2×C3×Dic3C2×D411yescharacteristic
191C2×C3×Dic3C2×D411yescharacteristic
192C3×C4×D3—22no—
193C3×C4×D3—22no—
194C3×C4×D3C2×Q812yes—
195C3×C4×D3#4112yes—
196C3×Dic6—21no—
197C3×Dic6—42no—
198C3×Dic6C2×Q812yescomplemented
199#627—44no—
200#626—24no—
201#624—24no—
202#624—42no—
203D3×Dic3—44no—
204C32×C8—22no—
205C3×C3⋊C8—22no—
206C2×C4⋊Q8—91no—
207C4×#41—91no—
208#477—92no—
209#476—92no—
210#475—31no—
211#475—91no—
212#474—91no—
213#474—91no—
214#428—92no—
215#423—31no—
216#417—92no—
217C2×C3×Q8—31no—
218C2×C3×Q8—61no—
219C22×C3×C4—31no—
220C22×C3×C4—31no—
221C22×C3×C4—31no—
222C2×#67—61no—
223C22×Dic3—62no—
224#239—34no—
225#239—62no—
226D3×Q8—124no—
227#235—34no—
228#235—62no—
229C2×D12—31no—
230C2×D12—31no—
231C2×D12—61no—
232C2×D12—61no—
233C2×C4×D3—61no—
234C2×C4×D3—61no—
235C2×C4×D3—61no—
236C2×C4×D3—62no—
237C2×C4×D3—61no—
238C2×C4×D3—61no—
239C2×C4×D3—61no—
240C2×C4×D3—121no—
241C2×C4×D3D1211yescharacteristic
242C2×C4×D3D1211yescharacteristic
243C2×C4×D3C22×D311yescharacteristic
244C2×Dic6—21no—
245C2×Dic6—62no—
246C2×Dic6—61no—
247C2×Dic6—61no—
248C2×Dic6—62no—
249C2×Dic6—121no—
250C2×Dic6—124no—
251C2×Dic6C22×D311yescharacteristic
252C3×M16—64no—
253C2×C3×C8—22no—
254C2×C3×C8—32no—
255C2×C3×C8C22×D312yes—
256C2×C3×C8C22×D312yes—
257C3×C4⋊C4—32no—
258C3×C4⋊C4—31no—
259C3×C4⋊C4—61no—
260C3×C4⋊C4—61no—
261C3×C42—21no—
262C3×C42—31no—
263C3×C42—31no—
264C3×C42—31no—
265C3×C42—61no—
266C3×C42C22×D311yescharacteristic
267C3×C42C22×D311yescharacteristic
268#217—61no—
269(C2×D3)⋊C4—61no—
270(C2×D3)⋊C4—61no—
271(C2×D3)⋊C4—61no—
272(C2×D3)⋊C4—61no—
273(C2×D3)⋊C4—61no—
274(C2×D3)⋊C4—121no—
275C4⋊Dic3—21no—
276C4⋊Dic3—31no—
277C4⋊Dic3—32no—
278C4⋊Dic3—32no—
279C4⋊Dic3—31no—
280C4⋊Dic3—61no—
281C4⋊Dic3—62no—
282C4⋊Dic3—62no—
283C4⋊Dic3—62no—
284C4⋊Dic3—61no—
285C4⋊Dic3—61no—
286C4⋊Dic3—61no—
287C4⋊Dic3—121no—
288C4⋊Dic3C22×D312yes—
289C4⋊Dic3C22×D311yescharacteristic
290Dic3⋊C4—21no—
291Dic3⋊C4—61no—
292Dic3⋊C4—62no—
293Dic3⋊C4—62no—
294C4×Dic3—21no—
295C4×Dic3—61no—
296C4×Dic3—61no—
297C4×Dic3—61no—
298C4×Dic3—61no—
299C4×Dic3D1211yescharacteristic
300C4×Dic3D1211yescharacteristic
301C4×Dic3C22×D311yescharacteristic
302C2×C3⋊C8C22×D312yes—
303ΓL(1,𝔽25)—24no—
304C22×C32C22×D411yescharacteristic
305C2×C3⋊D3—22no—
306C2×C3⋊D3—41no—
307C2×C3⋊D3—41no—
308C2×C3×D3—21no—
309C2×C3×D3—21no—
310C2×C3×D3C22⋊Q812yes—
311C32×C4—21no—
312C32×C4AGL(1,ℤ/8)12yes—
313C32×C4C22×Q811yescharacteristic
314C32×C4C2×#4111yescharacteristic
315C3⋊Dic3—42no—
316C3⋊Dic3—41no—
317C3×Dic3—22no—
318C3×Dic3—21no—
319C3×Dic3—42no—
320C3×Dic3—41no—
321C3×Dic3C22⋊Q812yes—
322C3×Dic3#13712yes—
323C2×#41—91no—
324C22×Q8—181no—
325C2×M16—32no—
326C4⋊Q8—31no—
327C4⋊Q8—92no—
328C4⋊Q8—91no—
329C4⋊Q8—181no—
330C4⋊Q8—181no—
331C4×Q8—31no—
332C4×Q8—91no—
333C4×D4—91no—
334C4×D4—91no—
335C4×D4—181no—
336C4×D4—181no—
337#117—91no—
338#117—181no—
339C2×C4⋊C4—92no—
340C2×C4⋊C4—181no—
341C2×C42—31no—
342C2×C42—181no—
343#107—92no—
344#107—92no—
345#106—32no—
346#106—92no—
347C4⋊C8—32no—
348C4⋊C8—31no—
349C4⋊C8D3211yescharacteristic
350#103—32no—
351#103—92no—
352#102—92no—
353#102—92no—
354C23×C3—31no—
355C22×D3—61no—
356C22×D3—61no—
357C22×D3—121no—
358C22×D3C2×D1211yescharacteristic
359C3×Q8—32no—
360C3×Q8—61no—
361C3×Q8—122no—
362C2×C3×C4—21no—
363C2×C3×C4—21no—
364C2×C3×C4—21no—
365C2×C3×C4—31no—
366C2×C3×C4—31no—
367C2×C3×C4—32no—
368C2×C3×C4—32no—
369C2×C3×C4—31no—
370C2×C3×C4—62no—
371C2×C3×C4—61no—
372C2×C3×C4—62no—
373C2×C3×C4—61no—
374C2×C3×C4—62no—
375C2×C3×C4C2×D1211yescharacteristic
376C2×C3×C4C2×D1211yescharacteristic
377C2×C3×C4D3×D411yescharacteristic
378C2×C3×C4D3×D411yescharacteristic
379C2×C3×C4C23×D311yescharacteristic
380C2×C3×C4C23×D311yescharacteristic
381#67—64no—
382C2×Dic3—21no—
383C2×Dic3—21no—
384C2×Dic3—22no—
385C2×Dic3—61no—
386C2×Dic3—62no—
387C2×Dic3—61no—
388C2×Dic3—62no—
389C2×Dic3—122no—
390C2×Dic3—121no—
391C2×Dic3—124no—
392C2×Dic3C2×D1211yescharacteristic
393C2×Dic3C2×D1211yescharacteristic
394C2×Dic3C2×D1211yescharacteristic
395D12—32no—
396D12—32no—
397D12—62no—
398D12—64no—
399D12—61no—
400D12—61no—
401D12—121no—
402C4×D3—22no—
403C4×D3—22no—
404C4×D3—64no—
405C4×D3—64no—
406C4×D3—122no—
407C4×D3—124no—
408C4×D3—122no—
409C4×D3—122no—
410C4×D3—122no—
411C4×D3—242no—
412C4×D3#23712yes—
413C4×D3D3×Q812yes—
414Dic6—21no—
415Dic6—42no—
416Dic6—124no—
417Dic6—124no—
418Dic6—122no—
419Dic6—122no—
420Dic6—242no—
421Dic6D3×Q812yescomplemented
422C3×C8—22no—
423C3×C8—22no—
424C3×C8—42no—
425C3×C8—62no—
426C3⋊C8—22no—
427C2×C32C2×C22⋊Q811yescharacteristic
428C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
429C2×C32C2×#13711yescharacteristic
430C3⋊D3—42no—
431C3×D3—22no—
432#41—94no—
433#41—182no—
434C2×Q8—31no—
435C2×Q8—61no—
436C2×Q8—182no—
437C2×Q8—181no—
438C2×Q8—364no—
439C2×D4—91no—
440C2×D4—181no—
441C22×C4—31no—
442C22×C4—31no—
443C22×C4—31no—
444C22×C4—181no—
445C22×C4—181no—
446C22×C4—182no—
447C22×C4—181no—
448M16—64no—
449C2×C8—32no—
450C2×C8C2×D3212yes—
451C4⋊C4—32no—
452C4⋊C4—31no—
453C4⋊C4—61no—
454C4⋊C4—61no—
455C4⋊C4—92no—
456C4⋊C4—91no—
457C4⋊C4—182no—
458C4⋊C4—182no—
459C4⋊C4—181no—
460C4⋊C4—181no—
461C22⋊C4—181no—
462C22⋊C4—181no—
463C22⋊C4—181no—
464C42—31no—
465C42—31no—
466C42—31no—
467C42—61no—
468C42—181no—
469C42—181no—
470C42C2×D3211yescharacteristic
471C22×C3—21no—
472C22×C3—32no—
473C22×C3—61no—
474C22×C3—61no—
475C22×C3C22×D1211yescharacteristic
476C22×C3C2×D3×D411yescharacteristic
477C2×D3—21no—
478C2×D3—21no—
479C2×D3—62no—
480C2×D3—62no—
481C2×D3—122no—
482C2×D3—121no—
483C2×D3—121no—
484C2×D3—121no—
485C2×D3—121no—
486C2×D3—241no—
487C2×D3—241no—
488C2×D3#89712yes—
489C3×C4—21no—
490C3×C4—21no—
491C3×C4—22no—
492C3×C4—21no—
493C3×C4—21no—
494C3×C4—32no—
495C3×C4—32no—
496C3×C4—41no—
497C3×C4—61no—
498C3×C4—62no—
499C3×C4—122no—
500C3×C4—121no—
501C3×C4#90812yes—
502C3×C4#91412yes—
503C3×C4C2×#23711yescharacteristic
504C3×C4C2×D3×Q811yescharacteristic
505C3×C4C2×D3×Q811yescharacteristic
506C3×C4D3×#4111yescharacteristic
507Dic3—21no—
508Dic3—22no—
509Dic3—42no—
510Dic3—41no—
511Dic3—122no—
512Dic3—121no—
513Dic3—122no—
514Dic3—121no—
515Dic3—242no—
516Dic3—241no—
517Dic3#89712yes—
518Dic3#90912yes—
519C32#307911yescharacteristic, complemented, Sylow
520C23—31no—
521C23—181no—
522Q8—32no—
523Q8—61no—
524Q8—122no—
525Q8—364no—
526Q8—362no—
527D4—92no—
528D4—184no—
529D4—181no—
530C2×C4—31no—
531C2×C4—31no—
532C2×C4—32no—
533C2×C4—32no—
534C2×C4—31no—
535C2×C4—62no—
536C2×C4—61no—
537C2×C4—62no—
538C2×C4—61no—
539C2×C4—62no—
540C2×C4—184no—
541C2×C4—181no—
542C2×C4—182no—
543C2×C4—362no—
544C2×C4—364no—
545C2×C4—362no—
546C2×C4D3×D1211yescharacteristic
547C2×C4D3×D1211yescharacteristic
548C2×C4C22×D3211yescharacteristic
549C8—22no—
550C8—62no—
551C2×C3—21no—
552C2×C3—21no—
553C2×C3—21no—
554C2×C3—62no—
555C2×C3C2×#89711yescharacteristic
556C2×C3D3×C22⋊Q811yescharacteristic
557C2×C3C2×#90811yescharacteristic
558C2×C3C2×#90911yescharacteristic
559C2×C3C2×#91411yescharacteristic
560C2×C3D3×#13711yescharacteristic
561D3—22no—
562D3—122no—
563D3—122no—
564D3—242no—
565C22—32no—
566C22—61no—
567C22—61no—
568C22—182no—
569C22—361no—
570C22—361no—
571C22C2×D3×D1211yescharacteristic
572C4—21no—
573C4—32no—
574C4—32no—
575C4—62no—
576C4—61no—
577C4—122no—
578C4—121no—
579C4—362no—
580C4—361no—
581C4#6379412yes—
582C4D3×#23711yescharacteristic
583C4D32×Q811yescharacteristic
584C3—21no—
585C3#7906011yescharacteristic, complemented
586C3#8101211yescharacteristic, complemented
587C2—62no—
588C2—362no—
589C2D3×#89711yescharacteristic
590C2C2×#6379411yescharacteristic
591C2D3×#90911yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radicalC2×#3799C22
hypercenterC4⋊C8D32
hypocenterC32#3079
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. D3×#869C2semidirect
3. #10592545C2semidirect
4. C3×#4851C2semidirect
5. C3×#4837C2semidirect
6. #10590804C2semidirect
7. #10590759C2semidirect
8. #10590681C2semidirect
10. #10590313C2semidirect
11. #10590301C2semidirect
58. #4851D3semidirect
65. #4837D3semidirect
82. #3799Q8semidirect
183. C4⋊(C3⋊D3)C2×Q8semidirect
198. C3×Dic6C2×Q8semidirect
421. Dic6D3×Q8semidirect
519. C32#3079semidirect
585. C3#79060semidirect
586. C3#81012semidirect

Maximal subgroups

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

subgroupindex
C4×#37992
D3×#8692
#105925452
C3×#48512
C3×#48372
#105908042
#105907592
#105906812
#105906712
#105903132
#105903012
#810123
#790603