Finite Group Databasebeta

← #11868806

Subgroups — #11868806

Order 1152.

895 conjugacy classes of subgroups.

The subgroup lattice has 597 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593909C211yesmaximal, characteristic, complemented
2C4×#3796C211yesmaximal, characteristic
3#10592536C211yesmaximal, characteristic, complemented
4C3×#4851C211yesmaximal, characteristic, complemented
5C3×#4846C211yesmaximal, characteristic, complemented
6#10590957C212yesmaximal
7#10590817C212yesmaximal, complemented
8#10590776C212yesmaximal, complemented
9#10590688C212yesmaximal, complemented
10#10590285C211yesmaximal, characteristic, complemented
11#10590269C211yesmaximal, characteristic, complemented
12#81012—31nomaximal
13#80966—31nomaximal
14C2×#3797—21no—
15C2×#3796C2211yescharacteristic
16C2×#3743C2212yes—
17C42×C3⋊D3C2211yescharacteristic
18C3×C4×D12C2211yescharacteristic
19C3×#869C2211yescharacteristic
20C3×#869C2211yescharacteristic
21C3×C4×Dic6C2211yescharacteristic
22#63919—21no—
23#63919C2212yes—
24C4×#626—21no—
25#63900—21no—
26#63900C2212yes—
27#63898C2211yescharacteristic
28#63881—21no—
29#63878—21no—
30C4×D3×Dic3—21no—
31#63873—21no—
32#63849C2211yescharacteristic
33#63843C2211yescharacteristic
34C32×C4⋊C8C2211yescharacteristic
35#63641C2212yes—
36C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
37C3×#821C2212yes—
38C3×#818C2212yes—
39C3×#817C2212yes—
40C3×#816C2212yes—
41#63576C2212yes—
42#63574C2212yes—
43#63565C2212yes—
44#63562C2212yes—
45D3×C4⋊Q8—31no—
46D3×C4⋊Q8—31no—
47C4×#239—31no—
48C4×#237—31no—
49C3×#475—31no—
50C3×#474—31no—
51#5094—31no—
52#5087—31no—
53#5020—31no—
54#5007—31no—
55#4881—32no—
56#4875—32no—
57#4870—32no—
58#4861—32no—
59#4851D311yescharacteristic, complemented
60#4846D311yescharacteristic, complemented
61#4837—31no—
62#4837—31no—
63#4837—61no—
64#4803—32no—
65#4793—32no—
66#4771—32no—
67#4761—32no—
68C2×C4×C3⋊D3D411yescharacteristic
69C2×C4×C3⋊D3D411yescharacteristic
70C2×C4×C3⋊D3C2311yescharacteristic
71C2×C3×D12C2311yescharacteristic
72C2×C3×C4×D3—21no—
73C2×C3×Dic6—21no—
74C2×C3×Dic6—21no—
75C2×C3×Dic6C2311yescharacteristic
76C2×#627—22no—
77C2×#626—21no—
78C2×#624—22no—
79C2×D3×Dic3—21no—
80C2×D3×Dic3—21no—
81#3797—44no—
82#3796—22no—
83#3796Q814yescomplemented
84C2×C32×C8C2312yes—
85C32×C42C2311yescharacteristic
86C4×C3⋊Dic3D411yescharacteristic
87C4×C3⋊Dic3D411yescharacteristic
88C4×C3⋊Dic3C2311yescharacteristic
89C2×C3⋊(C3⋊C8)C2312yes—
90#3743—24no—
91C3×(C2×D3)⋊C4—21no—
92C3×C4⋊Dic3—21no—
93C3×C4⋊Dic3—21no—
94C3×C4⋊Dic3C2312yes—
95C3×C4⋊Dic3C2312yes—
96C3×C4⋊Dic3C2311yescharacteristic
97C3×C4⋊Dic3C2311yescharacteristic
98C3×Dic3⋊C4—21no—
99C3×C4×Dic3—21no—
100#3724—22no—
101#3724—22no—
102Dic3⋊Dic3—21no—
103#3722—21no—
104(C2×D3)⋊Dic3—21no—
105Dic32—21no—
106Dic32—21no—
107#3079—91noSylow
108C2×#239—31no—
109C2×D3×Q8—61no—
110C2×D3×Q8—61no—
111C2×#237—31no—
112C3×C4⋊Q8—31no—
113C3×C4⋊Q8—31no—
114C3×C4×Q8—31no—
115C3×C4×D4—31no—
116Q8×Dic3—31no—
117#944—61no—
118#944—61no—
119D4×Dic3—31no—
120C4×#67—61no—
121C2×C4×Dic3—61no—
122C2×ΓL(1,𝔽25)—32no—
123C2×ΓL(1,𝔽25)—32no—
124C2×ΓL(1,𝔽25)—62no—
125#893—31no—
126#893—61no—
127#892—31no—
128#892—31no—
129#892—61no—
130D3×C4⋊C4—32no—
131D3×C4⋊C4—32no—
132D3×C4⋊C4—61no—
133D3×C4⋊C4—61no—
134#888—32no—
135#888—32no—
136#888—61no—
137#888—61no—
138#887—31no—
139#67⋊C4—61no—
140#877—61no—
141C4×D12—61no—
142C4×D12C2×D311yescharacteristic
143C42×D3—31no—
144C42×D3—31no—
145C42×D3—61no—
146C42×D3—61no—
147#869C2×D311yescharacteristic
148#869C2×D311yescharacteristic
149C4×Dic6C2×D311yescharacteristic
150C3×#107—32no—
151C3×#106—32no—
152C3×C4⋊C8—21no—
153C3×C4⋊C8C2×D311yescharacteristic
154C3×C4⋊C8C2×D311yescharacteristic
155C3×#103—32no—
156C3×#102—32no—
157#835—32no—
158#832—32no—
159#821C2×D312yes—
160#818C2×D312yes—
161#817C2×D312yes—
162#816C2×D312yes—
163Dic3⋊C8—32no—
164Dic3⋊C8—32no—
165Dic3⋊C8—62no—
166#810—32no—
167#809—32no—
168#808—32no—
169#808—32no—
170#807—32no—
171#807—32no—
172C4⋊(C3⋊C8)—31no—
173C4⋊(C3⋊C8)—31no—
174C4⋊(C3⋊C8)—61no—
175C22×C3⋊D3C2×D411yescharacteristic
176C22×C3×D3—21no—
177C2×C32×C4C2×D411yescharacteristic
178C2×C32×C4C2×D411yescharacteristic
179C2×C32×C4C2411yescharacteristic
180C2×C3⋊Dic3C2×D411yescharacteristic
181C2×C3⋊Dic3C2×D411yescharacteristic
182C2×C3⋊Dic3C2×D411yescharacteristic
183C4×C3⋊D3—22no—
184C4×C3⋊D3—22no—
185C4×C3⋊D3C2×Q812yes—
186C4×C3⋊D3#4112yes—
187C2×C3×Dic3—21no—
188C2×C3×Dic3—21no—
189C2×C3×Dic3—21no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3—22no—
192C3×D12—21no—
193C3×D12C2×Q812yescomplemented
194C3×C4×D3—42no—
195C3×Dic6—21no—
196C3×Dic6—42no—
197C3×Dic6—42no—
198C3×Dic6C2×Q812yescomplemented
199#627—44no—
200#626—24no—
201#624—44no—
202D3×Dic3—24no—
203D3×Dic3—42no—
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—31no—
213#474—91no—
214#428—92no—
215#423—91no—
216#417—92no—
217C2×C3×Q8—31no—
218C2×C3×Q8—61no—
219C2×C3×Q8—61no—
220C2×C3×D4—31no—
221C22×C3×C4—61no—
222C2×#67—61no—
223C22×Dic3—61no—
224C22×Dic3—61no—
225#239—34no—
226#239—62no—
227D3×Q8—124no—
228D3×Q8—124no—
229#237—34no—
230#237—62no—
231C2×D12—61no—
232C2×D12C22×D311yescharacteristic
233C2×C4×D3—21no—
234C2×C4×D3—31no—
235C2×C4×D3—31no—
236C2×C4×D3—31no—
237C2×C4×D3—31no—
238C2×C4×D3—31no—
239C2×C4×D3—31no—
240C2×C4×D3—61no—
241C2×C4×D3—61no—
242C2×C4×D3—61no—
243C2×C4×D3—61no—
244C2×C4×D3—62no—
245C2×C4×D3—62no—
246C2×C4×D3—61no—
247C2×Dic6—21no—
248C2×Dic6—21no—
249C2×Dic6—62no—
250C2×Dic6—62no—
251C2×Dic6C22×D311yescharacteristic
252C2×C3×C8—22no—
253C2×C3×C8C22×D312yes—
254C2×C3×C8C22×D312yes—
255C3×C4⋊C4—31no—
256C3×C4⋊C4—32no—
257C3×C4⋊C4—31no—
258C3×C4⋊C4—32no—
259C3×C4⋊C4—61no—
260C3×C4⋊C4—61no—
261C3×C4⋊C4—61no—
262C3×C22⋊C4—61no—
263C3×C42—21no—
264C3×C42—61no—
265C3×C42C22×D311yescharacteristic
266C3×C42C22×D311yescharacteristic
267#217—61no—
268(C2×D3)⋊C4—21no—
269(C2×D3)⋊C4—61no—
270(C2×D3)⋊C4—61no—
271(C2×D3)⋊C4—61no—
272C4⋊Dic3—21no—
273C4⋊Dic3—21no—
274C4⋊Dic3—61no—
275C4⋊Dic3C22×D311yescharacteristic
276C4⋊Dic3C22×D312yes—
277C4⋊Dic3C22×D311yescharacteristic
278C4⋊Dic3C22×D312yes—
279Dic3⋊C4—21no—
280Dic3⋊C4—61no—
281Dic3⋊C4—62no—
282Dic3⋊C4—62no—
283Dic3⋊C4—62no—
284Dic3⋊C4—62no—
285C4×Dic3—21no—
286C4×Dic3—31no—
287C4×Dic3—31no—
288C4×Dic3—31no—
289C4×Dic3—31no—
290C4×Dic3—31no—
291C4×Dic3—31no—
292C4×Dic3—61no—
293C4×Dic3—61no—
294C4×Dic3—61no—
295C4×Dic3—61no—
296C4×Dic3—61no—
297C4×Dic3—61no—
298C4×Dic3—61no—
299C2×C3⋊C8—32no—
300C2×C3⋊C8—32no—
301C2×C3⋊C8—62no—
302ΓL(1,𝔽25)—64no—
303ΓL(1,𝔽25)—64no—
304ΓL(1,𝔽25)—124no—
305C22×C32C22×D411yescharacteristic
306C2×C3⋊D3—21no—
307C2×C3⋊D3—21no—
308C2×C3⋊D3C22⋊Q812yes—
309C2×C3×D3—22no—
310C2×C3×D3—41no—
311C2×C3×D3—41no—
312C32×C4—21no—
313C32×C4AGL(1,ℤ/8)12yes—
314C32×C4C22×Q811yescharacteristic
315C32×C4C2×#4111yescharacteristic
316C3⋊Dic3—21no—
317C3⋊Dic3C22⋊Q812yes—
318C3⋊Dic3#13712yes—
319C3×Dic3—22no—
320C3×Dic3—42no—
321C3×Dic3—42no—
322C3×Dic3—41no—
323C3×Dic3—41no—
324C2×#41—91no—
325C22×Q8—181no—
326C2×M16—92no—
327C4⋊Q8—31no—
328C4⋊Q8—31no—
329C4⋊Q8—92no—
330C4⋊Q8—181no—
331C4⋊Q8—181no—
332C4×Q8—31no—
333C4×Q8—91no—
334C4×D4—31no—
335C4×D4—91no—
336C4×D4—181no—
337C4×D4—181no—
338#117—91no—
339#117—181no—
340C2×C4⋊C4—92no—
341C2×C4⋊C4—181no—
342C2×C42—91no—
343C2×C42—181no—
344#107—32no—
345#107—92no—
346#106—32no—
347#106—92no—
348C4⋊C8—92no—
349C4⋊C8—91no—
350C4⋊C8D3211yescharacteristic
351#103—32no—
352#103—92no—
353#102—32no—
354#102—92no—
355C23×C3—61no—
356C22×D3—21no—
357C22×D3—31no—
358C22×D3—31no—
359C22×D3—61no—
360C3×Q8—32no—
361C3×Q8—61no—
362C3×Q8—122no—
363C3×Q8—122no—
364C3×D4—32no—
365C3×D4—61no—
366C2×C3×C4—21no—
367C2×C3×C4—21no—
368C2×C3×C4—21no—
369C2×C3×C4—61no—
370C2×C3×C4—61no—
371C2×C3×C4—61no—
372C2×C3×C4—62no—
373C2×C3×C4—62no—
374C2×C3×C4—122no—
375C2×C3×C4D3×D411yescharacteristic
376C2×C3×C4D3×D411yescharacteristic
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—21no—
385C2×Dic3—22no—
386C2×Dic3—22no—
387C2×Dic3—31no—
388C2×Dic3—31no—
389C2×Dic3—31no—
390C2×Dic3—31no—
391C2×Dic3—31no—
392C2×Dic3—31no—
393C2×Dic3—61no—
394C2×Dic3—61no—
395C2×Dic3—61no—
396C2×Dic3—64no—
397C2×Dic3—122no—
398D12—21no—
399D12—64no—
400D12D3×Q812yescomplemented
401C4×D3—32no—
402C4×D3—32no—
403C4×D3—32no—
404C4×D3—32no—
405C4×D3—42no—
406C4×D3—62no—
407C4×D3—62no—
408C4×D3—62no—
409C4×D3—62no—
410C4×D3—64no—
411C4×D3—62no—
412C4×D3—62no—
413C4×D3—122no—
414C4×D3—122no—
415C4×D3—122no—
416C4×D3—124no—
417C4×D3—124no—
418Dic6—21no—
419Dic6—42no—
420Dic6—42no—
421Dic6—124no—
422Dic6—124no—
423Dic6D3×Q812yescomplemented
424C3×C8—22no—
425C3×C8—22no—
426C3×C8—42no—
427C3⋊C8—62no—
428C3⋊C8—62no—
429C3⋊C8—122no—
430C2×C32C2×C22⋊Q811yescharacteristic
431C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
432C2×C32C2×#13711yescharacteristic
433C3⋊D3—22no—
434C3×D3—42no—
435#41—94no—
436#41—182no—
437C2×Q8—31no—
438C2×Q8—61no—
439C2×Q8—61no—
440C2×Q8—182no—
441C2×Q8—364no—
442C2×D4—31no—
443C2×D4—181no—
444C22×C4—61no—
445C22×C4—91no—
446C22×C4—91no—
447C22×C4—91no—
448C22×C4—182no—
449C22×C4—181no—
450C22×C4—181no—
451M16—184no—
452C2×C8—92no—
453C2×C8C2×D3212yes—
454C4⋊C4—32no—
455C4⋊C4—32no—
456C4⋊C4—31no—
457C4⋊C4—31no—
458C4⋊C4—61no—
459C4⋊C4—61no—
460C4⋊C4—61no—
461C4⋊C4—182no—
462C4⋊C4—182no—
463C4⋊C4—181no—
464C22⋊C4—61no—
465C22⋊C4—181no—
466C22⋊C4—181no—
467C42—61no—
468C42—91no—
469C42—91no—
470C42—91no—
471C42—181no—
472C42—181no—
473C42C2×D3211yescharacteristic
474C22×C3—21no—
475C22×C3—62no—
476C22×C3—121no—
477C22×C3—121no—
478C22×C3C2×D3×D411yescharacteristic
479C22×C3C2×D3×D411yescharacteristic
480C2×D3—22no—
481C2×D3—32no—
482C2×D3—32no—
483C2×D3—41no—
484C2×D3—41no—
485C2×D3—62no—
486C2×D3—61no—
487C2×D3—61no—
488C2×D3—61no—
489C2×D3—61no—
490C2×D3—121no—
491C2×D3—121no—
492C3×C4—21no—
493C3×C4—21no—
494C3×C4—22no—
495C3×C4—21no—
496C3×C4—21no—
497C3×C4—41no—
498C3×C4—62no—
499C3×C4—122no—
500C3×C4—122no—
501C3×C4—121no—
502C3×C4—121no—
503C3×C4#91112yes—
504C3×C4#91412yes—
505C3×C4C2×D3×Q811yescharacteristic
506C3×C4C2×D3×Q811yescharacteristic
507C3×C4D3×#4111yescharacteristic
508C3×C4D3×#4111yescharacteristic
509Dic3—22no—
510Dic3—32no—
511Dic3—32no—
512Dic3—32no—
513Dic3—32no—
514Dic3—42no—
515Dic3—41no—
516Dic3—42no—
517Dic3—41no—
518Dic3—62no—
519Dic3—62no—
520Dic3—61no—
521Dic3—61no—
522Dic3—121no—
523C32#307911yescharacteristic, complemented, Sylow
524C23—61no—
525C23—91no—
526Q8—32no—
527Q8—61no—
528Q8—122no—
529Q8—122no—
530Q8—364no—
531D4—32no—
532D4—61no—
533D4—184no—
534C2×C4—61no—
535C2×C4—61no—
536C2×C4—61no—
537C2×C4—62no—
538C2×C4—62no—
539C2×C4—91no—
540C2×C4—91no—
541C2×C4—92no—
542C2×C4—92no—
543C2×C4—91no—
544C2×C4—122no—
545C2×C4—182no—
546C2×C4—184no—
547C2×C4—182no—
548C2×C4—362no—
549C2×C4—364no—
550C2×C4#380211yescharacteristic
551C2×C4#380211yescharacteristic
552C2×C4C22×D3211yescharacteristic
553C8—22no—
554C8—182no—
555C2×C3—21no—
556C2×C3—21no—
557C2×C3—21no—
558C2×C3—122no—
559C2×C3D3×C22⋊Q811yescharacteristic
560C2×C3D3×C22⋊Q811yescharacteristic
561C2×C3C2×#91111yescharacteristic
562C2×C3C2×#91411yescharacteristic
563C2×C3D3×#13711yescharacteristic
564C2×C3D3×#13711yescharacteristic
565D3—42no—
566D3—62no—
567D3—62no—
568D3—122no—
569C22—62no—
570C22—92no—
571C22—121no—
572C22—121no—
573C22—181no—
574C22—181no—
575C22C2×#380211yescharacteristic
576C4—21no—
577C4—62no—
578C4—92no—
579C4—92no—
580C4—121no—
581C4—122no—
582C4—122no—
583C4—121no—
584C4—181no—
585C4#6379812yes—
586C4#6431211yescharacteristic
587C4D32×Q811yescharacteristic
588C3—21no—
589C3#8096611yescharacteristic, complemented
590C3#8101211yescharacteristic, complemented
591C2—122no—
592C2—182no—
593C2#1059463111yescharacteristic
594C2C2×#6379811yescharacteristic
595C2#1059471711yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radicalC2×#3796C22
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
1. #10593909C2semidirect
3. #10592536C2semidirect
4. C3×#4851C2semidirect
5. C3×#4846C2semidirect
7. #10590817C2semidirect
8. #10590776C2semidirect
9. #10590688C2semidirect
10. #10590285C2semidirect
11. #10590269C2semidirect
59. #4851D3semidirect
60. #4846D3semidirect
83. #3796Q8semidirect
193. C3×D12C2×Q8semidirect
198. C3×Dic6C2×Q8semidirect
400. D12D3×Q8semidirect
423. Dic6D3×Q8semidirect
523. C32#3079semidirect
589. C3#80966semidirect
590. C3#81012semidirect

Maximal subgroups

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

subgroupindex
#105939092
C4×#37962
#105925362
C3×#48512
C3×#48462
#105909572
#105908172
#105907762
#105906882
#105902852
#105902692
#810123
#809663