Finite Group Databasebeta

← #11868802

Subgroups — #11868802

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
1C3×D3×C4⋊Q8C211yesmaximal, characteristic, complemented
2C4×#3799C211yesmaximal, characteristic
3#10592786C211yesmaximal, characteristic, complemented
4C3×#5094C211yesmaximal, characteristic, complemented
5#10590609C212yesmaximal
6#10590581C212yesmaximal, complemented
7#10590489C212yesmaximal, complemented
8#10590466C212yesmaximal, complemented
9#10590336C211yesmaximal, characteristic, complemented
10#10590313C211yesmaximal, characteristic, complemented
11#10590285C211yesmaximal, characteristic, complemented
12#83212—31nomaximal
13#81012—31nomaximal
14C2×C3×D3×Q8—21no—
15C2×#3799C2211yescharacteristic
16C32×C4⋊Q8C2211yescharacteristic
17C4×C4⋊(C3⋊D3)C2211yescharacteristic
18C3×#944—21no—
19C3×D3×C4⋊C4—21no—
20C3×D3×C4⋊C4C2212yes—
21C3×#888—21no—
22C3×#888C2212yes—
23C3×C42×D3C2211yescharacteristic
24C3×#869C2211yescharacteristic
25C3×C4×Dic6C2211yescharacteristic
26#63904—21no—
27C4×#626—21no—
28#63894C2211yescharacteristic
29C4×#624—21no—
30Dic3×Dic6C2211yescharacteristic
31#63841C2211yescharacteristic
32#63836—21no—
33C2×#3711C2212yes—
34#63636C2212yes—
35#63634C2212yes—
36C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
37C3×#810C2212yes—
38C3×#808C2212yes—
39C3×C4⋊(C3⋊C8)C2211yescharacteristic
40#63575C2212yes—
41#63574C2212yes—
42Dic3⋊(C3⋊C8)C2212yes—
43#63565C2212yes—
44#63564C2212yes—
45C2×C3×C4⋊Q8—31no—
46D3×C4⋊Q8D311yescharacteristic, complemented
47C4×#239—31no—
48C4×#235—31no—
49C3×#475—31no—
50#5094—31no—
51#5094D311yescharacteristic, complemented
52#5091—32no—
53#5087—31no—
54#5087—31no—
55#5087—31no—
56#5087—61no—
57#5084—32no—
58#5020—31no—
59#4966—32no—
60#4964—32no—
61#4924—31no—
62#4870—32no—
63#4861—32no—
64#4846—31no—
65#4837—31no—
66#4803—32no—
67#4793—32no—
68C2×C32×Q8—21no—
69C2×C4⋊(C3⋊D3)C2311yescharacteristic
70C2×C4×C3⋊D3—21no—
71C3×D3×Q8—44no—
72C2×C3×C4×D3—22no—
73C2×C3×C4×D3D411yescharacteristic
74C2×C3×C4×D3D411yescharacteristic
75C2×C3×C4×D3C2311yescharacteristic
76C2×C3×Dic6—21no—
77C2×C3×Dic6—22no—
78C2×C3×Dic6C2311yescharacteristic
79C2×#626—21no—
80C2×#624—21no—
81C2×#624—21no—
82#3799—22no—
83#3799Q814yescomplemented
84C32×C4⋊C4—21no—
85C32×C4⋊C4C2312yes—
86C32×C42C2311yescharacteristic
87#3752—21no—
88C4⋊(C3⋊Dic3)C2311yescharacteristic
89C2×C3⋊(C3⋊C8)C2312yes—
90C3×C4⋊Dic3—21no—
91C3×C4⋊Dic3C2312yes—
92C3×C4⋊Dic3C2311yescharacteristic
93C3×Dic3⋊C4—21no—
94C3×Dic3⋊C4—22no—
95C3×Dic3⋊C4—22no—
96C3×C4×Dic3—21no—
97C3×C4×Dic3D411yescharacteristic
98C3×C4×Dic3D411yescharacteristic
99C3×C4×Dic3C2311yescharacteristic
100C2×C3×C3⋊C8C2312yes—
101Dic3⋊Dic3—21no—
102#3722—21no—
103(C2×D3)⋊Dic3—21no—
104Dic32—21no—
105Dic32—21no—
106#3711—24no—
107#3079—91noSylow
108C22×C3×Q8—61no—
109C2×#239—31no—
110C2×D3×Q8—21no—
111C2×#235—31no—
112C3×C4⋊Q8—21no—
113C3×C4⋊Q8—32no—
114C3×C4⋊Q8—31no—
115C3×C4⋊Q8—61no—
116C3×C4⋊Q8—61no—
117C3×C4⋊Q8C2×D311yescharacteristic
118C3×C4⋊Q8C2×D311yescharacteristic
119C3×C4×Q8—31no—
120C2×C3×C4⋊C4—32no—
121C2×C3×C4⋊C4—61no—
122C2×C3×C42—31no—
123Q8×Dic3—31no—
124#944—21no—
125C4×#67—61no—
126C4×#67—61no—
127#926—31no—
128C2×#208—32no—
129C2×ΓL(1,𝔽25)—32no—
130#893—31no—
131#893—61no—
132#892—31no—
133#892—61no—
134D3×C4⋊C4—21no—
135D3×C4⋊C4C2×D312yes—
136#888—21no—
137#888C2×D312yes—
138C4×D12—31no—
139C4×D12—31no—
140C4×D12—31no—
141C4×D12—61no—
142C4×D12—61no—
143#872—61no—
144C42×D3—61no—
145C42×D3—61no—
146C42×D3C2×D311yescharacteristic
147#869C2×D311yescharacteristic
148C4×Dic6—31no—
149C4×Dic6C2×D311yescharacteristic
150C3×#106—32no—
151C3×C4⋊C8—31no—
152C3×#103—32no—
153#835—32no—
154#821—32no—
155#818—32no—
156Dic3⋊C8—32no—
157#810—32no—
158#810C2×D312yes—
159#809—32no—
160#809—32no—
161#809—32no—
162#809—62no—
163#808—32no—
164#808—32no—
165#808C2×D312yes—
166#807—32no—
167#807—32no—
168#807—32no—
169#807—62no—
170C4⋊(C3⋊C8)—31no—
171C4⋊(C3⋊C8)—31no—
172C4⋊(C3⋊C8)—32no—
173C4⋊(C3⋊C8)—61no—
174C4⋊(C3⋊C8)C2×D311yescharacteristic
175C22×C3⋊D3—21no—
176C22×C3×D3C2×D411yescharacteristic
177C32×Q8—42no—
178C2×C32×C4—22no—
179C2×C32×C4C2×D411yescharacteristic
180C2×C32×C4C2×D411yescharacteristic
181C2×C32×C4C2411yescharacteristic
182C2×C3⋊Dic3—21no—
183C4⋊(C3⋊D3)—21no—
184C4⋊(C3⋊D3)C2×Q812yescomplemented
185C4×C3⋊D3—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×D3—44no—
195C3×C4×D3C2×Q812yes—
196C3×C4×D3#4112yes—
197C3×Dic6—21no—
198C3×Dic6—44no—
199C3×Dic6—42no—
200C3×Dic6C2×Q812yescomplemented
201#626—24no—
202#624—24no—
203#624—42no—
204C3⋊(C3⋊C8)—22no—
205C3×C3⋊C8—22no—
206C2×C4⋊Q8—31no—
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—91no—
216#417—92no—
217C2×C3×Q8—21no—
218C2×C3×Q8—21no—
219C2×C3×Q8—31no—
220C2×C3×Q8—41no—
221C2×C3×Q8—62no—
222C2×C3×Q8—61no—
223C2×C3×Q8—124no—
224C22×C3×C4—31no—
225C22×C3×C4—31no—
226C22×C3×C4—31no—
227C22×C3×C4—62no—
228C2×#67—61no—
229#239—34no—
230#239—62no—
231D3×Q8—44no—
232#235—34no—
233#235—62no—
234C2×D12—31no—
235C2×D12—31no—
236C2×D12—61no—
237C2×D12—61no—
238C2×C4×D3—22no—
239C2×C4×D3—61no—
240C2×C4×D3—61no—
241C2×C4×D3—61no—
242C2×C4×D3—61no—
243C2×C4×D3—61no—
244C2×C4×D3—61no—
245C2×C4×D3—121no—
246C2×C4×D3#6711yescharacteristic
247C2×C4×D3#6711yescharacteristic
248C2×C4×D3C22×D311yescharacteristic
249C2×Dic6—21no—
250C2×Dic6—22no—
251C2×Dic6C22×D311yescharacteristic
252C2×C3×C8—32no—
253C3×C4⋊C4—21no—
254C3×C4⋊C4—21no—
255C3×C4⋊C4—22no—
256C3×C4⋊C4—32no—
257C3×C4⋊C4—31no—
258C3×C4⋊C4—41no—
259C3×C4⋊C4—62no—
260C3×C4⋊C4—62no—
261C3×C4⋊C4—61no—
262C3×C4⋊C4—61no—
263C3×C4⋊C4C22×D312yes—
264C3×C4⋊C4C22×D312yes—
265C3×C42—21no—
266C3×C42—31no—
267C3×C42—31no—
268C3×C42—31no—
269C3×C42—61no—
270C3×C42C22×D311yescharacteristic
271C3×C42C22×D311yescharacteristic
272#217—61no—
273(C2×D3)⋊C4—61no—
274(C2×D3)⋊C4—61no—
275(C2×D3)⋊C4—61no—
276(C2×D3)⋊C4—61no—
277(C2×D3)⋊C4—61no—
278(C2×D3)⋊C4—121no—
279C4⋊Dic3—21no—
280C4⋊Dic3—31no—
281C4⋊Dic3—31no—
282C4⋊Dic3—61no—
283C4⋊Dic3—61no—
284C4⋊Dic3C22×D311yescharacteristic
285C4⋊Dic3C22×D312yes—
286Dic3⋊C4—21no—
287Dic3⋊C4—22no—
288Dic3⋊C4—22no—
289Dic3⋊C4—61no—
290C4×Dic3—21no—
291C4×Dic3—61no—
292C4×Dic3—61no—
293C4×Dic3—61no—
294C4×Dic3—61no—
295C4×Dic3#6711yescharacteristic
296C4×Dic3#6711yescharacteristic
297C4×Dic3C22×D311yescharacteristic
298#208—64no—
299C2×C3⋊C8—32no—
300C2×C3⋊C8—32no—
301C2×C3⋊C8—62no—
302C2×C3⋊C8C22×D312yes—
303ΓL(1,𝔽25)—64no—
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×C4—42no—
313C32×C4AGL(1,ℤ/8)12yes—
314C32×C4C22×Q811yescharacteristic
315C32×C4C2×#4111yescharacteristic
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—61no—
325C2×M16—92no—
326C4⋊Q8—32no—
327C4⋊Q8—31no—
328C4⋊Q8—61no—
329C4⋊Q8—61no—
330C4⋊Q8D3211yescharacteristic
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—32no—
340C2×C4⋊C4—61no—
341C2×C42—31no—
342C2×C42—181no—
343#107—92no—
344#107—92no—
345#106—32no—
346#106—92no—
347C4⋊C8—31no—
348C4⋊C8—92no—
349C4⋊C8—91no—
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×#6711yescharacteristic
359C3×Q8—32no—
360C3×Q8—42no—
361C3×Q8—42no—
362C3×Q8—61no—
363C3×Q8—82no—
364C3×Q8—124no—
365C3×Q8—122no—
366C2×C3×C4—22no—
367C2×C3×C4—22no—
368C2×C3×C4—21no—
369C2×C3×C4—21no—
370C2×C3×C4—21no—
371C2×C3×C4—31no—
372C2×C3×C4—31no—
373C2×C3×C4—32no—
374C2×C3×C4—32no—
375C2×C3×C4—31no—
376C2×C3×C4—42no—
377C2×C3×C4—62no—
378C2×C3×C4—61no—
379C2×C3×C4—62no—
380C2×C3×C4—62no—
381C2×C3×C4—61no—
382C2×C3×C4—124no—
383C2×C3×C4D3×D411yescharacteristic
384C2×C3×C4D3×D411yescharacteristic
385C2×C3×C4C2×#6711yescharacteristic
386C2×C3×C4C2×#6711yescharacteristic
387C2×C3×C4C23×D311yescharacteristic
388C2×C3×C4C23×D311yescharacteristic
389#67—64no—
390C2×Dic3—21no—
391C2×Dic3—21no—
392C2×Dic3—22no—
393C2×Dic3—61no—
394C2×Dic3—61no—
395C2×Dic3—121no—
396C2×Dic3C2×#6711yescharacteristic
397C2×Dic3C2×#6711yescharacteristic
398C2×Dic3C2×#6711yescharacteristic
399D12—32no—
400D12—32no—
401D12—62no—
402D12—64no—
403D12—61no—
404D12—61no—
405D12—121no—
406C4×D3—22no—
407C4×D3—22no—
408C4×D3—44no—
409C4×D3—64no—
410C4×D3—64no—
411C4×D3—122no—
412C4×D3—122no—
413C4×D3—122no—
414C4×D3—122no—
415C4×D3—242no—
416C4×D3D3×Q812yes—
417C4×D3#23912yes—
418Dic6—21no—
419Dic6—44no—
420Dic6—42no—
421Dic6D3×Q812yescomplemented
422C3×C8—62no—
423C3⋊C8—22no—
424C3⋊C8—62no—
425C3⋊C8—62no—
426C3⋊C8—122no—
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—21no—
435C2×Q8—31no—
436C2×Q8—62no—
437C2×Q8—61no—
438C2×Q8—124no—
439C2×D4—91no—
440C2×D4—181no—
441C22×C4—31no—
442C22×C4—31no—
443C22×C4—31no—
444C22×C4—62no—
445C22×C4—181no—
446C22×C4—181no—
447C22×C4—181no—
448M16—184no—
449C2×C8—32no—
450C2×C8—92no—
451C4⋊C4—21no—
452C4⋊C4—32no—
453C4⋊C4—31no—
454C4⋊C4—62no—
455C4⋊C4—62no—
456C4⋊C4—61no—
457C4⋊C4—61no—
458C4⋊C4—91no—
459C4⋊C4—181no—
460C4⋊C4C2×D3212yes—
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×C3C2×D3×D411yescharacteristic
476C22×C3C22×#6711yescharacteristic
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#94612yes—
489C3×C4—21no—
490C3×C4—21no—
491C3×C4—21no—
492C3×C4—21no—
493C3×C4—22no—
494C3×C4—32no—
495C3×C4—32no—
496C3×C4—41no—
497C3×C4—42no—
498C3×C4—42no—
499C3×C4—61no—
500C3×C4—62no—
501C3×C4—82no—
502C3×C4—122no—
503C3×C4—121no—
504C3×C4#91412yes—
505C3×C4#93212yes—
506C3×C4C2×D3×Q811yescharacteristic
507C3×C4C2×D3×Q811yescharacteristic
508C3×C4C2×#23911yescharacteristic
509C3×C4D3×#4111yescharacteristic
510Dic3—21no—
511Dic3—22no—
512Dic3—41no—
513Dic3—42no—
514Dic3—121no—
515Dic3—121no—
516Dic3—241no—
517Dic3#94212yes—
518Dic3#94612yes—
519C32#307911yescharacteristic, complemented, Sylow
520C23—31no—
521C23—181no—
522Q8—32no—
523Q8—42no—
524Q8—61no—
525Q8—124no—
526Q8—122no—
527D4—92no—
528D4—184no—
529D4—181no—
530C2×C4—22no—
531C2×C4—31no—
532C2×C4—31no—
533C2×C4—32no—
534C2×C4—32no—
535C2×C4—31no—
536C2×C4—62no—
537C2×C4—61no—
538C2×C4—62no—
539C2×C4—61no—
540C2×C4—62no—
541C2×C4—124no—
542C2×C4—184no—
543C2×C4—181no—
544C2×C4—362no—
545C2×C4—362no—
546C2×C4D3×#6711yescharacteristic
547C2×C4D3×#6711yescharacteristic
548C2×C4C22×D3211yescharacteristic
549C8—62no—
550C8—182no—
551C2×C3—21no—
552C2×C3—21no—
553C2×C3—21no—
554C2×C3—62no—
555C2×C3D3×C22⋊Q811yescharacteristic
556C2×C3C2×#91411yescharacteristic
557C2×C3D3×#13711yescharacteristic
558C2×C3C2×#93211yescharacteristic
559C2×C3C2×#94211yescharacteristic
560C2×C3C2×#94611yescharacteristic
561D3—22no—
562D3—122no—
563D3—122no—
564D3—242no—
565C22—32no—
566C22—61no—
567C22—61no—
568C22—182no—
569C22—361no—
570C22—361no—
571C22C2×D3×#6711yescharacteristic
572C4—21no—
573C4—32no—
574C4—32no—
575C4—42no—
576C4—61no—
577C4—62no—
578C4—122no—
579C4—121no—
580C4—361no—
581C4#6393412yes—
582C4D32×Q811yescharacteristic
583C4D3×#23911yescharacteristic
584C3—21no—
585C3#8101211yescharacteristic, complemented
586C3#8321211yescharacteristic, complemented
587C2—62no—
588C2—362no—
589C2C2×#6393411yescharacteristic
590C2D3×#94211yescharacteristic
591C2D3×#94611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radicalC2×#3799C22
hypercenterC4⋊Q8D32
hypocenterC32#3079
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×D3×C4⋊Q8C2semidirect
3. #10592786C2semidirect
4. C3×#5094C2semidirect
6. #10590581C2semidirect
7. #10590489C2semidirect
8. #10590466C2semidirect
9. #10590336C2semidirect
10. #10590313C2semidirect
11. #10590285C2semidirect
46. D3×C4⋊Q8D3semidirect
51. #5094D3semidirect
83. #3799Q8semidirect
184. C4⋊(C3⋊D3)C2×Q8semidirect
200. C3×Dic6C2×Q8semidirect
421. Dic6D3×Q8semidirect
519. C32#3079semidirect
585. C3#81012semidirect
586. C3#83212semidirect

Maximal subgroups

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

subgroupindex
C3×D3×C4⋊Q82
C4×#37992
#105927862
C3×#50942
#105906092
#105905812
#105904892
#105904662
#105903362
#105903132
#105902852
#832123
#810123