Finite Group Databasebeta

← #11868804

Subgroups — #11868804

Order 1152.

880 conjugacy classes of subgroups.

The subgroup lattice has 589 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×C4⋊Q8C211yesmaximal, characteristic, complemented
2C4×#3795C211yesmaximal, characteristic
3#10592793C211yesmaximal, characteristic, complemented
4C3×#5087C211yesmaximal, characteristic, complemented
5#10590607C212yesmaximal
6#10590580C212yesmaximal, complemented
7#10590488C212yesmaximal, complemented
8#10590465C212yesmaximal, complemented
9#10590336C211yesmaximal, characteristic, complemented
10#10590307C211yesmaximal, characteristic, complemented
11#10590269C211yesmaximal, characteristic, complemented
12#83212—31nomaximal
13#80966—31nomaximal
14C2×C3×D3×Q8—21no—
15C2×#3795C2211yescharacteristic
16C32×C4⋊Q8C2211yescharacteristic
17C4×#634C2211yescharacteristic
18C3×#944—21no—
19C3×D3×C4⋊C4—21no—
20C3×D3×C4⋊C4C2212yes—
21C3×#888—21no—
22C3×#888C2212yes—
23C3×C4×D12C2211yescharacteristic
24C3×C42×D3C2211yescharacteristic
25C3×#869C2211yescharacteristic
26C4×#625—21no—
27Dic3×D12C2211yescharacteristic
28#63879—21no—
29#63877—21no—
30C4×D3×Dic3—21no—
31#63844C2211yescharacteristic
32#63841C2211yescharacteristic
33C2×#3711C2212yes—
34#63637C2212yes—
35#63635C2212yes—
36C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
37C3×#809C2212yes—
38C3×#807C2212yes—
39C3×C4⋊(C3⋊C8)C2211yescharacteristic
40#63576C2212yes—
41#63573C2212yes—
42Dic3⋊(C3⋊C8)C2212yes—
43#63567C2212yes—
44#63562C2212yes—
45C2×C3×C4⋊Q8—31no—
46D3×C4⋊Q8D311yescharacteristic, complemented
47C4×#237—31no—
48C4×#235—31no—
49C3×#474—31no—
50#5094—31no—
51#5094—31no—
52#5094—31no—
53#5094—61no—
54#5091—32no—
55#5087—31no—
56#5087D311yescharacteristic, complemented
57#5084—32no—
58#5007—31no—
59#4966—32no—
60#4964—32no—
61#4924—31no—
62#4881—32no—
63#4875—32no—
64#4851—31no—
65#4837—31no—
66#4771—32no—
67#4761—32no—
68C2×C32×Q8—21no—
69C2×#634C2311yescharacteristic
70C3×D3×Q8—44no—
71C2×C3×D12C2311yescharacteristic
72C2×C3×C4×D3—22no—
73C2×C3×C4×D3—21no—
74C2×C3×C4×D3D411yescharacteristic
75C2×C3×C4×D3D411yescharacteristic
76C2×C3×C4×D3C2311yescharacteristic
77C2×C3×Dic6—21no—
78C2×C3×Dic6—22no—
79C2×#625—21no—
80C2×D3×Dic3—21no—
81C2×D3×Dic3—21no—
82#3795—22no—
83#3795Q814yescomplemented
84C32×C4⋊C4—21no—
85C32×C4⋊C4C2312yes—
86C32×C42C2311yescharacteristic
87C4⋊(C3⋊Dic3)C2311yescharacteristic
88#3750—21no—
89C4×C3⋊Dic3—21no—
90C2×C3⋊(C3⋊C8)C2312yes—
91C3×(C2×D3)⋊C4—21no—
92C3×C4⋊Dic3—21no—
93C3×C4⋊Dic3C2312yes—
94C3×C4⋊Dic3C2311yescharacteristic
95C3×Dic3⋊C4—22no—
96C3×Dic3⋊C4—22no—
97C3×C4×Dic3D411yescharacteristic
98C3×C4×Dic3D411yescharacteristic
99C3×C4×Dic3C2311yescharacteristic
100C2×C3×C3⋊C8C2312yes—
101#3724—21no—
102(C2×D3)⋊Dic3—21no—
103(C2×D3)⋊Dic3—21no—
104Dic32—21no—
105Dic32—21no—
106#3711—24no—
107#3079—91noSylow
108C22×C3×Q8—61no—
109C2×D3×Q8—21no—
110C2×#237—31no—
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×D4—31no—
120C2×C3×C4⋊C4—32no—
121C2×C3×C4⋊C4—61no—
122C2×C3×C42—31no—
123#944—21no—
124D4×Dic3—31no—
125C4×#67—61no—
126C4×#67—61no—
127C4×#67—61no—
128#926—31no—
129C2×C4×Dic3—61no—
130C2×#208—32no—
131C2×ΓL(1,𝔽25)—32no—
132#892—31no—
133D3×C4⋊C4—21no—
134D3×C4⋊C4C2×D312yes—
135#888—21no—
136#888C2×D312yes—
137#887—31no—
138#67⋊C4—61no—
139#877—61no—
140C4×D12—31no—
141C4×D12C2×D311yescharacteristic
142#872—61no—
143C42×D3—61no—
144C42×D3C2×D311yescharacteristic
145#869C2×D311yescharacteristic
146C4×Dic6—31no—
147C4×Dic6—31no—
148C4×Dic6—31no—
149C4×Dic6—61no—
150C3×#107—32no—
151C3×C4⋊C8—31no—
152C3×#102—32no—
153#832—32no—
154#817—32no—
155#816—32no—
156Dic3⋊C8—32no—
157#810—32no—
158#810—32no—
159#810—32no—
160#810—62no—
161#809—32no—
162#809C2×D312yes—
163#808—32no—
164#808—32no—
165#808—32no—
166#808—62no—
167#807—32no—
168#807—32no—
169#807C2×D312yes—
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—
183C2×C3⋊Dic3—21no—
184#634—21no—
185#634C2×Q812yescomplemented
186C2×C3×Dic3—21no—
187C2×C3×Dic3—22no—
188C2×C3×Dic3C2×D411yescharacteristic
189C2×C3×Dic3C2×D411yescharacteristic
190C2×C3×Dic3C2×D411yescharacteristic
191C3×D12—21no—
192C3×D12C2×Q812yescomplemented
193C3×C4×D3—22no—
194C3×C4×D3—22no—
195C3×C4×D3—44no—
196C3×C4×D3—42no—
197C3×C4×D3C2×Q812yes—
198C3×C4×D3#4112yes—
199C3×Dic6—44no—
200C3×Dic6—42no—
201#625—24no—
202D3×Dic3—24no—
203D3×Dic3—42no—
204C3⋊(C3⋊C8)—22no—
205C3×C3⋊C8—22no—
206C2×C4⋊Q8—31no—
207C4×#41—91no—
208#477—92no—
209#476—92no—
210#475—91no—
211#475—91no—
212#474—31no—
213#474—91no—
214#428—92no—
215#423—91no—
216#417—92no—
217C2×C3×Q8—21no—
218C2×C3×Q8—21no—
219C2×C3×Q8—41no—
220C2×C3×Q8—62no—
221C2×C3×Q8—61no—
222C2×C3×Q8—124no—
223C2×C3×D4—31no—
224C22×C3×C4—31no—
225C22×C3×C4—31no—
226C22×C3×C4—31no—
227C22×C3×C4—62no—
228C22×C3×C4—61no—
229C2×#67—61no—
230C2×#67—61no—
231C22×Dic3—61no—
232C22×Dic3—61no—
233D3×Q8—44no—
234#237—34no—
235#237—62no—
236#235—34no—
237#235—62no—
238C2×D12C22×D311yescharacteristic
239C2×C4×D3—22no—
240C2×C4×D3—21no—
241C2×C4×D3—61no—
242C2×C4×D3—61no—
243C2×C4×D3#6711yescharacteristic
244C2×C4×D3#6711yescharacteristic
245C2×C4×D3C22×D311yescharacteristic
246C2×Dic6—21no—
247C2×Dic6—22no—
248C2×Dic6—31no—
249C2×Dic6—31no—
250C2×Dic6—61no—
251C2×C3×C8—32no—
252C3×C4⋊C4—21no—
253C3×C4⋊C4—21no—
254C3×C4⋊C4—22no—
255C3×C4⋊C4—31no—
256C3×C4⋊C4—32no—
257C3×C4⋊C4—41no—
258C3×C4⋊C4—62no—
259C3×C4⋊C4—62no—
260C3×C4⋊C4—61no—
261C3×C4⋊C4C22×D312yes—
262C3×C4⋊C4C22×D312yes—
263C3×C22⋊C4—61no—
264C3×C42—21no—
265C3×C42—31no—
266C3×C42—31no—
267C3×C42—31no—
268C3×C42C22×D311yescharacteristic
269C3×C42C22×D311yescharacteristic
270#217—61no—
271#217—61no—
272(C2×D3)⋊C4—21no—
273(C2×D3)⋊C4—61no—
274(C2×D3)⋊C4—61no—
275C4⋊Dic3—21no—
276C4⋊Dic3—31no—
277C4⋊Dic3—31no—
278C4⋊Dic3—61no—
279C4⋊Dic3C22×D311yescharacteristic
280C4⋊Dic3C22×D312yes—
281Dic3⋊C4—22no—
282Dic3⋊C4—22no—
283Dic3⋊C4—61no—
284Dic3⋊C4—61no—
285Dic3⋊C4—61no—
286Dic3⋊C4—61no—
287Dic3⋊C4—121no—
288C4×Dic3—61no—
289C4×Dic3—61no—
290C4×Dic3—61no—
291C4×Dic3—61no—
292C4×Dic3—61no—
293C4×Dic3—61no—
294C4×Dic3—121no—
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—21no—
306C2×C3×D3—21no—
307C2×C3×D3—22no—
308C2×C3×D3—41no—
309C2×C3×D3—41no—
310C2×C3×D3C22⋊Q812yes—
311C32×C4—21no—
312C32×C4—42no—
313C32×C4AGL(1,ℤ/8)12yes—
314C32×C4C22×Q811yescharacteristic
315C32×C4C2×#4111yescharacteristic
316C3⋊Dic3—22no—
317C3⋊Dic3—41no—
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—91no—
332C4×Q8—91no—
333C4×D4—31no—
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—32no—
344#107—92no—
345#106—92no—
346#106—92no—
347C4⋊C8—31no—
348C4⋊C8—92no—
349C4⋊C8—91no—
350#103—92no—
351#103—92no—
352#102—32no—
353#102—92no—
354C23×C3—31no—
355C23×C3—61no—
356C22×D3—21no—
357C22×D3C2×#6711yescharacteristic
358C3×Q8—42no—
359C3×Q8—42no—
360C3×Q8—82no—
361C3×Q8—124no—
362C3×Q8—122no—
363C3×D4—32no—
364C3×D4—61no—
365C2×C3×C4—22no—
366C2×C3×C4—22no—
367C2×C3×C4—21no—
368C2×C3×C4—21no—
369C2×C3×C4—21no—
370C2×C3×C4—31no—
371C2×C3×C4—31no—
372C2×C3×C4—32no—
373C2×C3×C4—32no—
374C2×C3×C4—31no—
375C2×C3×C4—42no—
376C2×C3×C4—62no—
377C2×C3×C4—62no—
378C2×C3×C4—62no—
379C2×C3×C4—61no—
380C2×C3×C4—124no—
381C2×C3×C4—122no—
382C2×C3×C4D3×D411yescharacteristic
383C2×C3×C4D3×D411yescharacteristic
384C2×C3×C4C2×#6711yescharacteristic
385C2×C3×C4C2×#6711yescharacteristic
386C2×C3×C4C23×D311yescharacteristic
387C2×C3×C4C23×D311yescharacteristic
388#67—64no—
389#67—64no—
390C2×Dic3—21no—
391C2×Dic3—22no—
392C2×Dic3—61no—
393C2×Dic3—61no—
394C2×Dic3—64no—
395C2×Dic3—61no—
396C2×Dic3—61no—
397C2×Dic3—121no—
398C2×Dic3—121no—
399C2×Dic3—122no—
400C2×Dic3C2×#6711yescharacteristic
401C2×Dic3C2×#6711yescharacteristic
402C2×Dic3C2×#6711yescharacteristic
403D12—21no—
404D12D3×Q812yescomplemented
405C4×D3—22no—
406C4×D3—22no—
407C4×D3—44no—
408C4×D3—42no—
409C4×D3—64no—
410C4×D3—122no—
411C4×D3D3×Q812yes—
412C4×D3#23912yes—
413Dic6—32no—
414Dic6—32no—
415Dic6—44no—
416Dic6—42no—
417Dic6—62no—
418Dic6—61no—
419Dic6—61no—
420Dic6—121no—
421C3×C8—62no—
422C3⋊C8—22no—
423C3⋊C8—62no—
424C3⋊C8—62no—
425C3⋊C8—122no—
426C2×C32C2×C22⋊Q811yescharacteristic
427C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
428C2×C32C2×#13711yescharacteristic
429C3×D3—22no—
430C3×D3—42no—
431#41—94no—
432#41—182no—
433C2×Q8—21no—
434C2×Q8—62no—
435C2×Q8—61no—
436C2×Q8—91no—
437C2×Q8—124no—
438C2×D4—31no—
439C2×D4—181no—
440C22×C4—31no—
441C22×C4—31no—
442C22×C4—31no—
443C22×C4—62no—
444C22×C4—61no—
445C22×C4—181no—
446C22×C4—181no—
447M16—184no—
448C2×C8—32no—
449C2×C8—92no—
450C4⋊C4—21no—
451C4⋊C4—32no—
452C4⋊C4—31no—
453C4⋊C4—62no—
454C4⋊C4—62no—
455C4⋊C4—61no—
456C4⋊C4—91no—
457C4⋊C4—181no—
458C4⋊C4—181no—
459C4⋊C4C2×D3212yes—
460C22⋊C4—61no—
461C22⋊C4—181no—
462C22⋊C4—181no—
463C42—31no—
464C42—31no—
465C42—31no—
466C42—181no—
467C42—181no—
468C42—181no—
469C42C2×D3211yescharacteristic
470C22×C3—21no—
471C22×C3—32no—
472C22×C3—61no—
473C22×C3—61no—
474C22×C3—62no—
475C22×C3—121no—
476C22×C3—121no—
477C22×C3C2×D3×D411yescharacteristic
478C22×C3C22×#6711yescharacteristic
479C2×D3—21no—
480C2×D3—21no—
481C2×D3—22no—
482C2×D3—41no—
483C2×D3—41no—
484C2×D3#94612yes—
485C3×C4—21no—
486C3×C4—21no—
487C3×C4—21no—
488C3×C4—21no—
489C3×C4—22no—
490C3×C4—32no—
491C3×C4—32no—
492C3×C4—41no—
493C3×C4—42no—
494C3×C4—42no—
495C3×C4—61no—
496C3×C4—82no—
497C3×C4—122no—
498C3×C4—121no—
499C3×C4#91112yes—
500C3×C4#93212yes—
501C3×C4C2×D3×Q811yescharacteristic
502C3×C4C2×D3×Q811yescharacteristic
503C3×C4C2×#23911yescharacteristic
504C3×C4D3×#4111yescharacteristic
505Dic3—21no—
506Dic3—41no—
507Dic3—42no—
508Dic3—62no—
509Dic3—62no—
510Dic3—122no—
511Dic3—121no—
512Dic3—121no—
513Dic3—241no—
514Dic3#94212yes—
515Dic3#94612yes—
516C32#307911yescharacteristic, complemented, Sylow
517C23—31no—
518C23—61no—
519Q8—42no—
520Q8—92no—
521Q8—124no—
522Q8—122no—
523Q8—181no—
524D4—32no—
525D4—61no—
526D4—184no—
527C2×C4—22no—
528C2×C4—31no—
529C2×C4—31no—
530C2×C4—32no—
531C2×C4—32no—
532C2×C4—31no—
533C2×C4—62no—
534C2×C4—62no—
535C2×C4—61no—
536C2×C4—62no—
537C2×C4—124no—
538C2×C4—122no—
539C2×C4—184no—
540C2×C4—181no—
541C2×C4—181no—
542C2×C4—362no—
543C2×C4D3×#6711yescharacteristic
544C2×C4D3×#6711yescharacteristic
545C2×C4C22×D3211yescharacteristic
546C8—62no—
547C8—182no—
548C2×C3—21no—
549C2×C3—21no—
550C2×C3—21no—
551C2×C3—62no—
552C2×C3—122no—
553C2×C3D3×C22⋊Q811yescharacteristic
554C2×C3C2×#91111yescharacteristic
555C2×C3D3×#13711yescharacteristic
556C2×C3C2×#93211yescharacteristic
557C2×C3C2×#94211yescharacteristic
558C2×C3C2×#94611yescharacteristic
559D3—22no—
560D3—42no—
561C22—32no—
562C22—61no—
563C22—61no—
564C22—62no—
565C22—121no—
566C22—121no—
567C22C2×D3×#6711yescharacteristic
568C4—21no—
569C4—32no—
570C4—32no—
571C4—42no—
572C4—61no—
573C4—122no—
574C4—121no—
575C4—182no—
576C4—361no—
577C4#6393212yes—
578C4D32×Q811yescharacteristic
579C4D3×#23911yescharacteristic
580C3—21no—
581C3#8096611yescharacteristic, complemented
582C3#8321211yescharacteristic, complemented
583C2—62no—
584C2—122no—
585C2C2×#6393211yescharacteristic
586C2D3×#94211yescharacteristic
587C2D3×#94611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radicalC2×#3795C22
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. #10592793C2semidirect
4. C3×#5087C2semidirect
6. #10590580C2semidirect
7. #10590488C2semidirect
8. #10590465C2semidirect
9. #10590336C2semidirect
10. #10590307C2semidirect
11. #10590269C2semidirect
46. D3×C4⋊Q8D3semidirect
56. #5087D3semidirect
83. #3795Q8semidirect
185. #634C2×Q8semidirect
192. C3×D12C2×Q8semidirect
404. D12D3×Q8semidirect
516. C32#3079semidirect
581. C3#80966semidirect
582. 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×#37952
#105927932
C3×#50872
#105906072
#105905802
#105904882
#105904652
#105903362
#105903072
#105902692
#832123
#809663