Finite Group Databasebeta

← #11775120

Subgroups — #11775120

Order 1152.

833 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 833 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594922C211yesmaximal, characteristic
2C3⋊D3×#95C211yesmaximal, characteristic, complemented
3#10591159C211yesmaximal, characteristic, complemented
4C3×#4452C211yesmaximal, characteristic, complemented
5C3×#4451C211yesmaximal, characteristic, complemented
6#10589152C211yesmaximal, characteristic, complemented
7#10589150C211yesmaximal, characteristic, complemented
8#68334—31nomaximal
9#68302—31nomaximal
10C22×C4×C3⋊D3—21no—
11C22×C4×C3⋊D3C2211yescharacteristic
12C2×#3796C411yescharacteristic, complemented
13C3×#930C2211yescharacteristic
14C3×#924C2211yescharacteristic
15#63981—21no—
16#67⋊Dic3—21no—
17#63916C411yescharacteristic, complemented
18#63881—21no—
19#63871C411yescharacteristic, complemented
20#63853—21no—
21#63849C411yescharacteristic, complemented
22C2×#3712—21no—
23C32×#95C2211yescharacteristic
24#63658—21no—
25#63658C2211yescharacteristic
26C3×#830C2211yescharacteristic
27C3×#830C2211yescharacteristic
28#63557—21no—
29#5627—31no—
30#5606—31no—
31#4726—31no—
32#4726—31no—
33D3×#95—31no—
34D3×#95—31no—
35D3×#95—61no—
36C3×#328—31no—
37C3×#327—31no—
38#4538—31no—
39#4537—31no—
40#4470—31no—
41#4467—31no—
42#4452D311yescharacteristic, complemented
43#4451D311yescharacteristic, complemented
44C23×C3⋊D3D411yescharacteristic
45C22×C32×C4—21no—
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3—21no—
48C22×C3⋊Dic3D411yescharacteristic
49C2×C4×C3⋊D3—24no—
50C2×C4×C3⋊D3—42no—
51C2×C4×C3⋊D3—42no—
52C2×C4×C3⋊D3—42no—
53C2×C4×C3⋊D3C2×C411yescharacteristic
54C2×C4×C3⋊D3C2×C411yescharacteristic
55C2×C4×C3⋊D3D411yescharacteristic
56C2×C4×C3⋊D3D411yescharacteristic
57C2×C3×#67—21no—
58C2×C3×D12C2×C411yescharacteristic, complemented
59C2×C3×Dic6C2×C411yescharacteristic, complemented
60C2×#626—21no—
61C2×#626—21no—
62C2×D3×Dic3—21no—
63#3796—42no—
64C3×#217—21no—
65C3×(C2×D3)⋊C4—21no—
66C3×C4⋊Dic3C2×C411yescharacteristic, complemented
67C3×C4⋊Dic3C2×C411yescharacteristic, complemented
68C3×Dic3⋊C4—21no—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71Dic3⋊Dic3—21no—
72#3722—21no—
73#3722—21no—
74(C2×D3)⋊Dic3—21no—
75Dic32—21no—
76#3712—42no—
77#1504—91noSylow
78C2×#239—31no—
79C2×#237—31no—
80C22×C4×D3—31no—
81C22×C4×D3—31no—
82C22×C4×D3—61no—
83C22×C4×D3—61no—
84C22×C4×D3—61no—
85C22×C4×D3—62no—
86C3×C22⋊Q8—31no—
87C3×#121—31no—
88#946—31no—
89#938—31no—
90#937—61no—
91D4×Dic3—61no—
92#930C2×D311yescharacteristic
93#924C2×D311yescharacteristic
94C2×ΓL(1,𝔽25)—61no—
95C2×ΓL(1,𝔽25)—61no—
96#897—31no—
97#895—31no—
98#894—61no—
99#893—61no—
100#892—31no—
101#892—31no—
102#883—61no—
103#882—61no—
104#67⋊C4—61no—
105#67⋊C4—61no—
106C3×C22⋊C8—31no—
107C3×C22⋊C8—31no—
108C3×#95—21no—
109C3×#95C2×D311yescharacteristic
110C3×#95C2×D311yescharacteristic
111C3⋊#95—31no—
112C3⋊#95—31no—
113C3⋊#95—61no—
114C3⋊#95—61no—
115C3⋊#95—61no—
116C3⋊#95—62no—
117#830C2×D311yescharacteristic
118#830C2×D311yescharacteristic
119(C2×D3)⋊C8—61no—
120(C2×D3)⋊C8—61no—
121C23×C32C2×D411yescharacteristic
122C22×C3⋊D3—21no—
123C22×C3⋊D3—21no—
124C22×C3⋊D3—22no—
125C22×C3⋊D3—22no—
126C22×C3⋊D3C22⋊C411yescharacteristic
127C22×C3⋊D3C22⋊C411yescharacteristic
128C22×C3×D3—21no—
129C2×C32×C4—22no—
130C2×C32×C4—41no—
131C2×C32×C4—41no—
132C2×C32×C4—41no—
133C2×C32×C4C22×C411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C3⋊Dic3—22no—
136C2×C3⋊Dic3—41no—
137C2×C3⋊Dic3—41no—
138C2×C3⋊Dic3—41no—
139C2×C3⋊Dic3C22⋊C411yescharacteristic
140C2×C3⋊Dic3C22⋊C411yescharacteristic
141C4×C3⋊D3—22no—
142C4×C3⋊D3—22no—
143C4×C3⋊D3—41no—
144C4×C3⋊D3—41no—
145C4×C3⋊D3—48no—
146C3×#67—41no—
147C3×#67—41no—
148C2×C3×Dic3—21no—
149C2×C3×Dic3—21no—
150C2×C3×Dic3—21no—
151C3×D12—41no—
152C3×Dic6—41no—
153#626—42no—
154#626—42no—
155D3×Dic3—42no—
156C3×C3⋊C8—41no—
157C3×C3⋊C8—41no—
158#525—91no—
159#407—91no—
160C2×#95—91no—
161#328—31no—
162#328—91no—
163#327—31no—
164#327—91no—
165C23×D3—31no—
166C23×D3—31no—
167C23×D3—61no—
168C2×C3×Q8—31no—
169C2×C3×D4—31no—
170C2×C3×D4—61no—
171C22×C3×C4—22no—
172C22×C3×C4—21no—
173C22×C3×C4—21no—
174C22×C3×C4—21no—
175C22×C3×C4C22×D311yescharacteristic
176C22×C3×C4C22×D311yescharacteristic
177C2×#67—21no—
178C2×#67—61no—
179C2×#67—61no—
180C22×Dic3—31no—
181C22×Dic3—31no—
182C22×Dic3—61no—
183C22×Dic3—61no—
184C22×Dic3—62no—
185C22×Dic3—61no—
186C22×Dic3—61no—
187#239—122no—
188#237—122no—
189C2×D12—61no—
190C2×D12—61no—
191C2×D12C4×D311yescharacteristic, complemented
192C2×C4×D3—31no—
193C2×C4×D3—31no—
194C2×C4×D3—31no—
195C2×C4×D3—31no—
196C2×C4×D3—31no—
197C2×C4×D3—31no—
198C2×C4×D3—31no—
199C2×C4×D3—31no—
200C2×C4×D3—61no—
201C2×C4×D3—61no—
202C2×C4×D3—61no—
203C2×C4×D3—61no—
204C2×C4×D3—61no—
205C2×C4×D3—64no—
206C2×C4×D3—64no—
207C2×C4×D3—68no—
208C2×C4×D3—122no—
209C2×C4×D3—122no—
210C2×C4×D3—124no—
211C2×C4×D3—122no—
212C2×C4×D3—122no—
213C2×C4×D3—124no—
214C2×C4×D3—124no—
215C2×C4×D3—122no—
216C2×C4×D3—122no—
217C2×Dic6C4×D311yescharacteristic, complemented
218C2×C3×C8—61no—
219C2×C3×C8—61no—
220C3×C4⋊C4—31no—
221C3×C4⋊C4—31no—
222C3×C4⋊C4—61no—
223C3×C22⋊C4—61no—
224C3×C22⋊C4—61no—
225#217—21no—
226#217—61no—
227(C2×D3)⋊C4—21no—
228(C2×D3)⋊C4—61no—
229(C2×D3)⋊C4—61no—
230(C2×D3)⋊C4—61no—
231(C2×D3)⋊C4—61no—
232(C2×D3)⋊C4—61no—
233C4⋊Dic3—61no—
234C4⋊Dic3C4×D311yescharacteristic, complemented
235C4⋊Dic3C4×D311yescharacteristic, complemented
236Dic3⋊C4—21no—
237Dic3⋊C4—61no—
238C4×Dic3—61no—
239C4×Dic3—61no—
240C2×C3⋊C8—21no—
241C2×C3⋊C8—21no—
242ΓL(1,𝔽25)—122no—
243ΓL(1,𝔽25)—122no—
244C22×C32—21no—
245C22×C32—21no—
246C22×C32C2×C22⋊C411yescharacteristic
247C22×C32AGL(1,ℤ/8)11yescharacteristic
248C22×C32#13711yescharacteristic
249C2×C3⋊D3—24no—
250C2×C3⋊D3—24no—
251C2×C3⋊D3—21no—
252C2×C3⋊D3—21no—
253C2×C3⋊D3—21no—
254C2×C3⋊D3—21no—
255C2×C3⋊D3#9912yes—
256C2×C3⋊D3#10412yes—
257C2×C3×D3—41no—
258C2×C3×D3—41no—
259C2×C3×D3—41no—
260C32×C4—21no—
261C32×C4—21no—
262C32×C4—42no—
263C3⋊Dic3—21no—
264C3⋊Dic3—21no—
265C3⋊Dic3—42no—
266C3×Dic3—41no—
267C3×Dic3—41no—
268C3×Dic3—41no—
269C2×#41—91no—
270C23×C4—91no—
271C23×C4—181no—
272C2×M16—181no—
273#123—181no—
274C22⋊Q8—31no—
275C22⋊Q8—91no—
276#121—31no—
277#121—91no—
278#120—181no—
279C4×D4—181no—
280C4×D4—181no—
281#117—91no—
282C22⋊C8—31no—
283C22⋊C8—31no—
284C22⋊C8—181no—
285#95—91no—
286#95—181no—
287#95D3211yescharacteristic
288C23×C3—21no—
289C23×C3—61no—
290C23×C3D3×D411yescharacteristic
291C23×C3D3×D411yescharacteristic
292C22×D3—21no—
293C22×D3—31no—
294C22×D3—31no—
295C22×D3—31no—
296C22×D3—31no—
297C22×D3—61no—
298C22×D3—61no—
299C22×D3—62no—
300C22×D3—62no—
301C22×D3—62no—
302C22×D3—62no—
303C22×D3—64no—
304C22×D3—64no—
305C22×D3—62no—
306C22×D3—62no—
307C22×D3—61no—
308C22×D3—61no—
309C22×D3—61no—
310C22×D3—61no—
311C3×Q8—121no—
312C3×D4—121no—
313C3×D4—121no—
314C3×D4—121no—
315C2×C3×C4—24no—
316C2×C3×C4—22no—
317C2×C3×C4—22no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—41no—
321C2×C3×C4—41no—
322C2×C3×C4—42no—
323C2×C3×C4—42no—
324C2×C3×C4—41no—
325C2×C3×C4—41no—
326C2×C3×C4—42no—
327C2×C3×C4—41no—
328C2×C3×C4—41no—
329C2×C3×C4—61no—
330C2×C3×C4—61no—
331C2×C3×C4—61no—
332C2×C3×C4C2×C4×D311yescharacteristic
333C2×C3×C4C2×C4×D311yescharacteristic
334C2×C3×C4D3×D411yescharacteristic
335C2×C3×C4D3×D411yescharacteristic
336#67—41no—
337#67—41no—
338#67—122no—
339#67—122no—
340C2×Dic3—21no—
341C2×Dic3—21no—
342C2×Dic3—21no—
343C2×Dic3—31no—
344C2×Dic3—31no—
345C2×Dic3—31no—
346C2×Dic3—31no—
347C2×Dic3—61no—
348C2×Dic3—61no—
349C2×Dic3—64no—
350C2×Dic3—62no—
351C2×Dic3—62no—
352C2×Dic3—122no—
353C2×Dic3—121no—
354C2×Dic3—121no—
355C2×Dic3—122no—
356C2×Dic3—122no—
357C2×Dic3—121no—
358C2×Dic3—121no—
359C2×Dic3—122no—
360C2×Dic3—121no—
361C2×Dic3—121no—
362D12—41no—
363D12—122no—
364D12—122no—
365C4×D3—62no—
366C4×D3—62no—
367C4×D3—62no—
368C4×D3—62no—
369C4×D3—122no—
370C4×D3—122no—
371C4×D3—121no—
372C4×D3—121no—
373C4×D3—121no—
374C4×D3—121no—
375C4×D3—122no—
376C4×D3—122no—
377C4×D3—122no—
378C4×D3—1216no—
379C4×D3—128no—
380C4×D3—128no—
381Dic6—41no—
382C3×C8—121no—
383C3×C8—121no—
384C3⋊C8—41no—
385C3⋊C8—41no—
386C2×C32—21no—
387C2×C32—21no—
388C2×C32C2×#9911yescharacteristic
389C2×C32#41711yescharacteristic
390C2×C32C2×#10411yescharacteristic
391C3⋊D3—22no—
392C3⋊D3—22no—
393C3×D3—81no—
394C24—91no—
395#41—362no—
396C2×Q8—31no—
397C2×D4—31no—
398C2×D4—61no—
399C2×D4—181no—
400C2×D4—181no—
401C22×C4—21no—
402C22×C4—91no—
403C22×C4—91no—
404C22×C4—91no—
405C22×C4—91no—
406C22×C4—91no—
407C22×C4—184no—
408C22×C4—181no—
409C22×C4—181no—
410C22×C4—362no—
411C22×C4—362no—
412C22×C4—362no—
413C22×C4C2×D3211yescharacteristic
414M16—362no—
415C2×C8—61no—
416C2×C8—61no—
417C4⋊C4—31no—
418C4⋊C4—31no—
419C4⋊C4—61no—
420C4⋊C4—181no—
421C22⋊C4—61no—
422C22⋊C4—61no—
423C22⋊C4—181no—
424C22⋊C4—181no—
425C22⋊C4—181no—
426C42—181no—
427C22×C3—22no—
428C22×C3—22no—
429C22×C3—21no—
430C22×C3—21no—
431C22×C3—21no—
432C22×C3—21no—
433C22×C3—21no—
434C22×C3—21no—
435C22×C3—21no—
436C22×C3—121no—
437C22×C3—121no—
438C22×C3—121no—
439C22×C3D3×C22⋊C411yescharacteristic
440C22×C3D3×C22⋊C411yescharacteristic
441C22×C3#91111yescharacteristic
442C22×C3#91411yescharacteristic
443C22×C3#91511yescharacteristic
444C22×C3#91811yescharacteristic
445C2×D3—32no—
446C2×D3—32no—
447C2×D3—32no—
448C2×D3—32no—
449C2×D3—41no—
450C2×D3—41no—
451C2×D3—41no—
452C2×D3—62no—
453C2×D3—62no—
454C2×D3—68no—
455C2×D3—64no—
456C2×D3—64no—
457C2×D3—62no—
458C2×D3—68no—
459C2×D3—64no—
460C2×D3—64no—
461C2×D3—62no—
462C2×D3—62no—
463C2×D3—62no—
464C2×D3—61no—
465C2×D3—61no—
466C2×D3—61no—
467C2×D3—61no—
468C2×D3—61no—
469C2×D3—61no—
470C2×D3—61no—
471C2×D3—61no—
472C3×C4—21no—
473C3×C4—21no—
474C3×C4—21no—
475C3×C4—21no—
476C3×C4—41no—
477C3×C4—41no—
478C3×C4—44no—
479C3×C4—42no—
480C3×C4—42no—
481C3×C4—121no—
482C3×C4—121no—
483C3×C4—121no—
484Dic3—41no—
485Dic3—41no—
486Dic3—41no—
487Dic3—61no—
488Dic3—61no—
489Dic3—61no—
490Dic3—61no—
491Dic3—121no—
492Dic3—121no—
493Dic3—124no—
494Dic3—122no—
495Dic3—122no—
496C32#150411yescharacteristic, complemented, Sylow
497C23—61no—
498C23—91no—
499C23—91no—
500C23—182no—
501C23—182no—
502C23—181no—
503C23—181no—
504C23#381111yescharacteristic
505Q8—121no—
506D4—121no—
507D4—121no—
508D4—121no—
509D4—362no—
510D4—362no—
511C2×C4—22no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—61no—
516C2×C4—61no—
517C2×C4—61no—
518C2×C4—91no—
519C2×C4—91no—
520C2×C4—182no—
521C2×C4—182no—
522C2×C4—182no—
523C2×C4—361no—
524C2×C4—361no—
525C2×C4—368no—
526C2×C4—362no—
527C2×C4—361no—
528C2×C4—361no—
529C2×C4—361no—
530C2×C4C4×D3211yescharacteristic
531C2×C4#380211yescharacteristic
532C8—121no—
533C8—121no—
534C2×C3—22no—
535C2×C3—22no—
536C2×C3—21no—
537C2×C3—21no—
538C2×C3—21no—
539C2×C3—21no—
540C2×C3—21no—
541C2×C3—21no—
542C2×C3—21no—
543C2×C3—241no—
544C2×C3D3×#9911yescharacteristic
545C2×C3D3×#9911yescharacteristic
546C2×C3#477111yescharacteristic
547C2×C3#480311yescharacteristic
548C2×C3D3×#10411yescharacteristic
549C2×C3D3×#10411yescharacteristic
550D3—64no—
551D3—64no—
552D3—62no—
553D3—62no—
554D3—62no—
555D3—62no—
556D3—81no—
557C22—21no—
558C22—21no—
559C22—92no—
560C22—92no—
561C22—121no—
562C22—121no—
563C22—121no—
564C22—184no—
565C22—184no—
566C22—181no—
567C22—181no—
568C22—181no—
569C22—181no—
570C22#6392111yescharacteristic
571C22#6393711yescharacteristic
572C22#6395111yescharacteristic
573C4—21no—
574C4—21no—
575C4—42no—
576C4—121no—
577C4—121no—
578C4—121no—
579C4—181no—
580C4—181no—
581C4—362no—
582C3—21no—
583C3#6830211yescharacteristic, complemented
584C3#6833411yescharacteristic, complemented
585C2—21no—
586C2—21no—
587C2—182no—
588C2—182no—
589C2—241no—
590C2#1059039311yescharacteristic
591C2#1059040411yescharacteristic
592C2#1059061211yescharacteristic
subgroupG/H
centerC22#63921
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#95C22
socleC22×C32C2×C22⋊C4
prime radical#10594922C2
cosocleC22×C32×C4C23
hypercenter#95D32
hypocenterC32#1504
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C3⋊D3×#95C2semidirect
3. #10591159C2semidirect
4. C3×#4452C2semidirect
5. C3×#4451C2semidirect
6. #10589152C2semidirect
7. #10589150C2semidirect
12. C2×#3796C4semidirect
17. #63916C4semidirect
19. #63871C4semidirect
21. #63849C4semidirect
42. #4452D3semidirect
43. #4451D3semidirect
58. C2×C3×D12C2×C4semidirect
59. C2×C3×Dic6C2×C4semidirect
66. C3×C4⋊Dic3C2×C4semidirect
67. C3×C4⋊Dic3C2×C4semidirect
191. C2×D12C4×D3semidirect
217. C2×Dic6C4×D3semidirect
234. C4⋊Dic3C4×D3semidirect
235. C4⋊Dic3C4×D3semidirect
496. C32#1504semidirect
583. C3#68302semidirect
584. C3#68334semidirect

Maximal subgroups

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

subgroupindex
#105949222
C3⋊D3×#952
#105911592
C3×#44522
C3×#44512
#105891522
#105891502
#683343
#683023