Finite Group Databasebeta

← #11872779

Subgroups — #11872779

Order 1152.

707 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 707 conjugacy classes of subgroups — too many to draw. Only its 97 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#10594223C211yesmaximal, characteristic, complemented
2#10594181C211yesmaximal, characteristic, complemented
3#10593744C211yesmaximal, characteristic, complemented
4#10593519C211yesmaximal, characteristic, complemented
5#10593519C211yesmaximal, characteristic, complemented
6#10593494C211yesmaximal, characteristic, complemented
7#10593494C211yesmaximal, characteristic, complemented
8#10593426C211yesmaximal, characteristic, complemented
9#10593420C211yesmaximal, characteristic, complemented
10#10593419C211yesmaximal, characteristic, complemented
11#10593419C211yesmaximal, characteristic, complemented
12#10593417C211yesmaximal, characteristic, complemented
13C4×#3774C211yesmaximal, characteristic, complemented
14#10593364C211yesmaximal, characteristic, complemented
15#10593350C211yesmaximal, characteristic, complemented
16C22×#625C2211yescharacteristic
17C2×#3774C2211yescharacteristic
18C2×#3774C2211yescharacteristic
19C2×#3774C2211yescharacteristic
20C2×#3774C2211yescharacteristic
21#64086C2211yescharacteristic
22C3×#884—21no—
23C3×D3×C22⋊C4—21no—
24#63980C2211yescharacteristic
25#63980C2211yescharacteristic
26#63970—21no—
27D3×#217—21no—
28#63957C2211yescharacteristic
29#63914C2211yescharacteristic, complemented
30#63905—21no—
31#63902C2211yescharacteristic
32#63902C2211yescharacteristic
33#63902C2211yescharacteristic, complemented
34C4×#625C2211yescharacteristic
35C4×#625C2211yescharacteristic
36C4×#625C2211yescharacteristic, complemented
37#63884—21no—
38#63879—21no—
39#63879—21no—
40#63870C2211yescharacteristic, complemented
41C22⋊#622C2211yescharacteristic
42C22⋊#622C2211yescharacteristic
43#63779C2211yescharacteristic, complemented
44#63777C2211yescharacteristic, complemented
45C4⋊#622C2211yescharacteristic, complemented
46C4×#622C2211yescharacteristic, complemented
47#63743C2211yescharacteristic, complemented
48#63743C2211yescharacteristic, complemented
49#63742C2211yescharacteristic, complemented
50#63742C2211yescharacteristic, complemented
51#63739C2211yescharacteristic
52#63739C2211yescharacteristic
53#63739C2211yescharacteristic
54#63739C2211yescharacteristic
55#63739C2211yescharacteristic, complemented
56#63739C2211yescharacteristic, complemented
57#63739C2211yescharacteristic, complemented
58#63739C2211yescharacteristic, complemented
59#5615—61no—
60#5486—61no—
61C23×C3×D3—21no—
62C22×C3⋊Dic3C2311yescharacteristic
63C2×C3×#67—21no—
64C2×C3×#67—21no—
65C2×C3×D12—21no—
66C2×C3×C4×D3—21no—
67C2×C3×C4×D3—21no—
68C2×C3×C4×D3—21no—
69C2×#625—21no—
70C2×#625—22no—
71C2×#625—22no—
72C2×#625—21no—
73C2×#625C2311yescharacteristic
74C2×#625C2311yescharacteristic
75C2×#625C2311yescharacteristic
76C2×#625C2311yescharacteristic
77C2×D3×Dic3—21no—
78C2×D3×Dic3—21no—
79C2×D3×Dic3—21no—
80C2×#622C2311yescharacteristic
81C2×#622C2311yescharacteristic
82C2×#622C2311yescharacteristic
83C2×#622C2311yescharacteristic
84#3774—22no—
85#3774—22no—
86#3774—22no—
87#3774—22no—
88C32×C22⋊C4D411yescharacteristic
89#3757D411yescharacteristic
90#3750D411yescharacteristic
91#3750D411yescharacteristic
92C4×C3⋊Dic3C2311yescharacteristic
93C4×C3⋊Dic3C2311yescharacteristic
94C3×#217—21no—
95C3×(C2×D3)⋊C4—21no—
96C3×(C2×D3)⋊C4—21no—
97C3×(C2×D3)⋊C4—21no—
98C3×Dic3⋊C4—21no—
99#3724C2311yescharacteristic
100#3724C2311yescharacteristic
101#3724C2311yescharacteristic
102#3724C2311yescharacteristic
103Dic3⋊Dic3—21no—
104(C2×D3)⋊Dic3—21no—
105(C2×D3)⋊Dic3—21no—
106(C2×D3)⋊Dic3—21no—
107(C2×D3)⋊Dic3—21no—
108(C2×D3)⋊Dic3—21no—
109Dic32—21no—
110#3122—91nomaximal, Sylow
111C22×#67—61no—
112C3×#121—61no—
113C2×C3×C22⋊C4—61no—
114C2×#217—61no—
115#940—61no—
116#939—61no—
117#939—61no—
118#939—61no—
119#938—61no—
120#935—61no—
121#929—61no—
122C4×#67—61no—
123C4×#67—61no—
124C4×#67—61no—
125C4×#67—61no—
126C4×#67—61no—
127#894—61no—
128#889—61no—
129#884—21no—
130#883—61no—
131#67⋊C4—61no—
132#67⋊C4—61no—
133#67⋊C4—61no—
134#67⋊C4—61no—
135#67⋊C4—61no—
136D3×C22⋊C4—21no—
137D3×C22⋊C4—61no—
138#877—61no—
139#877—61no—
140#877—61no—
141C23×C32C2×D411yescharacteristic
142C22×C3×D3—21no—
143C22×C3×D3—21no—
144C22×C3×D3—24no—
145C22×C3×D3—21no—
146C22×C3×D3—21no—
147C22×C3×D3—81no—
148C22×C3×D3—81no—
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4C2×D411yescharacteristic
151C2×C3⋊Dic3—21no—
152C2×C3⋊Dic3—21no—
153C2×C3⋊Dic3C2×D411yescharacteristic
154C2×C3⋊Dic3C2×D411yescharacteristic
155C2×C3⋊Dic3C2×D411yescharacteristic
156C2×C3⋊Dic3C2411yescharacteristic
157C3×#67—81no—
158C3×#67—81no—
159C2×C3×Dic3—21no—
160C2×C3×Dic3—21no—
161C2×C3×Dic3—21no—
162C2×C3×Dic3—21no—
163C3×D12—81no—
164C3×C4×D3—81no—
165C3×C4×D3—81no—
166C3×C4×D3—81no—
167#625—24no—
168#625—21no—
169#625—21no—
170#625—21no—
171#625—21no—
172#625—21no—
173#625—21no—
174#625—81no—
175#625#4112yes—
176#625#4112yes—
177D3×Dic3—81no—
178D3×Dic3—81no—
179D3×Dic3—81no—
180#622—21no—
181#622—21no—
182#622—21no—
183#622—21no—
184#540—91no—
185#518—91no—
186#482—91no—
187#482—91no—
188#478—91no—
189#478—91no—
190#459—91no—
191#459—91no—
192#447—91no—
193#447—91no—
194#442—91no—
195#442—91no—
196C4×D8—91no—
197C4×D8—91no—
198#433—91no—
199C24×C3—61no—
200C23×D3—21no—
201C2×C3×D4—61no—
202C2×C3×D4—61no—
203C2×C3×D4—61no—
204C22×C3×C4—61no—
205C22×C3×C4—61no—
206C22×C3×C4—61no—
207C2×#67—21no—
208C2×#67—21no—
209C2×#67—61no—
210C2×#67—61no—
211C2×#67—61no—
212C2×#67—61no—
213C2×#67—61no—
214C2×#67—61no—
215C2×#67—64no—
216C2×#67—64no—
217C2×#67—61no—
218C2×#67—61no—
219C22×Dic3—61no—
220C22×Dic3—61no—
221C22×Dic3—61no—
222C22×Dic3—61no—
223C22×Dic3—61no—
224C2×D12—21no—
225C2×C4×D3—21no—
226C2×C4×D3—21no—
227C2×C4×D3—21no—
228C2×C4×D3—61no—
229C2×C4×D3—61no—
230C2×C4×D3—61no—
231C3×C4⋊C4—61no—
232C3×C22⋊C4—21no—
233C3×C22⋊C4—21no—
234C3×C22⋊C4—61no—
235C3×C22⋊C4—61no—
236C3×C22⋊C4—61no—
237C3×C22⋊C4—61no—
238#217—21no—
239#217—61no—
240#217—61no—
241#217—61no—
242#217—61no—
243#217—61no—
244#217—61no—
245#217—61no—
246(C2×D3)⋊C4—21no—
247(C2×D3)⋊C4—21no—
248(C2×D3)⋊C4—21no—
249(C2×D3)⋊C4—61no—
250(C2×D3)⋊C4—61no—
251(C2×D3)⋊C4—61no—
252(C2×D3)⋊C4—61no—
253(C2×D3)⋊C4—61no—
254C4⋊Dic3—61no—
255Dic3⋊C4—21no—
256Dic3⋊C4—61no—
257Dic3⋊C4—61no—
258Dic3⋊C4—61no—
259Dic3⋊C4—61no—
260Dic3⋊C4—61no—
261Dic3⋊C4—61no—
262Dic3⋊C4—61no—
263Dic3⋊C4—61no—
264Dic3⋊C4—61no—
265C4×Dic3—61no—
266C4×Dic3—61no—
267C4×Dic3—61no—
268C4×Dic3—61no—
269C4×Dic3—61no—
270C4×Dic3—61no—
271C22×C32—21no—
272C22×C32—21no—
273C22×C32—21no—
274C22×C32C22×D411yescharacteristic
275C2×C3×D3—22no—
276C2×C3×D3—22no—
277C2×C3×D3—41no—
278C2×C3×D3—41no—
279C2×C3×D3—41no—
280C2×C3×D3—41no—
281C2×C3×D3—41no—
282C2×C3×D3—41no—
283C2×C3×D3—41no—
284C2×C3×D3—41no—
285C2×C3×D3—41no—
286C2×C3×D3—41no—
287C2×C3×D3—84no—
288C32×C4—21no—
289C32×C4—21no—
290C3⋊Dic3—21no—
291C3⋊Dic3—21no—
292C3⋊Dic3—21no—
293C3⋊Dic3C2×#4111yescharacteristic
294C3⋊Dic3C2×#4111yescharacteristic
295C3×Dic3—41no—
296C3×Dic3—41no—
297C3×Dic3—41no—
298C3×Dic3—41no—
299C22×D4—91no—
300C2×D8—91no—
301C2×D8—91no—
302C2×D8—91no—
303C2×D8—91no—
304#127—91no—
305#125—91no—
306#123—181no—
307#123—181no—
308#121—61no—
309#121—91no—
310#121—91no—
311#121—181no—
312C4×D4—91no—
313C4×D4—91no—
314C4×D4—91no—
315C4×D4—91no—
316C4×D4—91no—
317C4×D4—91no—
318C4×D4—181no—
319C4×D4—181no—
320#117—91no—
321#117—91no—
322C2×C22⋊C4—61no—
323C2×C22⋊C4—181no—
324#107—91no—
325#107—91no—
326#106—91no—
327#106—91no—
328C4⋊C8—91no—
329C4⋊C8—91no—
330#102—91no—
331#102—91no—
332#102—91no—
333#102—91no—
334#102—91no—
335#102—91no—
336#102—91no—
337#102—91no—
338C22⋊C8—91no—
339C22⋊C8—91no—
340#97—91no—
341C4×C8—91no—
342C23×C3—21no—
343C23×C3—21no—
344C23×C3—61no—
345C23×C3—61no—
346C23×C3—64no—
347C23×C3—61no—
348C23×C3—61no—
349C23×C3—241no—
350C23×C3—241no—
351C22×D3—21no—
352C22×D3—21no—
353C22×D3—24no—
354C22×D3—21no—
355C22×D3—21no—
356C22×D3—81no—
357C22×D3—81no—
358C3×D4—241no—
359C3×D4—241no—
360C3×D4—241no—
361C2×C3×C4—21no—
362C2×C3×C4—21no—
363C2×C3×C4—21no—
364C2×C3×C4—21no—
365C2×C3×C4—61no—
366C2×C3×C4—61no—
367C2×C3×C4—61no—
368C2×C3×C4—61no—
369C2×C3×C4—241no—
370C2×C3×C4—241no—
371C2×C3×C4—241no—
372#67—62no—
373#67—62no—
374#67—62no—
375#67—62no—
376#67—64no—
377#67—64no—
378#67—81no—
379#67—81no—
380#67—121no—
381#67—121no—
382#67—121no—
383#67—121no—
384#67—241no—
385#67—241no—
386C2×Dic3—21no—
387C2×Dic3—21no—
388C2×Dic3—21no—
389C2×Dic3—21no—
390C2×Dic3—61no—
391C2×Dic3—61no—
392C2×Dic3—61no—
393C2×Dic3—61no—
394C2×Dic3—61no—
395C2×Dic3—61no—
396C2×Dic3—61no—
397C2×Dic3—61no—
398C2×Dic3—62no—
399C2×Dic3—62no—
400C2×Dic3—121no—
401C2×Dic3—121no—
402C2×Dic3—241no—
403C2×Dic3—241no—
404C2×Dic3—241no—
405D12—81no—
406C4×D3—81no—
407C4×D3—81no—
408C4×D3—81no—
409C4×D3—241no—
410C4×D3—241no—
411C4×D3—241no—
412C2×C32—41no—
413C2×C32#52511yescharacteristic
414C2×C32#57611yescharacteristic
415C2×C32#57611yescharacteristic
416C3×D3—42no—
417C3×D3—42no—
418C3×D3—81no—
419C3×D3—81no—
420C24—61no—
421C2×D4—61no—
422C2×D4—61no—
423C2×D4—61no—
424C2×D4—91no—
425C2×D4—91no—
426C2×D4—91no—
427C2×D4—91no—
428C2×D4—181no—
429C2×D4—181no—
430C2×D4—182no—
431C2×D4—182no—
432C22×C4—61no—
433C22×C4—61no—
434C22×C4—61no—
435C22×C4—91no—
436C22×C4—181no—
437C22×C4—181no—
438C22×C4—181no—
439D8—182no—
440D8—182no—
441D8—182no—
442D8—182no—
443C2×C8—91no—
444C2×C8—91no—
445C2×C8—91no—
446C2×C8—91no—
447C4⋊C4—61no—
448C4⋊C4—91no—
449C4⋊C4—91no—
450C4⋊C4—91no—
451C4⋊C4—91no—
452C4⋊C4—91no—
453C4⋊C4—91no—
454C4⋊C4—181no—
455C22⋊C4—61no—
456C22⋊C4—61no—
457C22⋊C4—61no—
458C22⋊C4—61no—
459C22⋊C4—91no—
460C22⋊C4—181no—
461C22⋊C4—181no—
462C22⋊C4—181no—
463C22⋊C4—181no—
464C22⋊C4—181no—
465C22⋊C4GO+(4,𝔽2)11yescharacteristic
466C42—91no—
467C42—91no—
468C42—181no—
469C22×C3—22no—
470C22×C3—21no—
471C22×C3—21no—
472C22×C3—41no—
473C22×C3—41no—
474C22×C3—41no—
475C22×C3—41no—
476C22×C3—41no—
477C22×C3—62no—
478C22×C3—62no—
479C22×C3—121no—
480C22×C3—121no—
481C22×C3—121no—
482C22×C3—121no—
483C22×C3—121no—
484C22×C3—121no—
485C22×C3—121no—
486C22×C3—121no—
487C22×C3—121no—
488C22×C3—121no—
489C22×C3—244no—
490C2×D3—22no—
491C2×D3—22no—
492C2×D3—41no—
493C2×D3—41no—
494C2×D3—41no—
495C2×D3—41no—
496C2×D3—41no—
497C2×D3—41no—
498C2×D3—41no—
499C2×D3—41no—
500C2×D3—41no—
501C2×D3—41no—
502C2×D3—84no—
503C3×C4—41no—
504C3×C4—41no—
505C3×C4—41no—
506C3×C4—41no—
507C3×C4—121no—
508C3×C4—121no—
509C3×C4—121no—
510C3×C4—121no—
511Dic3—41no—
512Dic3—41no—
513Dic3—41no—
514Dic3—41no—
515Dic3—61no—
516Dic3—61no—
517Dic3—61no—
518Dic3—61no—
519Dic3—62no—
520Dic3—121no—
521Dic3—121no—
522Dic3—121no—
523Dic3—121no—
524Dic3—121no—
525C32#312211yescharacteristic, complemented, Sylow
526C23—64no—
527C23—61no—
528C23—61no—
529C23—61no—
530C23—61no—
531C23—241no—
532C23—241no—
533C23C2×GO+(4,𝔽2)11yescharacteristic
534D4—92no—
535D4—92no—
536D4—181no—
537D4—181no—
538D4—181no—
539D4—181no—
540D4—181no—
541D4—181no—
542D4—184no—
543D4—241no—
544D4—241no—
545D4—241no—
546D4—721no—
547C2×C4—61no—
548C2×C4—61no—
549C2×C4—61no—
550C2×C4—61no—
551C2×C4—91no—
552C2×C4—91no—
553C2×C4—91no—
554C2×C4—91no—
555C2×C4—181no—
556C2×C4—181no—
557C2×C4—241no—
558C2×C4—241no—
559C2×C4—241no—
560C2×C4—721no—
561C2×C4—721no—
562C2×C4—721no—
563C2×C4C2×GO+(4,𝔽2)11yescharacteristic
564C2×C4C2×GO+(4,𝔽2)11yescharacteristic
565C8—181no—
566C8—181no—
567C8—181no—
568C8—181no—
569C2×C3—21no—
570C2×C3—21no—
571C2×C3—21no—
572C2×C3—21no—
573C2×C3—21no—
574C2×C3—21no—
575C2×C3—42no—
576C2×C3—81no—
577C2×C3—122no—
578C2×C3—122no—
579C2×C3—241no—
580C2×C3—241no—
581D3—42no—
582D3—42no—
583D3—81no—
584D3—81no—
585C22—21no—
586C22—21no—
587C22—21no—
588C22—62no—
589C22—62no—
590C22—121no—
591C22—121no—
592C22—121no—
593C22—121no—
594C22—121no—
595C22—121no—
596C22—121no—
597C22—121no—
598C22—121no—
599C22—121no—
600C22—244no—
601C22C22×GO+(4,𝔽2)11yescharacteristic
602C4—21no—
603C4—21no—
604C4—91no—
605C4—91no—
606C4—121no—
607C4—121no—
608C4—121no—
609C4—121no—
610C4—181no—
611C4—181no—
612C4—181no—
613C3—21no—
614C3—21no—
615C2—41no—
616C2—122no—
617C2—122no—
618C2—241no—
619C2—241no—
620C2#1059651011yescharacteristic
621C2#1059651411yescharacteristic
622C2#1059651411yescharacteristic
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FittingC32×C22⋊C4D4
socleC22×C32C22×D4
hypercenterC22⋊C4GO+(4,𝔽2)
hypocenterC32#3122
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #10594223C2semidirect
2. #10594181C2semidirect
3. #10593744C2semidirect
4. #10593519C2semidirect
5. #10593519C2semidirect
6. #10593494C2semidirect
7. #10593494C2semidirect
8. #10593426C2semidirect
9. #10593420C2semidirect
10. #10593419C2semidirect
11. #10593419C2semidirect
12. #10593417C2semidirect
13. C4×#3774C2semidirect
14. #10593364C2semidirect
15. #10593350C2semidirect
29. #63914C22semidirect
33. #63902C22semidirect
36. C4×#625C22semidirect
40. #63870C22semidirect
43. #63779C22semidirect
44. #63777C22semidirect
45. C4⋊#622C22semidirect
46. C4×#622C22semidirect
47. #63743C22semidirect
48. #63743C22semidirect
49. #63742C22semidirect
50. #63742C22semidirect
55. #63739C22semidirect
56. #63739C22semidirect
57. #63739C22semidirect
58. #63739C22semidirect
525. C32#3122semidirect

Maximal subgroups

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

subgroupindex
#105942232
#105941812
#105937442
#105935192
#105934942
#105934262
#105934202
#105934192
#105934172
C4×#37742
#105933642
#105933502
#31229