Finite Group Databasebeta

← #11778446

Subgroups — #11778446

Order 1152.

733 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 733 conjugacy classes of subgroups — too many to draw. Only its 82 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#10596076C211yesmaximal, characteristic
2C3×#5033C211yesmaximal, characteristic, complemented
3#10591326C211yesmaximal, characteristic, complemented
4#10591133C211yesmaximal, characteristic, complemented
5C3×#4537C211yesmaximal, characteristic, complemented
6#10589151C211yesmaximal, characteristic, complemented
7#10589146C211yesmaximal, characteristic, complemented
8#71164—31nomaximal
9#68288—31nomaximal
10C2×D4×C3⋊D3—21no—
11C32×#121C2211yescharacteristic
12#64148—21no—
13#64146—21no—
14#64139C2211yescharacteristic
15C2×#3752C2211yescharacteristic
16#64103—21no—
17#64092—21no—
18#64091—21no—
19C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
20C2×#3722—21no—
21C3×#832—21no—
22C3×C3⋊#95C2211yescharacteristic, complemented
23C3×#830C2211yescharacteristic, complemented
24C3×#830C2211yescharacteristic, complemented
25C3×#807—21no—
26#63579—21no—
27#63575—21no—
28#63564—21no—
29#5605—31no—
30#5605—31no—
31#5605—61no—
32C3×#480—31no—
33#5033D311yescharacteristic, complemented
34#4992—31no—
35#4967—31no—
36#4736—31no—
37#4674—31no—
38C3×#327—31no—
39#4537D311yescharacteristic, complemented
40#4470—31no—
41#4468—31no—
42#4468—31no—
43#4451—31no—
44C23×C3⋊D3—21no—
45C23×C3⋊D3D411yescharacteristic
46C2×C32×D4—21no—
47C2×C32×D4D411yescharacteristic
48C22×C32×C4C2311yescharacteristic
49C2×#638—21no—
50C2×#638—21no—
51C2×#638—21no—
52C22×C3⋊Dic3D411yescharacteristic
53D4×C3⋊D3—42no—
54D4×C3⋊D3—42no—
55C2×C4⋊(C3⋊D3)—21no—
56C2×C4⋊(C3⋊D3)D411yescharacteristic
57C2×C4×C3⋊D3—21no—
58C22×C3×Dic3—21no—
59C22×C3×Dic3—21no—
60C32×C4⋊C4D411yescharacteristic
61C32×C22⋊C4—21no—
62#3757—21no—
63#3752—21no—
64#3752—21no—
65#3752—21no—
66#3752—21no—
67C4⋊(C3⋊Dic3)D411yescharacteristic
68#3750—21no—
69C3×C4⋊Dic3—21no—
70C3×C4⋊Dic3—21no—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
73#3722—42no—
74#1607—91noSylow
75C2×D3×D4—61no—
76C2×D3×D4—61no—
77C2×D3×D4—62no—
78C3×#121—21no—
79C3×#121C2×D311yescharacteristic
80C3×#121C2×D311yescharacteristic
81C2×C3×C4⋊C4—31no—
82#939—61no—
83#939—61no—
84#939—62no—
85#937—62no—
86#937—61no—
87#937—61no—
88#930—31no—
89#930—31no—
90#930—61no—
91C2×(C2×D3)⋊C4—31no—
92C2×(C2×D3)⋊C4—31no—
93C2×(C2×D3)⋊C4—61no—
94C2×(C2×D3)⋊C4—61no—
95C2×(C2×D3)⋊C4—61no—
96C2×C4⋊Dic3C2×D311yescharacteristic, complemented
97#894—62no—
98#894—61no—
99#894—61no—
100#883—61no—
101#883—61no—
102#883—62no—
103#882—61no—
104#882—61no—
105#882—62no—
106C3×#107—61no—
107C3×#102—61no—
108C3×C22⋊C8—31no—
109C3×C22⋊C8—31no—
110C3×#95—31no—
111#832—21no—
112C3⋊#95—61no—
113C3⋊#95—61no—
114C3⋊#95C2×D311yescharacteristic, complemented
115#830C2×D311yescharacteristic, complemented
116#830C2×D311yescharacteristic, complemented
117#821—61no—
118#818—61no—
119#809—61no—
120#807—21no—
121#807—61no—
122C23×C32—21no—
123C23×C32C2×D411yescharacteristic
124C22×C3⋊D3—21no—
125C22×C3⋊D3—21no—
126C22×C3⋊D3—21no—
127C22×C3⋊D3—42no—
128C22×C3⋊D3—41no—
129C22×C3⋊D3—41no—
130C22×C3⋊D3—81no—
131C22×C3⋊D3—81no—
132C22×C3⋊D3D812yes—
133C32×D4—41no—
134C32×D4—41no—
135C32×D4—41no—
136C2×C32×C4—21no—
137C2×C32×C4—41no—
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140#638—42no—
141#638—41no—
142#638—41no—
143#638—81no—
144C2×C3⋊Dic3—21no—
145C2×C3⋊Dic3—21no—
146C2×C3⋊Dic3—41no—
147C4⋊(C3⋊D3)—42no—
148C4⋊(C3⋊D3)—41no—
149C4×C3⋊D3—42no—
150C2×C3×Dic3—41no—
151C2×C3×Dic3—41no—
152C2×C3×Dic3—41no—
153C2×C3×Dic3—41no—
154C2×C3×Dic3—41no—
155C2×C3×Dic3—41no—
156C3×C3⋊C8—41no—
157C3×C3⋊C8—41no—
158#534—91no—
159#480—31no—
160#480—91no—
161#397—91no—
162#327—31no—
163#327—91no—
164#323—91no—
165C23×D3—31no—
166C23×D3—31no—
167C23×D3—61no—
168C23×D3—62no—
169C23×D3—61no—
170C23×D3—61no—
171C2×C3×D4—22no—
172C2×C3×D4—21no—
173C2×C3×D4—21no—
174C2×C3×D4—21no—
175C2×C3×D4D1211yescharacteristic
176C2×C3×D4#6711yescharacteristic
177C22×C3×C4—21no—
178C22×C3×C4—61no—
179C22×C3×C4—61no—
180C22×C3×C4C22×D311yescharacteristic
181C22×C3×C4C22×D311yescharacteristic
182C2×#67—62no—
183C2×#67—61no—
184C2×#67—61no—
185C2×#67—62no—
186C2×#67—61no—
187C2×#67—61no—
188C2×#67—62no—
189C2×#67—61no—
190C2×#67—61no—
191C22×Dic3—21no—
192C22×Dic3—21no—
193C22×Dic3—31no—
194C22×Dic3—31no—
195C22×Dic3—61no—
196D3×D4—122no—
197D3×D4—122no—
198D3×D4—124no—
199D3×D4—124no—
200D3×D4—122no—
201D3×D4—122no—
202C2×D12—31no—
203C2×D12—31no—
204C2×D12—61no—
205C2×D12—62no—
206C2×D12—61no—
207C2×D12—61no—
208C2×C4×D3—62no—
209C2×C4×D3—61no—
210C2×C4×D3—61no—
211C2×C3×C8—61no—
212C2×C3×C8—61no—
213C3×C4⋊C4—21no—
214C3×C4⋊C4—61no—
215C3×C4⋊C4—61no—
216C3×C4⋊C4D1211yescharacteristic
217C3×C4⋊C4#6711yescharacteristic
218C3×C22⋊C4—22no—
219C3×C22⋊C4—21no—
220C3×C22⋊C4—21no—
221#217—62no—
222#217—61no—
223#217—61no—
224(C2×D3)⋊C4—62no—
225(C2×D3)⋊C4—62no—
226(C2×D3)⋊C4—61no—
227(C2×D3)⋊C4—61no—
228(C2×D3)⋊C4—62no—
229(C2×D3)⋊C4—62no—
230(C2×D3)⋊C4—61no—
231(C2×D3)⋊C4—61no—
232(C2×D3)⋊C4—61no—
233(C2×D3)⋊C4—61no—
234(C2×D3)⋊C4—61no—
235(C2×D3)⋊C4—61no—
236(C2×D3)⋊C4—122no—
237(C2×D3)⋊C4—122no—
238C4⋊Dic3—21no—
239C4⋊Dic3—21no—
240C4⋊Dic3—31no—
241C4⋊Dic3—31no—
242C4⋊Dic3—61no—
243Dic3⋊C4—62no—
244Dic3⋊C4—61no—
245Dic3⋊C4—61no—
246C2×C3⋊C8—21no—
247C2×C3⋊C8—21no—
248C22×C32—21no—
249C22×C32—21no—
250C22×C32—41no—
251C22×C32—41no—
252C22×C32—41no—
253C22×C32#12011yescharacteristic
254C22×C32C2×D811yescharacteristic
255C22×C32AGL(1,ℤ/8)11yescharacteristic
256C2×C3⋊D3—22no—
257C2×C3⋊D3—41no—
258C2×C3⋊D3—41no—
259C2×C3⋊D3—41no—
260C2×C3⋊D3—41no—
261C2×C3⋊D3—41no—
262C2×C3⋊D3—42no—
263C2×C3⋊D3—81no—
264C2×C3⋊D3—84no—
265C32×C4—21no—
266C32×C4—21no—
267C32×C4—41no—
268C3⋊Dic3—41no—
269C3⋊Dic3—41no—
270C3×Dic3—81no—
271C3×Dic3—81no—
272C22×D4—181no—
273#123—181no—
274#123—181no—
275#121—91no—
276#121—181no—
277#121D3211yescharacteristic
278#120—181no—
279#120—181no—
280C2×C4⋊C4—31no—
281C2×C22⋊C4—91no—
282C2×C22⋊C4—181no—
283#107—61no—
284#107—181no—
285#102—61no—
286#102—181no—
287C22⋊C8—31no—
288C22⋊C8—31no—
289#95—31no—
290#95—181no—
291C23×C3—22no—
292C23×C3—21no—
293C23×C3—21no—
294C23×C3—21no—
295C23×C3D3×D411yescharacteristic
296C23×C3D3×D411yescharacteristic
297C22×D3—32no—
298C22×D3—32no—
299C22×D3—62no—
300C22×D3—62no—
301C22×D3—61no—
302C22×D3—61no—
303C22×D3—62no—
304C22×D3—61no—
305C22×D3—61no—
306C22×D3—62no—
307C22×D3—61no—
308C22×D3—61no—
309C22×D3—124no—
310C22×D3—122no—
311C22×D3—122no—
312C22×D3—121no—
313C22×D3—121no—
314C22×D3—121no—
315C22×D3—121no—
316C22×D3—241no—
317C22×D3—241no—
318C22×D3—242no—
319C22×D3—242no—
320C22×D3—241no—
321C22×D3—241no—
322C22×D3—241no—
323C22×D3—241no—
324C3×D4—41no—
325C3×D4—41no—
326C3×D4—42no—
327C3×D4—42no—
328C3×D4—41no—
329C3×D4—41no—
330C3×D4—41no—
331C3×D4—41no—
332C3×D4—81no—
333C2×C3×C4—22no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—41no—
339C2×C3×C4—41no—
340C2×C3×C4—81no—
341C2×C3×C4—121no—
342C2×C3×C4—121no—
343C2×C3×C4—121no—
344C2×C3×C4—121no—
345C2×C3×C4—121no—
346C2×C3×C4—121no—
347C2×C3×C4C2×D1211yescharacteristic
348C2×C3×C4D3×D411yescharacteristic
349C2×C3×C4D3×D411yescharacteristic
350C2×C3×C4C2×#6711yescharacteristic
351#67—124no—
352#67—122no—
353#67—122no—
354#67—122no—
355#67—122no—
356#67—121no—
357#67—121no—
358#67—121no—
359#67—121no—
360#67—242no—
361#67—241no—
362#67—241no—
363C2×Dic3—41no—
364C2×Dic3—41no—
365C2×Dic3—41no—
366C2×Dic3—41no—
367C2×Dic3—41no—
368C2×Dic3—41no—
369C2×Dic3—62no—
370C2×Dic3—62no—
371C2×Dic3—61no—
372C2×Dic3—61no—
373C2×Dic3—61no—
374C2×Dic3—61no—
375C2×Dic3—121no—
376C2×Dic3—121no—
377C2×Dic3—241no—
378D12—121no—
379D12—121no—
380D12—124no—
381D12—122no—
382D12—122no—
383D12—241no—
384C4×D3—124no—
385C4×D3—122no—
386C4×D3—122no—
387C3×C8—121no—
388C3×C8—121no—
389C3⋊C8—41no—
390C3⋊C8—41no—
391C2×C32—21no—
392C2×C32—21no—
393C2×C32—81no—
394C2×C32#44711yescharacteristic
395C2×C32#45511yescharacteristic
396C2×C32#45811yescharacteristic
397C3⋊D3—42no—
398C3⋊D3—81no—
399C24—91no—
400C24—181no—
401C2×D4—21no—
402C2×D4—91no—
403C2×D4—181no—
404C2×D4—181no—
405C2×D4—181no—
406C2×D4—181no—
407C2×D4—362no—
408C2×D4—362no—
409C2×D4#62611yescharacteristic
410C22×C4—61no—
411C22×C4—61no—
412C22×C4—91no—
413C22×C4—181no—
414C22×C4C2×D3211yescharacteristic
415C2×C8—61no—
416C2×C8—61no—
417C4⋊C4—61no—
418C4⋊C4—61no—
419C4⋊C4—91no—
420C4⋊C4—181no—
421C4⋊C4#62611yescharacteristic
422C22⋊C4—21no—
423C22⋊C4—181no—
424C22⋊C4—181no—
425C22⋊C4—181no—
426C22⋊C4—181no—
427C22⋊C4—181no—
428C22⋊C4—362no—
429C22×C3—21no—
430C22×C3—21no—
431C22×C3—21no—
432C22×C3—21no—
433C22×C3—21no—
434C22×C3—21no—
435C22×C3—21no—
436C22×C3—41no—
437C22×C3—41no—
438C22×C3—42no—
439C22×C3—42no—
440C22×C3—42no—
441C22×C3—41no—
442C22×C3—41no—
443C22×C3—41no—
444C22×C3—41no—
445C22×C3—41no—
446C22×C3—41no—
447C22×C3#88211yescharacteristic
448C22×C3D3×D811yescharacteristic
449C22×C3D3×D811yescharacteristic
450C22×C3#91111yescharacteristic
451C22×C3#91411yescharacteristic
452C22×C3#93711yescharacteristic
453C2×D3—64no—
454C2×D3—62no—
455C2×D3—62no—
456C2×D3—122no—
457C2×D3—122no—
458C2×D3—121no—
459C2×D3—121no—
460C2×D3—121no—
461C2×D3—121no—
462C2×D3—122no—
463C2×D3—122no—
464C2×D3—122no—
465C2×D3—122no—
466C2×D3—122no—
467C2×D3—121no—
468C2×D3—121no—
469C2×D3—121no—
470C2×D3—121no—
471C2×D3—121no—
472C2×D3—121no—
473C2×D3—242no—
474C2×D3—241no—
475C2×D3—241no—
476C2×D3—242no—
477C2×D3—248no—
478C2×D3—244no—
479C2×D3—244no—
480C3×C4—21no—
481C3×C4—21no—
482C3×C4—21no—
483C3×C4—21no—
484C3×C4—41no—
485C3×C4—41no—
486C3×C4—42no—
487C3×C4—41no—
488C3×C4—41no—
489C3×C4—241no—
490C3×C4—241no—
491Dic3—81no—
492Dic3—81no—
493Dic3—122no—
494Dic3—122no—
495Dic3—121no—
496Dic3—121no—
497Dic3—121no—
498Dic3—121no—
499C32#160711yescharacteristic, complemented, Sylow
500C23—21no—
501C23—92no—
502C23—181no—
503C23—181no—
504C23—181no—
505C23—361no—
506C23—361no—
507C23—362no—
508C23—721no—
509C23—721no—
510C23#381111yescharacteristic
511D4—41no—
512D4—41no—
513D4—41no—
514D4—361no—
515D4—362no—
516D4—362no—
517D4—361no—
518D4—361no—
519D4—721no—
520C2×C4—21no—
521C2×C4—41no—
522C2×C4—121no—
523C2×C4—121no—
524C2×C4—121no—
525C2×C4—121no—
526C2×C4—121no—
527C2×C4—121no—
528C2×C4—181no—
529C2×C4—181no—
530C2×C4—362no—
531C2×C4—361no—
532C2×C4C2×#62611yescharacteristic
533C2×C4#381111yescharacteristic
534C8—121no—
535C8—121no—
536C2×C3—21no—
537C2×C3—21no—
538C2×C3—21no—
539C2×C3—21no—
540C2×C3—21no—
541C2×C3—21no—
542C2×C3—21no—
543C2×C3—41no—
544C2×C3—41no—
545C2×C3—82no—
546C2×C3—81no—
547C2×C3—81no—
548C2×C3#474211yescharacteristic
549C2×C3#477311yescharacteristic
550C2×C3#482511yescharacteristic
551C2×C3#505311yescharacteristic
552C2×C3#515611yescharacteristic
553C2×C3#520211yescharacteristic
554D3—124no—
555D3—122no—
556D3—122no—
557D3—242no—
558D3—241no—
559D3—241no—
560C22—21no—
561C22—21no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—182no—
566C22—362no—
567C22—361no—
568C22—361no—
569C22—361no—
570C22—361no—
571C22—361no—
572C22—721no—
573C22—724no—
574C22#6392611yescharacteristic
575C22#6393711yescharacteristic
576C22#6398111yescharacteristic
577C4—21no—
578C4—21no—
579C4—41no—
580C4—241no—
581C4—241no—
582C4—361no—
583C4—361no—
584C3—21no—
585C3#6828811yescharacteristic, complemented
586C3#7116411yescharacteristic, complemented
587C2—21no—
588C2—21no—
589C2—81no—
590C2—362no—
591C2—721no—
592C2#1059145611yescharacteristic
593C2#1059153511yescharacteristic
594C2#1059169011yescharacteristic
subgroupG/H
centerC22#63981
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×#121C22
socleC22×C32#120
prime radical#10596076C2
hypercenter#121D32
hypocenterC32#1607
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
2. C3×#5033C2semidirect
3. #10591326C2semidirect
4. #10591133C2semidirect
5. C3×#4537C2semidirect
6. #10589151C2semidirect
7. #10589146C2semidirect
19. C2×C3×C4⋊Dic3C22semidirect
22. C3×C3⋊#95C22semidirect
23. C3×#830C22semidirect
24. C3×#830C22semidirect
33. #5033D3semidirect
39. #4537D3semidirect
96. C2×C4⋊Dic3C2×D3semidirect
114. C3⋊#95C2×D3semidirect
115. #830C2×D3semidirect
116. #830C2×D3semidirect
499. C32#1607semidirect
585. C3#68288semidirect
586. C3#71164semidirect

Maximal subgroups

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

subgroupindex
#105960762
C3×#50332
#105913262
#105911332
C3×#45372
#105891512
#105891462
#711643
#682883