Finite Group Databasebeta

← #11778453

Subgroups — #11778453

Order 1152.

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

normal subgroups only

This group has 605 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#10595072C211yesmaximal, characteristic
2C3×#4736C211yesmaximal, characteristic, complemented
3#10591314C211yesmaximal, characteristic, complemented
4#10591133C211yesmaximal, characteristic, complemented
5#10589336C211yesmaximal, characteristic, complemented
6C3×#4468C211yesmaximal, characteristic, complemented
7#10589150C211yesmaximal, characteristic, complemented
8#71164—31nomaximal
9#68110—31nomaximal
10C2×D3×#67—21no—
11#64139C2211yescharacteristic
12C3×#930C2211yescharacteristic
13C2×C3×(C2×D3)⋊C4C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
15#63978—21no—
16C2×(C2×D3)⋊Dic3—21no—
17#63923—21no—
18#63922—21no—
19#63891—21no—
20#63890—21no—
21C32×C22⋊C8C2211yescharacteristic, complemented
22#63658C2211yescharacteristic, complemented
23C3×#830C2211yescharacteristic, complemented
24C3×#821—21no—
25C3×#818—21no—
26#63579—21no—
27#63575—21no—
28#63564—21no—
29#5605—31no—
30#5493—31no—
31C3×#480—31no—
32#4992—31no—
33#4967—31no—
34#4953—31no—
35#4736—31no—
36#4736D311yescharacteristic, complemented
37C3×#323—31no—
38#4537—31no—
39#4470—31no—
40#4470—31no—
41#4470—31no—
42#4470—61no—
43#4468D311yescharacteristic, complemented
44C23×C3×D3D411yescharacteristic
45C22×D32—21no—
46C22×C32×C4C2311yescharacteristic
47C2×#638—21no—
48C22×C3⋊Dic3—21no—
49C2×C4⋊(C3⋊D3)D411yescharacteristic
50C2×C3×#67—21no—
51C22×C3×Dic3—21no—
52C22×C3×Dic3D411yescharacteristic
53C2×C3×D12D411yescharacteristic
54D3×#67—42no—
55D3×#67—42no—
56C2×#626—21no—
57C2×#626—21no—
58C2×#625—21no—
59C2×D3×Dic3—21no—
60C2×C32×C8—21no—
61#3752—21no—
62C4⋊(C3⋊Dic3)D411yescharacteristic
63C3×(C2×D3)⋊C4—21no—
64C3×(C2×D3)⋊C4—21no—
65C3×(C2×D3)⋊C4—21no—
66C3×C4⋊Dic3—21no—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3D411yescharacteristic
69C2×C3×C3⋊C8—21no—
70Dic3⋊Dic3—21no—
71#3722—21no—
72(C2×D3)⋊Dic3—21no—
73(C2×D3)⋊Dic3—42no—
74#1607—91noSylow
75C22×#67—61no—
76C2×D3×D4—61no—
77C3×#121—31no—
78C2×C3×C4⋊C4—31no—
79C2×C3×C22⋊C4—31no—
80C2×#217—61no—
81#939—61no—
82#937—61no—
83#930—31no—
84#930—31no—
85#930—61no—
86#930—61no—
87#930C2×D311yescharacteristic
88C2×(C2×D3)⋊C4—61no—
89C2×(C2×D3)⋊C4C2×D311yescharacteristic
90C2×C4⋊Dic3C2×D311yescharacteristic, complemented
91#894—61no—
92#886—61no—
93#886—61no—
94#883—61no—
95#882—61no—
96#882—61no—
97#882—61no—
98C3×#107—61no—
99C3×#102—61no—
100C3×C22⋊C8—21no—
101C3×C22⋊C8—31no—
102C3×C22⋊C8C2×D311yescharacteristic, complemented
103C3×C22⋊C8C2×D311yescharacteristic, complemented
104C3⋊#95—31no—
105C3⋊#95—31no—
106C3⋊#95—61no—
107C3⋊#95—61no—
108C3⋊#95—61no—
109#830C2×D311yescharacteristic, complemented
110#821—21no—
111#821—61no—
112#818—21no—
113#818—61no—
114#809—61no—
115#807—61no—
116C23×C32C2×D411yescharacteristic
117C22×C3⋊D3—21no—
118C22×C3×D3—21no—
119C22×C3×D3—21no—
120C22×C3×D3—21no—
121C22×C3×D3—41no—
122C22×C3×D3—41no—
123C22×C3×D3D812yes—
124C2×D32—42no—
125C2×D32—81no—
126C2×D32—81no—
127C2×C32×C4—41no—
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130#638—41no—
131#638—41no—
132C2×C3⋊Dic3—21no—
133C2×C3⋊Dic3—41no—
134C2×C3⋊Dic3—41no—
135C2×C3⋊Dic3—41no—
136C4⋊(C3⋊D3)—41no—
137C3×#67—41no—
138C3×#67—41no—
139C2×C3×Dic3—21no—
140C2×C3×Dic3—21no—
141C2×C3×Dic3—41no—
142C2×C3×Dic3—41no—
143C2×C3×Dic3—41no—
144C2×C3×Dic3—41no—
145C3×D12—41no—
146#626—42no—
147#626—81no—
148#625—42no—
149D3×Dic3—42no—
150C32×C8—41no—
151C3×C3⋊C8—41no—
152#534—91no—
153#480—31no—
154#480—91no—
155#397—91no—
156#327—91no—
157#327—91no—
158#323—31no—
159C24×C3—31no—
160C23×D3—61no—
161C23×D3—61no—
162C23×D3D1211yescharacteristic
163C2×C3×D4—31no—
164C2×C3×D4—61no—
165C22×C3×C4—21no—
166C22×C3×C4—31no—
167C22×C3×C4—61no—
168C22×C3×C4C22×D311yescharacteristic
169C22×C3×C4C22×D311yescharacteristic
170C2×#67—21no—
171C2×#67—61no—
172C2×#67—61no—
173C2×#67—61no—
174C2×#67—61no—
175C2×#67—61no—
176C2×#67—61no—
177C2×#67—121no—
178C2×#67—122no—
179C2×#67—122no—
180C22×Dic3—21no—
181C22×Dic3—61no—
182C22×Dic3—61no—
183C22×Dic3—61no—
184C22×Dic3—121no—
185C22×Dic3D1211yescharacteristic
186D3×D4—122no—
187D3×D4—122no—
188C2×D12—31no—
189C2×D12—31no—
190C2×D12—61no—
191C2×D12—61no—
192C2×D12—61no—
193C2×D12#6711yescharacteristic
194C2×C4×D3—61no—
195C2×C3×C8—21no—
196C2×C3×C8—21no—
197C2×C3×C8—41no—
198C2×C3×C8—61no—
199C3×C4⋊C4—31no—
200C3×C4⋊C4—61no—
201C3×C4⋊C4—61no—
202C3×C22⋊C4—61no—
203C3×C22⋊C4—61no—
204C3×C22⋊C4—61no—
205#217—61no—
206#217—122no—
207(C2×D3)⋊C4—21no—
208(C2×D3)⋊C4—21no—
209(C2×D3)⋊C4—21no—
210(C2×D3)⋊C4—61no—
211(C2×D3)⋊C4—61no—
212(C2×D3)⋊C4—61no—
213(C2×D3)⋊C4—61no—
214(C2×D3)⋊C4—61no—
215(C2×D3)⋊C4—121no—
216(C2×D3)⋊C4—122no—
217C4⋊Dic3—21no—
218C4⋊Dic3—21no—
219C4⋊Dic3—31no—
220C4⋊Dic3—31no—
221C4⋊Dic3—61no—
222C4⋊Dic3—61no—
223C4⋊Dic3#6711yescharacteristic
224Dic3⋊C4—61no—
225C2×C3⋊C8—21no—
226C22×C32—21no—
227C22×C32—21no—
228C22×C32#12011yescharacteristic
229C22×C32C2×D811yescharacteristic
230C22×C32AGL(1,ℤ/8)11yescharacteristic
231C2×C3⋊D3—41no—
232C2×C3⋊D3—41no—
233C2×C3⋊D3—41no—
234C2×C3×D3—22no—
235C2×C3×D3—41no—
236C2×C3×D3—41no—
237C2×C3×D3—42no—
238C2×C3×D3—41no—
239C2×C3×D3—41no—
240C2×C3×D3—41no—
241C2×C3×D3—81no—
242D32—84no—
243C32×C4—21no—
244C32×C4—21no—
245C3⋊Dic3—41no—
246C3⋊Dic3—81no—
247C3×Dic3—41no—
248C3×Dic3—41no—
249C3×Dic3—81no—
250C22×D4—181no—
251#123—181no—
252#123—181no—
253#121—31no—
254#121—91no—
255#121—181no—
256#120—181no—
257#120—181no—
258C2×C4⋊C4—31no—
259C2×C22⋊C4—31no—
260C2×C22⋊C4—181no—
261#107—61no—
262#107—181no—
263#102—61no—
264#102—181no—
265C22⋊C8—31no—
266C22⋊C8D3211yescharacteristic, complemented
267#95—91no—
268#95—181no—
269C23×C3—21no—
270C23×C3—32no—
271C23×C3—61no—
272C23×C3—61no—
273C23×C3—61no—
274C23×C3—121no—
275C23×C3—121no—
276C23×C3C2×D1211yescharacteristic
277C23×C3D3×D411yescharacteristic
278C22×D3—21no—
279C22×D3—21no—
280C22×D3—21no—
281C22×D3—41no—
282C22×D3—41no—
283C22×D3—61no—
284C22×D3—61no—
285C22×D3—121no—
286C22×D3—122no—
287C22×D3—122no—
288C22×D3—241no—
289C22×D3—241no—
290C22×D3—241no—
291C22×D3—241no—
292C22×D3D2412yes—
293C3×D4—121no—
294C3×D4—121no—
295C3×D4—121no—
296C2×C3×C4—21no—
297C2×C3×C4—21no—
298C2×C3×C4—41no—
299C2×C3×C4—41no—
300C2×C3×C4—61no—
301C2×C3×C4—61no—
302C2×C3×C4—81no—
303C2×C3×C4—121no—
304C2×C3×C4—121no—
305C2×C3×C4—121no—
306C2×C3×C4—121no—
307C2×C3×C4D3×D411yescharacteristic
308C2×C3×C4D3×D411yescharacteristic
309C2×C3×C4D3×D411yescharacteristic
310C2×C3×C4C2×#6711yescharacteristic
311#67—41no—
312#67—41no—
313#67—122no—
314#67—122no—
315#67—122no—
316#67—121no—
317#67—121no—
318#67—121no—
319#67—121no—
320#67—241no—
321#67—241no—
322#67—241no—
323C2×Dic3—21no—
324C2×Dic3—21no—
325C2×Dic3—41no—
326C2×Dic3—41no—
327C2×Dic3—41no—
328C2×Dic3—41no—
329C2×Dic3—61no—
330C2×Dic3—61no—
331C2×Dic3—121no—
332C2×Dic3—122no—
333C2×Dic3—121no—
334C2×Dic3—121no—
335C2×Dic3—121no—
336C2×Dic3—121no—
337C2×Dic3—122no—
338C2×Dic3—121no—
339C2×Dic3—121no—
340C2×Dic3—241no—
341C2×Dic3—241no—
342D12—41no—
343D12—121no—
344D12—121no—
345D12—122no—
346D12—241no—
347D12—241no—
348C4×D3—122no—
349C3×C8—41no—
350C3×C8—41no—
351C3×C8—81no—
352C3×C8—121no—
353C3⋊C8—41no—
354C2×C32—21no—
355C2×C32—21no—
356C2×C32#44711yescharacteristic
357C2×C32#45511yescharacteristic
358C2×C32#45811yescharacteristic
359C3⋊D3—81no—
360C3×D3—42no—
361C3×D3—81no—
362C24—31no—
363C24—181no—
364C2×D4—31no—
365C2×D4—61no—
366C2×D4—91no—
367C2×D4—181no—
368C2×D4—181no—
369C2×D4—181no—
370C2×D4—181no—
371C2×D4—362no—
372C2×D4—362no—
373C22×C4—31no—
374C22×C4—61no—
375C22×C4—181no—
376C22×C4—181no—
377C22×C4C2×D3211yescharacteristic
378C2×C8—21no—
379C2×C8—61no—
380C4⋊C4—31no—
381C4⋊C4—61no—
382C4⋊C4—61no—
383C4⋊C4—91no—
384C4⋊C4—181no—
385C22⋊C4—61no—
386C22⋊C4—61no—
387C22⋊C4—61no—
388C22⋊C4—181no—
389C22⋊C4—181no—
390C22⋊C4—181no—
391C22⋊C4—362no—
392C22×C3—21no—
393C22×C3—21no—
394C22×C3—21no—
395C22×C3—21no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—21no—
399C22×C3—41no—
400C22×C3—41no—
401C22×C3—62no—
402C22×C3—122no—
403C22×C3—121no—
404C22×C3—121no—
405C22×C3—121no—
406C22×C3—121no—
407C22×C3—121no—
408C22×C3—241no—
409C22×C3#88211yescharacteristic
410C22×C3C2×D2411yescharacteristic
411C22×C3#90811yescharacteristic
412C22×C3D3×D811yescharacteristic
413C22×C3#91111yescharacteristic
414C22×C3#93711yescharacteristic
415C2×D3—22no—
416C2×D3—41no—
417C2×D3—41no—
418C2×D3—42no—
419C2×D3—41no—
420C2×D3—41no—
421C2×D3—41no—
422C2×D3—81no—
423C2×D3—121no—
424C2×D3—121no—
425C2×D3—121no—
426C2×D3—121no—
427C2×D3—121no—
428C2×D3—121no—
429C2×D3—241no—
430C2×D3—241no—
431C2×D3—241no—
432C2×D3—244no—
433C2×D3—244no—
434C3×C4—21no—
435C3×C4—21no—
436C3×C4—21no—
437C3×C4—21no—
438C3×C4—41no—
439C3×C4—41no—
440C3×C4—121no—
441C3×C4—121no—
442C3×C4—241no—
443Dic3—41no—
444Dic3—41no—
445Dic3—81no—
446Dic3—121no—
447Dic3—121no—
448Dic3—241no—
449Dic3—241no—
450Dic3—241no—
451Dic3—242no—
452C32#160711yescharacteristic, complemented, Sylow
453C23—32no—
454C23—61no—
455C23—61no—
456C23—61no—
457C23—121no—
458C23—121no—
459C23—181no—
460C23—362no—
461C23—721no—
462C23—721no—
463C23D3×D1211yescharacteristic
464D4—121no—
465D4—121no—
466D4—121no—
467D4—361no—
468D4—362no—
469D4—362no—
470D4—361no—
471D4—361no—
472D4—721no—
473C2×C4—41no—
474C2×C4—61no—
475C2×C4—61no—
476C2×C4—121no—
477C2×C4—121no—
478C2×C4—121no—
479C2×C4—121no—
480C2×C4—181no—
481C2×C4—362no—
482C2×C4—361no—
483C2×C4—361no—
484C2×C4—361no—
485C2×C4#380211yescharacteristic
486C2×C4D3×#6711yescharacteristic
487C8—41no—
488C8—121no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3—21no—
495C2×C3—21no—
496C2×C3—41no—
497C2×C3—41no—
498C2×C3—122no—
499C2×C3—241no—
500C2×C3#473211yescharacteristic
501C2×C3#474211yescharacteristic
502C2×C3#474611yescharacteristic
503C2×C3#505311yescharacteristic
504C2×C3#515611yescharacteristic
505C2×C3#520211yescharacteristic
506D3—42no—
507D3—81no—
508D3—241no—
509D3—241no—
510D3—481no—
511C22—21no—
512C22—21no—
513C22—62no—
514C22—122no—
515C22—121no—
516C22—121no—
517C22—121no—
518C22—121no—
519C22—121no—
520C22—241no—
521C22—361no—
522C22—361no—
523C22—361no—
524C22—724no—
525C22D3×D2411yescharacteristic
526C22#6379511yescharacteristic
527C22#6392211yescharacteristic
528C4—21no—
529C4—21no—
530C4—121no—
531C4—121no—
532C4—241no—
533C4—361no—
534C4—721no—
535C3—21no—
536C3#6811011yescharacteristic, complemented
537C3#7116411yescharacteristic, complemented
538C2—21no—
539C2—21no—
540C2—122no—
541C2—241no—
542C2—721no—
543C2#1059040811yescharacteristic
544C2#1059094411yescharacteristic
545C2#1059101211yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32#120
prime radical#10595072C2
hypercenterC22⋊C8D32
hypocenterC32#1607
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C3×#4736C2semidirect
3. #10591314C2semidirect
4. #10591133C2semidirect
5. #10589336C2semidirect
6. C3×#4468C2semidirect
7. #10589150C2semidirect
14. C2×C3×C4⋊Dic3C22semidirect
21. C32×C22⋊C8C22semidirect
22. #63658C22semidirect
23. C3×#830C22semidirect
36. #4736D3semidirect
43. #4468D3semidirect
90. C2×C4⋊Dic3C2×D3semidirect
102. C3×C22⋊C8C2×D3semidirect
103. C3×C22⋊C8C2×D3semidirect
109. #830C2×D3semidirect
266. C22⋊C8D32semidirect
452. C32#1607semidirect
536. C3#68110semidirect
537. C3#71164semidirect

Maximal subgroups

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

subgroupindex
#105950722
C3×#47362
#105913142
#105911332
#105893362
C3×#44682
#105891502
#711643
#681103