Finite Group Databasebeta

← #11895967

Subgroups — #11895967

Order 1152.

864 conjugacy classes of subgroups.

The subgroup lattice has 551 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596038C211yesmaximal, characteristic, complemented
2C3×#5577C211yesmaximal, characteristic
3C3×#5024C211yesmaximal, characteristic, complemented
4#10590377C212yesmaximal, complemented
5#10590377C211yesmaximal, characteristic, complemented
6#10590360C212yesmaximal, complemented
7C4×#3716C211yesmaximal, characteristic, complemented
8#10590275C212yesmaximal, complemented
9#10590273C211yesmaximal, characteristic, complemented
10#10590272C211yesmaximal, characteristic, complemented
11#10590271C212yesmaximal, complemented
12#83587—31nomaximal
13#79980—31nomaximal
14C2×C3×#239—21no—
15C32×C4×Q8C2211yescharacteristic
16#64153—21no—
17#64098—22no—
18#64096—21no—
19#64079C2212yes—
20#64078C2211yescharacteristic
21C4×#634C2211yescharacteristic
22C4×#634C2212yes—
23C3×#895—21no—
24C3×#895—22no—
25C3×#874C2211yescharacteristic
26C3×#874C2212yes—
27C3×C4×D12C2212yes—
28C3×C4×D12C2211yescharacteristic
29C2×#3716C2211yescharacteristic
30C2×#3716C2212yes—
31C3×C4⋊(C3⋊C8)C2212yes—
32C3×C4⋊(C3⋊C8)C2211yescharacteristic
33C3×#803C2212yes—
34C3×C4×C3⋊C8C2211yescharacteristic
35#63575C2212yes—
36#63573C2211yescharacteristic
37#63567C2211yescharacteristic
38#63563C2212yes—
39#63563C2212yes—
40#63563C2212yes—
41#63563C2212yes—
42#63563C2211yescharacteristic
43C3×#550—31no—
44#5577D311yescharacteristic
45#5567—31no—
46#5567—31no—
47#5567—61no—
48C3×#446—31no—
49#5075—31no—
50#5075—32no—
51#5071—32no—
52#5070—31no—
53#5024D311yescharacteristic, complemented
54#5018—32no—
55C4×#214—31no—
56#5009—32no—
57#5007—31no—
58#4848—32no—
59#4848—31no—
60#4847—32no—
61#4846—31no—
62#4713—32no—
63#4710—32no—
64#4694—31no—
65C4×#204—31no—
66C2×C32×Q8D411yescharacteristic
67C2×#634—21no—
68C2×#634C2311yescharacteristic
69C3×#239—44no—
70C2×C3×D12—22no—
71C2×C3×D12—21no—
72C2×C3×D12—22no—
73C2×C3×D12—21no—
74C2×C3×D12C2312yes—
75C2×C3×D12C2311yescharacteristic
76C2×C3×C4×D3—22no—
77C2×C3×C4×D3—21no—
78C32×C4⋊C4D411yescharacteristic
79C32×C4⋊C4D412yes—
80C32×C42C2311yescharacteristic
81C32×C42C2312yes—
82C4⋊(C3⋊Dic3)—21no—
83C4⋊(C3⋊Dic3)C2312yes—
84C4⋊(C3⋊Dic3)C2311yescharacteristic
85#3750—21no—
86#3750—22no—
87#3750—22no—
88#3750—22no—
89C4×C3⋊Dic3—22no—
90C4×C3⋊Dic3—21no—
91C3×(C2×D3)⋊C4—22no—
92C3×(C2×D3)⋊C4—21no—
93C3×C4⋊Dic3C2311yescharacteristic
94C2×C3×C3⋊C8C2311yescharacteristic
95C2×C3×C3⋊C8C2311yescharacteristic
96C2×C3×C3⋊C8C2312yes—
97#3716—22no—
98#3716—24no—
99#3368—91noSylow
100C2×C3×#41—61no—
101C2×#239—21no—
102C3×#127—31no—
103C3×#127—32no—
104C3×#121—61no—
105C3×#121—62no—
106C3×C4×Q8—21no—
107C3×C4×Q8C2×D311yescharacteristic
108C3×C4×Q8C2×D311yescharacteristic
109C3×C4×D4—31no—
110C3×C4×D4—32no—
111#944—62no—
112#944—61no—
113#944—61no—
114C2×#214—31no—
115C2×#214—32no—
116C2×#204—31no—
117C2×#204—32no—
118#895—21no—
119#895—22no—
120#889—64no—
121#889—62no—
122#889—62no—
123#887—62no—
124#887—61no—
125#887—61no—
126#874C2×D311yescharacteristic
127#874C2×D312yes—
128C4×D12C2×D311yescharacteristic
129C4×D12C2×D312yes—
130#870—32no—
131#870—32no—
132#870—62no—
133#869—31no—
134#869—31no—
135#869—61no—
136C4×Dic6—31no—
137C4×Dic6—32no—
138C4×Dic6—31no—
139C4×Dic6—32no—
140C4×Dic6—61no—
141C4×Dic6—62no—
142C3×C4⋊C8—31no—
143C3×C4⋊C8—32no—
144C3×#97—32no—
145C3×C4×C8—31no—
146#832—32no—
147#832—32no—
148#832—32no—
149#832—31no—
150#832—32no—
151#821—31no—
152#821—32no—
153#821—32no—
154#821—32no—
155#821—32no—
156#818—32no—
157#817—31no—
158#816—31no—
159#810—31no—
160#808—31no—
161#807—32no—
162C4⋊(C3⋊C8)C2×D311yescharacteristic
163C4⋊(C3⋊C8)C2×D312yes—
164#803C2×D312yes—
165C4×C3⋊C8C2×D311yescharacteristic
166C22×C3×D3—22no—
167C22×C3×D3—21no—
168C32×Q8—22no—
169C2×C32×C4C2×D412yes—
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2×D412yes—
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2411yescharacteristic
174C2×C3⋊Dic3—21no—
175C2×C3⋊Dic3—21no—
176C2×C3⋊Dic3—22no—
177#634—21no—
178#634—42no—
179#634#4112yescomplemented
180C2×C3×Dic3—21no—
181C3×D12—21no—
182C3×D12—22no—
183C3×D12—22no—
184C3×D12—21no—
185C3×D12—44no—
186C3×D12—42no—
187C3×D12—82no—
188C3×D12—81no—
189C3×C4×D3—44no—
190C3×C4×D3—42no—
191C3×C3⋊C8—21no—
192C3×C3⋊C8—22no—
193C3×C3⋊C8—21no—
194#557—91no—
195#550—31no—
196#490—92no—
197#486—91no—
198#478—92no—
199#474—91no—
200#460—92no—
201#460—91no—
202#446—31no—
203#440—92no—
204C4×SD16—91no—
205C3×#41—124no—
206C2×C3×Q8—21no—
207C2×C3×Q8D1211yescharacteristic
208C2×C3×Q8#6711yescharacteristic
209C2×C3×D4—31no—
210C2×C3×D4—32no—
211C2×C3×D4—62no—
212C2×C3×D4—61no—
213C2×C3×D4—62no—
214C2×C3×D4—61no—
215C22×C3×C4—62no—
216C22×C3×C4—61no—
217#239—44no—
218C2×D12—22no—
219C2×D12—21no—
220C2×D12—22no—
221C2×D12—21no—
222C2×D12C22×D311yescharacteristic
223C2×D12C22×D312yes—
224C2×C4×D3—22no—
225C2×C4×D3—21no—
226C2×Dic6—31no—
227C2×Dic6—31no—
228C2×Dic6—61no—
229C2×Dic6—62no—
230C2×Dic6—61no—
231C2×Dic6—61no—
232C2×C3×C8—31no—
233C2×C3×C8—31no—
234C2×C3×C8—32no—
235C3×C4⋊C4—21no—
236C3×C4⋊C4—22no—
237C3×C4⋊C4—31no—
238C3×C4⋊C4D1211yescharacteristic
239C3×C4⋊C4D1212yes—
240C3×C4⋊C4#6711yescharacteristic
241C3×C4⋊C4#6712yes—
242C3×C22⋊C4—62no—
243C3×C22⋊C4—61no—
244C3×C42—21no—
245C3×C42—22no—
246C3×C42C22×D311yescharacteristic
247C3×C42C22×D312yes—
248C3×C42C22×D311yescharacteristic
249C3×C42C22×D312yes—
250#214—62no—
251#214—64no—
252(C2×D3)⋊C4—22no—
253(C2×D3)⋊C4—21no—
254C4⋊Dic3—32no—
255C4⋊Dic3—31no—
256C4⋊Dic3—31no—
257C4⋊Dic3—32no—
258C4⋊Dic3—62no—
259C4⋊Dic3—61no—
260C4⋊Dic3—62no—
261C4⋊Dic3—61no—
262C4⋊Dic3—61no—
263C4⋊Dic3C22×D311yescharacteristic
264Dic3⋊C4—62no—
265Dic3⋊C4—64no—
266Dic3⋊C4—64no—
267Dic3⋊C4—64no—
268Dic3⋊C4—61no—
269Dic3⋊C4—62no—
270Dic3⋊C4—62no—
271Dic3⋊C4—62no—
272Dic3⋊C4—61no—
273Dic3⋊C4—62no—
274Dic3⋊C4—62no—
275Dic3⋊C4—62no—
276C4×Dic3—64no—
277C4×Dic3—62no—
278C4×Dic3—62no—
279C4×Dic3—61no—
280C4×Dic3—62no—
281C4×Dic3—61no—
282C2×C3⋊C8C22×D311yescharacteristic
283C2×C3⋊C8C22×D311yescharacteristic
284C2×C3⋊C8C22×D312yes—
285#204—62no—
286#204—64no—
287C22×C32C22×D411yescharacteristic
288C2×C3×D3—42no—
289C2×C3×D3—41no—
290C2×C3×D3—42no—
291C2×C3×D3—41no—
292C2×C3×D3—42no—
293C2×C3×D3—41no—
294C32×C4—22no—
295C32×C4—22no—
296C32×C4—21no—
297C32×C4AGL(1,ℤ/8)12yes—
298C32×C4C2×#4111yescharacteristic
299C32×C42−1+411yescharacteristic
300C3⋊Dic3—22no—
301C3⋊Dic3—42no—
302C3⋊Dic3—41no—
303C3×Dic3—41no—
304C2×#41—61no—
305C2×SD16—91no—
306C2×SD16—92no—
307C4⋊Q8—91no—
308C4⋊Q8—181no—
309#127—31no—
310#127—32no—
311#125—92no—
312#125—182no—
313#121—61no—
314#121—62no—
315C4×Q8—91no—
316C4×Q8—92no—
317C4×Q8—181no—
318C4×Q8D3211yescharacteristic
319C4×D4—31no—
320C4×D4—32no—
321#107—92no—
322#106—91no—
323C4⋊C8—31no—
324C4⋊C8—32no—
325#103—91no—
326#102—91no—
327#102—92no—
328#102—92no—
329#102—92no—
330#102—92no—
331#97—32no—
332C4×C8—31no—
333C23×C3—62no—
334C23×C3—61no—
335C22×D3—22no—
336C22×D3—21no—
337C3×Q8—22no—
338C3×Q8—22no—
339C3×Q8—42no—
340C3×D4—61no—
341C3×D4—62no—
342C3×D4—61no—
343C3×D4—62no—
344C3×D4—124no—
345C3×D4—122no—
346C3×D4—242no—
347C3×D4—241no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—22no—
351C2×C3×C4—22no—
352C2×C3×C4—21no—
353C2×C3×C4—61no—
354C2×C3×C4—124no—
355C2×C3×C4—122no—
356C2×C3×C4C2×D1212yes—
357C2×C3×C4C2×D1212yes—
358C2×C3×C4C2×D1211yescharacteristic
359C2×C3×C4C2×D1211yescharacteristic
360C2×C3×C4C2×#6712yes—
361C2×C3×C4C2×#6712yes—
362C2×C3×C4C2×#6711yescharacteristic
363C2×C3×C4C2×#6711yescharacteristic
364C2×C3×C4C23×D311yescharacteristic
365C2×C3×C4C23×D311yescharacteristic
366C2×Dic3—21no—
367C2×Dic3—62no—
368C2×Dic3—61no—
369C2×Dic3—61no—
370C2×Dic3—62no—
371C2×Dic3—64no—
372C2×Dic3—61no—
373C2×Dic3—62no—
374C2×Dic3—61no—
375C2×Dic3—62no—
376D12—21no—
377D12—22no—
378D12—21no—
379D12—22no—
380D12—44no—
381D12—42no—
382D12—82no—
383D12—81no—
384C4×D3—44no—
385C4×D3—42no—
386Dic6—32no—
387Dic6—32no—
388Dic6—62no—
389Dic6—62no—
390Dic6—61no—
391Dic6—61no—
392Dic6—124no—
393Dic6—122no—
394Dic6—122no—
395C3×C8—61no—
396C3×C8—62no—
397C3×C8—61no—
398C3⋊C8—21no—
399C3⋊C8—21no—
400C3⋊C8—22no—
401C2×C32#54811yescharacteristic
402C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
403C2×C32#57711yescharacteristic
404C3×D3—82no—
405C3×D3—81no—
406#41—124no—
407C2×Q8—91no—
408C2×Q8—181no—
409C2×Q8#62611yescharacteristic
410C2×D4—31no—
411C2×D4—32no—
412C2×D4—62no—
413C2×D4—61no—
414C2×D4—62no—
415C2×D4—61no—
416C22×C4—62no—
417C22×C4—61no—
418SD16—182no—
419SD16—184no—
420C2×C8—31no—
421C2×C8—31no—
422C2×C8—32no—
423C4⋊C4—31no—
424C4⋊C4—91no—
425C4⋊C4—92no—
426C4⋊C4—181no—
427C4⋊C4—182no—
428C4⋊C4—182no—
429C4⋊C4—182no—
430C4⋊C4—181no—
431C4⋊C4#62611yescharacteristic
432C4⋊C4#62612yes—
433C22⋊C4—62no—
434C22⋊C4—61no—
435C42—182no—
436C42—181no—
437C42C2×D3211yescharacteristic
438C42C2×D3212yes—
439C22×C3—21no—
440C22×C3—122no—
441C22×C3—121no—
442C22×C3—122no—
443C22×C3—121no—
444C22×C3—122no—
445C22×C3—121no—
446C22×C3C22×D1211yescharacteristic
447C22×C3C22×#6711yescharacteristic
448C2×D3—42no—
449C2×D3—41no—
450C2×D3—42no—
451C2×D3—41no—
452C2×D3—42no—
453C2×D3—41no—
454C3×C4—22no—
455C3×C4—22no—
456C3×C4—21no—
457C3×C4—22no—
458C3×C4—22no—
459C3×C4—21no—
460C3×C4—21no—
461C3×C4—21no—
462C3×C4—22no—
463C3×C4—42no—
464C3×C4—42no—
465C3×C4—41no—
466C3×C4—121no—
467C3×C4#90812yes—
468C3×C4#93212yes—
469C3×C4#100711yescharacteristic
470C3×C4D3×#4111yescharacteristic
471C3×C4D3×#4111yescharacteristic
472C3×C4#101011yescharacteristic
473Dic3—41no—
474Dic3—64no—
475Dic3—62no—
476Dic3—62no—
477Dic3—124no—
478Dic3—122no—
479Dic3—122no—
480Dic3—121no—
481Dic3—122no—
482Dic3—121no—
483C32#336811yescharacteristic, complemented, Sylow
484C23—62no—
485C23—61no—
486Q8—22no—
487Q8—92no—
488Q8—181no—
489Q8—362no—
490D4—61no—
491D4—62no—
492D4—61no—
493D4—62no—
494D4—124no—
495D4—122no—
496D4—242no—
497D4—241no—
498C2×C4—61no—
499C2×C4—124no—
500C2×C4—122no—
501C2×C4—181no—
502C2×C4—181no—
503C2×C4—182no—
504C2×C4C2×#62612yes—
505C2×C4C2×#62611yescharacteristic
506C2×C4C2×#62612yes—
507C2×C4C2×#62611yescharacteristic
508C2×C4C22×D3211yescharacteristic
509C8—61no—
510C8—61no—
511C8—62no—
512C2×C3—21no—
513C2×C3—21no—
514C2×C3—21no—
515C2×C3—242no—
516C2×C3—241no—
517C2×C3#557611yescharacteristic
518C2×C3C2×#90811yescharacteristic
519C2×C3#575111yescharacteristic
520C2×C3C2×#93211yescharacteristic
521C2×C3#583111yescharacteristic
522C2×C3#583611yescharacteristic
523D3—82no—
524D3—81no—
525C22—122no—
526C22—121no—
527C22—122no—
528C22—121no—
529C22—122no—
530C22—121no—
531C22C22×#62611yescharacteristic
532C4—22no—
533C4—21no—
534C4—22no—
535C4—121no—
536C4—182no—
537C4—361no—
538C4—362no—
539C4#6383012yes—
540C4#6431511yescharacteristic
541C4#6431911yescharacteristic
542C3—21no—
543C3#7998011yescharacteristic, complemented
544C3#8358711yescharacteristic, complemented
545C2—242no—
546C2—241no—
547C2C2×#6383011yescharacteristic
548C2#1059541411yescharacteristic
549C2#1059544711yescharacteristic
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC3×#5577C2
hypercenterC4×Q8D32
hypocenterC32#3368
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #10596038C2semidirect
3. C3×#5024C2semidirect
4. #10590377C2semidirect
5. #10590377C2semidirect
6. #10590360C2semidirect
7. C4×#3716C2semidirect
8. #10590275C2semidirect
9. #10590273C2semidirect
10. #10590272C2semidirect
11. #10590271C2semidirect
53. #5024D3semidirect
179. #634#41semidirect
483. C32#3368semidirect
543. C3#79980semidirect
544. C3#83587semidirect

Maximal subgroups

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

subgroupindex
#105960382
C3×#55772
C3×#50242
#105903772
#105903602
C4×#37162
#105902752
#105902732
#105902722
#105902712
#835873
#799803