Finite Group Databasebeta

← #11895776

Subgroups — #11895776

Order 1152.

846 conjugacy classes of subgroups.

The subgroup lattice has 561 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5730C211yesmaximal, characteristic, complemented
2#10593900C211yesmaximal, characteristic, complemented
3#10592783C211yesmaximal, characteristic, complemented
4C3×#5088C211yesmaximal, characteristic, complemented
5#10590550C212yesmaximal, complemented
6#10590547C212yesmaximal, complemented
7#10590469C212yesmaximal, complemented
8#10590455C212yesmaximal, complemented
9#10590347C211yesmaximal, characteristic, complemented
10C4×#3714C211yesmaximal, characteristic, complemented
11#10590258C211yesmaximal, characteristic, complemented
12#83638—31nomaximal
13#81586—31nomaximal
14C2×#3796—21no—
15C32×C4⋊Q8C2211yescharacteristic
16C4×C4⋊(C3⋊D3)C2211yescharacteristic
17C3×#946—22no—
18C3×#897—21no—
19C3×#893C2212yes—
20C3×D3×C4⋊C4—21no—
21C3×#890C2212yes—
22C3×#874C2211yescharacteristic
23C3×C4×D12C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25#63916—21no—
26#63911C2212yes—
27Dic3×D12C2212yes—
28#63886—22no—
29C2×#3714C2211yescharacteristic
30C2×#3713C2212yes—
31#63636C2212yes—
32#63635C2212yes—
33C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
34C3×#809C2212yes—
35C3×#809C2212yes—
36C3×C4×C3⋊C8C2211yescharacteristic
37#63575C2211yescharacteristic
38Dic3⋊(C3⋊C8)C2212yes—
39#63564C2211yescharacteristic
40#63563C2211yescharacteristic
41#63562C2212yes—
42#63554C2212yes—
43C3×#554—31no—
44#5730D311yescharacteristic, complemented
45#5718—31no—
46#5577—31no—
47C3×#486—31no—
48#5088D311yescharacteristic, complemented
49#5084—31no—
50#5084—31no—
51#5084—61no—
52#5072—31no—
53#5067—32no—
54#5066—32no—
55#5024—31no—
56#5015—31no—
57#5015—32no—
58#5014—32no—
59C4×#213—31no—
60#4786—32no—
61#4785—32no—
62#4766—32no—
63#4764—32no—
64C4×D24—31no—
65#4679—31no—
66C2×C32×Q8—21no—
67C2×C4⋊(C3⋊D3)C2311yescharacteristic
68C2×C4×C3⋊D3—21no—
69C2×C3×D12—21no—
70C2×C3×D12—21no—
71C2×C3×D12C2312yes—
72C2×C3×D12C2311yescharacteristic
73C2×C3×C4×D3—21no—
74C2×C3×C4×D3—22no—
75C2×C3×Dic6D411yescharacteristic
76C2×#626—22no—
77C2×#626—22no—
78C2×D3×Dic3—22no—
79#3796—44no—
80C32×C4⋊C4—21no—
81C32×C4⋊C4C2312yes—
82C32×C42C2311yescharacteristic
83#3752—21no—
84C4⋊(C3⋊Dic3)C2311yescharacteristic
85C2×C3⋊(C3⋊C8)C2312yes—
86C3×(C2×D3)⋊C4—21no—
87C3×(C2×D3)⋊C4—22no—
88C3×C4⋊Dic3—22no—
89C3×C4⋊Dic3D411yescharacteristic
90C3×C4⋊Dic3C2311yescharacteristic
91C3×Dic3⋊C4—22no—
92C3×Dic3⋊C4D412yes—
93C3×C4×Dic3C2312yes—
94C2×C3×C3⋊C8C2311yescharacteristic
95C2×C3×C3⋊C8C2311yescharacteristic
96(C2×D3)⋊Dic3—22no—
97#3714—22no—
98#3713—24no—
99#3366—91noSylow
100C2×#239—61no—
101C2×#237—61no—
102C3×C4⋊Q8—21no—
103C3×C4⋊Q8C2×D311yescharacteristic
104C3×C4⋊Q8C2×D311yescharacteristic
105C3×#127—31no—
106C3×#125—32no—
107C3×C22⋊Q8—61no—
108C3×C22⋊Q8—62no—
109C3×C4×Q8—31no—
110C3×C4×D4—32no—
111C3×C4×D4—31no—
112C2×C3×C4⋊C4—61no—
113#946—22no—
114#940—32no—
115#939—62no—
116#938—61no—
117D4×Dic3—32no—
118C2×#213—32no—
119C2×#213—32no—
120C2×#213—31no—
121C2×D24—31no—
122#897—21no—
123#895—62no—
124#895—61no—
125#893C2×D312yes—
126D3×C4⋊C4—21no—
127#890C2×D312yes—
128#874—32no—
129#874C2×D311yescharacteristic
130C4×D12—32no—
131C4×D12—31no—
132C4×D12—31no—
133C4×D12—61no—
134C4×D12C2×D311yescharacteristic
135C4×Dic6C2×D311yescharacteristic
136C3×#102—32no—
137C3×#102—32no—
138C3×C4×C8—31no—
139#832—32no—
140#832—31no—
141#821—31no—
142#821—31no—
143#818—31no—
144#815—32no—
145Dic3⋊C8—32no—
146#809—32no—
147#809—32no—
148#809—32no—
149#809—31no—
150#809—62no—
151#809C2×D312yes—
152#809C2×D312yes—
153#808—32no—
154#808—32no—
155#808—62no—
156#807—31no—
157C4⋊(C3⋊C8)—31no—
158C4⋊(C3⋊C8)—31no—
159C4⋊(C3⋊C8)—32no—
160C4⋊(C3⋊C8)—61no—
161#803—32no—
162C4×C3⋊C8C2×D311yescharacteristic
163C22×C3⋊D3—21no—
164C22×C3×D3—21no—
165C22×C3×D3—22no—
166C32×Q8—81no—
167C2×C32×C4—22no—
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2411yescharacteristic
171C2×C3⋊Dic3—21no—
172C4⋊(C3⋊D3)—21no—
173C4⋊(C3⋊D3)—21no—
174C4×C3⋊D3—42no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3C2×D412yes—
177C2×C3×Dic3C2×D412yes—
178C3×D12—22no—
179C3×D12—21no—
180C3×D12—22no—
181C3×D12—42no—
182C3×D12—81no—
183C3×D12#4112yescomplemented
184C3×C4×D3—42no—
185C3×C4×D3—82no—
186C3×Dic6—22no—
187#626—44no—
188#626—82no—
189D3×Dic3—44no—
190C3⋊(C3⋊C8)—22no—
191C3×C3⋊C8—21no—
192C3×C3⋊C8—21no—
193#554—31no—
194#550—91no—
195#490—92no—
196#486—31no—
197#478—92no—
198#476—91no—
199#459—92no—
200#459—91no—
201#446—91no—
202#442—92no—
203C4×D8—91no—
204C2×C3×Q8—21no—
205C2×C3×Q8—21no—
206C2×C3×Q8—31no—
207C2×C3×Q8—41no—
208C2×C3×D4—31no—
209C2×C3×D4—32no—
210C2×C3×D4—61no—
211C2×C3×D4—61no—
212C22×C3×C4—62no—
213C22×C3×C4—61no—
214C2×#67—62no—
215C2×#67—62no—
216C22×Dic3—62no—
217#239—124no—
218#237—124no—
219C2×D12—21no—
220C2×D12—21no—
221C2×D12—31no—
222C2×D12—31no—
223C2×D12—61no—
224C2×D12—62no—
225C2×D12—62no—
226C2×D12C22×D312yes—
227C2×D12C22×D311yescharacteristic
228C2×C4×D3—21no—
229C2×C4×D3—22no—
230C2×C4×D3—62no—
231C2×C4×D3—61no—
232C2×C4×D3—61no—
233C2×C4×D3—121no—
234C2×Dic6#6711yescharacteristic
235C2×C3×C8—31no—
236C2×C3×C8—31no—
237C3×C4⋊C4—21no—
238C3×C4⋊C4—21no—
239C3×C4⋊C4—22no—
240C3×C4⋊C4—32no—
241C3×C4⋊C4—31no—
242C3×C4⋊C4—31no—
243C3×C4⋊C4—41no—
244C3×C4⋊C4—62no—
245C3×C4⋊C4—62no—
246C3×C4⋊C4C22×D312yes—
247C3×C4⋊C4C22×D312yes—
248C3×C22⋊C4—62no—
249C3×C22⋊C4—61no—
250C3×C42—21no—
251C3×C42—32no—
252C3×C42C22×D311yescharacteristic
253C3×C42C22×D311yescharacteristic
254#217—62no—
255#213—62no—
256#213—64no—
257#213—64no—
258(C2×D3)⋊C4—21no—
259(C2×D3)⋊C4—22no—
260(C2×D3)⋊C4—62no—
261(C2×D3)⋊C4—61no—
262(C2×D3)⋊C4—61no—
263(C2×D3)⋊C4—121no—
264C4⋊Dic3—22no—
265C4⋊Dic3—31no—
266C4⋊Dic3—31no—
267C4⋊Dic3—61no—
268C4⋊Dic3#6711yescharacteristic
269C4⋊Dic3C22×D311yescharacteristic
270Dic3⋊C4—22no—
271Dic3⋊C4#6712yes—
272C4×Dic3C22×D312yes—
273C2×C3⋊C8—32no—
274C2×C3⋊C8—32no—
275C2×C3⋊C8—62no—
276C2×C3⋊C8C22×D311yescharacteristic
277C2×C3⋊C8C22×D311yescharacteristic
278D24—62no—
279C22×C32C22×D411yescharacteristic
280C2×C3⋊D3—41no—
281C2×C3⋊D3—41no—
282C2×C3⋊D3—41no—
283C2×C3×D3—22no—
284C2×C3×D3—41no—
285C2×C3×D3—41no—
286C2×C3×D3—42no—
287C2×C3×D3—42no—
288C2×C3×D3—42no—
289C32×C4—21no—
290C32×C4—42no—
291C32×C4AGL(1,ℤ/8)12yes—
292C32×C4C2×#4111yescharacteristic
293C32×C42−1+411yescharacteristic
294C3⋊Dic3—41no—
295C3×Dic3—22no—
296C3×Dic3—22no—
297C3×Dic3—41no—
298C2×#41—181no—
299C2×D8—91no—
300C2×D8—92no—
301C4⋊Q8D3211yescharacteristic
302#127—31no—
303#127—92no—
304#125—32no—
305C22⋊Q8—61no—
306C22⋊Q8—62no—
307#121—181no—
308#121—182no—
309C4×Q8—31no—
310C4×D4—32no—
311C4×D4—31no—
312C4×D4—92no—
313C4×D4—91no—
314C2×C4⋊C4—61no—
315#107—91no—
316#106—92no—
317C4⋊C8—92no—
318C4⋊C8—91no—
319#102—32no—
320#102—32no—
321#102—91no—
322#102—92no—
323#102—91no—
324#102—92no—
325#97—92no—
326C4×C8—31no—
327C23×C3—61no—
328C23×C3—62no—
329C22×D3—21no—
330C22×D3—22no—
331C22×D3—61no—
332C22×D3—61no—
333C22×D3—121no—
334C3×Q8—62no—
335C3×Q8—81no—
336C3×Q8—81no—
337C3×Q8—82no—
338C3×D4—32no—
339C3×D4—62no—
340C3×D4—62no—
341C3×D4—61no—
342C3×D4—122no—
343C3×D4—241no—
344C2×C3×C4—22no—
345C2×C3×C4—22no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—32no—
350C2×C3×C4—32no—
351C2×C3×C4—42no—
352C2×C3×C4—61no—
353C2×C3×C4—122no—
354C2×C3×C4—242no—
355C2×C3×C4D3×D411yescharacteristic
356C2×C3×C4D3×D411yescharacteristic
357C2×C3×C4C2×#6711yescharacteristic
358C2×C3×C4C2×#6711yescharacteristic
359C2×C3×C4C23×D311yescharacteristic
360C2×C3×C4C23×D311yescharacteristic
361#67—124no—
362#67—242no—
363C2×Dic3—21no—
364C2×Dic3—61no—
365C2×Dic3—61no—
366C2×Dic3—121no—
367C2×Dic3—124no—
368C2×Dic3C2×#6712yes—
369C2×Dic3C2×#6712yes—
370D12—21no—
371D12—22no—
372D12—22no—
373D12—42no—
374D12—62no—
375D12—61no—
376D12—61no—
377D12—61no—
378D12—61no—
379D12—81no—
380D12—121no—
381D12—124no—
382D12—242no—
383D12#23912yescomplemented
384C4×D3—42no—
385C4×D3—82no—
386C4×D3—124no—
387C4×D3—122no—
388C4×D3—122no—
389C4×D3—242no—
390Dic6—22no—
391C3×C8—61no—
392C3×C8—61no—
393C3⋊C8—21no—
394C3⋊C8—21no—
395C3⋊C8—62no—
396C3⋊C8—62no—
397C3⋊C8—122no—
398C2×C32#54811yescharacteristic
399C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
400C2×C32#57611yescharacteristic
401C3⋊D3—81no—
402C3×D3—42no—
403C3×D3—82no—
404#41—364no—
405C2×Q8—21no—
406C2×Q8—31no—
407C2×D4—31no—
408C2×D4—32no—
409C2×D4—61no—
410C2×D4—61no—
411C2×D4—91no—
412C2×D4—182no—
413C2×D4—182no—
414C22×C4—62no—
415C22×C4—61no—
416C22×C4—182no—
417C22×C4—181no—
418D8—182no—
419D8—184no—
420C2×C8—31no—
421C2×C8—31no—
422C2×C8—92no—
423C4⋊C4—21no—
424C4⋊C4—31no—
425C4⋊C4—32no—
426C4⋊C4—31no—
427C4⋊C4—62no—
428C4⋊C4—62no—
429C4⋊C4—91no—
430C4⋊C4C2×D3212yes—
431C22⋊C4—62no—
432C22⋊C4—61no—
433C22⋊C4—182no—
434C22⋊C4—181no—
435C42—32no—
436C42C2×D3211yescharacteristic
437C22×C3—21no—
438C22×C3—62no—
439C22×C3—121no—
440C22×C3—121no—
441C22×C3—122no—
442C22×C3—122no—
443C22×C3—122no—
444C22×C3C2×D3×D411yescharacteristic
445C22×C3C22×#6711yescharacteristic
446C2×D3—22no—
447C2×D3—41no—
448C2×D3—41no—
449C2×D3—42no—
450C2×D3—42no—
451C2×D3—42no—
452C2×D3—122no—
453C2×D3—121no—
454C2×D3—121no—
455C2×D3—121no—
456C2×D3—121no—
457C2×D3—121no—
458C2×D3—121no—
459C2×D3—241no—
460C2×D3—241no—
461C3×C4—21no—
462C3×C4—21no—
463C3×C4—21no—
464C3×C4—21no—
465C3×C4—22no—
466C3×C4—41no—
467C3×C4—42no—
468C3×C4—42no—
469C3×C4—62no—
470C3×C4—62no—
471C3×C4—82no—
472C3×C4—121no—
473C3×C4#91412yes—
474C3×C4#94912yes—
475C3×C4C2×#23911yescharacteristic
476C3×C4#100711yescharacteristic
477C3×C4D3×#4111yescharacteristic
478C3×C4#101011yescharacteristic
479Dic3—22no—
480Dic3—22no—
481Dic3—41no—
482Dic3—121no—
483Dic3—121no—
484Dic3—241no—
485C32#336611yescharacteristic, complemented, Sylow
486C23—61no—
487C23—62no—
488C23—181no—
489Q8—62no—
490Q8—81no—
491D4—32no—
492D4—61no—
493D4—62no—
494D4—62no—
495D4—122no—
496D4—181no—
497D4—181no—
498D4—241no—
499D4—364no—
500D4—722no—
501C2×C4—22no—
502C2×C4—32no—
503C2×C4—32no—
504C2×C4—61no—
505C2×C4—122no—
506C2×C4—181no—
507C2×C4—242no—
508C2×C4—364no—
509C2×C4—362no—
510C2×C4D3×#6711yescharacteristic
511C2×C4D3×#6711yescharacteristic
512C2×C4C22×D3211yescharacteristic
513C8—61no—
514C8—61no—
515C8—182no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—122no—
520C2×C3—242no—
521C2×C3#567711yescharacteristic
522C2×C3#575711yescharacteristic
523C2×C3C2×#91411yescharacteristic
524C2×C3#581711yescharacteristic
525C2×C3C2×#94911yescharacteristic
526C2×C3#583511yescharacteristic
527D3—42no—
528D3—82no—
529D3—242no—
530D3—241no—
531D3—241no—
532C22—62no—
533C22—121no—
534C22—121no—
535C22—122no—
536C22—122no—
537C22—122no—
538C22—361no—
539C22—361no—
540C22—361no—
541C22C2×D3×#6711yescharacteristic
542C4—21no—
543C4—42no—
544C4—62no—
545C4—62no—
546C4—121no—
547C4—361no—
548C4#6393912yes—
549C4#6431511yescharacteristic
550C4D3×#23911yescharacteristic
551C3—21no—
552C3#8158611yescharacteristic, complemented
553C3#8363811yescharacteristic, complemented
554C2—122no—
555C2—242no—
556C2—721no—
557C2#1059509611yescharacteristic
558C2C2×#6393911yescharacteristic
559C2#1059540111yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
hypercenterC4⋊Q8D32
hypocenterC32#3366
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5730C2semidirect
2. #10593900C2semidirect
3. #10592783C2semidirect
4. C3×#5088C2semidirect
5. #10590550C2semidirect
6. #10590547C2semidirect
7. #10590469C2semidirect
8. #10590455C2semidirect
9. #10590347C2semidirect
10. C4×#3714C2semidirect
11. #10590258C2semidirect
44. #5730D3semidirect
48. #5088D3semidirect
183. C3×D12#41semidirect
383. D12#239semidirect
485. C32#3366semidirect
552. C3#81586semidirect
553. C3#83638semidirect

Maximal subgroups

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

subgroupindex
C3×#57302
#105939002
#105927832
C3×#50882
#105905502
#105905472
#105904692
#105904552
#105903472
C4×#37142
#105902582
#836383
#815863