Finite Group Databasebeta

← #11895432

Subgroups — #11895432

Order 1152.

845 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×Q8×Dic6C211yesmaximal, characteristic, complemented
2#10593900C211yesmaximal, characteristic
3C4×#3755C211yesmaximal, characteristic, complemented
4C3×#5027C211yesmaximal, characteristic, complemented
5#10591617C212yesmaximal, complemented
6Dic3×#215C212yesmaximal, complemented
7#10590548C212yesmaximal, complemented
8#10590465C212yesmaximal, complemented
9#10590300C211yesmaximal, characteristic, complemented
10#10590277C211yesmaximal, characteristic, complemented
11#10590250C211yesmaximal, characteristic, complemented
12#83703—31nomaximal
13#80369—31nomaximal
14C2×#3796—21no—
15C32×C4×Q8C2211yescharacteristic
16C2×#3755C2211yescharacteristic
17C4×C4⋊(C3⋊D3)C2211yescharacteristic
18C3×Q8×Dic3C2212yes—
19C2×C3×#215C2212yes—
20C3×#888—22no—
21C3×#888C2212yes—
22C3×#874C2211yescharacteristic
23C3×#869—21no—
24C3×#869C2211yescharacteristic
25C3×C4×Dic6—21no—
26C3×C4×Dic6C2211yescharacteristic
27#63916—21no—
28#63911C2212yes—
29Dic3×D12C2212yes—
30#63886—22no—
31#63662C2211yescharacteristic
32#63636C2211yescharacteristic
33#63635C2211yescharacteristic
34C4×C3⋊(C3⋊C8)C2211yescharacteristic
35C3×#809C2212yes—
36C3×C4⋊(C3⋊C8)C2211yescharacteristic
37#63573C2212yes—
38Dic3⋊(C3⋊C8)C2212yes—
39#63564C2212yes—
40#63562C2212yes—
41#63562C2212yes—
42Dic3×C3⋊C8C2212yes—
43C3×Q82—31no—
44#5718—31no—
45#5577—31no—
46Q8×Dic6D311yescharacteristic, complemented
47C3×#460—31no—
48#5163—32no—
49Dic3×SD16—32no—
50#5088—31no—
51#5088—32no—
52#5084—32no—
53#5084—31no—
54#5070—31no—
55#5027—32no—
56#5027D311yescharacteristic, complemented
57C4×#215—31no—
58C4×#215—31no—
59C4×#215—32no—
60C4×#215—61no—
61Q8×C3⋊C8—31no—
62#4842—31no—
63#4830—31no—
64#4761—32no—
65#4760—32no—
66C2×C32×Q8C2311yescharacteristic
67C2×C4⋊(C3⋊D3)C2311yescharacteristic
68C2×C4×C3⋊D3—21no—
69C2×C3×D12—21no—
70C2×C3×D12—21no—
71C2×C3×D12C2312yes—
72C2×C3×Dic6—21no—
73C2×C3×Dic6—22no—
74C2×C3×Dic6D411yescharacteristic
75C2×#626—22no—
76C2×#626—22no—
77C2×D3×Dic3—22no—
78#3796—44no—
79C32×C4⋊C4—21no—
80C32×C4⋊C4C2311yescharacteristic
81C32×C42—21no—
82C32×C42C2311yescharacteristic
83#3755—22no—
84#3752—21no—
85C4⋊(C3⋊Dic3)C2311yescharacteristic
86C2×C3⋊(C3⋊C8)C2311yescharacteristic
87C2×C3⋊(C3⋊C8)C2311yescharacteristic
88C3×#215—24no—
89C3×C4⋊Dic3—21no—
90C3×C4⋊Dic3—22no—
91C3×C4⋊Dic3D411yescharacteristic
92C3×C4⋊Dic3C2312yes—
93C3×Dic3⋊C4—22no—
94C3×Dic3⋊C4D412yes—
95C3×C4×Dic3—22no—
96C3×C4×Dic3C2312yes—
97C2×C3×C3⋊C8C2312yes—
98(C2×D3)⋊Dic3—22no—
99#3362—91noSylow
100C2×#239—61no—
101C2×#237—61no—
102C2×C3×SD16—32no—
103C3×C4⋊Q8—32no—
104C3×C4⋊Q8—31no—
105C3×C4⋊Q8—61no—
106C3×C4⋊Q8—62no—
107C3×#127—31no—
108C3×C4×Q8—21no—
109C3×C4×Q8—31no—
110C3×C4×Q8—32no—
111C3×C4×Q8—61no—
112C3×C4×Q8C2×D311yescharacteristic
113C3×C4×Q8C2×D311yescharacteristic
114Q8×Dic3C2×D312yes—
115C2×#215—31no—
116C2×#215—31no—
117C2×#215—61no—
118C2×#215C2×D312yes—
119#940—32no—
120#939—62no—
121#938—61no—
122D4×Dic3—32no—
123#895—62no—
124#895—61no—
125#888—22no—
126#888C2×D312yes—
127#874—32no—
128#874C2×D311yescharacteristic
129C4×D12—32no—
130C4×D12—31no—
131C4×D12—31no—
132C4×D12—61no—
133#869—21no—
134#869C2×D311yescharacteristic
135C4×Dic6—21no—
136C4×Dic6C2×D311yescharacteristic
137C3×C4⋊C8—31no—
138C3×#102—32no—
139#835—31no—
140#835—31no—
141#835—61no—
142#832—32no—
143#832—32no—
144#821—32no—
145#817—32no—
146Dic3⋊C8—32no—
147C8×Dic3—32no—
148#809—32no—
149#809—32no—
150#809—31no—
151#809—31no—
152#809—32no—
153#809—61no—
154#809C2×D312yes—
155#808—31no—
156#808—31no—
157#808—32no—
158#808—61no—
159C4⋊(C3⋊C8)—32no—
160C4⋊(C3⋊C8)C2×D311yescharacteristic
161C4×C3⋊C8—31no—
162C4×C3⋊C8—31no—
163C4×C3⋊C8—32no—
164C4×C3⋊C8—61no—
165C22×C3⋊D3—21no—
166C22×C3×D3—22no—
167C32×Q8—21no—
168C32×Q8#4112yescomplemented
169C2×C32×C4—21no—
170C2×C32×C4—21no—
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2411yescharacteristic
174C2×C3⋊Dic3—21no—
175C4⋊(C3⋊D3)—21no—
176C4⋊(C3⋊D3)—21no—
177C4×C3⋊D3—42no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3C2×D412yes—
180C2×C3×Dic3C2×D412yes—
181C3×D12—22no—
182C3×D12—22no—
183C3×D12—42no—
184C3×D12—81no—
185C3×Dic6—82no—
186C3×Dic6—81no—
187C3×Dic6SD1614yescomplemented
188#626—44no—
189#626—82no—
190D3×Dic3—44no—
191C3⋊(C3⋊C8)—21no—
192C3⋊(C3⋊C8)—21no—
193C3×C3⋊C8—22no—
194Q82—31no—
195#550—91no—
196#486—92no—
197#486—91no—
198#476—92no—
199#476—91no—
200#460—31no—
201#460—92no—
202C8×Q8—91no—
203C4×SD16—92no—
204C4×SD16—91no—
205C2×C3×Q8—21no—
206C2×C3×Q8—31no—
207C2×C3×Q8—62no—
208C2×C3×Q8—61no—
209C2×C3×Q8C22×D311yescharacteristic
210C2×C3×Q8C22×D311yescharacteristic
211C2×C3×D4—32no—
212C2×C3×D4—61no—
213C2×C3×D4—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×C4×D3—62no—
228C2×C4×D3—61no—
229C2×C4×D3—61no—
230C2×C4×D3—121no—
231C2×Dic6—21no—
232C2×Dic6—22no—
233C2×Dic6#6711yescharacteristic
234C3×SD16—64no—
235C2×C3×C8—32no—
236C3×C4⋊C4—21no—
237C3×C4⋊C4—21no—
238C3×C4⋊C4—21no—
239C3×C4⋊C4—32no—
240C3×C4⋊C4—31no—
241C3×C4⋊C4—32no—
242C3×C4⋊C4—41no—
243C3×C4⋊C4—62no—
244C3×C4⋊C4—62no—
245C3×C4⋊C4—61no—
246C3×C4⋊C4C22×D311yescharacteristic
247C3×C4⋊C4C22×D311yescharacteristic
248C3×C42—21no—
249C3×C42—21no—
250C3×C42—21no—
251C3×C42—32no—
252C3×C42—41no—
253C3×C42—62no—
254C3×C42C22×D311yescharacteristic
255C3×C42C22×D311yescharacteristic
256#217—62no—
257#215—24no—
258#215—64no—
259#215—62no—
260#215—62no—
261(C2×D3)⋊C4—62no—
262(C2×D3)⋊C4—61no—
263(C2×D3)⋊C4—61no—
264(C2×D3)⋊C4—121no—
265C4⋊Dic3—21no—
266C4⋊Dic3—22no—
267C4⋊Dic3—31no—
268C4⋊Dic3—31no—
269C4⋊Dic3—61no—
270C4⋊Dic3#6711yescharacteristic
271C4⋊Dic3C22×D312yes—
272Dic3⋊C4—22no—
273Dic3⋊C4#6712yes—
274C4×Dic3—22no—
275C4×Dic3C22×D312yes—
276C2×C3⋊C8—31no—
277C2×C3⋊C8—31no—
278C2×C3⋊C8—31no—
279C2×C3⋊C8—31no—
280C2×C3⋊C8—61no—
281C2×C3⋊C8—61no—
282C2×C3⋊C8C22×D312yes—
283C22×C32C22×D411yescharacteristic
284C2×C3⋊D3—41no—
285C2×C3⋊D3—41no—
286C2×C3⋊D3—41no—
287C2×C3×D3—42no—
288C2×C3×D3—42no—
289C2×C3×D3—42no—
290C32×C4—22no—
291C32×C4—21no—
292C32×C4—41no—
293C32×C4C2×SD1612yes—
294C32×C4C2×#4111yescharacteristic
295C32×C42−1+411yescharacteristic
296C3⋊Dic3—41no—
297C3×Dic3—22no—
298C3×Dic3—42no—
299C3×Dic3C2×SD1614yes—
300C2×#41—181no—
301C2×SD16—32no—
302C2×SD16—91no—
303C4⋊Q8—32no—
304C4⋊Q8—31no—
305C4⋊Q8—61no—
306C4⋊Q8—62no—
307#127—31no—
308#127—92no—
309#121—181no—
310#121—182no—
311C4×Q8—31no—
312C4×Q8—32no—
313C4×Q8—61no—
314C4×Q8D3211yescharacteristic
315C4×D4—92no—
316C4×D4—91no—
317#106—92no—
318#106—91no—
319C4⋊C8—31no—
320C4⋊C8—92no—
321#103—91no—
322#102—32no—
323#102—92no—
324#102—92no—
325#102—92no—
326#102—91no—
327C4×C8—92no—
328C4×C8—91no—
329C23×C3—62no—
330C22×D3—22no—
331C22×D3—61no—
332C22×D3—61no—
333C22×D3—121no—
334C3×Q8—21no—
335C3×Q8—21no—
336C3×Q8—22no—
337C3×Q8—34no—
338C3×Q8—41no—
339C3×Q8—241no—
340C3×Q8—242no—
341C3×Q8#23712yescomplemented
342C3×Q8#23912yescomplemented
343C3×D4—62no—
344C3×D4—62no—
345C3×D4—122no—
346C3×D4—241no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4—21no—
354C2×C3×C4—32no—
355C2×C3×C4—32no—
356C2×C3×C4—41no—
357C2×C3×C4—41no—
358C2×C3×C4—62no—
359C2×C3×C4D3×D411yescharacteristic
360C2×C3×C4D3×D411yescharacteristic
361C2×C3×C4C2×#6711yescharacteristic
362C2×C3×C4C2×#6711yescharacteristic
363C2×C3×C4C23×D311yescharacteristic
364C2×C3×C4C23×D311yescharacteristic
365#67—124no—
366#67—242no—
367C2×Dic3—22no—
368C2×Dic3—61no—
369C2×Dic3—61no—
370C2×Dic3—121no—
371C2×Dic3—124no—
372C2×Dic3C2×#6712yes—
373C2×Dic3C2×#6712yes—
374D12—22no—
375D12—22no—
376D12—42no—
377D12—62no—
378D12—61no—
379D12—61no—
380D12—61no—
381D12—61no—
382D12—81no—
383D12—121no—
384D12—124no—
385D12—242no—
386C4×D3—124no—
387C4×D3—122no—
388C4×D3—122no—
389C4×D3—242no—
390Dic6—82no—
391Dic6—81no—
392Dic6#21514yescomplemented
393C3×C8—62no—
394C3⋊C8—22no—
395C3⋊C8—62no—
396C3⋊C8—61no—
397C3⋊C8—61no—
398C3⋊C8—61no—
399C3⋊C8—61no—
400C3⋊C8—121no—
401C2×C32#54811yescharacteristic
402C2×C32C22×SD1611yescharacteristic
403C2×C32#57611yescharacteristic
404C3⋊D3—81no—
405C3×D3—82no—
406#41—364no—
407C2×Q8—31no—
408C2×Q8—62no—
409C2×Q8—61no—
410C2×Q8C2×D3211yescharacteristic
411C2×D4—32no—
412C2×D4—61no—
413C2×D4—61no—
414C2×D4—91no—
415C2×D4—182no—
416C2×D4—182no—
417C22×C4—182no—
418C22×C4—181no—
419SD16—64no—
420SD16—182no—
421C2×C8—32no—
422C2×C8—91no—
423C2×C8—91no—
424C4⋊C4—21no—
425C4⋊C4—32no—
426C4⋊C4—31no—
427C4⋊C4—32no—
428C4⋊C4—62no—
429C4⋊C4—62no—
430C4⋊C4—61no—
431C4⋊C4—91no—
432C4⋊C4C2×D3211yescharacteristic
433C22⋊C4—182no—
434C22⋊C4—181no—
435C42—21no—
436C42—32no—
437C42—62no—
438C42C2×D3211yescharacteristic
439C22×C3—21no—
440C22×C3—122no—
441C22×C3—122no—
442C22×C3—122no—
443C22×C3C2×D3×D411yescharacteristic
444C22×C3C22×#6711yescharacteristic
445C2×D3—42no—
446C2×D3—42no—
447C2×D3—42no—
448C2×D3—122no—
449C2×D3—121no—
450C2×D3—121no—
451C2×D3—121no—
452C2×D3—121no—
453C2×D3—121no—
454C2×D3—121no—
455C2×D3—241no—
456C2×D3—241no—
457C3×C4—21no—
458C3×C4—22no—
459C3×C4—21no—
460C3×C4—22no—
461C3×C4—21no—
462C3×C4—21no—
463C3×C4—22no—
464C3×C4—34no—
465C3×C4—41no—
466C3×C4—42no—
467C3×C4—41no—
468C3×C4—41no—
469C3×C4—62no—
470C3×C4—81no—
471C3×C4—122no—
472C3×C4D3×SD1612yes—
473C3×C4C2×#21512yes—
474C3×C4C2×#23711yescharacteristic
475C3×C4C2×#23911yescharacteristic
476C3×C4#100711yescharacteristic
477C3×C4#101011yescharacteristic
478Dic3—22no—
479Dic3—42no—
480Dic3—121no—
481Dic3—121no—
482Dic3—241no—
483Dic3C2×#21514yes—
484C32#336211yescharacteristic, complemented, Sylow
485C23—62no—
486C23—181no—
487Q8—21no—
488Q8—34no—
489Q8—241no—
490Q8—242no—
491Q8#379612yescomplemented
492D4—62no—
493D4—62no—
494D4—122no—
495D4—181no—
496D4—181no—
497D4—241no—
498D4—364no—
499D4—722no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—32no—
503C2×C4—32no—
504C2×C4—62no—
505C2×C4—181no—
506C2×C4—364no—
507C2×C4—362no—
508C2×C4D3×#6711yescharacteristic
509C2×C4D3×#6711yescharacteristic
510C2×C4C22×D3211yescharacteristic
511C8—62no—
512C8—181no—
513C8—181no—
514C2×C3—21no—
515C2×C3—21no—
516C2×C3—21no—
517C2×C3—242no—
518C2×C3#559811yescharacteristic
519C2×C3C2×D3×SD1611yescharacteristic
520C2×C3#577411yescharacteristic
521C2×C3C22×#21511yescharacteristic
522C2×C3#581711yescharacteristic
523C2×C3#583511yescharacteristic
524D3—82no—
525D3—242no—
526D3—241no—
527D3—241no—
528C22—122no—
529C22—122no—
530C22—122no—
531C22—361no—
532C22—361no—
533C22—361no—
534C22C2×D3×#6711yescharacteristic
535C4—22no—
536C4—21no—
537C4—34no—
538C4—41no—
539C4—62no—
540C4—122no—
541C4—361no—
542C4D3×#21512yes—
543C4C2×#379611yescharacteristic
544C4#6429711yescharacteristic
545C3—21no—
546C3#8036911yescharacteristic, complemented
547C3#8370311yescharacteristic, complemented
548C2—242no—
549C2—721no—
550C2#1059490011yescharacteristic
551C2C2×D3×#21511yescharacteristic
552C2#1059545411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radical#10593900C2
hypercenterC4×Q8D32
hypocenterC32#3362
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×Q8×Dic6C2semidirect
3. C4×#3755C2semidirect
4. C3×#5027C2semidirect
5. #10591617C2semidirect
6. Dic3×#215C2semidirect
7. #10590548C2semidirect
8. #10590465C2semidirect
9. #10590300C2semidirect
10. #10590277C2semidirect
11. #10590250C2semidirect
46. Q8×Dic6D3semidirect
56. #5027D3semidirect
168. C32×Q8#41semidirect
187. C3×Dic6SD16semidirect
341. C3×Q8#237semidirect
342. C3×Q8#239semidirect
392. Dic6#215semidirect
484. C32#3362semidirect
491. Q8#3796semidirect
546. C3#80369semidirect
547. C3#83703semidirect

Maximal subgroups

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

subgroupindex
C3×Q8×Dic62
#105939002
C4×#37552
C3×#50272
#105916172
Dic3×#2152
#105905482
#105904652
#105903002
#105902772
#105902502
#837033
#803693