Finite Group Databasebeta

← #11895430

Subgroups — #11895430

Order 1152.

848 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×Q8×Dic6C211yesmaximal, characteristic, complemented
2#10593902C211yesmaximal, characteristic
3#10592726C211yesmaximal, characteristic, complemented
4C3×C4×#215C211yesmaximal, characteristic, complemented
5#10591617C212yesmaximal, complemented
6#10591536C212yesmaximal, complemented
7#10590548C212yesmaximal, complemented
8#10590466C212yesmaximal, complemented
9#10590281C211yesmaximal, characteristic, complemented
10#10590266C211yesmaximal, characteristic, complemented
11C3⋊C8×Dic6C211yesmaximal, characteristic, complemented
12#83703—31nomaximal
13#79622—31nomaximal
14C2×#3799—21no—
15C32×C4×Q8C2211yescharacteristic
16C2×#3755C2212yes—
17#64083C2211yescharacteristic
18C3×Q8×Dic3C2212yes—
19C2×C3×#215C2211yescharacteristic
20C3×#888—22no—
21C3×#888C2212yes—
22C3×C4×D12C2211yescharacteristic
23C3×#869—21no—
24C3×#869C2211yescharacteristic
25C3×C4×Dic6—21no—
26C3×C4×Dic6C2211yescharacteristic
27#63911C2212yes—
28#63910—22no—
29#63909—21no—
30#63894C2212yes—
31#63636C2212yes—
32C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
33C3×#835C2211yescharacteristic
34C3×#809C2211yescharacteristic
35C3×#808C2211yescharacteristic
36C3×C4×C3⋊C8C2211yescharacteristic
37#63574C2212yes—
38Dic3⋊(C3⋊C8)C2212yes—
39#63564C2212yes—
40#63564C2212yes—
41#63562C2212yes—
42Dic3×C3⋊C8C2212yes—
43C3×Q82—31no—
44#5577—31no—
45Q8×Dic6D311yescharacteristic, complemented
46#5553—31no—
47C3×C4×SD16—31no—
48#5163—32no—
49#5088—32no—
50#5088—31no—
51#5084—31no—
52#5084—32no—
53#5027—31no—
54#5027—31no—
55#5027—32no—
56#5027—61no—
57C4×#215—32no—
58C4×#215D311yescharacteristic, complemented
59Q8×C3⋊C8—31no—
60#5008—31no—
61#4870—32no—
62#4788—32no—
63#4760—32no—
64#4694—31no—
65C8×Dic6—31no—
66C2×C32×Q8C2311yescharacteristic
67C2×C4⋊(C3⋊D3)—21no—
68C2×C4⋊(C3⋊D3)—21no—
69C2×C4⋊(C3⋊D3)C2312yes—
70C2×C3×D12C2311yescharacteristic
71C2×C3×C4×D3—21no—
72C2×C3×Dic6—21no—
73C2×C3×Dic6—22no—
74C2×C3×Dic6D411yescharacteristic
75C2×#626—22no—
76C2×#626—22no—
77C2×#624—22no—
78#3799—44no—
79C32×C4⋊C4—21no—
80C32×C4⋊C4C2311yescharacteristic
81C32×C42—21no—
82C32×C42C2311yescharacteristic
83#3755—24no—
84C2×C3⋊(C3⋊C8)C2312yes—
85C3×#215—22no—
86C3×(C2×D3)⋊C4—21no—
87C3×C4⋊Dic3—21no—
88C3×C4⋊Dic3—22no—
89C3×C4⋊Dic3D411yescharacteristic
90C3×C4⋊Dic3C2312yes—
91C3×C4⋊Dic3C2311yescharacteristic
92C3×Dic3⋊C4—22no—
93C3×Dic3⋊C4D412yes—
94C3×C4×Dic3—22no—
95C3×C4×Dic3C2312yes—
96C2×C3×C3⋊C8C2311yescharacteristic
97C2×C3×C3⋊C8C2311yescharacteristic
98#3722—22no—
99#3362—91noSylow
100C2×#239—61no—
101C2×#235—61no—
102C2×C3×SD16—31no—
103C3×C4⋊Q8—32no—
104C3×C4⋊Q8—31no—
105C3×C4⋊Q8—61no—
106C3×C4⋊Q8—62no—
107C3×C4×Q8—21no—
108C3×C4×Q8—31no—
109C3×C4×Q8—32no—
110C3×C4×Q8—61no—
111C3×C4×Q8C2×D311yescharacteristic
112C3×C4×Q8C2×D311yescharacteristic
113C3×C4×D4—31no—
114Q8×Dic3C2×D312yes—
115C2×#215—32no—
116C2×#215—32no—
117C2×#215—62no—
118C2×#215C2×D311yescharacteristic
119#940—32no—
120#930—61no—
121#895—62no—
122#895—61no—
123#893—32no—
124#888—22no—
125#888C2×D312yes—
126#884—62no—
127#874—32no—
128#874—31no—
129#874—31no—
130#874—61no—
131C4×D12—32no—
132C4×D12C2×D311yescharacteristic
133#869—21no—
134#869C2×D311yescharacteristic
135C4×Dic6—21no—
136C4×Dic6C2×D311yescharacteristic
137C3×#106—31no—
138C3×#103—31no—
139C3×#102—31no—
140C3×C4×C8—31no—
141#835C2×D311yescharacteristic
142#832—32no—
143#821—32no—
144#821—32no—
145Dic3⋊C8—32no—
146C8×Dic3—32no—
147#809—32no—
148#809—32no—
149#809—32no—
150#809—32no—
151#809—32no—
152#809—62no—
153#809C2×D311yescharacteristic
154#808—32no—
155#808—32no—
156#808C2×D311yescharacteristic
157C4⋊(C3⋊C8)—31no—
158C4⋊(C3⋊C8)—31no—
159C4⋊(C3⋊C8)—32no—
160C4⋊(C3⋊C8)—61no—
161C4×C3⋊C8—32no—
162C4×C3⋊C8C2×D311yescharacteristic
163C22×C3⋊D3—22no—
164C22×C3×D3—21no—
165C32×Q8—21no—
166C32×Q8#4112yescomplemented
167C2×C32×C4—21no—
168C2×C32×C4—21no—
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2411yescharacteristic
172C4⋊(C3⋊D3)—22no—
173C4⋊(C3⋊D3)—22no—
174C4⋊(C3⋊D3)—42no—
175C4⋊(C3⋊D3)—81no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3C2×D412yes—
179C2×C3×Dic3C2×D412yes—
180C3×D12—21no—
181C3×D12—21no—
182C3×C4×D3—42no—
183C3×Dic6—82no—
184C3×Dic6—81no—
185C3×Dic6SD1614yescomplemented
186#626—44no—
187#626—82no—
188#624—44no—
189C3⋊(C3⋊C8)—22no—
190C3×C3⋊C8—21no—
191C3×C3⋊C8—21no—
192Q82—31no—
193#550—91no—
194#486—91no—
195#486—92no—
196#476—92no—
197#476—91no—
198#460—92no—
199#460—91no—
200C8×Q8—91no—
201C4×SD16—31no—
202C4×SD16—92no—
203C2×C3×Q8—21no—
204C2×C3×Q8—31no—
205C2×C3×Q8—62no—
206C2×C3×Q8—61no—
207C2×C3×Q8C22×D311yescharacteristic
208C2×C3×Q8C22×D311yescharacteristic
209C2×C3×D4—31no—
210C22×C3×C4—61no—
211C2×#67—62no—
212C2×#67—62no—
213#239—124no—
214#235—124no—
215C2×D12—32no—
216C2×D12—32no—
217C2×D12—62no—
218C2×D12—62no—
219C2×D12—61no—
220C2×D12—61no—
221C2×D12—62no—
222C2×D12—61no—
223C2×D12—61no—
224C2×D12—121no—
225C2×D12—121no—
226C2×D12C22×D311yescharacteristic
227C2×C4×D3—21no—
228C2×C4×D3—62no—
229C2×C4×D3—62no—
230C2×Dic6—21no—
231C2×Dic6—22no—
232C2×Dic6#6711yescharacteristic
233C3×SD16—62no—
234C2×C3×C8—31no—
235C2×C3×C8—31no—
236C3×C4⋊C4—21no—
237C3×C4⋊C4—21no—
238C3×C4⋊C4—21no—
239C3×C4⋊C4—32no—
240C3×C4⋊C4—31no—
241C3×C4⋊C4—31no—
242C3×C4⋊C4—32no—
243C3×C4⋊C4—41no—
244C3×C4⋊C4—62no—
245C3×C4⋊C4—62no—
246C3×C4⋊C4—61no—
247C3×C4⋊C4C22×D311yescharacteristic
248C3×C4⋊C4C22×D311yescharacteristic
249C3×C22⋊C4—61no—
250C3×C42—21no—
251C3×C42—21no—
252C3×C42—21no—
253C3×C42—32no—
254C3×C42—41no—
255C3×C42—62no—
256C3×C42C22×D311yescharacteristic
257C3×C42C22×D311yescharacteristic
258#215—22no—
259#215—64no—
260#215—64no—
261#215—124no—
262(C2×D3)⋊C4—21no—
263(C2×D3)⋊C4—62no—
264(C2×D3)⋊C4—62no—
265C4⋊Dic3—21no—
266C4⋊Dic3—22no—
267C4⋊Dic3#6711yescharacteristic
268C4⋊Dic3C22×D311yescharacteristic
269C4⋊Dic3C22×D312yes—
270Dic3⋊C4—22no—
271Dic3⋊C4#6712yes—
272C4×Dic3—22no—
273C4×Dic3C22×D312yes—
274C2×C3⋊C8—32no—
275C2×C3⋊C8—32no—
276C2×C3⋊C8—62no—
277C2×C3⋊C8C22×D311yescharacteristic
278C2×C3⋊C8C22×D311yescharacteristic
279C22×C32C22×D411yescharacteristic
280C2×C3⋊D3—42no—
281C2×C3⋊D3—42no—
282C2×C3⋊D3—42no—
283C2×C3×D3—41no—
284C2×C3×D3—41no—
285C2×C3×D3—41no—
286C32×C4—22no—
287C32×C4—21no—
288C32×C4—41no—
289C32×C4C2×SD1612yes—
290C32×C4C2×#4111yescharacteristic
291C32×C42−1+411yescharacteristic
292C3×Dic3—22no—
293C3×Dic3—41no—
294C3×Dic3—42no—
295C3×Dic3C2×SD1614yes—
296C2×#41—181no—
297C2×SD16—31no—
298C2×SD16—92no—
299C4⋊Q8—32no—
300C4⋊Q8—31no—
301C4⋊Q8—61no—
302C4⋊Q8—62no—
303#127—92no—
304#127—91no—
305#121—182no—
306#121—181no—
307C4×Q8—31no—
308C4×Q8—32no—
309C4×Q8—61no—
310C4×Q8D3211yescharacteristic
311C4×D4—31no—
312C4×D4—92no—
313#106—31no—
314#106—92no—
315C4⋊C8—92no—
316C4⋊C8—91no—
317#103—31no—
318#102—31no—
319#102—92no—
320#102—92no—
321#102—92no—
322#102—92no—
323C4×C8—31no—
324C4×C8—92no—
325C23×C3—61no—
326C22×D3—21no—
327C22×D3—62no—
328C22×D3—62no—
329C22×D3—122no—
330C3×Q8—21no—
331C3×Q8—21no—
332C3×Q8—22no—
333C3×Q8—34no—
334C3×Q8—41no—
335C3×Q8—241no—
336C3×Q8—242no—
337C3×Q8#23512yescomplemented
338C3×Q8#23912yescomplemented
339C3×D4—61no—
340C3×D4—61no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—32no—
349C2×C3×C4—32no—
350C2×C3×C4—41no—
351C2×C3×C4—41no—
352C2×C3×C4—62no—
353C2×C3×C4—61no—
354C2×C3×C4—122no—
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—22no—
365C2×Dic3C2×#6712yes—
366C2×Dic3C2×#6712yes—
367D12—21no—
368D12—21no—
369D12—62no—
370D12—62no—
371D12—62no—
372D12—62no—
373D12—122no—
374D12—122no—
375D12—124no—
376D12—122no—
377D12—122no—
378D12—242no—
379D12—241no—
380D12—241no—
381D12—242no—
382D12—242no—
383C4×D3—42no—
384C4×D3—124no—
385C4×D3—124no—
386Dic6—82no—
387Dic6—81no—
388Dic6#21514yescomplemented
389C3×C8—61no—
390C3×C8—61no—
391C3⋊C8—21no—
392C3⋊C8—21no—
393C3⋊C8—62no—
394C3⋊C8—62no—
395C3⋊C8—122no—
396C2×C32#54811yescharacteristic
397C2×C32C22×SD1611yescharacteristic
398C2×C32#57611yescharacteristic
399C3⋊D3—82no—
400C3×D3—81no—
401#41—364no—
402C2×Q8—31no—
403C2×Q8—62no—
404C2×Q8—61no—
405C2×Q8C2×D3211yescharacteristic
406C2×D4—31no—
407C2×D4—92no—
408C2×D4—182no—
409C2×D4—182no—
410C2×D4—181no—
411C2×D4—181no—
412C22×C4—61no—
413C22×C4—182no—
414SD16—62no—
415SD16—184no—
416C2×C8—31no—
417C2×C8—31no—
418C2×C8—92no—
419C4⋊C4—21no—
420C4⋊C4—32no—
421C4⋊C4—31no—
422C4⋊C4—32no—
423C4⋊C4—31no—
424C4⋊C4—62no—
425C4⋊C4—62no—
426C4⋊C4—61no—
427C4⋊C4C2×D3211yescharacteristic
428C22⋊C4—61no—
429C22⋊C4—182no—
430C42—21no—
431C42—32no—
432C42—62no—
433C42C2×D3211yescharacteristic
434C22×C3—21no—
435C22×C3—121no—
436C22×C3—121no—
437C22×C3—121no—
438C22×C3C2×D3×D411yescharacteristic
439C22×C3C22×#6711yescharacteristic
440C2×D3—41no—
441C2×D3—41no—
442C2×D3—41no—
443C2×D3—122no—
444C2×D3—122no—
445C2×D3—122no—
446C2×D3—122no—
447C2×D3—122no—
448C2×D3—122no—
449C2×D3—242no—
450C2×D3—242no—
451C2×D3—242no—
452C3×C4—21no—
453C3×C4—22no—
454C3×C4—22no—
455C3×C4—21no—
456C3×C4—21no—
457C3×C4—21no—
458C3×C4—22no—
459C3×C4—34no—
460C3×C4—41no—
461C3×C4—42no—
462C3×C4—41no—
463C3×C4—41no—
464C3×C4—62no—
465C3×C4—81no—
466C3×C4—122no—
467C3×C4—121no—
468C3×C4D3×SD1612yes—
469C3×C4C2×#21512yes—
470C3×C4C2×#23511yescharacteristic
471C3×C4C2×#23911yescharacteristic
472C3×C4#100711yescharacteristic
473C3×C4#101011yescharacteristic
474Dic3—22no—
475Dic3—41no—
476Dic3—42no—
477Dic3C2×#21514yes—
478C32#336211yescharacteristic, complemented, Sylow
479C23—61no—
480C23—182no—
481Q8—21no—
482Q8—34no—
483Q8—241no—
484Q8—242no—
485Q8#379912yescomplemented
486D4—61no—
487D4—61no—
488D4—182no—
489D4—182no—
490D4—364no—
491D4—362no—
492D4—721no—
493D4—722no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—32no—
497C2×C4—32no—
498C2×C4—62no—
499C2×C4—61no—
500C2×C4—122no—
501C2×C4—364no—
502C2×C4D3×#6711yescharacteristic
503C2×C4D3×#6711yescharacteristic
504C2×C4C22×D3211yescharacteristic
505C8—61no—
506C8—61no—
507C8—182no—
508C2×C3—21no—
509C2×C3—21no—
510C2×C3—21no—
511C2×C3—241no—
512C2×C3#555211yescharacteristic
513C2×C3C2×D3×SD1611yescharacteristic
514C2×C3#576911yescharacteristic
515C2×C3C22×#21511yescharacteristic
516C2×C3#581711yescharacteristic
517C2×C3#583511yescharacteristic
518D3—81no—
519D3—242no—
520D3—242no—
521D3—482no—
522C22—121no—
523C22—121no—
524C22—121no—
525C22—362no—
526C22—362no—
527C22—362no—
528C22C2×D3×#6711yescharacteristic
529C4—22no—
530C4—21no—
531C4—34no—
532C4—41no—
533C4—62no—
534C4—122no—
535C4—121no—
536C4D3×#21512yes—
537C4#6429711yescharacteristic
538C4C2×#379911yescharacteristic
539C3—21no—
540C3#7962211yescharacteristic, complemented
541C3#8370311yescharacteristic, complemented
542C2—241no—
543C2—722no—
544C2#1059490211yescharacteristic
545C2C2×D3×#21511yescharacteristic
546C2#1059545611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radical#10593902C2
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. #10592726C2semidirect
4. C3×C4×#215C2semidirect
5. #10591617C2semidirect
6. #10591536C2semidirect
7. #10590548C2semidirect
8. #10590466C2semidirect
9. #10590281C2semidirect
10. #10590266C2semidirect
11. C3⋊C8×Dic6C2semidirect
45. Q8×Dic6D3semidirect
58. C4×#215D3semidirect
166. C32×Q8#41semidirect
185. C3×Dic6SD16semidirect
337. C3×Q8#235semidirect
338. C3×Q8#239semidirect
388. Dic6#215semidirect
478. C32#3362semidirect
485. Q8#3799semidirect
540. C3#79622semidirect
541. 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
#105939022
#105927262
C3×C4×#2152
#105916172
#105915362
#105905482
#105904662
#105902812
#105902662
C3⋊C8×Dic62
#837033
#796223