Finite Group Databasebeta

← #11898301

Subgroups — #11898301

Order 1152.

879 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5721C211yesmaximal, characteristic, complemented
2#10593902C211yesmaximal, characteristic
3#10592784C211yesmaximal, characteristic, complemented
4C3×#5083C211yesmaximal, characteristic, complemented
5#10591618C212yesmaximal, complemented
6#10591617C212yesmaximal, complemented
7#10591565C212yesmaximal, complemented
8#10591536C212yesmaximal, complemented
9#10590367C211yesmaximal, characteristic, complemented
10C4×#3715C211yesmaximal, characteristic, complemented
11#10590250C211yesmaximal, characteristic, complemented
12#83685—31nomaximal
13#80420—31nomaximal
14C2×#3799—21no—
15C32×C4⋊Q8C2211yescharacteristic
16C2×#3755C2212yes—
17C2×#3755C2212yes—
18#64083C2211yescharacteristic
19C3×Q8×Dic3C2212yes—
20C3×#944C2212yes—
21C2×C3×#215C2212yes—
22C3×#890—21no—
23C3×#889—22no—
24C3×#887—21no—
25C3×C4×D12C2211yescharacteristic
26C3×C4×Dic6C2211yescharacteristic
27C3×C4×Dic6C2211yescharacteristic
28#63911C2212yes—
29#63910—22no—
30#63909—21no—
31#63894C2212yes—
32C2×#3717C2212yes—
33C2×#3715C2211yescharacteristic
34C4×C3⋊(C3⋊C8)C2211yescharacteristic
35C3×#835C2212yes—
36C3×C4⋊(C3⋊C8)C2211yescharacteristic
37#63574C2211yescharacteristic
38Dic3⋊(C3⋊C8)C2212yes—
39#63565C2211yescharacteristic
40#63564C2212yes—
41#63562C2211yescharacteristic
42Dic3×C3⋊C8C2212yes—
43C3×#557—31no—
44#5721D311yescharacteristic, complemented
45#5577—31no—
46#5553—31no—
47C3×#461—31no—
48#5175—32no—
49#5163—32no—
50#5085—31no—
51#5085—31no—
52#5085—32no—
53#5085—61no—
54#5083—32no—
55#5083D311yescharacteristic, complemented
56#5027—32no—
57#5027—31no—
58C4×#215—31no—
59C4×#215—32no—
60Q8×C3⋊C8—31no—
61C4×#214—31no—
62#4848—31no—
63#4830—31no—
64#4818—32no—
65#4788—32no—
66C2×C32×Q8C2312yes—
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×Dic6D411yescharacteristic
73C2×C3×Dic6C2311yescharacteristic
74C2×#626—22no—
75C2×#626—22no—
76C2×#624—22no—
77#3799—44no—
78C32×C4⋊C4—21no—
79C32×C4⋊C4—21no—
80C32×C42C2311yescharacteristic
81#3755—24no—
82#3755—42no—
83C2×C3⋊(C3⋊C8)C2311yescharacteristic
84C2×C3⋊(C3⋊C8)C2311yescharacteristic
85C3×#215—42no—
86C3×(C2×D3)⋊C4—21no—
87C3×C4⋊Dic3—22no—
88C3×C4⋊Dic3D411yescharacteristic
89C3×C4⋊Dic3C2311yescharacteristic
90C3×C4⋊Dic3C2311yescharacteristic
91C3×Dic3⋊C4—21no—
92C3×Dic3⋊C4—22no—
93C3×Dic3⋊C4—22no—
94C3×Dic3⋊C4D412yes—
95C3×C4×Dic3—21no—
96C3×C4×Dic3—22no—
97C3×C4×Dic3C2312yes—
98C2×C3×C3⋊C8C2312yes—
99#3722—22no—
100#3717—42no—
101#3715—22no—
102#3392—91noSylow
103C2×#239—61no—
104C2×#235—61no—
105C2×C3×SD16—32no—
106C3×C4⋊Q8—21no—
107C3×C4⋊Q8—32no—
108C3×C4⋊Q8C2×D311yescharacteristic
109C3×C4⋊Q8C2×D311yescharacteristic
110C3×#125—62no—
111C3×#125—61no—
112C3×C4×Q8—31no—
113C3×C4×Q8—32no—
114C3×C4×Q8—31no—
115C3×C4×Q8—61no—
116C3×C4×D4—31no—
117Q8×Dic3C2×D312yes—
118#944C2×D312yes—
119C2×#215—32no—
120C2×#215—32no—
121C2×#215—31no—
122C2×#215—32no—
123C2×#215—32no—
124C2×#215—32no—
125C2×#215—62no—
126C2×#215—62no—
127C2×#215C2×D312yes—
128#940—32no—
129C2×#214—31no—
130#930—61no—
131C2×#204—32no—
132#895—62no—
133#895—61no—
134#893—32no—
135#890—21no—
136#889—22no—
137#887—21no—
138#884—62no—
139#874—32no—
140#874—31no—
141#874—31no—
142#874—61no—
143C4×D12—32no—
144C4×D12C2×D311yescharacteristic
145C4×Dic6C2×D311yescharacteristic
146C4×Dic6C2×D311yescharacteristic
147C3×C4⋊C8—31no—
148C3×#103—32no—
149#835—31no—
150#835C2×D312yes—
151#832—31no—
152#821—32no—
153Dic3⋊C8—32no—
154C8×Dic3—32no—
155#810—31no—
156#809—31no—
157#809—32no—
158#808—31no—
159#808—31no—
160C4⋊(C3⋊C8)—32no—
161C4⋊(C3⋊C8)C2×D311yescharacteristic
162C4×C3⋊C8—31no—
163C4×C3⋊C8—31no—
164C4×C3⋊C8—32no—
165C4×C3⋊C8—61no—
166C22×C3⋊D3—22no—
167C22×C3×D3—21no—
168C32×Q8—22no—
169C32×Q8—22no—
170C2×C32×C4—22no—
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2411yescharacteristic
174C4⋊(C3⋊D3)—22no—
175C4⋊(C3⋊D3)—22no—
176C4⋊(C3⋊D3)—42no—
177C4⋊(C3⋊D3)—81no—
178C2×C3×Dic3—21no—
179C2×C3×Dic3—21no—
180C2×C3×Dic3—21no—
181C2×C3×Dic3C2×D412yes—
182C2×C3×Dic3C2×D412yes—
183C3×D12—21no—
184C3×D12—21no—
185C3×C4×D3—42no—
186C3×Dic6—21no—
187C3×Dic6—21no—
188C3×Dic6SD1614yescomplemented
189#626—44no—
190#626—82no—
191#624—44no—
192C3⋊(C3⋊C8)—21no—
193C3⋊(C3⋊C8)#4112yescomplemented
194C3×C3⋊C8—22no—
195#557—31no—
196#550—91no—
197#492—92no—
198#492—91no—
199#461—31no—
200#461—92no—
201#460—91no—
202#460—92no—
203C8×Q8—91no—
204C4×SD16—92no—
205C4×SD16—91no—
206C2×C3×Q8—22no—
207C2×C3×Q8—31no—
208C2×C3×Q8—31no—
209C2×C3×Q8C22×D312yes—
210C2×C3×Q8C22×D312yes—
211C2×C3×D4—31no—
212C22×C3×C4—61no—
213C2×#67—62no—
214C2×#67—62no—
215#239—124no—
216#235—124no—
217C2×D12—32no—
218C2×D12—32no—
219C2×D12—62no—
220C2×D12—62no—
221C2×D12—61no—
222C2×D12—61no—
223C2×D12—62no—
224C2×D12—61no—
225C2×D12—61no—
226C2×D12—121no—
227C2×D12—121no—
228C2×D12C22×D311yescharacteristic
229C2×C4×D3—21no—
230C2×C4×D3—62no—
231C2×C4×D3—62no—
232C2×Dic6#6711yescharacteristic
233C2×Dic6C22×D311yescharacteristic
234C3×SD16—122no—
235C2×C3×C8—32no—
236C3×C4⋊C4—21no—
237C3×C4⋊C4—21no—
238C3×C4⋊C4—21no—
239C3×C4⋊C4—21no—
240C3×C4⋊C4—32no—
241C3×C4⋊C4—31no—
242C3×C4⋊C4—31no—
243C3×C4⋊C4—31no—
244C3×C4⋊C4—41no—
245C3×C4⋊C4—41no—
246C3×C4⋊C4—62no—
247C3×C4⋊C4—62no—
248C3×C4⋊C4—62no—
249C3×C4⋊C4—61no—
250C3×C22⋊C4—61no—
251C3×C42—21no—
252C3×C42—32no—
253C3×C42—62no—
254C3×C42—61no—
255C3×C42C22×D311yescharacteristic
256C3×C42C22×D311yescharacteristic
257#215—42no—
258#215—62no—
259#215—64no—
260#215—64no—
261#215—124no—
262#215—122no—
263#215—122no—
264#215—122no—
265#215—124no—
266#214—62no—
267(C2×D3)⋊C4—21no—
268(C2×D3)⋊C4—62no—
269(C2×D3)⋊C4—62no—
270C4⋊Dic3—22no—
271C4⋊Dic3#6711yescharacteristic
272C4⋊Dic3C22×D311yescharacteristic
273C4⋊Dic3C22×D311yescharacteristic
274Dic3⋊C4—21no—
275Dic3⋊C4—22no—
276Dic3⋊C4—22no—
277Dic3⋊C4#6712yes—
278C4×Dic3—21no—
279C4×Dic3—22no—
280C4×Dic3C22×D312yes—
281C2×C3⋊C8—31no—
282C2×C3⋊C8—31no—
283C2×C3⋊C8—31no—
284C2×C3⋊C8—31no—
285C2×C3⋊C8—61no—
286C2×C3⋊C8—61no—
287C2×C3⋊C8C22×D312yes—
288#204—122no—
289C22×C32C22×D411yescharacteristic
290C2×C3⋊D3—42no—
291C2×C3⋊D3—42no—
292C2×C3⋊D3—42no—
293C2×C3×D3—41no—
294C2×C3×D3—41no—
295C2×C3×D3—41no—
296C32×C4—21no—
297C32×C4—42no—
298C32×C4C2×SD1612yes—
299C32×C4C2×#4111yescharacteristic
300C32×C4H(5,𝔽2)11yescharacteristic
301C3×Dic3—22no—
302C3×Dic3—41no—
303C3×Dic3—41no—
304C3×Dic3—41no—
305C3×Dic3C2×SD1614yes—
306C2×#41—181no—
307C2×SD16—32no—
308C2×SD16—92no—
309C2×SD16—91no—
310C2×SD16—92no—
311C2×SD16—92no—
312C4⋊Q8—32no—
313C4⋊Q8D3211yescharacteristic
314#127—92no—
315#127—91no—
316#125—62no—
317#125—61no—
318#121—182no—
319#121—181no—
320C4×Q8—31no—
321C4×Q8—32no—
322C4×Q8—31no—
323C4×Q8—61no—
324C4×D4—31no—
325C4×D4—92no—
326#106—91no—
327C4⋊C8—31no—
328C4⋊C8—92no—
329#103—32no—
330#103—91no—
331#102—92no—
332#102—91no—
333C4×C8—92no—
334C4×C8—91no—
335C23×C3—61no—
336C22×D3—21no—
337C22×D3—62no—
338C22×D3—62no—
339C22×D3—122no—
340C3×Q8—22no—
341C3×Q8—22no—
342C3×Q8—22no—
343C3×Q8—22no—
344C3×Q8—34no—
345C3×Q8—42no—
346C3×Q8—42no—
347C3×Q8—61no—
348C3×Q8—61no—
349C3×D4—61no—
350C3×D4—61no—
351C2×C3×C4—22no—
352C2×C3×C4—22no—
353C2×C3×C4—21no—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—32no—
357C2×C3×C4—32no—
358C2×C3×C4—42no—
359C2×C3×C4—61no—
360C2×C3×C4—61no—
361C2×C3×C4—61no—
362C2×C3×C4—122no—
363C2×C3×C4D3×D411yescharacteristic
364C2×C3×C4D3×D411yescharacteristic
365C2×C3×C4C2×#6711yescharacteristic
366C2×C3×C4C2×#6711yescharacteristic
367C2×C3×C4C23×D311yescharacteristic
368C2×C3×C4C23×D311yescharacteristic
369#67—124no—
370#67—242no—
371C2×Dic3—21no—
372C2×Dic3—21no—
373C2×Dic3—21no—
374C2×Dic3C2×#6712yes—
375C2×Dic3C2×#6712yes—
376D12—21no—
377D12—21no—
378D12—62no—
379D12—62no—
380D12—62no—
381D12—62no—
382D12—122no—
383D12—122no—
384D12—124no—
385D12—122no—
386D12—122no—
387D12—242no—
388D12—241no—
389D12—241no—
390D12—242no—
391D12—242no—
392C4×D3—42no—
393C4×D3—124no—
394C4×D3—124no—
395Dic6—21no—
396Dic6—21no—
397Dic6#21514yescomplemented
398C3×C8—62no—
399C3⋊C8—22no—
400C3⋊C8—32no—
401C3⋊C8—32no—
402C3⋊C8—62no—
403C3⋊C8—62no—
404C3⋊C8—61no—
405C3⋊C8—61no—
406C2×C32#55011yescharacteristic
407C2×C32C22×SD1611yescharacteristic
408C2×C32#57711yescharacteristic
409C3⋊D3—82no—
410C3×D3—81no—
411#41—364no—
412C2×Q8—31no—
413C2×Q8—31no—
414C2×Q8C2×D3212yes—
415C2×D4—31no—
416C2×D4—92no—
417C2×D4—182no—
418C2×D4—182no—
419C2×D4—181no—
420C2×D4—181no—
421C22×C4—61no—
422C22×C4—182no—
423SD16—122no—
424SD16—182no—
425SD16—184no—
426SD16—362no—
427SD16—362no—
428C2×C8—32no—
429C2×C8—91no—
430C2×C8—91no—
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—32no—
434C4⋊C4—31no—
435C4⋊C4—31no—
436C4⋊C4—31no—
437C4⋊C4—62no—
438C4⋊C4—62no—
439C4⋊C4—62no—
440C4⋊C4—61no—
441C22⋊C4—61no—
442C22⋊C4—182no—
443C42—32no—
444C42—62no—
445C42—61no—
446C42C2×D3211yescharacteristic
447C22×C3—21no—
448C22×C3—121no—
449C22×C3—121no—
450C22×C3—121no—
451C22×C3C2×D3×D411yescharacteristic
452C22×C3C22×#6711yescharacteristic
453C2×D3—41no—
454C2×D3—41no—
455C2×D3—41no—
456C2×D3—122no—
457C2×D3—122no—
458C2×D3—122no—
459C2×D3—122no—
460C2×D3—122no—
461C2×D3—122no—
462C2×D3—242no—
463C2×D3—242no—
464C2×D3—242no—
465C3×C4—22no—
466C3×C4—21no—
467C3×C4—21no—
468C3×C4—21no—
469C3×C4—21no—
470C3×C4—22no—
471C3×C4—34no—
472C3×C4—42no—
473C3×C4—42no—
474C3×C4—62no—
475C3×C4—82no—
476C3×C4—121no—
477C3×C4—121no—
478C3×C4—121no—
479C3×C4D3×SD1612yes—
480C3×C4C2×#21512yes—
481C3×C4#100411yescharacteristic
482C3×C4D3×#4111yescharacteristic
483C3×C4D3×#4111yescharacteristic
484C3×C4#100911yescharacteristic
485Dic3—22no—
486Dic3—41no—
487Dic3—41no—
488Dic3—41no—
489Dic3C2×#21514yes—
490C32#339211yescharacteristic, complemented, Sylow
491C23—61no—
492C23—182no—
493Q8—22no—
494Q8—22no—
495Q8—34no—
496Q8—61no—
497Q8—61no—
498D4—61no—
499D4—61no—
500D4—182no—
501D4—182no—
502D4—364no—
503D4—362no—
504D4—721no—
505D4—722no—
506C2×C4—22no—
507C2×C4—32no—
508C2×C4—32no—
509C2×C4—61no—
510C2×C4—61no—
511C2×C4—61no—
512C2×C4—122no—
513C2×C4—364no—
514C2×C4D3×#6711yescharacteristic
515C2×C4D3×#6711yescharacteristic
516C2×C4C22×D3211yescharacteristic
517C8—62no—
518C8—92no—
519C8—181no—
520C2×C3—21no—
521C2×C3—21no—
522C2×C3—21no—
523C2×C3—241no—
524C2×C3#559911yescharacteristic
525C2×C3C2×D3×SD1611yescharacteristic
526C2×C3#577811yescharacteristic
527C2×C3C22×#21511yescharacteristic
528C2×C3#583411yescharacteristic
529C2×C3#583711yescharacteristic
530D3—81no—
531D3—242no—
532D3—242no—
533D3—482no—
534C22—121no—
535C22—121no—
536C22—121no—
537C22—362no—
538C22—362no—
539C22—362no—
540C22C2×D3×#6711yescharacteristic
541C4—21no—
542C4—34no—
543C4—42no—
544C4—62no—
545C4—121no—
546C4—121no—
547C4—121no—
548C4D3×#21512yes—
549C4#6431211yescharacteristic
550C4#6431411yescharacteristic
551C3—21no—
552C3#8042011yescharacteristic, complemented
553C3#8368511yescharacteristic, complemented
554C2—241no—
555C2—722no—
556C2#1059523611yescharacteristic
557C2C2×D3×#21511yescharacteristic
558C2#1059531911yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radical#10593902C2
hypercenterC4⋊Q8D32
hypocenterC32#3392
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×#5721C2semidirect
3. #10592784C2semidirect
4. C3×#5083C2semidirect
5. #10591618C2semidirect
6. #10591617C2semidirect
7. #10591565C2semidirect
8. #10591536C2semidirect
9. #10590367C2semidirect
10. C4×#3715C2semidirect
11. #10590250C2semidirect
44. #5721D3semidirect
55. #5083D3semidirect
188. C3×Dic6SD16semidirect
193. C3⋊(C3⋊C8)#41semidirect
397. Dic6#215semidirect
490. C32#3392semidirect
552. C3#80420semidirect
553. C3#83685semidirect

Maximal subgroups

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

subgroupindex
C3×#57212
#105939022
#105927842
C3×#50832
#105916182
#105916172
#105915652
#105915362
#105903672
C4×#37152
#105902502
#836853
#804203