Finite Group Databasebeta

← #11788577

Subgroups — #11788577

Order 1152.

719 conjugacy classes of subgroups.

The subgroup lattice has 563 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594958C211yesmaximal, characteristic, complemented
2#10594786C211yesmaximal, characteristic
3C3×#5006C211yesmaximal, characteristic, complemented
4C3×#5005C211yesmaximal, characteristic, complemented
5C2×#63568C211yesmaximal, characteristic, complemented
6#10589398C211yesmaximal, characteristic, complemented
7#10589169C211yesmaximal, characteristic, complemented
8#70395—31nomaximal
9#70055—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C32×#117C2211yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C3×#926C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17#67⋊Dic3—22no—
18#63898—21no—
19C4×D3×Dic3—21no—
20#63855—21no—
21#63843—21no—
22#63827—21no—
23#63827C412yescomplemented
24#63823—21no—
25#63823C412yescomplemented
26#63822—22no—
27C3×#806—22no—
28C3×#805—22no—
29#63568—21no—
30#63568—21no—
31Dic3×#41—31no—
32#5822—31no—
33#5822—31no—
34#5522—31no—
35C3×#421—31no—
36C3×#410—31no—
37C2×#837—31no—
38C2×#825—31no—
39#5006D311yescharacteristic, complemented
40#5005D311yescharacteristic, complemented
41#4556—31no—
42#4533—31no—
43#4532—31no—
44#4532—31no—
45#4532—61no—
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3—21no—
48C2×C3×#67—21no—
49C2×C3×#67—21no—
50C3×#235—21no—
51C3×#235—21no—
52C3×#235—21no—
53C3×#235—21no—
54C3×#235—21no—
55C3×#235—21no—
56C3×#235C2×C412yes—
57C3×#235D412yes—
58C2×C3×D12C2×C411yescharacteristic, complemented
59C2×C3×D12D411yescharacteristic
60C2×C3×C4×D3—21no—
61C2×C3×C4×D3—21no—
62C2×C3×Dic6C2×C411yescharacteristic, complemented
63C2×C3×Dic6D411yescharacteristic
64C2×D3×Dic3—22no—
65C32×C4⋊C4—21no—
66C32×C22⋊C4—21no—
67C32×C42—21no—
68C4×C3⋊Dic3—21no—
69C4×C3⋊Dic3D411yescharacteristic
70C4×C3⋊Dic3D411yescharacteristic
71#3748—21no—
72#3748C2×C412yescomplemented
73C2×C3⋊(C3⋊C8)—21no—
74C3×#217D412yes—
75C3×C4⋊Dic3—21no—
76C3×C4×Dic3—21no—
77C3×#208—21no—
78C3×#208—21no—
79C2×C3×C3⋊C8—21no—
80Dic3⋊Dic3—22no—
81(C2×D3)⋊Dic3—22no—
82Dic32—22no—
83#3718—22no—
84#3715—22no—
85#3715—22no—
86#3713—22no—
87#1906—91noSylow
88C2×C3×#41—31no—
89C2×C3×#41—31no—
90C2×#235C2×D311yescharacteristic
91C2×#235C2×D311yescharacteristic
92C2×C3×M16—31no—
93C3×#117—21no—
94C3×#117—31no—
95C3×#117C2×D311yescharacteristic
96C3×#117C2×D311yescharacteristic
97#951—32no—
98#951—61no—
99#950—62no—
100#950—62no—
101#949—32no—
102#949—61no—
103Q8×Dic3—61no—
104#942—32no—
105#942—61no—
106D4×Dic3—61no—
107D4×Dic3—62no—
108#932—32no—
109#932—61no—
110#926—61no—
111#926C2×D311yescharacteristic
112C2×C4×Dic3—31no—
113C2×C4×Dic3—31no—
114C2×C4×Dic3—61no—
115C2×C4×Dic3—61no—
116C2×#208—31no—
117C2×#208—31no—
118C2×#208—61no—
119C2×#208C2×D311yescharacteristic
120#893—61no—
121#887—61no—
122#67⋊C4—62no—
123#872—61no—
124C42×D3—61no—
125C3×#104—62no—
126C3×#99—62no—
127#837—61no—
128#837—61no—
129#825—61no—
130#825—61no—
131#806—22no—
132#805—22no—
133C23×C32C2×D411yescharacteristic
134C22×C3×D3—21no—
135C22×C3×D3—21no—
136C2×C32×C4—41no—
137C2×C32×C4C22×C411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4#4111yescharacteristic
142C2×C32×C4#4111yescharacteristic
143C2×C3⋊Dic3—21no—
144C2×C3⋊Dic3—21no—
145C2×C3⋊Dic3—42no—
146C3×#67—22no—
147C3×#67—22no—
148C3×#67—41no—
149C3×#67—41no—
150C2×C3×Dic3—21no—
151C2×C3×Dic3—21no—
152C2×C3×Dic3—22no—
153C3×D12—21no—
154C3×D12—21no—
155C3×D12—21no—
156C3×D12C22⋊C412yes—
157C3×C4×D3—22no—
158C3×C4×D3—22no—
159C3×C4×D3—41no—
160C3×C4×D3—41no—
161C3×Dic6—21no—
162C3×Dic6—21no—
163C3×Dic6—21no—
164C3×Dic6C22⋊C412yes—
165D3×Dic3—44no—
166C3⋊(C3⋊C8)—22no—
167C3×C3⋊C8—41no—
168#575—91no—
169C4×#41—91no—
170#421—31no—
171C2×#104—91no—
172#410—31no—
173#344—91no—
174#339—91no—
175C3×#41—32no—
176C3×#41—32no—
177C3×#41—61no—
178C3×#41—61no—
179C3×#41—61no—
180C3×#41—61no—
181C3×#41—61no—
182C3×#41—61no—
183C2×C3×Q8—31no—
184C2×C3×Q8—31no—
185C2×C3×D4—31no—
186C2×C3×D4—31no—
187C2×C3×D4—61no—
188C2×C3×D4—61no—
189C22×C3×C4—21no—
190C22×C3×C4—61no—
191C22×C3×C4—61no—
192C22×C3×C4C22×D311yescharacteristic
193C22×C3×C4C22×D311yescharacteristic
194C2×#67—21no—
195C2×#67—21no—
196C22×Dic3—62no—
197C22×Dic3—61no—
198C22×Dic3—61no—
199C22×Dic3—121no—
200#235—21no—
201#235—21no—
202#235—21no—
203#235—21no—
204#235—21no—
205#235—21no—
206#235C4×D312yes—
207#235#6712yes—
208C2×D12C4×D311yescharacteristic, complemented
209C2×D12D1211yescharacteristic
210C2×C4×D3—21no—
211C2×C4×D3—21no—
212C2×C4×D3—62no—
213C2×Dic6C4×D311yescharacteristic, complemented
214C2×Dic6D1211yescharacteristic
215C3×M16—61no—
216C3×M16—61no—
217C2×C3×C8—61no—
218C3×C4⋊C4—22no—
219C3×C4⋊C4—21no—
220C3×C4⋊C4—21no—
221C3×C4⋊C4—61no—
222C3×C22⋊C4—21no—
223C3×C22⋊C4—21no—
224C3×C22⋊C4—32no—
225C3×C22⋊C4—41no—
226C3×C42—21no—
227C3×C42—21no—
228C3×C42—41no—
229C3×C42—61no—
230#217—62no—
231#217#6712yes—
232#216—62no—
233#216—62no—
234#215—62no—
235#215—62no—
236#214—62no—
237#214—62no—
238#213—62no—
239#213—62no—
240(C2×D3)⋊C4—62no—
241C4⋊Dic3—21no—
242C4⋊Dic3—62no—
243Dic3⋊C4—62no—
244C4×Dic3—21no—
245C4×Dic3—31no—
246C4×Dic3—31no—
247C4×Dic3—31no—
248C4×Dic3—31no—
249C4×Dic3—61no—
250C4×Dic3—61no—
251C4×Dic3—62no—
252C4×Dic3—62no—
253C4×Dic3—61no—
254C4×Dic3—61no—
255C4×Dic3—121no—
256#208—21no—
257#208—21no—
258#208—32no—
259#208—32no—
260#208—62no—
261#208—61no—
262#208—61no—
263#208—121no—
264C2×C3⋊C8—21no—
265C2×C3⋊C8—61no—
266C2×C3⋊C8—61no—
267C2×C3⋊C8—121no—
268C22×C32—41no—
269C22×C32C4×D411yescharacteristic
270C22×C32#12011yescharacteristic
271C22×C32#12111yescharacteristic
272C2×C3×D3—22no—
273C2×C3×D3—42no—
274C2×C3×D3—41no—
275C2×C3×D3—81no—
276C32×C4—81no—
277C32×C4C2×C22⋊C411yescharacteristic
278C32×C4C4×D411yescharacteristic
279C32×C4#12111yescharacteristic
280C32×C4#12311yescharacteristic
281C3⋊Dic3—22no—
282C3⋊Dic3—41no—
283C3×Dic3—22no—
284C3×Dic3—42no—
285C3×Dic3—41no—
286C2×#41—31no—
287C2×#41—31no—
288#137—92no—
289#137—181no—
290AGL(1,ℤ/8)—92no—
291AGL(1,ℤ/8)—181no—
292#135—182no—
293C2×M16—31no—
294C2×M16—91no—
295C4×Q8—181no—
296C4×D4—182no—
297C4×D4—181no—
298#117—31no—
299#117—181no—
300#117D3211yescharacteristic
301C2×C42—91no—
302C2×C42—181no—
303#104—62no—
304#104—181no—
305#104—181no—
306#99—62no—
307C23×C3—21no—
308C23×C3—61no—
309C23×C3—61no—
310C23×C3D3×D411yescharacteristic
311C23×C3C2×#6711yescharacteristic
312C22×D3—21no—
313C22×D3—21no—
314C3×Q8—32no—
315C3×Q8—61no—
316C3×Q8—61no—
317C3×Q8—61no—
318C3×D4—32no—
319C3×D4—62no—
320C3×D4—62no—
321C3×D4—61no—
322C3×D4—61no—
323C3×D4—61no—
324C3×D4—121no—
325C3×D4—121no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—42no—
333C2×C3×C4—41no—
334C2×C3×C4—41no—
335C2×C3×C4—61no—
336C2×C3×C4—62no—
337C2×C3×C4—62no—
338C2×C3×C4—61no—
339C2×C3×C4—62no—
340C2×C3×C4—121no—
341C2×C3×C4—121no—
342C2×C3×C4C2×C4×D311yescharacteristic
343C2×C3×C4C2×C4×D311yescharacteristic
344C2×C3×C4C2×D1211yescharacteristic
345C2×C3×C4#23511yescharacteristic
346C2×C3×C4D3×D411yescharacteristic
347C2×C3×C4D3×D411yescharacteristic
348C2×C3×C4D3×D411yescharacteristic
349C2×C3×C4D3×D411yescharacteristic
350C2×C3×C4#23711yescharacteristic
351C2×C3×C4#23711yescharacteristic
352C2×C3×C4#23711yescharacteristic
353C2×C3×C4C2×#6711yescharacteristic
354#67—22no—
355#67—22no—
356#67—41no—
357#67—41no—
358C2×Dic3—21no—
359C2×Dic3—21no—
360C2×Dic3—22no—
361C2×Dic3—61no—
362C2×Dic3—61no—
363C2×Dic3—61no—
364C2×Dic3—61no—
365C2×Dic3—121no—
366C2×Dic3—121no—
367C2×Dic3—124no—
368C2×Dic3—122no—
369C2×Dic3—122no—
370C2×Dic3—124no—
371D12—21no—
372D12—21no—
373D12—21no—
374D12(C2×D3)⋊C412yes—
375C4×D3—22no—
376C4×D3—22no—
377C4×D3—41no—
378C4×D3—41no—
379C4×D3—124no—
380Dic6—21no—
381Dic6—21no—
382Dic6—21no—
383Dic6(C2×D3)⋊C412yes—
384C3×C8—121no—
385C3⋊C8—41no—
386C3⋊C8—62no—
387C3⋊C8—62no—
388C3⋊C8—122no—
389C2×C32—21no—
390C2×C32—21no—
391C2×C32—21no—
392C2×C32#38611yescharacteristic
393C3×D3—42no—
394C3×D3—81no—
395#41—32no—
396#41—32no—
397#41—61no—
398#41—61no—
399#41—61no—
400#41—61no—
401#41—61no—
402#41—61no—
403C2×Q8—31no—
404C2×Q8—31no—
405C2×D4—31no—
406C2×D4—31no—
407C2×D4—61no—
408C2×D4—61no—
409C22×C4—61no—
410C22×C4—61no—
411C22×C4—182no—
412C22×C4—181no—
413C22×C4C2×D3211yescharacteristic
414Q16—182no—
415SD16—182no—
416SD16—182no—
417D8—182no—
418M16—61no—
419M16—61no—
420M16—92no—
421M16—181no—
422C2×C8—61no—
423C2×C8—181no—
424C4⋊C4—21no—
425C4⋊C4—61no—
426C4⋊C4—182no—
427C22⋊C4—21no—
428C22⋊C4—32no—
429C22⋊C4—182no—
430C42—21no—
431C42—61no—
432C42—91no—
433C42—91no—
434C42—182no—
435C42—181no—
436C22×C3—21no—
437C22×C3—21no—
438C22×C3—21no—
439C22×C3—41no—
440C22×C3—41no—
441C22×C3—42no—
442C22×C3—62no—
443C22×C3—122no—
444C22×C3—121no—
445C22×C3—241no—
446C22×C3#67⋊C411yescharacteristic
447C22×C3#88211yescharacteristic
448C22×C3C4×#6711yescharacteristic
449C22×C3#93711yescharacteristic
450C22×C3#93811yescharacteristic
451C22×C3#93911yescharacteristic
452C2×D3—22no—
453C2×D3—42no—
454C2×D3—41no—
455C2×D3—81no—
456C3×C4—21no—
457C3×C4—21no—
458C3×C4—21no—
459C3×C4—21no—
460C3×C4—62no—
461C3×C4—82no—
462C3×C4—81no—
463C3×C4—81no—
464C3×C4—122no—
465C3×C4—121no—
466C3×C4D3×C22⋊C411yescharacteristic
467C3×C4#67⋊C411yescharacteristic
468C3×C4#67⋊C411yescharacteristic
469C3×C4#88311yescharacteristic
470C3×C4#88411yescharacteristic
471C3×C4#88611yescharacteristic
472C3×C4C2×(C2×D3)⋊C411yescharacteristic
473C3×C4#93911yescharacteristic
474Dic3—22no—
475Dic3—42no—
476Dic3—41no—
477Dic3—62no—
478Dic3—62no—
479Dic3—122no—
480Dic3—121no—
481Dic3—121no—
482Dic3—122no—
483C32#190611yescharacteristic, complemented, Sylow
484C23—61no—
485C23—61no—
486C23D3×#6711yescharacteristic
487Q8—32no—
488Q8—61no—
489Q8—61no—
490Q8—61no—
491D4—32no—
492D4—62no—
493D4—62no—
494D4—61no—
495D4—61no—
496D4—61no—
497D4—121no—
498D4—121no—
499C2×C4—41no—
500C2×C4—61no—
501C2×C4—62no—
502C2×C4—62no—
503C2×C4—61no—
504C2×C4—62no—
505C2×C4—121no—
506C2×C4—121no—
507C2×C4—181no—
508C2×C4—181no—
509C2×C4—364no—
510C2×C4—362no—
511C2×C4#379511yescharacteristic
512C2×C4C4×D3211yescharacteristic
513C2×C4D3×D1211yescharacteristic
514C2×C4#380211yescharacteristic
515C2×C4#380511yescharacteristic
516C2×C4D3×#6711yescharacteristic
517C8—121no—
518C8—182no—
519C2×C3—22no—
520C2×C3—21no—
521C2×C3—21no—
522C2×C3—21no—
523C2×C3—21no—
524C2×C3—21no—
525C2×C3—21no—
526C2×C3—21no—
527C2×C3—41no—
528C2×C3—41no—
529C2×C3—122no—
530C2×C3—241no—
531C2×C3#495611yescharacteristic
532C2×C3#495811yescharacteristic
533D3—42no—
534D3—81no—
535C22—41no—
536C22—62no—
537C22—122no—
538C22—121no—
539C22—241no—
540C22#6387911yescharacteristic
541C22#6392211yescharacteristic
542C22#6397011yescharacteristic
543C4—62no—
544C4—81no—
545C4—122no—
546C4—121no—
547C4—182no—
548C4—361no—
549C4#6388511yescharacteristic
550C4#6389111yescharacteristic
551C4#6390211yescharacteristic
552C4D3×(C2×D3)⋊C411yescharacteristic
553C3—21no—
554C3#7005511yescharacteristic, complemented
555C3#7039511yescharacteristic, complemented
556C2—21no—
557C2—21no—
558C2—21no—
559C2—122no—
560C2—241no—
561C2#1059136311yescharacteristic
subgroupG/H
centerC4#63885
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC2×C32#386
prime radical#10594786C2
cosocleC22×C32×C4C23
hypercenter#117D32
hypocenterC32#1906
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #10594958C2semidirect
3. C3×#5006C2semidirect
4. C3×#5005C2semidirect
5. C2×#63568C2semidirect
6. #10589398C2semidirect
7. #10589169C2semidirect
23. #63827C4semidirect
25. #63823C4semidirect
39. #5006D3semidirect
40. #5005D3semidirect
58. C2×C3×D12C2×C4semidirect
62. C2×C3×Dic6C2×C4semidirect
72. #3748C2×C4semidirect
208. C2×D12C4×D3semidirect
213. C2×Dic6C4×D3semidirect
483. C32#1906semidirect
554. C3#70055semidirect
555. C3#70395semidirect

Maximal subgroups

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

subgroupindex
#105949582
#105947862
C3×#50062
C3×#50052
C2×#635682
#105893982
#105891692
#703953
#700553