Finite Group Databasebeta

← #11860635

Subgroups — #11860635

Order 1152.

999 conjugacy classes of subgroups.

The subgroup lattice has 565 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5516C211yesmaximal, characteristic, complemented
2#10594992C211yesmaximal, characteristic
3C2×#63827C211yesmaximal, characteristic
4#10592694C211yesmaximal, characteristic, complemented
5C3×#5002C211yesmaximal, characteristic
6C2×#63566C211yesmaximal, characteristic, complemented
7#10591055C211yesmaximal, characteristic, complemented
8#10590477C212yesmaximal, complemented
9#10590476C212yesmaximal, complemented
10#10590454C212yesmaximal, complemented
11#10590453C212yesmaximal, complemented
12#82547—31nomaximal
13#78821—31nomaximal
14C2×C3×#235C2211yescharacteristic
15C22×C3×Dic6C2211yescharacteristic
16C32×#117C2211yescharacteristic
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C2×#3748C2211yescharacteristic
19C3×#926C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C3×#887C2212yes—
22C3×#887C2212yes—
23C3×#877—22no—
24C3×C4×Dic6—21no—
25C3×C4×Dic6—21no—
26#67⋊Dic3—22no—
27Dic3×D12C2212yes—
28D3×C4⋊Dic3—21no—
29Dic3×Dic6C2212yes—
30#63841—21no—
31C2×#3718C2212yes—
32#63827C418yescomplemented
33C2×#3715C2212yes—
34#63635C2212yes—
35#63634C2212yes—
36C3×#810C2211yescharacteristic
37C3×#810C2211yescharacteristic
38C3×#809C2211yescharacteristic
39C3×#809C2211yescharacteristic
40#63566C2212yes—
41#63566C2212yes—
42#63554C2212yes—
43Dic3×C3⋊C8C2212yes—
44C3×#519—31no—
45#5827—31no—
46C2×#951—31no—
47C2×#942—31no—
48#5523—31no—
49#5516D311yescharacteristic, complemented
50C3×#416—31no—
51C2×#835—31no—
52C2×#816—31no—
53#5101—31no—
54#5030—32no—
55C4×#216—32no—
56#5026—32no—
57C4×#215—32no—
58#5002D311yescharacteristic
59#4997—31no—
60#4995—31no—
61#4995—31no—
62#4995—61no—
63#4790—32no—
64#4789—32no—
65#4758—32no—
66#4757—32no—
67C22×C32×C4C2311yescharacteristic
68C22×C3⋊Dic3—21no—
69C2×C3×#67—21no—
70C22×C3×Dic3—21no—
71C3×#235—22no—
72C3×#235C2×C414yes—
73C2×C3×D12C2311yescharacteristic
74C2×C3×C4×D3—21no—
75C2×C3×Dic6—21no—
76C2×C3×Dic6—22no—
77C2×C3×Dic6C2×C414yescomplemented
78C2×C3×Dic6C2312yes—
79C2×C3×Dic6C2311yescharacteristic
80C2×D3×Dic3—22no—
81C32×C4⋊C4C2311yescharacteristic
82C32×C4⋊C4C2311yescharacteristic
83C32×C22⋊C4—21no—
84C32×C42—21no—
85C4⋊(C3⋊Dic3)—21no—
86C4⋊(C3⋊Dic3)C2312yes—
87#3748C2×C414yescomplemented
88C2×C3⋊(C3⋊C8)C2312yes—
89C3×#217D412yes—
90C3×C4⋊Dic3D411yescharacteristic
91C3×C4⋊Dic3D411yescharacteristic
92C3×Dic3⋊C4—22no—
93C3×Dic3⋊C4—22no—
94C3×C4×Dic3—22no—
95C3×C4×Dic3—22no—
96C3×C4×Dic3C2312yes—
97C2×C3×C3⋊C8—22no—
98C2×C3×C3⋊C8C2311yescharacteristic
99C2×C3×C3⋊C8C2311yescharacteristic
100Dic3⋊Dic3—22no—
101(C2×D3)⋊Dic3—22no—
102Dic32—22no—
103#3718C2×C418yescomplemented
104#3715C2×C418yescomplemented
105#2947—91noSylow
106C2×C3×#41—31no—
107C22×C3×Q8—31no—
108C2×#235C2×D311yescharacteristic
109C22×Dic6C2×D311yescharacteristic
110C22×C3×C8—31no—
111C3×C4×Q8—32no—
112C3×C4×Q8—32no—
113C3×C4×Q8—61no—
114C3×C4×Q8—61no—
115C3×#117—21no—
116C3×#117—31no—
117C3×#117—62no—
118C3×#117C2×D311yescharacteristic
119C3×#117C2×D311yescharacteristic
120#951—38no—
121Q8×Dic3—32no—
122C2×#216—32no—
123C2×#216—32no—
124#942—38no—
125C2×#215—32no—
126D4×Dic3—32no—
127D4×Dic3—62no—
128C2×#214—32no—
129#926—61no—
130#926C2×D311yescharacteristic
131C2×C4⋊Dic3—31no—
132C2×C4⋊Dic3—31no—
133C2×C4⋊Dic3—61no—
134C2×C4⋊Dic3—61no—
135C2×#208—31no—
136C2×#208—31no—
137C2×#208—61no—
138C22×C3⋊C8C2×D311yescharacteristic
139#892—61no—
140D3×C4⋊C4—61no—
141#887C2×D312yes—
142#887C2×D312yes—
143#67⋊C4—62no—
144#877—22no—
145C4×D12—32no—
146C4×Dic6—21no—
147C4×Dic6—21no—
148C4×Dic6—32no—
149C3×#103—31no—
150C3×#103—31no—
151C3×#102—31no—
152C3×#102—31no—
153#835—32no—
154#835—32no—
155#816—32no—
156#816—32no—
157#815—32no—
158C8×Dic3—32no—
159#810C2×D311yescharacteristic
160#810C2×D311yescharacteristic
161#809C2×D311yescharacteristic
162#809C2×D311yescharacteristic
163#808—32no—
164#808—32no—
165#808—62no—
166#807—32no—
167#807—32no—
168#807—62no—
169#803—32no—
170C4×C3⋊C8—32no—
171C23×C32C2×D411yescharacteristic
172C22×C3×D3—21no—
173C2×C32×C4—21no—
174C2×C32×C4—21no—
175C2×C32×C4C22×C412yes—
176C2×C32×C4C2×D411yescharacteristic
177C2×C32×C4#4112yes—
178C2×C32×C4C2411yescharacteristic
179C2×C3⋊Dic3—22no—
180C2×C3⋊Dic3—81no—
181C3×#67—24no—
182C2×C3×Dic3—24no—
183C2×C3×Dic3—21no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3C2×D412yes—
186C2×C3×Dic3C2×D412yes—
187C3×D12—21no—
188C3×D12C22×C412yes—
189C3×C4×D3—24no—
190C3×Dic6—24no—
191C3×Dic6—22no—
192C3×Dic6—21no—
193C3×Dic6C22×C414yes—
194C3×Dic6C22×C412yes—
195D3×Dic3—82no—
196C3⋊(C3⋊C8)C22×C414yes—
197C3×C3⋊C8—21no—
198C3×C3⋊C8—21no—
199C2×#137—91no—
200#520—91no—
201#519—31no—
202#441—92no—
203#440—92no—
204C4×Q16—92no—
205C4×SD16—92no—
206#428—91no—
207#416—31no—
208C2×#103—91no—
209#405—91no—
210C3×#41—34no—
211C3×#41—62no—
212C2×C3×Q8—34no—
213C2×C3×Q8—32no—
214C2×C3×Q8—31no—
215C2×C3×Q8—61no—
216C2×C3×Q8—62no—
217C2×C3×D4—31no—
218C2×C3×D4—61no—
219C22×C3×C4—21no—
220C22×C3×C4—61no—
221C22×C3×C4—61no—
222C22×C3×C4C22×D311yescharacteristic
223C22×C3×C4C22×D311yescharacteristic
224C2×#67—21no—
225C22×Dic3—21no—
226C22×Dic3—61no—
227C22×Dic3—61no—
228C22×Dic3—62no—
229C22×Dic3—121no—
230#235—22no—
231#235C4×D314yes—
232C2×D12C22×D311yescharacteristic
233C2×C4×D3—21no—
234C2×C4×D3—62no—
235C2×Dic6—22no—
236C2×Dic6—21no—
237C2×Dic6C4×D314yescomplemented
238C2×Dic6C22×D311yescharacteristic
239C2×Dic6C22×D312yes—
240C2×C3×C8—31no—
241C2×C3×C8—31no—
242C2×C3×C8—62no—
243C3×C4⋊C4—21no—
244C3×C4⋊C4—21no—
245C3×C4⋊C4—31no—
246C3×C4⋊C4—31no—
247C3×C4⋊C4—62no—
248C3×C4⋊C4—62no—
249C3×C4⋊C4C22×D311yescharacteristic
250C3×C4⋊C4C22×D311yescharacteristic
251C3×C4⋊C4C22×D311yescharacteristic
252C3×C4⋊C4C22×D311yescharacteristic
253C3×C22⋊C4—21no—
254C3×C22⋊C4—21no—
255C3×C22⋊C4—32no—
256C3×C22⋊C4—41no—
257C3×C42—21no—
258C3×C42—21no—
259C3×C42—32no—
260C3×C42—41no—
261C3×C42—62no—
262C3×C42—62no—
263#217—62no—
264#217#6712yes—
265#216—38no—
266#216—38no—
267#215—38no—
268#214—38no—
269(C2×D3)⋊C4—62no—
270C4⋊Dic3—32no—
271C4⋊Dic3—32no—
272C4⋊Dic3—62no—
273C4⋊Dic3—61no—
274C4⋊Dic3—61no—
275C4⋊Dic3—62no—
276C4⋊Dic3—121no—
277C4⋊Dic3#6711yescharacteristic
278C4⋊Dic3#6711yescharacteristic
279Dic3⋊C4—22no—
280Dic3⋊C4—22no—
281Dic3⋊C4—62no—
282C4×Dic3—22no—
283C4×Dic3—22no—
284C4×Dic3—62no—
285C4×Dic3—62no—
286C4×Dic3C22×D312yes—
287#208—34no—
288#208—34no—
289#208—64no—
290C2×C3⋊C8—22no—
291C2×C3⋊C8—32no—
292C2×C3⋊C8—32no—
293C2×C3⋊C8—62no—
294C2×C3⋊C8C22×D311yescharacteristic
295C2×C3⋊C8C22×D311yescharacteristic
296C22×C32—21no—
297C22×C32—21no—
298C22×C32C4×D412yes—
299C22×C32C22×D411yescharacteristic
300C2×C3×D3—22no—
301C2×C3×D3—41no—
302C2×C3×D3—41no—
303C32×C4—41no—
304C32×C4—41no—
305C32×C4C4×D412yes—
306C32×C4C23×C411yescharacteristic
307C32×C4C2×#4111yescharacteristic
308C3⋊Dic3—42no—
309C3×Dic3—24no—
310C3×Dic3—22no—
311C3×Dic3—22no—
312C3×Dic3—22no—
313C2×#41—31no—
314C22×Q8—31no—
315#137—98no—
316C2×Q16—92no—
317C2×SD16—92no—
318C2×M16—91no—
319C22×C8—31no—
320C4×Q8—32no—
321C4×Q8—32no—
322C4×Q8—61no—
323C4×Q8—61no—
324C4×Q8—92no—
325C4×D4—92no—
326C4×D4—182no—
327#117—31no—
328#117—62no—
329#117—181no—
330#117D3211yescharacteristic
331C2×C4⋊C4—91no—
332C2×C4⋊C4—181no—
333#107—92no—
334#106—92no—
335#103—31no—
336#103—31no—
337#103—92no—
338#103—92no—
339#102—31no—
340#102—31no—
341#97—92no—
342C4×C8—92no—
343C23×C3—21no—
344C23×C3—61no—
345C23×C3D3×D411yescharacteristic
346C23×C3C2×#6711yescharacteristic
347C22×D3—21no—
348C3×Q8—34no—
349C3×Q8—32no—
350C3×Q8—64no—
351C3×Q8—61no—
352C3×Q8—62no—
353C3×D4—32no—
354C3×D4—64no—
355C3×D4—61no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—21no—
360C2×C3×C4—21no—
361C2×C3×C4—22no—
362C2×C3×C4—22no—
363C2×C3×C4—21no—
364C2×C3×C4—32no—
365C2×C3×C4—32no—
366C2×C3×C4—41no—
367C2×C3×C4—41no—
368C2×C3×C4—64no—
369C2×C3×C4—62no—
370C2×C3×C4—61no—
371C2×C3×C4—64no—
372C2×C3×C4C2×C4×D312yes—
373C2×C3×C4C2×C4×D312yes—
374C2×C3×C4#23512yes—
375C2×C3×C4D3×D411yescharacteristic
376C2×C3×C4#23712yes—
377C2×C3×C4C2×#6711yescharacteristic
378C2×C3×C4C23×D311yescharacteristic
379C2×C3×C4C23×D311yescharacteristic
380#67—24no—
381C2×Dic3—24no—
382C2×Dic3—21no—
383C2×Dic3—22no—
384C2×Dic3—62no—
385C2×Dic3—62no—
386C2×Dic3—122no—
387C2×Dic3—242no—
388C2×Dic3—241no—
389C2×Dic3—241no—
390C2×Dic3—242no—
391C2×Dic3C2×#6712yes—
392C2×Dic3C2×#6712yes—
393D12—21no—
394D12C2×C4×D312yes—
395C4×D3—24no—
396C4×D3—242no—
397Dic6—24no—
398Dic6—22no—
399Dic6—21no—
400Dic6C2×C4×D314yes—
401Dic6C2×C4×D312yes—
402C3×C8—61no—
403C3×C8—61no—
404C3⋊C8—21no—
405C3⋊C8—21no—
406C3⋊C8—34no—
407C3⋊C8—34no—
408C3⋊C8—64no—
409C2×C32—22no—
410C2×C32C2×C4×D411yescharacteristic
411C2×C32#57711yescharacteristic
412C2×C32#57811yescharacteristic
413C3×D3—42no—
414#41—34no—
415#41—62no—
416C2×Q8—31no—
417C2×Q8—32no—
418C2×Q8—34no—
419C2×Q8—62no—
420C2×Q8—61no—
421C2×D4—31no—
422C2×D4—61no—
423C22×C4—61no—
424C22×C4—61no—
425C22×C4—182no—
426C22×C4—181no—
427C22×C4C2×D3211yescharacteristic
428Q16—98no—
429SD16—98no—
430M16—94no—
431C2×C8—31no—
432C2×C8—31no—
433C2×C8—62no—
434C2×C8—92no—
435C4⋊C4—31no—
436C4⋊C4—31no—
437C4⋊C4—62no—
438C4⋊C4—62no—
439C4⋊C4—92no—
440C4⋊C4—182no—
441C4⋊C4—181no—
442C4⋊C4C2×D3211yescharacteristic
443C4⋊C4C2×D3211yescharacteristic
444C22⋊C4—21no—
445C22⋊C4—32no—
446C22⋊C4—182no—
447C42—21no—
448C42—32no—
449C42—62no—
450C42—62no—
451C42—182no—
452C22×C3—21no—
453C22×C3—21no—
454C22×C3—21no—
455C22×C3—21no—
456C22×C3—21no—
457C22×C3—22no—
458C22×C3—41no—
459C22×C3—41no—
460C22×C3—62no—
461C22×C3—121no—
462C22×C3—121no—
463C22×C3#67⋊C412yes—
464C22×C3C4×#6712yes—
465C22×C3C2×D3×D411yescharacteristic
466C22×C3C22×#6711yescharacteristic
467C2×D3—22no—
468C2×D3—41no—
469C2×D3—41no—
470C3×C4—21no—
471C3×C4—21no—
472C3×C4—22no—
473C3×C4—41no—
474C3×C4—41no—
475C3×C4—41no—
476C3×C4—41no—
477C3×C4—64no—
478C3×C4—62no—
479C3×C4—62no—
480C3×C4—62no—
481C3×C4—81no—
482C3×C4—81no—
483C3×C4#67⋊C412yes—
484C3×C4C4×#6712yes—
485C3×C4C22×C4×D311yescharacteristic
486C3×C4C22×C4×D311yescharacteristic
487C3×C4C2×#23511yescharacteristic
488C3×C4C2×#23711yescharacteristic
489Dic3—22no—
490Dic3—24no—
491Dic3—22no—
492Dic3—22no—
493Dic3—122no—
494Dic3—122no—
495Dic3—242no—
496C32#294711yescharacteristic, complemented, Sylow
497C23—61no—
498C23D3×#6711yescharacteristic
499Q8—34no—
500Q8—32no—
501Q8—62no—
502Q8—61no—
503Q8—64no—
504D4—32no—
505D4—64no—
506D4—61no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—32no—
510C2×C4—32no—
511C2×C4—62no—
512C2×C4—61no—
513C2×C4—64no—
514C2×C4—64no—
515C2×C4—182no—
516C2×C4—722no—
517C2×C4—721no—
518C2×C4#379512yes—
519C2×C4C4×D3212yes—
520C2×C4D3×#6711yescharacteristic
521C2×C4C22×D3211yescharacteristic
522C8—61no—
523C8—61no—
524C8—94no—
525C2×C3—22no—
526C2×C3—22no—
527C2×C3—21no—
528C2×C3—21no—
529C2×C3—21no—
530C2×C3—42no—
531C2×C3—122no—
532C2×C3C2×#67⋊C411yescharacteristic
533C2×C3#577011yescharacteristic
534C2×C3#577111yescharacteristic
535C2×C3C2×C4×#6711yescharacteristic
536C2×C3#583711yescharacteristic
537C2×C3#583811yescharacteristic
538D3—42no—
539C22—21no—
540C22—21no—
541C22—62no—
542C22—121no—
543C22—121no—
544C22#6387912yes—
545C22C2×D3×#6711yescharacteristic
546C4—41no—
547C4—41no—
548C4—62no—
549C4—64no—
550C4—62no—
551C4—62no—
552C4—362no—
553C4#6387912yes—
554C4C2×#379511yescharacteristic
555C4C2×C4×D3211yescharacteristic
556C3—21no—
557C3#7882111yescharacteristic, complemented
558C3#8254711yescharacteristic, complemented
559C2—22no—
560C2—122no—
561C2C2×#6387911yescharacteristic
562C2#1059545711yescharacteristic
563C2#1059546711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radicalC2×C3×#235C22
cosocleC2×C32×C4C24
hypercenter#117D32
hypocenterC32#2947
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C3×#5516C2semidirect
4. #10592694C2semidirect
6. C2×#63566C2semidirect
7. #10591055C2semidirect
8. #10590477C2semidirect
9. #10590476C2semidirect
10. #10590454C2semidirect
11. #10590453C2semidirect
32. #63827C4semidirect
49. #5516D3semidirect
77. C2×C3×Dic6C2×C4semidirect
87. #3748C2×C4semidirect
103. #3718C2×C4semidirect
104. #3715C2×C4semidirect
237. C2×Dic6C4×D3semidirect
496. C32#2947semidirect
557. C3#78821semidirect
558. C3#82547semidirect

Maximal subgroups

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

subgroupindex
C3×#55162
#105949922
C2×#638272
#105926942
C3×#50022
C2×#635662
#105910552
#105904772
#105904762
#105904542
#105904532
#825473
#788213