Finite Group Databasebeta

← #11858592

Subgroups — #11858592

Order 1152.

1099 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595994C211yesmaximal, characteristic
2#10594990C211yesmaximal, characteristic
3C2×#63817C211yesmaximal, characteristic
4C3×#4998C211yesmaximal, characteristic, complemented
5C3×#4995C211yesmaximal, characteristic, complemented
6#10591131C211yesmaximal, characteristic, complemented
7C2×#63575C211yesmaximal, characteristic, complemented
8#10590584C212yesmaximal, complemented
9#10590583C212yesmaximal, complemented
10#10590574C212yesmaximal, complemented
11#10590573C212yesmaximal, complemented
12#79210—31nomaximal
13#79179—31nomaximal
14C2×#3828C2211yescharacteristic
15C32×#117C2211yescharacteristic
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17#64101C2212yes—
18C4⋊C4×C3⋊D3C2212yes—
19#64090—22no—
20C4×C4⋊(C3⋊D3)—21no—
21C4×#634—21no—
22C3×#926C2211yescharacteristic
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×#208C2211yescharacteristic
25C22×C3×C3⋊C8C2211yescharacteristic
26#63952—22no—
27#63900C2212yes—
28#63894—21no—
29#63849C2212yes—
30#63844—21no—
31C2×#3712C2212yes—
32#63817C418yescomplemented
33C2×#3710C2212yes—
34C3×#808C2212yes—
35C3×#808C2211yescharacteristic
36C3×#808C2211yescharacteristic
37C3×#807C2212yes—
38C3×#807C2211yescharacteristic
39C3×#807C2211yescharacteristic
40#63575C2212yes—
41#63575C2212yes—
42#63575C2212yes—
43#63573C2212yes—
44C2×#907—31no—
45C2×#901—31no—
46#5523—31no—
47#5523—31no—
48#5523—31no—
49#5523—61no—
50#5504—31no—
51C3×#428—31no—
52C3×#427—31no—
53#5121—31no—
54C2×#818—31no—
55#4998D311yescharacteristic, complemented
56#4995—31no—
57#4995D311yescharacteristic, complemented
58C2×#807—31no—
59#4881—32no—
60#4880—32no—
61D3×#107—32no—
62D3×#107—32no—
63#4861—32no—
64#4861—32no—
65#4861—32no—
66#4860—32no—
67C22×C32×C4C2311yescharacteristic
68C2×#638D412yes—
69C22×C3⋊Dic3—21no—
70#3828C2×C414yes—
71#3828Q814yes—
72C2×C4⋊(C3⋊D3)D411yescharacteristic
73C2×C4×C3⋊D3—22no—
74C2×C4×C3⋊D3C2312yes—
75C2×#634D411yescharacteristic
76C22×C3×Dic3—21no—
77C2×#624—22no—
78C32×C4⋊C4C2311yescharacteristic
79C32×C4⋊C4C2311yescharacteristic
80C32×C22⋊C4—21no—
81C32×C42—21no—
82#3752—22no—
83C4⋊(C3⋊Dic3)—21no—
84C4⋊(C3⋊Dic3)C2312yes—
85#3750—22no—
86C4×C3⋊Dic3—22no—
87C3×#217—21no—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3C2312yes—
90C3×C4⋊Dic3C2311yescharacteristic
91C3×C4⋊Dic3C2311yescharacteristic
92C3×C4×Dic3—21no—
93C3×#208C2×C414yescomplemented
94C2×C3×C3⋊C8C2×C414yescomplemented
95C2×C3×C3⋊C8C2311yescharacteristic
96C2×C3×C3⋊C8C2311yescharacteristic
97C2×C3×C3⋊C8C2312yes—
98#3724—22no—
99#3722—22no—
100Dic32—22no—
101#3712C2×C418yescomplemented
102#3710C2×C418yescomplemented
103#2913—91noSylow
104C2×#235—31no—
105C2×#235—31no—
106C2×#235—61no—
107C2×C3×M16—31no—
108C22×C3×C8—31no—
109C3×#117—21no—
110C3×#117—31no—
111C3×#117C2×D311yescharacteristic
112C3×#117C2×D311yescharacteristic
113C2×C3×C4⋊C4—31no—
114C4×#67—62no—
115#926C2×D311yescharacteristic
116C2×C4⋊Dic3—31no—
117C2×C4⋊Dic3—31no—
118C2×C4⋊Dic3—61no—
119C2×C4⋊Dic3C2×D311yescharacteristic
120C2×#208C2×D311yescharacteristic
121C22×C3⋊C8C2×D311yescharacteristic
122#907—38no—
123#901—38no—
124C2×ΓL(1,𝔽25)—32no—
125C2×ΓL(1,𝔽25)—32no—
126C2×D3×C8—32no—
127C2×D3×C8—32no—
128#893—61no—
129#892—32no—
130#892—32no—
131#892—32no—
132#892—32no—
133#892—62no—
134D3×C4⋊C4—32no—
135D3×C4⋊C4—32no—
136D3×C4⋊C4—32no—
137D3×C4⋊C4—32no—
138D3×C4⋊C4—62no—
139#887—61no—
140#67⋊C4—62no—
141#67⋊C4—62no—
142#67⋊C4—64no—
143#67⋊C4—62no—
144C4×D12—61no—
145C4×D12—61no—
146C4×D12—61no—
147C4×D12—62no—
148C4×Dic6—61no—
149C4×Dic6—61no—
150C4×Dic6—61no—
151C4×Dic6—62no—
152C3×#107—31no—
153C3×#107—32no—
154C3×#107—31no—
155C3×#106—31no—
156C3×#106—31no—
157C3×#106—32no—
158#818—32no—
159#818—32no—
160#818—32no—
161#817—32no—
162#808—32no—
163#808C2×D312yes—
164#808C2×D311yescharacteristic
165#808C2×D311yescharacteristic
166#807—32no—
167#807—32no—
168#807—32no—
169#807C2×D311yescharacteristic
170#807C2×D312yes—
171#807C2×D311yescharacteristic
172C23×C32C2×D411yescharacteristic
173C22×C3⋊D3C2×D412yes—
174C2×C32×C4—21no—
175C2×C32×C4—21no—
176C2×C32×C4C22×C412yes—
177C2×C32×C4C2×D411yescharacteristic
178C2×C32×C4C2×Q812yes—
179C2×C32×C4C2411yescharacteristic
180#638C4⋊C418yes—
181C2×C3⋊Dic3—22no—
182C2×C3⋊Dic3—81no—
183C2×C3⋊Dic3C2×D412yes—
184C4⋊(C3⋊D3)C4⋊C414yes—
185C4×C3⋊D3—82no—
186C4×C3⋊D3C22×C414yes—
187C4×C3⋊D3C2×Q814yes—
188#634C4⋊C414yes—
189C2×C3×Dic3—21no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3—81no—
193#624—82no—
194C3×C3⋊C8C22×C412yes—
195C3×C3⋊C8C22×C414yes—
196C3×C3⋊C8C22×C412yes—
197C2×#131—91no—
198#520—91no—
199#520—91no—
200#428—31no—
201#428—92no—
202#428—92no—
203#428—91no—
204#427—31no—
205#427—92no—
206C2×#107—92no—
207C2×#107—91no—
208C22×C3×C4—21no—
209C22×C3×C4—61no—
210C22×C3×C4C22×D311yescharacteristic
211C22×C3×C4C22×D311yescharacteristic
212C2×#67—32no—
213C2×#67—32no—
214C2×#67—62no—
215C22×Dic3—21no—
216C22×Dic3—62no—
217C22×Dic3—61no—
218C22×Dic3—61no—
219#235—34no—
220#235—34no—
221#235—34no—
222#235—34no—
223#235—64no—
224#235—64no—
225C2×D12—31no—
226C2×D12—31no—
227C2×D12—61no—
228C2×C4×D3—32no—
229C2×C4×D3—32no—
230C2×C4×D3—62no—
231C2×C4×D3—62no—
232C2×C4×D3—62no—
233C2×C4×D3—62no—
234C2×C4×D3—62no—
235C2×C4×D3—64no—
236C2×Dic6—31no—
237C2×Dic6—31no—
238C2×Dic6—61no—
239C3×M16—34no—
240C2×C3×C8—34no—
241C2×C3×C8—32no—
242C2×C3×C8—31no—
243C2×C3×C8—31no—
244C3×C4⋊C4—21no—
245C3×C4⋊C4—21no—
246C3×C4⋊C4—31no—
247C3×C4⋊C4—32no—
248C3×C4⋊C4—31no—
249C3×C4⋊C4—61no—
250C3×C4⋊C4C22×D311yescharacteristic
251C3×C4⋊C4C22×D311yescharacteristic
252C3×C4⋊C4C22×D311yescharacteristic
253C3×C4⋊C4C22×D311yescharacteristic
254C3×C22⋊C4—22no—
255C3×C22⋊C4—21no—
256C3×C22⋊C4—21no—
257C3×C22⋊C4—61no—
258C3×C42—22no—
259C3×C42—21no—
260C3×C42—21no—
261C3×C42—61no—
262#217—21no—
263(C2×D3)⋊C4—62no—
264(C2×D3)⋊C4—62no—
265(C2×D3)⋊C4—62no—
266(C2×D3)⋊C4—62no—
267(C2×D3)⋊C4—64no—
268C4⋊Dic3—21no—
269C4⋊Dic3—32no—
270C4⋊Dic3—32no—
271C4⋊Dic3—62no—
272C4⋊Dic3—62no—
273C4⋊Dic3—61no—
274C4⋊Dic3—61no—
275C4⋊Dic3C22×D311yescharacteristic
276C4⋊Dic3C22×D311yescharacteristic
277C4⋊Dic3C22×D312yes—
278Dic3⋊C4—62no—
279Dic3⋊C4—62no—
280Dic3⋊C4—62no—
281Dic3⋊C4—62no—
282Dic3⋊C4—64no—
283C4×Dic3—21no—
284C4×Dic3—62no—
285C4×Dic3—62no—
286C4×Dic3—62no—
287C4×Dic3—62no—
288C4×Dic3—64no—
289#208C4×D314yescomplemented
290C2×C3⋊C8C4×D314yescomplemented
291C2×C3⋊C8C22×D311yescharacteristic
292C2×C3⋊C8C22×D311yescharacteristic
293C2×C3⋊C8C22×D312yes—
294ΓL(1,𝔽25)—38no—
295ΓL(1,𝔽25)—38no—
296D3×C8—38no—
297D3×C8—38no—
298C22×C32—21no—
299C22×C32—21no—
300C22×C32C2×C4⋊C412yes—
301C22×C32C22×D411yescharacteristic
302C2×C3⋊D3—22no—
303C2×C3⋊D3—22no—
304C2×C3⋊D3C2×C4⋊C414yes—
305C32×C4—41no—
306C32×C4—41no—
307C32×C4C2×C4⋊C412yes—
308C32×C4C23×C411yescharacteristic
309C32×C4C22×Q811yescharacteristic
310C3⋊Dic3—42no—
311C3⋊Dic3C2×C4⋊C414yes—
312C3×Dic3—41no—
313C3×Dic3—42no—
314C3×Dic3—41no—
315C2×#41—91no—
316#131—98no—
317C2×M16—31no—
318C2×M16—92no—
319C22×C8—31no—
320C22×C8—92no—
321C4×Q8—181no—
322C4×Q8—181no—
323C4×D4—181no—
324C4×D4—181no—
325C4×D4—182no—
326C4×D4—182no—
327#117—31no—
328#117—92no—
329#117—92no—
330#117D3211yescharacteristic
331C2×C4⋊C4—31no—
332C2×C4⋊C4—92no—
333C2×C4⋊C4—91no—
334C2×C4⋊C4—92no—
335#107—31no—
336#107—32no—
337#107—31no—
338#107—92no—
339#107—92no—
340#107—92no—
341#106—31no—
342#106—31no—
343#106—32no—
344#106—92no—
345C23×C3—21no—
346C23×C3D3×D411yescharacteristic
347C23×C3D3×D411yescharacteristic
348C22×D3—32no—
349C22×D3—32no—
350C22×D3—62no—
351C2×C3×C4—22no—
352C2×C3×C4—22no—
353C2×C3×C4—21no—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—22no—
359C2×C3×C4—22no—
360C2×C3×C4—21no—
361C2×C3×C4—61no—
362C2×C3×C4—62no—
363C2×C3×C4—61no—
364C2×C3×C4—241no—
365C2×C3×C4C2×C4×D312yes—
366C2×C3×C4C2×C4×D312yes—
367C2×C3×C4D3×D411yescharacteristic
368C2×C3×C4D3×D411yescharacteristic
369C2×C3×C4D3×Q812yes—
370C2×C3×C4D3×Q812yes—
371C2×C3×C4C23×D311yescharacteristic
372C2×C3×C4C23×D311yescharacteristic
373#67—38no—
374#67—38no—
375#67—68no—
376C2×Dic3—21no—
377C2×Dic3—21no—
378C2×Dic3—22no—
379C2×Dic3—32no—
380C2×Dic3—32no—
381C2×Dic3—62no—
382C2×Dic3—64no—
383C2×Dic3—62no—
384C2×Dic3—62no—
385C2×Dic3—81no—
386C2×Dic3—241no—
387C2×Dic3—241no—
388C2×Dic3—242no—
389D12—34no—
390D12—34no—
391D12—64no—
392C4×D3—34no—
393C4×D3—34no—
394C4×D3—34no—
395C4×D3—34no—
396C4×D3—64no—
397C4×D3—64no—
398C4×D3—242no—
399C4×D3—242no—
400C4×D3—242no—
401C4×D3—242no—
402C4×D3—244no—
403Dic6—34no—
404Dic6—34no—
405Dic6—64no—
406C3×C8—32no—
407C3×C8—34no—
408C3×C8—32no—
409C3⋊C8C2×C4×D312yes—
410C3⋊C8C2×C4×D314yes—
411C3⋊C8C2×C4×D312yes—
412C2×C32—22no—
413C2×C32C22×C4⋊C411yescharacteristic
414C2×C32#57611yescharacteristic
415C2×C32#57811yescharacteristic
416C3⋊D3—24no—
417#41—94no—
418#41—94no—
419C2×Q8—91no—
420C2×D4—92no—
421C2×D4—91no—
422C22×C4—61no—
423C22×C4—92no—
424C22×C4—182no—
425C22×C4—182no—
426C22×C4—181no—
427C22×C4C2×D3211yescharacteristic
428M16—34no—
429M16—98no—
430C2×C8—31no—
431C2×C8—32no—
432C2×C8—31no—
433C2×C8—34no—
434C2×C8—98no—
435C4⋊C4—31no—
436C4⋊C4—32no—
437C4⋊C4—31no—
438C4⋊C4—61no—
439C4⋊C4—92no—
440C4⋊C4—182no—
441C4⋊C4—182no—
442C4⋊C4—181no—
443C4⋊C4C2×D3211yescharacteristic
444C4⋊C4C2×D3211yescharacteristic
445C22⋊C4—21no—
446C22⋊C4—61no—
447C22⋊C4—182no—
448C22⋊C4—182no—
449C42—21no—
450C42—61no—
451C42—182no—
452C42—182no—
453C22×C3—21no—
454C22×C3—21no—
455C22×C3—21no—
456C22×C3—21no—
457C22×C3—21no—
458C22×C3—22no—
459C22×C3—41no—
460C22×C3—41no—
461C22×C3D3×C4⋊C412yes—
462C22×C3D3×C4⋊C412yes—
463C22×C3C2×D3×D411yescharacteristic
464C22×C3C2×D3×D411yescharacteristic
465C2×D3—34no—
466C2×D3—34no—
467C2×D3—64no—
468C2×D3—62no—
469C2×D3—62no—
470C2×D3—62no—
471C2×D3—62no—
472C2×D3—122no—
473C2×D3—122no—
474C3×C4—21no—
475C3×C4—21no—
476C3×C4—22no—
477C3×C4—42no—
478C3×C4—42no—
479C3×C4—41no—
480C3×C4—41no—
481C3×C4—41no—
482C3×C4—41no—
483C3×C4—122no—
484C3×C4—121no—
485C3×C4—121no—
486C3×C4D3×C4⋊C412yes—
487C3×C4D3×C4⋊C412yes—
488C3×C4C22×C4×D311yescharacteristic
489C3×C4C22×C4×D311yescharacteristic
490C3×C4C2×D3×Q811yescharacteristic
491C3×C4C2×D3×Q811yescharacteristic
492Dic3—34no—
493Dic3—34no—
494Dic3—41no—
495Dic3—41no—
496Dic3—42no—
497Dic3—64no—
498Dic3—124no—
499Dic3—122no—
500Dic3—122no—
501C32#291311yescharacteristic, complemented, Sylow
502C23—92no—
503C23#381111yescharacteristic
504Q8—94no—
505D4—98no—
506D4—94no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—61no—
510C2×C4—61no—
511C2×C4—62no—
512C2×C4—92no—
513C2×C4—94no—
514C2×C4—94no—
515C2×C4—182no—
516C2×C4—241no—
517C2×C4—722no—
518C2×C4—722no—
519C2×C4—721no—
520C2×C4#379712yes—
521C2×C4C4×D3212yes—
522C2×C4#381111yescharacteristic
523C2×C4C22×D3211yescharacteristic
524C8—32no—
525C8—32no—
526C8—34no—
527C2×C3—22no—
528C2×C3—22no—
529C2×C3—21no—
530C2×C3—21no—
531C2×C3—21no—
532C2×C3—42no—
533C2×C3C2×D3×C4⋊C411yescharacteristic
534C2×C3C2×D3×C4⋊C411yescharacteristic
535C2×C3#576911yescharacteristic
536C2×C3#577111yescharacteristic
537C2×C3#577411yescharacteristic
538C2×C3#577911yescharacteristic
539D3—64no—
540D3—64no—
541D3—124no—
542C22—21no—
543C22—21no—
544C22—94no—
545C22—182no—
546C22—182no—
547C22#6388312yes—
548C22C2×#381111yescharacteristic
549C4—41no—
550C4—41no—
551C4—94no—
552C4—122no—
553C4—121no—
554C4—121no—
555C4—362no—
556C4#6388312yes—
557C4C2×#379711yescharacteristic
558C4C2×C4×D3211yescharacteristic
559C3—21no—
560C3#7917911yescharacteristic, complemented
561C3#7921011yescharacteristic, complemented
562C2—22no—
563C2—184no—
564C2C2×#6388311yescharacteristic
565C2#1059546111yescharacteristic
566C2#1059547211yescharacteristic
subgroupG/H
centerC22C2×#3811
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radicalC2×#3828C22
cosocleC2×C32×C4C24
hypercenter#117D32
hypocenterC32#2913
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
4. C3×#4998C2semidirect
5. C3×#4995C2semidirect
6. #10591131C2semidirect
7. C2×#63575C2semidirect
8. #10590584C2semidirect
9. #10590583C2semidirect
10. #10590574C2semidirect
11. #10590573C2semidirect
32. #63817C4semidirect
55. #4998D3semidirect
57. #4995D3semidirect
93. C3×#208C2×C4semidirect
94. C2×C3×C3⋊C8C2×C4semidirect
101. #3712C2×C4semidirect
102. #3710C2×C4semidirect
289. #208C4×D3semidirect
290. C2×C3⋊C8C4×D3semidirect
501. C32#2913semidirect
560. C3#79179semidirect
561. C3#79210semidirect

Maximal subgroups

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

subgroupindex
#105959942
#105949902
C2×#638172
C3×#49982
C3×#49952
#105911312
C2×#635752
#105905842
#105905832
#105905742
#105905732
#792103
#791793