Finite Group Databasebeta

← #11895181

Subgroups — #11895181

Order 1152.

880 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596198C211yesmaximal, characteristic
2#10593864C211yesmaximal, characteristic, complemented
3C3×#5094C211yesmaximal, characteristic, complemented
4C3×#5093C211yesmaximal, characteristic, complemented
5#10590567C212yesmaximal, complemented
6#10590565C212yesmaximal
7#10590497C212yesmaximal, complemented
8#10590483C212yesmaximal
9#10590379C211yesmaximal, characteristic
10C4×#3717C211yesmaximal, characteristic
11#10590254C211yesmaximal, characteristic, complemented
12#81620—31nomaximal
13#81037—31nomaximal
14C2×Q8×C3⋊D3—21no—
15C32×C4⋊Q8C2211yescharacteristic
16#64155—21no—
17#64105—22no—
18#64102C2212yes—
19#64097C2212yes—
20C4×C4⋊(C3⋊D3)C2211yescharacteristic
21C4×#634C2211yescharacteristic
22C3×#869C2211yescharacteristic
23C3×C4×Dic6C2211yescharacteristic
24#63873C2212yes—
25#63869—21no—
26#63847—22no—
27#63844—21no—
28#63843C2212yes—
29C2×#3717C2212yes—
30C2×#3717C2211yescharacteristic
31C3×#810C2212yes—
32C3×#810C2212yes—
33C3×#810C2212yes—
34C3×#808C2212yes—
35C3×C4⋊(C3⋊C8)C2211yescharacteristic
36C3×C4×C3⋊C8C2211yescharacteristic
37#63573C2211yescharacteristic
38#63572C2212yes—
39#63566C2212yes—
40#63566C2211yescharacteristic
41#63564C2211yescharacteristic
42#63553C2212yes—
43#5727—31no—
44#5727—31no—
45#5727—61no—
46#5721—31no—
47#5567—31no—
48C3×#487—31no—
49C3×#475—31no—
50#5094D311yescharacteristic, complemented
51#5093D311yescharacteristic, complemented
52#5083—31no—
53C4×#215—31no—
54#4854—32no—
55#4852—32no—
56#4841—31no—
57#4830—31no—
58#4818—32no—
59#4818—32no—
60#4792—32no—
61#4792—32no—
62#4791—32no—
63#4788—32no—
64C4×#204—31no—
65C8×Dic6—31no—
66C2×C32×Q8—21no—
67Q8×C3⋊D3—44no—
68C2×C4⋊(C3⋊D3)C2311yescharacteristic
69C2×C4×C3⋊D3—21no—
70C2×C4×C3⋊D3—22no—
71C2×#634—22no—
72C2×#634D411yescharacteristic
73C2×C3×Dic6C2312yes—
74C2×C3×Dic6C2311yescharacteristic
75C32×C4⋊C4—21no—
76C32×C4⋊C4C2312yes—
77C32×C42C2311yescharacteristic
78#3752—21no—
79#3752—22no—
80C4⋊(C3⋊Dic3)D411yescharacteristic
81C4⋊(C3⋊Dic3)C2311yescharacteristic
82#3750—22no—
83#3750D412yes—
84C4×C3⋊Dic3C2312yes—
85C3×C4⋊Dic3—21no—
86C3×C4⋊Dic3—21no—
87C3×C4⋊Dic3C2311yescharacteristic
88C3×Dic3⋊C4—21no—
89C3×C4×Dic3—21no—
90C2×C3×C3⋊C8C2311yescharacteristic
91C2×C3×C3⋊C8C2312yes—
92C2×C3×C3⋊C8C2311yescharacteristic
93#3724—22no—
94#3724—22no—
95Dic3⋊Dic3—22no—
96Dic32—22no—
97#3717—24no—
98#3717—22no—
99#3359—91noSylow
100C2×D3×Q8—61no—
101C2×D3×Q8—61no—
102C2×D3×Q8—62no—
103C3×C4⋊Q8—21no—
104C3×C4⋊Q8—31no—
105C3×C4⋊Q8C2×D311yescharacteristic
106C3×C4⋊Q8C2×D311yescharacteristic
107C3×C4×Q8—31no—
108#946—61no—
109#946—61no—
110#946—62no—
111Q8×Dic3—32no—
112#944—32no—
113#944—32no—
114C2×#215—31no—
115C2×#215—32no—
116C2×#204—31no—
117C2×#204—32no—
118#896—62no—
119#896—62no—
120#896—64no—
121#893—32no—
122#893—32no—
123#893—62no—
124#890—61no—
125#889—62no—
126#889—62no—
127#888—32no—
128#888—32no—
129#888—62no—
130#887—32no—
131#887—61no—
132C4×D12—31no—
133C4×D12—31no—
134C4×D12—61no—
135#870—61no—
136#869C2×D311yescharacteristic
137C4×Dic6—31no—
138C4×Dic6—31no—
139C4×Dic6—61no—
140C4×Dic6—61no—
141C4×Dic6C2×D311yescharacteristic
142C3×#106—32no—
143C3×C4⋊C8—31no—
144C3×#103—32no—
145C3×#103—32no—
146C3×#103—32no—
147C3×C4×C8—31no—
148#835—31no—
149#835—32no—
150#821—31no—
151#817—31no—
152#816—31no—
153#816—32no—
154Dic3⋊C8—32no—
155Dic3⋊C8—32no—
156C8×Dic3—32no—
157C8×Dic3—32no—
158#810C2×D312yes—
159#810C2×D312yes—
160#810C2×D312yes—
161#809—31no—
162#808—31no—
163#808C2×D312yes—
164C4⋊(C3⋊C8)C2×D311yescharacteristic
165C4×C3⋊C8C2×D311yescharacteristic
166C22×C3⋊D3—21no—
167C32×Q8—42no—
168C2×C32×C4—22no—
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2411yescharacteristic
172C2×C3⋊Dic3—21no—
173C2×C3⋊Dic3C2×D412yes—
174C2×C3⋊Dic3C2×D412yes—
175C4⋊(C3⋊D3)—21no—
176C4⋊(C3⋊D3)#4112yes—
177C4×C3⋊D3—42no—
178C4×C3⋊D3—44no—
179#634—44no—
180#634SD1614yescomplemented
181C2×C3×Dic3—21no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—21no—
184C3×Dic6—22no—
185C3×Dic6—21no—
186C3×Dic6—21no—
187C3×Dic6—22no—
188C3×C3⋊C8—22no—
189C3×C3⋊C8—21no—
190C3×C3⋊C8—21no—
191#557—91no—
192D4×Q8—91no—
193#487—31no—
194#487—92no—
195#475—31no—
196#475—92no—
197#461—92no—
198#461—91no—
199C8×Q8—91no—
200C4×SD16—91no—
201C4×SD16—92no—
202C2×C3×Q8—22no—
203C2×C3×Q8—21no—
204C2×C3×Q8—21no—
205C2×C3×Q8—31no—
206C2×C3×Q8—32no—
207D3×Q8—124no—
208D3×Q8—124no—
209D3×Q8—128no—
210C2×D12—31no—
211C2×D12—31no—
212C2×D12—61no—
213C2×C4×D3—62no—
214C2×C4×D3—62no—
215C2×C4×D3—62no—
216C2×C4×D3—64no—
217C2×C4×D3—61no—
218C2×C4×D3—61no—
219C2×Dic6—31no—
220C2×Dic6—31no—
221C2×Dic6—61no—
222C2×Dic6—62no—
223C2×Dic6—62no—
224C2×Dic6—64no—
225C2×Dic6C22×D311yescharacteristic
226C2×Dic6C22×D312yes—
227C2×C3×C8—31no—
228C2×C3×C8—32no—
229C2×C3×C8—31no—
230C3×C4⋊C4—22no—
231C3×C4⋊C4—21no—
232C3×C4⋊C4—21no—
233C3×C4⋊C4—22no—
234C3×C4⋊C4—31no—
235C3×C4⋊C4—61no—
236C3×C4⋊C4—61no—
237C3×C4⋊C4—61no—
238C3×C4⋊C4C22×D312yes—
239C3×C4⋊C4C22×D312yes—
240C3×C42—21no—
241C3×C42—61no—
242C3×C42C22×D311yescharacteristic
243C3×C42C22×D311yescharacteristic
244#215—62no—
245#215—64no—
246(C2×D3)⋊C4—62no—
247(C2×D3)⋊C4—62no—
248(C2×D3)⋊C4—62no—
249(C2×D3)⋊C4—64no—
250(C2×D3)⋊C4—61no—
251(C2×D3)⋊C4—61no—
252C4⋊Dic3—21no—
253C4⋊Dic3—21no—
254C4⋊Dic3—31no—
255C4⋊Dic3—31no—
256C4⋊Dic3—31no—
257C4⋊Dic3—31no—
258C4⋊Dic3—61no—
259C4⋊Dic3—61no—
260C4⋊Dic3—62no—
261C4⋊Dic3C22×D311yescharacteristic
262Dic3⋊C4—21no—
263Dic3⋊C4—32no—
264Dic3⋊C4—32no—
265Dic3⋊C4—62no—
266Dic3⋊C4—62no—
267Dic3⋊C4—62no—
268Dic3⋊C4—62no—
269Dic3⋊C4—62no—
270Dic3⋊C4—62no—
271Dic3⋊C4—62no—
272Dic3⋊C4—62no—
273Dic3⋊C4—64no—
274C4×Dic3—21no—
275C4×Dic3—32no—
276C4×Dic3—32no—
277C4×Dic3—62no—
278C4×Dic3—62no—
279C4×Dic3—62no—
280C2×C3⋊C8C22×D311yescharacteristic
281C2×C3⋊C8C22×D311yescharacteristic
282C2×C3⋊C8C22×D312yes—
283#204—64no—
284#204—62no—
285C22×C32C22×D411yescharacteristic
286C2×C3⋊D3—22no—
287C2×C3⋊D3—41no—
288C2×C3⋊D3—41no—
289C32×C4—21no—
290C32×C4—42no—
291C32×C4C2×SD1612yes—
292C32×C4C2×#4111yescharacteristic
293C32×C42−1+411yescharacteristic
294C3⋊Dic3—22no—
295C3⋊Dic3—41no—
296C3⋊Dic3C2×SD1614yes—
297C3×Dic3—41no—
298C3×Dic3—42no—
299C3×Dic3—41no—
300C22×Q8—181no—
301C2×SD16—91no—
302C2×SD16—92no—
303C4⋊Q8—31no—
304C4⋊Q8—92no—
305C4⋊Q8—92no—
306C4⋊Q8D3211yescharacteristic
307#125—181no—
308#125—182no—
309C22⋊Q8—182no—
310C22⋊Q8—181no—
311C4×Q8—31no—
312C4×Q8—91no—
313C4×Q8—92no—
314C4×Q8—181no—
315C4×D4—92no—
316C4×D4—91no—
317#106—32no—
318#106—91no—
319C4⋊C8—31no—
320C4⋊C8—92no—
321#103—32no—
322#103—32no—
323#103—32no—
324#103—91no—
325#103—92no—
326#102—91no—
327C4×C8—31no—
328C4×C8—92no—
329C22×D3—62no—
330C22×D3—61no—
331C22×D3—61no—
332C3×Q8—44no—
333C3×Q8—42no—
334C3×Q8—42no—
335C3×Q8—62no—
336C3×Q8—62no—
337C3×Q8—61no—
338C3×Q8—61no—
339C2×C3×C4—24no—
340C2×C3×C4—22no—
341C2×C3×C4—22no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—61no—
346C2×C3×C4—62no—
347C2×C3×C4—61no—
348C2×C3×C4D3×D411yescharacteristic
349C2×C3×C4D3×D411yescharacteristic
350C2×C3×C4D3×D411yescharacteristic
351C2×C3×C4D3×D411yescharacteristic
352C2×C3×C4C23×D311yescharacteristic
353C2×C3×C4C23×D311yescharacteristic
354C2×Dic3—21no—
355C2×Dic3—21no—
356C2×Dic3—22no—
357C2×Dic3—32no—
358C2×Dic3—32no—
359C2×Dic3—32no—
360C2×Dic3—32no—
361C2×Dic3—62no—
362C2×Dic3—62no—
363C2×Dic3—62no—
364C2×Dic3—61no—
365C2×Dic3—61no—
366D12—32no—
367D12—32no—
368D12—62no—
369D12—62no—
370D12—61no—
371D12—61no—
372C4×D3—124no—
373C4×D3—124no—
374C4×D3—128no—
375C4×D3—124no—
376C4×D3—122no—
377C4×D3—122no—
378Dic6—21no—
379Dic6—21no—
380Dic6—22no—
381Dic6—22no—
382Dic6—34no—
383Dic6—34no—
384Dic6—64no—
385Dic6—124no—
386Dic6—124no—
387Dic6—128no—
388C3×C8—61no—
389C3×C8—61no—
390C3×C8—62no—
391C3⋊C8—22no—
392C3⋊C8—21no—
393C3⋊C8—21no—
394C2×C32#54811yescharacteristic
395C2×C32C22×SD1611yescharacteristic
396C2×C32#57811yescharacteristic
397C3⋊D3—42no—
398C2×Q8—21no—
399C2×Q8—31no—
400C2×Q8—32no—
401C2×Q8—91no—
402C2×Q8—182no—
403C2×Q8—364no—
404C2×D4—91no—
405C22×C4—182no—
406C22×C4—181no—
407SD16—182no—
408SD16—184no—
409C2×C8—31no—
410C2×C8—31no—
411C2×C8—32no—
412C4⋊C4—21no—
413C4⋊C4—31no—
414C4⋊C4—61no—
415C4⋊C4—61no—
416C4⋊C4—61no—
417C4⋊C4—92no—
418C4⋊C4—91no—
419C4⋊C4—91no—
420C4⋊C4—182no—
421C4⋊C4—182no—
422C4⋊C4—182no—
423C4⋊C4—182no—
424C4⋊C4C2×D3212yes—
425C22⋊C4—182no—
426C22⋊C4—181no—
427C42—61no—
428C42—92no—
429C42—182no—
430C42C2×D3211yescharacteristic
431C22×C3—21no—
432C22×C3C2×D3×D411yescharacteristic
433C22×C3C2×D3×D411yescharacteristic
434C2×D3—64no—
435C2×D3—62no—
436C2×D3—62no—
437C2×D3—122no—
438C2×D3—122no—
439C2×D3—121no—
440C2×D3—121no—
441C2×D3—121no—
442C2×D3—121no—
443C3×C4—21no—
444C3×C4—21no—
445C3×C4—21no—
446C3×C4—21no—
447C3×C4—22no—
448C3×C4—41no—
449C3×C4—44no—
450C3×C4—42no—
451C3×C4—42no—
452C3×C4—122no—
453C3×C4—121no—
454C3×C4—121no—
455C3×C4D3×SD1612yes—
456C3×C4D3×SD1612yes—
457C3×C4#100711yescharacteristic
458C3×C4D3×#4111yescharacteristic
459C3×C4D3×#4111yescharacteristic
460C3×C4#101011yescharacteristic
461Dic3—34no—
462Dic3—34no—
463Dic3—41no—
464Dic3—42no—
465Dic3—41no—
466Dic3—64no—
467Dic3—62no—
468Dic3—62no—
469Dic3—122no—
470Dic3—122no—
471Dic3—121no—
472Dic3—121no—
473C32#335911yescharacteristic, complemented, Sylow
474C23—181no—
475Q8—42no—
476Q8—61no—
477Q8—62no—
478Q8—61no—
479Q8—62no—
480Q8—94no—
481Q8—364no—
482D4—92no—
483D4—181no—
484C2×C4—22no—
485C2×C4—61no—
486C2×C4—61no—
487C2×C4—62no—
488C2×C4—92no—
489C2×C4—92no—
490C2×C4—181no—
491C2×C4—364no—
492C2×C4—362no—
493C2×C4#381111yescharacteristic
494C2×C4#381111yescharacteristic
495C2×C4C22×D3211yescharacteristic
496C8—61no—
497C8—61no—
498C8—62no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3#563311yescharacteristic
503C2×C3#567711yescharacteristic
504C2×C3C2×D3×SD1611yescharacteristic
505C2×C3C2×D3×SD1611yescharacteristic
506C2×C3#576611yescharacteristic
507C2×C3#577911yescharacteristic
508D3—124no—
509D3—122no—
510D3—122no—
511C22—182no—
512C22—361no—
513C22—361no—
514C22C2×#381111yescharacteristic
515C4—21no—
516C4—42no—
517C4—94no—
518C4—121no—
519C4—121no—
520C4—122no—
521C4—182no—
522C4—361no—
523C4#6393012yes—
524C4#6431511yescharacteristic
525C4#6431911yescharacteristic
526C3—21no—
527C3#8103711yescharacteristic, complemented
528C3#8162011yescharacteristic, complemented
529C2—362no—
530C2C2×#6393011yescharacteristic
531C2#1059533711yescharacteristic
532C2#1059536211yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radicalC2×C4⋊(C3⋊D3)C23
hypercenterC4⋊Q8D32
hypocenterC32#3359
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
2. #10593864C2semidirect
3. C3×#5094C2semidirect
4. C3×#5093C2semidirect
5. #10590567C2semidirect
7. #10590497C2semidirect
11. #10590254C2semidirect
50. #5094D3semidirect
51. #5093D3semidirect
180. #634SD16semidirect
473. C32#3359semidirect
527. C3#81037semidirect
528. C3#81620semidirect

Maximal subgroups

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

subgroupindex
#105961982
#105938642
C3×#50942
C3×#50932
#105905672
#105905652
#105904972
#105904832
#105903792
C4×#37172
#105902542
#816203
#810373