Finite Group Databasebeta

← C2×#10591036 #11899563

Subgroups — C2×#10591036 #11899563

Order 1152.

969 conjugacy classes of subgroups; only the 156 normal subgroups are shown.

normal subgroups only

This group has 969 conjugacy classes of subgroups — too many to draw. Only its 156 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D8×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×#63810C211yesmaximal, characteristic, complemented
3C2×C3×#827C211yesmaximal, characteristic, complemented
4C2×C3×#826C211yesmaximal, characteristic, complemented
5#10591036C218yesmaximal, direct product factor
6C2×#63549C211yesmaximal, characteristic, complemented
7C2×#63546C211yesmaximal, characteristic, complemented
8C2×#63544C211yesmaximal, characteristic, complemented
9C2×#4914—31nomaximal
10C2×#4911—31nomaximal
11C2×D4×C3⋊D3—21no—
12C2×#3796—21no—
13C2×C32×D8C2211yescharacteristic
14C2×#3753—21no—
15D8×C3⋊D3—22no—
16D8×C3⋊D3C2214yescomplemented
17C2×#3745C2211yescharacteristic
18C2×C8×C3⋊D3C2211yescharacteristic
19C2×C3×Dic12C2211yescharacteristic, complemented
20C2×C3×D24C2211yescharacteristic, complemented
21C2×#3715—21no—
22#63810—22no—
23#63810C2214yescomplemented
24C3×#827C2214yescomplemented
25C3×#826C2214yescomplemented
26C2×C3×C3⋊C16C2211yescharacteristic, complemented
27C2×C3×C3⋊C16C2211yescharacteristic, complemented
28#63549C2214yescomplemented
29#63546C2214yescomplemented
30#63544C2214yescomplemented
31C2×#919—31no—
32C2×#912—31no—
33C2×D3×D8—31no—
34C2×D3×D8—31no—
35C2×D3×D8—61no—
36C2×C3×SD32—31no—
37C2×C3×D16—31no—
38C2×#828—31no—
39C2×#827D311yescharacteristic, complemented
40C2×#826—31no—
41C2×#826D311yescharacteristic, complemented
42#4914—38no—
43#4911—38no—
44C2×#800—31no—
45C2×D48—31no—
46C2×#798—31no—
47C2×#798—31no—
48C23×C3⋊D3—41no—
49C2×C32×D4—21no—
50C2×#638—41no—
51D4×C3⋊D3—24no—
52D4×C3⋊D3—42no—
53C2×C4⋊(C3⋊D3)—21no—
54C2×C4×C3⋊D3D411yescharacteristic
55C2×C3×D12—21no—
56C2×C3×Dic6—21no—
57C2×#626—41no—
58C2×D3×Dic3—41no—
59#3796—24no—
60#3796—42no—
61C32×D8—21no—
62C32×D8C2312yes—
63C2×C32×C8C2311yescharacteristic
64#3753—24no—
65C2×C3⋊(C3⋊C8)D411yescharacteristic
66#3745—21no—
67#3745C2312yes—
68C8×C3⋊D3D412yes—
69C8×C3⋊D3C2312yes—
70C3×Dic12—21no—
71C3×Dic12C2312yescomplemented
72C3×D24—21no—
73C3×D24C2312yescomplemented
74#3715—24no—
75C3×C3⋊C16C2312yescomplemented
76C3×C3⋊C16C2312yescomplemented
77C2×#509—91noSylow
78C2×#239—61no—
79C2×#237—61no—
80C2×D3×D4—61no—
81C2×D3×D4—61no—
82C2×D3×D4—62no—
83C2×C3×Q16—31no—
84C2×C3×D8—21no—
85C2×C3×D8—31no—
86C2×C3×D8C2×D311yescharacteristic
87C2×C3×D8C2×D311yescharacteristic
88C2×#215—61no—
89C2×#214—61no—
90C2×#213—61no—
91C2×#213—61no—
92C2×#213—62no—
93#919—34no—
94#919—62no—
95#912—34no—
96#912—62no—
97D3×D8—34no—
98D3×D8—34no—
99D3×D8—64no—
100D3×D8—62no—
101D3×D8—62no—
102D3×D8—64no—
103C2×Dic12C2×D311yescharacteristic, complemented
104C2×D24—31no—
105C2×D24—31no—
106C2×D24—61no—
107C2×D24C2×D311yescharacteristic, complemented
108C2×D3×C8—31no—
109C2×D3×C8—31no—
110C2×D3×C8—61no—
111C3×SD32—34no—
112C3×D16—34no—
113C2×C3×C16—31no—
114C2×C3×C16—31no—
115#828—34no—
116#827C2×D314yescomplemented
117#826—34no—
118#826C2×D314yescomplemented
119C2×C3⋊C16C2×D311yescharacteristic, complemented
120C2×C3⋊C16C2×D311yescharacteristic, complemented
121#800—34no—
122D48—34no—
123#798—34no—
124#798—34no—
125C23×C32—41no—
126C22×C3⋊D3—41no—
127C22×C3⋊D3—44no—
128C22×C3⋊D3—84no—
129C22×C3⋊D3D811yescharacteristic
130C22×C3×D3—41no—
131C32×D4—22no—
132C32×D4—41no—
133C2×C32×C4C2×D411yescharacteristic
134#638—44no—
135C2×C3⋊Dic3D811yescharacteristic
136C4⋊(C3⋊D3)—22no—
137C4⋊(C3⋊D3)—41no—
138C4×C3⋊D3D812yes—
139C4×C3⋊D3C2×D412yes—
140C2×C3×Dic3—41no—
141C3×D12—22no—
142C3×D12—41no—
143C3×Dic6—22no—
144C3×Dic6—41no—
145#626—44no—
146D3×Dic3—44no—
147C32×C8C2×D411yescharacteristic
148C32×C8C2411yescharacteristic
149C3⋊(C3⋊C8)C2×D412yes—
150C2×#135—91no—
151C22×D8—91no—
152#509—98no—
153C2×SD32—31no—
154C2×SD32—91no—
155C2×D16—31no—
156C2×D16—91no—
157C2×M32—91no—
158C23×D3—121no—
159C23×D3—121no—
160C23×D3—122no—
161C2×C3×Q8—61no—
162C2×C3×D4—22no—
163C2×C3×D4—21no—
164C2×C3×D4—21no—
165C2×C3×D4—61no—
166C2×#67—121no—
167C2×#67—121no—
168C2×#67—121no—
169C2×#67—122no—
170C22×Dic3—121no—
171#239—64no—
172#239—122no—
173#237—64no—
174#237—122no—
175D3×D4—64no—
176D3×D4—64no—
177D3×D4—68no—
178D3×D4—122no—
179D3×D4—122no—
180D3×D4—124no—
181C2×D12—21no—
182C2×D12—62no—
183C2×D12—61no—
184C2×D12—61no—
185C2×D12—121no—
186C2×C4×D3—31no—
187C2×C4×D3—31no—
188C2×C4×D3—61no—
189C2×C4×D3—121no—
190C2×Dic6—21no—
191C3×Q16—32no—
192C3×Q16—61no—
193C3×D8—22no—
194C3×D8—21no—
195C3×D8—21no—
196C3×D8—22no—
197C3×D8—32no—
198C3×D8—61no—
199C3×D8C22×D312yes—
200C3×D8C22×D312yes—
201C2×C3×C8—21no—
202C2×C3×C8C22×D311yescharacteristic
203C2×C3×C8C22×D311yescharacteristic
204#215—64no—
205#214—64no—
206#213—64no—
207#213—64no—
208#213—68no—
209C2×C3⋊C8—31no—
210C2×C3⋊C8—31no—
211C2×C3⋊C8—61no—
212Dic12—21no—
213Dic12C22×D312yescomplemented
214D24—21no—
215D24—32no—
216D24—32no—
217D24—62no—
218D24—62no—
219D24—61no—
220D24—61no—
221D24C22×D312yescomplemented
222D3×C8—32no—
223D3×C8—32no—
224D3×C8—32no—
225D3×C8—32no—
226D3×C8—62no—
227D3×C8—62no—
228C3×C16—32no—
229C3×C16—32no—
230C3⋊C16C22×D312yescomplemented
231C3⋊C16C22×D312yescomplemented
232C22×C32—42no—
233C22×C32—82no—
234C22×C32C2×D811yescharacteristic
235C2×C3⋊D3—22no—
236C2×C3⋊D3—42no—
237C2×C3⋊D3—88no—
238C2×C3⋊D3—82no—
239C2×C3⋊D3C2×D812yes—
240C2×C3×D3—42no—
241C2×C3×D3—82no—
242C32×C4C2×D811yescharacteristic
243C32×C4C22×D411yescharacteristic
244C3⋊Dic3C2×D812yes—
245C3×Dic3—42no—
246C2×#41—181no—
247C22×D4—181no—
248#135—94no—
249#135—182no—
250C2×Q16—31no—
251C2×SD16—181no—
252C2×D8—31no—
253C2×D8—94no—
254C2×D8—91no—
255C2×D8—182no—
256C2×D8—181no—
257C2×D8D3211yescharacteristic
258C22×C8—91no—
259SD32—34no—
260SD32—94no—
261D16—34no—
262D16—94no—
263M32—94no—
264C2×C16—31no—
265C2×C16—31no—
266C23×C3—42no—
267C23×C3—41no—
268C23×C3—41no—
269C23×C3—121no—
270C22×D3—31no—
271C22×D3—31no—
272C22×D3—41no—
273C22×D3—61no—
274C22×D3—124no—
275C22×D3—124no—
276C22×D3—128no—
277C22×D3—122no—
278C22×D3—121no—
279C22×D3—121no—
280C22×D3—248no—
281C22×D3—244no—
282C22×D3—244no—
283C3×Q8—62no—
284C3×Q8—121no—
285C3×D4—24no—
286C3×D4—22no—
287C3×D4—22no—
288C3×D4—42no—
289C3×D4—41no—
290C3×D4—41no—
291C3×D4—62no—
292C3×D4—121no—
293C2×C3×C4—21no—
294C2×C3×C4—121no—
295C2×C3×C4D3×D411yescharacteristic
296C2×C3×C4D3×D411yescharacteristic
297#67—124no—
298#67—124no—
299#67—124no—
300#67—128no—
301C2×Dic3—31no—
302C2×Dic3—31no—
303C2×Dic3—41no—
304C2×Dic3—61no—
305C2×Dic3—124no—
306D12—22no—
307D12—41no—
308D12—64no—
309D12—62no—
310D12—62no—
311D12—122no—
312D12—124no—
313D12—121no—
314D12—121no—
315C4×D3—32no—
316C4×D3—32no—
317C4×D3—32no—
318C4×D3—32no—
319C4×D3—62no—
320C4×D3—62no—
321C4×D3—124no—
322Dic6—22no—
323Dic6—41no—
324C3×C8—21no—
325C3×C8—21no—
326C3×C8D3×D411yescharacteristic
327C3×C8D3×D411yescharacteristic
328C3×C8C23×D311yescharacteristic
329C3×C8C23×D311yescharacteristic
330C3⋊C8—32no—
331C3⋊C8—32no—
332C3⋊C8—62no—
333C2×C32—82no—
334C2×C32#50912yescomplemented
335C2×C32C22×D811yescharacteristic
336C3⋊D3—22no—
337C3⋊D3—82no—
338C3×D3—82no—
339C24—361no—
340#41—184no—
341#41—362no—
342C2×Q8—61no—
343C2×D4—21no—
344C2×D4—61no—
345C2×D4—184no—
346C2×D4—181no—
347C2×D4—362no—
348C2×D4—361no—
349C2×D4—361no—
350C22×C4—91no—
351C22×C4—361no—
352Q16—32no—
353Q16—61no—
354SD16—184no—
355D8—21no—
356D8—32no—
357D8—61no—
358D8—92no—
359D8—184no—
360D8—181no—
361D8C2×D3212yes—
362C2×C8—91no—
363C2×C8—92no—
364C2×C8—92no—
365C2×C8C2×D3211yescharacteristic
366C16—32no—
367C16—32no—
368C22×C3—21no—
369C22×C3—44no—
370C22×C3—42no—
371C22×C3—42no—
372C22×C3—84no—
373C22×C3—82no—
374C22×C3—82no—
375C22×C3—122no—
376C22×C3—242no—
377C22×C3D3×D811yescharacteristic
378C22×C3D3×D811yescharacteristic
379C2×D3—32no—
380C2×D3—32no—
381C2×D3—42no—
382C2×D3—62no—
383C2×D3—64no—
384C2×D3—62no—
385C2×D3—62no—
386C2×D3—82no—
387C2×D3—124no—
388C2×D3—122no—
389C2×D3—122no—
390C2×D3—2416no—
391C2×D3—248no—
392C2×D3—248no—
393C2×D3—244no—
394C2×D3—242no—
395C2×D3—242no—
396C3×C4—21no—
397C3×C4—21no—
398C3×C4—122no—
399C3×C4D3×D811yescharacteristic
400C3×C4D3×D811yescharacteristic
401C3×C4C2×D3×D411yescharacteristic
402C3×C4C2×D3×D411yescharacteristic
403Dic3—32no—
404Dic3—32no—
405Dic3—42no—
406Dic3—62no—
407C32C2×#50911yescharacteristic, complemented, Sylow
408C23—41no—
409C23—91no—
410C23—121no—
411C23—364no—
412C23—361no—
413C23—724no—
414Q8—62no—
415Q8—121no—
416D4—22no—
417D4—41no—
418D4—62no—
419D4—121no—
420D4—182no—
421D4—364no—
422D4—364no—
423D4—361no—
424C2×C4—91no—
425C2×C4—92no—
426C2×C4—92no—
427C2×C4—121no—
428C2×C4—364no—
429C2×C4#381111yescharacteristic
430C8—92no—
431C8#381111yescharacteristic
432C8C22×D3211yescharacteristic
433C2×C3—21no—
434C2×C3—22no—
435C2×C3—84no—
436C2×C3—82no—
437C2×C3—82no—
438C2×C3—242no—
439C2×C3#491112yescomplemented
440C2×C3#491412yescomplemented
441C2×C3C2×D3×D811yescharacteristic
442C2×C3C2×D3×D811yescharacteristic
443D3—64no—
444D3—62no—
445D3—62no—
446D3—82no—
447D3—244no—
448D3—242no—
449D3—242no—
450C22—42no—
451C22—82no—
452C22—92no—
453C22—122no—
454C22—182no—
455C22—242no—
456C22—362no—
457C22—728no—
458C22—722no—
459C22#6392611yescharacteristic
460C4—92no—
461C4—122no—
462C4#6392611yescharacteristic
463C4C2×#381111yescharacteristic
464C3—21no—
465C3C2×#491111yescharacteristic, complemented
466C3C2×#491411yescharacteristic, complemented
467C2—82no—
468C2—182no—
469C2—242no—
470C2—722no—
471C2#1059103612yesdirect product factor
472C2C2×#6392611yescharacteristic
subgroupG/H
centerC22#63926
commutator, cosocleC32×C8C24
FrattiniC8C22×D32
FittingC2×C32×D8C22
socleC22×C32C2×D8
hypercenterC2×D8D32
hypocenterC32C2×#509
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×D8×C3⋊D3C2semidirect
2. C2×#63810C2semidirect
3. C2×C3×#827C2semidirect
4. C2×C3×#826C2semidirect
5. #10591036C2direct (N × H)
6. C2×#63549C2semidirect
7. C2×#63546C2semidirect
8. C2×#63544C2semidirect
16. D8×C3⋊D3C22semidirect
19. C2×C3×Dic12C22semidirect
20. C2×C3×D24C22semidirect
23. #63810C22semidirect
24. C3×#827C22semidirect
25. C3×#826C22semidirect
26. C2×C3×C3⋊C16C22semidirect
27. C2×C3×C3⋊C16C22semidirect
28. #63549C22semidirect
29. #63546C22semidirect
30. #63544C22semidirect
39. C2×#827D3semidirect
41. C2×#826D3semidirect
71. C3×Dic12C23semidirect
73. C3×D24C23semidirect
75. C3×C3⋊C16C23semidirect
76. C3×C3⋊C16C23semidirect
103. C2×Dic12C2×D3semidirect
107. C2×D24C2×D3semidirect
116. #827C2×D3semidirect
118. #826C2×D3semidirect
119. C2×C3⋊C16C2×D3semidirect
120. C2×C3⋊C16C2×D3semidirect
213. Dic12C22×D3semidirect
221. D24C22×D3semidirect
230. C3⋊C16C22×D3semidirect
231. C3⋊C16C22×D3semidirect
334. C2×C32#509semidirect
407. C32C2×#509semidirect
439. C2×C3#4911semidirect
440. C2×C3#4914semidirect
465. C3C2×#4911semidirect
466. C3C2×#4914semidirect
471. C2#10591036direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D8×C3⋊D32
C2×#638102
C2×C3×#8272
C2×C3×#8262
#105910362
C2×#635492
C2×#635462
C2×#635442
C2×#49143
C2×#49113