Finite Group Databasebeta

← #79787

Subgroups — #79787

Order 384.

394 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#5583C211yesmaximal, characteristic, complemented
2#5545C211yesmaximal, characteristic
3C3×#440C211yesmaximal, characteristic, complemented
4#5169C211yesmaximal, characteristic
5#5162C211yesmaximal, characteristic, complemented
6C4×#215C211yesmaximal, characteristic, complemented
7C4×#214C211yesmaximal, characteristic, complemented
8#4891C211yesmaximal, characteristic, complemented
9#4888C211yesmaximal, characteristic, complemented
10#4818C211yesmaximal, characteristic, complemented
11#4814C211yesmaximal, characteristic, complemented
12#4776C211yesmaximal, characteristic
13#4766C211yesmaximal, characteristic, complemented
14#4710C211yesmaximal, characteristic, complemented
15#4709C211yesmaximal, characteristic, complemented
16#3123—31nomaximal, Sylow
17C2×D3×D4C2211yescharacteristic
18C2×C3×SD16C2211yescharacteristic
19C3×C4×Q8C2211yescharacteristic, complemented
20C3×C4×D4C2211yescharacteristic
21#946C2211yescharacteristic
22#944C2211yescharacteristic, complemented
23C2×#215C2211yescharacteristic
24D4×Dic3C2211yescharacteristic
25C2×#214C2211yescharacteristic
26C4×#67—21no—
27C2×(C2×D3)⋊C4—21no—
28C2×#204C2211yescharacteristic
29#898—21no—
30#897C2211yescharacteristic
31#893C2211yescharacteristic
32#892C2211yescharacteristic
33#890C2211yescharacteristic, complemented
34#889—21no—
35#67⋊C4—21no—
36D3×C22⋊C4—21no—
37#876—21no—
38C4×D12C2211yescharacteristic
39#872C2211yescharacteristic
40#870—21no—
41C4×Dic6C2211yescharacteristic, complemented
42C3×#107C2211yescharacteristic, complemented
43C3×#103C2211yescharacteristic, complemented
44C3×#102C2211yescharacteristic
45C3×#97C2211yescharacteristic, complemented
46#835C2211yescharacteristic, complemented
47#832C2211yescharacteristic
48#821C2211yescharacteristic
49(C2×D3)⋊C8C2211yescharacteristic
50(C2×D3)⋊C8C2211yescharacteristic
51#818C2211yescharacteristic, complemented
52#816C2211yescharacteristic, complemented
53Dic3⋊C8C2211yescharacteristic, complemented
54Dic3⋊C8C2211yescharacteristic, complemented
55#810C2211yescharacteristic, complemented
56#809C2211yescharacteristic
57#808C2211yescharacteristic, complemented
58#808C2211yescharacteristic, complemented
59C4×C3⋊C8C2211yescharacteristic, complemented
60#541—31no—
61#518—31no—
62#485—31no—
63#485—31no—
64#478—31no—
65#478—31no—
66#461—31no—
67#461—31no—
68#450—31no—
69#450—31no—
70#440—31no—
71#440D311yescharacteristic, complemented
72C4×SD16—31no—
73C4×SD16—31no—
74#433—31no—
75C23×D3—21no—
76C2×C3×Q8C2311yescharacteristic
77C2×C3×D4C2311yescharacteristic
78C22×C3×C4—21no—
79C2×#67—21no—
80C22×Dic3—21no—
81D3×D4—22no—
82D3×D4—22no—
83C2×D12C2311yescharacteristic
84C2×C4×D3—21no—
85C2×C4×D3—21no—
86C2×C4×D3C2311yescharacteristic
87C2×Dic6C2311yescharacteristic
88C3×SD16—22no—
89C2×C3×C8C2311yescharacteristic
90C2×C3×C8C2311yescharacteristic
91C3×C4⋊C4—21no—
92C3×C4⋊C4C2311yescharacteristic
93C3×C4⋊C4C2311yescharacteristic
94C3×C22⋊C4—21no—
95C3×C42—21no—
96C3×C42C2311yescharacteristic
97#217—21no—
98#215—22no—
99#214—22no—
100(C2×D3)⋊C4—21no—
101(C2×D3)⋊C4—21no—
102(C2×D3)⋊C4—21no—
103(C2×D3)⋊C4—21no—
104(C2×D3)⋊C4—21no—
105(C2×D3)⋊C4D411yescharacteristic
106(C2×D3)⋊C4D411yescharacteristic
107C4⋊Dic3—21no—
108C4⋊Dic3—21no—
109C4⋊Dic3C2311yescharacteristic
110C4⋊Dic3C2311yescharacteristic
111Dic3⋊C4—21no—
112Dic3⋊C4—21no—
113Dic3⋊C4—21no—
114Dic3⋊C4—21no—
115Dic3⋊C4—21no—
116Dic3⋊C4D411yescharacteristic
117Dic3⋊C4D411yescharacteristic
118C4×Dic3—21no—
119C4×Dic3—21no—
120C4×Dic3C2311yescharacteristic
121C2×C3⋊C8C2311yescharacteristic
122C2×C3⋊C8C2311yescharacteristic
123#204—22no—
124C22×D4—31no—
125C2×SD16—31no—
126C2×SD16—31no—
127C2×SD16—31no—
128C2×SD16C2×D311yescharacteristic
129C4⋊Q8—31no—
130#126—61no—
131#126—61no—
132#125—31no—
133#125—61no—
134#125—61no—
135C22⋊Q8—31no—
136C22⋊Q8—31no—
137C4×Q8—31no—
138C4×Q8C2×D311yescharacteristic, complemented
139C4×D4—31no—
140C4×D4—31no—
141C4×D4—31no—
142C4×D4—61no—
143C4×D4—61no—
144C4×D4C2×D311yescharacteristic
145#117—31no—
146#117—31no—
147C2×C22⋊C4—61no—
148C2×C22⋊C4—61no—
149#107—31no—
150#107C2×D311yescharacteristic, complemented
151#106—31no—
152#106—31no—
153C4⋊C8—31no—
154C4⋊C8—31no—
155#103—31no—
156#103—31no—
157#103—31no—
158#103C2×D311yescharacteristic, complemented
159#102—31no—
160#102—31no—
161#102—31no—
162#102C2×D311yescharacteristic
163C22⋊C8—31no—
164C22⋊C8—31no—
165#97C2×D311yescharacteristic, complemented
166C4×C8—31no—
167C23×C3—21no—
168C22×D3—21no—
169C22×D3—24no—
170C22×D3—81no—
171C22×D3—81no—
172C22×D3C2×D411yescharacteristic
173C3×Q8—21no—
174C3×Q8—21no—
175C3×D4—21no—
176C3×D4#4112yes—
177C2×C3×C4—21no—
178C2×C3×C4—21no—
179C2×C3×C4—21no—
180C2×C3×C4—81no—
181C2×C3×C4C2×D411yescharacteristic
182C2×C3×C4C2×D411yescharacteristic
183C2×C3×C4C2411yescharacteristic
184#67—24no—
185C2×Dic3—21no—
186C2×Dic3—21no—
187C2×Dic3—21no—
188C2×Dic3—81no—
189C2×Dic3C2×D411yescharacteristic
190C2×Dic3C2×D411yescharacteristic
191C2×Dic3C2×D411yescharacteristic
192D12—21no—
193D12#4112yes—
194C4×D3—21no—
195C4×D3—21no—
196C4×D3—81no—
197C4×D3—81no—
198Dic6—21no—
199Dic6—21no—
200C3×C8—21no—
201C3×C8—21no—
202C3⋊C8—21no—
203C3⋊C8—21no—
204C24—61no—
205C2×Q8—31no—
206C2×Q8C22×D311yescharacteristic
207C2×D4—31no—
208C2×D4—61no—
209C2×D4—62no—
210C2×D4—62no—
211C2×D4C22×D311yescharacteristic
212C22×C4—21no—
213C22×C4—31no—
214C22×C4—61no—
215C22×C4—61no—
216C22×C4—61no—
217SD16—22no—
218SD16—62no—
219SD16—62no—
220SD16—62no—
221C2×C8—31no—
222C2×C8—31no—
223C2×C8C22×D311yescharacteristic
224C2×C8C22×D311yescharacteristic
225C4⋊C4—21no—
226C4⋊C4—31no—
227C4⋊C4—31no—
228C4⋊C4—31no—
229C4⋊C4—31no—
230C4⋊C4—61no—
231C4⋊C4—61no—
232C4⋊C4—61no—
233C4⋊C4—61no—
234C4⋊C4—61no—
235C4⋊C4—61no—
236C4⋊C4—61no—
237C4⋊C4C22×D311yescharacteristic
238C4⋊C4C22×D311yescharacteristic
239C22⋊C4—21no—
240C22⋊C4—31no—
241C22⋊C4—31no—
242C22⋊C4—61no—
243C22⋊C4—61no—
244C22⋊C4—61no—
245C22⋊C4—61no—
246C22⋊C4—61no—
247C22⋊C4—61no—
248C42—21no—
249C42—31no—
250C42—61no—
251C42—61no—
252C42C22×D311yescharacteristic
253C22×C3—22no—
254C22×C3—41no—
255C22×C3—41no—
256C22×C3C22×D411yescharacteristic
257C2×D3—21no—
258C2×D3—22no—
259C2×D3—21no—
260C2×D3—21no—
261C2×D3—41no—
262C2×D3—41no—
263C2×D3—84no—
264C3×C4—21no—
265C3×C4—21no—
266C3×C4—41no—
267C3×C4—41no—
268C3×C4—41no—
269C3×C4C2×#4111yescharacteristic
270C3×C4C2×#4111yescharacteristic
271Dic3—21no—
272Dic3—21no—
273Dic3—21no—
274Dic3—41no—
275Dic3—41no—
276Dic3—41no—
277C23—21no—
278C23—31no—
279C23—64no—
280C23—61no—
281C23—241no—
282C23—241no—
283Q8—21no—
284Q8—21no—
285Q8—61no—
286Q8—61no—
287D4—21no—
288D4—32no—
289D4—64no—
290D4—61no—
291D4#23512yes—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—31no—
296C2×C4—31no—
297C2×C4—31no—
298C2×C4—61no—
299C2×C4—61no—
300C2×C4—61no—
301C2×C4—61no—
302C2×C4—61no—
303C2×C4—81no—
304C2×C4—241no—
305C2×C4—241no—
306C2×C4—241no—
307C2×C4D3×D411yescharacteristic
308C2×C4D3×D411yescharacteristic
309C2×C4C23×D311yescharacteristic
310C8—21no—
311C8—21no—
312C8—61no—
313C8—61no—
314C2×C3—42no—
315C2×C3#52511yescharacteristic
316C2×C3#57711yescharacteristic
317C2×C3#57711yescharacteristic
318D3—41no—
319D3—42no—
320C22—22no—
321C22—41no—
322C22—41no—
323C22—61no—
324C22—61no—
325C22—61no—
326C22—62no—
327C22—121no—
328C22—121no—
329C22—244no—
330C22C2×D3×D411yescharacteristic
331C4—21no—
332C4—21no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—61no—
337C4—61no—
338C4—61no—
339C4—121no—
340C4—121no—
341C4—121no—
342C4C2×#23511yescharacteristic
343C4D3×#4111yescharacteristic
344C3#312311yescharacteristic, complemented, Sylow
345C2—42no—
346C2—121no—
347C2—122no—
348C2#554711yescharacteristic
349C2#577511yescharacteristic
350C2#577811yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#440C2
socleC22×C3C22×D4
prime radicalC2×D3×D4C22
hypercenter#440D3
hypocenterC3#3123
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #5583C2semidirect
3. C3×#440C2semidirect
5. #5162C2semidirect
6. C4×#215C2semidirect
7. C4×#214C2semidirect
8. #4891C2semidirect
9. #4888C2semidirect
10. #4818C2semidirect
11. #4814C2semidirect
13. #4766C2semidirect
14. #4710C2semidirect
15. #4709C2semidirect
19. C3×C4×Q8C22semidirect
22. #944C22semidirect
33. #890C22semidirect
41. C4×Dic6C22semidirect
42. C3×#107C22semidirect
43. C3×#103C22semidirect
45. C3×#97C22semidirect
46. #835C22semidirect
51. #818C22semidirect
52. #816C22semidirect
53. Dic3⋊C8C22semidirect
54. Dic3⋊C8C22semidirect
55. #810C22semidirect
57. #808C22semidirect
58. #808C22semidirect
59. C4×C3⋊C8C22semidirect
71. #440D3semidirect
138. C4×Q8C2×D3semidirect
150. #107C2×D3semidirect
158. #103C2×D3semidirect
165. #97C2×D3semidirect
344. C3#3123semidirect

Maximal subgroups

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

subgroupindex
#55832
#55452
C3×#4402
#51692
#51622
C4×#2152
C4×#2142
#48912
#48882
#48182
#48142
#47762
#47662
#47102
#47092
#31233