Finite Group Databasebeta

← #79653

Subgroups — #79653

Order 384.

428 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×D3×Q8C211yesmaximal, characteristic, complemented
2#5548C211yesmaximal, characteristic
3C3×C4×SD16C211yesmaximal, characteristic, complemented
4#5170C211yesmaximal, characteristic, complemented
5#5163C211yesmaximal, characteristic, complemented
6C4×#215C211yesmaximal, characteristic, complemented
7C4×#214C211yesmaximal, characteristic, complemented
8#4863C211yesmaximal, characteristic, complemented
9#4854C211yesmaximal, characteristic, complemented
10#4806C211yesmaximal, characteristic, complemented
11#4791C211yesmaximal, characteristic, complemented
12#4777C211yesmaximal, characteristic, complemented
13#4762C211yesmaximal, characteristic, complemented
14C4×#204C211yesmaximal, characteristic, complemented
15#4685C211yesmaximal, characteristic, complemented
16#3103—31nomaximal, Sylow
17C2×D3×Q8C2211yescharacteristic
18C2×#235—21no—
19C2×C3×SD16C2211yescharacteristic
20C3×C4×Q8C2211yescharacteristic
21C3×C4×D4C2211yescharacteristic
22Q8×Dic3C2211yescharacteristic
23C2×#215C2211yescharacteristic
24#940C2211yescharacteristic
25#938C2211yescharacteristic
26C2×#214C2211yescharacteristic
27C4×#67—21no—
28C2×#204C2211yescharacteristic
29#895C2211yescharacteristic
30D3×C4⋊C4—21no—
31D3×C4⋊C4C2211yescharacteristic
32#888C2211yescharacteristic
33#887—21no—
34#887C2211yescharacteristic
35#885—21no—
36#884—21no—
37C4×D12C2211yescharacteristic
38C42×D3—21no—
39C42×D3C2211yescharacteristic
40C4×Dic6—21no—
41C4×Dic6C2211yescharacteristic
42C3×#106C2211yescharacteristic
43C3×#103C2211yescharacteristic
44C3×#102C2211yescharacteristic
45C3×C4×C8C2211yescharacteristic
46#835C2211yescharacteristic
47#832C2211yescharacteristic
48#821C2211yescharacteristic
49(C2×D3)⋊C8C2211yescharacteristic
50(C2×D3)⋊C8C2211yescharacteristic
51#817C2211yescharacteristic
52#816C2211yescharacteristic
53Dic3⋊C8C2211yescharacteristic
54Dic3⋊C8C2211yescharacteristic
55#810C2211yescharacteristic
56#809C2211yescharacteristic
57#808C2211yescharacteristic
58#808C2211yescharacteristic
59C4×C3⋊C8C2211yescharacteristic
60#532—31no—
61C2×C4×Q8—31no—
62#481—31no—
63#481—31no—
64#475—31no—
65#475—31no—
66#460—31no—
67#460—31no—
68#448—31no—
69#448—31no—
70C4×SD16—31no—
71C4×SD16—31no—
72C4×SD16—31no—
73C4×SD16D311yescharacteristic, complemented
74#431—31no—
75C2×C3×Q8C2311yescharacteristic
76C2×C3×D4C2311yescharacteristic
77C22×C3×C4—21no—
78C2×#67—21no—
79C2×#67—21no—
80C2×#67—21no—
81D3×Q8—22no—
82D3×Q8—22no—
83#235—44no—
84C2×D12—21no—
85C2×D12C2311yescharacteristic
86C2×C4×D3—21no—
87C2×C4×D3—21no—
88C2×C4×D3—21no—
89C2×C4×D3D411yescharacteristic
90C2×C4×D3D411yescharacteristic
91C2×C4×D3C2311yescharacteristic
92C2×Dic6—21no—
93C2×Dic6—21no—
94C2×Dic6C2311yescharacteristic
95C3×SD16—22no—
96C2×C3×C8C2311yescharacteristic
97C2×C3×C8C2311yescharacteristic
98C3×C4⋊C4—21no—
99C3×C4⋊C4C2311yescharacteristic
100C3×C4⋊C4C2311yescharacteristic
101C3×C22⋊C4—21no—
102C3×C42—21no—
103C3×C42C2311yescharacteristic
104#217—21no—
105#215—22no—
106#214—22no—
107(C2×D3)⋊C4—21no—
108(C2×D3)⋊C4—21no—
109C4⋊Dic3—21no—
110C4⋊Dic3C2311yescharacteristic
111C4⋊Dic3C2311yescharacteristic
112Dic3⋊C4—21no—
113Dic3⋊C4—21no—
114Dic3⋊C4—21no—
115Dic3⋊C4—21no—
116C4×Dic3—21no—
117C4×Dic3—21no—
118C4×Dic3—21no—
119C4×Dic3D411yescharacteristic
120C4×Dic3D411yescharacteristic
121C4×Dic3C2311yescharacteristic
122C2×C3⋊C8C2311yescharacteristic
123C2×C3⋊C8C2311yescharacteristic
124#204—22no—
125C2×#41—61no—
126C22×Q8—31no—
127C2×SD16—31no—
128C2×SD16—31no—
129C2×SD16—31no—
130C2×SD16C2×D311yescharacteristic
131C4⋊Q8—31no—
132#127—31no—
133#124—61no—
134#121—31no—
135#121—31no—
136#121—61no—
137C4×Q8—31no—
138C4×Q8—31no—
139C4×Q8—31no—
140C4×Q8—61no—
141C4×Q8—61no—
142C4×Q8C2×D311yescharacteristic
143C4×D4—31no—
144C4×D4—61no—
145C4×D4C2×D311yescharacteristic
146C2×C4⋊C4—31no—
147C2×C4⋊C4—61no—
148C2×C42—31no—
149C2×C42—61no—
150#106—31no—
151#106—31no—
152#106—31no—
153#106C2×D311yescharacteristic
154C4⋊C8—31no—
155C4⋊C8—31no—
156#103—31no—
157#103—31no—
158#103—31no—
159#103C2×D311yescharacteristic
160#102—31no—
161#102—31no—
162#102—31no—
163#102C2×D311yescharacteristic
164C22⋊C8—31no—
165C22⋊C8—31no—
166C4×C8—31no—
167C4×C8C2×D311yescharacteristic
168C23×C3—21no—
169C22×D3—21no—
170C22×D3C2×D411yescharacteristic
171C3×Q8—21no—
172C3×Q8#4112yescomplemented
173C3×D4—21no—
174C3×D4—21no—
175C2×C3×C4—21no—
176C2×C3×C4—21no—
177C2×C3×C4—21no—
178C2×C3×C4—42no—
179C2×C3×C4C2×D411yescharacteristic
180C2×C3×C4C2×D411yescharacteristic
181C2×C3×C4C2411yescharacteristic
182#67—42no—
183#67—42no—
184#67—42no—
185C2×Dic3—21no—
186C2×Dic3—21no—
187C2×Dic3—21no—
188C2×Dic3C2×D411yescharacteristic
189C2×Dic3C2×D411yescharacteristic
190C2×Dic3C2×D411yescharacteristic
191D12—21no—
192D12—21no—
193D12—42no—
194C4×D3—24no—
195C4×D3—21no—
196C4×D3—21no—
197C4×D3—41no—
198C4×D3—42no—
199C4×D3—42no—
200C4×D3SD1614yescomplemented
201Dic6—24no—
202Dic6—21no—
203Dic6—42no—
204Dic6#4112yescomplemented
205C3×C8—21no—
206C3×C8—21no—
207C3⋊C8—21no—
208C3⋊C8—21no—
209#41—124no—
210C2×Q8—31no—
211C2×Q8—61no—
212C2×Q8—61no—
213C2×Q8—62no—
214C2×Q8—62no—
215C2×Q8C22×D311yescharacteristic
216C2×D4—31no—
217C2×D4—61no—
218C2×D4—61no—
219C2×D4—61no—
220C2×D4—61no—
221C2×D4C22×D311yescharacteristic
222C22×C4—21no—
223C22×C4—31no—
224C22×C4—31no—
225C22×C4—31no—
226C22×C4—61no—
227C22×C4—61no—
228C22×C4—61no—
229SD16—22no—
230SD16—62no—
231SD16—62no—
232SD16—62no—
233C2×C8—31no—
234C2×C8—31no—
235C2×C8C22×D311yescharacteristic
236C2×C8C22×D311yescharacteristic
237C4⋊C4—21no—
238C4⋊C4—31no—
239C4⋊C4—31no—
240C4⋊C4—61no—
241C4⋊C4—61no—
242C4⋊C4—61no—
243C4⋊C4—61no—
244C4⋊C4—61no—
245C4⋊C4C22×D311yescharacteristic
246C4⋊C4C22×D311yescharacteristic
247C22⋊C4—21no—
248C22⋊C4—61no—
249C22⋊C4—61no—
250C22⋊C4—61no—
251C42—21no—
252C42—31no—
253C42—31no—
254C42—31no—
255C42—61no—
256C42—61no—
257C42—61no—
258C42C22×D311yescharacteristic
259C22×C3—41no—
260C22×C3—41no—
261C22×C3—41no—
262C22×C3C22×D411yescharacteristic
263C2×D3—21no—
264C2×D3—21no—
265C2×D3—41no—
266C2×D3—41no—
267C2×D3—41no—
268C2×D3C2×SD1612yes—
269C3×C4—22no—
270C3×C4—21no—
271C3×C4—41no—
272C3×C4—41no—
273C3×C4C2×SD1612yes—
274C3×C4C2×#4111yescharacteristic
275C3×C4C2×#4111yescharacteristic
276Dic3—21no—
277Dic3—22no—
278Dic3—21no—
279Dic3—41no—
280Dic3—41no—
281Dic3C2×SD1612yes—
282C23—21no—
283C23—31no—
284C23—61no—
285Q8—21no—
286Q8—32no—
287Q8—64no—
288Q8—61no—
289Q8—122no—
290Q8#23512yescomplemented
291D4—21no—
292D4—21no—
293D4—61no—
294D4—61no—
295D4—122no—
296D4—122no—
297D4—122no—
298D4—122no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—31no—
303C2×C4—34no—
304C2×C4—31no—
305C2×C4—31no—
306C2×C4—42no—
307C2×C4—64no—
308C2×C4—61no—
309C2×C4—61no—
310C2×C4—61no—
311C2×C4—61no—
312C2×C4—61no—
313C2×C4—121no—
314C2×C4—122no—
315C2×C4—122no—
316C2×C4D3×D411yescharacteristic
317C2×C4D3×D411yescharacteristic
318C2×C4C23×D311yescharacteristic
319C8—21no—
320C8—21no—
321C8—61no—
322C8—61no—
323C2×C3—81no—
324C2×C3#52511yescharacteristic
325C2×C3C22×SD1611yescharacteristic
326C2×C3#57511yescharacteristic
327D3—22no—
328D3—81no—
329C22—32no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—61no—
334C22—61no—
335C22—121no—
336C22—121no—
337C22—121no—
338C22C2×D3×D411yescharacteristic
339C4—21no—
340C4—22no—
341C4—32no—
342C4—41no—
343C4—41no—
344C4—61no—
345C4—61no—
346C4—62no—
347C4—121no—
348C4—121no—
349C4D3×SD1612yes—
350C4C2×#23511yescharacteristic
351C4D3×#4111yescharacteristic
352C3#310311yescharacteristic, complemented, Sylow
353C2—62no—
354C2—81no—
355C2—241no—
356C2#554711yescharacteristic
357C2C2×D3×SD1611yescharacteristic
358C2#576811yescharacteristic
subgroupG/H
centerC2×C4D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×C4×SD16C2
socleC22×C3C22×D4
prime radical#5548C2
hypercenterC4×SD16D3
hypocenterC3#3103
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. C4×D3×Q8C2semidirect
3. C3×C4×SD16C2semidirect
4. #5170C2semidirect
5. #5163C2semidirect
6. C4×#215C2semidirect
7. C4×#214C2semidirect
8. #4863C2semidirect
9. #4854C2semidirect
10. #4806C2semidirect
11. #4791C2semidirect
12. #4777C2semidirect
13. #4762C2semidirect
14. C4×#204C2semidirect
15. #4685C2semidirect
73. C4×SD16D3semidirect
172. C3×Q8#41semidirect
200. C4×D3SD16semidirect
204. Dic6#41semidirect
290. Q8#235semidirect
352. C3#3103semidirect

Maximal subgroups

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

subgroupindex
C4×D3×Q82
#55482
C3×C4×SD162
#51702
#51632
C4×#2152
C4×#2142
#48632
#48542
#48062
#47912
#47772
#47622
C4×#2042
#46852
#31033