Finite Group Databasebeta

← #79666

Subgroups — #79666

Order 384.

362 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#5582C211yesmaximal, characteristic, complemented
2#5561C211yesmaximal, characteristic, complemented
3C3×C4×SD16C211yesmaximal, characteristic, complemented
4#5171C211yesmaximal, characteristic, complemented
5#5168C211yesmaximal, characteristic, complemented
6#5030C211yesmaximal, characteristic, complemented
7#5014C211yesmaximal, characteristic, complemented
8#4864C211yesmaximal, characteristic, complemented
9#4855C211yesmaximal, characteristic, complemented
10#4816C211yesmaximal, characteristic, complemented
11#4794C211yesmaximal, characteristic, complemented
12#4782C211yesmaximal, characteristic
13#4765C211yesmaximal, characteristic, complemented
14C4×#204C211yesmaximal, characteristic, complemented
15#4689C211yesmaximal, characteristic, complemented
16#3173—31nomaximal, Sylow
17C2×C3×SD16C2211yescharacteristic
18C3×C4×Q8C2211yescharacteristic
19C3×C4×D4C2211yescharacteristic
20#947C2211yescharacteristic
21#946C2211yescharacteristic
22C2×#216C2211yescharacteristic
23#938C2211yescharacteristic
24#936C2211yescharacteristic
25C2×#213C2211yescharacteristic
26#929—21no—
27#924—21no—
28C2×#204C2211yescharacteristic
29C2×ΓL(1,𝔽25)C2211yescharacteristic
30C2×D3×C8C2211yescharacteristic
31#897C2211yescharacteristic
32#896—21no—
33#895C2211yescharacteristic
34#894—21no—
35#888C2211yescharacteristic
36#888C2211yescharacteristic
37#885—21no—
38#879—21no—
39#876—21no—
40#875—21no—
41C4×D12C2211yescharacteristic
42#872C2211yescharacteristic
43C4×Dic6C2211yescharacteristic
44C3×#106C2211yescharacteristic
45C3×#103C2211yescharacteristic
46C3×#102C2211yescharacteristic
47C3×C4×C8C2211yescharacteristic
48#835C2211yescharacteristic
49#832C2211yescharacteristic
50#821C2211yescharacteristic
51#817C2211yescharacteristic
52#816C2211yescharacteristic
53#815C2211yescharacteristic
54C8×Dic3C2211yescharacteristic
55#810C2211yescharacteristic
56#809C2211yescharacteristic
57#808C2211yescharacteristic
58#808C2211yescharacteristic
59#803C2211yescharacteristic
60#542—31no—
61#542—31no—
62#498—31no—
63#495—31no—
64#489—31no—
65#489—31no—
66#470—31no—
67#469—31no—
68#465—31no—
69#465—31no—
70#442—31no—
71#441—31no—
72C4×SD16—31no—
73C4×SD16D311yescharacteristic, complemented
74#405—31no—
75C2×C3×Q8C2311yescharacteristic
76C2×C3×D4C2311yescharacteristic
77C22×C3×C4—21no—
78C2×#67—21no—
79C2×D12—21no—
80C2×D12C2311yescharacteristic
81C2×C4×D3—21no—
82C2×C4×D3C2311yescharacteristic
83C2×Dic6—21no—
84C2×Dic6—21no—
85C2×Dic6C2311yescharacteristic
86C3×SD16—22no—
87C2×C3×C8C2311yescharacteristic
88C2×C3×C8C2311yescharacteristic
89C3×C4⋊C4—21no—
90C3×C4⋊C4C2311yescharacteristic
91C3×C4⋊C4C2311yescharacteristic
92C3×C22⋊C4—21no—
93C3×C42—21no—
94C3×C42C2311yescharacteristic
95#217—21no—
96#217—21no—
97#217—21no—
98#216—22no—
99#213—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)⋊C4—21no—
106(C2×D3)⋊C4D411yescharacteristic
107(C2×D3)⋊C4D411yescharacteristic
108C4⋊Dic3—21no—
109C4⋊Dic3C2311yescharacteristic
110C4⋊Dic3C2311yescharacteristic
111Dic3⋊C4—21no—
112Dic3⋊C4—21no—
113Dic3⋊C4—21no—
114Dic3⋊C4—21no—
115Dic3⋊C4D411yescharacteristic
116Dic3⋊C4D411yescharacteristic
117C4×Dic3—21no—
118C4×Dic3C2311yescharacteristic
119C2×C3⋊C8C2311yescharacteristic
120C2×C3⋊C8C2311yescharacteristic
121#204—22no—
122ΓL(1,𝔽25)—22no—
123D3×C8—22no—
124C2×Q16—31no—
125C2×SD16—31no—
126C2×SD16C2×D311yescharacteristic
127C2×D8—31no—
128C2×M16—31no—
129C22×C8—31no—
130C4⋊Q8—31no—
131C4⋊Q8—31no—
132#126—61no—
133#126—61no—
134#124—31no—
135#124—31no—
136#124—61no—
137#124—61no—
138#123—61no—
139#123—61no—
140C22⋊Q8—31no—
141C22⋊Q8—31no—
142C22⋊Q8—61no—
143C22⋊Q8—61no—
144#121—31no—
145#121—31no—
146C4×Q8—31no—
147C4×Q8C2×D311yescharacteristic
148C4×D4—31no—
149C4×D4C2×D311yescharacteristic
150#117—31no—
151#106—31no—
152#106—31no—
153#106—31no—
154#106C2×D311yescharacteristic
155#103—31no—
156#103—31no—
157#103—31no—
158#103C2×D311yescharacteristic
159#102—31no—
160#102—31no—
161#102—31no—
162#102C2×D311yescharacteristic
163#97—31no—
164#97—31no—
165C4×C8—31no—
166C4×C8C2×D311yescharacteristic
167C23×C3—21no—
168C22×D3—21no—
169C22×D3C2×D411yescharacteristic
170C3×Q8—21no—
171C3×Q8—21no—
172C3×D4—21no—
173C3×D4—21no—
174C2×C3×C4—21no—
175C2×C3×C4—21no—
176C2×C3×C4—21no—
177C2×C3×C4—81no—
178C2×C3×C4C2×D411yescharacteristic
179C2×C3×C4C2×D411yescharacteristic
180C2×C3×C4C2411yescharacteristic
181#67—81no—
182C2×Dic3—21no—
183C2×Dic3—21no—
184C2×Dic3—21no—
185C2×Dic3C2×D411yescharacteristic
186C2×Dic3C2×D411yescharacteristic
187C2×Dic3C2×D411yescharacteristic
188D12—21no—
189D12—21no—
190D12—81no—
191C4×D3—21no—
192C4×D3—21no—
193C4×D3—81no—
194Dic6—21no—
195Dic6—21no—
196Dic6—81no—
197Dic6—81no—
198C3×C8—21no—
199C3×C8#4112yes—
200C3⋊C8—21no—
201C3⋊C8#4112yes—
202C2×Q8—31no—
203C2×Q8—61no—
204C2×Q8—61no—
205C2×Q8C22×D311yescharacteristic
206C2×D4—31no—
207C2×D4—61no—
208C2×D4—61no—
209C2×D4C22×D311yescharacteristic
210C22×C4—21no—
211C22×C4—31no—
212C22×C4—61no—
213Q16—62no—
214SD16—22no—
215SD16—62no—
216D8—62no—
217M16—62no—
218C2×C8—31no—
219C2×C8—31no—
220C2×C8—62no—
221C2×C8C22×D311yescharacteristic
222C2×C8C22×D311yescharacteristic
223C4⋊C4—21no—
224C4⋊C4—31no—
225C4⋊C4—31no—
226C4⋊C4—31no—
227C4⋊C4—31no—
228C4⋊C4—61no—
229C4⋊C4—61no—
230C4⋊C4—61no—
231C4⋊C4—61no—
232C4⋊C4—61no—
233C4⋊C4C22×D311yescharacteristic
234C4⋊C4C22×D311yescharacteristic
235C22⋊C4—21no—
236C22⋊C4—31no—
237C22⋊C4—31no—
238C22⋊C4—61no—
239C22⋊C4—61no—
240C22⋊C4—61no—
241C22⋊C4—61no—
242C22⋊C4—61no—
243C22⋊C4—61no—
244C22⋊C4—61no—
245C22⋊C4—61no—
246C22⋊C4—61no—
247C42—21no—
248C42—31no—
249C42—61no—
250C42C22×D311yescharacteristic
251C22×C3—41no—
252C22×C3—41no—
253C22×C3—41no—
254C22×C3C22×D411yescharacteristic
255C2×D3—21no—
256C2×D3—21no—
257C2×D3—21no—
258C2×D3—41no—
259C2×D3—41no—
260C2×D3—41no—
261C3×C4—21no—
262C3×C4—21no—
263C3×C4—41no—
264C3×C4—41no—
265C3×C4—41no—
266C3×C4C2×#4111yescharacteristic
267C3×C4C2×#4111yescharacteristic
268Dic3—21no—
269Dic3—21no—
270Dic3—21no—
271Dic3—41no—
272Dic3—41no—
273Dic3—41no—
274C23—21no—
275C23—31no—
276C23—61no—
277Q8—21no—
278Q8—21no—
279Q8—61no—
280Q8—61no—
281Q8—241no—
282Q8—241no—
283D4—21no—
284D4—21no—
285D4—61no—
286D4—61no—
287D4—241no—
288D4—241no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—31no—
293C2×C4—31no—
294C2×C4—31no—
295C2×C4—61no—
296C2×C4—61no—
297C2×C4—61no—
298C2×C4—61no—
299C2×C4—61no—
300C2×C4—81no—
301C2×C4—241no—
302C2×C4D3×D411yescharacteristic
303C2×C4D3×D411yescharacteristic
304C2×C4C23×D311yescharacteristic
305C8—21no—
306C8—32no—
307C8—61no—
308C8#23512yes—
309C2×C3—81no—
310C2×C3#53211yescharacteristic
311C2×C3#57711yescharacteristic
312C2×C3#57711yescharacteristic
313D3—41no—
314D3—81no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22—61no—
319C22—61no—
320C22—61no—
321C22—121no—
322C22—121no—
323C22—121no—
324C22C2×D3×D411yescharacteristic
325C4—21no—
326C4—21no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—61no—
331C4—61no—
332C4—61no—
333C4—121no—
334C4—121no—
335C4—121no—
336C4C2×#23511yescharacteristic
337C4D3×#4111yescharacteristic
338C3#317311yescharacteristic, complemented, Sylow
339C2—81no—
340C2—121no—
341C2—241no—
342C2#554811yescharacteristic
343C2#576211yescharacteristic
344C2#577011yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×C4×SD16C2
socleC22×C3C22×D4
prime radical#4782C2
hypercenterC4×SD16D3
hypocenterC3#3173
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #5582C2semidirect
2. #5561C2semidirect
3. C3×C4×SD16C2semidirect
4. #5171C2semidirect
5. #5168C2semidirect
6. #5030C2semidirect
7. #5014C2semidirect
8. #4864C2semidirect
9. #4855C2semidirect
10. #4816C2semidirect
11. #4794C2semidirect
13. #4765C2semidirect
14. C4×#204C2semidirect
15. #4689C2semidirect
73. C4×SD16D3semidirect
338. C3#3173semidirect

Maximal subgroups

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

subgroupindex
#55822
#55612
C3×C4×SD162
#51712
#51682
#50302
#50142
#48642
#48552
#48162
#47942
#47822
#47652
C4×#2042
#46892
#31733