Finite Group Databasebeta

← #79159

Subgroups — #79159

Order 384.

356 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#5514C211yesmaximal, characteristic
2#5511C211yesmaximal, characteristic, complemented
3C2×C3×#107C211yesmaximal, characteristic, complemented
4#5114C211yesmaximal, characteristic, complemented
5#5111C211yesmaximal, characteristic, complemented
6#4970C211yesmaximal, characteristic, complemented
7#4968C211yesmaximal, characteristic, complemented
8#4890C211yesmaximal, characteristic, complemented
9#4889C211yesmaximal, characteristic, complemented
10#4888C211yesmaximal, characteristic, complemented
11#4886C211yesmaximal, characteristic, complemented
12#4882C211yesmaximal, characteristic, complemented
13#4881C211yesmaximal, characteristic, complemented
14#4877C211yesmaximal, characteristic, complemented
15#4876C211yesmaximal, characteristic, complemented
16#3346—31nomaximal, Sylow
17C22×C3×C8C2211yescharacteristic
18C2×C3×C4⋊C4C2211yescharacteristic
19C2×C3×C4⋊C4C2211yescharacteristic
20#930—21no—
21#930C2211yescharacteristic
22C4×#67—21no—
23C4×#67—21no—
24C4×#67C2211yescharacteristic
25#924—21no—
26#924C2211yescharacteristic
27C2×#204C2211yescharacteristic
28C2×ΓL(1,𝔽25)C2211yescharacteristic
29#898—21no—
30#897C2211yescharacteristic
31#896—21no—
32#895C2211yescharacteristic
33#894—21no—
34#893C2211yescharacteristic
35#892C2211yescharacteristic
36D3×C4⋊C4C2211yescharacteristic
37#890C2211yescharacteristic
38#889—21no—
39#888C2211yescharacteristic
40#887C2211yescharacteristic
41C3×#107C2211yescharacteristic
42C3×#107C2211yescharacteristic
43C3×#107C2211yescharacteristic
44C3×#107C2211yescharacteristic
45#830C2211yescharacteristic
46#821C2211yescharacteristic
47(C2×D3)⋊C8C2211yescharacteristic
48#817C2211yescharacteristic
49#816C2211yescharacteristic
50#815C2211yescharacteristic
51Dic3⋊C8C2211yescharacteristic
52#810C2211yescharacteristic
53#810C2211yescharacteristic
54#809C2211yescharacteristic
55#809C2211yescharacteristic
56#808C2211yescharacteristic
57#808C2211yescharacteristic
58#807C2211yescharacteristic
59#807C2211yescharacteristic
60#554—31no—
61#553—31no—
62#501—31no—
63#485—31no—
64#484—31no—
65#481—31no—
66#480—31no—
67#479—31no—
68#474—31no—
69#468—31no—
70#465—31no—
71#440—31no—
72#435—31no—
73#428—31no—
74C2×#107D311yescharacteristic, complemented
75C22×C3×C4—21no—
76C22×C3×C4—21no—
77C22×C3×C4C2311yescharacteristic
78C2×#67—21no—
79C2×#67D411yescharacteristic
80C2×D12—21no—
81C2×D12C2311yescharacteristic
82C2×C4×D3—21no—
83C2×C4×D3—21no—
84C2×C4×D3C2311yescharacteristic
85C2×Dic6—21no—
86C2×Dic6C2311yescharacteristic
87C2×C3×C8—22no—
88C2×C3×C8C2311yescharacteristic
89C2×C3×C8C2311yescharacteristic
90C3×C4⋊C4—21no—
91C3×C4⋊C4—21no—
92C3×C4⋊C4C2311yescharacteristic
93C3×C4⋊C4C2311yescharacteristic
94C3×C4⋊C4C2311yescharacteristic
95C3×C4⋊C4C2311yescharacteristic
96#217—21no—
97#217D411yescharacteristic
98(C2×D3)⋊C4—21no—
99(C2×D3)⋊C4—21no—
100(C2×D3)⋊C4—21no—
101(C2×D3)⋊C4—21no—
102(C2×D3)⋊C4—21no—
103(C2×D3)⋊C4D411yescharacteristic
104C4⋊Dic3—21no—
105C4⋊Dic3—21no—
106C4⋊Dic3C2311yescharacteristic
107C4⋊Dic3C2311yescharacteristic
108Dic3⋊C4—21no—
109Dic3⋊C4—21no—
110Dic3⋊C4—21no—
111Dic3⋊C4—21no—
112Dic3⋊C4—21no—
113Dic3⋊C4D411yescharacteristic
114C4×Dic3—21no—
115C4×Dic3—21no—
116C4×Dic3C2311yescharacteristic
117C2×C3⋊C8C2311yescharacteristic
118C2×C3⋊C8C2311yescharacteristic
119#204—22no—
120ΓL(1,𝔽25)—22no—
121C2×SD16—31no—
122C2×M16—31no—
123C22×C8C2×D311yescharacteristic
124C4⋊Q8—31no—
125#126—61no—
126#125—31no—
127#125—61no—
128#123—61no—
129C22⋊Q8—31no—
130C22⋊Q8—31no—
131C22⋊Q8—61no—
132C22⋊Q8—61no—
133#121—31no—
134#121—31no—
135#121—61no—
136C4×Q8—31no—
137C4×D4—31no—
138C4×D4—31no—
139C4×D4—61no—
140C4×D4—61no—
141#117—31no—
142C2×C4⋊C4—31no—
143C2×C4⋊C4C2×D311yescharacteristic
144C2×C4⋊C4C2×D311yescharacteristic
145#107—31no—
146#107—31no—
147#107C2×D311yescharacteristic
148#107C2×D311yescharacteristic
149#107C2×D311yescharacteristic
150#107C2×D311yescharacteristic
151#106—31no—
152#106—31no—
153#106—31no—
154C4⋊C8—31no—
155#103—31no—
156#103—31no—
157#103—31no—
158#102—31no—
159#102—31no—
160#102—31no—
161C22⋊C8—31no—
162C22⋊C8—31no—
163#97—31no—
164C23×C3C2×D411yescharacteristic
165C22×D3—21no—
166C22×D3C2×D411yescharacteristic
167C2×C3×C4—21no—
168C2×C3×C4—21no—
169C2×C3×C4—21no—
170C2×C3×C4—21no—
171C2×C3×C4—21no—
172C2×C3×C4—21no—
173C2×C3×C4—81no—
174C2×C3×C4—81no—
175C2×C3×C4C2×D411yescharacteristic
176C2×C3×C4C2411yescharacteristic
177#67—22no—
178#67—42no—
179C2×Dic3—21no—
180C2×Dic3—21no—
181C2×Dic3—21no—
182C2×Dic3C2×D411yescharacteristic
183C2×Dic3C2×D411yescharacteristic
184C2×Dic3C2×D411yescharacteristic
185D12—21no—
186D12—21no—
187D12—81no—
188C4×D3—21no—
189C4×D3—21no—
190C4×D3—81no—
191C4×D3—81no—
192Dic6—21no—
193Dic6—21no—
194Dic6—81no—
195C3×C8—21no—
196C3×C8#4112yes—
197C3⋊C8—21no—
198C3⋊C8—21no—
199C2×Q8—31no—
200C2×Q8—61no—
201C2×D4—31no—
202C2×D4—31no—
203C2×D4—61no—
204C2×D4—61no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—31no—
208C22×C4—61no—
209C22×C4—61no—
210C22×C4C22×D311yescharacteristic
211SD16—62no—
212M16—62no—
213C2×C8—22no—
214C2×C8—31no—
215C2×C8—31no—
216C2×C8C22×D311yescharacteristic
217C2×C8C22×D311yescharacteristic
218C4⋊C4—21no—
219C4⋊C4—21no—
220C4⋊C4—31no—
221C4⋊C4—31no—
222C4⋊C4—31no—
223C4⋊C4—61no—
224C4⋊C4—61no—
225C4⋊C4—61no—
226C4⋊C4—61no—
227C4⋊C4—61no—
228C4⋊C4—61no—
229C4⋊C4—61no—
230C4⋊C4C22×D311yescharacteristic
231C4⋊C4C22×D311yescharacteristic
232C4⋊C4C22×D311yescharacteristic
233C4⋊C4C22×D311yescharacteristic
234C22⋊C4—31no—
235C22⋊C4—31no—
236C22⋊C4—61no—
237C22⋊C4—61no—
238C22⋊C4—61no—
239C22⋊C4—61no—
240C22⋊C4—61no—
241C22⋊C4—61no—
242C42—31no—
243C42—61no—
244C42—61no—
245C22×C3—21no—
246C22×C3—21no—
247C22×C3#13712yes—
248C22×C3C22×D411yescharacteristic
249C2×D3—21no—
250C2×D3—21no—
251C2×D3—21no—
252C2×D3—41no—
253C2×D3—41no—
254C2×D3—41no—
255C3×C4—21no—
256C3×C4—41no—
257C3×C4—41no—
258C3×C4—41no—
259C3×C4—41no—
260C3×C4C2×#4111yescharacteristic
261C3×C42−1+411yescharacteristic
262Dic3—21no—
263Dic3—21no—
264Dic3—21no—
265Dic3—41no—
266Dic3—41no—
267Dic3—41no—
268C23—31no—
269C23—61no—
270C23D3×D411yescharacteristic
271Q8—61no—
272Q8—61no—
273Q8—241no—
274D4—62no—
275D4—61no—
276D4—61no—
277D4—122no—
278D4—241no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—31no—
286C2×C4—31no—
287C2×C4—31no—
288C2×C4—61no—
289C2×C4—61no—
290C2×C4—61no—
291C2×C4—61no—
292C2×C4—61no—
293C2×C4—81no—
294C2×C4—81no—
295C2×C4—241no—
296C2×C4—241no—
297C2×C4D3×D411yescharacteristic
298C2×C4C23×D311yescharacteristic
299C8—21no—
300C8—61no—
301C8—61no—
302C8#23512yes—
303C2×C3—22no—
304C2×C3#54711yescharacteristic
305C2×C3C2×#13711yescharacteristic
306C2×C3#57611yescharacteristic
307D3—41no—
308D3—81no—
309C22—21no—
310C22—21no—
311C22—61no—
312C22—61no—
313C22—61no—
314C22—121no—
315C22—121no—
316C22—121no—
317C22#91812yes—
318C22C2×D3×D411yescharacteristic
319C4—21no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—61no—
325C4—61no—
326C4—61no—
327C4—121no—
328C4—121no—
329C4—121no—
330C4C2×#23511yescharacteristic
331C4#100711yescharacteristic
332C3#334611yescharacteristic, complemented, Sylow
333C2—22no—
334C2—121no—
335C2—241no—
336C2#550711yescharacteristic
337C2#575711yescharacteristic
338C2C2×#91811yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC2×C3×#107C2
socleC22×C3C22×D4
prime radical#5514C2
hypercenterC2×#107D3
hypocenterC3#3346
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
2. #5511C2semidirect
3. C2×C3×#107C2semidirect
4. #5114C2semidirect
5. #5111C2semidirect
6. #4970C2semidirect
7. #4968C2semidirect
8. #4890C2semidirect
9. #4889C2semidirect
10. #4888C2semidirect
11. #4886C2semidirect
12. #4882C2semidirect
13. #4881C2semidirect
14. #4877C2semidirect
15. #4876C2semidirect
74. C2×#107D3semidirect
332. C3#3346semidirect

Maximal subgroups

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

subgroupindex
#55142
#55112
C2×C3×#1072
#51142
#51112
#49702
#49682
#48902
#48892
#48882
#48862
#48822
#48812
#48772
#48762
#33463