Finite Group Databasebeta

← #79854

Subgroups — #79854

Order 384.

346 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#5542C211yesmaximal, characteristic, complemented
2#5539C211yesmaximal, characteristic, complemented
3C3×#442C211yesmaximal, characteristic
4#5153C211yesmaximal, characteristic
5#5153C211yesmaximal, characteristic
6#5019C211yesmaximal, characteristic, complemented
7#5009C211yesmaximal, characteristic, complemented
8#4857C211yesmaximal, characteristic, complemented
9#4854C211yesmaximal, characteristic, complemented
10#4768C211yesmaximal, characteristic, complemented
11#4765C211yesmaximal, characteristic, complemented
12#4758C211yesmaximal, characteristic, complemented
13#4757C211yesmaximal, characteristic, complemented
14#4703C211yesmaximal, characteristic, complemented
15#4701C211yesmaximal, characteristic, complemented
16#3376—31nomaximal, Sylow
17C2×C3×D8C2211yescharacteristic
18C3×C4×D4C2211yescharacteristic
19C3×C4×D4C2211yescharacteristic
20#936C2211yescharacteristic
21#936C2211yescharacteristic
22D4×Dic3C2211yescharacteristic
23D4×Dic3C2211yescharacteristic
24C2×#214C2211yescharacteristic
25C2×#214C2211yescharacteristic
26#926—21no—
27#924—21no—
28#924—21no—
29C2×Dic3⋊C4—21no—
30#890C2211yescharacteristic
31#888C2211yescharacteristic
32#887C2211yescharacteristic
33#887C2211yescharacteristic
34#879—21no—
35#879—21no—
36#878—21no—
37#878—21no—
38#870C2211yescharacteristic
39#869C2211yescharacteristic
40C4×Dic6C2211yescharacteristic
41C3×#106C2211yescharacteristic
42C3×#102C2211yescharacteristic
43C3×#102C2211yescharacteristic
44C3×#97C2211yescharacteristic
45#832C2211yescharacteristic
46#832C2211yescharacteristic
47#816C2211yescharacteristic
48#816C2211yescharacteristic
49#816C2211yescharacteristic
50#816C2211yescharacteristic
51#815C2211yescharacteristic
52Dic3⋊C8C2211yescharacteristic
53Dic3⋊C8C2211yescharacteristic
54C8×Dic3C2211yescharacteristic
55#810C2211yescharacteristic
56#810C2211yescharacteristic
57#808C2211yescharacteristic
58#807C2211yescharacteristic
59C4⋊(C3⋊C8)C2211yescharacteristic
60#556—31no—
61#554—31no—
62#491—31no—
63#489—31no—
64#488—31no—
65#479—31no—
66#478—31no—
67#475—31no—
68#463—31no—
69#463—31no—
70#461—31no—
71#446—31no—
72#442D311yescharacteristic
73#440—31no—
74C4×SD16—31no—
75C2×C3×D4C2311yescharacteristic
76C2×C3×D4C2311yescharacteristic
77C22×C3×C4—21no—
78C22×C3×C4—21no—
79C22×Dic3—21no—
80C22×Dic3—21no—
81C2×Dic6—21no—
82C2×Dic6D411yescharacteristic
83C2×Dic6C2311yescharacteristic
84C2×Dic6C2311yescharacteristic
85C3×D8—22no—
86C2×C3×C8C2311yescharacteristic
87C2×C3×C8C2311yescharacteristic
88C3×C4⋊C4C2311yescharacteristic
89C3×C4⋊C4C2311yescharacteristic
90C3×C22⋊C4—21no—
91C3×C22⋊C4—21no—
92C3×C42C2311yescharacteristic
93#217—21no—
94#217—21no—
95#217—21no—
96#217—21no—
97#217—21no—
98#217—21no—
99#214—22no—
100#214—22no—
101C4⋊Dic3—21no—
102C4⋊Dic3—21no—
103C4⋊Dic3—21no—
104C4⋊Dic3D411yescharacteristic
105C4⋊Dic3C2311yescharacteristic
106C4⋊Dic3C2311yescharacteristic
107Dic3⋊C4—21no—
108Dic3⋊C4—21no—
109Dic3⋊C4—21no—
110Dic3⋊C4—21no—
111Dic3⋊C4—21no—
112Dic3⋊C4—21no—
113Dic3⋊C4D411yescharacteristic
114Dic3⋊C4D411yescharacteristic
115C4×Dic3—21no—
116C4×Dic3—21no—
117C4×Dic3C2311yescharacteristic
118C4×Dic3C2311yescharacteristic
119C2×C3⋊C8C2311yescharacteristic
120C2×C3⋊C8C2311yescharacteristic
121C2×SD16—31no—
122C2×SD16—31no—
123C2×D8C2×D311yescharacteristic
124C4⋊Q8—31no—
125C4⋊Q8—31no—
126#126—61no—
127#126—61no—
128#125—31no—
129#125—31no—
130#124—31no—
131#124—31no—
132C22⋊Q8—61no—
133C22⋊Q8—61no—
134C22⋊Q8—61no—
135C22⋊Q8—61no—
136C4×Q8—31no—
137C4×Q8—31no—
138C4×Q8—31no—
139C4×D4—31no—
140C4×D4—31no—
141C4×D4C2×D311yescharacteristic
142C4×D4C2×D311yescharacteristic
143#117—61no—
144C2×C4⋊C4—61no—
145#107—31no—
146#106—31no—
147#106C2×D311yescharacteristic
148C4⋊C8—31no—
149C4⋊C8—31no—
150C4⋊C8—31no—
151#103—31no—
152#103—31no—
153#103—31no—
154#103—31no—
155#103—31no—
156#103—31no—
157#102—31no—
158#102—31no—
159#102C2×D311yescharacteristic
160#102C2×D311yescharacteristic
161#97—31no—
162#97C2×D311yescharacteristic
163C4×C8—31no—
164C23×C3—21no—
165C23×C3—21no—
166C3×D4—21no—
167C3×D4—21no—
168C3×D4—21no—
169C3×D4#4112yes—
170C2×C3×C4—21no—
171C2×C3×C4—21no—
172C2×C3×C4—42no—
173C2×C3×C4—81no—
174C2×C3×C4C2×D411yescharacteristic
175C2×C3×C4C2×D411yescharacteristic
176C2×C3×C4C2411yescharacteristic
177C2×Dic3—21no—
178C2×Dic3—21no—
179C2×Dic3—21no—
180C2×Dic3—21no—
181C2×Dic3—42no—
182C2×Dic3—81no—
183C2×Dic3C2×D411yescharacteristic
184C2×Dic3C2×D411yescharacteristic
185C2×Dic3C2×D411yescharacteristic
186C2×Dic3C2×D411yescharacteristic
187Dic6—21no—
188Dic6—21no—
189Dic6—21no—
190Dic6—21no—
191Dic6—41no—
192Dic6—81no—
193C3×C8—21no—
194C3×C8—21no—
195C3⋊C8—21no—
196C3⋊C8—21no—
197C2×Q8—31no—
198C2×Q8—31no—
199C2×Q8—31no—
200C2×Q8—61no—
201C2×D4C22×D311yescharacteristic
202C2×D4C22×D311yescharacteristic
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—61no—
206C22×C4—61no—
207SD16—62no—
208SD16—62no—
209D8—22no—
210C2×C8—31no—
211C2×C8—31no—
212C2×C8C22×D311yescharacteristic
213C2×C8C22×D311yescharacteristic
214C4⋊C4—31no—
215C4⋊C4—31no—
216C4⋊C4—31no—
217C4⋊C4—31no—
218C4⋊C4—31no—
219C4⋊C4—61no—
220C4⋊C4—61no—
221C4⋊C4—61no—
222C4⋊C4—61no—
223C4⋊C4—61no—
224C4⋊C4—61no—
225C4⋊C4—61no—
226C4⋊C4—61no—
227C4⋊C4—61no—
228C4⋊C4C22×D311yescharacteristic
229C4⋊C4C22×D311yescharacteristic
230C22⋊C4—21no—
231C22⋊C4—21no—
232C22⋊C4—61no—
233C22⋊C4—61no—
234C22⋊C4—61no—
235C22⋊C4—61no—
236C22⋊C4—61no—
237C22⋊C4—61no—
238C42—31no—
239C42—31no—
240C42—61no—
241C42—61no—
242C42C22×D311yescharacteristic
243C22×C3—22no—
244C22×C3—41no—
245C22×C3—41no—
246C22×C3—41no—
247C22×C3—41no—
248C22×C3—41no—
249C22×C3C22×D411yescharacteristic
250C3×C4—21no—
251C3×C4—21no—
252C3×C4—41no—
253C3×C4—41no—
254C3×C4C2×#4111yescharacteristic
255C3×C42−1+411yescharacteristic
256Dic3—21no—
257Dic3—21no—
258Dic3—21no—
259Dic3—21no—
260Dic3—41no—
261Dic3—41no—
262Dic3—41no—
263Dic3—41no—
264C23—21no—
265C23—21no—
266Q8—61no—
267Q8—61no—
268Q8—61no—
269Q8—61no—
270Q8—121no—
271Q8—241no—
272D4—21no—
273D4—21no—
274D4—21no—
275D4#23512yes—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—31no—
279C2×C4—31no—
280C2×C4—31no—
281C2×C4—31no—
282C2×C4—42no—
283C2×C4—61no—
284C2×C4—61no—
285C2×C4—61no—
286C2×C4—61no—
287C2×C4—81no—
288C2×C4—122no—
289C2×C4—241no—
290C2×C4D3×D411yescharacteristic
291C2×C4D3×D411yescharacteristic
292C2×C4C23×D311yescharacteristic
293C8—21no—
294C8—21no—
295C8—61no—
296C8—61no—
297C2×C3—42no—
298C2×C3—81no—
299C2×C3#54811yescharacteristic
300C2×C3#57511yescharacteristic
301C2×C3#57711yescharacteristic
302C22—22no—
303C22—41no—
304C22—41no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22C2×D3×D411yescharacteristic
309C4—21no—
310C4—21no—
311C4—41no—
312C4—41no—
313C4—61no—
314C4—61no—
315C4—61no—
316C4—61no—
317C4—121no—
318C4—121no—
319C4—121no—
320C4—121no—
321C4C2×#23511yescharacteristic
322C4#101011yescharacteristic
323C3#337611yescharacteristic, complemented, Sylow
324C2—42no—
325C2—81no—
326C2#555211yescharacteristic
327C2#577311yescharacteristic
328C2#577511yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#442C2
socleC22×C3C22×D4
prime radicalC2×C3×D8C22
hypercenter#442D3
hypocenterC3#3376
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #5542C2semidirect
2. #5539C2semidirect
6. #5019C2semidirect
7. #5009C2semidirect
8. #4857C2semidirect
9. #4854C2semidirect
10. #4768C2semidirect
11. #4765C2semidirect
12. #4758C2semidirect
13. #4757C2semidirect
14. #4703C2semidirect
15. #4701C2semidirect
323. C3#3376semidirect

Maximal subgroups

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

subgroupindex
#55422
#55392
C3×#4422
#51532
#50192
#50092
#48572
#48542
#47682
#47652
#47582
#47572
#47032
#47012
#33763