Finite Group Databasebeta

← #83606

Subgroups — #83606

Order 384.

354 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#553C211yesmaximal, characteristic
2#5541C211yesmaximal, characteristic, complemented
3#5065C211yesmaximal, characteristic, complemented
4#5063C211yesmaximal, characteristic, complemented
5#5041C211yesmaximal, characteristic, complemented
6#5041C211yesmaximal, characteristic, complemented
7#5035C211yesmaximal, characteristic, complemented
8#5033C211yesmaximal, characteristic, complemented
9C4×#214C211yesmaximal, characteristic, complemented
10D4×C3⋊C8C211yesmaximal, characteristic, complemented
11#5009C211yesmaximal, characteristic, complemented
12#4998C211yesmaximal, characteristic, complemented
13#4996C211yesmaximal, characteristic, complemented
14#4970C211yesmaximal, characteristic, complemented
15C2×#808C211yesmaximal, characteristic, complemented
16#3337—31nomaximal, Sylow
17C3×#126—21no—
18C3×#125C2211yescharacteristic
19C3×#123—21no—
20C3×#121—21no—
21C3×#121C2211yescharacteristic
22C3×#121C2211yescharacteristic
23C3×C4×D4—21no—
24C3×C4×D4C2211yescharacteristic
25C3×C4×D4C2211yescharacteristic
26C3×#117C2211yescharacteristic
27C2×C3×C4⋊C4C2211yescharacteristic
28#935—21no—
29C2×#214C2211yescharacteristic
30#926C2211yescharacteristic
31C2×C4⋊Dic3C2211yescharacteristic
32#924C2211yescharacteristic
33#924C2211yescharacteristic
34C22×C3⋊C8C2211yescharacteristic
35C22×C3⋊C8C2211yescharacteristic
36#889—21no—
37#879—21no—
38#877—21no—
39#870C2211yescharacteristic
40C4×Dic6C2211yescharacteristic
41#832C2211yescharacteristic
42#832C2211yescharacteristic
43#832C2211yescharacteristic
44#830C2211yescharacteristic
45#830C2211yescharacteristic
46#810C2211yescharacteristic
47#810C2211yescharacteristic
48#810C2211yescharacteristic
49#808C2211yescharacteristic
50#808C2211yescharacteristic
51#808C2211yescharacteristic
52#808C2211yescharacteristic
53#808C2211yescharacteristic
54#807C2211yescharacteristic
55#807C2211yescharacteristic
56#807C2211yescharacteristic
57#807C2211yescharacteristic
58C4⋊(C3⋊C8)C2211yescharacteristic
59C4×C3⋊C8C2211yescharacteristic
60#553D311yescharacteristic
61#552—31no—
62#499—31no—
63#485—31no—
64#484—31no—
65#482—31no—
66#480—31no—
67#479—31no—
68#478—31no—
69#465—31no—
70#465—31no—
71C4×SD16—31no—
72C8×D4—31no—
73#427—31no—
74C2×#106—31no—
75C2×C3×D4—21no—
76C2×C3×D4—21no—
77C2×C3×D4D411yescharacteristic
78C2×C3×D4C2311yescharacteristic
79C22×C3×C4—21no—
80C22×C3×C4—21no—
81C22×C3×C4C2311yescharacteristic
82C22×C3×C4C2311yescharacteristic
83C22×Dic3—21no—
84C2×Dic6C2311yescharacteristic
85C3×C4⋊C4—21no—
86C3×C4⋊C4—21no—
87C3×C4⋊C4—21no—
88C3×C4⋊C4D411yescharacteristic
89C3×C4⋊C4C2311yescharacteristic
90C3×C4⋊C4C2311yescharacteristic
91C3×C4⋊C4C2311yescharacteristic
92C3×C22⋊C4—21no—
93C3×C22⋊C4—21no—
94C3×C22⋊C4—21no—
95C3×C22⋊C4—21no—
96C3×C22⋊C4D411yescharacteristic
97C3×C22⋊C4D411yescharacteristic
98C3×C42—21no—
99C3×C42C2311yescharacteristic
100#217—21no—
101#217—21no—
102#217—21no—
103#214—22no—
104C4⋊Dic3—21no—
105C4⋊Dic3C2311yescharacteristic
106C4⋊Dic3C2311yescharacteristic
107C4⋊Dic3C2311yescharacteristic
108Dic3⋊C4—21no—
109Dic3⋊C4—21no—
110Dic3⋊C4—21no—
111Dic3⋊C4—21no—
112Dic3⋊C4—21no—
113C4×Dic3—21no—
114C4×Dic3—21no—
115C2×C3⋊C8—22no—
116C2×C3⋊C8—22no—
117C2×C3⋊C8C2311yescharacteristic
118C2×C3⋊C8C2311yescharacteristic
119C2×C3⋊C8C2311yescharacteristic
120C2×C3⋊C8C2311yescharacteristic
121C2×SD16—31no—
122C22×C8—31no—
123C22×C8—31no—
124#126—21no—
125#126—61no—
126#125—31no—
127#125—61no—
128#125C2×D311yescharacteristic
129#123—21no—
130#123—61no—
131C22⋊Q8—31no—
132C22⋊Q8—31no—
133#121—21no—
134#121C2×D311yescharacteristic
135#121C2×D311yescharacteristic
136C4×Q8—31no—
137C4×D4—21no—
138C4×D4C2×D311yescharacteristic
139C4×D4C2×D311yescharacteristic
140#117—31no—
141#117—61no—
142#117C2×D311yescharacteristic
143C2×C4⋊C4—31no—
144C2×C4⋊C4C2×D311yescharacteristic
145#107—31no—
146#107—31no—
147#107—31no—
148#107—31no—
149#106—31no—
150#106—31no—
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—
163C4×C8—31no—
164C23×C3—21no—
165C23×C3C2×D411yescharacteristic
166C23×C3C2×D411yescharacteristic
167C3×D4—22no—
168C3×D4—21no—
169C3×D4—21no—
170C3×D4—42no—
171C3×D4—81no—
172C2×C3×C4—21no—
173C2×C3×C4—21no—
174C2×C3×C4—21no—
175C2×C3×C4—21no—
176C2×C3×C4—21no—
177C2×C3×C4—21no—
178C2×C3×C4—21no—
179C2×C3×C4—81no—
180C2×C3×C4—81no—
181C2×C3×C4C2×D411yescharacteristic
182C2×C3×C4C2×D411yescharacteristic
183C2×C3×C4C2×D411yescharacteristic
184C2×C3×C4C2×D411yescharacteristic
185C2×C3×C4C2411yescharacteristic
186C2×Dic3—21no—
187C2×Dic3—21no—
188C2×Dic3—21no—
189C2×Dic3—21no—
190C2×Dic3—42no—
191Dic6—21no—
192Dic6—21no—
193C3⋊C8—21no—
194C3⋊C8—21no—
195C3⋊C8—21no—
196C3⋊C8#4112yes—
197C2×Q8—31no—
198C2×D4—21no—
199C2×D4—21no—
200C2×D4#6711yescharacteristic
201C2×D4C22×D311yescharacteristic
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—61no—
205C22×C4C22×D311yescharacteristic
206C22×C4C22×D311yescharacteristic
207SD16—62no—
208C2×C8—31no—
209C2×C8—31no—
210C2×C8—31no—
211C2×C8—31no—
212C2×C8—62no—
213C2×C8—62no—
214C4⋊C4—21no—
215C4⋊C4—21no—
216C4⋊C4—21no—
217C4⋊C4—31no—
218C4⋊C4—31no—
219C4⋊C4—31no—
220C4⋊C4—61no—
221C4⋊C4—61no—
222C4⋊C4—61no—
223C4⋊C4—61no—
224C4⋊C4—61no—
225C4⋊C4—61no—
226C4⋊C4#6711yescharacteristic
227C4⋊C4C22×D311yescharacteristic
228C4⋊C4C22×D311yescharacteristic
229C4⋊C4C22×D311yescharacteristic
230C22⋊C4—21no—
231C22⋊C4—21no—
232C22⋊C4—21no—
233C22⋊C4—21no—
234C22⋊C4—61no—
235C22⋊C4—61no—
236C22⋊C4—61no—
237C22⋊C4#6711yescharacteristic
238C22⋊C4#6711yescharacteristic
239C42—21no—
240C42—61no—
241C42—61no—
242C42C22×D311yescharacteristic
243C22×C3—21no—
244C22×C3—21no—
245C22×C3—21no—
246C22×C3—21no—
247C22×C3—21no—
248C22×C3—41no—
249C22×C3—41no—
250C22×C3—41no—
251C22×C3#13512yes—
252C22×C3C22×D411yescharacteristic
253C3×C4—21no—
254C3×C4—21no—
255C3×C4—21no—
256C3×C4—21no—
257C3×C4—41no—
258C3×C4—41no—
259C3×C4—41no—
260C3×C4C2×#4111yescharacteristic
261C3×C42−1+411yescharacteristic
262Dic3—41no—
263Dic3—41no—
264Dic3—41no—
265Dic3—41no—
266C23—21no—
267C23C2×#6711yescharacteristic
268C23C2×#6711yescharacteristic
269Q8—61no—
270Q8—61no—
271D4—22no—
272D4—21no—
273D4—21no—
274D4—42no—
275D4—81no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—61no—
284C2×C4—61no—
285C2×C4—61no—
286C2×C4—61no—
287C2×C4—81no—
288C2×C4—81no—
289C2×C4—122no—
290C2×C4C2×#6711yescharacteristic
291C2×C4C2×#6711yescharacteristic
292C2×C4C2×#6711yescharacteristic
293C2×C4C2×#6711yescharacteristic
294C2×C4C23×D311yescharacteristic
295C8—32no—
296C8—61no—
297C8—61no—
298C8—61no—
299C2×C3—22no—
300C2×C3—41no—
301C2×C3—81no—
302C2×C3#54711yescharacteristic
303C2×C3C2×#13511yescharacteristic
304C2×C3#57711yescharacteristic
305C22—21no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—41no—
311C22—41no—
312C22—41no—
313C22#95012yes—
314C22C22×#6711yescharacteristic
315C4—21no—
316C4—21no—
317C4—21no—
318C4—21no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—121no—
323C4—121no—
324C4—121no—
325C4—121no—
326C4D3×#4111yescharacteristic
327C4#101011yescharacteristic
328C3#333711yescharacteristic, complemented, Sylow
329C2—22no—
330C2—41no—
331C2—81no—
332C2C2×#95011yescharacteristic
333C2#582411yescharacteristic
334C2#583611yescharacteristic
subgroupG/H
centerC22C22×#67
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
Fitting, prime radicalC3×#553C2
socleC22×C3C22×D4
hypercenter#553D3
hypocenterC3#3337
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
2. #5541C2semidirect
3. #5065C2semidirect
4. #5063C2semidirect
5. #5041C2semidirect
6. #5041C2semidirect
7. #5035C2semidirect
8. #5033C2semidirect
9. C4×#214C2semidirect
10. D4×C3⋊C8C2semidirect
11. #5009C2semidirect
12. #4998C2semidirect
13. #4996C2semidirect
14. #4970C2semidirect
15. C2×#808C2semidirect
328. C3#3337semidirect

Maximal subgroups

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

subgroupindex
C3×#5532
#55412
#50652
#50632
#50412
#50352
#50332
C4×#2142
D4×C3⋊C82
#50092
#49982
#49962
#49702
C2×#8082
#33373