Finite Group Databasebeta

← #83607

Subgroups — #83607

Order 384.

366 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#553C211yesmaximal, characteristic, complemented
2#5565C211yesmaximal, characteristic, complemented
3#5066C211yesmaximal, characteristic, complemented
4#5065C211yesmaximal, characteristic, complemented
5#5038C211yesmaximal, characteristic, complemented
6#5038C211yesmaximal, characteristic, complemented
7#5035C211yesmaximal, characteristic, complemented
8#5034C211yesmaximal, characteristic, complemented
9C4×#213C211yesmaximal, characteristic, complemented
10D4×C3⋊C8C211yesmaximal, characteristic, complemented
11#5009C211yesmaximal, characteristic, complemented
12#5003C211yesmaximal, characteristic, complemented
13#4998C211yesmaximal, characteristic, complemented
14#4968C211yesmaximal, characteristic, complemented
15C2×#807C211yesmaximal, characteristic, complemented
16#3339—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#939—21no—
29C2×#213C2211yescharacteristic
30#930C2211yescharacteristic
31#930C2211yescharacteristic
32#926C2211yescharacteristic
33C2×C4⋊Dic3C2211yescharacteristic
34C22×C3⋊C8C2211yescharacteristic
35C22×C3⋊C8C2211yescharacteristic
36#898—21no—
37#883—21no—
38#67⋊C4—21no—
39C4×D12C2211yescharacteristic
40#870C2211yescharacteristic
41#832C2211yescharacteristic
42#832C2211yescharacteristic
43#832C2211yescharacteristic
44#830C2211yescharacteristic
45#830C2211yescharacteristic
46#809C2211yescharacteristic
47#809C2211yescharacteristic
48#809C2211yescharacteristic
49#808C2211yescharacteristic
50#808C2211yescharacteristic
51#808C2211yescharacteristic
52#808C2211yescharacteristic
53#807C2211yescharacteristic
54#807C2211yescharacteristic
55#807C2211yescharacteristic
56#807C2211yescharacteristic
57#807C2211yescharacteristic
58C4⋊(C3⋊C8)C2211yescharacteristic
59C4×C3⋊C8C2211yescharacteristic
60#553—31no—
61#553D311yescharacteristic, complemented
62#499—31no—
63#482—31no—
64#482—31no—
65#481—31no—
66#481—31no—
67#478—31no—
68#478—31no—
69#466—31no—
70#466—31no—
71C4×D8—31no—
72C8×D4—31no—
73#427—31no—
74C2×#107—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
83C2×#67—21no—
84C2×#67—21no—
85C22×Dic3—21no—
86C2×D12C2311yescharacteristic
87C2×C4×D3—21no—
88C3×C4⋊C4—21no—
89C3×C4⋊C4—21no—
90C3×C4⋊C4—21no—
91C3×C4⋊C4D411yescharacteristic
92C3×C4⋊C4C2311yescharacteristic
93C3×C4⋊C4C2311yescharacteristic
94C3×C4⋊C4C2311yescharacteristic
95C3×C22⋊C4—21no—
96C3×C22⋊C4—21no—
97C3×C22⋊C4—21no—
98C3×C22⋊C4—21no—
99C3×C22⋊C4D411yescharacteristic
100C3×C22⋊C4D411yescharacteristic
101C3×C42—21no—
102C3×C42C2311yescharacteristic
103#217—21no—
104#213—22no—
105(C2×D3)⋊C4—21no—
106(C2×D3)⋊C4—21no—
107(C2×D3)⋊C4—21no—
108C4⋊Dic3—21no—
109C4⋊Dic3C2311yescharacteristic
110C4⋊Dic3C2311yescharacteristic
111C4⋊Dic3C2311yescharacteristic
112Dic3⋊C4—21no—
113Dic3⋊C4—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×D8—31no—
122C22×C8—31no—
123C22×C8—31no—
124#126—21no—
125#126—61no—
126#125—31no—
127#125C2×D311yescharacteristic
128#123—21no—
129#123—61no—
130#121—21no—
131#121—31no—
132#121—31no—
133#121—61no—
134#121C2×D311yescharacteristic
135#121C2×D311yescharacteristic
136C4×D4—21no—
137C4×D4—31no—
138C4×D4—61no—
139C4×D4C2×D311yescharacteristic
140C4×D4C2×D311yescharacteristic
141#117—31no—
142#117C2×D311yescharacteristic
143C2×C4⋊C4—31no—
144C2×C4⋊C4C2×D311yescharacteristic
145#107—31no—
146#107—31no—
147#107—31no—
148#107—31no—
149#107—31no—
150#106—31no—
151#106—31no—
152#106—31no—
153#106—31no—
154C4⋊C8—31no—
155#102—31no—
156#102—31no—
157#102—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
167C22×D3—21no—
168C3×D4—22no—
169C3×D4—21no—
170C3×D4—21no—
171C3×D4—42no—
172C3×D4—81no—
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—21no—
180C2×C3×C4—81no—
181C2×C3×C4—81no—
182C2×C3×C4C2×D411yescharacteristic
183C2×C3×C4C2×D411yescharacteristic
184C2×C3×C4C2×D411yescharacteristic
185C2×C3×C4C2×D411yescharacteristic
186C2×C3×C4C2411yescharacteristic
187#67—42no—
188#67—81no—
189C2×Dic3—21no—
190C2×Dic3—21no—
191C2×Dic3—21no—
192C2×Dic3—81no—
193D12—21no—
194D12—21no—
195C4×D3—81no—
196C3⋊C8—21no—
197C3⋊C8—21no—
198C3⋊C8—21no—
199C3⋊C8#4112yes—
200C2×D4—21no—
201C2×D4—21no—
202C2×D4—31no—
203C2×D4—61no—
204C2×D4—61no—
205C2×D4#6711yescharacteristic
206C2×D4C22×D311yescharacteristic
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—61no—
210C22×C4—61no—
211C22×C4C22×D311yescharacteristic
212C22×C4C22×D311yescharacteristic
213D8—62no—
214C2×C8—31no—
215C2×C8—31no—
216C2×C8—31no—
217C2×C8—31no—
218C2×C8—62no—
219C2×C8—62no—
220C4⋊C4—21no—
221C4⋊C4—21no—
222C4⋊C4—21no—
223C4⋊C4—31no—
224C4⋊C4—31no—
225C4⋊C4—31no—
226C4⋊C4—61no—
227C4⋊C4—61no—
228C4⋊C4—61no—
229C4⋊C4#6711yescharacteristic
230C4⋊C4C22×D311yescharacteristic
231C4⋊C4C22×D311yescharacteristic
232C4⋊C4C22×D311yescharacteristic
233C22⋊C4—21no—
234C22⋊C4—21no—
235C22⋊C4—21no—
236C22⋊C4—21no—
237C22⋊C4—61no—
238C22⋊C4—61no—
239C22⋊C4—61no—
240C22⋊C4—61no—
241C22⋊C4#6711yescharacteristic
242C22⋊C4#6711yescharacteristic
243C42—21no—
244C42—61no—
245C42C22×D311yescharacteristic
246C22×C3—21no—
247C22×C3—21no—
248C22×C3—21no—
249C22×C3—21no—
250C22×C3—21no—
251C22×C3—41no—
252C22×C3—41no—
253C22×C3—41no—
254C22×C3#13512yes—
255C22×C3C22×D411yescharacteristic
256C2×D3—41no—
257C2×D3—41no—
258C2×D3—41no—
259C3×C4—21no—
260C3×C4—21no—
261C3×C4—21no—
262C3×C4—21no—
263C3×C4—41no—
264C3×C4—41no—
265C3×C4—41no—
266C3×C4C2×#4111yescharacteristic
267C3×C42−1+411yescharacteristic
268Dic3—41no—
269Dic3—41no—
270Dic3—41no—
271C23—21no—
272C23—61no—
273C23C2×#6711yescharacteristic
274C23C2×#6711yescharacteristic
275D4—22no—
276D4—21no—
277D4—21no—
278D4—42no—
279D4—61no—
280D4—61no—
281D4—81no—
282D4—122no—
283D4—241no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—61no—
292C2×C4—61no—
293C2×C4—61no—
294C2×C4—81no—
295C2×C4—81no—
296C2×C4—241no—
297C2×C4—241no—
298C2×C4C2×#6711yescharacteristic
299C2×C4C2×#6711yescharacteristic
300C2×C4C2×#6711yescharacteristic
301C2×C4C2×#6711yescharacteristic
302C2×C4C23×D311yescharacteristic
303C8—32no—
304C8—61no—
305C8—61no—
306C8—61no—
307C2×C3—22no—
308C2×C3—41no—
309C2×C3—81no—
310C2×C3#54711yescharacteristic
311C2×C3C2×#13511yescharacteristic
312C2×C3#57611yescharacteristic
313D3—81no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—121no—
323C22—121no—
324C22—121no—
325C22#95012yes—
326C22C22×#6711yescharacteristic
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—121no—
335C4—121no—
336C4—121no—
337C4D3×#4111yescharacteristic
338C4#101011yescharacteristic
339C3#333911yescharacteristic, complemented, Sylow
340C2—22no—
341C2—41no—
342C2—81no—
343C2—241no—
344C2C2×#95011yescharacteristic
345C2#582411yescharacteristic
346C2#583511yescharacteristic
subgroupG/H
centerC22C22×#67
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#553C2
socleC22×C3C22×D4
hypercenter#553D3
hypocenterC3#3339
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
1. C3×#553C2semidirect
2. #5565C2semidirect
3. #5066C2semidirect
4. #5065C2semidirect
5. #5038C2semidirect
6. #5038C2semidirect
7. #5035C2semidirect
8. #5034C2semidirect
9. C4×#213C2semidirect
10. D4×C3⋊C8C2semidirect
11. #5009C2semidirect
12. #5003C2semidirect
13. #4998C2semidirect
14. #4968C2semidirect
15. C2×#807C2semidirect
61. #553D3semidirect
339. C3#3339semidirect

Maximal subgroups

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

subgroupindex
C3×#5532
#55652
#50662
#50652
#50382
#50352
#50342
C4×#2132
D4×C3⋊C82
#50092
#50032
#49982
#49682
C2×#8072
#33393