Finite Group Databasebeta

← #83639

Subgroups — #83639

Order 384.

358 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#554C211yesmaximal, characteristic, complemented
2#5585C211yesmaximal, characteristic, complemented
3#5089C211yesmaximal, characteristic, complemented
4#5087C211yesmaximal, characteristic, complemented
5#5068C211yesmaximal, characteristic, complemented
6#5067C211yesmaximal, characteristic, complemented
7#5066C211yesmaximal, characteristic, complemented
8#5063C211yesmaximal, characteristic, complemented
9#5024C211yesmaximal, characteristic, complemented
10#5018C211yesmaximal, characteristic, complemented
11#5016C211yesmaximal, characteristic, complemented
12#5016C211yesmaximal, characteristic, complemented
13#5015C211yesmaximal, characteristic
14#5014C211yesmaximal, characteristic, complemented
15C4×#213C211yesmaximal, characteristic, complemented
16#3370—31nomaximal, Sylow
17C3×C4⋊Q8C2211yescharacteristic
18C3×#125C2211yescharacteristic
19C3×#125C2211yescharacteristic
20C3×C22⋊Q8—21no—
21C3×C22⋊Q8—21no—
22C3×C22⋊Q8—21no—
23C3×C4×Q8C2211yescharacteristic
24C3×C4×D4C2211yescharacteristic
25C3×C4×D4C2211yescharacteristic
26C3×C4×D4C2211yescharacteristic
27C2×C3×C4⋊C4—21no—
28#947—21no—
29C2×#214C2211yescharacteristic
30C2×#213C2211yescharacteristic
31C2×#213C2211yescharacteristic
32#894—21no—
33#894—21no—
34#893—21no—
35#875C2211yescharacteristic
36#875C2211yescharacteristic
37#874C2211yescharacteristic
38C4×D12C2211yescharacteristic
39C4×D12C2211yescharacteristic
40C4×Dic6C2211yescharacteristic
41#832C2211yescharacteristic
42#810C2211yescharacteristic
43#810C2211yescharacteristic
44#810C2211yescharacteristic
45#809C2211yescharacteristic
46#809C2211yescharacteristic
47#809C2211yescharacteristic
48#809C2211yescharacteristic
49#809C2211yescharacteristic
50#809C2211yescharacteristic
51#808C2211yescharacteristic
52#807C2211yescharacteristic
53#807C2211yescharacteristic
54C4⋊(C3⋊C8)C2211yescharacteristic
55C4⋊(C3⋊C8)C2211yescharacteristic
56C4⋊(C3⋊C8)C2211yescharacteristic
57#803C2211yescharacteristic
58#803C2211yescharacteristic
59C4×C3⋊C8C2211yescharacteristic
60#559—31no—
61#554D311yescharacteristic, complemented
62#490—31no—
63#489—31no—
64#488—31no—
65#479—31no—
66#478—31no—
67#474—31no—
68#463—31no—
69#463—31no—
70#459—31no—
71#446—31no—
72#442—31no—
73#440—31no—
74C4×D8—31no—
75C2×C3×Q8—21no—
76C2×C3×Q8D411yescharacteristic
77C2×C3×D4C2311yescharacteristic
78C22×C3×C4—21no—
79C22×C3×C4—21no—
80C22×C3×C4—21no—
81C2×D12—21no—
82C2×D12—21no—
83C2×D12C2311yescharacteristic
84C2×D12C2311yescharacteristic
85C2×C4×D3—21no—
86C2×C4×D3—21no—
87C2×Dic6C2311yescharacteristic
88C3×C4⋊C4—21no—
89C3×C4⋊C4—21no—
90C3×C4⋊C4—21no—
91C3×C4⋊C4—21no—
92C3×C4⋊C4—21no—
93C3×C4⋊C4D411yescharacteristic
94C3×C4⋊C4D411yescharacteristic
95C3×C4⋊C4D411yescharacteristic
96C3×C4⋊C4C2311yescharacteristic
97C3×C4⋊C4C2311yescharacteristic
98C3×C4⋊C4C2311yescharacteristic
99C3×C22⋊C4—21no—
100C3×C22⋊C4—21no—
101C3×C22⋊C4—21no—
102C3×C42C2311yescharacteristic
103C3×C42C2311yescharacteristic
104C3×C42C2311yescharacteristic
105#214—22no—
106#213—22no—
107#213—22no—
108(C2×D3)⋊C4—21no—
109(C2×D3)⋊C4—21no—
110(C2×D3)⋊C4—21no—
111(C2×D3)⋊C4—21no—
112(C2×D3)⋊C4—21no—
113(C2×D3)⋊C4—21no—
114C4⋊Dic3C2311yescharacteristic
115Dic3⋊C4—21no—
116C4×Dic3—21no—
117C2×C3⋊C8C2311yescharacteristic
118C2×C3⋊C8C2311yescharacteristic
119C2×C3⋊C8C2311yescharacteristic
120C2×C3⋊C8C2311yescharacteristic
121C2×SD16—31no—
122C2×D8—31no—
123C2×D8—31no—
124C4⋊Q8C2×D311yescharacteristic
125#127—31no—
126#125C2×D311yescharacteristic
127#125C2×D311yescharacteristic
128#124—31no—
129#124—31no—
130#124—61no—
131#123—61no—
132#123—61no—
133C22⋊Q8—21no—
134C22⋊Q8—21no—
135C22⋊Q8—21no—
136C4×Q8—31no—
137C4×Q8C2×D311yescharacteristic
138C4×D4—31no—
139C4×D4—31no—
140C4×D4—61no—
141C4×D4C2×D311yescharacteristic
142C4×D4C2×D311yescharacteristic
143C4×D4C2×D311yescharacteristic
144C2×C4⋊C4—21no—
145#107—31no—
146#107—31no—
147#106—31no—
148C4⋊C8—31no—
149C4⋊C8—31no—
150C4⋊C8—31no—
151#103—31no—
152#103—31no—
153#103—31no—
154#102—31no—
155#102—31no—
156#102—31no—
157#102—31no—
158#102—31no—
159#102—31no—
160#102—31no—
161#97—31no—
162#97—31no—
163C4×C8—31no—
164C23×C3—21no—
165C22×D3—21no—
166C22×D3—21no—
167C3×Q8—41no—
168C3×Q8—81no—
169C3×D4—21no—
170C3×D4#4112yes—
171C2×C3×C4—21no—
172C2×C3×C4—21no—
173C2×C3×C4—21no—
174C2×C3×C4—42no—
175C2×C3×C4—81no—
176C2×C3×C4—81no—
177C2×C3×C4C2×D411yescharacteristic
178C2×C3×C4C2×D411yescharacteristic
179C2×C3×C4C2×D411yescharacteristic
180C2×C3×C4C2×D411yescharacteristic
181C2×C3×C4C2×D411yescharacteristic
182C2×C3×C4C2×D411yescharacteristic
183C2×C3×C4C2411yescharacteristic
184C2×Dic3—21no—
185C2×Dic3—21no—
186D12—21no—
187D12—21no—
188D12—21no—
189D12—21no—
190D12—42no—
191D12—81no—
192C4×D3—81no—
193C4×D3—81no—
194Dic6—21no—
195Dic6—21no—
196C3⋊C8—21no—
197C3⋊C8—21no—
198C3⋊C8—21no—
199C3⋊C8—21no—
200C2×Q8—21no—
201C2×Q8—31no—
202C2×Q8#6711yescharacteristic
203C2×D4—31no—
204C2×D4—31no—
205C2×D4—61no—
206C2×D4—61no—
207C2×D4C22×D311yescharacteristic
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—61no—
212C22×C4—61no—
213SD16—62no—
214D8—62no—
215D8—62no—
216C2×C8—31no—
217C2×C8—31no—
218C2×C8—31no—
219C2×C8—31no—
220C4⋊C4—21no—
221C4⋊C4—21no—
222C4⋊C4—21no—
223C4⋊C4—21no—
224C4⋊C4—21no—
225C4⋊C4—31no—
226C4⋊C4—61no—
227C4⋊C4#6711yescharacteristic
228C4⋊C4#6711yescharacteristic
229C4⋊C4#6711yescharacteristic
230C4⋊C4C22×D311yescharacteristic
231C4⋊C4C22×D311yescharacteristic
232C4⋊C4C22×D311yescharacteristic
233C22⋊C4—21no—
234C22⋊C4—21no—
235C22⋊C4—21no—
236C22⋊C4—61no—
237C22⋊C4—61no—
238C22⋊C4—61no—
239C22⋊C4—61no—
240C22⋊C4—61no—
241C22⋊C4—61no—
242C42—61no—
243C42C22×D311yescharacteristic
244C42C22×D311yescharacteristic
245C42C22×D311yescharacteristic
246C22×C3—22no—
247C22×C3—41no—
248C22×C3—41no—
249C22×C3C22×D411yescharacteristic
250C2×D3—41no—
251C2×D3—41no—
252C2×D3—41no—
253C2×D3—41no—
254C2×D3—41no—
255C2×D3—41no—
256C3×C4—21no—
257C3×C4—21no—
258C3×C4—21no—
259C3×C4—21no—
260C3×C4—21no—
261C3×C4—21no—
262C3×C4—41no—
263C3×C4—41no—
264C3×C4—41no—
265C3×C4C2×#4111yescharacteristic
266C3×C42−1+411yescharacteristic
267Dic3—41no—
268Dic3—41no—
269C23—21no—
270C23—61no—
271C23—61no—
272Q8—41no—
273Q8—61no—
274Q8—61no—
275Q8—81no—
276D4—21no—
277D4—61no—
278D4—61no—
279D4—61no—
280D4—61no—
281D4—122no—
282D4—241no—
283D4#23912yes—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—42no—
288C2×C4—61no—
289C2×C4—61no—
290C2×C4—81no—
291C2×C4—81no—
292C2×C4—241no—
293C2×C4—241no—
294C2×C4C2×#6711yescharacteristic
295C2×C4C2×#6711yescharacteristic
296C2×C4C2×#6711yescharacteristic
297C2×C4C2×#6711yescharacteristic
298C2×C4C2×#6711yescharacteristic
299C2×C4C2×#6711yescharacteristic
300C2×C4C23×D311yescharacteristic
301C8—61no—
302C8—61no—
303C8—61no—
304C8—61no—
305C2×C3—42no—
306C2×C3#54811yescharacteristic
307C2×C3#57511yescharacteristic
308C2×C3#57611yescharacteristic
309D3—81no—
310D3—81no—
311C22—22no—
312C22—41no—
313C22—41no—
314C22—121no—
315C22—121no—
316C22—121no—
317C22—121no—
318C22—121no—
319C22—121no—
320C22C22×#6711yescharacteristic
321C4—21no—
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—21no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—121no—
331C4—121no—
332C4C2×#23911yescharacteristic
333C4#100711yescharacteristic
334C3#337011yescharacteristic, complemented, Sylow
335C2—42no—
336C2—241no—
337C2—241no—
338C2#581711yescharacteristic
339C2#582211yescharacteristic
340C2#583511yescharacteristic
subgroupG/H
centerC22C22×#67
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#554C2
socleC22×C3C22×D4
prime radical#5015C2
hypercenter#554D3
hypocenterC3#3370
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #554

Complements

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

NH ≅ G/Ntype
1. C3×#554C2semidirect
2. #5585C2semidirect
3. #5089C2semidirect
4. #5087C2semidirect
5. #5068C2semidirect
6. #5067C2semidirect
7. #5066C2semidirect
8. #5063C2semidirect
9. #5024C2semidirect
10. #5018C2semidirect
11. #5016C2semidirect
12. #5016C2semidirect
14. #5014C2semidirect
15. C4×#213C2semidirect
61. #554D3semidirect
334. C3#3370semidirect

Maximal subgroups

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

subgroupindex
C3×#5542
#55852
#50892
#50872
#50682
#50672
#50662
#50632
#50242
#50182
#50162
#50152
#50142
C4×#2132
#33703