Finite Group Databasebeta

← #83645

Subgroups — #83645

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
1C3×#554C211yesmaximal, characteristic, complemented
2#5584C211yesmaximal, characteristic, complemented
3#5094C211yesmaximal, characteristic, complemented
4#5089C211yesmaximal, characteristic, complemented
5#5069C211yesmaximal, characteristic, complemented
6#5068C211yesmaximal, characteristic, complemented
7#5066C211yesmaximal, characteristic, complemented
8#5063C211yesmaximal, characteristic, complemented
9#5024C211yesmaximal, characteristic, complemented
10#5019C211yesmaximal, characteristic, complemented
11#5018C211yesmaximal, characteristic, complemented
12C4×#214C211yesmaximal, characteristic, complemented
13#5016C211yesmaximal, characteristic
14#5016C211yesmaximal, characteristic
15#5014C211yesmaximal, characteristic
16#3376—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#946—21no—
29C2×#214C2211yescharacteristic
30C2×#214C2211yescharacteristic
31C2×#213C2211yescharacteristic
32#898—21no—
33#898—21no—
34#892—21no—
35#875C2211yescharacteristic
36#875C2211yescharacteristic
37C4×D12C2211yescharacteristic
38#869C2211yescharacteristic
39C4×Dic6C2211yescharacteristic
40C4×Dic6C2211yescharacteristic
41#832C2211yescharacteristic
42#810C2211yescharacteristic
43#810C2211yescharacteristic
44#810C2211yescharacteristic
45#810C2211yescharacteristic
46#810C2211yescharacteristic
47#810C2211yescharacteristic
48#809C2211yescharacteristic
49#809C2211yescharacteristic
50#809C2211yescharacteristic
51#808C2211yescharacteristic
52#808C2211yescharacteristic
53#807C2211yescharacteristic
54C4⋊(C3⋊C8)C2211yescharacteristic
55C4⋊(C3⋊C8)C2211yescharacteristic
56C4⋊(C3⋊C8)C2211yescharacteristic
57#803C2211yescharacteristic
58#803C2211yescharacteristic
59C4×C3⋊C8C2211yescharacteristic
60#556—31no—
61#554D311yescharacteristic, complemented
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#442—31no—
73#440—31no—
74C4×SD16—31no—
75C2×C3×Q8—21no—
76C2×C3×Q8D411yescharacteristic
77C2×C3×D4C2311yescharacteristic
78C22×C3×C4—21no—
79C22×C3×C4—21no—
80C22×C3×C4—21no—
81C2×D12C2311yescharacteristic
82C2×C4×D3—21no—
83C2×Dic6C2311yescharacteristic
84C2×Dic6C2311yescharacteristic
85C3×C4⋊C4—21no—
86C3×C4⋊C4—21no—
87C3×C4⋊C4—21no—
88C3×C4⋊C4—21no—
89C3×C4⋊C4—21no—
90C3×C4⋊C4D411yescharacteristic
91C3×C4⋊C4D411yescharacteristic
92C3×C4⋊C4D411yescharacteristic
93C3×C4⋊C4C2311yescharacteristic
94C3×C4⋊C4C2311yescharacteristic
95C3×C4⋊C4C2311yescharacteristic
96C3×C22⋊C4—21no—
97C3×C22⋊C4—21no—
98C3×C22⋊C4—21no—
99C3×C42C2311yescharacteristic
100C3×C42C2311yescharacteristic
101C3×C42C2311yescharacteristic
102#214—22no—
103#214—22no—
104#213—22no—
105(C2×D3)⋊C4—21no—
106(C2×D3)⋊C4—21no—
107(C2×D3)⋊C4—21no—
108(C2×D3)⋊C4—21no—
109(C2×D3)⋊C4—21no—
110C4⋊Dic3—21no—
111C4⋊Dic3—21no—
112C4⋊Dic3C2311yescharacteristic
113Dic3⋊C4—21no—
114Dic3⋊C4—21no—
115C4×Dic3—21no—
116C4×Dic3—21no—
117C2×C3⋊C8C2311yescharacteristic
118C2×C3⋊C8C2311yescharacteristic
119C2×C3⋊C8C2311yescharacteristic
120C2×C3⋊C8C2311yescharacteristic
121C2×SD16—31no—
122C2×SD16—31no—
123C2×D8—31no—
124C4⋊Q8—31no—
125C4⋊Q8C2×D311yescharacteristic
126#126—61no—
127#126—61no—
128#125C2×D311yescharacteristic
129#125C2×D311yescharacteristic
130#124—31no—
131#124—31no—
132C22⋊Q8—21no—
133C22⋊Q8—21no—
134C22⋊Q8—21no—
135C22⋊Q8—61no—
136C4×Q8—31no—
137C4×Q8—31no—
138C4×Q8C2×D311yescharacteristic
139C4×D4—31no—
140C4×D4C2×D311yescharacteristic
141C4×D4C2×D311yescharacteristic
142C4×D4C2×D311yescharacteristic
143#117—61no—
144C2×C4⋊C4—21no—
145#107—31no—
146#106—31no—
147#106—31no—
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#102—31no—
160#102—31no—
161#97—31no—
162#97—31no—
163C4×C8—31no—
164C23×C3—21no—
165C22×D3—21no—
166C3×Q8—41no—
167C3×Q8—81no—
168C3×D4—21no—
169C3×D4#4112yes—
170C2×C3×C4—21no—
171C2×C3×C4—21no—
172C2×C3×C4—21no—
173C2×C3×C4—42no—
174C2×C3×C4—81no—
175C2×C3×C4—81no—
176C2×C3×C4C2×D411yescharacteristic
177C2×C3×C4C2×D411yescharacteristic
178C2×C3×C4C2×D411yescharacteristic
179C2×C3×C4C2×D411yescharacteristic
180C2×C3×C4C2×D411yescharacteristic
181C2×C3×C4C2×D411yescharacteristic
182C2×C3×C4C2411yescharacteristic
183C2×Dic3—21no—
184C2×Dic3—21no—
185C2×Dic3—21no—
186D12—21no—
187D12—21no—
188C4×D3—42no—
189Dic6—21no—
190Dic6—21no—
191Dic6—21no—
192Dic6—21no—
193C3⋊C8—21no—
194C3⋊C8—21no—
195C3⋊C8—21no—
196C3⋊C8—21no—
197C2×Q8—21no—
198C2×Q8—31no—
199C2×Q8—31no—
200C2×Q8#6711yescharacteristic
201C2×D4—31no—
202C2×D4C22×D311yescharacteristic
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—61no—
207SD16—62no—
208SD16—62no—
209D8—62no—
210C2×C8—31no—
211C2×C8—31no—
212C2×C8—31no—
213C2×C8—31no—
214C4⋊C4—21no—
215C4⋊C4—21no—
216C4⋊C4—21no—
217C4⋊C4—21no—
218C4⋊C4—21no—
219C4⋊C4—31no—
220C4⋊C4—61no—
221C4⋊C4—61no—
222C4⋊C4—61no—
223C4⋊C4—61no—
224C4⋊C4#6711yescharacteristic
225C4⋊C4#6711yescharacteristic
226C4⋊C4#6711yescharacteristic
227C4⋊C4C22×D311yescharacteristic
228C4⋊C4C22×D311yescharacteristic
229C4⋊C4C22×D311yescharacteristic
230C22⋊C4—21no—
231C22⋊C4—21no—
232C22⋊C4—21no—
233C22⋊C4—61no—
234C22⋊C4—61no—
235C22⋊C4—61no—
236C22⋊C4—61no—
237C22⋊C4—61no—
238C42—61no—
239C42—61no—
240C42C22×D311yescharacteristic
241C42C22×D311yescharacteristic
242C42C22×D311yescharacteristic
243C22×C3—22no—
244C22×C3—41no—
245C22×C3—41no—
246C22×C3C22×D411yescharacteristic
247C2×D3—41no—
248C2×D3—41no—
249C2×D3—41no—
250C3×C4—21no—
251C3×C4—21no—
252C3×C4—21no—
253C3×C4—21no—
254C3×C4—21no—
255C3×C4—21no—
256C3×C4—41no—
257C3×C4—41no—
258C3×C4—41no—
259C3×C4C2×#4111yescharacteristic
260C3×C42−1+411yescharacteristic
261Dic3—41no—
262Dic3—41no—
263Dic3—41no—
264C23—21no—
265C23—61no—
266Q8—41no—
267Q8—61no—
268Q8—61no—
269Q8—61no—
270Q8—61no—
271Q8—81no—
272D4—21no—
273D4—61no—
274D4—61no—
275D4#23912yes—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—42no—
280C2×C4—61no—
281C2×C4—61no—
282C2×C4—61no—
283C2×C4—81no—
284C2×C4—81no—
285C2×C4—122no—
286C2×C4C2×#6711yescharacteristic
287C2×C4C2×#6711yescharacteristic
288C2×C4C2×#6711yescharacteristic
289C2×C4C2×#6711yescharacteristic
290C2×C4C2×#6711yescharacteristic
291C2×C4C2×#6711yescharacteristic
292C2×C4C23×D311yescharacteristic
293C8—61no—
294C8—61no—
295C8—61no—
296C8—61no—
297C2×C3—42no—
298C2×C3#54811yescharacteristic
299C2×C3#57511yescharacteristic
300C2×C3#57711yescharacteristic
301D3—81no—
302C22—22no—
303C22—41no—
304C22—41no—
305C22—121no—
306C22—121no—
307C22—121no—
308C22C22×#6711yescharacteristic
309C4—21no—
310C4—21no—
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—41no—
316C4—41no—
317C4—41no—
318C4—121no—
319C4—121no—
320C4—121no—
321C4C2×#23911yescharacteristic
322C4#100711yescharacteristic
323C3#337611yescharacteristic, complemented, Sylow
324C2—42no—
325C2—241no—
326C2#581711yescharacteristic
327C2#582211yescharacteristic
328C2#583611yescharacteristic
subgroupG/H
centerC22C22×#67
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#554C2
socleC22×C3C22×D4
prime radicalC2×#213C22
hypercenter#554D3
hypocenterC3#3376
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. #5584C2semidirect
3. #5094C2semidirect
4. #5089C2semidirect
5. #5069C2semidirect
6. #5068C2semidirect
7. #5066C2semidirect
8. #5063C2semidirect
9. #5024C2semidirect
10. #5019C2semidirect
11. #5018C2semidirect
12. C4×#214C2semidirect
61. #554D3semidirect
323. C3#3376semidirect

Maximal subgroups

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

subgroupindex
C3×#5542
#55842
#50942
#50892
#50692
#50682
#50662
#50632
#50242
#50192
#50182
C4×#2142
#50162
#50142
#33763