Finite Group Databasebeta

← #83661

Subgroups — #83661

Order 384.

348 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×#556C211yesmaximal, characteristic, complemented
2#5565C211yesmaximal, characteristic
3#5084C211yesmaximal, characteristic, complemented
4#5081C211yesmaximal, characteristic, complemented
5#5049C211yesmaximal, characteristic, complemented
6#5048C211yesmaximal, characteristic, complemented
7#5045C211yesmaximal, characteristic, complemented
8#5043C211yesmaximal, characteristic, complemented
9#5026C211yesmaximal, characteristic, complemented
10#5022C211yesmaximal, characteristic, complemented
11#5011C211yesmaximal, characteristic, complemented
12#5003C211yesmaximal, characteristic, complemented
13#5003C211yesmaximal, characteristic, complemented
14#4998C211yesmaximal, characteristic, complemented
15#4995C211yesmaximal, characteristic, complemented
16#3350—31nomaximal, Sylow
17C3×C4⋊Q8C2211yescharacteristic
18C3×#126—21no—
19C3×#126—21no—
20C3×#124—21no—
21C3×C22⋊Q8C2211yescharacteristic
22C3×C22⋊Q8C2211yescharacteristic
23C3×C4×Q8—21no—
24C3×C4×Q8C2211yescharacteristic
25C3×C4×D4C2211yescharacteristic
26C3×#117C2211yescharacteristic
27C3×#117C2211yescharacteristic
28C2×#215C2211yescharacteristic
29#939—21no—
30#930C2211yescharacteristic
31#930C2211yescharacteristic
32#926C2211yescharacteristic
33C2×C4⋊Dic3C2211yescharacteristic
34C2×#208C2211yescharacteristic
35C22×C3⋊C8C2211yescharacteristic
36#898—21no—
37#883—21no—
38#67⋊C4—21no—
39C4×D12C2211yescharacteristic
40#870C2211yescharacteristic
41#835C2211yescharacteristic
42#835C2211yescharacteristic
43#835C2211yescharacteristic
44#830C2211yescharacteristic
45#830C2211yescharacteristic
46#809C2211yescharacteristic
47#809C2211yescharacteristic
48#809C2211yescharacteristic
49#808C2211yescharacteristic
50#808C2211yescharacteristic
51#808C2211yescharacteristic
52#808C2211yescharacteristic
53#808C2211yescharacteristic
54#807C2211yescharacteristic
55#807C2211yescharacteristic
56#807C2211yescharacteristic
57#807C2211yescharacteristic
58C4⋊(C3⋊C8)C2211yescharacteristic
59#803C2211yescharacteristic
60#556D311yescharacteristic, complemented
61#553—31no—
62#501—31no—
63#485—31no—
64#483—31no—
65#482—31no—
66#482—31no—
67#479—31no—
68#476—31no—
69#468—31no—
70#465—31no—
71#440—31no—
72#435—31no—
73#428—31no—
74#427—31no—
75C2×C3×Q8—21no—
76C2×C3×Q8C2311yescharacteristic
77C2×C3×D4D411yescharacteristic
78C22×C3×C4C2311yescharacteristic
79C22×C3×C4C2311yescharacteristic
80C2×#67—21no—
81C2×#67—21no—
82C22×Dic3—21no—
83C2×D12C2311yescharacteristic
84C2×C4×D3—21no—
85C3×C4⋊C4—21no—
86C3×C4⋊C4—21no—
87C3×C4⋊C4—21no—
88C3×C4⋊C4—21no—
89C3×C4⋊C4D411yescharacteristic
90C3×C4⋊C4C2311yescharacteristic
91C3×C4⋊C4C2311yescharacteristic
92C3×C4⋊C4C2311yescharacteristic
93C3×C22⋊C4—21no—
94C3×C22⋊C4—21no—
95C3×C22⋊C4—21no—
96C3×C22⋊C4—21no—
97C3×C22⋊C4D411yescharacteristic
98C3×C22⋊C4D411yescharacteristic
99C3×C42—21no—
100C3×C42—21no—
101C3×C42—21no—
102C3×C42C2311yescharacteristic
103#217—21no—
104#215—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—
115#208—22no—
116C2×C3⋊C8—22no—
117C2×C3⋊C8C2311yescharacteristic
118C2×C3⋊C8C2311yescharacteristic
119C2×C3⋊C8C2311yescharacteristic
120C2×C3⋊C8C2311yescharacteristic
121C2×SD16—31no—
122C2×M16—31no—
123C22×C8—31no—
124C4⋊Q8C2×D311yescharacteristic
125#126—21no—
126#126—21no—
127#126—61no—
128#125—31no—
129#124—21no—
130#123—61no—
131C22⋊Q8C2×D311yescharacteristic
132C22⋊Q8C2×D311yescharacteristic
133#121—31no—
134#121—31no—
135#121—61no—
136C4×Q8—21no—
137C4×Q8C2×D311yescharacteristic
138C4×D4—31no—
139C4×D4—61no—
140C4×D4C2×D311yescharacteristic
141#117—31no—
142#117C2×D311yescharacteristic
143#117C2×D311yescharacteristic
144C2×C4⋊C4—31no—
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—
163#97—31no—
164C23×C3C2×D411yescharacteristic
165C23×C3C2×D411yescharacteristic
166C22×D3—21no—
167C3×Q8—21no—
168C3×Q8—21no—
169C3×Q8—42no—
170C3×D4—41no—
171C2×C3×C4—21no—
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×C4C2×D411yescharacteristic
180C2×C3×C4C2×D411yescharacteristic
181C2×C3×C4C2×D411yescharacteristic
182C2×C3×C4C2×D411yescharacteristic
183C2×C3×C4C2411yescharacteristic
184#67—42no—
185#67—81no—
186C2×Dic3—21no—
187C2×Dic3—21no—
188C2×Dic3—21no—
189C2×Dic3—81no—
190D12—21no—
191D12—21no—
192C4×D3—81no—
193C3⋊C8—21no—
194C3⋊C8—21no—
195C3⋊C8—21no—
196C3⋊C8#4112yes—
197C2×Q8—21no—
198C2×Q8C22×D311yescharacteristic
199C2×D4—31no—
200C2×D4—61no—
201C2×D4—61no—
202C2×D4#6711yescharacteristic
203C22×C4—61no—
204C22×C4—61no—
205C22×C4C22×D311yescharacteristic
206C22×C4C22×D311yescharacteristic
207SD16—62no—
208M16—62no—
209C2×C8—31no—
210C2×C8—31no—
211C2×C8—31no—
212C2×C8—31no—
213C2×C8—62no—
214C4⋊C4—21no—
215C4⋊C4—21no—
216C4⋊C4—21no—
217C4⋊C4—21no—
218C4⋊C4—31no—
219C4⋊C4—31no—
220C4⋊C4—31no—
221C4⋊C4—61no—
222C4⋊C4—61no—
223C4⋊C4—61no—
224C4⋊C4#6711yescharacteristic
225C4⋊C4C22×D311yescharacteristic
226C4⋊C4C22×D311yescharacteristic
227C4⋊C4C22×D311yescharacteristic
228C22⋊C4—21no—
229C22⋊C4—21no—
230C22⋊C4—21no—
231C22⋊C4—21no—
232C22⋊C4—61no—
233C22⋊C4—61no—
234C22⋊C4—61no—
235C22⋊C4—61no—
236C22⋊C4#6711yescharacteristic
237C22⋊C4#6711yescharacteristic
238C42—21no—
239C42—21no—
240C42—21no—
241C42—61no—
242C42C22×D311yescharacteristic
243C22×C3—21no—
244C22×C3—21no—
245C22×C3—21no—
246C22×C3—21no—
247C22×C3—21no—
248C22×C3—21no—
249C22×C3C22×D411yescharacteristic
250C2×D3—41no—
251C2×D3—41no—
252C2×D3—41no—
253C3×C4—21no—
254C3×C4—21no—
255C3×C4—21no—
256C3×C4—21no—
257C3×C4—41no—
258C3×C4—41no—
259C3×C4—41no—
260C3×C4—41no—
261C3×C4C2×#4111yescharacteristic
262C3×C42−1+411yescharacteristic
263Dic3—41no—
264Dic3—41no—
265Dic3—41no—
266C23—61no—
267C23C2×#6711yescharacteristic
268C23C2×#6711yescharacteristic
269Q8—21no—
270Q8—21no—
271Q8—42no—
272D4—41no—
273D4—61no—
274D4—61no—
275D4—122no—
276D4—241no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—61no—
286C2×C4—61no—
287C2×C4—61no—
288C2×C4—241no—
289C2×C4—241no—
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—41no—
300C2×C3—41no—
301C2×C3#54711yescharacteristic
302C2×C3#57511yescharacteristic
303C2×C3#57711yescharacteristic
304D3—81no—
305C22—21no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—121no—
312C22—121no—
313C22—121no—
314C22C22×#6711yescharacteristic
315C4—21no—
316C4—21no—
317C4—21no—
318C4—21no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—121no—
324C4—121no—
325C4—121no—
326C4D3×#4111yescharacteristic
327C4#101011yescharacteristic
328C3#335011yescharacteristic, complemented, Sylow
329C2—41no—
330C2—41no—
331C2—241no—
332C2#582211yescharacteristic
333C2#582411yescharacteristic
334C2#583711yescharacteristic
subgroupG/H
centerC22C22×#67
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#556C2
socleC22×C3C22×D4
prime radical#5565C2
hypercenter#556D3
hypocenterC3#3350
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C4×D4 ◁ #556

Complements

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

NH ≅ G/Ntype
1. C3×#556C2semidirect
3. #5084C2semidirect
4. #5081C2semidirect
5. #5049C2semidirect
6. #5048C2semidirect
7. #5045C2semidirect
8. #5043C2semidirect
9. #5026C2semidirect
10. #5022C2semidirect
11. #5011C2semidirect
12. #5003C2semidirect
13. #5003C2semidirect
14. #4998C2semidirect
15. #4995C2semidirect
60. #556D3semidirect
328. C3#3350semidirect

Maximal subgroups

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

subgroupindex
C3×#5562
#55652
#50842
#50812
#50492
#50482
#50452
#50432
#50262
#50222
#50112
#50032
#49982
#49952
#33503