Finite Group Databasebeta

← #79954

Subgroups — #79954

Order 384.

368 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#5585C211yesmaximal, characteristic, complemented
2#5584C211yesmaximal, characteristic, complemented
3C3×#446C211yesmaximal, characteristic, complemented
4#4848C211yesmaximal, characteristic, complemented
5#4845C211yesmaximal, characteristic, complemented
6#4845C211yesmaximal, characteristic, complemented
7#4844C211yesmaximal, characteristic, complemented
8#4844C211yesmaximal, characteristic, complemented
9#4841C211yesmaximal, characteristic, complemented
10#4716C211yesmaximal, characteristic, complemented
11#4715C211yesmaximal, characteristic, complemented
12#4712C211yesmaximal, characteristic
13#4711C211yesmaximal, characteristic, complemented
14#4696C211yesmaximal, characteristic, complemented
15C4×#204C211yesmaximal, characteristic, complemented
16#3401—31nomaximal, Sylow
17C3×C4×Q8C2211yescharacteristic
18#947—21no—
19#946—21no—
20C2×Dic12C2211yescharacteristic
21C2×Dic12C2211yescharacteristic
22C2×D24C2211yescharacteristic
23C2×D24C2211yescharacteristic
24C2×#204C2211yescharacteristic
25C2×#204C2211yescharacteristic
26C2×#204C2211yescharacteristic
27C2×#204C2211yescharacteristic
28C2×#204C2211yescharacteristic
29#898—21no—
30#898—21no—
31#894—21no—
32#894—21no—
33#893—21no—
34#892—21no—
35#875C2211yescharacteristic
36#875C2211yescharacteristic
37#875C2211yescharacteristic
38#875C2211yescharacteristic
39#874C2211yescharacteristic
40C4×D12C2211yescharacteristic
41C4×D12C2211yescharacteristic
42C4×D12C2211yescharacteristic
43#869C2211yescharacteristic
44C4×Dic6C2211yescharacteristic
45C4×Dic6C2211yescharacteristic
46C4×Dic6C2211yescharacteristic
47C3×C4⋊C8C2211yescharacteristic
48C3×C4⋊C8C2211yescharacteristic
49C3×C4⋊C8C2211yescharacteristic
50C3×#97C2211yescharacteristic
51C3×#97C2211yescharacteristic
52C3×C4×C8C2211yescharacteristic
53#821C2211yescharacteristic
54#821C2211yescharacteristic
55#821C2211yescharacteristic
56#817C2211yescharacteristic
57#816C2211yescharacteristic
58#816C2211yescharacteristic
59#816C2211yescharacteristic
60#559—31no—
61#556—31no—
62#497—31no—
63#496—31no—
64#495—31no—
65#464—31no—
66#464—31no—
67#463—31no—
68#463—31no—
69#461—31no—
70#460—31no—
71#446D311yescharacteristic, complemented
72#442—31no—
73#441—31no—
74C4×SD16—31no—
75C2×C3×Q8D411yescharacteristic
76C2×D12—21no—
77C2×D12—21no—
78C2×D12C2311yescharacteristic
79C2×D12C2311yescharacteristic
80C2×D12C2311yescharacteristic
81C2×C4×D3—21no—
82C2×C4×D3—21no—
83C2×C4×D3—21no—
84C2×Dic6C2311yescharacteristic
85C2×Dic6C2311yescharacteristic
86C2×Dic6C2311yescharacteristic
87C2×C3×C8C2311yescharacteristic
88C2×C3×C8C2311yescharacteristic
89C2×C3×C8C2311yescharacteristic
90C2×C3×C8C2311yescharacteristic
91C3×C4⋊C4D411yescharacteristic
92C3×C4⋊C4D411yescharacteristic
93C3×C4⋊C4D411yescharacteristic
94C3×C42C2311yescharacteristic
95C3×C42C2311yescharacteristic
96C3×C42C2311yescharacteristic
97(C2×D3)⋊C4—21no—
98(C2×D3)⋊C4—21no—
99(C2×D3)⋊C4—21no—
100(C2×D3)⋊C4—21no—
101(C2×D3)⋊C4—21no—
102(C2×D3)⋊C4—21no—
103(C2×D3)⋊C4—21no—
104(C2×D3)⋊C4—21no—
105(C2×D3)⋊C4—21no—
106(C2×D3)⋊C4—21no—
107(C2×D3)⋊C4—21no—
108C4⋊Dic3—21no—
109C4⋊Dic3—21no—
110C4⋊Dic3C2311yescharacteristic
111C4⋊Dic3C2311yescharacteristic
112Dic3⋊C4—21no—
113Dic3⋊C4—21no—
114Dic3⋊C4—21no—
115C4×Dic3—21no—
116C4×Dic3—21no—
117C4×Dic3—21no—
118Dic12—22no—
119Dic12—41no—
120D24—22no—
121D24—41no—
122#204—22no—
123#204—41no—
124#204—41no—
125#204—41no—
126#204—41no—
127C2×Q16—31no—
128C2×Q16—31no—
129C2×SD16—31no—
130C2×SD16—31no—
131C2×SD16—31no—
132C2×SD16—31no—
133C2×SD16—31no—
134C2×D8—31no—
135C2×D8—31no—
136C4⋊Q8—31no—
137#127—31no—
138#126—61no—
139#126—61no—
140#124—31no—
141#124—31no—
142#124—31no—
143#124—31no—
144#124—61no—
145#123—61no—
146#123—61no—
147C22⋊Q8—61no—
148C4×Q8—31no—
149C4×Q8—31no—
150C4×Q8—31no—
151C4×Q8C2×D311yescharacteristic
152C4×D4—31no—
153C4×D4—31no—
154C4×D4—31no—
155C4×D4—61no—
156#117—61no—
157#106—31no—
158C4⋊C8C2×D311yescharacteristic
159C4⋊C8C2×D311yescharacteristic
160C4⋊C8C2×D311yescharacteristic
161#103—31no—
162#103—31no—
163#103—31no—
164#102—31no—
165#102—31no—
166#102—31no—
167#97C2×D311yescharacteristic
168#97C2×D311yescharacteristic
169C4×C8C2×D311yescharacteristic
170C22×D3—21no—
171C22×D3—21no—
172C22×D3—21no—
173C3×Q8—41no—
174C2×C3×C4C2×D411yescharacteristic
175C2×C3×C4C2×D411yescharacteristic
176C2×C3×C4C2×D411yescharacteristic
177C2×C3×C4C2×D411yescharacteristic
178C2×C3×C4C2×D411yescharacteristic
179C2×C3×C4C2×D411yescharacteristic
180C2×C3×C4C2411yescharacteristic
181C2×Dic3—21no—
182C2×Dic3—21no—
183C2×Dic3—21no—
184C2×Dic3—21no—
185C2×Dic3—21no—
186D12—21no—
187D12—21no—
188D12—21no—
189D12—21no—
190D12—21no—
191D12—21no—
192D12—42no—
193D12—81no—
194C4×D3—42no—
195C4×D3—81no—
196C4×D3—81no—
197Dic6—21no—
198Dic6—21no—
199Dic6—21no—
200Dic6—21no—
201Dic6—21no—
202Dic6—21no—
203C3×C8—21no—
204C3×C8—21no—
205C3×C8—21no—
206C3×C8#4112yes—
207C2×Q8—31no—
208C2×Q8—31no—
209C2×Q8—31no—
210C2×Q8D1211yescharacteristic
211C2×D4—31no—
212C2×D4—31no—
213C2×D4—31no—
214C2×D4—61no—
215C2×D4—61no—
216C22×C4—61no—
217C22×C4—61no—
218C22×C4—61no—
219Q16—62no—
220Q16—121no—
221SD16—62no—
222SD16—121no—
223SD16—121no—
224SD16—121no—
225SD16—121no—
226D8—62no—
227D8—121no—
228C2×C8C22×D311yescharacteristic
229C2×C8C22×D311yescharacteristic
230C2×C8C22×D311yescharacteristic
231C2×C8C22×D311yescharacteristic
232C4⋊C4—31no—
233C4⋊C4—31no—
234C4⋊C4—61no—
235C4⋊C4—61no—
236C4⋊C4—61no—
237C4⋊C4—61no—
238C4⋊C4—61no—
239C4⋊C4D1211yescharacteristic
240C4⋊C4D1211yescharacteristic
241C4⋊C4D1211yescharacteristic
242C22⋊C4—61no—
243C22⋊C4—61no—
244C22⋊C4—61no—
245C22⋊C4—61no—
246C22⋊C4—61no—
247C22⋊C4—61no—
248C22⋊C4—61no—
249C22⋊C4—61no—
250C22⋊C4—61no—
251C22⋊C4—61no—
252C22⋊C4—61no—
253C42—61no—
254C42—61no—
255C42—61no—
256C42C22×D311yescharacteristic
257C42C22×D311yescharacteristic
258C42C22×D311yescharacteristic
259C22×C3C22×D411yescharacteristic
260C2×D3—41no—
261C2×D3—41no—
262C2×D3—41no—
263C2×D3—41no—
264C2×D3—41no—
265C2×D3—41no—
266C2×D3—41no—
267C2×D3—41no—
268C2×D3—41no—
269C3×C4—21no—
270C3×C4—21no—
271C3×C4—21no—
272C3×C4—21no—
273C3×C4—21no—
274C3×C4—21no—
275C3×C4C2×#4111yescharacteristic
276C3×C4H(5,𝔽2)11yescharacteristic
277Dic3—41no—
278Dic3—41no—
279Dic3—41no—
280Dic3—41no—
281Dic3—41no—
282C23—61no—
283C23—61no—
284C23—61no—
285Q8—41no—
286Q8—61no—
287Q8—61no—
288Q8—61no—
289Q8—61no—
290Q8—61no—
291Q8—61no—
292D4—61no—
293D4—61no—
294D4—61no—
295D4—61no—
296D4—61no—
297D4—61no—
298D4—122no—
299D4—241no—
300C2×C4—61no—
301C2×C4—61no—
302C2×C4—61no—
303C2×C4—61no—
304C2×C4—61no—
305C2×C4—122no—
306C2×C4—241no—
307C2×C4—241no—
308C2×C4C2×D1211yescharacteristic
309C2×C4C2×D1211yescharacteristic
310C2×C4C2×D1211yescharacteristic
311C2×C4C2×D1211yescharacteristic
312C2×C4C2×D1211yescharacteristic
313C2×C4C2×D1211yescharacteristic
314C2×C4C23×D311yescharacteristic
315C8—21no—
316C8—21no—
317C8—21no—
318C8#23912yes—
319C2×C3#55011yescharacteristic
320C2×C3#57511yescharacteristic
321C2×C3#57711yescharacteristic
322D3—81no—
323D3—81no—
324D3—81no—
325C22—121no—
326C22—121no—
327C22—121no—
328C22—121no—
329C22—121no—
330C22—121no—
331C22—121no—
332C22—121no—
333C22—121no—
334C22C22×D1211yescharacteristic
335C4—21no—
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—121no—
342C4—121no—
343C4—121no—
344C4—121no—
345C4—121no—
346C4C2×#23911yescharacteristic
347C4#100911yescharacteristic
348C3#340111yescharacteristic, complemented, Sylow
349C2—241no—
350C2—241no—
351C2—241no—
352C2#557711yescharacteristic
353C2#574811yescharacteristic
354C2#575111yescharacteristic
subgroupG/H
centerC22C22×D12
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#446C2
socleC22×C3C22×D4
prime radical#4712C2
hypercenter#446D3
hypocenterC3#3401
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #446

Complements

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

NH ≅ G/Ntype
1. #5585C2semidirect
2. #5584C2semidirect
3. C3×#446C2semidirect
4. #4848C2semidirect
5. #4845C2semidirect
6. #4845C2semidirect
7. #4844C2semidirect
8. #4844C2semidirect
9. #4841C2semidirect
10. #4716C2semidirect
11. #4715C2semidirect
13. #4711C2semidirect
14. #4696C2semidirect
15. C4×#204C2semidirect
71. #446D3semidirect
348. C3#3401semidirect

Maximal subgroups

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

subgroupindex
#55852
#55842
C3×#4462
#48482
#48452
#48442
#48412
#47162
#47152
#47122
#47112
#46962
C4×#2042
#34013