Finite Group Databasebeta

← #13081058

Subgroups — #13081058

Order 1408.

376 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
1#10623086C211yesmaximal, characteristic
2#10623072C211yesmaximal, characteristic, complemented
3C11×#435C211yesmaximal, characteristic, complemented
4#10622747C211yesmaximal, characteristic, complemented
5#10622734C211yesmaximal, characteristic, complemented
6#10622727C211yesmaximal, characteristic, complemented
7C2×#66882C211yesmaximal, characteristic, complemented
8#10622463C211yesmaximal, characteristic, complemented
9#10622460C211yesmaximal, characteristic, complemented
10#10622350C211yesmaximal, characteristic, complemented
11#10622349C211yesmaximal, characteristic, complemented
12#10622335C211yesmaximal, characteristic, complemented
13#10622334C211yesmaximal, characteristic, complemented
14#10622323C211yesmaximal, characteristic, complemented
15#10622315C211yesmaximal, characteristic, complemented
16C2×#4341—21no—
17C2×C11×M16C2211yescharacteristic
18C22×C8×C11C2211yescharacteristic
19C4×D4×C11C2211yescharacteristic
20#66988—21no—
21#66983C2211yescharacteristic
22#66983C2211yescharacteristic
23#66979C2211yescharacteristic
24C2×C4⋊Dic11C2211yescharacteristic
25C2×C4⋊Dic11C2211yescharacteristic
26C2×C4⋊Dic11C2211yescharacteristic
27#66977C2211yescharacteristic
28#66977C2211yescharacteristic
29C2×#4314C2211yescharacteristic
30#66950—21no—
31#66942—21no—
32#66939—21no—
33#66939—21no—
34#66932—21no—
35#66930—21no—
36C4×D44C2211yescharacteristic
37#66923C2211yescharacteristic
38#66922C2211yescharacteristic
39C4×Dic22C2211yescharacteristic
40C11×C4⋊C8C2211yescharacteristic
41C11×C22⋊C8C2211yescharacteristic
42C11×C22⋊C8C2211yescharacteristic
43C11×#97C2211yescharacteristic
44#66885C2211yescharacteristic
45#66885C2211yescharacteristic
46#66885C2211yescharacteristic
47#66882C2211yescharacteristic
48#66882C2211yescharacteristic
49#66882C2211yescharacteristic
50#66882C2211yescharacteristic
51#66882C2211yescharacteristic
52#66882C2211yescharacteristic
53#66881C2211yescharacteristic
54#66881C2211yescharacteristic
55#66881C2211yescharacteristic
56#66880C2211yescharacteristic
57#66880C2211yescharacteristic
58#66880C2211yescharacteristic
59C2×D4×C11D411yescharacteristic
60C22×C4×C11C2311yescharacteristic
61C22×C4×C11C2311yescharacteristic
62C2×C22⋊D11—21no—
63C2×C22⋊D11—21no—
64C22×Dic11—21no—
65C22×Dic11—21no—
66C22×Dic11—21no—
67#4341—44no—
68C2×D44C2311yescharacteristic
69C2×C4×D11—21no—
70C2×Dic22—21no—
71C2×Dic22C2311yescharacteristic
72C11×M16—22no—
73C2×C8×C11—22no—
74C2×C8×C11C2311yescharacteristic
75C2×C8×C11C2311yescharacteristic
76C2×C8×C11C2311yescharacteristic
77C2×C8×C11C2311yescharacteristic
78C11×C4⋊C4D411yescharacteristic
79C11×C22⋊C4D411yescharacteristic
80C11×C22⋊C4D411yescharacteristic
81C42×C11C2311yescharacteristic
82C22⋊Dic11—21no—
83C22⋊Dic11—21no—
84C22⋊Dic11—21no—
85(C2×D11)⋊C4—21no—
86(C2×D11)⋊C4—21no—
87(C2×D11)⋊C4—21no—
88C4⋊Dic11—21no—
89C4⋊Dic11—21no—
90C4⋊Dic11—21no—
91C4⋊Dic11—21no—
92C4⋊Dic11C2311yescharacteristic
93C4⋊Dic11C2311yescharacteristic
94C4⋊Dic11C2311yescharacteristic
95C4⋊Dic11C2311yescharacteristic
96C4⋊Dic11C2311yescharacteristic
97C4⋊Dic11C2311yescharacteristic
98Dic11⋊C4—21no—
99Dic11⋊C4—21no—
100Dic11⋊C4—21no—
101Dic11⋊C4—21no—
102Dic11⋊C4—21no—
103C4×Dic11—21no—
104C4×Dic11—21no—
105#4314—22no—
106#3343—111nomaximal, Sylow
107C23×C11C2×D411yescharacteristic
108C23×C11C2×D411yescharacteristic
109C22×D11—21no—
110D4×C11—22no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11C2×D411yescharacteristic
116C2×C4×C11C2×D411yescharacteristic
117C2×C4×C11C2×D411yescharacteristic
118C2×C4×C11C2×D411yescharacteristic
119C2×C4×C11C2411yescharacteristic
120C22⋊D11—42no—
121C22⋊D11—42no—
122C2×Dic11—21no—
123C2×Dic11—21no—
124C2×Dic11—21no—
125C2×Dic11—21no—
126C2×Dic11—21no—
127C2×Dic11—21no—
128C2×Dic11—21no—
129C2×Dic11—42no—
130C2×Dic11—42no—
131C2×Dic11—42no—
132D44—21no—
133D44—21no—
134C4×D11—42no—
135Dic22—21no—
136Dic22—21no—
137Dic22—42no—
138C8×C11—21no—
139C8×C11—21no—
140C8×C11—21no—
141C8×C11#4112yescomplemented
142#552—111no—
143#547—111no—
144#501—111no—
145#484—111no—
146#483—111no—
147#482—111no—
148#480—111no—
149#478—111no—
150#477—111no—
151#468—111no—
152#465—111no—
153#440—111no—
154#435D1111yescharacteristic, complemented
155#428—111no—
156C2×#107—111no—
157C22×C11—21no—
158C22×C11—21no—
159C22×C11—21no—
160C22×C11—21no—
161C22×C11—21no—
162C22×C11AGL(1,ℤ/8)12yes—
163C22×C11C22×D411yescharacteristic
164C2×D11—41no—
165C2×D11—41no—
166C2×D11—41no—
167C4×C11—21no—
168C4×C11—21no—
169C4×C11—21no—
170C4×C11—21no—
171C4×C11C2×#4111yescharacteristic
172C4×C112−1+411yescharacteristic
173Dic11—41no—
174Dic11—41no—
175Dic11—41no—
176Dic11—41no—
177Dic11—41no—
178Dic11—41no—
179Dic11—41no—
180C2×#41—221no—
181C2×SD16—111no—
182C2×M16C2×D1111yescharacteristic
183C22×C8C2×D1111yescharacteristic
184C4⋊Q8—111no—
185#126—221no—
186#125—111no—
187#125—221no—
188#123—221no—
189#123—221no—
190#123—221no—
191C22⋊Q8—111no—
192C22⋊Q8—111no—
193C22⋊Q8—221no—
194#121—111no—
195#121—111no—
196C4×Q8—111no—
197C4×D4—111no—
198C4×D4C2×D1111yescharacteristic
199#117—111no—
200#117—221no—
201C2×C4⋊C4—111no—
202C2×C4⋊C4—111no—
203C2×C4⋊C4—111no—
204#107—111no—
205#107—111no—
206#107—111no—
207#107—111no—
208#107—111no—
209#107—111no—
210#106—111no—
211#106—111no—
212#106—111no—
213C4⋊C8C2×D1111yescharacteristic
214#103—111no—
215#103—111no—
216#103—111no—
217#102—111no—
218#102—111no—
219#102—111no—
220C22⋊C8C2×D1111yescharacteristic
221C22⋊C8C2×D1111yescharacteristic
222#97C2×D1111yescharacteristic
223C2×C11—22no—
224C2×C11—41no—
225C2×C11#54711yescharacteristic
226C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
227C2×C11#57811yescharacteristic
228D11—81no—
229#41—444no—
230C2×Q8—111no—
231C2×Q8—221no—
232C2×D4—111no—
233C2×D4—221no—
234C2×D4—221no—
235C2×D4D4411yescharacteristic
236C22×C4—221no—
237C22×C4—221no—
238C22×C4—221no—
239C22×C4—221no—
240C22×C4C22×D1111yescharacteristic
241C22×C4C22×D1111yescharacteristic
242SD16—222no—
243M16—22no—
244C2×C8—22no—
245C2×C8C22×D1111yescharacteristic
246C2×C8C22×D1111yescharacteristic
247C2×C8C22×D1111yescharacteristic
248C2×C8C22×D1111yescharacteristic
249C4⋊C4—111no—
250C4⋊C4—111no—
251C4⋊C4—111no—
252C4⋊C4—111no—
253C4⋊C4—111no—
254C4⋊C4—111no—
255C4⋊C4—221no—
256C4⋊C4—221no—
257C4⋊C4—221no—
258C4⋊C4—221no—
259C4⋊C4—221no—
260C4⋊C4—221no—
261C4⋊C4—221no—
262C4⋊C4—221no—
263C4⋊C4—221no—
264C4⋊C4D4411yescharacteristic
265C22⋊C4—221no—
266C22⋊C4—221no—
267C22⋊C4—221no—
268C22⋊C4—221no—
269C22⋊C4—221no—
270C22⋊C4—221no—
271C22⋊C4D4411yescharacteristic
272C22⋊C4D4411yescharacteristic
273C42—221no—
274C42—221no—
275C42C22×D1111yescharacteristic
276C11#334311yescharacteristic, complemented, Sylow
277C23—221no—
278C23C2×D4411yescharacteristic
279C23C2×D4411yescharacteristic
280Q8—221no—
281Q8—221no—
282Q8—442no—
283D4—22no—
284D4—221no—
285D4—221no—
286D4—442no—
287D4—442no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—221no—
293C2×C4—221no—
294C2×C4—221no—
295C2×C4—221no—
296C2×C4—221no—
297C2×C4—221no—
298C2×C4—221no—
299C2×C4—442no—
300C2×C4—442no—
301C2×C4—442no—
302C2×C4—442no—
303C2×C4C2×D4411yescharacteristic
304C2×C4C2×D4411yescharacteristic
305C2×C4C2×D4411yescharacteristic
306C2×C4C2×D4411yescharacteristic
307C2×C4C23×D1111yescharacteristic
308C8—21no—
309C8—21no—
310C8—21no—
311C8#434112yescomplemented
312C22—21no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—441no—
318C22—441no—
319C22—441no—
320C22#6696112yes—
321C22C22×D4411yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—441no—
327C4—441no—
328C4—441no—
329C4—441no—
330C4—441no—
331C4—441no—
332C4—441no—
333C4C2×#434111yescharacteristic
334C4#6704311yescharacteristic
335C2—22no—
336C2—41no—
337C2—881no—
338C2#1062308611yescharacteristic
339C2C2×#6696111yescharacteristic
340C2#1062328411yescharacteristic
subgroupG/H
centerC22C22×D44
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#435C2
socleC22×C11C22×D4
prime radical#10623086C2
hypercenter#435D11
hypocenterC11#3343
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
2. #10623072C2semidirect
3. C11×#435C2semidirect
4. #10622747C2semidirect
5. #10622734C2semidirect
6. #10622727C2semidirect
7. C2×#66882C2semidirect
8. #10622463C2semidirect
9. #10622460C2semidirect
10. #10622350C2semidirect
11. #10622349C2semidirect
12. #10622335C2semidirect
13. #10622334C2semidirect
14. #10622323C2semidirect
15. #10622315C2semidirect
141. C8×C11#41semidirect
154. #435D11semidirect
276. C11#3343semidirect
311. C8#4341semidirect

Maximal subgroups

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

subgroupindex
#106230862
#106230722
C11×#4352
#106227472
#106227342
#106227272
C2×#668822
#106224632
#106224602
#106223502
#106223492
#106223352
#106223342
#106223232
#106223152
#334311