Finite Group Databasebeta

← #13081055

Subgroups — #13081055

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#10623257C211yesmaximal, characteristic
2#10623225C211yesmaximal, characteristic, complemented
3C11×#501C211yesmaximal, characteristic, complemented
4#10622704C211yesmaximal, characteristic, complemented
5#10622679C211yesmaximal, characteristic, complemented
6#10622499C211yesmaximal, characteristic, complemented
7#10622497C211yesmaximal, characteristic, complemented
8#10622495C211yesmaximal, characteristic, complemented
9D11×#107C211yesmaximal, characteristic, complemented
10#10622479C211yesmaximal, characteristic, complemented
11#10622477C211yesmaximal, characteristic, complemented
12#10622475C211yesmaximal, characteristic, complemented
13#10622474C211yesmaximal, characteristic, complemented
14#10622323C211yesmaximal, characteristic, complemented
15#10622319C211yesmaximal, characteristic, complemented
16C2×#4343—21no—
17C11×C4⋊Q8C2211yescharacteristic
18C11×#125C2211yescharacteristic
19#66999—21no—
20C2×#4314C2211yescharacteristic
21C2×#4313C2211yescharacteristic
22C2×C8×D11C2211yescharacteristic
23#66951—21no—
24#66950C2211yescharacteristic
25#66950C2211yescharacteristic
26#66948C2211yescharacteristic
27#66948C2211yescharacteristic
28#66947—21no—
29#66947—21no—
30#66947—21no—
31#66945—21no—
32#66945C2211yescharacteristic
33C4⋊C4×D11C2211yescharacteristic
34C4⋊C4×D11C2211yescharacteristic
35C4⋊C4×D11C2211yescharacteristic
36#66943—21no—
37C4×D44C2211yescharacteristic
38C4×D44C2211yescharacteristic
39C4×Dic22C2211yescharacteristic
40C11×#107C2211yescharacteristic
41C11×#107C2211yescharacteristic
42C11×#106C2211yescharacteristic
43C11×#106C2211yescharacteristic
44C11×#97C2211yescharacteristic
45#66885C2211yescharacteristic
46(C2×D11)⋊C8C2211yescharacteristic
47(C2×D11)⋊C8C2211yescharacteristic
48#66882C2211yescharacteristic
49#66880C2211yescharacteristic
50#66874C2211yescharacteristic
51#66874C2211yescharacteristic
52#66873C2211yescharacteristic
53#66873C2211yescharacteristic
54#66872C2211yescharacteristic
55#66871C2211yescharacteristic
56#66871C2211yescharacteristic
57#66871C2211yescharacteristic
58C4⋊(C11⋊C8)C2211yescharacteristic
59C2×Q8×C11—21no—
60#4343—44no—
61C2×D44—21no—
62C2×D44—21no—
63C2×D44D411yescharacteristic
64C2×D44C2311yescharacteristic
65C2×C4×D11—21no—
66C2×C4×D11—21no—
67C2×C4×D11—21no—
68C2×C4×D11—21no—
69C2×C4×D11C2311yescharacteristic
70C2×C4×D11C2311yescharacteristic
71C2×Dic22C2311yescharacteristic
72C2×C8×C11C2311yescharacteristic
73C2×C8×C11C2311yescharacteristic
74C11×C4⋊C4—21no—
75C11×C4⋊C4—21no—
76C11×C4⋊C4—21no—
77C11×C4⋊C4C2311yescharacteristic
78C11×C4⋊C4C2311yescharacteristic
79C11×C4⋊C4C2311yescharacteristic
80C11×C4⋊C4C2311yescharacteristic
81C42×C11C2311yescharacteristic
82(C2×D11)⋊C4—21no—
83(C2×D11)⋊C4—21no—
84(C2×D11)⋊C4—21no—
85(C2×D11)⋊C4—21no—
86(C2×D11)⋊C4—21no—
87(C2×D11)⋊C4—21no—
88(C2×D11)⋊C4D411yescharacteristic
89(C2×D11)⋊C4D411yescharacteristic
90C4⋊Dic11—21no—
91C4⋊Dic11—21no—
92C4⋊Dic11D411yescharacteristic
93C4⋊Dic11C2311yescharacteristic
94C4⋊Dic11C2311yescharacteristic
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99C4×Dic11—21no—
100C4×Dic11—21no—
101C2×C11⋊C8C2311yescharacteristic
102C2×C11⋊C8C2311yescharacteristic
103#4314—22no—
104#4313—22no—
105C8×D11—22no—
106#3343—111nomaximal, Sylow
107C22×D11—21no—
108C22×D11C2×D411yescharacteristic
109C22×D11C2×D411yescharacteristic
110Q8×C11—42no—
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×C11C2411yescharacteristic
118C2×Dic11—21no—
119C2×Dic11—21no—
120C2×Dic11—21no—
121C2×Dic11C2×D411yescharacteristic
122C2×Dic11C2×D411yescharacteristic
123D44—22no—
124D44—21no—
125D44—21no—
126D44—42no—
127D44—42no—
128C4×D11—21no—
129C4×D11—21no—
130C4×D11—21no—
131C4×D11—21no—
132C4×D11—42no—
133C4×D11—42no—
134C4×D11—42no—
135C4×D11—42no—
136Dic22—21no—
137Dic22—21no—
138C8×C11—21no—
139C8×C11#4112yescomplemented
140C11⋊C8—21no—
141C11⋊C8—21no—
142#552—111no—
143#547—111no—
144#501D1111yescharacteristic, complemented
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#435—111no—
155#428—111no—
156C2×#107—111no—
157C22×C11C22×D411yescharacteristic
158C2×D11—21no—
159C2×D11—21no—
160C2×D11—21no—
161C2×D11—21no—
162C2×D11—21no—
163C2×D11—41no—
164C2×D11—41no—
165C2×D11—41no—
166C2×D11AGL(1,ℤ/8)12yes—
167C4×C11—21no—
168C4×C11—21no—
169C4×C11—41no—
170C4×C11—41no—
171C4×C11—41no—
172C4×C11—41no—
173C4×C11C2×#4111yescharacteristic
174C4×C112−1+411yescharacteristic
175Dic11—21no—
176Dic11—21no—
177Dic11—41no—
178Dic11—41no—
179Dic11—41no—
180C2×#41—221no—
181C2×SD16—111no—
182C2×M16—111no—
183C22×C8—111no—
184C4⋊Q8C2×D1111yescharacteristic
185#126—221no—
186#125—221no—
187#125C2×D1111yescharacteristic
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×D4—111no—
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#107C2×D1111yescharacteristic
209#107C2×D1111yescharacteristic
210#106—111no—
211#106C2×D1111yescharacteristic
212#106C2×D1111yescharacteristic
213C4⋊C8—111no—
214#103—111no—
215#103—111no—
216#103—111no—
217#102—111no—
218#102—111no—
219#102—111no—
220C22⋊C8—111no—
221C22⋊C8—111no—
222#97C2×D1111yescharacteristic
223C2×C11#54711yescharacteristic
224C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
225C2×C11#57811yescharacteristic
226D11—22no—
227D11—41no—
228D11—81no—
229#41—444no—
230C2×Q8—21no—
231C2×Q8—111no—
232C2×D4—111no—
233C2×D4—111no—
234C2×D4—221no—
235C2×D4—221no—
236C22×C4—111no—
237C22×C4—111no—
238C22×C4—221no—
239C22×C4—221no—
240C22×C4—221no—
241C22×C4—221no—
242SD16—222no—
243M16—222no—
244C2×C8—111no—
245C2×C8—111no—
246C2×C8—222no—
247C2×C8C22×D1111yescharacteristic
248C2×C8C22×D1111yescharacteristic
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—21no—
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⋊C4C22×D1111yescharacteristic
262C4⋊C4C22×D1111yescharacteristic
263C4⋊C4C22×D1111yescharacteristic
264C4⋊C4C22×D1111yescharacteristic
265C22⋊C4—111no—
266C22⋊C4—111no—
267C22⋊C4—221no—
268C22⋊C4—221no—
269C22⋊C4—221no—
270C22⋊C4—221no—
271C22⋊C4—221no—
272C22⋊C4—221no—
273C42—221no—
274C42—221no—
275C42C22×D1111yescharacteristic
276C11#334311yescharacteristic, complemented, Sylow
277C23—111no—
278C23—111no—
279C23—221no—
280Q8—42no—
281Q8—221no—
282Q8—221no—
283D4—222no—
284D4—221no—
285D4—221no—
286D4—442no—
287D4—442no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—111no—
293C2×C4—111no—
294C2×C4—221no—
295C2×C4—221no—
296C2×C4—221no—
297C2×C4—221no—
298C2×C4—221no—
299C2×C4—221no—
300C2×C4—221no—
301C2×C4—442no—
302C2×C4—442no—
303C2×C4—442no—
304C2×C4—442no—
305C2×C4D4×D1111yescharacteristic
306C2×C4D4×D1111yescharacteristic
307C2×C4C23×D1111yescharacteristic
308C8—21no—
309C8—221no—
310C8—221no—
311C8#434312yescomplemented
312C22—112no—
313C22—221no—
314C22—221no—
315C22—221no—
316C22—221no—
317C22—221no—
318C22—441no—
319C22—441no—
320C22—441no—
321C22C2×D4×D1111yescharacteristic
322C4—21no—
323C4—21no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—41no—
328C4—221no—
329C4—221no—
330C4—441no—
331C4—441no—
332C4—441no—
333C4C2×#434311yescharacteristic
334C4#6704011yescharacteristic
335C2—222no—
336C2—441no—
337C2—881no—
338C2#1062325711yescharacteristic
339C2D11×AGL(1,ℤ/8)11yescharacteristic
340C2#1062331011yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#501C2
socleC22×C11C22×D4
prime radical#10623257C2
hypercenter#501D11
hypocenterC11#3343
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
2. #10623225C2semidirect
3. C11×#501C2semidirect
4. #10622704C2semidirect
5. #10622679C2semidirect
6. #10622499C2semidirect
7. #10622497C2semidirect
8. #10622495C2semidirect
9. D11×#107C2semidirect
10. #10622479C2semidirect
11. #10622477C2semidirect
12. #10622475C2semidirect
13. #10622474C2semidirect
14. #10622323C2semidirect
15. #10622319C2semidirect
139. C8×C11#41semidirect
144. #501D11semidirect
276. C11#3343semidirect
311. C8#4343semidirect

Maximal subgroups

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

subgroupindex
#106232572
#106232252
C11×#5012
#106227042
#106226792
#106224992
#106224972
#106224952
D11×#1072
#106224792
#106224772
#106224752
#106224742
#106223232
#106223192
#334311