Finite Group Databasebeta

← #13081337

Subgroups — #13081337

Order 1408.

372 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
1#10623258C211yesmaximal, characteristic, complemented
2#10623099C211yesmaximal, characteristic, complemented
3C11×#477C211yesmaximal, characteristic, complemented
4#10622702C211yesmaximal, characteristic, complemented
5#10622639C211yesmaximal, characteristic, complemented
6#10622503C211yesmaximal, characteristic, complemented
7#10622502C211yesmaximal, characteristic, complemented
8#10622488C211yesmaximal, characteristic, complemented
9#10622485C211yesmaximal, characteristic
10#10622457C211yesmaximal, characteristic
11#10622441C211yesmaximal, characteristic, complemented
12#10622432C211yesmaximal, characteristic
13#10622431C211yesmaximal, characteristic, complemented
14#10622408C211yesmaximal, characteristic, complemented
15#10622405C211yesmaximal, characteristic, complemented
16C2×Q8×D11—21no—
17C11×C4⋊Q8C2211yescharacteristic
18C4×Q8×C11C2211yescharacteristic
19#67000C2211yescharacteristic
20#66999—21no—
21#66997C2211yescharacteristic
22C2×#4325C2211yescharacteristic
23C2×D88C2211yescharacteristic
24C2×#4314C2211yescharacteristic
25#66951—21no—
26#66949—21no—
27#66949—21no—
28#66949—21no—
29#66946C2211yescharacteristic
30#66946C2211yescharacteristic
31#66946C2211yescharacteristic
32#66941C2211yescharacteristic
33#66941C2211yescharacteristic
34#66940C2211yescharacteristic
35#66929—21no—
36#66928C2211yescharacteristic
37C4×D44C2211yescharacteristic
38#66925—21no—
39C4×Dic22C2211yescharacteristic
40C11×#107C2211yescharacteristic
41C11×#107C2211yescharacteristic
42C11×C4⋊C8C2211yescharacteristic
43C11×#103C2211yescharacteristic
44C11×#103C2211yescharacteristic
45#66899C2211yescharacteristic
46#66885C2211yescharacteristic
47#66880C2211yescharacteristic
48#66879C2211yescharacteristic
49Dic11⋊C8C2211yescharacteristic
50Dic11⋊C8C2211yescharacteristic
51C8×Dic11C2211yescharacteristic
52#66874C2211yescharacteristic
53#66874C2211yescharacteristic
54#66873C2211yescharacteristic
55#66873C2211yescharacteristic
56#66873C2211yescharacteristic
57#66871C2211yescharacteristic
58#66867C2211yescharacteristic
59C2×Q8×C11—21no—
60C2×Q8×C11C2311yescharacteristic
61Q8×D11—44no—
62C2×D44C2311yescharacteristic
63C2×D44C2311yescharacteristic
64C2×C4×D11—21no—
65C2×C4×D11—21no—
66C2×C4×D11—21no—
67C2×C4×D11—21no—
68C2×Dic22—21no—
69C2×Dic22—21no—
70C2×Dic22D411yescharacteristic
71C2×Dic22C2311yescharacteristic
72C2×C8×C11C2311yescharacteristic
73C2×C8×C11C2311yescharacteristic
74C11×C4⋊C4—21no—
75C11×C4⋊C4—21no—
76C11×C4⋊C4C2311yescharacteristic
77C11×C4⋊C4C2311yescharacteristic
78C11×C4⋊C4C2311yescharacteristic
79C42×C11—21no—
80C42×C11C2311yescharacteristic
81#4325—22no—
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)⋊C4—21no—
89(C2×D11)⋊C4—21no—
90C4⋊Dic11D411yescharacteristic
91C4⋊Dic11C2311yescharacteristic
92Dic11⋊C4—21no—
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4D411yescharacteristic
98Dic11⋊C4D411yescharacteristic
99C4×Dic11—21no—
100C4×Dic11C2311yescharacteristic
101C4×Dic11C2311yescharacteristic
102C2×C11⋊C8C2311yescharacteristic
103C2×C11⋊C8C2311yescharacteristic
104D88—22no—
105#4314—22no—
106#3367—111nomaximal, Sylow
107C22×D11—21no—
108C22×D11—21no—
109Q8×C11—21no—
110Q8×C11—21no—
111Q8×C11—42no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11C2×D411yescharacteristic
117C2×C4×C11C2×D411yescharacteristic
118C2×C4×C11C2411yescharacteristic
119C2×Dic11—21no—
120C2×Dic11—21no—
121C2×Dic11C2×D411yescharacteristic
122C2×Dic11C2×D411yescharacteristic
123C2×Dic11C2×D411yescharacteristic
124C2×Dic11C2×D411yescharacteristic
125D44—21no—
126D44—21no—
127D44—21no—
128D44#4112yes—
129C4×D11—42no—
130C4×D11—42no—
131C4×D11—42no—
132C4×D11—42no—
133Dic22—22no—
134Dic22—21no—
135Dic22—21no—
136Dic22—42no—
137Dic22—42no—
138C8×C11—21no—
139C8×C11—21no—
140C11⋊C8—21no—
141C11⋊C8—21no—
142#556—111no—
143D4×Q8—111no—
144#489—111no—
145#489—111no—
146#487—111no—
147#477—111no—
148#477D1111yescharacteristic, complemented
149#474—111no—
150#463—111no—
151#463—111no—
152#461—111no—
153#446—111no—
154#440—111no—
155#440—111no—
156C4×D8—111no—
157C22×C11C22×D411yescharacteristic
158C2×D11—22no—
159C2×D11—41no—
160C2×D11—41no—
161C2×D11—41no—
162C2×D11—41no—
163C2×D11—41no—
164C4×C11—21no—
165C4×C11—21no—
166C4×C11—41no—
167C4×C11—41no—
168C4×C11—41no—
169C4×C11—41no—
170C4×C11C2×#4111yescharacteristic
171C4×C112−1+411yescharacteristic
172Dic11—21no—
173Dic11—21no—
174Dic11—21no—
175Dic11—41no—
176Dic11—41no—
177Dic11AGL(1,ℤ/8)12yes—
178C22×Q8—221no—
179C2×SD16—111no—
180C2×SD16—111no—
181C2×D8—111no—
182C4⋊Q8—111no—
183C4⋊Q8—111no—
184C4⋊Q8—111no—
185C4⋊Q8C2×D1111yescharacteristic
186#126—221no—
187#126—221no—
188#124—111no—
189#124—111no—
190C22⋊Q8—221no—
191C22⋊Q8—221no—
192C22⋊Q8—221no—
193C22⋊Q8—221no—
194C4×Q8—111no—
195C4×Q8—111no—
196C4×Q8C2×D1111yescharacteristic
197C4×D4—111no—
198C4×D4—111no—
199C4×D4—111no—
200C4×D4—111no—
201#117—221no—
202#107—111no—
203#107C2×D1111yescharacteristic
204#107C2×D1111yescharacteristic
205C4⋊C8—111no—
206C4⋊C8—111no—
207C4⋊C8C2×D1111yescharacteristic
208#103—111no—
209#103—111no—
210#103—111no—
211#103—111no—
212#103C2×D1111yescharacteristic
213#103C2×D1111yescharacteristic
214#102—111no—
215#102—111no—
216#102—111no—
217#102—111no—
218#97—111no—
219#97—111no—
220C4×C8—111no—
221C2×C11#54811yescharacteristic
222C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
223C2×C11#57811yescharacteristic
224D11—42no—
225D11—81no—
226C2×Q8—21no—
227C2×Q8—111no—
228C2×Q8—111no—
229C2×Q8—221no—
230C2×Q8—221no—
231C2×Q8—444no—
232C2×Q8C22×D1111yescharacteristic
233C2×D4—111no—
234C2×D4—111no—
235C22×C4—221no—
236C22×C4—221no—
237C22×C4—221no—
238C22×C4—221no—
239SD16—222no—
240SD16—222no—
241D8—222no—
242C2×C8—111no—
243C2×C8—111no—
244C2×C8C22×D1111yescharacteristic
245C2×C8C22×D1111yescharacteristic
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—111no—
249C4⋊C4—111no—
250C4⋊C4—111no—
251C4⋊C4—111no—
252C4⋊C4—221no—
253C4⋊C4—221no—
254C4⋊C4—221no—
255C4⋊C4—221no—
256C4⋊C4—221no—
257C4⋊C4C22×D1111yescharacteristic
258C4⋊C4C22×D1111yescharacteristic
259C4⋊C4C22×D1111yescharacteristic
260C22⋊C4—221no—
261C22⋊C4—221no—
262C22⋊C4—221no—
263C22⋊C4—221no—
264C22⋊C4—221no—
265C22⋊C4—221no—
266C22⋊C4—221no—
267C22⋊C4—221no—
268C42—21no—
269C42—111no—
270C42—111no—
271C42—221no—
272C42C22×D1111yescharacteristic
273C11#336711yescharacteristic, complemented, Sylow
274C23—221no—
275C23—221no—
276Q8—21no—
277Q8—21no—
278Q8—42no—
279Q8—222no—
280Q8—221no—
281Q8—221no—
282Q8—442no—
283Q8—442no—
284D4—112no—
285D4—221no—
286D4—221no—
287D4—221no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—111no—
293C2×C4—111no—
294C2×C4—111no—
295C2×C4—111no—
296C2×C4—221no—
297C2×C4—221no—
298C2×C4—442no—
299C2×C4—442no—
300C2×C4—442no—
301C2×C4—442no—
302C2×C4D4×D1111yescharacteristic
303C2×C4D4×D1111yescharacteristic
304C2×C4C23×D1111yescharacteristic
305C8—21no—
306C8—21no—
307C8—221no—
308C8—221no—
309C22—222no—
310C22—441no—
311C22—441no—
312C22—441no—
313C22—441no—
314C22—441no—
315C22C2×D4×D1111yescharacteristic
316C4—21no—
317C4—21no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—112no—
323C4—221no—
324C4—221no—
325C4—221no—
326C4—441no—
327C4—441no—
328C4#6704011yescharacteristic
329C4#41×D1111yescharacteristic
330C2—442no—
331C2—881no—
332C2#1062316411yescharacteristic
333C2#1062329711yescharacteristic
334C2D11×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#477C2
socleC22×C11C22×D4
prime radicalC2×D88C22
hypercenter#477D11
hypocenterC11#3367
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
1. #10623258C2semidirect
2. #10623099C2semidirect
3. C11×#477C2semidirect
4. #10622702C2semidirect
5. #10622639C2semidirect
6. #10622503C2semidirect
7. #10622502C2semidirect
8. #10622488C2semidirect
11. #10622441C2semidirect
13. #10622431C2semidirect
14. #10622408C2semidirect
15. #10622405C2semidirect
148. #477D11semidirect
273. C11#3367semidirect

Maximal subgroups

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

subgroupindex
#106232582
#106230992
C11×#4772
#106227022
#106226392
#106225032
#106225022
#106224882
#106224852
#106224572
#106224412
#106224322
#106224312
#106224082
#106224052
#336711