Finite Group Databasebeta

← #13080674

Subgroups — #13080674

Order 1408.

376 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623258C211yesmaximal, characteristic
2#10623112C211yesmaximal, characteristic
3C11×#462C211yesmaximal, characteristic, complemented
4#10622802C211yesmaximal, characteristic, complemented
5#10622801C211yesmaximal, characteristic, complemented
6#10622799C211yesmaximal, characteristic, complemented
7#10622799C211yesmaximal, characteristic, complemented
8#10622695C211yesmaximal, characteristic, complemented
9#10622643C211yesmaximal, characteristic, complemented
10#10622449C211yesmaximal, characteristic
11#10622442C211yesmaximal, characteristic, complemented
12#10622427C211yesmaximal, characteristic, complemented
13#10622418C211yesmaximal, characteristic, complemented
14#10622415C211yesmaximal, characteristic, complemented
15D11×#103C211yesmaximal, characteristic, complemented
16C2×Q8×D11C2211yescharacteristic
17C2×Q8×D11C2211yescharacteristic
18C2×C11×Q16C2211yescharacteristic
19C2×C11×Q16C2211yescharacteristic
20C11×C4⋊Q8C2211yescharacteristic
21C4×Q8×C11C2211yescharacteristic
22#66999C2211yescharacteristic
23#66999C2211yescharacteristic
24#66999C2211yescharacteristic
25#66999C2211yescharacteristic
26C2×#4326C2211yescharacteristic
27C2×#4313C2211yescharacteristic
28C2×C8×D11C2211yescharacteristic
29#66949—21no—
30#66949—21no—
31#66947—21no—
32#66946—21no—
33#66945C2211yescharacteristic
34C4⋊C4×D11C2211yescharacteristic
35#66942—21no—
36#66941—21no—
37#66929—21no—
38C4×D44C2211yescharacteristic
39#66925—21no—
40#66923C2211yescharacteristic
41C4×Dic22C2211yescharacteristic
42C11×C4⋊C8C2211yescharacteristic
43C11×#103C2211yescharacteristic
44C11×#103C2211yescharacteristic
45#66899C2211yescharacteristic
46#66899C2211yescharacteristic
47#66899C2211yescharacteristic
48#66899C2211yescharacteristic
49#66899C2211yescharacteristic
50(C2×D11)⋊C8C2211yescharacteristic
51(C2×D11)⋊C8C2211yescharacteristic
52#66882C2211yescharacteristic
53#66881C2211yescharacteristic
54#66880C2211yescharacteristic
55#66880C2211yescharacteristic
56#66874C2211yescharacteristic
57#66872C2211yescharacteristic
58#66867C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×Q8×C11C2311yescharacteristic
61C2×Q8×C11C2311yescharacteristic
62Q8×D11—22no—
63Q8×D11—22no—
64Q8×D11—41no—
65Q8×D11—41no—
66C2×D44D411yescharacteristic
67C2×C4×D11—21no—
68C2×C4×D11—21no—
69C2×C4×D11—21no—
70C2×C4×D11C2311yescharacteristic
71C2×C4×D11C2311yescharacteristic
72C2×Dic22—21no—
73C2×Dic22—21no—
74C2×Dic22C2311yescharacteristic
75C11×Q16—41no—
76C11×Q16—41no—
77C2×C8×C11C2311yescharacteristic
78C2×C8×C11C2311yescharacteristic
79C11×C4⋊C4—21no—
80C11×C4⋊C4—21no—
81C11×C4⋊C4—21no—
82C11×C4⋊C4C2311yescharacteristic
83C42×C11—21no—
84C42×C11C2311yescharacteristic
85#4326—22no—
86(C2×D11)⋊C4—21no—
87(C2×D11)⋊C4—21no—
88(C2×D11)⋊C4—21no—
89(C2×D11)⋊C4—21no—
90(C2×D11)⋊C4—21no—
91(C2×D11)⋊C4D411yescharacteristic
92(C2×D11)⋊C4D411yescharacteristic
93C4⋊Dic11D411yescharacteristic
94C4⋊Dic11C2311yescharacteristic
95C4⋊Dic11C2311yescharacteristic
96C4⋊Dic11C2311yescharacteristic
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99Dic11⋊C4—21no—
100Dic11⋊C4—21no—
101Dic11⋊C4—21no—
102Dic11⋊C4—21no—
103Dic11⋊C4—21no—
104Dic11⋊C4—21no—
105C4×Dic11—21no—
106C4×Dic11—21no—
107C2×C11⋊C8C2311yescharacteristic
108C2×C11⋊C8C2311yescharacteristic
109#4313—41no—
110C8×D11—41no—
111#3312—111nomaximal, Sylow
112C22×D11C2×D411yescharacteristic
113C22×D11C2×D411yescharacteristic
114Q8×C11—21no—
115Q8×C11—21no—
116Q8×C11—21no—
117Q8×C11—21no—
118Q8×C11—21no—
119Q8×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11C2×D411yescharacteristic
125C2×C4×C11C2×D411yescharacteristic
126C2×C4×C11C2411yescharacteristic
127C2×Dic11—21no—
128C2×Dic11—21no—
129C2×Dic11—21no—
130C2×Dic11—21no—
131C2×Dic11C2×D411yescharacteristic
132C2×Dic11C2×D411yescharacteristic
133D44—22no—
134C4×D11—21no—
135C4×D11—21no—
136C4×D11—21no—
137C4×D11—21no—
138C4×D11—42no—
139C4×D11—42no—
140C4×D11—42no—
141Dic22—21no—
142Dic22—42no—
143Dic22—42no—
144Dic22#4112yes—
145C8×C11—21no—
146C8×C11—21no—
147C11⋊C8—21no—
148C11⋊C8—21no—
149#552—111no—
150D4×Q8—111no—
151#491—111no—
152#485—111no—
153#483—111no—
154#479—111no—
155#470—111no—
156#467—111no—
157#462D1111yescharacteristic, complemented
158#451—111no—
159#451—111no—
160#441—111no—
161#435—111no—
162#419—111no—
163C2×#103—111no—
164C22×C11C22×D411yescharacteristic
165C2×D11—21no—
166C2×D11—21no—
167C2×D11—21no—
168C2×D11—21no—
169C2×D11—21no—
170C2×D11#13712yes—
171C4×C11—21no—
172C4×C11—21no—
173C4×C11—41no—
174C4×C11—41no—
175C4×C11—41no—
176C4×C11—41no—
177C4×C11C2×#4111yescharacteristic
178C4×C11H(5,𝔽2)11yescharacteristic
179Dic11—22no—
180Dic11—21no—
181Dic11—21no—
182Dic11—41no—
183Dic11—41no—
184Dic11—41no—
185C22×Q8—111no—
186C22×Q8—111no—
187C2×Q16—111no—
188C2×Q16C2×D1111yescharacteristic
189C2×Q16C2×D1111yescharacteristic
190C2×M16—111no—
191C22×C8—111no—
192C4⋊Q8—221no—
193C4⋊Q8C2×D1111yescharacteristic
194#126—221no—
195#125—111no—
196#125—221no—
197#123—221no—
198C22⋊Q8—111no—
199C22⋊Q8—111no—
200C22⋊Q8—111no—
201C22⋊Q8—111no—
202C22⋊Q8—221no—
203C22⋊Q8—221no—
204C4×Q8—111no—
205C4×Q8C2×D1111yescharacteristic
206C4×D4—111no—
207C4×D4—221no—
208#117—111no—
209#117—221no—
210C2×C4⋊C4—111no—
211#107—111no—
212#106—111no—
213#106—111no—
214C4⋊C8C2×D1111yescharacteristic
215#103—111no—
216#103—111no—
217#103—111no—
218#103—111no—
219#103—111no—
220#103—111no—
221#103—111no—
222#103—111no—
223#103C2×D1111yescharacteristic
224#103C2×D1111yescharacteristic
225C22⋊C8—111no—
226C22⋊C8—111no—
227#97—111no—
228C2×C11#54611yescharacteristic
229C2×C11C2×#13711yescharacteristic
230C2×C11#57811yescharacteristic
231D11—22no—
232D11—41no—
233C2×Q8—111no—
234C2×Q8—221no—
235C2×Q8—221no—
236C2×Q8—222no—
237C2×Q8—222no—
238C2×Q8—441no—
239C2×Q8—441no—
240C2×Q8C22×D1111yescharacteristic
241C2×Q8C22×D1111yescharacteristic
242C2×Q8C22×D1111yescharacteristic
243C2×D4—111no—
244C22×C4—111no—
245C22×C4—111no—
246C22×C4—221no—
247C22×C4—221no—
248C22×C4—221no—
249Q16—41no—
250Q16—41no—
251Q16—222no—
252M16—441no—
253C2×C8—111no—
254C2×C8—111no—
255C2×C8—441no—
256C2×C8C22×D1111yescharacteristic
257C2×C8C22×D1111yescharacteristic
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—111no—
262C4⋊C4—111no—
263C4⋊C4—111no—
264C4⋊C4—111no—
265C4⋊C4—221no—
266C4⋊C4—221no—
267C4⋊C4—221no—
268C4⋊C4—221no—
269C4⋊C4—221no—
270C4⋊C4—221no—
271C4⋊C4—221no—
272C4⋊C4—221no—
273C4⋊C4C22×D1111yescharacteristic
274C22⋊C4—111no—
275C22⋊C4—111no—
276C22⋊C4—221no—
277C22⋊C4—221no—
278C22⋊C4—221no—
279C22⋊C4—221no—
280C22⋊C4—221no—
281C42—21no—
282C42—221no—
283C42—221no—
284C42C22×D1111yescharacteristic
285C11#331211yescharacteristic, complemented, Sylow
286C23—111no—
287C23—111no—
288Q8—21no—
289Q8—21no—
290Q8—21no—
291Q8—21no—
292Q8—21no—
293Q8—21no—
294Q8—112no—
295Q8—221no—
296Q8—442no—
297Q8—442no—
298D4—222no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—111no—
304C2×C4—111no—
305C2×C4—221no—
306C2×C4—221no—
307C2×C4—221no—
308C2×C4—221no—
309C2×C4—221no—
310C2×C4—221no—
311C2×C4—221no—
312C2×C4—221no—
313C2×C4—442no—
314C2×C4—442no—
315C2×C4—442no—
316C2×C4D4×D1111yescharacteristic
317C2×C4D4×D1111yescharacteristic
318C2×C4C23×D1111yescharacteristic
319C8—21no—
320C8—21no—
321C8—221no—
322C8—221no—
323C22—112no—
324C22—221no—
325C22—221no—
326C22—221no—
327C22—221no—
328C22—221no—
329C22C2×D4×D1111yescharacteristic
330C4—21no—
331C4—21no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—221no—
337C4—221no—
338C4—222no—
339C4—441no—
340C4—441no—
341C4—441no—
342C4#6703711yescharacteristic
343C4#41×D1111yescharacteristic
344C2—222no—
345C2—441no—
346C2#1062314311yescharacteristic
347C2#1062329711yescharacteristic
348C2D11×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#462C2
socleC22×C11C22×D4
prime radicalC2×D44D4
hypercenter#462D11
hypocenterC11#3312
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
3. C11×#462C2semidirect
4. #10622802C2semidirect
5. #10622801C2semidirect
6. #10622799C2semidirect
7. #10622799C2semidirect
8. #10622695C2semidirect
9. #10622643C2semidirect
11. #10622442C2semidirect
12. #10622427C2semidirect
13. #10622418C2semidirect
14. #10622415C2semidirect
15. D11×#103C2semidirect
157. #462D11semidirect
285. C11#3312semidirect

Maximal subgroups

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

subgroupindex
#106232582
#106231122
C11×#4622
#106228022
#106228012
#106227992
#106226952
#106226432
#106224492
#106224422
#106224272
#106224182
#106224152
D11×#1032
#331211