Finite Group Databasebeta

← #13080949

Subgroups — #13080949

Order 1408.

398 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623166C211yesmaximal, characteristic, complemented
2#10623130C211yesmaximal, characteristic
3C11×#468C211yesmaximal, characteristic, complemented
4#10622786C211yesmaximal, characteristic, complemented
5#10622776C211yesmaximal, characteristic, complemented
6#10622746C211yesmaximal, characteristic, complemented
7#10622741C211yesmaximal, characteristic, complemented
8#10622660C211yesmaximal, characteristic, complemented
9#10622646C211yesmaximal, characteristic, complemented
10#10622495C211yesmaximal, characteristic, complemented
11#10622488C211yesmaximal, characteristic, complemented
12#10622425C211yesmaximal, characteristic, complemented
13#10622403C211yesmaximal, characteristic, complemented
14#10622384C211yesmaximal, characteristic, complemented
15#10622373C211yesmaximal, characteristic, complemented
16C2×#4341C2211yescharacteristic
17C2×#4339C2211yescharacteristic
18C2×C11×SD16C2211yescharacteristic
19C2×C11×M16C2211yescharacteristic
20C11×C22⋊Q8C2211yescharacteristic
21C11×#121C2211yescharacteristic
22#66999C2211yescharacteristic
23Q8×Dic11C2211yescharacteristic
24C2×#4326C2211yescharacteristic
25C2×#4325C2211yescharacteristic
26#66993—21no—
27#66993C2211yescharacteristic
28#66992—21no—
29C4×C22⋊D11C2211yescharacteristic
30C2×C4⋊Dic11C2211yescharacteristic
31C2×#4313C2211yescharacteristic
32#66950—21no—
33#66948C2211yescharacteristic
34C4⋊C4×D11C2211yescharacteristic
35#66942—21no—
36#66941C2211yescharacteristic
37#66940C2211yescharacteristic
38#66937—21no—
39(C22⋊D11)⋊C4—21no—
40(C22⋊D11)⋊C4—21no—
41#66931—21no—
42C11×#107C2211yescharacteristic
43C11×#103C2211yescharacteristic
44C11×#102C2211yescharacteristic
45#66896C2211yescharacteristic
46#66896C2211yescharacteristic
47C22⋊(C11⋊C8)C2211yescharacteristic
48#66885C2211yescharacteristic
49#66885C2211yescharacteristic
50(C2×D11)⋊C8C2211yescharacteristic
51#66880C2211yescharacteristic
52#66880C2211yescharacteristic
53Dic11⋊C8C2211yescharacteristic
54C8×Dic11C2211yescharacteristic
55#66874C2211yescharacteristic
56#66873C2211yescharacteristic
57#66871C2211yescharacteristic
58#66871C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×D4×C11—21no—
61C2×D4×C11C2311yescharacteristic
62C22×C4×C11C2311yescharacteristic
63C2×C22⋊D11—21no—
64C2×C22⋊D11—21no—
65C2×C22⋊D11—21no—
66C2×C22⋊D11—21no—
67C2×C22⋊D11D411yescharacteristic
68C22×Dic11—21no—
69C22×Dic11—21no—
70#4341—22no—
71#4341—41no—
72#4339—22no—
73#4339—41no—
74C2×D44—21no—
75C2×D44C2311yescharacteristic
76C2×C4×D11—21no—
77C2×C4×D11—21no—
78C2×C4×D11C2311yescharacteristic
79C2×Dic22—21no—
80C2×Dic22C2311yescharacteristic
81C11×SD16—41no—
82C11×M16—41no—
83C2×C8×C11C2311yescharacteristic
84C2×C8×C11C2311yescharacteristic
85C11×C4⋊C4—21no—
86C11×C4⋊C4C2311yescharacteristic
87C11×C4⋊C4C2311yescharacteristic
88C11×C22⋊C4—21no—
89C11×C22⋊C4—21no—
90C22⋊Dic11D411yescharacteristic
91#4326—22no—
92#4325—41no—
93(C2×D11)⋊C4—21no—
94(C2×D11)⋊C4—21no—
95(C2×D11)⋊C4D411yescharacteristic
96C4⋊Dic11—21no—
97C4⋊Dic11—21no—
98C4⋊Dic11C2311yescharacteristic
99C4⋊Dic11C2311yescharacteristic
100Dic11⋊C4—21no—
101Dic11⋊C4—21no—
102Dic11⋊C4—21no—
103Dic11⋊C4—21no—
104Dic11⋊C4D411yescharacteristic
105C4×Dic11—21no—
106C4×Dic11—21no—
107C4×Dic11C2311yescharacteristic
108C2×C11⋊C8C2311yescharacteristic
109C2×C11⋊C8C2311yescharacteristic
110#4313—41no—
111#3333—111nomaximal, Sylow
112C23×C11—21no—
113C23×C11C2×D411yescharacteristic
114C22×D11—21no—
115C22×D11C2×D411yescharacteristic
116Q8×C11—21no—
117Q8×C11—21no—
118D4×C11—21no—
119D4×C11—21no—
120D4×C11—81no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11C2×D411yescharacteristic
127C2×C4×C11C2411yescharacteristic
128C22⋊D11—22no—
129C22⋊D11—42no—
130C22⋊D11—42no—
131C22⋊D11—42no—
132C22⋊D11—81no—
133C2×Dic11—21no—
134C2×Dic11—21no—
135C2×Dic11—21no—
136C2×Dic11—42no—
137C2×Dic11—81no—
138C2×Dic11C2×D411yescharacteristic
139C2×Dic11C2×D411yescharacteristic
140C2×Dic11C2×D411yescharacteristic
141D44—21no—
142D44—21no—
143D44—81no—
144C4×D11—21no—
145C4×D11—21no—
146C4×D11—42no—
147C4×D11—81no—
148Dic22—21no—
149Dic22—81no—
150Dic22#4112yes—
151C8×C11—21no—
152C8×C11—21no—
153C11⋊C8—21no—
154C11⋊C8—21no—
155#554—111no—
156#550—111no—
157#486—111no—
158#480—111no—
159#480—111no—
160#477—111no—
161#468—111no—
162#468D1111yescharacteristic, complemented
163#460—111no—
164#452—111no—
165#452—111no—
166C4×Q16—111no—
167#436—111no—
168#417—111no—
169#417—111no—
170C22×C11—21no—
171C22×C11—21no—
172C22×C11—21no—
173C22×C11—41no—
174C22×C11—41no—
175C22×C11—41no—
176C22×C11C22×D411yescharacteristic
177C2×D11—21no—
178C2×D11—21no—
179C2×D11—21no—
180C2×D11—41no—
181C2×D11—41no—
182C2×D11—41no—
183C4×C11—21no—
184C4×C11—41no—
185C4×C11—41no—
186C4×C11—41no—
187C4×C11C2×#4111yescharacteristic
188C4×C11H(5,𝔽2)11yescharacteristic
189Dic11—22no—
190Dic11—21no—
191Dic11—21no—
192Dic11—41no—
193Dic11—41no—
194Dic11#13712yes—
195C2×#41—111no—
196C2×#41—111no—
197C2×Q16—111no—
198C2×SD16—111no—
199C2×SD16C2×D1111yescharacteristic
200C2×M16—111no—
201C2×M16C2×D1111yescharacteristic
202C4⋊Q8—111no—
203#127—111no—
204#127—221no—
205#125—221no—
206C22⋊Q8—111no—
207C22⋊Q8—221no—
208C22⋊Q8—221no—
209C22⋊Q8C2×D1111yescharacteristic
210#121—111no—
211#121—221no—
212#121—221no—
213#121C2×D1111yescharacteristic
214C4×Q8—111no—
215C4×Q8—111no—
216C4×D4—111no—
217C4×D4—221no—
218C4×D4—221no—
219C2×C4⋊C4—111no—
220C2×C4⋊C4—111no—
221#107—111no—
222#107—111no—
223#107C2×D1111yescharacteristic
224C4⋊C8—111no—
225#103—111no—
226#103—111no—
227#103—111no—
228#103C2×D1111yescharacteristic
229#102—111no—
230#102—111no—
231#102—111no—
232#102—111no—
233#102—111no—
234#102C2×D1111yescharacteristic
235C22⋊C8—111no—
236C22⋊C8—111no—
237C4×C8—111no—
238C2×C11—41no—
239C2×C11—81no—
240C2×C11#54611yescharacteristic
241C2×C11C2×#13711yescharacteristic
242C2×C11#57611yescharacteristic
243D11—41no—
244D11—81no—
245#41—222no—
246#41—222no—
247#41—441no—
248#41—441no—
249C2×Q8—111no—
250C2×Q8—221no—
251C2×Q8C22×D1111yescharacteristic
252C2×D4—21no—
253C2×D4—111no—
254C2×D4—111no—
255C2×D4—221no—
256C2×D4—221no—
257C2×D4—221no—
258C2×D4—221no—
259C2×D4—221no—
260C2×D4C22×D1111yescharacteristic
261C22×C4—111no—
262C22×C4—221no—
263C22×C4—221no—
264C22×C4—221no—
265C22×C4—221no—
266C22×C4C22×D1111yescharacteristic
267Q16—222no—
268SD16—41no—
269SD16—441no—
270M16—41no—
271M16—441no—
272C2×C8—111no—
273C2×C8—111no—
274C2×C8C22×D1111yescharacteristic
275C2×C8C22×D1111yescharacteristic
276C4⋊C4—21no—
277C4⋊C4—111no—
278C4⋊C4—111no—
279C4⋊C4—111no—
280C4⋊C4—221no—
281C4⋊C4—221no—
282C4⋊C4—221no—
283C4⋊C4—221no—
284C4⋊C4—221no—
285C4⋊C4—221no—
286C4⋊C4C22×D1111yescharacteristic
287C4⋊C4C22×D1111yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—111no—
291C22⋊C4—111no—
292C22⋊C4—221no—
293C22⋊C4—221no—
294C42—111no—
295C42—221no—
296C42—221no—
297C11#333311yescharacteristic, complemented, Sylow
298C23—21no—
299C23—111no—
300C23—221no—
301C23D4×D1111yescharacteristic
302Q8—21no—
303Q8—21no—
304Q8—112no—
305Q8—221no—
306Q8—881no—
307D4—21no—
308D4—21no—
309D4—81no—
310D4—222no—
311D4—221no—
312D4—221no—
313D4—442no—
314D4—442no—
315D4—442no—
316D4—881no—
317D4—881no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—111no—
324C2×C4—111no—
325C2×C4—111no—
326C2×C4—221no—
327C2×C4—221no—
328C2×C4—221no—
329C2×C4—221no—
330C2×C4—221no—
331C2×C4—442no—
332C2×C4—442no—
333C2×C4—881no—
334C2×C4—881no—
335C2×C4D4×D1111yescharacteristic
336C2×C4C23×D1111yescharacteristic
337C8—21no—
338C8—21no—
339C8—221no—
340C8—221no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—221no—
348C22—221no—
349C22—221no—
350C22—441no—
351C22—441no—
352C22—441no—
353C22C2×D4×D1111yescharacteristic
354C4—21no—
355C4—41no—
356C4—41no—
357C4—41no—
358C4—112no—
359C4—221no—
360C4—221no—
361C4—222no—
362C4—441no—
363C4—441no—
364C4#6703711yescharacteristic
365C4#41×D1111yescharacteristic
366C2—41no—
367C2—81no—
368C2—441no—
369C2—881no—
370C2#1062314111yescharacteristic
371C2#1062330511yescharacteristic
372C2D11×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#468C2
socleC22×C11C22×D4
prime radical#10623130C2
hypercenter#468D11
hypocenterC11#3333
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. #10623166C2semidirect
3. C11×#468C2semidirect
4. #10622786C2semidirect
5. #10622776C2semidirect
6. #10622746C2semidirect
7. #10622741C2semidirect
8. #10622660C2semidirect
9. #10622646C2semidirect
10. #10622495C2semidirect
11. #10622488C2semidirect
12. #10622425C2semidirect
13. #10622403C2semidirect
14. #10622384C2semidirect
15. #10622373C2semidirect
162. #468D11semidirect
297. C11#3333semidirect

Maximal subgroups

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

subgroupindex
#106231662
#106231302
C11×#4682
#106227862
#106227762
#106227462
#106227412
#106226602
#106226462
#106224952
#106224882
#106224252
#106224032
#106223842
#106223732
#333311