Finite Group Databasebeta

← #13080748

Subgroups — #13080748

Order 1408.

392 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623170C211yesmaximal, characteristic, complemented
2#10623130C211yesmaximal, characteristic
3C11×#465C211yesmaximal, characteristic, complemented
4#10622786C211yesmaximal, characteristic, complemented
5#10622776C211yesmaximal, characteristic, complemented
6#10622726C211yesmaximal, characteristic, complemented
7#10622724C211yesmaximal, characteristic, complemented
8#10622660C211yesmaximal, characteristic, complemented
9#10622648C211yesmaximal, characteristic, complemented
10#10622476C211yesmaximal, characteristic, complemented
11#10622470C211yesmaximal, characteristic, complemented
12#10622425C211yesmaximal, characteristic, complemented
13#10622402C211yesmaximal, characteristic, complemented
14#10622384C211yesmaximal, characteristic, complemented
15#10622377C211yesmaximal, characteristic, complemented
16C2×#4341C2211yescharacteristic
17C2×#4339C2211yescharacteristic
18C2×C11×SD16C2211yescharacteristic
19C22×C8×C11C2211yescharacteristic
20C11×C22⋊Q8C2211yescharacteristic
21C11×#121C2211yescharacteristic
22#66999C2211yescharacteristic
23Q8×Dic11C2211yescharacteristic
24C2×#4326C2211yescharacteristic
25C2×#4325C2211yescharacteristic
26#66993—21no—
27#66993C2211yescharacteristic
28#66992—21no—
29C4×C22⋊D11C2211yescharacteristic
30#66979C2211yescharacteristic
31C2×#4313C2211yescharacteristic
32#66948C2211yescharacteristic
33#66945—21no—
34C4⋊C4×D11C2211yescharacteristic
35#66943C2211yescharacteristic
36#66942—21no—
37#66940C2211yescharacteristic
38#66937—21no—
39#66936—21no—
40(C22⋊D11)⋊C4—21no—
41#66932—21no—
42C11×#106C2211yescharacteristic
43C11×#103C2211yescharacteristic
44C11×#102C2211yescharacteristic
45#66896C2211yescharacteristic
46#66896C2211yescharacteristic
47C22⋊(C11⋊C8)C2211yescharacteristic
48#66885C2211yescharacteristic
49#66885C2211yescharacteristic
50(C2×D11)⋊C8C2211yescharacteristic
51#66880C2211yescharacteristic
52#66880C2211yescharacteristic
53#66879C2211yescharacteristic
54Dic11⋊C8C2211yescharacteristic
55#66874C2211yescharacteristic
56#66873C2211yescharacteristic
57#66872C2211yescharacteristic
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—
69#4341—22no—
70#4341—41no—
71#4339—22no—
72#4339—41no—
73C2×D44—21no—
74C2×D44C2311yescharacteristic
75C2×C4×D11—21no—
76C2×C4×D11—21no—
77C2×C4×D11C2311yescharacteristic
78C2×Dic22C2311yescharacteristic
79C11×SD16—41no—
80C2×C8×C11—41no—
81C2×C8×C11C2311yescharacteristic
82C2×C8×C11C2311yescharacteristic
83C11×C4⋊C4—21no—
84C11×C4⋊C4C2311yescharacteristic
85C11×C4⋊C4C2311yescharacteristic
86C11×C22⋊C4—21no—
87C11×C22⋊C4—21no—
88C22⋊Dic11—21no—
89C22⋊Dic11D411yescharacteristic
90#4326—22no—
91#4325—41no—
92(C2×D11)⋊C4—21no—
93(C2×D11)⋊C4—21no—
94(C2×D11)⋊C4D411yescharacteristic
95C4⋊Dic11—21no—
96C4⋊Dic11—21no—
97C4⋊Dic11C2311yescharacteristic
98C4⋊Dic11C2311yescharacteristic
99Dic11⋊C4—21no—
100Dic11⋊C4—21no—
101Dic11⋊C4—21no—
102Dic11⋊C4—21no—
103Dic11⋊C4D411yescharacteristic
104C4×Dic11—21no—
105C4×Dic11—21no—
106C4×Dic11—21no—
107C4×Dic11C2311yescharacteristic
108C2×C11⋊C8C2311yescharacteristic
109C2×C11⋊C8C2311yescharacteristic
110#4313—41no—
111#3317—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—41no—
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×Dic11C2×D411yescharacteristic
138C2×Dic11C2×D411yescharacteristic
139C2×Dic11C2×D411yescharacteristic
140D44—21no—
141D44—21no—
142D44—81no—
143C4×D11—21no—
144C4×D11—21no—
145C4×D11—42no—
146C4×D11—42no—
147Dic22—21no—
148Dic22#4112yes—
149C8×C11—21no—
150C8×C11—21no—
151C11⋊C8—21no—
152C11⋊C8—21no—
153#552—111no—
154#550—111no—
155#490—111no—
156#482—111no—
157#481—111no—
158#479—111no—
159#468—111no—
160#465D1111yescharacteristic, complemented
161#460—111no—
162#452—111no—
163#452—111no—
164#441—111no—
165#435—111no—
166#417—111no—
167#416—111no—
168C22×C11—21no—
169C22×C11—21no—
170C22×C11—21no—
171C22×C11—41no—
172C22×C11—41no—
173C22×C11—41no—
174C22×C11C22×D411yescharacteristic
175C2×D11—21no—
176C2×D11—21no—
177C2×D11—21no—
178C2×D11—41no—
179C2×D11—41no—
180C2×D11—41no—
181C4×C11—21no—
182C4×C11—41no—
183C4×C11—41no—
184C4×C11—41no—
185C4×C11C2×#4111yescharacteristic
186C4×C11H(5,𝔽2)11yescharacteristic
187Dic11—22no—
188Dic11—21no—
189Dic11—21no—
190Dic11—21no—
191Dic11—41no—
192Dic11—41no—
193C2×#41—111no—
194C2×#41—111no—
195C2×Q16—111no—
196C2×SD16—111no—
197C2×SD16C2×D1111yescharacteristic
198C2×M16—111no—
199C22×C8C2×D1111yescharacteristic
200#127—111no—
201#127—221no—
202#126—221no—
203#125—111no—
204#125—221no—
205#123—221no—
206C22⋊Q8—111no—
207C22⋊Q8C2×D1111yescharacteristic
208#121—111no—
209#121—221no—
210#121—221no—
211#121C2×D1111yescharacteristic
212C4×Q8—111no—
213C4×Q8—111no—
214C4×D4—111no—
215C4×D4—221no—
216#117—111no—
217#117—221no—
218C2×C4⋊C4—111no—
219#107—111no—
220#106—111no—
221#106C2×D1111yescharacteristic
222C4⋊C8—111no—
223#103—111no—
224#103—111no—
225#103—111no—
226#103C2×D1111yescharacteristic
227#102—111no—
228#102—111no—
229#102—111no—
230#102—111no—
231#102—111no—
232#102C2×D1111yescharacteristic
233C22⋊C8—111no—
234C22⋊C8—111no—
235#97—111no—
236C2×C11—41no—
237C2×C11—81no—
238C2×C11#54611yescharacteristic
239C2×C11#57511yescharacteristic
240C2×C11#57711yescharacteristic
241D11—41no—
242D11—81no—
243#41—222no—
244#41—222no—
245#41—441no—
246#41—441no—
247C2×Q8—111no—
248C2×Q8C22×D1111yescharacteristic
249C2×D4—21no—
250C2×D4—111no—
251C2×D4—111no—
252C2×D4—221no—
253C2×D4—221no—
254C2×D4—221no—
255C2×D4—221no—
256C2×D4—221no—
257C2×D4C22×D1111yescharacteristic
258C22×C4—111no—
259C22×C4—221no—
260C22×C4—221no—
261C22×C4—221no—
262C22×C4C22×D1111yescharacteristic
263Q16—222no—
264SD16—41no—
265SD16—441no—
266M16—441no—
267C2×C8—41no—
268C2×C8—111no—
269C2×C8—111no—
270C2×C8C22×D1111yescharacteristic
271C2×C8C22×D1111yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—111no—
274C4⋊C4—111no—
275C4⋊C4—111no—
276C4⋊C4—221no—
277C4⋊C4—221no—
278C4⋊C4—221no—
279C4⋊C4—221no—
280C4⋊C4—221no—
281C4⋊C4—221no—
282C4⋊C4C22×D1111yescharacteristic
283C4⋊C4C22×D1111yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—111no—
287C22⋊C4—111no—
288C22⋊C4—221no—
289C22⋊C4—221no—
290C22⋊C4—221no—
291C42—111no—
292C42—221no—
293C42—221no—
294C42—221no—
295C11#331711yescharacteristic, complemented, Sylow
296C23—21no—
297C23—111no—
298C23—221no—
299C23D4×D1111yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—112no—
303Q8—221no—
304D4—21no—
305D4—21no—
306D4—81no—
307D4—221no—
308D4—221no—
309D4—441no—
310D4—442no—
311D4—442no—
312D4—442no—
313D4—881no—
314D4—881no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—111no—
321C2×C4—111no—
322C2×C4—111no—
323C2×C4—221no—
324C2×C4—221no—
325C2×C4—221no—
326C2×C4—221no—
327C2×C4—221no—
328C2×C4—442no—
329C2×C4—442no—
330C2×C4—442no—
331C2×C4D4×D1111yescharacteristic
332C2×C4C23×D1111yescharacteristic
333C8—21no—
334C8—21no—
335C8—221no—
336C8—221no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—221no—
344C22—221no—
345C22—221no—
346C22—441no—
347C22—441no—
348C22—441no—
349C22C2×D4×D1111yescharacteristic
350C4—21no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4—221no—
355C4—221no—
356C4—221no—
357C4—222no—
358C4—441no—
359C4—441no—
360C4#6703711yescharacteristic
361C4#41×D1111yescharacteristic
362C2—41no—
363C2—81no—
364C2—441no—
365C2—881no—
366C2#1062314111yescharacteristic
367C2#1062329311yescharacteristic
368C2#1062329911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#465C2
socleC22×C11C22×D4
prime radical#10623130C2
hypercenter#465D11
hypocenterC11#3317
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #10623170C2semidirect
3. C11×#465C2semidirect
4. #10622786C2semidirect
5. #10622776C2semidirect
6. #10622726C2semidirect
7. #10622724C2semidirect
8. #10622660C2semidirect
9. #10622648C2semidirect
10. #10622476C2semidirect
11. #10622470C2semidirect
12. #10622425C2semidirect
13. #10622402C2semidirect
14. #10622384C2semidirect
15. #10622377C2semidirect
160. #465D11semidirect
295. C11#3317semidirect

Maximal subgroups

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

subgroupindex
#106231702
#106231302
C11×#4652
#106227862
#106227762
#106227262
#106227242
#106226602
#106226482
#106224762
#106224702
#106224252
#106224022
#106223842
#106223772
#331711