Finite Group Databasebeta

← #13080746

Subgroups — #13080746

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#10623365C211yesmaximal, characteristic
2#10623170C211yesmaximal, characteristic, complemented
3C11×#452C211yesmaximal, characteristic, complemented
4#10622846C211yesmaximal, characteristic, complemented
5#10622800C211yesmaximal, characteristic, complemented
6#10622797C211yesmaximal, characteristic, complemented
7#10622787C211yesmaximal, characteristic, complemented
8#10622776C211yesmaximal, characteristic, complemented
9#10622661C211yesmaximal, characteristic, complemented
10#10622416C211yesmaximal, characteristic, complemented
11#10622409C211yesmaximal, characteristic, complemented
12#10622390C211yesmaximal, characteristic, complemented
13#10622377C211yesmaximal, characteristic, complemented
14#10622350C211yesmaximal, characteristic, complemented
15#10622343C211yesmaximal, characteristic, complemented
16C2×C11×#41C2211yescharacteristic
17C2×#4343C2211yescharacteristic
18C2×C11×Q16C2211yescharacteristic
19C2×C11×SD16C2211yescharacteristic
20C11×C22⋊Q8C2211yescharacteristic
21#66999C2211yescharacteristic
22Q8×Dic11C2211yescharacteristic
23Q8×Dic11C2211yescharacteristic
24C2×#4325C2211yescharacteristic
25#66993—21no—
26#66993C2211yescharacteristic
27#66991—21no—
28#66991C2211yescharacteristic
29#66983—21no—
30#66983C2211yescharacteristic
31C4×C22⋊D11—21no—
32C4×C22⋊D11C2211yescharacteristic
33#66979C2211yescharacteristic
34C22×C11⋊C8C2211yescharacteristic
35C2×#4313C2211yescharacteristic
36#66945—21no—
37C4⋊C4×D11C2211yescharacteristic
38#66943C2211yescharacteristic
39#66942—21no—
40#66936—21no—
41#66932—21no—
42C11×#103C2211yescharacteristic
43C11×#102C2211yescharacteristic
44C11×C22⋊C8C2211yescharacteristic
45#66899C2211yescharacteristic
46#66899C2211yescharacteristic
47#66899C2211yescharacteristic
48#66896C2211yescharacteristic
49#66896C2211yescharacteristic
50#66885C2211yescharacteristic
51#66885C2211yescharacteristic
52(C2×D11)⋊C8C2211yescharacteristic
53#66882C2211yescharacteristic
54#66881C2211yescharacteristic
55#66879C2211yescharacteristic
56Dic11⋊C8C2211yescharacteristic
57#66873C2211yescharacteristic
58#66872C2211yescharacteristic
59C11×#41—22no—
60C11×#41—41no—
61C2×Q8×C11C2311yescharacteristic
62C2×Q8×C11C2311yescharacteristic
63C2×D4×C11—21no—
64C2×D4×C11C2311yescharacteristic
65C22×C4×C11—21no—
66C22×C4×C11C2311yescharacteristic
67C2×C22⋊D11—21no—
68C2×C22⋊D11—21no—
69C2×C22⋊D11—21no—
70C2×C22⋊D11—21no—
71C2×C22⋊D11D411yescharacteristic
72#4343—22no—
73#4343—41no—
74C2×D44—21no—
75C2×D44C2311yescharacteristic
76C2×C4×D11—21no—
77C2×C4×D11—21no—
78C2×C4×D11C2311yescharacteristic
79C11×Q16—22no—
80C11×SD16—41no—
81C2×C8×C11C2311yescharacteristic
82C2×C8×C11C2311yescharacteristic
83C11×C4⋊C4—21no—
84C11×C4⋊C4C2311yescharacteristic
85C11×C22⋊C4—21no—
86C22⋊Dic11—21no—
87C22⋊Dic11—21no—
88C22⋊Dic11D411yescharacteristic
89#4325—41no—
90(C2×D11)⋊C4—21no—
91(C2×D11)⋊C4—21no—
92(C2×D11)⋊C4D411yescharacteristic
93C4⋊Dic11—21no—
94C4⋊Dic11—21no—
95C4⋊Dic11—21no—
96C4⋊Dic11C2311yescharacteristic
97C4⋊Dic11C2311yescharacteristic
98C4⋊Dic11C2311yescharacteristic
99Dic11⋊C4—21no—
100Dic11⋊C4—21no—
101Dic11⋊C4—21no—
102Dic11⋊C4D411yescharacteristic
103C4×Dic11—21no—
104C4×Dic11—21no—
105C4×Dic11—21no—
106C4×Dic11C2311yescharacteristic
107C2×C11⋊C8—41no—
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—
118Q8×C11—21no—
119Q8×C11#4112yes—
120D4×C11—21no—
121D4×C11—21no—
122D4×C11—42no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—42no—
129C2×C4×C11C2×D411yescharacteristic
130C2×C4×C11C2411yescharacteristic
131C22⋊D11—41no—
132C22⋊D11—42no—
133C22⋊D11—81no—
134C22⋊D11—81no—
135C22⋊D11—81no—
136C2×Dic11—21no—
137C2×Dic11—21no—
138C2×Dic11—21no—
139C2×Dic11C2×D411yescharacteristic
140C2×Dic11C2×D411yescharacteristic
141C2×Dic11C2×D411yescharacteristic
142D44—21no—
143D44—21no—
144D44—42no—
145C4×D11—21no—
146C4×D11—21no—
147C4×D11—42no—
148C4×D11—42no—
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#465—111no—
161#460—111no—
162#452—111no—
163#452D1111yescharacteristic, complemented
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—22no—
183C4×C11—41no—
184C4×C11—41no—
185C4×C11C2×#4111yescharacteristic
186C4×C11H(5,𝔽2)11yescharacteristic
187Dic11—21no—
188Dic11—21no—
189Dic11—21no—
190Dic11—41no—
191Dic11—41no—
192Dic11—41no—
193C2×#41—111no—
194C2×#41C2×D1111yescharacteristic
195C2×Q16C2×D1111yescharacteristic
196C2×SD16—111no—
197C2×SD16C2×D1111yescharacteristic
198C2×M16—111no—
199C22×C8—111no—
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—111no—
210#121—221no—
211#121—221no—
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#106—111no—
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⋊C8C2×D1111yescharacteristic
235#97—111no—
236C2×C11—41no—
237C2×C11—81no—
238C2×C11#54611yescharacteristic
239C2×C11#57511yescharacteristic
240C2×C11#57711yescharacteristic
241D11—41no—
242D11—81no—
243#41—22no—
244#41—41no—
245#41—222no—
246#41—441no—
247C2×Q8C22×D1111yescharacteristic
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—21no—
259C22×C4—111no—
260C22×C4—221no—
261C22×C4—221no—
262C22×C4C22×D1111yescharacteristic
263Q16—22no—
264SD16—41no—
265SD16—441no—
266M16—441no—
267C2×C8—111no—
268C2×C8—111no—
269C2×C8—441no—
270C2×C8C22×D1111yescharacteristic
271C2×C8C22×D1111yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—111no—
274C4⋊C4—111no—
275C4⋊C4—111no—
276C4⋊C4—111no—
277C4⋊C4—221no—
278C4⋊C4—221no—
279C4⋊C4—221no—
280C4⋊C4—221no—
281C4⋊C4—221no—
282C4⋊C4—221no—
283C4⋊C4C22×D1111yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—111no—
286C22⋊C4—111no—
287C22⋊C4—221no—
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—21no—
303Q8#434112yes—
304D4—21no—
305D4—21no—
306D4—42no—
307D4—221no—
308D4—221no—
309D4—442no—
310D4—441no—
311D4—442no—
312D4—881no—
313D4—881no—
314D4—881no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—42no—
321C2×C4—111no—
322C2×C4—111no—
323C2×C4—111no—
324C2×C4—221no—
325C2×C4—221no—
326C2×C4—221no—
327C2×C4—221no—
328C2×C4—221no—
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—22no—
352C4—41no—
353C4—41no—
354C4—221no—
355C4—221no—
356C4—221no—
357C4—441no—
358C4—441no—
359C4—441no—
360C4C2×#434111yescharacteristic
361C4#6703711yescharacteristic
362C2—41no—
363C2—81no—
364C2—441no—
365C2—881no—
366C2#1062312211yescharacteristic
367C2#1062329911yescharacteristic
368C2#1062330911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#452C2
socleC22×C11C22×D4
prime radical#10623365C2
hypercenter#452D11
hypocenterC11#3317
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
2. #10623170C2semidirect
3. C11×#452C2semidirect
4. #10622846C2semidirect
5. #10622800C2semidirect
6. #10622797C2semidirect
7. #10622787C2semidirect
8. #10622776C2semidirect
9. #10622661C2semidirect
10. #10622416C2semidirect
11. #10622409C2semidirect
12. #10622390C2semidirect
13. #10622377C2semidirect
14. #10622350C2semidirect
15. #10622343C2semidirect
163. #452D11semidirect
295. C11#3317semidirect

Maximal subgroups

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

subgroupindex
#106233652
#106231702
C11×#4522
#106228462
#106228002
#106227972
#106227872
#106227762
#106226612
#106224162
#106224092
#106223902
#106223772
#106223502
#106223432
#331711