Finite Group Databasebeta

← #13080878

Subgroups — #13080878

Order 1408.

380 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#552C211yesmaximal, characteristic, complemented
2#10623083C211yesmaximal, characteristic
3#10622681C211yesmaximal, characteristic, complemented
4#10622676C211yesmaximal, characteristic, complemented
5#10622665C211yesmaximal, characteristic, complemented
6#10622663C211yesmaximal, characteristic, complemented
7#10622662C211yesmaximal, characteristic, complemented
8#10622660C211yesmaximal, characteristic, complemented
9C4×#4326C211yesmaximal, characteristic, complemented
10#10622641C211yesmaximal, characteristic, complemented
11#10622625C211yesmaximal, characteristic, complemented
12#10622617C211yesmaximal, characteristic, complemented
13#10622616C211yesmaximal, characteristic, complemented
14#10622583C211yesmaximal, characteristic, complemented
15#10622579C211yesmaximal, characteristic, complemented
16C2×#4339C2211yescharacteristic
17C22×Dic22C2211yescharacteristic
18C11×#126—21no—
19C11×#125—21no—
20C11×#125C2211yescharacteristic
21C11×#123—21no—
22C11×C22⋊Q8C2211yescharacteristic
23C11×C22⋊Q8C2211yescharacteristic
24C4×Q8×C11C2211yescharacteristic
25C4×D4×C11C2211yescharacteristic
26C11×#117—21no—
27C11×#117C2211yescharacteristic
28C2×C11×C4⋊C4C2211yescharacteristic
29C2×#4326C2211yescharacteristic
30C2×#4326C2211yescharacteristic
31C2×#4325C2211yescharacteristic
32#66992—21no—
33#66983C2211yescharacteristic
34#66977C2211yescharacteristic
35C2×#4318C2211yescharacteristic
36C2×#4318C2211yescharacteristic
37#66949—21no—
38#66938—21no—
39(C22⋊D11)⋊C4—21no—
40#66928C2211yescharacteristic
41C4×Dic22C2211yescharacteristic
42#66899C2211yescharacteristic
43C22⋊(C11⋊C8)C2211yescharacteristic
44C22⋊(C11⋊C8)C2211yescharacteristic
45#66874C2211yescharacteristic
46#66874C2211yescharacteristic
47#66874C2211yescharacteristic
48#66874C2211yescharacteristic
49#66874C2211yescharacteristic
50#66874C2211yescharacteristic
51#66873C2211yescharacteristic
52#66873C2211yescharacteristic
53#66873C2211yescharacteristic
54#66872C2211yescharacteristic
55#66871C2211yescharacteristic
56#66871C2211yescharacteristic
57C4⋊(C11⋊C8)C2211yescharacteristic
58C4×C11⋊C8C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×D4×C11D411yescharacteristic
61C22×C4×C11—21no—
62C22×C4×C11C2311yescharacteristic
63C22×C4×C11C2311yescharacteristic
64C2×C22⋊D11—21no—
65C2×C22⋊D11—21no—
66C22×Dic11—21no—
67#4339—22no—
68#4339—41no—
69C2×D44C2311yescharacteristic
70C2×C4×D11—21no—
71C2×Dic22—22no—
72C2×Dic22—21no—
73C2×Dic22—41no—
74C2×Dic22C2311yescharacteristic
75C2×Dic22C2311yescharacteristic
76C11×C4⋊C4—21no—
77C11×C4⋊C4—21no—
78C11×C4⋊C4—21no—
79C11×C4⋊C4—21no—
80C11×C4⋊C4—21no—
81C11×C4⋊C4—21no—
82C11×C4⋊C4D411yescharacteristic
83C11×C4⋊C4C2311yescharacteristic
84C11×C4⋊C4C2311yescharacteristic
85C11×C4⋊C4C2311yescharacteristic
86C11×C22⋊C4—21no—
87C11×C22⋊C4—21no—
88C11×C22⋊C4—21no—
89C11×C22⋊C4D411yescharacteristic
90C11×C22⋊C4D411yescharacteristic
91C42×C11—21no—
92C42×C11—21no—
93C42×C11C2311yescharacteristic
94C22⋊Dic11—21no—
95#4326—22no—
96#4326—41no—
97#4325—41no—
98(C2×D11)⋊C4—21no—
99(C2×D11)⋊C4—21no—
100(C2×D11)⋊C4—21no—
101C4⋊Dic11C2311yescharacteristic
102Dic11⋊C4—21no—
103Dic11⋊C4—21no—
104C4×Dic11—21no—
105#4318—41no—
106#4318—41no—
107C2×C11⋊C8C2311yescharacteristic
108C2×C11⋊C8C2311yescharacteristic
109C2×C11⋊C8C2311yescharacteristic
110C2×C11⋊C8C2311yescharacteristic
111#3327—111nomaximal, Sylow
112C23×C11C2×D411yescharacteristic
113C23×C11C2×D411yescharacteristic
114C22×D11—21no—
115Q8×C11—21no—
116Q8×C11—21no—
117D4×C11—41no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—42no—
127C2×C4×C11C2×D411yescharacteristic
128C2×C4×C11C2×D411yescharacteristic
129C2×C4×C11C2×D411yescharacteristic
130C2×C4×C11C2×D411yescharacteristic
131C2×C4×C11C2411yescharacteristic
132C22⋊D11—42no—
133C22⋊D11—42no—
134C2×Dic11—21no—
135C2×Dic11—21no—
136C2×Dic11—21no—
137C2×Dic11—42no—
138D44—21no—
139D44—21no—
140C4×D11—42no—
141Dic22—21no—
142Dic22—21no—
143Dic22—21no—
144Dic22—42no—
145Dic22#4112yes—
146C11⋊C8—21no—
147C11⋊C8—21no—
148C11⋊C8—21no—
149C11⋊C8—21no—
150#552D1111yescharacteristic, complemented
151#548—111no—
152#488—111no—
153#484—111no—
154#482—111no—
155#479—111no—
156#470—111no—
157#468—111no—
158#464—111no—
159#452—111no—
160#451—111no—
161C4×Q16—111no—
162#436—111no—
163#419—111no—
164#417—111no—
165C22×C11—21no—
166C22×C11—21no—
167C22×C11—21no—
168C22×C11—21no—
169C22×C11—21no—
170C22×C11—21no—
171C22×C11C22×D411yescharacteristic
172C2×D11—41no—
173C2×D11—41no—
174C2×D11—41no—
175C4×C11—21no—
176C4×C11—21no—
177C4×C11—21no—
178C4×C11—21no—
179C4×C11—41no—
180C4×C11—41no—
181C4×C11—41no—
182C4×C11—41no—
183C4×C11C2×#4111yescharacteristic
184C4×C11H(5,𝔽2)11yescharacteristic
185Dic11—22no—
186Dic11—41no—
187Dic11—41no—
188C2×#41—111no—
189C22×Q8—111no—
190C2×Q16—111no—
191C2×Q16—111no—
192C2×SD16—111no—
193C2×M16—111no—
194C2×M16—111no—
195#126—21no—
196#125—21no—
197#125C2×D1111yescharacteristic
198#124—111no—
199#124—221no—
200#123—21no—
201C22⋊Q8—111no—
202C22⋊Q8—221no—
203C22⋊Q8C2×D1111yescharacteristic
204C22⋊Q8C2×D1111yescharacteristic
205#121—111no—
206#121—221no—
207C4×Q8—111no—
208C4×Q8C2×D1111yescharacteristic
209C4×D4—221no—
210C4×D4C2×D1111yescharacteristic
211#117—21no—
212#117C2×D1111yescharacteristic
213C2×C4⋊C4C2×D1111yescharacteristic
214#107—111no—
215#107—111no—
216#106—111no—
217C4⋊C8—111no—
218#103—111no—
219#103—111no—
220#103—111no—
221#103—111no—
222#103—111no—
223#103—111no—
224#103—111no—
225#102—111no—
226#102—111no—
227#102—111no—
228C22⋊C8—111no—
229C22⋊C8—111no—
230C4×C8—111no—
231C2×C11—41no—
232C2×C11—41no—
233C2×C11#54611yescharacteristic
234C2×C11#57511yescharacteristic
235C2×C11#57811yescharacteristic
236D11—81no—
237#41—222no—
238#41—441no—
239C2×Q8—111no—
240C2×Q8—111no—
241C2×Q8—222no—
242C2×Q8—221no—
243C2×Q8—441no—
244C2×Q8C22×D1111yescharacteristic
245C2×D4—111no—
246C2×D4—221no—
247C2×D4—221no—
248C2×D4C22⋊D1111yescharacteristic
249C22×C4—21no—
250C22×C4—221no—
251C22×C4—221no—
252C22×C4C22×D1111yescharacteristic
253C22×C4C22×D1111yescharacteristic
254Q16—222no—
255Q16—441no—
256SD16—441no—
257M16—441no—
258M16—441no—
259C2×C8—111no—
260C2×C8—111no—
261C2×C8—111no—
262C2×C8—111no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—111no—
270C4⋊C4—221no—
271C4⋊C4—221no—
272C4⋊C4C22⋊D1111yescharacteristic
273C4⋊C4C22×D1111yescharacteristic
274C4⋊C4C22×D1111yescharacteristic
275C4⋊C4C22×D1111yescharacteristic
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—221no—
280C22⋊C4—221no—
281C22⋊C4—221no—
282C22⋊C4—221no—
283C22⋊C4C22⋊D1111yescharacteristic
284C22⋊C4C22⋊D1111yescharacteristic
285C42—21no—
286C42—21no—
287C42—221no—
288C42C22×D1111yescharacteristic
289C11#332711yescharacteristic, complemented, Sylow
290C23—221no—
291C23C2×C22⋊D1111yescharacteristic
292C23C2×C22⋊D1111yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—112no—
296Q8—221no—
297Q8—221no—
298Q8—221no—
299Q8—442no—
300D4—41no—
301D4—221no—
302D4—221no—
303D4—442no—
304D4—442no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—42no—
314C2×C4—221no—
315C2×C4—221no—
316C2×C4—221no—
317C2×C4—442no—
318C2×C4—442no—
319C2×C4C2×C22⋊D1111yescharacteristic
320C2×C4C2×C22⋊D1111yescharacteristic
321C2×C4C2×C22⋊D1111yescharacteristic
322C2×C4C2×C22⋊D1111yescharacteristic
323C2×C4C23×D1111yescharacteristic
324C8—221no—
325C8—221no—
326C8—221no—
327C8—221no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—441no—
335C22—441no—
336C22—441no—
337C22C22×C22⋊D1111yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—222no—
347C4—441no—
348C4—441no—
349C4#41×D1111yescharacteristic
350C4#6704211yescharacteristic
351C2—41no—
352C2—41no—
353C2—881no—
354C2#1062335311yescharacteristic
355C2#1062336011yescharacteristic
356C2#1062336911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#552C2
socleC22×C11C22×D4
prime radical#10623083C2
hypercenter#552D11
hypocenterC11#3327
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ #552

Complements

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

NH ≅ G/Ntype
1. C11×#552C2semidirect
3. #10622681C2semidirect
4. #10622676C2semidirect
5. #10622665C2semidirect
6. #10622663C2semidirect
7. #10622662C2semidirect
8. #10622660C2semidirect
9. C4×#4326C2semidirect
10. #10622641C2semidirect
11. #10622625C2semidirect
12. #10622617C2semidirect
13. #10622616C2semidirect
14. #10622583C2semidirect
15. #10622579C2semidirect
150. #552D11semidirect
289. C11#3327semidirect

Maximal subgroups

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

subgroupindex
C11×#5522
#106230832
#106226812
#106226762
#106226652
#106226632
#106226622
#106226602
C4×#43262
#106226412
#106226252
#106226172
#106226162
#106225832
#106225792
#332711