Finite Group Databasebeta

← #13079998

Subgroups — #13079998

Order 1408.

386 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623153C211yesmaximal, characteristic, complemented
2#10623127C211yesmaximal, characteristic
3C11×#468C211yesmaximal, characteristic, complemented
4#10622776C211yesmaximal, characteristic, complemented
5#10622775C211yesmaximal, characteristic, complemented
6#10622747C211yesmaximal, characteristic, complemented
7#10622731C211yesmaximal, characteristic, complemented
8#10622662C211yesmaximal, characteristic, complemented
9#10622655C211yesmaximal, characteristic, complemented
10#10622503C211yesmaximal, characteristic, complemented
11#10622488C211yesmaximal, characteristic, complemented
12#10622431C211yesmaximal, characteristic, complemented
13#10622407C211yesmaximal, characteristic, complemented
14#10622375C211yesmaximal, characteristic, complemented
15#10622372C211yesmaximal, characteristic, complemented
16C2×#4341—21no—
17C2×C11×SD16C2211yescharacteristic
18C2×C11×M16C2211yescharacteristic
19C11×C22⋊Q8C2211yescharacteristic
20C11×#121C2211yescharacteristic
21Q8×Dic11C2211yescharacteristic
22#66997C2211yescharacteristic
23C2×#4325C2211yescharacteristic
24#66993C2211yescharacteristic
25#66992—21no—
26D4×Dic11C2211yescharacteristic
27C2×#4324C2211yescharacteristic
28#66983C2211yescharacteristic
29#66977C2211yescharacteristic
30C2×C4×Dic11C2211yescharacteristic
31C2×#4318C2211yescharacteristic
32C2×#4314C2211yescharacteristic
33#66946C2211yescharacteristic
34#66942—21no—
35#66941C2211yescharacteristic
36#66941C2211yescharacteristic
37#66940—21no—
38#66940C2211yescharacteristic
39#66938—21no—
40(C22⋊D11)⋊C4—21no—
41#66931—21no—
42#66930—21no—
43C11×#107C2211yescharacteristic
44C11×#103C2211yescharacteristic
45C11×#102C2211yescharacteristic
46#66899C2211yescharacteristic
47#66896C2211yescharacteristic
48#66885C2211yescharacteristic
49#66882C2211yescharacteristic
50#66880C2211yescharacteristic
51Dic11⋊C8C2211yescharacteristic
52Dic11⋊C8C2211yescharacteristic
53Dic11⋊C8C2211yescharacteristic
54Dic11⋊C8C2211yescharacteristic
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—
66C22×Dic11—21no—
67C22×Dic11D411yescharacteristic
68C22×Dic11D411yescharacteristic
69#4341—44no—
70C2×D44C2311yescharacteristic
71C2×C4×D11—21no—
72C2×Dic22—21no—
73C2×Dic22—21no—
74C2×Dic22C2311yescharacteristic
75C11×SD16—41no—
76C11×M16—41no—
77C2×C8×C11C2311yescharacteristic
78C2×C8×C11C2311yescharacteristic
79C11×C4⋊C4—21no—
80C11×C4⋊C4C2311yescharacteristic
81C11×C4⋊C4C2311yescharacteristic
82C11×C22⋊C4—21no—
83C11×C22⋊C4—21no—
84C22⋊Dic11—21no—
85C22⋊Dic11—21no—
86#4325—41no—
87#4324—41no—
88(C2×D11)⋊C4—21no—
89(C2×D11)⋊C4—21no—
90C4⋊Dic11—21no—
91C4⋊Dic11C2311yescharacteristic
92C4⋊Dic11C2311yescharacteristic
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99C4×Dic11—21no—
100C4×Dic11—21no—
101C4×Dic11D411yescharacteristic
102C4×Dic11D411yescharacteristic
103C4×Dic11C2311yescharacteristic
104C4×Dic11C2311yescharacteristic
105#4318—41no—
106C2×C11⋊C8C2311yescharacteristic
107C2×C11⋊C8C2311yescharacteristic
108#4314—41no—
109#3254—111nomaximal, Sylow
110C23×C11—21no—
111C23×C11C2×D411yescharacteristic
112C22×D11—21no—
113Q8×C11—21no—
114Q8×C11—21no—
115D4×C11—21no—
116D4×C11—21no—
117D4×C11—42no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11C2×D411yescharacteristic
124C2×C4×C11C2411yescharacteristic
125C22⋊D11—42no—
126C22⋊D11—42no—
127C22⋊D11—42no—
128C2×Dic11—22no—
129C2×Dic11—22no—
130C2×Dic11—21no—
131C2×Dic11—21no—
132C2×Dic11—21no—
133C2×Dic11—42no—
134C2×Dic11C2×D411yescharacteristic
135C2×Dic11C2×D411yescharacteristic
136C2×Dic11C2×D411yescharacteristic
137C2×Dic11C2×D411yescharacteristic
138D44—21no—
139D44—21no—
140C4×D11—42no—
141Dic22—21no—
142Dic22—21no—
143Dic22—42no—
144Dic22—42no—
145C8×C11—21no—
146C8×C11—21no—
147C11⋊C8—21no—
148C11⋊C8—21no—
149#533—111no—
150#532—111no—
151#477—111no—
152#477—111no—
153#474—111no—
154#474—111no—
155#468—111no—
156#468—111no—
157#468—111no—
158#468D1111yescharacteristic, complemented
159#461—111no—
160#461—111no—
161#460—111no—
162#460—111no—
163#423—111no—
164C22×C11—21no—
165C22×C11—21no—
166C22×C11—21no—
167C22×C11—41no—
168C22×C11—41no—
169C22×C11—41no—
170C22×C11C22×D411yescharacteristic
171C2×D11—41no—
172C2×D11—41no—
173C2×D11—41no—
174C4×C11—21no—
175C4×C11—41no—
176C4×C11—41no—
177C4×C11—41no—
178C4×C11H(5,𝔽2)11yescharacteristic
179C4×C112−1+411yescharacteristic
180Dic11—21no—
181Dic11—21no—
182Dic11—41no—
183Dic11—41no—
184Dic11—41no—
185Dic11AGL(1,ℤ/8)12yes—
186Dic11#13712yes—
187C2×#41—221no—
188C2×SD16—111no—
189C2×SD16—111no—
190C2×SD16—111no—
191C2×SD16C2×D1111yescharacteristic
192C2×M16—111no—
193C2×M16C2×D1111yescharacteristic
194C4⋊Q8—111no—
195C4⋊Q8—111no—
196C4⋊Q8—111no—
197#127—111no—
198#125—221no—
199#124—221no—
200C22⋊Q8—111no—
201C22⋊Q8—221no—
202C22⋊Q8C2×D1111yescharacteristic
203#121—111no—
204#121—221no—
205#121C2×D1111yescharacteristic
206C4×Q8—111no—
207C4×Q8—111no—
208C4×Q8—221no—
209C4×D4—111no—
210C4×D4—111no—
211C4×D4—221no—
212#117—221no—
213C2×C42—111no—
214#107—111no—
215#107—111no—
216#107—111no—
217#107C2×D1111yescharacteristic
218C4⋊C8—111no—
219C4⋊C8—111no—
220C4⋊C8—111no—
221C4⋊C8—111no—
222#103—111no—
223#103—111no—
224#103—111no—
225#103C2×D1111yescharacteristic
226#102—111no—
227#102—111no—
228#102—111no—
229#102C2×D1111yescharacteristic
230C2×C11—41no—
231C2×C11—81no—
232C2×C11#53711yescharacteristic
233C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
234C2×C11C2×#13711yescharacteristic
235D11—81no—
236#41—444no—
237C2×Q8—111no—
238C2×Q8—221no—
239C2×Q8—221no—
240C2×Q8C22×D1111yescharacteristic
241C2×D4—21no—
242C2×D4—111no—
243C2×D4—221no—
244C2×D4—221no—
245C2×D4—221no—
246C2×D4C22×D1111yescharacteristic
247C22×C4—111no—
248C22×C4—111no—
249C22×C4—221no—
250C22×C4—221no—
251C22×C4C22×D1111yescharacteristic
252SD16—41no—
253SD16—441no—
254SD16—441no—
255SD16—441no—
256M16—41no—
257M16—441no—
258C2×C8—111no—
259C2×C8—111no—
260C2×C8C22×D1111yescharacteristic
261C2×C8C22×D1111yescharacteristic
262C4⋊C4—21no—
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⋊C4C22×D1111yescharacteristic
273C4⋊C4C22×D1111yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—221no—
277C22⋊C4—221no—
278C22⋊C4—221no—
279C22⋊C4—221no—
280C42—111no—
281C42—111no—
282C42—111no—
283C42—111no—
284C42—221no—
285C42—221no—
286C11#325411yescharacteristic, complemented, Sylow
287C23—21no—
288C23—221no—
289C23D4×D1111yescharacteristic
290Q8—21no—
291Q8—21no—
292Q8—221no—
293Q8—221no—
294Q8—442no—
295Q8—442no—
296D4—21no—
297D4—21no—
298D4—42no—
299D4—221no—
300D4—221no—
301D4—442no—
302D4—442no—
303D4—442no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—111no—
310C2×C4—111no—
311C2×C4—111no—
312C2×C4—111no—
313C2×C4—222no—
314C2×C4—222no—
315C2×C4—221no—
316C2×C4—221no—
317C2×C4—221no—
318C2×C4—442no—
319C2×C4—442no—
320C2×C4D4×D1111yescharacteristic
321C2×C4C23×D1111yescharacteristic
322C8—21no—
323C8—21no—
324C8—221no—
325C8—221no—
326C22—21no—
327C22—21no—
328C22—21no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—441no—
333C22—441no—
334C22—441no—
335C22C2×D4×D1111yescharacteristic
336C4—21no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—112no—
341C4—112no—
342C4—221no—
343C4—221no—
344C4—441no—
345C4—441no—
346C4—441no—
347C4#6703711yescharacteristic
348C4#6704311yescharacteristic
349C2—41no—
350C2—81no—
351C2—881no—
352C2#1062312811yescharacteristic
353C2D11×AGL(1,ℤ/8)11yescharacteristic
354C2D11×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#468C2
socleC22×C11C22×D4
prime radical#10623127C2
hypercenter#468D11
hypocenterC11#3254
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. #10623153C2semidirect
3. C11×#468C2semidirect
4. #10622776C2semidirect
5. #10622775C2semidirect
6. #10622747C2semidirect
7. #10622731C2semidirect
8. #10622662C2semidirect
9. #10622655C2semidirect
10. #10622503C2semidirect
11. #10622488C2semidirect
12. #10622431C2semidirect
13. #10622407C2semidirect
14. #10622375C2semidirect
15. #10622372C2semidirect
158. #468D11semidirect
286. C11#3254semidirect

Maximal subgroups

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

subgroupindex
#106231532
#106231272
C11×#4682
#106227762
#106227752
#106227472
#106227312
#106226622
#106226552
#106225032
#106224882
#106224312
#106224072
#106223752
#106223722
#325411