Finite Group Databasebeta

← #13079331

Subgroups — #13079331

Order 1408.

402 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#10623109C211yesmaximal, characteristic, complemented
2#10623079C211yesmaximal, characteristic
3C11×#440C211yesmaximal, characteristic, complemented
4#10622788C211yesmaximal, characteristic, complemented
5#10622787C211yesmaximal, characteristic, complemented
6#10622639C211yesmaximal, characteristic, complemented
7#10622631C211yesmaximal, characteristic, complemented
8#10622499C211yesmaximal, characteristic, complemented
9#10622487C211yesmaximal, characteristic, complemented
10#10622425C211yesmaximal, characteristic, complemented
11#10622405C211yesmaximal, characteristic, complemented
12#10622393C211yesmaximal, characteristic, complemented
13#10622373C211yesmaximal, characteristic, complemented
14#10622323C211yesmaximal, characteristic, complemented
15#10622320C211yesmaximal, characteristic, complemented
16C2×#4339—21no—
17C2×C11×SD16C2211yescharacteristic
18C4×Q8×C11C2211yescharacteristic
19C4×D4×C11C2211yescharacteristic
20#66999C2211yescharacteristic
21#66997C2211yescharacteristic
22C2×#4325C2211yescharacteristic
23#66993C2211yescharacteristic
24#66991C2211yescharacteristic
25C2×#4324C2211yescharacteristic
26C4×C22⋊D11—21no—
27C2×#4314C2211yescharacteristic
28C2×#4313C2211yescharacteristic
29C2×#4313C2211yescharacteristic
30#66950C2211yescharacteristic
31#66949—21no—
32#66948C2211yescharacteristic
33#66942—21no—
34#66941C2211yescharacteristic
35#66941C2211yescharacteristic
36#66938—21no—
37#66937—21no—
38C4×D44C2211yescharacteristic
39#66925—21no—
40C42×D11C2211yescharacteristic
41C4×Dic22—21no—
42C4×Dic22C2211yescharacteristic
43C11×#107C2211yescharacteristic
44C11×#103C2211yescharacteristic
45C11×#102C2211yescharacteristic
46C11×#97C2211yescharacteristic
47#66899C2211yescharacteristic
48#66896C2211yescharacteristic
49#66885C2211yescharacteristic
50#66882C2211yescharacteristic
51#66880C2211yescharacteristic
52C8×Dic11C2211yescharacteristic
53C8×Dic11C2211yescharacteristic
54#66874C2211yescharacteristic
55#66873C2211yescharacteristic
56#66871C2211yescharacteristic
57#66871C2211yescharacteristic
58#66867C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×D4×C11C2311yescharacteristic
61C22×C4×C11—21no—
62C2×C22⋊D11—21no—
63C2×C22⋊D11—21no—
64C2×C22⋊D11—21no—
65#4339—44no—
66C2×D44—21no—
67C2×D44C2311yescharacteristic
68C2×C4×D11—21no—
69C2×C4×D11D411yescharacteristic
70C2×C4×D11D411yescharacteristic
71C2×C4×D11C2311yescharacteristic
72C2×Dic22—21no—
73C2×Dic22—21no—
74C2×Dic22C2311yescharacteristic
75C11×SD16—22no—
76C2×C8×C11C2311yescharacteristic
77C2×C8×C11C2311yescharacteristic
78C11×C4⋊C4—21no—
79C11×C4⋊C4C2311yescharacteristic
80C11×C4⋊C4C2311yescharacteristic
81C11×C22⋊C4—21no—
82C42×C11—21no—
83C42×C11C2311yescharacteristic
84C22⋊Dic11—21no—
85#4325—22no—
86#4324—22no—
87(C2×D11)⋊C4—21no—
88(C2×D11)⋊C4—21no—
89(C2×D11)⋊C4—21no—
90(C2×D11)⋊C4—21no—
91C4⋊Dic11—21no—
92C4⋊Dic11C2311yescharacteristic
93C4⋊Dic11C2311yescharacteristic
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99Dic11⋊C4—21no—
100C4×Dic11—21no—
101C4×Dic11D411yescharacteristic
102C4×Dic11D411yescharacteristic
103C4×Dic11C2311yescharacteristic
104C2×C11⋊C8C2311yescharacteristic
105C2×C11⋊C8C2311yescharacteristic
106#4314—22no—
107#4313—22no—
108#4313—22no—
109#3182—111nomaximal, Sylow
110C23×C11—21no—
111C22×D11—21no—
112C22×D11C2×D411yescharacteristic
113Q8×C11—21no—
114Q8×C11—21no—
115D4×C11—21no—
116D4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—42no—
121C2×C4×C11C2×D411yescharacteristic
122C2×C4×C11C2×D411yescharacteristic
123C2×C4×C11C2411yescharacteristic
124C22⋊D11—42no—
125C22⋊D11—42no—
126C22⋊D11—42no—
127C2×Dic11—21no—
128C2×Dic11—21no—
129C2×Dic11—21no—
130C2×Dic11C2×D411yescharacteristic
131C2×Dic11C2×D411yescharacteristic
132C2×Dic11C2×D411yescharacteristic
133D44—21no—
134D44—21no—
135D44—42no—
136C4×D11—21no—
137C4×D11—21no—
138C4×D11—22no—
139C4×D11—22no—
140C4×D11—42no—
141Dic22—21no—
142Dic22—21no—
143Dic22—42no—
144Dic22—42no—
145C8×C11—21no—
146C8×C11#4112yescomplemented
147C11⋊C8—21no—
148C11⋊C8#4112yescomplemented
149#533—111no—
150#532—111no—
151#500—111no—
152#492—111no—
153#487—111no—
154#486—111no—
155#468—111no—
156#468—111no—
157#468—111no—
158#468—111no—
159#440—111no—
160#440—111no—
161#440—111no—
162#440D1111yescharacteristic, complemented
163C4×M16—111no—
164C22×C11—41no—
165C22×C11—41no—
166C22×C11—41no—
167C22×C11C22×D411yescharacteristic
168C2×D11—21no—
169C2×D11—21no—
170C2×D11—21no—
171C2×D11—41no—
172C2×D11—41no—
173C2×D11—41no—
174C4×C11—21no—
175C4×C11—21no—
176C4×C11—41no—
177C4×C11—41no—
178C4×C11—41no—
179C4×C11C2×#4111yescharacteristic
180C4×C11C2×#4111yescharacteristic
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×M16—111no—
194C4⋊Q8—111no—
195C4⋊Q8—111no—
196C4⋊Q8—111no—
197#127—111no—
198#125—221no—
199#124—221no—
200C22⋊Q8—111no—
201C22⋊Q8—111no—
202C22⋊Q8—221no—
203#121—111no—
204#121—111no—
205#121—221no—
206C4×Q8—111no—
207C4×Q8—221no—
208C4×Q8C2×D1111yescharacteristic
209C4×D4—111no—
210C4×D4—221no—
211C4×D4C2×D1111yescharacteristic
212#117—221no—
213C2×C42—111no—
214#107—111no—
215#107—111no—
216#107—111no—
217#107C2×D1111yescharacteristic
218#103—111no—
219#103—111no—
220#103—111no—
221#103C2×D1111yescharacteristic
222#102—111no—
223#102—111no—
224#102—111no—
225#102C2×D1111yescharacteristic
226#97—111no—
227#97C2×D1111yescharacteristic
228C4×C8—111no—
229C4×C8—111no—
230C2×C11—81no—
231C2×C11#53211yescharacteristic
232C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
233C2×C11C2×#13711yescharacteristic
234D11—41no—
235D11—81no—
236#41—444no—
237C2×Q8—111no—
238C2×Q8—221no—
239C2×Q8—221no—
240C2×Q8C22×D1111yescharacteristic
241C2×D4—111no—
242C2×D4—221no—
243C2×D4—221no—
244C2×D4—221no—
245C2×D4—221no—
246C2×D4C22×D1111yescharacteristic
247C22×C4—21no—
248C22×C4—111no—
249C22×C4—111no—
250C22×C4—111no—
251C22×C4—221no—
252SD16—22no—
253SD16—222no—
254SD16—222no—
255SD16—222no—
256M16—222no—
257M16—222no—
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—221no—
276C22⋊C4—221no—
277C22⋊C4—221no—
278C22⋊C4—221no—
279C22⋊C4—221no—
280C42—21no—
281C42—111no—
282C42—111no—
283C42—111no—
284C42—221no—
285C42C22×D1111yescharacteristic
286C11#318211yescharacteristic, complemented, Sylow
287C23—21no—
288C23—111no—
289C23—221no—
290Q8—21no—
291Q8—21no—
292Q8—221no—
293Q8—221no—
294Q8—442no—
295Q8—442no—
296D4—21no—
297D4—21no—
298D4—221no—
299D4—221no—
300D4—442no—
301D4—442no—
302D4—442no—
303D4—442no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—42no—
308C2×C4—111no—
309C2×C4—111no—
310C2×C4—111no—
311C2×C4—222no—
312C2×C4—222no—
313C2×C4—221no—
314C2×C4—221no—
315C2×C4—221no—
316C2×C4—221no—
317C2×C4—221no—
318C2×C4—442no—
319C2×C4D4×D1111yescharacteristic
320C2×C4D4×D1111yescharacteristic
321C2×C4C23×D1111yescharacteristic
322C8—21no—
323C8—112no—
324C8—221no—
325C8#433912yescomplemented
326C22—41no—
327C22—41no—
328C22—41no—
329C22—221no—
330C22—221no—
331C22—221no—
332C22—441no—
333C22—441no—
334C22—441no—
335C22C2×D4×D1111yescharacteristic
336C4—21no—
337C4—21no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—112no—
342C4—112no—
343C4—221no—
344C4—441no—
345C4—441no—
346C4—441no—
347C4C2×#433911yescharacteristic
348C4#41×D1111yescharacteristic
349C2—81no—
350C2—441no—
351C2—881no—
352C2#1062307911yescharacteristic
353C2D11×AGL(1,ℤ/8)11yescharacteristic
354C2D11×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#440C2
socleC22×C11C22×D4
prime radical#10623079C2
hypercenter#440D11
hypocenterC11#3182
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #10623109C2semidirect
3. C11×#440C2semidirect
4. #10622788C2semidirect
5. #10622787C2semidirect
6. #10622639C2semidirect
7. #10622631C2semidirect
8. #10622499C2semidirect
9. #10622487C2semidirect
10. #10622425C2semidirect
11. #10622405C2semidirect
12. #10622393C2semidirect
13. #10622373C2semidirect
14. #10622323C2semidirect
15. #10622320C2semidirect
146. C8×C11#41semidirect
148. C11⋊C8#41semidirect
162. #440D11semidirect
286. C11#3182semidirect
325. C8#4339semidirect

Maximal subgroups

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

subgroupindex
#106231092
#106230792
C11×#4402
#106227882
#106227872
#106226392
#106226312
#106224992
#106224872
#106224252
#106224052
#106223932
#106223732
#106223232
#106223202
#318211