Finite Group Databasebeta

← #13078736

Subgroups — #13078736

Order 1408.

424 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×Q8×D11C211yesmaximal, characteristic, complemented
2#10623079C211yesmaximal, characteristic
3C11×#440C211yesmaximal, characteristic, complemented
4#10622783C211yesmaximal, characteristic, complemented
5#10622776C211yesmaximal, characteristic, complemented
6#10622639C211yesmaximal, characteristic, complemented
7#10622631C211yesmaximal, characteristic, complemented
8#10622495C211yesmaximal, characteristic, complemented
9#10622488C211yesmaximal, characteristic, complemented
10#10622419C211yesmaximal, characteristic, complemented
11#10622407C211yesmaximal, characteristic, complemented
12#10622387C211yesmaximal, characteristic, complemented
13#10622375C211yesmaximal, characteristic, complemented
14#10622323C211yesmaximal, characteristic, complemented
15#10622318C211yesmaximal, characteristic, complemented
16C2×Q8×D11C2211yescharacteristic
17C2×#4339—21no—
18C2×C11×SD16C2211yescharacteristic
19C4×Q8×C11C2211yescharacteristic
20C4×D4×C11C2211yescharacteristic
21Q8×Dic11C2211yescharacteristic
22C2×#4325C2211yescharacteristic
23#66993C2211yescharacteristic
24#66991C2211yescharacteristic
25C2×#4324C2211yescharacteristic
26C4×C22⋊D11—21no—
27C2×#4314C2211yescharacteristic
28#66948C2211yescharacteristic
29C4⋊C4×D11—21no—
30C4⋊C4×D11C2211yescharacteristic
31#66941C2211yescharacteristic
32#66940—21no—
33#66940C2211yescharacteristic
34#66938—21no—
35#66937—21no—
36C4×D44C2211yescharacteristic
37C42×D11—21no—
38C42×D11C2211yescharacteristic
39C4×Dic22—21no—
40C4×Dic22C2211yescharacteristic
41C11×#107C2211yescharacteristic
42C11×#103C2211yescharacteristic
43C11×#102C2211yescharacteristic
44C11×#97C2211yescharacteristic
45#66899C2211yescharacteristic
46#66896C2211yescharacteristic
47#66885C2211yescharacteristic
48(C2×D11)⋊C8C2211yescharacteristic
49(C2×D11)⋊C8C2211yescharacteristic
50#66882C2211yescharacteristic
51#66880C2211yescharacteristic
52Dic11⋊C8C2211yescharacteristic
53Dic11⋊C8C2211yescharacteristic
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—
65Q8×D11—22no—
66Q8×D11—22no—
67#4339—44no—
68C2×D44—21no—
69C2×D44C2311yescharacteristic
70C2×C4×D11—21no—
71C2×C4×D11—21no—
72C2×C4×D11—21no—
73C2×C4×D11D411yescharacteristic
74C2×C4×D11D411yescharacteristic
75C2×C4×D11C2311yescharacteristic
76C2×Dic22—21no—
77C2×Dic22—21no—
78C2×Dic22C2311yescharacteristic
79C11×SD16—22no—
80C2×C8×C11C2311yescharacteristic
81C2×C8×C11C2311yescharacteristic
82C11×C4⋊C4—21no—
83C11×C4⋊C4C2311yescharacteristic
84C11×C4⋊C4C2311yescharacteristic
85C11×C22⋊C4—21no—
86C42×C11—21no—
87C42×C11C2311yescharacteristic
88C22⋊Dic11—21no—
89#4325—22no—
90#4324—22no—
91(C2×D11)⋊C4—21no—
92(C2×D11)⋊C4—21no—
93C4⋊Dic11—21no—
94C4⋊Dic11C2311yescharacteristic
95C4⋊Dic11C2311yescharacteristic
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99Dic11⋊C4—21no—
100C4×Dic11—21no—
101C4×Dic11—21no—
102C4×Dic11—21no—
103C4×Dic11D411yescharacteristic
104C4×Dic11D411yescharacteristic
105C4×Dic11C2311yescharacteristic
106C2×C11⋊C8C2311yescharacteristic
107C2×C11⋊C8C2311yescharacteristic
108#4314—22no—
109#3112—111nomaximal, Sylow
110C23×C11—21no—
111C22×D11—21no—
112C22×D11C2×D411yescharacteristic
113Q8×C11—21no—
114Q8×C11#4112yescomplemented
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—24no—
137C4×D11—22no—
138C4×D11—21no—
139C4×D11—21no—
140C4×D11—22no—
141C4×D11—42no—
142C4×D11—42no—
143Dic22—24no—
144Dic22—21no—
145Dic22—42no—
146Dic22#4112yescomplemented
147C8×C11—21no—
148C8×C11—21no—
149C11⋊C8—21no—
150C11⋊C8—21no—
151#532—111no—
152C2×C4×Q8—111no—
153#480—111no—
154#480—111no—
155#477—111no—
156#477—111no—
157#460—111no—
158#460—111no—
159#448—111no—
160#448—111no—
161#440—111no—
162#440—111no—
163#440—111no—
164#440D1111yescharacteristic, complemented
165#432—111no—
166C22×C11—41no—
167C22×C11—41no—
168C22×C11—41no—
169C22×C11C22×D411yescharacteristic
170C2×D11—21no—
171C2×D11—21no—
172C2×D11—41no—
173C2×D11—41no—
174C2×D11—41no—
175C2×D11AGL(1,ℤ/8)12yes—
176C4×C11—22no—
177C4×C11—21no—
178C4×C11—21no—
179C4×C11—41no—
180C4×C11—41no—
181C4×C11C2×#4111yescharacteristic
182C4×C11C2×#4111yescharacteristic
183Dic11—21no—
184Dic11—22no—
185Dic11—21no—
186Dic11—41no—
187Dic11—41no—
188Dic11#13712yes—
189C2×#41—221no—
190C22×Q8—111no—
191C2×SD16—111no—
192C2×SD16—111no—
193C2×SD16—111no—
194C2×SD16C2×D1111yescharacteristic
195C4⋊Q8—111no—
196#127—111no—
197#124—221no—
198#121—111no—
199#121—111no—
200#121—221no—
201C4×Q8—111no—
202C4×Q8—111no—
203C4×Q8—111no—
204C4×Q8—221no—
205C4×Q8—221no—
206C4×Q8C2×D1111yescharacteristic
207C4×D4—111no—
208C4×D4—221no—
209C4×D4C2×D1111yescharacteristic
210C2×C4⋊C4—111no—
211C2×C4⋊C4—221no—
212C2×C42—111no—
213C2×C42—221no—
214#107—111no—
215#107—111no—
216#107—111no—
217#107C2×D1111yescharacteristic
218C4⋊C8—111no—
219C4⋊C8—111no—
220#103—111no—
221#103—111no—
222#103—111no—
223#103C2×D1111yescharacteristic
224#102—111no—
225#102—111no—
226#102—111no—
227#102C2×D1111yescharacteristic
228C22⋊C8—111no—
229C22⋊C8—111no—
230#97—111no—
231#97C2×D1111yescharacteristic
232C2×C11—81no—
233C2×C11#52511yescharacteristic
234C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
235C2×C11C2×#13711yescharacteristic
236D11—22no—
237D11—81no—
238#41—444no—
239C2×Q8—111no—
240C2×Q8—221no—
241C2×Q8—221no—
242C2×Q8—222no—
243C2×Q8—222no—
244C2×Q8C22×D1111yescharacteristic
245C2×D4—111no—
246C2×D4—221no—
247C2×D4—221no—
248C2×D4—221no—
249C2×D4—221no—
250C2×D4C22×D1111yescharacteristic
251C22×C4—21no—
252C22×C4—111no—
253C22×C4—111no—
254C22×C4—111no—
255C22×C4—221no—
256C22×C4—221no—
257C22×C4—221no—
258SD16—22no—
259SD16—222no—
260SD16—222no—
261SD16—222no—
262C2×C8—111no—
263C2×C8—111no—
264C2×C8C22×D1111yescharacteristic
265C2×C8C22×D1111yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—111no—
268C4⋊C4—111no—
269C4⋊C4—221no—
270C4⋊C4—221no—
271C4⋊C4—221no—
272C4⋊C4—221no—
273C4⋊C4—221no—
274C4⋊C4C22×D1111yescharacteristic
275C4⋊C4C22×D1111yescharacteristic
276C22⋊C4—21no—
277C22⋊C4—221no—
278C22⋊C4—221no—
279C22⋊C4—221no—
280C42—21no—
281C42—111no—
282C42—111no—
283C42—111no—
284C42—221no—
285C42—221no—
286C42—221no—
287C42C22×D1111yescharacteristic
288C11#311211yescharacteristic, complemented, Sylow
289C23—21no—
290C23—111no—
291C23—221no—
292Q8—21no—
293Q8—112no—
294Q8—224no—
295Q8—221no—
296Q8—442no—
297Q8#433912yescomplemented
298D4—21no—
299D4—21no—
300D4—221no—
301D4—221no—
302D4—442no—
303D4—442no—
304D4—442no—
305D4—442no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—42no—
310C2×C4—111no—
311C2×C4—111no—
312C2×C4—111no—
313C2×C4—222no—
314C2×C4—222no—
315C2×C4—224no—
316C2×C4—221no—
317C2×C4—221no—
318C2×C4—221no—
319C2×C4—221no—
320C2×C4—221no—
321C2×C4—442no—
322C2×C4—442no—
323C2×C4D4×D1111yescharacteristic
324C2×C4D4×D1111yescharacteristic
325C2×C4C23×D1111yescharacteristic
326C8—21no—
327C8—21no—
328C8—221no—
329C8—221no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—112no—
334C22—221no—
335C22—221no—
336C22—441no—
337C22—441no—
338C22—441no—
339C22C2×D4×D1111yescharacteristic
340C4—21no—
341C4—21no—
342C4—22no—
343C4—41no—
344C4—41no—
345C4—112no—
346C4—221no—
347C4—221no—
348C4—222no—
349C4—441no—
350C4—441no—
351C4C2×#433911yescharacteristic
352C4#41×D1111yescharacteristic
353C2—81no—
354C2—222no—
355C2—881no—
356C2#1062307811yescharacteristic
357C2D11×AGL(1,ℤ/8)11yescharacteristic
358C2D11×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#440C2
socleC22×C11C22×D4
prime radical#10623079C2
hypercenter#440D11
hypocenterC11#3112
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. C4×Q8×D11C2semidirect
3. C11×#440C2semidirect
4. #10622783C2semidirect
5. #10622776C2semidirect
6. #10622639C2semidirect
7. #10622631C2semidirect
8. #10622495C2semidirect
9. #10622488C2semidirect
10. #10622419C2semidirect
11. #10622407C2semidirect
12. #10622387C2semidirect
13. #10622375C2semidirect
14. #10622323C2semidirect
15. #10622318C2semidirect
114. Q8×C11#41semidirect
146. Dic22#41semidirect
164. #440D11semidirect
288. C11#3112semidirect
297. Q8#4339semidirect

Maximal subgroups

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

subgroupindex
C4×Q8×D112
#106230792
C11×#4402
#106227832
#106227762
#106226392
#106226312
#106224952
#106224882
#106224192
#106224072
#106223872
#106223752
#106223232
#106223182
#311211