Finite Group Databasebeta

← #13080917

Subgroups — #13080917

Order 1408.

420 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623355C211yesmaximal, characteristic, complemented
2#10623038C211yesmaximal, characteristic, complemented
3C11×#417C211yesmaximal, characteristic, complemented
4#10622851C211yesmaximal, characteristic, complemented
5#10622747C211yesmaximal, characteristic, complemented
6#10622741C211yesmaximal, characteristic, complemented
7#10622583C211yesmaximal, characteristic, complemented
8#10622431C211yesmaximal, characteristic, complemented
9#10622425C211yesmaximal, characteristic, complemented
10#10622422C211yesmaximal, characteristic, complemented
11#10622405C211yesmaximal, characteristic, complemented
12#10622394C211yesmaximal, characteristic, complemented
13#10622384C211yesmaximal, characteristic, complemented
14#10622372C211yesmaximal, characteristic, complemented
15#10622369C211yesmaximal, characteristic, complemented
16C2×C11×#41C2211yescharacteristic
17C2×#4341C2211yescharacteristic
18C2×#4339—21no—
19C2×C11×M16C2211yescharacteristic
20C2×C11×C4⋊C4C2211yescharacteristic
21#66999C2211yescharacteristic
22#66997C2211yescharacteristic
23C2×#4325C2211yescharacteristic
24#66992—21no—
25#66988—21no—
26D4×Dic11C2211yescharacteristic
27C2×#4323C2211yescharacteristic
28#66983C2211yescharacteristic
29#66982—21no—
30#66982—21no—
31C4×C22⋊D11C2211yescharacteristic
32#66977C2211yescharacteristic
33C2×Dic11⋊C4—21no—
34C2×#4314C2211yescharacteristic
35C2×#4313C2211yescharacteristic
36#66949—21no—
37#66948C2211yescharacteristic
38#66947—21no—
39#66946C2211yescharacteristic
40C4⋊C4×D11C2211yescharacteristic
41#66941C2211yescharacteristic
42C11×#103C2211yescharacteristic
43C11×#103C2211yescharacteristic
44C11×#102C2211yescharacteristic
45C11×#102C2211yescharacteristic
46#66899C2211yescharacteristic
47#66896C2211yescharacteristic
48C22⋊(C11⋊C8)C2211yescharacteristic
49#66885C2211yescharacteristic
50(C2×D11)⋊C8C2211yescharacteristic
51#66882C2211yescharacteristic
52#66880C2211yescharacteristic
53Dic11⋊C8C2211yescharacteristic
54C8×Dic11C2211yescharacteristic
55#66874C2211yescharacteristic
56#66874C2211yescharacteristic
57#66871C2211yescharacteristic
58#66871C2211yescharacteristic
59C11×#41—22no—
60C11×#41—41no—
61C2×Q8×C11C2311yescharacteristic
62C2×D4×C11—21no—
63C2×D4×C11C2311yescharacteristic
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11C2311yescharacteristic
67C2×C22⋊D11—21no—
68C2×C22⋊D11—21no—
69C2×C22⋊D11D411yescharacteristic
70C22×Dic11—21no—
71C22×Dic11—21no—
72#4341—22no—
73#4341—41no—
74#4339—44no—
75C2×D44—21no—
76C2×D44C2311yescharacteristic
77C2×C4×D11—21no—
78C2×C4×D11—21no—
79C2×C4×D11C2311yescharacteristic
80C2×Dic22—21no—
81C2×Dic22C2311yescharacteristic
82C11×M16—41no—
83C2×C8×C11C2311yescharacteristic
84C2×C8×C11C2311yescharacteristic
85C11×C4⋊C4—21no—
86C11×C4⋊C4C2311yescharacteristic
87C11×C4⋊C4C2311yescharacteristic
88C22⋊Dic11—21no—
89C22⋊Dic11—21no—
90C22⋊Dic11D411yescharacteristic
91#4325—41no—
92#4323—22no—
93(C2×D11)⋊C4—21no—
94(C2×D11)⋊C4—21no—
95(C2×D11)⋊C4—21no—
96(C2×D11)⋊C4—21no—
97(C2×D11)⋊C4D411yescharacteristic
98C4⋊Dic11C2311yescharacteristic
99C4⋊Dic11C2311yescharacteristic
100Dic11⋊C4—21no—
101Dic11⋊C4—21no—
102Dic11⋊C4—21no—
103Dic11⋊C4—21no—
104Dic11⋊C4—21no—
105Dic11⋊C4—21no—
106Dic11⋊C4D411yescharacteristic
107C4×Dic11C2311yescharacteristic
108C2×C11⋊C8C2311yescharacteristic
109C2×C11⋊C8C2311yescharacteristic
110#4314—41no—
111#4313—41no—
112#3330—111nomaximal, Sylow
113C23×C11—21no—
114C23×C11C2×D411yescharacteristic
115C22×D11—21no—
116C22×D11C2×D411yescharacteristic
117Q8×C11—21no—
118Q8×C11—21no—
119D4×C11—21no—
120D4×C11—42no—
121D4×C11#4112yescomplemented
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—42no—
128C2×C4×C11—42no—
129C2×C4×C11C2×D411yescharacteristic
130C2×C4×C11C2411yescharacteristic
131C22⋊D11—22no—
132C22⋊D11—42no—
133C22⋊D11—42no—
134C2×Dic11—21no—
135C2×Dic11—21no—
136C2×Dic11—21no—
137C2×Dic11—42no—
138C2×Dic11—42no—
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—
149Dic22—21no—
150Dic22—21no—
151Dic22—42no—
152C8×C11—21no—
153C8×C11—21no—
154C11⋊C8—21no—
155C11⋊C8—21no—
156#547—111no—
157#547—111no—
158#487—111no—
159#484—111no—
160#484—111no—
161#474—111no—
162#468—111no—
163#468—111no—
164#461—111no—
165#449—111no—
166#449—111no—
167C4×D8—111no—
168#436—111no—
169#417—111no—
170#417D1111yescharacteristic, complemented
171C22×C11—21no—
172C22×C11—22no—
173C22×C11—21no—
174C22×C11—21no—
175C22×C11—41no—
176C22×C11—41no—
177C22×C11C22×D411yescharacteristic
178C2×D11—21no—
179C2×D11—21no—
180C2×D11—21no—
181C2×D11—41no—
182C2×D11—41no—
183C2×D11—41no—
184C4×C11—21no—
185C4×C11—41no—
186C4×C11—41no—
187C4×C11—41no—
188C4×C11C2×#4111yescharacteristic
189C4×C11H(5,𝔽2)11yescharacteristic
190Dic11—21no—
191Dic11—21no—
192Dic11—41no—
193Dic11—41no—
194Dic11—41no—
195Dic11AGL(1,ℤ/8)12yes—
196C2×#41—111no—
197C2×#41—221no—
198C2×#41C2×D1111yescharacteristic
199C2×SD16—111no—
200C2×SD16—111no—
201C2×D8—111no—
202C2×M16—111no—
203C2×M16C2×D1111yescharacteristic
204C4⋊Q8—111no—
205C4⋊Q8—111no—
206#123—221no—
207#123—221no—
208#123—221no—
209#123—221no—
210C22⋊Q8—111no—
211C22⋊Q8—111no—
212C22⋊Q8—221no—
213#121—111no—
214#121—111no—
215#121—221no—
216C4×D4—111no—
217C4×D4—111no—
218C4×D4—111no—
219C2×C4⋊C4—111no—
220C2×C4⋊C4—221no—
221C2×C4⋊C4C2×D1111yescharacteristic
222#107—111no—
223#107—111no—
224#107—111no—
225C4⋊C8—111no—
226#103—111no—
227#103—111no—
228#103—111no—
229#103—111no—
230#103C2×D1111yescharacteristic
231#103C2×D1111yescharacteristic
232#102—111no—
233#102—111no—
234#102C2×D1111yescharacteristic
235#102C2×D1111yescharacteristic
236C22⋊C8—111no—
237C22⋊C8—111no—
238C4×C8—111no—
239C2×C11—41no—
240C2×C11—42no—
241C2×C11#54611yescharacteristic
242C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
243C2×C11#57811yescharacteristic
244D11—41no—
245D11—81no—
246#41—22no—
247#41—41no—
248#41—222no—
249#41—444no—
250#41—441no—
251C2×Q8—111no—
252C2×Q8—221no—
253C2×Q8C22×D1111yescharacteristic
254C2×D4—21no—
255C2×D4—111no—
256C2×D4—111no—
257C2×D4—221no—
258C2×D4—221no—
259C2×D4—221no—
260C2×D4C22×D1111yescharacteristic
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—111no—
264C22×C4—221no—
265C22×C4—221no—
266C22×C4—221no—
267C22×C4—221no—
268C22×C4C22×D1111yescharacteristic
269SD16—441no—
270SD16—441no—
271D8—222no—
272M16—41no—
273M16—441no—
274C2×C8—111no—
275C2×C8—111no—
276C2×C8C22×D1111yescharacteristic
277C2×C8C22×D1111yescharacteristic
278C4⋊C4—21no—
279C4⋊C4—111no—
280C4⋊C4—111no—
281C4⋊C4—111no—
282C4⋊C4—221no—
283C4⋊C4—221no—
284C4⋊C4—221no—
285C4⋊C4—221no—
286C4⋊C4—221no—
287C4⋊C4—221no—
288C4⋊C4C22×D1111yescharacteristic
289C4⋊C4C22×D1111yescharacteristic
290C22⋊C4—111no—
291C22⋊C4—111no—
292C22⋊C4—221no—
293C22⋊C4—221no—
294C22⋊C4—221no—
295C22⋊C4—221no—
296C22⋊C4—221no—
297C22⋊C4—221no—
298C42—111no—
299C11#333011yescharacteristic, complemented, Sylow
300C23—21no—
301C23—111no—
302C23—221no—
303C23D4×D1111yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—221no—
307Q8—221no—
308Q8—442no—
309D4—21no—
310D4—42no—
311D4—222no—
312D4—221no—
313D4—221no—
314D4—442no—
315D4—442no—
316D4—442no—
317D4#433912yescomplemented
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—111no—
326C2×C4—111no—
327C2×C4—111no—
328C2×C4—221no—
329C2×C4—221no—
330C2×C4—221no—
331C2×C4—221no—
332C2×C4—221no—
333C2×C4—442no—
334C2×C4—442no—
335C2×C4—442no—
336C2×C4—442no—
337C2×C4D4×D1111yescharacteristic
338C2×C4C23×D1111yescharacteristic
339C8—21no—
340C8—21no—
341C8—221no—
342C8—221no—
343C22—21no—
344C22—22no—
345C22—21no—
346C22—21no—
347C22—41no—
348C22—41no—
349C22—221no—
350C22—221no—
351C22—221no—
352C22—441no—
353C22—441no—
354C22—441no—
355C22C2×D4×D1111yescharacteristic
356C4—21no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—112no—
361C4—221no—
362C4—221no—
363C4—441no—
364C4—441no—
365C4—441no—
366C4C2×#433911yescharacteristic
367C4#6703711yescharacteristic
368C2—41no—
369C2—42no—
370C2—441no—
371C2—881no—
372C2#1062302111yescharacteristic
373C2D11×AGL(1,ℤ/8)11yescharacteristic
374C2#1062331011yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#417C2
socleC22×C11C22×D4
hypercenter#417D11
hypocenterC11#3330
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. #10623355C2semidirect
2. #10623038C2semidirect
3. C11×#417C2semidirect
4. #10622851C2semidirect
5. #10622747C2semidirect
6. #10622741C2semidirect
7. #10622583C2semidirect
8. #10622431C2semidirect
9. #10622425C2semidirect
10. #10622422C2semidirect
11. #10622405C2semidirect
12. #10622394C2semidirect
13. #10622384C2semidirect
14. #10622372C2semidirect
15. #10622369C2semidirect
121. D4×C11#41semidirect
170. #417D11semidirect
299. C11#3330semidirect
317. D4#4339semidirect

Maximal subgroups

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

subgroupindex
#106233552
#106230382
C11×#4172
#106228512
#106227472
#106227412
#106225832
#106224312
#106224252
#106224222
#106224052
#106223942
#106223842
#106223722
#106223692
#333011