Finite Group Databasebeta

← #13078762

Subgroups — #13078762

Order 1408.

430 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623127C211yesmaximal, characteristic, complemented
2#10623053C211yesmaximal, characteristic, complemented
3C11×#482C211yesmaximal, characteristic, complemented
4#10622650C211yesmaximal, characteristic, complemented
5#10622616C211yesmaximal, characteristic, complemented
6#10622503C211yesmaximal, characteristic, complemented
7#10622502C211yesmaximal, characteristic, complemented
8#10622482C211yesmaximal, characteristic, complemented
9#10622467C211yesmaximal, characteristic, complemented
10#10622399C211yesmaximal, characteristic, complemented
11#10622398C211yesmaximal, characteristic, complemented
12#10622375C211yesmaximal, characteristic, complemented
13#10622370C211yesmaximal, characteristic, complemented
14#10622347C211yesmaximal, characteristic, complemented
15#10622332C211yesmaximal, characteristic, complemented
16C2×#4341—21no—
17C2×#4339C2211yescharacteristic
18C11×#121C2211yescharacteristic
19C11×#117C2211yescharacteristic
20#66993C2211yescharacteristic
21#66992—21no—
22D4×Dic11C2211yescharacteristic
23C2×#4324C2211yescharacteristic
24C2×#4323C2211yescharacteristic
25#66983C2211yescharacteristic
26C2×C4×Dic11C2211yescharacteristic
27C2×D88C2211yescharacteristic
28C2×#4314C2211yescharacteristic
29#66946C2211yescharacteristic
30#66946C2211yescharacteristic
31#66946C2211yescharacteristic
32#66941C2211yescharacteristic
33#66940C2211yescharacteristic
34#66940C2211yescharacteristic
35#66938—21no—
36(C22⋊D11)⋊C4—21no—
37(C22⋊D11)⋊C4—21no—
38(C22⋊D11)⋊C4—21no—
39#66925—21no—
40C42×D11—21no—
41C11×#107C2211yescharacteristic
42C11×#106C2211yescharacteristic
43C11×#102C2211yescharacteristic
44C11×#102C2211yescharacteristic
45C11×C22⋊C8C2211yescharacteristic
46C22⋊(C11⋊C8)C2211yescharacteristic
47#66885C2211yescharacteristic
48#66880C2211yescharacteristic
49#66879C2211yescharacteristic
50#66879C2211yescharacteristic
51Dic11⋊C8C2211yescharacteristic
52Dic11⋊C8C2211yescharacteristic
53#66874C2211yescharacteristic
54#66873C2211yescharacteristic
55#66873C2211yescharacteristic
56#66873C2211yescharacteristic
57#66872C2211yescharacteristic
58#66871C2211yescharacteristic
59C2×D4×C11—21no—
60C2×D4×C11C2311yescharacteristic
61C22×C4×C11C2311yescharacteristic
62C2×C22⋊D11—21no—
63C2×C22⋊D11—21no—
64C2×C22⋊D11—21no—
65C2×C22⋊D11—21no—
66C22×Dic11—21no—
67C22×Dic11D411yescharacteristic
68C22×Dic11D411yescharacteristic
69#4341—44no—
70#4339—22no—
71#4339—22no—
72C2×D44C2311yescharacteristic
73C2×D44C2311yescharacteristic
74C2×C4×D11—21no—
75C2×C4×D11—21no—
76C2×C4×D11—21no—
77C2×C4×D11—21no—
78C2×Dic22—21no—
79C2×Dic22C2311yescharacteristic
80C2×C8×C11C2311yescharacteristic
81C2×C8×C11C2311yescharacteristic
82C11×C4⋊C4C2311yescharacteristic
83C11×C4⋊C4C2311yescharacteristic
84C11×C4⋊C4C2311yescharacteristic
85C11×C22⋊C4—21no—
86C11×C22⋊C4—21no—
87C42×C11—21no—
88C22⋊Dic11—21no—
89#4324—22no—
90#4323—22no—
91(C2×D11)⋊C4—21no—
92(C2×D11)⋊C4—21no—
93(C2×D11)⋊C4—21no—
94(C2×D11)⋊C4—21no—
95C4⋊Dic11C2311yescharacteristic
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99C4×Dic11—21no—
100C4×Dic11—21no—
101C4×Dic11D411yescharacteristic
102C4×Dic11D411yescharacteristic
103C4×Dic11C2311yescharacteristic
104C4×Dic11C2311yescharacteristic
105C2×C11⋊C8C2311yescharacteristic
106C2×C11⋊C8C2311yescharacteristic
107D88—22no—
108#4314—22no—
109#3115—111nomaximal, Sylow
110C23×C11—21no—
111C23×C11C2×D411yescharacteristic
112C22×D11—21no—
113C22×D11—21no—
114D4×C11—21no—
115D4×C11—21no—
116D4×C11—42no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11C2×D411yescharacteristic
123C2×C4×C11C2411yescharacteristic
124C22⋊D11—24no—
125C22⋊D11—42no—
126C22⋊D11—42no—
127C22⋊D11—42no—
128C2×Dic11—21no—
129C2×Dic11—22no—
130C2×Dic11—21no—
131C2×Dic11—41no—
132C2×Dic11—42no—
133C2×Dic11C2×D411yescharacteristic
134C2×Dic11C2×D411yescharacteristic
135C2×Dic11C2×D411yescharacteristic
136C2×Dic11C2×D411yescharacteristic
137D44—21no—
138D44—21no—
139D44—21no—
140D44#4112yescomplemented
141C4×D11—24no—
142C4×D11—42no—
143C4×D11—42no—
144C4×D11—42no—
145Dic22—21no—
146Dic22—42no—
147Dic22#4112yescomplemented
148C8×C11—21no—
149C8×C11—21no—
150C11⋊C8—21no—
151C11⋊C8—21no—
152#532—111no—
153C4×#41—111no—
154#482—111no—
155#482D1111yescharacteristic, complemented
156#475—111no—
157#474—111no—
158#460—111no—
159#459—111no—
160#449—111no—
161#449—111no—
162#442—111no—
163#442—111no—
164#440—111no—
165#440—111no—
166#432—111no—
167C22×C11—21no—
168C22×C11—21no—
169C22×C11—21no—
170C22×C11—41no—
171C22×C11—41no—
172C22×C11—41no—
173C22×C11C22×D411yescharacteristic
174C2×D11—22no—
175C2×D11—41no—
176C2×D11—41no—
177C2×D11—41no—
178C2×D11—41no—
179C2×D11—41no—
180C4×C11—21no—
181C4×C11—41no—
182C4×C11—41no—
183C4×C11—41no—
184C4×C11C2×#4111yescharacteristic
185C4×C11C2×#4111yescharacteristic
186Dic11—22no—
187Dic11—21no—
188Dic11—21no—
189Dic11—21no—
190Dic11—41no—
191Dic11AGL(1,ℤ/8)12yes—
192C2×#41—111no—
193C2×#41—221no—
194C2×SD16—111no—
195C2×SD16—111no—
196C2×D8—111no—
197C2×D8—111no—
198C4⋊Q8—111no—
199#127—111no—
200#124—221no—
201#121—111no—
202#121—221no—
203#121C2×D1111yescharacteristic
204C4×Q8—111no—
205C4×Q8—111no—
206C4×D4—111no—
207C4×D4—111no—
208C4×D4—111no—
209C4×D4—111no—
210C4×D4—221no—
211C4×D4—221no—
212C4×D4—221no—
213#117—221no—
214#117C2×D1111yescharacteristic
215C2×C42—111no—
216C2×C42—221no—
217#107—111no—
218#107C2×D1111yescharacteristic
219#106—111no—
220#106C2×D1111yescharacteristic
221C4⋊C8—111no—
222C4⋊C8—111no—
223#103—111no—
224#103—111no—
225#102—111no—
226#102—111no—
227#102—111no—
228#102—111no—
229#102C2×D1111yescharacteristic
230#102C2×D1111yescharacteristic
231C22⋊C8—111no—
232C22⋊C8C2×D1111yescharacteristic
233#97—111no—
234#97—111no—
235C2×C11—41no—
236C2×C11—81no—
237C2×C11#52511yescharacteristic
238C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
239C2×C11#57511yescharacteristic
240D11—42no—
241D11—81no—
242#41—222no—
243#41—222no—
244#41—444no—
245C2×Q8—111no—
246C2×Q8—221no—
247C2×D4—21no—
248C2×D4—111no—
249C2×D4—111no—
250C2×D4—221no—
251C2×D4—221no—
252C2×D4—221no—
253C2×D4—221no—
254C2×D4C22×D1111yescharacteristic
255C22×C4—111no—
256C22×C4—111no—
257C22×C4—221no—
258C22×C4—221no—
259C22×C4—221no—
260C22×C4—221no—
261C22×C4—221no—
262C22×C4C22×D1111yescharacteristic
263SD16—222no—
264SD16—222no—
265D8—222no—
266D8—222no—
267C2×C8—111no—
268C2×C8—111no—
269C2×C8C22×D1111yescharacteristic
270C2×C8C22×D1111yescharacteristic
271C4⋊C4—111no—
272C4⋊C4—221no—
273C4⋊C4—221no—
274C4⋊C4—221no—
275C4⋊C4C22×D1111yescharacteristic
276C4⋊C4C22×D1111yescharacteristic
277C4⋊C4C22×D1111yescharacteristic
278C22⋊C4—21no—
279C22⋊C4—21no—
280C22⋊C4—221no—
281C22⋊C4—221no—
282C22⋊C4—221no—
283C22⋊C4—221no—
284C22⋊C4—221no—
285C42—21no—
286C42—111no—
287C42—111no—
288C42—111no—
289C42—111no—
290C42—221no—
291C42—221no—
292C11#311511yescharacteristic, complemented, Sylow
293C23—21no—
294C23—221no—
295C23—221no—
296C23D4×D1111yescharacteristic
297Q8—112no—
298Q8—221no—
299Q8—442no—
300D4—21no—
301D4—21no—
302D4—42no—
303D4—112no—
304D4—224no—
305D4—221no—
306D4—221no—
307D4—221no—
308D4—442no—
309D4—442no—
310D4—442no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—111no—
317C2×C4—111no—
318C2×C4—111no—
319C2×C4—111no—
320C2×C4—224no—
321C2×C4—222no—
322C2×C4—221no—
323C2×C4—221no—
324C2×C4—442no—
325C2×C4—442no—
326C2×C4—442no—
327C2×C4—441no—
328C2×C4—442no—
329C2×C4D4×D1111yescharacteristic
330C2×C4C23×D1111yescharacteristic
331C8—21no—
332C8—21no—
333C8—221no—
334C8—221no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—222no—
342C22—441no—
343C22—441no—
344C22—441no—
345C22—441no—
346C22—441no—
347C22C2×D4×D1111yescharacteristic
348C4—21no—
349C4—41no—
350C4—41no—
351C4—41no—
352C4—112no—
353C4—221no—
354C4—221no—
355C4—221no—
356C4—222no—
357C4—441no—
358C4#41×D1111yescharacteristic
359C4#41×D1111yescharacteristic
360C2—41no—
361C2—81no—
362C2—442no—
363C2—881no—
364C2#1062318711yescharacteristic
365C2#1062329911yescharacteristic
366C2D11×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#482C2
socleC22×C11C22×D4
hypercenter#482D11
hypocenterC11#3115
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #10623127C2semidirect
2. #10623053C2semidirect
3. C11×#482C2semidirect
4. #10622650C2semidirect
5. #10622616C2semidirect
6. #10622503C2semidirect
7. #10622502C2semidirect
8. #10622482C2semidirect
9. #10622467C2semidirect
10. #10622399C2semidirect
11. #10622398C2semidirect
12. #10622375C2semidirect
13. #10622370C2semidirect
14. #10622347C2semidirect
15. #10622332C2semidirect
140. D44#41semidirect
147. Dic22#41semidirect
155. #482D11semidirect
292. C11#3115semidirect

Maximal subgroups

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

subgroupindex
#106231272
#106230532
C11×#4822
#106226502
#106226162
#106225032
#106225022
#106224822
#106224672
#106223992
#106223982
#106223752
#106223702
#106223472
#106223322
#311511