Finite Group Databasebeta

← #13079182

Subgroups — #13079182

Order 1408.

380 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623111C211yesmaximal, characteristic, complemented
2#10623088C211yesmaximal, characteristic, complemented
3C4×C11×SD16C211yesmaximal, characteristic, complemented
4#10622784C211yesmaximal, characteristic, complemented
5#10622781C211yesmaximal, characteristic, complemented
6C4×#4326C211yesmaximal, characteristic, complemented
7C4×#4323C211yesmaximal, characteristic, complemented
8#10622477C211yesmaximal, characteristic, complemented
9#10622471C211yesmaximal, characteristic, complemented
10#10622426C211yesmaximal, characteristic, complemented
11#10622413C211yesmaximal, characteristic, complemented
12#10622388C211yesmaximal, characteristic
13#10622381C211yesmaximal, characteristic, complemented
14C4×#4314C211yesmaximal, characteristic, complemented
15C4×C8×D11C211yesmaximal, characteristic, complemented
16C2×C11×SD16C2211yescharacteristic
17C4×Q8×C11C2211yescharacteristic
18C4×D4×C11C2211yescharacteristic
19#67000C2211yescharacteristic
20#66999C2211yescharacteristic
21C2×#4326C2211yescharacteristic
22#66991C2211yescharacteristic
23#66989C2211yescharacteristic
24C2×#4323C2211yescharacteristic
25C4×C22⋊D11—21no—
26#66979—21no—
27C2×#4314C2211yescharacteristic
28C2×C8×D11C2211yescharacteristic
29C2×C8×D11C2211yescharacteristic
30#66951—21no—
31#66950C2211yescharacteristic
32#66948C2211yescharacteristic
33#66947—21no—
34#66943C2211yescharacteristic
35#66943C2211yescharacteristic
36#66936—21no—
37#66932—21no—
38C4×D44—21no—
39C4×D44C2211yescharacteristic
40#66925—21no—
41C42×D11C2211yescharacteristic
42C4×Dic22C2211yescharacteristic
43C11×#106C2211yescharacteristic
44C11×#103C2211yescharacteristic
45C11×#102C2211yescharacteristic
46C4×C8×C11C2211yescharacteristic
47#66899C2211yescharacteristic
48#66896C2211yescharacteristic
49#66885C2211yescharacteristic
50#66881C2211yescharacteristic
51#66880C2211yescharacteristic
52C8×Dic11C2211yescharacteristic
53C8×Dic11C2211yescharacteristic
54#66874C2211yescharacteristic
55#66873C2211yescharacteristic
56#66871C2211yescharacteristic
57#66871C2211yescharacteristic
58C4×C11⋊C8C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×D4×C11C2311yescharacteristic
61C22×C4×C11—21no—
62C2×C22⋊D11—21no—
63C2×D44—21no—
64C2×D44C2311yescharacteristic
65C2×C4×D11—21no—
66C2×C4×D11D411yescharacteristic
67C2×C4×D11D411yescharacteristic
68C2×C4×D11C2311yescharacteristic
69C2×Dic22C2311yescharacteristic
70C11×SD16—22no—
71C2×C8×C11C2311yescharacteristic
72C2×C8×C11C2311yescharacteristic
73C11×C4⋊C4—21no—
74C11×C4⋊C4C2311yescharacteristic
75C11×C4⋊C4C2311yescharacteristic
76C11×C22⋊C4—21no—
77C42×C11—21no—
78C42×C11C2311yescharacteristic
79C22⋊Dic11—21no—
80C22⋊Dic11—21no—
81C22⋊Dic11—21no—
82#4326—22no—
83#4323—22no—
84(C2×D11)⋊C4—21no—
85(C2×D11)⋊C4—21no—
86(C2×D11)⋊C4—21no—
87(C2×D11)⋊C4—21no—
88(C2×D11)⋊C4—21no—
89(C2×D11)⋊C4—21no—
90C4⋊Dic11—21no—
91C4⋊Dic11—21no—
92C4⋊Dic11—21no—
93C4⋊Dic11C2311yescharacteristic
94C4⋊Dic11C2311yescharacteristic
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99C4×Dic11—21no—
100C4×Dic11D411yescharacteristic
101C4×Dic11D411yescharacteristic
102C4×Dic11C2311yescharacteristic
103C2×C11⋊C8C2311yescharacteristic
104C2×C11⋊C8C2311yescharacteristic
105#4314—22no—
106C8×D11—22no—
107C8×D11—22no—
108#3168—111nomaximal, Sylow
109C23×C11—21no—
110C22×D11—21no—
111C22×D11C2×D411yescharacteristic
112Q8×C11—21no—
113Q8×C11—21no—
114D4×C11—21no—
115D4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—42no—
120C2×C4×C11C2×D411yescharacteristic
121C2×C4×C11C2×D411yescharacteristic
122C2×C4×C11C2411yescharacteristic
123C22⋊D11—42no—
124C2×Dic11—21no—
125C2×Dic11—21no—
126C2×Dic11—21no—
127C2×Dic11C2×D411yescharacteristic
128C2×Dic11C2×D411yescharacteristic
129C2×Dic11C2×D411yescharacteristic
130D44—21no—
131D44—21no—
132D44—42no—
133C4×D11—22no—
134C4×D11—22no—
135C4×D11—21no—
136C4×D11—21no—
137C4×D11—42no—
138Dic22—21no—
139Dic22—21no—
140C8×C11—21no—
141C8×C11#4112yes—
142C11⋊C8—21no—
143C11⋊C8#4112yes—
144#529—111no—
145#529—111no—
146#499—111no—
147#495—111no—
148#488—111no—
149#488—111no—
150#467—111no—
151#466—111no—
152#465—111no—
153#465—111no—
154C4×Q16—111no—
155C4×SD16—111no—
156C4×SD16D1111yescharacteristic, complemented
157C4×D8—111no—
158C2×C4×C8—111no—
159C22×C11—41no—
160C22×C11—41no—
161C22×C11—41no—
162C22×C11C22×D411yescharacteristic
163C2×D11—21no—
164C2×D11—21no—
165C2×D11—41no—
166C2×D11—41no—
167C2×D11—41no—
168C2×D11#13512yes—
169C4×C11—21no—
170C4×C11—41no—
171C4×C11—41no—
172C4×C11—41no—
173C4×C11#13512yes—
174C4×C11C2×#4111yescharacteristic
175C4×C11C2×#4111yescharacteristic
176Dic11—21no—
177Dic11—21no—
178Dic11—21no—
179Dic11—41no—
180Dic11—41no—
181Dic11—41no—
182C2×Q16—111no—
183C2×SD16—111no—
184C2×SD16C2×D1111yescharacteristic
185C2×D8—111no—
186C22×C8—111no—
187C22×C8—111no—
188#126—221no—
189#126—221no—
190#125—111no—
191#125—111no—
192#124—111no—
193#124—111no—
194#123—221no—
195#123—221no—
196C22⋊Q8—111no—
197C22⋊Q8—111no—
198#121—111no—
199#121—111no—
200C4×Q8—111no—
201C4×Q8C2×D1111yescharacteristic
202C4×D4—111no—
203C4×D4—221no—
204C4×D4—221no—
205C4×D4C2×D1111yescharacteristic
206#117—221no—
207#117—221no—
208C2×C42—111no—
209#107—111no—
210#107—111no—
211#106—111no—
212#106C2×D1111yescharacteristic
213#103—111no—
214#103—111no—
215#103—111no—
216#103C2×D1111yescharacteristic
217#102—111no—
218#102—111no—
219#102—111no—
220#102C2×D1111yescharacteristic
221C4×C8—111no—
222C4×C8—111no—
223C4×C8—111no—
224C4×C8C2×D1111yescharacteristic
225C2×C11—81no—
226C2×C11#53211yescharacteristic
227C2×C11C2×#13511yescharacteristic
228C2×C11C2×#13511yescharacteristic
229D11—22no—
230D11—81no—
231C2×Q8—111no—
232C2×Q8C22×D1111yescharacteristic
233C2×D4—111no—
234C2×D4—221no—
235C2×D4—221no—
236C2×D4C22×D1111yescharacteristic
237C22×C4—21no—
238C22×C4—111no—
239C22×C4—111no—
240C22×C4—111no—
241C22×C4—221no—
242Q16—222no—
243SD16—22no—
244SD16—222no—
245D8—222no—
246C2×C8—111no—
247C2×C8—111no—
248C2×C8—222no—
249C2×C8—222no—
250C2×C8C22×D1111yescharacteristic
251C2×C8C22×D1111yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—111no—
254C4⋊C4—111no—
255C4⋊C4—221no—
256C4⋊C4—221no—
257C4⋊C4—221no—
258C4⋊C4—221no—
259C4⋊C4—221no—
260C4⋊C4—221no—
261C4⋊C4—221no—
262C4⋊C4C22×D1111yescharacteristic
263C4⋊C4C22×D1111yescharacteristic
264C22⋊C4—21no—
265C22⋊C4—221no—
266C22⋊C4—221no—
267C22⋊C4—221no—
268C22⋊C4—221no—
269C22⋊C4—221no—
270C22⋊C4—221no—
271C22⋊C4—221no—
272C22⋊C4—221no—
273C22⋊C4—221no—
274C42—21no—
275C42—111no—
276C42—111no—
277C42—111no—
278C42—221no—
279C42C22×D1111yescharacteristic
280C11#316811yescharacteristic, complemented, Sylow
281C23—21no—
282C23—111no—
283C23—221no—
284Q8—21no—
285Q8—21no—
286Q8—221no—
287Q8—221no—
288D4—21no—
289D4—21no—
290D4—221no—
291D4—221no—
292D4—442no—
293D4—442no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—42no—
298C2×C4—111no—
299C2×C4—111no—
300C2×C4—111no—
301C2×C4—222no—
302C2×C4—222no—
303C2×C4—221no—
304C2×C4—221no—
305C2×C4—221no—
306C2×C4—221no—
307C2×C4—221no—
308C2×C4—442no—
309C2×C4D4×D1111yescharacteristic
310C2×C4D4×D1111yescharacteristic
311C2×C4C23×D1111yescharacteristic
312C8—21no—
313C8—112no—
314C8—221no—
315C8#433912yes—
316C22—41no—
317C22—41no—
318C22—41no—
319C22—112no—
320C22—221no—
321C22—221no—
322C22—441no—
323C22—441no—
324C22—441no—
325C22C2×D4×D1111yescharacteristic
326C4—21no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—221no—
331C4—221no—
332C4—221no—
333C4—441no—
334C4—441no—
335C4—441no—
336C4#6696912yes—
337C4C2×#433911yescharacteristic
338C4#41×D1111yescharacteristic
339C2—81no—
340C2—222no—
341C2—881no—
342C2#1062307911yescharacteristic
343C2C2×#6696911yescharacteristic
344C2D11×#13511yescharacteristic
subgroupG/H
centerC2×C4D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC4×C11×SD16C2
socleC22×C11C22×D4
prime radical#10622388C2
hypercenterC4×SD16D11
hypocenterC11#3168
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #10623111C2semidirect
2. #10623088C2semidirect
3. C4×C11×SD16C2semidirect
4. #10622784C2semidirect
5. #10622781C2semidirect
6. C4×#4326C2semidirect
7. C4×#4323C2semidirect
8. #10622477C2semidirect
9. #10622471C2semidirect
10. #10622426C2semidirect
11. #10622413C2semidirect
13. #10622381C2semidirect
14. C4×#4314C2semidirect
15. C4×C8×D11C2semidirect
156. C4×SD16D11semidirect
280. C11#3168semidirect

Maximal subgroups

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

subgroupindex
#106231112
#106230882
C4×C11×SD162
#106227842
#106227812
C4×#43262
C4×#43232
#106224772
#106224712
#106224262
#106224132
#106223882
#106223812
C4×#43142
C4×C8×D112
#316811