Finite Group Databasebeta

← #13079946

Subgroups — #13079946

Order 1408.

354 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623153C211yesmaximal, characteristic, complemented
2#10623131C211yesmaximal, characteristic
3C11×#465C211yesmaximal, characteristic
4#10622779C211yesmaximal, characteristic, complemented
5#10622775C211yesmaximal, characteristic, complemented
6#10622729C211yesmaximal, characteristic, complemented
7C2×Dic11⋊C8C211yesmaximal, characteristic, complemented
8#10622664C211yesmaximal, characteristic, complemented
9#10622654C211yesmaximal, characteristic
10#10622470C211yesmaximal, characteristic, complemented
11#10622467C211yesmaximal, characteristic, complemented
12#10622409C211yesmaximal, characteristic, complemented
13#10622406C211yesmaximal, characteristic, complemented
14#10622380C211yesmaximal, characteristic, complemented
15#10622372C211yesmaximal, characteristic, complemented
16C2×C11×SD16C2211yescharacteristic
17C22×C8×C11C2211yescharacteristic
18C11×C22⋊Q8C2211yescharacteristic
19C11×#121C2211yescharacteristic
20Q8×Dic11C2211yescharacteristic
21#66997C2211yescharacteristic
22C2×#4326C2211yescharacteristic
23#66989C2211yescharacteristic
24#66988—21no—
25D4×Dic11—21no—
26D4×Dic11C2211yescharacteristic
27C2×#4324C2211yescharacteristic
28#66977C2211yescharacteristic
29#66977C2211yescharacteristic
30C2×C4×Dic11C2211yescharacteristic
31C22×C11⋊C8C2211yescharacteristic
32C2×Dic44C2211yescharacteristic
33#66943C2211yescharacteristic
34#66942—21no—
35#66941C2211yescharacteristic
36#66940—21no—
37#66940C2211yescharacteristic
38#66940C2211yescharacteristic
39#66932—21no—
40#66931—21no—
41#66930—21no—
42#66930—21no—
43C11×#106C2211yescharacteristic
44C11×#103C2211yescharacteristic
45C11×#102C2211yescharacteristic
46#66899C2211yescharacteristic
47#66896C2211yescharacteristic
48#66882C2211yescharacteristic
49#66880C2211yescharacteristic
50#66880C2211yescharacteristic
51Dic11⋊C8C2211yescharacteristic
52Dic11⋊C8C2211yescharacteristic
53Dic11⋊C8C2211yescharacteristic
54Dic11⋊C8C2211yescharacteristic
55#66874C2211yescharacteristic
56#66874C2211yescharacteristic
57#66872C2211yescharacteristic
58#66871C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×D4×C11—21no—
61C2×D4×C11C2311yescharacteristic
62C22×C4×C11C2311yescharacteristic
63C22×Dic11—21no—
64C22×Dic11D411yescharacteristic
65C22×Dic11D411yescharacteristic
66C2×Dic22—21no—
67C2×Dic22C2311yescharacteristic
68C2×Dic22C2311yescharacteristic
69C11×SD16—41no—
70C2×C8×C11—41no—
71C2×C8×C11C2311yescharacteristic
72C2×C8×C11C2311yescharacteristic
73C11×C4⋊C4—21no—
74C11×C4⋊C4C2311yescharacteristic
75C11×C4⋊C4C2311yescharacteristic
76C11×C22⋊C4—21no—
77C11×C22⋊C4—21no—
78C22⋊Dic11—21no—
79C22⋊Dic11—21no—
80C22⋊Dic11—21no—
81C22⋊Dic11—21no—
82C22⋊Dic11—21no—
83#4326—41no—
84#4324—41no—
85C4⋊Dic11—21no—
86C4⋊Dic11—21no—
87C4⋊Dic11C2311yescharacteristic
88C4⋊Dic11C2311yescharacteristic
89Dic11⋊C4—21no—
90Dic11⋊C4—21no—
91Dic11⋊C4—21no—
92Dic11⋊C4—21no—
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97C4×Dic11—21no—
98C4×Dic11—21no—
99C4×Dic11—21no—
100C4×Dic11D411yescharacteristic
101C4×Dic11D411yescharacteristic
102C4×Dic11C2311yescharacteristic
103C4×Dic11C2311yescharacteristic
104C2×C11⋊C8—41no—
105C2×C11⋊C8C2311yescharacteristic
106C2×C11⋊C8C2311yescharacteristic
107Dic44—41no—
108#3248—111nomaximal, Sylow
109C23×C11—21no—
110C23×C11C2×D411yescharacteristic
111Q8×C11—21no—
112Q8×C11—21no—
113D4×C11—21no—
114D4×C11—21no—
115D4×C11—42no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11C2×D411yescharacteristic
122C2×C4×C11C2411yescharacteristic
123C2×Dic11—22no—
124C2×Dic11—22no—
125C2×Dic11—21no—
126C2×Dic11—21no—
127C2×Dic11—21no—
128C2×Dic11—21no—
129C2×Dic11—42no—
130C2×Dic11C2×D411yescharacteristic
131C2×Dic11C2×D411yescharacteristic
132C2×Dic11C2×D411yescharacteristic
133C2×Dic11C2×D411yescharacteristic
134Dic22—21no—
135Dic22—21no—
136Dic22—21no—
137Dic22—21no—
138Dic22—42no—
139C8×C11—21no—
140C8×C11—21no—
141C11⋊C8—21no—
142C11⋊C8—21no—
143#533—111no—
144#529—111no—
145#479—111no—
146#479—111no—
147#475—111no—
148#474—111no—
149#467—111no—
150#467—111no—
151#465—111no—
152#465D1111yescharacteristic
153#464—111no—
154#464—111no—
155#462—111no—
156#461—111no—
157C2×C4⋊C8—111no—
158C22×C11—21no—
159C22×C11—21no—
160C22×C11—41no—
161C22×C11—41no—
162C22×C11—41no—
163C22×C11#13712yes—
164C22×C11C22×D411yescharacteristic
165C4×C11—21no—
166C4×C11—41no—
167C4×C11—41no—
168C4×C11—41no—
169C4×C11H(5,𝔽2)11yescharacteristic
170C4×C112−1+411yescharacteristic
171Dic11—21no—
172Dic11—21no—
173Dic11—21no—
174Dic11—41no—
175Dic11—41no—
176Dic11—41no—
177Dic11—41no—
178Dic11#13512yes—
179C2×Q16—111no—
180C2×Q16—111no—
181C2×SD16—111no—
182C2×SD16C2×D1111yescharacteristic
183C22×C8—111no—
184C22×C8C2×D1111yescharacteristic
185C4⋊Q8—111no—
186C4⋊Q8—111no—
187#126—221no—
188#125—111no—
189#125—221no—
190#124—111no—
191#123—221no—
192C22⋊Q8—111no—
193C22⋊Q8—111no—
194C22⋊Q8—221no—
195C22⋊Q8C2×D1111yescharacteristic
196#121C2×D1111yescharacteristic
197C4×Q8—111no—
198C4×Q8—111no—
199C4×Q8—111no—
200C4×Q8—221no—
201C4×D4—111no—
202C4×D4—221no—
203#117—221no—
204#117—221no—
205C2×C42—111no—
206#107—111no—
207#107—111no—
208#106—111no—
209#106C2×D1111yescharacteristic
210C4⋊C8—111no—
211C4⋊C8—111no—
212C4⋊C8—111no—
213C4⋊C8—111no—
214#103—111no—
215#103—111no—
216#103—111no—
217#103—111no—
218#103—111no—
219#103C2×D1111yescharacteristic
220#102—111no—
221#102C2×D1111yescharacteristic
222C2×C11—22no—
223C2×C11—81no—
224C2×C11#53711yescharacteristic
225C2×C11C2×#13511yescharacteristic
226C2×C11C2×#13711yescharacteristic
227C2×Q8—111no—
228C2×Q8—111no—
229C2×Q8—221no—
230C2×Q8C22×D1111yescharacteristic
231C2×D4—21no—
232C2×D4C22×D1111yescharacteristic
233C22×C4—111no—
234C22×C4—111no—
235C22×C4—221no—
236C22×C4C22×D1111yescharacteristic
237Q16—441no—
238Q16—441no—
239SD16—41no—
240SD16—441no—
241C2×C8—41no—
242C2×C8—111no—
243C2×C8—111no—
244C2×C8—441no—
245C2×C8C22×D1111yescharacteristic
246C2×C8C22×D1111yescharacteristic
247C4⋊C4—21no—
248C4⋊C4—111no—
249C4⋊C4—111no—
250C4⋊C4—221no—
251C4⋊C4—221no—
252C4⋊C4—221no—
253C4⋊C4—221no—
254C4⋊C4—221no—
255C4⋊C4—221no—
256C4⋊C4—221no—
257C4⋊C4—221no—
258C4⋊C4—221no—
259C4⋊C4—221no—
260C4⋊C4C22×D1111yescharacteristic
261C4⋊C4C22×D1111yescharacteristic
262C22⋊C4—21no—
263C22⋊C4—21no—
264C22⋊C4—221no—
265C22⋊C4—221no—
266C22⋊C4—221no—
267C22⋊C4—221no—
268C22⋊C4—221no—
269C42—111no—
270C42—111no—
271C42—111no—
272C42—111no—
273C42—221no—
274C42—221no—
275C42—221no—
276C11#324811yescharacteristic, complemented, Sylow
277C23—21no—
278C23D4×D1111yescharacteristic
279Q8—21no—
280Q8—21no—
281Q8—221no—
282Q8—221no—
283Q8—221no—
284Q8—221no—
285Q8—442no—
286D4—21no—
287D4—21no—
288D4—42no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—111no—
295C2×C4—111no—
296C2×C4—111no—
297C2×C4—111no—
298C2×C4—222no—
299C2×C4—222no—
300C2×C4—221no—
301C2×C4—221no—
302C2×C4—221no—
303C2×C4—221no—
304C2×C4—442no—
305C2×C4D4×D1111yescharacteristic
306C2×C4C23×D1111yescharacteristic
307C8—21no—
308C8—21no—
309C8—221no—
310C8—221no—
311C22—21no—
312C22—21no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22#6696812yes—
317C22C2×D4×D1111yescharacteristic
318C4—21no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—112no—
323C4—221no—
324C4—221no—
325C4—221no—
326C4—441no—
327C4—441no—
328C4—441no—
329C4—441no—
330C4#6703711yescharacteristic
331C4#6704311yescharacteristic
332C2—22no—
333C2—81no—
334C2#1062312811yescharacteristic
335C2C2×#6696811yescharacteristic
336C2D11×#13511yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#465C2
socleC22×C11C22×D4
prime radicalC11×#121C22
hypercenter#465D11
hypocenterC11#3248
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #10623153C2semidirect
4. #10622779C2semidirect
5. #10622775C2semidirect
6. #10622729C2semidirect
7. C2×Dic11⋊C8C2semidirect
8. #10622664C2semidirect
10. #10622470C2semidirect
11. #10622467C2semidirect
12. #10622409C2semidirect
13. #10622406C2semidirect
14. #10622380C2semidirect
15. #10622372C2semidirect
276. C11#3248semidirect

Maximal subgroups

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

subgroupindex
#106231532
#106231312
C11×#4652
#106227792
#106227752
#106227292
C2×Dic11⋊C82
#106226642
#106226542
#106224702
#106224672
#106224092
#106224062
#106223802
#106223722
#324811