Finite Group Databasebeta

← #13069616

Subgroups — #13069616

Order 1408.

444 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×SD16C211yesmaximal, characteristic, complemented
2C2×#66999C211yesmaximal, characteristic, complemented
3C2×#66991C211yesmaximal, characteristic
4C2×#66899C211yesmaximal, characteristic, complemented
5C2×#66896C211yesmaximal, characteristic, complemented
6C2×(C2×D11)⋊C8C211yesmaximal, characteristic, complemented
7#10622189C211yesmaximal, characteristic, complemented
8C22×Q8×C11C2211yescharacteristic
9C22×D4×C11C2211yescharacteristic
10C22×C22⋊D11—21no—
11C22×C4×D11C2211yescharacteristic
12C2×C11×SD16—22no—
13C2×C11×SD16—22no—
14C2×C11×SD16—22no—
15C22×C8×C11C2211yescharacteristic
16C2×C22⋊Dic11—21no—
17#66999—22no—
18#66999—22no—
19#66991—22no—
20#66991—22no—
21C2×(C2×D11)⋊C4—21no—
22C2×C4⋊Dic11C2211yescharacteristic
23C2×C4⋊Dic11C2211yescharacteristic
24C2×Dic11⋊C4—21no—
25C22×C11⋊C8C2211yescharacteristic
26#66899—22no—
27#66896—22no—
28(C2×D11)⋊C8—22no—
29C24×C11—21no—
30C23×D11D411yescharacteristic
31C2×Q8×C11—21no—
32C2×Q8×C11—21no—
33C2×Q8×C11—21no—
34C2×Q8×C11—21no—
35C2×Q8×C11—21no—
36C2×Q8×C11D412yescomplemented
37C2×D4×C11—21no—
38C2×D4×C11—21no—
39C2×D4×C11—21no—
40C2×D4×C11—21no—
41C2×D4×C11—21no—
42C2×D4×C11D412yes—
43C22×C4×C11—21no—
44C22×C4×C11C2311yescharacteristic
45C2×C22⋊D11—24no—
46C2×C22⋊D11—42no—
47C2×C22⋊D11—42no—
48C22×Dic11—21no—
49C22×Dic11—21no—
50C22×Dic11D411yescharacteristic
51C2×C4×D11—21no—
52C2×C4×D11—21no—
53C2×C4×D11—21no—
54C2×C4×D11—21no—
55C2×C4×D11—21no—
56C2×C4×D11—21no—
57C11×SD16—28no—
58C2×C8×C11—21no—
59C2×C8×C11—21no—
60C2×C8×C11D412yescomplemented
61C22⋊Dic11—24no—
62(C2×D11)⋊C4—24no—
63C4⋊Dic11—21no—
64C4⋊Dic11—21no—
65C4⋊Dic11D412yes—
66C4⋊Dic11D412yescomplemented
67Dic11⋊C4—24no—
68C2×C11⋊C8—21no—
69C2×C11⋊C8—21no—
70C2×C11⋊C8—21no—
71#2000—111nomaximal, Sylow
72C23×C11—22no—
73C23×C11—41no—
74C23×C11—41no—
75C23×C11—41no—
76C23×C11—41no—
77C23×C11—41no—
78C23×C11—41no—
79C23×C11C2×D411yescharacteristic
80C22×D11—21no—
81C22×D11—21no—
82C22×D11—21no—
83C22×D11—21no—
84C22×D11—21no—
85C22×D11—21no—
86C22×D11SD1612yescomplemented
87Q8×C11—22no—
88Q8×C11—22no—
89Q8×C11—41no—
90Q8×C11—41no—
91D4×C11—22no—
92D4×C11—22no—
93D4×C11—41no—
94D4×C11—41no—
95C2×C4×C11—22no—
96C2×C4×C11—41no—
97C2×C4×C11—41no—
98C2×C4×C11C2×D411yescharacteristic
99C2×C4×C11C2×D411yescharacteristic
100C2×C4×C11C2×D411yescharacteristic
101C2×C4×C11C2×D411yescharacteristic
102C2×C4×C11C2×D411yescharacteristic
103C2×C4×C11#4111yescharacteristic
104C22⋊D11—48no—
105C2×Dic11—21no—
106C2×Dic11—22no—
107C2×Dic11—22no—
108C2×Dic11—21no—
109C2×Dic11—21no—
110C2×Dic11—41no—
111C2×Dic11—41no—
112C2×Dic11—41no—
113C2×Dic11—41no—
114C4×D11—41no—
115C4×D11—41no—
116C4×D11—41no—
117C4×D11—41no—
118C8×C11—22no—
119C11⋊C8—41no—
120C22×SD16D1111yescharacteristic, complemented
121C2×C22⋊Q8—111no—
122C2×#121—111no—
123C2×#103—111no—
124C2×#102—111no—
125C2×C22⋊C8—111no—
126#340—111no—
127C22×C11—42no—
128C22×C11—42no—
129C22×C11—42no—
130C22×C11—81no—
131C22×C11—81no—
132C22×C11—81no—
133C22×C11—81no—
134C22×C11#12011yescharacteristic
135C22×C11#12011yescharacteristic
136C22×C11#12111yescharacteristic
137C22×C11C2×SD1611yescharacteristic
138C22×C11#13511yescharacteristic
139C22×C11AGL(1,ℤ/8)11yescharacteristic
140C22×C11#13711yescharacteristic
141C2×D11—22no—
142C2×D11—22no—
143C2×D11—22no—
144C2×D11—41no—
145C2×D11—41no—
146C2×D11—41no—
147C2×D11—41no—
148C4×C11—42no—
149C4×C11#12011yescharacteristic
150C4×C11#12111yescharacteristic
151C4×C11#12111yescharacteristic
152C4×C11#12711yescharacteristic
153Dic11—41no—
154Dic11—42no—
155Dic11—42no—
156C22×Q8C2×D1111yescharacteristic
157C22×D4—221no—
158C22×D4C2×D1111yescharacteristic
159C23×C4—111no—
160C2×SD16—22no—
161C2×SD16—22no—
162C2×SD16—22no—
163C22×C8—111no—
164C22×C8C2×D1111yescharacteristic
165C22⋊Q8—222no—
166C22⋊Q8—222no—
167#121—222no—
168#121—222no—
169C2×C4⋊C4—111no—
170C2×C4⋊C4—111no—
171C2×C4⋊C4—221no—
172C2×C22⋊C4—221no—
173C2×C22⋊C4—221no—
174#103—222no—
175#102—222no—
176C22⋊C8—222no—
177C2×C11—82no—
178C2×C11#39211yescharacteristic
179C2×C11#44811yescharacteristic
180C2×C11#44911yescharacteristic
181C2×C11#45011yescharacteristic
182C2×C11#45211yescharacteristic
183C2×C11#46511yescharacteristic
184C2×C11#46811yescharacteristic
185D11—42no—
186C24—21no—
187C24—111no—
188C2×Q8—21no—
189C2×Q8—21no—
190C2×Q8—21no—
191C2×Q8—21no—
192C2×Q8—21no—
193C2×Q8C22⋊D1112yescomplemented
194C2×D4—21no—
195C2×D4—21no—
196C2×D4—21no—
197C2×D4—21no—
198C2×D4—21no—
199C2×D4—224no—
200C2×D4—442no—
201C2×D4—442no—
202C2×D4C22⋊D1112yes—
203C22×C4—21no—
204C22×C4—111no—
205C22×C4—221no—
206C22×C4—221no—
207C22×C4—221no—
208C22×C4—221no—
209C22×C4—221no—
210C22×C4—221no—
211C22×C4—221no—
212C22×C4—221no—
213C22×C4C22×D1111yescharacteristic
214SD16—28no—
215C2×C8—21no—
216C2×C8—21no—
217C2×C8—221no—
218C2×C8—221no—
219C2×C8—221no—
220C2×C8C22⋊D1112yescomplemented
221C4⋊C4—112no—
222C4⋊C4—112no—
223C4⋊C4—224no—
224C4⋊C4—221no—
225C4⋊C4—221no—
226C22⋊C4—224no—
227C22⋊C4—224no—
228C11#200011yescharacteristic, complemented, Sylow
229C23—22no—
230C23—41no—
231C23—41no—
232C23—41no—
233C23—41no—
234C23—41no—
235C23—41no—
236C23—112no—
237C23—221no—
238C23—221no—
239C23—221no—
240C23—221no—
241C23—221no—
242C23—221no—
243C23D4×D1111yescharacteristic
244Q8—22no—
245Q8—22no—
246Q8—41no—
247Q8—41no—
248D4—22no—
249D4—22no—
250D4—41no—
251D4—41no—
252D4—448no—
253C2×C4—22no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—221no—
257C2×C4—222no—
258C2×C4—222no—
259C2×C4—221no—
260C2×C4—221no—
261C2×C4—441no—
262C2×C4—441no—
263C2×C4—441no—
264C2×C4—441no—
265C2×C4—441no—
266C2×C4—441no—
267C2×C4—441no—
268C2×C4—441no—
269C2×C4D4×D1111yescharacteristic
270C2×C4D4×D1111yescharacteristic
271C2×C4#434111yescharacteristic
272C2×C4C2×C22⋊D1111yescharacteristic
273C2×C4C2×C22⋊D1111yescharacteristic
274C2×C4C2×C22⋊D1111yescharacteristic
275C8—22no—
276C8—441no—
277C22—42no—
278C22—42no—
279C22—42no—
280C22—81no—
281C22—81no—
282C22—81no—
283C22—81no—
284C22—222no—
285C22—222no—
286C22—222no—
287C22—441no—
288C22—441no—
289C22—441no—
290C22—441no—
291C22SD16×D1111yescharacteristic
292C22#6696711yescharacteristic
293C22#6696811yescharacteristic
294C22#6696911yescharacteristic
295C22#6699011yescharacteristic
296C22#6699011yescharacteristic
297C22#6699111yescharacteristic
298C4—42no—
299C4—442no—
300C4—442no—
301C4—441no—
302C4#6699211yescharacteristic
303C4#6699211yescharacteristic
304C4#6699311yescharacteristic
305C4#6700611yescharacteristic
306C2—82no—
307C2—442no—
308C2#1062278211yescharacteristic
309C2#1062278311yescharacteristic
310C2#1062278411yescharacteristic
311C2#1062278511yescharacteristic
312C2#1062278611yescharacteristic
313C2#1062278711yescharacteristic
314C2#1062283611yescharacteristic
subgroupG/H
centerC23D4×D11
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC22×C11×SD16C2
socleC23×C11C2×D4
prime radicalC2×#66991C2
hypercenterC22×SD16D11
hypocenterC11#2000
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C22×C11×SD16C2semidirect
2. C2×#66999C2semidirect
4. C2×#66899C2semidirect
5. C2×#66896C2semidirect
6. C2×(C2×D11)⋊C8C2semidirect
7. #10622189C2semidirect
36. C2×Q8×C11D4semidirect
60. C2×C8×C11D4semidirect
66. C4⋊Dic11D4semidirect
86. C22×D11SD16semidirect
120. C22×SD16D11semidirect
193. C2×Q8C22⋊D11semidirect
220. C2×C8C22⋊D11semidirect
228. C11#2000semidirect

Maximal subgroups

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

subgroupindex
C22×C11×SD162
C2×#669992
C2×#669912
C2×#668992
C2×#668962
C2×(C2×D11)⋊C82
#106221892
#200011