Finite Group Databasebeta

← #13069804

Subgroups — #13069804

Order 1408.

368 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 87 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
1C2×#66991C211yesmaximal, characteristic
2C2×C11×#102C211yesmaximal, characteristic, complemented
3C2×#66896C211yesmaximal, characteristic, complemented
4C2×(C2×D11)⋊C8C211yesmaximal, characteristic, complemented
5C2×#66881C211yesmaximal, characteristic, complemented
6#10622600C211yesmaximal, characteristic, complemented
7#10622167C211yesmaximal, characteristic, complemented
8C22×D4×C11C2211yescharacteristic
9C22×C22⋊D11—21no—
10C22×C4×D11C2211yescharacteristic
11C22×C8×C11C2211yescharacteristic
12C2×C11×C4⋊C4C2211yescharacteristic
13C2×C22⋊Dic11—21no—
14#66991—22no—
15#66991—22no—
16C2×(C2×D11)⋊C4—21no—
17C2×C4⋊Dic11C2211yescharacteristic
18C2×C4⋊Dic11C2211yescharacteristic
19C22×C11⋊C8C2211yescharacteristic
20C11×#102—22no—
21#66896—22no—
22C11⋊#95—21no—
23(C2×D11)⋊C8—22no—
24#66881—22no—
25C24×C11—21no—
26C23×D11D411yescharacteristic
27C2×D4×C11—21no—
28C2×D4×C11—21no—
29C2×D4×C11—21no—
30C2×D4×C11—21no—
31C2×D4×C11—21no—
32C2×D4×C11D412yes—
33C22×C4×C11—21no—
34C22×C4×C11C2311yescharacteristic
35C2×C22⋊D11—24no—
36C2×C22⋊D11—42no—
37C2×C22⋊D11—42no—
38C22×Dic11—21no—
39C22×Dic11—21no—
40C22×Dic11D411yescharacteristic
41C2×C4×D11—21no—
42C2×C4×D11—21no—
43C2×C4×D11—21no—
44C2×C4×D11—21no—
45C2×C4×D11—21no—
46C2×C4×D11—21no—
47C2×C8×C11—21no—
48C2×C8×C11—21no—
49C2×C8×C11D412yescomplemented
50C11×C4⋊C4—21no—
51C11×C4⋊C4—21no—
52C22⋊Dic11—24no—
53(C2×D11)⋊C4—42no—
54C4⋊Dic11—21no—
55C4⋊Dic11—21no—
56C4⋊Dic11—21no—
57C4⋊Dic11D412yes—
58C2×C11⋊C8—21no—
59C2×C11⋊C8—21no—
60C2×C11⋊C8—21no—
61#2034—111nomaximal, Sylow
62C23×C11—22no—
63C23×C11—41no—
64C23×C11—41no—
65C23×C11—41no—
66C23×C11—41no—
67C23×C11—41no—
68C23×C11—41no—
69C23×C11C2×D411yescharacteristic
70C22×D11—21no—
71C22×D11—21no—
72C22×D11—21no—
73C22×D11—21no—
74C22×D11—21no—
75C22×D11—21no—
76C22×D11SD1612yes—
77D4×C11—22no—
78D4×C11—22no—
79D4×C11—41no—
80D4×C11—41no—
81C2×C4×C11—41no—
82C2×C4×C11—41no—
83C2×C4×C11—41no—
84C2×C4×C11C2×D411yescharacteristic
85C2×C4×C11C2×D411yescharacteristic
86C2×C4×C11C2×D411yescharacteristic
87C2×C4×C11#4111yescharacteristic
88C2×C4×C11#4111yescharacteristic
89C2×C4×C11#4111yescharacteristic
90C22⋊D11—48no—
91C2×Dic11—22no—
92C2×Dic11—21no—
93C2×Dic11—21no—
94C2×Dic11—21no—
95C2×Dic11—41no—
96C2×Dic11—41no—
97C2×Dic11—41no—
98C2×Dic11—41no—
99C2×Dic11—41no—
100C4×D11—41no—
101C4×D11—41no—
102C4×D11—41no—
103C4×D11—41no—
104C8×C11—22no—
105C11⋊C8—41no—
106C2×#121—111no—
107C2×#106—111no—
108C2×#102—111no—
109C2×#102D1111yescharacteristic, complemented
110C2×C22⋊C8—111no—
111#380—111no—
112#340—111no—
113C22×C11—42no—
114C22×C11—42no—
115C22×C11—42no—
116C22×C11—81no—
117C22×C11—81no—
118C22×C11—81no—
119C22×C11—81no—
120C22×C11#12011yescharacteristic
121C22×C11#12111yescharacteristic
122C22×C11#12311yescharacteristic
123C22×C11C2×SD1611yescharacteristic
124C22×C11#13511yescharacteristic
125C22×C11AGL(1,ℤ/8)11yescharacteristic
126C22×C11AGL(1,ℤ/8)11yescharacteristic
127C2×D11—22no—
128C2×D11—22no—
129C2×D11—22no—
130C2×D11—41no—
131C2×D11—41no—
132C2×D11—41no—
133C2×D11—41no—
134C4×C11—81no—
135C4×C11#12111yescharacteristic
136C4×C11#12111yescharacteristic
137C4×C11#12311yescharacteristic
138C4×C11#12411yescharacteristic
139Dic11—41no—
140Dic11—42no—
141Dic11—81no—
142C22×D4—221no—
143C22×D4C2×D1111yescharacteristic
144C23×C4—111no—
145C22×C8—111no—
146C22×C8C2×D1111yescharacteristic
147#121—222no—
148#121—222no—
149C2×C4⋊C4—111no—
150C2×C4⋊C4—111no—
151C2×C4⋊C4C2×D1111yescharacteristic
152C2×C22⋊C4—221no—
153C2×C22⋊C4—221no—
154#106—222no—
155#102—22no—
156#102—222no—
157C22⋊C8—222no—
158#95—221no—
159C2×C11—82no—
160C2×C11#39411yescharacteristic
161C2×C11#44911yescharacteristic
162C2×C11#45011yescharacteristic
163C2×C11#46511yescharacteristic
164C2×C11#46911yescharacteristic
165C2×C11#48111yescharacteristic
166C2×C11#48211yescharacteristic
167D11—42no—
168C24—21no—
169C24—111no—
170C2×D4—21no—
171C2×D4—21no—
172C2×D4—21no—
173C2×D4—21no—
174C2×D4—21no—
175C2×D4—224no—
176C2×D4—442no—
177C2×D4—442no—
178C2×D4D4412yes—
179C22×C4—21no—
180C22×C4—111no—
181C22×C4—221no—
182C22×C4—221no—
183C22×C4—221no—
184C22×C4—221no—
185C22×C4—221no—
186C22×C4—221no—
187C22×C4—221no—
188C22×C4—221no—
189C22×C4C22×D1111yescharacteristic
190C2×C8—21no—
191C2×C8—21no—
192C2×C8—221no—
193C2×C8—221no—
194C2×C8—221no—
195C2×C8C22⋊D1112yescomplemented
196C4⋊C4—21no—
197C4⋊C4—21no—
198C4⋊C4—112no—
199C4⋊C4—221no—
200C4⋊C4—221no—
201C4⋊C4—221no—
202C22⋊C4—224no—
203C22⋊C4—442no—
204C11#203411yescharacteristic, complemented, Sylow
205C23—22no—
206C23—41no—
207C23—41no—
208C23—41no—
209C23—41no—
210C23—41no—
211C23—41no—
212C23—112no—
213C23—221no—
214C23—221no—
215C23—221no—
216C23—221no—
217C23—221no—
218C23—221no—
219C23D4×D1111yescharacteristic
220D4—22no—
221D4—22no—
222D4—41no—
223D4—41no—
224D4—448no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—221no—
229C2×C4—222no—
230C2×C4—221no—
231C2×C4—221no—
232C2×C4—441no—
233C2×C4—441no—
234C2×C4—441no—
235C2×C4—441no—
236C2×C4—441no—
237C2×C4—441no—
238C2×C4—441no—
239C2×C4—441no—
240C2×C4—441no—
241C2×C4C2×D4411yescharacteristic
242C2×C4#433911yescharacteristic
243C2×C4D4×D1111yescharacteristic
244C2×C4#434111yescharacteristic
245C2×C4#434111yescharacteristic
246C2×C4C2×C22⋊D1111yescharacteristic
247C8—22no—
248C8—441no—
249C22—42no—
250C22—42no—
251C22—42no—
252C22—81no—
253C22—81no—
254C22—81no—
255C22—81no—
256C22—222no—
257C22—222no—
258C22—222no—
259C22—441no—
260C22—441no—
261C22—441no—
262C22—441no—
263C22#6693511yescharacteristic
264C22#6693611yescharacteristic
265C22#6696411yescharacteristic
266C22#6696411yescharacteristic
267C22SD16×D1111yescharacteristic
268C22#6696911yescharacteristic
269C22#6699111yescharacteristic
270C4—81no—
271C4—441no—
272C4—442no—
273C4—881no—
274C4#6693811yescharacteristic
275C4#6693911yescharacteristic
276C4#6698311yescharacteristic
277C4#6699211yescharacteristic
278C2—82no—
279C2—442no—
280C2#1062238911yescharacteristic
281C2#1062239011yescharacteristic
282C2#1062239211yescharacteristic
283C2#1062239411yescharacteristic
284C2#1062257411yescharacteristic
285C2#1062277211yescharacteristic
286C2#1062278411yescharacteristic
subgroupG/H
centerC23D4×D11
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC2×C11×#102C2
socleC23×C11C2×D4
prime radicalC2×#66991C2
hypercenterC2×#102D11
hypocenterC11#2034
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
2. C2×C11×#102C2semidirect
3. C2×#66896C2semidirect
4. C2×(C2×D11)⋊C8C2semidirect
5. C2×#66881C2semidirect
6. #10622600C2semidirect
7. #10622167C2semidirect
49. C2×C8×C11D4semidirect
109. C2×#102D11semidirect
195. C2×C8C22⋊D11semidirect
204. C11#2034semidirect

Maximal subgroups

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

subgroupindex
C2×#669912
C2×C11×#1022
C2×#668962
C2×(C2×D11)⋊C82
C2×#668812
#106226002
#106221672
#203411