Finite Group Databasebeta

← #13069798

Subgroups — #13069798

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×#66983C211yesmaximal, characteristic
2C11×#380C211yesmaximal, characteristic, complemented
3C2×C22⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
4C2×#66873C211yesmaximal, characteristic, complemented
5C2×#66873C211yesmaximal, characteristic, complemented
6C2×#66871C211yesmaximal, characteristic, complemented
7#10622167C211yesmaximal, characteristic, complemented
8C23×C4×C11C2211yescharacteristic
9C22×C22⋊D11—21no—
10C22×D44C2211yescharacteristic
11C2×C11×C4⋊C4C2211yescharacteristic
12C2×C11×C4⋊C4C2211yescharacteristic
13C2×C11×C22⋊C4—21no—
14#66983—22no—
15#66983—22no—
16C2×(C2×D11)⋊C4—21no—
17C2×C4⋊Dic11C2211yescharacteristic
18C22×C11⋊C8C2211yescharacteristic
19C22×C11⋊C8C2211yescharacteristic
20C11×#95—21no—
21C22⋊(C11⋊C8)—22no—
22#66873—22no—
23#66873—22no—
24#66871—22no—
25C24×C11D411yescharacteristic
26C23×D11—21no—
27C22×C4×C11—21no—
28C22×C4×C11—21no—
29C22×C4×C11—21no—
30C22×C4×C11—21no—
31C22×C4×C11—21no—
32C22×C4×C11—21no—
33C22×C4×C11—21no—
34C22×C4×C11—21no—
35C22×C4×C11D411yescharacteristic
36C22×C4×C11C2311yescharacteristic
37C2×C22⋊D11—24no—
38C2×C22⋊D11—42no—
39C2×C22⋊D11—42no—
40C22×Dic11—21no—
41C2×D44—21no—
42C2×D44—21no—
43C2×D44—21no—
44C2×D44—21no—
45C2×D44—21no—
46C2×D44D412yes—
47C11×C4⋊C4—21no—
48C11×C4⋊C4—21no—
49C11×C4⋊C4—21no—
50C11×C4⋊C4—21no—
51C11×C22⋊C4—42no—
52(C2×D11)⋊C4—24no—
53C4⋊Dic11—21no—
54C4⋊Dic11D412yes—
55C2×C11⋊C8—21no—
56C2×C11⋊C8—21no—
57C2×C11⋊C8—21no—
58C2×C11⋊C8—21no—
59C2×C11⋊C8—21no—
60C2×C11⋊C8D412yescomplemented
61#2033—111nomaximal, Sylow
62C23×C11—21no—
63C23×C11—21no—
64C23×C11—21no—
65C23×C11—21no—
66C23×C11—21no—
67C23×C11—21no—
68C23×C11D812yes—
69C23×C11C2×D411yescharacteristic
70C22×D11—22no—
71C22×D11—41no—
72C22×D11—41no—
73C22×D11—41no—
74C22×D11—41no—
75C22×D11—41no—
76C22×D11—41no—
77C2×C4×C11—21no—
78C2×C4×C11—21no—
79C2×C4×C11—21no—
80C2×C4×C11—41no—
81C2×C4×C11—41no—
82C2×C4×C11—41no—
83C2×C4×C11—41no—
84C2×C4×C11—41no—
85C2×C4×C11—41no—
86C2×C4×C11—41no—
87C2×C4×C11—41no—
88C2×C4×C11—41no—
89C2×C4×C11—41no—
90C2×C4×C11C2×D411yescharacteristic
91C2×C4×C11C2×D411yescharacteristic
92C2×C4×C11C2×D411yescharacteristic
93C2×C4×C11#4111yescharacteristic
94C2×C4×C11#4111yescharacteristic
95C2×C4×C11#4111yescharacteristic
96C22⋊D11—48no—
97C2×Dic11—22no—
98C2×Dic11—41no—
99C2×Dic11—41no—
100D44—22no—
101D44—22no—
102D44—41no—
103D44—41no—
104C11⋊C8—22no—
105C11⋊C8—41no—
106C2×#121—111no—
107C2×#107—111no—
108C2×#102—111no—
109C2×#102—111no—
110C2×C22⋊C8—111no—
111#380D1111yescharacteristic, complemented
112#340—111no—
113C22×C11—22no—
114C22×C11—22no—
115C22×C11—22no—
116C22×C11—41no—
117C22×C11—41no—
118C22×C11—41no—
119C22×C11—41no—
120C22×C11#12011yescharacteristic
121C22×C11#12111yescharacteristic
122C22×C11#12311yescharacteristic
123C22×C11C2×D811yescharacteristic
124C22×C11#13511yescharacteristic
125C22×C11AGL(1,ℤ/8)11yescharacteristic
126C22×C11#13711yescharacteristic
127C2×D11—42no—
128C2×D11—42no—
129C2×D11—42no—
130C2×D11—81no—
131C2×D11—81no—
132C2×D11—81no—
133C2×D11—81no—
134C4×C11—41no—
135C4×C11—81no—
136C4×C11—81no—
137C4×C11#12111yescharacteristic
138C4×C11#12111yescharacteristic
139C4×C11#12311yescharacteristic
140C4×C11#12411yescharacteristic
141Dic11—42no—
142C22×D4—111no—
143C22×D4—221no—
144C23×C4C2×D1111yescharacteristic
145C22×C8—111no—
146C22×C8—111no—
147#121—222no—
148#121—222no—
149C2×C4⋊C4—111no—
150C2×C4⋊C4C2×D1111yescharacteristic
151C2×C4⋊C4C2×D1111yescharacteristic
152C2×C22⋊C4—21no—
153C2×C22⋊C4—221no—
154#107—222no—
155#102—222no—
156#102—222no—
157C22⋊C8—222no—
158#95—21no—
159C2×C11—42no—
160C2×C11#39411yescharacteristic
161C2×C11#44711yescharacteristic
162C2×C11#45211yescharacteristic
163C2×C11#46611yescharacteristic
164C2×C11#46811yescharacteristic
165C2×C11#48011yescharacteristic
166C2×C11#48211yescharacteristic
167D11—82no—
168C24—221no—
169C24C22⋊D1111yescharacteristic
170C2×D4—112no—
171C2×D4—224no—
172C2×D4—221no—
173C2×D4—221no—
174C2×D4—221no—
175C2×D4—221no—
176C2×D4—221no—
177C2×D4—442no—
178C2×D4—442no—
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—21no—
187C22×C4—221no—
188C22×C4C22⋊D1111yescharacteristic
189C22×C4C22×D1111yescharacteristic
190C2×C8—112no—
191C2×C8—221no—
192C2×C8—221no—
193C2×C8—221no—
194C2×C8—221no—
195C2×C8—221no—
196C4⋊C4—21no—
197C4⋊C4—21no—
198C4⋊C4—21no—
199C4⋊C4—21no—
200C4⋊C4—112no—
201C4⋊C4—221no—
202C22⋊C4—42no—
203C22⋊C4—224no—
204C11#203311yescharacteristic, complemented, Sylow
205C23—21no—
206C23—21no—
207C23—21no—
208C23—21no—
209C23—21no—
210C23—21no—
211C23—222no—
212C23—441no—
213C23—441no—
214C23—441no—
215C23—441no—
216C23—441no—
217C23—441no—
218C23#432312yes—
219C23C2×C22⋊D1111yescharacteristic
220D4—222no—
221D4—222no—
222D4—448no—
223D4—441no—
224D4—441no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—222no—
239C2×C4—441no—
240C2×C4—441no—
241C2×C4#433911yescharacteristic
242C2×C4#433911yescharacteristic
243C2×C4D4×D1111yescharacteristic
244C2×C4D4×D1111yescharacteristic
245C2×C4D4×D1111yescharacteristic
246C2×C4#434111yescharacteristic
247C8—222no—
248C8—441no—
249C22—22no—
250C22—22no—
251C22—22no—
252C22—41no—
253C22—41no—
254C22—41no—
255C22—41no—
256C22—442no—
257C22—442no—
258C22—442no—
259C22—881no—
260C22—881no—
261C22—881no—
262C22—881no—
263C22#6698211yescharacteristic
264C22C2×#432311yescharacteristic
265C22#6699011yescharacteristic
266C22#6699211yescharacteristic
267C22#6699511yescharacteristic
268C22#6700211yescharacteristic
269C22#6700311yescharacteristic
270C4—41no—
271C4—81no—
272C4—81no—
273C4—442no—
274C4#6693611yescharacteristic
275C4#6693711yescharacteristic
276C4#6693711yescharacteristic
277C4#6693811yescharacteristic
278C2—42no—
279C2—882no—
280C2#1062257211yescharacteristic
281C2#1062258011yescharacteristic
282C2#1062261611yescharacteristic
283C2#1062264911yescharacteristic
284C2#1062265111yescharacteristic
285C2#1062266011yescharacteristic
286C2#1062266211yescharacteristic
subgroupG/H
centerC23C2×C22⋊D11
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC11×#380C2
socleC23×C11C2×D4
prime radicalC2×#66983C2
hypercenter#380D11
hypocenterC11#2033
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
2. C11×#380C2semidirect
3. C2×C22⋊(C11⋊C8)C2semidirect
4. C2×#66873C2semidirect
5. C2×#66873C2semidirect
6. C2×#66871C2semidirect
7. #10622167C2semidirect
60. C2×C11⋊C8D4semidirect
111. #380D11semidirect
204. C11#2033semidirect

Maximal subgroups

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

subgroupindex
C2×#669832
C11×#3802
C2×C22⋊(C11⋊C8)2
C2×#668732
C2×#668712
#106221672
#203311