Finite Group Databasebeta

← #13078594

Subgroups — #13078594

Order 1408.

398 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 133 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
1C11×#520C211yesmaximal, characteristic, complemented
2#10623364C211yesmaximal, characteristic
3#10622847C211yesmaximal, characteristic, complemented
4#10622616C212yesmaximal, complemented
5#10622615C211yesmaximal, characteristic, complemented
6#10622609C212yesmaximal, complemented
7#10622608C211yesmaximal, characteristic, complemented
8#10622583C212yesmaximal, complemented
9#10622580C212yesmaximal, complemented
10#10622579C211yesmaximal, characteristic, complemented
11C2×#66871C211yesmaximal, characteristic, complemented
12C2×C11×#41C2211yescharacteristic
13C2×#4339C2211yescharacteristic
14C4×Q8×C11—21no—
15C4×D4×C11—21no—
16C4×D4×C11—22no—
17C11×#117C2211yescharacteristic
18C11×#117C2212yes—
19C2×C11×C4⋊C4C2211yescharacteristic
20C2×C11×C4⋊C4C2212yes—
21#66999—21no—
22#66992—22no—
23#66991—21no—
24#66983C2212yes—
25C2×C4⋊Dic11C2211yescharacteristic
26#66977C2212yes—
27C2×#4318C2211yescharacteristic
28C22×C11⋊C8C2211yescharacteristic
29C22⋊(C11⋊C8)C2212yes—
30C22⋊(C11⋊C8)C2212yes—
31#66874C2212yes—
32#66874C2211yescharacteristic
33#66874C2211yescharacteristic
34#66873C2212yes—
35#66873C2211yescharacteristic
36#66873C2211yescharacteristic
37#66872C2212yes—
38#66871C2212yes—
39#66871C2212yes—
40#66871C2212yes—
41C11×#41—22no—
42C11×#41—22no—
43C2×Q8×C11D411yescharacteristic
44C2×D4×C11D411yescharacteristic
45C2×D4×C11D412yes—
46C22×C4×C11—22no—
47C22×C4×C11—21no—
48C22×C4×C11C2312yes—
49C22×C4×C11C2311yescharacteristic
50C2×C22⋊D11—21no—
51C2×C22⋊D11—22no—
52C22×Dic11—21no—
53#4339—22no—
54#4339—22no—
55C2×D44C2311yescharacteristic
56C2×C4×D11—21no—
57C2×Dic22C2311yescharacteristic
58C11×C4⋊C4—22no—
59C11×C4⋊C4—21no—
60C11×C4⋊C4C2312yes—
61C11×C4⋊C4C2311yescharacteristic
62C11×C4⋊C4C2311yescharacteristic
63C11×C22⋊C4—22no—
64C11×C22⋊C4—21no—
65C42×C11—22no—
66C42×C11—21no—
67C22⋊Dic11—22no—
68(C2×D11)⋊C4—22no—
69C4⋊Dic11—21no—
70C4⋊Dic11C2312yes—
71Dic11⋊C4—22no—
72#4318—22no—
73C2×C11⋊C8—22no—
74C2×C11⋊C8C2311yescharacteristic
75C2×C11⋊C8C2311yescharacteristic
76C2×C11⋊C8C2312yes—
77#3098—111nomaximal, Sylow
78C23×C11C2×D412yes—
79C23×C11C2×D411yescharacteristic
80C22×D11—21no—
81Q8×C11—22no—
82D4×C11—24no—
83D4×C11—22no—
84C2×C4×C11—22no—
85C2×C4×C11—22no—
86C2×C4×C11—21no—
87C2×C4×C11—22no—
88C2×C4×C11—21no—
89C2×C4×C11—81no—
90C2×C4×C11—82no—
91C2×C4×C11C2×D412yes—
92C2×C4×C11C2×D411yescharacteristic
93C2×C4×C11#4112yes—
94C2×C4×C11#4112yes—
95C2×C4×C11C2411yescharacteristic
96C22⋊D11—42no—
97C22⋊D11—82no—
98C2×Dic11—21no—
99C2×Dic11—22no—
100C2×Dic11—81no—
101D44—21no—
102D44—21no—
103C4×D11—42no—
104Dic22—21no—
105Dic22—21no—
106C11⋊C8—21no—
107C11⋊C8—21no—
108C11⋊C8—22no—
109#537—111no—
110#520D1111yescharacteristic, complemented
111#485—112no—
112#484—112no—
113#482—112no—
114#480—112no—
115#428—111no—
116C2×#107—111no—
117#417—111no—
118#416—111no—
119#408—111no—
120C22×C11—21no—
121C22×C11—21no—
122C22×C11—22no—
123C22×C11—22no—
124C22×C11—22no—
125C22×C11#12312yes—
126C22×C11C22×D411yescharacteristic
127C2×D11—41no—
128C2×D11—41no—
129C2×D11—41no—
130C4×C11—22no—
131C4×C11—42no—
132C4×C11—41no—
133C4×C11—41no—
134C4×C11#12312yes—
135C4×C11C2×#4111yescharacteristic
136C4×C11C2×#4111yescharacteristic
137Dic11—41no—
138Dic11—42no—
139C2×#41—111no—
140C2×#41C2×D1111yescharacteristic
141C2×M16—111no—
142C22×C8—111no—
143C22⋊Q8—112no—
144C22⋊Q8—221no—
145#121—112no—
146#121—221no—
147#121—222no—
148C4×Q8—21no—
149C4×D4—22no—
150C4×D4—21no—
151#117C2×D1111yescharacteristic
152#117C2×D1112yes—
153C2×C4⋊C4—111no—
154C2×C4⋊C4C2×D1111yescharacteristic
155C2×C4⋊C4C2×D1112yes—
156#107—112no—
157#107—112no—
158#107—112no—
159#106—112no—
160#103—111no—
161#103—111no—
162#103—112no—
163#102—111no—
164#102—111no—
165#102—112no—
166C22⋊C8—112no—
167C22⋊C8—112no—
168C2×C11—22no—
169C2×C11—42no—
170C2×C11C2×#12311yescharacteristic
171C2×C11#57611yescharacteristic
172C2×C11#57811yescharacteristic
173D11—81no—
174#41—22no—
175#41—22no—
176#41—222no—
177#41—222no—
178C2×Q8—111no—
179C2×Q8C22⋊D1111yescharacteristic
180C2×D4—111no—
181C2×D4—221no—
182C2×D4—222no—
183C2×D4C22⋊D1112yes—
184C2×D4C22⋊D1111yescharacteristic
185C22×C4—22no—
186C22×C4—21no—
187C22×C4—221no—
188C22×C4—221no—
189C22×C4C22×D1112yes—
190C22×C4C22×D1111yescharacteristic
191M16—222no—
192C2×C8—112no—
193C2×C8—111no—
194C2×C8—111no—
195C2×C8—222no—
196C4⋊C4—22no—
197C4⋊C4—21no—
198C4⋊C4—112no—
199C4⋊C4—221no—
200C4⋊C4—222no—
201C4⋊C4C22×D1111yescharacteristic
202C4⋊C4C22×D1111yescharacteristic
203C4⋊C4C22×D1112yes—
204C22⋊C4—22no—
205C22⋊C4—21no—
206C22⋊C4—222no—
207C22⋊C4—222no—
208C42—22no—
209C42—21no—
210C11#309811yescharacteristic, complemented, Sylow
211C23—221no—
212C23C2×C22⋊D1112yes—
213C23C2×C22⋊D1111yescharacteristic
214Q8—22no—
215Q8—221no—
216Q8—221no—
217D4—24no—
218D4—22no—
219D4—221no—
220D4—221no—
221D4—442no—
222D4—882no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—21no—
228C2×C4—81no—
229C2×C4—82no—
230C2×C4—222no—
231C2×C4—221no—
232C2×C4—442no—
233C2×C4—881no—
234C2×C4#433912yes—
235C2×C4#433912yes—
236C2×C4C2×C22⋊D1112yes—
237C2×C4C2×C22⋊D1111yescharacteristic
238C2×C4C23×D1111yescharacteristic
239C8—221no—
240C8—221no—
241C8—222no—
242C22—21no—
243C22—21no—
244C22—22no—
245C22—22no—
246C22—22no—
247C22—441no—
248C22—441no—
249C22—441no—
250C22#6698212yes—
251C22C22×C22⋊D1111yescharacteristic
252C4—22no—
253C4—42no—
254C4—41no—
255C4—41no—
256C4—441no—
257C4—442no—
258C4#6698212yes—
259C4C2×#433911yescharacteristic
260C4C2×#433911yescharacteristic
261C2—22no—
262C2—42no—
263C2—881no—
264C2C2×#6698211yescharacteristic
265C2#1062336611yescharacteristic
266C2#1062336911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#520C2
socleC22×C11C22×D4
prime radical#10623364C2
hypercenter#520D11
hypocenterC11#3098
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#41 ◁ #520

Complements

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

NH ≅ G/Ntype
1. C11×#520C2semidirect
3. #10622847C2semidirect
4. #10622616C2semidirect
5. #10622615C2semidirect
6. #10622609C2semidirect
7. #10622608C2semidirect
8. #10622583C2semidirect
9. #10622580C2semidirect
10. #10622579C2semidirect
11. C2×#66871C2semidirect
110. #520D11semidirect
210. C11#3098semidirect

Maximal subgroups

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

subgroupindex
C11×#5202
#106233642
#106228472
#106226162
#106226152
#106226092
#106226082
#106225832
#106225802
#106225792
C2×#668712
#309811