Finite Group Databasebeta

← #13080910

Subgroups — #13080910

Order 1408.

386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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
1D4×Q8×C11C211yesmaximal, characteristic, complemented
2#10623094C211yesmaximal, characteristic
3#10622840C212yesmaximal, complemented
4#10622838C212yesmaximal, complemented
5#10622696C211yesmaximal, characteristic, complemented
6#10622694C211yesmaximal, characteristic, complemented
7#10622662C212yesmaximal, complemented
8#10622658C212yesmaximal, complemented
9C4×#4325C211yesmaximal, characteristic, complemented
10#10622634C211yesmaximal, characteristic, complemented
11#10622625C211yesmaximal, characteristic, complemented
12C22×Q8×C11C2212yes—
13C11×C4⋊Q8—21no—
14C11×C4⋊Q8C2211yescharacteristic
15C11×C22⋊Q8—22no—
16C11×C22⋊Q8C2212yes—
17C4×Q8×C11C2211yescharacteristic
18C4×D4×C11—21no—
19C4×D4×C11C2211yescharacteristic
20C2×#4325C2211yescharacteristic
21C2×#4325C2212yes—
22#66991—21no—
23#66983C2212yes—
24#66979C2212yes—
25C2×#4318C2212yes—
26#66945—21no—
27#66938—22no—
28C4×D44C2211yescharacteristic
29#66922C2211yescharacteristic
30#66899C2211yescharacteristic
31#66899C2212yes—
32#66899C2212yes—
33#66899C2212yes—
34#66899C2212yes—
35C22⋊(C11⋊C8)C2212yes—
36#66873C2211yescharacteristic
37#66872C2211yescharacteristic
38#66871C2212yes—
39C4⋊(C11⋊C8)C2211yescharacteristic
40C4×C11⋊C8C2211yescharacteristic
41C2×Q8×C11—22no—
42C2×Q8×C11—24no—
43C2×Q8×C11—42no—
44C2×Q8×C11C2312yes—
45C2×Q8×C11C2311yescharacteristic
46C2×D4×C11D411yescharacteristic
47C22×C4×C11—22no—
48C22×C4×C11C2312yes—
49C2×C22⋊D11—22no—
50C2×D44C2311yescharacteristic
51C2×C4×D11—21no—
52C2×Dic22—21no—
53C11×C4⋊C4—21no—
54C11×C4⋊C4—21no—
55C11×C4⋊C4—21no—
56C11×C4⋊C4—22no—
57C11×C4⋊C4D411yescharacteristic
58C11×C4⋊C4C2311yescharacteristic
59C11×C22⋊C4—22no—
60C11×C22⋊C4D412yes—
61C42×C11—21no—
62C42×C11C2311yescharacteristic
63C22⋊Dic11—22no—
64#4325—22no—
65#4325—42no—
66(C2×D11)⋊C4—21no—
67(C2×D11)⋊C4—22no—
68C4⋊Dic11—21no—
69C4⋊Dic11C2312yes—
70C4⋊Dic11C2311yescharacteristic
71C4×Dic11—22no—
72#4318—42no—
73C2×C11⋊C8C2311yescharacteristic
74C2×C11⋊C8C2311yescharacteristic
75C2×C11⋊C8C2312yes—
76#3329—111nomaximal, Sylow
77C23×C11C2×D412yes—
78C22×D11—21no—
79Q8×C11—21no—
80Q8×C11—22no—
81Q8×C11—22no—
82Q8×C11—44no—
83Q8×C11#4112yes—
84D4×C11—22no—
85C2×C4×C11—21no—
86C2×C4×C11—22no—
87C2×C4×C11—22no—
88C2×C4×C11—21no—
89C2×C4×C11—22no—
90C2×C4×C11—44no—
91C2×C4×C11C2×D412yes—
92C2×C4×C11C2×D411yescharacteristic
93C2×C4×C11C2×D411yescharacteristic
94C2×C4×C11C2411yescharacteristic
95C22⋊D11—82no—
96C2×Dic11—21no—
97C2×Dic11—22no—
98D44—21no—
99D44—21no—
100C4×D11—42no—
101Dic22—81no—
102C11⋊C8—21no—
103C11⋊C8—21no—
104C11⋊C8—22no—
105#555—111no—
106D4×Q8D1111yescharacteristic, complemented
107#487—111no—
108#485—112no—
109#477—111no—
110#468—112no—
111#461—111no—
112#448—112no—
113C4×SD16—111no—
114#436—111no—
115#419—112no—
116C22×C11—22no—
117C22×C11—22no—
118C22×C11—22no—
119C22×C11C22×D411yescharacteristic
120C2×D11—41no—
121C2×D11—41no—
122C2×D11—41no—
123C4×C11—22no—
124C4×C11—22no—
125C4×C11—21no—
126C4×C11—42no—
127C4×C11—41no—
128C4×C11#13712yes—
129C4×C11C2×#4111yescharacteristic
130C4×C11H(5,𝔽2)11yescharacteristic
131Dic11—41no—
132Dic11—42no—
133C22×Q8C2×D1112yes—
134C2×SD16—111no—
135C2×SD16—112no—
136C2×M16—112no—
137C4⋊Q8—21no—
138C4⋊Q8—111no—
139C4⋊Q8C2×D1111yescharacteristic
140#124—222no—
141C22⋊Q8—22no—
142C22⋊Q8C2×D1112yes—
143#121—112no—
144#121—221no—
145C4×Q8C2×D1111yescharacteristic
146C4×D4—21no—
147C4×D4—111no—
148C4×D4C2×D1111yescharacteristic
149#117—112no—
150#117—221no—
151#107—112no—
152#106—111no—
153C4⋊C8—111no—
154#103—111no—
155#103—112no—
156#103—112no—
157#103—112no—
158#103—112no—
159#102—111no—
160C22⋊C8—112no—
161C4×C8—111no—
162C2×C11—42no—
163C2×C11#54611yescharacteristic
164C2×C11C2×#13711yescharacteristic
165C2×C11#57711yescharacteristic
166D11—81no—
167C2×Q8—22no—
168C2×Q8—24no—
169C2×Q8—42no—
170C2×Q8—221no—
171C2×Q8C22×D1112yes—
172C2×Q8C22×D1111yescharacteristic
173C2×D4—111no—
174C2×D4—222no—
175C2×D4C22⋊D1111yescharacteristic
176C22×C4—22no—
177C22×C4—221no—
178C22×C4C22×D1112yes—
179SD16—222no—
180SD16—442no—
181M16—442no—
182C2×C8—111no—
183C2×C8—111no—
184C2×C8—112no—
185C4⋊C4—21no—
186C4⋊C4—21no—
187C4⋊C4—21no—
188C4⋊C4—22no—
189C4⋊C4—111no—
190C4⋊C4—112no—
191C4⋊C4—221no—
192C4⋊C4C22⋊D1111yescharacteristic
193C4⋊C4C22×D1111yescharacteristic
194C22⋊C4—22no—
195C22⋊C4—222no—
196C22⋊C4—222no—
197C22⋊C4—221no—
198C22⋊C4C22⋊D1112yes—
199C42—21no—
200C42—222no—
201C42C22×D1111yescharacteristic
202C11#332911yescharacteristic, complemented, Sylow
203C23—221no—
204C23C2×C22⋊D1112yes—
205Q8—21no—
206Q8—22no—
207Q8—22no—
208Q8—44no—
209Q8—881no—
210Q8#434112yes—
211D4—22no—
212D4—221no—
213D4—221no—
214D4—882no—
215C2×C4—21no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—44no—
221C2×C4—221no—
222C2×C4—222no—
223C2×C4—442no—
224C2×C4C2×C22⋊D1112yes—
225C2×C4C2×C22⋊D1111yescharacteristic
226C2×C4C2×C22⋊D1111yescharacteristic
227C2×C4C23×D1111yescharacteristic
228C8—221no—
229C8—221no—
230C8—222no—
231C22—22no—
232C22—22no—
233C22—22no—
234C22—441no—
235C22—441no—
236C22—441no—
237C22C22×C22⋊D1111yescharacteristic
238C4—22no—
239C4—22no—
240C4—21no—
241C4—42no—
242C4—41no—
243C4—441no—
244C4—442no—
245C4#6699512yes—
246C4C2×#434111yescharacteristic
247C4#6703711yescharacteristic
248C2—42no—
249C2—881no—
250C2#1062333711yescharacteristic
251C2C2×#6699511yescharacteristic
252C2#1062336811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingD4×Q8×C11C2
socleC22×C11C22×D4
prime radical#10623094C2
hypercenterD4×Q8D11
hypocenterC11#3329
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
1. D4×Q8×C11C2semidirect
3. #10622840C2semidirect
4. #10622838C2semidirect
5. #10622696C2semidirect
6. #10622694C2semidirect
7. #10622662C2semidirect
8. #10622658C2semidirect
9. C4×#4325C2semidirect
10. #10622634C2semidirect
11. #10622625C2semidirect
106. D4×Q8D11semidirect
202. C11#3329semidirect

Maximal subgroups

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

subgroupindex
D4×Q8×C112
#106230942
#106228402
#106228382
#106226962
#106226942
#106226622
#106226582
C4×#43252
#106226342
#106226252
#332911