Finite Group Databasebeta

← #13078601

Subgroups — #13078601

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×#537C211yesmaximal, characteristic
2#10623358C211yesmaximal, characteristic, complemented
3#10622847C211yesmaximal, characteristic, complemented
4#10622846C211yesmaximal, characteristic, complemented
5#10622845C211yesmaximal, characteristic, complemented
6#10622658C212yesmaximal, complemented
7#10622656C212yesmaximal, complemented
8#10622648C212yesmaximal, complemented
9#10622647C212yesmaximal, complemented
10#10622577C211yesmaximal, characteristic, complemented
11C2×#66872C211yesmaximal, characteristic, complemented
12C2×C11×#41C2211yescharacteristic
13C2×C11×#41C2211yescharacteristic
14C11×C22⋊Q8—21no—
15C11×C22⋊Q8C2212yes—
16C11×#121—21no—
17C11×#121—22no—
18C11×#121C2212yes—
19C2×C11×C4⋊C4C2211yescharacteristic
20Q8×Dic11—21no—
21D4×Dic11—22no—
22D4×Dic11—21no—
23#66979C2211yescharacteristic
24#66979C2212yes—
25C2×C4⋊Dic11C2211yescharacteristic
26C2×C4⋊Dic11C2212yes—
27C2×#4318C2211yescharacteristic
28C22×C11⋊C8C2211yescharacteristic
29#66899C2212yes—
30#66899C2211yescharacteristic
31#66899C2211yescharacteristic
32#66896C2212yes—
33#66896C2211yescharacteristic
34#66896C2211yescharacteristic
35C22⋊(C11⋊C8)C2212yes—
36C22⋊(C11⋊C8)C2212yes—
37#66872C2212yes—
38#66872C2212yes—
39#66872C2212yes—
40#66871C2212yes—
41C11×#41—22no—
42C11×#41—22no—
43C11×#41—22no—
44C11×#41—22no—
45C2×Q8×C11D411yescharacteristic
46C2×Q8×C11C2311yescharacteristic
47C2×D4×C11—21no—
48C2×D4×C11—22no—
49C2×D4×C11D412yes—
50C2×D4×C11D411yescharacteristic
51C2×D4×C11C2311yescharacteristic
52C22×C4×C11—21no—
53C22×C4×C11—21no—
54C22×C4×C11C2312yes—
55C22×C4×C11C2311yescharacteristic
56C22×Dic11—22no—
57C22×Dic11—21no—
58C11×C4⋊C4—21no—
59C11×C4⋊C4—22no—
60C11×C4⋊C4C2312yes—
61C11×C22⋊C4—22no—
62C11×C22⋊C4—22no—
63C22⋊Dic11—22no—
64C22⋊Dic11—21no—
65C4⋊Dic11—22no—
66C4⋊Dic11—21no—
67C4⋊Dic11C2311yescharacteristic
68C4⋊Dic11C2312yes—
69C4⋊Dic11C2311yescharacteristic
70C4×Dic11—22no—
71C4×Dic11—21no—
72#4318—22no—
73C2×C11⋊C8—22no—
74C2×C11⋊C8C2312yes—
75C2×C11⋊C8C2311yescharacteristic
76C2×C11⋊C8C2311yescharacteristic
77#3099—111nomaximal, Sylow
78C23×C11—21no—
79C23×C11C2×D412yes—
80C23×C11C2×D411yescharacteristic
81Q8×C11—22no—
82Q8×C11—21no—
83Q8×C11—21no—
84D4×C11—24no—
85D4×C11—22no—
86D4×C11—21no—
87D4×C11—21no—
88D4×C11—42no—
89D4×C11—82no—
90C2×C4×C11—22no—
91C2×C4×C11—22no—
92C2×C4×C11—22no—
93C2×C4×C11—21no—
94C2×C4×C11—42no—
95C2×C4×C11—81no—
96C2×C4×C11C2×D412yes—
97C2×C4×C11C2×D411yescharacteristic
98C2×C4×C11#4112yes—
99C2×C4×C11#4112yes—
100C2×C4×C11C2411yescharacteristic
101C2×Dic11—21no—
102C2×Dic11—22no—
103C2×Dic11—21no—
104C2×Dic11—81no—
105C2×Dic11—82no—
106C11⋊C8—21no—
107C11⋊C8—21no—
108C11⋊C8—22no—
109#537D1111yescharacteristic
110#520—111no—
111#485—112no—
112#483—112no—
113#482—112no—
114#481—112no—
115#428—111no—
116C2×#106—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—41no—
126C22×C11—41no—
127C22×C11—41no—
128C22×C11#12312yes—
129C22×C11C22×D411yescharacteristic
130C4×C11—22no—
131C4×C11—41no—
132C4×C11—42no—
133C4×C11#12312yes—
134C4×C11C2×#4111yescharacteristic
135C4×C11C2×#4111yescharacteristic
136Dic11—41no—
137Dic11—42no—
138Dic11—41no—
139C2×#41C2×D1111yescharacteristic
140C2×#41C2×D1111yescharacteristic
141C2×M16—111no—
142C22×C8—111no—
143C22⋊Q8—21no—
144C22⋊Q8C2×D1112yes—
145#121—21no—
146#121—22no—
147#121C2×D1112yes—
148C4×Q8—221no—
149C4×D4—222no—
150C4×D4—221no—
151#117—111no—
152#117—112no—
153C2×C4⋊C4—111no—
154C2×C4⋊C4—112no—
155C2×C4⋊C4C2×D1111yescharacteristic
156#107—112no—
157#106—112no—
158#106—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×C11—81no—
171C2×C11C2×#12311yescharacteristic
172C2×C11#57711yescharacteristic
173C2×C11#57711yescharacteristic
174#41—22no—
175#41—22no—
176#41—22no—
177#41—22no—
178C2×Q8C22⋊D1111yescharacteristic
179C2×Q8C22×D1111yescharacteristic
180C2×D4—21no—
181C2×D4—22no—
182C2×D4C22⋊D1112yes—
183C2×D4C22⋊D1111yescharacteristic
184C2×D4C22×D1111yescharacteristic
185C22×C4—21no—
186C22×C4—21no—
187C22×C4—222no—
188C22×C4—221no—
189C22×C4C22×D1112yes—
190C22×C4C22×D1111yescharacteristic
191M16—222no—
192C2×C8—111no—
193C2×C8—111no—
194C2×C8—112no—
195C2×C8—222no—
196C4⋊C4—21no—
197C4⋊C4—22no—
198C4⋊C4—111no—
199C4⋊C4—112no—
200C4⋊C4—111no—
201C4⋊C4—222no—
202C4⋊C4—221no—
203C4⋊C4C22×D1112yes—
204C22⋊C4—22no—
205C22⋊C4—22no—
206C22⋊C4—222no—
207C22⋊C4—221no—
208C42—222no—
209C42—221no—
210C11#309911yescharacteristic, complemented, Sylow
211C23—21no—
212C23C2×C22⋊D1112yes—
213C23C2×C22⋊D1111yescharacteristic
214Q8—22no—
215Q8—21no—
216Q8—21no—
217D4—24no—
218D4—22no—
219D4—21no—
220D4—21no—
221D4—42no—
222D4—82no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—21no—
227C2×C4—42no—
228C2×C4—81no—
229C2×C4—221no—
230C2×C4—222no—
231C2×C4—221no—
232C2×C4—881no—
233C2×C4—882no—
234C2×C4#434112yes—
235C2×C4#434112yes—
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—41no—
248C22—41no—
249C22—41no—
250C22#6698812yes—
251C22C22×C22⋊D1111yescharacteristic
252C4—22no—
253C4—41no—
254C4—42no—
255C4—441no—
256C4—442no—
257C4—441no—
258C4#6698812yes—
259C4C2×#434111yescharacteristic
260C4C2×#434111yescharacteristic
261C2—22no—
262C2—42no—
263C2—81no—
264C2C2×#6698811yescharacteristic
265C2#1062336711yescharacteristic
266C2#1062336811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
Fitting, prime radicalC11×#537C2
socleC22×C11C22×D4
hypercenter#537D11
hypocenterC11#3099
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#41 ◁ #537

Complements

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

NH ≅ G/Ntype
2. #10623358C2semidirect
3. #10622847C2semidirect
4. #10622846C2semidirect
5. #10622845C2semidirect
6. #10622658C2semidirect
7. #10622656C2semidirect
8. #10622648C2semidirect
9. #10622647C2semidirect
10. #10622577C2semidirect
11. C2×#66872C2semidirect
210. C11#3099semidirect

Maximal subgroups

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

subgroupindex
C11×#5372
#106233582
#106228472
#106228462
#106228452
#106226582
#106226562
#106226482
#106226472
#106225772
C2×#668722
#309911