Finite Group Databasebeta

← #13069692

Subgroups — #13069692

Order 1408.

426 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 89 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
1C22×#4324C211yesmaximal, characteristic, complemented
2C22×#4323C211yesmaximal, characteristic
3C2×#66928C211yesmaximal, characteristic, complemented
4C11×#390C211yesmaximal, characteristic, complemented
5C2×#66874C211yesmaximal, characteristic, complemented
6C2×#66873C211yesmaximal, characteristic, complemented
7#10622162C211yesmaximal, characteristic, complemented
8C22×D4×C11C2211yescharacteristic
9C22×D44C2211yescharacteristic
10C22×Dic22C2211yescharacteristic
11C2×C11×C4⋊C4C2211yescharacteristic
12C2×C11×C22⋊C4—22no—
13C2×C42×C11C2211yescharacteristic
14C2×#4324—22no—
15C2×#4324—22no—
16C2×#4324—22no—
17C2×#4323—22no—
18C2×#4323—22no—
19C2×#4323—22no—
20C2×(C2×D11)⋊C4—22no—
21C22×C11⋊C8C2211yescharacteristic
22C22×C11⋊C8C2211yescharacteristic
23#66928—22no—
24#66928—22no—
25#66874—22no—
26#66873—22no—
27C24×C11—21no—
28C23×D11—21no—
29C2×D4×C11—21no—
30C2×D4×C11—21no—
31C2×D4×C11—21no—
32C2×D4×C11—21no—
33C2×D4×C11—21no—
34C2×D4×C11D412yes—
35C22×C4×C11—21no—
36C22×C4×C11D412yes—
37C22×C4×C11C2311yescharacteristic
38C22×Dic11—21no—
39C2×D44—21no—
40C2×D44—21no—
41C2×D44—21no—
42C2×D44—21no—
43C2×D44—21no—
44C2×D44D412yes—
45C2×Dic22—21no—
46C2×Dic22—21no—
47C2×Dic22—21no—
48C2×Dic22—21no—
49C2×Dic22—21no—
50C2×Dic22D412yes—
51C11×C4⋊C4—21no—
52C11×C4⋊C4—21no—
53C11×C22⋊C4—44no—
54C42×C11—21no—
55C42×C11—21no—
56#4324—28no—
57#4323—28no—
58(C2×D11)⋊C4—28no—
59C2×C11⋊C8—21no—
60C2×C11⋊C8—21no—
61C2×C11⋊C8—21no—
62C2×C11⋊C8—21no—
63C2×C11⋊C8D412yes—
64C2×C11⋊C8D412yes—
65#2012—111nomaximal, Sylow
66C23×C11—22no—
67C23×C11—41no—
68C23×C11—41no—
69C23×C11—42no—
70C23×C11—42no—
71C23×C11C2×D411yescharacteristic
72C22×D11—22no—
73C22×D11—41no—
74C22×D11—41no—
75C22×D11—42no—
76C22×D11—42no—
77D4×C11—22no—
78D4×C11—22no—
79D4×C11—41no—
80D4×C11—41no—
81C2×C4×C11—22no—
82C2×C4×C11—22no—
83C2×C4×C11—22no—
84C2×C4×C11—41no—
85C2×C4×C11—42no—
86C2×C4×C11C2×D411yescharacteristic
87C2×C4×C11C2×D411yescharacteristic
88C2×C4×C11C2×D411yescharacteristic
89C2×C4×C11C2×D411yescharacteristic
90C2×C4×C11C2×D411yescharacteristic
91C2×C4×C11#4111yescharacteristic
92C2×Dic11—22no—
93C2×Dic11—41no—
94C2×Dic11—41no—
95D44—22no—
96D44—22no—
97D44—41no—
98D44—41no—
99Dic22—22no—
100Dic22—22no—
101Dic22—41no—
102Dic22—41no—
103C11⋊C8—22no—
104C11⋊C8—22no—
105C22×SD16—111no—
106C22×D8—111no—
107C2×#124—111no—
108C2×#103—111no—
109C2×#102—111no—
110#390D1111yescharacteristic, complemented
111#336—111no—
112C22×C11—42no—
113C22×C11—44no—
114C22×C11—82no—
115C22×C11—81no—
116C22×C11—81no—
117C22×C11#12011yescharacteristic
118C22×C11#12111yescharacteristic
119C22×C11#12711yescharacteristic
120C22×C11#13512yes—
121C22×C11AGL(1,ℤ/8)12yes—
122C2×D11—42no—
123C2×D11—44no—
124C2×D11—82no—
125C2×D11—81no—
126C2×D11—81no—
127C4×C11—42no—
128C4×C11—81no—
129C4×C11#12011yescharacteristic
130C4×C11#12011yescharacteristic
131C4×C11#12111yescharacteristic
132C4×C11#12111yescharacteristic
133Dic11—42no—
134C22×Q8—111no—
135C22×D4—111no—
136C22×D4C2×D1111yescharacteristic
137C2×SD16—222no—
138C2×SD16—222no—
139C2×SD16—222no—
140C2×D8—222no—
141C2×D8—222no—
142C2×D8—222no—
143C22×C8—111no—
144C22×C8—111no—
145#124—222no—
146#124—222no—
147C2×C4⋊C4C2×D1111yescharacteristic
148C2×C22⋊C4—22no—
149C2×C22⋊C4—222no—
150C2×C42C2×D1111yescharacteristic
151#103—222no—
152#102—222no—
153C2×C11—82no—
154C2×C11#39211yescharacteristic
155C2×C11#44912yes—
156C2×C11#46312yes—
157C2×C11#49511yescharacteristic
158C2×C11#49611yescharacteristic
159D11—82no—
160C24—21no—
161C24—221no—
162C2×Q8—112no—
163C2×Q8—221no—
164C2×Q8—221no—
165C2×Q8—221no—
166C2×Q8—221no—
167C2×Q8—221no—
168C2×D4—21no—
169C2×D4—21no—
170C2×D4—21no—
171C2×D4—21no—
172C2×D4—21no—
173C2×D4—112no—
174C2×D4—221no—
175C2×D4—221no—
176C2×D4—221no—
177C2×D4—221no—
178C2×D4—221no—
179C2×D4D4412yes—
180C22×C4—21no—
181C22×C4—221no—
182C22×C4C22⋊D1112yes—
183C22×C4C22×D1111yescharacteristic
184SD16—228no—
185D8—228no—
186C2×C8—112no—
187C2×C8—112no—
188C2×C8—221no—
189C2×C8—221no—
190C2×C8—221no—
191C2×C8—221no—
192C4⋊C4—21no—
193C4⋊C4—21no—
194C22⋊C4—44no—
195C22⋊C4—228no—
196C42—21no—
197C42—21no—
198C11#201211yescharacteristic, complemented, Sylow
199C23—22no—
200C23—42no—
201C23—41no—
202C23—41no—
203C23—42no—
204C23—222no—
205C23—441no—
206C23—442no—
207C23—441no—
208C23—442no—
209C23C2×C22⋊D1111yescharacteristic
210Q8—222no—
211Q8—222no—
212Q8—441no—
213Q8—441no—
214D4—22no—
215D4—22no—
216D4—41no—
217D4—41no—
218D4—222no—
219D4—222no—
220D4—441no—
221D4—441no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—42no—
226C2×C4—41no—
227C2×C4—222no—
228C2×C4—441no—
229C2×C4—441no—
230C2×C4C2×D4411yescharacteristic
231C2×C4#433911yescharacteristic
232C2×C4D4×D1111yescharacteristic
233C2×C4D4×D1111yescharacteristic
234C2×C4D4×D1111yescharacteristic
235C2×C4D4×D1111yescharacteristic
236C8—222no—
237C8—222no—
238C22—42no—
239C22—44no—
240C22—82no—
241C22—81no—
242C22—81no—
243C22—442no—
244C22—444no—
245C22—882no—
246C22—881no—
247C22—881no—
248C22#6698311yescharacteristic
249C22#6698512yes—
250C22#6699011yescharacteristic
251C22#6699311yescharacteristic
252C22#6700312yes—
253C4—42no—
254C4—81no—
255C4—442no—
256C4#6693511yescharacteristic
257C4#6693511yescharacteristic
258C4#6693711yescharacteristic
259C4#6693711yescharacteristic
260C2—82no—
261C2—882no—
262C2#1062257311yescharacteristic
263C2#1062262912yes—
264C2#1062265012yes—
265C2#1062267211yescharacteristic
266C2#1062268711yescharacteristic
subgroupG/H
centerC23C2×C22⋊D11
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC11×#390C2
socleC23×C11C2×D4
prime radicalC22×#4323C2
hypercenter#390D11
hypocenterC11#2012
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C22×#4324C2semidirect
3. C2×#66928C2semidirect
4. C11×#390C2semidirect
5. C2×#66874C2semidirect
6. C2×#66873C2semidirect
7. #10622162C2semidirect
110. #390D11semidirect
198. C11#2012semidirect

Maximal subgroups

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

subgroupindex
C22×#43242
C22×#43232
C2×#669282
C11×#3902
C2×#668742
C2×#668732
#106221622
#201211