Finite Group Databasebeta

← #27205694

Subgroups — #27205694

Order 13184.

348 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 149 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
1#20268344C211yesmaximal, characteristic
2C2×#15693012C211yesmaximal, characteristic
3#20268199C212yesmaximal, complemented
4#20268198C212yesmaximal, complemented
5#20268192C212yesmaximal, complemented
6#20268191C212yesmaximal, complemented
7#20267834C211yesmaximal, characteristic
8#20267833C211yesmaximal, characteristic
9#20267831C211yesmaximal, characteristic
10M16×Dic103C211yesmaximal, characteristic
11#428×C103C211yesmaximal, characteristic
12C2×#13110089C2211yescharacteristic
13#15693020C2211yescharacteristic
14#15693020C2211yescharacteristic
15#15693012—21no—
16#15693012—21no—
17#15693012C2212yes—
18#15693012C2212yes—
19#15693012C2211yescharacteristic
20#15693012C2211yescharacteristic
21#15692998—21no—
22#15692998—21no—
23C4×Dic206—21no—
24C4×Dic206—21no—
25#15692980C2211yescharacteristic
26C2×C4⋊Dic103—21no—
27C2×C4⋊Dic103C2211yescharacteristic
28C2×Dic103⋊C4—21no—
29C2×C4×Dic103C2211yescharacteristic
30#15692955C2212yes—
31#15692954C2212yes—
32#15692954C2212yes—
33#15692953C2212yes—
34#15692952C2212yes—
35#15692952C2212yes—
36#15692931C2212yes—
37C8×Dic103C2212yes—
38C2×M16×C103C2211yescharacteristic
39#117×C103C2211yescharacteristic
40C2×C4⋊C4×C103C2211yescharacteristic
41#107×C103C2212yes—
42#106×C103C2212yes—
43C2×Dic206—21no—
44C2×Dic206—21no—
45C22×Dic103—21no—
46C22×Dic103D411yescharacteristic
47C22×Dic103D411yescharacteristic
48#13110089Q814yescomplemented
49C2×C103⋊C8C2312yes—
50C4⋊Dic103—21no—
51C4⋊Dic103—22no—
52C4⋊Dic103—22no—
53C4⋊Dic103—21no—
54C4⋊Dic103—21no—
55C4⋊Dic103C2311yescharacteristic
56C4⋊Dic103C2312yes—
57C4⋊Dic103C2311yescharacteristic
58Dic103⋊C4—22no—
59Dic103⋊C4—22no—
60Dic103⋊C4—21no—
61Dic103⋊C4—21no—
62Dic103⋊C4—21no—
63Dic103⋊C4—21no—
64C22⋊Dic103—21no—
65C4×Dic103—21no—
66C4×Dic103D411yescharacteristic
67C4×Dic103D411yescharacteristic
68C4×Dic103C2311yescharacteristic
69C4×Dic103C2311yescharacteristic
70C22×C4×C103—21no—
71C22×C4×C103C2311yescharacteristic
72M16×C103Q814yescomplemented
73C2×C8×C103C2312yes—
74C4⋊C4×C103—21no—
75C4⋊C4×C103C2311yescharacteristic
76C4⋊C4×C103C2312yes—
77C4⋊C4×C103C2311yescharacteristic
78C22⋊C4×C103—21no—
79C42×C103—21no—
80C23×C103C2×D411yescharacteristic
81C2×C4×C103—21no—
82C2×C4×C103—21no—
83C2×C4×C103—22no—
84C2×C4×C103—42no—
85C2×C4×C103C2×D411yescharacteristic
86C2×C4×C103C2×Q812yes—
87C2×C4×C103C2×Q812yes—
88C2×C4×C103C2411yescharacteristic
89C2×Dic103—21no—
90C2×Dic103—21no—
91C2×Dic103—22no—
92C2×Dic103—41no—
93C2×Dic103—41no—
94C2×Dic103—42no—
95C2×Dic103C2×D411yescharacteristic
96C2×Dic103C2×D411yescharacteristic
97C2×Dic103C2×D411yescharacteristic
98C2×Dic103C2×D411yescharacteristic
99Dic206—42no—
100Dic206—42no—
101C8×C103C2×Q814yes—
102C103⋊C8C2×Q814yes—
103C22×C103—21no—
104C22×C103—21no—
105C22×C103C4⋊Q812yes—
106C22×C103C22×D411yescharacteristic
107C4×C103—41no—
108C4×C103—41no—
109C4×C103—42no—
110C4×C103C4⋊Q812yes—
111C4×C103C22×Q811yescharacteristic
112C4×C103C22×Q811yescharacteristic
113Dic103—21no—
114Dic103—21no—
115Dic103—21no—
116Dic103—21no—
117Dic103—41no—
118Dic103—41no—
119Dic103—42no—
120C2×C103—22no—
121C2×C103C2×C4⋊Q811yescharacteristic
122C2×C103#57511yescharacteristic
123C2×C103#57511yescharacteristic
124#3166—1031nomaximal, Sylow
125C103#316611yescharacteristic, complemented, Sylow
126#533—1031no—
127C2×#125—1031no—
128#501—1032no—
129#501—1032no—
130#499—1032no—
131#499—1032no—
132#428—1031no—
133#428—1031no—
134#428—1031no—
135#428D10311yescharacteristic
136C4×M16—1031no—
137C2×M16—1031no—
138C2×M16C2×D10311yescharacteristic
139C4⋊Q8—1031no—
140C4⋊Q8—1031no—
141#125—1032no—
142#125—1032no—
143#125—1031no—
144#125—1031no—
145#125—2061no—
146#125—2061no—
147C22⋊Q8—2061no—
148C22⋊Q8—2061no—
149C4×Q8—2061no—
150C4×Q8—2061no—
151#117—1031no—
152#117C2×D10311yescharacteristic
153C2×C4⋊C4—1031no—
154C2×C4⋊C4—2061no—
155C2×C4⋊C4—2061no—
156C2×C4⋊C4C2×D10311yescharacteristic
157C2×C42—1031no—
158#107—1032no—
159#107—1032no—
160#107—1032no—
161#107C2×D10312yes—
162#106—1032no—
163#106—1032no—
164#106—1032no—
165#106C2×D10312yes—
166#97—1032no—
167C4×C8—1032no—
168C2×Q8—2061no—
169C2×Q8—2061no—
170C22×C4—21no—
171C22×C4—1031no—
172C22×C4—1031no—
173C22×C4—2061no—
174C22×C4C22×D10311yescharacteristic
175M16—1034no—
176M16Dic20614yescomplemented
177C2×C8—1032no—
178C2×C8C22×D10312yes—
179C4⋊C4—21no—
180C4⋊C4—1032no—
181C4⋊C4—1031no—
182C4⋊C4—1031no—
183C4⋊C4—2062no—
184C4⋊C4—2062no—
185C4⋊C4—2061no—
186C4⋊C4—2061no—
187C4⋊C4—2061no—
188C4⋊C4—2061no—
189C4⋊C4—2062no—
190C4⋊C4—2062no—
191C4⋊C4—2061no—
192C4⋊C4—2061no—
193C4⋊C4—2061no—
194C4⋊C4C22×D10311yescharacteristic
195C4⋊C4C22×D10312yes—
196C4⋊C4C22×D10311yescharacteristic
197C22⋊C4—21no—
198C22⋊C4—2061no—
199C42—21no—
200C42—1031no—
201C42—1031no—
202C42—1031no—
203C42—1031no—
204C42—2061no—
205C23D4×D10311yescharacteristic
206Q8—4122no—
207Q8—4122no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—42no—
212C2×C4—1031no—
213C2×C4—1031no—
214C2×C4—1031no—
215C2×C4—1031no—
216C2×C4—4122no—
217C2×C4—4121no—
218C2×C4—4121no—
219C2×C4—2061no—
220C2×C4—2061no—
221C2×C4—2062no—
222C2×C4D4×D10311yescharacteristic
223C2×C4Q8×D10312yes—
224C2×C4C2×Dic20612yes—
225C2×C4C23×D10311yescharacteristic
226C8—1034no—
227C8C2×Dic20614yes—
228C22—21no—
229C22—21no—
230C22#1569302012yes—
231C22C2×D4×D10311yescharacteristic
232C4—42no—
233C4—41no—
234C4—41no—
235C4—4121no—
236C4—4122no—
237C4—4121no—
238C4—2061no—
239C4—2061no—
240C4—2061no—
241C4—2061no—
242C4#1569302012yes—
243C4C2×Q8×D10311yescharacteristic
244C4C22×Dic20611yescharacteristic
245C2—22no—
246C2C2×#1569302011yescharacteristic
247C2#2026858711yescharacteristic
248C2#2026859011yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#428×C103C2
socleC22×C103C22×D4
prime radicalC23×C103C2×D4
hypercenter#428D103
hypocenterC103#3166
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
3. #20268199C2semidirect
4. #20268198C2semidirect
5. #20268192C2semidirect
6. #20268191C2semidirect
48. #13110089Q8semidirect
72. M16×C103Q8semidirect
125. C103#3166semidirect
176. M16Dic206semidirect

Maximal subgroups

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

subgroupindex
#202683442
C2×#156930122
#202681992
#202681982
#202681922
#202681912
#202678342
#202678332
#202678312
M16×Dic1032
#428×C1032
#3166103