Finite Group Databasebeta

← #27193662

Subgroups — #27193662

Order 13184.

294 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 65 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⋊Q8×D103C211yesmaximal, characteristic
2#20267753C211yesmaximal, characteristic
3#20267638C211yesmaximal, characteristic
4#20267529C211yesmaximal, characteristic, complemented
5#20267528C211yesmaximal, characteristic, complemented
6#20267527C211yesmaximal, characteristic, complemented
7#328×C103C211yesmaximal, characteristic, complemented
8C2×Q8×D103C411yescharacteristic, complemented
9C22×C4×D103C2211yescharacteristic
10C2×#13110088—21no—
11#15693001C411yescharacteristic, complemented
12#15693000C2211yescharacteristic
13#15692999—21no—
14#15692998—21no—
15#15692997C411yescharacteristic, complemented
16C4⋊C4×D103—21no—
17C4⋊C4×D103C411yescharacteristic, complemented
18C2×(C2×D103)⋊C4—21no—
19C22⋊C4×D103—21no—
20C2×C4×Dic103—21no—
21C22⋊(C103⋊C8)C2211yescharacteristic
22(C2×D103)⋊C8—21no—
23C103⋊#95C2211yescharacteristic
24C22⋊Q8×C103C2211yescharacteristic
25C22⋊C8×C103C2211yescharacteristic
26#95×C103C2211yescharacteristic
27C23×D103D411yescharacteristic
28C2×Dic206—21no—
29C2×Dic206C2×C411yescharacteristic
30Q8×D103—42no—
31C22×Dic103—21no—
32C22×Dic103D411yescharacteristic
33C2×C4×D103—21no—
34C2×C4×D103—21no—
35C2×C4×D103—42no—
36C2×C4×D103C2×C411yescharacteristic
37C2×C4×D103C2×C411yescharacteristic
38C2×C4×D103D411yescharacteristic
39C2×C4×D103D411yescharacteristic
40#13110088—42no—
41C2×C103⋊C8—21no—
42C4⋊Dic103—21no—
43C4⋊Dic103C2×C411yescharacteristic
44Dic103⋊C4—21no—
45Dic103⋊C4—21no—
46Dic103⋊C4—21no—
47C22⋊Dic103—21no—
48(C2×D103)⋊C4—24no—
49(C2×D103)⋊C4—21no—
50(C2×D103)⋊C4—21no—
51C4×Dic103—42no—
52C2×Q8×C103C2×C411yescharacteristic
53C22×C4×C103—21no—
54C22×C4×C103C2311yescharacteristic
55C2×C8×C103—21no—
56C4⋊C4×C103—21no—
57C4⋊C4×C103C2×C411yescharacteristic
58C22⋊C4×C103—21no—
59C23×C103C2×D411yescharacteristic
60C22×D103—21no—
61C22×D103—21no—
62C22×D103—22no—
63C22×D103—41no—
64C22×D103C22⋊C411yescharacteristic
65C22×D103C22⋊C411yescharacteristic
66Q8×C103—41no—
67C2×C4×C103—22no—
68C2×C4×C103—21no—
69C2×C4×C103—21no—
70C2×C4×C103—41no—
71C2×C4×C103—41no—
72C2×C4×C103—41no—
73C2×C4×C103C22×C411yescharacteristic
74C2×C4×C103C2×D411yescharacteristic
75C2×Dic103—22no—
76C2×Dic103—22no—
77C2×Dic103—21no—
78C2×Dic103—21no—
79C2×Dic103—41no—
80C2×Dic103—41no—
81C2×Dic103C22⋊C411yescharacteristic
82C2×Dic103C22⋊C411yescharacteristic
83C4×D103—22no—
84C4×D103—22no—
85C4×D103—41no—
86C4×D103—41no—
87C4×D103—42no—
88C4×D103—42no—
89Dic206—42no—
90Dic206—41no—
91C8×C103—41no—
92C103⋊C8—41no—
93C22×C103—21no—
94C22×C103—21no—
95C22×C103C2×C22⋊C411yescharacteristic
96C22×C103#13711yescharacteristic
97C22×C103#13711yescharacteristic
98C2×D103—21no—
99C2×D103—21no—
100C2×D103—21no—
101C2×D103—21no—
102C2×D103—21no—
103C2×D103—42no—
104C2×D103—42no—
105C2×D103#10412yes—
106C4×C103—21no—
107C4×C103—21no—
108C4×C103—42no—
109C4×C103—41no—
110C4×C103—41no—
111Dic103—21no—
112Dic103—42no—
113Dic103—41no—
114Dic103—41no—
115Dic103#9912yes—
116C2×C103—21no—
117C2×C103—21no—
118C2×C103C2×#9911yescharacteristic
119C2×C103#41911yescharacteristic
120C2×C103C2×#10411yescharacteristic
121D103—22no—
122D103—41no—
123#1508—1031nomaximal, Sylow
124C103#150811yescharacteristic, complemented, Sylow
125C2×C22⋊Q8—1031no—
126#407—1031no—
127C4×C22⋊C4—1031no—
128#328—1031no—
129#328—1031no—
130#328—1031no—
131#328D10311yescharacteristic, complemented
132C22×Q8—1031no—
133C23×C4—1031no—
134C2×M16—2061no—
135C22⋊Q8—1031no—
136C22⋊Q8—1031no—
137C22⋊Q8—1031no—
138C22⋊Q8—2061no—
139C22⋊Q8—2061no—
140C22⋊Q8C2×D10311yescharacteristic
141C2×C4⋊C4—1031no—
142C2×C4⋊C4—2061no—
143C2×C22⋊C4—2061no—
144C2×C22⋊C4—2061no—
145C2×C42—2061no—
146C22⋊C8—1031no—
147C22⋊C8—2061no—
148C22⋊C8C2×D10311yescharacteristic
149#95—1031no—
150#95C2×D10311yescharacteristic
151C24—1031no—
152C2×Q8—1031no—
153C2×Q8—4122no—
154C2×Q8—2061no—
155C2×Q8C4×D10311yescharacteristic
156C22×C4—21no—
157C22×C4—1031no—
158C22×C4—1031no—
159C22×C4—1031no—
160C22×C4—1031no—
161C22×C4—1031no—
162C22×C4—4122no—
163C22×C4—2061no—
164C22×C4—2061no—
165C22×C4—2061no—
166C22×C4C22×D10311yescharacteristic
167M16—4122no—
168C2×C8—21no—
169C2×C8—2061no—
170C4⋊C4—21no—
171C4⋊C4—1031no—
172C4⋊C4—2061no—
173C4⋊C4—2061no—
174C4⋊C4—2061no—
175C4⋊C4—2061no—
176C4⋊C4C4×D10311yescharacteristic
177C22⋊C4—21no—
178C22⋊C4—2061no—
179C22⋊C4—2061no—
180C22⋊C4—2064no—
181C22⋊C4—2061no—
182C42—4122no—
183C23—1031no—
184C23—1031no—
185C23—4121no—
186C23—2062no—
187C23—2061no—
188C23—2061no—
189C23D4×D10311yescharacteristic
190Q8—41no—
191Q8—4121no—
192Q8—4122no—
193C2×C4—22no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—1031no—
200C2×C4—1031no—
201C2×C4—4121no—
202C2×C4—4121no—
203C2×C4—4122no—
204C2×C4—4122no—
205C2×C4—4121no—
206C2×C4—4121no—
207C2×C4—2062no—
208C2×C4—2062no—
209C2×C4—2062no—
210C2×C4—2062no—
211C2×C4—2061no—
212C2×C4—2061no—
213C2×C4C2×C4×D10311yescharacteristic
214C2×C4D4×D10311yescharacteristic
215C8—41no—
216C8—4121no—
217C22—21no—
218C22—21no—
219C22—1032no—
220C22—4122no—
221C22—4122no—
222C22—2061no—
223C22—2061no—
224C22—2061no—
225C22—2061no—
226C22—2061no—
227C22C22⋊C4×D10311yescharacteristic
228C22#1569305011yescharacteristic
229C22#1569305311yescharacteristic
230C4—21no—
231C4—21no—
232C4—42no—
233C4—41no—
234C4—41no—
235C4—1032no—
236C4—4122no—
237C4—4121no—
238C4—4121no—
239C4—2061no—
240C2—21no—
241C2—21no—
242C2—4121no—
243C2—2062no—
244C2#99×D10311yescharacteristic
245C2#2026779811yescharacteristic
246C2#104×D10311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D103
commutatorC2×C4×C103C22×C4
FrattiniC22×C4C22×D103
Fitting#328×C103C2
socleC22×C103C2×C22⋊C4
prime radicalC23×D103D4
cosocleC22×C4×C103C23
hypercenter#328D103
hypocenterC103#1508
LCSG ▷ C2×C4×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
4. #20267529C2semidirect
5. #20267528C2semidirect
6. #20267527C2semidirect
7. #328×C103C2semidirect
8. C2×Q8×D103C4semidirect
11. #15693001C4semidirect
15. #15692997C4semidirect
17. C4⋊C4×D103C4semidirect
124. C103#1508semidirect
131. #328D103semidirect

Maximal subgroups

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

subgroupindex
C22⋊Q8×D1032
#202677532
#202676382
#202675292
#202675282
#202675272
#328×C1032
#1508103