Finite Group Databasebeta

← #27198413

Subgroups — #27198413

Order 13184.

528 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 155 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
1C2×#15692986C211yesmaximal, characteristic, complemented
2C2×#15692977C211yesmaximal, characteristic
3#20267729C211yesmaximal, characteristic, complemented
4#20267722C212yesmaximal, complemented
5#20267714C212yesmaximal
6#20267712C211yesmaximal, characteristic, complemented
7#20267703C211yesmaximal, characteristic
8C4⋊C4×Dic103C212yesmaximal, complemented
9#20267642C211yesmaximal, characteristic, complemented
10C22⋊C4×Dic103C212yesmaximal
11#399×C103C211yesmaximal, characteristic
12C22×Dic206C2211yescharacteristic
13C23×Dic103C2211yescharacteristic
14#15692986—24no—
15#15692977—24no—
16C2×C4⋊Dic103C2212yes—
17C2×Dic103⋊C4C2212yes—
18C2×Dic103⋊C4C2211yescharacteristic
19C2×Dic103⋊C4C2212yes—
20C2×Dic103⋊C4C2211yescharacteristic
21C2×C22⋊Dic103C2212yes—
22C2×C22⋊Dic103C2211yescharacteristic
23C2×C4×Dic103C2212yes—
24C2×C4×Dic103C2212yes—
25C2×C4×Dic103C2211yescharacteristic
26C2×C4×Dic103C2211yescharacteristic
27C103⋊#95C2212yes—
28C103⋊#95C2212yes—
29C103⋊#95C2211yescharacteristic
30C103⋊#95C2212yes—
31C103⋊#95C2212yes—
32C2×C4⋊C4×C103C2212yes—
33C2×C4⋊C4×C103C2211yescharacteristic
34C2×C22⋊C4×C103C2212yes—
35C2×C22⋊C4×C103C2211yescharacteristic
36#95×C103C2211yescharacteristic
37C2×Dic206—22no—
38C2×Dic206—24no—
39C22×Dic103—22no—
40C22×Dic103—22no—
41C22×Dic103Q814yescomplemented
42C22×Dic103C2312yes—
43C22×Dic103C2311yescharacteristic
44C22×Dic103C2311yescharacteristic
45C22×Dic103C2311yescharacteristic
46C22×Dic103C2312yes—
47C22×Dic103C2311yescharacteristic
48C4⋊Dic103—24no—
49Dic103⋊C4—22no—
50Dic103⋊C4—24no—
51Dic103⋊C4—22no—
52Dic103⋊C4—24no—
53C22⋊Dic103—22no—
54C22⋊Dic103—24no—
55C4×Dic103—22no—
56C4×Dic103—24no—
57C4×Dic103—24no—
58C4×Dic103D414yes—
59C24×C103C2311yescharacteristic
60C22×C4×C103C2311yescharacteristic
61C22×C4×C103C2312yes—
62C22×C4×C103C2311yescharacteristic
63C22×C4×C103C2312yes—
64C4⋊C4×C103—22no—
65C4⋊C4×C103—24no—
66C22⋊C4×C103—22no—
67C22⋊C4×C103—24no—
68C23×C103—21no—
69C23×C103—22no—
70C23×C103—22no—
71C23×C103—21no—
72C23×C103C2×Q812yes—
73C23×C103C2411yescharacteristic
74C2×C4×C103—22no—
75C2×C4×C103—22no—
76C2×C4×C103—22no—
77C2×C4×C103—21no—
78C2×C4×C103—22no—
79C2×C4×C103—22no—
80C2×C4×C103—22no—
81C2×C4×C103—22no—
82C2×C4×C103C2×D412yes—
83C2×C4×C103#4114yes—
84C2×Dic103—22no—
85C2×Dic103—21no—
86C2×Dic103—22no—
87C2×Dic103—21no—
88C2×Dic103—22no—
89C2×Dic103—28no—
90C2×Dic103—21no—
91C2×Dic103—22no—
92C2×Dic103—22no—
93C2×Dic103—22no—
94C2×Dic103—22no—
95C2×Dic103C2×D412yes—
96C2×Dic103C2×D412yes—
97C2×Dic103C2×Q812yes—
98C2×Dic103C2×Q812yes—
99C2×Dic103#4114yes—
100C2×Dic103#4112yes—
101Dic206—28no—
102C22×C103—22no—
103C22×C103—24no—
104C22×C103—41no—
105C22×C103—42no—
106C22×C103—41no—
107C22×C103C22×D411yescharacteristic
108C22×C103C22×Q811yescharacteristic
109C22×C103C2×#4111yescharacteristic
110C22×C103C2×#4112yes—
111C22×C103C2×#4112yes—
112C4×C103—22no—
113C4×C103—24no—
114C4×C103—41no—
115C4×C103—42no—
116Dic103—22no—
117Dic103—24no—
118Dic103—22no—
119Dic103—41no—
120Dic103—42no—
121Dic103C22⋊Q814yes—
122C2×C103—42no—
123C2×C103C2×C22⋊Q811yescharacteristic
124C2×C103#52511yescharacteristic
125C2×C103#52912yes—
126C2×C103#53211yescharacteristic
127C2×C103#53312yes—
128#2396—1031nomaximal, Sylow
129C103#239611yescharacteristic, complemented, Sylow
130C2×C4×Q8—1031no—
131C2×#117—1031no—
132#400—1031no—
133#399D10311yescharacteristic
134#398—1032no—
135#396—1032no—
136#395—1031no—
137#393—1031no—
138C4×C4⋊C4—1032no—
139C4×C4⋊C4—1031no—
140C4×C22⋊C4—1032no—
141C22×Q8—1031no—
142C23×C4—1031no—
143C4×Q8—2064no—
144#117—2064no—
145C2×C4⋊C4—1031no—
146C2×C4⋊C4—1031no—
147C2×C4⋊C4—1032no—
148C2×C4⋊C4—1032no—
149C2×C4⋊C4—1032no—
150C2×C4⋊C4C2×D10311yescharacteristic
151C2×C4⋊C4C2×D10312yes—
152C2×C22⋊C4—1031no—
153C2×C22⋊C4—1032no—
154C2×C22⋊C4C2×D10311yescharacteristic
155C2×C22⋊C4C2×D10312yes—
156C2×C42—1031no—
157C2×C42—1031no—
158C2×C42—1032no—
159C2×C42—1032no—
160#95—1032no—
161#95—1032no—
162#95—1032no—
163#95—1031no—
164#95—1032no—
165#95C2×D10311yescharacteristic
166C24C22×D10311yescharacteristic
167C2×Q8—2064no—
168C2×Q8—2062no—
169C22×C4—1031no—
170C22×C4—1034no—
171C22×C4—1031no—
172C22×C4—1032no—
173C22×C4—1031no—
174C22×C4—1032no—
175C22×C4—1031no—
176C22×C4—2062no—
177C22×C4—2062no—
178C22×C4C22×D10311yescharacteristic
179C22×C4C22×D10312yes—
180C22×C4C22×D10311yescharacteristic
181C22×C4C22×D10312yes—
182C4⋊C4—22no—
183C4⋊C4—24no—
184C4⋊C4—2062no—
185C4⋊C4—2064no—
186C4⋊C4—2064no—
187C4⋊C4—2062no—
188C4⋊C4—2064no—
189C22⋊C4—22no—
190C22⋊C4—24no—
191C22⋊C4—2064no—
192C22⋊C4—2062no—
193C42—1034no—
194C42—2064no—
195C42—2062no—
196C42—2064no—
197C23—21no—
198C23—22no—
199C23—21no—
200C23—22no—
201C23Q8×D10312yes—
202C23C23×D10311yescharacteristic
203Q8—2068no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—21no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—1032no—
213C2×C4—1032no—
214C2×C4—1032no—
215C2×C4—1032no—
216C2×C4—1032no—
217C2×C4—1034no—
218C2×C4—2068no—
219C2×C4—2061no—
220C2×C4—2062no—
221C2×C4—2062no—
222C2×C4—2062no—
223C2×C4—2062no—
224C2×C4—2062no—
225C2×C4—2061no—
226C2×C4—2061no—
227C2×C4—2062no—
228C2×C4—2062no—
229C2×C4D4×D10312yes—
230C2×C4#1311010414yes—
231C22—24no—
232C22—22no—
233C22—41no—
234C22—42no—
235C22—41no—
236C22C2×D4×D10311yescharacteristic
237C22C2×Q8×D10311yescharacteristic
238C22#41×D10312yes—
239C22#41×D10311yescharacteristic
240C22C2×#1311010412yes—
241C4—22no—
242C4—24no—
243C4—41no—
244C4—42no—
245C4—1034no—
246C4—4121no—
247C4—4122no—
248C4—2064no—
249C4—2062no—
250C4—2062no—
251C2—42no—
252C2C22⋊Q8×D10311yescharacteristic
253C2#2026829911yescharacteristic
254C2#2026831812yes—
255C2#2026833911yescharacteristic
256C2#2026834312yes—
subgroupG/H
center, FrattiniC23C23×D103
commutator, socle, cosocleC23×C103C24
Fitting#399×C103C2
prime radicalC24×C103C23
hypercenter#399D103
hypocenterC103#2396
LCSG ▷ C23×C103 ▷ C103
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×#15692986C2semidirect
3. #20267729C2semidirect
4. #20267722C2semidirect
6. #20267712C2semidirect
8. C4⋊C4×Dic103C2semidirect
9. #20267642C2semidirect
41. C22×Dic103Q8semidirect
129. C103#2396semidirect

Maximal subgroups

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

subgroupindex
C2×#156929862
C2×#156929772
#202677292
#202677222
#202677142
#202677122
#202677032
C4⋊C4×Dic1032
#202676422
C22⋊C4×Dic1032
#399×C1032
#2396103