Finite Group Databasebeta

← #27198409

Subgroups — #27198409

Order 13184.

560 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 147 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×(C22⋊D103)⋊C4C211yesmaximal, characteristic
2C2×#15692979C211yesmaximal, characteristic, complemented
3#20267729C211yesmaximal, characteristic, complemented
4#20267723C211yesmaximal, characteristic, complemented
5#20267717C212yesmaximal, complemented
6#20267716C211yesmaximal, characteristic, complemented
7#20267707C212yesmaximal
8C4⋊C4×Dic103C212yesmaximal, complemented
9C22⋊C4×Dic103C212yesmaximal, complemented
10#20267638C211yesmaximal, characteristic, complemented
11#399×C103C211yesmaximal, characteristic, complemented
12C22×C22⋊D103C2211yescharacteristic
13C23×Dic103C2211yescharacteristic
14C22×C4×D103C2211yescharacteristic
15(C22⋊D103)⋊C4—24no—
16#15692979—24no—
17C2×C4⋊Dic103C2212yes—
18C2×C4⋊Dic103C2211yescharacteristic
19C2×Dic103⋊C4C2211yescharacteristic
20C2×C22⋊Dic103C2212yes—
21C2×(C2×D103)⋊C4C2212yes—
22C2×(C2×D103)⋊C4C2212yes—
23C2×(C2×D103)⋊C4C2211yescharacteristic
24C2×C4×Dic103C2212yes—
25C2×C4×Dic103C2212yes—
26C2×C4×Dic103C2211yescharacteristic
27C103⋊#95C2211yescharacteristic
28C103⋊#95C2212yes—
29C103⋊#95C2212yes—
30C103⋊#95C2212yes—
31C103⋊#95C2212yes—
32C2×C4⋊C4×C103C2212yes—
33C2×C4⋊C4×C103C2211yescharacteristic
34C2×C22⋊C4×C103C2212yes—
35C2×C22⋊C4×C103C2211yescharacteristic
36#95×C103C2211yescharacteristic
37C23×D103C2311yescharacteristic
38C2×C22⋊D103—22no—
39C2×C22⋊D103—22no—
40C2×C22⋊D103—22no—
41C22×Dic103—22no—
42C22×Dic103—24no—
43C22×Dic103C2311yescharacteristic
44C22×Dic103C2312yes—
45C22×Dic103C2312yes—
46C22×Dic103C2311yescharacteristic
47C22×Dic103C2311yescharacteristic
48C2×C4×D103—24no—
49C2×C4×D103D414yes—
50C4⋊Dic103—22no—
51C4⋊Dic103—24no—
52Dic103⋊C4—22no—
53C22⋊Dic103—24no—
54(C2×D103)⋊C4—24no—
55(C2×D103)⋊C4—22no—
56(C2×D103)⋊C4—24no—
57C4×Dic103—24no—
58C4×Dic103—22no—
59C4×Dic103—24no—
60C24×C103C2311yescharacteristic
61C22×C4×C103C2311yescharacteristic
62C22×C4×C103C2312yes—
63C22×C4×C103C2311yescharacteristic
64C22×C4×C103C2312yes—
65C4⋊C4×C103—22no—
66C4⋊C4×C103—24no—
67C22⋊C4×C103—22no—
68C22⋊C4×C103—24no—
69C23×C103—21no—
70C23×C103—22no—
71C23×C103—22no—
72C23×C103—21no—
73C23×C103#4112yes—
74C23×C103C2411yescharacteristic
75C22×D103—22no—
76C22×D103—22no—
77C22×D103—21no—
78C22×D103—21no—
79C22×D103C2×D412yes—
80C2×C4×C103—22no—
81C2×C4×C103—22no—
82C2×C4×C103—22no—
83C2×C4×C103—21no—
84C2×C4×C103—22no—
85C2×C4×C103—22no—
86C2×C4×C103—22no—
87C2×C4×C103—22no—
88C2×C4×C103C2×D412yes—
89C2×C4×C103#4114yes—
90C22⋊D103—28no—
91C2×Dic103—21no—
92C2×Dic103—21no—
93C2×Dic103—22no—
94C2×Dic103—21no—
95C2×Dic103—22no—
96C2×Dic103—22no—
97C2×Dic103—22no—
98C2×Dic103—22no—
99C2×Dic103—22no—
100C2×Dic103—22no—
101C2×Dic103—44no—
102C2×Dic103C2×D412yes—
103C2×Dic103#4112yes—
104C2×Dic103#4114yes—
105C4×D103—28no—
106C22×C103—22no—
107C22×C103—24no—
108C22×C103—41no—
109C22×C103—42no—
110C22×C103—41no—
111C22×C103C22×D411yescharacteristic
112C22×C103C2×#4112yes—
113C22×C103C2×#4111yescharacteristic
114C22×C103C2×#4112yes—
115C22×C103C2×#4111yescharacteristic
116C2×D103—22no—
117C2×D103—22no—
118C2×D103—22no—
119C2×D103—42no—
120C2×D103—42no—
121C4×C103—22no—
122C4×C103—24no—
123C4×C103—41no—
124C4×C103—42no—
125Dic103—22no—
126Dic103—41no—
127Dic103—42no—
128Dic103—42no—
129Dic103#12314yes—
130C2×C103—42no—
131C2×C103C2×#12311yescharacteristic
132C2×C103#52511yescharacteristic
133C2×C103#52912yes—
134C2×C103#52912yes—
135C2×C103#53211yescharacteristic
136D103—42no—
137#2395—1031nomaximal, Sylow
138C103#239511yescharacteristic, complemented, Sylow
139C2×C4×D4—1031no—
140C2×#117—1031no—
141#400—1031no—
142#399D10311yescharacteristic, complemented
143#398—1031no—
144#397—1032no—
145#397—1031no—
146#394—1032no—
147C4×C4⋊C4—1032no—
148C4×C22⋊C4—1032no—
149C4×C22⋊C4—1031no—
150C22×D4—1031no—
151C23×C4—1031no—
152C23×C4—1031no—
153C4×D4—2064no—
154#117—2064no—
155C2×C4⋊C4—1031no—
156C2×C4⋊C4—1031no—
157C2×C4⋊C4—1032no—
158C2×C4⋊C4C2×D10311yescharacteristic
159C2×C4⋊C4C2×D10312yes—
160C2×C22⋊C4—1032no—
161C2×C22⋊C4—1032no—
162C2×C22⋊C4—1031no—
163C2×C22⋊C4—1032no—
164C2×C22⋊C4C2×D10311yescharacteristic
165C2×C22⋊C4C2×D10312yes—
166C2×C42—1032no—
167C2×C42—1031no—
168C2×C42—1032no—
169#95—1032no—
170#95—1031no—
171#95—1032no—
172#95—1032no—
173#95—1032no—
174#95C2×D10311yescharacteristic
175C24—1031no—
176C24C22×D10311yescharacteristic
177C2×D4—2062no—
178C2×D4—2062no—
179C2×D4—2062no—
180C22×C4—1031no—
181C22×C4—1031no—
182C22×C4—1034no—
183C22×C4—1032no—
184C22×C4—1031no—
185C22×C4—1032no—
186C22×C4—2064no—
187C22×C4—2062no—
188C22×C4—2064no—
189C22×C4C22×D10311yescharacteristic
190C22×C4C22×D10312yes—
191C22×C4C22×D10311yescharacteristic
192C22×C4C22×D10312yes—
193C4⋊C4—22no—
194C4⋊C4—24no—
195C4⋊C4—2064no—
196C4⋊C4—2062no—
197C4⋊C4—2062no—
198C22⋊C4—22no—
199C22⋊C4—24no—
200C22⋊C4—2064no—
201C22⋊C4—2062no—
202C22⋊C4—2064no—
203C22⋊C4—2064no—
204C42—2064no—
205C42—2064no—
206C42—2062no—
207C23—21no—
208C23—22no—
209C23—21no—
210C23—22no—
211C23—1032no—
212C23—2062no—
213C23—2061no—
214C23—2062no—
215C23—2061no—
216C23#1311010612yes—
217C23C23×D10311yescharacteristic
218D4—2068no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—1032no—
228C2×C4—1034no—
229C2×C4—1032no—
230C2×C4—4124no—
231C2×C4—2068no—
232C2×C4—2062no—
233C2×C4—2061no—
234C2×C4—2062no—
235C2×C4—2062no—
236C2×C4—2062no—
237C2×C4—2062no—
238C2×C4—2062no—
239C2×C4—2062no—
240C2×C4—2061no—
241C2×C4—2061no—
242C2×C4D4×D10312yes—
243C2×C4#1311010414yes—
244C22—22no—
245C22—24no—
246C22—41no—
247C22—42no—
248C22—41no—
249C22—4122no—
250C22—4122no—
251C22—2062no—
252C22—2062no—
253C22—2062no—
254C22C2×D4×D10311yescharacteristic
255C22#41×D10312yes—
256C22#41×D10311yescharacteristic
257C22C2×#1311010412yes—
258C22C2×#1311010611yescharacteristic
259C4—22no—
260C4—24no—
261C4—41no—
262C4—42no—
263C4—1034no—
264C4—4121no—
265C4—4122no—
266C4—4122no—
267C4—2062no—
268C2—42no—
269C2—4122no—
270C2#123×D10311yescharacteristic
271C2#2026830411yescharacteristic
272C2#2026831812yes—
273C2#2026832712yes—
274C2#2026833911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D103
commutator, socle, cosocleC23×C103C24
Fitting#399×C103C2
prime radicalC22×C22⋊D103C22
hypercenter#399D103
hypocenterC103#2395
LCSG ▷ C23×C103 ▷ C103
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
2. C2×#15692979C2semidirect
3. #20267729C2semidirect
4. #20267723C2semidirect
5. #20267717C2semidirect
6. #20267716C2semidirect
8. C4⋊C4×Dic103C2semidirect
9. C22⋊C4×Dic103C2semidirect
10. #20267638C2semidirect
11. #399×C103C2semidirect
138. C103#2395semidirect
142. #399D103semidirect

Maximal subgroups

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

subgroupindex
C2×(C22⋊D103)⋊C42
C2×#156929792
#202677292
#202677232
#202677172
#202677162
#202677072
C4⋊C4×Dic1032
C22⋊C4×Dic1032
#202676382
#399×C1032
#2395103