Finite Group Databasebeta

← #27198433

Subgroups — #27198433

Order 13184.

568 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 143 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×#15692983C211yesmaximal, characteristic
3#20267729C211yesmaximal, characteristic, complemented
4#20267720C212yesmaximal, complemented
5#20267709C211yesmaximal, characteristic
6#20267708C211yesmaximal, characteristic
7#20267704C212yesmaximal, complemented
8#20267638C212yesmaximal, complemented
9#20267638C212yesmaximal, complemented
10#20267636C211yesmaximal, characteristic, complemented
11#400×C103C211yesmaximal, characteristic, complemented
12C22×Dic206C2211yescharacteristic
13C22×D412C2211yescharacteristic
14C22×C4×D103C2212yes—
15#15692986—24no—
16#15692983—24no—
17C2×Dic103⋊C4C2211yescharacteristic
18C2×Dic103⋊C4C2211yescharacteristic
19C2×(C2×D103)⋊C4C2212yes—
20C2×(C2×D103)⋊C4C2212yes—
21C2×(C2×D103)⋊C4C2212yes—
22C2×(C2×D103)⋊C4C2212yes—
23C2×(C2×D103)⋊C4C2212yes—
24C2×C4×Dic103C2212yes—
25C2×C4×Dic103C2211yescharacteristic
26C2×C4×Dic103C2211yescharacteristic
27C2×C4×Dic103C2211yescharacteristic
28C103⋊#95C2212yes—
29C103⋊#95C2211yescharacteristic
30C103⋊#95C2212yes—
31C103⋊#95C2212yes—
32C2×C4⋊C4×C103C2211yescharacteristic
33C2×C4⋊C4×C103C2211yescharacteristic
34#95×C103C2211yescharacteristic
35#95×C103C2212yes—
36#95×C103C2212yes—
37C23×D103C2312yes—
38C2×Dic206—22no—
39C2×Dic206—22no—
40C2×Dic206—22no—
41C2×D412—24no—
42C2×D412—22no—
43C22×Dic103C2312yes—
44C22×Dic103C2311yescharacteristic
45C22×Dic103C2311yescharacteristic
46C22×Dic103C2311yescharacteristic
47C22×Dic103C2311yescharacteristic
48C2×C4×D103—24no—
49C2×C4×D103—24no—
50C2×C4×D103—24no—
51Dic103⋊C4—22no—
52Dic103⋊C4—22no—
53(C2×D103)⋊C4—24no—
54(C2×D103)⋊C4—24no—
55(C2×D103)⋊C4—24no—
56(C2×D103)⋊C4—24no—
57(C2×D103)⋊C4—24no—
58C4×Dic103—22no—
59C4×Dic103—22no—
60C4×Dic103—24no—
61C4×Dic103D414yes—
62C22×C4×C103C2312yes—
63C22×C4×C103C2312yes—
64C22×C4×C103C2311yescharacteristic
65C22×C4×C103C2311yescharacteristic
66C22×C4×C103C2311yescharacteristic
67C4⋊C4×C103—22no—
68C4⋊C4×C103—22no—
69C23×C103C2411yescharacteristic
70C22×D103—22no—
71C22×D103—22no—
72C22×D103—22no—
73C22×D103—22no—
74C22×D103—22no—
75C22×D103—22no—
76C22×D103#4114yes—
77C2×C4×C103—21no—
78C2×C4×C103—22no—
79C2×C4×C103—21no—
80C2×C4×C103—21no—
81C2×C4×C103—22no—
82C2×C4×C103—22no—
83C2×C4×C103—22no—
84C2×C4×C103—22no—
85C2×C4×C103—22no—
86C2×C4×C103—22no—
87C2×C4×C103—22no—
88C2×C4×C103C2×D412yes—
89C2×C4×C103#4112yes—
90C2×Dic103—21no—
91C2×Dic103—21no—
92C2×Dic103—21no—
93C2×Dic103—21no—
94C2×Dic103—21no—
95C2×Dic103—22no—
96C2×Dic103—22no—
97C2×Dic103—22no—
98C2×Dic103—22no—
99C2×Dic103C2×D412yes—
100C2×Dic103C2×D412yes—
101C2×Dic103#4112yes—
102C2×Dic103#4114yes—
103D412—28no—
104C4×D103—48no—
105Dic206—28no—
106C22×C103C22×D411yescharacteristic
107C22×C103C2×#4112yes—
108C22×C103C2×#4111yescharacteristic
109C22×C103C2×#4112yes—
110C22×C103C2×#4111yescharacteristic
111C2×D103—24no—
112C2×D103—24no—
113C2×D103—24no—
114C2×D103—42no—
115C2×D103—42no—
116C2×D103—42no—
117C2×D103—42no—
118C4×C103—22no—
119C4×C103—22no—
120C4×C103—41no—
121C4×C103—42no—
122C4×C103—42no—
123Dic103—22no—
124Dic103—22no—
125Dic103—41no—
126Dic103—42no—
127Dic103#12414yes—
128C2×C103#52511yescharacteristic
129C2×C103#52511yescharacteristic
130C2×C103C2×#12411yescharacteristic
131C2×C103#52912yes—
132C2×C103#52912yes—
133D103—44no—
134#2398—1031nomaximal, Sylow
135C103#239811yescharacteristic, complemented, Sylow
136C2×C4×Q8—1031no—
137C2×C4×D4—1031no—
138#400—1031no—
139#400D10311yescharacteristic, complemented
140#397—1032no—
141#394—1031no—
142#394—1031no—
143#393—1032no—
144C4×C22⋊C4—1032no—
145C4×C22⋊C4—1032no—
146#376—1031no—
147C22×Q8—1031no—
148C22×D4—1031no—
149C23×C4—1032no—
150C4×Q8—2064no—
151C4×D4—2064no—
152C2×C4⋊C4—1031no—
153C2×C4⋊C4—1031no—
154C2×C4⋊C4C2×D10311yescharacteristic
155C2×C4⋊C4C2×D10311yescharacteristic
156C2×C22⋊C4—1032no—
157C2×C22⋊C4—1032no—
158C2×C22⋊C4—1032no—
159C2×C22⋊C4—1032no—
160C2×C22⋊C4—1032no—
161C2×C42—1031no—
162C2×C42—1031no—
163C2×C42—1031no—
164C2×C42—1032no—
165#95—1032no—
166#95—1031no—
167#95—1032no—
168#95—1032no—
169#95C2×D10311yescharacteristic
170#95C2×D10312yes—
171#95C2×D10312yes—
172C24—1032no—
173C2×Q8—2062no—
174C2×Q8—2062no—
175C2×Q8—2062no—
176C2×D4—2064no—
177C2×D4—2062no—
178C22×C4—1031no—
179C22×C4—1031no—
180C22×C4—1031no—
181C22×C4—1032no—
182C22×C4—1031no—
183C22×C4—2064no—
184C22×C4—2064no—
185C22×C4—2064no—
186C22×C4C22×D10312yes—
187C22×C4C22×D10312yes—
188C22×C4C22×D10311yescharacteristic
189C22×C4C22×D10311yescharacteristic
190C22×C4C22×D10311yescharacteristic
191C4⋊C4—22no—
192C4⋊C4—22no—
193C4⋊C4—2062no—
194C4⋊C4—2062no—
195C22⋊C4—2064no—
196C22⋊C4—2064no—
197C22⋊C4—2064no—
198C22⋊C4—2064no—
199C22⋊C4—2064no—
200C42—1034no—
201C42—2064no—
202C42—2062no—
203C42—2062no—
204C23—1034no—
205C23—2062no—
206C23—2062no—
207C23—2062no—
208C23—2062no—
209C23—2062no—
210C23—2062no—
211C23C23×D10311yescharacteristic
212Q8—2068no—
213D4—2068no—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—1032no—
226C2×C4—1034no—
227C2×C4—1032no—
228C2×C4—1032no—
229C2×C4—4128no—
230C2×C4—2061no—
231C2×C4—2062no—
232C2×C4—2062no—
233C2×C4—2062no—
234C2×C4—2062no—
235C2×C4—2061no—
236C2×C4—2061no—
237C2×C4—2061no—
238C2×C4—2061no—
239C2×C4D4×D10312yes—
240C2×C4#1311010612yes—
241C22—4122no—
242C22—4122no—
243C22—4122no—
244C22—4122no—
245C22—2064no—
246C22—2064no—
247C22—2064no—
248C22C2×D4×D10311yescharacteristic
249C22#41×D10312yes—
250C22#41×D10311yescharacteristic
251C22#41×D10312yes—
252C22C2×#1311010611yescharacteristic
253C4—22no—
254C4—22no—
255C4—41no—
256C4—42no—
257C4—42no—
258C4—1034no—
259C4—4121no—
260C4—4122no—
261C4—2062no—
262C4—2062no—
263C2—4124no—
264C2#2026829911yescharacteristic
265C2#2026830411yescharacteristic
266C2#124×D10311yescharacteristic
267C2#2026832412yes—
268C2#2026832612yes—
subgroupG/H
center, FrattiniC23C23×D103
commutator, socle, cosocleC23×C103C24
Fitting#400×C103C2
prime radicalC22×D412C22
hypercenter#400D103
hypocenterC103#2398
LCSG ▷ C23×C103 ▷ C103
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. C2×#15692986C2semidirect
3. #20267729C2semidirect
4. #20267720C2semidirect
7. #20267704C2semidirect
8. #20267638C2semidirect
9. #20267638C2semidirect
10. #20267636C2semidirect
11. #400×C103C2semidirect
135. C103#2398semidirect
139. #400D103semidirect

Maximal subgroups

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

subgroupindex
C2×#156929862
C2×#156929832
#202677292
#202677202
#202677092
#202677082
#202677042
#202676382
#202676362
#400×C1032
#2398103