Finite Group Databasebeta

← #27205315

Subgroups — #27205315

Order 13184.

386 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 129 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#20268325C211yesmaximal, characteristic
2#20268126C211yesmaximal, characteristic, complemented
3#20268109C211yesmaximal, characteristic
4#20268098C212yesmaximal, complemented
5#20268013C212yesmaximal, complemented
6#20267947C211yesmaximal, characteristic, complemented
7#20267930C211yesmaximal, characteristic
8#20267896C212yesmaximal, complemented
9#20267889C212yesmaximal, complemented
10#20267848C211yesmaximal, characteristic, complemented
11C2×C4×Q8×C103C211yesmaximal, characteristic, complemented
12C2×#13110095C2212yes—
13C2×#13110092C2212yes—
14#15693015—21no—
15#15693013C2211yescharacteristic
16#15693009C2211yescharacteristic
17#15693004—21no—
18#15693000C2211yescharacteristic
19#15692995C2211yescharacteristic
20C4×Dic206C2211yescharacteristic
21C4×D412C2211yescharacteristic
22C4×C22⋊D103—21no—
23#15692978—21no—
24#15692954C2212yes—
25#15692952C2212yes—
26C4⋊(C103⋊C8)C2212yes—
27#15692945C2212yes—
28#15692945C2212yes—
29#15692944C2212yes—
30#15692941C2212yes—
31C22⋊(C103⋊C8)C2211yescharacteristic
32C22⋊(C103⋊C8)C2211yescharacteristic
33#15692932C2212yes—
34C22×Q8×C103C2211yescharacteristic
35C4×Q8×C103—21no—
36C4×Q8×C103—21no—
37C4×Q8×C103C2212yes—
38C4×Q8×C103C2212yes—
39C2×C4⋊C4×C103—21no—
40C2×C4⋊C4×C103C2211yescharacteristic
41C2×C42×C103—21no—
42C2×C42×C103C2211yescharacteristic
43C2×Dic206C2311yescharacteristic
44C2×D412C2311yescharacteristic
45C2×C22⋊D103—21no—
46C2×C4×D103—21no—
47#13110095—24no—
48#13110092—24no—
49C2×C103⋊C8C2312yes—
50C2×C103⋊C8C2312yes—
51C4⋊Dic103C2311yescharacteristic
52C4⋊Dic103C2311yescharacteristic
53Dic103⋊C4—21no—
54Dic103⋊C4—21no—
55Dic103⋊C4—21no—
56Dic103⋊C4—21no—
57C22⋊Dic103—21no—
58(C2×D103)⋊C4—21no—
59(C2×D103)⋊C4—21no—
60(C2×D103)⋊C4—21no—
61(C2×D103)⋊C4—21no—
62C4×Dic103—21no—
63C2×Q8×C103—24no—
64C2×Q8×C103—21no—
65C2×Q8×C103C2312yes—
66C22×C4×C103—21no—
67C22×C4×C103—21no—
68C22×C4×C103D411yescharacteristic
69C22×C4×C103D411yescharacteristic
70C22×C4×C103C2311yescharacteristic
71C4⋊C4×C103—22no—
72C4⋊C4×C103—22no—
73C4⋊C4×C103—21no—
74C4⋊C4×C103C2312yes—
75C42×C103—22no—
76C42×C103—22no—
77C42×C103D411yescharacteristic
78C42×C103D411yescharacteristic
79C42×C103C2311yescharacteristic
80C42×C103C2311yescharacteristic
81C23×C103C2×D411yescharacteristic
82C22×D103—21no—
83Q8×C103—24no—
84Q8×C103—22no—
85Q8×C103#4114yes—
86C2×C4×C103—24no—
87C2×C4×C103—22no—
88C2×C4×C103—22no—
89C2×C4×C103—22no—
90C2×C4×C103—22no—
91C2×C4×C103—41no—
92C2×C4×C103—42no—
93C2×C4×C103C2×D411yescharacteristic
94C2×C4×C103C2×D411yescharacteristic
95C2×C4×C103C2×D411yescharacteristic
96C2×C4×C103C2×D411yescharacteristic
97C2×C4×C103C2×D411yescharacteristic
98C2×C4×C103C2411yescharacteristic
99C22⋊D103—42no—
100C2×Dic103—21no—
101C2×Dic103—21no—
102C2×Dic103—21no—
103D412—22no—
104C4×D103—42no—
105Dic206—22no—
106C103⋊C8—22no—
107C103⋊C8—22no—
108C22×C103—21no—
109C22×C103—21no—
110C22×C103#13712yes—
111C22×C103C22×D411yescharacteristic
112C2×D103—41no—
113C2×D103—41no—
114C2×D103—41no—
115C4×C103—24no—
116C4×C103—21no—
117C4×C103—21no—
118C4×C103—21no—
119C4×C103—21no—
120C4×C103—21no—
121C4×C103—42no—
122C4×C103C2×#4112yes—
123Dic103—41no—
124Dic103—41no—
125Dic103—41no—
126C2×C103—22no—
127C2×C103#52511yescharacteristic
128C2×C103C2×#13711yescharacteristic
129C2×C103#57511yescharacteristic
130D103—81no—
131#3117—1031nomaximal, Sylow
132C103#311711yescharacteristic, complemented, Sylow
133#529—1031no—
134C2×C4×Q8D10311yescharacteristic, complemented
135#484—1031no—
136#481—1031no—
137#479—1032no—
138#464—1032no—
139#451—1031no—
140#448—1031no—
141#441—1032no—
142#440—1032no—
143#432—1031no—
144C22×Q8C2×D10311yescharacteristic
145C2×Q16—1032no—
146C2×SD16—1032no—
147#126—2061no—
148#125—1031no—
149#124—1031no—
150#123—2061no—
151C22⋊Q8—1031no—
152#121—1031no—
153C4×Q8—21no—
154C4×Q8—21no—
155C4×Q8—1031no—
156C4×Q8C2×D10312yes—
157C4×Q8C2×D10312yes—
158C4×D4—1031no—
159C4×D4—2061no—
160#117—2061no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4C2×D10311yescharacteristic
163C2×C42—21no—
164C2×C42C2×D10311yescharacteristic
165#107—1032no—
166#106—1032no—
167C4⋊C8—1032no—
168#103—1032no—
169#103—1032no—
170#103—1032no—
171#102—1032no—
172C22⋊C8—1031no—
173C22⋊C8—1031no—
174#97—1032no—
175C2×Q8—24no—
176C2×Q8—21no—
177C2×Q8—1031no—
178C2×Q8C22×D10312yes—
179C2×D4—1031no—
180C2×D4—2061no—
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—2061no—
184C22×C4C22⋊D10311yescharacteristic
185C22×C4C22⋊D10311yescharacteristic
186C22×C4C22×D10311yescharacteristic
187Q16—2064no—
188SD16—2064no—
189C2×C8—1032no—
190C2×C8—1032no—
191C4⋊C4—22no—
192C4⋊C4—22no—
193C4⋊C4—21no—
194C4⋊C4—1031no—
195C4⋊C4—1031no—
196C4⋊C4—2061no—
197C4⋊C4—2061no—
198C4⋊C4—2061no—
199C4⋊C4—2061no—
200C4⋊C4C22×D10312yes—
201C22⋊C4—2061no—
202C22⋊C4—2061no—
203C22⋊C4—2061no—
204C22⋊C4—2061no—
205C22⋊C4—2061no—
206C42—22no—
207C42—22no—
208C42—2061no—
209C42C22⋊D10311yescharacteristic
210C42C22⋊D10311yescharacteristic
211C42C22×D10311yescharacteristic
212C42C22×D10311yescharacteristic
213C23—2061no—
214C23C2×C22⋊D10311yescharacteristic
215Q8—24no—
216Q8—22no—
217Q8—2062no—
218Q8#1311010514yes—
219D4—4122no—
220D4—2062no—
221C2×C4—24no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—4122no—
229C2×C4—2061no—
230C2×C4—2061no—
231C2×C4—2061no—
232C2×C4C2×C22⋊D10311yescharacteristic
233C2×C4C2×C22⋊D10311yescharacteristic
234C2×C4C2×C22⋊D10311yescharacteristic
235C2×C4C2×C22⋊D10311yescharacteristic
236C2×C4C2×C22⋊D10311yescharacteristic
237C2×C4C23×D10311yescharacteristic
238C8—2062no—
239C8—2062no—
240C22—21no—
241C22—21no—
242C22—4121no—
243C22—4121no—
244C22—4121no—
245C22#1569305212yes—
246C22C22×C22⋊D10311yescharacteristic
247C4—24no—
248C4—21no—
249C4—21no—
250C4—21no—
251C4—21no—
252C4—21no—
253C4—42no—
254C4—4121no—
255C4—4121no—
256C4—4121no—
257C4C2×#1311010512yes—
258C2—22no—
259C2—8241no—
260C2#2026830211yescharacteristic
261C2C2×#1569305211yescharacteristic
262C2#2026858911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
FittingC2×C4×Q8×C103C2
socleC22×C103C22×D4
prime radical#15692995C22
hypercenterC2×C4×Q8D103
hypocenterC103#3117
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
2. #20268126C2semidirect
4. #20268098C2semidirect
5. #20268013C2semidirect
6. #20267947C2semidirect
8. #20267896C2semidirect
9. #20267889C2semidirect
10. #20267848C2semidirect
11. C2×C4×Q8×C103C2semidirect
132. C103#3117semidirect
134. C2×C4×Q8D103semidirect

Maximal subgroups

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

subgroupindex
#202683252
#202681262
#202681092
#202680982
#202680132
#202679472
#202679302
#202678962
#202678892
#202678482
C2×C4×Q8×C1032
#3117103