Finite Group Databasebeta

← #27205915

Subgroups — #27205915

Order 13184.

416 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 121 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×D103C212yesmaximal
2#20268128C212yesmaximal, complemented
3#20268125C212yesmaximal, complemented
4#20268032C211yesmaximal, characteristic, complemented
5#20268030C212yesmaximal, complemented
6#20267948C212yesmaximal, complemented
7#20267945C212yesmaximal, complemented
8C2×(C2×D103)⋊C8C211yesmaximal, characteristic
9#467×C103C211yesmaximal, characteristic, complemented
10C2×Q8×D103C2212yes—
11C22×C4×D103C2211yescharacteristic
12C2×Dic412C2211yescharacteristic, complemented
13C2×#13110095C2212yescomplemented
14C22×C103⋊C8C2211yescharacteristic
15#15693001C2212yes—
16#15693000C2212yes—
17#15692999—22no—
18#15692998—22no—
19#15692997C2212yes—
20C4⋊C4×D103—22no—
21C4⋊C4×D103C2212yes—
22C22⋊C4×D103—22no—
23#15692955C2211yescharacteristic, complemented
24#15692954C2212yescomplemented
25#15692946C2212yescomplemented
26#15692945C2212yescomplemented
27#15692944C2212yescomplemented
28(C2×D103)⋊C8C2212yes—
29(C2×D103)⋊C8C2212yes—
30C2×Q16×C103C2211yescharacteristic, complemented
31C22×C8×C103C2211yescharacteristic
32C22⋊Q8×C103C2212yes—
33#107×C103C2211yescharacteristic, complemented
34#103×C103C2212yescomplemented
35C23×D103D411yescharacteristic
36C2×Dic206—22no—
37C2×Dic206C2312yes—
38Q8×D103—42no—
39Q8×D103—42no—
40C22×Dic103D411yescharacteristic
41C2×C4×D103—22no—
42C2×C4×D103—22no—
43C2×C4×D103—41no—
44C2×C4×D103—41no—
45C2×C4×D103D412yes—
46C2×C4×D103C2312yes—
47Dic412—41no—
48#13110095—42no—
49C2×C103⋊C8—41no—
50C2×C103⋊C8C2312yes—
51C4⋊Dic103—22no—
52C4⋊Dic103C2312yes—
53Dic103⋊C4—22no—
54Dic103⋊C4—22no—
55Dic103⋊C4—22no—
56C22⋊Dic103—22no—
57(C2×D103)⋊C4—22no—
58(C2×D103)⋊C4—22no—
59C2×Q8×C103C2312yes—
60C22×C4×C103C2311yescharacteristic
61Q16×C103—41no—
62C2×C8×C103—41no—
63C2×C8×C103C2311yescharacteristic
64C2×C8×C103C2311yescharacteristic
65C4⋊C4×C103—22no—
66C4⋊C4×C103C2312yes—
67C22⋊C4×C103—22no—
68C23×C103C2×D411yescharacteristic
69C22×D103—41no—
70C22×D103—41no—
71C22×D103Q1614yescomplemented
72C22×D103C2×D412yes—
73Q8×C103—22no—
74Q8×C103—22no—
75C2×C4×C103—21no—
76C2×C4×C103—21no—
77C2×C4×C103—22no—
78C2×C4×C103—22no—
79C2×C4×C103C2×D411yescharacteristic
80C2×C4×C103C2411yescharacteristic
81C2×Dic103—22no—
82C2×Dic103—22no—
83C2×Dic103—41no—
84C2×Dic103C2×D412yes—
85C4×D103—22no—
86C4×D103—22no—
87C4×D103—42no—
88C4×D103—44no—
89C4×D103—44no—
90Dic206—22no—
91Dic206—22no—
92Dic206—44no—
93C8×C103—21no—
94C8×C103—21no—
95C103⋊C8—22no—
96C22×C103—21no—
97C22×C103—21no—
98C22×C103C2×Q1612yes—
99C22×C103C22×D411yescharacteristic
100C2×D103—22no—
101C2×D103—22no—
102C2×D103—44no—
103C2×D103C2×Q1614yes—
104C4×C103—21no—
105C4×C103—42no—
106C4×C103—42no—
107C4×C103H(5,𝔽2)11yescharacteristic
108C4×C103H(5,𝔽2)11yescharacteristic
109Dic103—22no—
110Dic103—42no—
111Dic103—42no—
112C2×C103—22no—
113C2×C103#53411yescharacteristic
114C2×C103C22×Q1611yescharacteristic
115C2×C103#57511yescharacteristic
116D103—24no—
117#3189—1031nomaximal, Sylow
118C103#318911yescharacteristic, complemented, Sylow
119C2×C22⋊Q8—1032no—
120#484—1032no—
121#484—1032no—
122#467—1031no—
123#467—1032no—
124#467D10311yescharacteristic, complemented
125#451—1032no—
126#451—1032no—
127C2×C22⋊C8—1031no—
128C22×Q8—1032no—
129C23×C4—1031no—
130C2×Q16—1032no—
131C2×Q16—1031no—
132C2×Q16C2×D10311yescharacteristic, complemented
133C22×C8—1031no—
134C22×C8C2×D10311yescharacteristic
135C22⋊Q8—1032no—
136C22⋊Q8—1032no—
137C22⋊Q8—1032no—
138C22⋊Q8—2062no—
139C22⋊Q8—2062no—
140C22⋊Q8C2×D10312yes—
141C2×C4⋊C4—1032no—
142C2×C4⋊C4—2062no—
143C2×C22⋊C4—2062no—
144#107—1031no—
145#107—1032no—
146#107C2×D10311yescharacteristic, complemented
147#103—1032no—
148#103—1032no—
149#103—1032no—
150#103C2×D10312yescomplemented
151C22⋊C8—1032no—
152C22⋊C8—1032no—
153C24—1031no—
154C2×Q8—1032no—
155C2×Q8—4122no—
156C2×Q8—4122no—
157C2×Q8—2062no—
158C2×Q8C22×D10312yes—
159C22×C4—1031no—
160C22×C4—1032no—
161C22×C4—1032no—
162C22×C4—4121no—
163C22×C4—4121no—
164C22×C4—2062no—
165C22×C4—2062no—
166C22×C4C22×D10311yescharacteristic
167Q16—41no—
168Q16—4121no—
169Q16—4122no—
170C2×C8—41no—
171C2×C8—1032no—
172C2×C8—4121no—
173C2×C8C22×D10311yescharacteristic
174C2×C8C22×D10311yescharacteristic
175C4⋊C4—22no—
176C4⋊C4—1032no—
177C4⋊C4—2062no—
178C4⋊C4—2062no—
179C4⋊C4—2062no—
180C4⋊C4—2062no—
181C4⋊C4C22×D10312yes—
182C22⋊C4—22no—
183C22⋊C4—2062no—
184C22⋊C4—2062no—
185C22⋊C4—2062no—
186C23—1034no—
187C23—1032no—
188C23—4121no—
189C23—4121no—
190C23D4×D10311yescharacteristic
191Q8—22no—
192Q8—22no—
193Q8—4124no—
194Q8—2062no—
195Q8—2062no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—1032no—
201C2×C4—4122no—
202C2×C4—4124no—
203C2×C4—4124no—
204C2×C4—4121no—
205C2×C4—2062no—
206C2×C4—2062no—
207C2×C4—2062no—
208C2×C4—2062no—
209C2×C4D4×D10311yescharacteristic
210C2×C4C23×D10311yescharacteristic
211C8—21no—
212C8—21no—
213C8—2062no—
214C22—21no—
215C22—21no—
216C22—1034no—
217C22—4124no—
218C22—2062no—
219C22—2062no—
220C22Q16×D10312yes—
221C22C2×D4×D10311yescharacteristic
222C4—21no—
223C4—42no—
224C4—42no—
225C4—4122no—
226C4—4122no—
227C4—2062no—
228C4#1569306611yescharacteristic
229C4#1569306711yescharacteristic
230C2—22no—
231C2—2064no—
232C2#2026834911yescharacteristic
233C2C2×Q16×D10311yescharacteristic
234C2#2026858811yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#467×C103C2
socleC22×C103C22×D4
prime radicalC23×D103D4
hypercenter#467D103
hypocenterC103#3189
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
2. #20268128C2semidirect
3. #20268125C2semidirect
4. #20268032C2semidirect
5. #20268030C2semidirect
6. #20267948C2semidirect
7. #20267945C2semidirect
9. #467×C103C2semidirect
12. C2×Dic412C22semidirect
13. C2×#13110095C22semidirect
23. #15692955C22semidirect
24. #15692954C22semidirect
25. #15692946C22semidirect
26. #15692945C22semidirect
27. #15692944C22semidirect
30. C2×Q16×C103C22semidirect
33. #107×C103C22semidirect
34. #103×C103C22semidirect
71. C22×D103Q16semidirect
118. C103#3189semidirect
124. #467D103semidirect
132. C2×Q16C2×D103semidirect
146. #107C2×D103semidirect
150. #103C2×D103semidirect

Maximal subgroups

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

subgroupindex
C22⋊Q8×D1032
#202681282
#202681252
#202680322
#202680302
#202679482
#202679452
C2×(C2×D103)⋊C82
#467×C1032
#3189103