Finite Group Databasebeta

← #501×D103 #27205659

Subgroups — #501×D103 #27205659

Order 13184.

384 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 145 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
1C4⋊Q8×D103C211yesmaximal, characteristic
2#125×D103C211yesmaximal, characteristic
3#20268201C211yesmaximal, characteristic, complemented
4#20268200C211yesmaximal, characteristic, complemented
5#20268199C212yesmaximal, complemented
6#20268198C212yesmaximal, complemented
7#20268197C211yesmaximal, characteristic, complemented
8#107×D103C212yesmaximal
9#106×D103C212yesmaximal
10#97×D103C211yesmaximal, characteristic
11#501×C103C211yesmaximal, characteristic, complemented
12C2×Q8×D103—21no—
13C2×C8×D103C2212yes—
14#15693021C2211yescharacteristic
15#15693020—21no—
16#15693020C2212yes—
17#15693019—21no—
18#15693013C2211yescharacteristic
19#15693012C2211yescharacteristic
20#15693012C2211yescharacteristic
21#15693011—21no—
22#15693011—21no—
23C4⋊C4×D103—21no—
24C4⋊C4×D103—21no—
25C4⋊C4×D103—21no—
26C4⋊C4×D103C2211yescharacteristic
27C4⋊C4×D103C2211yescharacteristic
28C4⋊C4×D103C2212yes—
29C42×D103C2211yescharacteristic
30#15692955C2212yes—
31#15692954C2212yes—
32#15692954C2212yes—
33#15692953C2212yes—
34#15692952C2212yes—
35#15692952C2212yes—
36#15692932C2211yescharacteristic
37#15692931C2212yes—
38C4⋊Q8×C103C2211yescharacteristic
39#125×C103C2211yescharacteristic
40#107×C103C2212yes—
41#106×C103C2212yes—
42#97×C103C2211yescharacteristic
43C2×Dic206—21no—
44C2×Dic206—22no—
45Q8×D103—44no—
46C2×C4×D103—22no—
47C2×C4×D103—21no—
48C2×C4×D103—21no—
49C2×C4×D103D411yescharacteristic
50C2×C4×D103D411yescharacteristic
51C2×C4×D103C2311yescharacteristic
52C2×C103⋊C8C2312yes—
53C8×D103Q818yescomplemented
54C4⋊Dic103—21no—
55C4⋊Dic103—21no—
56C4⋊Dic103—21no—
57C4⋊Dic103C2311yescharacteristic
58C4⋊Dic103C2312yes—
59C4⋊Dic103C2311yescharacteristic
60Dic103⋊C4—21no—
61Dic103⋊C4—21no—
62Dic103⋊C4—21no—
63Dic103⋊C4—21no—
64Dic103⋊C4—22no—
65Dic103⋊C4—21no—
66Dic103⋊C4—21no—
67Dic103⋊C4—22no—
68C4×Dic103D411yescharacteristic
69C4×Dic103D411yescharacteristic
70C4×Dic103C2311yescharacteristic
71C2×Q8×C103—21no—
72C2×C8×C103C2312yes—
73C4⋊C4×C103—21no—
74C4⋊C4×C103—21no—
75C4⋊C4×C103—21no—
76C4⋊C4×C103C2311yescharacteristic
77C4⋊C4×C103C2312yes—
78C4⋊C4×C103C2311yescharacteristic
79C42×C103C2311yescharacteristic
80C22×D103C2×D411yescharacteristic
81Q8×C103—42no—
82C2×C4×C103—21no—
83C2×C4×C103—21no—
84C2×C4×C103—22no—
85C2×C4×C103C2×D411yescharacteristic
86C2×C4×C103C2×D411yescharacteristic
87C2×C4×C103C2411yescharacteristic
88C2×Dic103—21no—
89C2×Dic103—21no—
90C2×Dic103—22no—
91C2×Dic103C2×D411yescharacteristic
92C2×Dic103C2×D411yescharacteristic
93C2×Dic103C2×D411yescharacteristic
94C4×D103—22no—
95C4×D103—22no—
96C4×D103—42no—
97C4×D103—44no—
98C4×D103—42no—
99C4×D103C2×Q814yes—
100Dic206—44no—
101Dic206—42no—
102C8×C103C2×Q814yescomplemented
103C103⋊C8C2×Q814yescomplemented
104C22×C103C22×D411yescharacteristic
105C2×D103C4⋊Q812yes—
106C2×D103AGL(1,ℤ/8)12yes—
107C2×D103#13712yes—
108C4×C103—21no—
109C4×C103—21no—
110C4×C103—42no—
111C4×C103—41no—
112C4×C103—41no—
113C4×C103C22×Q812yes—
114Dic103—21no—
115Dic103—21no—
116Dic103—42no—
117Dic103—41no—
118Dic103—41no—
119Dic103C4⋊Q812yes—
120C2×C103C2×C4⋊Q811yescharacteristic
121C2×C103C2×AGL(1,ℤ/8)11yescharacteristic
122C2×C103C2×#13711yescharacteristic
123D103#50114yesdirect product factor
124C2×#501—1031nomaximal, Sylow
125C103C2×#50111yescharacteristic, complemented, Sylow
126C2×C4⋊Q8—1031no—
127C2×#125—1031no—
128#501—1031no—
129#501—1031no—
130#501—1032no—
131#501—1032no—
132#501—1031no—
133#501D10311yescharacteristic, direct product factor
134C2×#107—1032no—
135C2×#106—1032no—
136C2×#97—1031no—
137C22×Q8—2061no—
138C22×C8—1032no—
139C4⋊Q8—1032no—
140C4⋊Q8—1031no—
141C4⋊Q8—2061no—
142C4⋊Q8—2061no—
143C4⋊Q8C2×D10311yescharacteristic
144#125—1031no—
145#125—1031no—
146#125—1031no—
147#125—2061no—
148#125—2061no—
149#125C2×D10311yescharacteristic
150C2×C4⋊C4—1031no—
151C2×C4⋊C4—1031no—
152C2×C4⋊C4—1032no—
153C2×C4⋊C4—2061no—
154C2×C4⋊C4—2061no—
155C2×C4⋊C4—2061no—
156C2×C42—1031no—
157#107—1032no—
158#107—1032no—
159#107—1032no—
160#107C2×D10312yes—
161#106—1032no—
162#106—1032no—
163#106—1032no—
164#106C2×D10312yes—
165#97—1032no—
166#97—1031no—
167#97C2×D10311yescharacteristic
168C2×Q8—21no—
169C2×Q8—4124no—
170C2×Q8—2062no—
171C2×Q8—2061no—
172C22×C4—1031no—
173C22×C4—1031no—
174C22×C4—1031no—
175C22×C4—2061no—
176C22×C4—2061no—
177C22×C4—2062no—
178C2×C8—1032no—
179C2×C8—1038no—
180C2×C8C22×D10312yes—
181C4⋊C4—21no—
182C4⋊C4—21no—
183C4⋊C4—21no—
184C4⋊C4—1031no—
185C4⋊C4—1032no—
186C4⋊C4—1031no—
187C4⋊C4—2061no—
188C4⋊C4—2061no—
189C4⋊C4—2062no—
190C4⋊C4—2061no—
191C4⋊C4—2061no—
192C4⋊C4—2062no—
193C4⋊C4—2061no—
194C4⋊C4—2061no—
195C4⋊C4—2061no—
196C4⋊C4—2061no—
197C4⋊C4—2061no—
198C4⋊C4C22×D10311yescharacteristic
199C4⋊C4C22×D10312yes—
200C4⋊C4C22×D10311yescharacteristic
201C42—1031no—
202C42—1031no—
203C42—1031no—
204C42C22×D10311yescharacteristic
205C23—1031no—
206Q8—42no—
207Q8—4122no—
208Q8—4124no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—1031no—
213C2×C4—1034no—
214C2×C4—1031no—
215C2×C4—1031no—
216C2×C4—4124no—
217C2×C4—4122no—
218C2×C4—4122no—
219C2×C4—2062no—
220C2×C4—2062no—
221C2×C4—2061no—
222C2×C4—2061no—
223C2×C4—2062no—
224C2×C4D4×D10311yescharacteristic
225C2×C4D4×D10311yescharacteristic
226C2×C4C23×D10311yescharacteristic
227C8—1034no—
228C8Q8×D10314yescomplemented
229C22—1032no—
230C22—1032no—
231C22—1032no—
232C22C2×D4×D10311yescharacteristic
233C4—21no—
234C4—21no—
235C4—42no—
236C4—41no—
237C4—41no—
238C4—1032no—
239C4—4122no—
240C4—4121no—
241C4—4121no—
242C4—2061no—
243C4—2061no—
244C4C2×Q8×D10312yes—
245C2—1034no—
246C2C4⋊Q8×D10311yescharacteristic
247C2AGL(1,ℤ/8)×D10311yescharacteristic
248C2#137×D10311yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#501×C103C2
socleC22×C103C22×D4
prime radicalC22×D103C2×D4
hypercenter#501D103
hypocenterC103C2×#501
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
3. #20268201C2semidirect
4. #20268200C2semidirect
5. #20268199C2semidirect
6. #20268198C2semidirect
7. #20268197C2semidirect
11. #501×C103C2semidirect
53. C8×D103Q8semidirect
102. C8×C103C2×Q8semidirect
103. C103⋊C8C2×Q8semidirect
123. D103#501direct (N × H)
125. C103C2×#501semidirect
133. #501D103direct (N × H)
228. C8Q8×D103semidirect

Maximal subgroups

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

subgroupindex
C4⋊Q8×D1032
#125×D1032
#202682012
#202682002
#202681992
#202681982
#202681972
#107×D1032
#106×D1032
#97×D1032
#501×C1032
C2×#501103