Finite Group Databasebeta

← #27205799

Subgroups — #27205799

Order 13184.

338 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 115 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#20268399C212yesmaximal
2#20268192C211yesmaximal, characteristic, complemented
3#20268169C211yesmaximal, characteristic, complemented
4#20268158C212yesmaximal, complemented
5#20268048C212yesmaximal
6#20268033C211yesmaximal, characteristic
7#20268029C211yesmaximal, characteristic
8#20267896C212yesmaximal, complemented
9C4×Dic412C211yesmaximal, characteristic, complemented
10#20267745C211yesmaximal, characteristic
11C4×Q16×C103C211yesmaximal, characteristic, complemented
12C2×Dic412C2211yescharacteristic
13C2×#13110095C2212yes—
14C2×#13110088C2211yescharacteristic
15C2×C8×D103C2211yescharacteristic
16#15693019C2212yes—
17#15693016—22no—
18#15693015—22no—
19#15693013—22no—
20#15693012C2212yes—
21#15693011—22no—
22#15693001C2212yes—
23#15692997C2212yes—
24C4×Dic206C2212yes—
25#15692978C2211yescharacteristic
26#15692955C2211yescharacteristic
27#15692952C2212yes—
28#15692946C2212yes—
29#15692945C2212yes—
30#15692944C2212yes—
31#15692932C2211yescharacteristic
32#15692931C2211yescharacteristic
33C8×Dic103C2211yescharacteristic
34C2×Q16×C103C2211yescharacteristic
35C4×Q8×C103C2212yes—
36#107×C103C2211yescharacteristic
37#103×C103C2212yes—
38C4×C8×C103C2211yescharacteristic
39C2×Dic206C2312yes—
40C2×C4×D103C2311yescharacteristic
41Dic412—22no—
42#13110095—24no—
43#13110088—22no—
44C2×C103⋊C8C2311yescharacteristic
45C2×C103⋊C8C2311yescharacteristic
46C8×D103—22no—
47C4⋊Dic103—22no—
48C4⋊Dic103—22no—
49C4⋊Dic103C2312yes—
50Dic103⋊C4—22no—
51Dic103⋊C4—22no—
52Dic103⋊C4—22no—
53Dic103⋊C4—22no—
54Dic103⋊C4—22no—
55Dic103⋊C4D411yescharacteristic
56Dic103⋊C4D411yescharacteristic
57(C2×D103)⋊C4—22no—
58(C2×D103)⋊C4—22no—
59(C2×D103)⋊C4D411yescharacteristic
60(C2×D103)⋊C4D411yescharacteristic
61C4×Dic103—22no—
62C4×Dic103C2311yescharacteristic
63C2×Q8×C103C2312yes—
64Q16×C103—22no—
65C2×C8×C103C2311yescharacteristic
66C2×C8×C103C2311yescharacteristic
67C4⋊C4×C103—22no—
68C4⋊C4×C103C2312yes—
69C42×C103—22no—
70C42×C103C2311yescharacteristic
71C22×D103C2×D411yescharacteristic
72Q8×C103—22no—
73Q8×C103—22no—
74C2×C4×C103—22no—
75C2×C4×C103—22no—
76C2×C4×C103C2×D411yescharacteristic
77C2×C4×C103C2×D411yescharacteristic
78C2×C4×C103C2411yescharacteristic
79C2×Dic103—22no—
80C2×Dic103—22no—
81C2×Dic103C2×D411yescharacteristic
82C2×Dic103C2×D411yescharacteristic
83C2×Dic103C2×D411yescharacteristic
84C4×D103—21no—
85C4×D103—21no—
86Dic206—22no—
87Dic206—22no—
88C8×C103—21no—
89C8×C103#4112yes—
90C103⋊C8—21no—
91C103⋊C8#4112yes—
92C22×C103C22×D411yescharacteristic
93C2×D103—21no—
94C2×D103—21no—
95C2×D103—21no—
96C4×C103—21no—
97C4×C103—21no—
98C4×C103—42no—
99C4×C103—42no—
100C4×C103C2×#4111yescharacteristic
101C4×C103C2×#4111yescharacteristic
102Dic103—21no—
103Dic103—21no—
104Dic103—21no—
105Dic103—42no—
106Dic103—42no—
107C2×C103#53211yescharacteristic
108C2×C103#57811yescharacteristic
109C2×C103#57811yescharacteristic
110D103—41no—
111#3177—1031nomaximal, Sylow
112C103#317711yescharacteristic, complemented, Sylow
113#541—1032no—
114#499—1031no—
115#494—1031no—
116#491—1032no—
117#470—1032no—
118#467—1031no—
119#467—1031no—
120#441—1032no—
121C4×Q16—1031no—
122C4×Q16D10311yescharacteristic, complemented
123#405—1031no—
124C2×Q16—1032no—
125C2×Q16—1031no—
126C2×Q16C2×D10311yescharacteristic
127C2×M16—1031no—
128C22×C8—1031no—
129C4⋊Q8—1032no—
130#126—2062no—
131#126—2062no—
132#125—1032no—
133#125—2062no—
134#125—2062no—
135C22⋊Q8—1032no—
136C22⋊Q8—1032no—
137C4×Q8—1032no—
138C4×Q8C2×D10312yes—
139#117—1031no—
140#107—1031no—
141#107C2×D10311yescharacteristic
142#106—1032no—
143#103—1032no—
144#103—1032no—
145#103—1032no—
146#103C2×D10312yes—
147#97—1031no—
148#97—1031no—
149C4×C8—1031no—
150C4×C8C2×D10311yescharacteristic
151C2×Q8—1032no—
152C2×Q8C22×D10312yes—
153C22×C4—1031no—
154Q16—22no—
155Q16—2064no—
156Q16—2062no—
157M16—2062no—
158C2×C8—1031no—
159C2×C8—1031no—
160C2×C8—2062no—
161C2×C8C22×D10311yescharacteristic
162C2×C8C22×D10311yescharacteristic
163C4⋊C4—22no—
164C4⋊C4—1031no—
165C4⋊C4—1031no—
166C4⋊C4—1032no—
167C4⋊C4—2062no—
168C4⋊C4—2062no—
169C4⋊C4—2062no—
170C4⋊C4—2062no—
171C4⋊C4—2062no—
172C4⋊C4—2062no—
173C4⋊C4—2062no—
174C4⋊C4C22×D10312yes—
175C22⋊C4—1031no—
176C22⋊C4—1031no—
177C22⋊C4—2062no—
178C22⋊C4—2062no—
179C42—22no—
180C42—1031no—
181C42—2062no—
182C42C22×D10311yescharacteristic
183C23—1031no—
184Q8—22no—
185Q8—22no—
186Q8—2062no—
187Q8—2062no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—1031no—
191C2×C4—1031no—
192C2×C4—1031no—
193C2×C4—2062no—
194C2×C4—2062no—
195C2×C4—2061no—
196C2×C4—2061no—
197C2×C4D4×D10311yescharacteristic
198C2×C4D4×D10311yescharacteristic
199C2×C4C23×D10311yescharacteristic
200C8—21no—
201C8—1032no—
202C8—2061no—
203C8#1311010512yes—
204C22—2061no—
205C22—2061no—
206C22—2061no—
207C22C2×D4×D10311yescharacteristic
208C4—21no—
209C4—21no—
210C4—42no—
211C4—42no—
212C4—4122no—
213C4—4122no—
214C4—2061no—
215C4—2061no—
216C4—2061no—
217C4#41×D10311yescharacteristic
218C4C2×#1311010511yescharacteristic
219C2—4121no—
220C2#2026833811yescharacteristic
221C2#2026860411yescharacteristic
222C2#2026860511yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
FittingC4×Q16×C103C2
socleC22×C103C22×D4
prime radicalC22×D103C2×D4
hypercenterC4×Q16D103
hypocenterC103#3177
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
2. #20268192C2semidirect
3. #20268169C2semidirect
4. #20268158C2semidirect
8. #20267896C2semidirect
9. C4×Dic412C2semidirect
11. C4×Q16×C103C2semidirect
112. C103#3177semidirect
122. C4×Q16D103semidirect

Maximal subgroups

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

subgroupindex
#202683992
#202681922
#202681692
#202681582
#202680482
#202680332
#202680292
#202678962
C4×Dic4122
#202677452
C4×Q16×C1032
#3177103