Finite Group Databasebeta

← #27195959

Subgroups — #27195959

Order 13184.

344 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 99 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×#15693008C211yesmaximal, characteristic
2C2×#15692946C211yesmaximal, characteristic, complemented
3C2×#15692944C211yesmaximal, characteristic, complemented
4C2×#15692942C211yesmaximal, characteristic
5C2×#15692931C211yesmaximal, characteristic, complemented
6#20267660C211yesmaximal, characteristic, complemented
7C2×#102×C103C211yesmaximal, characteristic
8C22×Dic206C2211yescharacteristic
9C22×C103⋊C8C2211yescharacteristic
10#15693008—22no—
11#15693008C414yescomplemented
12C2×C4⋊Dic103C2211yescharacteristic
13C2×Dic103⋊C4—22no—
14C2×C22⋊Dic103—22no—
15C2×C4×Dic103C2211yescharacteristic
16#15692946—22no—
17#15692944—22no—
18#15692942—22no—
19#15692931—22no—
20C22×D4×C103C2211yescharacteristic
21C22×C8×C103C2211yescharacteristic
22C2×C4⋊C4×C103C2211yescharacteristic
23#102×C103—22no—
24C2×Dic206—21no—
25C2×Dic206—21no—
26C2×Dic206—21no—
27C2×Dic206—21no—
28C2×Dic206—21no—
29C2×Dic206C2×C412yes—
30C22×Dic103—21no—
31C22×Dic103—21no—
32C22×Dic103D412yes—
33C2×C103⋊C8—21no—
34C2×C103⋊C8—21no—
35C2×C103⋊C8D412yes—
36C4⋊Dic103—21no—
37C4⋊Dic103—21no—
38Dic103⋊C4—44no—
39C22⋊Dic103—28no—
40C4×Dic103C2×C412yes—
41C4×Dic103D412yes—
42C24×C103—21no—
43C2×D4×C103—21no—
44C2×D4×C103—21no—
45C2×D4×C103—21no—
46C2×D4×C103—21no—
47C2×D4×C103—21no—
48C2×D4×C103C2×C412yes—
49C22×C4×C103—21no—
50C22×C4×C103C2311yescharacteristic
51C2×C8×C103—21no—
52C2×C8×C103—21no—
53C2×C8×C103D412yes—
54C4⋊C4×C103—21no—
55C4⋊C4×C103—21no—
56C23×C103—22no—
57C23×C103—41no—
58C23×C103—41no—
59C23×C103—42no—
60C23×C103—42no—
61C23×C103C2×D411yescharacteristic
62D4×C103—22no—
63D4×C103—22no—
64D4×C103—41no—
65D4×C103—41no—
66C2×C4×C103—41no—
67C2×C4×C103—42no—
68C2×C4×C103C22×C411yescharacteristic
69C2×C4×C103C2×D411yescharacteristic
70C2×C4×C103C2×D411yescharacteristic
71C2×C4×C103C2×D411yescharacteristic
72C2×C4×C103#4111yescharacteristic
73C2×C4×C103#4111yescharacteristic
74C2×Dic103—22no—
75C2×Dic103—22no—
76C2×Dic103—22no—
77C2×Dic103—41no—
78C2×Dic103—41no—
79C2×Dic103—41no—
80C2×Dic103—42no—
81C2×Dic103C22⋊C414yes—
82Dic206—22no—
83Dic206—22no—
84Dic206—41no—
85Dic206—41no—
86C8×C103—22no—
87C103⋊C8—22no—
88C22×C103—42no—
89C22×C103—44no—
90C22×C103—82no—
91C22×C103—81no—
92C22×C103—81no—
93C22×C103C2×C22⋊C411yescharacteristic
94C22×C103#12411yescharacteristic
95C22×C103#12711yescharacteristic
96C22×C103AGL(1,ℤ/8)12yes—
97C22×C103#13712yes—
98C4×C103—81no—
99C4×C103C4×D411yescharacteristic
100C4×C103C4×D411yescharacteristic
101C4×C103#12111yescharacteristic
102C4×C103#12111yescharacteristic
103Dic103—24no—
104Dic103—42no—
105Dic103—81no—
106C2×C103—82no—
107C2×C103#39011yescharacteristic
108C2×C103#41712yes—
109C2×C103#48912yes—
110C2×C103#49611yescharacteristic
111C2×C103#49711yescharacteristic
112#1959—1031nomaximal, Sylow
113C103#195911yescharacteristic, complemented, Sylow
114C2×#124—1031no—
115C2×#103—1031no—
116C2×#103—1031no—
117C2×#102—1031no—
118C2×#102D10311yescharacteristic
119C2×#97—1031no—
120#384—1031no—
121C22×Q8—1031no—
122C22×D4C2×D10311yescharacteristic
123C22×C8—1031no—
124C22×C8C2×D10311yescharacteristic
125#124—1034no—
126#124—2062no—
127C2×C4⋊C4—1031no—
128C2×C4⋊C4—2062no—
129C2×C4⋊C4C2×D10311yescharacteristic
130C2×C22⋊C4—2062no—
131C2×C42—1031no—
132#103—2062no—
133#103—2062no—
134#102—22no—
135#102—2062no—
136#97—2062no—
137C24—21no—
138C2×Q8—1032no—
139C2×Q8—2061no—
140C2×Q8—2061no—
141C2×Q8—2061no—
142C2×Q8—2061no—
143C2×Q8—2061no—
144C2×D4—21no—
145C2×D4—21no—
146C2×D4—21no—
147C2×D4—21no—
148C2×D4—21no—
149C2×D4C4×D10312yes—
150C22×C4—21no—
151C22×C4—1032no—
152C22×C4—2061no—
153C22×C4—2061no—
154C22×C4C22×D10311yescharacteristic
155C2×C8—21no—
156C2×C8—21no—
157C2×C8—1032no—
158C2×C8—2061no—
159C2×C8—2061no—
160C2×C8C22⋊D10312yes—
161C4⋊C4—21no—
162C4⋊C4—21no—
163C4⋊C4—4124no—
164C4⋊C4—2061no—
165C4⋊C4—2061no—
166C22⋊C4—2068no—
167C42—1032no—
168C42—1032no—
169C23—22no—
170C23—41no—
171C23—41no—
172C23—42no—
173C23—42no—
174C23D4×D10311yescharacteristic
175Q8—4121no—
176Q8—4121no—
177Q8—2062no—
178Q8—2062no—
179D4—22no—
180D4—22no—
181D4—41no—
182D4—41no—
183C2×C4—41no—
184C2×C4—42no—
185C2×C4—1034no—
186C2×C4—4121no—
187C2×C4—4122no—
188C2×C4—4121no—
189C2×C4—4121no—
190C2×C4—2062no—
191C2×C4—2062no—
192C2×C4—2062no—
193C2×C4C2×C4×D10311yescharacteristic
194C2×C4D4×D10311yescharacteristic
195C2×C4D4×D10311yescharacteristic
196C2×C4C2×C22⋊D10311yescharacteristic
197C2×C4#1311010411yescharacteristic
198C2×C4#1311010511yescharacteristic
199C8—22no—
200C8—2062no—
201C22—44no—
202C22—42no—
203C22—82no—
204C22—81no—
205C22—81no—
206C22C22⋊C4×D10311yescharacteristic
207C22#1569300711yescharacteristic
208C22#1569301711yescharacteristic
209C22#1569304512yes—
210C22#1569305012yes—
211C4—81no—
212C4—8241no—
213C4—4122no—
214C4—2064no—
215C4(C22⋊D103)⋊C411yescharacteristic
216C4C4×C22⋊D10311yescharacteristic
217C4#1569299311yescharacteristic
218C4#1569299411yescharacteristic
219C2—82no—
220C2#2026769111yescharacteristic
221C2#2026778912yes—
222C2#2026814912yes—
223C2#2026817911yescharacteristic
224C2#2026818211yescharacteristic
subgroupG/H
centerC23D4×D103
commutatorC2×C4×C103C22×C4
FrattiniC22×C4C22×D103
FittingC2×#102×C103C2
socleC23×C103C2×D4
prime radicalC22×D4×C103C22
cosocleC22×C4×C103C23
hypercenterC2×#102D103
hypocenterC103#1959
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
2. C2×#15692946C2semidirect
3. C2×#15692944C2semidirect
5. C2×#15692931C2semidirect
6. #20267660C2semidirect
11. #15693008C4semidirect
113. C103#1959semidirect

Maximal subgroups

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

subgroupindex
C2×#156930082
C2×#156929462
C2×#156929442
C2×#156929422
C2×#156929312
#202676602
C2×#102×C1032
#1959103