Finite Group Databasebeta

← #27196294

Subgroups — #27196294

Order 13184.

258 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 83 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×#15693012C211yesmaximal, characteristic
2C2×#15692946C211yesmaximal, characteristic
3C2×#15692944C211yesmaximal, characteristic
4#20267696C211yesmaximal, characteristic
5#20267553C211yesmaximal, characteristic
6#20267545C211yesmaximal, characteristic
7#340×C103C211yesmaximal, characteristic
8C22×Dic206C2211yescharacteristic
9C22×C103⋊C8C2211yescharacteristic
10#15693012—22no—
11#15693012—22no—
12C2×C4⋊Dic103—21no—
13C2×C4⋊Dic103C2211yescharacteristic
14C2×Dic103⋊C4—21no—
15C2×C4×Dic103C2211yescharacteristic
16#15692946—22no—
17#15692944—22no—
18C103⋊#95—21no—
19C103⋊#95—21no—
20C22×C8×C103C2211yescharacteristic
21C2×C4⋊C4×C103C2211yescharacteristic
22C2×C4⋊C4×C103C2211yescharacteristic
23C2×Dic206—21no—
24C2×Dic206—21no—
25C2×Dic206—21no—
26C2×Dic206—21no—
27C2×Dic206—21no—
28C2×Dic206Q812yes—
29C22×Dic103—21no—
30C22×Dic103—21no—
31C22×Dic103D411yescharacteristic
32C22×Dic103D411yescharacteristic
33C2×C103⋊C8—21no—
34C2×C103⋊C8—21no—
35C2×C103⋊C8—21no—
36C4⋊Dic103—24no—
37C4⋊Dic103—21no—
38C4⋊Dic103D412yes—
39Dic103⋊C4—24no—
40C4×Dic103—21no—
41C4×Dic103—21no—
42C22×C4×C103—21no—
43C22×C4×C103—21no—
44C22×C4×C103C2311yescharacteristic
45C2×C8×C103—21no—
46C2×C8×C103—21no—
47C2×C8×C103—21no—
48C4⋊C4×C103—21no—
49C4⋊C4×C103—21no—
50C4⋊C4×C103—21no—
51C4⋊C4×C103D412yes—
52C23×C103C2×D411yescharacteristic
53C2×C4×C103—22no—
54C2×C4×C103—41no—
55C2×C4×C103—41no—
56C2×C4×C103—41no—
57C2×C4×C103—41no—
58C2×C4×C103—41no—
59C2×C4×C103C2×D411yescharacteristic
60C2×C4×C103C2×D411yescharacteristic
61C2×C4×C103C2×Q811yescharacteristic
62C2×C4×C103#4111yescharacteristic
63C2×C4×C103#4111yescharacteristic
64C2×C4×C103#4111yescharacteristic
65C2×Dic103—21no—
66C2×Dic103—21no—
67C2×Dic103—22no—
68C2×Dic103—22no—
69C2×Dic103—21no—
70C2×Dic103—21no—
71C2×Dic103—21no—
72C2×Dic103—21no—
73C2×Dic103—41no—
74C2×Dic103—41no—
75C2×Dic103—41no—
76C2×Dic103—41no—
77Dic206—22no—
78Dic206—22no—
79Dic206—41no—
80Dic206—41no—
81C8×C103—41no—
82C103⋊C8—41no—
83C22×C103#12011yescharacteristic
84C22×C103C22⋊Q811yescharacteristic
85C22×C103#12411yescharacteristic
86C22×C103#13511yescharacteristic
87C22×C103#13511yescharacteristic
88C22×C103#13711yescharacteristic
89C22×C103#13711yescharacteristic
90C4×C103—42no—
91C4×C103—81no—
92C4×C103C22⋊Q811yescharacteristic
93C4×C103C22⋊Q811yescharacteristic
94C4×C103#12411yescharacteristic
95C4×C103#12411yescharacteristic
96Dic103—42no—
97Dic103—41no—
98Dic103—41no—
99Dic103—42no—
100C2×C103#39311yescharacteristic
101C2×C103#45211yescharacteristic
102C2×C103#45211yescharacteristic
103C2×C103#47911yescharacteristic
104C2×C103#47911yescharacteristic
105C2×C103#48811yescharacteristic
106C2×C103#49111yescharacteristic
107#2026—1031nomaximal, Sylow
108C103#202611yescharacteristic, complemented, Sylow
109C2×#125—1031no—
110C2×#103—1031no—
111C2×#103—1031no—
112#391—1031no—
113#340—1031no—
114#340D10311yescharacteristic
115#336—1031no—
116C22×Q8—1031no—
117C22×C8—1031no—
118C22×C8C2×D10311yescharacteristic
119#125—2062no—
120#125—2062no—
121C2×C4⋊C4—1031no—
122C2×C4⋊C4—2061no—
123C2×C4⋊C4—2061no—
124C2×C4⋊C4C2×D10311yescharacteristic
125C2×C4⋊C4C2×D10311yescharacteristic
126C2×C42—1031no—
127#103—2062no—
128#103—2062no—
129#95—2061no—
130#95—2061no—
131C2×Q8—1032no—
132C2×Q8—2061no—
133C2×Q8—2061no—
134C2×Q8—2061no—
135C2×Q8—2061no—
136C2×Q8—2061no—
137C22×C4—21no—
138C22×C4—21no—
139C22×C4—1031no—
140C22×C4—1031no—
141C22×C4—2061no—
142C22×C4—2061no—
143C22×C4C22×D10311yescharacteristic
144C2×C8—21no—
145C2×C8—21no—
146C2×C8—21no—
147C2×C8—2061no—
148C2×C8—2061no—
149C2×C8—2061no—
150C4⋊C4—21no—
151C4⋊C4—21no—
152C4⋊C4—21no—
153C4⋊C4—1032no—
154C4⋊C4—2064no—
155C4⋊C4—2064no—
156C4⋊C4—2061no—
157C4⋊C4D41212yes—
158C42—2061no—
159C42—2061no—
160C23D4×D10311yescharacteristic
161Q8—4121no—
162Q8—4121no—
163Q8—2062no—
164Q8—2062no—
165C2×C4—22no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—4121no—
172C2×C4—4121no—
173C2×C4—4121no—
174C2×C4—4121no—
175C2×C4—2061no—
176C2×C4—2061no—
177C2×C4—2062no—
178C2×C4—2062no—
179C2×C4—2061no—
180C2×C4—2061no—
181C2×C4—2061no—
182C2×C4—2061no—
183C2×C4D4×D10311yescharacteristic
184C2×C4C2×D41211yescharacteristic
185C2×C4Q8×D10311yescharacteristic
186C2×C4#1311010411yescharacteristic
187C2×C4#1311010511yescharacteristic
188C2×C4#1311010511yescharacteristic
189C8—41no—
190C8—4121no—
191C22#1569299111yescharacteristic
192C22#1569299911yescharacteristic
193C22#1569300711yescharacteristic
194C22#1569304011yescharacteristic
195C22#1569304211yescharacteristic
196C22#1569305011yescharacteristic
197C22#1569305311yescharacteristic
198C4—42no—
199C4—81no—
200C4—4121no—
201C4—4122no—
202C4—4121no—
203C4—4122no—
204C4#1569299911yescharacteristic
205C4#1569300111yescharacteristic
206C4#1569300711yescharacteristic
207C4#1569300911yescharacteristic
208C2#2026770411yescharacteristic
209C2#2026795411yescharacteristic
210C2#2026795611yescharacteristic
211C2#2026809711yescharacteristic
212C2#2026810111yescharacteristic
213C2#2026814411yescharacteristic
214C2#2026815811yescharacteristic
subgroupG/H
centerC23D4×D103
commutator, cosocleC22×C4×C103C23
FrattiniC22×C4C22×D103
Fitting#340×C103C2
socle, prime radicalC23×C103C2×D4
hypercenter#340D103
hypocenterC103#2026
LCSG ▷ C22×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
108. C103#2026semidirect

Maximal subgroups

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

subgroupindex
C2×#156930122
C2×#156929462
C2×#156929442
#202676962
#202675532
#202675452
#340×C1032
#2026103