Finite Group Databasebeta

← #27194171

Subgroups — #27194171

Order 13184.

236 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 53 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#20268417C211yesmaximal, characteristic
2#20268127C212yesmaximal, complemented
3#20267727C211yesmaximal, characteristic
4#20267529C212yesmaximal, complemented
5#323×C103C211yesmaximal, characteristic
6#15693000—21no—
7#15693000C2212yes—
8#15692998—22no—
9#15692998—22no—
10C2×C4⋊Dic103C2211yescharacteristic
11C2×Dic103⋊C4—21no—
12C2×C22⋊Dic103—21no—
13C2×C22⋊Dic103—21no—
14#15692955—22no—
15#15692946—22no—
16C103⋊#95C2211yescharacteristic
17C2×C22⋊C4×C103C2211yescharacteristic
18C22⋊C8×C103C2212yes—
19C2×Dic206—21no—
20C2×Dic206D412yes—
21C22×Dic103—21no—
22C22×Dic103—21no—
23C22×Dic103—21no—
24C22×Dic103—21no—
25C4⋊Dic103—21no—
26C4⋊Dic103—22no—
27C4⋊Dic103D412yes—
28Dic103⋊C4—22no—
29Dic103⋊C4—22no—
30Dic103⋊C4—42no—
31C22⋊Dic103—22no—
32C22⋊Dic103—22no—
33C22⋊Dic103—42no—
34C24×C103D411yescharacteristic
35C22×C4×C103D411yescharacteristic
36C22×C4×C103C2311yescharacteristic
37C2×C8×C103—22no—
38C22⋊C4×C103—22no—
39C23×C103—21no—
40C23×C103—21no—
41C23×C103—41no—
42C23×C103—41no—
43C23×C103Q1612yes—
44C23×C103C2×D411yescharacteristic
45C2×C4×C103—21no—
46C2×C4×C103—41no—
47C2×C4×C103—41no—
48C2×C4×C103C2×D412yes—
49C2×Dic103—22no—
50C2×Dic103—22no—
51C2×Dic103—22no—
52C2×Dic103—41no—
53C2×Dic103—41no—
54C2×Dic103—41no—
55C2×Dic103—41no—
56C2×Dic103—41no—
57C2×Dic103—81no—
58C2×Dic103—81no—
59Dic206—42no—
60Dic206—81no—
61C8×C103—42no—
62C22×C103—21no—
63C22×C103—21no—
64C22×C103—22no—
65C22×C103—42no—
66C22×C103—41no—
67C22×C103—41no—
68C22×C103—81no—
69C22×C103#12011yescharacteristic
70C22×C103C2×Q1611yescharacteristic
71C22×C103#13711yescharacteristic
72C4×C103—22no—
73C4×C103—41no—
74Dic103—42no—
75Dic103—42no—
76Dic103—42no—
77Dic103—81no—
78C2×C103—21no—
79C2×C103—21no—
80C2×C103—42no—
81C2×C103#45111yescharacteristic
82C2×C103#45311yescharacteristic
83C2×C103#45811yescharacteristic
84#1614—1031nomaximal, Sylow
85C103#161411yescharacteristic, complemented, Sylow
86#543—1031no—
87#484—1032no—
88#399—1031no—
89#328—1032no—
90#323D10311yescharacteristic
91C22⋊Q8—1032no—
92C22⋊Q8—2062no—
93C22⋊Q8—2062no—
94C22⋊Q8—2061no—
95C2×C4⋊C4—1031no—
96C2×C4⋊C4—2061no—
97C2×C22⋊C4—2061no—
98C2×C22⋊C4—2061no—
99C2×C22⋊C4C2×D10311yescharacteristic
100#107—2062no—
101#103—2062no—
102C22⋊C8C2×D10312yes—
103#95—1031no—
104C24D41211yescharacteristic
105C2×Q8—1032no—
106C2×Q8—2061no—
107C22×C4—2061no—
108C22×C4—2061no—
109C22×C4—2061no—
110C22×C4—2061no—
111C22×C4D41211yescharacteristic
112C22×C4C22×D10311yescharacteristic
113C2×C8—22no—
114C4⋊C4—1032no—
115C4⋊C4—4122no—
116C4⋊C4—2062no—
117C4⋊C4—2061no—
118C4⋊C4—2062no—
119C4⋊C4—2062no—
120C22⋊C4—22no—
121C22⋊C4—4122no—
122C22⋊C4—2062no—
123C22⋊C4—2062no—
124C23—21no—
125C23—21no—
126C23—41no—
127C23—41no—
128C23Dic41212yes—
129C23C2×D41211yescharacteristic
130Q8—8241no—
131Q8—4122no—
132C2×C4—21no—
133C2×C4—41no—
134C2×C4—41no—
135C2×C4—8241no—
136C2×C4—8241no—
137C2×C4—4121no—
138C2×C4—4121no—
139C2×C4—4121no—
140C2×C4—4121no—
141C2×C4—4121no—
142C2×C4—2062no—
143C2×C4—2062no—
144C2×C4—2062no—
145C2×C4D4×D10312yes—
146C8—42no—
147C22—21no—
148C22—21no—
149C22—22no—
150C22—42no—
151C22—41no—
152C22—41no—
153C22—81no—
154C22#1569299111yescharacteristic
155C22C2×Dic41211yescharacteristic
156C22#1569305411yescharacteristic
157C4—22no—
158C4—41no—
159C4—8241no—
160C4—4122no—
161C4—4122no—
162C4—4122no—
163C2—21no—
164C2—21no—
165C2—42no—
166C2#2026794911yescharacteristic
167C2#2026796111yescharacteristic
168C2#2026798211yescharacteristic
subgroupG/H
centerC22#15692991
commutator, cosocleC22×C4×C103C23
FrattiniC22×C4C22×D103
Fitting#323×C103C2
socleC22×C103#120
prime radicalC24×C103D4
hypercenter#323D103
hypocenterC103#1614
LCSG ▷ C22×C4×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #20268127C2semidirect
4. #20267529C2semidirect
85. C103#1614semidirect

Maximal subgroups

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

subgroupindex
#202684172
#202681272
#202677272
#202675292
#323×C1032
#1614103