Finite Group Databasebeta

← #27196830

Subgroups — #27196830

Order 13184.

230 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 55 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#20268361C211yesmaximal, characteristic
2#101×D103C212yesmaximal, complemented
3#20267589C212yesmaximal, complemented
4#20267588C211yesmaximal, characteristic, complemented
5#355×C103C211yesmaximal, characteristic, complemented
6C2×#13110104C411yescharacteristic
7C2×Q8×D103C2211yescharacteristic
8M16×D103—22no—
9#15693021C411yescharacteristic
10#15693019C2211yescharacteristic
11#15693008C411yescharacteristic
12#15693003—22no—
13#15692998—22no—
14#15692978C411yescharacteristic
15#15692940C2212yes—
16#15692939—22no—
17#124×C103C2211yescharacteristic
18#101×C103C2212yes—
19#13110104—42no—
20C2×Dic206C2×C411yescharacteristic
21C2×Dic206C2×C411yescharacteristic
22C2×Dic206D412yes—
23Q8×D103—42no—
24C2×C22⋊D103—21no—
25C22×Dic103—21no—
26C2×C4×D103C2×C411yescharacteristic
27C2×C4×D103D412yes—
28#13110089—22no—
29#13110088—42no—
30C8×D103—42no—
31C4⋊Dic103—22no—
32Dic103⋊C4—22no—
33Dic103⋊C4—21no—
34C22⋊Dic103—22no—
35(C2×D103)⋊C4—21no—
36C4×Dic103C2×C411yescharacteristic
37C2×Q8×C103C2311yescharacteristic
38C2×D4×C103C2×C411yescharacteristic
39M16×C103—22no—
40C22⋊C4×C103—22no—
41C42×C103C2×C411yescharacteristic
42C23×C103—21no—
43C22×D103C22⋊C411yescharacteristic
44Q8×C103—41no—
45D4×C103—41no—
46C2×C4×C103—21no—
47C2×C4×C103C22×C411yescharacteristic
48C2×C4×C103C2×D412yes—
49C22⋊D103—42no—
50C2×Dic103—21no—
51C2×Dic103—21no—
52C2×Dic103—42no—
53C2×Dic103C22⋊C412yes—
54C2×Dic103C22⋊C411yescharacteristic
55C4×D103—22no—
56C4×D103—22no—
57C4×D103—22no—
58Dic206—41no—
59Dic206—42no—
60Dic206—41no—
61C8×C103—42no—
62C103⋊C8—42no—
63C22×C103—42no—
64C22×C103—41no—
65C22×C103C2×C22⋊C411yescharacteristic
66C2×D103—41no—
67C2×D103#9912yes—
68C4×C103—22no—
69C4×C103—21no—
70C4×C103—41no—
71Dic103—21no—
72Dic103—22no—
73Dic103—41no—
74Dic103—41no—
75C2×C103—21no—
76C2×C103—81no—
77C2×C103C2×#9911yescharacteristic
78D103—22no—
79#2133—1031nomaximal, Sylow
80C103#213311yescharacteristic, complemented, Sylow
81#536—1031no—
82C2×#101—1032no—
83#356—1032no—
84#355—1031no—
85#355D10311yescharacteristic, complemented
86C2×#41—1031no—
87C22×Q8—1031no—
88C2×M16—2062no—
89C4⋊Q8—1031no—
90C4⋊Q8—1031no—
91#124—1031no—
92#124C2×D10311yescharacteristic
93#123—2062no—
94C22⋊Q8—2062no—
95#117—1031no—
96#101—1032no—
97#101—2062no—
98#101C2×D10312yes—
99#41—4122no—
100C2×Q8—1031no—
101C2×Q8—1032no—
102C2×Q8—1031no—
103C2×Q8—4122no—
104C2×Q8C22×D10311yescharacteristic
105C2×D4—2061no—
106C2×D4C4×D10311yescharacteristic
107C22×C4—1031no—
108C22×C4—1032no—
109C22×C4—2061no—
110M16—22no—
111M16—4122no—
112M16—2062no—
113C2×C8—4122no—
114C4⋊C4—2061no—
115C4⋊C4—2062no—
116C4⋊C4—2062no—
117C22⋊C4—22no—
118C22⋊C4—2061no—
119C22⋊C4—2062no—
120C42—1031no—
121C42C4×D10311yescharacteristic
122C23—21no—
123C23—1031no—
124Q8—41no—
125Q8—4121no—
126Q8—4122no—
127Q8—4121no—
128D4—41no—
129D4—4122no—
130C2×C4—21no—
131C2×C4—1032no—
132C2×C4—1031no—
133C2×C4—4122no—
134C2×C4—2062no—
135C2×C4—2062no—
136C2×C4—2062no—
137C2×C4—2061no—
138C2×C4—2061no—
139C2×C4C2×C4×D10311yescharacteristic
140C2×C4D4×D10312yes—
141C8—42no—
142C8—4122no—
143C22—42no—
144C22—41no—
145C22—1032no—
146C22—4121no—
147C22C22⋊C4×D10311yescharacteristic
148C4—22no—
149C4—21no—
150C4—41no—
151C4—4121no—
152C4—4121no—
153C4—2061no—
154C4—2062no—
155C2—21no—
156C2—81no—
157C2—2062no—
158C2#99×D10311yescharacteristic
subgroupG/H
centerC2#99×D103
commutatorC2×C4×C103C22×C4
FrattiniC2×Q8C22×D103
Fitting#355×C103C2
socleC2×C103C2×#99
prime radicalC2×#13110104C4
cosocleC2×Q8×C103C23
hypercenter#355D103
hypocenterC103#2133
LCSG ▷ C2×C4×C103 ▷ C22×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #355

Complements

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

NH ≅ G/Ntype
2. #101×D103C2semidirect
3. #20267589C2semidirect
4. #20267588C2semidirect
5. #355×C103C2semidirect
80. C103#2133semidirect
85. #355D103semidirect

Maximal subgroups

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

subgroupindex
#202683612
#101×D1032
#202675892
#202675882
#355×C1032
#2133103