Finite Group Databasebeta

← #27196837

Subgroups — #27196837

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#20268366C211yesmaximal, characteristic
2#20267774C212yesmaximal
3#20267590C211yesmaximal, characteristic, complemented
4#20267589C212yesmaximal, complemented
5#356×C103C211yesmaximal, characteristic, complemented
6C2×#13110106C2211yescharacteristic
7C2×Q8×D103C411yescharacteristic
8M16×D103—22no—
9#15693019C2211yescharacteristic
10#15693010C411yescharacteristic
11#15693009C411yescharacteristic
12#15693006—22no—
13#15692999—22no—
14#15692978C411yescharacteristic
15#15692940C2212yes—
16#15692937—22no—
17C4⋊Q8×C103C2211yescharacteristic
18#101×C103C2212yes—
19#13110106—42no—
20C2×Dic206—21no—
21C2×Dic206C2×C411yescharacteristic
22Q8×D103—42no—
23C2×D412C2×C411yescharacteristic
24C2×D412D412yes—
25C2×C4×D103—21no—
26C2×C4×D103C2×C411yescharacteristic
27C2×C4×D103D412yes—
28#13110089—22no—
29#13110088—42no—
30C8×D103—42no—
31Dic103⋊C4—22no—
32Dic103⋊C4—21no—
33(C2×D103)⋊C4—21no—
34(C2×D103)⋊C4—22no—
35(C2×D103)⋊C4—22no—
36C4×Dic103C2×C411yescharacteristic
37C2×Q8×C103C2×C411yescharacteristic
38C2×Q8×C103C2311yescharacteristic
39M16×C103—22no—
40C4⋊C4×C103—22no—
41C42×C103C2×C411yescharacteristic
42C22×D103C22⋊C412yes—
43C22×D103C22⋊C411yescharacteristic
44Q8×C103—41no—
45Q8×C103—41no—
46C2×C4×C103—21no—
47C2×C4×C103—21no—
48C2×C4×C103C22×C411yescharacteristic
49C2×C4×C103C2×D412yes—
50C2×Dic103—21no—
51C2×Dic103—21no—
52C2×Dic103C22⋊C411yescharacteristic
53D412—41no—
54D412—42no—
55C4×D103—22no—
56C4×D103—22no—
57C4×D103—22no—
58C4×D103—42no—
59Dic206—42no—
60Dic206—41no—
61C8×C103—42no—
62C103⋊C8—42no—
63C22×C103C2×C22⋊C411yescharacteristic
64C2×D103—21no—
65C2×D103—22no—
66C2×D103—42no—
67C2×D103—41no—
68C4×C103—22no—
69C4×C103—21no—
70C4×C103—41no—
71C4×C103—41no—
72Dic103—41no—
73Dic103—41no—
74Dic103#9912yes—
75C2×C103—21no—
76C2×C103C2×#9911yescharacteristic
77D103—41no—
78D103—42no—
79#2135—1031nomaximal, Sylow
80C103#213511yescharacteristic, complemented, Sylow
81#536—1031no—
82#413—1032no—
83#356—1031no—
84#356—1032no—
85#356D10311yescharacteristic, complemented
86C2×#41—1031no—
87C22×Q8—1031no—
88C2×M16—2062no—
89C4⋊Q8—1031no—
90C4⋊Q8C2×D10311yescharacteristic
91#124—1031no—
92#124—1031no—
93#123—2062no—
94C22⋊Q8—2062no—
95#117—1031no—
96#101—1032no—
97#101C2×D10312yes—
98#100—2062no—
99#41—4122no—
100C2×Q8—1031no—
101C2×Q8—4122no—
102C2×Q8—2061no—
103C2×Q8C4×D10311yescharacteristic
104C2×Q8C22×D10311yescharacteristic
105C2×D4—1031no—
106C2×D4—1032no—
107C22×C4—1031no—
108C22×C4—1032no—
109C22×C4—2061no—
110M16—22no—
111M16—4122no—
112M16—2062no—
113C2×C8—4122no—
114C4⋊C4—22no—
115C4⋊C4—2061no—
116C4⋊C4—2062no—
117C22⋊C4—2061no—
118C22⋊C4—2062no—
119C22⋊C4—2062no—
120C42—1031no—
121C42C4×D10311yescharacteristic
122C23—1032no—
123C23—1031no—
124Q8—41no—
125Q8—41no—
126Q8—4121no—
127Q8—4122no—
128D4—4122no—
129D4—4121no—
130C2×C4—21no—
131C2×C4—21no—
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—4122no—
144C22—4121no—
145C22—2061no—
146C22—2062no—
147C22C22⋊C4×D10311yescharacteristic
148C4—22no—
149C4—21no—
150C4—41no—
151C4—41no—
152C4—1032no—
153C4—4121no—
154C4—4121no—
155C2—21no—
156C2—4121no—
157C2—4122no—
158C2#99×D10311yescharacteristic
subgroupG/H
centerC2#99×D103
commutatorC2×C4×C103C22×C4
FrattiniC2×Q8C22×D103
Fitting#356×C103C2
socleC2×C103C2×#99
prime radicalC2×#13110106C22
cosocleC2×Q8×C103C23
hypercenter#356D103
hypocenterC103#2135
LCSG ▷ C2×C4×C103 ▷ C22×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #356

Complements

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

NH ≅ G/Ntype
3. #20267590C2semidirect
4. #20267589C2semidirect
5. #356×C103C2semidirect
80. C103#2135semidirect
85. #356D103semidirect

Maximal subgroups

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

subgroupindex
#202683662
#202677742
#202675902
#202675892
#356×C1032
#2135103