Finite Group Databasebeta

← #14545084

Subgroups — #14545084

Order 2176.

262 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 52 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#11763796C212yesmaximal, complemented
2#11763718C212yesmaximal, complemented
3#11763717C212yesmaximal, complemented
4#11763372C211yesmaximal, characteristic
5C2×#63254C2211yescharacteristic
6C2×D4×D17C411yescharacteristic
7C2×#63247—22no—
8C17×#127C411yescharacteristic
9#10587626C411yescharacteristic
10#10587625—22no—
11#10587623—22no—
12#10587622C2211yescharacteristic
13#10587561C2211yescharacteristic
14#10587558C411yescharacteristic
15#10587553—22no—
16#10587545C2214yescomplemented
17C23×D17—21no—
18C2×D4×C17—22no—
19C2×D4×C17C2×C411yescharacteristic
20C2×D4×C17C2×C411yescharacteristic
21C2×C22⋊D17—22no—
22C2×C22⋊D17—21no—
23C2×C22⋊D17D412yes—
24C22×Dic17D412yes—
25#63254—42no—
26D4×D17—42no—
27C2×D68C2×C411yescharacteristic
28C2×C4×D17C2×C411yescharacteristic
29C2×Dic34C2311yescharacteristic
30#63247—24no—
31#63247—42no—
32C2×#3624—42no—
33C42×C17C2×C411yescharacteristic
34C22⋊Dic17—22no—
35#63227—21no—
36#63227—22no—
37#63225—21no—
38C4×Dic17C2×C411yescharacteristic
39C23×C17—21no—
40C23×C17C22⋊C412yes—
41C22×D17—21no—
42C22×D17—42no—
43C22×D17—82no—
44C22×D17C22⋊C411yescharacteristic
45D4×C17—41no—
46D4×C17—41no—
47D4×C17—82no—
48C2×C4×C17—21no—
49C2×C4×C17C22×C411yescharacteristic
50C22⋊D17—42no—
51C22⋊D17—42no—
52C22⋊D17—82no—
53C2×Dic17—22no—
54C2×Dic17—22no—
55C2×Dic17—21no—
56C2×Dic17C22⋊C411yescharacteristic
57C2×Dic17C2×D412yes—
58D68—41no—
59C4×D17—22no—
60Dic34—41no—
61#3624—44no—
62#2134—171nomaximal, Sylow
63C22×C17—22no—
64C22×C17—42no—
65C22×C17—42no—
66C22×C17—41no—
67C22×C17C2×C22⋊C411yescharacteristic
68C2×D17—21no—
69C2×D17—41no—
70C2×D17—42no—
71C2×D17—41no—
72C2×D17—84no—
73C4×C17—21no—
74C4×C17—41no—
75Dic17—22no—
76Dic17—41no—
77Dic17#9912yes—
78#535—171no—
79#413—172no—
80#355—172no—
81#355—172no—
82C2×C17—21no—
83C2×C17—42no—
84C2×C17—81no—
85C2×C17C2×#9911yescharacteristic
86D17—41no—
87D17—81no—
88C2×#41—171no—
89C22×D4—171no—
90C2×M16—342no—
91#127—171no—
92#127#59511yescharacteristic
93#124—171no—
94#124—171no—
95#121—342no—
96#120—342no—
97#117—171no—
98#101—174no—
99#100—342no—
100C17#213411yescharacteristic, complemented, Sylow
101C24—341no—
102#41—682no—
103C2×Q8—171no—
104C2×D4—22no—
105C2×D4—172no—
106C2×D4—171no—
107C2×D4—341no—
108C2×D4—342no—
109C2×D4—682no—
110C2×D4C2×#59511yescharacteristic
111C2×D4C2×#59511yescharacteristic
112C22×C4—172no—
113C22×C4—171no—
114M16—344no—
115M16—682no—
116C2×C8—682no—
117C4⋊C4—341no—
118C22⋊C4—342no—
119C22⋊C4—341no—
120C22⋊C4—342no—
121C42—171no—
122C42C2×#59511yescharacteristic
123C23—21no—
124C23—171no—
125C23—341no—
126C23—682no—
127C23—1362no—
128C23C22⋊#59512yes—
129Q8—681no—
130D4—41no—
131D4—41no—
132D4—82no—
133D4—681no—
134D4—682no—
135D4—682no—
136D4—1362no—
137C2×C4—21no—
138C2×C4—171no—
139C2×C4—172no—
140C2×C4—342no—
141C2×C4—342no—
142C2×C4—342no—
143C2×C4—341no—
144C2×C4C22×#59511yescharacteristic
145C8—684no—
146C22—22no—
147C22—42no—
148C22—42no—
149C22—41no—
150C22—341no—
151C22—681no—
152C22—682no—
153C22—681no—
154C22—1364no—
155C22C2×C22⋊#59511yescharacteristic
156C4—21no—
157C4—41no—
158C4—172no—
159C4—342no—
160C4—681no—
161C2—21no—
162C2—42no—
163C2—81no—
164C2—681no—
165C2—1361no—
166C2D17⋊#9911yescharacteristic
subgroupG/H
centerC2D17⋊#99
commutatorC2×C4×C17C22×C4
FrattiniC2×C4C22×#595
FittingC17×#127C4
socleC2×C17C2×#99
prime radical#11763372C2
cosocleC2×Dic34C23
hypercenter#127#595
hypocenterC17#2134
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #11763796C2semidirect
2. #11763718C2semidirect
3. #11763717C2semidirect
16. #10587545C22semidirect
100. C17#2134semidirect

Maximal subgroups

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

subgroupindex
#117637962
#117637182
#117637172
#117633722
#213417