Finite Group Databasebeta

← #14545055

Subgroups — #14545055

Order 2176.

258 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 54 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#11763788C212yesmaximal, complemented
2#11763715C212yesmaximal, complemented
3#11763713C212yesmaximal, complemented
4#11763355C211yesmaximal, characteristic
5C2×#41×C17C411yescharacteristic, complemented
6C2×#63252C2211yescharacteristic
7#10587677—22no—
8#10587633C2211yescharacteristic
9#10587630C411yescharacteristic, complemented
10#10587626C2211yescharacteristic
11#10587625—22no—
12#10587622C411yescharacteristic, complemented
13C4×C22⋊D17—22no—
14C2×C4×Dic17C411yescharacteristic, complemented
15#10587551—22no—
16#10587539C2214yes—
17#41×C17—41no—
18#41×C17—41no—
19C2×Q8×C17C2×C411yescharacteristic
20C2×D4×C17—21no—
21C2×D4×C17C2×C411yescharacteristic
22C22×C4×C17—21no—
23C22×C4×C17C2×C411yescharacteristic
24C2×C22⋊D17—22no—
25C2×C22⋊D17D412yes—
26C22×Dic17—21no—
27#63252—41no—
28#63252—41no—
29C2×D68C2311yescharacteristic
30C2×C4×D17D412yes—
31C2×Dic34C2×C411yescharacteristic
32C22⋊#595—24no—
33C4⋊#595—42no—
34C4×#595—42no—
35C22⋊Dic17—22no—
36#63227—22no—
37#63225—22no—
38C4×Dic17—21no—
39C4×Dic17C2×C411yescharacteristic
40C4×Dic17C2×C411yescharacteristic
41C23×C17—21no—
42C23×C17C22⋊C411yescharacteristic
43C22×D17C2×D412yes—
44C2×#595—44no—
45Q8×C17—41no—
46D4×C17—41no—
47D4×C17—42no—
48C2×C4×C17—21no—
49C2×C4×C17—21no—
50C2×C4×C17—21no—
51C2×C4×C17—41no—
52C2×C4×C17—41no—
53C2×C4×C17C22⋊C411yescharacteristic
54C2×C4×C17C22×C411yescharacteristic
55C22⋊D17—42no—
56C22⋊D17—44no—
57C2×Dic17—21no—
58C2×Dic17—21no—
59C2×Dic17—42no—
60C2×Dic17C22⋊C412yes—
61D68—41no—
62C4×D17—22no—
63C4×D17—22no—
64Dic34—41no—
65#2126—171nomaximal, Sylow
66C22×C17—21no—
67C22×C17—41no—
68C22×C17—42no—
69C22×C17—41no—
70C22×C17C2×C22⋊C411yescharacteristic
71C2×D17—22no—
72C2×D17—42no—
73#595—84no—
74C4×C17—21no—
75C4×C17—41no—
76C4×C17#9911yescharacteristic
77C4×C17#9911yescharacteristic
78Dic17—22no—
79Dic17—22no—
80Dic17—41no—
81#532—171no—
82#410—172no—
83#354—172no—
84#353—172no—
85C2×C17—21no—
86C2×C17—41no—
87C2×C17—81no—
88C2×C17C2×#9911yescharacteristic
89D17—42no—
90C2×#41—171no—
91C2×#41#59511yescharacteristic, complemented
92C4⋊Q8—171no—
93#127—171no—
94#124—171no—
95#124—171no—
96#121—342no—
97C4×D4—342no—
98#117—342no—
99C2×C42—171no—
100#99—174no—
101#99—342no—
102C17#212611yescharacteristic, complemented, Sylow
103#41—41no—
104#41—41no—
105#41—681no—
106#41—681no—
107C2×Q8—171no—
108C2×Q8C2×#59511yescharacteristic
109C2×D4—21no—
110C2×D4—172no—
111C2×D4—171no—
112C2×D4—342no—
113C2×D4C2×#59511yescharacteristic
114C22×C4—21no—
115C22×C4—172no—
116C22×C4—341no—
117C22×C4C2×#59511yescharacteristic
118C4⋊C4—342no—
119C4⋊C4—682no—
120C22⋊C4—342no—
121C22⋊C4—342no—
122C22⋊C4—344no—
123C42—171no—
124C42—171no—
125C42—341no—
126C42—682no—
127C23—21no—
128C23—172no—
129C23C22⋊#59511yescharacteristic
130Q8—41no—
131Q8—681no—
132D4—41no—
133D4—42no—
134D4—681no—
135D4—682no—
136D4—684no—
137C2×C4—21no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—41no—
141C2×C4—41no—
142C2×C4—172no—
143C2×C4—341no—
144C2×C4—342no—
145C2×C4—342no—
146C2×C4—341no—
147C2×C4—682no—
148C2×C4—684no—
149C2×C4C22⋊#59511yescharacteristic
150C2×C4C22×#59511yescharacteristic
151C22—21no—
152C22—41no—
153C22—42no—
154C22—41no—
155C22—342no—
156C22—682no—
157C22C2×C22⋊#59511yescharacteristic
158C4—21no—
159C4—41no—
160C4—342no—
161C4—342no—
162C4—681no—
163C4—1364no—
164C4#1058755111yescharacteristic
165C4#1058755111yescharacteristic
166C2—21no—
167C2—41no—
168C2—81no—
169C2—682no—
170C2C2×#1058755111yescharacteristic
subgroupG/H
centerC4#10587551
commutatorC2×C4×C17C22×C4
FrattiniC2×C4C22×#595
FittingC2×#41×C17C4
socleC2×C17C2×#99
prime radical#11763355C2
cosocleC2×D68C23
hypercenterC2×#41#595
hypocenterC17#2126
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #11763788C2semidirect
2. #11763715C2semidirect
3. #11763713C2semidirect
5. C2×#41×C17C4semidirect
9. #10587630C4semidirect
12. #10587622C4semidirect
14. C2×C4×Dic17C4semidirect
91. C2×#41#595semidirect
102. C17#2126semidirect

Maximal subgroups

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

subgroupindex
#117637882
#117637152
#117637132
#117633552
#212617