Finite Group Databasebeta

← #14545086

Subgroups — #14545086

Order 2176.

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

normal subgroups only

This group has 230 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#11763795C212yesmaximal
2#11763719C214yesmaximal, complemented
3#11763383C211yesmaximal, characteristic
4C22×Q8×C17C411yescharacteristic
5C2×#63252C2211yescharacteristic
6D17⋊M16—22no—
7#10587633C412yes—
8#10587632—22no—
9#10587630C2212yes—
10#10587615—22no—
11#10587612C411yescharacteristic
12#10587553—22no—
13#10587545C2214yes—
14C2×Q8×C17—21no—
15C2×Q8×C17—42no—
16C2×Q8×C17C2×C412yes—
17C22×C4×C17—21no—
18C22×C4×C17C2×C411yescharacteristic
19C2×C22⋊D17D412yes—
20#63252—42no—
21C2×D68C2×C411yescharacteristic
22C2×C4×D17D412yes—
23C2×Dic34C2311yescharacteristic
24#63247—24no—
25#63243—42no—
26#63242—42no—
27C22⋊Dic17—21no—
28#63227—24no—
29C4⋊Dic17—21no—
30#63225—24no—
31C4×Dic17C2×C412yes—
32C23×C17C22⋊C411yescharacteristic
33C22×D17C22⋊C412yes—
34Q8×C17—42no—
35Q8×C17—42no—
36C2×C4×C17—22no—
37C2×C4×C17—22no—
38C2×C4×C17—42no—
39C2×C4×C17C22⋊C411yescharacteristic
40C2×C4×C17C22×C411yescharacteristic
41C22⋊D17—42no—
42C2×Dic17—22no—
43C2×Dic17C2×D412yes—
44D68—41no—
45C4×D17—22no—
46C4×D17—22no—
47Dic34—41no—
48#3624—44no—
49#2135—171nomaximal, Sylow
50C22×C17—21no—
51C22×C17—41no—
52C22×C17C2×C22⋊C411yescharacteristic
53C2×D17—22no—
54C2×D17—42no—
55C4×C17—21no—
56C4×C17—42no—
57C4×C17#9912yes—
58Dic17—22no—
59Dic17—42no—
60#536—171no—
61#413—172no—
62#356—174no—
63C2×C17—21no—
64C2×C17—41no—
65C2×C17C2×#9911yescharacteristic
66D17—42no—
67C2×#41—171no—
68C22×Q8#59511yescharacteristic
69C2×M16—342no—
70C4⋊Q8—172no—
71#124—172no—
72#123—342no—
73C22⋊Q8—342no—
74#117—171no—
75#101—174no—
76#100—342no—
77C17#213511yescharacteristic, complemented, Sylow
78#41—682no—
79C2×Q8—21no—
80C2×Q8—42no—
81C2×Q8—171no—
82C2×Q8C2×#59512yes—
83C2×D4—172no—
84C2×D4—171no—
85C22×C4—21no—
86C22×C4—172no—
87C22×C4C2×#59511yescharacteristic
88M16—344no—
89M16—682no—
90C2×C8—682no—
91C4⋊C4—344no—
92C4⋊C4—341no—
93C22⋊C4—344no—
94C22⋊C4—341no—
95C42—172no—
96C23—172no—
97C23C22⋊#59511yescharacteristic
98Q8—42no—
99Q8—42no—
100Q8—681no—
101D4—681no—
102D4—682no—
103C2×C4—22no—
104C2×C4—22no—
105C2×C4—42no—
106C2×C4—172no—
107C2×C4—342no—
108C2×C4—342no—
109C2×C4—342no—
110C2×C4C22⋊#59511yescharacteristic
111C2×C4C22×#59511yescharacteristic
112C8—684no—
113C22—21no—
114C22—41no—
115C22—342no—
116C22—682no—
117C22C2×C22⋊#59511yescharacteristic
118C4—21no—
119C4—42no—
120C4—342no—
121C4—682no—
122C4#1058755112yes—
123C2—21no—
124C2—41no—
125C2—682no—
126C2C2×#1058755111yescharacteristic
subgroupG/H
centerC2C2×#10587551
commutatorC2×C4×C17C22×C4
FrattiniC2×C4C22×#595
FittingC22×Q8×C17C4
socleC2×C17C2×#99
prime radicalC2×#63252C22
cosocleC2×Dic34C23
hypercenterC22×Q8#595
hypocenterC17#2135
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. #11763719C2semidirect
77. C17#2135semidirect

Maximal subgroups

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

subgroupindex
#117637952
#117637192
#117633832
#213517