Finite Group Databasebeta

← #14545076

Subgroups — #14545076

Order 2176.

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

normal subgroups only

This group has 250 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#11763720C212yesmaximal, complemented
3#11763717C212yesmaximal, complemented
4#11763357C211yesmaximal, characteristic
5C2×#63254C411yescharacteristic
6C2×#63254C2211yescharacteristic
7C2×#63247—22no—
8C17×#127C411yescharacteristic
9#10587624—22no—
10#10587622C411yescharacteristic
11#10587622C2211yescharacteristic
12D4×Dic17—22no—
13C42×D17C411yescharacteristic
14#10587555C2211yescharacteristic
15#10587553—22no—
16#10587545C2214yes—
17C2×D4×C17—22no—
18C2×D4×C17C2×C411yescharacteristic
19C2×D4×C17C2×C411yescharacteristic
20C2×C22⋊D17—21no—
21C2×C22⋊D17D412yes—
22C22×Dic17—21no—
23C22×Dic17D412yes—
24#63254—41no—
25#63254—41no—
26#63254—41no—
27#63254—41no—
28C2×C4×D17—21no—
29C2×C4×D17C2×C411yescharacteristic
30C2×Dic34C2×C411yescharacteristic
31C2×Dic34C2311yescharacteristic
32#63247—24no—
33#63247—42no—
34C2×#3624—42no—
35C42×C17C2×C411yescharacteristic
36C22⋊Dic17—22no—
37C22⋊Dic17—22no—
38C4⋊Dic17—22no—
39C4×Dic17—21no—
40C4×Dic17C2×C411yescharacteristic
41C23×C17—21no—
42C23×C17C22⋊C412yes—
43C22×D17C22⋊C411yescharacteristic
44D4×C17—41no—
45D4×C17—41no—
46D4×C17—44no—
47C2×C4×C17—21no—
48C2×C4×C17C22×C411yescharacteristic
49C22⋊D17—42no—
50C22⋊D17—42no—
51C2×Dic17—22no—
52C2×Dic17—22no—
53C2×Dic17—21no—
54C2×Dic17—21no—
55C2×Dic17—41no—
56C2×Dic17—41no—
57C2×Dic17C22⋊C411yescharacteristic
58C2×Dic17C2×D412yes—
59C4×D17—21no—
60C4×D17—21no—
61C4×D17—42no—
62Dic34—41no—
63Dic34—41no—
64#3624—44no—
65#2132—171nomaximal, Sylow
66C22×C17—22no—
67C22×C17—42no—
68C22×C17—42no—
69C22×C17—41no—
70C22×C17C2×C22⋊C411yescharacteristic
71C2×D17—21no—
72C2×D17—41no—
73C4×C17—22no—
74C4×C17—21no—
75Dic17—22no—
76Dic17—41no—
77Dic17—41no—
78Dic17#9911yescharacteristic
79Dic17#9911yescharacteristic
80#532—171no—
81#413—172no—
82#356—172no—
83#355—172no—
84C2×C17—21no—
85C2×C17—42no—
86C2×C17—81no—
87C2×C17C2×#9911yescharacteristic
88D17—41no—
89C2×#41—171no—
90C2×#41—171no—
91C2×M16—342no—
92C4⋊Q8—171no—
93#127#59511yescharacteristic
94#124—171no—
95#124—171no—
96#121—342no—
97C4×D4—342no—
98C2×C42—171no—
99#101—174no—
100#100—342no—
101C17#213211yescharacteristic, complemented, Sylow
102#41—681no—
103#41—681no—
104#41—681no—
105#41—681no—
106C2×Q8—171no—
107C2×Q8—171no—
108C2×D4—22no—
109C2×D4—172no—
110C2×D4—341no—
111C2×D4C2×#59511yescharacteristic
112C2×D4C2×#59511yescharacteristic
113C22×C4—172no—
114C22×C4—171no—
115C22×C4—341no—
116C22×C4—341no—
117M16—344no—
118M16—682no—
119C2×C8—682no—
120C4⋊C4—342no—
121C22⋊C4—342no—
122C22⋊C4—342no—
123C42—171no—
124C42—341no—
125C42C2×#59511yescharacteristic
126C23—21no—
127C23—171no—
128C23C22⋊#59512yes—
129Q8—681no—
130Q8—681no—
131D4—41no—
132D4—41no—
133D4—44no—
134D4—682no—
135D4—682no—
136C2×C4—21no—
137C2×C4—171no—
138C2×C4—172no—
139C2×C4—341no—
140C2×C4—341no—
141C2×C4—342no—
142C2×C4—342no—
143C2×C4—341no—
144C2×C4—341no—
145C2×C4—682no—
146C2×C4—681no—
147C2×C4—681no—
148C2×C4C22×#59511yescharacteristic
149C8—684no—
150C22—22no—
151C22—42no—
152C22—42no—
153C22—41no—
154C22—341no—
155C22—681no—
156C22C2×C22⋊#59511yescharacteristic
157C4—22no—
158C4—21no—
159C4—171no—
160C4—171no—
161C4—342no—
162C4—681no—
163C4—681no—
164C2—21no—
165C2—42no—
166C2—81no—
167C2—681no—
168C2D17⋊#9911yescharacteristic
subgroupG/H
centerC2D17⋊#99
commutatorC2×C4×C17C22×C4
FrattiniC2×C4C22×#595
FittingC17×#127C4
socleC2×C17C2×#99
prime radical#11763357C2
cosocleC2×Dic34C23
hypercenter#127#595
hypocenterC17#2132
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. #11763720C2semidirect
3. #11763717C2semidirect
101. C17#2132semidirect

Maximal subgroups

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

subgroupindex
#117637962
#117637202
#117637172
#117633572
#213217