Finite Group Databasebeta

← #17958527

Subgroups — #17958527

Order 4352.

270 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 70 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#14545158C212yesmaximal
2#14543733C212yesmaximal
3#14543730C212yesmaximal
4#14537718C211yesmaximal, characteristic
5#11763731—22no—
6#11763705C2214yes—
7#11763702—22no—
8#11763366C411yescharacteristic
9#11762939—22no—
10C8×Dic34—22no—
11#11762835C411yescharacteristic
12#11762835C2211yescharacteristic
13#11762833C2211yescharacteristic
14#11762764C411yescharacteristic
15#11762764C2211yescharacteristic
16C2×C4×C8×C17C411yescharacteristic
17C22×C8×C17C2×C411yescharacteristic
18C22×C8×C17C2×C411yescharacteristic
19C2×C42×C17C2×C411yescharacteristic
20#10587612C2×C411yescharacteristic
21#10587612C2×C411yescharacteristic
22#10587610—22no—
23C2×#63223C2×C411yescharacteristic
24C2×#63223C2311yescharacteristic
25#10587556—21no—
26#10587555—21no—
27C4×Dic34—22no—
28#10587538—24no—
29C4×C8×C17—21no—
30C4×C8×C17—21no—
31#10587486—21no—
32#10587486D412yes—
33#10587485—22no—
34#10587485—22no—
35C8×Dic17—21no—
36C8×Dic17D412yes—
37C4⋊#3622—22no—
38C22×C4×C17—21no—
39C22×C4×C17C22×C411yescharacteristic
40C2×Dic34—22no—
41C2×C8×C17—22no—
42C2×C8×C17—21no—
43C2×C8×C17—41no—
44C2×C8×C17C22⋊C411yescharacteristic
45C2×C8×C17C22⋊C411yescharacteristic
46C42×C17—21no—
47C42×C17M1611yescharacteristic
48C42×C17M1611yescharacteristic
49C22⋊Dic17—21no—
50C22⋊Dic17M1612yes—
51C4⋊Dic17—22no—
52C4⋊Dic17—21no—
53C4⋊Dic17—21no—
54#63225—24no—
55C4×Dic17—21no—
56C4×Dic17C22⋊C412yes—
57#63223—41no—
58#63223—41no—
59C2×#3622—21no—
60C2×#3622C2×D412yes—
61#63216—44no—
62#11539—171nomaximal, Sylow
63C23×C17C2×M1611yescharacteristic
64C2×C4×C17—21no—
65C2×C4×C17—21no—
66C2×C4×C17—21no—
67C2×C4×C17—21no—
68C2×C4×C17—42no—
69C2×C4×C17C2×C22⋊C411yescharacteristic
70C2×C4×C17C2×M1611yescharacteristic
71C2×Dic17—22no—
72C2×Dic17—22no—
73Dic34—44no—
74C8×C17—21no—
75C8×C17—41no—
76C8×C17#10112yes—
77#3622—22no—
78#3622—41no—
79#2960—171no—
80#2166—172no—
81#1328—172no—
82#1327—172no—
83C22×C17—21no—
84C22×C17—41no—
85C22×C17#40711yescharacteristic
86C4×C17—22no—
87C4×C17—21no—
88C4×C17—41no—
89C4×C17#41011yescharacteristic
90C4×C17C2×#10111yescharacteristic
91Dic17—42no—
92Dic17—42no—
93#533—171no—
94#446—342no—
95C8×Q8—342no—
96#424—171no—
97#424—171no—
98#423—171no—
99#405—171no—
100#405—171no—
101C2×C4×C8#59511yescharacteristic
102#364—342no—
103#349—174no—
104#347—342no—
105C2×C17—21no—
106C2×C17—41no—
107C2×C17#146711yescharacteristic
108C2×M16—171no—
109C2×M16—171no—
110C22×C8C2×#59511yescharacteristic
111C22×C8C2×#59511yescharacteristic
112C4⋊Q8—341no—
113#125—341no—
114C22⋊Q8—342no—
115C4×Q8—342no—
116#117—171no—
117#117—171no—
118C2×C42C2×#59511yescharacteristic
119M32—344no—
120C4⋊C8—342no—
121C4⋊C8—342no—
122C4⋊C8—342no—
123#97—172no—
124#97—341no—
125C4×C8—21no—
126C4×C8—21no—
127C4×C8—172no—
128C4×C8—341no—
129C17#1153911yescharacteristic, complemented, Sylow
130C2×Q8—342no—
131C22×C4—21no—
132C22×C4C22×#59511yescharacteristic
133M16—681no—
134M16—681no—
135C2×C8—22no—
136C2×C8—21no—
137C2×C8—41no—
138C2×C8—172no—
139C2×C8—341no—
140C2×C8C22⋊#59511yescharacteristic
141C2×C8C22⋊#59511yescharacteristic
142C4⋊C4—344no—
143C4⋊C4—342no—
144C4⋊C4—341no—
145C4⋊C4—341no—
146C22⋊C4—172no—
147C22⋊C4—341no—
148C42—21no—
149C42—172no—
150C42—341no—
151C42#6324311yescharacteristic
152C42#6324311yescharacteristic
153C16—684no—
154C23D17⋊M1611yescharacteristic
155Q8—684no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—42no—
161C2×C4—342no—
162C2×C4—342no—
163C2×C4C2×#6324311yescharacteristic
164C2×C4C2×C22⋊#59511yescharacteristic
165C8—21no—
166C8—41no—
167C8—342no—
168C8—681no—
169C8#1058754512yes—
170C22—21no—
171C22—41no—
172C22#1176378011yescharacteristic
173C4—22no—
174C4—21no—
175C4—41no—
176C4—682no—
177C4—682no—
178C4#1176378811yescharacteristic
179C4C2×#1058754511yescharacteristic
180C2—21no—
181C2—41no—
182C2#1454404611yescharacteristic
subgroupG/H
centerC4#11763788
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC2×C4×C8×C17C4
socleC2×C17#1467
prime radicalC23×C17C2×M16
cosocleC2×#63223C23
hypercenterC2×C4×C8#595
hypocenterC17#11539
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C4 ◁ C2×C8 ◁ C22×C8 ◁ C2×C4×C8

Complements

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

NH ≅ G/Ntype
129. C17#11539semidirect

Maximal subgroups

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

subgroupindex
#145451582
#145437332
#145437302
#145377182
#1153917