Finite Group Databasebeta

← #14544961

Subgroups — #14544961

Order 2176.

260 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 72 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
1C4×#63243C211yesmaximal, characteristic
2C4×C4⋊#595C211yesmaximal, characteristic
3#11763679C212yesmaximal
4#11763679C212yesmaximal
5#11763365C211yesmaximal, characteristic
6C2×C4⋊#595—21no—
7C2×C4×#595C2212yes—
8C2×#63243C2212yes—
9C17×#125C411yescharacteristic, complemented
10#10587582—21no—
11#10587582—21no—
12#10587578C2211yescharacteristic
13#10587578C2211yescharacteristic
14#10587574C411yescharacteristic, complemented
15#10587574C411yescharacteristic, complemented
16#10587573—21no—
17#10587573—21no—
18C42×D17C2211yescharacteristic
19#10587556C411yescharacteristic, complemented
20(C2×#595)⋊C4—21no—
21#10587542—21no—
22C4×#3624—21no—
23C22×#595—22no—
24C2×C4×D17D411yescharacteristic
25C2×C4×D17D411yescharacteristic
26C2×C4×D17C2311yescharacteristic
27C2×Dic34—21no—
28C2×Dic34—21no—
29C2×#3624—22no—
30C4⋊#595—24no—
31C4×#595—24no—
32#63243—22no—
33#63243Q814yescomplemented
34C4⋊C4×C17—21no—
35C4⋊C4×C17—21no—
36C4⋊C4×C17C2×C411yescharacteristic
37C4⋊C4×C17C2×C411yescharacteristic
38C42×C17C2×C411yescharacteristic
39#63227—21no—
40#63227—21no—
41C4⋊Dic17C2×C411yescharacteristic
42C4⋊Dic17C2×C411yescharacteristic
43#63225—21no—
44#63225—21no—
45#63225—21no—
46#63225—21no—
47C4×Dic17—21no—
48C4×Dic17—21no—
49C4×Dic17C2×C411yescharacteristic
50C4×Dic17D411yescharacteristic
51C4×Dic17D411yescharacteristic
52C22×D17C2×D411yescharacteristic
53C2×#595—24no—
54C2×#595—42no—
55C2×#595—42no—
56C2×C4×C17—21no—
57C2×C4×C17—21no—
58C2×C4×C17C22⋊C411yescharacteristic
59C2×C4×C17C22⋊C411yescharacteristic
60C2×C4×C17C22×C411yescharacteristic
61C2×Dic17—21no—
62C2×Dic17—21no—
63C2×Dic17C22⋊C411yescharacteristic
64C2×Dic17C22⋊C411yescharacteristic
65C2×Dic17C2×D411yescharacteristic
66C4×D17—22no—
67C4×D17—41no—
68C4×D17C2×Q812yes—
69C4×D17#4112yes—
70Dic34—42no—
71Dic34—42no—
72#3624—24no—
73#1986—171nomaximal, Sylow
74C22×C17C2×C22⋊C411yescharacteristic
75C2×D17—21no—
76C2×D17—21no—
77C2×D17#12411yescharacteristic
78C2×D17C4⋊Q811yescharacteristic
79#595—44no—
80C4×C17—21no—
81C4×C17—21no—
82C4×C17—41no—
83C4×C17—41no—
84C4×C17C4×Q812yes—
85Dic17—21no—
86Dic17—41no—
87Dic17—41no—
88Dic17#10412yes—
89Dic17C22⋊Q812yes—
90#533—171no—
91C4×M16—171no—
92C4×C4⋊C4—171no—
93#339—172no—
94#339—172no—
95C2×C17#39111yescharacteristic
96C2×C17C2×#10411yescharacteristic
97C2×C17#42111yescharacteristic
98D17—21no—
99D17—21no—
100C2×M16—172no—
101C4⋊Q8—171no—
102C4⋊Q8—171no—
103#125—171no—
104#125#59511yescharacteristic, complemented
105C22⋊Q8—341no—
106C22⋊Q8—341no—
107C4×Q8—341no—
108C4×Q8—341no—
109#117—171no—
110#117—171no—
111C2×C4⋊C4—341no—
112C2×C42—171no—
113C2×C42—172no—
114#97—341no—
115C4×C8—341no—
116#95—341no—
117C17#198611yescharacteristic, complemented, Sylow
118C2×Q8—341no—
119C2×Q8—341no—
120C22×C4—171no—
121C22×C4—171no—
122C22×C4—171no—
123C22×C4—342no—
124M16—174no—
125M16—342no—
126C2×C8—342no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—171no—
130C4⋊C4—171no—
131C4⋊C4—341no—
132C4⋊C4—341no—
133C4⋊C4—344no—
134C4⋊C4—341no—
135C4⋊C4—341no—
136C4⋊C4C2×#59511yescharacteristic
137C4⋊C4C2×#59511yescharacteristic
138C22⋊C4—341no—
139C22⋊C4—341no—
140C42—171no—
141C42—171no—
142C42—171no—
143C42—341no—
144C42—341no—
145C42—344no—
146C42C2×#59511yescharacteristic
147C23—171no—
148Q8—682no—
149Q8—682no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—171no—
153C2×C4—171no—
154C2×C4—172no—
155C2×C4—172no—
156C2×C4—171no—
157C2×C4—342no—
158C2×C4—344no—
159C2×C4—341no—
160C2×C4—341no—
161C2×C4—681no—
162C2×C4—682no—
163C2×C4—682no—
164C2×C4C22⋊#59511yescharacteristic
165C2×C4C22⋊#59511yescharacteristic
166C2×C4C22×#59511yescharacteristic
167C8—344no—
168C22—171no—
169C22—171no—
170C22—341no—
171C22—341no—
172C22C2×C22⋊#59511yescharacteristic
173C4—21no—
174C4—21no—
175C4—41no—
176C4—41no—
177C4—172no—
178C4—172no—
179C4—341no—
180C4—684no—
181C4—681no—
182C4—681no—
183C4Q8×#59512yes—
184C2—341no—
185C2—341no—
186C2(C2×#595)⋊Q811yescharacteristic
187C2D17⋊#10411yescharacteristic
188C2#1176380611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#595
commutatorC2×C4×C17C22×C4
FrattiniC2×C4C22×#595
FittingC17×#125C4
socleC22×C17C2×C22⋊C4
prime radicalC22×D17C2×D4
cosocleC2×C4×D17C23
hypercenter#125#595
hypocenterC17#1986
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
9. C17×#125C4semidirect
14. #10587574C4semidirect
15. #10587574C4semidirect
19. #10587556C4semidirect
33. #63243Q8semidirect
104. #125#595semidirect
117. C17#1986semidirect

Maximal subgroups

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

subgroupindex
C4×#632432
C4×C4⋊#5952
#117636792
#117633652
#198617