Finite Group Databasebeta

← #14544206

Subgroups — #14544206

Order 2176.

208 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 56 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#11763831C211yesmaximal, characteristic
2#11763754C211yesmaximal, characteristic
3#11763663C212yesmaximal
4#11763662C212yesmaximal
5#11763363C211yesmaximal, characteristic
6C4×Q8×C17C411yescharacteristic, complemented
7#10587632C2211yescharacteristic
8#10587630C411yescharacteristic, complemented
9#10587583C2211yescharacteristic
10#10587582—21no—
11#10587575—21no—
12#10587574C411yescharacteristic, complemented
13#10587558—21no—
14C42×D17C2211yescharacteristic
15C4×Dic34—21no—
16C4×Dic34C411yescharacteristic, complemented
17(C2×#595)⋊C4—21no—
18(C2×#595)⋊C4—21no—
19(C2×#595)⋊C4C2212yes—
20#10587543C2212yes—
21#10587542—21no—
22C4⋊#3624—21no—
23C22×#595—22no—
24C2×Q8×C17C2×C411yescharacteristic
25C2×C4×D17D411yescharacteristic
26C2×C4×D17D411yescharacteristic
27C2×C4×D17C2311yescharacteristic
28C2×Dic34—21no—
29C2×Dic34C2×C411yescharacteristic
30C2×#3624—22no—
31C4⋊C4×C17—21no—
32C4⋊C4×C17C2×C411yescharacteristic
33C42×C17—21no—
34C42×C17C2×C411yescharacteristic
35#63227—21no—
36#63227—21no—
37C4⋊Dic17—21no—
38C4⋊Dic17C2×C411yescharacteristic
39#63225—21no—
40#63225—21no—
41#63225—21no—
42#63225—21no—
43#63225—21no—
44C4×Dic17—21no—
45C4×Dic17C2×C411yescharacteristic
46C4×Dic17D411yescharacteristic
47C4×Dic17D411yescharacteristic
48C22×D17C2×D411yescharacteristic
49C2×#595—42no—
50C2×#595—42no—
51C2×#595—42no—
52Q8×C17—41no—
53C2×C4×C17—21no—
54C2×C4×C17—21no—
55C2×C4×C17C22⋊C411yescharacteristic
56C2×C4×C17C22⋊C411yescharacteristic
57C2×C4×C17C22×C411yescharacteristic
58C2×Dic17—21no—
59C2×Dic17—21no—
60C2×Dic17C22⋊C411yescharacteristic
61C2×Dic17C22⋊C411yescharacteristic
62C2×Dic17C2×D411yescharacteristic
63C4×D17—22no—
64C4×D17—41no—
65C4×D17—41no—
66Dic34—42no—
67Dic34—41no—
68#3624—42no—
69#1515—171nomaximal, Sylow
70C22×C17C2×C22⋊C411yescharacteristic
71C2×D17—21no—
72C2×D17—21no—
73C2×D17#13712yes—
74#595—82no—
75C4×C17—21no—
76C4×C17—21no—
77C4×C17—21no—
78C4×C17—41no—
79C4×C17—41no—
80Dic17—21no—
81Dic17—21no—
82Dic17—21no—
83Dic17—41no—
84Dic17—41no—
85#533—171no—
86#432—171no—
87#383—171no—
88#328—172no—
89#328—172no—
90C2×C17#41011yescharacteristic
91C2×C17#41911yescharacteristic
92C2×C17#42111yescharacteristic
93D17—22no—
94C4⋊Q8—171no—
95C4⋊Q8—171no—
96#125—341no—
97C22⋊Q8—171no—
98C22⋊Q8—171no—
99C22⋊Q8—341no—
100C4×Q8—171no—
101C4×Q8—341no—
102C4×Q8#59511yescharacteristic, complemented
103#117—341no—
104C2×C42—171no—
105C4⋊C8—341no—
106C22⋊C8—172no—
107#97—341no—
108#95—172no—
109#95—341no—
110#95—341no—
111C17#151511yescharacteristic, complemented, Sylow
112C2×Q8—171no—
113C2×Q8—341no—
114C2×Q8C2×#59511yescharacteristic
115C22×C4—171no—
116C22×C4—171no—
117C22×C4—171no—
118C22×C4—342no—
119C2×C8—342no—
120C4⋊C4—21no—
121C4⋊C4—171no—
122C4⋊C4—341no—
123C4⋊C4—341no—
124C4⋊C4—341no—
125C4⋊C4—341no—
126C4⋊C4—341no—
127C4⋊C4—341no—
128C4⋊C4C2×#59511yescharacteristic
129C22⋊C4—341no—
130C22⋊C4—341no—
131C42—21no—
132C42—171no—
133C42—171no—
134C42—171no—
135C42—341no—
136C42C2×#59511yescharacteristic
137C23—171no—
138Q8—41no—
139Q8—681no—
140Q8—682no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—171no—
144C2×C4—171no—
145C2×C4—171no—
146C2×C4—342no—
147C2×C4—341no—
148C2×C4—341no—
149C2×C4—681no—
150C2×C4—681no—
151C2×C4—682no—
152C2×C4—682no—
153C2×C4—682no—
154C2×C4C22⋊#59511yescharacteristic
155C2×C4C22⋊#59511yescharacteristic
156C2×C4C22×#59511yescharacteristic
157C8—682no—
158C22—172no—
159C22—341no—
160C22—341no—
161C22C2×C22⋊#59511yescharacteristic
162C4—21no—
163C4—21no—
164C4—21no—
165C4—41no—
166C4—41no—
167C4—341no—
168C4—341no—
169C4—341no—
170C4—681no—
171C4—681no—
172C4—1362no—
173C2—342no—
174C2#1176378811yescharacteristic
175C2#1176380211yescharacteristic
176C2#1176380611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#595
commutatorC2×C4×C17C22×C4
FrattiniC2×C4C22×#595
FittingC4×Q8×C17C4
socleC22×C17C2×C22⋊C4
prime radicalC22×D17C2×D4
cosocleC2×C4×D17C23
hypercenterC4×Q8#595
hypocenterC17#1515
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
6. C4×Q8×C17C4semidirect
8. #10587630C4semidirect
12. #10587574C4semidirect
16. C4×Dic34C4semidirect
102. C4×Q8#595semidirect
111. C17#1515semidirect

Maximal subgroups

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

subgroupindex
#117638312
#117637542
#117636632
#117636622
#117633632
#151517