Finite Group Databasebeta

← #14544227

Subgroups — #14544227

Order 2176.

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

normal subgroups only

This group has 218 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#11763828C211yesmaximal, characteristic, complemented
2#11763754C211yesmaximal, characteristic, complemented
3#11763662C212yesmaximal, complemented
4#11763661C212yesmaximal
5#11763344C211yesmaximal, characteristic
6C17×#125C411yescharacteristic, complemented
7#10587584—21no—
8#10587583C2211yescharacteristic
9#10587581C2211yescharacteristic
10#10587580—21no—
11#10587579—21no—
12#10587579C411yescharacteristic, complemented
13#10587578—21no—
14#10587573C411yescharacteristic, complemented
15#10587561C411yescharacteristic, complemented
16C42×D17C2211yescharacteristic
17(C2×#595)⋊C4—21no—
18(C2×#595)⋊C4—21no—
19(C2×#595)⋊C4C2212yes—
20#10587543C2212yes—
21C4⋊#3624—21no—
22C4×#3624—21no—
23C22×#595—22no—
24C2×D68—21no—
25C2×D68C2×C411yescharacteristic
26C2×C4×D17—21no—
27C2×C4×D17D411yescharacteristic
28C2×C4×D17D411yescharacteristic
29C2×C4×D17C2311yescharacteristic
30C2×Dic34C2×C411yescharacteristic
31C2×#3624—22no—
32C4⋊C4×C17—21no—
33C4⋊C4×C17—21no—
34C4⋊C4×C17C2×C411yescharacteristic
35C4⋊C4×C17C2×C411yescharacteristic
36C42×C17C2×C411yescharacteristic
37#63227—21no—
38#63227—21no—
39#63227—21no—
40#63227—21no—
41#63227—21no—
42C4⋊Dic17—21no—
43#63225—21no—
44C4×Dic17—21no—
45C4×Dic17C2×C411yescharacteristic
46C4×Dic17D411yescharacteristic
47C4×Dic17D411yescharacteristic
48C22×D17—21no—
49C22×D17C2×D411yescharacteristic
50C2×#595—42no—
51C2×#595—42no—
52C2×#595—42no—
53C2×C4×C17—21no—
54C2×C4×C17—21no—
55C2×C4×C17C22⋊C411yescharacteristic
56C2×C4×C17C22⋊C411yescharacteristic
57C2×C4×C17C22×C411yescharacteristic
58C2×Dic17—21no—
59C2×Dic17C22⋊C411yescharacteristic
60C2×Dic17C22⋊C411yescharacteristic
61C2×Dic17C2×D411yescharacteristic
62D68—41no—
63D68—42no—
64C4×D17—22no—
65C4×D17—41no—
66C4×D17—41no—
67C4×D17—42no—
68Dic34—41no—
69#3624—42no—
70#1521—171nomaximal, Sylow
71C22×C17C2×C22⋊C411yescharacteristic
72C2×D17—21no—
73C2×D17—21no—
74C2×D17—41no—
75C2×D17—41no—
76C2×D17—41no—
77C2×D17#13512yes—
78#595—82no—
79C4×C17—21no—
80C4×C17—21no—
81C4×C17—21no—
82C4×C17—41no—
83C4×C17—41no—
84Dic17—21no—
85Dic17—21no—
86Dic17—21no—
87Dic17—41no—
88#529—171no—
89#431—171no—
90#383—171no—
91#328—172no—
92#327—172no—
93C2×C17#41011yescharacteristic
94C2×C17#41611yescharacteristic
95C2×C17#42111yescharacteristic
96D17—22no—
97D17—81no—
98#126—341no—
99#125#59511yescharacteristic, complemented
100#124—171no—
101#123—341no—
102C22⋊Q8—171no—
103#121—171no—
104C4×Q8—171no—
105C4×D4—171no—
106C4×D4—341no—
107#117—341no—
108C2×C42—171no—
109C4⋊C8—341no—
110C22⋊C8—172no—
111C4×C8—341no—
112#95—172no—
113#95—341no—
114#95—341no—
115C17#152111yescharacteristic, complemented, Sylow
116C2×Q8—171no—
117C2×D4—171no—
118C2×D4—341no—
119C22×C4—171no—
120C22×C4—171no—
121C22×C4—171no—
122C22×C4—341no—
123C22×C4—342no—
124C2×C8—342no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—341no—
128C4⋊C4—341no—
129C4⋊C4C2×#59511yescharacteristic
130C4⋊C4C2×#59511yescharacteristic
131C22⋊C4—341no—
132C22⋊C4—341no—
133C22⋊C4—341no—
134C22⋊C4—341no—
135C22⋊C4—341no—
136C42—171no—
137C42—171no—
138C42—171no—
139C42—341no—
140C42C2×#59511yescharacteristic
141C23—171no—
142C23—341no—
143Q8—681no—
144D4—681no—
145D4—682no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—171no—
149C2×C4—171no—
150C2×C4—171no—
151C2×C4—342no—
152C2×C4—341no—
153C2×C4—681no—
154C2×C4—681no—
155C2×C4—682no—
156C2×C4—682no—
157C2×C4—682no—
158C2×C4—682no—
159C2×C4C22⋊#59511yescharacteristic
160C2×C4C22⋊#59511yescharacteristic
161C2×C4C22×#59511yescharacteristic
162C8—682no—
163C22—172no—
164C22—341no—
165C22—341no—
166C22—681no—
167C22—681no—
168C22—681no—
169C22C2×C22⋊#59511yescharacteristic
170C4—21no—
171C4—21no—
172C4—21no—
173C4—41no—
174C4—41no—
175C4—341no—
176C4—341no—
177C4—341no—
178C4—681no—
179C4—1362no—
180C2—342no—
181C2—1361no—
182C2#1176379011yescharacteristic
183C2#1176379911yescharacteristic
184C2#1176380611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#595
commutatorC2×C4×C17C22×C4
FrattiniC2×C4C22×#595
FittingC17×#125C4
socleC22×C17C2×C22⋊C4
prime radical#10587581C22
cosocleC2×C4×D17C23
hypercenter#125#595
hypocenterC17#1521
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
1. #11763828C2semidirect
2. #11763754C2semidirect
3. #11763662C2semidirect
6. C17×#125C4semidirect
12. #10587579C4semidirect
14. #10587573C4semidirect
15. #10587561C4semidirect
99. #125#595semidirect
115. C17#1521semidirect

Maximal subgroups

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

subgroupindex
#117638282
#117637542
#117636622
#117636612
#117633442
#152117