Finite Group Databasebeta

← #14543646

Subgroups — #14543646

Order 2176.

228 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 54 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#11763777C211yesmaximal, characteristic
2#11763751C211yesmaximal, characteristic
3#11762668C211yesmaximal, characteristic
4C22×C4×D17C2211yescharacteristic
5C2×C22⋊#595—21no—
6C2×C4⋊#595—21no—
7C2×#63242C412yescomplemented
8C2×#63227—21no—
9C2×#63225—21no—
10C22⋊#3624—21no—
11(C2×#595)⋊C4C412yescomplemented
12#10587543—21no—
13C17×#95C411yescharacteristic, complemented
14#10587502C411yescharacteristic, complemented
15C23×D17D411yescharacteristic
16C22×#595—22no—
17C22×C4×C17—21no—
18C22×C4×C17C2×C411yescharacteristic
19C22×Dic17—21no—
20C22×Dic17D411yescharacteristic
21C2×C4×D17—42no—
22C2×C4×D17C2×C411yescharacteristic
23C2×C4×D17C2×C411yescharacteristic
24C2×C4×D17D411yescharacteristic
25C2×C4×D17Q811yescharacteristic
26C22⋊#595—41no—
27C22⋊#595—41no—
28C2×#3624—22no—
29C4⋊#595—42no—
30#63242—42no—
31#63227—41no—
32#63227—41no—
33#63225—42no—
34C23×C17C22⋊C411yescharacteristic
35C22×D17—41no—
36C22×D17—41no—
37C22×D17C22⋊C411yescharacteristic
38C22×D17C4⋊C411yescharacteristic
39C22×D17D811yescharacteristic
40C22×D17SD1611yescharacteristic
41C22×D17SD1611yescharacteristic
42C22×D17Q1611yescharacteristic
43C2×#595—42no—
44C2×#595—42no—
45C2×#595—42no—
46C2×C4×C17—41no—
47C2×C4×C17—41no—
48C2×C4×C17—41no—
49C2×C4×C17—41no—
50C2×C4×C17C4211yescharacteristic
51C2×C4×C17C4⋊C411yescharacteristic
52C2×Dic17—22no—
53C2×Dic17—41no—
54C2×Dic17—41no—
55C2×Dic17—41no—
56C2×Dic17C22⋊C411yescharacteristic
57C2×Dic17C4⋊C411yescharacteristic
58C4×D17—22no—
59C4×D17—22no—
60C4×D17—41no—
61C4×D17—41no—
62#3624—42no—
63#1289—171nomaximal, Sylow
64C22×C17—21no—
65C22×C17—21no—
66C22×C17#9511yescharacteristic
67C22×C17#10211yescharacteristic
68C22×C17#10311yescharacteristic
69C2×D17—21no—
70C2×D17—21no—
71C2×D17—21no—
72C2×D17—21no—
73C2×D17—41no—
74C2×D17—41no—
75C2×D17—41no—
76C2×D17—41no—
77C2×D17#10211yescharacteristic
78C2×D17#10311yescharacteristic
79C2×D17#10611yescharacteristic
80C2×D17#10711yescharacteristic
81#595—82no—
82C4×C17—21no—
83C4×C17—21no—
84C4×C17—81no—
85Dic17—21no—
86Dic17—81no—
87Dic17#9912yes—
88C2×C22⋊C8—171no—
89#380—171no—
90#380—171no—
91C2×C17—21no—
92C2×C17—21no—
93C2×C17H(3,ℤ/4)11yescharacteristic
94C2×C17#34011yescharacteristic
95C2×C17#34211yescharacteristic
96D17—21no—
97D17—21no—
98D17—21no—
99D17—21no—
100C23×C4—171no—
101C22×C8—172no—
102C2×C4⋊C4—341no—
103C2×C4⋊C4—341no—
104C2×C22⋊C4—341no—
105C2×C22⋊C4—341no—
106C22⋊C8—341no—
107C22⋊C8—341no—
108#95—172no—
109#95—171no—
110#95#59511yescharacteristic, complemented
111C17#128911yescharacteristic, complemented, Sylow
112C24—171no—
113C22×C4—21no—
114C22×C4—171no—
115C22×C4—171no—
116C22×C4—171no—
117C22×C4—171no—
118C22×C4—171no—
119C22×C4—342no—
120C22×C4—341no—
121C22×C4—682no—
122C22×C4C2×#59511yescharacteristic
123C2×C8—342no—
124C2×C8—682no—
125C4⋊C4—682no—
126C4⋊C4—682no—
127C22⋊C4—681no—
128C22⋊C4—681no—
129C22⋊C4—681no—
130C22⋊C4—681no—
131C23—171no—
132C23—171no—
133C23—171no—
134C23—171no—
135C23—171no—
136C23—171no—
137C23—681no—
138C23—681no—
139C23C22⋊#59511yescharacteristic
140C2×C4—41no—
141C2×C4—41no—
142C2×C4—41no—
143C2×C4—41no—
144C2×C4—171no—
145C2×C4—171no—
146C2×C4—342no—
147C2×C4—342no—
148C2×C4—342no—
149C2×C4—681no—
150C2×C4—681no—
151C2×C4—681no—
152C2×C4—681no—
153C2×C4—682no—
154C2×C4—682no—
155C2×C4—682no—
156C2×C4—681no—
157C2×C4C4×#59511yescharacteristic
158C2×C4C4⋊#59511yescharacteristic
159C8—682no—
160C22—21no—
161C22—21no—
162C22—171no—
163C22—171no—
164C22—171no—
165C22—171no—
166C22—341no—
167C22—341no—
168C22—341no—
169C22—341no—
170C22—681no—
171C22—681no—
172C22—681no—
173C22—681no—
174C22(C2×#595)⋊C411yescharacteristic
175C22#1058754711yescharacteristic
176C22#1058754911yescharacteristic
177C4—21no—
178C4—21no—
179C4—81no—
180C4—172no—
181C4—341no—
182C4—1361no—
183C4—1362no—
184C2—21no—
185C2—21no—
186C2—341no—
187C2—341no—
188C2—341no—
189C2—341no—
190C2#1176367611yescharacteristic
191C2#1176368211yescharacteristic
192C2#1176368611yescharacteristic
subgroupG/H
centerC22(C2×#595)⋊C4
commutatorC2×C4×C17C42
FrattiniC22×C4C2×#595
FittingC17×#95C4
socleC22×C17#95
prime radicalC23×D17D4
cosocleC22×C4×D17C22
hypercenter#95#595
hypocenterC17#1289
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
7. C2×#63242C4semidirect
11. (C2×#595)⋊C4C4semidirect
13. C17×#95C4semidirect
14. #10587502C4semidirect
110. #95#595semidirect
111. C17#1289semidirect

Maximal subgroups

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

subgroupindex
#117637772
#117637512
#117626682
#128917