Finite Group Databasebeta

← #17949802

Subgroups — #17949802

Order 4352.

440 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 118 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#14544711C212yesmaximal
2#14543604C214yesmaximal
3C4⋊Q8×Dic17C211yesmaximal, characteristic
4#11763675—22no—
5#11763675—22no—
6#11763675C2214yes—
7C2×Q8×Dic17C412yes—
8#11762716C2212yes—
9#11762708—22no—
10#11762679C411yescharacteristic
11C4⋊C4×Dic17—22no—
12C42×Dic17C2211yescharacteristic
13C2×C17×C4⋊Q8C411yescharacteristic
14C22×Q8×C17C2×C412yes—
15C22×#3624—24no—
16C17×C4⋊Q8—22no—
17C17×C4⋊Q8C814yescomplemented
18C2×C4⋊C4×C17—22no—
19C2×C42×C17C2×C411yescharacteristic
20Q8×Dic17—44no—
21C2×C4⋊Dic17—22no—
22C2×C4⋊Dic17—22no—
23C2×C4⋊Dic17C2×C412yes—
24C2×C4×Dic17—22no—
25C2×C4×Dic17C2×C411yescharacteristic
26C2×C4×Dic17D412yes—
27C2×C4×Dic17D412yes—
28C2×C4×Dic17C2311yescharacteristic
29#10587502—24no—
30C2×Q8×C17—22no—
31C2×Q8×C17—42no—
32C2×Q8×C17—42no—
33C2×Q8×C17C2×C814yes—
34C22×C4×C17—22no—
35C22×C4×C17C22⋊C412yes—
36C22×C4×C17C22×C411yescharacteristic
37C22×Dic17—22no—
38C22×Dic17C22⋊C411yescharacteristic
39C22×Dic17C22⋊C411yescharacteristic
40C22×Dic17C2×D412yes—
41C2×#3624—44no—
42C2×#3624—44no—
43C2×#3624—44no—
44C4⋊C4×C17—28no—
45C42×C17C2×C812yes—
46C42×C17M1612yes—
47C4⋊Dic17—44no—
48C4⋊Dic17—44no—
49C4⋊Dic17—42no—
50C4×Dic17—22no—
51C4×Dic17—24no—
52C4×Dic17—42no—
53C4×Dic17—41no—
54C4×Dic17—44no—
55#7605—171nomaximal, Sylow
56C23×C17C2×C22⋊C411yescharacteristic
57Q8×C17—44no—
58Q8×C17—44no—
59C2×C4×C17—21no—
60C2×C4×C17—21no—
61C2×C4×C17—22no—
62C2×C4×C17—22no—
63C2×C4×C17—24no—
64C2×C4×C17—42no—
65C2×C4×C17—42no—
66C2×C4×C17C22⋊C814yes—
67C2×C4×C17C22×C811yescharacteristic
68C2×C4×C17C2×M1611yescharacteristic
69C2×Dic17—22no—
70C2×Dic17—22no—
71C2×Dic17—22no—
72C2×Dic17—21no—
73C2×Dic17—22no—
74C2×Dic17—42no—
75C2×Dic17—44no—
76C2×Dic17#10012yes—
77C2×Dic17#13714yes—
78#3624—84no—
79C4×C4⋊Q8—171no—
80#1839—172no—
81#1272—174no—
82C22×C17C2×C22⋊C811yescharacteristic
83C22×C17#41011yescharacteristic
84C22×C17C2×#10011yescharacteristic
85C22×C17#41912yes—
86C22×C17#42112yes—
87C4×C17—21no—
88C4×C17—21no—
89C4×C17—24no—
90C4×C17—44no—
91Dic17—22no—
92Dic17—24no—
93Dic17—41no—
94Dic17—82no—
95C2×C4⋊Q8#59511yescharacteristic
96C2×C4×Q8—172no—
97#391—172no—
98#389—342no—
99#384—171no—
100C4×C4⋊C4—342no—
101C43—171no—
102#336—174no—
103#336—342no—
104#336—342no—
105C2×C17#146011yescharacteristic
106C2×C17#147912yes—
107C2×C17#151512yes—
108C2×C17#153611yescharacteristic
109C2×C17#155811yescharacteristic
110C22×Q8C2×#59512yes—
111C22×C8—344no—
112C4⋊Q8—22no—
113C4⋊Q8#362414yescomplemented
114C4×Q8—684no—
115C2×C4⋊C4—22no—
116C2×C4⋊C4—172no—
117C2×C4⋊C4—342no—
118C2×C4⋊C4—342no—
119C2×C42—172no—
120C2×C42—171no—
121C2×C42—172no—
122C2×C42—171no—
123C2×C42—342no—
124C2×C42C2×#59511yescharacteristic
125#95—344no—
126C17#760511yescharacteristic, complemented, Sylow
127C2×Q8—22no—
128C2×Q8—42no—
129C2×Q8—42no—
130C2×Q8C2×#362414yes—
131C22×C4—22no—
132C22×C4—171no—
133C22×C4—172no—
134C22×C4—171no—
135C22×C4—342no—
136C22×C4C22⋊#59512yes—
137C22×C4C22×#59511yescharacteristic
138C2×C8—684no—
139C2×C8—684no—
140C2×C8—684no—
141C4⋊C4—28no—
142C4⋊C4—682no—
143C4⋊C4—684no—
144C4⋊C4—684no—
145C42—342no—
146C42—344no—
147C42—681no—
148C42—682no—
149C42—684no—
150C42C2×#362412yes—
151C42#6324712yes—
152C23C2×C22⋊#59511yescharacteristic
153Q8—44no—
154Q8—44no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—24no—
160C2×C4—42no—
161C2×C4—42no—
162C2×C4—172no—
163C2×C4—174no—
164C2×C4—342no—
165C2×C4—342no—
166C2×C4—342no—
167C2×C4—341no—
168C2×C4—342no—
169C2×C4—682no—
170C2×C4—684no—
171C2×C4C22⋊#362414yes—
172C2×C4C22×#362411yescharacteristic
173C2×C4C2×#6324711yescharacteristic
174C8—1364no—
175C22C2×C22⋊#362411yescharacteristic
176C22#1176378911yescharacteristic
177C22D17⋊#10011yescharacteristic
178C22#1176380212yes—
179C22#1176380812yes—
180C4—21no—
181C4—21no—
182C4—24no—
183C4—44no—
184C4—344no—
185C4—342no—
186C4—681no—
187C4—1362no—
188C2#1454402411yescharacteristic
189C2#1454408612yes—
190C2#1454420812yes—
191C2#1454427411yescharacteristic
192C2#1454431811yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC2×C4×C17C22×C8
FrattiniC22×C4C22×#595
FittingC2×C17×C4⋊Q8C4
socle, prime radicalC23×C17C2×C22⋊C4
cosocleC2×C4×Dic17C23
hypercenterC2×C4⋊Q8#595
hypocenterC17#7605
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
17. C17×C4⋊Q8C8semidirect
113. C4⋊Q8#3624semidirect
126. C17#7605semidirect

Maximal subgroups

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

subgroupindex
#145447112
#145436042
C4⋊Q8×Dic172
#760517