Finite Group Databasebeta

← #17958420

Subgroups — #17958420

Order 4352.

510 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 80 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#14544035C212yesmaximal
2#14543714C214yesmaximal, complemented
3#14531370C211yesmaximal, characteristic
4#11763829—22no—
5#11763654C2214yes—
6#11763652—22no—
7C2×#10587612C411yescharacteristic
8C2×#10587612C2211yescharacteristic
9#11762716—22no—
10#11762716C412yes—
11#11762716C2212yes—
12#11762672—22no—
13C23×Q8×C17C411yescharacteristic
14C22×Q8×C17—24no—
15C22×Q8×C17—21no—
16C22×Q8×C17—42no—
17C22×Q8×C17—42no—
18C22×Q8×C17C2×C412yes—
19C23×C4×C17—21no—
20C23×C4×C17C2×C411yescharacteristic
21C2×C22⋊Dic17—21no—
22C2×C22⋊Dic17D412yes—
23#10587612—42no—
24#10587612—42no—
25C2×C4⋊Dic17—21no—
26C2×C4⋊Dic17C2×C411yescharacteristic
27C2×C4⋊Dic17C2311yescharacteristic
28C2×C4×Dic17C2×C412yes—
29C2×C4×Dic17D412yes—
30C22⋊#3624—24no—
31#10587544—42no—
32#10587542—42no—
33#10587502—24no—
34#10587502—24no—
35C24×C17C22⋊C411yescharacteristic
36C2×Q8×C17—24no—
37C2×Q8×C17—22no—
38C2×Q8×C17—416no—
39C2×Q8×C17—42no—
40C2×Q8×C17—42no—
41C2×Q8×C17—42no—
42C2×Q8×C17—42no—
43C2×Q8×C17M1614yes—
44C22×C4×C17—22no—
45C22×C4×C17—22no—
46C22×C4×C17—22no—
47C22×C4×C17—24no—
48C22×C4×C17—22no—
49C22×C4×C17—42no—
50C22×C4×C17—42no—
51C22×C4×C17C22⋊C411yescharacteristic
52C22×C4×C17C22×C411yescharacteristic
53C22×Dic17—22no—
54C22×Dic17C22⋊C412yes—
55C22×Dic17C2×D412yes—
56C2×#3624—44no—
57C22⋊Dic17—42no—
58C22⋊Dic17—42no—
59C4⋊Dic17—41no—
60C4⋊Dic17—41no—
61C4⋊Dic17—42no—
62C4×Dic17—22no—
63C4×Dic17—22no—
64C4×Dic17—42no—
65#11510—171nomaximal, Sylow
66C23×C17—21no—
67C23×C17—21no—
68C23×C17—41no—
69C23×C17—41no—
70C23×C17#10012yes—
71C23×C17C2×C22⋊C411yescharacteristic
72Q8×C17—44no—
73Q8×C17—48no—
74Q8×C17—44no—
75C2×C4×C17—28no—
76C2×C4×C17—21no—
77C2×C4×C17—21no—
78C2×C4×C17—21no—
79C2×C4×C17—21no—
80C2×C4×C17—24no—
81C2×C4×C17—48no—
82C2×C4×C17—42no—
83C2×C4×C17—42no—
84C2×C4×C17#9912yes—
85C2×C4×C17C2×M1612yes—
86C2×Dic17—22no—
87C2×Dic17—22no—
88C2×Dic17—42no—
89C2×Dic17—42no—
90C2×Dic17—42no—
91C2×Dic17—42no—
92C2×Dic17—42no—
93#3624—84no—
94#2310—171no—
95#1464—172no—
96#1319—174no—
97C22×C17—21no—
98C22×C17—21no—
99C22×C17—22no—
100C22×C17—42no—
101C22×C17—42no—
102C22×C17—41no—
103C22×C17—41no—
104C22×C17#40711yescharacteristic
105C22×C17C2×#9911yescharacteristic
106C22×C17C2×#10011yescharacteristic
107C4×C17—22no—
108C4×C17—22no—
109C4×C17—44no—
110Dic17—42no—
111Dic17—42no—
112Dic17—82no—
113C23×Q8#59511yescharacteristic
114C2×#117—171no—
115C2×#117—171no—
116#432—342no—
117#391—172no—
118#391—172no—
119#391—342no—
120#381—342no—
121#324—174no—
122#323—342no—
123C2×C17—21no—
124C2×C17—21no—
125C2×C17—42no—
126C2×C17#146211yescharacteristic
127C2×C17#212911yescharacteristic
128C2×C17#213511yescharacteristic
129C22×Q8—24no—
130C22×Q8—21no—
131C22×Q8—42no—
132C22×Q8—42no—
133C22×Q8C2×#59512yes—
134C23×C4—21no—
135C23×C4C2×#59511yescharacteristic
136#117—682no—
137#117—682no—
138C2×C4⋊C4—171no—
139C2×C4⋊C4—171no—
140C2×C4⋊C4—341no—
141C2×C22⋊C4—172no—
142C2×C22⋊C4—341no—
143C2×C42—172no—
144C2×C42—172no—
145C4⋊C8—682no—
146C22⋊C8—344no—
147#97—682no—
148#95—344no—
149#95—344no—
150C17#1151011yescharacteristic, complemented, Sylow
151C24C22⋊#59511yescharacteristic
152C2×Q8—24no—
153C2×Q8—22no—
154C2×Q8—416no—
155C2×Q8—42no—
156C2×Q8—42no—
157C2×Q8—42no—
158C2×Q8—42no—
159C2×Q8#6324714yes—
160C22×C4—22no—
161C22×C4—22no—
162C22×C4—22no—
163C22×C4—24no—
164C22×C4—22no—
165C22×C4—42no—
166C22×C4—42no—
167C22×C4—172no—
168C22×C4—172no—
169C22×C4—342no—
170C22×C4C22⋊#59511yescharacteristic
171C22×C4C22×#59511yescharacteristic
172C2×C8—684no—
173C4⋊C4—681no—
174C4⋊C4—681no—
175C4⋊C4—682no—
176C22⋊C4—682no—
177C22⋊C4—682no—
178C42—342no—
179C42—342no—
180C42—682no—
181C23—21no—
182C23—21no—
183C23—41no—
184C23—41no—
185C23#1058755312yes—
186C23C2×C22⋊#59511yescharacteristic
187Q8—44no—
188Q8—44no—
189Q8—48no—
190C2×C4—28no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—24no—
196C2×C4—48no—
197C2×C4—42no—
198C2×C4—42no—
199C2×C4—342no—
200C2×C4—342no—
201C2×C4—682no—
202C2×C4—682no—
203C2×C4—682no—
204C2×C4—682no—
205C2×C4—682no—
206C2×C4#1058755112yes—
207C2×C4C2×#6324712yes—
208C8—1364no—
209C22—21no—
210C22—21no—
211C22—22no—
212C22—42no—
213C22—42no—
214C22—41no—
215C22—41no—
216C22#1176377911yescharacteristic
217C22C2×#1058755111yescharacteristic
218C22C2×#1058755311yescharacteristic
219C4—22no—
220C4—22no—
221C4—44no—
222C4—682no—
223C4—682no—
224C4—1362no—
225C2—21no—
226C2—21no—
227C2—42no—
228C2#1454402911yescharacteristic
229C2#1454506611yescharacteristic
230C2#1454508611yescharacteristic
subgroupG/H
centerC22C2×#10587551
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC23×Q8×C17C4
socleC22×C17C2×#99
prime radicalC24×C17C22⋊C4
cosocleC2×C4⋊Dic17C23
hypercenterC23×Q8#595
hypocenterC17#11510
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C23×Q8

Complements

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

NH ≅ G/Ntype
2. #14543714C2semidirect
150. C17#11510semidirect

Maximal subgroups

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

subgroupindex
#145440352
#145437142
#145313702
#1151017