Finite Group Databasebeta

← #17958458

Subgroups — #17958458

Order 4352.

330 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 66 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#14545154C212yesmaximal, complemented
2#14543730C212yesmaximal, complemented
3#14543717C212yesmaximal
4#14537416C211yesmaximal, characteristic
5#11763731—22no—
6#11763705C2214yes—
7#11763702—22no—
8C2×C42×D17C411yescharacteristic
9#11762865—22no—
10#11762861—22no—
11#11762833C2211yescharacteristic
12#11762772C411yescharacteristic
13#11762772C2211yescharacteristic
14M16×Dic17C411yescharacteristic
15M16×Dic17C2211yescharacteristic
16C17×#423C411yescharacteristic
17C22×C4×D17—21no—
18C22×C4×D17C2×C411yescharacteristic
19C2×M16×C17C2×C411yescharacteristic
20C2×M16×C17C2×C411yescharacteristic
21C2×C42×C17C2×C411yescharacteristic
22C2×C4×Dic17—21no—
23C2×C4×Dic17C2×C411yescharacteristic
24C2×#63223C2×C411yescharacteristic
25C2×#63223C2311yescharacteristic
26C42×D17—21no—
27C42×D17—21no—
28C42×D17—21no—
29C42×D17—21no—
30#10587538—24no—
31C17×C4⋊C8—22no—
32#10587491—22no—
33#10587491—22no—
34#10587486—21no—
35#10587486D412yes—
36C8×Dic17—21no—
37C8×Dic17D412yes—
38C4⋊#3622—22no—
39C23×D17M1611yescharacteristic
40C22×C4×C17—21no—
41C22×C4×C17C22×C411yescharacteristic
42C22×Dic17—21no—
43C22×Dic17M1611yescharacteristic
44C2×C4×D17—21no—
45C2×C4×D17—21no—
46C2×C4×D17—21no—
47C2×C4×D17—21no—
48C2×C4×D17—21no—
49C2×C4×D17—21no—
50C2×C4×D17—44no—
51C2×C4×D17—41no—
52C2×C4×D17—41no—
53M16×C17—41no—
54M16×C17—41no—
55C2×C8×C17—21no—
56C2×C8×C17C22⋊C412yes—
57C42×C17—21no—
58C42×C17M1611yescharacteristic
59C42×C17M1611yescharacteristic
60C4×Dic17—21no—
61C4×Dic17—21no—
62C4×Dic17—21no—
63C4×Dic17—21no—
64C4×Dic17—21no—
65C4×Dic17C22⋊C411yescharacteristic
66C4×Dic17C22⋊C411yescharacteristic
67#63223—41no—
68#63223—41no—
69C2×#3622—21no—
70C2×#3622C2×D412yes—
71#63216—44no—
72#11521—171nomaximal, Sylow
73C23×C17C2×M1611yescharacteristic
74C22×D17—21no—
75C22×D17—42no—
76C22×D17—41no—
77C2×C4×C17—21no—
78C2×C4×C17—21no—
79C2×C4×C17—21no—
80C2×C4×C17—21no—
81C2×C4×C17—42no—
82C2×C4×C17C2×C22⋊C411yescharacteristic
83C2×C4×C17C2×M1611yescharacteristic
84C2×Dic17—21no—
85C2×Dic17—21no—
86C2×Dic17—21no—
87C2×Dic17—42no—
88C2×Dic17—41no—
89C4×D17—24no—
90C4×D17—42no—
91C4×D17—42no—
92C4×D17—42no—
93C4×D17—42no—
94C4×D17—41no—
95C4×D17—41no—
96C8×C17—22no—
97C8×C17—41no—
98#3622—22no—
99#3622—41no—
100#2920—171no—
101#2165—172no—
102#1327—172no—
103#1320—172no—
104C22×C17—21no—
105C22×C17—41no—
106C22×C17#40711yescharacteristic
107C2×D17—22no—
108C2×D17—41no—
109C2×D17—42no—
110C2×D17—41no—
111C2×D17—42no—
112C4×C17—22no—
113C4×C17—21no—
114C4×C17—41no—
115C4×C17#41011yescharacteristic
116C4×C17#41311yescharacteristic
117Dic17—22no—
118Dic17—41no—
119Dic17—41no—
120C22×C42—171no—
121#432—342no—
122#431—342no—
123#423—171no—
124#423#59511yescharacteristic
125#407—171no—
126#407—171no—
127C4×M16—171no—
128C4×M16—171no—
129#364—342no—
130#349—174no—
131#347—342no—
132C2×C17—21no—
133C2×C17—41no—
134C2×C17#146411yescharacteristic
135D17—42no—
136C23×C4—171no—
137C23×C4—341no—
138C2×M16—171no—
139C2×M16—171no—
140C2×M16C2×#59511yescharacteristic
141C2×M16C2×#59511yescharacteristic
142C2×C42—171no—
143C2×C42—341no—
144C2×C42—341no—
145C2×C42—341no—
146C2×C42—341no—
147C2×C42—341no—
148C2×C42C2×#59511yescharacteristic
149M32—344no—
150C4⋊C8—22no—
151C4⋊C8—342no—
152C22⋊C8—342no—
153C22⋊C8—342no—
154#97—172no—
155#97—341no—
156C4×C8—172no—
157C4×C8—341no—
158C17#1152111yescharacteristic, complemented, Sylow
159C24—171no—
160C22×C4—21no—
161C22×C4—171no—
162C22×C4—341no—
163C22×C4—341no—
164C22×C4—341no—
165C22×C4—341no—
166C22×C4—341no—
167C22×C4—341no—
168C22×C4—341no—
169C22×C4—681no—
170C22×C4—681no—
171C22×C4—684no—
172C22×C4C22×#59511yescharacteristic
173M16—41no—
174M16—41no—
175M16—681no—
176M16—681no—
177C2×C8—21no—
178C2×C8—172no—
179C2×C8—341no—
180C2×C8C22⋊#59512yes—
181C42—21no—
182C42—171no—
183C42—171no—
184C42—341no—
185C42—341no—
186C42—341no—
187C42—341no—
188C42—341no—
189C42#6324311yescharacteristic
190C42#6324311yescharacteristic
191C16—684no—
192C23—341no—
193C23—681no—
194C23—682no—
195C23D17⋊M1611yescharacteristic
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—42no—
201C2×C4—344no—
202C2×C4—341no—
203C2×C4—341no—
204C2×C4—341no—
205C2×C4—682no—
206C2×C4—682no—
207C2×C4—682no—
208C2×C4—682no—
209C2×C4—682no—
210C2×C4—681no—
211C2×C4—681no—
212C2×C4—681no—
213C2×C4C2×#6324311yescharacteristic
214C2×C4C2×C22⋊#59511yescharacteristic
215C8—22no—
216C8—41no—
217C8—342no—
218C8—681no—
219C22—21no—
220C22—41no—
221C22—342no—
222C22—681no—
223C22—682no—
224C22—682no—
225C22—681no—
226C22#1176378011yescharacteristic
227C4—22no—
228C4—21no—
229C4—41no—
230C4—342no—
231C4—681no—
232C4—681no—
233C4#1176379011yescharacteristic
234C4#1176379611yescharacteristic
235C2—21no—
236C2—41no—
237C2—682no—
238C2#1454403811yescharacteristic
subgroupG/H
centerC4#11763790
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC17×#423C4
socleC2×C17#1464
prime radicalC23×D17M16
cosocleC2×#63223C23
hypercenter#423#595
hypocenterC17#11521
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #423

Complements

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

NH ≅ G/Ntype
1. #14545154C2semidirect
2. #14543730C2semidirect
158. C17#11521semidirect

Maximal subgroups

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

subgroupindex
#145451542
#145437302
#145437172
#145374162
#1152117