Finite Group Databasebeta

← #17958331

Subgroups — #17958331

Order 4352.

382 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 82 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#14545021C212yesmaximal, complemented
2#14543733C212yesmaximal, complemented
3#14543716C212yesmaximal, complemented
4#14537478C211yesmaximal, characteristic
5#11763865—22no—
6#11763706—22no—
7#11763705C2214yes—
8C2×#10587587C2211yescharacteristic
9#11763320C411yescharacteristic
10#11762880—22no—
11C8×C22⋊D17—22no—
12#11762835C2211yescharacteristic
13#11762775C411yescharacteristic
14#11762773C2211yescharacteristic
15#11762764C411yescharacteristic
16C23×C8×C17C411yescharacteristic
17C23×C4×C17C2×C411yescharacteristic
18C2×#63252C2×C411yescharacteristic
19C22×C8×C17—21no—
20C22×C8×C17—21no—
21C22×C8×C17—41no—
22C22×C8×C17—41no—
23C22×C8×C17C2×C411yescharacteristic
24C22×C8×C17C2×C411yescharacteristic
25#10587639C812yes—
26#10587616—21no—
27#10587615C812yes—
28C4×C22⋊D17—22no—
29#10587612C2×C411yescharacteristic
30#10587610—21no—
31C2×#63223C2×C411yescharacteristic
32C2×#63223C2311yescharacteristic
33#10587587—41no—
34#10587587—41no—
35C2×#63218D412yes—
36C2×C8×D17D412yes—
37#10587538—24no—
38#10587530—42no—
39#10587529—42no—
40C22⋊#3622—22no—
41#10587491—22no—
42#10587486—21no—
43#10587485—22no—
44C8×Dic17—21no—
45C24×C17C2×C811yescharacteristic
46C22×C4×C17—21no—
47C22×C4×C17—21no—
48C22×C4×C17—41no—
49C22×C4×C17—41no—
50C22×C4×C17C2×C811yescharacteristic
51C22×C4×C17C22×C411yescharacteristic
52C2×C22⋊D17—22no—
53C2×C22⋊D17C2×C812yes—
54#63252—41no—
55#63252—41no—
56C2×D68M1611yescharacteristic
57C2×C4×D17C22⋊C412yes—
58C2×Dic34M1611yescharacteristic
59C2×C8×C17—21no—
60C2×C8×C17—21no—
61C2×C8×C17—21no—
62C2×C8×C17—42no—
63C2×C8×C17—41no—
64C2×C8×C17—41no—
65C2×C8×C17—41no—
66C2×C8×C17C22⋊C411yescharacteristic
67C2×C8×C17C22⋊C411yescharacteristic
68C22⋊Dic17—22no—
69C22⋊Dic17C2×C812yes—
70#63227—22no—
71C4⋊Dic17—21no—
72#63225—22no—
73C4×Dic17—21no—
74#63223—41no—
75#63223—41no—
76C2×#3622—21no—
77C2×#3622C2×D412yes—
78#63218—42no—
79C8×D17—22no—
80C8×D17—22no—
81#63216—44no—
82#11483—171nomaximal, Sylow
83C23×C17—21no—
84C23×C17—41no—
85C23×C17—42no—
86C23×C17C22×C811yescharacteristic
87C22×D17C22⋊C812yes—
88C2×C4×C17—21no—
89C2×C4×C17—21no—
90C2×C4×C17—21no—
91C2×C4×C17—42no—
92C2×C4×C17—41no—
93C2×C4×C17—41no—
94C2×C4×C17—41no—
95C2×C4×C17C2×C22⋊C411yescharacteristic
96C2×C4×C17C2×M1611yescharacteristic
97C22⋊D17—42no—
98C22⋊D17—44no—
99C2×Dic17—22no—
100C2×Dic17C22⋊C812yes—
101D68—41no—
102C4×D17—22no—
103C4×D17—22no—
104Dic34—41no—
105C8×C17—21no—
106C8×C17—41no—
107C8×C17#9911yescharacteristic
108C8×C17#9911yescharacteristic
109#3622—22no—
110#3622—41no—
111#2929—171no—
112#2115—172no—
113#1328—172no—
114#1320—172no—
115C22×C17—22no—
116C22×C17—21no—
117C22×C17—41no—
118C22×C17—41no—
119C22×C17—42no—
120C22×C17—42no—
121C22×C17—41no—
122C22×C17C2×C22⋊C811yescharacteristic
123C2×D17—22no—
124C2×D17—42no—
125C4×C17—21no—
126C4×C17—41no—
127C4×C17C2×#9911yescharacteristic
128C4×C17#41311yescharacteristic
129Dic17—22no—
130Dic17—42no—
131C2×#131—171no—
132C23×C8#59511yescharacteristic
133#525—171no—
134C2×M32—342no—
135#435—342no—
136C8×D4—342no—
137#424—171no—
138#408—171no—
139#407—171no—
140#405—171no—
141#349—174no—
142#349—342no—
143C2×C17—21no—
144C2×C17—42no—
145C2×C17—41no—
146C2×C17#145911yescharacteristic
147D17—42no—
148C2×#41—171no—
149C23×C4C2×#59511yescharacteristic
150#131—681no—
151#131—681no—
152C2×M16—171no—
153C2×M16—172no—
154C2×M16—171no—
155C22×C8—21no—
156C22×C8—21no—
157C22×C8—41no—
158C22×C8—41no—
159C22×C8—172no—
160C22×C8C2×#59511yescharacteristic
161C22×C8C2×#59511yescharacteristic
162#123—172no—
163C22⋊Q8—341no—
164#121—341no—
165#120—172no—
166C4×D4—342no—
167#117—171no—
168M32—344no—
169M32—682no—
170C2×C16—682no—
171C4⋊C8—342no—
172C22⋊C8—342no—
173C22⋊C8—342no—
174#97—341no—
175C4×C8—341no—
176C17#1148311yescharacteristic, complemented, Sylow
177C24#6324211yescharacteristic
178#41—681no—
179#41—681no—
180C2×Q8—171no—
181C2×D4—172no—
182C2×D4—171no—
183C2×D4—342no—
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—41no—
187C22×C4—41no—
188C22×C4—172no—
189C22×C4#6324211yescharacteristic
190C22×C4C22×#59511yescharacteristic
191M16—682no—
192M16—681no—
193M16—681no—
194C2×C8—21no—
195C2×C8—21no—
196C2×C8—21no—
197C2×C8—42no—
198C2×C8—41no—
199C2×C8—41no—
200C2×C8—41no—
201C2×C8—172no—
202C2×C8—342no—
203C2×C8—342no—
204C2×C8—341no—
205C2×C8C22⋊#59511yescharacteristic
206C2×C8C22⋊#59511yescharacteristic
207C4⋊C4—342no—
208C4⋊C4—341no—
209C22⋊C4—172no—
210C22⋊C4—342no—
211C22⋊C4—342no—
212C42—341no—
213C16—684no—
214C23—21no—
215C23—41no—
216C23—42no—
217C23—172no—
218C23C2×#6324211yescharacteristic
219Q8—681no—
220D4—681no—
221D4—682no—
222D4—684no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—42no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—172no—
231C2×C4—342no—
232C2×C4—342no—
233C2×C4—342no—
234C2×C4D17⋊M1611yescharacteristic
235C2×C4C2×C22⋊#59511yescharacteristic
236C8—21no—
237C8—41no—
238C8—342no—
239C8—681no—
240C8#1058755111yescharacteristic
241C8#1058755111yescharacteristic
242C22—22no—
243C22—21no—
244C22—41no—
245C22—41no—
246C22—42no—
247C22—42no—
248C22—41no—
249C22—342no—
250C22—682no—
251C22#1176377711yescharacteristic
252C4—21no—
253C4—41no—
254C4—342no—
255C4—682no—
256C4C2×#1058755111yescharacteristic
257C4#1176379511yescharacteristic
258C2—21no—
259C2—42no—
260C2—41no—
261C2—682no—
262C2#1454401911yescharacteristic
subgroupG/H
centerC8#10587551
commutatorC23×C17C22×C8
FrattiniC22×C4C22×#595
FittingC23×C8×C17C4
socleC2×C17#1459
prime radical#11763320C4
cosocleC2×#63223C23
hypercenterC23×C8#595
hypocenterC17#11483
LCSG ▷ C23×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C8 ◁ C2×C8 ◁ C22×C8 ◁ C23×C8

Complements

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

NH ≅ G/Ntype
1. #14545021C2semidirect
2. #14543733C2semidirect
3. #14543716C2semidirect
176. C17#11483semidirect

Maximal subgroups

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

subgroupindex
#145450212
#145437332
#145437162
#145374782
#1148317