Finite Group Databasebeta

← #17958335

Subgroups — #17958335

Order 4352.

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

normal subgroups only

This group has 368 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#14537487C211yesmaximal, characteristic
5#11763865—22no—
6#11763706—22no—
7#11763705C2214yes—
8C2×#10587587C2211yescharacteristic
9#11763320C411yescharacteristic
10#11762885—22no—
11#11762878—22no—
12#11762835C2211yescharacteristic
13#11762775C411yescharacteristic
14#11762773C2211yescharacteristic
15#11762764C411yescharacteristic
16C22×M16×C17C411yescharacteristic
17C23×C4×C17C2×C411yescharacteristic
18C2×#63252C2×C411yescharacteristic
19C2×M16×C17—21no—
20C2×M16×C17—21no—
21C2×M16×C17—42no—
22C22×C8×C17C2×C411yescharacteristic
23C22×C8×C17C2×C411yescharacteristic
24#10587639C812yes—
25#10587616—21no—
26#10587615C812yes—
27C4×C22⋊D17—22no—
28#10587612C2×C411yescharacteristic
29#10587610—21no—
30C2×#63223C2×C411yescharacteristic
31C2×#63223C2311yescharacteristic
32#10587587—42no—
33C2×#63218D412yes—
34C2×C8×D17D412yes—
35#10587538—24no—
36#10587530—42no—
37#10587529—42no—
38C22⋊#3622—22no—
39#10587491—22no—
40#10587486—21no—
41#10587485—22no—
42C8×Dic17—21no—
43C24×C17C2×C811yescharacteristic
44C22×C4×C17—21no—
45C22×C4×C17—21no—
46C22×C4×C17—41no—
47C22×C4×C17—41no—
48C22×C4×C17C2×C811yescharacteristic
49C22×C4×C17C22×C411yescharacteristic
50C2×C22⋊D17—22no—
51C2×C22⋊D17C2×C812yes—
52#63252—41no—
53#63252—41no—
54C2×D68M1611yescharacteristic
55C2×C4×D17C22⋊C412yes—
56C2×Dic34M1611yescharacteristic
57M16×C17—42no—
58M16×C17—42no—
59C2×C8×C17—22no—
60C2×C8×C17—21no—
61C2×C8×C17—41no—
62C2×C8×C17C22⋊C411yescharacteristic
63C2×C8×C17C22⋊C411yescharacteristic
64C22⋊Dic17—22no—
65C22⋊Dic17C2×C812yes—
66#63227—22no—
67C4⋊Dic17—21no—
68#63225—22no—
69C4×Dic17—21no—
70#63223—41no—
71#63223—41no—
72C2×#3622—21no—
73C2×#3622C2×D412yes—
74#63218—42no—
75C8×D17—22no—
76C8×D17—22no—
77#63216—44no—
78#11484—171nomaximal, Sylow
79C23×C17—21no—
80C23×C17—41no—
81C23×C17—81no—
82C23×C17C22×C811yescharacteristic
83C22×D17C22⋊C812yes—
84C2×C4×C17—21no—
85C2×C4×C17—21no—
86C2×C4×C17—21no—
87C2×C4×C17—42no—
88C2×C4×C17—41no—
89C2×C4×C17—41no—
90C2×C4×C17—41no—
91C2×C4×C17C2×C22⋊C411yescharacteristic
92C2×C4×C17C2×M1611yescharacteristic
93C22⋊D17—42no—
94C22⋊D17—82no—
95C2×Dic17—22no—
96C2×Dic17C22⋊C812yes—
97D68—41no—
98C4×D17—22no—
99C4×D17—22no—
100Dic34—41no—
101C8×C17—21no—
102C8×C17—41no—
103C8×C17#9912yes—
104#3622—22no—
105#3622—41no—
106#2930—171no—
107#2115—172no—
108#1328—172no—
109#1320—172no—
110C22×C17—21no—
111C22×C17—41no—
112C22×C17—41no—
113C22×C17—41no—
114C22×C17—41no—
115C22×C17—82no—
116C22×C17C2×C22⋊C811yescharacteristic
117C2×D17—22no—
118C2×D17—42no—
119C4×C17—21no—
120C4×C17—41no—
121C4×C17C2×#9911yescharacteristic
122C4×C17#41311yescharacteristic
123Dic17—22no—
124Dic17—42no—
125C2×#131—171no—
126C22×M16#59511yescharacteristic
127#525—171no—
128C2×M32—342no—
129#436—342no—
130#435—342no—
131#424—171no—
132#408—171no—
133#407—171no—
134#405—171no—
135#349—174no—
136#349—342no—
137C2×C17—21no—
138C2×C17—41no—
139C2×C17—81no—
140C2×C17#145911yescharacteristic
141D17—42no—
142C2×#41—171no—
143C23×C4C2×#59511yescharacteristic
144#131—682no—
145C2×M16—21no—
146C2×M16—21no—
147C2×M16—42no—
148C2×M16—171no—
149C2×M16—172no—
150C2×M16—171no—
151C22×C8—172no—
152C22×C8C2×#59511yescharacteristic
153C22×C8C2×#59511yescharacteristic
154#123—172no—
155C22⋊Q8—341no—
156#121—341no—
157#120—172no—
158C4×D4—342no—
159#117—171no—
160M32—344no—
161M32—682no—
162C2×C16—682no—
163C4⋊C8—342no—
164C22⋊C8—342no—
165C22⋊C8—342no—
166#97—341no—
167C4×C8—341no—
168C17#1148411yescharacteristic, complemented, Sylow
169C24#6324211yescharacteristic
170#41—681no—
171#41—681no—
172C2×Q8—171no—
173C2×D4—172no—
174C2×D4—171no—
175C2×D4—342no—
176C22×C4—21no—
177C22×C4—21no—
178C22×C4—41no—
179C22×C4—41no—
180C22×C4—172no—
181C22×C4#6324211yescharacteristic
182C22×C4C22×#59511yescharacteristic
183M16—42no—
184M16—42no—
185M16—682no—
186M16—681no—
187M16—681no—
188C2×C8—22no—
189C2×C8—21no—
190C2×C8—41no—
191C2×C8—172no—
192C2×C8—342no—
193C2×C8—342no—
194C2×C8—341no—
195C2×C8C22⋊#59511yescharacteristic
196C2×C8C22⋊#59511yescharacteristic
197C4⋊C4—342no—
198C4⋊C4—341no—
199C22⋊C4—172no—
200C22⋊C4—342no—
201C22⋊C4—342no—
202C42—341no—
203C16—684no—
204C23—21no—
205C23—41no—
206C23—81no—
207C23—172no—
208C23C2×#6324211yescharacteristic
209Q8—681no—
210D4—681no—
211D4—682no—
212D4—1362no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—42no—
217C2×C4—41no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—172no—
221C2×C4—342no—
222C2×C4—342no—
223C2×C4—342no—
224C2×C4D17⋊M1611yescharacteristic
225C2×C4C2×C22⋊#59511yescharacteristic
226C8—21no—
227C8—41no—
228C8—342no—
229C8—681no—
230C8#1058755112yes—
231C22—21no—
232C22—41no—
233C22—41no—
234C22—41no—
235C22—41no—
236C22—82no—
237C22—342no—
238C22—682no—
239C22#1176377711yescharacteristic
240C4—21no—
241C4—41no—
242C4—342no—
243C4—682no—
244C4C2×#1058755111yescharacteristic
245C4#1176379511yescharacteristic
246C2—21no—
247C2—41no—
248C2—81no—
249C2—682no—
250C2#1454401911yescharacteristic
subgroupG/H
centerC4C2×#10587551
commutatorC23×C17C22×C8
FrattiniC22×C4C22×#595
FittingC22×M16×C17C4
socleC2×C17#1459
prime radical#11763320C4
cosocleC2×#63223C23
hypercenterC22×M16#595
hypocenterC17#11484
LCSG ▷ C23×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C4 ◁ C2×C8 ◁ C22×C8 ◁ C22×M16

Complements

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

NH ≅ G/Ntype
1. #14545021C2semidirect
2. #14543733C2semidirect
3. #14543716C2semidirect
168. C17#11484semidirect

Maximal subgroups

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

subgroupindex
#145450212
#145437332
#145437162
#145374872
#1148417