Finite Group Databasebeta

← #17958337

Subgroups — #17958337

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#14543732C212yesmaximal, complemented
3#14543717C212yesmaximal, complemented
4#14537489C211yesmaximal, characteristic
5#11763865—22no—
6#11763706—22no—
7#11763705C2214yes—
8C2×#10587587C2211yescharacteristic
9C22×#63218C411yescharacteristic
10#11763321C411yescharacteristic
11#11762888—22no—
12#11762882—22no—
13#11762836C2211yescharacteristic
14#11762777C411yescharacteristic
15#11762772C2211yescharacteristic
16C17×#405C411yescharacteristic
17C2×#63252C2×C411yescharacteristic
18C22×C4×D17C2×C411yescharacteristic
19C2×M16×C17C2×C411yescharacteristic
20C22×C8×C17C2×C411yescharacteristic
21C17×#117C2×C411yescharacteristic
22C2×#63223C2311yescharacteristic
23C22×#3622C2×C411yescharacteristic
24#10587587—42no—
25C2×#63218—21no—
26C2×#63218—21no—
27C2×#63218—42no—
28C2×#63218D412yes—
29C2×C8×D17D412yes—
30#10587583—21no—
31#10587581—21no—
32#10587572C812yes—
33#10587568C812yes—
34C4×D68—22no—
35#10587538—24no—
36#10587530—42no—
37#10587529—42no—
38C17×#97—21no—
39C4×C8×C17—21no—
40#10587491—22no—
41#10587491—22no—
42C4⋊#3622—22no—
43C23×D17C2×C811yescharacteristic
44C22×C4×C17C22×C411yescharacteristic
45C2×C22⋊D17C2×C812yes—
46C22×Dic17C2×C811yescharacteristic
47#63252—41no—
48#63252—41no—
49C2×D68—22no—
50C2×D68M1611yescharacteristic
51C2×C4×D17—21no—
52C2×C4×D17—21no—
53C2×C4×D17—41no—
54C2×C4×D17—41no—
55C2×C4×D17C22⋊C412yes—
56C2×Dic34M1611yescharacteristic
57M16×C17—41no—
58C2×C8×C17—22no—
59C2×C8×C17—21no—
60C2×C8×C17C22⋊C411yescharacteristic
61C2×C8×C17C22⋊C411yescharacteristic
62C4⋊C4×C17—21no—
63C22⋊C4×C17C2×C812yes—
64C42×C17—21no—
65#63227—22no—
66#63227—22no—
67C4⋊Dic17—22no—
68#63223—41no—
69C2×#3622—21no—
70C2×#3622—41no—
71C2×#3622C2×D412yes—
72#63218—42no—
73#63218—42no—
74#63218—42no—
75C8×D17—22no—
76C8×D17—22no—
77#63216—44no—
78#11484—171nomaximal, Sylow
79C23×C17C22×C811yescharacteristic
80C22×D17—21no—
81C22×D17—41no—
82C22×D17—81no—
83C22×D17C22⋊C812yes—
84C2×C4×C17—21no—
85C2×C4×C17—21no—
86C2×C4×C17—22no—
87C2×C4×C17C2×C22⋊C411yescharacteristic
88C2×C4×C17C2×M1611yescharacteristic
89C22⋊D17—42no—
90C2×Dic17—21no—
91C2×Dic17—41no—
92C2×Dic17C22⋊C812yes—
93D68—41no—
94D68—82no—
95C4×D17—22no—
96C4×D17—22no—
97C4×D17—42no—
98C4×D17—41no—
99C4×D17—41no—
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×C17C2×C22⋊C811yescharacteristic
113C2×D17—22no—
114C2×D17—42no—
115C2×D17—41no—
116C2×D17—41no—
117C2×D17—41no—
118C2×D17—82no—
119C4×C17—21no—
120C4×C17—42no—
121C4×C17C2×#9911yescharacteristic
122C4×C17#41311yescharacteristic
123Dic17—22no—
124Dic17—41no—
125C2×#131—171no—
126C22×M16—171no—
127#525—171no—
128C2×M32—342no—
129#436—342no—
130#435—342no—
131#424—171no—
132#408—171no—
133#407—171no—
134#405#59511yescharacteristic
135#349—174no—
136#349—342no—
137C2×C17—21no—
138C2×C17—41no—
139C2×C17#145911yescharacteristic
140D17—42no—
141D17—81no—
142C2×#41—171no—
143C23×C4—171no—
144#131—682no—
145C2×M16—171no—
146C2×M16—172no—
147C2×M16—341no—
148C2×M16—341no—
149C2×M16—682no—
150C2×M16C2×#59511yescharacteristic
151C22×C8—172no—
152C22×C8—171no—
153C22×C8C2×#59511yescharacteristic
154#123—172no—
155C22⋊Q8—341no—
156#121—341no—
157#120—172no—
158C4×D4—342no—
159#117C2×#59511yescharacteristic
160M32—344no—
161M32—682no—
162C2×C16—682no—
163C4⋊C8—342no—
164C22⋊C8—342no—
165C22⋊C8—342no—
166#97—21no—
167C4×C8—21no—
168C17#1148411yescharacteristic, complemented, Sylow
169C24—171no—
170#41—681no—
171#41—681no—
172C2×Q8—171no—
173C2×D4—172no—
174C2×D4—171no—
175C2×D4—342no—
176C22×C4—172no—
177C22×C4—171no—
178C22×C4—341no—
179C22×C4—341no—
180C22×C4—681no—
181C22×C4—681no—
182C22×C4C22×#59511yescharacteristic
183M16—41no—
184M16—682no—
185M16—682no—
186M16—681no—
187M16—682no—
188C2×C8—22no—
189C2×C8—21no—
190C2×C8—172no—
191C2×C8—342no—
192C2×C8—342no—
193C2×C8—341no—
194C2×C8—681no—
195C2×C8C22⋊#59511yescharacteristic
196C2×C8C22⋊#59511yescharacteristic
197C4⋊C4—21no—
198C4⋊C4—342no—
199C22⋊C4—342no—
200C22⋊C4—342no—
201C22⋊C4#6324212yes—
202C42—21no—
203C16—684no—
204C23—172no—
205C23—341no—
206C23—681no—
207C23—1361no—
208C23C2×#6324211yescharacteristic
209Q8—681no—
210D4—681no—
211D4—682no—
212D4—1362no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—172no—
217C2×C4—342no—
218C2×C4—342no—
219C2×C4—341no—
220C2×C4—682no—
221C2×C4—681no—
222C2×C4—681no—
223C2×C4—681no—
224C2×C4D17⋊M1611yescharacteristic
225C2×C4C2×C22⋊#59511yescharacteristic
226C8—21no—
227C8—41no—
228C8—342no—
229C8—681no—
230C8#1058753912yes—
231C22—21no—
232C22—41no—
233C22—342no—
234C22—682no—
235C22—681no—
236C22—681no—
237C22—681no—
238C22—1362no—
239C22#1176377711yescharacteristic
240C4—21no—
241C4—42no—
242C4—342no—
243C4—681no—
244C4C2×#1058753911yescharacteristic
245C4#1176379511yescharacteristic
246C2—21no—
247C2—41no—
248C2—682no—
249C2—1361no—
250C2#1454402111yescharacteristic
subgroupG/H
centerC4C2×#10587539
commutatorC23×C17C22×C8
FrattiniC22×C4C22×#595
FittingC17×#405C4
socleC2×C17#1459
prime radical#11763321C4
cosocleC2×#63223C23
hypercenter#405#595
hypocenterC17#11484
LCSG ▷ C23×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C4 ◁ C2×C8 ◁ C22×C8 ◁ #405

Complements

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

NH ≅ G/Ntype
1. #14545021C2semidirect
2. #14543732C2semidirect
3. #14543717C2semidirect
168. C17#11484semidirect

Maximal subgroups

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

subgroupindex
#145450212
#145437322
#145437172
#145374892
#1148417