Finite Group Databasebeta

← #17958333

Subgroups — #17958333

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#14543732C212yesmaximal, complemented
3#14543717C212yesmaximal, complemented
4#14537480C211yesmaximal, characteristic
5#11763865—22no—
6#11763706—22no—
7#11763705C2214yes—
8C2×#10587587C2211yescharacteristic
9C22×C8×D17C411yescharacteristic
10#11763321C411yescharacteristic
11#11762882—22no—
12C8×D68—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—41no—
25#10587587—41no—
26C2×#63218D412yes—
27C2×C8×D17—21no—
28C2×C8×D17—21no—
29C2×C8×D17—41no—
30C2×C8×D17—41no—
31C2×C8×D17D412yes—
32#10587583—21no—
33#10587581—21no—
34#10587572C812yes—
35#10587568C812yes—
36C4×D68—22no—
37#10587538—24no—
38#10587530—42no—
39#10587529—42no—
40C17×#97—21no—
41C4×C8×C17—21no—
42#10587491—22no—
43#10587491—22no—
44C4⋊#3622—22no—
45C23×D17C2×C811yescharacteristic
46C22×C4×C17C22×C411yescharacteristic
47C2×C22⋊D17C2×C812yes—
48C22×Dic17C2×C811yescharacteristic
49#63252—41no—
50#63252—41no—
51C2×D68—22no—
52C2×D68M1611yescharacteristic
53C2×C4×D17—21no—
54C2×C4×D17—21no—
55C2×C4×D17—41no—
56C2×C4×D17—41no—
57C2×C4×D17C22⋊C412yes—
58C2×Dic34M1611yescharacteristic
59M16×C17—41no—
60C2×C8×C17—21no—
61C2×C8×C17—21no—
62C2×C8×C17—21no—
63C2×C8×C17C22⋊C411yescharacteristic
64C2×C8×C17C22⋊C411yescharacteristic
65C4⋊C4×C17—21no—
66C22⋊C4×C17C2×C812yes—
67C42×C17—21no—
68#63227—22no—
69#63227—22no—
70C4⋊Dic17—22no—
71#63223—41no—
72C2×#3622—21no—
73C2×#3622—41no—
74C2×#3622C2×D412yes—
75#63218—42no—
76C8×D17—22no—
77C8×D17—22no—
78C8×D17—42no—
79C8×D17—41no—
80C8×D17—41no—
81#63216—44no—
82#11483—171nomaximal, Sylow
83C23×C17C22×C811yescharacteristic
84C22×D17—21no—
85C22×D17—42no—
86C22×D17—41no—
87C22×D17C22⋊C812yes—
88C2×C4×C17—21no—
89C2×C4×C17—21no—
90C2×C4×C17—22no—
91C2×C4×C17C2×C22⋊C411yescharacteristic
92C2×C4×C17C2×M1611yescharacteristic
93C22⋊D17—42no—
94C2×Dic17—21no—
95C2×Dic17—41no—
96C2×Dic17C22⋊C812yes—
97D68—41no—
98D68—44no—
99C4×D17—22no—
100C4×D17—22no—
101C4×D17—42no—
102C4×D17—41no—
103C4×D17—41no—
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—21no—
116C22×C17—41no—
117C22×C17C2×C22⋊C811yescharacteristic
118C2×D17—22no—
119C2×D17—22no—
120C2×D17—41no—
121C2×D17—42no—
122C2×D17—41no—
123C2×D17—42no—
124C2×D17—42no—
125C4×C17—21no—
126C4×C17—42no—
127C4×C17C2×#9911yescharacteristic
128C4×C17#41311yescharacteristic
129Dic17—22no—
130Dic17—41no—
131C2×#131—171no—
132C23×C8—171no—
133#525—171no—
134C2×M32—342no—
135#435—342no—
136C8×D4—342no—
137#424—171no—
138#408—171no—
139#407—171no—
140#405#59511yescharacteristic
141#349—174no—
142#349—342no—
143C2×C17—21no—
144C2×C17—41no—
145C2×C17#145911yescharacteristic
146D17—42no—
147D17—42no—
148C2×#41—171no—
149C23×C4—171no—
150#131—681no—
151#131—681no—
152C2×M16—171no—
153C2×M16—172no—
154C2×M16C2×#59511yescharacteristic
155C22×C8—172no—
156C22×C8—171no—
157C22×C8—341no—
158C22×C8—341no—
159C22×C8—681no—
160C22×C8—681no—
161C22×C8C2×#59511yescharacteristic
162#123—172no—
163C22⋊Q8—341no—
164#121—341no—
165#120—172no—
166C4×D4—342no—
167#117C2×#59511yescharacteristic
168M32—344no—
169M32—682no—
170C2×C16—682no—
171C4⋊C8—342no—
172C22⋊C8—342no—
173C22⋊C8—342no—
174#97—21no—
175C4×C8—21no—
176C17#1148311yescharacteristic, complemented, Sylow
177C24—171no—
178#41—681no—
179#41—681no—
180C2×Q8—171no—
181C2×D4—172no—
182C2×D4—171no—
183C2×D4—342no—
184C22×C4—172no—
185C22×C4—171no—
186C22×C4—341no—
187C22×C4—341no—
188C22×C4—681no—
189C22×C4—681no—
190C22×C4C22×#59511yescharacteristic
191M16—41no—
192M16—682no—
193M16—681no—
194C2×C8—21no—
195C2×C8—21no—
196C2×C8—21no—
197C2×C8—172no—
198C2×C8—342no—
199C2×C8—342no—
200C2×C8—341no—
201C2×C8—682no—
202C2×C8—681no—
203C2×C8—681no—
204C2×C8—681no—
205C2×C8C22⋊#59511yescharacteristic
206C2×C8C22⋊#59511yescharacteristic
207C4⋊C4—21no—
208C4⋊C4—342no—
209C22⋊C4—342no—
210C22⋊C4—342no—
211C22⋊C4#6324212yes—
212C42—21no—
213C16—684no—
214C23—172no—
215C23—341no—
216C23—681no—
217C23—682no—
218C23C2×#6324211yescharacteristic
219Q8—681no—
220D4—681no—
221D4—684no—
222D4—682no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—172no—
227C2×C4—342no—
228C2×C4—342no—
229C2×C4—341no—
230C2×C4—682no—
231C2×C4—681no—
232C2×C4—681no—
233C2×C4—681no—
234C2×C4D17⋊M1611yescharacteristic
235C2×C4C2×C22⋊#59511yescharacteristic
236C8—21no—
237C8—41no—
238C8—342no—
239C8—681no—
240C8#1058753911yescharacteristic
241C8#1058753911yescharacteristic
242C22—21no—
243C22—41no—
244C22—342no—
245C22—342no—
246C22—682no—
247C22—681no—
248C22—682no—
249C22—682no—
250C22—681no—
251C22#1176377711yescharacteristic
252C4—21no—
253C4—42no—
254C4—342no—
255C4—681no—
256C4C2×#1058753911yescharacteristic
257C4#1176379511yescharacteristic
258C2—21no—
259C2—41no—
260C2—682no—
261C2—682no—
262C2#1454402111yescharacteristic
subgroupG/H
centerC8#10587539
commutatorC23×C17C22×C8
FrattiniC22×C4C22×#595
FittingC17×#405C4
socleC2×C17#1459
prime radical#11763321C4
cosocleC2×#63223C23
hypercenter#405#595
hypocenterC17#11483
LCSG ▷ C23×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C8 ◁ 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
176. C17#11483semidirect

Maximal subgroups

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

subgroupindex
#145450212
#145437322
#145437172
#145374802
#1148317