Finite Group Databasebeta

← #17958334

Subgroups — #17958334

Order 4352.

382 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 86 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#14545020C212yesmaximal, complemented
2#14543733C212yesmaximal, complemented
3#14543717C212yesmaximal, complemented
4#14537481C211yesmaximal, characteristic
5C2×#10587538—22no—
6#11763705—22no—
7#11763705C2214yes—
8C2×#10587634C2211yescharacteristic
9C22×C8×D17C411yescharacteristic
10#11763316C411yescharacteristic
11#11762883—22no—
12#11762872—22no—
13#11762835C2211yescharacteristic
14#11762772C2211yescharacteristic
15#11762767C411yescharacteristic
16C17×#408C411yescharacteristic
17C2×#41×C17C2×C411yescharacteristic
18C22×C4×D17C2×C411yescharacteristic
19C2×M16×C17C2×C411yescharacteristic
20C22×C8×C17C2×C411yescharacteristic
21#10587634—41no—
22#10587634—41no—
23#10587632—21no—
24#10587624—21no—
25#10587623C812yes—
26#10587621C812yes—
27C4×C22⋊D17—22no—
28#10587612C2×C411yescharacteristic
29C2×#63223D412yes—
30C2×#63223C2311yescharacteristic
31C22×#3622C2×C411yescharacteristic
32C22×#3622D412yes—
33C2×C8×D17—21no—
34C2×C8×D17—21no—
35C2×C8×D17—41no—
36C2×C8×D17—41no—
37#10587538—24no—
38#10587538—42no—
39C2×#63216—42no—
40C17×C22⋊C8—22no—
41#10587491—22no—
42#10587486—21no—
43#10587485—22no—
44C8×Dic17—21no—
45C23×D17C2×C811yescharacteristic
46#41×C17—41no—
47#41×C17—41no—
48C2×Q8×C17M1611yescharacteristic
49C2×D4×C17C2×C812yes—
50C2×D4×C17M1611yescharacteristic
51C22×C4×C17C22⋊C412yes—
52C22×C4×C17C22×C411yescharacteristic
53C2×C22⋊D17—22no—
54C22×Dic17C2×C811yescharacteristic
55C2×C4×D17—21no—
56C2×C4×D17—21no—
57C2×C4×D17—41no—
58C2×C4×D17—41no—
59M16×C17—41no—
60C2×C8×C17—21no—
61C2×C8×C17—21no—
62C2×C8×C17—41no—
63C22⋊Dic17—22no—
64C22⋊Dic17C2×C812yes—
65#63227—22no—
66C4⋊Dic17—21no—
67#63225—22no—
68C4×Dic17—21no—
69#63223—42no—
70#63223—41no—
71C2×#3622—22no—
72C2×#3622—22no—
73C2×#3622—21no—
74C2×#3622—21no—
75C2×#3622C22⋊C411yescharacteristic
76C2×#3622C22⋊C411yescharacteristic
77C2×#3622C2×D412yes—
78C8×D17—42no—
79C8×D17—41no—
80C8×D17—41no—
81#63216—44no—
82#11483—171nomaximal, Sylow
83C23×C17C22⋊C812yes—
84C23×C17C22×C811yescharacteristic
85C22×D17—21no—
86C22×D17—42no—
87C22×D17—41no—
88Q8×C17—41no—
89D4×C17—42no—
90D4×C17—41no—
91C2×C4×C17—21no—
92C2×C4×C17—22no—
93C2×C4×C17—21no—
94C2×C4×C17—22no—
95C2×C4×C17C22⋊C812yes—
96C2×C4×C17C2×C22⋊C411yescharacteristic
97C2×C4×C17C2×M1611yescharacteristic
98C22⋊D17—44no—
99C2×Dic17—21no—
100C2×Dic17—22no—
101C2×Dic17—41no—
102C4×D17—42no—
103C4×D17—41no—
104C4×D17—41no—
105C8×C17—41no—
106C8×C17—41no—
107#3622—22no—
108#3622—21no—
109#3622#9911yescharacteristic
110#3622#9911yescharacteristic
111#2929—171no—
112#2115—172no—
113#1328—172no—
114#1320—172no—
115C22×C17—21no—
116C22×C17—22no—
117C22×C17—42no—
118C22×C17—41no—
119C22×C17C2×C22⋊C811yescharacteristic
120C2×D17—22no—
121C2×D17—41no—
122C2×D17—42no—
123C2×D17—41no—
124C2×D17—42no—
125C4×C17—21no—
126C4×C17—22no—
127C4×C17C2×#9911yescharacteristic
128C4×C17#41311yescharacteristic
129Dic17—42no—
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#59511yescharacteristic
139#407—171no—
140#405—171no—
141#349—174no—
142#349—342no—
143C2×C17—21no—
144C2×C17—41no—
145C2×C17—42no—
146C2×C17#145911yescharacteristic
147D17—42no—
148C2×#41C2×#59511yescharacteristic
149C23×C4—171no—
150#131—681no—
151#131—681no—
152C2×M16—172no—
153C2×M16—171no—
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#117—171no—
168M32—344no—
169M32—682no—
170C2×C16—682no—
171C4⋊C8—342no—
172C22⋊C8—22no—
173C22⋊C8—342no—
174#97—341no—
175C4×C8—341no—
176C17#1148311yescharacteristic, complemented, Sylow
177C24—171no—
178#41—41no—
179#41—41no—
180C2×Q8#6324311yescharacteristic
181C2×D4—342no—
182C2×D4#6324212yes—
183C2×D4#6324311yescharacteristic
184C22×C4—171no—
185C22×C4—341no—
186C22×C4—341no—
187C22×C4—681no—
188C22×C4—681no—
189C22×C4C22⋊#59512yes—
190C22×C4C22×#59511yescharacteristic
191M16—41no—
192M16—681no—
193M16—682no—
194C2×C8—21no—
195C2×C8—21no—
196C2×C8—41no—
197C2×C8—171no—
198C2×C8—171no—
199C2×C8—172no—
200C2×C8—342no—
201C2×C8—342no—
202C2×C8—341no—
203C2×C8—341no—
204C2×C8—681no—
205C2×C8—681no—
206C2×C8—682no—
207C4⋊C4—341no—
208C4⋊C4—342no—
209C22⋊C4—172no—
210C22⋊C4—342no—
211C22⋊C4—342no—
212C42—341no—
213C16—684no—
214C23—341no—
215C23—681no—
216C23—682no—
217C23#1058754312yes—
218C23C2×#6324211yescharacteristic
219Q8—41no—
220D4—42no—
221D4—41no—
222D4—684no—
223C2×C4—21no—
224C2×C4—22no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—342no—
228C2×C4—341no—
229C2×C4—682no—
230C2×C4—681no—
231C2×C4—681no—
232C2×C4—681no—
233C2×C4#1058754312yes—
234C2×C4C2×#6324311yescharacteristic
235C2×C4C2×C22⋊#59511yescharacteristic
236C8—41no—
237C8—41no—
238C8—171no—
239C8—171no—
240C8—342no—
241C8—341no—
242C22—21no—
243C22—22no—
244C22—42no—
245C22—41no—
246C22—342no—
247C22—681no—
248C22—682no—
249C22—682no—
250C22—681no—
251C22C2×#1058754311yescharacteristic
252C4—21no—
253C4—22no—
254C4—682no—
255C4—681no—
256C4D17⋊#9911yescharacteristic
257C4#1176379611yescharacteristic
258C2—21no—
259C2—41no—
260C2—42no—
261C2—682no—
262C2#1454402211yescharacteristic
subgroupG/H
centerC4D17⋊#99
commutatorC23×C17C22×C8
FrattiniC22×C4C22×#595
FittingC17×#408C4
socleC2×C17#1459
prime radical#11763316C4
cosocleC2×#63223C23
hypercenter#408#595
hypocenterC17#11483
LCSG ▷ C23×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
1. #14545020C2semidirect
2. #14543733C2semidirect
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
#145450202
#145437332
#145437172
#145374812
#1148317