Finite Group Databasebeta

← #17958338

Subgroups — #17958338

Order 4352.

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

normal subgroups only

This group has 368 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#14537490C211yesmaximal, characteristic
5C2×#10587538—22no—
6#11763705—22no—
7#11763705C2214yes—
8C2×#10587634C2211yescharacteristic
9C22×#63218C411yescharacteristic
10#11763316C411yescharacteristic
11#11762884—22no—
12#11762877—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—42no—
22#10587632—21no—
23#10587624—21no—
24#10587623C812yes—
25#10587621C812yes—
26C4×C22⋊D17—22no—
27#10587612C2×C411yescharacteristic
28C2×#63223D412yes—
29C2×#63223C2311yescharacteristic
30C22×#3622C2×C411yescharacteristic
31C22×#3622D412yes—
32C2×#63218—21no—
33C2×#63218—21no—
34C2×#63218—42no—
35#10587538—24no—
36#10587538—42no—
37C2×#63216—42no—
38C17×C22⋊C8—22no—
39#10587491—22no—
40#10587486—21no—
41#10587485—22no—
42C8×Dic17—21no—
43C23×D17C2×C811yescharacteristic
44#41×C17—41no—
45#41×C17—41no—
46C2×Q8×C17M1611yescharacteristic
47C2×D4×C17C2×C812yes—
48C2×D4×C17M1611yescharacteristic
49C22×C4×C17C22⋊C412yes—
50C22×C4×C17C22×C411yescharacteristic
51C2×C22⋊D17—22no—
52C22×Dic17C2×C811yescharacteristic
53C2×C4×D17—21no—
54C2×C4×D17—21no—
55C2×C4×D17—41no—
56C2×C4×D17—41no—
57M16×C17—41no—
58C2×C8×C17—21no—
59C2×C8×C17—21no—
60C2×C8×C17—41no—
61C22⋊Dic17—22no—
62C22⋊Dic17C2×C812yes—
63#63227—22no—
64C4⋊Dic17—21no—
65#63225—22no—
66C4×Dic17—21no—
67#63223—42no—
68#63223—41no—
69C2×#3622—22no—
70C2×#3622—22no—
71C2×#3622—22no—
72C2×#3622C22⋊C411yescharacteristic
73C2×#3622C22⋊C411yescharacteristic
74C2×#3622C2×D412yes—
75#63218—42no—
76#63218—42no—
77#63216—44no—
78#11484—171nomaximal, Sylow
79C23×C17C22⋊C812yes—
80C23×C17C22×C811yescharacteristic
81C22×D17—21no—
82C22×D17—41no—
83C22×D17—81no—
84Q8×C17—41no—
85D4×C17—42no—
86D4×C17—41no—
87C2×C4×C17—21no—
88C2×C4×C17—22no—
89C2×C4×C17—21no—
90C2×C4×C17—22no—
91C2×C4×C17C22⋊C812yes—
92C2×C4×C17C2×C22⋊C411yescharacteristic
93C2×C4×C17C2×M1611yescharacteristic
94C22⋊D17—82no—
95C2×Dic17—21no—
96C2×Dic17—22no—
97C2×Dic17—41no—
98C4×D17—42no—
99C4×D17—41no—
100C4×D17—41no—
101C8×C17—41no—
102C8×C17—41no—
103#3622—22no—
104#3622—21no—
105#3622#9912yes—
106#2930—171no—
107#2115—172no—
108#1328—172no—
109#1320—172no—
110C22×C17—21no—
111C22×C17—22no—
112C22×C17—42no—
113C22×C17—41no—
114C22×C17C2×C22⋊C811yescharacteristic
115C2×D17—41no—
116C2×D17—41no—
117C2×D17—41no—
118C2×D17—82no—
119C4×C17—21no—
120C4×C17—22no—
121C4×C17C2×#9911yescharacteristic
122C4×C17#41311yescharacteristic
123Dic17—42no—
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#59511yescharacteristic
133#407—171no—
134#405—171no—
135#349—174no—
136#349—342no—
137C2×C17—21no—
138C2×C17—41no—
139C2×C17—42no—
140C2×C17#145911yescharacteristic
141D17—81no—
142C2×#41C2×#59511yescharacteristic
143C23×C4—171no—
144#131—682no—
145C2×M16—172no—
146C2×M16—171no—
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#117—171no—
160M32—344no—
161M32—682no—
162C2×C16—682no—
163C4⋊C8—342no—
164C22⋊C8—22no—
165C22⋊C8—342no—
166#97—341no—
167C4×C8—341no—
168C17#1148411yescharacteristic, complemented, Sylow
169C24—171no—
170#41—41no—
171#41—41no—
172C2×Q8#6324311yescharacteristic
173C2×D4—342no—
174C2×D4#6324212yes—
175C2×D4#6324311yescharacteristic
176C22×C4—171no—
177C22×C4—341no—
178C22×C4—341no—
179C22×C4—681no—
180C22×C4—681no—
181C22×C4C22⋊#59512yes—
182C22×C4C22×#59511yescharacteristic
183M16—41no—
184M16—682no—
185M16—682no—
186M16—681no—
187M16—682no—
188C2×C8—21no—
189C2×C8—21no—
190C2×C8—41no—
191C2×C8—171no—
192C2×C8—171no—
193C2×C8—172no—
194C2×C8—342no—
195C2×C8—342no—
196C2×C8—342no—
197C4⋊C4—341no—
198C4⋊C4—342no—
199C22⋊C4—172no—
200C22⋊C4—342no—
201C22⋊C4—342no—
202C42—341no—
203C16—684no—
204C23—341no—
205C23—681no—
206C23—1361no—
207C23#1058754312yes—
208C23C2×#6324211yescharacteristic
209Q8—41no—
210D4—42no—
211D4—41no—
212D4—1362no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—21no—
216C2×C4—22no—
217C2×C4—342no—
218C2×C4—341no—
219C2×C4—682no—
220C2×C4—681no—
221C2×C4—681no—
222C2×C4—681no—
223C2×C4#1058754312yes—
224C2×C4C2×#6324311yescharacteristic
225C2×C4C2×C22⋊#59511yescharacteristic
226C8—41no—
227C8—41no—
228C8—172no—
229C8—342no—
230C8—341no—
231C22—21no—
232C22—22no—
233C22—42no—
234C22—41no—
235C22—681no—
236C22—681no—
237C22—681no—
238C22—1362no—
239C22C2×#1058754311yescharacteristic
240C4—21no—
241C4—22no—
242C4—682no—
243C4—681no—
244C4D17⋊#9911yescharacteristic
245C4#1176379611yescharacteristic
246C2—21no—
247C2—41no—
248C2—42no—
249C2—1361no—
250C2#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#11484
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
168. C17#11484semidirect

Maximal subgroups

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

subgroupindex
#145450202
#145437332
#145437172
#145374902
#1148417