Finite Group Databasebeta

← #17958933

Subgroups — #17958933

Order 4352.

430 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 92 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#14545142C211yesmaximal, characteristic, complemented
2#14544341C211yesmaximal, characteristic, complemented
3#14543739C214yesmaximal, complemented
4C2×#11762891C211yesmaximal, characteristic
5#11763812—21no—
6#11763730—21no—
7C22⋊#63216—21no—
8#11763695C2212yescomplemented
9#11763673—21no—
10#11763672C2212yescomplemented
11C22×D136C411yescharacteristic
12C2×#10587579—21no—
13#11762891—21no—
14#11762891—21no—
15#11762891C412yes—
16#11762891C2212yes—
17C2×#10587480—21no—
18C2×C8×Dic17C2211yescharacteristic
19C2×C17×#107C411yescharacteristic
20C22×D68—21no—
21C22×C4×D17—41no—
22C2×#63247—41no—
23C22×C8×C17C2×C411yescharacteristic
24C2×C4⋊C4×C17—21no—
25C2×#63227—41no—
26C2×C4×Dic17D411yescharacteristic
27C22×#3622D411yescharacteristic
28C2×D136—24no—
29C2×D136—21no—
30C2×D136C2×C412yes—
31#10587579—22no—
32#10587579—22no—
33#10587579—41no—
34#10587579—41no—
35#10587544—41no—
36C4⋊#3624—22no—
37C2×#63216—22no—
38C17×#107—21no—
39C17×#107C2×C412yes—
40C8×Dic17C2×C411yescharacteristic
41C8×Dic17D411yescharacteristic
42C8×Dic17D411yescharacteristic
43C8×Dic17C2311yescharacteristic
44#10587480—22no—
45#10587480—22no—
46C23×D17—41no—
47C22×C4×C17—41no—
48C22×C4×C17C22⋊C411yescharacteristic
49C22×Dic17D811yescharacteristic
50C22×Dic17SD1611yescharacteristic
51C2×D68—24no—
52C2×D68—22no—
53C2×D68—42no—
54C2×D68—41no—
55C2×C4×D17—42no—
56C2×C4×D17—42no—
57C2×C4×D17—82no—
58C2×C4×D17—82no—
59#63247—82no—
60C2×#3624—42no—
61C2×C8×C17—22no—
62C2×C8×C17C22⋊C411yescharacteristic
63C2×C8×C17C22×C411yescharacteristic
64C4⋊C4×C17—22no—
65C4⋊C4×C17—41no—
66#63227—42no—
67#63227—42no—
68C4×Dic17C22⋊C411yescharacteristic
69C4×Dic17D811yescharacteristic
70C4×Dic17SD1611yescharacteristic
71C4×Dic17C2×D411yescharacteristic
72C2×#3622—41no—
73C2×#3622C22⋊C411yescharacteristic
74C2×#3622C2×D411yescharacteristic
75D136—24no—
76D136—22no—
77D136M1614yescomplemented
78#63216—42no—
79#11657—171nomaximal, Sylow
80C23×C17#10211yescharacteristic
81C22×D17—44no—
82C22×D17—42no—
83C22×D17—82no—
84C22×D17—82no—
85C2×C4×C17—21no—
86C2×C4×C17—21no—
87C2×C4×C17—42no—
88C2×C4×C17—82no—
89C2×C4×C17#10211yescharacteristic
90C2×C4×C17C2×C22⋊C411yescharacteristic
91C2×Dic17—41no—
92C2×Dic17#10211yescharacteristic
93C2×Dic17#10211yescharacteristic
94C2×Dic17D1612yes—
95C2×Dic17SD3212yes—
96C2×Dic17C2×D811yescharacteristic
97C2×Dic17C2×SD1611yescharacteristic
98D68—24no—
99D68—44no—
100D68—42no—
101C4×D17—84no—
102C4×D17—82no—
103C4×D17—82no—
104#3624—82no—
105C8×C17—21no—
106C8×C17C2×M1612yes—
107#3622—21no—
108#3622—21no—
109C2×C4×D8—171no—
110#2162—171no—
111#1567—171no—
112#1331—174no—
113C22×C17—21no—
114C22×C17—21no—
115C22×C17#35712yes—
116C22×C17C2×#10211yescharacteristic
117C2×D17—44no—
118C2×D17—88no—
119C2×D17—82no—
120C2×D17—82no—
121C4×C17—21no—
122C4×C17—82no—
123C4×C17#40711yescharacteristic
124C4×C17#42111yescharacteristic
125Dic17—21no—
126Dic17—21no—
127Dic17#35712yes—
128Dic17C2×D1611yescharacteristic
129Dic17C2×SD3211yescharacteristic
130C22×D8—171no—
131C2×C4×D4—341no—
132C4×D8—172no—
133C4×D8—172no—
134C4×D8—341no—
135C4×D8—341no—
136C2×#107#59511yescharacteristic
137#423—341no—
138C2×#102—341no—
139C2×C4×C8—171no—
140C4⋊C16—341no—
141C22⋊C16—341no—
142C4×C16—172no—
143#335—172no—
144#335—341no—
145C2×C17—22no—
146C2×C17#148611yescharacteristic
147C2×C17C2×#35711yescharacteristic
148C2×C17#214311yescharacteristic
149D17—84no—
150C22×D4—341no—
151C23×C4—681no—
152C2×D8—172no—
153C2×D8—344no—
154C2×D8—341no—
155C2×M16—681no—
156C22×C8—171no—
157C22×C8C2×#59511yescharacteristic
158C4×D4—342no—
159C4×D4—342no—
160C4×D4—681no—
161C4×D4—681no—
162C2×C4⋊C4—21no—
163C2×C22⋊C4—681no—
164C2×C42—171no—
165C2×C16—342no—
166#107—21no—
167#107C2×#59512yes—
168C4⋊C8—342no—
169C4⋊C8—681no—
170#102—342no—
171#102—342no—
172C4×C8—171no—
173C4×C8—171no—
174C4×C8—171no—
175C4×C8—171no—
176C17#1165711yescharacteristic, complemented, Sylow
177C24—681no—
178C2×D4—344no—
179C2×D4—342no—
180C2×D4—682no—
181C2×D4—681no—
182C22×C4—41no—
183C22×C4—171no—
184C22×C4—171no—
185C22×C4—682no—
186C22×C4—682no—
187C22×C4—1362no—
188C22×C4—1362no—
189C22×C4C22⋊#59511yescharacteristic
190D8—174no—
191D8—344no—
192D8—342no—
193M16—1362no—
194C2×C8—22no—
195C2×C8—171no—
196C2×C8—171no—
197C2×C8—681no—
198C2×C8—682no—
199C2×C8C22⋊#59511yescharacteristic
200C2×C8C22×#59511yescharacteristic
201C4⋊C4—22no—
202C4⋊C4—41no—
203C22⋊C4—682no—
204C22⋊C4—682no—
205C42—171no—
206C42—171no—
207C42—171no—
208C42—171no—
209C16—682no—
210C23—684no—
211C23—682no—
212C23—1362no—
213C23—1362no—
214C23#1058754711yescharacteristic
215D4—344no—
216D4—684no—
217D4—682no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—42no—
221C2×C4—82no—
222C2×C4—172no—
223C2×C4—172no—
224C2×C4—171no—
225C2×C4—171no—
226C2×C4—171no—
227C2×C4—171no—
228C2×C4—681no—
229C2×C4—1362no—
230C2×C4—1364no—
231C2×C4—1362no—
232C2×C4#1058754711yescharacteristic
233C2×C4C2×C22⋊#59511yescharacteristic
234C8—21no—
235C8—341no—
236C8—341no—
237C8—1362no—
238C8D17⋊M1612yes—
239C22—21no—
240C22—21no—
241C22—684no—
242C22—1368no—
243C22—1362no—
244C22—1362no—
245C22#1176372112yes—
246C22C2×#1058754711yescharacteristic
247C4—21no—
248C4—82no—
249C4—171no—
250C4—172no—
251C4—171no—
252C4—341no—
253C4—341no—
254C4#1176378111yescharacteristic
255C4#1176380811yescharacteristic
256C2—22no—
257C2—1364no—
258C2#1454411111yescharacteristic
259C2C2×#1176372111yescharacteristic
260C2#1454510011yescharacteristic
subgroupG/H
centerC22C2×#10587547
commutatorC2×C8×C17C22×C4
FrattiniC2×C8C22×#595
FittingC2×C17×#107C4
socleC22×C17C2×#102
prime radicalC22×D136C4
cosocleC8×Dic17C23
hypercenterC2×#107#595
hypocenterC17#11657
LCSG ▷ C2×C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
1. #14545142C2semidirect
2. #14544341C2semidirect
3. #14543739C2semidirect
8. #11763695C22semidirect
10. #11763672C22semidirect
77. D136M16semidirect
176. C17#11657semidirect

Maximal subgroups

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

subgroupindex
#145451422
#145443412
#145437392
C2×#117628912
#1165717