Finite Group Databasebeta

← #17959812

Subgroups — #17959812

Order 4352.

388 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 80 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#14544650C211yesmaximal, characteristic
2#14544026C211yesmaximal, characteristic
3#14543785C214yesmaximal
4#14533993C211yesmaximal, characteristic
5#11763826—21no—
6#11763812—21no—
7C2×#10587545—21no—
8#11763689C2212yes—
9#11763655C2212yes—
10#11763654—21no—
11C2×C4×Dic34C2211yescharacteristic
12#11762728C412yes—
13#11762728C2212yes—
14#11762714—21no—
15#11762705—21no—
16#11762705—21no—
17#11762678—21no—
18C4×C4⋊Dic17C411yescharacteristic
19C2×C17×C4⋊Q8C411yescharacteristic
20C22×Q8×C17C2×C412yes—
21C22×Dic34D411yescharacteristic
22C2×#63247—22no—
23C17×C4⋊Q8—41no—
24C17×C4⋊Q8—41no—
25C2×C4⋊C4×C17—21no—
26C2×C4⋊C4×C17—21no—
27C2×C42×C17C2×C411yescharacteristic
28C2×C4⋊Dic17—21no—
29C2×C4⋊Dic17D411yescharacteristic
30C2×#63225—22no—
31C2×#63225—22no—
32C2×#63225C2×C411yescharacteristic
33C2×#63225C2311yescharacteristic
34C2×C4×Dic17—21no—
35C2×C4×Dic17D411yescharacteristic
36C2×C4×Dic17D411yescharacteristic
37C4×Dic34—41no—
38C4×Dic34—41no—
39C22⋊#3624—22no—
40#10587545—42no—
41#10587544—41no—
42#10587544—41no—
43C4⋊#3624—41no—
44C4×#3624—41no—
45#10587502—22no—
46#10587502—22no—
47#10587502C2×C412yes—
48C2×Q8×C17—42no—
49C2×Q8×C17—82no—
50C22×C4×C17—22no—
51C22×C4×C17C22⋊C411yescharacteristic
52C22×C4×C17C22⋊C411yescharacteristic
53C22×C4×C17C22×C411yescharacteristic
54C22×Dic17—22no—
55C22×Dic17C22⋊C411yescharacteristic
56C22×Dic17C22⋊C411yescharacteristic
57C22×Dic17C2×D411yescharacteristic
58C22×Dic17C2×D411yescharacteristic
59C2×Dic34—41no—
60C2×Dic34—41no—
61C2×Dic34SD1612yes—
62C2×Dic34Q1612yes—
63#63247—42no—
64#63247—42no—
65C2×#3624—42no—
66C2×#3624—42no—
67C4⋊C4×C17—42no—
68C4⋊C4×C17—41no—
69C4⋊C4×C17—41no—
70C42×C17—21no—
71C42×C17—21no—
72C4⋊Dic17—24no—
73C4⋊Dic17—41no—
74#63225—41no—
75#63225—41no—
76#63225—82no—
77#63225—82no—
78C4×Dic17—21no—
79C4×Dic17—21no—
80C4×Dic17—21no—
81C4×Dic17—21no—
82C4×Dic17—42no—
83#11908—171nomaximal, Sylow
84C23×C17C2×C22⋊C411yescharacteristic
85Q8×C17—84no—
86C2×C4×C17—21no—
87C2×C4×C17—21no—
88C2×C4×C17—22no—
89C2×C4×C17—21no—
90C2×C4×C17—41no—
91C2×C4×C17—42no—
92C2×C4×C17—42no—
93C2×C4×C17—42no—
94C2×C4×C17#9911yescharacteristic
95C2×C4×C17#9911yescharacteristic
96C2×C4×C17#10312yes—
97C2×Dic17—21no—
98C2×Dic17—21no—
99C2×Dic17—21no—
100C2×Dic17—21no—
101C2×Dic17—24no—
102C2×Dic17—21no—
103C2×Dic17—21no—
104C2×Dic17—42no—
105C2×Dic17—42no—
106C2×Dic17—41no—
107C2×Dic17—41no—
108C2×Dic17#10312yes—
109C2×Dic17C2×SD1611yescharacteristic
110C2×Dic17C2×Q1611yescharacteristic
111Dic34—42no—
112Dic34—42no—
113#3624—82no—
114#3624—82no—
115#2567—171no—
116#1801—171no—
117#1461—171no—
118#1354—174no—
119C22×C17—21no—
120C22×C17—21no—
121C22×C17C2×#9911yescharacteristic
122C22×C17C2×#10311yescharacteristic
123C22×C17#42111yescharacteristic
124C4×C17—21no—
125C4×C17—22no—
126C4×C17—41no—
127C4×C17—82no—
128C4×C17#35612yes—
129Dic17—21no—
130Dic17—22no—
131Dic17—21no—
132Dic17—44no—
133Dic17—41no—
134Dic17—41no—
135C2×C4⋊Q8#59511yescharacteristic
136C2×C4×Q8—171no—
137#431—341no—
138#423—341no—
139C2×#101—341no—
140#395—172no—
141#395—172no—
142#391—341no—
143#389—341no—
144#389—341no—
145#384—341no—
146C4×C4⋊C4—171no—
147#343—172no—
148#324—172no—
149#324—341no—
150C2×C17—21no—
151C2×C17—21no—
152C2×C17#152011yescharacteristic
153C2×C17#212211yescharacteristic
154C2×C17C2×#35611yescharacteristic
155C22×Q8—171no—
156C22×Q8C2×#59512yes—
157C2×M16—342no—
158C4⋊Q8—41no—
159C4⋊Q8—41no—
160C4×Q8—681no—
161C4×Q8—681no—
162C2×C4⋊C4—21no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4—171no—
165C2×C4⋊C4—171no—
166C2×C4⋊C4—171no—
167C2×C4⋊C4—341no—
168C2×C4⋊C4—342no—
169C2×C4⋊C4—342no—
170C2×C42—171no—
171C2×C42—171no—
172C2×C42—341no—
173C2×C42C2×#59511yescharacteristic
174C4⋊C8—681no—
175C4⋊C8—681no—
176C4⋊C8—681no—
177#101—682no—
178C22⋊C8—342no—
179C4×C8—681no—
180#95—172no—
181#95—342no—
182#95—342no—
183C17#1190811yescharacteristic, complemented, Sylow
184C2×Q8—42no—
185C2×Q8—82no—
186C2×Q8—172no—
187C2×Q8—172no—
188C2×Q8—681no—
189C2×Q8—681no—
190C22×C4—22no—
191C22×C4—171no—
192C22×C4—171no—
193C22×C4—171no—
194C22×C4—171no—
195C22×C4—342no—
196C22×C4C22⋊#59511yescharacteristic
197C22×C4C22⋊#59511yescharacteristic
198C22×C4C22×#59511yescharacteristic
199M16—682no—
200M16—682no—
201C2×C8—682no—
202C2×C8—682no—
203C4⋊C4—42no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—344no—
207C4⋊C4—681no—
208C4⋊C4—681no—
209C4⋊C4—681no—
210C4⋊C4—1362no—
211C4⋊C4—1362no—
212C42—21no—
213C42—21no—
214C42—341no—
215C42—341no—
216C42—341no—
217C42—341no—
218C42—682no—
219C23C2×C22⋊#59511yescharacteristic
220Q8—84no—
221Q8—682no—
222Q8—682no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—21no—
227C2×C4—41no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—171no—
232C2×C4—172no—
233C2×C4—171no—
234C2×C4—341no—
235C2×C4—341no—
236C2×C4—341no—
237C2×C4—341no—
238C2×C4—344no—
239C2×C4—341no—
240C2×C4—341no—
241C2×C4—682no—
242C2×C4—682no—
243C2×C4—681no—
244C2×C4—681no—
245C2×C4#1058754912yes—
246C2×C4#1058755111yescharacteristic
247C2×C4#1058755111yescharacteristic
248C8—1362no—
249C8—1362no—
250C22—21no—
251C22—21no—
252C22C2×#1058755111yescharacteristic
253C22C2×#1058754911yescharacteristic
254C22#1176380811yescharacteristic
255C4—22no—
256C4—21no—
257C4—41no—
258C4—82no—
259C4—341no—
260C4—342no—
261C4—341no—
262C4—684no—
263C4—681no—
264C4—681no—
265C4#1176371912yes—
266C2—21no—
267C2—21no—
268C2#1454422411yescharacteristic
269C2#1454504311yescharacteristic
270C2C2×#1176371911yescharacteristic
subgroupG/H
centerC22C2×#10587551
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC2×C17×C4⋊Q8C4
socleC22×C17C2×#99
prime radicalC23×C17C2×C22⋊C4
cosocleC2×#63225C23
hypercenterC2×C4⋊Q8#595
hypocenterC17#11908
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
183. C17#11908semidirect

Maximal subgroups

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

subgroupindex
#145446502
#145440262
#145437852
#145339932
#1190817