Finite Group Databasebeta

← #17959369

Subgroups — #17959369

Order 4352.

414 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 74 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
1C4×#10587545C211yesmaximal, characteristic
2#14544046C211yesmaximal, characteristic
3#14543768C214yesmaximal
4#14533773C211yesmaximal, characteristic
5#11763830—21no—
6C2×#10587545—21no—
7C4×#63247—21no—
8#11763689C2212yes—
9#11763655C2212yes—
10#11763654—21no—
11C2×#10587630—21no—
12C2×C4×Dic34C2211yescharacteristic
13#11762740C412yes—
14#11762740C2212yes—
15#11762716—21no—
16#11762705—21no—
17#11762705—21no—
18C4×C4⋊Dic17C411yescharacteristic
19C2×C17×C4⋊Q8C411yescharacteristic
20C22×Q8×C17—21no—
21C22×Dic34D411yescharacteristic
22C2×#63247—22no—
23C17×C4⋊Q8—41no—
24C17×C4⋊Q8—41no—
25C2×C4⋊C4×C17—21no—
26C2×C4⋊C4×C17C2×C412yes—
27C2×C42×C17C2×C411yescharacteristic
28#10587630—44no—
29C2×C4⋊Dic17—21no—
30C2×C4⋊Dic17D411yescharacteristic
31C2×#63225—22no—
32C2×#63225—22no—
33C2×#63225C2×C411yescharacteristic
34C2×#63225C2311yescharacteristic
35C2×C4×Dic17—21no—
36C2×C4×Dic17D411yescharacteristic
37C2×C4×Dic17D411yescharacteristic
38C4×Dic34—41no—
39C4×Dic34—41no—
40C22⋊#3624—22no—
41#10587545—24no—
42#10587542—41no—
43#10587542—41no—
44C4⋊#3624—41no—
45C4×#3624—41no—
46#10587502—22no—
47#10587502—22no—
48#10587502C2×C412yes—
49C2×Q8×C17—42no—
50C2×Q8×C17—42no—
51C2×Q8×C17—42no—
52C22×C4×C17—22no—
53C22×C4×C17C22⋊C411yescharacteristic
54C22×C4×C17C22⋊C411yescharacteristic
55C22×C4×C17C22×C411yescharacteristic
56C22×Dic17—22no—
57C22×Dic17C22⋊C411yescharacteristic
58C22×Dic17C22⋊C411yescharacteristic
59C22×Dic17C2×D411yescharacteristic
60C22×Dic17C2×D411yescharacteristic
61C2×Dic34—22no—
62C2×Dic34—22no—
63C2×Dic34—41no—
64#63247—24no—
65#63247—42no—
66C2×#3624—42no—
67C2×#3624—42no—
68C4⋊C4×C17—42no—
69C4⋊C4×C17—41no—
70C4⋊C4×C17—41no—
71C42×C17—21no—
72C42×C17—21no—
73C4⋊Dic17—24no—
74C4⋊Dic17—41no—
75#63225—41no—
76#63225—41no—
77#63225—44no—
78#63225—44no—
79C4×Dic17—21no—
80C4×Dic17—21no—
81C4×Dic17—21no—
82C4×Dic17—21no—
83C4×Dic17—42no—
84#11782—171nomaximal, Sylow
85C23×C17C2×C22⋊C411yescharacteristic
86Q8×C17—84no—
87C2×C4×C17—21no—
88C2×C4×C17—21no—
89C2×C4×C17—22no—
90C2×C4×C17—21no—
91C2×C4×C17—41no—
92C2×C4×C17—42no—
93C2×C4×C17—42no—
94C2×C4×C17—42no—
95C2×C4×C17#9911yescharacteristic
96C2×C4×C17#9911yescharacteristic
97C2×C4×C17#10412yes—
98C2×Dic17—21no—
99C2×Dic17—21no—
100C2×Dic17—24no—
101C2×Dic17—21no—
102C2×Dic17—21no—
103C2×Dic17—21no—
104C2×Dic17—21no—
105C2×Dic17—21no—
106C2×Dic17—42no—
107C2×Dic17—42no—
108C2×Dic17—41no—
109C2×Dic17—41no—
110C2×Dic17AGL(1,ℤ/8)12yes—
111Dic34—44no—
112#3624—44no—
113#3624—82no—
114#2546—171no—
115C4×#101—171no—
116#1467—171no—
117#1346—174no—
118C22×C17—21no—
119C22×C17—21no—
120C22×C17C2×#9911yescharacteristic
121C22×C17#41811yescharacteristic
122C22×C17C2×#10411yescharacteristic
123C4×C17—21no—
124C4×C17—22no—
125C4×C17—41no—
126C4×C17—82no—
127C4×C17#35612yes—
128Dic17—22no—
129Dic17—44no—
130Dic17—41no—
131Dic17—41no—
132Dic17—41no—
133C2×C4⋊Q8—341no—
134C2×C4⋊Q8#59511yescharacteristic
135C2×C4×Q8—171no—
136#432—341no—
137C2×#101—341no—
138C4×M16—341no—
139#398—172no—
140#398—172no—
141#391—341no—
142#389—341no—
143#389—341no—
144C4×C4⋊C4—171no—
145#343—172no—
146#324—172no—
147#324—341no—
148C2×C17—21no—
149C2×C17—21no—
150C2×C17#150711yescharacteristic
151C2×C17#212311yescharacteristic
152C2×C17C2×#35611yescharacteristic
153C22×Q8—21no—
154C22×Q8—171no—
155C2×M16—342no—
156C4⋊Q8—41no—
157C4⋊Q8—41no—
158C4⋊Q8—684no—
159C4×Q8—681no—
160C4×Q8—681no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4—171no—
163C2×C4⋊C4—171no—
164C2×C4⋊C4—171no—
165C2×C4⋊C4—341no—
166C2×C4⋊C4—342no—
167C2×C4⋊C4—342no—
168C2×C4⋊C4C2×#59512yes—
169C2×C42—171no—
170C2×C42—171no—
171C2×C42—341no—
172C2×C42C2×#59511yescharacteristic
173C4⋊C8—681no—
174#101—344no—
175C22⋊C8—342no—
176#97—681no—
177#97—681no—
178C4×C8—681no—
179#95—172no—
180#95—342no—
181#95—342no—
182C17#1178211yescharacteristic, complemented, Sylow
183C2×Q8—42no—
184C2×Q8—42no—
185C2×Q8—42no—
186C2×Q8—342no—
187C2×Q8—342no—
188C2×Q8—681no—
189C22×C4—22no—
190C22×C4—171no—
191C22×C4—171no—
192C22×C4—171no—
193C22×C4—171no—
194C22×C4—342no—
195C22×C4C22⋊#59511yescharacteristic
196C22×C4C22⋊#59511yescharacteristic
197C22×C4C22×#59511yescharacteristic
198M16—344no—
199M16—682no—
200C2×C8—682no—
201C2×C8—682no—
202C4⋊C4—42no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—344no—
206C4⋊C4—681no—
207C4⋊C4—681no—
208C4⋊C4—681no—
209C4⋊C4—684no—
210C4⋊C4—684no—
211C42—21no—
212C42—21no—
213C42—341no—
214C42—341no—
215C42—341no—
216C42—341no—
217C42—682no—
218C23C2×C22⋊#59511yescharacteristic
219Q8—84no—
220Q8—684no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—21no—
225C2×C4—41no—
226C2×C4—42no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—172no—
230C2×C4—341no—
231C2×C4—341no—
232C2×C4—344no—
233C2×C4—341no—
234C2×C4—341no—
235C2×C4—341no—
236C2×C4—341no—
237C2×C4—341no—
238C2×C4—682no—
239C2×C4—682no—
240C2×C4—681no—
241C2×C4—681no—
242C2×C4#1058754812yes—
243C2×C4#1058755111yescharacteristic
244C2×C4#1058755111yescharacteristic
245C8—684no—
246C8—1362no—
247C22—21no—
248C22—21no—
249C22C2×#1058755111yescharacteristic
250C22#1176380111yescharacteristic
251C22C2×#1058754811yescharacteristic
252C4—22no—
253C4—21no—
254C4—41no—
255C4—82no—
256C4—342no—
257C4—684no—
258C4—681no—
259C4—681no—
260C4—681no—
261C4#1176371912yes—
262C2—21no—
263C2—21no—
264C2#1454418011yescharacteristic
265C2#1454504611yescharacteristic
266C2C2×#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#11782
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
182. C17#11782semidirect

Maximal subgroups

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

subgroupindex
C4×#105875452
#145440462
#145437682
#145337732
#1178217