Finite Group Databasebeta

← #17959413

Subgroups — #17959413

Order 4352.

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

normal subgroups only

This group has 394 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#14543784C214yesmaximal
4#14533992C211yesmaximal, characteristic
5#11763830—21no—
6C2×#10587545—21no—
7C4×#63247—21no—
8#11763689C2212yes—
9#11763655C2212yes—
10#11763654—21no—
11C2×#10587555C411yescharacteristic
12C2×C4×Dic34C2211yescharacteristic
13#11762730C412yes—
14#11762730C2212yes—
15#11762715—21no—
16#11762708—21no—
17#11762708—21no—
18#11762679—21no—
19C4×C4⋊C4×C17C411yescharacteristic
20C22×Dic34C2×C412yes—
21C22×Dic34D411yescharacteristic
22C2×#63247—22no—
23C2×C4⋊C4×C17—21no—
24C2×C42×C17—21no—
25C2×C42×C17C2×C411yescharacteristic
26C2×C4⋊Dic17—21no—
27C2×C4⋊Dic17—21no—
28C2×C4⋊Dic17—22no—
29C2×C4⋊Dic17—22no—
30C2×C4⋊Dic17D411yescharacteristic
31C2×#63225C2×C411yescharacteristic
32C2×#63225C2311yescharacteristic
33C2×C4×Dic17D411yescharacteristic
34C2×C4×Dic17D411yescharacteristic
35#10587555—41no—
36#10587555—41no—
37C4×Dic34—41no—
38C4×Dic34—41no—
39C22⋊#3624—22no—
40#10587545—24no—
41#10587542—41no—
42#10587542—41no—
43C4⋊#3624—41no—
44C4×#3624—41no—
45C17×#95C2×C412yes—
46#10587502—22no—
47#10587502—22no—
48C22×C4×C17—22no—
49C22×C4×C17C22⋊C411yescharacteristic
50C22×C4×C17C22⋊C411yescharacteristic
51C22×C4×C17C22×C411yescharacteristic
52C22×Dic17—22no—
53C22×Dic17C22⋊C411yescharacteristic
54C22×Dic17C22⋊C411yescharacteristic
55C22×Dic17C2×D411yescharacteristic
56C22×Dic17C2×D411yescharacteristic
57C2×Dic34—22no—
58C2×Dic34—22no—
59C2×Dic34—41no—
60C2×Dic34—42no—
61C2×Dic34—82no—
62#63247—24no—
63#63247—42no—
64C2×#3624—42no—
65C2×#3624—42no—
66C4⋊C4×C17—24no—
67C42×C17—21no—
68C42×C17—21no—
69C42×C17—42no—
70C4⋊Dic17—41no—
71C4⋊Dic17—42no—
72C4⋊Dic17—41no—
73C4⋊Dic17—41no—
74C4⋊Dic17—82no—
75C4⋊Dic17—82no—
76#63225—41no—
77#63225—41no—
78C4×Dic17—21no—
79C4×Dic17—21no—
80C4×Dic17—21no—
81C4×Dic17—21no—
82#11795—171nomaximal, Sylow
83C23×C17C2×C22⋊C411yescharacteristic
84C2×C4×C17—21no—
85C2×C4×C17—21no—
86C2×C4×C17—22no—
87C2×C4×C17—24no—
88C2×C4×C17—21no—
89C2×C4×C17—42no—
90C2×C4×C17—42no—
91C2×C4×C17—41no—
92C2×C4×C17#9911yescharacteristic
93C2×C4×C17#9911yescharacteristic
94C2×C4×C17#10412yes—
95C2×Dic17—21no—
96C2×Dic17—21no—
97C2×Dic17—21no—
98C2×Dic17—21no—
99C2×Dic17—21no—
100C2×Dic17—21no—
101C2×Dic17—21no—
102C2×Dic17—41no—
103C2×Dic17—41no—
104C2×Dic17—42no—
105C2×Dic17—42no—
106C2×Dic17—42no—
107C2×Dic17#13712yes—
108Dic34—44no—
109Dic34—84no—
110#3624—44no—
111#3624—82no—
112#2567—171no—
113C4×#101—171no—
114#1467—171no—
115#1354—174no—
116C22×C17—21no—
117C22×C17—21no—
118C22×C17C2×#9911yescharacteristic
119C22×C17#41911yescharacteristic
120C22×C17C2×#10411yescharacteristic
121C4×C17—21no—
122C4×C17—22no—
123C4×C17—44no—
124C4×C17—41no—
125C4×C17#35612yes—
126Dic17—22no—
127Dic17—41no—
128Dic17—41no—
129Dic17—41no—
130Dic17—82no—
131C2×C4⋊Q8—171no—
132C2×C4×Q8—171no—
133#432—341no—
134C2×#101—341no—
135C4×M16—341no—
136#395—172no—
137#395—172no—
138#391—341no—
139#389—341no—
140#389—341no—
141#384—341no—
142C4×C4⋊C4#59511yescharacteristic
143#343—172no—
144#324—172no—
145#324—341no—
146C2×C17—21no—
147C2×C17—21no—
148C2×C17#150811yescharacteristic
149C2×C17#212211yescharacteristic
150C2×C17C2×#35611yescharacteristic
151C22×Q8—171no—
152C22×Q8—172no—
153C2×M16—342no—
154C4⋊Q8—681no—
155C4⋊Q8—681no—
156C4×Q8—681no—
157C4×Q8—681no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—171no—
160C2×C4⋊C4—171no—
161C2×C4⋊C4—171no—
162C2×C4⋊C4—341no—
163C2×C4⋊C4—341no—
164C2×C4⋊C4—342no—
165C2×C4⋊C4—342no—
166C2×C42—21no—
167C2×C42—171no—
168C2×C42—171no—
169C2×C42C2×#59511yescharacteristic
170C4⋊C8—681no—
171#101—344no—
172C22⋊C8—342no—
173#97—681no—
174#97—681no—
175C4×C8—681no—
176#95—342no—
177#95—342no—
178#95C2×#59512yes—
179C17#1179511yescharacteristic, complemented, Sylow
180C2×Q8—342no—
181C2×Q8—342no—
182C2×Q8—681no—
183C2×Q8—682no—
184C2×Q8—1362no—
185C22×C4—22no—
186C22×C4—171no—
187C22×C4—171no—
188C22×C4—171no—
189C22×C4—171no—
190C22×C4—342no—
191C22×C4C22⋊#59511yescharacteristic
192C22×C4C22⋊#59511yescharacteristic
193C22×C4C22×#59511yescharacteristic
194M16—344no—
195M16—682no—
196C2×C8—682no—
197C2×C8—682no—
198C4⋊C4—24no—
199C4⋊C4—681no—
200C4⋊C4—681no—
201C4⋊C4—681no—
202C4⋊C4—682no—
203C4⋊C4—681no—
204C4⋊C4—681no—
205C4⋊C4—1362no—
206C4⋊C4—1362no—
207C42—21no—
208C42—21no—
209C42—42no—
210C42—341no—
211C42—341no—
212C42—341no—
213C42—341no—
214C23C2×C22⋊#59511yescharacteristic
215Q8—684no—
216Q8—1364no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—24no—
221C2×C4—21no—
222C2×C4—42no—
223C2×C4—42no—
224C2×C4—41no—
225C2×C4—172no—
226C2×C4—341no—
227C2×C4—341no—
228C2×C4—341no—
229C2×C4—341no—
230C2×C4—341no—
231C2×C4—341no—
232C2×C4—341no—
233C2×C4—681no—
234C2×C4—681no—
235C2×C4—682no—
236C2×C4—682no—
237C2×C4—682no—
238C2×C4#1058753911yescharacteristic
239C2×C4#1058753911yescharacteristic
240C2×C4#1058754812yes—
241C8—684no—
242C8—1362no—
243C22—21no—
244C22—21no—
245C22C2×#1058753911yescharacteristic
246C22#1176380211yescharacteristic
247C22C2×#1058754811yescharacteristic
248C4—22no—
249C4—21no—
250C4—44no—
251C4—41no—
252C4—342no—
253C4—681no—
254C4—681no—
255C4—681no—
256C4—1362no—
257C4#1176372012yes—
258C2—21no—
259C2—21no—
260C2#1454418311yescharacteristic
261C2#1454504511yescharacteristic
262C2C2×#1176372011yescharacteristic
subgroupG/H
centerC22C2×#10587539
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC4×C4⋊C4×C17C4
socleC22×C17C2×#99
prime radicalC23×C17C2×C22⋊C4
cosocleC2×#63225C23
hypercenterC4×C4⋊C4#595
hypocenterC17#11795
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
179. C17#11795semidirect

Maximal subgroups

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

subgroupindex
C4×#105875452
#145440462
#145437842
#145339922
#1179517