Finite Group Databasebeta

← #17958633

Subgroups — #17958633

Order 4352.

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

normal subgroups only

This group has 462 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
1#14544046C211yesmaximal, characteristic, complemented
2#14544026C211yesmaximal, characteristic, complemented
3#14543712C214yesmaximal, complemented
4#14533787C211yesmaximal, characteristic
5#11763830—21no—
6#11763826—21no—
7#11763655—21no—
8#11763655—21no—
9#11763654C2212yes—
10#11763654C2212yes—
11C2×#10587622C412yes—
12C2×C4×Dic34C2211yescharacteristic
13#11762723—21no—
14#11762723—21no—
15#11762712—21no—
16#11762712—21no—
17#11762712C2212yes—
18C4×C4⋊Dic17C411yescharacteristic
19C2×C17×#127C411yescharacteristic
20C22×D4×C17—21no—
21C22×D4×C17—21no—
22C22×D4×C17C2×C412yes—
23C22×Dic34C2×C411yescharacteristic
24C17×#127—41no—
25C17×#127—41no—
26C2×C42×C17C2×C411yescharacteristic
27C2×C22⋊Dic17—22no—
28C2×C22⋊Dic17—22no—
29C2×C22⋊Dic17—22no—
30C2×C22⋊Dic17—22no—
31#10587622—44no—
32C2×C4⋊Dic17—21no—
33C2×C4⋊Dic17C2311yescharacteristic
34C2×#63225D411yescharacteristic
35C2×#63225D411yescharacteristic
36C2×C4×Dic17C2×C412yes—
37C2×C4×Dic17D411yescharacteristic
38C2×C4×Dic17D411yescharacteristic
39C4×Dic34—41no—
40C4×Dic34—41no—
41C22⋊#3624—22no—
42C22⋊#3624—22no—
43#10587544—41no—
44#10587542—41no—
45C4⋊#3624—41no—
46C4×#3624—41no—
47#10587502—21no—
48C24×C17—22no—
49C2×D4×C17—24no—
50C2×D4×C17—42no—
51C2×D4×C17—42no—
52C2×D4×C17—42no—
53C2×D4×C17—42no—
54C2×D4×C17—42no—
55C2×D4×C17—41no—
56C2×D4×C17—41no—
57C2×D4×C17—82no—
58C22×C4×C17C22⋊C411yescharacteristic
59C22×C4×C17C22⋊C411yescharacteristic
60C22×C4×C17C22×C411yescharacteristic
61C22×Dic17—22no—
62C22×Dic17C22⋊C411yescharacteristic
63C22×Dic17C22⋊C411yescharacteristic
64C22×Dic17C2×D411yescharacteristic
65C22×Dic17C2×D411yescharacteristic
66C2×Dic34—22no—
67C2×Dic34—22no—
68C2×Dic34—41no—
69C2×#3624—42no—
70C2×#3624—42no—
71C42×C17—21no—
72C42×C17—21no—
73C22⋊Dic17—44no—
74C22⋊Dic17—44no—
75C22⋊Dic17—82no—
76C22⋊Dic17—82no—
77C4⋊Dic17—41no—
78C4⋊Dic17—42no—
79#63225—41no—
80#63225—41no—
81C4×Dic17—21no—
82C4×Dic17—21no—
83C4×Dic17—21no—
84C4×Dic17—21no—
85C4×Dic17—42no—
86#11567—171nomaximal, Sylow
87C23×C17—42no—
88C23×C17—42no—
89C23×C17—42no—
90C23×C17—42no—
91C23×C17—42no—
92C23×C17—42no—
93C23×C17—42no—
94C23×C17C2×C22⋊C411yescharacteristic
95D4×C17—84no—
96D4×C17—82no—
97D4×C17—84no—
98D4×C17—82no—
99C2×C4×C17—21no—
100C2×C4×C17—21no—
101C2×C4×C17—22no—
102C2×C4×C17—21no—
103C2×C4×C17—41no—
104C2×C4×C17#9911yescharacteristic
105C2×C4×C17#9911yescharacteristic
106C2×C4×C17#13112yes—
107C2×Dic17—21no—
108C2×Dic17—21no—
109C2×Dic17—21no—
110C2×Dic17—21no—
111C2×Dic17—21no—
112C2×Dic17—21no—
113C2×Dic17—21no—
114C2×Dic17—41no—
115C2×Dic17—41no—
116C2×Dic17—42no—
117C2×Dic17—42no—
118C2×Dic17—42no—
119C2×Dic17#10012yes—
120Dic34—44no—
121#3624—82no—
122#3624—82no—
123#2548—171no—
124#1467—171no—
125#1461—171no—
126#1318—174no—
127C22×C17—21no—
128C22×C17—21no—
129C22×C17—82no—
130C22×C17—82no—
131C22×C17—82no—
132C22×C17—82no—
133C22×C17—82no—
134C22×C17—82no—
135C22×C17—82no—
136C22×C17#40811yescharacteristic
137C22×C17C2×#9911yescharacteristic
138C22×C17C2×#10011yescharacteristic
139C4×C17—21no—
140C4×C17—22no—
141C4×C17—41no—
142C4×C17#35512yes—
143Dic17—22no—
144Dic17—41no—
145Dic17—41no—
146Dic17—41no—
147Dic17—82no—
148C2×#127#59511yescharacteristic
149C2×#124—172no—
150C2×C4×Q8—171no—
151#432—341no—
152#431—341no—
153#394—341no—
154#394—341no—
155#390—172no—
156#390—341no—
157#390—341no—
158C4×C4⋊C4—171no—
159#324—172no—
160#324—172no—
161#324—341no—
162#324—341no—
163C2×C17—21no—
164C2×C17—21no—
165C2×C17—162no—
166C2×C17#147111yescharacteristic
167C2×C17#212811yescharacteristic
168C2×C17C2×#35511yescharacteristic
169C22×Q8—171no—
170C22×D4—21no—
171C22×D4—21no—
172C22×D4C2×#59512yes—
173#127—41no—
174#127—41no—
175#124—684no—
176C4×Q8—681no—
177C4×Q8—681no—
178C2×C4⋊C4—171no—
179C2×C4⋊C4—171no—
180C2×C4⋊C4—171no—
181C2×C4⋊C4—341no—
182C2×C22⋊C4—342no—
183C2×C22⋊C4—342no—
184C2×C22⋊C4—342no—
185C2×C22⋊C4—342no—
186C2×C42—171no—
187C2×C42—171no—
188C2×C42—172no—
189C2×C42C2×#59511yescharacteristic
190C4⋊C8—681no—
191C4⋊C8—681no—
192C22⋊C8—342no—
193C22⋊C8—342no—
194#97—681no—
195C4×C8—681no—
196#95—341no—
197C17#1156711yescharacteristic, complemented, Sylow
198C24—22no—
199C2×Q8—342no—
200C2×Q8—342no—
201C2×Q8—681no—
202C2×D4—24no—
203C2×D4—42no—
204C2×D4—42no—
205C2×D4—42no—
206C2×D4—42no—
207C2×D4—42no—
208C2×D4—41no—
209C2×D4—41no—
210C2×D4—82no—
211C22×C4—171no—
212C22×C4—171no—
213C22×C4—171no—
214C22×C4—171no—
215C22×C4—342no—
216C22×C4C22⋊#59511yescharacteristic
217C22×C4C22⋊#59511yescharacteristic
218C22×C4C22×#59511yescharacteristic
219C2×C8—682no—
220C2×C8—682no—
221C4⋊C4—681no—
222C4⋊C4—681no—
223C4⋊C4—681no—
224C4⋊C4—682no—
225C22⋊C4—684no—
226C22⋊C4—684no—
227C22⋊C4—1362no—
228C22⋊C4—1362no—
229C42—21no—
230C42—21no—
231C42—341no—
232C42—341no—
233C42—341no—
234C42—341no—
235C42—682no—
236C23—42no—
237C23—42no—
238C23—42no—
239C23—42no—
240C23—42no—
241C23—42no—
242C23—42no—
243C23C2×C22⋊#59511yescharacteristic
244Q8—684no—
245D4—84no—
246D4—82no—
247D4—84no—
248D4—82no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—22no—
252C2×C4—21no—
253C2×C4—41no—
254C2×C4—172no—
255C2×C4—341no—
256C2×C4—341no—
257C2×C4—341no—
258C2×C4—341no—
259C2×C4—341no—
260C2×C4—341no—
261C2×C4—341no—
262C2×C4—681no—
263C2×C4—681no—
264C2×C4—682no—
265C2×C4—682no—
266C2×C4—682no—
267C2×C4#1058755111yescharacteristic
268C2×C4#1058755111yescharacteristic
269C2×C4#1058767812yes—
270C8—1362no—
271C8—1362no—
272C22—21no—
273C22—21no—
274C22—82no—
275C22—82no—
276C22—82no—
277C22—82no—
278C22—82no—
279C22—82no—
280C22—82no—
281C22#1176378311yescharacteristic
282C22C2×#1058755111yescharacteristic
283C22D17⋊#10011yescharacteristic
284C4—21no—
285C4—22no—
286C4—41no—
287C4—342no—
288C4—681no—
289C4—681no—
290C4—681no—
291C4—1362no—
292C4#1176371712yes—
293C2—21no—
294C2—21no—
295C2—162no—
296C2#1454405911yescharacteristic
297C2#1454506311yescharacteristic
298C2C2×#1176371711yescharacteristic
subgroupG/H
centerC22C2×#10587551
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
Fitting, prime radicalC2×C17×#127C4
socleC22×C17C2×#99
cosocleC2×C4⋊Dic17C23
hypercenterC2×#127#595
hypocenterC17#11567
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. #14544046C2semidirect
2. #14544026C2semidirect
3. #14543712C2semidirect
197. C17#11567semidirect

Maximal subgroups

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

subgroupindex
#145440462
#145440262
#145437122
#145337872
#1156717