Finite Group Databasebeta

← #17949915

Subgroups — #17949915

Order 4352.

636 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 636 conjugacy classes of subgroups — too many to draw. Only its 98 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#14544501C212yesmaximal, complemented
2#14543601C212yesmaximal, complemented
3#14543600C212yesmaximal, complemented
4C4×#10587626C211yesmaximal, characteristic
5C2×#10587542—22no—
6#11763675—22no—
7#11763675C2214yes—
8C2×#10587626C411yescharacteristic
9C2×C4×D68C411yescharacteristic
10C2×C4×C22⋊D17—22no—
11#11762712C2211yescharacteristic
12#11762710C2211yescharacteristic
13#11762709—22no—
14#11762678C411yescharacteristic
15C42×Dic17C2211yescharacteristic
16C2×C4×D4×C17C411yescharacteristic
17C22×D4×C17C2×C411yescharacteristic
18C23×C4×C17—21no—
19C22×C22⋊D17—22no—
20C22×D68C2×C411yescharacteristic
21C22×C4×D17—21no—
22C22×#3624—24no—
23C4×D4×C17—42no—
24C2×C4⋊C4×C17C2×C411yescharacteristic
25C2×C22⋊C4×C17—21no—
26C2×C42×C17C2×C411yescharacteristic
27C2×C22⋊Dic17—22no—
28#10587626—22no—
29#10587626—22no—
30C4×C22⋊D17—48no—
31C2×#63227—21no—
32C2×#63227—22no—
33C2×C4⋊Dic17C2×C411yescharacteristic
34C2×#63225—22no—
35C2×C4×Dic17C2×C411yescharacteristic
36C2×C4×Dic17D412yes—
37C2×C4×Dic17D412yes—
38C2×C4×Dic17C2311yescharacteristic
39C4×D68—42no—
40#10587542—28no—
41C24×C17—21no—
42C23×D17—21no—
43C2×D4×C17—21no—
44C2×D4×C17—41no—
45C2×D4×C17—41no—
46C2×D4×C17M1612yes—
47C22×C4×C17—21no—
48C22×C4×C17—44no—
49C22×C4×C17—42no—
50C22×C4×C17C22⋊C411yescharacteristic
51C22×C4×C17C22⋊C411yescharacteristic
52C22×C4×C17C22×C411yescharacteristic
53C2×C22⋊D17—28no—
54C2×C22⋊D17—44no—
55C2×C22⋊D17—44no—
56C22×Dic17—21no—
57C22×Dic17C22⋊C412yes—
58C22×Dic17C2×D412yes—
59C2×D68—21no—
60C2×D68—41no—
61C2×D68—41no—
62C2×D68M1612yes—
63C2×C4×D17—44no—
64C2×C4×D17—42no—
65C2×#3624—28no—
66C2×#3624—44no—
67C2×#3624—44no—
68C4⋊C4×C17—41no—
69C22⋊C4×C17—42no—
70C42×C17—22no—
71C22⋊Dic17—44no—
72#63227—42no—
73#63227—44no—
74C4⋊Dic17—41no—
75#63225—44no—
76C4×Dic17—21no—
77C4×Dic17—21no—
78C4×Dic17—24no—
79C4×Dic17—24no—
80C4×Dic17—41no—
81#7637—171nomaximal, Sylow
82C23×C17—22no—
83C23×C17—41no—
84C23×C17—41no—
85C23×C17—42no—
86C23×C17—42no—
87C23×C17C2×C22⋊C411yescharacteristic
88C22×D17—22no—
89C22×D17—41no—
90C22×D17—41no—
91C22×D17—42no—
92C22×D17—42no—
93D4×C17—42no—
94D4×C17—42no—
95C2×C4×C17—21no—
96C2×C4×C17—21no—
97C2×C4×C17—22no—
98C2×C4×C17—21no—
99C2×C4×C17—22no—
100C2×C4×C17—41no—
101C2×C4×C17—42no—
102C2×C4×C17—84no—
103C2×C4×C17#10012yes—
104C2×C4×C17C2×M1611yescharacteristic
105C2×C4×C17C2×M1611yescharacteristic
106C22⋊D17—416no—
107C2×Dic17—22no—
108C2×Dic17—22no—
109C2×Dic17—22no—
110C2×Dic17—22no—
111C2×Dic17—41no—
112C2×Dic17—42no—
113C2×Dic17#10414yes—
114C2×Dic17AGL(1,ℤ/8)14yes—
115D68—42no—
116D68—42no—
117C4×D17—84no—
118#3624—48no—
119C4×#127—171no—
120#1745—172no—
121#1270—172no—
122#1270—172no—
123C22×C17—42no—
124C22×C17—44no—
125C22×C17—81no—
126C22×C17—82no—
127C22×C17—81no—
128C22×C17#40711yescharacteristic
129C22×C17#41011yescharacteristic
130C22×C17C2×#10011yescharacteristic
131C22×C17#41812yes—
132C22×C17C2×#10412yes—
133C2×D17—42no—
134C2×D17—44no—
135C2×D17—81no—
136C2×D17—82no—
137C2×D17—81no—
138C4×C17—22no—
139C4×C17—21no—
140C4×C17—21no—
141C4×C17—41no—
142C4×C17—81no—
143Dic17—24no—
144Dic17—24no—
145Dic17—81no—
146C2×#127—171no—
147C2×C4×D4—171no—
148C2×C4×D4—342no—
149C2×C4×D4#59511yescharacteristic
150C2×#97—342no—
151#390—171no—
152#390—171no—
153#390—342no—
154#384—171no—
155C43—171no—
156#336—174no—
157#336—342no—
158C2×C17—82no—
159C2×C17#146611yescharacteristic
160C2×C17#149012yes—
161C2×C17#150512yes—
162C2×C17#152511yescharacteristic
163C2×C17#155511yescharacteristic
164D17—82no—
165C22×D4—171no—
166C22×D4—342no—
167C22×D4C2×#59511yescharacteristic
168C23×C4—21no—
169C23×C4—341no—
170C22×C8—344no—
171#127—342no—
172#127—342no—
173C4×D4—42no—
174C4×D4—682no—
175C4×D4—688no—
176C2×C4⋊C4—171no—
177C2×C4⋊C4—342no—
178C2×C4⋊C4C2×#59511yescharacteristic
179C2×C22⋊C4—21no—
180C2×C22⋊C4—342no—
181C2×C22⋊C4—342no—
182C2×C22⋊C4—341no—
183C2×C42—172no—
184C2×C42—172no—
185C2×C42—171no—
186C2×C42—171no—
187C2×C42C2×#59511yescharacteristic
188#97—348no—
189C17#763711yescharacteristic, complemented, Sylow
190C24—21no—
191C24—341no—
192C2×D4—21no—
193C2×D4—41no—
194C2×D4—41no—
195C2×D4—172no—
196C2×D4—348no—
197C2×D4—341no—
198C2×D4—681no—
199C2×D4—681no—
200C2×D4—684no—
201C2×D4—684no—
202C2×D4#6324312yes—
203C22×C4—21no—
204C22×C4—44no—
205C22×C4—42no—
206C22×C4—172no—
207C22×C4—172no—
208C22×C4—341no—
209C22×C4—684no—
210C22×C4—682no—
211C22×C4C22⋊#59511yescharacteristic
212C22×C4C22⋊#59511yescharacteristic
213C22×C4C22×#59511yescharacteristic
214C2×C8—348no—
215C2×C8—684no—
216C2×C8—684no—
217C4⋊C4—41no—
218C4⋊C4—681no—
219C4⋊C4—684no—
220C22⋊C4—42no—
221C22⋊C4—682no—
222C22⋊C4—684no—
223C22⋊C4—684no—
224C42—22no—
225C42—344no—
226C42—344no—
227C42—341no—
228C42—341no—
229C42—681no—
230C23—22no—
231C23—41no—
232C23—41no—
233C23—42no—
234C23—42no—
235C23—342no—
236C23—681no—
237C23—681no—
238C23—682no—
239C23—682no—
240C23C2×C22⋊#59511yescharacteristic
241D4—42no—
242D4—42no—
243D4—682no—
244D4—682no—
245D4—6816no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—22no—
249C2×C4—21no—
250C2×C4—22no—
251C2×C4—41no—
252C2×C4—42no—
253C2×C4—84no—
254C2×C4—174no—
255C2×C4—174no—
256C2×C4—342no—
257C2×C4—342no—
258C2×C4—342no—
259C2×C4—342no—
260C2×C4—681no—
261C2×C4—682no—
262C2×C4—1364no—
263C2×C4#1058755312yes—
264C2×C4C2×#6324311yescharacteristic
265C2×C4D17⋊M1611yescharacteristic
266C8—688no—
267C22—42no—
268C22—44no—
269C22—82no—
270C22—81no—
271C22—81no—
272C22—682no—
273C22—684no—
274C22—1362no—
275C22—1361no—
276C22—1361no—
277C22#1176378011yescharacteristic
278C22#1176378811yescharacteristic
279C22C2×#1058755311yescharacteristic
280C22#1176380112yes—
281C22D17⋊#10412yes—
282C4—21no—
283C4—21no—
284C4—22no—
285C4—41no—
286C4—81no—
287C4—344no—
288C4—344no—
289C4—1361no—
290C2—82no—
291C2—1362no—
292C2#1454404311yescharacteristic
293C2#1454412412yes—
294C2#1454417412yes—
295C2#1454423811yescharacteristic
296C2#1454431111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC2×C4×D4×C17C4
socleC23×C17C2×C22⋊C4
prime radicalC2×#10587626C4
cosocleC2×C4×Dic17C23
hypercenterC2×C4×D4#595
hypocenterC17#7637
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #14544501C2semidirect
2. #14543601C2semidirect
3. #14543600C2semidirect
189. C17#7637semidirect

Maximal subgroups

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

subgroupindex
#145445012
#145436012
#145436002
C4×#105876262
#763717