Finite Group Databasebeta

← #17949963

Subgroups — #17949963

Order 4352.

624 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 624 conjugacy classes of subgroups — too many to draw. Only its 122 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#14544701C212yesmaximal, complemented
2#14543601C212yesmaximal, complemented
3#14543600C212yesmaximal, complemented
4C4×#10587626C211yesmaximal, characteristic
5C2×C4⋊#3624—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—44no—
31C4×C22⋊D17—44no—
32C2×#63227—21no—
33C2×#63227—22no—
34C2×C4⋊Dic17C2×C411yescharacteristic
35C2×#63225—22no—
36C2×C4×Dic17C2×C411yescharacteristic
37C2×C4×Dic17D412yes—
38C2×C4×Dic17D412yes—
39C2×C4×Dic17C2311yescharacteristic
40C4×D68—42no—
41C4⋊#3624—44no—
42C24×C17—21no—
43C23×D17—21no—
44C2×D4×C17—21no—
45C2×D4×C17—41no—
46C2×D4×C17—41no—
47C2×D4×C17M1612yes—
48C22×C4×C17—21no—
49C22×C4×C17—42no—
50C22×C4×C17—44no—
51C22×C4×C17C22⋊C411yescharacteristic
52C22×C4×C17C22⋊C411yescharacteristic
53C22×C4×C17C22×C411yescharacteristic
54C2×C22⋊D17—28no—
55C2×C22⋊D17—44no—
56C2×C22⋊D17—44no—
57C22×Dic17—21no—
58C22×Dic17C22⋊C412yes—
59C22×Dic17C2×D412yes—
60C2×D68—21no—
61C2×D68—41no—
62C2×D68—41no—
63C2×D68M1612yes—
64C2×C4×D17—42no—
65C2×C4×D17—44no—
66C2×#3624—44no—
67C2×#3624—44no—
68C2×#3624—44no—
69C4⋊C4×C17—41no—
70C22⋊C4×C17—42no—
71C42×C17—22no—
72C22⋊Dic17—42no—
73C22⋊Dic17—42no—
74#63227—42no—
75#63227—42no—
76#63227—42no—
77C4⋊Dic17—41no—
78#63225—44no—
79C4×Dic17—21no—
80C4×Dic17—21no—
81C4×Dic17—42no—
82C4×Dic17—41no—
83C4×Dic17D814yes—
84C4×Dic17SD1614yes—
85#7651—171nomaximal, Sylow
86C23×C17—22no—
87C23×C17—41no—
88C23×C17—41no—
89C23×C17—42no—
90C23×C17—42no—
91C23×C17C2×C22⋊C411yescharacteristic
92C22×D17—22no—
93C22×D17—41no—
94C22×D17—41no—
95C22×D17—42no—
96C22×D17—42no—
97D4×C17—42no—
98D4×C17—42no—
99C2×C4×C17—21no—
100C2×C4×C17—21no—
101C2×C4×C17—21no—
102C2×C4×C17—22no—
103C2×C4×C17—41no—
104C2×C4×C17—42no—
105C2×C4×C17—84no—
106C2×C4×C17#10012yes—
107C2×C4×C17#10214yes—
108C2×C4×C17C2×M1611yescharacteristic
109C2×C4×C17C2×M1611yescharacteristic
110C22⋊D17—416no—
111C2×Dic17—22no—
112C2×Dic17—22no—
113C2×Dic17—22no—
114C2×Dic17—22no—
115C2×Dic17—41no—
116C2×Dic17—42no—
117C2×Dic17#10214yes—
118C2×Dic17C2×D812yes—
119C2×Dic17C2×SD1612yes—
120D68—42no—
121D68—42no—
122C4×D17—84no—
123#3624—84no—
124C4×#127—171no—
125#1831—172no—
126#1270—172no—
127#1270—172no—
128C22×C17—42no—
129C22×C17—44no—
130C22×C17—81no—
131C22×C17—81no—
132C22×C17—82no—
133C22×C17#40711yescharacteristic
134C22×C17#41011yescharacteristic
135C22×C17C2×#10011yescharacteristic
136C22×C17C2×#10212yes—
137C22×C17#42112yes—
138C2×D17—42no—
139C2×D17—44no—
140C2×D17—81no—
141C2×D17—81no—
142C2×D17—82no—
143C4×C17—21no—
144C4×C17—21no—
145C4×C17—41no—
146C4×C17—81no—
147C4×C17#33114yes—
148Dic17—24no—
149Dic17—22no—
150Dic17—22no—
151Dic17—81no—
152C2×#127—171no—
153C2×C4×D4—171no—
154C2×C4×D4—342no—
155C2×C4×D4#59511yescharacteristic
156C2×C4⋊C8—342no—
157#390—171no—
158#390—171no—
159#390—342no—
160#384—171no—
161C43—171no—
162#336—174no—
163#336—342no—
164C2×C17—82no—
165C2×C17#146611yescharacteristic
166C2×C17#148612yes—
167C2×C17#151712yes—
168C2×C17#153611yescharacteristic
169C2×C17C2×#33111yescharacteristic
170D17—82no—
171C22×D4—171no—
172C22×D4—342no—
173C22×D4C2×#59511yescharacteristic
174C23×C4—21no—
175C23×C4—341no—
176C22×C8—344no—
177#127—342no—
178#127—342no—
179C4×D4—42no—
180C4×D4—682no—
181C4×D4—684no—
182C4×D4—684no—
183C2×C4⋊C4—171no—
184C2×C4⋊C4—342no—
185C2×C4⋊C4C2×#59511yescharacteristic
186C2×C22⋊C4—21no—
187C2×C22⋊C4—342no—
188C2×C22⋊C4—342no—
189C2×C22⋊C4—341no—
190C2×C42—172no—
191C2×C42—171no—
192C2×C42—172no—
193C2×C42—171no—
194C2×C42C2×#59511yescharacteristic
195C4⋊C8—684no—
196C17#765111yescharacteristic, complemented, Sylow
197C24—21no—
198C24—341no—
199C2×D4—21no—
200C2×D4—41no—
201C2×D4—41no—
202C2×D4—172no—
203C2×D4—348no—
204C2×D4—341no—
205C2×D4—681no—
206C2×D4—681no—
207C2×D4—684no—
208C2×D4—684no—
209C2×D4#6324312yes—
210C22×C4—21no—
211C22×C4—44no—
212C22×C4—42no—
213C22×C4—172no—
214C22×C4—172no—
215C22×C4—341no—
216C22×C4—684no—
217C22×C4—682no—
218C22×C4C22⋊#59511yescharacteristic
219C22×C4C22⋊#59511yescharacteristic
220C22×C4C22×#59511yescharacteristic
221C2×C8—684no—
222C2×C8—684no—
223C2×C8—684no—
224C4⋊C4—41no—
225C4⋊C4—681no—
226C4⋊C4—684no—
227C22⋊C4—42no—
228C22⋊C4—682no—
229C22⋊C4—682no—
230C22⋊C4—682no—
231C22⋊C4—682no—
232C22⋊C4—682no—
233C42—22no—
234C42—174no—
235C42—174no—
236C42—341no—
237C42—341no—
238C42—681no—
239C42—682no—
240C23—22no—
241C23—41no—
242C23—41no—
243C23—42no—
244C23—42no—
245C23—342no—
246C23—681no—
247C23—681no—
248C23—682no—
249C23—682no—
250C23C2×C22⋊#59511yescharacteristic
251D4—42no—
252D4—42no—
253D4—682no—
254D4—682no—
255D4—6816no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—22no—
260C2×C4—41no—
261C2×C4—42no—
262C2×C4—84no—
263C2×C4—172no—
264C2×C4—172no—
265C2×C4—174no—
266C2×C4—342no—
267C2×C4—342no—
268C2×C4—342no—
269C2×C4—342no—
270C2×C4—681no—
271C2×C4—682no—
272C2×C4—1364no—
273C2×C4#1058754714yes—
274C2×C4#1058755312yes—
275C2×C4C2×#6324311yescharacteristic
276C2×C4D17⋊M1611yescharacteristic
277C8—1364no—
278C22—42no—
279C22—44no—
280C22—82no—
281C22—81no—
282C22—81no—
283C22—682no—
284C22—684no—
285C22—1362no—
286C22—1361no—
287C22—1361no—
288C22#1176378011yescharacteristic
289C22#1176378811yescharacteristic
290C22C2×#1058755311yescharacteristic
291C22C2×#1058754712yes—
292C22#1176380612yes—
293C4—21no—
294C4—21no—
295C4—41no—
296C4—81no—
297C4—342no—
298C4—342no—
299C4—344no—
300C4—1361no—
301C4#1176366714yes—
302C2—82no—
303C2—1362no—
304C2#1454404311yescharacteristic
305C2#1454411012yes—
306C2#1454421412yes—
307C2#1454427211yescharacteristic
308C2C2×#1176366711yescharacteristic
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#7651
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. #14544701C2semidirect
2. #14543601C2semidirect
3. #14543600C2semidirect
196. C17#7651semidirect

Maximal subgroups

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

subgroupindex
#145447012
#145436012
#145436002
C4×#105876262
#765117