Finite Group Databasebeta

← #17955945

Subgroups — #17955945

Order 4352.

558 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 558 conjugacy classes of subgroups — too many to draw. Only its 120 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#14544701C211yesmaximal, characteristic, complemented
2#14544499C211yesmaximal, characteristic, complemented
3C2×#11763659C212yesmaximal, complemented
4C2×#11763657C212yesmaximal
5#14531323C211yesmaximal, characteristic
6C2×C4⋊#3624C2212yes—
7C2×C4×#3624C2212yes—
8#11763675—22no—
9#11763675—22no—
10#11763659—24no—
11#11763657—24no—
12C2×#10587561C411yescharacteristic
13C2×#10587573C2211yescharacteristic
14C2×#10587579C2211yescharacteristic
15#11762714C411yescharacteristic
16#11762710C411yescharacteristic
17#11762698—22no—
18#11762656—22no—
19C42×Dic17C2211yescharacteristic
20C17×#382C411yescharacteristic
21C22×D68C2×C411yescharacteristic
22C22×C4×D17—21no—
23C22×Dic34C2×C411yescharacteristic
24C22×#3624—22no—
25C22×#3624—22no—
26C2×C4⋊C4×C17C2×C411yescharacteristic
27C2×C4⋊C4×C17C2×C411yescharacteristic
28C2×C42×C17C2×C411yescharacteristic
29C2×#63227—22no—
30C2×#63227—22no—
31C2×#63227—21no—
32C2×#63225—21no—
33C2×C4×Dic17—21no—
34C2×C4×Dic17C2×C411yescharacteristic
35C2×C4×Dic17D412yes—
36C2×C4×Dic17D412yes—
37C2×C4×Dic17C2311yescharacteristic
38#10587579—22no—
39#10587579—22no—
40#10587573—22no—
41#10587573—22no—
42#10587561—22no—
43#10587561—22no—
44C4⋊#3624—22no—
45C4⋊#3624—22no—
46C4×#3624—22no—
47C4×#3624D414yes—
48C17×#95—22no—
49#10587502—22no—
50C23×D17—21no—
51C22×C4×C17—21no—
52C22×C4×C17—21no—
53C22×C4×C17C22⋊C412yes—
54C22×C4×C17C22×C411yescharacteristic
55C22×Dic17—21no—
56C22×Dic17C22⋊C412yes—
57C22×Dic17C2×D411yescharacteristic
58C22×Dic17C2×D411yescharacteristic
59C2×D68—22no—
60C2×D68—22no—
61C2×D68—21no—
62C2×D68M1612yes—
63C2×C4×D17—41no—
64C2×C4×D17—41no—
65C2×C4×D17—44no—
66C2×Dic34—22no—
67C2×Dic34—22no—
68C2×Dic34—21no—
69C2×Dic34M1612yes—
70C2×#3624—24no—
71C2×#3624—44no—
72C2×#3624—42no—
73C2×#3624—44no—
74C4⋊C4×C17—22no—
75C4⋊C4×C17—22no—
76C42×C17—21no—
77C42×C17—21no—
78#63227—28no—
79#63227—44no—
80#63227—42no—
81#63225—42no—
82C4×Dic17—22no—
83C4×Dic17—24no—
84C4×Dic17—42no—
85C4×Dic17—41no—
86C4×Dic17—41no—
87C4×Dic17C2×D412yes—
88C4×Dic17#4112yes—
89#9645—171nomaximal, Sylow
90C23×C17C2×C22⋊C411yescharacteristic
91C22×D17—22no—
92C22×D17—41no—
93C22×D17—41no—
94C22×D17—42no—
95C22×D17—42no—
96C2×C4×C17—22no—
97C2×C4×C17—22no—
98C2×C4×C17—22no—
99C2×C4×C17—41no—
100C2×C4×C17—41no—
101C2×C4×C17—42no—
102C2×C4×C17—42no—
103C2×C4×C17C4×D412yes—
104C2×C4×C17C2×M1611yescharacteristic
105C2×C4×C17C2×M1611yescharacteristic
106C2×C4×C17#13112yes—
107C2×Dic17—22no—
108C2×Dic17—22no—
109C2×Dic17—22no—
110C2×Dic17—22no—
111C2×Dic17—22no—
112C2×Dic17—41no—
113C2×Dic17—41no—
114C2×Dic17#12112yes—
115C2×Dic17#12411yescharacteristic
116C2×Dic17#12711yescharacteristic
117C2×Dic17#13514yes—
118D68—24no—
119D68—42no—
120C4×D17—82no—
121C4×D17—82no—
122Dic34—24no—
123Dic34—42no—
124#3624—44no—
125#3624—82no—
126C4×#124—171no—
127#1831—171no—
128#1744—171no—
129C2×Q8⋊C8—172no—
130C2×D4⋊C8—172no—
131C22×C17#39011yescharacteristic
132C22×C17#40711yescharacteristic
133C22×C17#40811yescharacteristic
134C22×C17#41612yes—
135C22×C17#42112yes—
136C2×D17—42no—
137C2×D17—44no—
138C2×D17—81no—
139C2×D17—81no—
140C2×D17—82no—
141C4×C17—42no—
142C4×C17—81no—
143C4×C17—81no—
144C4×C17#43512yes—
145C4×C17#43512yes—
146Dic17—22no—
147Dic17—42no—
148Dic17—42no—
149Dic17#48812yes—
150Dic17#49512yes—
151C2×#124—171no—
152C2×C4×Q8—171no—
153C2×C4×D4—171no—
154C2×C4⋊C8—172no—
155C2×C4×C8—172no—
156#391—171no—
157#390—171no—
158#388—342no—
159#382#59511yescharacteristic
160C4×C22⋊C4—342no—
161C43—171no—
162#336—342no—
163#336—342no—
164Q8⋊C8—344no—
165D4⋊C8—344no—
166C2×C17#148212yes—
167C2×C17#148812yes—
168C2×C17#195511yescharacteristic
169C2×C17#195811yescharacteristic
170C2×C17#196311yescharacteristic
171D17—82no—
172C22×Q8—171no—
173C22×D4—171no—
174C23×C4—341no—
175C22×C8—342no—
176C22×C8—342no—
177#124—342no—
178#124—342no—
179C4×Q8—342no—
180C4×Q8—342no—
181C4×D4—342no—
182C4×D4—342no—
183C2×C4⋊C4—341no—
184C2×C4⋊C4C2×#59511yescharacteristic
185C2×C4⋊C4C2×#59511yescharacteristic
186C2×C22⋊C4—342no—
187C2×C22⋊C4—341no—
188C2×C22⋊C4—342no—
189C2×C42—171no—
190C2×C42—172no—
191C2×C42—171no—
192C2×C42—172no—
193C2×C42—341no—
194C2×C42C2×#59511yescharacteristic
195C4⋊C8—342no—
196C4⋊C8—342no—
197C4×C8—174no—
198C4×C8—342no—
199#95—22no—
200#95—342no—
201C17#964511yescharacteristic, complemented, Sylow
202C24—341no—
203C2×Q8—172no—
204C2×Q8—341no—
205C2×Q8—342no—
206C2×Q8—342no—
207C2×D4—172no—
208C2×D4—341no—
209C2×D4—342no—
210C2×D4—342no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—171no—
214C22×C4—171no—
215C22×C4—172no—
216C22×C4—341no—
217C22×C4—681no—
218C22×C4—681no—
219C22×C4—684no—
220C22×C4C22⋊#59512yes—
221C22×C4C22×#59511yescharacteristic
222C2×C8—344no—
223C2×C8—684no—
224C2×C8—682no—
225C2×C8—684no—
226C4⋊C4—22no—
227C4⋊C4—22no—
228C4⋊C4—682no—
229C22⋊C4—348no—
230C22⋊C4—682no—
231C22⋊C4—684no—
232C42—21no—
233C42—21no—
234C42—172no—
235C42—172no—
236C42—344no—
237C42—342no—
238C42—682no—
239C42—681no—
240C42—681no—
241C23—342no—
242C23—681no—
243C23—681no—
244C23—682no—
245C23—682no—
246C23C2×C22⋊#59511yescharacteristic
247Q8—344no—
248Q8—682no—
249D4—344no—
250D4—682no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—171no—
259C2×C4—171no—
260C2×C4—174no—
261C2×C4—172no—
262C2×C4—342no—
263C2×C4—342no—
264C2×C4—342no—
265C2×C4—342no—
266C2×C4—342no—
267C2×C4—681no—
268C2×C4—681no—
269C2×C4—1362no—
270C2×C4—1362no—
271C2×C4D17⋊M1611yescharacteristic
272C2×C4D17⋊M1611yescharacteristic
273C2×C4D4×#59512yes—
274C2×C4#1058768012yes—
275C8—684no—
276C8—1362no—
277C22—682no—
278C22—684no—
279C22—1361no—
280C22—1361no—
281C22—1362no—
282C22#1176376111yescharacteristic
283C22#1176378111yescharacteristic
284C22#1176378411yescharacteristic
285C22#1176379912yes—
286C22#1176380612yes—
287C4—42no—
288C4—81no—
289C4—81no—
290C4—172no—
291C4—172no—
292C4—342no—
293C4—682no—
294C4—682no—
295C4#1176383912yes—
296C4#1176383912yes—
297C2—1362no—
298C2#1454409812yes—
299C2#1454411712yes—
300C2#1454491011yescharacteristic
301C2#1454491311yescharacteristic
302C2#1454492111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC17×#382C4
socleC23×C17C2×C22⋊C4
prime radicalC22×D68C2×C4
cosocleC2×C4×Dic17C23
hypercenter#382#595
hypocenterC17#9645
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #382

Complements

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

NH ≅ G/Ntype
1. #14544701C2semidirect
2. #14544499C2semidirect
3. C2×#11763659C2semidirect
201. C17#9645semidirect

Maximal subgroups

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

subgroupindex
#145447012
#145444992
C2×#117636592
C2×#117636572
#145313232
#964517