Finite Group Databasebeta

← #17959383

Subgroups — #17959383

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
1C4×#10587551C211yesmaximal, characteristic
2#14544043C211yesmaximal, characteristic
3#14543780C214yesmaximal, complemented
4#14533102C211yesmaximal, characteristic
5#11763830—21no—
6C2×#10587551—21no—
7C4×C22⋊#595—21no—
8#11763687C2212yes—
9#11763653C2212yes—
10#11763652—21no—
11C2×C4×C22⋊D17C2211yescharacteristic
12C22×C4⋊Dic17C411yescharacteristic, complemented
13#11762749C412yescomplemented
14#11762746C2212yes—
15#11762708—21no—
16#11762686—21no—
17#11762684—21no—
18#11762666—21no—
19C17×#380C411yescharacteristic, complemented
20C23×C4×C17C2×C411yescharacteristic
21C22×C22⋊D17D411yescharacteristic
22C23×Dic17—21no—
23C22×C4×D17D411yescharacteristic
24C2×C22⋊#595—22no—
25C2×C4×#595—41no—
26C2×C4⋊C4×C17—21no—
27C2×C22⋊C4×C17—21no—
28C2×C22⋊Dic17D411yescharacteristic
29C4×C22⋊D17—41no—
30C4×C22⋊D17—41no—
31C2×#63227—22no—
32C2×#63227C2311yescharacteristic
33C2×C4⋊Dic17—21no—
34C2×C4⋊Dic17—22no—
35C2×C4⋊Dic17—41no—
36C2×C4⋊Dic17—41no—
37C2×C4⋊Dic17C2×C412yes—
38C2×#63225C2×C411yescharacteristic
39C2×C4×Dic17D411yescharacteristic
40C22⋊#3624—22no—
41#10587551—24no—
42(C2×#595)⋊C4—41no—
43#10587542—41no—
44C4⋊#3624—41no—
45C17×#95C2×C412yes—
46#10587502—22no—
47#10587502—22no—
48C24×C17C22⋊C411yescharacteristic
49C23×D17C2×D411yescharacteristic
50C22×#595—42no—
51C22×C4×C17—21no—
52C22×C4×C17—21no—
53C22×C4×C17—22no—
54C22×C4×C17—42no—
55C22×C4×C17C22⋊C411yescharacteristic
56C22×C4×C17C22×C411yescharacteristic
57C2×C22⋊D17—22no—
58C2×C22⋊D17—22no—
59C2×C22⋊D17—41no—
60C22×Dic17—22no—
61C22×Dic17—42no—
62C22×Dic17—82no—
63C22×Dic17C22⋊C411yescharacteristic
64C22×Dic17C22⋊C411yescharacteristic
65C22×Dic17C2×D411yescharacteristic
66C2×C4×D17—21no—
67C2×C4×D17—21no—
68C2×C4×D17—42no—
69C22⋊#595—24no—
70C22⋊#595—42no—
71C2×#3624—42no—
72C4×#595—82no—
73C4⋊C4×C17—42no—
74C22⋊C4×C17—42no—
75C22⋊Dic17—41no—
76#63227—41no—
77#63227—82no—
78C4⋊Dic17—41no—
79C4⋊Dic17—41no—
80C4⋊Dic17—42no—
81C4⋊Dic17—82no—
82#63225—41no—
83C4×Dic17—21no—
84C4×Dic17—21no—
85#11786—171nomaximal, Sylow
86C23×C17—21no—
87C23×C17—21no—
88C23×C17—41no—
89C23×C17—41no—
90C23×C17#10412yes—
91C23×C17C2×C22⋊C411yescharacteristic
92C22×D17—21no—
93C22×D17—21no—
94C22×D17—41no—
95C22×D17—41no—
96C22×D17#13712yes—
97C2×#595—44no—
98C2×#595—82no—
99C2×#595—82no—
100C2×C4×C17—22no—
101C2×C4×C17—21no—
102C2×C4×C17—42no—
103C2×C4×C17—42no—
104C2×C4×C17—41no—
105C2×C4×C17—42no—
106C2×C4×C17—42no—
107C2×C4×C17—42no—
108C2×C4×C17#9911yescharacteristic
109C2×C4×C17#9911yescharacteristic
110C22⋊D17—44no—
111C2×Dic17—21no—
112C2×Dic17—21no—
113C2×Dic17—21no—
114C2×Dic17—21no—
115C2×Dic17—21no—
116C2×Dic17—41no—
117C2×Dic17—41no—
118C2×Dic17—42no—
119C2×Dic17—42no—
120C2×Dic17—42no—
121C2×Dic17—84no—
122C4×D17—42no—
123C4×D17—81no—
124#3624—82no—
125#2487—171no—
126C4×#99—171no—
127#1466—171no—
128#1352—174no—
129C22×C17—21no—
130C22×C17—21no—
131C22×C17—22no—
132C22×C17—42no—
133C22×C17—42no—
134C22×C17—41no—
135C22×C17—41no—
136C22×C17C2×#9911yescharacteristic
137C22×C17#41911yescharacteristic
138C22×C17C2×#10411yescharacteristic
139C2×D17—22no—
140C2×D17—41no—
141C2×D17—41no—
142C2×D17—42no—
143C2×D17—81no—
144#595—84no—
145C4×C17—21no—
146C4×C17—41no—
147C4×C17—82no—
148C4×C17#35212yes—
149Dic17—41no—
150Dic17—41no—
151Dic17—41no—
152Dic17—82no—
153C2×C4×D4—171no—
154C22×C4⋊C4—171no—
155#432—341no—
156C2×#99—341no—
157#400—172no—
158#399—172no—
159#389—341no—
160#386—341no—
161#385—341no—
162#380—341no—
163#380#59511yescharacteristic, complemented
164C4×C22⋊C4—341no—
165#342—172no—
166#323—172no—
167#323—341no—
168C2×C17—21no—
169C2×C17—21no—
170C2×C17—42no—
171C2×C17#150811yescharacteristic
172C2×C17C2×#35211yescharacteristic
173C2×C17#212811yescharacteristic
174D17—42no—
175C22×D4—171no—
176C23×C4—171no—
177C23×C4—341no—
178C23×C4C2×#59511yescharacteristic
179C4×D4—681no—
180C4×D4—681no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4—171no—
183C2×C4⋊C4—172no—
184C2×C4⋊C4—341no—
185C2×C4⋊C4—342no—
186C2×C4⋊C4—681no—
187C2×C4⋊C4—681no—
188C2×C22⋊C4—21no—
189C2×C22⋊C4—171no—
190C2×C22⋊C4—171no—
191C2×C22⋊C4—342no—
192C2×C22⋊C4—342no—
193C2×C42—171no—
194C2×C42—681no—
195C4⋊C8—681no—
196#99—344no—
197C22⋊C8—342no—
198#97—681no—
199#95—342no—
200#95—342no—
201#95—681no—
202#95C2×#59512yes—
203C17#1178611yescharacteristic, complemented, Sylow
204C24—171no—
205C24C22⋊#59511yescharacteristic
206C2×D4—342no—
207C2×D4—342no—
208C2×D4—681no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—22no—
212C22×C4—42no—
213C22×C4—171no—
214C22×C4—171no—
215C22×C4—171no—
216C22×C4—341no—
217C22×C4—341no—
218C22×C4—342no—
219C22×C4—682no—
220C22×C4—682no—
221C22×C4—682no—
222C22×C4—1362no—
223C22×C4C22⋊#59511yescharacteristic
224C22×C4C22×#59511yescharacteristic
225C2×C8—682no—
226C4⋊C4—42no—
227C4⋊C4—681no—
228C4⋊C4—682no—
229C4⋊C4—681no—
230C4⋊C4—681no—
231C4⋊C4—1362no—
232C22⋊C4—42no—
233C22⋊C4—344no—
234C22⋊C4—681no—
235C22⋊C4—681no—
236C22⋊C4—682no—
237C22⋊C4—1362no—
238C42—341no—
239C42—341no—
240C42—1362no—
241C23—21no—
242C23—21no—
243C23—41no—
244C23—41no—
245C23—172no—
246C23—341no—
247C23—341no—
248C23—681no—
249C23—681no—
250C23#1058754812yes—
251C23C2×C22⋊#59511yescharacteristic
252D4—684no—
253C2×C4—22no—
254C2×C4—21no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—41no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—341no—
262C2×C4—341no—
263C2×C4—341no—
264C2×C4—341no—
265C2×C4—341no—
266C2×C4—682no—
267C2×C4—681no—
268C2×C4—681no—
269C2×C4—682no—
270C2×C4—682no—
271C2×C4—684no—
272C2×C4—682no—
273C2×C4—1361no—
274C2×C4—1364no—
275C2×C4—1362no—
276C2×C4—1362no—
277C2×C4#1058753911yescharacteristic
278C2×C4#1058753911yescharacteristic
279C8—1362no—
280C22—21no—
281C22—21no—
282C22—22no—
283C22—42no—
284C22—42no—
285C22—41no—
286C22—41no—
287C22—342no—
288C22—682no—
289C22—681no—
290C22—681no—
291C22—1361no—
292C22C2×#1058753911yescharacteristic
293C22#1176380211yescharacteristic
294C22C2×#1058754811yescharacteristic
295C4—21no—
296C4—41no—
297C4—82no—
298C4—681no—
299C4—681no—
300C4—681no—
301C4—1364no—
302C4—1362no—
303C4#1176371212yes—
304C2—21no—
305C2—21no—
306C2—42no—
307C2—682no—
308C2#1454418311yescharacteristic
309C2C2×#1176371211yescharacteristic
310C2#1454506511yescharacteristic
subgroupG/H
centerC22C2×#10587539
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC17×#380C4
socleC22×C17C2×#99
prime radicalC22×C22⋊D17D4
cosocleC2×#63227C23
hypercenter#380#595
hypocenterC17#11786
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
3. #14543780C2semidirect
12. C22×C4⋊Dic17C4semidirect
13. #11762749C4semidirect
19. C17×#380C4semidirect
163. #380#595semidirect
203. C17#11786semidirect

Maximal subgroups

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

subgroupindex
C4×#105875512
#145440432
#145437802
#145331022
#1178617