Finite Group Databasebeta

← #17959782

Subgroups — #17959782

Order 4352.

452 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 80 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#14544644C211yesmaximal, characteristic
2#14544023C211yesmaximal, characteristic
3#14543781C214yesmaximal, complemented
4#14533095C211yesmaximal, characteristic
5#11763826—21no—
6C2×#10587551—21no—
7#11763751—21no—
8#11763687C2212yes—
9#11763653C2212yes—
10#11763652—21no—
11C2×C4×C22⋊D17C2211yescharacteristic
12#11762747C412yescomplemented
13#11762744C2212yes—
14#11762705—21no—
15#11762688—21no—
16#11762682—21no—
17#11762669C411yescharacteristic, complemented
18#11762666—21no—
19C22×C4⋊C4×C17C411yescharacteristic, complemented
20C23×C4×C17—21no—
21C23×C4×C17C2×C411yescharacteristic
22C22×C22⋊D17D411yescharacteristic
23C22×C4×D17D411yescharacteristic
24C2×C22⋊#595—22no—
25C2×C4⋊#595—41no—
26C2×C4⋊C4×C17—21no—
27C2×C4⋊C4×C17—41no—
28C2×C4⋊C4×C17—41no—
29C2×C4⋊C4×C17C2×C412yes—
30C2×C22⋊Dic17—21no—
31C2×C22⋊Dic17D411yescharacteristic
32C4×C22⋊D17—41no—
33C4×C22⋊D17—41no—
34C2×#63227—22no—
35C2×#63227C2311yescharacteristic
36C2×C4⋊Dic17—21no—
37C2×#63225—22no—
38C2×#63225C2×C411yescharacteristic
39C2×C4×Dic17D411yescharacteristic
40C22⋊#3624—22no—
41#10587551—42no—
42(C2×#595)⋊C4—41no—
43#10587544—41no—
44C4×#3624—41no—
45#10587502—22no—
46#10587502—22no—
47#10587502C2×C412yes—
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×C17—42no—
56C22×C4×C17—82no—
57C22×C4×C17C22⋊C411yescharacteristic
58C22×C4×C17C22×C411yescharacteristic
59C2×C22⋊D17—41no—
60C2×C22⋊D17—41no—
61C2×C22⋊D17SD1612yes—
62C2×C22⋊D17Q1612yes—
63C22×Dic17—22no—
64C22×Dic17C22⋊C411yescharacteristic
65C22×Dic17C22⋊C411yescharacteristic
66C22×Dic17C2×D411yescharacteristic
67C2×C4×D17—21no—
68C2×C4×D17—21no—
69C2×C4×D17—42no—
70C22⋊#595—42no—
71C22⋊#595—42no—
72C2×#3624—42no—
73C4⋊#595—82no—
74C4⋊C4×C17—42no—
75C4⋊C4×C17—41no—
76C4⋊C4×C17—41no—
77C22⋊Dic17—41no—
78C22⋊Dic17—42no—
79#63227—41no—
80#63227—82no—
81C4⋊Dic17—42no—
82#63225—41no—
83#63225—82no—
84C4×Dic17—21no—
85C4×Dic17—21no—
86#11899—171nomaximal, Sylow
87C23×C17—21no—
88C23×C17—21no—
89C23×C17—41no—
90C23×C17—41no—
91C23×C17#10312yes—
92C23×C17C2×C22⋊C411yescharacteristic
93C22×D17—21no—
94C22×D17—21no—
95C22×D17—41no—
96C22×D17—41no—
97C22×D17C2×SD1611yescharacteristic
98C22×D17C2×Q1611yescharacteristic
99C2×#595—82no—
100C2×#595—82no—
101C2×#595—82no—
102C2×C4×C17—22no—
103C2×C4×C17—21no—
104C2×C4×C17—42no—
105C2×C4×C17—42no—
106C2×C4×C17—41no—
107C2×C4×C17—42no—
108C2×C4×C17—42no—
109C2×C4×C17—42no—
110C2×C4×C17—84no—
111C2×C4×C17#9911yescharacteristic
112C2×C4×C17#9911yescharacteristic
113C22⋊D17—42no—
114C22⋊D17—42no—
115C2×Dic17—21no—
116C2×Dic17—21no—
117C2×Dic17—21no—
118C2×Dic17—21no—
119C2×Dic17—41no—
120C2×Dic17—41no—
121C2×Dic17—42no—
122C2×Dic17—42no—
123C2×Dic17—42no—
124C2×Dic17#10312yes—
125C4×D17—42no—
126C4×D17—81no—
127#3624—82no—
128#2487—171no—
129#1799—171no—
130#1460—171no—
131#1352—174no—
132C22×C17—21no—
133C22×C17—21no—
134C22×C17—22no—
135C22×C17—42no—
136C22×C17—42no—
137C22×C17—41no—
138C22×C17—41no—
139C22×C17C2×#9911yescharacteristic
140C22×C17C2×#10311yescharacteristic
141C22×C17#42111yescharacteristic
142C2×D17—21no—
143C2×D17—21no—
144C2×D17—41no—
145C2×D17—41no—
146C2×D17—41no—
147C2×D17—41no—
148C2×D17—81no—
149#595—162no—
150C4×C17—21no—
151C4×C17—41no—
152C4×C17—82no—
153C4×C17#35212yes—
154Dic17—22no—
155Dic17—41no—
156Dic17—41no—
157Dic17—82no—
158C2×C4×D4—171no—
159C22×C4⋊C4#59511yescharacteristic, complemented
160#431—341no—
161C2×#99—341no—
162#400—172no—
163#399—172no—
164#389—341no—
165#386—341no—
166#385—341no—
167#380—171no—
168#380—341no—
169#380—341no—
170#342—172no—
171#323—172no—
172#323—341no—
173C2×C17—21no—
174C2×C17—21no—
175C2×C17—42no—
176C2×C17#152011yescharacteristic
177C2×C17C2×#35211yescharacteristic
178C2×C17#212811yescharacteristic
179D17—41no—
180D17—41no—
181C22×D4—171no—
182C23×C4—21no—
183C23×C4—171no—
184C23×C4C2×#59511yescharacteristic
185C4×D4—681no—
186C4×D4—681no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—41no—
189C2×C4⋊C4—41no—
190C2×C4⋊C4—171no—
191C2×C4⋊C4—341no—
192C2×C4⋊C4—342no—
193C2×C4⋊C4—681no—
194C2×C4⋊C4C2×#59512yes—
195C2×C22⋊C4—171no—
196C2×C22⋊C4—171no—
197C2×C22⋊C4—341no—
198C2×C22⋊C4—342no—
199C2×C22⋊C4—342no—
200C2×C42—171no—
201C4⋊C8—681no—
202#99—682no—
203C22⋊C8—342no—
204C4×C8—681no—
205#95—172no—
206#95—342no—
207#95—342no—
208#95—681no—
209C17#1189911yescharacteristic, complemented, Sylow
210C24—171no—
211C24C22⋊#59511yescharacteristic
212C2×D4—172no—
213C2×D4—172no—
214C2×D4—681no—
215C2×D4—681no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—22no—
219C22×C4—42no—
220C22×C4—42no—
221C22×C4—82no—
222C22×C4—171no—
223C22×C4—171no—
224C22×C4—171no—
225C22×C4—341no—
226C22×C4—341no—
227C22×C4—342no—
228C22×C4—682no—
229C22×C4—682no—
230C22×C4C22⋊#59511yescharacteristic
231C22×C4C22×#59511yescharacteristic
232C2×C8—682no—
233C4⋊C4—42no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—681no—
237C4⋊C4—682no—
238C4⋊C4—1362no—
239C4⋊C4—1362no—
240C22⋊C4—681no—
241C22⋊C4—681no—
242C22⋊C4—682no—
243C22⋊C4—682no—
244C22⋊C4—682no—
245C22⋊C4—1362no—
246C42—341no—
247C42—341no—
248C23—21no—
249C23—21no—
250C23—41no—
251C23—41no—
252C23—171no—
253C23—171no—
254C23—341no—
255C23—341no—
256C23—681no—
257C23—681no—
258C23#1058754912yes—
259C23C2×C22⋊#59511yescharacteristic
260D4—682no—
261D4—682no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—41no—
267C2×C4—42no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4—84no—
271C2×C4—172no—
272C2×C4—341no—
273C2×C4—341no—
274C2×C4—341no—
275C2×C4—341no—
276C2×C4—682no—
277C2×C4—681no—
278C2×C4—681no—
279C2×C4—682no—
280C2×C4—682no—
281C2×C4—682no—
282C2×C4—1361no—
283C2×C4—1362no—
284C2×C4—1362no—
285C2×C4—1362no—
286C2×C4#1058755111yescharacteristic
287C2×C4#1058755111yescharacteristic
288C8—1362no—
289C22—21no—
290C22—21no—
291C22—22no—
292C22—42no—
293C22—42no—
294C22—41no—
295C22—41no—
296C22—341no—
297C22—341no—
298C22—681no—
299C22—681no—
300C22—681no—
301C22—681no—
302C22—1361no—
303C22C2×#1058755111yescharacteristic
304C22C2×#1058754911yescharacteristic
305C22#1176380811yescharacteristic
306C4—21no—
307C4—41no—
308C4—82no—
309C4—2722no—
310C4—342no—
311C4—681no—
312C4—681no—
313C4—1362no—
314C4#1176371112yes—
315C2—21no—
316C2—21no—
317C2—42no—
318C2—681no—
319C2—681no—
320C2#1454422411yescharacteristic
321C2C2×#1176371111yescharacteristic
322C2#1454506311yescharacteristic
subgroupG/H
centerC22C2×#10587551
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC22×C4⋊C4×C17C4
socleC22×C17C2×#99
prime radicalC22×C22⋊D17D4
cosocleC2×#63227C23
hypercenterC22×C4⋊C4#595
hypocenterC17#11899
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #14543781C2semidirect
12. #11762747C4semidirect
17. #11762669C4semidirect
19. C22×C4⋊C4×C17C4semidirect
159. C22×C4⋊C4#595semidirect
209. C17#11899semidirect

Maximal subgroups

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

subgroupindex
#145446442
#145440232
#145437812
#145330952
#1189917