Finite Group Databasebeta

← #17959472

Subgroups — #17959472

Order 4352.

382 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 66 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#14544681C211yesmaximal, characteristic
2#14544037C211yesmaximal, characteristic
3#14543780C214yesmaximal
4#14534608C211yesmaximal, characteristic
5#11763829—21no—
6#11763752—21no—
7#11763687—21no—
8#11763687C2212yes—
9#11763655—21no—
10#11763653C2212yes—
11C2×#10587555C411yescharacteristic, complemented
12C2×#10587558C2211yescharacteristic
13#11762749C412yescomplemented
14#11762746C2212yes—
15#11762730—21no—
16#11762722—21no—
17#11762708—21no—
18#11762666—21no—
19C17×#382C411yescharacteristic, complemented
20C22×C4×D17D411yescharacteristic
21C22×Dic34—21no—
22C2×C22⋊#595—22no—
23C2×C4⋊C4×C17—21no—
24C2×C42×C17C2×C411yescharacteristic
25C2×#63227—22no—
26C2×#63227D411yescharacteristic
27C2×#63227C2311yescharacteristic
28C2×C4⋊Dic17—21no—
29C2×C4⋊Dic17—22no—
30C2×C4⋊Dic17C2×C412yes—
31C2×#63225C2×C411yescharacteristic
32C2×#63225D411yescharacteristic
33C2×C4×Dic17D411yescharacteristic
34#10587558—41no—
35#10587558—41no—
36#10587555—41no—
37#10587555—41no—
38C22⋊#3624—22no—
39(C2×#595)⋊C4—41no—
40(C2×#595)⋊C4—41no—
41#10587544—41no—
42#10587542—41no—
43C17×#95—21no—
44C17×#95C2×C412yes—
45#10587502—22no—
46#10587502—22no—
47C23×D17C2×D411yescharacteristic
48C22×#595—42no—
49C22×C4×C17—22no—
50C22×C4×C17C22⋊C411yescharacteristic
51C22×C4×C17C22⋊C411yescharacteristic
52C22×C4×C17C22×C411yescharacteristic
53C22×Dic17—22no—
54C22×Dic17C22⋊C411yescharacteristic
55C22×Dic17C22⋊C411yescharacteristic
56C22×Dic17C2×D411yescharacteristic
57C2×C4×D17—22no—
58C2×C4×D17—21no—
59C2×C4×D17—21no—
60C2×C4×D17—41no—
61C2×Dic34—42no—
62C2×Dic34—82no—
63C22⋊#595—42no—
64C22⋊#595—42no—
65C2×#3624—42no—
66C4⋊C4×C17—42no—
67C42×C17—21no—
68C42×C17—21no—
69#63227—41no—
70#63227—41no—
71#63227—82no—
72C4⋊Dic17—41no—
73C4⋊Dic17—41no—
74C4⋊Dic17—42no—
75C4⋊Dic17—82no—
76#63225—41no—
77#63225—41no—
78C4×Dic17—21no—
79C4×Dic17—21no—
80#11813—171nomaximal, Sylow
81C23×C17C2×C22⋊C411yescharacteristic
82C22×D17—21no—
83C22×D17—21no—
84C22×D17—41no—
85C22×D17—41no—
86C22×D17#13712yes—
87C2×#595—82no—
88C2×#595—82no—
89C2×#595—82no—
90C2×C4×C17—21no—
91C2×C4×C17—21no—
92C2×C4×C17—21no—
93C2×C4×C17—21no—
94C2×C4×C17—41no—
95C2×C4×C17—41no—
96C2×C4×C17—42no—
97C2×C4×C17—42no—
98C2×C4×C17—42no—
99C2×C4×C17#9911yescharacteristic
100C2×C4×C17#9911yescharacteristic
101C2×Dic17—21no—
102C2×Dic17—21no—
103C2×Dic17—21no—
104C2×Dic17—21no—
105C2×Dic17—21no—
106C2×Dic17—41no—
107C2×Dic17—41no—
108C2×Dic17—42no—
109C2×Dic17—42no—
110C2×Dic17—42no—
111C4×D17—42no—
112C4×D17—42no—
113Dic34—84no—
114#3624—82no—
115#2628—171no—
116#1820—171no—
117#1464—171no—
118#1352—174no—
119C22×C17—21no—
120C22×C17—21no—
121C22×C17C2×#9911yescharacteristic
122C22×C17#41911yescharacteristic
123C22×C17#42111yescharacteristic
124C2×D17—22no—
125C2×D17—41no—
126C2×D17—41no—
127C2×D17—42no—
128C2×D17—81no—
129#595—162no—
130C4×C17—21no—
131C4×C17—21no—
132C4×C17—41no—
133C4×C17—41no—
134C4×C17—82no—
135Dic17—41no—
136Dic17—41no—
137Dic17—41no—
138Dic17—82no—
139C2×C4⋊Q8—171no—
140C2×#117—171no—
141#432—341no—
142#400—172no—
143#399—172no—
144#395—341no—
145#393—341no—
146#389—341no—
147#382#59511yescharacteristic, complemented
148#381—341no—
149#380—341no—
150#342—172no—
151#342—341no—
152#324—341no—
153#323—172no—
154C2×C17—21no—
155C2×C17—21no—
156C2×C17#151111yescharacteristic
157C2×C17#212311yescharacteristic
158C2×C17#212811yescharacteristic
159D17—42no—
160C22×Q8—341no—
161C23×C4—171no—
162C4⋊Q8—681no—
163C4⋊Q8—681no—
164#117—681no—
165#117—681no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4—171no—
168C2×C4⋊C4—171no—
169C2×C4⋊C4—172no—
170C2×C4⋊C4—341no—
171C2×C4⋊C4—342no—
172C2×C22⋊C4—171no—
173C2×C22⋊C4—171no—
174C2×C22⋊C4—342no—
175C2×C22⋊C4—342no—
176C2×C42—171no—
177C2×C42C2×#59511yescharacteristic
178C4⋊C8—681no—
179C22⋊C8—342no—
180#97—681no—
181#95—21no—
182#95—342no—
183#95—342no—
184#95—681no—
185#95—681no—
186#95C2×#59512yes—
187C17#1181311yescharacteristic, complemented, Sylow
188C24—171no—
189C2×Q8—682no—
190C2×Q8—1362no—
191C22×C4—22no—
192C22×C4—171no—
193C22×C4—171no—
194C22×C4—171no—
195C22×C4—342no—
196C22×C4—341no—
197C22×C4—341no—
198C22×C4—342no—
199C22×C4—681no—
200C22×C4—682no—
201C22×C4C22⋊#59511yescharacteristic
202C22×C4C22⋊#59511yescharacteristic
203C22×C4C22×#59511yescharacteristic
204C2×C8—682no—
205C4⋊C4—42no—
206C4⋊C4—681no—
207C4⋊C4—681no—
208C4⋊C4—682no—
209C4⋊C4—681no—
210C4⋊C4—681no—
211C4⋊C4—1362no—
212C22⋊C4—681no—
213C22⋊C4—681no—
214C22⋊C4—682no—
215C22⋊C4—682no—
216C22⋊C4—1362no—
217C42—21no—
218C42—21no—
219C42—341no—
220C42—341no—
221C23—172no—
222C23—341no—
223C23—341no—
224C23—681no—
225C23—681no—
226C23C2×C22⋊#59511yescharacteristic
227Q8—1364no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—341no—
238C2×C4—341no—
239C2×C4—341no—
240C2×C4—341no—
241C2×C4—341no—
242C2×C4—682no—
243C2×C4—682no—
244C2×C4—681no—
245C2×C4—681no—
246C2×C4—682no—
247C2×C4—682no—
248C2×C4—682no—
249C2×C4—1362no—
250C2×C4—1362no—
251C2×C4—1362no—
252C2×C4#1058753911yescharacteristic
253C2×C4#1058753911yescharacteristic
254C8—1362no—
255C22—21no—
256C22—21no—
257C22—342no—
258C22—682no—
259C22—681no—
260C22—681no—
261C22—1361no—
262C22C2×#1058753911yescharacteristic
263C22#1176380211yescharacteristic
264C22#1176380711yescharacteristic
265C4—21no—
266C4—21no—
267C4—41no—
268C4—41no—
269C4—82no—
270C4—2722no—
271C4—681no—
272C4—681no—
273C4—681no—
274C4—1362no—
275C2—21no—
276C2—21no—
277C2—682no—
278C2#1454419211yescharacteristic
279C2#1454504811yescharacteristic
280C2#1454506511yescharacteristic
subgroupG/H
centerC22C2×#10587539
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC17×#382C4
socleC22×C17C2×#99
prime radicalC23×D17C2×D4
cosocleC2×#63227C23
hypercenter#382#595
hypocenterC17#11813
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ #382

Complements

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

NH ≅ G/Ntype
11. C2×#10587555C4semidirect
13. #11762749C4semidirect
19. C17×#382C4semidirect
147. #382#595semidirect
187. C17#11813semidirect

Maximal subgroups

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

subgroupindex
#145446812
#145440372
#145437802
#145346082
#1181317