Finite Group Databasebeta

← #17950239

Subgroups — #17950239

Order 4352.

494 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 100 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#14544676C211yesmaximal, characteristic
2#14544641C211yesmaximal, characteristic
3#14543603C214yesmaximal, complemented
4#14537131C211yesmaximal, characteristic
5C2×#10587544—21no—
6C2×#10587543—21no—
7C2×#10587543—21no—
8#11763675—21no—
9#11763675C2212yes—
10#11763675C2212yes—
11C2×#10587632—21no—
12C2×C42×D17C2211yescharacteristic
13#11762716—21no—
14#11762705—21no—
15#11762705C2212yes—
16#11762679C411yescharacteristic
17#11762666—21no—
18#11762666C412yes—
19C2×C17×C4⋊Q8C411yescharacteristic
20C22×Q8×C17—21no—
21C22×C4×D17C2×C411yescharacteristic
22C22×C4×D17D411yescharacteristic
23C22×C4×D17D411yescharacteristic
24C22×#3624—22no—
25C22×#3624—22no—
26C17×C4⋊Q8—42no—
27C2×C4⋊C4×C17—21no—
28C2×C4⋊C4×C17C2×C412yes—
29C2×C42×C17C2×C411yescharacteristic
30#10587632—42no—
31#10587632—42no—
32C2×#63227—22no—
33C2×C4⋊Dic17—21no—
34C2×C4⋊Dic17—21no—
35C2×C4⋊Dic17C2×C412yes—
36C2×#63225—22no—
37C2×C4×Dic17D411yescharacteristic
38C2×C4×Dic17D411yescharacteristic
39C2×C4×Dic17C2311yescharacteristic
40C42×D17—42no—
41#10587544—42no—
42#10587543—42no—
43#10587543—42no—
44#10587502—22no—
45#10587502—22no—
46C23×D17C22⋊C411yescharacteristic
47C2×Q8×C17—42no—
48C2×Q8×C17—42no—
49C2×Q8×C17—42no—
50C22×C4×C17—22no—
51C22×C4×C17C22⋊C411yescharacteristic
52C22×C4×C17C22⋊C411yescharacteristic
53C22×C4×C17C22×C411yescharacteristic
54C22×Dic17—22no—
55C22×Dic17C22⋊C411yescharacteristic
56C22×Dic17C2×D411yescharacteristic
57C22×Dic17C2×D411yescharacteristic
58C2×C4×D17—22no—
59C2×C4×D17—22no—
60C2×C4×D17—22no—
61C2×C4×D17—22no—
62C2×C4×D17—41no—
63C2×C4×D17—41no—
64C2×C4×D17—41no—
65C2×C4×D17—41no—
66C2×C4×D17D812yes—
67C2×C4×D17SD1612yes—
68C2×#3624—42no—
69C2×#3624—42no—
70C2×#3624—42no—
71C2×#3624—42no—
72C2×#3624—42no—
73C2×#3624—42no—
74C4⋊C4×C17—42no—
75C4⋊C4×C17—42no—
76C42×C17—22no—
77#63227—44no—
78C4⋊Dic17—24no—
79C4⋊Dic17—42no—
80C4⋊Dic17—42no—
81#63225—42no—
82#63225—42no—
83C4×Dic17—22no—
84C4×Dic17—41no—
85C4×Dic17—41no—
86#7728—171nomaximal, Sylow
87C23×C17C2×C22⋊C411yescharacteristic
88C22×D17—21no—
89C22×D17—21no—
90C22×D17—21no—
91C22×D17—21no—
92C22×D17—21no—
93C22×D17—21no—
94C22×D17#10212yes—
95Q8×C17—84no—
96C2×C4×C17—21no—
97C2×C4×C17—21no—
98C2×C4×C17—21no—
99C2×C4×C17—21no—
100C2×C4×C17—21no—
101C2×C4×C17—21no—
102C2×C4×C17—42no—
103C2×C4×C17—42no—
104C2×C4×C17—42no—
105C2×C4×C17#9912yes—
106C2×C4×C17#10212yes—
107C2×C4×C17#13112yes—
108C2×Dic17—21no—
109C2×Dic17—21no—
110C2×Dic17—21no—
111C2×Dic17—21no—
112C2×Dic17—21no—
113C2×Dic17—21no—
114C2×Dic17—42no—
115C2×Dic17—42no—
116C2×Dic17—42no—
117C2×Dic17#10112yes—
118C2×Dic17C2×D811yescharacteristic
119C2×Dic17C2×SD1611yescharacteristic
120C2×Dic17#13712yes—
121C4×D17—42no—
122C4×D17—42no—
123C4×D17—44no—
124C4×D17—44no—
125#3624—82no—
126#3624—82no—
127#2857—171no—
128#1817—171no—
129#1797—171no—
130#1271—174no—
131C22×C17#40811yescharacteristic
132C22×C17C2×#9911yescharacteristic
133C22×C17C2×#10111yescharacteristic
134C22×C17C2×#10211yescharacteristic
135C22×C17#41911yescharacteristic
136C22×C17#42111yescharacteristic
137C22×C17#42111yescharacteristic
138C2×D17—22no—
139C2×D17—22no—
140C2×D17—22no—
141C2×D17—41no—
142C2×D17—41no—
143C2×D17—41no—
144C2×D17—41no—
145C4×C17—22no—
146C4×C17—22no—
147C4×C17—22no—
148C4×C17—82no—
149Dic17—22no—
150Dic17—22no—
151Dic17—21no—
152Dic17—21no—
153Dic17—82no—
154C2×C4⋊Q8#59511yescharacteristic
155C2×C22⋊Q8—341no—
156C22×C42—171no—
157C2×C4⋊C8—341no—
158C2×C22⋊C8—341no—
159C2×C22⋊C8—341no—
160#391—341no—
161#389—172no—
162#389—341no—
163#384—171no—
164#380—172no—
165#380—341no—
166#336—172no—
167#336—172no—
168#336—341no—
169C2×C17#147211yescharacteristic
170C2×C17#148011yescharacteristic
171C2×C17#149711yescharacteristic
172C2×C17#151111yescharacteristic
173C2×C17#151911yescharacteristic
174C2×C17#153711yescharacteristic
175C2×C17#154611yescharacteristic
176D17—42no—
177C22×Q8—21no—
178C23×C4—171no—
179C23×C4—171no—
180C23×C4—171no—
181C22×C8—342no—
182C22×C8—342no—
183C4⋊Q8—42no—
184C22⋊Q8—682no—
185C22⋊Q8—682no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—172no—
188C2×C4⋊C4—342no—
189C2×C4⋊C4—341no—
190C2×C4⋊C4—341no—
191C2×C4⋊C4C2×#59512yes—
192C2×C22⋊C4—342no—
193C2×C42—171no—
194C2×C42—171no—
195C2×C42—171no—
196C2×C42—682no—
197C2×C42C2×#59511yescharacteristic
198C4⋊C8—682no—
199C22⋊C8—682no—
200C22⋊C8—682no—
201#95—342no—
202#95—342no—
203C17#772811yescharacteristic, complemented, Sylow
204C24—171no—
205C2×Q8—42no—
206C2×Q8—42no—
207C2×Q8—42no—
208C22×C4—22no—
209C22×C4—171no—
210C22×C4—171no—
211C22×C4—171no—
212C22×C4—172no—
213C22×C4—172no—
214C22×C4—342no—
215C22×C4—342no—
216C22×C4—342no—
217C22×C4—342no—
218C22×C4—342no—
219C22×C4—681no—
220C22×C4—681no—
221C22×C4—681no—
222C22×C4—681no—
223C22×C4C22⋊#59511yescharacteristic
224C22×C4C22⋊#59511yescharacteristic
225C22×C4C22×#59511yescharacteristic
226C2×C8—682no—
227C2×C8—682no—
228C2×C8—682no—
229C2×C8—682no—
230C2×C8—682no—
231C2×C8—682no—
232C4⋊C4—42no—
233C4⋊C4—42no—
234C4⋊C4—344no—
235C4⋊C4—682no—
236C4⋊C4—682no—
237C4⋊C4—682no—
238C4⋊C4—682no—
239C22⋊C4—684no—
240C42—22no—
241C42—342no—
242C42—681no—
243C42—681no—
244C23—172no—
245C23—341no—
246C23—341no—
247C23—341no—
248C23—341no—
249C23—341no—
250C23—341no—
251C23C2×C22⋊#59511yescharacteristic
252Q8—84no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—172no—
263C2×C4—171no—
264C2×C4—171no—
265C2×C4—172no—
266C2×C4—341no—
267C2×C4—341no—
268C2×C4—341no—
269C2×C4—341no—
270C2×C4—341no—
271C2×C4—341no—
272C2×C4—682no—
273C2×C4—682no—
274C2×C4—684no—
275C2×C4—684no—
276C2×C4—682no—
277C2×C4—682no—
278C2×C4—682no—
279C2×C4#1058754712yes—
280C2×C4#1058755112yes—
281C2×C4#1058768012yes—
282C8—1362no—
283C8—1362no—
284C22—342no—
285C22—342no—
286C22—342no—
287C22—681no—
288C22—681no—
289C22—681no—
290C22—681no—
291C22#1176378411yescharacteristic
292C22C2×#1058755111yescharacteristic
293C22D17⋊#10111yescharacteristic
294C22C2×#1058754711yescharacteristic
295C22#1176380211yescharacteristic
296C22#1176380711yescharacteristic
297C22#1176380811yescharacteristic
298C4—22no—
299C4—22no—
300C4—22no—
301C4—82no—
302C4—342no—
303C4—341no—
304C4—341no—
305C4—342no—
306C4—1362no—
307C2—682no—
308C2#1454406411yescharacteristic
309C2#1454409111yescharacteristic
310C2#1454414811yescharacteristic
311C2#1454419411yescharacteristic
312C2#1454422011yescharacteristic
313C2#1454427611yescharacteristic
314C2#1454429411yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC2×C17×C4⋊Q8C4
socleC23×C17C2×C22⋊C4
prime radicalC23×D17C22⋊C4
cosocleC2×C4×Dic17C23
hypercenterC2×C4⋊Q8#595
hypocenterC17#7728
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. #14543603C2semidirect
203. C17#7728semidirect

Maximal subgroups

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

subgroupindex
#145446762
#145446412
#145436032
#145371312
#772817