Finite Group Databasebeta

← #17950090

Subgroups — #17950090

Order 4352.

562 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 562 conjugacy classes of subgroups — too many to draw. Only its 116 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×#10587543C211yesmaximal, characteristic
2#14544448C211yesmaximal, characteristic
3#14543604C214yesmaximal, complemented
4#14537131C211yesmaximal, characteristic
5C22×#63243—21no—
6C2×#10587543—21no—
7C2×C4×#3624—21no—
8#11763675—21no—
9#11763675C2212yes—
10#11763675C2212yes—
11C2×#10587632C412yes—
12C2×C42×D17C2211yescharacteristic
13#11762716C2212yes—
14#11762705—21no—
15#11762705—21no—
16#11762679C411yescharacteristic
17#11762666—21no—
18#11762666—21no—
19C2×C17×C4⋊Q8C411yescharacteristic
20C22×Q8×C17C2×C412yes—
21C22×C4×D17C2×C411yescharacteristic
22C22×C4×D17D411yescharacteristic
23C22×C4×D17D411yescharacteristic
24C22×#3624—22no—
25C22×#3624—22no—
26C2×#63243—24no—
27C2×#63243—42no—
28C2×#63243—42no—
29C17×C4⋊Q8—42no—
30C2×C4⋊C4×C17—21no—
31C2×C4⋊C4×C17—21no—
32C2×C42×C17C2×C411yescharacteristic
33#10587632—44no—
34C2×#63227—22no—
35C2×C4⋊Dic17—21no—
36C2×C4⋊Dic17—21no—
37C2×C4⋊Dic17C2×C412yes—
38C2×#63225—22no—
39C2×C4×Dic17D411yescharacteristic
40C2×C4×Dic17D411yescharacteristic
41C2×C4×Dic17C2311yescharacteristic
42C42×D17—42no—
43#10587543—24no—
44C4×#3624—42no—
45#10587502—22no—
46#10587502—22no—
47C23×D17C22⋊C411yescharacteristic
48C2×Q8×C17—24no—
49C2×Q8×C17—42no—
50C2×Q8×C17—42no—
51C22×C4×C17—22no—
52C22×C4×C17C22⋊C411yescharacteristic
53C22×C4×C17C22⋊C411yescharacteristic
54C22×C4×C17C22×C411yescharacteristic
55C22×Dic17—22no—
56C22×Dic17C22⋊C411yescharacteristic
57C22×Dic17C2×D411yescharacteristic
58C22×Dic17C2×D411yescharacteristic
59C2×C4×D17—22no—
60C2×C4×D17—22no—
61C2×C4×D17—22no—
62C2×C4×D17—22no—
63C2×C4×D17—22no—
64C2×C4×D17—22no—
65C2×C4×D17—41no—
66C2×C4×D17—41no—
67C2×C4×D17SD1612yes—
68C2×C4×D17Q1612yes—
69C2×#3624—24no—
70C2×#3624—24no—
71C2×#3624—42no—
72C2×#3624—42no—
73C2×#3624—42no—
74C2×#3624—42no—
75#63243—48no—
76C4⋊C4×C17—42no—
77C4⋊C4×C17—42no—
78C42×C17—22no—
79#63227—44no—
80C4⋊Dic17—42no—
81C4⋊Dic17—42no—
82C4⋊Dic17—42no—
83#63225—44no—
84C4×Dic17—22no—
85C4×Dic17—41no—
86C4×Dic17—41no—
87#7687—171nomaximal, Sylow
88C23×C17C2×C22⋊C411yescharacteristic
89C22×D17—21no—
90C22×D17—21no—
91C22×D17—21no—
92C22×D17—21no—
93C22×D17—21no—
94C22×D17—21no—
95C22×D17#10312yes—
96Q8×C17—84no—
97C2×C4×C17—21no—
98C2×C4×C17—21no—
99C2×C4×C17—21no—
100C2×C4×C17—21no—
101C2×C4×C17—42no—
102C2×C4×C17—42no—
103C2×C4×C17—42no—
104C2×C4×C17#9912yes—
105C2×C4×C17#10312yes—
106C2×C4×C17#10412yes—
107C2×C4×C17#10412yes—
108C2×C4×C17#13112yes—
109C2×Dic17—21no—
110C2×Dic17—21no—
111C2×Dic17—21no—
112C2×Dic17—21no—
113C2×Dic17—21no—
114C2×Dic17—21no—
115C2×Dic17—42no—
116C2×Dic17—42no—
117C2×Dic17—42no—
118C2×Dic17#10012yes—
119C2×Dic17C2×SD1611yescharacteristic
120C2×Dic17C2×Q1611yescharacteristic
121C2×Dic17#13712yes—
122C4×D17—24no—
123C4×D17—24no—
124C4×D17—44no—
125C4×D17—44no—
126#3624—44no—
127#3624—44no—
128#2857—171no—
129C4×C22⋊C8—171no—
130#1728—171no—
131#1272—174no—
132C22×C17#40811yescharacteristic
133C22×C17C2×#9911yescharacteristic
134C22×C17C2×#10011yescharacteristic
135C22×C17C2×#10311yescharacteristic
136C22×C17#41911yescharacteristic
137C22×C17C2×#10411yescharacteristic
138C22×C17C2×#10411yescharacteristic
139C2×D17—22no—
140C2×D17—22no—
141C2×D17—22no—
142C2×D17—41no—
143C2×D17—41no—
144C2×D17—41no—
145C2×D17—41no—
146C4×C17—22no—
147C4×C17—22no—
148C4×C17—82no—
149C4×C17#32814yes—
150Dic17—22no—
151Dic17—21no—
152Dic17—21no—
153Dic17—22no—
154Dic17—82no—
155C22×M16—341no—
156C2×C4⋊Q8#59511yescharacteristic
157C2×C22⋊Q8—172no—
158C22×C42—171no—
159C2×C22⋊C8—341no—
160C2×C4×C8—341no—
161#391—172no—
162#389—341no—
163#389—341no—
164#384—171no—
165#380—341no—
166#380—341no—
167#336—172no—
168#336—172no—
169#336—341no—
170C2×C17#147111yescharacteristic
171C2×C17#148511yescharacteristic
172C2×C17#149311yescharacteristic
173C2×C17C2×#32811yescharacteristic
174C2×C17#150811yescharacteristic
175C2×C17#152511yescharacteristic
176C2×C17#154811yescharacteristic
177D17—42no—
178C22×Q8C2×#59512yes—
179C23×C4—171no—
180C23×C4—171no—
181C23×C4—171no—
182C2×M16—344no—
183C2×M16—682no—
184C2×M16—682no—
185C22×C8—342no—
186C22×C8—342no—
187C4⋊Q8—42no—
188C22⋊Q8—684no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—172no—
192C2×C4⋊C4—342no—
193C2×C4⋊C4—341no—
194C2×C4⋊C4—341no—
195C2×C22⋊C4—342no—
196C2×C42—171no—
197C2×C42—171no—
198C2×C42—171no—
199C2×C42—682no—
200C2×C42C2×#59511yescharacteristic
201C22⋊C8—344no—
202C4×C8—682no—
203#95—342no—
204#95—342no—
205C17#768711yescharacteristic, complemented, Sylow
206C24—171no—
207C2×Q8—24no—
208C2×Q8—42no—
209C2×Q8—42no—
210C22×C4—22no—
211C22×C4—171no—
212C22×C4—171no—
213C22×C4—171no—
214C22×C4—172no—
215C22×C4—172no—
216C22×C4—342no—
217C22×C4—342no—
218C22×C4—342no—
219C22×C4—342no—
220C22×C4—342no—
221C22×C4—342no—
222C22×C4—342no—
223C22×C4—681no—
224C22×C4—681no—
225C22×C4C22⋊#59511yescharacteristic
226C22×C4C22⋊#59511yescharacteristic
227C22×C4C22×#59511yescharacteristic
228M16—688no—
229C2×C8—344no—
230C2×C8—344no—
231C2×C8—682no—
232C2×C8—682no—
233C2×C8—682no—
234C2×C8—682no—
235C4⋊C4—42no—
236C4⋊C4—42no—
237C4⋊C4—682no—
238C4⋊C4—684no—
239C4⋊C4—682no—
240C4⋊C4—682no—
241C22⋊C4—684no—
242C42—22no—
243C42—342no—
244C42—681no—
245C42—681no—
246C23—172no—
247C23—341no—
248C23—341no—
249C23—341no—
250C23—341no—
251C23—341no—
252C23—341no—
253C23C2×C22⋊#59511yescharacteristic
254Q8—84no—
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—344no—
273C2×C4—344no—
274C2×C4—684no—
275C2×C4—684no—
276C2×C4—682no—
277C2×C4—682no—
278C2×C4—682no—
279C2×C4#1058754912yes—
280C2×C4#1058755012yes—
281C2×C4#1058755012yes—
282C2×C4#1058755112yes—
283C2×C4#1058767812yes—
284C8—684no—
285C8—684no—
286C22—342no—
287C22—342no—
288C22—342no—
289C22—681no—
290C22—681no—
291C22—681no—
292C22—681no—
293C22#1176378311yescharacteristic
294C22C2×#1058755111yescharacteristic
295C22D17⋊#10011yescharacteristic
296C22C2×#1058754911yescharacteristic
297C22#1176380211yescharacteristic
298C22C2×#1058755011yescharacteristic
299C22C2×#1058755011yescharacteristic
300C4—22no—
301C4—22no—
302C4—82no—
303C4—341no—
304C4—341no—
305C4—342no—
306C4—342no—
307C4—1362no—
308C4#1176366314yes—
309C2—682no—
310C2#1454405911yescharacteristic
311C2#1454410711yescharacteristic
312C2#1454413311yescharacteristic
313C2C2×#1176366311yescharacteristic
314C2#1454418411yescharacteristic
315C2#1454424011yescharacteristic
316C2#1454429811yescharacteristic
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#7687
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. #14543604C2semidirect
205. C17#7687semidirect

Maximal subgroups

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

subgroupindex
C4×#105875432
#145444482
#145436042
#145371312
#768717