Finite Group Databasebeta

← #17951825

Subgroups — #17951825

Order 4352.

542 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 138 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×#10587553C211yesmaximal, characteristic
2#14544023C211yesmaximal, characteristic
3C8×#63247C212yesmaximal, complemented
4#14543629C212yesmaximal, complemented
5C2×#11762872C211yesmaximal, characteristic
6#11763826C2212yes—
7C2×#10587553C412yes—
8C4×#63247C2212yes—
9#11763689C412yes—
10#11763653C412yes—
11#11763652C412yes—
12#11763651—22no—
13C8×#3624—22no—
14C23×#3622C411yescharacteristic
15C22×C8×D17C411yescharacteristic
16C2×C4×C22⋊D17C2211yescharacteristic
17#11762872—22no—
18#11762872—22no—
19C2×#10587485C2211yescharacteristic
20C2×#10587491C411yescharacteristic
21C2×C8×Dic17C2211yescharacteristic
22C2×C17×C22⋊C8C411yescharacteristic
23C23×C4×C17C2×C411yescharacteristic
24C22×C22⋊D17C2×C411yescharacteristic
25C22×C4×D17C2×C411yescharacteristic
26C2×#63247C2×C414yes—
27C22×C8×C17C2×C411yescharacteristic
28C22×C8×C17C2×C411yescharacteristic
29C2×C22⋊Dic17C2×C411yescharacteristic
30C4×C22⋊D17—22no—
31C4×C22⋊D17—22no—
32C2×#63227C2×C411yescharacteristic
33C2×#63225C2×C411yescharacteristic
34C2×C4×Dic17C2311yescharacteristic
35C22×#3622—21no—
36C22×#3622—21no—
37C22×#3622—42no—
38C22×#3622C2×C411yescharacteristic
39C22×#3622C2×C411yescharacteristic
40C2×C8×D17—21no—
41C2×C8×D17—21no—
42C2×C8×D17—42no—
43#10587553C818yescomplemented
44C22⋊#3624C2×C414yes—
45#10587544—22no—
46#10587542—22no—
47C4×#3624—22no—
48C4×#3624—22no—
49C17×C22⋊C8—22no—
50#10587491—22no—
51#10587485—22no—
52C8×Dic17D412yes—
53C8×Dic17D412yes—
54C24×C17C4211yescharacteristic
55C23×D17C4211yescharacteristic
56C22×C4×C17—21no—
57C22×C4×C17—21no—
58C22×C4×C17—41no—
59C22×C4×C17—41no—
60C22×C4×C17C4211yescharacteristic
61C22×C4×C17C22×C411yescharacteristic
62C2×C22⋊D17—22no—
63C2×C22⋊D17—22no—
64C2×C22⋊D17C2×C814yes—
65C22×Dic17C4211yescharacteristic
66C22×Dic17C22×C411yescharacteristic
67C22×Dic17C22×C411yescharacteristic
68C2×C4×D17—21no—
69C2×C4×D17—21no—
70C2×C4×D17—41no—
71C2×C4×D17—41no—
72#63247—24no—
73#63247C2×C818yescomplemented
74C2×#3624—24no—
75C2×#3624—24no—
76C2×C8×C17—21no—
77C2×C8×C17—41no—
78C2×C8×C17—41no—
79C2×C8×C17C22⋊C412yes—
80C22⋊Dic17—22no—
81#63227—22no—
82#63225—22no—
83C4×Dic17C2×D412yes—
84C4×Dic17#4112yes—
85C2×#3622—22no—
86C2×#3622—21no—
87C2×#3622—42no—
88C2×#3622—42no—
89C2×#3622—41no—
90C2×#3622C22⋊C411yescharacteristic
91C2×#3622C22⋊C411yescharacteristic
92C8×D17—42no—
93C8×D17—42no—
94C8×#100—171nomaximal, Sylow
95C23×C17—21no—
96C23×C17—21no—
97C23×C17—41no—
98C23×C17—41no—
99C23×C17C4×C812yes—
100C23×C17C2×C4211yescharacteristic
101C22×D17—21no—
102C22×D17—21no—
103C22×D17—41no—
104C22×D17—41no—
105C22×D17C4×C812yes—
106C2×C4×C17—21no—
107C2×C4×C17—21no—
108C2×C4×C17—21no—
109C2×C4×C17—42no—
110C2×C4×C17—41no—
111C2×C4×C17—41no—
112C2×C4×C17—41no—
113C2×C4×C17C2×C22⋊C411yescharacteristic
114C2×C4×C17#11711yescharacteristic
115C22⋊D17—28no—
116C2×Dic17—21no—
117C2×Dic17—41no—
118C2×Dic17—41no—
119C2×Dic17C4×D412yes—
120C2×Dic17C4×D412yes—
121C2×Dic17C22×C812yes—
122C2×Dic17#13112yes—
123C4×D17—42no—
124C4×D17—41no—
125C4×D17—41no—
126#3624—28no—
127#3624—44no—
128C8×C17—22no—
129C8×C17—41no—
130#3622—21no—
131#3622—41no—
132#3622#10012yescomplemented
133C2×C8×D4—171no—
134C4×#100—171no—
135#1460—171no—
136C8×M16—172no—
137#1283—172no—
138C22×C17—21no—
139C22×C17—21no—
140C22×C17—22no—
141C22×C17—42no—
142C22×C17—42no—
143C22×C17—41no—
144C22×C17—41no—
145C22×C17C4×C22⋊C411yescharacteristic
146C22×C17C2×C4×C811yescharacteristic
147C22×C17#40511yescharacteristic
148C2×D17—22no—
149C2×D17—42no—
150C2×D17—41no—
151C2×D17—41no—
152C2×D17—42no—
153C4×C17—21no—
154C4×C17—41no—
155C4×C17C2×#10011yescharacteristic
156C4×C17#41311yescharacteristic
157Dic17—22no—
158Dic17—41no—
159Dic17C8×D414yes—
160C23×C8—171no—
161C23×C8—171no—
162C2×C4×D4—171no—
163C8×D4—342no—
164C8×D4—342no—
165#431—172no—
166C2×C4⋊C8—171no—
167C2×#100—172no—
168C2×C22⋊C8—171no—
169C2×C22⋊C8#59511yescharacteristic
170C4×M16—172no—
171C2×C4×C8—171no—
172#343—172no—
173#323—172no—
174#323—172no—
175#322—342no—
176C82—342no—
177C2×C17—21no—
178C2×C17—21no—
179C2×C17—42no—
180C2×C17C8×C22⋊C411yescharacteristic
181C2×C17C4×#10011yescharacteristic
182C2×C17#175711yescharacteristic
183D17—42no—
184C22×D4—171no—
185C23×C4—171no—
186C23×C4C2×#59511yescharacteristic
187C2×M16—174no—
188C22×C8—171no—
189C22×C8—171no—
190C22×C8—341no—
191C22×C8—341no—
192C22×C8—341no—
193C22×C8—341no—
194C22×C8—682no—
195C22×C8—682no—
196C22×C8C2×#59511yescharacteristic
197C22×C8C2×#59511yescharacteristic
198C4×D4—342no—
199C4×D4—342no—
200C2×C4⋊C4—171no—
201C2×C22⋊C4—171no—
202C2×C22⋊C4—171no—
203C2×C42—171no—
204C4⋊C8—342no—
205C4⋊C8—342no—
206#100—178no—
207C22⋊C8—22no—
208C22⋊C8—174no—
209C22⋊C8—342no—
210#97—342no—
211C4×C8—172no—
212C4×C8—172no—
213C4×C8—342no—
214C4×C8—342no—
215C17C8×#10011yescharacteristic, complemented, Sylow
216C24—171no—
217C24C4×#59511yescharacteristic
218C2×D4—174no—
219C2×D4—342no—
220C2×D4—342no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—41no—
224C22×C4—41no—
225C22×C4—171no—
226C22×C4—171no—
227C22×C4—171no—
228C22×C4—341no—
229C22×C4—341no—
230C22×C4—681no—
231C22×C4—681no—
232C22×C4C4×#59511yescharacteristic
233C22×C4C22×#59511yescharacteristic
234M16—178no—
235M16—344no—
236C2×C8—21no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—171no—
240C2×C8—171no—
241C2×C8—342no—
242C2×C8—344no—
243C2×C8—344no—
244C2×C8—341no—
245C2×C8—682no—
246C2×C8—682no—
247C2×C8—682no—
248C2×C8—682no—
249C2×C8—681no—
250C2×C8C22⋊#59512yes—
251C4⋊C4—342no—
252C22⋊C4—342no—
253C22⋊C4—342no—
254C42—172no—
255C42—172no—
256C23—21no—
257C23—21no—
258C23—41no—
259C23—41no—
260C23—172no—
261C23—341no—
262C23—341no—
263C23—681no—
264C23—681no—
265C23C8×#59512yes—
266C23C2×C4×#59511yescharacteristic
267D4—348no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—42no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—172no—
276C2×C4—172no—
277C2×C4—172no—
278C2×C4—172no—
279C2×C4—341no—
280C2×C4—682no—
281C2×C4—681no—
282C2×C4—681no—
283C2×C4—681no—
284C2×C4—681no—
285C2×C4#1058767711yescharacteristic
286C2×C4C2×C22⋊#59511yescharacteristic
287C8—22no—
288C8—41no—
289C8—172no—
290C8—348no—
291C8—341no—
292C8—684no—
293C8—681no—
294C22—21no—
295C22—21no—
296C22—22no—
297C22—42no—
298C22—42no—
299C22—41no—
300C22—41no—
301C22—342no—
302C22—682no—
303C22—682no—
304C22—681no—
305C22—681no—
306C22C4×C22⋊#59511yescharacteristic
307C22C2×C8×#59511yescharacteristic
308C22#1176377211yescharacteristic
309C4—21no—
310C4—41no—
311C4—174no—
312C4—342no—
313C4—681no—
314C4D17⋊#10011yescharacteristic
315C4#1176379611yescharacteristic
316C2—21no—
317C2—21no—
318C2—42no—
319C2—682no—
320C2C8×C22⋊#59511yescharacteristic
321C2#1454453411yescharacteristic
322C2#1454454011yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#595
commutatorC22×C17C2×C4×C8
FrattiniC22×C4C22×#595
FittingC2×C17×C22⋊C8C4
socleC22×C17C4×C22⋊C4
prime radicalC22×C22⋊D17C2×C4
cosocleC2×C4×Dic17C23
hypercenterC2×C22⋊C8#595
hypocenterC17C8×#100
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
3. C8×#63247C2semidirect
4. #14543629C2semidirect
43. #10587553C8semidirect
73. #63247C2×C8semidirect
132. #3622#100semidirect
215. C17C8×#100semidirect

Maximal subgroups

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

subgroupindex
C4×#105875532
#145440232
C8×#632472
#145436292
C2×#117628722
C8×#10017