Finite Group Databasebeta

← #16944830

Subgroups — #16944830

Order 4352.

428 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 91 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#14528523C211yesmaximal, characteristic
2#14527118C211yesmaximal, characteristic
3#14526814C212yesmaximal, complemented
4#14526790C212yesmaximal, complemented
5C17×#2599C211yesmaximal, characteristic
6C22×#63223—21no—
7#11762866—21no—
8#11762578—21no—
9#11762578C2212yes—
10#11762535C2212yes—
11#11762533—21no—
12C2×C4×Q8×C17C411yescharacteristic
13C2×C17×#117C2211yescharacteristic
14C17×#398C2211yescharacteristic
15C17×#397C411yescharacteristic
16C17×#395C2211yescharacteristic
17C17×#393C411yescharacteristic
18C17×#388—21no—
19C17×#387—21no—
20C17×#387—21no—
21C17×#385—21no—
22C17×#383C411yescharacteristic
23C22×Q8×C17C2×C411yescharacteristic
24C23×C4×C17D411yescharacteristic
25C4×Q8×C17—41no—
26C4×Q8×C17—41no—
27C17×#117—41no—
28C17×#117—41no—
29C2×C4⋊C4×C17—21no—
30C2×C4⋊C4×C17—21no—
31C2×C4⋊C4×C17—21no—
32C2×C4⋊C4×C17C2×C411yescharacteristic
33C2×C4⋊C4×C17D411yescharacteristic
34C2×C4⋊C4×C17C2311yescharacteristic
35C2×C22⋊C4×C17—21no—
36C2×C22⋊C4×C17—21no—
37C2×C22⋊C4×C17C2×C411yescharacteristic
38C2×C22⋊C4×C17D411yescharacteristic
39C2×C42×C17—21no—
40C2×C42×C17C2×C411yescharacteristic
41C2×C42×C17D411yescharacteristic
42C2×#63223—24no—
43C2×#63223—22no—
44C2×#63223—41no—
45C2×#63223—42no—
46C22×#3622—41no—
47C17×#95—21no—
48C17×#95—21no—
49C17×#95—21no—
50C17×#95—21no—
51C17×#95—21no—
52C17×#95—21no—
53C17×#95C2×C411yescharacteristic
54C17×#95C2×C411yescharacteristic
55C22⋊#3622—22no—
56C4⋊#3622—41no—
57#10587474—41no—
58C24×C17C22⋊C411yescharacteristic
59C2×Q8×C17—42no—
60C2×Q8×C17—41no—
61C22×C4×C17—22no—
62C22×C4×C17—21no—
63C22×C4×C17—21no—
64C22×C4×C17—21no—
65C22×C4×C17—21no—
66C22×C4×C17—21no—
67C22×C4×C17—21no—
68C22×C4×C17—21no—
69C22×C4×C17—21no—
70C22×C4×C17C22⋊C411yescharacteristic
71C22×C4×C17C22⋊C411yescharacteristic
72C22×C4×C17C22⋊C411yescharacteristic
73C22×C4×C17C22×C411yescharacteristic
74C22×C4×C17C2×D411yescharacteristic
75C22×C4×C17C2×D411yescharacteristic
76C4⋊C4×C17—41no—
77C4⋊C4×C17—41no—
78C4⋊C4×C17—41no—
79C4⋊C4×C17—42no—
80C4⋊C4×C17—41no—
81C4⋊C4×C17—41no—
82C4⋊C4×C17—41no—
83C4⋊C4×C17—41no—
84C22⋊C4×C17—41no—
85C22⋊C4×C17—41no—
86C22⋊C4×C17—42no—
87C22⋊C4×C17—42no—
88C42×C17—21no—
89C42×C17—21no—
90C42×C17—21no—
91C42×C17—21no—
92C42×C17—42no—
93#63223—24no—
94#63223—44no—
95#63223—42no—
96C2×#3622—44no—
97C2×#3622—42no—
98C2×#3622—42no—
99#11763—171nomaximal, Sylow
100C23×C17—21no—
101C23×C17—21no—
102C23×C17—41no—
103C23×C17—41no—
104C23×C17#10412yes—
105C23×C17C2×C22⋊C411yescharacteristic
106Q8×C17—42no—
107Q8×C17—42no—
108C2×C4×C17—22no—
109C2×C4×C17—22no—
110C2×C4×C17—22no—
111C2×C4×C17—22no—
112C2×C4×C17—21no—
113C2×C4×C17—21no—
114C2×C4×C17—21no—
115C2×C4×C17—21no—
116C2×C4×C17—22no—
117C2×C4×C17—21no—
118C2×C4×C17—21no—
119C2×C4×C17—21no—
120C2×C4×C17—21no—
121C2×C4×C17—41no—
122C2×C4×C17—41no—
123C2×C4×C17—41no—
124C2×C4×C17—41no—
125C2×C4×C17—41no—
126C2×C4×C17—41no—
127C2×C4×C17—41no—
128C2×C4×C17—41no—
129C2×C4×C17—41no—
130C2×C4×C17—41no—
131C2×C4×C17—41no—
132C2×C4×C17—41no—
133C2×C4×C17—41no—
134C2×C4×C17—41no—
135C2×C4×C17—41no—
136C2×C4×C17#9911yescharacteristic
137C2×C4×C17#9911yescharacteristic
138C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C17#13711yescharacteristic
140#3622—44no—
141#3622—82no—
142#2599D1711yescharacteristic
143#1742—171no—
144#1464—171no—
145#1354—172no—
146#1346—172no—
147C22×C17—21no—
148C22×C17—21no—
149C22×C17—22no—
150C22×C17—42no—
151C22×C17—41no—
152C22×C17—41no—
153C22×C17—81no—
154C22×C17C2×#9911yescharacteristic
155C22×C17#41711yescharacteristic
156C22×C17C2×#10411yescharacteristic
157C4×C17—21no—
158C4×C17—21no—
159C4×C17—21no—
160C4×C17—21no—
161C4×C17—41no—
162C4×C17—42no—
163C4×C17—41no—
164C4×C17—41no—
165C4×C17—41no—
166C4×C17—81no—
167C4×C17—81no—
168C4×C17—81no—
169C22×M16—341no—
170C2×C4×Q8Dic1711yescharacteristic
171C2×#117C2×D1711yescharacteristic
172#432—341no—
173#398C2×D1711yescharacteristic
174#397Dic1711yescharacteristic
175#395C2×D1711yescharacteristic
176#393Dic1711yescharacteristic
177#388—21no—
178#387—21no—
179#387—21no—
180#385—21no—
181#383Dic1711yescharacteristic
182#343—172no—
183#343—341no—
184#324—172no—
185#323—341no—
186C2×C17—21no—
187C2×C17—21no—
188C2×C17—42no—
189C2×C17#150411yescharacteristic
190C2×C17#212011yescharacteristic
191C2×C17#213511yescharacteristic
192C22×Q8C2×Dic1711yescharacteristic
193C23×C4C22⋊D1711yescharacteristic
194C2×M16—344no—
195C2×M16—342no—
196C2×M16—681no—
197C2×M16—682no—
198C22×C8—681no—
199C4×Q8—41no—
200C4×Q8—41no—
201#117—41no—
202#117—41no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4C2×Dic1711yescharacteristic
207C2×C4⋊C4C22⋊D1711yescharacteristic
208C2×C4⋊C4C22×D1711yescharacteristic
209C2×C22⋊C4—21no—
210C2×C22⋊C4—21no—
211C2×C22⋊C4C2×Dic1711yescharacteristic
212C2×C22⋊C4C22⋊D1711yescharacteristic
213C2×C42—21no—
214C2×C42C2×Dic1711yescharacteristic
215C2×C42C22⋊D1711yescharacteristic
216C4⋊C8—681no—
217C22⋊C8—342no—
218#97—681no—
219#95—21no—
220#95—21no—
221#95—21no—
222#95—21no—
223#95—21no—
224#95—21no—
225#95C2×Dic1711yescharacteristic
226#95C2×Dic1711yescharacteristic
227C17#1176311yescharacteristic, complemented, Sylow
228C24C22⋊Dic1711yescharacteristic
229C2×Q8—42no—
230C2×Q8—41no—
231C22×C4—22no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4C22⋊Dic1711yescharacteristic
241C22×C4C22⋊Dic1711yescharacteristic
242C22×C4C22⋊Dic1711yescharacteristic
243C22×C4C22×Dic1711yescharacteristic
244C22×C4C2×C22⋊D1711yescharacteristic
245C22×C4C2×C22⋊D1711yescharacteristic
246M16—344no—
247M16—684no—
248M16—682no—
249C2×C8—684no—
250C2×C8—682no—
251C2×C8—682no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—42no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C22⋊C4—41no—
261C22⋊C4—41no—
262C22⋊C4—42no—
263C22⋊C4—42no—
264C42—21no—
265C42—21no—
266C42—21no—
267C42—21no—
268C42—42no—
269C23—21no—
270C23—21no—
271C23—41no—
272C23—41no—
273C23#1058750812yes—
274C23C2×C22⋊Dic1711yescharacteristic
275Q8—42no—
276Q8—42no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—22no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4#1058750511yescharacteristic
306C2×C4#1058750511yescharacteristic
307C2×C4#1058763511yescharacteristic
308C2×C4#1058763711yescharacteristic
309C8—684no—
310C8—1362no—
311C22—21no—
312C22—21no—
313C22—22no—
314C22—42no—
315C22—41no—
316C22—41no—
317C22—81no—
318C22C2×#1058750511yescharacteristic
319C22#1176281011yescharacteristic
320C22C2×#1058750811yescharacteristic
321C4—21no—
322C4—21no—
323C4—21no—
324C4—21no—
325C4—41no—
326C4—42no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—81no—
331C4—81no—
332C4—81no—
333C2—21no—
334C2—21no—
335C2—42no—
336C2#1452728811yescharacteristic
337C2#1453042511yescharacteristic
338C2#1453047911yescharacteristic
subgroupG/H
centerC22C2×#10587505
commutatorC22×C4×C17C22×C4
FrattiniC2×C4⋊C4C22×D17
FittingC17×#2599C2
socleC22×C17C2×#99
prime radicalC24×C17C22⋊C4
cosocleC2×C4⋊C4×C17C23
hypercenter#2599D17
hypocenterC17#11763
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #2599

Complements

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

NH ≅ G/Ntype
3. #14526814C2semidirect
4. #14526790C2semidirect
227. C17#11763semidirect

Maximal subgroups

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

subgroupindex
#145285232
#145271182
#145268142
#145267902
C17×#25992
#1176317