Finite Group Databasebeta

← #16943985

Subgroups — #16943985

Order 4352.

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

normal subgroups only

This group has 416 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#14527122C211yesmaximal, characteristic
2#14527102C211yesmaximal, characteristic
3#14526730C212yesmaximal, complemented
4#14526728C212yesmaximal, complemented
5C17×#2566C211yesmaximal, characteristic
6#11762773—21no—
7C2×C22⋊#3622—21no—
8#11762535C2212yes—
9#11762535C2212yes—
10#11762533—21no—
11#11762533—21no—
12C2×C17×#125C411yescharacteristic
13C2×C4×D4×C17C2211yescharacteristic
14C17×#396—21no—
15C17×#396—21no—
16C17×#390C411yescharacteristic
17C17×#390C411yescharacteristic
18C17×#385—21no—
19C17×#385—21no—
20C17×#384C2211yescharacteristic
21C17×#382C2211yescharacteristic
22C4×C4⋊C4×C17C411yescharacteristic
23C22×D4×C17C2×C411yescharacteristic
24C23×C4×C17D411yescharacteristic
25C23×C4×C17D411yescharacteristic
26C17×#125—41no—
27C17×#125—41no—
28C4×D4×C17—41no—
29C4×D4×C17—41no—
30C2×C4⋊C4×C17—21no—
31C2×C4⋊C4×C17—21no—
32C2×C4⋊C4×C17—21no—
33C2×C4⋊C4×C17—21no—
34C2×C4⋊C4×C17—21no—
35C2×C4⋊C4×C17C2×C411yescharacteristic
36C2×C4⋊C4×C17C2×C411yescharacteristic
37C2×C4⋊C4×C17C2311yescharacteristic
38C2×C22⋊C4×C17—21no—
39C2×C22⋊C4×C17—21no—
40C2×C22⋊C4×C17—21no—
41C2×C22⋊C4×C17—21no—
42C2×C22⋊C4×C17D411yescharacteristic
43C2×C22⋊C4×C17D411yescharacteristic
44C2×C42×C17C2×C411yescharacteristic
45C2×C42×C17C2×C411yescharacteristic
46C2×C42×C17C2×C411yescharacteristic
47C2×#63223—41no—
48C22×#3622—41no—
49C17×#95—21no—
50C17×#95—21no—
51C17×#95—21no—
52C22⋊#3622—22no—
53C22⋊#3622—22no—
54C22⋊#3622—41no—
55C22⋊#3622—41no—
56C24×C17C22⋊C411yescharacteristic
57C24×C17C22⋊C411yescharacteristic
58C2×D4×C17—22no—
59C2×D4×C17—22no—
60C2×D4×C17—41no—
61C22×C4×C17—21no—
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—81no—
70C22×C4×C17—81no—
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—42no—
81C4⋊C4×C17—41no—
82C4⋊C4×C17—41no—
83C4⋊C4×C17—81no—
84C4⋊C4×C17—81no—
85C22⋊C4×C17—41no—
86C22⋊C4×C17—41no—
87C22⋊C4×C17—42no—
88C22⋊C4×C17—42no—
89C22⋊C4×C17—81no—
90C22⋊C4×C17—81no—
91C42×C17—21no—
92C42×C17—21no—
93C42×C17—22no—
94C42×C17—22no—
95#63223—82no—
96C2×#3622—42no—
97C2×#3622—42no—
98C2×#3622—82no—
99#11572—171nomaximal, Sylow
100C23×C17—21no—
101C23×C17—21no—
102C23×C17—21no—
103C23×C17—21no—
104C23×C17—21no—
105C23×C17—41no—
106C23×C17—41no—
107C23×C17—41no—
108C23×C17—41no—
109C23×C17#10112yes—
110C23×C17C2×C22⋊C411yescharacteristic
111D4×C17—44no—
112C2×C4×C17—21no—
113C2×C4×C17—21no—
114C2×C4×C17—22no—
115C2×C4×C17—21no—
116C2×C4×C17—21no—
117C2×C4×C17—21no—
118C2×C4×C17—41no—
119C2×C4×C17—42no—
120C2×C4×C17—42no—
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—81no—
136C2×C4×C17—81no—
137C2×C4×C17#9911yescharacteristic
138C2×C4×C17#9911yescharacteristic
139C2×C4×C17#13112yes—
140#3622—82no—
141#3622—82no—
142#2566D1711yescharacteristic
143#1465—171no—
144#1459—171no—
145#1325—172no—
146#1324—172no—
147C22×C17—21no—
148C22×C17—21no—
149C22×C17—22no—
150C22×C17—42no—
151C22×C17—42no—
152C22×C17—41no—
153C22×C17—41no—
154C22×C17—41no—
155C22×C17—41no—
156C22×C17—41no—
157C22×C17—81no—
158C22×C17—81no—
159C22×C17#40811yescharacteristic
160C22×C17C2×#9911yescharacteristic
161C22×C17C2×#10111yescharacteristic
162C4×C17—21no—
163C4×C17—21no—
164C4×C17—22no—
165C4×C17—42no—
166C4×C17—41no—
167C4×C17—41no—
168C4×C17—41no—
169C4×C17—81no—
170C4×C17—81no—
171C4×C17—81no—
172C2×#125Dic1711yescharacteristic
173C2×C4×D4C2×D1711yescharacteristic
174#407—341no—
175C2×C22⋊C8—341no—
176#396—21no—
177#396—21no—
178#390Dic1711yescharacteristic
179#390Dic1711yescharacteristic
180#385—21no—
181#385—21no—
182#384C2×D1711yescharacteristic
183#382C2×D1711yescharacteristic
184C4×C4⋊C4Dic1711yescharacteristic
185#324—172no—
186#324—172no—
187#323—341no—
188#323—341no—
189C2×C17—21no—
190C2×C17—21no—
191C2×C17—42no—
192C2×C17—81no—
193C2×C17#147211yescharacteristic
194C2×C17#212711yescharacteristic
195C2×C17#213211yescharacteristic
196C22×D4C2×Dic1711yescharacteristic
197C23×C4C22⋊D1711yescharacteristic
198C23×C4C22⋊D1711yescharacteristic
199C2×M16—681no—
200C22×C8—681no—
201#125—41no—
202#125—41no—
203C4×D4—41no—
204C4×D4—41no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4C2×Dic1711yescharacteristic
211C2×C4⋊C4C2×Dic1711yescharacteristic
212C2×C4⋊C4C22×D1711yescharacteristic
213C2×C22⋊C4—21no—
214C2×C22⋊C4—21no—
215C2×C22⋊C4—21no—
216C2×C22⋊C4—21no—
217C2×C22⋊C4C22⋊D1711yescharacteristic
218C2×C22⋊C4C22⋊D1711yescharacteristic
219C2×C42C2×Dic1711yescharacteristic
220C2×C42C2×Dic1711yescharacteristic
221C2×C42C2×Dic1711yescharacteristic
222C22⋊C8—342no—
223C22⋊C8—342no—
224C22⋊C8—681no—
225C22⋊C8—681no—
226#95—21no—
227#95—21no—
228#95—21no—
229C17#1157211yescharacteristic, complemented, Sylow
230C24C22⋊Dic1711yescharacteristic
231C24C22⋊Dic1711yescharacteristic
232C2×D4—22no—
233C2×D4—22no—
234C2×D4—41no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—81no—
244C22×C4—81no—
245C22×C4C22⋊Dic1711yescharacteristic
246C22×C4C22⋊Dic1711yescharacteristic
247C22×C4C22×Dic1711yescharacteristic
248C22×C4C2×C22⋊D1711yescharacteristic
249C22×C4C2×C22⋊D1711yescharacteristic
250M16—1362no—
251C2×C8—682no—
252C2×C8—682no—
253C2×C8—1362no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—42no—
258C4⋊C4—42no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—81no—
262C4⋊C4—81no—
263C22⋊C4—41no—
264C22⋊C4—41no—
265C22⋊C4—42no—
266C22⋊C4—42no—
267C22⋊C4—81no—
268C22⋊C4—81no—
269C42—21no—
270C42—21no—
271C42—22no—
272C42—22no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23—41no—
279C23—41no—
280C23—41no—
281C23—41no—
282C23#1058750712yes—
283C23C2×C22⋊Dic1711yescharacteristic
284D4—44no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—22no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—41no—
292C2×C4—42no—
293C2×C4—42no—
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—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—81no—
309C2×C4—81no—
310C2×C4#1058750511yescharacteristic
311C2×C4#1058750511yescharacteristic
312C2×C4#1058763412yes—
313C8—1362no—
314C8—1362no—
315C22—21no—
316C22—21no—
317C22—22no—
318C22—42no—
319C22—42no—
320C22—41no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—41no—
325C22—81no—
326C22—81no—
327C22#1176277611yescharacteristic
328C22C2×#1058750511yescharacteristic
329C22C2×#1058750711yescharacteristic
330C4—21no—
331C4—21no—
332C4—22no—
333C4—42no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—81no—
338C4—81no—
339C4—81no—
340C2—21no—
341C2—21no—
342C2—42no—
343C2—81no—
344C2#1452714811yescharacteristic
345C2#1453045311yescharacteristic
346C2#1453046911yescharacteristic
subgroupG/H
centerC22C2×#10587505
commutatorC22×C4×C17C22×C4
FrattiniC2×C4⋊C4C22×D17
FittingC17×#2566C2
socleC22×C17C2×#99
prime radicalC22×D4×C17C2×C4
cosocleC2×C4⋊C4×C17C23
hypercenter#2566D17
hypocenterC17#11572
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2566

Complements

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

NH ≅ G/Ntype
3. #14526730C2semidirect
4. #14526728C2semidirect
229. C17#11572semidirect

Maximal subgroups

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

subgroupindex
#145271222
#145271022
#145267302
#145267282
C17×#25662
#1157217