Finite Group Databasebeta

← #16944698

Subgroups — #16944698

Order 4352.

440 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 95 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×#10587504C211yesmaximal, characteristic
2#14527102C211yesmaximal, characteristic
3#14526811C212yesmaximal, complemented
4#14526790C212yesmaximal, complemented
5C17×#2395C211yesmaximal, characteristic
6C2×#10587504—21no—
7C2×C22⋊#3622—21no—
8C4×#63223—21no—
9#11762578C2212yes—
10#11762535C2212yes—
11#11762533—21no—
12C2×C4×D4×C17C2211yescharacteristic
13C2×C17×#117C411yescharacteristic
14C17×#400C2211yescharacteristic
15C17×#399C411yescharacteristic
16C17×#398C2211yescharacteristic
17C17×#397—21no—
18C17×#397C411yescharacteristic
19C17×#394—21no—
20C4×C4⋊C4×C17—21no—
21C4×C22⋊C4×C17—21no—
22C4×C22⋊C4×C17C411yescharacteristic
23C22×D4×C17D411yescharacteristic
24C23×C4×C17C2×C411yescharacteristic
25C23×C4×C17D411yescharacteristic
26C4×D4×C17—41no—
27C4×D4×C17—41no—
28C17×#117—41no—
29C17×#117—41no—
30C2×C4⋊C4×C17—21no—
31C2×C4⋊C4×C17—21no—
32C2×C4⋊C4×C17C2×C411yescharacteristic
33C2×C4⋊C4×C17C2×C411yescharacteristic
34C2×C4⋊C4×C17C2311yescharacteristic
35C2×C22⋊C4×C17—21no—
36C2×C22⋊C4×C17—21no—
37C2×C22⋊C4×C17—21no—
38C2×C22⋊C4×C17—21no—
39C2×C22⋊C4×C17C2×C411yescharacteristic
40C2×C22⋊C4×C17D411yescharacteristic
41C2×C42×C17—21no—
42C2×C42×C17—21no—
43C2×C42×C17D411yescharacteristic
44C2×#63223—22no—
45C22×#3622—41no—
46C17×#95—21no—
47C17×#95—21no—
48C17×#95—21no—
49C17×#95—21no—
50C17×#95C2×C411yescharacteristic
51C17×#95C2×C411yescharacteristic
52#10587504—24no—
53C22⋊#3622—22no—
54C22⋊#3622—41no—
55#10587474—41no—
56C4×#3622—41no—
57C24×C17C22⋊C411yescharacteristic
58C24×C17C22⋊C411yescharacteristic
59C2×D4×C17—22no—
60C2×D4×C17—22no—
61C2×D4×C17—41no—
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×C17—42no—
71C22×C4×C17—42no—
72C22×C4×C17C22⋊C411yescharacteristic
73C22×C4×C17C22⋊C411yescharacteristic
74C22×C4×C17C22×C411yescharacteristic
75C22×C4×C17C2×D411yescharacteristic
76C22×C4×C17C2×D411yescharacteristic
77C4⋊C4×C17—41no—
78C4⋊C4×C17—41no—
79C4⋊C4×C17—41no—
80C4⋊C4×C17—42no—
81C4⋊C4×C17—42no—
82C22⋊C4×C17—41no—
83C22⋊C4×C17—41no—
84C22⋊C4×C17—42no—
85C22⋊C4×C17—42no—
86C22⋊C4×C17—42no—
87C22⋊C4×C17—42no—
88C42×C17—21no—
89C42×C17—21no—
90C42×C17—42no—
91C42×C17—41no—
92C42×C17—41no—
93#63223—24no—
94#63223—42no—
95C2×#3622—42no—
96C2×#3622—42no—
97C2×#3622—82no—
98#11735—171nomaximal, Sylow
99C23×C17—21no—
100C23×C17—21no—
101C23×C17—21no—
102C23×C17—21no—
103C23×C17—21no—
104C23×C17—41no—
105C23×C17—41no—
106C23×C17—41no—
107C23×C17—41no—
108C23×C17#10412yes—
109C23×C17C2×C22⋊C411yescharacteristic
110D4×C17—44no—
111C2×C4×C17—21no—
112C2×C4×C17—21no—
113C2×C4×C17—22no—
114C2×C4×C17—22no—
115C2×C4×C17—21no—
116C2×C4×C17—21no—
117C2×C4×C17—21no—
118C2×C4×C17—42no—
119C2×C4×C17—41no—
120C2×C4×C17—41no—
121C2×C4×C17—42no—
122C2×C4×C17—42no—
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#9911yescharacteristic
137C2×C4×C17#9911yescharacteristic
138C2×C4×C17#13512yes—
139#3622—44no—
140#3622—82no—
141#2395D1711yescharacteristic
142C4×#100—171no—
143#1459—171no—
144#1353—172no—
145#1346—172no—
146C22×C17—21no—
147C22×C17—21no—
148C22×C17—22no—
149C22×C17—42no—
150C22×C17—41no—
151C22×C17—41no—
152C22×C17—41no—
153C22×C17—41no—
154C22×C17—41no—
155C22×C17—81no—
156C22×C17—81no—
157C22×C17—81no—
158C22×C17C2×#9911yescharacteristic
159C22×C17#41611yescharacteristic
160C22×C17C2×#10411yescharacteristic
161C4×C17—21no—
162C4×C17—22no—
163C4×C17—42no—
164C4×C17—41no—
165C4×C17—41no—
166C4×C17—41no—
167C4×C17—81no—
168C4×C17—81no—
169C4×C17—81no—
170C4×C17#35212yes—
171C2×C4×D4C2×D1711yescharacteristic
172C2×#117Dic1711yescharacteristic
173C2×#100—341no—
174C2×C22⋊C8—341no—
175C4×M16—341no—
176#400C2×D1711yescharacteristic
177#399Dic1711yescharacteristic
178#398C2×D1711yescharacteristic
179#397—21no—
180#397Dic1711yescharacteristic
181#394—21no—
182C4×C4⋊C4—21no—
183C4×C22⋊C4—21no—
184C4×C22⋊C4Dic1711yescharacteristic
185#343—172no—
186#324—172no—
187#323—341no—
188C2×C17—21no—
189C2×C17—21no—
190C2×C17—42no—
191C2×C17—81no—
192C2×C17#150111yescharacteristic
193C2×C17C2×#35211yescharacteristic
194C2×C17#213211yescharacteristic
195C22×D4C22⋊D1711yescharacteristic
196C23×C4C2×Dic1711yescharacteristic
197C23×C4C22⋊D1711yescharacteristic
198C2×M16—342no—
199C22×C8—681no—
200C4×D4—41no—
201C4×D4—41no—
202#117—41no—
203#117—41no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4C2×Dic1711yescharacteristic
207C2×C4⋊C4C2×Dic1711yescharacteristic
208C2×C4⋊C4C22×D1711yescharacteristic
209C2×C22⋊C4—21no—
210C2×C22⋊C4—21no—
211C2×C22⋊C4—21no—
212C2×C22⋊C4—21no—
213C2×C22⋊C4C2×Dic1711yescharacteristic
214C2×C22⋊C4C22⋊D1711yescharacteristic
215C2×C42—21no—
216C2×C42—21no—
217C2×C42C22⋊D1711yescharacteristic
218#100—344no—
219C22⋊C8—342no—
220C22⋊C8—681no—
221#97—681no—
222C4×C8—681no—
223#95—21no—
224#95—21no—
225#95—21no—
226#95—21no—
227#95C2×Dic1711yescharacteristic
228#95C2×Dic1711yescharacteristic
229C17#1173511yescharacteristic, 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—42no—
244C22×C4—42no—
245C22×C4C22⋊Dic1711yescharacteristic
246C22×C4C22⋊Dic1711yescharacteristic
247C22×C4C22×Dic1711yescharacteristic
248C22×C4C2×C22⋊D1711yescharacteristic
249C22×C4C2×C22⋊D1711yescharacteristic
250M16—344no—
251M16—682no—
252C2×C8—682no—
253C2×C8—682no—
254C2×C8—1362no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—42no—
259C4⋊C4—42no—
260C22⋊C4—41no—
261C22⋊C4—41no—
262C22⋊C4—42no—
263C22⋊C4—42no—
264C22⋊C4—42no—
265C22⋊C4—42no—
266C42—21no—
267C42—21no—
268C42—42no—
269C42—41no—
270C42—41no—
271C23—21no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—41no—
277C23—41no—
278C23—41no—
279C23—41no—
280C23#1058750812yes—
281C23C2×C22⋊Dic1711yescharacteristic
282D4—44no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—42no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4—42no—
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—81no—
308C2×C4#1058750511yescharacteristic
309C2×C4#1058750511yescharacteristic
310C2×C4#1058763612yes—
311C8—684no—
312C8—1362no—
313C22—21no—
314C22—21no—
315C22—22no—
316C22—42no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—81no—
323C22—81no—
324C22—81no—
325C22C2×#1058750511yescharacteristic
326C22#1176280511yescharacteristic
327C22C2×#1058750811yescharacteristic
328C4—22no—
329C4—21no—
330C4—42no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—81no—
335C4—81no—
336C4—81no—
337C4#1176259912yes—
338C2—21no—
339C2—21no—
340C2—42no—
341C2—81no—
342C2#1452727511yescharacteristic
343C2C2×#1176259911yescharacteristic
344C2#1453046911yescharacteristic
subgroupG/H
centerC2×C4#10587505
commutatorC22×C4×C17C22×C4
FrattiniC2×C4⋊C4C22×D17
FittingC17×#2395C2
socleC22×C17C2×#99
prime radicalC22×D4×C17D4
cosocleC2×C4⋊C4×C17C23
hypercenter#2395D17
hypocenterC17#11735
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2395

Complements

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

NH ≅ G/Ntype
3. #14526811C2semidirect
4. #14526790C2semidirect
229. C17#11735semidirect

Maximal subgroups

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

subgroupindex
C4×#105875042
#145271022
#145268112
#145267902
C17×#23952
#1173517