Finite Group Databasebeta

← #16944963

Subgroups — #16944963

Order 4352.

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

normal subgroups only

This group has 378 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
1C4×#10587507C211yesmaximal, characteristic
2#14527128C211yesmaximal, characteristic
3#14526814C212yesmaximal
4#14526811C212yesmaximal
5C17×#2581C211yesmaximal, characteristic
6#11762866—21no—
7C2×#10587507—21no—
8C4×#63223—21no—
9#11762578C2212yes—
10#11762535—21no—
11#11762535C2212yes—
12C2×C4×Q8×C17C411yescharacteristic
13C2×C4×Q8×C17C2211yescharacteristic
14C17×#400C411yescharacteristic
15C17×#400C2211yescharacteristic
16C17×#395C411yescharacteristic
17C17×#395C2211yescharacteristic
18C17×#391—21no—
19C17×#389—21no—
20C17×#387—21no—
21C17×#387—21no—
22C17×#382C411yescharacteristic
23C22×Q8×C17C2×C411yescharacteristic
24C22×Q8×C17D411yescharacteristic
25C4×Q8×C17—41no—
26C4×Q8×C17—41no—
27C4×Q8×C17—41no—
28C4×Q8×C17—41no—
29C2×C4⋊C4×C17—21no—
30C2×C4⋊C4×C17—21no—
31C2×C4⋊C4×C17—21no—
32C2×C4⋊C4×C17—21no—
33C2×C4⋊C4×C17C2×C411yescharacteristic
34C2×C4⋊C4×C17C2×C411yescharacteristic
35C2×C4⋊C4×C17D411yescharacteristic
36C2×C4⋊C4×C17C2311yescharacteristic
37C2×C42×C17—21no—
38C2×C42×C17C2×C411yescharacteristic
39C2×C42×C17D411yescharacteristic
40C2×C42×C17D411yescharacteristic
41C2×#63223—22no—
42C17×#95—21no—
43C17×#95—21no—
44C17×#95—21no—
45C17×#95—21no—
46C17×#95—21no—
47C17×#95—21no—
48C17×#95—21no—
49C17×#95C2×C411yescharacteristic
50C17×#95C2×C411yescharacteristic
51#10587507—24no—
52C22⋊#3622—22no—
53C4⋊#3622—41no—
54#10587474—41no—
55#10587474—41no—
56C4×#3622—41no—
57C2×Q8×C17—22no—
58C2×Q8×C17—22no—
59C2×Q8×C17—41no—
60C2×Q8×C17—42no—
61C2×Q8×C17—41no—
62C22×C4×C17—21no—
63C22×C4×C17—21no—
64C22×C4×C17—21no—
65C22×C4×C17—21no—
66C22×C4×C17C22⋊C411yescharacteristic
67C22×C4×C17C22⋊C411yescharacteristic
68C22×C4×C17C22⋊C411yescharacteristic
69C22×C4×C17C22⋊C411yescharacteristic
70C22×C4×C17C22×C411yescharacteristic
71C22×C4×C17C2×D411yescharacteristic
72C22×C4×C17C2×D411yescharacteristic
73C4⋊C4×C17—41no—
74C4⋊C4×C17—41no—
75C4⋊C4×C17—41no—
76C4⋊C4×C17—41no—
77C4⋊C4×C17—42no—
78C4⋊C4×C17—42no—
79C4⋊C4×C17—41no—
80C4⋊C4×C17—41no—
81C4⋊C4×C17—42no—
82C42×C17—21no—
83C42×C17—21no—
84C42×C17—21no—
85C42×C17—21no—
86C42×C17—21no—
87C42×C17—21no—
88C42×C17—42no—
89#63223—24no—
90#63223—42no—
91C2×#3622—42no—
92C2×#3622—42no—
93#11792—171nomaximal, Sylow
94C23×C17C2×C22⋊C411yescharacteristic
95Q8×C17—44no—
96Q8×C17—42no—
97Q8×C17—42no—
98C2×C4×C17—21no—
99C2×C4×C17—21no—
100C2×C4×C17—21no—
101C2×C4×C17—21no—
102C2×C4×C17—22no—
103C2×C4×C17—21no—
104C2×C4×C17—21no—
105C2×C4×C17—21no—
106C2×C4×C17—21no—
107C2×C4×C17—21no—
108C2×C4×C17—21no—
109C2×C4×C17—41no—
110C2×C4×C17—41no—
111C2×C4×C17—41no—
112C2×C4×C17—41no—
113C2×C4×C17—41no—
114C2×C4×C17—41no—
115C2×C4×C17—41no—
116C2×C4×C17—41no—
117C2×C4×C17—41no—
118C2×C4×C17—41no—
119C2×C4×C17—42no—
120C2×C4×C17—41no—
121C2×C4×C17—41no—
122C2×C4×C17—41no—
123C2×C4×C17#9911yescharacteristic
124C2×C4×C17#9911yescharacteristic
125C2×C4×C17#10412yes—
126C2×C4×C17#13712yes—
127#3622—44no—
128#3622—82no—
129#2581D1711yescharacteristic
130C4×#101—171no—
131#1467—171no—
132#1354—172no—
133#1353—172no—
134C22×C17—21no—
135C22×C17—21no—
136C22×C17C2×#9911yescharacteristic
137C22×C17#41911yescharacteristic
138C22×C17C2×#10411yescharacteristic
139C4×C17—21no—
140C4×C17—21no—
141C4×C17—22no—
142C4×C17—22no—
143C4×C17—41no—
144C4×C17—41no—
145C4×C17—42no—
146C4×C17—41no—
147C4×C17—41no—
148C4×C17—81no—
149C4×C17—81no—
150C4×C17—81no—
151C2×C4×Q8Dic1711yescharacteristic
152C2×C4×Q8C2×D1711yescharacteristic
153#432—341no—
154C2×#101—341no—
155C4×M16—341no—
156#400Dic1711yescharacteristic
157#400C2×D1711yescharacteristic
158#395Dic1711yescharacteristic
159#395C2×D1711yescharacteristic
160#391—21no—
161#389—21no—
162#387—21no—
163#387—21no—
164#382Dic1711yescharacteristic
165#343—172no—
166#324—172no—
167#324—341no—
168C2×C17—21no—
169C2×C17—21no—
170C2×C17#150811yescharacteristic
171C2×C17#212011yescharacteristic
172C2×C17#213311yescharacteristic
173C22×Q8C2×Dic1711yescharacteristic
174C22×Q8C22⋊D1711yescharacteristic
175C2×M16—342no—
176C4×Q8—41no—
177C4×Q8—41no—
178C4×Q8—41no—
179C4×Q8—41no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4C2×Dic1711yescharacteristic
185C2×C4⋊C4C2×Dic1711yescharacteristic
186C2×C4⋊C4C22⋊D1711yescharacteristic
187C2×C4⋊C4C22×D1711yescharacteristic
188C2×C42—21no—
189C2×C42C2×Dic1711yescharacteristic
190C2×C42C22⋊D1711yescharacteristic
191C2×C42C22⋊D1711yescharacteristic
192C4⋊C8—681no—
193#101—344no—
194C22⋊C8—342no—
195#97—681no—
196#97—681no—
197C4×C8—681no—
198#95—21no—
199#95—21no—
200#95—21no—
201#95—21no—
202#95—21no—
203#95—21no—
204#95—21no—
205#95C2×Dic1711yescharacteristic
206#95C2×Dic1711yescharacteristic
207C17#1179211yescharacteristic, complemented, Sylow
208C2×Q8—22no—
209C2×Q8—22no—
210C2×Q8—41no—
211C2×Q8—42no—
212C2×Q8—41no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4C22⋊Dic1711yescharacteristic
218C22×C4C22⋊Dic1711yescharacteristic
219C22×C4C22⋊Dic1711yescharacteristic
220C22×C4C22⋊Dic1711yescharacteristic
221C22×C4C22×Dic1711yescharacteristic
222C22×C4C2×C22⋊D1711yescharacteristic
223C22×C4C2×C22⋊D1711yescharacteristic
224M16—344no—
225M16—682no—
226C2×C8—682no—
227C2×C8—682no—
228C4⋊C4—41no—
229C4⋊C4—41no—
230C4⋊C4—41no—
231C4⋊C4—41no—
232C4⋊C4—42no—
233C4⋊C4—42no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—42no—
237C42—21no—
238C42—21no—
239C42—21no—
240C42—21no—
241C42—21no—
242C42—21no—
243C42—42no—
244C23C2×C22⋊Dic1711yescharacteristic
245Q8—44no—
246Q8—42no—
247Q8—42no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—22no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—42no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4#1058750511yescharacteristic
274C2×C4#1058750511yescharacteristic
275C2×C4#1058750812yes—
276C2×C4#1058762812yes—
277C8—684no—
278C8—1362no—
279C22—21no—
280C22—21no—
281C22C2×#1058750511yescharacteristic
282C22#1176281811yescharacteristic
283C22C2×#1058750811yescharacteristic
284C4—22no—
285C4—22no—
286C4—21no—
287C4—21no—
288C4—41no—
289C4—41no—
290C4—42no—
291C4—41no—
292C4—41no—
293C4—81no—
294C4—81no—
295C4—81no—
296C2—21no—
297C2—21no—
298C2#1452730411yescharacteristic
299C2#1453042511yescharacteristic
300C2#1453047311yescharacteristic
subgroupG/H
centerC22C2×#10587505
commutatorC22×C4×C17C22×C4
FrattiniC2×C4⋊C4C22×D17
FittingC17×#2581C2
socleC22×C17C2×#99
prime radicalC23×C17C2×C22⋊C4
cosocleC2×C4⋊C4×C17C23
hypercenter#2581D17
hypocenterC17#11792
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2581

Complements

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

NH ≅ G/Ntype
207. C17#11792semidirect

Maximal subgroups

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

subgroupindex
C4×#105875072
#145271282
#145268142
#145268112
C17×#25812
#1179217