Finite Group Databasebeta

← #16944701

Subgroups — #16944701

Order 4352.

402 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 87 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#14532075C211yesmaximal, characteristic
2#14527108C211yesmaximal, characteristic
3#14526813C212yesmaximal
4#14526789C212yesmaximal
5C4×C17×#101C211yesmaximal, characteristic
6C2×C4×Dic34C411yescharacteristic
7#11762862—21no—
8#11762740—21no—
9#11762739C411yescharacteristic
10#11762739C2211yescharacteristic
11#11762729C411yescharacteristic
12#11762729C2211yescharacteristic
13#11762728—21no—
14C4×#63225—21no—
15C4×#63225—21no—
16#11762655C411yescharacteristic
17#11762535—21no—
18#11762535C2212yes—
19C2×C4×Q8×C17C2211yescharacteristic
20C2×C17×#101—21no—
21C4×M16×C17—21no—
22C17×#343C2212yes—
23C22×Q8×C17D411yescharacteristic
24C22×Dic34C2×C411yescharacteristic
25C2×M16×C17—22no—
26C4×Q8×C17—41no—
27C4×Q8×C17—41no—
28C2×C4⋊C4×C17C2×C411yescharacteristic
29C2×C4⋊C4×C17D411yescharacteristic
30C2×C4⋊C4×C17C2311yescharacteristic
31C2×C42×C17C2×C411yescharacteristic
32C2×C42×C17D411yescharacteristic
33C2×C42×C17D411yescharacteristic
34C2×C4⋊Dic17C2×C411yescharacteristic
35C2×#63225—21no—
36C2×#63225—21no—
37C2×#63225—21no—
38C2×#63225—21no—
39C2×#63225—21no—
40C2×C4×Dic17—21no—
41C2×C4×Dic17—21no—
42C4×Dic34—41no—
43C4×Dic34—41no—
44C17×#101—24no—
45C17×#97—41no—
46C4×C8×C17—41no—
47#10587502—21no—
48#10587502—21no—
49#10587502—21no—
50#10587502—21no—
51#10587502—21no—
52#10587502C2×C411yescharacteristic
53#10587502C2×C411yescharacteristic
54C22⋊#3622—22no—
55C4⋊#3622—41no—
56C4×#3622—41no—
57C2×Q8×C17—22no—
58C2×Q8×C17—22no—
59C2×Q8×C17—41no—
60C22×C4×C17C22⋊C411yescharacteristic
61C22×C4×C17C22⋊C411yescharacteristic
62C22×C4×C17C22⋊C411yescharacteristic
63C22×C4×C17C22⋊C411yescharacteristic
64C22×C4×C17C22×C411yescharacteristic
65C22×C4×C17C2×D411yescharacteristic
66C22×C4×C17C2×D411yescharacteristic
67C22×Dic17—21no—
68C22×Dic17—21no—
69C22×Dic17—21no—
70C22×Dic17—21no—
71C2×Dic34—41no—
72C2×Dic34—42no—
73M16×C17—24no—
74M16×C17—42no—
75C2×C8×C17—42no—
76C4⋊C4×C17—41no—
77C4⋊C4×C17—41no—
78C4⋊C4×C17—41no—
79C42×C17—21no—
80C42×C17—21no—
81C42×C17—21no—
82C42×C17—21no—
83C42×C17—21no—
84C42×C17—21no—
85C4⋊Dic17—41no—
86#63225—42no—
87#63225—42no—
88#63225—42no—
89#63225—42no—
90#63225—42no—
91C4×Dic17—24no—
92C4×Dic17—41no—
93C4×Dic17—41no—
94C2×#3622—42no—
95#11736—171nomaximal, Sylow
96C23×C17C2×C22⋊C411yescharacteristic
97Q8×C17—44no—
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#9911yescharacteristic
113C2×C4×C17#9911yescharacteristic
114C2×C4×C17#10412yes—
115C2×C4×C17#13512yes—
116C2×Dic17—22no—
117C2×Dic17—22no—
118C2×Dic17—22no—
119C2×Dic17—41no—
120C2×Dic17—41no—
121C2×Dic17—41no—
122C2×Dic17—41no—
123C2×Dic17—41no—
124C2×Dic17—41no—
125C2×Dic17—41no—
126C2×Dic17—41no—
127C2×Dic17—41no—
128Dic34—42no—
129Dic34—42no—
130C8×C17—44no—
131#3622—82no—
132#2399—171no—
133C4×#101D1711yescharacteristic
134#1461—171no—
135#1354—172no—
136#1346—172no—
137C22×C17—21no—
138C22×C17—21no—
139C22×C17C2×#9911yescharacteristic
140C22×C17#41611yescharacteristic
141C22×C17C2×#10411yescharacteristic
142C4×C17—21no—
143C4×C17—22no—
144C4×C17—22no—
145C4×C17—41no—
146C4×C17—41no—
147C4×C17—41no—
148C4×C17—41no—
149C4×C17#35612yes—
150Dic17—42no—
151Dic17—42no—
152Dic17—42no—
153Dic17—81no—
154C2×C4×Q8—171no—
155C2×C4×Q8C2×D1711yescharacteristic
156#431—341no—
157C2×#101—21no—
158C4×M16—21no—
159#398—171no—
160#398—171no—
161#398—341no—
162#395—171no—
163#395—171no—
164#395—341no—
165C4×C4⋊C4—341no—
166C4×C4⋊C4—341no—
167#376—171no—
168#343C2×D1712yes—
169#324—172no—
170#324—341no—
171C2×C17—21no—
172C2×C17—21no—
173C2×C17#150111yescharacteristic
174C2×C17#212011yescharacteristic
175C2×C17C2×#35611yescharacteristic
176C22×Q8—171no—
177C22×Q8C22⋊D1711yescharacteristic
178C2×M16—22no—
179C4×Q8—41no—
180C4×Q8—41no—
181C4×Q8—681no—
182C4×Q8—681no—
183C2×C4⋊C4—171no—
184C2×C4⋊C4—341no—
185C2×C4⋊C4—341no—
186C2×C4⋊C4—341no—
187C2×C4⋊C4—341no—
188C2×C4⋊C4—341no—
189C2×C4⋊C4C4×D1711yescharacteristic
190C2×C4⋊C4D6811yescharacteristic
191C2×C4⋊C4C22×D1711yescharacteristic
192C2×C42—341no—
193C2×C42—341no—
194C2×C42C4×D1711yescharacteristic
195C2×C42D6811yescharacteristic
196C2×C42C22⋊D1711yescharacteristic
197C4⋊C8—681no—
198#101—24no—
199C22⋊C8—342no—
200#97—41no—
201C4×C8—41no—
202C4×C8—681no—
203#95—171no—
204#95—171no—
205#95—341no—
206#95—341no—
207#95—341no—
208#95—341no—
209#95—341no—
210C17#1173611yescharacteristic, complemented, Sylow
211C2×Q8—22no—
212C2×Q8—22no—
213C2×Q8—41no—
214C2×Q8—681no—
215C2×Q8—682no—
216C22×C4—341no—
217C22×C4—341no—
218C22×C4—341no—
219C22×C4—341no—
220C22×C4#6322711yescharacteristic
221C22×C4#6322711yescharacteristic
222C22×C4#6322711yescharacteristic
223C22×C4#6322711yescharacteristic
224C22×C4C2×C4×D1711yescharacteristic
225C22×C4C2×D6811yescharacteristic
226C22×C4C2×C22⋊D1711yescharacteristic
227M16—24no—
228M16—42no—
229C2×C8—42no—
230C2×C8—682no—
231C4⋊C4—41no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—681no—
235C4⋊C4—682no—
236C4⋊C4—682no—
237C4⋊C4—682no—
238C4⋊C4—682no—
239C4⋊C4—682no—
240C42—21no—
241C42—21no—
242C42—21no—
243C42—21no—
244C42—21no—
245C42—21no—
246C42—344no—
247C42—681no—
248C42—681no—
249C23C2×#6322711yescharacteristic
250Q8—44no—
251Q8—682no—
252Q8—682no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—22no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—342no—
268C2×C4—342no—
269C2×C4—342no—
270C2×C4—681no—
271C2×C4—681no—
272C2×C4—681no—
273C2×C4—681no—
274C2×C4—681no—
275C2×C4—681no—
276C2×C4—681no—
277C2×C4—681no—
278C2×C4—681no—
279C2×C4#1058747612yes—
280C2×C4#1058747711yescharacteristic
281C2×C4#1058747711yescharacteristic
282C2×C4#1058763612yes—
283C8—44no—
284C8—1362no—
285C22—21no—
286C22—21no—
287C22C2×#1058747711yescharacteristic
288C22#1176280311yescharacteristic
289C22C2×#1058747611yescharacteristic
290C4—22no—
291C4—22no—
292C4—21no—
293C4—41no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4—682no—
298C4—682no—
299C4—682no—
300C4—1361no—
301C4#1176260712yes—
302C2—21no—
303C2—21no—
304C2#1452727311yescharacteristic
305C2#1453042611yescharacteristic
306C2C2×#1176260711yescharacteristic
subgroupG/H
centerC2×C4#10587477
commutatorC22×C4×C17C22×C4
FrattiniC2×C4⋊C4C22×D17
FittingC4×C17×#101C2
socleC22×C17C2×#99
prime radicalC23×C17C2×C22⋊C4
cosocleC2×C4⋊C4×C17C23
hypercenterC4×#101D17
hypocenterC17#11736
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C4×Q8 ◁ C4×#101

Complements

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

NH ≅ G/Ntype
210. C17#11736semidirect

Maximal subgroups

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

subgroupindex
#145320752
#145271082
#145268132
#145267892
C4×C17×#1012
#1173617