Finite Group Databasebeta

← #16943873

Subgroups — #16943873

Order 4352.

380 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 79 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#14533067C211yesmaximal, characteristic
2#14527118C211yesmaximal, characteristic
3#14526733C212yesmaximal
4#14526713C212yesmaximal
5C17×#1458C211yesmaximal, characteristic
6C22×#63225C411yescharacteristic
7#11762866—21no—
8#11762747—21no—
9#11762740—21no—
10#11762693—21no—
11#11762693—21no—
12#11762681C411yescharacteristic
13#11762681C2211yescharacteristic
14#11762672C411yescharacteristic
15#11762670C411yescharacteristic
16#11762670C2211yescharacteristic
17#11762535—21no—
18#11762533C2212yes—
19C2×C17×#117C2211yescharacteristic
20C17×#431—21no—
21C17×#324—21no—
22C17×#323C2212yes—
23C23×C4×C17C2×C411yescharacteristic
24C23×Dic17C2×C411yescharacteristic
25C23×Dic17C2×C411yescharacteristic
26C17×#117—41no—
27C17×#117—41no—
28C2×C4⋊C4×C17D411yescharacteristic
29C2×C4⋊C4×C17D411yescharacteristic
30C2×C22⋊C4×C17C2×C411yescharacteristic
31C2×C22⋊C4×C17C2311yescharacteristic
32C2×C42×C17D411yescharacteristic
33C2×C42×C17D411yescharacteristic
34C2×C22⋊Dic17C2×C411yescharacteristic
35C2×C22⋊Dic17C2×C411yescharacteristic
36C2×#63225—21no—
37C2×#63225—21no—
38C2×#63225—21no—
39C2×#63225—21no—
40C2×#63225—41no—
41C2×#63225—41no—
42C17×C4⋊C8—41no—
43C17×C22⋊C8—22no—
44C4×C8×C17—41no—
45#10587502—21no—
46#10587502—21no—
47#10587502—21no—
48#10587502—21no—
49#10587502—21no—
50#10587502—21no—
51#10587502—21no—
52#10587502—21no—
53C22⋊#3622—22no—
54C4⋊#3622—41no—
55#10587474—41no—
56C24×C17C22×C411yescharacteristic
57C22×C4×C17—22no—
58C22×C4×C17—21no—
59C22×C4×C17—21no—
60C22×C4×C17—41no—
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—
71C22×Dic17—22no—
72C22×Dic17—42no—
73C22×Dic17—41no—
74C22×Dic17—41no—
75C22×Dic17—41no—
76C2×C8×C17—42no—
77C4⋊C4×C17—41no—
78C4⋊C4×C17—41no—
79C22⋊C4×C17—41no—
80C22⋊C4×C17—41no—
81C42×C17—21no—
82C42×C17—21no—
83C42×C17—21no—
84C42×C17—21no—
85C22⋊Dic17—22no—
86C22⋊Dic17—41no—
87#63225—42no—
88#63225—42no—
89#63225—42no—
90#63225—41no—
91#63225—41no—
92C2×#3622—42no—
93#11548—171nomaximal, Sylow
94C23×C17—21no—
95C23×C17—21no—
96C23×C17—41no—
97C23×C17—41no—
98C23×C17C2×C22⋊C411yescharacteristic
99C23×C17#13112yes—
100C2×C4×C17—21no—
101C2×C4×C17—21no—
102C2×C4×C17—21no—
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—42no—
110C2×C4×C17—42no—
111C2×C4×C17—41no—
112C2×C4×C17—41no—
113C2×C4×C17—41no—
114C2×C4×C17—41no—
115C2×C4×C17#9911yescharacteristic
116C2×C4×C17#9911yescharacteristic
117C2×Dic17—22no—
118C2×Dic17—41no—
119C2×Dic17—42no—
120C2×Dic17—41no—
121C2×Dic17—42no—
122C2×Dic17—41no—
123C2×Dic17—41no—
124C2×Dic17—41no—
125C2×Dic17—41no—
126C2×Dic17—41no—
127C2×Dic17—41no—
128C2×Dic17—41no—
129C2×Dic17—41no—
130C2×Dic17—41no—
131C2×Dic17—82no—
132C8×C17—82no—
133#3622—82no—
134#2484—171no—
135#1464—171no—
136#1458D1711yescharacteristic
137#1326—172no—
138#1317—172no—
139C22×C17—21no—
140C22×C17—21no—
141C22×C17—22no—
142C22×C17—42no—
143C22×C17—42no—
144C22×C17—41no—
145C22×C17—41no—
146C22×C17#40811yescharacteristic
147C22×C17C2×#9911yescharacteristic
148C22×C17#41311yescharacteristic
149C4×C17—21no—
150C4×C17—21no—
151C4×C17—41no—
152C4×C17—41no—
153C4×C17—41no—
154C4×C17—41no—
155C4×C17—41no—
156Dic17—42no—
157Dic17—81no—
158Dic17—81no—
159Dic17—81no—
160C2×#117C2×D1711yescharacteristic
161C22×C4⋊C4—171no—
162#432—341no—
163#431—21no—
164#400—341no—
165#398—341no—
166#387—341no—
167#387—341no—
168#385—171no—
169#385—171no—
170#381—171no—
171#381—171no—
172#381—171no—
173#324—21no—
174#324—341no—
175#323—172no—
176#323C2×D1712yes—
177C2×C17—21no—
178C2×C17—21no—
179C2×C17—42no—
180C2×C17#146811yescharacteristic
181C2×C17#212011yescharacteristic
182C2×C17#212311yescharacteristic
183C23×C4—171no—
184C23×C4—171no—
185C23×C4C4×D1711yescharacteristic
186#117—41no—
187#117—41no—
188C2×C4⋊C4—341no—
189C2×C4⋊C4—341no—
190C2×C4⋊C4—341no—
191C2×C4⋊C4—341no—
192C2×C4⋊C4—681no—
193C2×C4⋊C4—681no—
194C2×C4⋊C4D6811yescharacteristic
195C2×C4⋊C4C22⋊D1711yescharacteristic
196C2×C22⋊C4—171no—
197C2×C22⋊C4—171no—
198C2×C22⋊C4C4×D1711yescharacteristic
199C2×C22⋊C4C22×D1711yescharacteristic
200C2×C42D6811yescharacteristic
201C2×C42C22⋊D1711yescharacteristic
202C4⋊C8—41no—
203C4⋊C8—681no—
204C22⋊C8—22no—
205C22⋊C8—342no—
206#97—681no—
207C4×C8—41no—
208#95—341no—
209#95—341no—
210#95—341no—
211#95—341no—
212#95—341no—
213#95—341no—
214#95—341no—
215#95—341no—
216C17#1154811yescharacteristic, complemented, Sylow
217C24C2×C4×D1711yescharacteristic
218C22×C4—22no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—41no—
222C22×C4—341no—
223C22×C4—341no—
224C22×C4—341no—
225C22×C4—341no—
226C22×C4—342no—
227C22×C4—682no—
228C22×C4—681no—
229C22×C4—681no—
230C22×C4—681no—
231C22×C4#6322711yescharacteristic
232C22×C4#6322711yescharacteristic
233C22×C4#6322711yescharacteristic
234C22×C4#6322711yescharacteristic
235C22×C4C2×D6811yescharacteristic
236C22×C4C2×C22⋊D1711yescharacteristic
237C2×C8—42no—
238C2×C8—682no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—682no—
242C4⋊C4—682no—
243C4⋊C4—682no—
244C4⋊C4—681no—
245C4⋊C4—681no—
246C22⋊C4—41no—
247C22⋊C4—41no—
248C22⋊C4—342no—
249C22⋊C4—681no—
250C42—21no—
251C42—21no—
252C42—21no—
253C42—21no—
254C23—21no—
255C23—21no—
256C23—41no—
257C23—41no—
258C23#1058758712yes—
259C23C2×#6322711yescharacteristic
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—342no—
276C2×C4—681no—
277C2×C4—682no—
278C2×C4—681no—
279C2×C4—682no—
280C2×C4—681no—
281C2×C4—681no—
282C2×C4—681no—
283C2×C4—681no—
284C2×C4—681no—
285C2×C4—681no—
286C2×C4—681no—
287C2×C4—681no—
288C2×C4—681no—
289C2×C4—1362no—
290C2×C4#1058747711yescharacteristic
291C2×C4#1058747711yescharacteristic
292C8—82no—
293C8—1362no—
294C22—21no—
295C22—21no—
296C22—22no—
297C22—42no—
298C22—42no—
299C22—41no—
300C22—41no—
301C22#1176277511yescharacteristic
302C22C2×#1058747711yescharacteristic
303C22#1176279111yescharacteristic
304C4—21no—
305C4—21no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—41no—
310C4—41no—
311C4—682no—
312C4—1361no—
313C4—1361no—
314C4—1361no—
315C2—21no—
316C2—21no—
317C2—42no—
318C2#1452713011yescharacteristic
319C2#1453042611yescharacteristic
320C2#1453043711yescharacteristic
subgroupG/H
centerC22C2×#10587477
commutator, prime radicalC24×C17C22×C4
FrattiniC2×C22⋊C4C22×D17
FittingC17×#1458C2
socleC22×C17C2×#99
cosocleC2×C22⋊C4×C17C23
hypercenter#1458D17
hypocenterC17#11548
LCSG ▷ C24×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1458

Complements

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

NH ≅ G/Ntype
216. C17#11548semidirect

Maximal subgroups

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

subgroupindex
#145330672
#145271182
#145267332
#145267132
C17×#14582
#1154817