Finite Group Databasebeta

← #16945233

Subgroups — #16945233

Order 4352.

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

normal subgroups only

This group has 376 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#14534361C211yesmaximal, characteristic
2#14528867C211yesmaximal, characteristic
3#14526815C212yesmaximal, complemented
4#14526791C212yesmaximal, complemented
5C17×#1458C211yesmaximal, characteristic
6C2×C4×Dic34C411yescharacteristic
7#11762773—21no—
8#11762739C2211yescharacteristic
9#11762734C411yescharacteristic
10#11762729C2211yescharacteristic
11#11762721C411yescharacteristic
12#11762697—21no—
13#11762693—21no—
14#11762690—21no—
15#11762682—21no—
16#11762677C411yescharacteristic
17#11762578—21no—
18#11762578C2212yes—
19C2×C17×#117C2211yescharacteristic
20C17×#431—21no—
21C17×#324C2212yes—
22C17×#323—21no—
23C23×C4×C17D411yescharacteristic
24C22×Dic34C2×C411yescharacteristic
25C17×#117—41no—
26C17×#117—41no—
27C2×C4⋊C4×C17D411yescharacteristic
28C2×C4⋊C4×C17C2311yescharacteristic
29C2×C22⋊C4×C17C2×C411yescharacteristic
30C2×C22⋊C4×C17D411yescharacteristic
31C2×C42×C17C2×C411yescharacteristic
32C2×C42×C17D411yescharacteristic
33C2×C22⋊Dic17—21no—
34C2×C22⋊Dic17—21no—
35C2×C4⋊Dic17C2×C411yescharacteristic
36C2×#63225—21no—
37C2×#63225—21no—
38C2×#63225—21no—
39C2×C4×Dic17—21no—
40C2×#63223—22no—
41C4×Dic34—41no—
42C4×Dic34—41no—
43C17×C4⋊C8—41no—
44C17×C22⋊C8—22no—
45C4×C8×C17—41no—
46#10587502—21no—
47#10587502—21no—
48#10587502—21no—
49#10587502—21no—
50#10587502—21no—
51#10587502—21no—
52#10587502C2×C411yescharacteristic
53#10587502C2×C411yescharacteristic
54C22⋊#3622—41no—
55C22⋊#3622—41no—
56C24×C17C22⋊C411yescharacteristic
57C22×C4×C17—21no—
58C22×C4×C17—21no—
59C22×C4×C17—22no—
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—
71C2×Dic34—41no—
72C2×Dic34—42no—
73C2×C8×C17—42no—
74C4⋊C4×C17—41no—
75C4⋊C4×C17—41no—
76C22⋊C4×C17—41no—
77C22⋊C4×C17—41no—
78C42×C17—21no—
79C42×C17—21no—
80C42×C17—21no—
81C42×C17—21no—
82C22⋊Dic17—42no—
83C22⋊Dic17—42no—
84C4⋊Dic17—41no—
85#63225—42no—
86#63225—41no—
87#63225—41no—
88#63225—42no—
89C4×Dic17—42no—
90#63223—42no—
91#63223—42no—
92C2×#3622—42no—
93#11849—171nomaximal, Sylow
94C23×C17—21no—
95C23×C17—21no—
96C23×C17—21no—
97C23×C17—41no—
98C23×C17—41no—
99C23×C17C2×C22⋊C411yescharacteristic
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—42no—
109C2×C4×C17—42no—
110C2×C4×C17—41no—
111C2×C4×C17—41no—
112C2×C4×C17—41no—
113C2×C4×C17—41no—
114C2×C4×C17#9911yescharacteristic
115C2×C4×C17#9911yescharacteristic
116C2×C4×C17#13512yes—
117C2×Dic17—22no—
118C2×Dic17—41no—
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—
128C2×Dic17—41no—
129Dic34—42no—
130Dic34—42no—
131C8×C17—82no—
132#3622—82no—
133#2599—171no—
134#1822—171no—
135#1458D1711yescharacteristic
136#1354—172no—
137#1346—172no—
138C22×C17—21no—
139C22×C17—21no—
140C22×C17—42no—
141C22×C17—41no—
142C22×C17—41no—
143C22×C17—41no—
144C22×C17—81no—
145C22×C17C2×#9911yescharacteristic
146C22×C17#41611yescharacteristic
147C22×C17#42111yescharacteristic
148C4×C17—22no—
149C4×C17—21no—
150C4×C17—21no—
151C4×C17—41no—
152C4×C17—41no—
153C4×C17—41no—
154C4×C17—41no—
155Dic17—42no—
156Dic17—81no—
157Dic17—81no—
158Dic17—81no—
159C2×C4×Q8—171no—
160C2×#117C2×D1711yescharacteristic
161#431—21no—
162#407—341no—
163#398—171no—
164#397—171no—
165#395—171no—
166#393—171no—
167#388—341no—
168#387—341no—
169#387—341no—
170#385—341no—
171#383—171no—
172#343—172no—
173#343—341no—
174#324C2×D1712yes—
175#323—21no—
176C2×C17—21no—
177C2×C17—21no—
178C2×C17—81no—
179C2×C17#151611yescharacteristic
180C2×C17#212011yescharacteristic
181C2×C17#213511yescharacteristic
182C22×Q8—171no—
183C23×C4D6811yescharacteristic
184C2×M16—342no—
185C4×Q8—681no—
186C4×Q8—681no—
187#117—41no—
188#117—41no—
189C2×C4⋊C4—171no—
190C2×C4⋊C4—341no—
191C2×C4⋊C4—341no—
192C2×C4⋊C4—341no—
193C2×C4⋊C4D6811yescharacteristic
194C2×C4⋊C4C22×D1711yescharacteristic
195C2×C22⋊C4—341no—
196C2×C22⋊C4—341no—
197C2×C22⋊C4C4×D1711yescharacteristic
198C2×C22⋊C4C22⋊D1711yescharacteristic
199C2×C42—341no—
200C2×C42C4×D1711yescharacteristic
201C2×C42C22⋊D1711yescharacteristic
202C4⋊C8—41no—
203C22⋊C8—22no—
204C22⋊C8—681no—
205C22⋊C8—681no—
206C4×C8—41no—
207#95—171no—
208#95—171no—
209#95—341no—
210#95—341no—
211#95—341no—
212#95—341no—
213#95—341no—
214#95—341no—
215C17#1184911yescharacteristic, complemented, Sylow
216C24#6322711yescharacteristic
217C2×Q8—681no—
218C2×Q8—682no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—22no—
222C22×C4—41no—
223C22×C4—341no—
224C22×C4—341no—
225C22×C4—341no—
226C22×C4—341no—
227C22×C4#6322711yescharacteristic
228C22×C4#6322711yescharacteristic
229C22×C4#6322711yescharacteristic
230C22×C4C2×C4×D1711yescharacteristic
231C22×C4C2×D6811yescharacteristic
232C22×C4C2×C22⋊D1711yescharacteristic
233M16—682no—
234M16—682no—
235C2×C8—42no—
236C2×C8—682no—
237C4⋊C4—41no—
238C4⋊C4—41no—
239C4⋊C4—681no—
240C4⋊C4—682no—
241C4⋊C4—681no—
242C4⋊C4—681no—
243C4⋊C4—682no—
244C22⋊C4—41no—
245C22⋊C4—41no—
246C22⋊C4—682no—
247C22⋊C4—682no—
248C42—21no—
249C42—21no—
250C42—21no—
251C42—21no—
252C42—682no—
253C23—21no—
254C23—21no—
255C23—21no—
256C23—41no—
257C23—41no—
258C23C2×#6322711yescharacteristic
259Q8—682no—
260Q8—682no—
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—681no—
278C2×C4—681no—
279C2×C4—681no—
280C2×C4—681no—
281C2×C4—681no—
282C2×C4—681no—
283C2×C4—681no—
284C2×C4—681no—
285C2×C4—681no—
286C2×C4—681no—
287C2×C4#1058747711yescharacteristic
288C2×C4#1058747711yescharacteristic
289C2×C4#1058759012yes—
290C8—82no—
291C8—1362no—
292C22—21no—
293C22—21no—
294C22—42no—
295C22—41no—
296C22—41no—
297C22—41no—
298C22—81no—
299C22C2×#1058747711yescharacteristic
300C22#1176280611yescharacteristic
301C22#1176282511yescharacteristic
302C4—22no—
303C4—21no—
304C4—21no—
305C4—41no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—682no—
310C4—1361no—
311C4—1361no—
312C4—1361no—
313C2—21no—
314C2—21no—
315C2—81no—
316C2#1452734111yescharacteristic
317C2#1453042311yescharacteristic
318C2#1453047811yescharacteristic
subgroupG/H
centerC22C2×#10587477
commutatorC22×C4×C17C22×C4
FrattiniC2×C4⋊C4C22×D17
FittingC17×#1458C2
socleC22×C17C2×#99
prime radicalC24×C17C22⋊C4
cosocleC2×C4⋊C4×C17C23
hypercenter#1458D17
hypocenterC17#11849
LCSG ▷ C22×C4×C17 ▷ C23×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
3. #14526815C2semidirect
4. #14526791C2semidirect
215. C17#11849semidirect

Maximal subgroups

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

subgroupindex
#145343612
#145288672
#145268152
#145267912
C17×#14582
#1184917