Finite Group Databasebeta

← #16943893

Subgroups — #16943893

Order 4352.

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

normal subgroups only

This group has 366 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#14533233C211yesmaximal, characteristic
2#14527118C211yesmaximal, characteristic
3#14526729C212yesmaximal, complemented
4#14526717C212yesmaximal, complemented
5C17×#1458C211yesmaximal, characteristic
6C2×#10587610C411yescharacteristic
7#11762866—21no—
8#11762737—21no—
9#11762737—21no—
10#11762714C411yescharacteristic
11#11762714C2211yescharacteristic
12#11762693—21no—
13#11762693—21no—
14#11762678C2211yescharacteristic
15#11762674C411yescharacteristic
16C4×C22⋊Dic17C411yescharacteristic
17#11762535C2212yes—
18#11762533—21no—
19C2×C17×#117C2211yescharacteristic
20C17×#431—21no—
21C17×#324C2212yes—
22C17×#323—21no—
23C23×C4×C17C2×C411yescharacteristic
24C22×Dic34C2×C411yescharacteristic
25C17×#117—41no—
26C17×#117—41no—
27C2×C4⋊C4×C17C2×C411yescharacteristic
28C2×C4⋊C4×C17C2311yescharacteristic
29C2×C22⋊C4×C17D411yescharacteristic
30C2×C22⋊C4×C17D411yescharacteristic
31C2×C42×C17D411yescharacteristic
32C2×C42×C17D411yescharacteristic
33C2×C22⋊Dic17—21no—
34C2×C22⋊Dic17—21no—
35C2×C4⋊Dic17C2×C411yescharacteristic
36#10587610—41no—
37#10587610—41no—
38C2×#63225—21no—
39C2×#63225—21no—
40C2×#63225—21no—
41C2×C4×Dic17C2×C411yescharacteristic
42C2×C4×Dic17C2×C411yescharacteristic
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#10587502—21no—
53C22⋊#3622—22no—
54C4⋊#3622—41no—
55#10587474—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—22no—
72C2×Dic34—41no—
73C2×Dic34—41no—
74C2×C8×C17—42no—
75C4⋊C4×C17—41no—
76C4⋊C4×C17—41no—
77C22⋊C4×C17—41no—
78C22⋊C4×C17—41no—
79C42×C17—21no—
80C42×C17—21no—
81C42×C17—21no—
82C42×C17—21no—
83C22⋊Dic17—42no—
84C22⋊Dic17—42no—
85C4⋊Dic17—41no—
86#63225—42no—
87#63225—42no—
88#63225—41no—
89#63225—41no—
90C4×Dic17—22no—
91C4×Dic17—41no—
92C2×#3622—42no—
93#11552—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#13112yes—
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—82no—
130C8×C17—82no—
131#3622—82no—
132#2499—171no—
133#1464—171no—
134#1458D1711yescharacteristic
135#1325—172no—
136#1319—172no—
137C22×C17—21no—
138C22×C17—21no—
139C22×C17—41no—
140C22×C17—41no—
141C22×C17—41no—
142C22×C17—81no—
143C22×C17—81no—
144C22×C17#40811yescharacteristic
145C22×C17C2×#9911yescharacteristic
146C22×C17#41311yescharacteristic
147C4×C17—22no—
148C4×C17—21no—
149C4×C17—21no—
150C4×C17—41no—
151C4×C17—41no—
152C4×C17—41no—
153C4×C17—41no—
154Dic17—42no—
155Dic17—81no—
156Dic17—81no—
157Dic17—81no—
158C2×C22⋊Q8—171no—
159C2×#117C2×D1711yescharacteristic
160#432—341no—
161#431—21no—
162#397—341no—
163#397—341no—
164#391—171no—
165#391—171no—
166#387—341no—
167#387—341no—
168#384—171no—
169#382—171no—
170C4×C22⋊C4—171no—
171#324—172no—
172#324C2×D1712yes—
173#323—21no—
174#323—341no—
175C2×C17—21no—
176C2×C17—21no—
177C2×C17—81no—
178C2×C17#146811yescharacteristic
179C2×C17#212611yescharacteristic
180C2×C17#213511yescharacteristic
181C22×Q8—171no—
182C23×C4C4×D1711yescharacteristic
183C22⋊Q8—681no—
184C22⋊Q8—681no—
185#117—41no—
186#117—41no—
187C2×C4⋊C4—171no—
188C2×C4⋊C4—341no—
189C2×C4⋊C4—341no—
190C2×C4⋊C4—341no—
191C2×C4⋊C4C4×D1711yescharacteristic
192C2×C4⋊C4C22×D1711yescharacteristic
193C2×C22⋊C4—341no—
194C2×C22⋊C4—341no—
195C2×C22⋊C4D6811yescharacteristic
196C2×C22⋊C4C22⋊D1711yescharacteristic
197C2×C42—171no—
198C2×C42—171no—
199C2×C42D6811yescharacteristic
200C2×C42C22⋊D1711yescharacteristic
201C4⋊C8—41no—
202C4⋊C8—681no—
203C22⋊C8—22no—
204C22⋊C8—342no—
205#97—681no—
206C4×C8—41no—
207#95—341no—
208#95—341no—
209#95—341no—
210#95—341no—
211#95—341no—
212#95—341no—
213#95—341no—
214C17#1155211yescharacteristic, complemented, Sylow
215C24#6322711yescharacteristic
216C2×Q8—342no—
217C2×Q8—681no—
218C2×Q8—681no—
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
233C2×C8—42no—
234C2×C8—682no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4—681no—
238C4⋊C4—682no—
239C4⋊C4—682no—
240C4⋊C4—681no—
241C4⋊C4—681no—
242C22⋊C4—41no—
243C22⋊C4—41no—
244C22⋊C4—682no—
245C22⋊C4—682no—
246C42—21no—
247C42—21no—
248C42—21no—
249C42—21no—
250C42—342no—
251C42—681no—
252C23—21no—
253C23—21no—
254C23—21no—
255C23—41no—
256C23—41no—
257C23C2×#6322711yescharacteristic
258Q8—1362no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—42no—
268C2×C4—42no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—342no—
274C2×C4—681no—
275C2×C4—681no—
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#1058747711yescharacteristic
286C2×C4#1058747711yescharacteristic
287C2×C4#1058758712yes—
288C8—82no—
289C8—1362no—
290C22—21no—
291C22—21no—
292C22—41no—
293C22—41no—
294C22—41no—
295C22—81no—
296C22—81no—
297C22#1176277511yescharacteristic
298C22C2×#1058747711yescharacteristic
299C22#1176279111yescharacteristic
300C4—21no—
301C4—21no—
302C4—22no—
303C4—41no—
304C4—41no—
305C4—41no—
306C4—41no—
307C4—682no—
308C4—1361no—
309C4—1361no—
310C4—1361no—
311C2—21no—
312C2—21no—
313C2—81no—
314C2#1452713011yescharacteristic
315C2#1453044711yescharacteristic
316C2#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#11552
LCSG ▷ C22×C4×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
3. #14526729C2semidirect
4. #14526717C2semidirect
214. C17#11552semidirect

Maximal subgroups

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

subgroupindex
#145332332
#145271182
#145267292
#145267172
C17×#14582
#1155217