Finite Group Databasebeta

← #16943807

Subgroups — #16943807

Order 4352.

504 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 75 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#14531507C211yesmaximal, characteristic
2#14527121C212yesmaximal, complemented
3#14526728C211yesmaximal, characteristic, complemented
4#14526715C212yesmaximal, complemented
5C17×#1324C211yesmaximal, characteristic, complemented
6C2×#10587560C411yescharacteristic
7C2×#10587579C411yescharacteristic
8C2×#10587579C2211yescharacteristic
9#11762771—22no—
10#11762710C411yescharacteristic
11#11762710C2211yescharacteristic
12#11762687—22no—
13#11762687—22no—
14#11762655C411yescharacteristic
15#11762535C2212yes—
16#11762532—22no—
17C17×#382C2211yescharacteristic
18C17×#324C2212yes—
19C22×D68—22no—
20C22×D68C2×C411yescharacteristic
21C22×D68C2×C411yescharacteristic
22C22×C4×D17—21no—
23C22×C4×D17D412yes—
24C2×C4⋊C4×C17C2×C411yescharacteristic
25C2×C4⋊C4×C17C2311yescharacteristic
26C2×C42×C17C2×C411yescharacteristic
27C2×#63227—22no—
28C2×#63227—22no—
29C2×#63227—21no—
30C2×#63227D412yes—
31C2×C4×Dic17C2×C411yescharacteristic
32C2×C4×Dic17C2×C411yescharacteristic
33C2×#63218—42no—
34#10587579—42no—
35#10587579—42no—
36#10587560—22no—
37#10587560—22no—
38C17×C22⋊C8—22no—
39C17×#95—22no—
40#10587502—21no—
41#10587502—21no—
42C22⋊#3622—22no—
43#10587491—42no—
44C23×D17—21no—
45C23×D17C22⋊C412yes—
46C22×C4×C17—21no—
47C22×C4×C17—21no—
48C22×C4×C17C22×C411yescharacteristic
49C22×C4×C17C2×D412yes—
50C22×Dic17—21no—
51C22×Dic17C22⋊C411yescharacteristic
52C22×Dic17C22⋊C411yescharacteristic
53C2×D68—21no—
54C2×D68—21no—
55C2×D68—21no—
56C2×D68—28no—
57C2×D68—41no—
58C2×D68—41no—
59C2×D68—41no—
60C2×D68—41no—
61C2×D68—82no—
62C2×D68—82no—
63C2×D68M1612yescomplemented
64C2×C4×D17—22no—
65C2×C4×D17—22no—
66C2×C4×D17—42no—
67C2×C4×D17—82no—
68C2×C4×D17—82no—
69C2×C8×C17—42no—
70C4⋊C4×C17—41no—
71C4⋊C4×C17—41no—
72C42×C17—21no—
73C42×C17M1612yescomplemented
74#63227—42no—
75#63227—42no—
76#63227—82no—
77#63227—82no—
78C4×Dic17—22no—
79C4×Dic17—41no—
80C2×#3622—42no—
81#63218—84no—
82#11533—171nomaximal, Sylow
83C23×C17C2×C22⋊C411yescharacteristic
84C22×D17—22no—
85C22×D17—22no—
86C22×D17—22no—
87C22×D17—22no—
88C22×D17—42no—
89C22×D17—42no—
90C22×D17—42no—
91C22×D17—42no—
92C22×D17—41no—
93C22×D17—41no—
94C2×C4×C17—21no—
95C2×C4×C17—21no—
96C2×C4×C17—22no—
97C2×C4×C17—22no—
98C2×C4×C17—41no—
99C2×C4×C17—41no—
100C2×C4×C17—42no—
101C2×C4×C17—42no—
102C2×C4×C17—41no—
103C2×C4×C17C2×M1611yescharacteristic
104C2×C4×C17C2×M1611yescharacteristic
105C2×Dic17—21no—
106C2×Dic17—41no—
107C2×Dic17—41no—
108C2×Dic17—41no—
109C2×Dic17—41no—
110C2×Dic17—41no—
111C2×Dic17#9912yes—
112D68—42no—
113D68—42no—
114D68—42no—
115D68—42no—
116D68—88no—
117C4×D17—44no—
118C4×D17—82no—
119C4×D17—84no—
120C8×C17—82no—
121#3622—82no—
122#2328—171no—
123#1465—172no—
124#1324—171no—
125#1324D1711yescharacteristic, complemented
126#1318—172no—
127C22×C17—21no—
128C22×C17—21no—
129C22×C17#40711yescharacteristic
130C22×C17C2×#9911yescharacteristic
131C22×C17#41311yescharacteristic
132C2×D17—44no—
133C2×D17—44no—
134C2×D17—42no—
135C2×D17—42no—
136C2×D17—42no—
137C2×D17—42no—
138C2×D17—82no—
139C2×D17—81no—
140C2×D17—81no—
141C2×D17—82no—
142C4×C17—21no—
143C4×C17—21no—
144C4×C17—42no—
145C4×C17—42no—
146C4×C17—81no—
147Dic17—22no—
148Dic17—41no—
149Dic17—81no—
150C2×#127—171no—
151C2×C4×D4—171no—
152C2×C4×D4—171no—
153#407—342no—
154#390—171no—
155#390—171no—
156#386—342no—
157#386—342no—
158#382C2×D1711yescharacteristic
159#376—171no—
160#324—172no—
161#324C2×D1712yes—
162#323—342no—
163C2×C17—21no—
164C2×C17—21no—
165C2×C17#146511yescharacteristic
166C2×C17#212711yescharacteristic
167C2×C17#213411yescharacteristic
168D17—82no—
169D17—82no—
170C22×D4—171no—
171C22×D4—171no—
172C22×D4—342no—
173C23×C4—172no—
174C23×C4—341no—
175C2×M16—682no—
176#127—342no—
177#127—342no—
178C4×D4—682no—
179C4×D4—682no—
180C2×C4⋊C4C4×D1711yescharacteristic
181C2×C4⋊C4C22×D1711yescharacteristic
182C2×C22⋊C4—172no—
183C2×C22⋊C4—341no—
184C2×C22⋊C4—342no—
185C2×C22⋊C4—342no—
186C2×C42—171no—
187C2×C42—171no—
188C2×C42C4×D1711yescharacteristic
189C22⋊C8—22no—
190C22⋊C8—342no—
191C22⋊C8—682no—
192#95—22no—
193#95—341no—
194#95—341no—
195C17#1153311yescharacteristic, complemented, Sylow
196C24—172no—
197C24—341no—
198C2×D4—172no—
199C2×D4—348no—
200C2×D4—341no—
201C2×D4—341no—
202C2×D4—341no—
203C2×D4—681no—
204C2×D4—681no—
205C2×D4—681no—
206C2×D4—681no—
207C2×D4—1362no—
208C2×D4—1362no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—171no—
212C22×C4—171no—
213C22×C4—342no—
214C22×C4—342no—
215C22×C4—341no—
216C22×C4—682no—
217C22×C4—1362no—
218C22×C4—1362no—
219C22×C4C2×C4×D1711yescharacteristic
220C22×C4D4×D1712yes—
221M16—1364no—
222C2×C8—42no—
223C2×C8—682no—
224C4⋊C4—41no—
225C4⋊C4—41no—
226C22⋊C4—682no—
227C22⋊C4—682no—
228C22⋊C4—1362no—
229C22⋊C4—1362no—
230C42—21no—
231C42—342no—
232C42—681no—
233C42#6321812yescomplemented
234C23—342no—
235C23—342no—
236C23—342no—
237C23—342no—
238C23—682no—
239C23—682no—
240C23—682no—
241C23—682no—
242C23—681no—
243C23—681no—
244C23C22⋊C4×D1711yescharacteristic
245D4—682no—
246D4—682no—
247D4—682no—
248D4—682no—
249D4—1368no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—41no—
259C2×C4—172no—
260C2×C4—341no—
261C2×C4—684no—
262C2×C4—681no—
263C2×C4—681no—
264C2×C4—681no—
265C2×C4—681no—
266C2×C4—681no—
267C2×C4—1362no—
268C2×C4—1364no—
269C2×C4C2×#6321811yescharacteristic
270C2×C4M16×D1711yescharacteristic
271C8—82no—
272C8—1362no—
273C22—21no—
274C22—21no—
275C22—684no—
276C22—684no—
277C22—682no—
278C22—682no—
279C22—682no—
280C22—682no—
281C22—1362no—
282C22—1362no—
283C22—1361no—
284C22—1361no—
285C22#1176277111yescharacteristic
286C22#99×D1711yescharacteristic
287C22#1176279211yescharacteristic
288C4—21no—
289C4—21no—
290C4—42no—
291C4—42no—
292C4—81no—
293C4—342no—
294C4—681no—
295C4—1361no—
296C2—21no—
297C2—21no—
298C2—1362no—
299C2—1362no—
300C2#1452712111yescharacteristic
301C2#1453045211yescharacteristic
302C2#1453047411yescharacteristic
subgroupG/H
centerC22#99×D17
commutatorC22×C4×C17C22×C4
FrattiniC2×C4⋊C4C22×D17
FittingC17×#1324C2
socleC22×C17C2×#99
prime radicalC2×#10587560C4
cosocleC2×C4⋊C4×C17C23
hypercenter#1324D17
hypocenterC17#11533
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1324

Complements

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

NH ≅ G/Ntype
2. #14527121C2semidirect
3. #14526728C2semidirect
4. #14526715C2semidirect
5. C17×#1324C2semidirect
63. C2×D68M16semidirect
73. C42×C17M16semidirect
125. #1324D17semidirect
195. C17#11533semidirect
233. C42#63218semidirect

Maximal subgroups

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

subgroupindex
#145315072
#145271212
#145267282
#145267152
C17×#13242
#1153317