Finite Group Databasebeta

← #17949887

Subgroups — #17949887

Order 4352.

658 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 658 conjugacy classes of subgroups — too many to draw. Only its 102 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#14544511C212yesmaximal
2#14543605C212yesmaximal, complemented
3#14543604C212yesmaximal, complemented
4D17×#391C211yesmaximal, characteristic
5C2×#10587543—22no—
6C2×#10587542—22no—
7#11763675C2214yes—
8C22×Q8×D17C411yescharacteristic
9C2×C4⋊C4×D17C411yescharacteristic
10C2×C42×D17C2211yescharacteristic
11#11762716C2211yescharacteristic
12#11762715C411yescharacteristic
13#11762714C2211yescharacteristic
14#11762713—22no—
15#95×D17—22no—
16C17×#391C411yescharacteristic
17C22×Q8×C17C2×C411yescharacteristic
18C2×Q8×D17—22no—
19C2×Q8×D17—22no—
20C2×Q8×D17—42no—
21C2×Q8×D17—42no—
22C22×C4×D17—21no—
23C22×C4×D17—21no—
24C22×C4×D17C2×C411yescharacteristic
25C22×C4×D17D412yes—
26C22×Dic34—21no—
27C22×Dic34C2×C411yescharacteristic
28C22×#3624—24no—
29C2×C4⋊C4×C17C2×C411yescharacteristic
30C2×C42×C17C2×C411yescharacteristic
31C2×C4⋊Dic17C2×C411yescharacteristic
32C2×#63225—21no—
33C2×C4×Dic17D412yes—
34C2×C4×Dic17C2311yescharacteristic
35C4⋊C4×D17—42no—
36C42×D17—42no—
37#10587543—28no—
38#10587542—44no—
39C17×#95—22no—
40#10587502—22no—
41#10587502—22no—
42#10587502—22no—
43C23×D17C22⋊C411yescharacteristic
44C2×Q8×C17—21no—
45C2×Q8×C17—41no—
46C2×Q8×C17—41no—
47C2×Q8×C17M1612yes—
48C22×C4×C17—21no—
49C22×C4×C17—21no—
50C22×C4×C17C22⋊C412yes—
51C22×C4×C17C22×C411yescharacteristic
52C22×Dic17—21no—
53C22×Dic17—21no—
54C22×Dic17C22⋊C411yescharacteristic
55C22×Dic17C2×D412yes—
56Q8×D17—48no—
57Q8×D17—48no—
58C2×C4×D17—22no—
59C2×C4×D17—21no—
60C2×C4×D17—21no—
61C2×C4×D17—22no—
62C2×C4×D17—24no—
63C2×C4×D17—24no—
64C2×C4×D17—24no—
65C2×C4×D17—42no—
66C2×C4×D17—42no—
67C2×C4×D17—42no—
68C2×C4×D17—42no—
69C2×C4×D17—44no—
70C2×Dic34—24no—
71C2×Dic34—21no—
72C2×Dic34—42no—
73C2×Dic34—42no—
74C2×Dic34—41no—
75C2×Dic34—41no—
76C2×Dic34M1612yes—
77C2×#3624—28no—
78C2×#3624—44no—
79C2×#3624—44no—
80C4⋊C4×C17—41no—
81C42×C17—41no—
82C4⋊Dic17—41no—
83#63225—42no—
84C4×Dic17—24no—
85C4×Dic17—41no—
86#7629—171nomaximal, Sylow
87C23×C17C2×C22⋊C411yescharacteristic
88C22×D17—21no—
89C22×D17—21no—
90C22×D17—22no—
91C22×D17#10012yes—
92C22×D17#10414yes—
93Q8×C17—42no—
94Q8×C17—42no—
95C2×C4×C17—21no—
96C2×C4×C17—21no—
97C2×C4×C17—22no—
98C2×C4×C17—22no—
99C2×C4×C17—22no—
100C2×C4×C17—22no—
101C2×C4×C17—41no—
102C2×C4×C17—41no—
103C2×C4×C17—41no—
104C2×C4×C17—42no—
105C2×C4×C17C2×M1611yescharacteristic
106C2×C4×C17C2×M1611yescharacteristic
107C2×Dic17—21no—
108C2×Dic17—22no—
109C2×Dic17—21no—
110C2×Dic17—22no—
111C2×Dic17—22no—
112C2×Dic17—41no—
113C2×Dic17—41no—
114C2×Dic17—41no—
115C2×Dic17—42no—
116C2×Dic17#9912yes—
117C2×Dic17#13714yes—
118C4×D17—24no—
119C4×D17—24no—
120C4×D17—48no—
121C4×D17—48no—
122C4×D17—84no—
123Dic34—48no—
124Dic34—42no—
125Dic34—42no—
126#3624—48no—
127C2×#391—171no—
128#1749—172no—
129#1272—172no—
130#1272—172no—
131C22×C17#40711yescharacteristic
132C22×C17C2×#9911yescharacteristic
133C22×C17C2×#10011yescharacteristic
134C22×C17#41912yes—
135C22×C17C2×#10412yes—
136C2×D17—22no—
137C2×D17—22no—
138C2×D17—24no—
139C2×D17—24no—
140C2×D17#32914yes—
141C4×C17—21no—
142C4×C17—21no—
143C4×C17—42no—
144C4×C17—42no—
145C4×C17—81no—
146Dic17—22no—
147Dic17—24no—
148Dic17—42no—
149Dic17—81no—
150C23×Q8—171no—
151C22×C4⋊C4—171no—
152C22×C42—171no—
153C2×C22⋊C8—342no—
154C2×#97—342no—
155#391—171no—
156#391—171no—
157#391—171no—
158#391—342no—
159#391#59511yescharacteristic
160C2×#95—342no—
161#336—174no—
162C2×C17#146211yescharacteristic
163C2×C17#149112yes—
164C2×C17#150812yes—
165C2×C17C2×#32911yescharacteristic
166C2×C17#155811yescharacteristic
167D17—24no—
168C22×Q8—171no—
169C22×Q8—341no—
170C22×Q8—342no—
171C22×Q8—342no—
172C22×Q8—682no—
173C22×Q8—682no—
174C22×Q8C2×#59511yescharacteristic
175C23×C4—171no—
176C23×C4—172no—
177C23×C4—341no—
178C23×C4—341no—
179C22×C8—344no—
180C2×C4⋊C4—171no—
181C2×C4⋊C4—341no—
182C2×C4⋊C4—682no—
183C2×C4⋊C4C2×#59511yescharacteristic
184C2×C42—172no—
185C2×C42—171no—
186C2×C42—682no—
187C2×C42C2×#59511yescharacteristic
188C22⋊C8—348no—
189#97—684no—
190#95—22no—
191#95—342no—
192#95—342no—
193#95—342no—
194C17#762911yescharacteristic, complemented, Sylow
195C24—171no—
196C2×Q8—21no—
197C2×Q8—41no—
198C2×Q8—41no—
199C2×Q8—172no—
200C2×Q8—344no—
201C2×Q8—341no—
202C2×Q8—681no—
203C2×Q8—681no—
204C2×Q8—682no—
205C2×Q8—682no—
206C2×Q8—688no—
207C2×Q8—688no—
208C2×Q8#6324312yes—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—171no—
212C22×C4—172no—
213C22×C4—342no—
214C22×C4—344no—
215C22×C4—342no—
216C22×C4—344no—
217C22×C4—344no—
218C22×C4—341no—
219C22×C4—341no—
220C22×C4—341no—
221C22×C4—341no—
222C22×C4—682no—
223C22×C4—682no—
224C22×C4—682no—
225C22×C4—682no—
226C22×C4—684no—
227C22×C4C22⋊#59512yes—
228C22×C4C22×#59511yescharacteristic
229C2×C8—348no—
230C2×C8—684no—
231C2×C8—684no—
232C4⋊C4—41no—
233C4⋊C4—681no—
234C4⋊C4—682no—
235C42—41no—
236C42—344no—
237C42—681no—
238C23—172no—
239C23—174no—
240C23—341no—
241C23—341no—
242C23—342no—
243C23C2×C22⋊#59511yescharacteristic
244Q8—42no—
245Q8—42no—
246Q8—682no—
247Q8—682no—
248Q8—688no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—42no—
259C2×C4—172no—
260C2×C4—174no—
261C2×C4—344no—
262C2×C4—344no—
263C2×C4—341no—
264C2×C4—342no—
265C2×C4—341no—
266C2×C4—342no—
267C2×C4—342no—
268C2×C4—688no—
269C2×C4—688no—
270C2×C4—681no—
271C2×C4—681no—
272C2×C4—681no—
273C2×C4—682no—
274C2×C4—1364no—
275C2×C4C2×#6324311yescharacteristic
276C2×C4D17⋊M1611yescharacteristic
277C8—688no—
278C22—174no—
279C22—344no—
280C22—342no—
281C22—342no—
282C22—344no—
283C22#1176378011yescharacteristic
284C22D17⋊#9911yescharacteristic
285C22D17⋊#10011yescharacteristic
286C22#1176380212yes—
287C22D17⋊#10412yes—
288C4—21no—
289C4—21no—
290C4—42no—
291C4—42no—
292C4—81no—
293C4—344no—
294C4—342no—
295C4—682no—
296C4—1361no—
297C2—344no—
298C2#1454403011yescharacteristic
299C2#1454412712yes—
300C2#1454418212yes—
301C2D17⋊#32911yescharacteristic
302C2#1454431811yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC17×#391C4
socleC23×C17C2×C22⋊C4
prime radicalC23×D17C22⋊C4
cosocleC2×C4×Dic17C23
hypercenter#391#595
hypocenterC17#7629
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #391

Complements

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

NH ≅ G/Ntype
2. #14543605C2semidirect
3. #14543604C2semidirect
194. C17#7629semidirect

Maximal subgroups

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

subgroupindex
#145445112
#145436052
#145436042
D17×#3912
#762917