Finite Group Databasebeta

← #17949944

Subgroups — #17949944

Order 4352.

630 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 94 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#14544676C212yesmaximal, complemented
2#14543604C212yesmaximal, complemented
3#14543601C212yesmaximal, complemented
4#14531273C211yesmaximal, characteristic
5C2×#10587543—22no—
6#11763675—22no—
7#11763675C2214yes—
8C22×#63256C411yescharacteristic
9C2×#10587578C411yescharacteristic
10C2×C42×D17C2211yescharacteristic
11#11762716C2211yescharacteristic
12#11762711C411yescharacteristic
13#11762710C2211yescharacteristic
14#11762687—22no—
15#11762656—22no—
16C17×#391C411yescharacteristic
17C22×Q8×C17C2×C411yescharacteristic
18C2×#63256—22no—
19C2×#63256—22no—
20C2×#63256—42no—
21C2×#63256—42no—
22C22×D68—21no—
23C22×D68C2×C411yescharacteristic
24C22×C4×D17—21no—
25C22×C4×D17C2×C411yescharacteristic
26C22×C4×D17D412yes—
27C22×#3624—24no—
28C2×C4⋊C4×C17C2×C411yescharacteristic
29C2×C42×C17C2×C411yescharacteristic
30C2×#63227—21no—
31C2×#63227—22no—
32C2×#63227—22no—
33C2×C4⋊Dic17C2×C411yescharacteristic
34C2×C4×Dic17—21no—
35C2×C4×Dic17D412yes—
36C2×C4×Dic17C2311yescharacteristic
37#10587578—42no—
38C42×D17—42no—
39#10587543—44no—
40C17×#95—22no—
41#10587502—22no—
42C23×D17—21no—
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×Dic17C22⋊C411yescharacteristic
54C22×Dic17C2×D412yes—
55#63256—48no—
56#63256—48no—
57C2×D68—24no—
58C2×D68—21no—
59C2×D68—41no—
60C2×D68—41no—
61C2×D68—42no—
62C2×D68—42no—
63C2×D68M1612yes—
64C2×C4×D17—22no—
65C2×C4×D17—21no—
66C2×C4×D17—21no—
67C2×C4×D17—22no—
68C2×C4×D17—24no—
69C2×C4×D17—24no—
70C2×C4×D17—24no—
71C2×C4×D17—42no—
72C2×C4×D17—42no—
73C2×C4×D17—42no—
74C2×#3624—44no—
75C2×#3624—44no—
76C2×#3624—44no—
77C4⋊C4×C17—41no—
78C42×C17—41no—
79#63227—44no—
80#63227—42no—
81#63227—44no—
82C4⋊Dic17—41no—
83C4×Dic17—42no—
84C4×Dic17—41no—
85C4×Dic17—42no—
86#7645—171nomaximal, Sylow
87C23×C17C2×C22⋊C411yescharacteristic
88C22×D17—21no—
89C22×D17—21no—
90C22×D17—22no—
91C22×D17—22no—
92C22×D17—22no—
93C22×D17—41no—
94C22×D17—41no—
95C22×D17—42no—
96C22×D17—42no—
97C22×D17#9912yes—
98Q8×C17—42no—
99Q8×C17—42no—
100C2×C4×C17—21no—
101C2×C4×C17—21no—
102C2×C4×C17—22no—
103C2×C4×C17—22no—
104C2×C4×C17—22no—
105C2×C4×C17—22no—
106C2×C4×C17—41no—
107C2×C4×C17—41no—
108C2×C4×C17—41no—
109C2×C4×C17—42no—
110C2×C4×C17C2×M1611yescharacteristic
111C2×C4×C17C2×M1611yescharacteristic
112C2×Dic17—21no—
113C2×Dic17—22no—
114C2×Dic17—21no—
115C2×Dic17—22no—
116C2×Dic17—41no—
117C2×Dic17—42no—
118C2×Dic17#10012yes—
119C2×Dic17#13514yes—
120D68—42no—
121D68—42no—
122D68—48no—
123C4×D17—24no—
124C4×D17—24no—
125C4×D17—48no—
126C4×D17—48no—
127#3624—84no—
128#2297—171no—
129#1817—172no—
130#1272—172no—
131#1270—172no—
132C22×C17#40711yescharacteristic
133C22×C17C2×#9911yescharacteristic
134C22×C17C2×#10011yescharacteristic
135C22×C17#41612yes—
136C22×C17#42112yes—
137C2×D17—22no—
138C2×D17—24no—
139C2×D17—41no—
140C2×D17—41no—
141C2×D17—42no—
142C2×D17—42no—
143C2×D17—44no—
144C2×D17—81no—
145C2×D17—81no—
146C2×D17—82no—
147C4×C17—21no—
148C4×C17—21no—
149C4×C17—42no—
150C4×C17—42no—
151C4×C17—81no—
152Dic17—22no—
153Dic17—24no—
154Dic17—81no—
155C22×#41—171no—
156C2×#117—171no—
157C22×C42—171no—
158C2×C22⋊C8—342no—
159#391—171no—
160#391#59511yescharacteristic
161#390—171no—
162#390—171no—
163#386—342no—
164C4×C22⋊C4—342no—
165#336—174no—
166#336—342no—
167C2×C17#146211yescharacteristic
168C2×C17#148812yes—
169C2×C17#151612yes—
170C2×C17#153611yescharacteristic
171C2×C17#154311yescharacteristic
172D17—42no—
173D17—82no—
174C2×#41—342no—
175C2×#41—342no—
176C2×#41—682no—
177C2×#41—682no—
178C22×Q8C2×#59511yescharacteristic
179C22×D4—171no—
180C22×D4—341no—
181C23×C4—171no—
182C23×C4—172no—
183C23×C4—341no—
184C22×C8—344no—
185#117—682no—
186C2×C4⋊C4—171no—
187C2×C4⋊C4C2×#59511yescharacteristic
188C2×C22⋊C4—342no—
189C2×C22⋊C4—341no—
190C2×C22⋊C4—342no—
191C2×C42—172no—
192C2×C42—171no—
193C2×C42—341no—
194C2×C42—682no—
195C2×C42C2×#59511yescharacteristic
196C22⋊C8—684no—
197#95—22no—
198#95—342no—
199C17#764511yescharacteristic, complemented, Sylow
200C24—171no—
201C24—341no—
202#41—688no—
203#41—688no—
204C2×Q8—21no—
205C2×Q8—41no—
206C2×Q8—41no—
207C2×Q8#6324312yes—
208C2×D4—172no—
209C2×D4—344no—
210C2×D4—341no—
211C2×D4—681no—
212C2×D4—681no—
213C2×D4—682no—
214C2×D4—682no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—171no—
218C22×C4—172no—
219C22×C4—342no—
220C22×C4—344no—
221C22×C4—342no—
222C22×C4—344no—
223C22×C4—344no—
224C22×C4—341no—
225C22×C4—341no—
226C22×C4—341no—
227C22×C4—682no—
228C22×C4—682no—
229C22×C4—682no—
230C22×C4C22⋊#59512yes—
231C22×C4C22×#59511yescharacteristic
232C2×C8—684no—
233C2×C8—684no—
234C2×C8—684no—
235C4⋊C4—41no—
236C4⋊C4—681no—
237C22⋊C4—684no—
238C22⋊C4—684no—
239C22⋊C4—682no—
240C42—41no—
241C42—681no—
242C42—682no—
243C42—682no—
244C23—172no—
245C23—341no—
246C23—341no—
247C23—342no—
248C23—342no—
249C23—342no—
250C23—681no—
251C23—681no—
252C23—682no—
253C23—682no—
254C23C2×C22⋊#59511yescharacteristic
255Q8—42no—
256Q8—42no—
257D4—682no—
258D4—682no—
259D4—688no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—42no—
270C2×C4—172no—
271C2×C4—174no—
272C2×C4—344no—
273C2×C4—344no—
274C2×C4—341no—
275C2×C4—342no—
276C2×C4—341no—
277C2×C4—342no—
278C2×C4—688no—
279C2×C4—688no—
280C2×C4—681no—
281C2×C4—682no—
282C2×C4C2×#6324311yescharacteristic
283C2×C4D17⋊M1611yescharacteristic
284C8—1364no—
285C22—344no—
286C22—342no—
287C22—681no—
288C22—681no—
289C22—682no—
290C22—682no—
291C22—684no—
292C22—1362no—
293C22—1361no—
294C22—1361no—
295C22#1176378011yescharacteristic
296C22D17⋊#9911yescharacteristic
297C22D17⋊#10011yescharacteristic
298C22#1176379912yes—
299C22#1176380812yes—
300C4—21no—
301C4—21no—
302C4—42no—
303C4—42no—
304C4—81no—
305C4—344no—
306C4—342no—
307C4—1361no—
308C2—682no—
309C2—1362no—
310C2#1454403011yescharacteristic
311C2#1454411812yes—
312C2#1454421112yes—
313C2#1454427411yescharacteristic
314C2#1454428811yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC17×#391C4
socleC23×C17C2×C22⋊C4
prime radicalC22×#63256C4
cosocleC2×C4×Dic17C23
hypercenter#391#595
hypocenterC17#7645
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
1. #14544676C2semidirect
2. #14543604C2semidirect
3. #14543601C2semidirect
199. C17#7645semidirect

Maximal subgroups

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

subgroupindex
#145446762
#145436042
#145436012
#145312732
#764517