Finite Group Databasebeta

← #17949943

Subgroups — #17949943

Order 4352.

630 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 96 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#14544675C212yesmaximal, complemented
2#14543605C212yesmaximal, complemented
3#14543601C212yesmaximal, complemented
4#14531272C211yesmaximal, characteristic
5C2×C22⋊#3624—22no—
6#11763675—22no—
7#11763675C2214yes—
8C22×#63252C411yescharacteristic
9C22×C4×Dic17C2211yescharacteristic
10#11762714C411yescharacteristic
11#11762714C2211yescharacteristic
12#11762710C411yescharacteristic
13#11762710C2211yescharacteristic
14#11762686—22no—
15C4×#63227—22no—
16C2×C17×#117C411yescharacteristic
17C23×C4×C17C2×C411yescharacteristic
18C22×C22⋊D17—21no—
19C23×Dic17D412yes—
20C2×#63252—22no—
21C2×#63252—22no—
22C2×#63252—42no—
23C2×#63252—42no—
24C22×D68C2×C411yescharacteristic
25C22×C4×D17—21no—
26C22×Dic34C2×C411yescharacteristic
27C22×#3624—24no—
28C17×#117—42no—
29C2×C4⋊C4×C17C2×C411yescharacteristic
30C2×C4⋊C4×C17C2×C411yescharacteristic
31C2×C22⋊C4×C17—21no—
32C2×C42×C17—21no—
33C2×#63227—22no—
34C2×#63227—22no—
35C2×C4×Dic17—42no—
36C2×C4×Dic17C2×C411yescharacteristic
37C2×C4×Dic17D412yes—
38C2×C4×Dic17C2311yescharacteristic
39C22⋊#3624—44no—
40#10587502—22no—
41#10587502—22no—
42C24×C17C22⋊C411yescharacteristic
43C23×D17—21no—
44C22×C4×C17—22no—
45C22×C4×C17—22no—
46C22×C4×C17—21no—
47C22×C4×C17—21no—
48C22×C4×C17—21no—
49C22×C4×C17—21no—
50C22×C4×C17C22⋊C411yescharacteristic
51C22×C4×C17C22×C411yescharacteristic
52C2×C22⋊D17—24no—
53C2×C22⋊D17—42no—
54C2×C22⋊D17—42no—
55C22×Dic17—24no—
56C22×Dic17—21no—
57C22×Dic17—24no—
58C22×Dic17—42no—
59C22×Dic17C22⋊C412yes—
60C22×Dic17C2×D412yes—
61#63252—48no—
62#63252—48no—
63C2×D68—21no—
64C2×D68—41no—
65C2×D68—41no—
66C2×D68M1612yes—
67C2×C4×D17—24no—
68C2×C4×D17—42no—
69C2×C4×D17—42no—
70C2×Dic34—21no—
71C2×Dic34—41no—
72C2×Dic34—41no—
73C2×Dic34M1612yes—
74C2×#3624—44no—
75C2×#3624—44no—
76C2×#3624—44no—
77C4⋊C4×C17—41no—
78C4⋊C4×C17—41no—
79C22⋊C4×C17—42no—
80C42×C17—42no—
81#63227—44no—
82#63227—44no—
83C4×Dic17—41no—
84C4×Dic17—42no—
85C4×Dic17—41no—
86#7645—171nomaximal, Sylow
87C23×C17—21no—
88C23×C17—21no—
89C23×C17—22no—
90C23×C17—22no—
91C23×C17#9912yes—
92C23×C17C2×C22⋊C411yescharacteristic
93C22×D17—22no—
94C22×D17—41no—
95C22×D17—41no—
96C22×D17—42no—
97C22×D17—42no—
98C2×C4×C17—24no—
99C2×C4×C17—24no—
100C2×C4×C17—21no—
101C2×C4×C17—21no—
102C2×C4×C17—21no—
103C2×C4×C17—21no—
104C2×C4×C17—41no—
105C2×C4×C17—41no—
106C2×C4×C17—42no—
107C2×C4×C17—42no—
108C2×C4×C17#10012yes—
109C2×C4×C17C2×M1611yescharacteristic
110C2×C4×C17C2×M1611yescharacteristic
111C22⋊D17—48no—
112C2×Dic17—22no—
113C2×Dic17—22no—
114C2×Dic17—22no—
115C2×Dic17—22no—
116C2×Dic17—22no—
117C2×Dic17—22no—
118C2×Dic17—48no—
119C2×Dic17—41no—
120C2×Dic17—41no—
121C2×Dic17#13514yes—
122D68—42no—
123D68—42no—
124C4×D17—48no—
125Dic34—42no—
126Dic34—42no—
127#3624—84no—
128#2297—171no—
129#1817—172no—
130#1272—172no—
131#1270—172no—
132C22×C17—22no—
133C22×C17—24no—
134C22×C17—41no—
135C22×C17—41no—
136C22×C17—42no—
137C22×C17#40711yescharacteristic
138C22×C17C2×#9911yescharacteristic
139C22×C17C2×#10011yescharacteristic
140C22×C17#41612yes—
141C22×C17#42112yes—
142C2×D17—42no—
143C2×D17—44no—
144C2×D17—81no—
145C2×D17—81no—
146C2×D17—82no—
147C4×C17—21no—
148C4×C17—21no—
149C4×C17—22no—
150C4×C17—81no—
151C4×C17—81no—
152Dic17—24no—
153Dic17—42no—
154Dic17—42no—
155C22×#41—171no—
156C2×#117#59511yescharacteristic
157C22×C42—171no—
158C2×C22⋊C8—342no—
159#391—171no—
160#391—171no—
161#390—171no—
162#390—171no—
163#386—342no—
164C4×C22⋊C4—342no—
165#336—174no—
166#336—342no—
167C2×C17—42no—
168C2×C17#146211yescharacteristic
169C2×C17#148812yes—
170C2×C17#151612yes—
171C2×C17#153611yescharacteristic
172C2×C17#154311yescharacteristic
173D17—82no—
174C2×#41—342no—
175C2×#41—342no—
176C2×#41—682no—
177C2×#41—682no—
178C22×Q8—171no—
179C22×D4—171no—
180C22×D4—341no—
181C23×C4—172no—
182C23×C4—341no—
183C23×C4C2×#59511yescharacteristic
184C22×C8—344no—
185#117—42no—
186C2×C4⋊C4C2×#59511yescharacteristic
187C2×C4⋊C4C2×#59511yescharacteristic
188C2×C22⋊C4—21no—
189C2×C22⋊C4—342no—
190C2×C22⋊C4—342no—
191C2×C42—21no—
192C2×C42—172no—
193C2×C42—171no—
194C2×C42—171no—
195C2×C42—682no—
196C22⋊C8—684no—
197#95—342no—
198#95—342no—
199C17#764511yescharacteristic, complemented, Sylow
200C24—341no—
201C24C22⋊#59511yescharacteristic
202#41—688no—
203#41—688no—
204C2×Q8—172no—
205C2×Q8—341no—
206C2×Q8—681no—
207C2×Q8—681no—
208C2×D4—172no—
209C2×D4—344no—
210C2×D4—341no—
211C2×D4—681no—
212C2×D4—681no—
213C2×D4—682no—
214C2×D4—682no—
215C22×C4—22no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—22no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—172no—
222C22×C4—172no—
223C22×C4—344no—
224C22×C4—344no—
225C22×C4—341no—
226C22×C4—344no—
227C22×C4—682no—
228C22×C4—682no—
229C22×C4—682no—
230C22×C4C22⋊#59511yescharacteristic
231C22×C4C22×#59511yescharacteristic
232C2×C8—684no—
233C2×C8—684no—
234C2×C8—684no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C22⋊C4—42no—
238C22⋊C4—684no—
239C22⋊C4—684no—
240C42—42no—
241C42—682no—
242C42—681no—
243C42—681no—
244C23—21no—
245C23—21no—
246C23—22no—
247C23—22no—
248C23—342no—
249C23—681no—
250C23—681no—
251C23—682no—
252C23—682no—
253C23#1058753912yes—
254C23C2×C22⋊#59511yescharacteristic
255Q8—682no—
256Q8—682no—
257D4—682no—
258D4—682no—
259D4—688no—
260C2×C4—24no—
261C2×C4—24no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4—174no—
271C2×C4—342no—
272C2×C4—342no—
273C2×C4—342no—
274C2×C4—342no—
275C2×C4—342no—
276C2×C4—342no—
277C2×C4—688no—
278C2×C4—688no—
279C2×C4—681no—
280C2×C4—681no—
281C2×C4#1058755312yes—
282C2×C4D17⋊M1611yescharacteristic
283C2×C4D17⋊M1611yescharacteristic
284C8—1364no—
285C22—24no—
286C22—22no—
287C22—41no—
288C22—41no—
289C22—42no—
290C22—682no—
291C22—684no—
292C22—1362no—
293C22—1361no—
294C22—1361no—
295C22#1176378111yescharacteristic
296C22C2×#1058753911yescharacteristic
297C22C2×#1058755311yescharacteristic
298C22#1176379912yes—
299C22#1176380612yes—
300C4—22no—
301C4—21no—
302C4—21no—
303C4—81no—
304C4—81no—
305C4—344no—
306C4—682no—
307C4—682no—
308C2—42no—
309C2—1362no—
310C2#1454403111yescharacteristic
311C2#1454411712yes—
312C2#1454421212yes—
313C2#1454427211yescharacteristic
314C2#1454428711yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC2×C17×#117C4
socleC23×C17C2×C22⋊C4
prime radicalC22×#63252C4
cosocleC2×C4×Dic17C23
hypercenterC2×#117#595
hypocenterC17#7645
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
1. #14544675C2semidirect
2. #14543605C2semidirect
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
#145446752
#145436052
#145436012
#145312722
#764517