Finite Group Databasebeta

← #17949941

Subgroups — #17949941

Order 4352.

630 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 100 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#14543604C212yesmaximal, complemented
3#14543600C212yesmaximal, complemented
4#14531275C211yesmaximal, characteristic
5C2×C22⋊#3624—22no—
6#11763675—22no—
7#11763675C2214yes—
8C2×#10587612C411yescharacteristic
9C22×C4×Dic17C2211yescharacteristic
10#11762716C411yescharacteristic
11#11762716C2211yescharacteristic
12#11762712C411yescharacteristic
13#11762712C2211yescharacteristic
14#11762689—22no—
15C4×C22⋊Dic17—22no—
16C22×#41×C17C411yescharacteristic
17C2×#41×C17—22no—
18C2×#41×C17—22no—
19C2×#41×C17—42no—
20C2×#41×C17—42no—
21C22×Q8×C17C2×C411yescharacteristic
22C22×D4×C17—21no—
23C22×D4×C17C2×C411yescharacteristic
24C23×C4×C17—21no—
25C23×C4×C17C2×C411yescharacteristic
26C23×Dic17D412yes—
27C22×#3624—24no—
28C2×C22⋊Dic17—21no—
29C2×C22⋊Dic17—22no—
30C2×C22⋊Dic17—22no—
31#10587612—42no—
32C2×C4⋊Dic17C2×C411yescharacteristic
33C2×C4⋊Dic17C2×C411yescharacteristic
34C2×C4×Dic17—21no—
35C2×C4×Dic17—42no—
36C2×C4×Dic17C2×C411yescharacteristic
37C2×C4×Dic17D412yes—
38C2×C4×Dic17C2311yescharacteristic
39C22⋊#3624—44no—
40#10587502—22no—
41#10587502—22no—
42C24×C17—21no—
43C24×C17C22⋊C411yescharacteristic
44#41×C17—48no—
45#41×C17—48no—
46C2×Q8×C17—21no—
47C2×Q8×C17—41no—
48C2×Q8×C17—41no—
49C2×Q8×C17M1612yes—
50C2×D4×C17—24no—
51C2×D4×C17—21no—
52C2×D4×C17—41no—
53C2×D4×C17—41no—
54C2×D4×C17—42no—
55C2×D4×C17—42no—
56C2×D4×C17M1612yes—
57C22×C4×C17—22no—
58C22×C4×C17—22no—
59C22×C4×C17—21no—
60C22×C4×C17—21no—
61C22×C4×C17—24no—
62C22×C4×C17—21no—
63C22×C4×C17—42no—
64C22×C4×C17—42no—
65C22×C4×C17C22⋊C411yescharacteristic
66C22×C4×C17C22×C411yescharacteristic
67C22×Dic17—24no—
68C22×Dic17—24no—
69C22×Dic17—21no—
70C22×Dic17—21no—
71C22×Dic17—42no—
72C22×Dic17C22⋊C412yes—
73C22×Dic17C2×D412yes—
74C2×#3624—44no—
75C2×#3624—44no—
76C2×#3624—44no—
77C22⋊Dic17—44no—
78C22⋊Dic17—42no—
79C22⋊Dic17—44no—
80C4⋊Dic17—41no—
81C4⋊Dic17—41no—
82C4×Dic17—41no—
83C4×Dic17—42no—
84C4×Dic17—41no—
85C4×Dic17—42no—
86#7645—171nomaximal, Sylow
87C23×C17—21no—
88C23×C17—21no—
89C23×C17—22no—
90C23×C17—22no—
91C23×C17—22no—
92C23×C17—41no—
93C23×C17—41no—
94C23×C17—42no—
95C23×C17—42no—
96C23×C17#9912yes—
97C23×C17C2×C22⋊C411yescharacteristic
98Q8×C17—42no—
99Q8×C17—42no—
100D4×C17—42no—
101D4×C17—42no—
102D4×C17—48no—
103C2×C4×C17—24no—
104C2×C4×C17—24no—
105C2×C4×C17—21no—
106C2×C4×C17—21no—
107C2×C4×C17—21no—
108C2×C4×C17—21no—
109C2×C4×C17—22no—
110C2×C4×C17—48no—
111C2×C4×C17—41no—
112C2×C4×C17—41no—
113C2×C4×C17#10012yes—
114C2×C4×C17C2×M1611yescharacteristic
115C2×C4×C17C2×M1611yescharacteristic
116C2×Dic17—22no—
117C2×Dic17—22no—
118C2×Dic17—22no—
119C2×Dic17—22no—
120C2×Dic17—22no—
121C2×Dic17—48no—
122C2×Dic17—41no—
123C2×Dic17—41no—
124C2×Dic17—42no—
125C2×Dic17—42no—
126C2×Dic17#13514yes—
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—42no—
138C22×C17—44no—
139C22×C17—81no—
140C22×C17—81no—
141C22×C17—82no—
142C22×C17#40711yescharacteristic
143C22×C17C2×#9911yescharacteristic
144C22×C17C2×#10011yescharacteristic
145C22×C17#41612yes—
146C22×C17#42112yes—
147C4×C17—22no—
148C4×C17—21no—
149C4×C17—21no—
150C4×C17—42no—
151Dic17—24no—
152Dic17—42no—
153Dic17—81no—
154Dic17—81no—
155C22×#41#59511yescharacteristic
156C2×#117—171no—
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—82no—
169C2×C17#146211yescharacteristic
170C2×C17#148812yes—
171C2×C17#151612yes—
172C2×C17#153611yescharacteristic
173C2×C17#154311yescharacteristic
174C2×#41—22no—
175C2×#41—22no—
176C2×#41—42no—
177C2×#41—42no—
178C22×Q8C2×#59511yescharacteristic
179C22×D4—21no—
180C22×D4C2×#59511yescharacteristic
181C23×C4—21no—
182C23×C4—172no—
183C23×C4C2×#59511yescharacteristic
184C22×C8—344no—
185#117—682no—
186C2×C4⋊C4—171no—
187C2×C4⋊C4—171no—
188C2×C22⋊C4—342no—
189C2×C22⋊C4—342no—
190C2×C22⋊C4—341no—
191C2×C42—172no—
192C2×C42—171no—
193C2×C42—171no—
194C2×C42—341no—
195C2×C42—682no—
196C22⋊C8—684no—
197#95—342no—
198#95—342no—
199C17#764511yescharacteristic, complemented, Sylow
200C24—21no—
201C24C22⋊#59511yescharacteristic
202#41—48no—
203#41—48no—
204C2×Q8—21no—
205C2×Q8—41no—
206C2×Q8—41no—
207C2×Q8#6324712yes—
208C2×D4—24no—
209C2×D4—21no—
210C2×D4—41no—
211C2×D4—41no—
212C2×D4—42no—
213C2×D4—42no—
214C2×D4#6324712yes—
215C22×C4—22no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—22no—
219C22×C4—24no—
220C22×C4—21no—
221C22×C4—42no—
222C22×C4—42no—
223C22×C4—172no—
224C22×C4—172no—
225C22×C4—344no—
226C22×C4—344no—
227C22×C4—341no—
228C22×C4—341no—
229C22×C4—682no—
230C22×C4C22⋊#59511yescharacteristic
231C22×C4C22×#59511yescharacteristic
232C2×C8—684no—
233C2×C8—684no—
234C2×C8—684no—
235C4⋊C4—681no—
236C4⋊C4—681no—
237C22⋊C4—684no—
238C22⋊C4—684no—
239C22⋊C4—682no—
240C42—682no—
241C42—681no—
242C42—681no—
243C42—682no—
244C23—21no—
245C23—21no—
246C23—22no—
247C23—22no—
248C23—22no—
249C23—41no—
250C23—41no—
251C23—42no—
252C23—42no—
253C23#1058755112yes—
254C23C2×C22⋊#59511yescharacteristic
255Q8—42no—
256Q8—42no—
257D4—42no—
258D4—42no—
259D4—48no—
260C2×C4—24no—
261C2×C4—24no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—22no—
267C2×C4—48no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—174no—
271C2×C4—342no—
272C2×C4—342no—
273C2×C4—342no—
274C2×C4—342no—
275C2×C4—342no—
276C2×C4—688no—
277C2×C4—681no—
278C2×C4—681no—
279C2×C4—682no—
280C2×C4—682no—
281C2×C4#1058755312yes—
282C2×C4C2×#6324711yescharacteristic
283C2×C4C2×#6324711yescharacteristic
284C8—1364no—
285C22—24no—
286C22—22no—
287C22—41no—
288C22—41no—
289C22—42no—
290C22—42no—
291C22—44no—
292C22—82no—
293C22—81no—
294C22—81no—
295C22#1176377911yescharacteristic
296C22C2×#1058755111yescharacteristic
297C22C2×#1058755311yescharacteristic
298C22#1176379912yes—
299C22#1176380612yes—
300C4—22no—
301C4—21no—
302C4—21no—
303C4—42no—
304C4—344no—
305C4—682no—
306C4—1361no—
307C4—1361no—
308C2—42no—
309C2—82no—
310C2#1454402911yescharacteristic
311C2#1454411512yes—
312C2#1454421012yes—
313C2#1454427211yescharacteristic
314C2#1454428711yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
Fitting, prime radicalC22×#41×C17C4
socleC23×C17C2×C22⋊C4
cosocleC2×C4×Dic17C23
hypercenterC22×#41#595
hypocenterC17#7645
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. #14544675C2semidirect
2. #14543604C2semidirect
3. #14543600C2semidirect
199. C17#7645semidirect

Maximal subgroups

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

subgroupindex
#145446752
#145436042
#145436002
#145312752
#764517