Finite Group Databasebeta

← #17949655

Subgroups — #17949655

Order 4352.

690 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 690 conjugacy classes of subgroups — too many to draw. Only its 128 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
1C4×C22⋊#3624C212yesmaximal, complemented
2#14543605C212yesmaximal, complemented
3#14543601C212yesmaximal, complemented
4#14531272C211yesmaximal, characteristic
5C2×C22⋊#3624—22no—
6C2×C4×#3624—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—42no—
22C2×#63252—42no—
23C2×#63252C814yescomplemented
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—28no—
40C4×#3624—44no—
41#10587502—22no—
42#10587502—22no—
43C24×C17C22⋊C411yescharacteristic
44C23×D17—21no—
45C22×C4×C17—22no—
46C22×C4×C17—22no—
47C22×C4×C17—21no—
48C22×C4×C17—21no—
49C22×C4×C17C22⋊C411yescharacteristic
50C22×C4×C17C2×C812yes—
51C22×C4×C17M1612yes—
52C22×C4×C17C22×C411yescharacteristic
53C2×C22⋊D17—24no—
54C2×C22⋊D17—42no—
55C2×C22⋊D17—42no—
56C22×Dic17—21no—
57C22×Dic17—24no—
58C22×Dic17—24no—
59C22×Dic17—42no—
60C22×Dic17C22⋊C412yes—
61C22×Dic17C2×D412yes—
62#63252—48no—
63#63252—48no—
64C2×D68—21no—
65C2×D68—41no—
66C2×D68—41no—
67C2×D68C2×C812yes—
68C2×C4×D17—24no—
69C2×C4×D17—42no—
70C2×C4×D17—42no—
71C2×Dic34—21no—
72C2×Dic34—41no—
73C2×Dic34—41no—
74C2×Dic34C2×C812yes—
75C2×#3624—28no—
76C2×#3624—44no—
77C2×#3624—44no—
78C4⋊C4×C17—41no—
79C4⋊C4×C17—41no—
80C22⋊C4×C17—42no—
81C42×C17—42no—
82#63227—44no—
83#63227—44no—
84C4×Dic17—24no—
85C4×Dic17—41no—
86C4×Dic17—41no—
87#7563—171nomaximal, Sylow
88C23×C17—21no—
89C23×C17—21no—
90C23×C17—22no—
91C23×C17—22no—
92C23×C17C22⋊C812yes—
93C23×C17C2×C22⋊C411yescharacteristic
94C22×D17—22no—
95C22×D17—41no—
96C22×D17—41no—
97C22×D17—42no—
98C22×D17—42no—
99C2×C4×C17—21no—
100C2×C4×C17—21no—
101C2×C4×C17—24no—
102C2×C4×C17—24no—
103C2×C4×C17—41no—
104C2×C4×C17—41no—
105C2×C4×C17—42no—
106C2×C4×C17—42no—
107C2×C4×C17C22⋊C812yes—
108C2×C4×C17#9912yes—
109C2×C4×C17#10012yes—
110C2×C4×C17C22×C811yescharacteristic
111C2×C4×C17C2×M1611yescharacteristic
112C22⋊D17—48no—
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#10414yes—
122C2×Dic17#13514yes—
123D68—42no—
124D68—42no—
125C4×D17—48no—
126Dic34—42no—
127Dic34—42no—
128#3624—48no—
129#2297—171no—
130C4×C22⋊C8—172no—
131#1272—172no—
132#1270—172no—
133C22×C17—22no—
134C22×C17—24no—
135C22×C17—41no—
136C22×C17—42no—
137C22×C17—41no—
138C22×C17C2×C22⋊C811yescharacteristic
139C22×C17C2×#9911yescharacteristic
140C22×C17C2×#10011yescharacteristic
141C22×C17#41612yes—
142C22×C17C2×#10412yes—
143C2×D17—42no—
144C2×D17—44no—
145C2×D17—81no—
146C2×D17—82no—
147C2×D17—81no—
148C4×C17—21no—
149C4×C17—21no—
150C4×C17—81no—
151C4×C17—81no—
152C4×C17#32314yes—
153Dic17—24no—
154Dic17—24no—
155Dic17—42no—
156C22×#41—171no—
157C2×#117#59511yescharacteristic
158C22×C42—171no—
159C2×C22⋊C8—342no—
160C2×C4×C8—342no—
161#391—171no—
162#391—171no—
163#390—171no—
164#390—171no—
165#386—342no—
166C4×C22⋊C4—342no—
167#336—174no—
168C2×C17—42no—
169C2×C17C2×#32311yescharacteristic
170C2×C17#147612yes—
171C2×C17#150112yes—
172C2×C17#152511yescharacteristic
173C2×C17#154311yescharacteristic
174D17—82no—
175C2×#41—174no—
176C2×#41—342no—
177C2×#41—682no—
178C2×#41—682no—
179C22×Q8—171no—
180C22×D4—171no—
181C22×D4—341no—
182C23×C4—172no—
183C23×C4—341no—
184C23×C4C2×#59511yescharacteristic
185C22×C8—344no—
186#117—42no—
187C2×C4⋊C4C2×#59511yescharacteristic
188C2×C4⋊C4C2×#59511yescharacteristic
189C2×C22⋊C4—21no—
190C2×C22⋊C4—342no—
191C2×C22⋊C4—342no—
192C2×C42—21no—
193C2×C42—172no—
194C2×C42—171no—
195C2×C42—171no—
196C2×C42—682no—
197C22⋊C8—348no—
198C4×C8—684no—
199#95—342no—
200#95—342no—
201C17#756311yescharacteristic, complemented, Sylow
202C24—341no—
203C24C22⋊#59511yescharacteristic
204#41—688no—
205#41—688no—
206C2×Q8—172no—
207C2×Q8—341no—
208C2×Q8—681no—
209C2×Q8—681no—
210C2×D4—172no—
211C2×D4—344no—
212C2×D4—341no—
213C2×D4—681no—
214C2×D4—681no—
215C2×D4—682no—
216C2×D4—682no—
217C22×C4—22no—
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×C4#6324212yes—
231C22×C4#6324312yes—
232C22×C4C22⋊#59511yescharacteristic
233C22×C4C22×#59511yescharacteristic
234C2×C8—348no—
235C2×C8—684no—
236C2×C8—684no—
237C4⋊C4—41no—
238C4⋊C4—41no—
239C22⋊C4—42no—
240C22⋊C4—684no—
241C22⋊C4—684no—
242C42—42no—
243C42—344no—
244C42—681no—
245C42—681no—
246C23—21no—
247C23—21no—
248C23—22no—
249C23—22no—
250C23—342no—
251C23—681no—
252C23—681no—
253C23—682no—
254C23—682no—
255C23#1058754312yes—
256C23C2×C22⋊#59511yescharacteristic
257Q8—682no—
258Q8—682no—
259D4—682no—
260D4—682no—
261D4—688no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—24no—
265C2×C4—24no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4—174no—
271C2×C4—174no—
272C2×C4—342no—
273C2×C4—342no—
274C2×C4—342no—
275C2×C4—342no—
276C2×C4—342no—
277C2×C4—688no—
278C2×C4—681no—
279C2×C4—681no—
280C2×C4—688no—
281C2×C4#1058753912yes—
282C2×C4#1058754312yes—
283C2×C4#1058755312yes—
284C2×C4C2×#6324211yescharacteristic
285C2×C4C2×#6324311yescharacteristic
286C8—688no—
287C22—22no—
288C22—24no—
289C22—42no—
290C22—41no—
291C22—41no—
292C22—682no—
293C22—684no—
294C22—1362no—
295C22—1361no—
296C22—1361no—
297C22C2×#1058754311yescharacteristic
298C22C2×#1058753911yescharacteristic
299C22C2×#1058755311yescharacteristic
300C22#1176379912yes—
301C22D17⋊#10412yes—
302C4—21no—
303C4—21no—
304C4—81no—
305C4—81no—
306C4—344no—
307C4—344no—
308C4—682no—
309C4#1176365314yes—
310C2—42no—
311C2—1362no—
312C2C2×#1176365311yescharacteristic
313C2#1454407712yes—
314C2#1454416112yes—
315C2#1454423811yescharacteristic
316C2#1454428711yescharacteristic
subgroupG/H
centerC22×C4C22⋊#595
commutatorC2×C4×C17C22×C8
FrattiniC22×C4C22×#595
FittingC2×C17×#117C4
socleC23×C17C2×C22⋊C4
prime radicalC22×#63252C4
cosocleC2×C4×Dic17C23
hypercenterC2×#117#595
hypocenterC17#7563
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
1. C4×C22⋊#3624C2semidirect
2. #14543605C2semidirect
3. #14543601C2semidirect
23. C2×#63252C8semidirect
201. C17#7563semidirect

Maximal subgroups

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

subgroupindex
C4×C22⋊#36242
#145436052
#145436012
#145312722
#756317