Finite Group Databasebeta

← #17949767

Subgroups — #17949767

Order 4352.

630 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 110 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
2#14543605C212yesmaximal, complemented
3#14543604C212yesmaximal, complemented
4D17×#391C211yesmaximal, characteristic
5C2×#10587543—22no—
6#11763675—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—42no—
20C2×Q8×D17—42no—
21C2×Q8×D17C814yescomplemented
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—44no—
38C17×#95—22no—
39#10587502—22no—
40#10587502—22no—
41#10587502—22no—
42C23×D17C22⋊C411yescharacteristic
43C2×Q8×C17—21no—
44C2×Q8×C17—41no—
45C2×Q8×C17—41no—
46C2×Q8×C17C2×C812yes—
47C22×C4×C17—21no—
48C22×C4×C17—21no—
49C22×C4×C17C22⋊C412yes—
50C22×C4×C17C22×C411yescharacteristic
51C22×Dic17—21no—
52C22×Dic17—21no—
53C22×Dic17C22⋊C411yescharacteristic
54C22×Dic17C2×D412yes—
55Q8×D17—48no—
56Q8×D17—48no—
57C2×C4×D17—22no—
58C2×C4×D17—22no—
59C2×C4×D17—24no—
60C2×C4×D17—24no—
61C2×C4×D17—24no—
62C2×C4×D17—42no—
63C2×C4×D17—42no—
64C2×C4×D17—42no—
65C2×C4×D17—44no—
66C2×C4×D17—42no—
67C2×C4×D17C2×C812yes—
68C2×C4×D17M1612yes—
69C2×Dic34—21no—
70C2×Dic34—24no—
71C2×Dic34—42no—
72C2×Dic34—42no—
73C2×Dic34—41no—
74C2×Dic34—41no—
75C2×Dic34C2×C812yes—
76C2×#3624—44no—
77C2×#3624—44no—
78C2×#3624—44no—
79C4⋊C4×C17—41no—
80C42×C17—41no—
81C4⋊Dic17—41no—
82#63225—42no—
83C4×Dic17—42no—
84C4×Dic17—41no—
85#7595—171nomaximal, Sylow
86C23×C17C2×C22⋊C411yescharacteristic
87C22×D17—22no—
88C22×D17—22no—
89C22×D17C22⋊C812yes—
90C22×D17#9912yes—
91C22×D17#10012yes—
92Q8×C17—42no—
93Q8×C17—42no—
94C2×C4×C17—21no—
95C2×C4×C17—21no—
96C2×C4×C17—22no—
97C2×C4×C17—22no—
98C2×C4×C17—22no—
99C2×C4×C17—22no—
100C2×C4×C17—41no—
101C2×C4×C17—41no—
102C2×C4×C17—41no—
103C2×C4×C17—42no—
104C2×C4×C17C22×C811yescharacteristic
105C2×C4×C17C2×M1611yescharacteristic
106C2×Dic17—22no—
107C2×Dic17—21no—
108C2×Dic17—21no—
109C2×Dic17—22no—
110C2×Dic17—22no—
111C2×Dic17—41no—
112C2×Dic17—41no—
113C2×Dic17—41no—
114C2×Dic17—42no—
115C2×Dic17C22⋊C812yes—
116C2×Dic17#13714yes—
117C4×D17—24no—
118C4×D17—24no—
119C4×D17—48no—
120C4×D17—48no—
121C4×D17—84no—
122Dic34—48no—
123Dic34—42no—
124Dic34—42no—
125#3624—84no—
126C2×#391—171no—
127#1817—172no—
128#1272—172no—
129#1272—172no—
130C22×C17C2×C22⋊C811yescharacteristic
131C22×C17C2×#9911yescharacteristic
132C22×C17C2×#10011yescharacteristic
133C22×C17#41912yes—
134C22×C17#42112yes—
135C2×D17—22no—
136C2×D17—24no—
137C2×D17—24no—
138C2×D17—22no—
139C2×D17#32314yes—
140C4×C17—21no—
141C4×C17—21no—
142C4×C17—42no—
143C4×C17—42no—
144C4×C17—81no—
145Dic17—22no—
146Dic17—24no—
147Dic17—42no—
148Dic17—81no—
149C23×Q8—171no—
150C22×C4⋊C4—171no—
151C22×C42—171no—
152C2×C22⋊C8—342no—
153#391—171no—
154#391—171no—
155#391—171no—
156#391—342no—
157#391#59511yescharacteristic
158C2×#95—342no—
159#336—174no—
160#336—342no—
161C2×C17C2×#32311yescharacteristic
162C2×C17#147912yes—
163C2×C17#151112yes—
164C2×C17#153311yescharacteristic
165C2×C17#155811yescharacteristic
166D17—24no—
167C22×Q8—174no—
168C22×Q8—171no—
169C22×Q8—341no—
170C22×Q8—342no—
171C22×Q8—682no—
172C22×Q8—682no—
173C22×Q8C2×#59511yescharacteristic
174C23×C4—171no—
175C23×C4—172no—
176C23×C4—341no—
177C23×C4—341no—
178C22×C8—344no—
179C2×C4⋊C4—171no—
180C2×C4⋊C4—341no—
181C2×C4⋊C4—682no—
182C2×C4⋊C4C2×#59511yescharacteristic
183C2×C42—172no—
184C2×C42—171no—
185C2×C42—682no—
186C2×C42C2×#59511yescharacteristic
187C22⋊C8—684no—
188#95—22no—
189#95—342no—
190#95—342no—
191#95—342no—
192C17#759511yescharacteristic, complemented, Sylow
193C24—171no—
194C2×Q8—21no—
195C2×Q8—41no—
196C2×Q8—41no—
197C2×Q8—172no—
198C2×Q8—344no—
199C2×Q8—341no—
200C2×Q8—681no—
201C2×Q8—681no—
202C2×Q8—682no—
203C2×Q8—682no—
204C2×Q8—688no—
205C2×Q8—688no—
206C2×Q8#6324212yes—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—171no—
210C22×C4—172no—
211C22×C4—172no—
212C22×C4—172no—
213C22×C4—344no—
214C22×C4—342no—
215C22×C4—342no—
216C22×C4—344no—
217C22×C4—344no—
218C22×C4—341no—
219C22×C4—341no—
220C22×C4—682no—
221C22×C4—682no—
222C22×C4—682no—
223C22×C4—682no—
224C22×C4—684no—
225C22×C4C22⋊#59512yes—
226C22×C4C22×#59511yescharacteristic
227C2×C8—684no—
228C2×C8—684no—
229C2×C8—684no—
230C4⋊C4—41no—
231C4⋊C4—681no—
232C4⋊C4—682no—
233C42—41no—
234C42—681no—
235C42—682no—
236C23—172no—
237C23—172no—
238C23—172no—
239C23—342no—
240C23—342no—
241C23C2×C22⋊#59511yescharacteristic
242Q8—42no—
243Q8—42no—
244Q8—682no—
245Q8—682no—
246Q8—688no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—42no—
257C2×C4—172no—
258C2×C4—174no—
259C2×C4—344no—
260C2×C4—344no—
261C2×C4—342no—
262C2×C4—341no—
263C2×C4—341no—
264C2×C4—342no—
265C2×C4—342no—
266C2×C4—688no—
267C2×C4—688no—
268C2×C4—681no—
269C2×C4—681no—
270C2×C4—681no—
271C2×C4—682no—
272C2×C4—1364no—
273C2×C4C2×#6324211yescharacteristic
274C2×C4D17⋊M1611yescharacteristic
275C8—1364no—
276C22—174no—
277C22—344no—
278C22—342no—
279C22—342no—
280C22—344no—
281C22#1176377711yescharacteristic
282C22D17⋊#9911yescharacteristic
283C22D17⋊#10011yescharacteristic
284C22#1176380212yes—
285C22#1176380612yes—
286C4—21no—
287C4—21no—
288C4—42no—
289C4—42no—
290C4—81no—
291C4—344no—
292C4—342no—
293C4—682no—
294C4—1361no—
295C2—344no—
296C2#1454401011yescharacteristic
297C2#1454408712yes—
298C2#1454419312yes—
299C2#1454426411yescharacteristic
300C2#1454431811yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC2×C4×C17C22×C8
FrattiniC22×C4C22×#595
FittingC17×#391C4
socleC23×C17C2×C22⋊C4
prime radicalC23×D17C22⋊C4
cosocleC2×C4×Dic17C23
hypercenter#391#595
hypocenterC17#7595
LCSG ▷ C2×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
21. C2×Q8×D17C8semidirect
192. C17#7595semidirect

Maximal subgroups

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

subgroupindex
#145446762
#145436052
#145436042
D17×#3912
#759517