Finite Group Databasebeta

← #16952969

Subgroups — #16952969

Order 4352.

484 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 111 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#14528772C211yesmaximal, characteristic
2C4×#10587504C211yesmaximal, characteristic
3#14526902C214yesmaximal
4C17×#2487C211yesmaximal, characteristic
5C2×#10587504C2212yes—
6C2×#10587505C2212yes—
7C4×#63223—21no—
8#11762669—21no—
9#11762578—21no—
10#11762576—21no—
11C2×C4×D4×C17C2211yescharacteristic
12C22×C4⋊C4×C17C411yescharacteristic, complemented
13C17×#400—21no—
14C17×#399—21no—
15C17×#389—21no—
16C17×#386C2212yes—
17C17×#385C412yescomplemented
18C17×#380—21no—
19C17×#380C411yescharacteristic, complemented
20C22×D4×C17C2311yescharacteristic
21C23×C4×C17C2×C411yescharacteristic
22C23×C4×C17C2×C412yes—
23C23×C4×C17D411yescharacteristic
24C4×D4×C17—41no—
25C4×D4×C17—41no—
26C2×C4⋊C4×C17—21no—
27C2×C4⋊C4×C17—21no—
28C2×C4⋊C4×C17—21no—
29C2×C4⋊C4×C17—22no—
30C2×C4⋊C4×C17—41no—
31C2×C4⋊C4×C17—41no—
32C2×C4⋊C4×C17D411yescharacteristic
33C2×C22⋊C4×C17—22no—
34C2×C22⋊C4×C17C2×C412yes—
35C2×C22⋊C4×C17C2×C411yescharacteristic
36C2×C22⋊C4×C17D411yescharacteristic
37C2×C42×C17D411yescharacteristic
38C2×C22⋊Dic17—22no—
39C2×C4⋊Dic17—41no—
40C2×#63223—22no—
41C17×#95—22no—
42C17×#95—21no—
43C17×#95—22no—
44#10587505—24no—
45#10587504—22no—
46#10587504Q814yes—
47#10587502—41no—
48#10587474—41no—
49C4×#3622—41no—
50C24×C17C22×C411yescharacteristic
51C24×C17C2×D411yescharacteristic
52C2×D4×C17—41no—
53C2×D4×C17—41no—
54C2×D4×C17C2×Q812yes—
55C2×D4×C17#4112yes—
56C22×C4×C17—21no—
57C22×C4×C17—21no—
58C22×C4×C17—21no—
59C22×C4×C17—21no—
60C22×C4×C17—22no—
61C22×C4×C17—22no—
62C22×C4×C17—42no—
63C22×C4×C17—42no—
64C22×C4×C17—42no—
65C22×C4×C17—82no—
66C22×C4×C17C22⋊C411yescharacteristic
67C22×C4×C17C22⋊C411yescharacteristic
68C22×C4×C17C22⋊C411yescharacteristic
69C22×C4×C17C22⋊C411yescharacteristic
70C22×C4×C17C2×D411yescharacteristic
71C22×Dic17—42no—
72C4⋊C4×C17—41no—
73C4⋊C4×C17—42no—
74C4⋊C4×C17—42no—
75C4⋊C4×C17—41no—
76C4⋊C4×C17—41no—
77C4⋊C4×C17—82no—
78C22⋊C4×C17—41no—
79C22⋊C4×C17—41no—
80C22⋊C4×C17—42no—
81C22⋊C4×C17—82no—
82C42×C17—21no—
83C42×C17—21no—
84C22⋊Dic17—42no—
85C22⋊Dic17—42no—
86C4⋊Dic17—82no—
87#63223—24no—
88#63223—42no—
89C2×#3622—42no—
90#13292—171nomaximal, Sylow
91C23×C17—21no—
92C23×C17—21no—
93C23×C17—21no—
94C23×C17—21no—
95C23×C17—41no—
96C23×C17—41no—
97C23×C17—41no—
98C23×C17—41no—
99C23×C17C2×C22⋊C411yescharacteristic
100C23×C17C4×Q812yes—
101C23×C17#12411yescharacteristic
102C23×C17C4⋊Q811yescharacteristic
103D4×C17—42no—
104D4×C17—42no—
105C2×C4×C17—21no—
106C2×C4×C17—21no—
107C2×C4×C17—22no—
108C2×C4×C17—21no—
109C2×C4×C17—21no—
110C2×C4×C17—21no—
111C2×C4×C17—42no—
112C2×C4×C17—42no—
113C2×C4×C17—42no—
114C2×C4×C17—41no—
115C2×C4×C17—41no—
116C2×C4×C17—41no—
117C2×C4×C17—42no—
118C2×C4×C17—42no—
119C2×C4×C17—42no—
120C2×C4×C17—42no—
121C2×C4×C17—42no—
122C2×C4×C17—42no—
123C2×C4×C17—81no—
124C2×C4×C17—84no—
125C2×C4×C17#9911yescharacteristic
126C2×C4×C17#9911yescharacteristic
127C2×C4×C17C22⋊Q812yes—
128C2×Dic17—82no—
129C2×Dic17—82no—
130C2×Dic17—82no—
131#3622—44no—
132#2487D1711yescharacteristic
133#1799—171no—
134C4×#100—171no—
135#1390—174no—
136C22×C17—21no—
137C22×C17—21no—
138C22×C17—21no—
139C22×C17—22no—
140C22×C17—21no—
141C22×C17—42no—
142C22×C17—41no—
143C22×C17—41no—
144C22×C17—42no—
145C22×C17—41no—
146C22×C17—41no—
147C22×C17—41no—
148C22×C17—41no—
149C22×C17—81no—
150C22×C17#39111yescharacteristic
151C22×C17C2×#9911yescharacteristic
152C22×C17#41011yescharacteristic
153C4×C17—21no—
154C4×C17—22no—
155C4×C17—41no—
156C4×C17—41no—
157C4×C17—41no—
158C4×C17—82no—
159C4×C17—82no—
160C4×C17#35212yes—
161Dic17—162no—
162C2×C4×D4C2×D1711yescharacteristic
163C22×C4⋊C4Dic1711yescharacteristic, complemented
164C2×#100—172no—
165C2×#99—172no—
166C4×M16—341no—
167#400—21no—
168#399—21no—
169#389—21no—
170#386C2×D1712yes—
171#385Dic1712yescomplemented
172#380—21no—
173#380—341no—
174#380Dic1711yescharacteristic, complemented
175#343—341no—
176#342—341no—
177C2×C17—21no—
178C2×C17—21no—
179C2×C17—41no—
180C2×C17—42no—
181C2×C17—41no—
182C2×C17#199611yescharacteristic
183C2×C17C2×#35211yescharacteristic
184C2×C17#212211yescharacteristic
185C22×D4C22×D1711yescharacteristic
186C23×C4C2×Dic1711yescharacteristic
187C23×C4C2×Dic1712yes—
188C23×C4C22⋊D1711yescharacteristic
189C2×M16—342no—
190C4×D4—41no—
191C4×D4—41no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—22no—
196C2×C4⋊C4—41no—
197C2×C4⋊C4—41no—
198C2×C4⋊C4—681no—
199C2×C4⋊C4C22⋊D1711yescharacteristic
200C2×C22⋊C4—22no—
201C2×C22⋊C4—342no—
202C2×C22⋊C4C2×Dic1712yes—
203C2×C22⋊C4C2×Dic1711yescharacteristic
204C2×C22⋊C4C22⋊D1711yescharacteristic
205C2×C42C22⋊D1711yescharacteristic
206#100—174no—
207#100—342no—
208#99—344no—
209#97—681no—
210C4×C8—681no—
211#95—22no—
212#95—21no—
213#95—22no—
214#95—681no—
215C17#1329211yescharacteristic, complemented, Sylow
216C24C22×Dic1711yescharacteristic
217C24C2×C22⋊D1711yescharacteristic
218C2×D4—41no—
219C2×D4—41no—
220C2×D4Q8×D1712yes—
221C2×D4#6325612yes—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—42no—
229C22×C4—42no—
230C22×C4—42no—
231C22×C4—82no—
232C22×C4—682no—
233C22×C4C22⋊Dic1711yescharacteristic
234C22×C4C22⋊Dic1711yescharacteristic
235C22×C4C22⋊Dic1711yescharacteristic
236C22×C4C22⋊Dic1711yescharacteristic
237C22×C4C2×C22⋊D1711yescharacteristic
238M16—344no—
239M16—682no—
240C2×C8—682no—
241C4⋊C4—41no—
242C4⋊C4—42no—
243C4⋊C4—42no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—82no—
247C4⋊C4—1362no—
248C22⋊C4—41no—
249C22⋊C4—41no—
250C22⋊C4—42no—
251C22⋊C4—82no—
252C22⋊C4—682no—
253C22⋊C4—682no—
254C42—21no—
255C42—21no—
256C23—21no—
257C23—21no—
258C23—21no—
259C23—21no—
260C23—41no—
261C23—41no—
262C23—41no—
263C23—41no—
264C23#1058763011yescharacteristic
265C23Q8×Dic1712yes—
266C23#1058763311yescharacteristic
267C23C2×C22⋊Dic1711yescharacteristic
268D4—42no—
269D4—42no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—22no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—81no—
289C2×C4—84no—
290C2×C4—1362no—
291C2×C4—1362no—
292C2×C4—1362no—
293C2×C4#1058750511yescharacteristic
294C2×C4#1058750511yescharacteristic
295C2×C4#1058763212yes—
296C8—684no—
297C22—21no—
298C22—21no—
299C22—21no—
300C22—21no—
301C22—22no—
302C22—41no—
303C22—42no—
304C22—41no—
305C22—42no—
306C22—41no—
307C22—41no—
308C22—41no—
309C22—41no—
310C22—81no—
311C22#1176271611yescharacteristic
312C22C2×#1058750511yescharacteristic
313C22#1176278311yescharacteristic
314C4—21no—
315C4—22no—
316C4—41no—
317C4—41no—
318C4—41no—
319C4—82no—
320C4—82no—
321C4—2722no—
322C4#1176259912yes—
323C2—21no—
324C2—21no—
325C2—41no—
326C2—42no—
327C2—41no—
328C2#1452977011yescharacteristic
329C2C2×#1176259911yescharacteristic
330C2#1453043411yescharacteristic
subgroupG/H
centerC22C2×#10587505
commutatorC24×C17C22×C4
FrattiniC22×D4C22×D17
FittingC17×#2487C2
socleC22×C17C2×#99
prime radical, cosocleC22×D4×C17C23
hypercenter#2487D17
hypocenterC17#13292
LCSG ▷ C24×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2487

Complements

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

NH ≅ G/Ntype
12. C22×C4⋊C4×C17C4semidirect
17. C17×#385C4semidirect
19. C17×#380C4semidirect
163. C22×C4⋊C4Dic17semidirect
171. #385Dic17semidirect
174. #380Dic17semidirect
215. C17#13292semidirect

Maximal subgroups

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

subgroupindex
#145287722
C4×#105875042
#145269022
C17×#24872
#1329217