Finite Group Databasebeta

← #16944897

Subgroups — #16944897

Order 4352.

480 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 87 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#14533776C211yesmaximal, characteristic
2#14527122C211yesmaximal, characteristic
3#14526783C214yesmaximal, complemented
4C4×C17×#99C211yesmaximal, characteristic
5C2×#10587555C411yescharacteristic, complemented
6C2×#10587622—21no—
7#11762773—21no—
8#11762734C412yescomplemented
9#11762734C2212yes—
10#11762714—21no—
11#11762669—21no—
12#11762669—21no—
13C4×C4⋊Dic17C411yescharacteristic, complemented
14#11762535—21no—
15#11762533C2212yes—
16C2×C4×D4×C17C2211yescharacteristic
17C2×C17×#99—21no—
18C4×C22⋊C4×C17—21no—
19C17×#342C2212yes—
20C22×D4×C17D411yescharacteristic
21C23×C4×C17D411yescharacteristic
22C23×C4×C17D411yescharacteristic
23C22×Dic34—21no—
24C4×D4×C17—41no—
25C4×D4×C17—41no—
26C2×C4⋊C4×C17D411yescharacteristic
27C2×C22⋊C4×C17—22no—
28C2×C22⋊C4×C17C2×C411yescharacteristic
29C2×C22⋊C4×C17C2311yescharacteristic
30C2×C42×C17—41no—
31C2×C42×C17C2×C411yescharacteristic
32C2×C22⋊Dic17—22no—
33C2×C22⋊Dic17—22no—
34#10587622—44no—
35C2×C4⋊Dic17—21no—
36C2×C4⋊Dic17—21no—
37C2×C4⋊Dic17C2×C412yes—
38C2×C4×Dic17—21no—
39C2×#63223—41no—
40#10587555—41no—
41#10587555—41no—
42C17×#99—24no—
43C17×#95—41no—
44#10587502—22no—
45#10587502—22no—
46#10587502C2×C412yes—
47C22⋊#3622—22no—
48C22⋊#3622—41no—
49C24×C17C22⋊C411yescharacteristic
50C24×C17C2×D411yescharacteristic
51C2×D4×C17—22no—
52C2×D4×C17—22no—
53C2×D4×C17—41no—
54C22×C4×C17—21no—
55C22×C4×C17—21no—
56C22×C4×C17—21no—
57C22×C4×C17—21no—
58C22×C4×C17—42no—
59C22×C4×C17—42no—
60C22×C4×C17—42no—
61C22×C4×C17C22⋊C411yescharacteristic
62C22×C4×C17C22⋊C411yescharacteristic
63C22×C4×C17C22⋊C411yescharacteristic
64C22×C4×C17C22×C411yescharacteristic
65C22×C4×C17C2×D411yescharacteristic
66C22×Dic17—22no—
67C22×Dic17—22no—
68C2×Dic34—42no—
69C2×Dic34—42no—
70C2×Dic34—42no—
71C4⋊C4×C17—41no—
72C22⋊C4×C17—24no—
73C22⋊C4×C17—41no—
74C22⋊C4×C17—41no—
75C22⋊C4×C17—42no—
76C42×C17—21no—
77C42×C17—21no—
78C42×C17—82no—
79C22⋊Dic17—44no—
80C22⋊Dic17—44no—
81C4⋊Dic17—42no—
82C4⋊Dic17—41no—
83C4⋊Dic17—41no—
84C4⋊Dic17—42no—
85C4×Dic17—42no—
86#63223—82no—
87C2×#3622—42no—
88#11777—171nomaximal, Sylow
89C23×C17—21no—
90C23×C17—21no—
91C23×C17—21no—
92C23×C17—21no—
93C23×C17—21no—
94C23×C17—41no—
95C23×C17—41no—
96C23×C17—41no—
97C23×C17—41no—
98C23×C17C2×C22⋊C411yescharacteristic
99C23×C17AGL(1,ℤ/8)12yes—
100D4×C17—44no—
101C2×C4×C17—21no—
102C2×C4×C17—21no—
103C2×C4×C17—22no—
104C2×C4×C17—21no—
105C2×C4×C17—21no—
106C2×C4×C17—21no—
107C2×C4×C17—42no—
108C2×C4×C17—42no—
109C2×C4×C17—41no—
110C2×C4×C17—41no—
111C2×C4×C17—41no—
112C2×C4×C17—44no—
113C2×C4×C17—81no—
114C2×C4×C17—81no—
115C2×C4×C17—82no—
116C2×C4×C17—82no—
117C2×C4×C17#9911yescharacteristic
118C2×C4×C17#9911yescharacteristic
119C2×C4×C17#10412yes—
120C2×Dic17—42no—
121C2×Dic17—42no—
122C2×Dic17—42no—
123C2×Dic17—42no—
124C2×Dic17—42no—
125C2×Dic17—42no—
126Dic34—84no—
127#3622—82no—
128#2547—171no—
129C4×#99D1711yescharacteristic
130#1465—171no—
131#1344—174no—
132C22×C17—21no—
133C22×C17—21no—
134C22×C17—22no—
135C22×C17—42no—
136C22×C17—42no—
137C22×C17—41no—
138C22×C17—41no—
139C22×C17—41no—
140C22×C17—41no—
141C22×C17—41no—
142C22×C17—81no—
143C22×C17—81no—
144C22×C17C2×#9911yescharacteristic
145C22×C17#41811yescharacteristic
146C22×C17C2×#10411yescharacteristic
147C4×C17—21no—
148C4×C17—22no—
149C4×C17—41no—
150C4×C17—41no—
151C4×C17—41no—
152C4×C17—84no—
153C4×C17#35412yes—
154Dic17—82no—
155Dic17—82no—
156C2×C4⋊Q8—171no—
157C2×#124—341no—
158C2×C4×D4C2×D1711yescharacteristic
159C2×#99—21no—
160#407—341no—
161#397—172no—
162#397—172no—
163#391—341no—
164#380—341no—
165#380—341no—
166C4×C4⋊C4—171no—
167C4×C22⋊C4—21no—
168#342C2×D1712yes—
169#324—341no—
170#323—172no—
171C2×C17—21no—
172C2×C17—21no—
173C2×C17—42no—
174C2×C17—81no—
175C2×C17#150711yescharacteristic
176C2×C17#212311yescharacteristic
177C2×C17C2×#35411yescharacteristic
178C22×Q8—341no—
179C22×D4C22⋊D1711yescharacteristic
180C23×C4D6811yescharacteristic
181C23×C4C22⋊D1711yescharacteristic
182C2×M16—681no—
183C4⋊Q8—681no—
184C4⋊Q8—681no—
185#124—684no—
186C4×D4—41no—
187C4×D4—41no—
188C2×C4⋊C4—172no—
189C2×C4⋊C4—341no—
190C2×C4⋊C4—341no—
191C2×C4⋊C4D6811yescharacteristic
192C2×C22⋊C4—22no—
193C2×C22⋊C4—342no—
194C2×C22⋊C4—342no—
195C2×C22⋊C4C4×D1711yescharacteristic
196C2×C22⋊C4C22×D1711yescharacteristic
197C2×C42—41no—
198C2×C42—341no—
199C2×C42C4×D1711yescharacteristic
200#99—24no—
201C22⋊C8—342no—
202C22⋊C8—681no—
203#95—41no—
204#95—172no—
205#95—342no—
206#95—342no—
207C17#1177711yescharacteristic, complemented, Sylow
208C24#6322711yescharacteristic
209C24C2×C22⋊D1711yescharacteristic
210C2×Q8—682no—
211C2×Q8—682no—
212C2×Q8—682no—
213C2×D4—22no—
214C2×D4—22no—
215C2×D4—41no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—42no—
221C22×C4—42no—
222C22×C4—42no—
223C22×C4—342no—
224C22×C4—342no—
225C22×C4#6322711yescharacteristic
226C22×C4#6322711yescharacteristic
227C22×C4#6322711yescharacteristic
228C22×C4C2×C4×D1711yescharacteristic
229C22×C4C2×D6811yescharacteristic
230M16—1362no—
231C2×C8—682no—
232C4⋊C4—41no—
233C4⋊C4—682no—
234C4⋊C4—682no—
235C4⋊C4—681no—
236C4⋊C4—681no—
237C22⋊C4—24no—
238C22⋊C4—41no—
239C22⋊C4—41no—
240C22⋊C4—42no—
241C22⋊C4—684no—
242C22⋊C4—684no—
243C42—21no—
244C42—21no—
245C42—82no—
246C42—682no—
247C23—21no—
248C23—21no—
249C23—21no—
250C23—21no—
251C23—21no—
252C23—41no—
253C23—41no—
254C23—41no—
255C23—41no—
256C23C2×#6322711yescharacteristic
257C23#1058763512yes—
258Q8—1364no—
259D4—44no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—44no—
272C2×C4—81no—
273C2×C4—81no—
274C2×C4—82no—
275C2×C4—82no—
276C2×C4—682no—
277C2×C4—682no—
278C2×C4—682no—
279C2×C4—682no—
280C2×C4—682no—
281C2×C4—682no—
282C2×C4#1058747612yes—
283C2×C4#1058747711yescharacteristic
284C2×C4#1058747711yescharacteristic
285C8—1362no—
286C22—21no—
287C22—21no—
288C22—22no—
289C22—42no—
290C22—42no—
291C22—41no—
292C22—41no—
293C22—41no—
294C22—41no—
295C22—41no—
296C22—81no—
297C22—81no—
298C22C2×#1058747711yescharacteristic
299C22#1176281311yescharacteristic
300C22C2×#1058747611yescharacteristic
301C4—22no—
302C4—21no—
303C4—41no—
304C4—41no—
305C4—41no—
306C4—84no—
307C4—1362no—
308C4—1362no—
309C4#1176260312yes—
310C2—21no—
311C2—21no—
312C2—42no—
313C2—81no—
314C2#1452729911yescharacteristic
315C2#1453043711yescharacteristic
316C2C2×#1176260311yescharacteristic
subgroupG/H
centerC22C2×#10587477
commutatorC22×C4×C17C22×C4
FrattiniC2×C22⋊C4C22×D17
FittingC4×C17×#99C2
socleC22×C17C2×#99
prime radicalC22×D4×C17D4
cosocleC2×C22⋊C4×C17C23
hypercenterC4×#99D17
hypocenterC17#11777
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
3. #14526783C2semidirect
5. C2×#10587555C4semidirect
8. #11762734C4semidirect
13. C4×C4⋊Dic17C4semidirect
207. C17#11777semidirect

Maximal subgroups

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

subgroupindex
#145337762
#145271222
#145267832
C4×C17×#992
#1177717