Finite Group Databasebeta

← #17959363

Subgroups — #17959363

Order 4352.

464 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 74 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×#10587553C211yesmaximal, characteristic
2#14544039C211yesmaximal, characteristic
3#14543768C214yesmaximal, complemented
4#14533086C211yesmaximal, characteristic
5C2×#10587553—21no—
6#11763780—21no—
7C4×#63247—21no—
8#11763689C2212yes—
9#11763655C2212yes—
10#11763652—21no—
11C2×#10587615—21no—
12C2×C4×C22⋊D17C2211yescharacteristic
13#11762740C2212yes—
14#11762735C412yes—
15#11762705—21no—
16#11762672—21no—
17#11762669C411yescharacteristic
18#11762666—21no—
19C22×C4⋊C4×C17C411yescharacteristic
20C23×C4×C17—21no—
21C23×C4×C17C2×C411yescharacteristic
22C22×C22⋊D17D411yescharacteristic
23C22×C4×D17D411yescharacteristic
24C2×#63247—22no—
25C2×#63243—41no—
26C2×C4⋊C4×C17—21no—
27C2×C4⋊C4×C17—41no—
28C2×C4⋊C4×C17—41no—
29C2×C4⋊C4×C17C2×C412yes—
30C2×C22⋊Dic17—21no—
31C2×C22⋊Dic17D411yescharacteristic
32#10587615—44no—
33C4×C22⋊D17—41no—
34C4×C22⋊D17—41no—
35C2×#63227—22no—
36C2×#63227C2×C411yescharacteristic
37C2×C4⋊Dic17—21no—
38C2×#63225—22no—
39C2×#63225C2311yescharacteristic
40C2×C4×Dic17D411yescharacteristic
41#10587553—24no—
42C22⋊#3624—22no—
43#10587543—41no—
44#10587542—41no—
45C4×#3624—41no—
46#10587502—22no—
47#10587502—22no—
48#10587502C2×C412yes—
49C24×C17C22⋊C411yescharacteristic
50C23×D17C22⋊C411yescharacteristic
51C22×C4×C17—21no—
52C22×C4×C17—21no—
53C22×C4×C17—22no—
54C22×C4×C17—42no—
55C22×C4×C17—42no—
56C22×C4×C17—42no—
57C22×C4×C17—42no—
58C22×C4×C17C22⋊C411yescharacteristic
59C22×C4×C17C22×C411yescharacteristic
60C2×C22⋊D17—22no—
61C2×C22⋊D17—22no—
62C2×C22⋊D17—41no—
63C22×Dic17—22no—
64C22×Dic17C22⋊C411yescharacteristic
65C22×Dic17C2×D411yescharacteristic
66C22×Dic17C2×D411yescharacteristic
67C2×C4×D17—21no—
68C2×C4×D17—21no—
69C2×C4×D17—42no—
70#63247—24no—
71#63247—42no—
72C2×#3624—42no—
73C2×#3624—42no—
74#63243—82no—
75C4⋊C4×C17—42no—
76C4⋊C4×C17—41no—
77C4⋊C4×C17—41no—
78C22⋊Dic17—41no—
79C22⋊Dic17—42no—
80#63227—41no—
81#63227—44no—
82C4⋊Dic17—42no—
83#63225—41no—
84#63225—44no—
85C4×Dic17—21no—
86C4×Dic17—21no—
87#11780—171nomaximal, Sylow
88C23×C17—21no—
89C23×C17—21no—
90C23×C17—41no—
91C23×C17—41no—
92C23×C17#10412yes—
93C23×C17C2×C22⋊C411yescharacteristic
94C22×D17—21no—
95C22×D17—21no—
96C22×D17—21no—
97C22×D17—41no—
98C22×D17—41no—
99C2×C4×C17—22no—
100C2×C4×C17—21no—
101C2×C4×C17—42no—
102C2×C4×C17—42no—
103C2×C4×C17—41no—
104C2×C4×C17—42no—
105C2×C4×C17—42no—
106C2×C4×C17—42no—
107C2×C4×C17—84no—
108C2×C4×C17#9911yescharacteristic
109C2×C4×C17#9911yescharacteristic
110C22⋊D17—44no—
111C2×Dic17—21no—
112C2×Dic17—21no—
113C2×Dic17—21no—
114C2×Dic17—21no—
115C2×Dic17—41no—
116C2×Dic17—41no—
117C2×Dic17—42no—
118C2×Dic17—42no—
119C2×Dic17—42no—
120C2×Dic17AGL(1,ℤ/8)12yes—
121C4×D17—42no—
122C4×D17—81no—
123#3624—44no—
124#3624—82no—
125#2486—171no—
126C4×#100—171no—
127#1465—171no—
128#1346—174no—
129C22×C17—21no—
130C22×C17—21no—
131C22×C17—22no—
132C22×C17—42no—
133C22×C17—42no—
134C22×C17—41no—
135C22×C17—41no—
136C22×C17C2×#9911yescharacteristic
137C22×C17#41811yescharacteristic
138C22×C17C2×#10411yescharacteristic
139C2×D17—42no—
140C2×D17—41no—
141C2×D17—41no—
142C2×D17—41no—
143C2×D17—81no—
144C4×C17—21no—
145C4×C17—41no—
146C4×C17—82no—
147C4×C17#35212yes—
148Dic17—22no—
149Dic17—41no—
150Dic17—41no—
151Dic17—82no—
152C2×#123—341no—
153C2×C4×D4—171no—
154C22×C4⋊C4#59511yescharacteristic
155C2×#100—341no—
156#407—341no—
157C4×M16—341no—
158#398—172no—
159#397—172no—
160#389—341no—
161#381—341no—
162#380—171no—
163#380—341no—
164#343—172no—
165#324—172no—
166#323—341no—
167C2×C17—21no—
168C2×C17—21no—
169C2×C17—42no—
170C2×C17#150711yescharacteristic
171C2×C17C2×#35211yescharacteristic
172C2×C17#213511yescharacteristic
173D17—81no—
174C22×D4—171no—
175C23×C4—21no—
176C23×C4—171no—
177C23×C4C2×#59511yescharacteristic
178C2×M16—342no—
179C2×M16—681no—
180#123—684no—
181C4×D4—681no—
182C4×D4—681no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—41no—
185C2×C4⋊C4—41no—
186C2×C4⋊C4—171no—
187C2×C4⋊C4—342no—
188C2×C4⋊C4—341no—
189C2×C4⋊C4C2×#59512yes—
190C2×C22⋊C4—171no—
191C2×C22⋊C4—171no—
192C2×C22⋊C4—342no—
193C2×C22⋊C4—341no—
194C2×C42—171no—
195#100—344no—
196C22⋊C8—342no—
197C22⋊C8—681no—
198#97—681no—
199C4×C8—681no—
200#95—172no—
201#95—342no—
202#95—342no—
203C17#1178011yescharacteristic, complemented, Sylow
204C24—171no—
205C24C22⋊#59511yescharacteristic
206C2×D4—342no—
207C2×D4—342no—
208C2×D4—681no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—22no—
212C22×C4—42no—
213C22×C4—42no—
214C22×C4—42no—
215C22×C4—42no—
216C22×C4—171no—
217C22×C4—171no—
218C22×C4—171no—
219C22×C4—341no—
220C22×C4—341no—
221C22×C4—342no—
222C22×C4—682no—
223C22×C4C22⋊#59511yescharacteristic
224C22×C4C22×#59511yescharacteristic
225M16—344no—
226M16—682no—
227M16—1362no—
228C2×C8—682no—
229C2×C8—682no—
230C4⋊C4—42no—
231C4⋊C4—41no—
232C4⋊C4—41no—
233C4⋊C4—681no—
234C4⋊C4—682no—
235C4⋊C4—684no—
236C22⋊C4—681no—
237C22⋊C4—684no—
238C22⋊C4—681no—
239C22⋊C4—682no—
240C42—341no—
241C42—341no—
242C23—21no—
243C23—21no—
244C23—41no—
245C23—41no—
246C23—341no—
247C23—341no—
248C23—341no—
249C23—681no—
250C23—681no—
251C23#1058754812yes—
252C23C2×C22⋊#59511yescharacteristic
253D4—684no—
254C2×C4—22no—
255C2×C4—21no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—41no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—84no—
263C2×C4—172no—
264C2×C4—341no—
265C2×C4—341no—
266C2×C4—341no—
267C2×C4—341no—
268C2×C4—682no—
269C2×C4—681no—
270C2×C4—681no—
271C2×C4—682no—
272C2×C4—682no—
273C2×C4—682no—
274C2×C4—1361no—
275C2×C4#1058755111yescharacteristic
276C2×C4#1058755111yescharacteristic
277C8—684no—
278C8—1362no—
279C22—21no—
280C22—21no—
281C22—22no—
282C22—42no—
283C22—42no—
284C22—41no—
285C22—41no—
286C22—682no—
287C22—681no—
288C22—681no—
289C22—681no—
290C22—1361no—
291C22C2×#1058755111yescharacteristic
292C22#1176380111yescharacteristic
293C22C2×#1058754811yescharacteristic
294C4—21no—
295C4—41no—
296C4—82no—
297C4—342no—
298C4—681no—
299C4—681no—
300C4—1362no—
301C4#1176371112yes—
302C2—21no—
303C2—21no—
304C2—42no—
305C2—1361no—
306C2#1454418011yescharacteristic
307C2C2×#1176371111yescharacteristic
308C2#1454508611yescharacteristic
subgroupG/H
centerC22C2×#10587551
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC22×C4⋊C4×C17C4
socleC22×C17C2×#99
prime radicalC22×C22⋊D17D4
cosocleC2×#63225C23
hypercenterC22×C4⋊C4#595
hypocenterC17#11780
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #14543768C2semidirect
203. C17#11780semidirect

Maximal subgroups

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

subgroupindex
C4×#105875532
#145440392
#145437682
#145330862
#1178017