Finite Group Databasebeta

← #17958301

Subgroups — #17958301

Order 4352.

616 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 616 conjugacy classes of subgroups — too many to draw. Only its 90 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#14544021C212yesmaximal, complemented
2#14543726C212yesmaximal, complemented
3#14543713C212yesmaximal, complemented
4C4×#10587560C211yesmaximal, characteristic
5#11763777—22no—
6#11763654C2214yes—
7#11763653—22no—
8C2×#10587560C411yescharacteristic
9C2×C4×D68—22no—
10C2×C4×D68C411yescharacteristic
11C2×C4×D68C2211yescharacteristic
12#11762711—22no—
13#11762711C411yescharacteristic
14#11762711C2211yescharacteristic
15#11762679C2211yescharacteristic
16C43×C17C411yescharacteristic
17C22×D68—22no—
18C22×D68C2×C411yescharacteristic
19C22×D68C2×C411yescharacteristic
20C22×C4×D17—21no—
21C22×C4×D17D412yes—
22C2×#63242—42no—
23C2×C42×C17—21no—
24C2×C42×C17—21no—
25C2×C42×C17C2×C411yescharacteristic
26C2×C42×C17C2×C411yescharacteristic
27C2×C42×C17C2×C411yescharacteristic
28C2×#63227—22no—
29C2×#63227—21no—
30C2×#63227—22no—
31C2×#63227D412yes—
32C2×C4⋊Dic17—22no—
33C2×C4⋊Dic17C2×C411yescharacteristic
34C2×C4⋊Dic17C2311yescharacteristic
35#10587560—22no—
36#10587560C814yescomplemented
37C4×D68—41no—
38C4×D68—41no—
39C4×D68—48no—
40C4×D68—41no—
41C4×D68—41no—
42C22⋊#3624—24no—
43#10587543—42no—
44C23×D17—21no—
45C23×D17C22⋊C412yes—
46C22×C4×C17—21no—
47C22×C4×C17—21no—
48C22×C4×C17C22⋊C411yescharacteristic
49C22×C4×C17C22⋊C411yescharacteristic
50C22×C4×C17C22×C411yescharacteristic
51C22×Dic17—21no—
52C22×Dic17C2×D412yes—
53C2×D68—28no—
54C2×D68—21no—
55C2×D68—41no—
56C2×D68—41no—
57C2×D68—41no—
58C2×D68—41no—
59C2×D68—44no—
60C2×D68—44no—
61C2×D68C2×C812yes—
62C2×D68C2×C812yescomplemented
63C2×D68M1612yes—
64C2×C4×D17—22no—
65C2×C4×D17—22no—
66C2×C4×D17—44no—
67C2×C4×D17—44no—
68C2×C4×D17—41no—
69C2×C4×D17—41no—
70C2×#3624—44no—
71#63242—84no—
72C42×C17—24no—
73C42×C17—21no—
74C42×C17—21no—
75C42×C17—21no—
76C42×C17—41no—
77C42×C17—42no—
78C42×C17C2×C812yescomplemented
79#63227—42no—
80#63227—44no—
81#63227—44no—
82#63227—42no—
83C4⋊Dic17—41no—
84C4⋊Dic17—44no—
85C4⋊Dic17—41no—
86#11475—171nomaximal, Sylow
87C23×C17C2×C22⋊C411yescharacteristic
88C22×D17—22no—
89C22×D17—22no—
90C22×D17—22no—
91C22×D17—42no—
92C22×D17—42no—
93C22×D17—42no—
94C22×D17—42no—
95C22×D17—41no—
96C22×D17—41no—
97C22×D17C22⋊C814yes—
98C2×C4×C17—22no—
99C2×C4×C17—22no—
100C2×C4×C17—22no—
101C2×C4×C17—21no—
102C2×C4×C17—21no—
103C2×C4×C17—22no—
104C2×C4×C17—22no—
105C2×C4×C17—21no—
106C2×C4×C17—41no—
107C2×C4×C17—41no—
108C2×C4×C17—41no—
109C2×C4×C17#9911yescharacteristic
110C2×C4×C17#9911yescharacteristic
111C2×C4×C17C22×C811yescharacteristic
112C2×C4×C17C2×M1611yescharacteristic
113C2×Dic17—22no—
114C2×Dic17—42no—
115C2×Dic17—42no—
116C2×Dic17—41no—
117D68—42no—
118D68—42no—
119D68—42no—
120D68—416no—
121D68—42no—
122C4×D17—44no—
123C4×D17—82no—
124C4×D17—82no—
125C4×D17—82no—
126#3624—84no—
127C4×#127—171no—
128#1459—172no—
129#1325—172no—
130#1318—172no—
131C22×C17—21no—
132C22×C17—21no—
133C22×C17C2×C22⋊C811yescharacteristic
134C22×C17C2×#9911yescharacteristic
135C22×C17#41311yescharacteristic
136C2×D17—24no—
137C2×D17—42no—
138C2×D17—42no—
139C2×D17—44no—
140C2×D17—44no—
141C2×D17—42no—
142C2×D17—82no—
143C2×D17—82no—
144C2×D17—81no—
145C2×D17—81no—
146C4×C17—24no—
147C4×C17—21no—
148C4×C17—21no—
149C4×C17—21no—
150C4×C17—42no—
151C4×C17—41no—
152C4×C17#35312yes—
153Dic17—42no—
154Dic17—81no—
155C2×#127—171no—
156C2×C4×D4—171no—
157C2×C4×D4—171no—
158C2×C4×D4—342no—
159C2×C22⋊C8—342no—
160#390—171no—
161#390—171no—
162#390—342no—
163#384—171no—
164C43#59511yescharacteristic
165#324—174no—
166#323—342no—
167C2×C17—21no—
168C2×C17—21no—
169C2×C17#145911yescharacteristic
170C2×C17C2×#35311yescharacteristic
171C2×C17#213211yescharacteristic
172D17—44no—
173D17—82no—
174C22×D4—171no—
175C22×D4—171no—
176C22×D4—342no—
177C23×C4—172no—
178C23×C4—341no—
179C22×C8—682no—
180#127—174no—
181#127—342no—
182C4×D4—681no—
183C4×D4—681no—
184C4×D4—688no—
185C4×D4—681no—
186C4×D4—681no—
187C2×C4⋊C4—171no—
188C2×C4⋊C4—171no—
189C2×C4⋊C4—342no—
190C2×C22⋊C4—172no—
191C2×C22⋊C4—342no—
192C2×C22⋊C4—342no—
193C2×C22⋊C4—341no—
194C2×C42—21no—
195C2×C42—21no—
196C2×C42C2×#59511yescharacteristic
197C2×C42C2×#59511yescharacteristic
198C2×C42C2×#59511yescharacteristic
199C22⋊C8—344no—
200C22⋊C8—682no—
201C17#1147511yescharacteristic, complemented, Sylow
202C24—172no—
203C24—341no—
204C2×D4—172no—
205C2×D4—172no—
206C2×D4—172no—
207C2×D4—348no—
208C2×D4—341no—
209C2×D4—681no—
210C2×D4—681no—
211C2×D4—681no—
212C2×D4—681no—
213C2×D4—684no—
214C2×D4—684no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—172no—
218C22×C4—342no—
219C22×C4—342no—
220C22×C4—341no—
221C22×C4—684no—
222C22×C4—684no—
223C22×C4—681no—
224C22×C4—681no—
225C22×C4C22⋊#59511yescharacteristic
226C22×C4C22⋊#59511yescharacteristic
227C22×C4C22×#59511yescharacteristic
228C2×C8—684no—
229C2×C8—1364no—
230C4⋊C4—681no—
231C4⋊C4—681no—
232C4⋊C4—684no—
233C22⋊C4—682no—
234C22⋊C4—684no—
235C22⋊C4—684no—
236C22⋊C4—682no—
237C42—24no—
238C42—21no—
239C42—21no—
240C42—21no—
241C42—41no—
242C42—42no—
243C42#6324212yescomplemented
244C23—174no—
245C23—342no—
246C23—342no—
247C23—342no—
248C23—682no—
249C23—682no—
250C23—682no—
251C23—682no—
252C23—681no—
253C23—681no—
254C23C2×C22⋊#59511yescharacteristic
255D4—682no—
256D4—682no—
257D4—682no—
258D4—6816no—
259D4—682no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—21no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—342no—
272C2×C4—684no—
273C2×C4—682no—
274C2×C4—682no—
275C2×C4—681no—
276C2×C4—1362no—
277C2×C4—1362no—
278C2×C4—1362no—
279C2×C4#1058753911yescharacteristic
280C2×C4#1058753911yescharacteristic
281C2×C4C2×#6324211yescharacteristic
282C2×C4D17⋊M1611yescharacteristic
283C8—1364no—
284C22—21no—
285C22—21no—
286C22—344no—
287C22—684no—
288C22—684no—
289C22—682no—
290C22—682no—
291C22—682no—
292C22—1362no—
293C22—1362no—
294C22—1361no—
295C22—1361no—
296C22#1176377711yescharacteristic
297C22C2×#1058753911yescharacteristic
298C22#1176379511yescharacteristic
299C4—24no—
300C4—21no—
301C4—21no—
302C4—21no—
303C4—42no—
304C4—41no—
305C4—682no—
306C4—1361no—
307C4#1176371412yes—
308C2—21no—
309C2—21no—
310C2—684no—
311C2—1362no—
312C2#1454402111yescharacteristic
313C2C2×#1176371411yescharacteristic
314C2#1454507711yescharacteristic
subgroupG/H
centerC2×C4#10587539
commutatorC2×C4×C17C22×C8
FrattiniC22×C4C22×#595
FittingC43×C17C4
socleC22×C17C2×#99
prime radicalC2×#10587560C4
cosocleC2×C4⋊Dic17C23
hypercenterC43#595
hypocenterC17#11475
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ C43

Complements

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

NH ≅ G/Ntype
1. #14544021C2semidirect
2. #14543726C2semidirect
3. #14543713C2semidirect
36. #10587560C8semidirect
62. C2×D68C2×C8semidirect
78. C42×C17C2×C8semidirect
201. C17#11475semidirect
243. C42#63242semidirect

Maximal subgroups

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

subgroupindex
#145440212
#145437262
#145437132
C4×#105875602
#1147517