Finite Group Databasebeta

← C22×#11763839 #17979655

Subgroups — C22×#11763839 #17979655

Order 4352.

3350 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#63243C211yesmaximal, characteristic, complemented
2C23×#63242C211yesmaximal, characteristic, complemented
3C2×#11763839C2124yesmaximal, direct product factor
4C22×#10587544C211yesmaximal, characteristic, complemented
5C22×#10587543C211yesmaximal, characteristic, complemented
6C22×#10587543C211yesmaximal, characteristic, complemented
7C22×#10587542C211yesmaximal, characteristic, complemented
8C22×#10587579C211yesmaximal, characteristic
9C22×#63243—28no—
10C22×#63243C22112yescomplemented
11C22×#63242—28no—
12C22×#63242C22112yescomplemented
13C23×#3624C2211yescharacteristic
14C23×#3624C2211yescharacteristic
15C23×#3624C2211yescharacteristic
16C23×#3624C2211yescharacteristic
17#11763839C22164yesdirect product factor
18C2×#10587544C22112yescomplemented
19C2×#10587543C22112yescomplemented
20C2×#10587543C22112yescomplemented
21C2×#10587542C22112yescomplemented
22C23×D68C411yescharacteristic
23C23×C4×D17C2211yescharacteristic
24C23×C4×D17C2211yescharacteristic
25C2×#10587579C4112yes—
26C2×#10587579C22112yes—
27C22×#63227C411yescharacteristic
28C22×#63227C411yescharacteristic
29C22×C4×Dic17C2211yescharacteristic
30C22×C4⋊C4×C17C411yescharacteristic
31C24×D17C2×C411yescharacteristic
32C24×D17C2×C411yescharacteristic
33C23×C4×C17C2×C411yescharacteristic
34C23×C4×C17C2×C411yescharacteristic
35C23×C4×C17C2×C411yescharacteristic
36C23×Dic17C2×C411yescharacteristic
37C23×Dic17C2311yescharacteristic
38C22×D68—28no—
39C22×D68C2×C4112yes—
40C22×C4×D17—24no—
41C22×C4×D17—24no—
42C22×C4×D17—24no—
43C22×C4×D17—24no—
44C22×C4×D17C2×C416yes—
45C22×C4×D17C2×C416yes—
46C22×C4×D17C2316yes—
47C22×C4×D17C2316yes—
48C22×#3624—24no—
49C22×#3624—24no—
50C22×#3624—24no—
51C22×#3624D418yescomplemented
52C22×#3624C2316yes—
53C22×#3624C2316yes—
54C22×#3624C2316yes—
55C22×#3624C2316yes—
56C2×#63243—248no—
57C2×#63243C23116yescomplemented
58C2×#63242—248no—
59C2×#63242C23116yescomplemented
60C2×C4⋊C4×C17C2×C4112yes—
61C2×#63227C2×C4112yes—
62C2×#63227C2×C4112yes—
63C2×C4×Dic17C2×C416yes—
64C2×C4×Dic17C2316yes—
65#10587579C2×C4148yes—
66#10587579C23116yes—
67#10587544C23116yescomplemented
68#10587543C23116yescomplemented
69#10587543C23116yescomplemented
70#10587542C23116yescomplemented
71C24×C17C22×C411yescharacteristic
72C23×D17—24no—
73C23×D17—24no—
74C23×D17—24no—
75C23×D17—24no—
76C23×D17—24no—
77C23×D17M1618yescomplemented
78C23×D17C22×C416yes—
79C23×D17C22×C416yes—
80C22×C4×C17—24no—
81C22×C4×C17—24no—
82C22×C4×C17—24no—
83C22×C4×C17C22×C416yes—
84C22×C4×C17C22×C416yes—
85C22×C4×C17C22×C416yes—
86C22×Dic17—24no—
87C22×Dic17C22×C416yes—
88C22×Dic17C22×C413yes—
89C22×Dic17C2×D414yes—
90C22×Dic17#4114yes—
91C22×Dic17C2413yes—
92C2×D68—248no—
93C2×D68C22×C4116yes—
94C2×C4×D17—224no—
95C2×C4×D17—224no—
96C2×C4×D17—212no—
97C2×C4×D17—212no—
98C2×C4×D17—212no—
99C2×C4×D17—212no—
100C2×C4×D17C22×C4112yes—
101C2×C4×D17C22×C4112yes—
102C2×C4×D17C2414yes—
103C2×C4×D17C2414yes—
104C2×#3624—212no—
105C2×#3624—212no—
106C2×#3624—212no—
107C2×#3624C2×D4124yescomplemented
108C2×#3624C2414yes—
109C2×#3624C2414yes—
110C2×#3624C2414yes—
111C2×#3624C2414yes—
112#63243—232no—
113#63242—232no—
114C4⋊C4×C17C22×C4116yes—
115#63227C22×C4116yes—
116#63227C22×C4116yes—
117C4×Dic17C22×C4112yes—
118C4×Dic17C2414yes—
119C22×#435—171nomaximal, Sylow
120C23×C17C4×D414yes—
121C23×C17C2×M1614yes—
122C23×C17#13114yes—
123C23×C17C23×C413yes—
124C22×D17—212no—
125C22×D17—212no—
126C22×D17—232no—
127C22×D17—212no—
128C22×D17—212no—
129C22×D17—212no—
130C22×D17—416no—
131C22×D17C2×M16124yescomplemented
132C22×D17C23×C414yes—
133C22×D17C23×C414yes—
134C2×C4×C17—212no—
135C2×C4×C17—212no—
136C2×C4×C17—212no—
137C2×C4×C17C23×C414yes—
138C2×C4×C17C23×C414yes—
139C2×C4×C17C23×C414yes—
140C2×Dic17—212no—
141C2×Dic17C4×D4112yes—
142C2×Dic17C23×C414yes—
143C2×Dic17C23×C413yes—
144C2×Dic17C22×D416yes—
145C2×Dic17C2×#4116yes—
146C2×Dic17C2511yescharacteristic
147D68—232no—
148C4×D17—224no—
149C4×D17—224no—
150C4×D17—24no—
151C4×D17—24no—
152C4×D17—24no—
153C4×D17—24no—
154#3624—24no—
155#3624—24no—
156#3624—24no—
157#3624C22×D418yescomplemented
158C23×M16—171no—
159C24×C8—171no—
160C22×C4×D4—171no—
161C2×#435—1724no—
162C22×C4⋊C8—171no—
163C22×C22⋊C8—171no—
164C22×C22⋊C8—171no—
165C22×#97—171no—
166C22×C17#435116yescomplemented
167C22×C17C2×C4×D416yes—
168C22×C17C22×M1616yes—
169C22×C17C2×#13116yes—
170C22×C17C24×C411yescharacteristic
171C2×D17—24no—
172C2×D17—248no—
173C2×D17—24no—
174C2×D17—24no—
175C2×D17—24no—
176C2×D17—24no—
177C2×D17—424no—
178C2×D17C22×M1618yescomplemented
179C4×C17—24no—
180C4×C17—24no—
181C4×C17—24no—
182Dic17—24no—
183Dic17C2×C4×D416yes—
184Dic17C23×D411yescharacteristic
185Dic17C22×#4111yescharacteristic
186C23×D4—171no—
187C24×C4—171no—
188C24×C4—171no—
189C22×M16—1712no—
190C22×M16—348no—
191C23×C8—171no—
192C23×C8—171no—
193C23×C8—171no—
194C23×C8—171no—
195C23×C8—1712no—
196C23×C8—348no—
197C2×C4×D4—1712no—
198C2×C4×D4—1712no—
199C22×C4⋊C4#59511yescharacteristic
200C22×C22⋊C4—171no—
201C22×C22⋊C4—171no—
202C22×C42—171no—
203#435—1764no—
204C2×C4⋊C8—1712no—
205C2×C22⋊C8—1712no—
206C2×C22⋊C8—1712no—
207C2×#97—1712no—
208C2×C17C2×#435112yescomplemented
209C2×C17C22×C4×D411yescharacteristic
210C2×C17C23×M1611yescharacteristic
211C2×C17C22×#13111yescharacteristic
212D17—28no—
213D17—44no—
214C25—171no—
215C25—171no—
216C22×D4—1712no—
217C22×D4—348no—
218C23×C4—171no—
219C23×C4—171no—
220C23×C4—176no—
221C23×C4—176no—
222C23×C4—176no—
223C23×C4—176no—
224C23×C4—344no—
225C23×C4—344no—
226C23×C4—344no—
227C23×C4—344no—
228C23×C4C2×#59511yescharacteristic
229C23×C4C2×#59511yescharacteristic
230C23×C4C2×#59511yescharacteristic
231C2×M16—1716no—
232C2×M16—3448no—
233C22×C8—178no—
234C22×C8—176no—
235C22×C8—1716no—
236C22×C8—176no—
237C22×C8—176no—
238C22×C8—176no—
239C22×C8—3448no—
240C22×C8—344no—
241C22×C8—344no—
242C22×C8—344no—
243C4×D4—1716no—
244C4×D4—1748no—
245C2×C4⋊C4C2×#595112yes—
246C2×C22⋊C4—1712no—
247C2×C22⋊C4—1712no—
248C2×C42—176no—
249C2×C42—176no—
250C4⋊C8—1716no—
251C22⋊C8—1716no—
252C22⋊C8—1716no—
253#97—1716no—
254C17C22×#43511yescharacteristic, complemented, Sylow
255C24—178no—
256C24—176no—
257C24—176no—
258C24—344no—
259C24—344no—
260C24—344no—
261C24—344no—
262C24—344no—
263C24C22×#59511yescharacteristic
264C2×D4—1716no—
265C2×D4—3448no—
266C22×C4—24no—
267C22×C4—24no—
268C22×C4—24no—
269C22×C4—174no—
270C22×C4—174no—
271C22×C4—173no—
272C22×C4—173no—
273C22×C4—176no—
274C22×C4—1712no—
275C22×C4—1712no—
276C22×C4—174no—
277C22×C4—174no—
278C22×C4—3412no—
279C22×C4—3412no—
280C22×C4—3412no—
281C22×C4—3412no—
282C22×C4—3424no—
283C22×C4—3424no—
284C22×C4—344no—
285C22×C4C22×#59516yes—
286C22×C4C22×#59516yes—
287C22×C4C22×#59516yes—
288M16—3432no—
289C2×C8—1724no—
290C2×C8—174no—
291C2×C8—174no—
292C2×C8—174no—
293C2×C8—174no—
294C2×C8—3432no—
295C2×C8—3412no—
296C2×C8—3412no—
297C2×C8—3412no—
298C4⋊C4C22×#595116yes—
299C22⋊C4—1716no—
300C22⋊C4—1716no—
301C42—174no—
302C42—1712no—
303C23—1724no—
304C23—174no—
305C23—174no—
306C23—3432no—
307C23—3412no—
308C23—3412no—
309C23—3412no—
310C23—3412no—
311C23—3412no—
312C23—6816no—
313C23D17⋊M1614yes—
314C23D4×#59514yes—
315C23#1058768014yes—
316C23C23×#59513yes—
317D4—3432no—
318C2×C4—212no—
319C2×C4—212no—
320C2×C4—212no—
321C2×C4—176no—
322C2×C4—176no—
323C2×C4—1712no—
324C2×C4—171no—
325C2×C4—173no—
326C2×C4—174no—
327C2×C4—344no—
328C2×C4—344no—
329C2×C4—344no—
330C2×C4—344no—
331C2×C4—3424no—
332C2×C4—3424no—
333C2×C4—3412no—
334C2×C4C23×#59514yes—
335C2×C4C23×#59514yes—
336C2×C4C23×#59514yes—
337C8—178no—
338C8—344no—
339C8—344no—
340C8—344no—
341C22—178no—
342C22—3448no—
343C22—344no—
344C22—344no—
345C22—344no—
346C22—344no—
347C22—344no—
348C22—6824no—
349C22#11763839116yesdirect product factor
350C22C2×D4×#59516yes—
351C22C2×D17⋊M1616yes—
352C22C2×#1058768016yes—
353C22C24×#59511yescharacteristic
354C4—24no—
355C4—24no—
356C4—24no—
357C4—171no—
358C4—171no—
359C4—176no—
360C4—344no—
361C2—348no—
362C2—684no—
363C2C2×#11763839112yesdirect product factor
364C2C22×D4×#59511yescharacteristic
365C2C22×D17⋊M1611yescharacteristic
366C2C22×#1058768011yescharacteristic
subgroupG/H
centerC24C22×#595
commutatorC22×C17C24×C4
FrattiniC22C24×#595
FittingC22×C4⋊C4×C17C4
socleC24×C17C22×C4
prime radicalC23×D68C4
cosocleC2×Dic17C25
hypercenterC22×C4⋊C4#595
hypocenterC17C22×#435
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C24 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C23×#63243C2semidirect
2. C23×#63242C2semidirect
3. C2×#11763839C2direct (N × H)
4. C22×#10587544C2semidirect
5. C22×#10587543C2semidirect
6. C22×#10587543C2semidirect
7. C22×#10587542C2semidirect
10. C22×#63243C22semidirect
12. C22×#63242C22semidirect
17. #11763839C22direct (N × H)
18. C2×#10587544C22semidirect
19. C2×#10587543C22semidirect
20. C2×#10587543C22semidirect
21. C2×#10587542C22semidirect
51. C22×#3624D4semidirect
57. C2×#63243C23semidirect
59. C2×#63242C23semidirect
67. #10587544C23semidirect
68. #10587543C23semidirect
69. #10587543C23semidirect
70. #10587542C23semidirect
77. C23×D17M16semidirect
107. C2×#3624C2×D4semidirect
131. C22×D17C2×M16semidirect
157. #3624C22×D4semidirect
166. C22×C17#435semidirect
178. C2×D17C22×M16semidirect
208. C2×C17C2×#435semidirect
254. C17C22×#435semidirect
349. C22#11763839direct (N × H)
363. C2C2×#11763839direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#632432
C23×#632422
C2×#117638392
C22×#105875442
C22×#105875432
C22×#105875422
C22×#105875792
C22×#43517