Finite Group Databasebeta

← #36444976

Subgroups — #36444976

Order 22784.

582 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×#10623494C211yesmaximal, characteristic
2#26020030C212yesmaximal, complemented
3#26018570C211yesmaximal, characteristic
4#26018100C212yesmaximal, complemented
5C4×#99×C89C211yesmaximal, characteristic
6C23×#10623494C411yescharacteristic, complemented
7C23×#10623494C2211yescharacteristic
8D4×#10623494—22no—
9D4×#10623494—22no—
10C2×C4⋊#10623494C411yescharacteristic, complemented
11C2×C22⋊#10623494C411yescharacteristic, complemented
12C2×C22⋊#10623494C2212yes—
13C2×C22⋊#10623494C2211yescharacteristic
14C2×#15667923—22no—
15C2×C4×#10623494C411yescharacteristic, complemented
16#19151353—22no—
17#19151324C412yescomplemented
18#19151322C412yescomplemented
19C2×C4×D4×C89C2211yescharacteristic
20C2×#99×C89C412yes—
21C4×C22⋊C4×C89C2212yes—
22#342×C89C412yes—
23C22×#10623494—21no—
24C22×#10623494—21no—
25C22×#10623494—22no—
26C22×#10623494—42no—
27C22×#10623494—42no—
28C22×#10623494C2×C411yescharacteristic
29C22×#10623494C2×C411yescharacteristic
30C22×#10623494C2×C411yescharacteristic
31C22×#10623494C2×C411yescharacteristic
32C22×#10623494D412yes—
33C22×#10623494D412yes—
34C4⋊#10623494—22no—
35C22⋊#10623494—22no—
36C22⋊#10623494—22no—
37C22⋊#10623494—22no—
38C22⋊#10623494C2×C414yes—
39#15667923—44no—
40C4×#10623494—21no—
41C4×#10623494—21no—
42C22×D4×C89C2×C411yescharacteristic
43C23×C4×C89C2×C411yescharacteristic
44C23×C4×C89C2311yescharacteristic
45C4×D4×C89—22no—
46C4×D4×C89—22no—
47C2×C4⋊C4×C89C2×C411yescharacteristic
48C2×C22⋊C4×C89C2×C411yescharacteristic
49C2×C22⋊C4×C89C2×C414yes—
50C2×C22⋊C4×C89C2×C411yescharacteristic
51C2×C42×C89—22no—
52C2×C42×C89C2×C411yescharacteristic
53#99×C89—24no—
54#95×C89—22no—
55C2×#10623494—22no—
56C2×#10623494—24no—
57C2×#10623494—21no—
58C2×#10623494—21no—
59C2×#10623494—24no—
60C2×#10623494—41no—
61C2×#10623494—42no—
62C2×#10623494—42no—
63C2×#10623494—42no—
64C2×#10623494—42no—
65C2×#10623494—42no—
66C2×#10623494—41no—
67C2×#10623494—41no—
68C2×#10623494C22⋊C411yescharacteristic
69C2×#10623494C22⋊C412yes—
70C2×#10623494C22⋊C411yescharacteristic
71C24×C89C4211yescharacteristic
72C24×C89C22×C411yescharacteristic
73C2×D4×C89—22no—
74C2×D4×C89—22no—
75C2×D4×C89M1614yes—
76C22×C4×C89—21no—
77C22×C4×C89—21no—
78C22×C4×C89—24no—
79C22×C4×C89—41no—
80C22×C4×C89—41no—
81C22×C4×C89—41no—
82C22×C4×C89—41no—
83C22×C4×C89C4211yescharacteristic
84C22×C4×C89C4211yescharacteristic
85C22×C4×C89C4211yescharacteristic
86C22×C4×C89C22×C411yescharacteristic
87C22×C4×C89C22×C411yescharacteristic
88C22×C4×C89C2×D412yes—
89C22×C4×C89#4112yes—
90C4⋊C4×C89—22no—
91C22⋊C4×C89—22no—
92C22⋊C4×C89—22no—
93C22⋊C4×C89—24no—
94C22⋊C4×C89—24no—
95C42×C89—21no—
96C42×C89—21no—
97C42×C89—42no—
98C42×C89—42no—
99C23×C89—21no—
100C23×C89—21no—
101C23×C89—41no—
102C23×C89—41no—
103C23×C89—41no—
104C23×C89—41no—
105C23×C89#9712yescomplemented
106C23×C89C2×C4211yescharacteristic
107C23×C89C4×D412yes—
108C23×C89C2×M1612yes—
109C23×C89#13112yes—
110D4×C89—28no—
111C2×C4×C89—21no—
112C2×C4×C89—21no—
113C2×C4×C89—22no—
114C2×C4×C89—21no—
115C2×C4×C89—22no—
116C2×C4×C89—21no—
117C2×C4×C89—21no—
118C2×C4×C89—21no—
119C2×C4×C89—41no—
120C2×C4×C89—42no—
121C2×C4×C89—42no—
122C2×C4×C89—41no—
123C2×C4×C89—41no—
124C2×C4×C89—41no—
125C2×C4×C89—41no—
126C2×C4×C89—44no—
127C2×C4×C89—44no—
128C2×C4×C89—44no—
129C2×C4×C89#9712yescomplemented
130C2×C4×C89C2×C22⋊C411yescharacteristic
131C2×C4×C89#11711yescharacteristic
132C2×C4×C89C4×D412yes—
133#10623494—21no—
134#10623494—22no—
135#10623494—44no—
136#10623494—41no—
137#10623494—41no—
138#10623494#9912yescomplemented
139C22×C89—22no—
140C22×C89—21no—
141C22×C89—22no—
142C22×C89—21no—
143C22×C89—22no—
144C22×C89—42no—
145C22×C89—42no—
146C22×C89—42no—
147C22×C89—42no—
148C22×C89—41no—
149C22×C89—41no—
150C22×C89C4×C22⋊C411yescharacteristic
151C22×C89C2×#9711yescharacteristic
152C22×C89#40511yescharacteristic
153C22×C89#43514yes—
154C4×C89—22no—
155C4×C89—22no—
156C4×C89—21no—
157C4×C89—41no—
158C4×C89—41no—
159C4×C89—84no—
160C4×C89C2×#9911yescharacteristic
161C4×C89#41011yescharacteristic
162#8160—891nomaximal, Sylow
163C2×C89—24no—
164C2×C89—21no—
165C2×C89—21no—
166C2×C89—42no—
167C2×C89#175211yescharacteristic
168C2×C89C4×#9911yescharacteristic
169C2×C89#175711yescharacteristic
170C2×C8×D4—891no—
171C4×#99D8911yescharacteristic
172#1752—892no—
173#1459—891no—
174#1282—892no—
175C89#816011yescharacteristic, complemented, Sylow
176C23×C8—891no—
177C23×C8—891no—
178C2×C4×D4C2×D8911yescharacteristic
179C8×D4—1782no—
180C8×D4—1782no—
181C2×C4⋊C8—891no—
182C2×#99Dic8912yes—
183C2×C22⋊C8—892no—
184C2×C22⋊C8—891no—
185C2×C22⋊C8—891no—
186C2×#97—1782no—
187C2×C4×C8—891no—
188C4×C22⋊C4C2×D8912yes—
189#342Dic8912yes—
190#336—1782no—
191#324—892no—
192#323—892no—
193C22×D4C2×Dic8911yescharacteristic
194C23×C4C4×D8911yescharacteristic
195C23×C4C22×D8911yescharacteristic
196C22×C8—891no—
197C22×C8—892no—
198C22×C8—891no—
199C22×C8—892no—
200C22×C8—891no—
201C22×C8—891no—
202C22×C8—3562no—
203C22×C8—3562no—
204C22×C8—1781no—
205C22×C8—1781no—
206C22×C8—1782no—
207C4×D4—22no—
208C4×D4—22no—
209C2×C4⋊C4C4×D8911yescharacteristic
210C2×C22⋊C4C4×D8911yescharacteristic
211C2×C22⋊C4C2×Dic8914yes—
212C2×C22⋊C4C2×Dic8911yescharacteristic
213C2×C42—22no—
214C2×C42C4×D8911yescharacteristic
215C4⋊C8—1782no—
216#99—24no—
217C22⋊C8—894no—
218C22⋊C8—1782no—
219C22⋊C8—1782no—
220C22⋊C8—1782no—
221#97—3564no—
222C4×C8—1781no—
223C4×C8—1781no—
224#95—22no—
225C24C4×Dic8911yescharacteristic
226C24C22×Dic8911yescharacteristic
227C2×D4—22no—
228C2×D4—22no—
229C2×D4#1308355814yes—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—24no—
233C22×C4—41no—
234C22×C4—41no—
235C22×C4—41no—
236C22×C4—41no—
237C22×C4C4×Dic8911yescharacteristic
238C22×C4C4×Dic8911yescharacteristic
239C22×C4C4×Dic8911yescharacteristic
240C22×C4C2×C4×D8911yescharacteristic
241C22×C4C2×C4×D8911yescharacteristic
242C22×C4D4×D8912yes—
243C22×C4#1308357312yes—
244C2×C8—891no—
245C2×C8—891no—
246C2×C8—892no—
247C2×C8—3562no—
248C2×C8—3562no—
249C2×C8—3562no—
250C2×C8—3562no—
251C2×C8—3561no—
252C2×C8—3561no—
253C2×C8—3562no—
254C2×C8—3561no—
255C2×C8—1784no—
256C2×C8—1782no—
257C2×C8—1784no—
258C2×C8—1781no—
259C2×C8—1781no—
260C4⋊C4—22no—
261C22⋊C4—22no—
262C22⋊C4—22no—
263C22⋊C4—24no—
264C22⋊C4—24no—
265C42—21no—
266C42—21no—
267C42—42no—
268C42—42no—
269C23—21no—
270C23—21no—
271C23—41no—
272C23—41no—
273C23—41no—
274C23—41no—
275C23#1566792312yescomplemented
276C23C2×C4×Dic8911yescharacteristic
277C23D4×Dic8912yes—
278C23C2×#1308355812yes—
279C23#1566801912yes—
280D4—28no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—22no—
284C2×C4—21no—
285C2×C4—22no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—41no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—44no—
297C2×C4—44no—
298C2×C4—44no—
299C2×C4#1566792312yescomplemented
300C2×C4C22⋊C4×D8911yescharacteristic
301C2×C4#1566796811yescharacteristic
302C2×C4#1566797212yes—
303C8—892no—
304C8—3564no—
305C8—3561no—
306C8—3561no—
307C8—1781no—
308C8—1782no—
309C22—22no—
310C22—21no—
311C22—22no—
312C22—21no—
313C22—22no—
314C22—42no—
315C22—42no—
316C22—42no—
317C22—42no—
318C22—41no—
319C22—41no—
320C22C22⋊C4×Dic8911yescharacteristic
321C22C2×#1566792311yescharacteristic
322C22#1915155411yescharacteristic
323C22#1915167014yes—
324C4—22no—
325C4—22no—
326C4—21no—
327C4—41no—
328C4—41no—
329C4—84no—
330C4#99×D8911yescharacteristic
331C4#1915157011yescharacteristic
332C2—24no—
333C2—21no—
334C2—21no—
335C2—42no—
336C2#2602003011yescharacteristic
337C2#99×Dic8911yescharacteristic
338C2#2602005411yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D89
commutatorC23×C89C2×C42
FrattiniC23×C4C22×D89
FittingC4×#99×C89C2
socleC22×C89C4×C22⋊C4
prime radicalC22×D4×C89C2×C4
cosocleC23×C4×C89C23
hypercenterC4×#99D89
hypocenterC89#8160
LCSG ▷ C23×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
2. #26020030C2semidirect
4. #26018100C2semidirect
6. C23×#10623494C4semidirect
10. C2×C4⋊#10623494C4semidirect
11. C2×C22⋊#10623494C4semidirect
15. C2×C4×#10623494C4semidirect
17. #19151324C4semidirect
18. #19151322C4semidirect
105. C23×C89#97semidirect
129. C2×C4×C89#97semidirect
138. #10623494#99semidirect
175. C89#8160semidirect
275. C23#15667923semidirect
299. C2×C4#15667923semidirect

Maximal subgroups

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

subgroupindex
C2×D4×#106234942
#260200302
#260185702
#260181002
C4×#99×C892
#816089