Finite Group Databasebeta

← #36443046

Subgroups — #36443046

Order 22784.

414 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
1#26020395C211yesmaximal, characteristic, complemented
2#26020369C211yesmaximal, characteristic, complemented
3#26018078C212yesmaximal, complemented
4#26018073C212yesmaximal
5C89×#2861C211yesmaximal, characteristic
6C2×C4⋊#10623494—21no—
7#19151353—21no—
8#19151353—21no—
9#19151353—21no—
10#19151353C2212yes—
11#19151353C2212yes—
12C2×#125×C89C411yescharacteristic
13C2×#124×C89C411yescharacteristic
14#391×C89C411yescharacteristic
15#391×C89C2211yescharacteristic
16#390×C89C411yescharacteristic
17#390×C89C2211yescharacteristic
18#388×C89—21no—
19#388×C89—21no—
20#388×C89—21no—
21#388×C89—21no—
22C43×C89C2211yescharacteristic
23C22×#10623494—22no—
24C22×#10623494—22no—
25C4⋊#10623494—42no—
26C22×Q8×C89C2×C411yescharacteristic
27C22×D4×C89C2×C411yescharacteristic
28#125×C89—42no—
29#124×C89—42no—
30C2×C4⋊C4×C89—21no—
31C2×C4⋊C4×C89—21no—
32C2×C4⋊C4×C89C2×C411yescharacteristic
33C2×C4⋊C4×C89C2×C411yescharacteristic
34C2×C22⋊C4×C89—21no—
35C2×C22⋊C4×C89—21no—
36C2×C22⋊C4×C89—21no—
37C2×C22⋊C4×C89—21no—
38C2×C22⋊C4×C89—21no—
39C2×C22⋊C4×C89—21no—
40C2×C42×C89C2×C411yescharacteristic
41C2×C42×C89C2×C411yescharacteristic
42C2×C42×C89D411yescharacteristic
43C2×C42×C89D411yescharacteristic
44C2×C42×C89D411yescharacteristic
45C2×C42×C89D411yescharacteristic
46C2×C42×C89C2311yescharacteristic
47#95×C89—21no—
48#95×C89—21no—
49#95×C89—21no—
50#95×C89—21no—
51C2×#10623494—42no—
52C2×#10623494—42no—
53C2×#10623494—42no—
54C2×#10623494—42no—
55C2×#10623494—42no—
56C2×#10623494—42no—
57C24×C89—21no—
58C2×Q8×C89—22no—
59C2×Q8×C89—41no—
60C2×Q8×C89—41no—
61C2×D4×C89—22no—
62C2×D4×C89—41no—
63C2×D4×C89—41no—
64C22×C4×C89—21no—
65C22×C4×C89—21no—
66C22×C4×C89—21no—
67C22×C4×C89C22⋊C411yescharacteristic
68C22×C4×C89C22⋊C411yescharacteristic
69C22×C4×C89C22⋊C411yescharacteristic
70C22×C4×C89C22⋊C411yescharacteristic
71C22×C4×C89C22×C411yescharacteristic
72C22×C4×C89C2×D411yescharacteristic
73C22×C4×C89C2×D411yescharacteristic
74C4⋊C4×C89—42no—
75C4⋊C4×C89—41no—
76C4⋊C4×C89—41no—
77C4⋊C4×C89—42no—
78C22⋊C4×C89—42no—
79C22⋊C4×C89—42no—
80C22⋊C4×C89—42no—
81C22⋊C4×C89—42no—
82C22⋊C4×C89—42no—
83C22⋊C4×C89—41no—
84C22⋊C4×C89—41no—
85C42×C89—22no—
86C42×C89—22no—
87C42×C89—22no—
88C42×C89—21no—
89C42×C89—21no—
90C42×C89—41no—
91C42×C89—41no—
92C42×C89—41no—
93C23×C89—41no—
94C23×C89—41no—
95C23×C89—41no—
96C23×C89—41no—
97C23×C89—41no—
98C23×C89—41no—
99C23×C89—41no—
100C23×C89C2×C22⋊C411yescharacteristic
101Q8×C89—82no—
102D4×C89—82no—
103C2×C4×C89—21no—
104C2×C4×C89—21no—
105C2×C4×C89—21no—
106C2×C4×C89—21no—
107C2×C4×C89—21no—
108C2×C4×C89—21no—
109C2×C4×C89—21no—
110C2×C4×C89—21no—
111C2×C4×C89—21no—
112C2×C4×C89—21no—
113C2×C4×C89—21no—
114C2×C4×C89—21no—
115C2×C4×C89—21no—
116C2×C4×C89—21no—
117C2×C4×C89—21no—
118C2×C4×C89—21no—
119C2×C4×C89—21no—
120C2×C4×C89—41no—
121C2×C4×C89—41no—
122C2×C4×C89—41no—
123C2×C4×C89—41no—
124C2×C4×C89—41no—
125C2×C4×C89—41no—
126C2×C4×C89—41no—
127C2×C4×C89—41no—
128C2×C4×C89—41no—
129C2×C4×C89#10012yes—
130C2×C4×C89#13112yes—
131C2×C4×C89#13512yes—
132C2×C4×C89AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C89#13711yescharacteristic
134#10623494—82no—
135#10623494—82no—
136C22×C89—81no—
137C22×C89—81no—
138C22×C89—81no—
139C22×C89—81no—
140C22×C89—81no—
141C22×C89—81no—
142C22×C89—81no—
143C22×C89#40811yescharacteristic
144C22×C89#41011yescharacteristic
145C22×C89C2×#10011yescharacteristic
146C22×C89#41611yescharacteristic
147C22×C89#41711yescharacteristic
148C22×C89#42111yescharacteristic
149C22×C89#42111yescharacteristic
150C4×C89—22no—
151C4×C89—22no—
152C4×C89—21no—
153C4×C89—21no—
154C4×C89—22no—
155C4×C89—41no—
156C4×C89—41no—
157C4×C89—41no—
158C4×C89—81no—
159C4×C89—81no—
160C4×C89—81no—
161#7716—891nomaximal, Sylow
162C2×C89—161no—
163C2×C89#146911yescharacteristic
164C2×C89#148211yescharacteristic
165C2×C89#149511yescharacteristic
166C2×C89#151211yescharacteristic
167C2×C89#152111yescharacteristic
168C2×C89#153611yescharacteristic
169C2×C89#155111yescharacteristic
170#2861D8911yescharacteristic
171#1839—891no—
172#1831—891no—
173#1272—892no—
174#1270—892no—
175C89#771611yescharacteristic, complemented, Sylow
176C2×#125Dic8911yescharacteristic
177C2×#124Dic8911yescharacteristic
178C2×C4⋊C8—1781no—
179#391Dic8911yescharacteristic
180#391C2×D8911yescharacteristic
181#390Dic8911yescharacteristic
182#390C2×D8911yescharacteristic
183#388—21no—
184#388—21no—
185#388—21no—
186#388—21no—
187C43C2×D8911yescharacteristic
188#336—892no—
189#336—892no—
190#336—1781no—
191#336—1781no—
192#336—1781no—
193C22×Q8C2×Dic8911yescharacteristic
194C22×D4C2×Dic8911yescharacteristic
195C22×C8—1782no—
196C22×C8—1782no—
197#125—42no—
198#124—42no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4C2×Dic8911yescharacteristic
202C2×C4⋊C4C2×Dic8911yescharacteristic
203C2×C22⋊C4—21no—
204C2×C22⋊C4—21no—
205C2×C22⋊C4—21no—
206C2×C22⋊C4—21no—
207C2×C22⋊C4—21no—
208C2×C22⋊C4—21no—
209C2×C42C2×Dic8911yescharacteristic
210C2×C42C2×Dic8911yescharacteristic
211C2×C42C22⋊D8911yescharacteristic
212C2×C42C22⋊D8911yescharacteristic
213C2×C42C22⋊D8911yescharacteristic
214C2×C42C22⋊D8911yescharacteristic
215C2×C42C22×D8911yescharacteristic
216C4⋊C8—3562no—
217#95—21no—
218#95—21no—
219#95—21no—
220#95—21no—
221C24—21no—
222C2×Q8—22no—
223C2×Q8—41no—
224C2×Q8—41no—
225C2×D4—22no—
226C2×D4—41no—
227C2×D4—41no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4C22⋊Dic8911yescharacteristic
232C22×C4C22⋊Dic8911yescharacteristic
233C22×C4C22⋊Dic8911yescharacteristic
234C22×C4C22⋊Dic8911yescharacteristic
235C22×C4C22×Dic8911yescharacteristic
236C22×C4C2×C22⋊D8911yescharacteristic
237C22×C4C2×C22⋊D8911yescharacteristic
238C2×C8—3562no—
239C2×C8—3562no—
240C2×C8—3562no—
241C2×C8—3562no—
242C2×C8—3562no—
243C2×C8—3562no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—42no—
247C4⋊C4—42no—
248C22⋊C4—42no—
249C22⋊C4—42no—
250C22⋊C4—42no—
251C22⋊C4—42no—
252C22⋊C4—41no—
253C22⋊C4—41no—
254C22⋊C4—42no—
255C42—22no—
256C42—22no—
257C42—21no—
258C42—21no—
259C42—22no—
260C42—41no—
261C42—41no—
262C42—41no—
263C23—41no—
264C23—41no—
265C23—41no—
266C23—41no—
267C23—41no—
268C23—41no—
269C23—41no—
270C23C2×C22⋊Dic8911yescharacteristic
271Q8—82no—
272D4—82no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4#1566792912yes—
300C2×C4#1566801912yes—
301C2×C4#1566803212yes—
302C2×C4#1566803711yescharacteristic
303C2×C4#1566804211yescharacteristic
304C8—7122no—
305C8—7122no—
306C22—81no—
307C22—81no—
308C22—81no—
309C22—81no—
310C22—81no—
311C22—81no—
312C22—81no—
313C22#1915156511yescharacteristic
314C22#1915157211yescharacteristic
315C22C2×#1566792911yescharacteristic
316C22#1915159411yescharacteristic
317C22#1915159911yescharacteristic
318C22#1915161511yescharacteristic
319C22#1915161511yescharacteristic
320C4—22no—
321C4—22no—
322C4—22no—
323C4—21no—
324C4—21no—
325C4—41no—
326C4—41no—
327C4—41no—
328C4—81no—
329C4—81no—
330C4—81no—
331C2—161no—
332C2#2601860411yescharacteristic
333C2#2601866011yescharacteristic
334C2#2601871711yescharacteristic
335C2#2601879011yescharacteristic
336C2#2601882911yescharacteristic
337C2#2601888711yescharacteristic
338C2#2601894711yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic89
commutatorC22×C4×C89C22×C4
FrattiniC2×C42C22×D89
FittingC89×#2861C2
socleC23×C89C2×C22⋊C4
prime radicalC22×D4×C89C2×C4
cosocleC2×C42×C89C23
hypercenter#2861D89
hypocenterC89#7716
LCSG ▷ C22×C4×C89 ▷ C22×C89 ▷ C89
UCSC1 ◁ C23 ◁ C43 ◁ #2861

Complements

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

NH ≅ G/Ntype
1. #26020395C2semidirect
2. #26020369C2semidirect
3. #26018078C2semidirect
175. C89#7716semidirect

Maximal subgroups

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

subgroupindex
#260203952
#260203692
#260180782
#260180732
C89×#28612
#771689