Finite Group Databasebeta

← #36453032

Subgroups — #36453032

Order 22784.

368 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26020369C211yesmaximal, characteristic
2C4×C4⋊#10623494C211yesmaximal, characteristic
3C2×#19151350C211yesmaximal, characteristic
4C2×#19151348C211yesmaximal, characteristic
5#26018086C211yesmaximal, characteristic
6#26018086C211yesmaximal, characteristic
7C89×#1767C211yesmaximal, characteristic
8C2×C4⋊#10623494C411yescharacteristic
9C2×C4⋊#10623494C411yescharacteristic
10C2×C4⋊#10623494C2211yescharacteristic
11C2×C4⋊#10623494C2211yescharacteristic
12C2×C4×#10623494C2211yescharacteristic
13C2×C4×#10623494C2211yescharacteristic
14#19151353—21no—
15#19151353—21no—
16#19151353C411yescharacteristic
17#19151353C411yescharacteristic
18#19151350—22no—
19#19151348—22no—
20C2×C4⋊C8×C89C2211yescharacteristic
21C2×C4⋊C8×C89C2211yescharacteristic
22C2×#97×C89—21no—
23C43×C89C2211yescharacteristic
24#336×C89—21no—
25C22×#10623494—21no—
26C22×#10623494—21no—
27C22×#10623494C2×C411yescharacteristic
28C22×#10623494C2×C411yescharacteristic
29C22×#10623494C2×C411yescharacteristic
30C22×#10623494C2×C411yescharacteristic
31C4⋊#10623494—22no—
32C4⋊#10623494—22no—
33C4⋊#10623494—21no—
34C4⋊#10623494—21no—
35C4⋊#10623494—21no—
36C4⋊#10623494—21no—
37C4×#10623494—21no—
38C4×#10623494—21no—
39C4×#10623494—21no—
40C4×#10623494—21no—
41C22×C8×C89—21no—
42C22×C8×C89—21no—
43C2×C42×C89C2×C411yescharacteristic
44C2×C42×C89C2×C411yescharacteristic
45C2×C42×C89D411yescharacteristic
46C2×C42×C89D411yescharacteristic
47C2×C42×C89Q811yescharacteristic
48C2×C42×C89Q811yescharacteristic
49C2×C42×C89C2311yescharacteristic
50C4⋊C8×C89—21no—
51C4⋊C8×C89—21no—
52C4⋊C8×C89D412yes—
53C4⋊C8×C89Q812yes—
54#97×C89—42no—
55C2×#10623494—21no—
56C2×#10623494—21no—
57C2×#10623494—21no—
58C2×#10623494—21no—
59C2×#10623494—21no—
60C2×#10623494—21no—
61C2×#10623494—21no—
62C2×#10623494—21no—
63C2×#10623494—21no—
64C2×#10623494—21no—
65C2×#10623494—41no—
66C2×#10623494—41no—
67C2×#10623494—41no—
68C2×#10623494—41no—
69C2×#10623494—41no—
70C2×#10623494—41no—
71C2×#10623494M1612yes—
72C2×#10623494M1612yes—
73C22×C4×C89C4⋊C411yescharacteristic
74C22×C4×C89C4⋊C411yescharacteristic
75C22×C4×C89C4⋊C411yescharacteristic
76C22×C4×C89C4⋊C411yescharacteristic
77C22×C4×C89C22×C411yescharacteristic
78C22×C4×C89C2×D411yescharacteristic
79C22×C4×C89C2×Q811yescharacteristic
80C2×C8×C89—22no—
81C2×C8×C89—22no—
82C2×C8×C89—41no—
83C2×C8×C89—41no—
84C2×C8×C89—41no—
85C2×C8×C89—41no—
86C42×C89—22no—
87C42×C89—21no—
88C42×C89—21no—
89C42×C89—21no—
90C42×C89—21no—
91C42×C89—21no—
92C42×C89—21no—
93C42×C89—21no—
94C42×C89—21no—
95C42×C89—41no—
96C42×C89C2×D411yescharacteristic
97C42×C89C2×Q811yescharacteristic
98C42×C89#4111yescharacteristic
99C42×C89#4111yescharacteristic
100C23×C89C2×C4⋊C411yescharacteristic
101C2×C4×C89—21no—
102C2×C4×C89—21no—
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#10812yes—
115C2×C4×C89C4×D411yescharacteristic
116C2×C4×C89C4×Q811yescharacteristic
117C2×C4×C89#12111yescharacteristic
118C2×C4×C89C22⋊Q811yescharacteristic
119C2×C4×C89#12511yescharacteristic
120C2×C4×C89C4⋊Q811yescharacteristic
121C2×C4×C89C2×M1611yescharacteristic
122C2×C4×C89C2×M1611yescharacteristic
123C2×C4×C89#13111yescharacteristic
124C2×C4×C89#13111yescharacteristic
125C2×C4×C89#13511yescharacteristic
126C2×C4×C89#13511yescharacteristic
127C2×C4×C89AGL(1,ℤ/8)11yescharacteristic
128C2×C4×C89#13711yescharacteristic
129C8×C89—42no—
130C8×C89—42no—
131#10623494—22no—
132#10623494—22no—
133#10623494—41no—
134#10623494—41no—
135#10623494—81no—
136#10623494—81no—
137C22×C89#38911yescharacteristic
138C22×C89#42311yescharacteristic
139C22×C89#42411yescharacteristic
140C22×C89#42711yescharacteristic
141C22×C89#42811yescharacteristic
142C22×C89C2×#10811yescharacteristic
143C22×C89#43011yescharacteristic
144C4×C89—22no—
145C4×C89—21no—
146C4×C89—21no—
147C4×C89—41no—
148C4×C89—41no—
149C4×C89—41no—
150C4×C89#43511yescharacteristic
151C4×C89#43511yescharacteristic
152C4×C89#44611yescharacteristic
153C4×C89#44611yescharacteristic
154C4×C89#46311yescharacteristic
155C4×C89#46411yescharacteristic
156C4×C89#47811yescharacteristic
157C4×C89#47911yescharacteristic
158#9606—891nomaximal, Sylow
159C2×C89#156811yescharacteristic
160C2×C89#156911yescharacteristic
161C2×C89#157211yescharacteristic
162C2×C89#157411yescharacteristic
163C2×C89#194011yescharacteristic
164C2×C89#194911yescharacteristic
165C2×C89#195011yescharacteristic
166#1831—891no—
167#1767D8911yescharacteristic
168C4×C4⋊C8—891no—
169C2×#335—891no—
170C2×#334—891no—
171#1277—891no—
172#1277—891no—
173C89#960611yescharacteristic, complemented, Sylow
174C2×C4⋊C8—891no—
175C2×C4⋊C8—891no—
176C2×C4⋊C8—891no—
177C2×C4⋊C8—891no—
178C2×C4⋊C8C2×D8911yescharacteristic
179C2×C4⋊C8C2×D8911yescharacteristic
180C2×#97—21no—
181C2×C4×C8—891no—
182C2×C4×C8—891no—
183C43C2×D8911yescharacteristic
184#336—21no—
185#336—891no—
186#336—891no—
187#336—1781no—
188#336—1781no—
189#335—1782no—
190#334—1782no—
191C22×C8—21no—
192C22×C8—21no—
193C22×C8—891no—
194C22×C8—891no—
195C22×C8—891no—
196C22×C8—891no—
197C22×C8—1781no—
198C22×C8—1781no—
199C2×C42Dic17811yescharacteristic
200C2×C42Dic17811yescharacteristic
201C2×C42C4×D8911yescharacteristic
202C2×C42C4×D8911yescharacteristic
203C2×C42C22⋊D8911yescharacteristic
204C2×C42C22⋊D8911yescharacteristic
205C2×C42C22×D8911yescharacteristic
206C4⋊C8—21no—
207C4⋊C8—21no—
208C4⋊C8—1782no—
209C4⋊C8—1782no—
210C4⋊C8—1781no—
211C4⋊C8—1781no—
212C4⋊C8—1781no—
213C4⋊C8—1781no—
214C4⋊C8Dic17812yes—
215C4⋊C8D35612yes—
216#97—42no—
217C4×C8—1781no—
218C4×C8—1781no—
219C4×C8—1781no—
220C4×C8—1781no—
221C22×C4#1308355311yescharacteristic
222C22×C4#1308355311yescharacteristic
223C22×C4#1308355311yescharacteristic
224C22×C4#1308355311yescharacteristic
225C22×C4C2×C4×D8911yescharacteristic
226C22×C4C2×C22⋊D8911yescharacteristic
227C22×C4C2×Dic17811yescharacteristic
228C2×C8—22no—
229C2×C8—22no—
230C2×C8—41no—
231C2×C8—41no—
232C2×C8—41no—
233C2×C8—41no—
234C2×C8—892no—
235C2×C8—892no—
236C2×C8—3561no—
237C2×C8—3561no—
238C2×C8—3561no—
239C2×C8—3561no—
240C2×C8—3561no—
241C2×C8—3561no—
242C2×C8—1781no—
243C2×C8—1781no—
244C2×C8—1781no—
245C2×C8—1781no—
246C2×C8—1781no—
247C2×C8—1781no—
248C2×C8—1781no—
249C2×C8—1781no—
250C2×C8—1781no—
251C2×C8—1781no—
252C42—21no—
253C42—21no—
254C42—21no—
255C42—21no—
256C42—21no—
257C42—21no—
258C42—21no—
259C42—21no—
260C42—22no—
261C42—41no—
262C42C2×D35611yescharacteristic
263C42C2×Dic17811yescharacteristic
264C42#1308357411yescharacteristic
265C42#1308357411yescharacteristic
266C23C2×#1308355311yescharacteristic
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4#1566794712yes—
281C2×C4C4×D35611yescharacteristic
282C2×C4C4×Dic17811yescharacteristic
283C2×C4#1566798611yescharacteristic
284C2×C4#1566799111yescharacteristic
285C2×C4#1566800411yescharacteristic
286C2×C4#1566801211yescharacteristic
287C2×C4M16×D8911yescharacteristic
288C2×C4M16×D8911yescharacteristic
289C2×C4#1566802011yescharacteristic
290C2×C4#1566802011yescharacteristic
291C2×C4#1566803211yescharacteristic
292C2×C4#1566803211yescharacteristic
293C2×C4#1566803811yescharacteristic
294C2×C4#1566804311yescharacteristic
295C8—42no—
296C8—42no—
297C8—3561no—
298C8—3561no—
299C8—1782no—
300C8—1782no—
301C8—7121no—
302C8—7121no—
303C22#1915149611yescharacteristic
304C22#1915162111yescharacteristic
305C22#1915162611yescharacteristic
306C22#1915163411yescharacteristic
307C22#1915163811yescharacteristic
308C22C2×#1566794711yescharacteristic
309C22#1915164611yescharacteristic
310C4—21no—
311C4—21no—
312C4—22no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4#1915167111yescharacteristic
317C4#1915167111yescharacteristic
318C4#1915172611yescharacteristic
319C4#1915172611yescharacteristic
320C4#1915181311yescharacteristic
321C4#1915182011yescharacteristic
322C4#1915189811yescharacteristic
323C4#1915190511yescharacteristic
324C2#2601901311yescharacteristic
325C2#2601901711yescharacteristic
326C2#2601903311yescharacteristic
327C2#2601904311yescharacteristic
328C2#2602097511yescharacteristic
329C2#2602102011yescharacteristic
330C2#2602102711yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D89
commutatorC22×C4×C89C22×C4
FrattiniC2×C42C22×D89
FittingC89×#1767C2
socle, prime radicalC23×C89C2×C4⋊C4
cosocleC2×C42×C89C23
hypercenter#1767D89
hypocenterC89#9606
LCSG ▷ C22×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22×C4 ◁ C43 ◁ #1767

Complements

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

NH ≅ G/Ntype
173. C89#9606semidirect

Maximal subgroups

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

subgroupindex
#260203692
C4×C4⋊#106234942
C2×#191513502
C2×#191513482
#260180862
C89×#17672
#960689