Finite Group Databasebeta

← #36458888

Subgroups — #36458888

Order 22784.

406 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#26025491C211yesmaximal, characteristic
2#26021011C211yesmaximal, characteristic
3#26021010C211yesmaximal, characteristic
4#26020409C211yesmaximal, characteristic
5#26018136C211yesmaximal, characteristic
6#26018092C211yesmaximal, characteristic
7C89×#1279C211yesmaximal, characteristic
8C2×#15667946—21no—
9C2×#15667945—21no—
10C2×#15667944—22no—
11C2×C4⋊#10623494C2211yescharacteristic
12#19151540—22no—
13#19151496—21no—
14#19151494—21no—
15#19151468C2211yescharacteristic
16#19151468C2211yescharacteristic
17#19151464—21no—
18#19151463—21no—
19C4×C4⋊Dic89C2211yescharacteristic
20#19151361—21no—
21#19151360—21no—
22C2×C4⋊C8×C89C2211yescharacteristic
23C2×C4×C8×C89C2211yescharacteristic
24C4×C4⋊C4×C89C2211yescharacteristic
25C22×#10623494—21no—
26C2×C4⋊Dic89—21no—
27C2×C4⋊Dic89—21no—
28C2×C4⋊Dic89—21no—
29C2×C4⋊Dic89—21no—
30C2×C4⋊Dic89—21no—
31C2×C4⋊Dic89D411yescharacteristic
32C2×C4⋊Dic89D411yescharacteristic
33C2×C4⋊Dic89D412yes—
34C2×#13083553—22no—
35C2×C4×Dic89—21no—
36#15667946—42no—
37#15667945—42no—
38#15667944—44no—
39C4⋊#10623494—21no—
40C4⋊#10623494Q812yes—
41#15667919—22no—
42#15667919—22no—
43#15667919—22no—
44#15667919—21no—
45C22×C8×C89—21no—
46C22×C8×C89—21no—
47C2×C4⋊C4×C89D411yescharacteristic
48C2×C4⋊C4×C89D411yescharacteristic
49C2×C42×C89—21no—
50C2×C42×C89C2311yescharacteristic
51C4⋊C8×C89—21no—
52C4⋊C8×C89Q812yes—
53C4×C8×C89—21no—
54C4×C8×C89Q812yes—
55#95×C89—21no—
56C22×Dic89—21no—
57C22×Dic89—21no—
58C22×Dic89—22no—
59C22×Dic89—41no—
60C2×#10623494—22no—
61C2×#10623494—41no—
62C2×#10623494—41no—
63C4⋊Dic89—21no—
64C4⋊Dic89—21no—
65C4⋊Dic89—21no—
66C4⋊Dic89—21no—
67C4⋊Dic89—41no—
68C4⋊Dic89—41no—
69C4⋊Dic89—41no—
70C4⋊Dic89—41no—
71C4⋊Dic89—42no—
72C4⋊Dic89—42no—
73C4⋊Dic89—41no—
74C4⋊Dic89—41no—
75C4⋊Dic89—41no—
76C4⋊Dic89—41no—
77#13083553—82no—
78C4×Dic89—41no—
79C4×Dic89—41no—
80C22×C4×C89—21no—
81C22×C4×C89—21no—
82C22×C4×C89C2×D411yescharacteristic
83C22×C4×C89C2×D411yescharacteristic
84C22×C4×C89C2×D411yescharacteristic
85C2×C8×C89—22no—
86C2×C8×C89—22no—
87C2×C8×C89—22no—
88C2×C8×C89—22no—
89C2×C8×C89—41no—
90C2×C8×C89—41no—
91C4⋊C4×C89—21no—
92C4⋊C4×C89—21no—
93C4⋊C4×C89—21no—
94C4⋊C4×C89—21no—
95C42×C89—41no—
96C42×C89—41no—
97C42×C89C2×Q811yescharacteristic
98C42×C89C2×Q811yescharacteristic
99C42×C89C2×Q811yescharacteristic
100C42×C89#4111yescharacteristic
101C23×C89#12011yescharacteristic
102C2×C4×C89—21no—
103C2×C4×C89—21no—
104C2×C4×C89—41no—
105C2×C4×C89—41no—
106C2×C4×C89—41no—
107C2×C4×C89—41no—
108C2×C4×C89—41no—
109C2×C4×C89—41no—
110C2×C4×C89C22⋊Q811yescharacteristic
111C2×C4×C89C22⋊Q811yescharacteristic
112C2×C4×C89C22⋊Q811yescharacteristic
113C2×C4×C89C4⋊Q811yescharacteristic
114C2×C4×C89C4⋊Q811yescharacteristic
115C2×C4×C89C4⋊Q811yescharacteristic
116C2×C4×C89#13511yescharacteristic
117C2×C4×C89#13511yescharacteristic
118C2×C4×C89#13511yescharacteristic
119C2×C4×C89#13511yescharacteristic
120C2×C4×C89AGL(1,ℤ/8)11yescharacteristic
121C2×C4×C89AGL(1,ℤ/8)11yescharacteristic
122C2×C4×C89#13711yescharacteristic
123C2×C4×C89#13711yescharacteristic
124C2×Dic89—41no—
125C2×Dic89—41no—
126C2×Dic89—41no—
127C2×Dic89—41no—
128C2×Dic89—42no—
129C2×Dic89—42no—
130C2×Dic89—41no—
131C2×Dic89—42no—
132C2×Dic89—41no—
133C2×Dic89—81no—
134C2×Dic89—81no—
135C2×Dic89—81no—
136C8×C89—24no—
137C8×C89—42no—
138#10623494—42no—
139C22×C89#39511yescharacteristic
140C22×C89#44911yescharacteristic
141C22×C89#44911yescharacteristic
142C22×C89#45211yescharacteristic
143C22×C89#45211yescharacteristic
144C22×C89#45311yescharacteristic
145C22×C89#45611yescharacteristic
146C4×C89—21no—
147C4×C89—21no—
148C4×C89—81no—
149C4×C89—81no—
150C4×C89#47811yescharacteristic
151C4×C89#47811yescharacteristic
152C4×C89#47911yescharacteristic
153C4×C89#47911yescharacteristic
154C4×C89#49911yescharacteristic
155C4×C89#49911yescharacteristic
156C4×C89#50111yescharacteristic
157C4×C89#50111yescharacteristic
158Dic89—81no—
159Dic89—82no—
160Dic89—81no—
161Dic89—161no—
162#10577—891nomaximal, Sylow
163C2×C89#162411yescharacteristic
164C2×C89#163011yescharacteristic
165C2×C89#165211yescharacteristic
166C2×C89#165211yescharacteristic
167C2×C89#205911yescharacteristic
168C2×C89#205911yescharacteristic
169C2×C89#206011yescharacteristic
170#2571—891no—
171#1947—891no—
172#1947—891no—
173#1844—891no—
174#1296—891no—
175#1279—891no—
176#1279D8911yescharacteristic
177C89#1057711yescharacteristic, complemented, Sylow
178C2×#107—1781no—
179C2×#107—1781no—
180C2×#106—1782no—
181C2×C4⋊C8—891no—
182C2×C4⋊C8C2×D8911yescharacteristic
183C2×C4×C8C2×D8911yescharacteristic
184#400—1782no—
185#389—1781no—
186#389—1781no—
187#384—891no—
188#384—891no—
189#382—1781no—
190#382—1781no—
191C4×C4⋊C4—891no—
192C4×C4⋊C4C2×D8911yescharacteristic
193#340—1781no—
194#340—1781no—
195C22×C8—21no—
196C22×C8—21no—
197C22×C8—1781no—
198C2×C4⋊C4—892no—
199C2×C4⋊C4—891no—
200C2×C4⋊C4—891no—
201C2×C4⋊C4—1781no—
202C2×C4⋊C4—1781no—
203C2×C4⋊C4—1781no—
204C2×C4⋊C4—1781no—
205C2×C4⋊C4—1781no—
206C2×C4⋊C4—1782no—
207C2×C4⋊C4D35611yescharacteristic
208C2×C4⋊C4D35611yescharacteristic
209C2×C42—21no—
210C2×C42—1781no—
211C2×C42C22×D8911yescharacteristic
212#107—3562no—
213#107—3562no—
214#106—3564no—
215C4⋊C8—21no—
216C4⋊C8—892no—
217C4⋊C8—1781no—
218C4⋊C8Dic17812yes—
219C4×C8—21no—
220C4×C8Dic17812yes—
221#95—21no—
222#95—1782no—
223#95—1782no—
224#95—1782no—
225#95—1781no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—3561no—
229C22×C4—1781no—
230C22×C4—1781no—
231C22×C4—1782no—
232C22×C4D4×D8911yescharacteristic
233C22×C4D4×D8911yescharacteristic
234C22×C4C2×D35611yescharacteristic
235C2×C8—22no—
236C2×C8—22no—
237C2×C8—22no—
238C2×C8—22no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—3561no—
242C2×C8—3561no—
243C2×C8—1782no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—3562no—
249C4⋊C4—3562no—
250C4⋊C4—3561no—
251C4⋊C4—3561no—
252C4⋊C4—3561no—
253C4⋊C4—3561no—
254C4⋊C4—3561no—
255C4⋊C4—3561no—
256C4⋊C4—3561no—
257C4⋊C4—3561no—
258C4⋊C4—1781no—
259C4⋊C4—1781no—
260C4⋊C4—1781no—
261C4⋊C4—1781no—
262C4⋊C4—7122no—
263C42—41no—
264C42—41no—
265C42—3561no—
266C42—3561no—
267C42Q8×D8911yescharacteristic
268C42C2×Dic17811yescharacteristic
269C42C2×Dic17811yescharacteristic
270C42#1308357311yescharacteristic
271C23#1566798211yescharacteristic
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—3561no—
281C2×C4—3561no—
282C2×C4—3561no—
283C2×C4—3562no—
284C2×C4—3562no—
285C2×C4—3561no—
286C2×C4—3562no—
287C2×C4—3561no—
288C2×C4—3561no—
289C2×C4—7121no—
290C2×C4—7121no—
291C2×C4—7121no—
292C2×C4#1566798911yescharacteristic
293C2×C4#1566798911yescharacteristic
294C2×C4#1566799211yescharacteristic
295C2×C4#1566801111yescharacteristic
296C2×C4#1566801111yescharacteristic
297C2×C4#1566801211yescharacteristic
298C2×C4#1566803311yescharacteristic
299C2×C4#1566803311yescharacteristic
300C2×C4#1566803411yescharacteristic
301C2×C4#1566803411yescharacteristic
302C2×C4#1566803611yescharacteristic
303C2×C4#1566804011yescharacteristic
304C2×C4#1566804411yescharacteristic
305C2×C4#1566804511yescharacteristic
306C8—24no—
307C8—42no—
308C8—3562no—
309C22#1915151911yescharacteristic
310C22#1915174411yescharacteristic
311C22#1915174511yescharacteristic
312C22#1915176211yescharacteristic
313C22#1915176311yescharacteristic
314C22#1915176711yescharacteristic
315C22#1915178211yescharacteristic
316C4—21no—
317C4—21no—
318C4—81no—
319C4—81no—
320C4—14241no—
321C4—7121no—
322C4—7122no—
323C4—7121no—
324C4#1915189911yescharacteristic
325C4#1915190011yescharacteristic
326C4#1915190311yescharacteristic
327C4#1915190611yescharacteristic
328C4#1915199811yescharacteristic
329C4#1915200011yescharacteristic
330C4#1915200611yescharacteristic
331C4#1915200711yescharacteristic
332C2#2601933711yescharacteristic
333C2#2601937511yescharacteristic
334C2#2601952411yescharacteristic
335C2#2601952511yescharacteristic
336C2#2602158911yescharacteristic
337C2#2602159111yescharacteristic
338C2#2602159611yescharacteristic
subgroupG/H
centerC23#15667982
commutator, cosocleC2×C42×C89C23
FrattiniC2×C42C22×D89
FittingC89×#1279C2
socle, prime radicalC23×C89#120
hypercenter#1279D89
hypocenterC89#10577
LCSG ▷ C2×C42×C89 ▷ C22×C89 ▷ C89
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
177. C89#10577semidirect

Maximal subgroups

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

subgroupindex
#260254912
#260210112
#260210102
#260204092
#260181362
#260180922
C89×#12792
#1057789