Finite Group Databasebeta

← #36459155

Subgroups — #36459155

Order 22784.

366 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#26020409C211yesmaximal, characteristic
2#26020257C211yesmaximal, characteristic
3#26020257C211yesmaximal, characteristic
4#26018136C211yesmaximal, characteristic
5#26018136C211yesmaximal, characteristic
6#26018087C211yesmaximal, characteristic
7C89×#1984C211yesmaximal, characteristic
8C2×#15667944—21no—
9C2×#15667944—21no—
10C2×C4⋊#10623494C2211yescharacteristic
11C2×C4⋊#10623494C2211yescharacteristic
12C2×#15667936—21no—
13C2×#15667936—21no—
14#19151468C2211yescharacteristic
15#19151468C2211yescharacteristic
16#19151360—21no—
17#19151360—21no—
18C2×C4×Q8×C89C2211yescharacteristic
19C2×C4⋊C8×C89C2211yescharacteristic
20C2×C4×C8×C89C2211yescharacteristic
21#336×C89—21no—
22#336×C89—21no—
23C22×#10623494—21no—
24C22×#10623494—21no—
25C2×C4⋊Dic89—21no—
26C2×C4⋊Dic89—21no—
27C2×C4⋊Dic89—21no—
28C2×C4⋊Dic89—21no—
29C2×C4⋊Dic89—21no—
30C2×C4⋊Dic89—21no—
31#15667944—42no—
32#15667944—42no—
33C4⋊#10623494—21no—
34C4⋊#10623494—21no—
35C4⋊#10623494—21no—
36C4⋊#10623494—21no—
37#15667936—42no—
38#15667936—42no—
39C22×Q8×C89D411yescharacteristic
40C22×C8×C89—21no—
41C22×C8×C89D411yescharacteristic
42C22×C8×C89D411yescharacteristic
43C4×Q8×C89—21no—
44C4×Q8×C89—21no—
45C4×Q8×C89—21no—
46C4×Q8×C89—21no—
47C2×C4⋊C4×C89—21no—
48C2×C4⋊C4×C89D411yescharacteristic
49C2×C42×C89—21no—
50C2×C42×C89C2311yescharacteristic
51C4⋊C8×C89—21no—
52C4⋊C8×C89—21no—
53C4×C8×C89—21no—
54C4×C8×C89—21no—
55C22×Dic89—41no—
56C22×Dic89—41no—
57C2×#10623494—41no—
58C2×#10623494—41no—
59C2×#10623494—41no—
60C2×#10623494—41no—
61C2×#10623494—41no—
62C2×#10623494—41no—
63C4⋊Dic89—41no—
64C4⋊Dic89—41no—
65C4⋊Dic89—41no—
66C4⋊Dic89—41no—
67C4⋊Dic89—41no—
68C4⋊Dic89—41no—
69C4⋊Dic89—41no—
70C4⋊Dic89—41no—
71C4⋊Dic89—81no—
72C4⋊Dic89—81no—
73C2×Q8×C89—21no—
74C2×Q8×C89—21no—
75C2×Q8×C89—21no—
76C2×Q8×C89—21no—
77C2×Q8×C89—21no—
78C2×Q8×C89SD1612yes—
79C22×C4×C89—21no—
80C22×C4×C89—21no—
81C22×C4×C89C2×D411yescharacteristic
82C22×C4×C89C2×D411yescharacteristic
83C22×C4×C89#4111yescharacteristic
84C2×C8×C89—21no—
85C2×C8×C89—21no—
86C2×C8×C89—21no—
87C2×C8×C89—21no—
88C2×C8×C89—41no—
89C2×C8×C89—41no—
90C2×C8×C89—41no—
91C2×C8×C89SD1612yes—
92C2×C8×C89Q1612yes—
93C4⋊C4×C89—21no—
94C4⋊C4×C89—21no—
95C4⋊C4×C89—41no—
96C4⋊C4×C89—41no—
97C42×C89—41no—
98C42×C89—41no—
99C42×C89#4111yescharacteristic
100C42×C89#4111yescharacteristic
101C42×C89#4111yescharacteristic
102C42×C89#4111yescharacteristic
103C23×C89#12111yescharacteristic
104Q8×C89—22no—
105Q8×C89—22no—
106Q8×C89—41no—
107Q8×C89—41no—
108C2×C4×C89—21no—
109C2×C4×C89—21no—
110C2×C4×C89—22no—
111C2×C4×C89—41no—
112C2×C4×C89—41no—
113C2×C4×C89—41no—
114C2×C4×C89—41no—
115C2×C4×C89—41no—
116C2×C4×C89#12311yescharacteristic
117C2×C4×C89#12311yescharacteristic
118C2×C4×C89#12311yescharacteristic
119C2×C4×C89#12411yescharacteristic
120C2×C4×C89#12611yescharacteristic
121C2×C4×C89#12611yescharacteristic
122C2×C4×C89C2×SD1611yescharacteristic
123C2×C4×C89C2×SD1611yescharacteristic
124C2×C4×C89C2×Q1611yescharacteristic
125C2×C4×C89#13511yescharacteristic
126C2×C4×C89AGL(1,ℤ/8)11yescharacteristic
127C2×C4×C89AGL(1,ℤ/8)11yescharacteristic
128C2×C4×C89#13711yescharacteristic
129C2×C4×C89#13711yescharacteristic
130C2×Dic89—81no—
131C2×Dic89—81no—
132C2×Dic89—81no—
133C2×Dic89—81no—
134C2×Dic89—81no—
135C2×Dic89—81no—
136C8×C89—22no—
137C8×C89—22no—
138C8×C89—81no—
139#10623494—81no—
140#10623494—81no—
141C22×C89#39711yescharacteristic
142C22×C89#46011yescharacteristic
143C22×C89#46211yescharacteristic
144C22×C89#46511yescharacteristic
145C22×C89#46811yescharacteristic
146C22×C89#47111yescharacteristic
147C22×C89#47111yescharacteristic
148C4×C89—21no—
149C4×C89—21no—
150C4×C89—42no—
151C4×C89—81no—
152C4×C89#48111yescharacteristic
153C4×C89#48211yescharacteristic
154C4×C89#48311yescharacteristic
155C4×C89#48311yescharacteristic
156C4×C89#48411yescharacteristic
157C4×C89#48511yescharacteristic
158C4×C89#48711yescharacteristic
159C4×C89#48911yescharacteristic
160Dic89—161no—
161Dic89—161no—
162#10620—891nomaximal, Sylow
163C2×C89#166611yescharacteristic
164C2×C89#167211yescharacteristic
165C2×C89#168611yescharacteristic
166C2×C89#169211yescharacteristic
167C2×C89#207211yescharacteristic
168C2×C89#207711yescharacteristic
169C2×C89#207911yescharacteristic
170#1984D8911yescharacteristic
171#1844—891no—
172#1803—891no—
173#1803—891no—
174#1296—891no—
175#1296—891no—
176#1277—891no—
177C89#1062011yescharacteristic, complemented, Sylow
178C2×C4×Q8C2×D8911yescharacteristic
179C2×#106—1781no—
180C2×#106—1781no—
181C2×C4⋊C8—891no—
182C2×C4⋊C8—891no—
183C2×C4⋊C8C2×D8911yescharacteristic
184C2×#103—1781no—
185C2×#103—1781no—
186C2×C4×C8C2×D8911yescharacteristic
187#384—891no—
188#384—891no—
189#340—1781no—
190#340—1781no—
191#336—21no—
192#336—21no—
193C22×Q8D35611yescharacteristic
194C22×C8—21no—
195C22×C8—1781no—
196C22×C8—1781no—
197C22×C8C22⋊D8911yescharacteristic
198C22×C8C22⋊D8911yescharacteristic
199C4×Q8—21no—
200C4×Q8—21no—
201C4×Q8—21no—
202C4×Q8—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—1781no—
205C2×C4⋊C4—1781no—
206C2×C4⋊C4—1781no—
207C2×C4⋊C4—1781no—
208C2×C4⋊C4—1781no—
209C2×C4⋊C4—1781no—
210C2×C4⋊C4D35611yescharacteristic
211C2×C42—21no—
212C2×C42C22×D8911yescharacteristic
213#106—3562no—
214#106—3562no—
215C4⋊C8—21no—
216C4⋊C8—21no—
217C4⋊C8—1781no—
218C4⋊C8—1781no—
219C4⋊C8—1781no—
220C4⋊C8—1781no—
221#103—3562no—
222#103—3562no—
223C4×C8—21no—
224C4×C8—21no—
225C2×Q8—21no—
226C2×Q8—21no—
227C2×Q8—21no—
228C2×Q8—21no—
229C2×Q8—21no—
230C2×Q8#1308356312yes—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—3561no—
234C22×C4—3561no—
235C22×C4C2×C22⋊D8911yescharacteristic
236C22×C4C2×D35611yescharacteristic
237C22×C4#1308357411yescharacteristic
238C2×C8—21no—
239C2×C8—21no—
240C2×C8—21no—
241C2×C8—21no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—3561no—
246C2×C8—3561no—
247C2×C8—3561no—
248C2×C8—3561no—
249C2×C8—3561no—
250C2×C8—3561no—
251C2×C8#1308356112yes—
252C2×C8#1308356412yes—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—3561no—
258C4⋊C4—3561no—
259C4⋊C4—3561no—
260C4⋊C4—3561no—
261C4⋊C4—3561no—
262C4⋊C4—3561no—
263C4⋊C4—3561no—
264C4⋊C4—3561no—
265C4⋊C4—7121no—
266C4⋊C4—7121no—
267C42—41no—
268C42—41no—
269C42#1308357311yescharacteristic
270C42#1308357311yescharacteristic
271C42#1308357311yescharacteristic
272C42#1308357311yescharacteristic
273C23#1566798611yescharacteristic
274Q8—22no—
275Q8—22no—
276Q8—41no—
277Q8—41no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—22no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—7121no—
287C2×C4—7121no—
288C2×C4—7121no—
289C2×C4—7121no—
290C2×C4—7121no—
291C2×C4—7121no—
292C2×C4#1566799311yescharacteristic
293C2×C4#1566799611yescharacteristic
294C2×C4#1566799611yescharacteristic
295C2×C4#1566799911yescharacteristic
296C2×C4#1566800511yescharacteristic
297C2×C4#1566800511yescharacteristic
298C2×C4C2×#1308356111yescharacteristic
299C2×C4C2×#1308356311yescharacteristic
300C2×C4C2×#1308356411yescharacteristic
301C2×C4#1566803411yescharacteristic
302C2×C4#1566803711yescharacteristic
303C2×C4#1566804011yescharacteristic
304C2×C4#1566804211yescharacteristic
305C2×C4#1566804511yescharacteristic
306C8—22no—
307C8—22no—
308C8—81no—
309C8—7121no—
310C8—7121no—
311C22#1915152311yescharacteristic
312C22#1915179811yescharacteristic
313C22#1915180811yescharacteristic
314C22#1915182711yescharacteristic
315C22#1915184411yescharacteristic
316C22#1915186111yescharacteristic
317C22#1915186111yescharacteristic
318C4—21no—
319C4—21no—
320C4—42no—
321C4—81no—
322C4—14241no—
323C4—14241no—
324C4#1915191711yescharacteristic
325C4#1915192311yescharacteristic
326C4#1915192611yescharacteristic
327C4#1915192911yescharacteristic
328C4#1915193111yescharacteristic
329C4#1915194011yescharacteristic
330C4#1915194811yescharacteristic
331C4#1915195711yescharacteristic
332C2#2601960011yescharacteristic
333C2#2601963411yescharacteristic
334C2#2601972411yescharacteristic
335C2#2601975811yescharacteristic
336C2#2602166011yescharacteristic
337C2#2602168511yescharacteristic
338C2#2602169711yescharacteristic
subgroupG/H
centerC23#15667986
commutator, cosocleC2×C42×C89C23
FrattiniC2×C42C22×D89
FittingC89×#1984C2
socle, prime radicalC23×C89#121
hypercenter#1984D89
hypocenterC89#10620
LCSG ▷ C2×C42×C89 ▷ C22×C89 ▷ C89
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1984

Complements

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

NH ≅ G/Ntype
177. C89#10620semidirect

Maximal subgroups

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

subgroupindex
#260204092
#260202572
#260181362
#260180872
C89×#19842
#1062089