Finite Group Databasebeta

← #36459159

Subgroups — #36459159

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#26021189C211yesmaximal, characteristic
2#26020408C211yesmaximal, characteristic
3#26020257C211yesmaximal, characteristic
4#26018136C211yesmaximal, characteristic
5#26018135C211yesmaximal, characteristic
6#26018086C211yesmaximal, characteristic
7C89×#1803C211yesmaximal, characteristic
8C2×#15667943—21no—
9C2×#15667943—21no—
10C2×C4⋊#10623494C2211yescharacteristic
11C2×C4⋊#10623494C2211yescharacteristic
12C2×#15667936—21no—
13C2×C4×#10623494C2211yescharacteristic
14#19151468C2211yescharacteristic
15#19151360—21no—
16#19151353—21no—
17#19151353—21no—
18C2×C4×Q8×C89C2211yescharacteristic
19C2×C4⋊C8×C89C2211yescharacteristic
20C2×#103×C89—21no—
21#384×C89C2211yescharacteristic
22#340×C89—21no—
23C22×#10623494—21no—
24C22×#10623494—21no—
25C22×#10623494D411yescharacteristic
26C22×#10623494D411yescharacteristic
27C2×C4⋊Dic89—21no—
28C2×C4⋊Dic89—21no—
29C2×C4⋊Dic89—21no—
30#15667943—42no—
31#15667943—42no—
32C4⋊#10623494—21no—
33C4⋊#10623494—21no—
34C4⋊#10623494—21no—
35C4⋊#10623494—21no—
36#15667936—42no—
37C4×#10623494—21no—
38C4×#10623494—21no—
39C22×Q8×C89D411yescharacteristic
40C22×C8×C89—21no—
41C4×Q8×C89—21no—
42C4×Q8×C89—21no—
43C4×Q8×C89—21no—
44C4×Q8×C89—21no—
45C2×C4⋊C4×C89—21no—
46C2×C4⋊C4×C89—21no—
47C2×C4⋊C4×C89—21no—
48C2×C4⋊C4×C89—21no—
49C2×C4⋊C4×C89D411yescharacteristic
50C2×C42×C89—21no—
51C2×C42×C89C2311yescharacteristic
52C4⋊C8×C89—21no—
53C4⋊C8×C89—21no—
54#103×C89—42no—
55C22×Dic89—41no—
56C2×#10623494—21no—
57C2×#10623494—21no—
58C2×#10623494—21no—
59C2×#10623494—21no—
60C2×#10623494—41no—
61C2×#10623494—41no—
62C2×#10623494—41no—
63C2×#10623494—41no—
64C2×#10623494—41no—
65C2×#10623494—41no—
66C2×#10623494SD1612yes—
67C2×#10623494Q1612yes—
68C4⋊Dic89—41no—
69C4⋊Dic89—41no—
70C4⋊Dic89—41no—
71C4⋊Dic89—41no—
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×C89—41no—
82C22×C4×C89C2×D411yescharacteristic
83C22×C4×C89C2×D411yescharacteristic
84C22×C4×C89#4111yescharacteristic
85C2×C8×C89—41no—
86C2×C8×C89—41no—
87C2×C8×C89—41no—
88C4⋊C4×C89—21no—
89C4⋊C4×C89—21no—
90C4⋊C4×C89—41no—
91C4⋊C4×C89—41no—
92C4⋊C4×C89—41no—
93C4⋊C4×C89—41no—
94C4⋊C4×C89—41no—
95C4⋊C4×C89—41no—
96C4⋊C4×C89—81no—
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—81no—
117C2×C4×C89—81no—
118C2×C4×C89—81no—
119C2×C4×C89#12311yescharacteristic
120C2×C4×C89#12311yescharacteristic
121C2×C4×C89#12311yescharacteristic
122C2×C4×C89#12411yescharacteristic
123C2×C4×C89#12611yescharacteristic
124C2×C4×C89#12611yescharacteristic
125C2×C4×C89C2×SD1611yescharacteristic
126C2×C4×C89C2×SD1611yescharacteristic
127C2×C4×C89C2×Q1611yescharacteristic
128C2×C4×C89#13511yescharacteristic
129C2×C4×C89AGL(1,ℤ/8)11yescharacteristic
130C2×C4×C89AGL(1,ℤ/8)11yescharacteristic
131C2×C4×C89#13711yescharacteristic
132C2×C4×C89#13711yescharacteristic
133C2×Dic89—81no—
134C2×Dic89—81no—
135C2×Dic89—81no—
136C8×C89—81no—
137#10623494—22no—
138#10623494—22no—
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—161no—
153C4×C89#48111yescharacteristic
154C4×C89#48211yescharacteristic
155C4×C89#48311yescharacteristic
156C4×C89#48311yescharacteristic
157C4×C89#48411yescharacteristic
158C4×C89#48511yescharacteristic
159C4×C89#48711yescharacteristic
160C4×C89#48911yescharacteristic
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#1984—891no—
171#1844—891no—
172#1803—891no—
173#1803D8911yescharacteristic
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—21no—
185C2×#103—1781no—
186C2×C4×C8—891no—
187#384—891no—
188#384C2×D8911yescharacteristic
189#340—21no—
190#340—1781no—
191#336—1781no—
192#336—1781no—
193C22×Q8C22⋊D8911yescharacteristic
194C22×C8—21no—
195C22×C8—891no—
196C22×C8—891no—
197C22×C8—1781no—
198C22×C8—1781no—
199C4×Q8—21no—
200C4×Q8—21no—
201C4×Q8—21no—
202C4×Q8—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—1781no—
208C2×C4⋊C4—1781no—
209C2×C4⋊C4—1781no—
210C2×C4⋊C4C22⋊D8911yescharacteristic
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—42no—
222#103—3562no—
223C4×C8—1781no—
224C4×C8—1781no—
225C2×Q8—21no—
226C2×Q8—21no—
227C2×Q8—21no—
228C2×Q8—21no—
229C2×Q8—21no—
230C2×Q8#1308356112yes—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—41no—
234C22×C4—3561no—
235C22×C4D4×D8911yescharacteristic
236C22×C4C2×C22⋊D8911yescharacteristic
237C22×C4#1308357311yescharacteristic
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—892no—
242C2×C8—892no—
243C2×C8—3561no—
244C2×C8—3561no—
245C2×C8—3561no—
246C2×C8—3561no—
247C2×C8—3561no—
248C2×C8—3561no—
249C2×C8—1781no—
250C2×C8—1781no—
251C2×C8—1781no—
252C2×C8—1781no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—81no—
262C4⋊C4—3561no—
263C4⋊C4—3561no—
264C4⋊C4—3561no—
265C4⋊C4—3561no—
266C4⋊C4—7121no—
267C42—41no—
268C42—41no—
269C42#1308357311yescharacteristic
270C42#1308357311yescharacteristic
271C42#1308357411yescharacteristic
272C42#1308357411yescharacteristic
273C23#1566798411yescharacteristic
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—81no—
287C2×C4—81no—
288C2×C4—81no—
289C2×C4—7121no—
290C2×C4—7121no—
291C2×C4—7121no—
292C2×C4#1566799311yescharacteristic
293C2×C4#1566799411yescharacteristic
294C2×C4#1566799511yescharacteristic
295C2×C4#1566799811yescharacteristic
296C2×C4#1566800511yescharacteristic
297C2×C4#1566800511yescharacteristic
298C2×C4SD16×D8911yescharacteristic
299C2×C4C2×#1308356111yescharacteristic
300C2×C4Q16×D8911yescharacteristic
301C2×C4#1566803211yescharacteristic
302C2×C4#1566803811yescharacteristic
303C2×C4#1566803911yescharacteristic
304C2×C4#1566804211yescharacteristic
305C2×C4#1566804411yescharacteristic
306C8—81no—
307C8—1782no—
308C8—1782no—
309C8—7121no—
310C8—7121no—
311C22#1915152611yescharacteristic
312C22#1915179611yescharacteristic
313C22#1915180611yescharacteristic
314C22#1915182911yescharacteristic
315C22#1915184211yescharacteristic
316C22#1915185911yescharacteristic
317C22#1915186311yescharacteristic
318C4—21no—
319C4—21no—
320C4—42no—
321C4—81no—
322C4—161no—
323C4—14241no—
324C4#1915191611yescharacteristic
325C4#1915191911yescharacteristic
326C4#1915192611yescharacteristic
327C4#1915192711yescharacteristic
328C4#1915193211yescharacteristic
329C4#1915193911yescharacteristic
330C4#1915194711yescharacteristic
331C4#1915195911yescharacteristic
332C2#2601960211yescharacteristic
333C2#2601963611yescharacteristic
334C2#2601972211yescharacteristic
335C2#2601975611yescharacteristic
336C2#2602166311yescharacteristic
337C2#2602168911yescharacteristic
338C2#2602170011yescharacteristic
subgroupG/H
centerC23#15667984
commutator, cosocleC2×C42×C89C23
FrattiniC2×C42C22×D89
FittingC89×#1803C2
socle, prime radicalC23×C89#121
hypercenter#1803D89
hypocenterC89#10620
LCSG ▷ C2×C42×C89 ▷ C22×C89 ▷ C89
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1803

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
#260211892
#260204082
#260202572
#260181362
#260181352
#260180862
C89×#18032
#1062089