Finite Group Databasebeta

← #36459147

Subgroups — #36459147

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#26021187C211yesmaximal, characteristic
2#26020411C211yesmaximal, characteristic
3#26020258C211yesmaximal, characteristic
4#26020254C211yesmaximal, characteristic
5#26018136C211yesmaximal, characteristic
6#26018086C211yesmaximal, characteristic
7C89×#1296C211yesmaximal, characteristic
8C2×C4×Dic178C2211yescharacteristic
9C2×#15667945—21no—
10C2×#15667945—21no—
11C2×C4⋊#10623494C2211yescharacteristic
12C2×#15667937—21no—
13C2×#15667935—21no—
14C2×C4×#10623494C2211yescharacteristic
15#19151468C2211yescharacteristic
16#19151361—21no—
17#19151360—21no—
18#19151352—21no—
19#19151352—21no—
20C2×C4⋊C8×C89C2211yescharacteristic
21C2×C4⋊C8×C89C2211yescharacteristic
22#384×C89C2211yescharacteristic
23C22×Dic178D411yescharacteristic
24C22×#10623494—21no—
25C22×#10623494D411yescharacteristic
26C22×#10623494D411yescharacteristic
27C4×Dic178—21no—
28C4×Dic178—21no—
29C4×Dic178—21no—
30C4×Dic178—21no—
31C2×C4⋊Dic89—21no—
32C2×C4⋊Dic89—21no—
33C2×C4⋊Dic89—21no—
34C2×C4⋊Dic89D411yescharacteristic
35C2×#13083553—21no—
36C2×C4×Dic89—21no—
37#15667945—42no—
38#15667945—42no—
39C4⋊#10623494—21no—
40C4⋊#10623494—21no—
41#15667937—42no—
42#15667935—42no—
43C4×#10623494—21no—
44C4×#10623494—21no—
45C22×C8×C89—21no—
46C22×C8×C89—21no—
47C2×C4⋊C4×C89—21no—
48C2×C4⋊C4×C89—21no—
49C2×C4⋊C4×C89—21no—
50C2×C42×C89C2311yescharacteristic
51C4⋊C8×C89—21no—
52C4⋊C8×C89—21no—
53C4⋊C8×C89—21no—
54C4⋊C8×C89—21no—
55C2×Dic178—21no—
56C2×Dic178—21no—
57C2×Dic178—21no—
58C2×Dic178—21no—
59C2×Dic178—21no—
60C2×Dic178Q1612yes—
61C22×Dic89—21no—
62C22×Dic89—21no—
63C22×Dic89—41no—
64C2×#10623494—21no—
65C2×#10623494—21no—
66C2×#10623494—21no—
67C2×#10623494—21no—
68C2×#10623494—41no—
69C2×#10623494—41no—
70C2×#10623494—41no—
71C2×#10623494SD1612yes—
72C2×#10623494Q1612yes—
73C4⋊Dic89—21no—
74C4⋊Dic89—21no—
75C4⋊Dic89—41no—
76C4⋊Dic89—41no—
77C4⋊Dic89—41no—
78C4⋊Dic89—41no—
79C4⋊Dic89—81no—
80#13083553—41no—
81#13083553—41no—
82C4×Dic89—41no—
83C4×Dic89—41no—
84C22×C4×C89—41no—
85C22×C4×C89C2×D411yescharacteristic
86C22×C4×C89C2×D411yescharacteristic
87C22×C4×C89#4111yescharacteristic
88C2×C8×C89—41no—
89C2×C8×C89—41no—
90C2×C8×C89—41no—
91C2×C8×C89—41no—
92C2×C8×C89—41no—
93C2×C8×C89—41no—
94C4⋊C4×C89—41no—
95C4⋊C4×C89—41no—
96C4⋊C4×C89—41no—
97C4⋊C4×C89—41no—
98C4⋊C4×C89—81no—
99C42×C89#4111yescharacteristic
100C42×C89#4111yescharacteristic
101C42×C89#4111yescharacteristic
102C42×C89#4111yescharacteristic
103C23×C89#12111yescharacteristic
104C2×C4×C89—21no—
105C2×C4×C89—21no—
106C2×C4×C89—81no—
107C2×C4×C89—81no—
108C2×C4×C89—81no—
109C2×C4×C89#12311yescharacteristic
110C2×C4×C89#12311yescharacteristic
111C2×C4×C89#12311yescharacteristic
112C2×C4×C89#12411yescharacteristic
113C2×C4×C89#12611yescharacteristic
114C2×C4×C89#12611yescharacteristic
115C2×C4×C89C2×SD1611yescharacteristic
116C2×C4×C89C2×Q1611yescharacteristic
117C2×C4×C89C2×Q1611yescharacteristic
118C2×C4×C89#13511yescharacteristic
119C2×C4×C89AGL(1,ℤ/8)11yescharacteristic
120C2×C4×C89AGL(1,ℤ/8)11yescharacteristic
121C2×C4×C89AGL(1,ℤ/8)11yescharacteristic
122C2×C4×C89#13711yescharacteristic
123C2×Dic89—22no—
124C2×Dic89—41no—
125C2×Dic89—41no—
126C2×Dic89—41no—
127C2×Dic89—41no—
128C2×Dic89—41no—
129C2×Dic89—81no—
130C2×Dic89—81no—
131C2×Dic89—81no—
132Dic178—22no—
133Dic178—22no—
134Dic178—41no—
135Dic178—41no—
136C8×C89—81no—
137C8×C89—81no—
138#10623494—22no—
139#10623494—22no—
140#10623494—81no—
141C22×C89#39711yescharacteristic
142C22×C89#46011yescharacteristic
143C22×C89#46211yescharacteristic
144C22×C89#46711yescharacteristic
145C22×C89#46911yescharacteristic
146C22×C89#47211yescharacteristic
147C22×C89#47311yescharacteristic
148C4×C89—21no—
149C4×C89—21no—
150C4×C89—161no—
151C4×C89#48211yescharacteristic
152C4×C89#48211yescharacteristic
153C4×C89#48311yescharacteristic
154C4×C89#48411yescharacteristic
155C4×C89#48411yescharacteristic
156C4×C89#48411yescharacteristic
157C4×C89#48711yescharacteristic
158C4×C89#48911yescharacteristic
159Dic89—42no—
160Dic89—81no—
161Dic89—161no—
162#10618—891nomaximal, Sylow
163C2×C89#167011yescharacteristic
164C2×C89#167611yescharacteristic
165C2×C89#168811yescharacteristic
166C2×C89#169411yescharacteristic
167C2×C89#207211yescharacteristic
168C2×C89#207611yescharacteristic
169C2×C89#207811yescharacteristic
170#1984—891no—
171#1845—891no—
172#1803—891no—
173#1803—891no—
174#1296—891no—
175#1296D8911yescharacteristic
176#1277—891no—
177C89#1061811yescharacteristic, complemented, Sylow
178C2×C4×Q8—891no—
179C2×#107—1781no—
180C2×#107—1781no—
181C2×C4⋊C8—891no—
182C2×C4⋊C8C2×D8911yescharacteristic
183C2×C4⋊C8C2×D8911yescharacteristic
184C2×#103—1781no—
185C2×#103—1781no—
186C2×C4×C8—891no—
187#384—891no—
188#384C2×D8911yescharacteristic
189#340—1781no—
190#340—1781no—
191#336—1781no—
192#336—1781no—
193C22×Q8—891no—
194C22×C8—21no—
195C22×C8—21no—
196C22×C8—891no—
197C22×C8—891no—
198C22×C8—1781no—
199C4×Q8—1781no—
200C4×Q8—1781no—
201C4×Q8—1781no—
202C4×Q8—1781no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—891no—
207C2×C4⋊C4—1781no—
208C2×C4⋊C4—1781no—
209C2×C4⋊C4—1781no—
210C2×C4⋊C4—1781no—
211C2×C42—1781no—
212C2×C42C22×D8911yescharacteristic
213#107—3562no—
214#107—3562no—
215C4⋊C8—21no—
216C4⋊C8—21no—
217C4⋊C8—21no—
218C4⋊C8—21no—
219C4⋊C8—1781no—
220C4⋊C8—1781no—
221#103—3562no—
222#103—3562no—
223C4×C8—1781no—
224C4×C8—1781no—
225C2×Q8—892no—
226C2×Q8—1781no—
227C2×Q8—1781no—
228C2×Q8—1781no—
229C2×Q8—1781no—
230C2×Q8—1781no—
231C22×C4—41no—
232C22×C4—3561no—
233C22×C4—1781no—
234C22×C4—1781no—
235C22×C4D4×D8911yescharacteristic
236C22×C4D4×D8911yescharacteristic
237C22×C4#1308357411yescharacteristic
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—892no—
245C2×C8—892no—
246C2×C8—3561no—
247C2×C8—3561no—
248C2×C8—3561no—
249C2×C8—1781no—
250C2×C8—1781no—
251C2×C8—1781no—
252C2×C8—1781no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—81no—
258C4⋊C4—3561no—
259C4⋊C4—3561no—
260C4⋊C4—3561no—
261C4⋊C4—3561no—
262C4⋊C4—3561no—
263C4⋊C4—3561no—
264C4⋊C4—1781no—
265C4⋊C4—1781no—
266C4⋊C4—7121no—
267C42—3561no—
268C42—3561no—
269C42#1308357311yescharacteristic
270C42#1308357411yescharacteristic
271C42#1308357411yescharacteristic
272C42#1308357511yescharacteristic
273C23#1566798511yescharacteristic
274Q8—3561no—
275Q8—3561no—
276Q8—1782no—
277Q8—1782no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—81no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4—3561no—
284C2×C4—3561no—
285C2×C4—3561no—
286C2×C4—3561no—
287C2×C4—3561no—
288C2×C4—1782no—
289C2×C4—7121no—
290C2×C4—7121no—
291C2×C4—7121no—
292C2×C4#1566799411yescharacteristic
293C2×C4#1566799711yescharacteristic
294C2×C4#1566799711yescharacteristic
295C2×C4#1566799811yescharacteristic
296C2×C4#1566800611yescharacteristic
297C2×C4#1566800711yescharacteristic
298C2×C4SD16×D8911yescharacteristic
299C2×C4Q16×D8911yescharacteristic
300C2×C4Q16×D8911yescharacteristic
301C2×C4#1566803311yescharacteristic
302C2×C4#1566803611yescharacteristic
303C2×C4#1566803611yescharacteristic
304C2×C4#1566803911yescharacteristic
305C2×C4#1566804111yescharacteristic
306C8—81no—
307C8—81no—
308C8—1782no—
309C8—1782no—
310C8—7121no—
311C22#1915152711yescharacteristic
312C22#1915179711yescharacteristic
313C22#1915180711yescharacteristic
314C22#1915183811yescharacteristic
315C22#1915185011yescharacteristic
316C22#1915186711yescharacteristic
317C22#1915187211yescharacteristic
318C4—21no—
319C4—21no—
320C4—161no—
321C4—3562no—
322C4—14241no—
323C4—7121no—
324C4#1915192111yescharacteristic
325C4#1915192411yescharacteristic
326C4#1915193011yescharacteristic
327C4#1915193211yescharacteristic
328C4#1915193511yescharacteristic
329C4#1915193511yescharacteristic
330C4#1915194711yescharacteristic
331C4#1915195611yescharacteristic
332C2#2601962111yescharacteristic
333C2#2601965511yescharacteristic
334C2#2601973511yescharacteristic
335C2#2601976911yescharacteristic
336C2#2602166411yescharacteristic
337C2#2602168411yescharacteristic
338C2#2602169611yescharacteristic
subgroupG/H
centerC23#15667985
commutator, cosocleC2×C42×C89C23
FrattiniC2×C42C22×D89
FittingC89×#1296C2
socle, prime radicalC23×C89#121
hypercenter#1296D89
hypocenterC89#10618
LCSG ▷ C2×C42×C89 ▷ C22×C89 ▷ C89
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
177. C89#10618semidirect

Maximal subgroups

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

subgroupindex
#260211872
#260204112
#260202582
#260202542
#260181362
#260180862
C89×#12962
#1061889