Finite Group Databasebeta

← #36459191

Subgroups — #36459191

Order 22784.

350 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26021188C211yesmaximal, characteristic
2#26020380C211yesmaximal, characteristic
3#26020258C211yesmaximal, characteristic
4#26020258C211yesmaximal, characteristic
5#26018136C211yesmaximal, characteristic
6#26018136C211yesmaximal, characteristic
7C89×#1277C211yesmaximal, characteristic
8C2×C4×Dic178C2211yescharacteristic
9C2×C4⋊#10623494C2211yescharacteristic
10C2×#15667937—21no—
11C2×#15667937—21no—
12#19151468C2211yescharacteristic
13#19151468C2211yescharacteristic
14#19151361—21no—
15#19151361—21no—
16#19151361—21no—
17#19151361—21no—
18#19151352—21no—
19#19151352—21no—
20C2×C4⋊C8×C89C2211yescharacteristic
21C2×C4⋊C8×C89C2211yescharacteristic
22C2×C4×C8×C89C2211yescharacteristic
23C22×Dic178D411yescharacteristic
24C22×#10623494—21no—
25C4×Dic178—21no—
26C4×Dic178—21no—
27C4×Dic178—21no—
28C4×Dic178—21no—
29C2×C4⋊Dic89—21no—
30C2×C4⋊Dic89—21no—
31C2×C4⋊Dic89—21no—
32C2×C4⋊Dic89—21no—
33C2×C4⋊Dic89—21no—
34C2×C4⋊Dic89—21no—
35C2×C4⋊Dic89D411yescharacteristic
36C2×#13083553—21no—
37C2×C4×Dic89—21no—
38C4⋊#10623494—21no—
39C4⋊#10623494—21no—
40#15667937—42no—
41#15667937—42no—
42C22×C8×C89—21no—
43C22×C8×C89—21no—
44C22×C8×C89D411yescharacteristic
45C22×C8×C89D411yescharacteristic
46C2×C42×C89C2311yescharacteristic
47C4⋊C8×C89—21no—
48C4⋊C8×C89—21no—
49C4⋊C8×C89—21no—
50C4⋊C8×C89—21no—
51C4×C8×C89—21no—
52C4×C8×C89—21no—
53C2×Dic178—21no—
54C2×Dic178—21no—
55C2×Dic178—21no—
56C2×Dic178—21no—
57C2×Dic178—21no—
58C2×Dic178SD1612yes—
59C22×Dic89—21no—
60C22×Dic89—21no—
61C22×Dic89—41no—
62C22×Dic89—41no—
63C2×#10623494—41no—
64C2×#10623494—41no—
65C2×#10623494—41no—
66C4⋊Dic89—21no—
67C4⋊Dic89—21no—
68C4⋊Dic89—41no—
69C4⋊Dic89—41no—
70C4⋊Dic89—41no—
71C4⋊Dic89—41no—
72C4⋊Dic89—41no—
73C4⋊Dic89—41no—
74C4⋊Dic89—41no—
75C4⋊Dic89—41no—
76C4⋊Dic89—81no—
77C4⋊Dic89—81no—
78#13083553—41no—
79#13083553—41no—
80C4×Dic89—41no—
81C4×Dic89—41no—
82C22×C4×C89C2×D411yescharacteristic
83C22×C4×C89C2×D411yescharacteristic
84C22×C4×C89#4111yescharacteristic
85C2×C8×C89—21no—
86C2×C8×C89—21no—
87C2×C8×C89—21no—
88C2×C8×C89—21no—
89C2×C8×C89—21no—
90C2×C8×C89—21no—
91C2×C8×C89—41no—
92C2×C8×C89—41no—
93C2×C8×C89—41no—
94C2×C8×C89—41no—
95C2×C8×C89—41no—
96C2×C8×C89—41no—
97C42×C89#4111yescharacteristic
98C42×C89#4111yescharacteristic
99C42×C89#4111yescharacteristic
100C42×C89#4111yescharacteristic
101C23×C89#12111yescharacteristic
102C2×C4×C89—21no—
103C2×C4×C89—21no—
104C2×C4×C89#12311yescharacteristic
105C2×C4×C89#12311yescharacteristic
106C2×C4×C89#12311yescharacteristic
107C2×C4×C89#12411yescharacteristic
108C2×C4×C89#12611yescharacteristic
109C2×C4×C89#12611yescharacteristic
110C2×C4×C89C2×SD1611yescharacteristic
111C2×C4×C89#13511yescharacteristic
112C2×C4×C89#13511yescharacteristic
113C2×C4×C89#13511yescharacteristic
114C2×C4×C89AGL(1,ℤ/8)11yescharacteristic
115C2×C4×C89#13711yescharacteristic
116C2×C4×C89#13711yescharacteristic
117C2×C4×C89#13711yescharacteristic
118C2×Dic89—22no—
119C2×Dic89—41no—
120C2×Dic89—41no—
121C2×Dic89—41no—
122C2×Dic89—41no—
123C2×Dic89—41no—
124C2×Dic89—81no—
125C2×Dic89—81no—
126C2×Dic89—81no—
127C2×Dic89—81no—
128C2×Dic89—81no—
129C2×Dic89—81no—
130Dic178—22no—
131Dic178—22no—
132Dic178—41no—
133Dic178—41no—
134C8×C89—41no—
135C8×C89—41no—
136C8×C89—81no—
137C8×C89—81no—
138#10623494—81no—
139C22×C89#39711yescharacteristic
140C22×C89#46411yescharacteristic
141C22×C89#46411yescharacteristic
142C22×C89#46511yescharacteristic
143C22×C89#46811yescharacteristic
144C22×C89#47211yescharacteristic
145C22×C89#47311yescharacteristic
146C4×C89—21no—
147C4×C89—21no—
148C4×C89#48111yescharacteristic
149C4×C89#48211yescharacteristic
150C4×C89#48311yescharacteristic
151C4×C89#48511yescharacteristic
152C4×C89#48511yescharacteristic
153C4×C89#48511yescharacteristic
154C4×C89#48811yescharacteristic
155C4×C89#49111yescharacteristic
156Dic89—42no—
157Dic89—81no—
158Dic89—161no—
159Dic89—161no—
160#10626—891nomaximal, Sylow
161C2×C89#167811yescharacteristic
162C2×C89#168011yescharacteristic
163C2×C89#169811yescharacteristic
164C2×C89#170011yescharacteristic
165C2×C89#207411yescharacteristic
166C2×C89#207711yescharacteristic
167C2×C89#207811yescharacteristic
168#1984—891no—
169#1834—891no—
170#1803—891no—
171#1803—891no—
172#1296—891no—
173#1296—891no—
174#1277D8911yescharacteristic
175C89#1062611yescharacteristic, complemented, Sylow
176C2×C4×Q8—891no—
177C2×C4⋊C8—891no—
178C2×C4⋊C8C2×D8911yescharacteristic
179C2×C4⋊C8C2×D8911yescharacteristic
180C2×#103—1781no—
181C2×#103—1781no—
182C2×C4×C8C2×D8911yescharacteristic
183#384—891no—
184#384—891no—
185#340—1781no—
186#340—1781no—
187#340—1781no—
188#340—1781no—
189#336—1781no—
190#336—1781no—
191C22×Q8—891no—
192C22×C8—21no—
193C22×C8—21no—
194C22×C8—1781no—
195C22×C8D35611yescharacteristic
196C22×C8D35611yescharacteristic
197C4×Q8—1781no—
198C4×Q8—1781no—
199C4×Q8—1781no—
200C4×Q8—1781no—
201C2×C4⋊C4—891no—
202C2×C4⋊C4—1781no—
203C2×C4⋊C4—1781no—
204C2×C4⋊C4—1781no—
205C2×C4⋊C4—1781no—
206C2×C4⋊C4—1781no—
207C2×C4⋊C4—1781no—
208C2×C4⋊C4—1781no—
209C2×C42—1781no—
210C2×C42C22×D8911yescharacteristic
211C4⋊C8—21no—
212C4⋊C8—21no—
213C4⋊C8—21no—
214C4⋊C8—21no—
215C4⋊C8—1781no—
216C4⋊C8—1781no—
217#103—3562no—
218#103—3562no—
219C4×C8—21no—
220C4×C8—21no—
221C2×Q8—892no—
222C2×Q8—1781no—
223C2×Q8—1781no—
224C2×Q8—1781no—
225C2×Q8—1781no—
226C2×Q8—1781no—
227C22×C4—3561no—
228C22×C4—3561no—
229C22×C4—1781no—
230C22×C4—1781no—
231C22×C4D4×D8911yescharacteristic
232C22×C4C2×D35611yescharacteristic
233C22×C4#1308357511yescharacteristic
234C2×C8—21no—
235C2×C8—21no—
236C2×C8—21no—
237C2×C8—21no—
238C2×C8—21no—
239C2×C8—21no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—3561no—
247C2×C8—3561no—
248C2×C8—3561no—
249C4⋊C4—3561no—
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—3561no—
259C4⋊C4—1781no—
260C4⋊C4—1781no—
261C4⋊C4—7121no—
262C4⋊C4—7121no—
263C42—3561no—
264C42—3561no—
265C42#1308357311yescharacteristic
266C42#1308357311yescharacteristic
267C42#1308357411yescharacteristic
268C42#1308357411yescharacteristic
269C23#1566798711yescharacteristic
270Q8—3561no—
271Q8—3561no—
272Q8—1782no—
273Q8—1782no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—3561no—
277C2×C4—3561no—
278C2×C4—3561no—
279C2×C4—3561no—
280C2×C4—3561no—
281C2×C4—1782no—
282C2×C4—7121no—
283C2×C4—7121no—
284C2×C4—7121no—
285C2×C4—7121no—
286C2×C4—7121no—
287C2×C4—7121no—
288C2×C4#1566799411yescharacteristic
289C2×C4#1566799411yescharacteristic
290C2×C4#1566799611yescharacteristic
291C2×C4#1566800011yescharacteristic
292C2×C4#1566800711yescharacteristic
293C2×C4#1566800711yescharacteristic
294C2×C4SD16×D8911yescharacteristic
295C2×C4#1566803311yescharacteristic
296C2×C4#1566803411yescharacteristic
297C2×C4#1566803411yescharacteristic
298C2×C4#1566803611yescharacteristic
299C2×C4#1566804411yescharacteristic
300C2×C4#1566804511yescharacteristic
301C2×C4#1566804511yescharacteristic
302C8—41no—
303C8—41no—
304C8—81no—
305C8—81no—
306C8—7121no—
307C22#1915152511yescharacteristic
308C22#1915182111yescharacteristic
309C22#1915182111yescharacteristic
310C22#1915182811yescharacteristic
311C22#1915184511yescharacteristic
312C22#1915186911yescharacteristic
313C22#1915187411yescharacteristic
314C4—21no—
315C4—21no—
316C4—3562no—
317C4—14241no—
318C4—14241no—
319C4—7121no—
320C4#1915191511yescharacteristic
321C4#1915192111yescharacteristic
322C4#1915192711yescharacteristic
323C4#1915193711yescharacteristic
324C4#1915194011yescharacteristic
325C4#1915194011yescharacteristic
326C4#1915195311yescharacteristic
327C4#1915196711yescharacteristic
328C2#2601966911yescharacteristic
329C2#2601968311yescharacteristic
330C2#2601979311yescharacteristic
331C2#2601980711yescharacteristic
332C2#2602167211yescharacteristic
333C2#2602168711yescharacteristic
334C2#2602169411yescharacteristic
subgroupG/H
centerC23#15667987
commutator, cosocleC2×C42×C89C23
FrattiniC2×C42C22×D89
FittingC89×#1277C2
socle, prime radicalC23×C89#121
hypercenter#1277D89
hypocenterC89#10626
LCSG ▷ C2×C42×C89 ▷ C22×C89 ▷ C89
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1277

Complements

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

NH ≅ G/Ntype
175. C89#10626semidirect

Maximal subgroups

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

subgroupindex
#260211882
#260203802
#260202582
#260181362
C89×#12772
#1062689