Finite Group Databasebeta

← #36523646

Subgroups — #36523646

Order 22784.

572 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26029369C212yesmaximal
2#26019041C212yesmaximal, complemented
3#26019037C212yesmaximal, complemented
4#26019032C212yesmaximal, complemented
5#26019027C212yesmaximal, complemented
6#26019019C212yesmaximal, complemented
7#26019015C211yesmaximal, characteristic, complemented
8#26019011C211yesmaximal, characteristic, complemented
9C89×#2922C211yesmaximal, characteristic
10#19151729—22no—
11#19151676—22no—
12#19151670—22no—
13#19151670—22no—
14#19151655C2212yes—
15#19151655C2212yes—
16#19151651C2212yes—
17#19151622C2212yes—
18#19151622C2212yes—
19C2×C4⋊#10623494C2212yes—
20#19151351C2212yes—
21#19151351C2211yescharacteristic
22#19151351C2211yescharacteristic
23#19151351C2211yescharacteristic
24#19151351C2211yescharacteristic
25#19151351C2212yes—
26#19151351C2212yes—
27#19151349C2212yes—
28#19151349C2212yes—
29#19151349C2212yes—
30C4×#41×C89C2211yescharacteristic
31#433×C89C414yes—
32#431×C89C2212yes—
33#431×C89C2212yes—
34#424×C89C412yes—
35#408×C89C412yes—
36C4×M16×C89C2211yescharacteristic
37C2×C4×C8×C89C2211yescharacteristic
38C2×#13083558—22no—
39C2×#13083558—22no—
40C22×#10623494—22no—
41C4⋊#10623494—22no—
42C4⋊#10623494—22no—
43C4⋊#10623494—22no—
44C4⋊#10623494C2312yes—
45C4⋊#10623494C2312yes—
46C4⋊#10623494C2312yes—
47C4⋊#10623494C2312yes—
48C22⋊#10623494—22no—
49C22⋊#10623494—22no—
50C22⋊#10623494—22no—
51#15667923—22no—
52#15667923—22no—
53C4×#10623494—22no—
54C2×#41×C89C2×C411yescharacteristic
55C2×M16×C89C2×C412yes—
56C22×C8×C89C2×C412yes—
57C4×Q8×C89D411yescharacteristic
58C4×Q8×C89Q811yescharacteristic
59C4×D4×C89D411yescharacteristic
60C4×D4×C89D412yes—
61C4×D4×C89Q812yes—
62C4×D4×C89Q811yescharacteristic
63#117×C89C2×C411yescharacteristic
64#117×C89C2×C412yes—
65C2×C42×C89C2312yes—
66C2×C42×C89C2311yescharacteristic
67C4⋊C8×C89C2×C414yes—
68C4⋊C8×C89C2×C414yes—
69C22⋊C8×C89C2×C414yes—
70C22⋊C8×C89C2×C414yes—
71#97×C89C2×C412yes—
72C4×C8×C89C2×C412yes—
73C4×C8×C89C2311yescharacteristic
74C4×C8×C89C2311yescharacteristic
75C4×C8×C89C2312yes—
76#13083558—82no—
77#13083558—82no—
78C2×#10623494—22no—
79C2×#10623494—22no—
80C2×#10623494—22no—
81C2×#10623494—22no—
82C2×#10623494—82no—
83#41×C89—42no—
84C2×Q8×C89C4⋊C411yescharacteristic
85C2×D4×C89C4⋊C411yescharacteristic
86C2×D4×C89C4⋊C412yes—
87C22×C4×C89C22×C412yes—
88C22×C4×C89C22×C411yescharacteristic
89C22×C4×C89C2×D412yes—
90C22×C4×C89C2×D411yescharacteristic
91C22×C4×C89C2×Q812yes—
92C22×C4×C89C2×Q811yescharacteristic
93M16×C89—42no—
94C2×C8×C89—42no—
95C2×C8×C89C22×C412yes—
96C2×C8×C89C22×C412yes—
97C2×C8×C89C22×C414yes—
98C4⋊C4×C89C4⋊C411yescharacteristic
99C4⋊C4×C89C4⋊C412yes—
100C4⋊C4×C89C4⋊C411yescharacteristic
101C4⋊C4×C89C4⋊C412yes—
102C22⋊C4×C89C4⋊C412yes—
103C22⋊C4×C89C4⋊C412yes—
104C22⋊C4×C89C4⋊C412yes—
105C42×C89C22×C411yescharacteristic
106C42×C89C22×C412yes—
107C42×C89C2×D412yes—
108C42×C89C2×D411yescharacteristic
109C42×C89C2×Q812yes—
110C42×C89C2×Q811yescharacteristic
111C42×C89C2411yescharacteristic
112C23×C89C2×C4⋊C412yes—
113C23×C89C2×C4⋊C411yescharacteristic
114Q8×C89—41no—
115D4×C89—41no—
116D4×C89—42no—
117C2×C4×C89—22no—
118C2×C4×C89—24no—
119C2×C4×C89—22no—
120C2×C4×C89—21no—
121C2×C4×C89—22no—
122C2×C4×C89—21no—
123C2×C4×C89—42no—
124C2×C4×C89—41no—
125C2×C4×C89C2×C4⋊C411yescharacteristic
126C2×C4×C89C2×C4⋊C412yes—
127C2×C4×C89C2×C4⋊C411yescharacteristic
128C2×C4×C89C2×C4⋊C412yes—
129C2×C4×C89C2×C4⋊C412yes—
130C2×C4×C89C2×C4⋊C411yescharacteristic
131C2×C4×C89C23×C411yescharacteristic
132C2×C4×C89C22×D411yescharacteristic
133C2×C4×C89C22×Q811yescharacteristic
134C8×C89—22no—
135C8×C89—22no—
136C8×C89—24no—
137#10623494—42no—
138#10623494—42no—
139#10623494—42no—
140#10623494—42no—
141C22×C89—21no—
142C22×C89—22no—
143C22×C89—22no—
144C22×C89—21no—
145C22×C89—22no—
146C22×C89—21no—
147C22×C89C22×C4⋊C411yescharacteristic
148C4×C89—21no—
149C4×C89—22no—
150C4×C89—22no—
151C4×C89—21no—
152C4×C89—21no—
153C4×C89—21no—
154C4×C89—22no—
155C4×C89#56812yes—
156C4×C89#57611yescharacteristic
157C4×C89#57811yescharacteristic
158#17825—891nomaximal, Sylow
159C2×C89—41no—
160C2×C89—42no—
161C2×C89#290511yescharacteristic
162C2×C89#291311yescharacteristic
163C2×C89#291611yescharacteristic
164#2989—892no—
165#2922D8911yescharacteristic
166#1574—892no—
167#1573—892no—
168#1572—892no—
169#1571—892no—
170#1569—892no—
171#1568—891no—
172#1567—891no—
173C89#1782511yescharacteristic, complemented, Sylow
174C4×#41C2×D8911yescharacteristic
175#446—1782no—
176#436—1782no—
177#435—1782no—
178#435—1782no—
179#433Dic8914yes—
180#432—892no—
181#432—892no—
182#431—892no—
183#431C2×D8912yes—
184#431C2×D8912yes—
185#424Dic8912yes—
186#423—892no—
187#423—892no—
188C2×C4⋊C8—892no—
189#408Dic8912yes—
190C4×M16C2×D8911yescharacteristic
191C2×C4×C8C2×D8911yescharacteristic
192#335—892no—
193#335—891no—
194#335—891no—
195#335—891no—
196#335—891no—
197#335—892no—
198#335—892no—
199#334—892no—
200#334—892no—
201#334—892no—
202C2×#41C2×Dic8911yescharacteristic
203C2×M16—1782no—
204C2×M16—1782no—
205C2×M16C2×Dic8912yes—
206C22×C8—1782no—
207C22×C8C2×Dic8912yes—
208C4×Q8Dic17811yescharacteristic
209C4×Q8D35611yescharacteristic
210C4×D4Dic17811yescharacteristic
211C4×D4Dic17812yes—
212C4×D4D35611yescharacteristic
213C4×D4D35612yes—
214#117C2×Dic8911yescharacteristic
215#117C2×Dic8912yes—
216C2×C42C22×D8911yescharacteristic
217C2×C42C22×D8912yes—
218C4⋊C8—892no—
219C4⋊C8—892no—
220C4⋊C8—892no—
221C4⋊C8—892no—
222C4⋊C8—1782no—
223C4⋊C8—1782no—
224C4⋊C8—1782no—
225C4⋊C8C2×Dic8914yes—
226C4⋊C8C2×Dic8914yes—
227C22⋊C8—1782no—
228C22⋊C8—1782no—
229C22⋊C8—1782no—
230C22⋊C8C2×Dic8914yes—
231C22⋊C8C2×Dic8914yes—
232#97—1782no—
233#97—1782no—
234#97C2×Dic8912yes—
235C4×C8—1782no—
236C4×C8C2×Dic8912yes—
237C4×C8C22×D8911yescharacteristic
238C4×C8C22×D8912yes—
239C4×C8C22×D8911yescharacteristic
240#41—42no—
241C2×Q8C4⋊Dic8911yescharacteristic
242C2×D4C4⋊Dic8911yescharacteristic
243C2×D4C4⋊Dic8912yes—
244C22×C4C22×Dic8912yes—
245C22×C4C22×Dic8911yescharacteristic
246C22×C4C2×D35612yes—
247C22×C4C2×D35611yescharacteristic
248C22×C4C2×Dic17811yescharacteristic
249C22×C4C2×Dic17812yes—
250M16—42no—
251M16—7122no—
252M16—7122no—
253C2×C8—42no—
254C2×C8—1782no—
255C2×C8—1782no—
256C2×C8—1782no—
257C2×C8—1782no—
258C2×C8—7122no—
259C2×C8C22×Dic8912yes—
260C2×C8C22×Dic8912yes—
261C2×C8C22×Dic8914yes—
262C4⋊C4C4⋊Dic8911yescharacteristic
263C4⋊C4C4⋊Dic8912yes—
264C4⋊C4C4⋊Dic8911yescharacteristic
265C4⋊C4C4⋊Dic8912yes—
266C22⋊C4C4⋊Dic8912yes—
267C22⋊C4C4⋊Dic8912yes—
268C22⋊C4C4⋊Dic8912yes—
269C42C22×Dic8911yescharacteristic
270C42C22×Dic8912yes—
271C42C2×D35612yes—
272C42C2×D35611yescharacteristic
273C42C2×Dic17811yescharacteristic
274C42C2×Dic17812yes—
275C42C23×D8911yescharacteristic
276C23C2×C4⋊Dic8912yes—
277C23C2×C4⋊Dic8911yescharacteristic
278Q8—41no—
279D4—41no—
280D4—42no—
281C2×C4—22no—
282C2×C4—21no—
283C2×C4—22no—
284C2×C4—21no—
285C2×C4—22no—
286C2×C4—24no—
287C2×C4—41no—
288C2×C4—42no—
289C2×C4C2×C4⋊Dic8911yescharacteristic
290C2×C4C2×C4⋊Dic8912yes—
291C2×C4C2×C4⋊Dic8911yescharacteristic
292C2×C4C2×C4⋊Dic8912yes—
293C2×C4C2×C4⋊Dic8912yes—
294C2×C4C2×C4⋊Dic8911yescharacteristic
295C2×C4C23×Dic8911yescharacteristic
296C2×C4C22×D35611yescharacteristic
297C2×C4C22×Dic17811yescharacteristic
298C8—22no—
299C8—22no—
300C8—24no—
301C8—3562no—
302C8—3562no—
303C8—3562no—
304C8—3562no—
305C22—21no—
306C22—22no—
307C22—22no—
308C22—21no—
309C22—22no—
310C22—21no—
311C22C22×C4⋊Dic8911yescharacteristic
312C4—21no—
313C4—22no—
314C4—22no—
315C4—21no—
316C4—21no—
317C4—21no—
318C4—22no—
319C4#1915236512yes—
320C4#1915240311yescharacteristic
321C4#1915241511yescharacteristic
322C2—41no—
323C2—42no—
324C2#2602881611yescharacteristic
325C2#2602885211yescharacteristic
326C2#2602886311yescharacteristic
subgroupG/H
centerC2×C4C22×D356
commutatorC2×C4×C89C23×C4
FrattiniC42C23×D89
FittingC89×#2922C2
socleC22×C89C22×C4⋊C4
prime radicalC2×#41×C89C2×C4
cosocleC42×C89C24
hypercenter#2922D89
hypocenterC89#17825
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #2922

Complements

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

NH ≅ G/Ntype
2. #26019041C2semidirect
3. #26019037C2semidirect
4. #26019032C2semidirect
5. #26019027C2semidirect
6. #26019019C2semidirect
7. #26019015C2semidirect
8. #26019011C2semidirect
173. C89#17825semidirect

Maximal subgroups

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

subgroupindex
#260293692
#260190412
#260190372
#260190322
#260190272
#260190192
#260190152
#260190112
C89×#29222
#1782589