Finite Group Databasebeta

← #36452802

Subgroups — #36452802

Order 22784.

386 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#26021203C211yesmaximal, characteristic
2#26021053C211yesmaximal, characteristic
3#26021013C211yesmaximal, characteristic
4#26020122C211yesmaximal, characteristic
5C2×#19151345C211yesmaximal, characteristic
6#26018086C211yesmaximal, characteristic
7C89×#1296C211yesmaximal, characteristic
8C2×#15668012C2211yescharacteristic
9C2×#15667943—21no—
10C2×C4⋊#10623494C2211yescharacteristic
11C2×#15667935—21no—
12C2×#15667935—21no—
13C2×#15667922—21no—
14C2×C4×#10623494C2211yescharacteristic
15C4×C4⋊Dic89C2211yescharacteristic
16#19151361—21no—
17#19151361—21no—
18#19151360—21no—
19#19151352—21no—
20#19151345C414yescomplemented
21C2×C4⋊C8×C89C2211yescharacteristic
22C2×C4⋊C8×C89C2211yescharacteristic
23#384×C89C2211yescharacteristic
24C22×Dic178—21no—
25C22×#10623494—21no—
26C22×#10623494D411yescharacteristic
27C22×#10623494D411yescharacteristic
28#15668012—21no—
29#15668012—21no—
30#15668012—21no—
31#15668012C2×C412yes—
32C2×C4⋊Dic89—21no—
33C2×C4⋊Dic89—21no—
34C2×C4⋊Dic89D411yescharacteristic
35C2×C4⋊Dic89D411yescharacteristic
36C2×C4×Dic89—21no—
37#15667943—42no—
38C4⋊#10623494—21no—
39C4⋊#10623494C2×C412yes—
40#15667935—42no—
41#15667935—42no—
42#15667922—42no—
43C4×#10623494—21no—
44C4×#10623494—21no—
45#15667919—21no—
46C22×C8×C89—21no—
47C22×C8×C89—21no—
48C2×C4⋊C4×C89—21no—
49C2×C4⋊C4×C89—21no—
50C2×C4⋊C4×C89—21no—
51C2×C42×C89C2311yescharacteristic
52C4⋊C8×C89—21no—
53C4⋊C8×C89—21no—
54C4⋊C8×C89—21no—
55C4⋊C8×C89C2×C412yes—
56C2×Dic178—22no—
57C2×Dic178—41no—
58C2×Dic178—41no—
59C2×Dic178—41no—
60C2×Dic178—41no—
61C2×Dic178—41no—
62C22×Dic89—21no—
63C22×Dic89—21no—
64C22×Dic89—41no—
65C2×#10623494—21no—
66C2×#10623494—21no—
67C2×#10623494—22no—
68C2×#10623494—21no—
69C2×#10623494—21no—
70C2×#10623494—21no—
71C2×#10623494—41no—
72C2×#10623494—41no—
73C2×#10623494SD1612yes—
74C4⋊Dic89—22no—
75C4⋊Dic89—22no—
76C4⋊Dic89—21no—
77C4⋊Dic89—21no—
78C4⋊Dic89—21no—
79C4⋊Dic89—21no—
80C4⋊Dic89—41no—
81C4⋊Dic89—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—22no—
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×C89C22×C411yescharacteristic
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#11711yescharacteristic
110C2×C4×C89C4×D411yescharacteristic
111C2×C4×C89C4×D411yescharacteristic
112C2×C4×C89#12311yescharacteristic
113C2×C4×C89#12411yescharacteristic
114C2×C4×C89#12611yescharacteristic
115C2×C4×C89C2×SD1611yescharacteristic
116C2×C4×C89#13511yescharacteristic
117C2×C4×C89AGL(1,ℤ/8)11yescharacteristic
118C2×C4×C89AGL(1,ℤ/8)11yescharacteristic
119C2×C4×C89AGL(1,ℤ/8)11yescharacteristic
120C2×C4×C89#13711yescharacteristic
121C2×C4×C89#13711yescharacteristic
122C2×C4×C89#13711yescharacteristic
123C2×Dic89—42no—
124C2×Dic89—41no—
125C2×Dic89—41no—
126C2×Dic89—41no—
127C2×Dic89—41no—
128C2×Dic89—41no—
129C2×Dic89—41no—
130C2×Dic89—81no—
131C2×Dic89—81no—
132Dic178—42no—
133Dic178—42no—
134Dic178—81no—
135Dic178—81no—
136C8×C89—42no—
137C8×C89—81no—
138#10623494—22no—
139#10623494—42no—
140#10623494—41no—
141C22×C89#38811yescharacteristic
142C22×C89#46011yescharacteristic
143C22×C89#46311yescharacteristic
144C22×C89#46811yescharacteristic
145C22×C89#47011yescharacteristic
146C22×C89#47111yescharacteristic
147C22×C89#47311yescharacteristic
148C4×C89—21no—
149C4×C89—21no—
150C4×C89—161no—
151C4×C89C4×SD1611yescharacteristic
152C4×C89#44011yescharacteristic
153C4×C89#44111yescharacteristic
154C4×C89#44211yescharacteristic
155C4×C89#48111yescharacteristic
156C4×C89#48211yescharacteristic
157C4×C89#48911yescharacteristic
158C4×C89#49111yescharacteristic
159Dic89—82no—
160Dic89—81no—
161Dic89—81no—
162#9570—891nomaximal, Sylow
163C2×C89#168611yescharacteristic
164C2×C89#169011yescharacteristic
165C2×C89#169911yescharacteristic
166C2×C89#170311yescharacteristic
167C2×C89#192611yescharacteristic
168C2×C89#193011yescharacteristic
169C2×C89#193511yescharacteristic
170#1988—891no—
171#1956—891no—
172#1948—891no—
173#1770—891no—
174C2×#332—891no—
175#1296D8911yescharacteristic
176#1277—891no—
177C89#957011yescharacteristic, complemented, Sylow
178C2×C4⋊Q8—891no—
179C2×#106—1781no—
180C2×C4⋊C8—891no—
181C2×C4⋊C8C2×D8911yescharacteristic
182C2×C4⋊C8C2×D8911yescharacteristic
183C2×#103—1781no—
184C2×#103—1781no—
185C2×#97—1781no—
186C2×C4×C8—891no—
187#384C2×D8911yescharacteristic
188C4×C4⋊C4—891no—
189#340—1781no—
190#340—1781no—
191#340—1781no—
192#336—1781no—
193#332—894no—
194C22×Q8—1781no—
195C22×C8—21no—
196C22×C8—21no—
197C22×C8—891no—
198C22×C8—891no—
199C22×C8—1781no—
200C4⋊Q8—892no—
201C4⋊Q8—1781no—
202C4⋊Q8—1781no—
203C4⋊Q8—1781no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—891no—
208C2×C4⋊C4—891no—
209C2×C4⋊C4—1781no—
210C2×C4⋊C4—1781no—
211C2×C42—1781no—
212C2×C42C22×D8911yescharacteristic
213#106—3562no—
214C4⋊C8—21no—
215C4⋊C8—21no—
216C4⋊C8—21no—
217C4⋊C8—892no—
218C4⋊C8—1781no—
219C4⋊C8C4×D8912yes—
220#103—3562no—
221#103—3562no—
222#97—3562no—
223C4×C8—1781no—
224C4×C8—1781no—
225#95—1781no—
226C2×Q8—3561no—
227C2×Q8—3561no—
228C2×Q8—3561no—
229C2×Q8—3561no—
230C2×Q8—3561no—
231C2×Q8—1782no—
232C22×C4—41no—
233C22×C4—3561no—
234C22×C4—1781no—
235C22×C4—1781no—
236C22×C4D4×D8911yescharacteristic
237C22×C4D4×D8911yescharacteristic
238C22×C4#1308357411yescharacteristic
239C2×C8—22no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—892no—
246C2×C8—3561no—
247C2×C8—3561no—
248C2×C8—1782no—
249C2×C8—1781no—
250C2×C8—1781no—
251C2×C8—1781no—
252C2×C8—1781no—
253C2×C8—1781no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—81no—
259C4⋊C4—3561no—
260C4⋊C4—3561no—
261C4⋊C4—1782no—
262C4⋊C4—1782no—
263C4⋊C4—1781no—
264C4⋊C4—1781no—
265C4⋊C4—1781no—
266C4⋊C4—1781no—
267C42—3561no—
268C42—3561no—
269C42C2×C4×D8911yescharacteristic
270C42#1308357311yescharacteristic
271C42#1308357411yescharacteristic
272C42#1308357511yescharacteristic
273C23#1566798511yescharacteristic
274Q8—3562no—
275Q8—3562no—
276Q8—7121no—
277Q8—7121no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—81no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4—3561no—
284C2×C4—3562no—
285C2×C4—3561no—
286C2×C4—3561no—
287C2×C4—3561no—
288C2×C4—3561no—
289C2×C4—3561no—
290C2×C4—7121no—
291C2×C4—7121no—
292C2×C4#1566796911yescharacteristic
293C2×C4#1566797211yescharacteristic
294C2×C4#1566797411yescharacteristic
295C2×C4#1566799711yescharacteristic
296C2×C4#1566799811yescharacteristic
297C2×C4#1566800711yescharacteristic
298C2×C4SD16×D8911yescharacteristic
299C2×C4#1566803511yescharacteristic
300C2×C4#1566803611yescharacteristic
301C2×C4#1566803611yescharacteristic
302C2×C4#1566803911yescharacteristic
303C2×C4#1566804111yescharacteristic
304C2×C4#1566804111yescharacteristic
305C2×C4#1566804411yescharacteristic
306C8—42no—
307C8—81no—
308C8—3561no—
309C8—3562no—
310C8—1782no—
311C22#1915148711yescharacteristic
312C22#1915179711yescharacteristic
313C22#1915181611yescharacteristic
314C22#1915184311yescharacteristic
315C22#1915185511yescharacteristic
316C22#1915186011yescharacteristic
317C22#1915187211yescharacteristic
318C4—21no—
319C4—21no—
320C4—161no—
321C4—7122no—
322C4—7121no—
323C4—7121no—
324C4#1915168311yescharacteristic
325C4#1915169711yescharacteristic
326C4#1915170411yescharacteristic
327C4#1915170711yescharacteristic
328C4#1915191811yescharacteristic
329C4#1915192511yescharacteristic
330C4#1915195611yescharacteristic
331C4#1915196511yescharacteristic
332C2#2601972311yescharacteristic
333C2#2601974511yescharacteristic
334C2#2601980211yescharacteristic
335C2#2601983011yescharacteristic
336C2#2602087711yescharacteristic
337C2#2602090511yescharacteristic
338C2#2602094011yescharacteristic
subgroupG/H
centerC23#15667985
commutatorC42×C89C22×C4
FrattiniC2×C42C22×D89
FittingC89×#1296C2
socle, prime radicalC23×C89#121
cosocleC2×C42×C89C23
hypercenter#1296D89
hypocenterC89#9570
LCSG ▷ C42×C89 ▷ C22×C89 ▷ C89
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
20. #19151345C4semidirect
177. C89#9570semidirect

Maximal subgroups

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

subgroupindex
#260212032
#260210532
#260210132
#260201222
C2×#191513452
#260180862
C89×#12962
#957089