Finite Group Databasebeta

← #36458949

Subgroups — #36458949

Order 22784.

386 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26021204C211yesmaximal, characteristic
2#26021053C211yesmaximal, characteristic
3#26020971C211yesmaximal, characteristic
4C2×#19151348C211yesmaximal, characteristic
5C2×#19151343C211yesmaximal, characteristic
6#26018135C211yesmaximal, characteristic
7C89×#1947C211yesmaximal, characteristic
8C2×#15668012C2211yescharacteristic
9C2×C4⋊#10623494—21no—
10C2×C4⋊#10623494C2211yescharacteristic
11C2×C4⋊#10623494C2211yescharacteristic
12C2×#15667935—21no—
13C2×#15667935—21no—
14C2×C4×#10623494C2211yescharacteristic
15#19151360—21no—
16#19151360—21no—
17#19151353—21no—
18#19151348—22no—
19#19151343—22no—
20C2×#107×C89—21no—
21C2×C4⋊C8×C89C2211yescharacteristic
22#384×C89C2211yescharacteristic
23C4×C4⋊C4×C89C2211yescharacteristic
24#340×C89—21no—
25C22×Dic178—21no—
26C22×#10623494—21no—
27C22×#10623494—21no—
28C22×#10623494D411yescharacteristic
29C22×#10623494D411yescharacteristic
30#15668012—21no—
31#15668012—21no—
32#15668012—21no—
33#15668012Q812yes—
34C2×C4⋊Dic89—21no—
35C2×C4⋊Dic89—21no—
36C4⋊#10623494—21no—
37C4⋊#10623494—21no—
38C4⋊#10623494—21no—
39C4⋊#10623494—21no—
40C4⋊#10623494—42no—
41#15667935—42no—
42#15667935—42no—
43C4×#10623494—21no—
44C4×#10623494—21no—
45C22×C8×C89—21no—
46C2×C4⋊C4×C89—21no—
47C2×C4⋊C4×C89—21no—
48C2×C4⋊C4×C89—21no—
49C2×C4⋊C4×C89D411yescharacteristic
50C2×C4⋊C4×C89D411yescharacteristic
51C2×C42×C89—21no—
52C2×C42×C89C2311yescharacteristic
53#107×C89—42no—
54C4⋊C8×C89—21no—
55C4⋊C8×C89D412yes—
56#95×C89—21no—
57C2×Dic178—22no—
58C2×Dic178—41no—
59C2×Dic178—41no—
60C2×Dic178—41no—
61C2×Dic178—41no—
62C2×Dic178—41no—
63C22×Dic89—41no—
64C2×#10623494—21no—
65C2×#10623494—21no—
66C2×#10623494—21no—
67C2×#10623494—21no—
68C2×#10623494—21no—
69C2×#10623494—41no—
70C2×#10623494—41no—
71C2×#10623494—41no—
72C2×#10623494—41no—
73C2×#10623494—41no—
74C2×#10623494—41no—
75C2×#10623494D812yes—
76C4⋊Dic89—22no—
77C4⋊Dic89—22no—
78C4⋊Dic89—41no—
79C4⋊Dic89—41no—
80C22×C4×C89—21no—
81C22×C4×C89—21no—
82C22×C4×C89—41no—
83C22×C4×C89C2×D411yescharacteristic
84C22×C4×C89C2×D411yescharacteristic
85C22×C4×C89#4111yescharacteristic
86C2×C8×C89—22no—
87C2×C8×C89—41no—
88C2×C8×C89—41no—
89C4⋊C4×C89—21no—
90C4⋊C4×C89—21no—
91C4⋊C4×C89—21no—
92C4⋊C4×C89—41no—
93C4⋊C4×C89—41no—
94C4⋊C4×C89—41no—
95C4⋊C4×C89—41no—
96C4⋊C4×C89—81no—
97C4⋊C4×C89SD1612yes—
98C42×C89—41no—
99C42×C89—41no—
100C42×C89C2×D411yescharacteristic
101C42×C89C2×Q811yescharacteristic
102C42×C89#4111yescharacteristic
103C42×C89#4111yescharacteristic
104C23×C89#12111yescharacteristic
105C2×C4×C89—21no—
106C2×C4×C89—21no—
107C2×C4×C89—22no—
108C2×C4×C89—41no—
109C2×C4×C89—41no—
110C2×C4×C89—41no—
111C2×C4×C89—41no—
112C2×C4×C89—41no—
113C2×C4×C89—81no—
114C2×C4×C89—81no—
115C2×C4×C89—81no—
116C2×C4×C89#12111yescharacteristic
117C2×C4×C89#12111yescharacteristic
118C2×C4×C89C22⋊Q811yescharacteristic
119C2×C4×C89C22⋊Q811yescharacteristic
120C2×C4×C89C22⋊Q811yescharacteristic
121C2×C4×C89#12611yescharacteristic
122C2×C4×C89C2×D811yescharacteristic
123C2×C4×C89C2×SD1611yescharacteristic
124C2×C4×C89#13511yescharacteristic
125C2×C4×C89#13511yescharacteristic
126C2×C4×C89AGL(1,ℤ/8)11yescharacteristic
127C2×C4×C89#13711yescharacteristic
128C2×C4×C89#13711yescharacteristic
129C2×C4×C89#13711yescharacteristic
130C2×Dic89—42no—
131C2×Dic89—81no—
132C2×Dic89—81no—
133Dic178—42no—
134Dic178—42no—
135Dic178—81no—
136Dic178—81no—
137C8×C89—42no—
138#10623494—22no—
139#10623494—41no—
140#10623494—81no—
141#10623494—81no—
142C22×C89#39611yescharacteristic
143C22×C89#45911yescharacteristic
144C22×C89#46411yescharacteristic
145C22×C89#46511yescharacteristic
146C22×C89#47011yescharacteristic
147C22×C89#47111yescharacteristic
148C22×C89#47311yescharacteristic
149C4×C89—21no—
150C4×C89—21no—
151C4×C89—42no—
152C4×C89—81no—
153C4×C89—161no—
154C4×C89#46111yescharacteristic
155C4×C89#46411yescharacteristic
156C4×C89#46611yescharacteristic
157C4×C89#46811yescharacteristic
158C4×C89#47411yescharacteristic
159C4×C89#47511yescharacteristic
160C4×C89#47811yescharacteristic
161C4×C89#47911yescharacteristic
162Dic89—82no—
163#10588—891nomaximal, Sylow
164C2×C89#166511yescharacteristic
165C2×C89#168011yescharacteristic
166C2×C89#168911yescharacteristic
167C2×C89#170411yescharacteristic
168C2×C89#206411yescharacteristic
169C2×C89#206611yescharacteristic
170C2×C89#206711yescharacteristic
171#1988—891no—
172#1956—891no—
173#1947D8911yescharacteristic
174#1939—891no—
175C2×#334—891no—
176C2×#332—891no—
177#1296—891no—
178C89#1058811yescharacteristic, complemented, Sylow
179C2×C4⋊Q8—891no—
180C2×#107—21no—
181C2×C4⋊C8—891no—
182C2×C4⋊C8—891no—
183C2×C4⋊C8—1781no—
184C2×C4⋊C8C2×D8911yescharacteristic
185C2×#103—1781no—
186C2×#103—1781no—
187C2×C4×C8—891no—
188#384C2×D8911yescharacteristic
189C4×C4⋊C4C2×D8911yescharacteristic
190#340—21no—
191#340—1781no—
192#340—1781no—
193#336—1781no—
194#334—1782no—
195#332—1782no—
196C22×Q8—1781no—
197C22×C8—21no—
198C22×C8—891no—
199C22×C8—891no—
200C22×C8—1781no—
201C22×C8—1781no—
202C4⋊Q8—892no—
203C4⋊Q8—1781no—
204C4⋊Q8—1781no—
205C4⋊Q8—1781no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—1781no—
210C2×C4⋊C4—1781no—
211C2×C4⋊C4C22⋊D8911yescharacteristic
212C2×C4⋊C4C22⋊D8911yescharacteristic
213C2×C42—21no—
214C2×C42C22×D8911yescharacteristic
215#107—42no—
216C4⋊C8—21no—
217C4⋊C8—3562no—
218C4⋊C8—1781no—
219C4⋊C8—1781no—
220C4⋊C8—1781no—
221C4⋊C8—1781no—
222C4⋊C8D35612yes—
223#103—3562no—
224#103—3562no—
225C4×C8—1781no—
226C4×C8—1781no—
227#95—21no—
228C2×Q8—3561no—
229C2×Q8—3561no—
230C2×Q8—3561no—
231C2×Q8—3561no—
232C2×Q8—3561no—
233C2×Q8—1782no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—41no—
237C22×C4—3561no—
238C22×C4D4×D8911yescharacteristic
239C22×C4C2×C22⋊D8911yescharacteristic
240C22×C4#1308357311yescharacteristic
241C2×C8—22no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—892no—
245C2×C8—3561no—
246C2×C8—3561no—
247C2×C8—3561no—
248C2×C8—3561no—
249C2×C8—3561no—
250C2×C8—3561no—
251C2×C8—1781no—
252C2×C8—1781no—
253C2×C8—1781no—
254C2×C8—1781no—
255C2×C8—1781no—
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—81no—
264C4⋊C4—3561no—
265C4⋊C4—3561no—
266C4⋊C4—1782no—
267C4⋊C4—1782no—
268C4⋊C4#1308356212yes—
269C42—41no—
270C42—41no—
271C42C2×D35611yescharacteristic
272C42Q8×D8911yescharacteristic
273C42#1308357411yescharacteristic
274C42#1308357511yescharacteristic
275C23#1566798411yescharacteristic
276Q8—3562no—
277Q8—3562no—
278Q8—7121no—
279Q8—7121no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—22no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—81no—
289C2×C4—81no—
290C2×C4—81no—
291C2×C4—3562no—
292C2×C4—7121no—
293C2×C4—7121no—
294C2×C4#1566798611yescharacteristic
295C2×C4#1566798711yescharacteristic
296C2×C4#1566798811yescharacteristic
297C2×C4#1566799011yescharacteristic
298C2×C4#1566799211yescharacteristic
299C2×C4#1566800711yescharacteristic
300C2×C4D8×D8911yescharacteristic
301C2×C4C2×#1308356211yescharacteristic
302C2×C4#1566803211yescharacteristic
303C2×C4#1566803511yescharacteristic
304C2×C4#1566803611yescharacteristic
305C2×C4#1566804211yescharacteristic
306C2×C4#1566804311yescharacteristic
307C2×C4#1566804411yescharacteristic
308C8—42no—
309C8—3561no—
310C8—1782no—
311C8—7121no—
312C8—7121no—
313C22#1915152011yescharacteristic
314C22#1915179111yescharacteristic
315C22#1915182211yescharacteristic
316C22#1915182511yescharacteristic
317C22#1915185411yescharacteristic
318C22#1915185911yescharacteristic
319C22#1915187111yescharacteristic
320C4—21no—
321C4—21no—
322C4—42no—
323C4—81no—
324C4—161no—
325C4—7122no—
326C4#1915180311yescharacteristic
327C4#1915182011yescharacteristic
328C4#1915183511yescharacteristic
329C4#1915184511yescharacteristic
330C4#1915187711yescharacteristic
331C4#1915188011yescharacteristic
332C4#1915190111yescharacteristic
333C4#1915190211yescharacteristic
334C2#2601959111yescharacteristic
335C2#2601968411yescharacteristic
336C2#2601973911yescharacteristic
337C2#2601983611yescharacteristic
338C2#2602161611yescharacteristic
339C2#2602163011yescharacteristic
340C2#2602163511yescharacteristic
subgroupG/H
centerC23#15667984
commutator, cosocleC2×C42×C89C23
FrattiniC2×C42C22×D89
FittingC89×#1947C2
socle, prime radicalC23×C89#121
hypercenter#1947D89
hypocenterC89#10588
LCSG ▷ C2×C42×C89 ▷ C22×C89 ▷ C89
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1947

Complements

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

NH ≅ G/Ntype
178. C89#10588semidirect

Maximal subgroups

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

subgroupindex
#260212042
#260210532
#260209712
C2×#191513482
C2×#191513432
#260181352
C89×#19472
#1058889