Finite Group Databasebeta

← #36458951

Subgroups — #36458951

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#26021054C211yesmaximal, characteristic
3#26021010C211yesmaximal, characteristic
4C2×#19151349C211yesmaximal, characteristic
5C2×#19151345C211yesmaximal, characteristic
6#26018136C211yesmaximal, characteristic
7C89×#1939C211yesmaximal, characteristic
8C2×#15668012C2211yescharacteristic
9C2×#15667945—21no—
10C2×C4⋊#10623494C2211yescharacteristic
11C2×C4⋊#10623494C2211yescharacteristic
12C2×#15667937—21no—
13C2×#15667937—21no—
14#19151468C2211yescharacteristic
15#19151360—21no—
16#19151360—21no—
17#19151360—21no—
18#19151349—22no—
19#19151345—22no—
20C2×C4⋊C8×C89—21no—
21C2×C4⋊C8×C89C2211yescharacteristic
22C2×C4×C8×C89C2211yescharacteristic
23C4×C4⋊C4×C89C2211yescharacteristic
24#336×C89—21no—
25C22×Dic178—21no—
26C22×#10623494—21no—
27C22×#10623494—21no—
28#15668012—21no—
29#15668012—21no—
30#15668012—21no—
31#15668012Q812yes—
32C2×C4⋊Dic89—21no—
33C2×C4⋊Dic89—21no—
34C2×C4⋊Dic89—21no—
35C2×C4⋊Dic89—21no—
36C2×C4⋊Dic89—21no—
37#15667945—42no—
38C4⋊#10623494—21no—
39C4⋊#10623494—21no—
40C4⋊#10623494—21no—
41C4⋊#10623494D412yes—
42#15667937—42no—
43#15667937—42no—
44C22×C8×C89—21no—
45C22×C8×C89D411yescharacteristic
46C22×C8×C89D411yescharacteristic
47C2×C4⋊C4×C89D411yescharacteristic
48C2×C4⋊C4×C89D411yescharacteristic
49C2×C42×C89—21no—
50C2×C42×C89C2311yescharacteristic
51C4⋊C8×C89—21no—
52C4⋊C8×C89—21no—
53C4⋊C8×C89—42no—
54C4×C8×C89—21no—
55C4×C8×C89—21no—
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—
64C22×Dic89—41no—
65C2×#10623494—22no—
66C2×#10623494—41no—
67C2×#10623494—41no—
68C2×#10623494—41no—
69C2×#10623494—41no—
70C2×#10623494—41no—
71C4⋊Dic89—22no—
72C4⋊Dic89—22no—
73C4⋊Dic89—41no—
74C4⋊Dic89—41no—
75C4⋊Dic89—41no—
76C4⋊Dic89—41no—
77C4⋊Dic89—41no—
78C4⋊Dic89—41no—
79C4⋊Dic89—81no—
80C22×C4×C89—21no—
81C22×C4×C89—21no—
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—41no—
91C2×C8×C89—41no—
92C2×C8×C89—41no—
93C2×C8×C89D812yes—
94C4⋊C4×C89—21no—
95C4⋊C4×C89—21no—
96C4⋊C4×C89—21no—
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#12111yescharacteristic
114C2×C4×C89#12111yescharacteristic
115C2×C4×C89C22⋊Q811yescharacteristic
116C2×C4×C89C22⋊Q811yescharacteristic
117C2×C4×C89C22⋊Q811yescharacteristic
118C2×C4×C89#12611yescharacteristic
119C2×C4×C89C2×D811yescharacteristic
120C2×C4×C89C2×SD1611yescharacteristic
121C2×C4×C89#13511yescharacteristic
122C2×C4×C89#13511yescharacteristic
123C2×C4×C89AGL(1,ℤ/8)11yescharacteristic
124C2×C4×C89#13711yescharacteristic
125C2×C4×C89#13711yescharacteristic
126C2×C4×C89#13711yescharacteristic
127C2×Dic89—42no—
128C2×Dic89—81no—
129C2×Dic89—81no—
130C2×Dic89—81no—
131C2×Dic89—81no—
132C2×Dic89—81no—
133Dic178—42no—
134Dic178—42no—
135Dic178—81no—
136Dic178—81no—
137C8×C89—22no—
138C8×C89—41no—
139C8×C89—81no—
140#10623494—42no—
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#46111yescharacteristic
154C4×C89#46411yescharacteristic
155C4×C89#46611yescharacteristic
156C4×C89#46811yescharacteristic
157C4×C89#47411yescharacteristic
158C4×C89#47511yescharacteristic
159C4×C89#47811yescharacteristic
160C4×C89#47911yescharacteristic
161Dic89—82no—
162Dic89—161no—
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#1947—891no—
174#1939D8911yescharacteristic
175C2×#334—891no—
176C2×#332—891no—
177#1296—891no—
178C89#1058811yescharacteristic, complemented, Sylow
179C2×C4⋊Q8—891no—
180C2×#107—1781no—
181C2×C4⋊C8—21no—
182C2×C4⋊C8—891no—
183C2×C4⋊C8—891no—
184C2×C4⋊C8C2×D8911yescharacteristic
185C2×#103—1781no—
186C2×#103—1781no—
187C2×C4×C8C2×D8911yescharacteristic
188#384—891no—
189C4×C4⋊C4C2×D8911yescharacteristic
190#340—1781no—
191#340—1781no—
192#340—1781no—
193#336—21no—
194#334—1782no—
195#332—1782no—
196C22×Q8—1781no—
197C22×C8—21no—
198C22×C8—1781no—
199C22×C8—1781no—
200C22×C8C22⋊D8911yescharacteristic
201C22×C8C22⋊D8911yescharacteristic
202C4⋊Q8—892no—
203C4⋊Q8—1781no—
204C4⋊Q8—1781no—
205C4⋊Q8—1781no—
206C2×C4⋊C4—1781no—
207C2×C4⋊C4—1781no—
208C2×C4⋊C4—1781no—
209C2×C4⋊C4—1781no—
210C2×C4⋊C4—1781no—
211C2×C4⋊C4D35611yescharacteristic
212C2×C4⋊C4D35611yescharacteristic
213C2×C42—21no—
214C2×C42C22×D8911yescharacteristic
215#107—3562no—
216C4⋊C8—21no—
217C4⋊C8—21no—
218C4⋊C8—42no—
219C4⋊C8—892no—
220C4⋊C8—1781no—
221C4⋊C8—1781no—
222C4⋊C8—1781no—
223#103—3562no—
224#103—3562no—
225C4×C8—21no—
226C4×C8—21no—
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—3561no—
237C22×C4—3561no—
238C22×C4C2×C22⋊D8911yescharacteristic
239C22×C4C2×D35611yescharacteristic
240C22×C4#1308357411yescharacteristic
241C2×C8—21no—
242C2×C8—21no—
243C2×C8—21no—
244C2×C8—21no—
245C2×C8—21no—
246C2×C8—41no—
247C2×C8—41no—
248C2×C8—41no—
249C2×C8—3561no—
250C2×C8—3561no—
251C2×C8—3561no—
252C2×C8—3561no—
253C2×C8—3561no—
254C2×C8—1782no—
255C2×C8#1308355912yes—
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—3561no—
260C4⋊C4—3561no—
261C4⋊C4—3561no—
262C4⋊C4—3561no—
263C4⋊C4—3561no—
264C4⋊C4—3561no—
265C4⋊C4—1782no—
266C4⋊C4—1782no—
267C4⋊C4—7121no—
268C4⋊C4#1308356312yes—
269C42—41no—
270C42—41no—
271C42D4×D8911yescharacteristic
272C42Q8×D8911yescharacteristic
273C42#1308357311yescharacteristic
274C42#1308357511yescharacteristic
275C23#1566798611yescharacteristic
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—3562no—
289C2×C4—7121no—
290C2×C4—7121no—
291C2×C4—7121no—
292C2×C4—7121no—
293C2×C4—7121no—
294C2×C4#1566798411yescharacteristic
295C2×C4#1566798711yescharacteristic
296C2×C4#1566798811yescharacteristic
297C2×C4#1566799011yescharacteristic
298C2×C4#1566799211yescharacteristic
299C2×C4#1566800711yescharacteristic
300C2×C4C2×#1308355911yescharacteristic
301C2×C4C2×#1308356311yescharacteristic
302C2×C4#1566803211yescharacteristic
303C2×C4#1566803411yescharacteristic
304C2×C4#1566803711yescharacteristic
305C2×C4#1566804311yescharacteristic
306C2×C4#1566804511yescharacteristic
307C2×C4#1566804511yescharacteristic
308C8—22no—
309C8—41no—
310C8—81no—
311C8—3562no—
312C8—7121no—
313C22#1915152011yescharacteristic
314C22#1915179311yescharacteristic
315C22#1915182011yescharacteristic
316C22#1915182711yescharacteristic
317C22#1915185611yescharacteristic
318C22#1915186111yescharacteristic
319C22#1915187311yescharacteristic
320C4—21no—
321C4—21no—
322C4—42no—
323C4—81no—
324C4—14241no—
325C4—7122no—
326C4#1915180411yescharacteristic
327C4#1915182111yescharacteristic
328C4#1915183211yescharacteristic
329C4#1915184611yescharacteristic
330C4#1915187511yescharacteristic
331C4#1915188411yescharacteristic
332C4#1915189511yescharacteristic
333C4#1915190611yescharacteristic
334C2#2601959311yescharacteristic
335C2#2601968211yescharacteristic
336C2#2601974111yescharacteristic
337C2#2601983411yescharacteristic
338C2#2602161811yescharacteristic
339C2#2602163211yescharacteristic
340C2#2602163711yescharacteristic
subgroupG/H
centerC23#15667986
commutator, cosocleC2×C42×C89C23
FrattiniC2×C42C22×D89
FittingC89×#1939C2
socle, prime radicalC23×C89#121
hypercenter#1939D89
hypocenterC89#10588
LCSG ▷ C2×C42×C89 ▷ C22×C89 ▷ C89
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1939

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
#260210542
#260210102
C2×#191513492
C2×#191513452
#260181362
C89×#19392
#1058889