Finite Group Databasebeta

← #36459183

Subgroups — #36459183

Order 22784.

402 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26021046C211yesmaximal, characteristic
2#26020249C211yesmaximal, characteristic
3#26020249C211yesmaximal, characteristic
4#26018135C211yesmaximal, characteristic, complemented
5#26018135C211yesmaximal, characteristic, complemented
6#26018087C211yesmaximal, characteristic, complemented
7C89×#1834C211yesmaximal, characteristic, complemented
8C2×C4×D356C2211yescharacteristic
9C2×C4⋊#10623494C2211yescharacteristic
10C2×C4⋊#10623494C2211yescharacteristic
11C2×C4⋊#10623494C2211yescharacteristic
12C2×#15667932—21no—
13C2×#15667932—21no—
14C2×#15667924—21no—
15C2×#15667924—21no—
16#19151360—21no—
17#19151360—21no—
18C2×C4×C8×C89C2211yescharacteristic
19#384×C89C2211yescharacteristic
20#384×C89C2211yescharacteristic
21#340×C89—21no—
22#340×C89—21no—
23C22×D356D411yescharacteristic
24C22×C4×D89—21no—
25C22×#10623494—21no—
26C22×#10623494—21no—
27C22×#10623494—21no—
28C4×D356—21no—
29C4×D356—21no—
30C4×D356—21no—
31C4×D356—21no—
32C2×C4⋊Dic89D411yescharacteristic
33C2×#13083551—21no—
34C4⋊#10623494—21no—
35C4⋊#10623494—21no—
36C4⋊#10623494—21no—
37C4⋊#10623494—21no—
38C4⋊#10623494—21no—
39C4⋊#10623494—21no—
40#15667932—42no—
41#15667932—42no—
42#15667924—42no—
43#15667924—42no—
44C22×C8×C89D411yescharacteristic
45C22×C8×C89D411yescharacteristic
46C2×C4⋊C4×C89—21no—
47C2×C4⋊C4×C89—21no—
48C2×C4⋊C4×C89—21no—
49C2×C4⋊C4×C89—21no—
50C2×C4⋊C4×C89—21no—
51C2×C4⋊C4×C89—21no—
52C2×C42×C89C2311yescharacteristic
53C4×C8×C89—21no—
54C4×C8×C89—21no—
55C23×D89—21no—
56C2×D356—21no—
57C2×D356—21no—
58C2×D356—21no—
59C2×D356—21no—
60C2×D356—21no—
61C2×D356SD1612yes—
62C22×Dic89—21no—
63C2×C4×D89—41no—
64C2×C4×D89—41no—
65C2×C4×D89—41no—
66C2×C4×D89—41no—
67C2×C4×D89—41no—
68C2×C4×D89—41no—
69C2×#10623494—41no—
70C2×#10623494—41no—
71C2×#10623494—41no—
72C2×#10623494—41no—
73C2×#10623494—41no—
74C2×#10623494—41no—
75C2×#10623494—41no—
76C2×#10623494—41no—
77C2×#10623494—41no—
78C4⋊Dic89—21no—
79C4⋊Dic89—21no—
80#13083551—41no—
81#13083551—41no—
82C22×C4×C89—41no—
83C22×C4×C89—41no—
84C22×C4×C89C2×D411yescharacteristic
85C22×C4×C89C2×D411yescharacteristic
86C22×C4×C89#4111yescharacteristic
87C2×C8×C89—21no—
88C2×C8×C89—21no—
89C2×C8×C89—21no—
90C2×C8×C89—21no—
91C2×C8×C89—21no—
92C2×C8×C89—21no—
93C4⋊C4×C89—41no—
94C4⋊C4×C89—41no—
95C4⋊C4×C89—41no—
96C4⋊C4×C89—41no—
97C4⋊C4×C89—41no—
98C4⋊C4×C89—41no—
99C4⋊C4×C89—41no—
100C4⋊C4×C89—41no—
101C4⋊C4×C89—81no—
102C4⋊C4×C89—81no—
103C42×C89#4111yescharacteristic
104C42×C89#4111yescharacteristic
105C42×C89#4111yescharacteristic
106C42×C89#4111yescharacteristic
107C23×C89#12111yescharacteristic
108C22×D89—22no—
109C22×D89—41no—
110C22×D89—41no—
111C22×D89—41no—
112C22×D89—41no—
113C22×D89—41no—
114C22×D89—41no—
115C2×C4×C89—21no—
116C2×C4×C89—21no—
117C2×C4×C89—81no—
118C2×C4×C89—81no—
119C2×C4×C89—81no—
120C2×C4×C89—81no—
121C2×C4×C89—81no—
122C2×C4×C89—81no—
123C2×C4×C89#12311yescharacteristic
124C2×C4×C89#12311yescharacteristic
125C2×C4×C89#12311yescharacteristic
126C2×C4×C89#12411yescharacteristic
127C2×C4×C89#12611yescharacteristic
128C2×C4×C89#12611yescharacteristic
129C2×C4×C89C2×SD1611yescharacteristic
130C2×C4×C89#13511yescharacteristic
131C2×C4×C89#13511yescharacteristic
132C2×C4×C89#13511yescharacteristic
133C2×C4×C89AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C89AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C89AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C89#13711yescharacteristic
137C2×Dic89—41no—
138C2×Dic89—41no—
139C2×Dic89—41no—
140D356—22no—
141D356—22no—
142D356—41no—
143D356—41no—
144C4×D89—81no—
145C4×D89—81no—
146C4×D89—81no—
147C4×D89—81no—
148C8×C89—41no—
149C8×C89—41no—
150#10623494—81no—
151#10623494—81no—
152#10623494—81no—
153C22×C89#39711yescharacteristic
154C22×C89#46311yescharacteristic
155C22×C89#46311yescharacteristic
156C22×C89#46511yescharacteristic
157C22×C89#46811yescharacteristic
158C22×C89#47211yescharacteristic
159C22×C89#47311yescharacteristic
160C2×D89—42no—
161C2×D89—42no—
162C2×D89—42no—
163C2×D89—81no—
164C2×D89—81no—
165C2×D89—81no—
166C2×D89—81no—
167C4×C89—21no—
168C4×C89—21no—
169C4×C89—161no—
170C4×C89—161no—
171C4×C89#48111yescharacteristic
172C4×C89#48211yescharacteristic
173C4×C89#48211yescharacteristic
174C4×C89#48211yescharacteristic
175C4×C89#48311yescharacteristic
176C4×C89#48511yescharacteristic
177C4×C89#48811yescharacteristic
178C4×C89#49011yescharacteristic
179Dic89—81no—
180#10625—891nomaximal, Sylow
181C2×C89#167711yescharacteristic
182C2×C89#167911yescharacteristic
183C2×C89#169711yescharacteristic
184C2×C89#169911yescharacteristic
185C2×C89#207311yescharacteristic
186C2×C89#207711yescharacteristic
187C2×C89#207811yescharacteristic
188D89—82no—
189#1954—891no—
190#1834D8911yescharacteristic, complemented
191#1802—891no—
192#1802—891no—
193#1296—891no—
194#1296—891no—
195#1277—891no—
196C89#1062511yescharacteristic, complemented, Sylow
197C2×C4×D4—891no—
198C2×C4⋊C8—891no—
199C2×C4⋊C8—891no—
200C2×C4⋊C8—891no—
201C2×#102—1781no—
202C2×#102—1781no—
203C2×C22⋊C8—1781no—
204C2×C22⋊C8—1781no—
205C2×C4×C8C2×D8911yescharacteristic
206#384C2×D8911yescharacteristic
207#384C2×D8911yescharacteristic
208#340—21no—
209#340—21no—
210#340—1781no—
211#340—1781no—
212C22×D4—891no—
213C23×C4—1781no—
214C22×C8—1781no—
215C22×C8—1781no—
216C22×C8—1781no—
217C22×C8C22⋊D8911yescharacteristic
218C22×C8C22⋊D8911yescharacteristic
219C4×D4—1781no—
220C4×D4—1781no—
221C4×D4—1781no—
222C4×D4—1781no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—891no—
230C2×C22⋊C4—1781no—
231C2×C42C22×D8911yescharacteristic
232C4⋊C8—1781no—
233C4⋊C8—1781no—
234C4⋊C8—1781no—
235C4⋊C8—1781no—
236C4⋊C8—1781no—
237C4⋊C8—1781no—
238#102—3562no—
239#102—3562no—
240C22⋊C8—3562no—
241C22⋊C8—3562no—
242C4×C8—21no—
243C4×C8—21no—
244C24—1781no—
245C2×D4—892no—
246C2×D4—1781no—
247C2×D4—1781no—
248C2×D4—1781no—
249C2×D4—1781no—
250C2×D4—1781no—
251C22×C4—41no—
252C22×C4—41no—
253C22×C4—3561no—
254C22×C4—3561no—
255C22×C4—3561no—
256C22×C4—3561no—
257C22×C4—3561no—
258C22×C4—3561no—
259C22×C4—1781no—
260C22×C4D4×D8911yescharacteristic
261C22×C4C2×C22⋊D8911yescharacteristic
262C22×C4#1308357311yescharacteristic
263C2×C8—21no—
264C2×C8—21no—
265C2×C8—21no—
266C2×C8—21no—
267C2×C8—21no—
268C2×C8—21no—
269C2×C8—3561no—
270C2×C8—3561no—
271C2×C8—3561no—
272C2×C8—3561no—
273C2×C8—3561no—
274C2×C8—3561no—
275C2×C8—3561no—
276C2×C8—3561no—
277C2×C8—3561no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—81no—
287C4⋊C4—81no—
288C4⋊C4—1781no—
289C4⋊C4—1781no—
290C22⋊C4—3561no—
291C22⋊C4—3561no—
292C42#1308357411yescharacteristic
293C42#1308357411yescharacteristic
294C42#1308357511yescharacteristic
295C42#1308357511yescharacteristic
296C23—3561no—
297C23—3561no—
298C23—3561no—
299C23—3561no—
300C23—3561no—
301C23—3561no—
302C23—1782no—
303C23#1566798311yescharacteristic
304D4—3561no—
305D4—3561no—
306D4—1782no—
307D4—1782no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—3561no—
317C2×C4—3561no—
318C2×C4—3561no—
319C2×C4—7121no—
320C2×C4—7121no—
321C2×C4—7121no—
322C2×C4—7121no—
323C2×C4#1566799511yescharacteristic
324C2×C4#1566799711yescharacteristic
325C2×C4#1566799711yescharacteristic
326C2×C4#1566800111yescharacteristic
327C2×C4#1566800711yescharacteristic
328C2×C4#1566800711yescharacteristic
329C2×C4SD16×D8911yescharacteristic
330C2×C4#1566803211yescharacteristic
331C2×C4#1566803211yescharacteristic
332C2×C4#1566803311yescharacteristic
333C2×C4#1566803711yescharacteristic
334C2×C4#1566803711yescharacteristic
335C2×C4#1566803911yescharacteristic
336C2×C4#1566804111yescharacteristic
337C8—41no—
338C8—41no—
339C8—7121no—
340C8—7121no—
341C8—7121no—
342C22—3562no—
343C22—3562no—
344C22—3562no—
345C22—7121no—
346C22—7121no—
347C22—7121no—
348C22—7121no—
349C22#1915152411yescharacteristic
350C22#1915181011yescharacteristic
351C22#1915181011yescharacteristic
352C22#1915182411yescharacteristic
353C22#1915184111yescharacteristic
354C22#1915186511yescharacteristic
355C22#1915187011yescharacteristic
356C4—21no—
357C4—21no—
358C4—161no—
359C4—161no—
360C4—7121no—
361C4#1915191811yescharacteristic
362C4#1915192211yescharacteristic
363C4#1915192211yescharacteristic
364C4#1915192411yescharacteristic
365C4#1915193011yescharacteristic
366C4#1915194211yescharacteristic
367C4#1915195511yescharacteristic
368C4#1915196411yescharacteristic
369C2—7122no—
370C2#2601965811yescharacteristic
371C2#2601967211yescharacteristic
372C2#2601978211yescharacteristic
373C2#2601979611yescharacteristic
374C2#2602166611yescharacteristic
375C2#2602168611yescharacteristic
376C2#2602169311yescharacteristic
subgroupG/H
centerC23#15667983
commutator, cosocleC2×C42×C89C23
FrattiniC2×C42C22×D89
FittingC89×#1834C2
socleC23×C89#121
prime radicalC22×D356D4
hypercenter#1834D89
hypocenterC89#10625
LCSG ▷ C2×C42×C89 ▷ C22×C89 ▷ C89
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1834

Complements

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

NH ≅ G/Ntype
4. #26018135C2semidirect
5. #26018135C2semidirect
6. #26018087C2semidirect
7. C89×#1834C2semidirect
190. #1834D89semidirect
196. C89#10625semidirect

Maximal subgroups

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

subgroupindex
#260210462
#260202492
#260181352
#260180872
C89×#18342
#1062589