Finite Group Databasebeta

← #36452811

Subgroups — #36452811

Order 22784.

454 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26021179C211yesmaximal, characteristic
2#26021058C211yesmaximal, characteristic
3#26021010C211yesmaximal, characteristic, complemented
4C2×#19151341C211yesmaximal, characteristic
5#26018136C211yesmaximal, characteristic, complemented
6#26018087C211yesmaximal, characteristic, complemented
7C89×#1770C211yesmaximal, characteristic, complemented
8C2×#15668009C2211yescharacteristic
9C2×#15667945—21no—
10C2×C4⋊#10623494C2211yescharacteristic
11C2×C4⋊#10623494C2211yescharacteristic
12C2×#15667934—21no—
13C2×#15667934—21no—
14C2×#15667932—21no—
15C2×#15667932—21no—
16#19151468C2211yescharacteristic
17#19151360—21no—
18#19151341C414yescomplemented
19C2×C4⋊C8×C89C2211yescharacteristic
20C2×#97×C89—21no—
21C2×C4×C8×C89C2211yescharacteristic
22C4×C4⋊C4×C89C2211yescharacteristic
23#336×C89—21no—
24C22×D356—21no—
25C22×D356—21no—
26C22×D356—21no—
27C22×#10623494—21no—
28C22×#10623494—21no—
29#15668009—21no—
30#15668009—21no—
31#15668009—21no—
32#15668009C2×C412yes—
33C2×C4⋊Dic89—21no—
34C2×C4⋊Dic89—21no—
35C2×C4⋊Dic89—21no—
36#15667945—42no—
37C4⋊#10623494—21no—
38C4⋊#10623494—21no—
39C4⋊#10623494—21no—
40C4⋊#10623494C2×C412yes—
41#15667934—42no—
42#15667934—42no—
43#15667932—42no—
44#15667932—42no—
45C22×C8×C89—21no—
46C22×C8×C89D411yescharacteristic
47C22×C8×C89D411yescharacteristic
48C2×C4⋊C4×C89D411yescharacteristic
49C2×C4⋊C4×C89D411yescharacteristic
50C2×C42×C89—21no—
51C2×C42×C89C2311yescharacteristic
52C4⋊C8×C89—21no—
53C4⋊C8×C89C2×C412yes—
54#97×C89—42no—
55C4×C8×C89—21no—
56C4×C8×C89—21no—
57#95×C89—21no—
58C23×D89—41no—
59C2×D356—22no—
60C2×D356—22no—
61C2×D356—22no—
62C2×D356—41no—
63C2×D356—41no—
64C2×D356—41no—
65C2×D356—41no—
66C2×D356—41no—
67C2×D356—41no—
68C2×D356—41no—
69C2×D356—41no—
70C2×D356—41no—
71C2×D356—41no—
72C2×D356—41no—
73C2×D356—81no—
74C2×D356—81no—
75C22×Dic89—41no—
76C2×#10623494—22no—
77C2×#10623494—41no—
78C2×#10623494—41no—
79C2×#10623494—41no—
80C2×#10623494—41no—
81C2×#10623494—41no—
82C4⋊Dic89—41no—
83C4⋊Dic89—41no—
84C4⋊Dic89—41no—
85C4⋊Dic89—41no—
86C4⋊Dic89—81no—
87C22×C4×C89—21no—
88C22×C4×C89—21no—
89C22×C4×C89C2×D411yescharacteristic
90C22×C4×C89C2×D411yescharacteristic
91C22×C4×C89#4111yescharacteristic
92C2×C8×C89—21no—
93C2×C8×C89—21no—
94C2×C8×C89—22no—
95C2×C8×C89—21no—
96C2×C8×C89—21no—
97C2×C8×C89—21no—
98C2×C8×C89—41no—
99C2×C8×C89—41no—
100C2×C8×C89D812yes—
101C4⋊C4×C89—21no—
102C4⋊C4×C89—21no—
103C4⋊C4×C89—21no—
104C4⋊C4×C89—21no—
105C42×C89—41no—
106C42×C89—41no—
107C42×C89C22×C411yescharacteristic
108C42×C89#4111yescharacteristic
109C42×C89#4111yescharacteristic
110C42×C89#4111yescharacteristic
111C23×C89#12111yescharacteristic
112C22×D89—42no—
113C22×D89—81no—
114C22×D89—81no—
115C22×D89—81no—
116C22×D89—81no—
117C22×D89—81no—
118C22×D89—81no—
119C2×C4×C89—21no—
120C2×C4×C89—21no—
121C2×C4×C89—41no—
122C2×C4×C89—41no—
123C2×C4×C89—41no—
124C2×C4×C89—41no—
125C2×C4×C89—41no—
126C2×C4×C89—41no—
127C2×C4×C89#11711yescharacteristic
128C2×C4×C89C4×D411yescharacteristic
129C2×C4×C89C4×D411yescharacteristic
130C2×C4×C89#12311yescharacteristic
131C2×C4×C89#12411yescharacteristic
132C2×C4×C89#12611yescharacteristic
133C2×C4×C89C2×D811yescharacteristic
134C2×C4×C89#13511yescharacteristic
135C2×C4×C89AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C89AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C89AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C89AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C89#13711yescharacteristic
140C2×C4×C89#13711yescharacteristic
141C2×Dic89—81no—
142C2×Dic89—81no—
143C2×Dic89—81no—
144D356—42no—
145D356—42no—
146D356—42no—
147D356—42no—
148D356—82no—
149D356—82no—
150D356—81no—
151D356—81no—
152D356—81no—
153D356—81no—
154C8×C89—22no—
155C8×C89—42no—
156C8×C89—41no—
157#10623494—42no—
158#10623494—81no—
159C22×C89#38811yescharacteristic
160C22×C89#45911yescharacteristic
161C22×C89#46411yescharacteristic
162C22×C89#46811yescharacteristic
163C22×C89#46911yescharacteristic
164C22×C89#47111yescharacteristic
165C22×C89#47211yescharacteristic
166C2×D89—82no—
167C2×D89—82no—
168C2×D89—82no—
169C2×D89—161no—
170C2×D89—161no—
171C2×D89—161no—
172C2×D89—161no—
173C4×C89—21no—
174C4×C89—21no—
175C4×C89—81no—
176C4×C89—81no—
177C4×C89C4×D811yescharacteristic
178C4×C89#44011yescharacteristic
179C4×C89#44011yescharacteristic
180C4×C89#44211yescharacteristic
181C4×C89#48011yescharacteristic
182C4×C89#48211yescharacteristic
183C4×C89#48911yescharacteristic
184C4×C89#49011yescharacteristic
185Dic89—161no—
186#9571—891nomaximal, Sylow
187C2×C89#168511yescharacteristic
188C2×C89#168711yescharacteristic
189C2×C89#169811yescharacteristic
190C2×C89#170211yescharacteristic
191C2×C89#192511yescharacteristic
192C2×C89#193111yescharacteristic
193C2×C89#193611yescharacteristic
194D89—162no—
195#1982—891no—
196#1957—891no—
197#1947—891no—
198#1770D8911yescharacteristic, complemented
199C2×#331—891no—
200#1296—891no—
201#1277—891no—
202C89#957111yescharacteristic, complemented, Sylow
203C2×#127—891no—
204C2×#107—1781no—
205C2×C4⋊C8—891no—
206C2×C4⋊C8—891no—
207C2×C4⋊C8C2×D8911yescharacteristic
208C2×#102—1781no—
209C2×#102—1781no—
210C2×#102—1781no—
211C2×#102—1781no—
212C2×#97—21no—
213C2×C4×C8C2×D8911yescharacteristic
214#384—891no—
215C4×C4⋊C4C2×D8911yescharacteristic
216#340—1781no—
217#336—21no—
218#331—894no—
219C22×D4—1781no—
220C22×D4—1781no—
221C22×D4—1781no—
222C22×C8—21no—
223C22×C8—1781no—
224C22×C8—1781no—
225C22×C8C22⋊D8911yescharacteristic
226C22×C8C22⋊D8911yescharacteristic
227#127—892no—
228#127—1781no—
229#127—1781no—
230#127—1781no—
231C2×C4⋊C4—1781no—
232C2×C4⋊C4—1781no—
233C2×C4⋊C4—1781no—
234C2×C4⋊C4D35611yescharacteristic
235C2×C4⋊C4D35611yescharacteristic
236C2×C42—21no—
237C2×C42C22×D8911yescharacteristic
238#107—3562no—
239C4⋊C8—21no—
240C4⋊C8—892no—
241C4⋊C8—1781no—
242C4⋊C8—1781no—
243C4⋊C8—1781no—
244C4⋊C8C4×D8912yes—
245#102—3562no—
246#102—3562no—
247#102—3562no—
248#102—3562no—
249#97—42no—
250C4×C8—21no—
251C4×C8—21no—
252#95—21no—
253C24—3561no—
254C2×D4—3561no—
255C2×D4—3561no—
256C2×D4—3561no—
257C2×D4—3561no—
258C2×D4—3561no—
259C2×D4—3561no—
260C2×D4—3561no—
261C2×D4—3561no—
262C2×D4—3561no—
263C2×D4—3561no—
264C2×D4—3561no—
265C2×D4—1782no—
266C2×D4—1782no—
267C2×D4—1782no—
268C2×D4—7121no—
269C2×D4—7121no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—3561no—
273C22×C4C2×C22⋊D8911yescharacteristic
274C22×C4C2×D35611yescharacteristic
275C22×C4#1308357411yescharacteristic
276C2×C8—21no—
277C2×C8—21no—
278C2×C8—22no—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8—21no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8—3561no—
285C2×C8—3561no—
286C2×C8—3561no—
287C2×C8—3561no—
288C2×C8—3561no—
289C2×C8—1782no—
290C2×C8#1308355912yes—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—3561no—
296C4⋊C4—3561no—
297C4⋊C4—3561no—
298C4⋊C4—3561no—
299C4⋊C4—7121no—
300C42—41no—
301C42—41no—
302C42C2×C4×D8911yescharacteristic
303C42#1308357411yescharacteristic
304C42#1308357411yescharacteristic
305C42#1308357411yescharacteristic
306C23—3562no—
307C23—7121no—
308C23—7121no—
309C23—7121no—
310C23—7121no—
311C23—7121no—
312C23—7121no—
313C23#1566798611yescharacteristic
314D4—3562no—
315D4—3562no—
316D4—3562no—
317D4—3562no—
318D4—7122no—
319D4—7122no—
320D4—7121no—
321D4—7121no—
322D4—7121no—
323D4—7121no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—7121no—
333C2×C4—7121no—
334C2×C4—7121no—
335C2×C4#1566796911yescharacteristic
336C2×C4C4×C22⋊D8911yescharacteristic
337C2×C4C4×D35611yescharacteristic
338C2×C4#1566799511yescharacteristic
339C2×C4#1566800011yescharacteristic
340C2×C4#1566800611yescharacteristic
341C2×C4C2×#1308355911yescharacteristic
342C2×C4#1566803211yescharacteristic
343C2×C4#1566803711yescharacteristic
344C2×C4#1566804011yescharacteristic
345C2×C4#1566804011yescharacteristic
346C2×C4#1566804011yescharacteristic
347C2×C4#1566804311yescharacteristic
348C2×C4#1566804511yescharacteristic
349C8—22no—
350C8—41no—
351C8—42no—
352C8—3562no—
353C8—7121no—
354C22—14241no—
355C22—14241no—
356C22—14241no—
357C22—14241no—
358C22—7122no—
359C22—7122no—
360C22—7122no—
361C22#1915148911yescharacteristic
362C22#1915179311yescharacteristic
363C22#1915182011yescharacteristic
364C22#1915184411yescharacteristic
365C22#1915185111yescharacteristic
366C22#1915186111yescharacteristic
367C22#1915186811yescharacteristic
368C4—21no—
369C4—21no—
370C4—81no—
371C4—81no—
372C4—14241no—
373C4C4×#1308355911yescharacteristic
374C4#1915169611yescharacteristic
375C4#1915170011yescharacteristic
376C4#1915171111yescharacteristic
377C4#1915191111yescharacteristic
378C4#1915192211yescharacteristic
379C4#1915195811yescharacteristic
380C4#1915196311yescharacteristic
381C2—14242no—
382C2#2601971711yescharacteristic
383C2#2601973111yescharacteristic
384C2#2601979211yescharacteristic
385C2#2601982011yescharacteristic
386C2#2602087211yescharacteristic
387C2#2602091411yescharacteristic
388C2#2602094911yescharacteristic
subgroupG/H
centerC23#15667986
commutatorC42×C89C22×C4
FrattiniC2×C42C22×D89
FittingC89×#1770C2
socleC23×C89#121
prime radicalC2×#15668009C22
cosocleC2×C42×C89C23
hypercenter#1770D89
hypocenterC89#9571
LCSG ▷ C42×C89 ▷ C22×C89 ▷ C89
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1770

Complements

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

NH ≅ G/Ntype
3. #26021010C2semidirect
5. #26018136C2semidirect
6. #26018087C2semidirect
7. C89×#1770C2semidirect
18. #19151341C4semidirect
198. #1770D89semidirect
202. C89#9571semidirect

Maximal subgroups

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

subgroupindex
#260211792
#260210582
#260210102
C2×#191513412
#260181362
#260180872
C89×#17702
#957189