Finite Group Databasebeta

← #26028087

Subgroups — #26028087

Order 11392.

434 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19151535C211yesmaximal, characteristic, complemented
2#19151527C211yesmaximal, characteristic, complemented
3#19151527C211yesmaximal, characteristic, complemented
4#19151527C211yesmaximal, characteristic, complemented
5#19151515C211yesmaximal, characteristic
6#19151499C211yesmaximal, characteristic
7#19151495C211yesmaximal, characteristic, complemented
8#19151490C211yesmaximal, characteristic, complemented
9#19151487C211yesmaximal, characteristic, complemented
10#19151484C211yesmaximal, characteristic, complemented
11#19151484C211yesmaximal, characteristic, complemented
12#19151476C211yesmaximal, characteristic
13#19151472C211yesmaximal, characteristic, complemented
14#19151472C211yesmaximal, characteristic, complemented
15#400×C89C211yesmaximal, characteristic, complemented
16C22×D356C2211yescharacteristic
17C22×C4×D89C2211yescharacteristic
18C2×C4⋊Dic89C2211yescharacteristic
19C2×C4⋊Dic89C2211yescharacteristic
20C2×C4⋊Dic89C2211yescharacteristic
21C2×#13083553C2211yescharacteristic
22C2×#13083553C2211yescharacteristic
23C2×#13083553C2211yescharacteristic
24C2×#13083551C2211yescharacteristic
25C2×#13083551C2211yescharacteristic
26C2×#13083551C2211yescharacteristic
27C2×#13083551C2211yescharacteristic
28C2×#13083551C2211yescharacteristic
29C2×#13083551C2211yescharacteristic
30C2×#13083551C2211yescharacteristic
31C2×#13083551C2211yescharacteristic
32C2×#13083551C2211yescharacteristic
33C2×#13083551C2211yescharacteristic
34C2×#13083551C2211yescharacteristic
35C2×C4×Dic89C2211yescharacteristic
36C2×C4×Dic89C2211yescharacteristic
37#15667919C2211yescharacteristic
38#15667919C2211yescharacteristic
39#15667919C2211yescharacteristic
40#15667919C2211yescharacteristic
41#15667919C2211yescharacteristic
42#15667919C2211yescharacteristic
43#15667919C2211yescharacteristic
44C2×C4⋊C4×C89C2211yescharacteristic
45C2×C4⋊C4×C89C2211yescharacteristic
46#95×C89C2211yescharacteristic
47#95×C89C2211yescharacteristic
48#95×C89C2211yescharacteristic
49#95×C89C2211yescharacteristic
50#95×C89C2211yescharacteristic
51C23×D89C2311yescharacteristic
52C23×D89C2311yescharacteristic
53C2×D356—22no—
54C2×D356—22no—
55C2×D356—41no—
56C22×Dic89C2311yescharacteristic
57C22×Dic89C2311yescharacteristic
58C22×Dic89C2311yescharacteristic
59C22×Dic89C2311yescharacteristic
60C22×Dic89C2311yescharacteristic
61C22×Dic89C2311yescharacteristic
62C2×C4×D89—41no—
63C2×C4×D89—41no—
64C2×C4×D89—41no—
65C4⋊Dic89—41no—
66C4⋊Dic89—41no—
67C4⋊Dic89—41no—
68#13083553—22no—
69#13083553—41no—
70#13083553—41no—
71#13083551—22no—
72#13083551—22no—
73#13083551—22no—
74#13083551—22no—
75#13083551—41no—
76#13083551—41no—
77#13083551—41no—
78#13083551—41no—
79#13083551—41no—
80#13083551—41no—
81#13083551—41no—
82C4×Dic89—41no—
83C4×Dic89—41no—
84C22×C4×C89C2311yescharacteristic
85C22×C4×C89C2311yescharacteristic
86C22×C4×C89C2311yescharacteristic
87C22×C4×C89C2311yescharacteristic
88C22×C4×C89C2311yescharacteristic
89C22×C4×C89C2311yescharacteristic
90C22×C4×C89C2311yescharacteristic
91C4⋊C4×C89—22no—
92C4⋊C4×C89—22no—
93C23×C89C2411yescharacteristic
94C22×D89—21no—
95C22×D89—21no—
96C22×D89—21no—
97C22×D89—21no—
98C22×D89—21no—
99C22×D89—21no—
100C22×D89—21no—
101C22×D89—21no—
102C22×D89—21no—
103C22×D89—21no—
104C22×D89—21no—
105C22×D89—21no—
106C22×D89—21no—
107C22×D89#4112yes—
108C2×C4×C89—21no—
109C2×C4×C89—21no—
110C2×C4×C89—21no—
111C2×C4×C89—21no—
112C2×C4×C89—21no—
113C2×C4×C89—21no—
114C2×C4×C89—21no—
115C2×C4×C89—21no—
116C2×C4×C89—21no—
117C2×C4×C89—21no—
118C2×C4×C89—21no—
119C2×C4×C89—21no—
120C2×C4×C89—21no—
121C2×C4×C89—21no—
122C2×C4×C89—21no—
123C2×C4×C89—21no—
124C2×C4×C89—21no—
125C2×C4×C89—21no—
126C2×C4×C89—21no—
127C2×C4×C89—21no—
128C2×C4×C89#4112yes—
129C2×Dic89—21no—
130C2×Dic89—21no—
131C2×Dic89—21no—
132C2×Dic89—21no—
133C2×Dic89—21no—
134C2×Dic89—21no—
135C2×Dic89—21no—
136C2×Dic89—21no—
137C2×Dic89—21no—
138C2×Dic89—21no—
139C2×Dic89—21no—
140C2×Dic89—21no—
141C2×Dic89—21no—
142C2×Dic89—21no—
143C2×Dic89—21no—
144C2×Dic89—21no—
145C2×Dic89—21no—
146C2×Dic89#4112yes—
147D356—44no—
148C4×D89—44no—
149C22×C89C2×#4111yescharacteristic
150C22×C89C2×#4111yescharacteristic
151C22×C89C2×#4111yescharacteristic
152C22×C89H(5,𝔽2)11yescharacteristic
153C22×C89H(5,𝔽2)11yescharacteristic
154C22×C89H(5,𝔽2)11yescharacteristic
155C22×C892−1+411yescharacteristic
156C2×D89—22no—
157C2×D89—22no—
158C2×D89—22no—
159C2×D89—41no—
160C2×D89—41no—
161C2×D89—41no—
162C2×D89—41no—
163C2×D89—41no—
164C2×D89—41no—
165C2×D89—41no—
166C2×D89—41no—
167C2×D89—41no—
168C2×D89—41no—
169C2×D89—41no—
170C4×C89—22no—
171C4×C89—41no—
172C4×C89—41no—
173C4×C89—41no—
174C4×C89—41no—
175C4×C89—41no—
176C4×C89—41no—
177Dic89—22no—
178Dic89—41no—
179Dic89—41no—
180Dic89—41no—
181Dic89—41no—
182Dic89—41no—
183C2×C89#53911yescharacteristic
184C2×C89#53911yescharacteristic
185C2×C89#54211yescharacteristic
186C2×C89#55111yescharacteristic
187C2×C89#55311yescharacteristic
188C2×C89#55911yescharacteristic
189C2×C89#56011yescharacteristic
190D89—42no—
191D89—81no—
192#2796—891nomaximal, Sylow
193C89#279611yescharacteristic, complemented, Sylow
194#400D8911yescharacteristic, complemented
195#399—891no—
196#397—891no—
197#397—891no—
198#397—891no—
199#394—891no—
200#390—891no—
201#389—891no—
202#388—891no—
203#388—891no—
204#387—891no—
205#387—891no—
206#386—891no—
207#385—891no—
208#385—891no—
209C22×D4—891no—
210C23×C4—891no—
211C2×C4⋊C4—891no—
212C2×C4⋊C4—891no—
213C2×C4⋊C4—891no—
214C2×C4⋊C4—891no—
215C2×C4⋊C4—891no—
216C2×C4⋊C4—891no—
217C2×C4⋊C4C2×D8911yescharacteristic
218C2×C4⋊C4C2×D8911yescharacteristic
219C2×C22⋊C4—891no—
220C2×C22⋊C4—891no—
221C2×C22⋊C4—891no—
222C2×C22⋊C4—891no—
223C2×C22⋊C4—891no—
224C2×C22⋊C4—891no—
225C2×C22⋊C4—891no—
226C2×C22⋊C4—891no—
227C2×C22⋊C4—891no—
228C2×C22⋊C4—891no—
229C2×C22⋊C4—891no—
230C2×C42—891no—
231C2×C42—891no—
232#95—891no—
233#95—891no—
234#95—891no—
235#95—891no—
236#95—891no—
237#95—891no—
238#95—891no—
239#95C2×D8911yescharacteristic
240#95C2×D8911yescharacteristic
241#95C2×D8911yescharacteristic
242#95C2×D8911yescharacteristic
243#95C2×D8911yescharacteristic
244C24—891no—
245C24—891no—
246C2×D4—3561no—
247C2×D4—1782no—
248C2×D4—1782no—
249C22×C4—891no—
250C22×C4—891no—
251C22×C4—891no—
252C22×C4—891no—
253C22×C4—891no—
254C22×C4—891no—
255C22×C4—3561no—
256C22×C4—3561no—
257C22×C4—3561no—
258C22×C4C22×D8911yescharacteristic
259C22×C4C22×D8911yescharacteristic
260C22×C4C22×D8911yescharacteristic
261C22×C4C22×D8911yescharacteristic
262C22×C4C22×D8911yescharacteristic
263C22×C4C22×D8911yescharacteristic
264C22×C4C22×D8911yescharacteristic
265C4⋊C4—22no—
266C4⋊C4—22no—
267C4⋊C4—3561no—
268C4⋊C4—3561no—
269C4⋊C4—3561no—
270C4⋊C4—3561no—
271C4⋊C4—3561no—
272C4⋊C4—1782no—
273C22⋊C4—3561no—
274C22⋊C4—3561no—
275C22⋊C4—3561no—
276C22⋊C4—3561no—
277C22⋊C4—3561no—
278C22⋊C4—3561no—
279C22⋊C4—3561no—
280C22⋊C4—1782no—
281C22⋊C4—1782no—
282C22⋊C4—1782no—
283C22⋊C4—1782no—
284C42—3561no—
285C42—3561no—
286C23—892no—
287C23—1781no—
288C23—1781no—
289C23—1781no—
290C23—1781no—
291C23—1781no—
292C23—1781no—
293C23—1781no—
294C23—1781no—
295C23—1781no—
296C23—1781no—
297C23—1781no—
298C23—1781no—
299C23—1781no—
300C23C23×D8911yescharacteristic
301D4—3564no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—892no—
323C2×C4—3564no—
324C2×C4—1781no—
325C2×C4—1781no—
326C2×C4—1781no—
327C2×C4—1781no—
328C2×C4—1781no—
329C2×C4—1781no—
330C2×C4—1781no—
331C2×C4—1781no—
332C2×C4—1781no—
333C2×C4—1781no—
334C2×C4—1781no—
335C2×C4—1781no—
336C2×C4—1781no—
337C2×C4—1781no—
338C2×C4—1781no—
339C2×C4—1781no—
340C2×C4—1781no—
341C2×C4#1308357312yes—
342C22—3561no—
343C22—3561no—
344C22—3561no—
345C22—3561no—
346C22—3561no—
347C22—3561no—
348C22—3561no—
349C22—3561no—
350C22—3561no—
351C22—3561no—
352C22—3561no—
353C22—1782no—
354C22—1782no—
355C22—1782no—
356C22#41×D8911yescharacteristic
357C22#41×D8911yescharacteristic
358C22C2×#1308357311yescharacteristic
359C22#1566805811yescharacteristic
360C22#1566805811yescharacteristic
361C22#1566805811yescharacteristic
362C22#1566806011yescharacteristic
363C4—22no—
364C4—41no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—41no—
370C4—3561no—
371C4—3561no—
372C4—3561no—
373C4—3561no—
374C4—3561no—
375C4—1782no—
376C2—3562no—
377C2—7121no—
378C2#1915219611yescharacteristic
379C2#1915219611yescharacteristic
380C2#1915222111yescharacteristic
381C2#1915227111yescharacteristic
382C2#1915229911yescharacteristic
383C2#1915233011yescharacteristic
384C2#1915233911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#400×C89C2
prime radicalC22×D356C22
hypercenter#400D89
hypocenterC89#2796
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. #19151535C2semidirect
2. #19151527C2semidirect
3. #19151527C2semidirect
4. #19151527C2semidirect
7. #19151495C2semidirect
8. #19151490C2semidirect
9. #19151487C2semidirect
10. #19151484C2semidirect
11. #19151484C2semidirect
13. #19151472C2semidirect
14. #19151472C2semidirect
15. #400×C89C2semidirect
193. C89#2796semidirect
194. #400D89semidirect

Maximal subgroups

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

subgroupindex
#191515352
#191515272
#191515152
#191514992
#191514952
#191514902
#191514872
#191514842
#191514762
#191514722
#400×C892
#279689