Finite Group Databasebeta

← #26027288

Subgroups — #26027288

Order 11392.

552 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19151533C211yesmaximal, characteristic, complemented
2#19151527C211yesmaximal, characteristic, complemented
3#19151526C211yesmaximal, characteristic, complemented
4#19151525C211yesmaximal, characteristic, complemented
5#19151521C211yesmaximal, characteristic, complemented
6#19151520C211yesmaximal, characteristic, complemented
7#19151489C211yesmaximal, characteristic, complemented
8#19151489C211yesmaximal, characteristic, complemented
9#19151487C211yesmaximal, characteristic, complemented
10#19151487C211yesmaximal, characteristic, complemented
11#19151486C211yesmaximal, characteristic, complemented
12#19151453C211yesmaximal, characteristic
13#19151453C211yesmaximal, characteristic
14#19151453C211yesmaximal, characteristic
15#388×C89C211yesmaximal, characteristic, complemented
16C24×D89C2211yescharacteristic
17C2×C4⋊Dic89C2211yescharacteristic, complemented
18C2×#13083553C2211yescharacteristic, complemented
19C2×#13083553C2211yescharacteristic, complemented
20C2×#13083553C2211yescharacteristic, complemented
21C2×#13083553C2211yescharacteristic, complemented
22C2×C22⋊Dic89C2211yescharacteristic
23C2×C22⋊Dic89C2211yescharacteristic
24C2×C22⋊Dic89C2211yescharacteristic
25C2×#13083551C2211yescharacteristic
26C2×#13083551C2211yescharacteristic
27C2×#13083551C2211yescharacteristic
28C2×#13083551C2211yescharacteristic
29C2×#13083551C2211yescharacteristic
30C2×#13083551C2211yescharacteristic
31C2×#13083551C2211yescharacteristic
32C2×#13083551C2211yescharacteristic
33C2×#13083551C2211yescharacteristic
34C2×#13083551C2211yescharacteristic
35C2×#13083551C2211yescharacteristic
36C2×#13083551C2211yescharacteristic
37C2×C4×Dic89C2211yescharacteristic, complemented
38#15667919C2211yescharacteristic, complemented
39#15667919C2211yescharacteristic, complemented
40#15667919C2211yescharacteristic, complemented
41#15667919C2211yescharacteristic, complemented
42#15667919C2211yescharacteristic, complemented
43#15667919C2211yescharacteristic, complemented
44C2×C4⋊C4×C89C2211yescharacteristic, complemented
45C2×C22⋊C4×C89C2211yescharacteristic
46C2×C22⋊C4×C89C2211yescharacteristic
47C2×C22⋊C4×C89C2211yescharacteristic
48C2×C42×C89C2211yescharacteristic, complemented
49#95×C89C2211yescharacteristic, complemented
50#95×C89C2211yescharacteristic, complemented
51C23×D89—22no—
52C23×D89—22no—
53C23×D89—22no—
54C23×D89—41no—
55C23×D89—41no—
56C23×D89—41no—
57C23×D89—41no—
58C23×D89C2311yescharacteristic
59C23×D89C2311yescharacteristic
60C22×Dic89C2311yescharacteristic
61C22×Dic89C2311yescharacteristic
62C22×Dic89C2311yescharacteristic
63C22×Dic89C2311yescharacteristic
64C22×Dic89C2311yescharacteristic
65C22×Dic89C2311yescharacteristic
66C4⋊Dic89—41no—
67#13083553—41no—
68#13083553—41no—
69#13083553—41no—
70#13083553—41no—
71C22⋊Dic89—22no—
72C22⋊Dic89—41no—
73C22⋊Dic89—41no—
74#13083551—22no—
75#13083551—22no—
76#13083551—22no—
77#13083551—22no—
78#13083551—41no—
79#13083551—41no—
80#13083551—41no—
81#13083551—41no—
82#13083551—41no—
83#13083551—41no—
84#13083551—41no—
85#13083551—41no—
86C4×Dic89—41no—
87C24×C89C2311yescharacteristic
88C22×C4×C89C2311yescharacteristic
89C22×C4×C89C2311yescharacteristic
90C22×C4×C89C2311yescharacteristic
91C22×C4×C89C2311yescharacteristic
92C22×C4×C89C2311yescharacteristic
93C22×C4×C89C2311yescharacteristic
94C4⋊C4×C89—41no—
95C22⋊C4×C89—22no—
96C22⋊C4×C89—41no—
97C22⋊C4×C89—41no—
98C42×C89—41no—
99C23×C89—21no—
100C23×C89—21no—
101C23×C89—21no—
102C23×C89—21no—
103C23×C89—21no—
104C23×C89—21no—
105C23×C89#4112yes—
106C23×C89C2411yescharacteristic
107C22×D89—21no—
108C22×D89—21no—
109C22×D89—21no—
110C22×D89—21no—
111C22×D89—21no—
112C22×D89—21no—
113C22×D89—21no—
114C22×D89—21no—
115C22×D89—21no—
116C22×D89—21no—
117C22×D89—21no—
118C22×D89—21no—
119C22×D89—44no—
120C22×D89—44no—
121C22×D89—44no—
122C22×D89—44no—
123C22×D89—44no—
124C22×D89—44no—
125C22×D89—44no—
126C22×D89#4112yes—
127C22×D89#4112yes—
128C2×C4×C89—21no—
129C2×C4×C89—21no—
130C2×C4×C89—21no—
131C2×C4×C89—21no—
132C2×C4×C89—21no—
133C2×C4×C89—21no—
134C2×C4×C89—21no—
135C2×C4×C89—21no—
136C2×C4×C89—21no—
137C2×C4×C89—21no—
138C2×C4×C89—21no—
139C2×C4×C89—21no—
140C2×C4×C89—21no—
141C2×C4×C89—21no—
142C2×C4×C89—21no—
143C2×C4×C89—21no—
144C2×C4×C89—21no—
145C2×C4×C89—21no—
146C2×Dic89—21no—
147C2×Dic89—21no—
148C2×Dic89—21no—
149C2×Dic89—21no—
150C2×Dic89—21no—
151C2×Dic89—21no—
152C2×Dic89—21no—
153C2×Dic89—21no—
154C2×Dic89—21no—
155C2×Dic89—21no—
156C2×Dic89—21no—
157C2×Dic89—21no—
158C2×Dic89—21no—
159C2×Dic89—21no—
160C2×Dic89—21no—
161C2×Dic89—21no—
162C2×Dic89—21no—
163C2×Dic89—21no—
164C22×C89—22no—
165C22×C89—22no—
166C22×C89—22no—
167C22×C89—41no—
168C22×C89—41no—
169C22×C89—41no—
170C22×C89—41no—
171C22×C89C2×#4111yescharacteristic
172C22×C89C2×#4111yescharacteristic
173C22×C89C2×#4111yescharacteristic
174C22×C89H(5,𝔽2)11yescharacteristic
175C22×C89H(5,𝔽2)11yescharacteristic
176C22×C89H(5,𝔽2)11yescharacteristic
177C22×C89H(5,𝔽2)11yescharacteristic
178C2×D89—22no—
179C2×D89—22no—
180C2×D89—22no—
181C2×D89—22no—
182C2×D89—22no—
183C2×D89—22no—
184C2×D89—416no—
185C2×D89—41no—
186C2×D89—41no—
187C2×D89—41no—
188C2×D89—41no—
189C2×D89—41no—
190C2×D89—41no—
191C2×D89—41no—
192C2×D89—41no—
193C4×C89—41no—
194C4×C89—41no—
195C4×C89—41no—
196C4×C89—41no—
197C4×C89—41no—
198C4×C89—41no—
199Dic89—41no—
200Dic89—41no—
201Dic89—41no—
202Dic89—41no—
203Dic89—41no—
204Dic89—41no—
205C2×C89—42no—
206C2×C89#53811yescharacteristic
207C2×C89#53811yescharacteristic
208C2×C89#53811yescharacteristic
209C2×C89#55111yescharacteristic
210C2×C89#55111yescharacteristic
211C2×C89#55111yescharacteristic
212C2×C89#56011yescharacteristic
213D89—42no—
214D89—42no—
215#2735—891nomaximal, Sylow
216C89#273511yescharacteristic, complemented, Sylow
217#399—891no—
218#397—891no—
219#397—891no—
220#397—891no—
221#396—891no—
222#396—891no—
223#388—891no—
224#388—891no—
225#388—891no—
226#388—891no—
227#388—891no—
228#388D8911yescharacteristic, complemented
229#379—891no—
230#379—891no—
231#379—891no—
232C25—891no—
233C2×C4⋊C4—891no—
234C2×C4⋊C4—891no—
235C2×C4⋊C4—891no—
236C2×C4⋊C4—891no—
237C2×C4⋊C4—891no—
238C2×C4⋊C4C2×D8911yescharacteristic, complemented
239C2×C22⋊C4—891no—
240C2×C22⋊C4—891no—
241C2×C22⋊C4—891no—
242C2×C22⋊C4—891no—
243C2×C22⋊C4—891no—
244C2×C22⋊C4—891no—
245C2×C22⋊C4—891no—
246C2×C22⋊C4—891no—
247C2×C22⋊C4—891no—
248C2×C22⋊C4—891no—
249C2×C22⋊C4—891no—
250C2×C22⋊C4—891no—
251C2×C22⋊C4—891no—
252C2×C22⋊C4—891no—
253C2×C22⋊C4—891no—
254C2×C22⋊C4C2×D8911yescharacteristic
255C2×C22⋊C4C2×D8911yescharacteristic
256C2×C22⋊C4C2×D8911yescharacteristic
257C2×C42—891no—
258C2×C42C2×D8911yescharacteristic, complemented
259#95—891no—
260#95—891no—
261#95—891no—
262#95—891no—
263#95—891no—
264#95—891no—
265#95C2×D8911yescharacteristic, complemented
266#95C2×D8911yescharacteristic, complemented
267C24—891no—
268C24—891no—
269C24—3561no—
270C24—3561no—
271C24—3561no—
272C24—3561no—
273C24—1782no—
274C24—1782no—
275C24—1782no—
276C24C22×D8911yescharacteristic
277C22×C4—891no—
278C22×C4—891no—
279C22×C4—891no—
280C22×C4—891no—
281C22×C4—891no—
282C22×C4—891no—
283C22×C4C22×D8911yescharacteristic
284C22×C4C22×D8911yescharacteristic
285C22×C4C22×D8911yescharacteristic
286C22×C4C22×D8911yescharacteristic
287C22×C4C22×D8911yescharacteristic
288C22×C4C22×D8911yescharacteristic
289C4⋊C4—41no—
290C4⋊C4—3561no—
291C4⋊C4—3561no—
292C4⋊C4—3561no—
293C4⋊C4—3561no—
294C4⋊C4—3561no—
295C22⋊C4—22no—
296C22⋊C4—41no—
297C22⋊C4—41no—
298C22⋊C4—3561no—
299C22⋊C4—3561no—
300C22⋊C4—3561no—
301C22⋊C4—3561no—
302C22⋊C4—3561no—
303C22⋊C4—3561no—
304C22⋊C4—3561no—
305C22⋊C4—3561no—
306C22⋊C4—3561no—
307C22⋊C4—3561no—
308C22⋊C4—1782no—
309C22⋊C4—1782no—
310C22⋊C4—1782no—
311C22⋊C4—1782no—
312C22⋊C4—1782no—
313C42—41no—
314C42—3561no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—892no—
322C23—892no—
323C23—3564no—
324C23—3564no—
325C23—3564no—
326C23—3564no—
327C23—3564no—
328C23—3564no—
329C23—3564no—
330C23—1781no—
331C23—1781no—
332C23—1781no—
333C23—1781no—
334C23—1781no—
335C23—1781no—
336C23—1781no—
337C23—1781no—
338C23—1781no—
339C23—1781no—
340C23—1781no—
341C23—1781no—
342C23#1308357412yes—
343C23C23×D8911yescharacteristic
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—1781no—
363C2×C4—1781no—
364C2×C4—1781no—
365C2×C4—1781no—
366C2×C4—1781no—
367C2×C4—1781no—
368C2×C4—1781no—
369C2×C4—1781no—
370C2×C4—1781no—
371C2×C4—1781no—
372C2×C4—1781no—
373C2×C4—1781no—
374C2×C4—1781no—
375C2×C4—1781no—
376C2×C4—1781no—
377C2×C4—1781no—
378C2×C4—1781no—
379C2×C4—1781no—
380C22—22no—
381C22—22no—
382C22—22no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—35616no—
388C22—3561no—
389C22—3561no—
390C22—3561no—
391C22—3561no—
392C22—3561no—
393C22—3561no—
394C22—3561no—
395C22—3561no—
396C22—1782no—
397C22—1782no—
398C22—1782no—
399C22—1782no—
400C22—1782no—
401C22—1782no—
402C22#41×D8911yescharacteristic
403C22#41×D8911yescharacteristic
404C22C2×#1308357411yescharacteristic
405C22#1566805711yescharacteristic
406C22#1566805711yescharacteristic
407C22#1566805811yescharacteristic
408C22#1566805811yescharacteristic
409C4—41no—
410C4—41no—
411C4—41no—
412C4—41no—
413C4—41no—
414C4—41no—
415C4—3561no—
416C4—3561no—
417C4—3561no—
418C4—3561no—
419C4—3561no—
420C4—3561no—
421C2—42no—
422C2—3562no—
423C2—3562no—
424C2#1915218111yescharacteristic
425C2#1915218411yescharacteristic
426C2#1915218711yescharacteristic
427C2#1915227211yescharacteristic
428C2#1915227711yescharacteristic
429C2#1915227811yescharacteristic
430C2#1915233611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#388×C89C2
prime radicalC24×D89C22
hypercenter#388D89
hypocenterC89#2735
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. #19151533C2semidirect
2. #19151527C2semidirect
3. #19151526C2semidirect
4. #19151525C2semidirect
5. #19151521C2semidirect
6. #19151520C2semidirect
7. #19151489C2semidirect
8. #19151489C2semidirect
9. #19151487C2semidirect
10. #19151487C2semidirect
11. #19151486C2semidirect
15. #388×C89C2semidirect
17. C2×C4⋊Dic89C22semidirect
18. C2×#13083553C22semidirect
19. C2×#13083553C22semidirect
20. C2×#13083553C22semidirect
21. C2×#13083553C22semidirect
37. C2×C4×Dic89C22semidirect
38. #15667919C22semidirect
39. #15667919C22semidirect
40. #15667919C22semidirect
41. #15667919C22semidirect
42. #15667919C22semidirect
43. #15667919C22semidirect
44. C2×C4⋊C4×C89C22semidirect
48. C2×C42×C89C22semidirect
49. #95×C89C22semidirect
50. #95×C89C22semidirect
216. C89#2735semidirect
228. #388D89semidirect
238. C2×C4⋊C4C2×D89semidirect
258. C2×C42C2×D89semidirect
265. #95C2×D89semidirect
266. #95C2×D89semidirect

Maximal subgroups

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

subgroupindex
#191515332
#191515272
#191515262
#191515252
#191515212
#191515202
#191514892
#191514872
#191514862
#191514532
#388×C892
#273589