Finite Group Databasebeta

← #37582657

Subgroups — #37582657

Order 24448.

450 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#27133192C211yesmaximal, characteristic, complemented
2C4×D4×D191C211yesmaximal, characteristic, complemented
3#27132992C211yesmaximal, characteristic, complemented
4#27132975C211yesmaximal, characteristic, complemented
5#27132964C211yesmaximal, characteristic, complemented
6#27132963C211yesmaximal, characteristic, complemented
7#27132875C211yesmaximal, characteristic, complemented
8#27132812C211yesmaximal, characteristic, complemented
9#27132795C211yesmaximal, characteristic
10#27132775C211yesmaximal, characteristic, complemented
11#27132772C211yesmaximal, characteristic, complemented
12#27132766C211yesmaximal, characteristic, complemented
13#27132764C211yesmaximal, characteristic, complemented
14#27132719C211yesmaximal, characteristic, complemented
15#463×C191C211yesmaximal, characteristic, complemented
16C2×D4×D191C2211yescharacteristic
17C22×C4×D191—21no—
18C2×#15690274C2211yescharacteristic
19C2×#15690272C2211yescharacteristic
20#20259315—21no—
21#20259314C2211yescharacteristic, complemented
22#20259304—21no—
23#20259298C2211yescharacteristic
24#20259293C2211yescharacteristic
25Q8×Dic191C2211yescharacteristic, complemented
26C4×D764C2211yescharacteristic
27D4×Dic191C2211yescharacteristic
28D4×Dic191C2211yescharacteristic, complemented
29#20259284C2211yescharacteristic
30C4×C22⋊D191—21no—
31(C22⋊D191)⋊C4—21no—
32(C22⋊D191)⋊C4—21no—
33#20259278—21no—
34C4⋊C4×D191C2211yescharacteristic
35C22⋊C4×D191—21no—
36C42×D191C2211yescharacteristic
37#20259256C2211yescharacteristic, complemented
38#20259255C2211yescharacteristic, complemented
39#20259254C2211yescharacteristic, complemented
40#20259253C2211yescharacteristic, complemented
41C4⋊(C191⋊C8)C2211yescharacteristic, complemented
42#20259246C2211yescharacteristic, complemented
43#20259244C2211yescharacteristic
44#20259244C2211yescharacteristic
45#20259243C2211yescharacteristic
46#20259243C2211yescharacteristic
47#20259243C2211yescharacteristic, complemented
48(C2×D191)⋊C8C2211yescharacteristic
49(C2×D191)⋊C8C2211yescharacteristic
50#20259232C2211yescharacteristic, complemented
51#20259232C2211yescharacteristic, complemented
52C2×SD16×C191C2211yescharacteristic
53C2×D8×C191C2211yescharacteristic
54#124×C191C2211yescharacteristic, complemented
55C4×D4×C191C2211yescharacteristic
56C4⋊C8×C191C2211yescharacteristic, complemented
57#103×C191C2211yescharacteristic, complemented
58#102×C191C2211yescharacteristic, complemented
59C23×D191—21no—
60C2×D764C2311yescharacteristic
61C2×C22⋊D191—21no—
62C2×C22⋊D191—21no—
63D4×D191—22no—
64D4×D191—22no—
65C22×Dic191—21no—
66C22×Dic191—21no—
67C2×C4×D191—21no—
68C2×C4×D191—21no—
69C2×C4×D191—21no—
70C2×C4×D191—44no—
71C2×C4×D191D411yescharacteristic
72C2×C4×D191D411yescharacteristic
73C2×C4×D191C2311yescharacteristic
74#15690274—22no—
75#15690272—22no—
76C2×C191⋊C8C2311yescharacteristic
77C2×C191⋊C8C2311yescharacteristic
78C4⋊Dic191—21no—
79C4⋊Dic191C2311yescharacteristic
80C4⋊Dic191C2311yescharacteristic
81C4⋊Dic191C2311yescharacteristic
82Dic191⋊C4—21no—
83Dic191⋊C4—21no—
84Dic191⋊C4—21no—
85Dic191⋊C4—21no—
86C22⋊Dic191—21no—
87C22⋊Dic191—21no—
88C22⋊Dic191—21no—
89(C2×D191)⋊C4—21no—
90(C2×D191)⋊C4—21no—
91(C2×D191)⋊C4—21no—
92C4×Dic191—21no—
93C4×Dic191D411yescharacteristic
94C4×Dic191D411yescharacteristic
95C4×Dic191C2311yescharacteristic
96C2×Q8×C191C2311yescharacteristic
97C2×D4×C191C2311yescharacteristic
98C2×D4×C191C2311yescharacteristic
99C22×C4×C191—21no—
100SD16×C191—22no—
101D8×C191—22no—
102C2×C8×C191C2311yescharacteristic
103C2×C8×C191C2311yescharacteristic
104C4⋊C4×C191C2311yescharacteristic
105C22⋊C4×C191—21no—
106C22⋊C4×C191—21no—
107C22⋊C4×C191—21no—
108C42×C191C2311yescharacteristic
109C22×D191—24no—
110C22×D191—21no—
111C22×D191—42no—
112C22×D191—42no—
113C22×D191C2×D411yescharacteristic
114D764—21no—
115D764#4112yes—
116C22⋊D191—24no—
117C22⋊D191—42no—
118C2×Dic191—21no—
119C2×Dic191—21no—
120C2×Dic191—21no—
121C2×Dic191—42no—
122C2×Dic191—42no—
123C2×Dic191C2×D411yescharacteristic
124C2×Dic191C2×D411yescharacteristic
125C2×Dic191C2×D411yescharacteristic
126C4×D191—22no—
127C4×D191—21no—
128C4×D191—21no—
129C4×D191—41no—
130C4×D191—42no—
131C4×D191—42no—
132C4×D191—42no—
133C191⋊C8—21no—
134C191⋊C8—21no—
135C23×C191—21no—
136C23×C191—21no—
137Q8×C191—21no—
138Q8×C191—21no—
139D4×C191—21no—
140D4×C191—21no—
141D4×C191—21no—
142D4×C191#4112yes—
143C2×C4×C191—21no—
144C2×C4×C191—21no—
145C2×C4×C191—42no—
146C2×C4×C191C2×D411yescharacteristic
147C2×C4×C191C2×D411yescharacteristic
148C2×C4×C191C2411yescharacteristic
149C8×C191—21no—
150C8×C191—21no—
151C22×C191—22no—
152C22×C191—41no—
153C22×C191—41no—
154C22×C191—41no—
155C22×C191—41no—
156C22×C191—41no—
157C22×C191C22×D411yescharacteristic
158C2×D191—21no—
159C2×D191—21no—
160C2×D191—22no—
161C2×D191—48no—
162C2×D191—41no—
163C2×D191—41no—
164C2×D191AGL(1,ℤ/8)12yes—
165C4×C191—21no—
166C4×C191—21no—
167C4×C191—41no—
168C4×C191—41no—
169C4×C191C2×#4111yescharacteristic
170C4×C191C2×#4111yescharacteristic
171Dic191—21no—
172Dic191—21no—
173Dic191—21no—
174Dic191—41no—
175Dic191—41no—
176Dic191—41no—
177C2×C191—42no—
178C2×C191—81no—
179C2×C191#52511yescharacteristic
180C2×C191C2×AGL(1,ℤ/8)11yescharacteristic
181C2×C191#57511yescharacteristic
182D191—22no—
183D191—42no—
184C191#311411yescharacteristic, complemented, Sylow
185#3114—1911nomaximal, Sylow
186#529—1911no—
187C2×C4×D4—1911no—
188#483—1911no—
189#480—1911no—
190#478—1911no—
191#478—1911no—
192#463—1911no—
193#463D19111yescharacteristic, complemented
194#450—1911no—
195#447—1911no—
196#442—1911no—
197#442—1911no—
198#440—1911no—
199#440—1911no—
200#432—1911no—
201C22×D4—1911no—
202C23×C4—3821no—
203C2×SD16—1911no—
204C2×SD16C2×D19111yescharacteristic
205C2×D8—1911no—
206C2×D8C2×D19111yescharacteristic
207#126—3821no—
208#125—1911no—
209#124C2×D19111yescharacteristic, complemented
210#123—3821no—
211C22⋊Q8—1911no—
212#121—1911no—
213C4×Q8—1911no—
214C4×D4—3821no—
215C4×D4—3821no—
216C4×D4—3821no—
217C4×D4—1911no—
218C4×D4—1911no—
219C4×D4—1911no—
220C4×D4—1911no—
221C4×D4C2×D19111yescharacteristic
222#117—3821no—
223C2×C4⋊C4—1911no—
224C2×C22⋊C4—3821no—
225C2×C42—1911no—
226#107—1911no—
227#107—1911no—
228#106—1911no—
229#106—1911no—
230C4⋊C8—1911no—
231C4⋊C8C2×D19111yescharacteristic, complemented
232#103—1911no—
233#103C2×D19111yescharacteristic, complemented
234#102—1911no—
235#102—1911no—
236#102—1911no—
237#102—1911no—
238#102—1911no—
239#102C2×D19111yescharacteristic, complemented
240C22⋊C8—1911no—
241C22⋊C8—1911no—
242#97—1911no—
243#97—1911no—
244C24—3821no—
245C2×Q8C22×D19111yescharacteristic
246C2×D4—3822no—
247C2×D4—3822no—
248C2×D4—3821no—
249C2×D4—3821no—
250C2×D4—1911no—
251C2×D4C22×D19111yescharacteristic
252C2×D4C22×D19111yescharacteristic
253C22×C4—21no—
254C22×C4—3821no—
255C22×C4—3821no—
256C22×C4—3821no—
257C22×C4—3821no—
258C22×C4—3821no—
259C22×C4—1911no—
260C22×C4—1911no—
261C22×C4—1911no—
262C22×C4—7644no—
263SD16—22no—
264SD16—3822no—
265D8—22no—
266D8—3822no—
267C2×C8—1911no—
268C2×C8—1911no—
269C2×C8C22×D19111yescharacteristic
270C2×C8C22×D19111yescharacteristic
271C4⋊C4—3821no—
272C4⋊C4—3821no—
273C4⋊C4—3821no—
274C4⋊C4—3821no—
275C4⋊C4—3821no—
276C4⋊C4—1911no—
277C4⋊C4—1911no—
278C4⋊C4—1911no—
279C4⋊C4C22×D19111yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—3821no—
284C22⋊C4—3821no—
285C22⋊C4—3821no—
286C22⋊C4—3821no—
287C22⋊C4—3821no—
288C22⋊C4—3821no—
289C42—3821no—
290C42—1911no—
291C42—1911no—
292C42—1911no—
293C42C22×D19111yescharacteristic
294C23—21no—
295C23—21no—
296C23—3824no—
297C23—3821no—
298C23—1911no—
299C23—7642no—
300C23—7642no—
301Q8—21no—
302Q8—21no—
303D4—21no—
304D4—21no—
305D4—21no—
306D4—3824no—
307D4—3821no—
308D4—1912no—
309D4—7642no—
310D4#1569028612yes—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—42no—
314C2×C4—3822no—
315C2×C4—3821no—
316C2×C4—3821no—
317C2×C4—3821no—
318C2×C4—3821no—
319C2×C4—3821no—
320C2×C4—1911no—
321C2×C4—1911no—
322C2×C4—1911no—
323C2×C4—7641no—
324C2×C4—7642no—
325C2×C4—7642no—
326C2×C4—7642no—
327C2×C4—7642no—
328C2×C4—7642no—
329C2×C4D4×D19111yescharacteristic
330C2×C4D4×D19111yescharacteristic
331C2×C4C23×D19111yescharacteristic
332C8—21no—
333C8—21no—
334C8—3821no—
335C8—3821no—
336C22—22no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—3821no—
343C22—3821no—
344C22—3822no—
345C22—1912no—
346C22—7648no—
347C22—7641no—
348C22—7641no—
349C22C2×D4×D19111yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—3821no—
355C4—3821no—
356C4—3821no—
357C4—7641no—
358C4—7641no—
359C4—7641no—
360C4#41×D19111yescharacteristic
361C4C2×#1569028611yescharacteristic
362C2—42no—
363C2—81no—
364C2—3822no—
365C2—7642no—
366C2#2713317311yescharacteristic
367C2AGL(1,ℤ/8)×D19111yescharacteristic
368C2#2713346011yescharacteristic
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#463×C191C2
socleC22×C191C22×D4
prime radical#27132795C2
hypercenter#463D191
hypocenterC191#3114
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #27133192C2semidirect
2. C4×D4×D191C2semidirect
3. #27132992C2semidirect
4. #27132975C2semidirect
5. #27132964C2semidirect
6. #27132963C2semidirect
7. #27132875C2semidirect
8. #27132812C2semidirect
10. #27132775C2semidirect
11. #27132772C2semidirect
12. #27132766C2semidirect
13. #27132764C2semidirect
14. #27132719C2semidirect
15. #463×C191C2semidirect
21. #20259314C22semidirect
25. Q8×Dic191C22semidirect
28. D4×Dic191C22semidirect
37. #20259256C22semidirect
38. #20259255C22semidirect
39. #20259254C22semidirect
40. #20259253C22semidirect
41. C4⋊(C191⋊C8)C22semidirect
42. #20259246C22semidirect
47. #20259243C22semidirect
50. #20259232C22semidirect
51. #20259232C22semidirect
54. #124×C191C22semidirect
56. C4⋊C8×C191C22semidirect
57. #103×C191C22semidirect
58. #102×C191C22semidirect
184. C191#3114semidirect
193. #463D191semidirect
209. #124C2×D191semidirect
231. C4⋊C8C2×D191semidirect
233. #103C2×D191semidirect
239. #102C2×D191semidirect

Maximal subgroups

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

subgroupindex
#271331922
C4×D4×D1912
#271329922
#271329752
#271329642
#271329632
#271328752
#271328122
#271327952
#271327752
#271327722
#271327662
#271327642
#271327192
#463×C1912
#3114191