Finite Group Databasebeta

← #37582701

Subgroups — #37582701

Order 24448.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#27133282C211yesmaximal, characteristic, complemented
2#27133135C211yesmaximal, characteristic, complemented
3#27133003C211yesmaximal, characteristic, complemented
4#27132985C211yesmaximal, characteristic, complemented
5#27132953C211yesmaximal, characteristic, complemented
6#27132944C211yesmaximal, characteristic, complemented
7#27132875C211yesmaximal, characteristic, complemented
8#27132812C211yesmaximal, characteristic, complemented
9#27132795C211yesmaximal, characteristic
10#27132772C211yesmaximal, characteristic, complemented
11#27132764C211yesmaximal, characteristic, complemented
12#27132748C211yesmaximal, characteristic, complemented
13D8×Dic191C211yesmaximal, characteristic, complemented
14#27132723C211yesmaximal, characteristic, complemented
15#463×C191C211yesmaximal, characteristic, complemented
16C2×D4×D191C2211yescharacteristic
17C2×#15690274C2211yescharacteristic
18C2×#15690272C2211yescharacteristic
19#20259322C2211yescharacteristic, complemented
20#20259315—21no—
21#20259308—21no—
22#20259306—21no—
23#20259299—21no—
24#20259298C2211yescharacteristic
25#20259293C2211yescharacteristic
26Q8×Dic191C2211yescharacteristic, complemented
27C4×D764C2211yescharacteristic
28D4×Dic191C2211yescharacteristic
29D4×Dic191C2211yescharacteristic, complemented
30#20259284C2211yescharacteristic
31C4×C22⋊D191—21no—
32(C22⋊D191)⋊C4—21no—
33#20259280C2211yescharacteristic
34#20259279C2211yescharacteristic
35C2×(C2×D191)⋊C4—21no—
36C22⋊C4×D191—21no—
37#20259256C2211yescharacteristic, complemented
38#20259256C2211yescharacteristic, complemented
39#20259253C2211yescharacteristic, 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
51C8×Dic191C2211yescharacteristic, 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×Dic382—21no—
61C2×D764C2311yescharacteristic
62C2×C22⋊D191—21no—
63C2×C22⋊D191—21no—
64D4×D191—22no—
65D4×D191—22no—
66C22×Dic191—21no—
67C22×Dic191—21no—
68C2×C4×D191—21no—
69C2×C4×D191—21no—
70C2×C4×D191C2311yescharacteristic
71#15690274—22no—
72#15690272—22no—
73C2×C191⋊C8C2311yescharacteristic
74C2×C191⋊C8C2311yescharacteristic
75C4⋊Dic191—21no—
76C4⋊Dic191—21no—
77C4⋊Dic191C2311yescharacteristic
78C4⋊Dic191C2311yescharacteristic
79C4⋊Dic191C2311yescharacteristic
80Dic191⋊C4—21no—
81Dic191⋊C4D411yescharacteristic
82Dic191⋊C4D411yescharacteristic
83C22⋊Dic191—21no—
84C22⋊Dic191—21no—
85C22⋊Dic191—21no—
86(C2×D191)⋊C4—21no—
87(C2×D191)⋊C4—21no—
88(C2×D191)⋊C4—21no—
89(C2×D191)⋊C4—21no—
90(C2×D191)⋊C4D411yescharacteristic
91(C2×D191)⋊C4D411yescharacteristic
92C4×Dic191—21no—
93C4×Dic191—21no—
94C4×Dic191C2311yescharacteristic
95C2×Q8×C191C2311yescharacteristic
96C2×D4×C191C2311yescharacteristic
97C2×D4×C191C2311yescharacteristic
98C22×C4×C191—21no—
99SD16×C191—22no—
100D8×C191—22no—
101C2×C8×C191C2311yescharacteristic
102C2×C8×C191C2311yescharacteristic
103C4⋊C4×C191C2311yescharacteristic
104C22⋊C4×C191—21no—
105C22⋊C4×C191—21no—
106C22⋊C4×C191—21no—
107C42×C191C2311yescharacteristic
108C22×D191—21no—
109C22×D191—24no—
110C22×D191—81no—
111C22×D191—81no—
112C22×D191C2×D411yescharacteristic
113Dic382—81no—
114D764—21no—
115D764#4112yes—
116C22⋊D191—24no—
117C22⋊D191—81no—
118C2×Dic191—21no—
119C2×Dic191—21no—
120C2×Dic191—21no—
121C2×Dic191—81no—
122C2×Dic191—81no—
123C2×Dic191C2×D411yescharacteristic
124C2×Dic191C2×D411yescharacteristic
125C2×Dic191C2×D411yescharacteristic
126C4×D191—21no—
127C4×D191—21no—
128C4×D191—81no—
129C4×D191—81no—
130C191⋊C8—21no—
131C191⋊C8—21no—
132C23×C191—21no—
133C23×C191—21no—
134Q8×C191—21no—
135Q8×C191—21no—
136D4×C191—21no—
137D4×C191—21no—
138D4×C191—21no—
139D4×C191#4112yes—
140C2×C4×C191—21no—
141C2×C4×C191—21no—
142C2×C4×C191—81no—
143C2×C4×C191C2×D411yescharacteristic
144C2×C4×C191C2×D411yescharacteristic
145C2×C4×C191C2411yescharacteristic
146C8×C191—21no—
147C8×C191—21no—
148C22×C191—22no—
149C22×C191—41no—
150C22×C191—41no—
151C22×C191—41no—
152C22×C191—41no—
153C22×C191—41no—
154C22×C191C22×D411yescharacteristic
155C2×D191—21no—
156C2×D191—22no—
157C2×D191—21no—
158C2×D191—21no—
159C2×D191—41no—
160C2×D191—41no—
161C2×D191—84no—
162C4×C191—21no—
163C4×C191—21no—
164C4×C191—41no—
165C4×C191—41no—
166C4×C191C2×#4111yescharacteristic
167C4×C191C2×#4111yescharacteristic
168Dic191—21no—
169Dic191—21no—
170Dic191—21no—
171Dic191—41no—
172Dic191—41no—
173Dic191—41no—
174C2×C191—42no—
175C2×C191—81no—
176C2×C191#52511yescharacteristic
177C2×C191#57611yescharacteristic
178C2×C191#57711yescharacteristic
179D191—41no—
180D191—42no—
181C191#311811yescharacteristic, complemented, Sylow
182#3118—1911nomaximal, Sylow
183#542—1911no—
184#518—1911no—
185#485—1911no—
186#482—1911no—
187#476—1911no—
188#474—1911no—
189#463—1911no—
190#463D19111yescharacteristic, complemented
191#450—1911no—
192#447—1911no—
193#442—1911no—
194#440—1911no—
195C4×SD16—1911no—
196C4×D8—1911no—
197#433—1911no—
198C22×D4—1911no—
199C2×SD16—1911no—
200C2×SD16C2×D19111yescharacteristic
201C2×D8—1911no—
202C2×D8C2×D19111yescharacteristic
203C4⋊Q8—1911no—
204#126—3821no—
205#124—3821no—
206#124C2×D19111yescharacteristic, complemented
207#123—3821no—
208C22⋊Q8—3821no—
209C22⋊Q8—1911no—
210#121—1911no—
211C4×Q8—1911no—
212C4×D4—3821no—
213C4×D4—3821no—
214C4×D4—1911no—
215C4×D4—1911no—
216C4×D4—1911no—
217C4×D4—1911no—
218C4×D4C2×D19111yescharacteristic
219#117—1911no—
220#117—1911no—
221C2×C22⋊C4—3821no—
222C2×C22⋊C4—3821no—
223#107—1911no—
224#107—1911no—
225#106—1911no—
226#106—1911no—
227C4⋊C8—1911no—
228C4⋊C8C2×D19111yescharacteristic, complemented
229#103—1911no—
230#103C2×D19111yescharacteristic, complemented
231#102—1911no—
232#102—1911no—
233#102—1911no—
234#102—1911no—
235#102—1911no—
236#102C2×D19111yescharacteristic, complemented
237C22⋊C8—1911no—
238C22⋊C8—1911no—
239#97—1911no—
240C4×C8—1911no—
241C24—3821no—
242C2×Q8—3821no—
243C2×Q8C22×D19111yescharacteristic
244C2×D4—3822no—
245C2×D4—3822no—
246C2×D4—3821no—
247C2×D4—3821no—
248C2×D4—1911no—
249C2×D4C22×D19111yescharacteristic
250C2×D4C22×D19111yescharacteristic
251C22×C4—21no—
252C22×C4—3821no—
253C22×C4—3821no—
254C22×C4—3821no—
255C22×C4—3821no—
256C22×C4—1911no—
257SD16—22no—
258SD16—3822no—
259D8—22no—
260D8—3822no—
261C2×C8—1911no—
262C2×C8—1911no—
263C2×C8C22×D19111yescharacteristic
264C2×C8C22×D19111yescharacteristic
265C4⋊C4—3821no—
266C4⋊C4—3821no—
267C4⋊C4—3821no—
268C4⋊C4—1911no—
269C4⋊C4—1911no—
270C4⋊C4—1911no—
271C4⋊C4—1911no—
272C4⋊C4—1911no—
273C4⋊C4C22×D19111yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—3821no—
278C22⋊C4—3821no—
279C22⋊C4—3821no—
280C22⋊C4—3821no—
281C22⋊C4—3821no—
282C22⋊C4—3821no—
283C22⋊C4—3821no—
284C22⋊C4—1911no—
285C22⋊C4—1911no—
286C42—3821no—
287C42—3821no—
288C42—1911no—
289C42C22×D19111yescharacteristic
290C23—21no—
291C23—21no—
292C23—3824no—
293C23—3821no—
294C23—1911no—
295C23—15281no—
296C23—15281no—
297Q8—21no—
298Q8—21no—
299Q8—15281no—
300D4—21no—
301D4—21no—
302D4—21no—
303D4—3824no—
304D4—3821no—
305D4—1912no—
306D4—15281no—
307D4#1569028612yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—81no—
311C2×C4—3821no—
312C2×C4—3821no—
313C2×C4—3821no—
314C2×C4—3821no—
315C2×C4—3821no—
316C2×C4—1911no—
317C2×C4—1911no—
318C2×C4—1911no—
319C2×C4—15281no—
320C2×C4—15281no—
321C2×C4—15281no—
322C2×C4—15281no—
323C2×C4D4×D19111yescharacteristic
324C2×C4D4×D19111yescharacteristic
325C2×C4C23×D19111yescharacteristic
326C8—21no—
327C8—21no—
328C8—3821no—
329C8—3821no—
330C22—22no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—3821no—
337C22—3821no—
338C22—3821no—
339C22—3822no—
340C22—15284no—
341C22—7641no—
342C22—7641no—
343C22C2×D4×D19111yescharacteristic
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—3821no—
349C4—3821no—
350C4—3821no—
351C4—7641no—
352C4—7641no—
353C4—7641no—
354C4#41×D19111yescharacteristic
355C4C2×#1569028611yescharacteristic
356C2—42no—
357C2—81no—
358C2—7641no—
359C2—7642no—
360C2#2713317311yescharacteristic
361C2#2713346511yescharacteristic
362C2#2713347311yescharacteristic
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#463×C191C2
socleC22×C191C22×D4
prime radical#27132795C2
hypercenter#463D191
hypocenterC191#3118
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. #27133282C2semidirect
2. #27133135C2semidirect
3. #27133003C2semidirect
4. #27132985C2semidirect
5. #27132953C2semidirect
6. #27132944C2semidirect
7. #27132875C2semidirect
8. #27132812C2semidirect
10. #27132772C2semidirect
11. #27132764C2semidirect
12. #27132748C2semidirect
13. D8×Dic191C2semidirect
14. #27132723C2semidirect
15. #463×C191C2semidirect
19. #20259322C22semidirect
26. Q8×Dic191C22semidirect
29. D4×Dic191C22semidirect
37. #20259256C22semidirect
38. #20259256C22semidirect
39. #20259253C22semidirect
40. #20259253C22semidirect
41. C4⋊(C191⋊C8)C22semidirect
42. #20259246C22semidirect
47. #20259243C22semidirect
50. #20259232C22semidirect
51. C8×Dic191C22semidirect
54. #124×C191C22semidirect
56. C4⋊C8×C191C22semidirect
57. #103×C191C22semidirect
58. #102×C191C22semidirect
181. C191#3118semidirect
190. #463D191semidirect
206. #124C2×D191semidirect
228. C4⋊C8C2×D191semidirect
230. #103C2×D191semidirect
236. #102C2×D191semidirect

Maximal subgroups

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

subgroupindex
#271332822
#271331352
#271330032
#271329852
#271329532
#271329442
#271328752
#271328122
#271327952
#271327722
#271327642
#271327482
D8×Dic1912
#271327232
#463×C1912
#3118191