Finite Group Databasebeta

← #37582708

Subgroups — #37582708

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#27133285C211yesmaximal, characteristic, complemented
2#27133135C211yesmaximal, characteristic, complemented
3#27133002C211yesmaximal, characteristic, complemented
4#27132990C211yesmaximal, characteristic, complemented
5#27132951C211yesmaximal, characteristic, complemented
6#27132942C211yesmaximal, characteristic, complemented
7#27132881C211yesmaximal, characteristic, complemented
8#27132880C211yesmaximal, characteristic, complemented
9#27132812C211yesmaximal, characteristic, complemented
10#27132798C211yesmaximal, characteristic
11#27132776C211yesmaximal, characteristic, complemented
12C4×#15690274C211yesmaximal, characteristic, complemented
13C4×#15690272C211yesmaximal, characteristic, complemented
14#27132725C211yesmaximal, characteristic, complemented
15#440×C191C211yesmaximal, characteristic, complemented
16C2×D4×D191C2211yescharacteristic
17C2×#15690274C2211yescharacteristic
18C2×D1528C2211yescharacteristic
19C2×#15690272C2211yescharacteristic
20#20259321C2211yescharacteristic, complemented
21#20259316—21no—
22#20259311C2211yescharacteristic, complemented
23#20259310—21no—
24#20259307—21no—
25#20259300—21no—
26#20259298C2211yescharacteristic
27#20259297C2211yescharacteristic
28C4×D764C2211yescharacteristic
29C4×D764C2211yescharacteristic, complemented
30D4×Dic191C2211yescharacteristic
31#20259284C2211yescharacteristic
32C4×C22⋊D191—21no—
33(C22⋊D191)⋊C4—21no—
34#20259280C2211yescharacteristic
35#20259279C2211yescharacteristic
36C2×(C2×D191)⋊C4—21no—
37C22⋊C4×D191—21no—
38#20259255C2211yescharacteristic, complemented
39#20259254C2211yescharacteristic, complemented
40#20259253C2211yescharacteristic, complemented
41Dic191⋊C8C2211yescharacteristic, complemented
42Dic191⋊C8C2211yescharacteristic, complemented
43#20259246C2211yescharacteristic, complemented
44#20259244C2211yescharacteristic
45#20259244C2211yescharacteristic, complemented
46#20259243C2211yescharacteristic
47#20259242C2211yescharacteristic
48#20259242C2211yescharacteristic, complemented
49(C2×D191)⋊C8C2211yescharacteristic
50(C2×D191)⋊C8C2211yescharacteristic
51C4×C191⋊C8C2211yescharacteristic, complemented
52C2×SD16×C191C2211yescharacteristic
53C4×Q8×C191C2211yescharacteristic, complemented
54C4×D4×C191C2211yescharacteristic
55#107×C191C2211yescharacteristic, complemented
56#103×C191C2211yescharacteristic, complemented
57#102×C191C2211yescharacteristic
58#97×C191C2211yescharacteristic, complemented
59C23×D191—21no—
60C2×Dic382—21no—
61C2×D764—21no—
62C2×D764C2311yescharacteristic
63C2×D764C2311yescharacteristic
64C2×C22⋊D191—21no—
65D4×D191—22no—
66D4×D191—22no—
67C22×Dic191—21no—
68C2×C4×D191—21no—
69C2×C4×D191—21no—
70C2×C4×D191—21no—
71C2×C4×D191C2311yescharacteristic
72#15690274—22no—
73D1528—22no—
74#15690272—22no—
75C2×C191⋊C8C2311yescharacteristic
76C2×C191⋊C8C2311yescharacteristic
77C4⋊Dic191C2311yescharacteristic
78C4⋊Dic191C2311yescharacteristic
79Dic191⋊C4—21no—
80Dic191⋊C4—21no—
81Dic191⋊C4D411yescharacteristic
82Dic191⋊C4D411yescharacteristic
83C22⋊Dic191—21no—
84(C2×D191)⋊C4—21no—
85(C2×D191)⋊C4—21no—
86(C2×D191)⋊C4—21no—
87(C2×D191)⋊C4—21no—
88(C2×D191)⋊C4—21no—
89(C2×D191)⋊C4—21no—
90(C2×D191)⋊C4—21no—
91(C2×D191)⋊C4—21no—
92(C2×D191)⋊C4D411yescharacteristic
93(C2×D191)⋊C4D411yescharacteristic
94C4×Dic191—21no—
95C4×Dic191C2311yescharacteristic
96C2×Q8×C191C2311yescharacteristic
97C2×D4×C191C2311yescharacteristic
98C22×C4×C191—21no—
99SD16×C191—22no—
100C2×C8×C191C2311yescharacteristic
101C2×C8×C191C2311yescharacteristic
102C4⋊C4×C191—21no—
103C4⋊C4×C191C2311yescharacteristic
104C4⋊C4×C191C2311yescharacteristic
105C22⋊C4×C191—21no—
106C42×C191—21no—
107C42×C191C2311yescharacteristic
108C22×D191—21no—
109C22×D191—24no—
110C22×D191—21no—
111C22×D191—81no—
112C22×D191—81no—
113C22×D191C2×D411yescharacteristic
114Dic382—81no—
115D764—21no—
116D764—21no—
117D764—21no—
118D764—81no—
119D764#4112yes—
120C22⋊D191—24no—
121C2×Dic191—21no—
122C2×Dic191—21no—
123C2×Dic191—81no—
124C2×Dic191C2×D411yescharacteristic
125C2×Dic191C2×D411yescharacteristic
126C2×Dic191C2×D411yescharacteristic
127C4×D191—21no—
128C4×D191—21no—
129C4×D191—81no—
130C4×D191—81no—
131C4×D191—81no—
132C191⋊C8—21no—
133C191⋊C8—21no—
134C23×C191—21no—
135Q8×C191—21no—
136Q8×C191—21no—
137D4×C191—21no—
138D4×C191#4112yes—
139C2×C4×C191—21no—
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×C191C22×D411yescharacteristic
152C2×D191—21no—
153C2×D191—22no—
154C2×D191—21no—
155C2×D191—21no—
156C2×D191—41no—
157C2×D191—41no—
158C2×D191—41no—
159C2×D191—41no—
160C2×D191—41no—
161C2×D191—84no—
162C4×C191—21no—
163C4×C191—21no—
164C4×C191—41no—
165C4×C191—41no—
166C4×C191—41no—
167C4×C191C2×#4111yescharacteristic
168C4×C191C2×#4111yescharacteristic
169Dic191—21no—
170Dic191—21no—
171Dic191—21no—
172Dic191—41no—
173Dic191—41no—
174C2×C191—42no—
175C2×C191#52511yescharacteristic
176C2×C191#57611yescharacteristic
177C2×C191#57711yescharacteristic
178D191—41no—
179D191—42no—
180D191—81no—
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#463—1911no—
191#450—1911no—
192#447—1911no—
193#442—1911no—
194#440D19111yescharacteristic, complemented
195C4×SD16—1911no—
196C4×D8—1911no—
197#433—1911no—
198C22×D4—1911no—
199C2×SD16—1911no—
200C2×SD16C2×D19111yescharacteristic
201C2×D8—1911no—
202C2×D8—1911no—
203C4⋊Q8—1911no—
204#126—3821no—
205#124—3821no—
206#124—1911no—
207#123—3821no—
208C22⋊Q8—3821no—
209C22⋊Q8—1911no—
210#121—1911no—
211C4×Q8C2×D19111yescharacteristic, complemented
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#107C2×D19111yescharacteristic, complemented
225#106—1911no—
226#106—1911no—
227C4⋊C8—1911no—
228C4⋊C8—1911no—
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
237C22⋊C8—1911no—
238C22⋊C8—1911no—
239#97C2×D19111yescharacteristic, complemented
240C4×C8—1911no—
241C24—3821no—
242C2×Q8—3821no—
243C2×Q8C22×D19111yescharacteristic
244C2×D4—3821no—
245C2×D4—3822no—
246C2×D4—3822no—
247C2×D4—3821no—
248C2×D4—1911no—
249C2×D4—1911no—
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—3822no—
260D8—3822no—
261C2×C8—1911no—
262C2×C8—1911no—
263C2×C8C22×D19111yescharacteristic
264C2×C8C22×D19111yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—3821no—
267C4⋊C4—3821no—
268C4⋊C4—1911no—
269C4⋊C4—1911no—
270C4⋊C4—1911no—
271C4⋊C4—1911no—
272C4⋊C4C22×D19111yescharacteristic
273C4⋊C4C22×D19111yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—3821no—
276C22⋊C4—3821no—
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—21no—
287C42—3821no—
288C42—1911no—
289C42C22×D19111yescharacteristic
290C23—21no—
291C23—3824no—
292C23—3821no—
293C23—3821no—
294C23—1911no—
295C23—15281no—
296C23—15281no—
297Q8—21no—
298Q8—21no—
299Q8—15281no—
300D4—21no—
301D4—3824no—
302D4—3821no—
303D4—3821no—
304D4—3821no—
305D4—1912no—
306D4—15281no—
307D4#1569028712yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—81no—
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—3821no—
334C22—3821no—
335C22—3821no—
336C22—3822no—
337C22—15284no—
338C22—7641no—
339C22—7641no—
340C22—7641no—
341C22—7641no—
342C22—7641no—
343C22C2×D4×D19111yescharacteristic
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—3821no—
350C4—3821no—
351C4—3821no—
352C4—7641no—
353C4—7641no—
354C4#41×D19111yescharacteristic
355C4C2×#1569028711yescharacteristic
356C2—42no—
357C2—15281no—
358C2—7641no—
359C2—7642no—
360C2#2713317211yescharacteristic
361C2#2713346711yescharacteristic
362C2#2713347211yescharacteristic
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#440×C191C2
socleC22×C191C22×D4
prime radical#27132798C2
hypercenter#440D191
hypocenterC191#3118
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #27133285C2semidirect
2. #27133135C2semidirect
3. #27133002C2semidirect
4. #27132990C2semidirect
5. #27132951C2semidirect
6. #27132942C2semidirect
7. #27132881C2semidirect
8. #27132880C2semidirect
9. #27132812C2semidirect
11. #27132776C2semidirect
12. C4×#15690274C2semidirect
13. C4×#15690272C2semidirect
14. #27132725C2semidirect
15. #440×C191C2semidirect
20. #20259321C22semidirect
22. #20259311C22semidirect
29. C4×D764C22semidirect
38. #20259255C22semidirect
39. #20259254C22semidirect
40. #20259253C22semidirect
41. Dic191⋊C8C22semidirect
42. Dic191⋊C8C22semidirect
43. #20259246C22semidirect
45. #20259244C22semidirect
48. #20259242C22semidirect
51. C4×C191⋊C8C22semidirect
53. C4×Q8×C191C22semidirect
55. #107×C191C22semidirect
56. #103×C191C22semidirect
58. #97×C191C22semidirect
181. C191#3118semidirect
194. #440D191semidirect
211. C4×Q8C2×D191semidirect
224. #107C2×D191semidirect
230. #103C2×D191semidirect
239. #97C2×D191semidirect

Maximal subgroups

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

subgroupindex
#271332852
#271331352
#271330022
#271329902
#271329512
#271329422
#271328812
#271328802
#271328122
#271327982
#271327762
C4×#156902742
C4×#156902722
#271327252
#440×C1912
#3118191