Finite Group Databasebeta

← #37582706

Subgroups — #37582706

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#27133284C211yesmaximal, characteristic, complemented
2#27133137C211yesmaximal, characteristic, complemented
3#27133005C211yesmaximal, characteristic, complemented
4#27132988C211yesmaximal, characteristic, complemented
5#27132954C211yesmaximal, characteristic, complemented
6#27132944C211yesmaximal, characteristic, complemented
7#27132879C211yesmaximal, characteristic, complemented
8#27132879C211yesmaximal, characteristic, complemented
9#27132816C211yesmaximal, characteristic, complemented
10#27132799C211yesmaximal, characteristic
11#27132776C211yesmaximal, characteristic, complemented
12#27132765C211yesmaximal, characteristic, complemented
13C4×#15690276C211yesmaximal, characteristic, complemented
14C4×D1528C211yesmaximal, characteristic, complemented
15#433×C191C211yesmaximal, characteristic, complemented
16C22×D764C2211yescharacteristic
17C2×#15690276C2211yescharacteristic
18C2×#15690276C2211yescharacteristic
19C2×D1528C2211yescharacteristic
20C2×D1528C2211yescharacteristic
21#20259322C2211yescharacteristic, complemented
22#20259317—21no—
23#20259310C2211yescharacteristic, complemented
24#20259308—21no—
25#20259304—21no—
26#20259301C2211yescharacteristic
27#20259300—21no—
28#20259296C2211yescharacteristic
29C4×Dic382C2211yescharacteristic, complemented
30C4×D764C2211yescharacteristic
31C4×D764C2211yescharacteristic
32C4×D764C2211yescharacteristic
33C4×D764C2211yescharacteristic
34C4×D764C2211yescharacteristic, complemented
35#20259284—21no—
36#20259284—21no—
37#20259281C2211yescharacteristic
38C22⋊C4×D191—21no—
39C22⋊C4×D191—21no—
40#20259256C2211yescharacteristic, complemented
41#20259256C2211yescharacteristic, complemented
42#20259254C2211yescharacteristic, complemented
43#20259254C2211yescharacteristic, complemented
44#20259247C2211yescharacteristic, complemented
45#20259247C2211yescharacteristic, complemented
46#20259244C2211yescharacteristic
47#20259244C2211yescharacteristic
48#20259244C2211yescharacteristic
49#20259244C2211yescharacteristic
50#20259244C2211yescharacteristic, complemented
51#20259244C2211yescharacteristic, complemented
52#117×C191C2211yescharacteristic
53C4⋊C8×C191C2211yescharacteristic, complemented
54C4⋊C8×C191C2211yescharacteristic, complemented
55C22⋊C8×C191C2211yescharacteristic
56C22⋊C8×C191C2211yescharacteristic
57#97×C191C2211yescharacteristic, complemented
58C4×C8×C191C2211yescharacteristic, complemented
59C23×D191—21no—
60C2×Dic382—21no—
61C2×Dic382C2311yescharacteristic
62C2×D764—22no—
63C2×D764—22no—
64C2×D764—21no—
65C2×D764C2311yescharacteristic
66C2×D764C2311yescharacteristic
67C2×D764C2311yescharacteristic
68C2×C22⋊D191—21no—
69C2×C4×D191—21no—
70C2×C4×D191—21no—
71C2×C4×D191—21no—
72C2×C4×D191—21no—
73C2×C4×D191—21no—
74#15690276—22no—
75#15690276—22no—
76D1528—22no—
77D1528—22no—
78C4⋊Dic191—21no—
79C4⋊Dic191C2311yescharacteristic
80C4⋊Dic191C2311yescharacteristic
81C4⋊Dic191C2311yescharacteristic
82C4⋊Dic191C2311yescharacteristic
83Dic191⋊C4—21no—
84Dic191⋊C4—21no—
85C22⋊Dic191—21no—
86C22⋊Dic191—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)⋊C4—21no—
93(C2×D191)⋊C4—21no—
94(C2×D191)⋊C4—21no—
95C4×Dic191—21no—
96C4×Dic191—21no—
97C22×C4×C191C2311yescharacteristic
98C2×C8×C191C2311yescharacteristic
99C2×C8×C191C2311yescharacteristic
100C2×C8×C191C2311yescharacteristic
101C2×C8×C191C2311yescharacteristic
102C4⋊C4×C191D411yescharacteristic
103C4⋊C4×C191D411yescharacteristic
104C22⋊C4×C191D411yescharacteristic
105C22⋊C4×C191D411yescharacteristic
106C42×C191C2311yescharacteristic
107C42×C191C2311yescharacteristic
108C22×D191—21no—
109C22×D191—21no—
110C22×D191—24no—
111C22×D191—21no—
112C22×D191—81no—
113C22×D191—81no—
114Dic382—21no—
115Dic382—21no—
116Dic382—81no—
117D764—24no—
118D764—21no—
119D764—21no—
120D764—21no—
121D764—21no—
122D764#4112yes—
123D764#4112yes—
124C22⋊D191—81no—
125C2×Dic191—21no—
126C2×Dic191—21no—
127C2×Dic191—21no—
128C2×Dic191—21no—
129C2×Dic191—21no—
130C4×D191—81no—
131C4×D191—81no—
132C4×D191—81no—
133C4×D191—81no—
134C4×D191—81no—
135C23×C191C2×D411yescharacteristic
136C2×C4×C191—21no—
137C2×C4×C191—21no—
138C2×C4×C191C2×D411yescharacteristic
139C2×C4×C191C2×D411yescharacteristic
140C2×C4×C191C2×D411yescharacteristic
141C2×C4×C191C2×D411yescharacteristic
142C2×C4×C191C2×D411yescharacteristic
143C2×C4×C191C2411yescharacteristic
144C8×C191—21no—
145C8×C191—21no—
146C8×C191—21no—
147C8×C191—21no—
148C22×C191—21no—
149C22×C191—21no—
150C22×C191—21no—
151C22×C191C22×D411yescharacteristic
152C2×D191—22no—
153C2×D191—22no—
154C2×D191—41no—
155C2×D191—41no—
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—21no—
165C4×C191—21no—
166C4×C191—21no—
167C4×C191C2×#4111yescharacteristic
168C4×C191C2×#4111yescharacteristic
169Dic191—41no—
170Dic191—41no—
171Dic191—41no—
172Dic191—41no—
173Dic191—41no—
174C2×C191—41no—
175C2×C191#52511yescharacteristic
176C2×C191#57611yescharacteristic
177C2×C191#57711yescharacteristic
178D191—42no—
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#440—1911no—
195C4×SD16—1911no—
196C4×D8—1911no—
197#433D19111yescharacteristic, complemented
198C22×D4—1911no—
199C2×SD16—1911no—
200C2×SD16—1911no—
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×Q8—1911no—
212C4×D4—3821no—
213C4×D4—3821no—
214C4×D4—1911no—
215C4×D4—1911no—
216C4×D4—1911no—
217C4×D4—1911no—
218C4×D4—1911no—
219#117—1911no—
220#117C2×D19111yescharacteristic
221C2×C22⋊C4—3821no—
222C2×C22⋊C4—3821no—
223#107—1911no—
224#107—1911no—
225#106—1911no—
226#106—1911no—
227C4⋊C8C2×D19111yescharacteristic, complemented
228C4⋊C8C2×D19111yescharacteristic, complemented
229#103—1911no—
230#103—1911no—
231#102—1911no—
232#102—1911no—
233#102—1911no—
234#102—1911no—
235#102—1911no—
236#102—1911no—
237C22⋊C8C2×D19111yescharacteristic
238C22⋊C8C2×D19111yescharacteristic
239#97C2×D19111yescharacteristic, complemented
240C4×C8C2×D19111yescharacteristic, complemented
241C24—3821no—
242C2×Q8—3821no—
243C2×Q8—1911no—
244C2×D4—3822no—
245C2×D4—3822no—
246C2×D4—3821no—
247C2×D4—3821no—
248C2×D4—1911no—
249C2×D4—1911no—
250C2×D4—1911no—
251C22×C4—3821no—
252C22×C4—3821no—
253C22×C4—3821no—
254C22×C4—3821no—
255C22×C4—3821no—
256C22×C4C22×D19111yescharacteristic
257SD16—3822no—
258SD16—3822no—
259D8—3822no—
260D8—3822no—
261C2×C8C22×D19111yescharacteristic
262C2×C8C22×D19111yescharacteristic
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⋊C4D76411yescharacteristic
273C4⋊C4D76411yescharacteristic
274C22⋊C4—3821no—
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⋊C4D76411yescharacteristic
285C22⋊C4D76411yescharacteristic
286C42—3821no—
287C42—3821no—
288C42C22×D19111yescharacteristic
289C42C22×D19111yescharacteristic
290C23—3824no—
291C23—3821no—
292C23—3821no—
293C23—3821no—
294C23—15281no—
295C23—15281no—
296C23C2×D76411yescharacteristic
297Q8—3821no—
298Q8—3821no—
299Q8—15281no—
300D4—3824no—
301D4—3821no—
302D4—3821no—
303D4—3821no—
304D4—3821no—
305D4—1912no—
306D4—1912no—
307D4—15281no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—3821no—
311C2×C4—3821no—
312C2×C4—3821no—
313C2×C4—3821no—
314C2×C4—3821no—
315C2×C4—15281no—
316C2×C4—15281no—
317C2×C4—15281no—
318C2×C4—15281no—
319C2×C4—15281no—
320C2×C4C2×D76411yescharacteristic
321C2×C4C2×D76411yescharacteristic
322C2×C4C2×D76411yescharacteristic
323C2×C4C2×D76411yescharacteristic
324C2×C4C2×D76411yescharacteristic
325C2×C4C23×D19111yescharacteristic
326C8—21no—
327C8—21no—
328C8—21no—
329C8—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—3822no—
334C22—3822no—
335C22—15284no—
336C22—7641no—
337C22—7641no—
338C22—7641no—
339C22—7641no—
340C22—7641no—
341C22—7641no—
342C22—7641no—
343C22C22×D76411yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—7641no—
350C4—7641no—
351C4—7641no—
352C4—7641no—
353C4—7641no—
354C4#41×D19111yescharacteristic
355C4#41×D19111yescharacteristic
356C2—41no—
357C2—15281no—
358C2—7642no—
359C2—7642no—
360C2#2713317511yescharacteristic
361C2#2713346811yescharacteristic
362C2#2713347511yescharacteristic
subgroupG/H
centerC22C22×D764
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#433×C191C2
socleC22×C191C22×D4
prime radical#27132799C2
hypercenter#433D191
hypocenterC191#3118
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #27133284C2semidirect
2. #27133137C2semidirect
3. #27133005C2semidirect
4. #27132988C2semidirect
5. #27132954C2semidirect
6. #27132944C2semidirect
7. #27132879C2semidirect
8. #27132879C2semidirect
9. #27132816C2semidirect
11. #27132776C2semidirect
12. #27132765C2semidirect
13. C4×#15690276C2semidirect
14. C4×D1528C2semidirect
15. #433×C191C2semidirect
21. #20259322C22semidirect
23. #20259310C22semidirect
29. C4×Dic382C22semidirect
34. C4×D764C22semidirect
40. #20259256C22semidirect
41. #20259256C22semidirect
42. #20259254C22semidirect
43. #20259254C22semidirect
44. #20259247C22semidirect
45. #20259247C22semidirect
50. #20259244C22semidirect
51. #20259244C22semidirect
53. C4⋊C8×C191C22semidirect
54. C4⋊C8×C191C22semidirect
57. #97×C191C22semidirect
58. C4×C8×C191C22semidirect
181. C191#3118semidirect
197. #433D191semidirect
227. C4⋊C8C2×D191semidirect
228. C4⋊C8C2×D191semidirect
239. #97C2×D191semidirect
240. C4×C8C2×D191semidirect

Maximal subgroups

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

subgroupindex
#271332842
#271331372
#271330052
#271329882
#271329542
#271329442
#271328792
#271328162
#271327992
#271327762
#271327652
C4×#156902762
C4×D15282
#433×C1912
#3118191