Finite Group Databasebeta

← #37582760

Subgroups — #37582760

Order 24448.

418 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#27133264C211yesmaximal, characteristic, complemented
2#27133135C211yesmaximal, characteristic, complemented
3#27132990C211yesmaximal, characteristic, complemented
4#27132985C211yesmaximal, characteristic, complemented
5#27132966C211yesmaximal, characteristic, complemented
6#27132961C211yesmaximal, characteristic, complemented
7#27132857C211yesmaximal, characteristic, complemented
8#27132856C211yesmaximal, characteristic, complemented
9#27132798C211yesmaximal, characteristic, complemented
10#27132795C211yesmaximal, characteristic, complemented
11#27132773C211yesmaximal, characteristic, complemented
12#27132773C211yesmaximal, characteristic, complemented
13C4×D1528C211yesmaximal, characteristic, complemented
14#27132722C211yesmaximal, characteristic, complemented
15C4×D8×C191C211yesmaximal, characteristic, complemented
16C2×D4×D191C2211yescharacteristic
17C2×D1528C2211yescharacteristic
18C2×#15690272C2211yescharacteristic
19C2×#15690272C2211yescharacteristic
20#20259318C2211yescharacteristic, complemented
21#20259313C2211yescharacteristic, complemented
22#20259305—21no—
23#20259304—21no—
24#20259297C2211yescharacteristic
25#20259296—21no—
26#20259295—21no—
27#20259293C2211yescharacteristic
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#20259256C2211yescharacteristic, complemented
39#20259253C2211yescharacteristic, complemented
40#20259253C2211yescharacteristic, complemented
41Dic191⋊C8C2211yescharacteristic, complemented
42Dic191⋊C8C2211yescharacteristic, complemented
43#20259244C2211yescharacteristic
44#20259244C2211yescharacteristic, complemented
45#20259243C2211yescharacteristic
46#20259243C2211yescharacteristic, complemented
47#20259242C2211yescharacteristic
48#20259242C2211yescharacteristic, complemented
49(C2×D191)⋊C8C2211yescharacteristic
50(C2×D191)⋊C8C2211yescharacteristic
51#20259233C2211yescharacteristic, complemented
52C2×D8×C191C2211yescharacteristic
53C4×D4×C191C2211yescharacteristic
54C4×D4×C191C2211yescharacteristic, complemented
55#107×C191C2211yescharacteristic, complemented
56#102×C191C2211yescharacteristic
57#102×C191C2211yescharacteristic, complemented
58C4×C8×C191C2211yescharacteristic, complemented
59C23×D191—21no—
60C2×D764—21no—
61C2×D764C2311yescharacteristic
62C2×D764C2311yescharacteristic
63C2×C22⋊D191—21no—
64C2×C22⋊D191—21no—
65C2×C22⋊D191—21no—
66C2×C22⋊D191—21no—
67D4×D191—22no—
68D4×D191—22no—
69C22×Dic191—21no—
70C2×C4×D191—21no—
71C2×C4×D191—21no—
72C2×C4×D191—21no—
73C2×C4×D191C2311yescharacteristic
74D1528—22no—
75#15690272—22no—
76#15690272—22no—
77C2×C191⋊C8C2311yescharacteristic
78C2×C191⋊C8C2311yescharacteristic
79C4⋊Dic191—21no—
80C4⋊Dic191C2311yescharacteristic
81C4⋊Dic191C2311yescharacteristic
82Dic191⋊C4—21no—
83Dic191⋊C4D411yescharacteristic
84Dic191⋊C4D411yescharacteristic
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)⋊C4D411yescharacteristic
93(C2×D191)⋊C4D411yescharacteristic
94C4×Dic191—21no—
95C4×Dic191C2311yescharacteristic
96C2×D4×C191C2311yescharacteristic
97C2×D4×C191C2311yescharacteristic
98C22×C4×C191—21no—
99C22×C4×C191—21no—
100D8×C191—22no—
101C2×C8×C191C2311yescharacteristic
102C2×C8×C191C2311yescharacteristic
103C4⋊C4×C191C2311yescharacteristic
104C4⋊C4×C191C2311yescharacteristic
105C22⋊C4×C191—21no—
106C22⋊C4×C191—21no—
107C42×C191C2311yescharacteristic
108C22×D191—21no—
109C22×D191—24no—
110C22×D191—21no—
111C22×D191—81no—
112C22×D191—81no—
113C22×D191C2×D411yescharacteristic
114D764—21no—
115D764—21no—
116D764—21no—
117D764—81no—
118D764#4112yes—
119C22⋊D191—24no—
120C22⋊D191—81no—
121C22⋊D191—81no—
122C22⋊D191—81no—
123C2×Dic191—21no—
124C2×Dic191—21no—
125C2×Dic191—81no—
126C2×Dic191C2×D411yescharacteristic
127C2×Dic191C2×D411yescharacteristic
128C2×Dic191C2×D411yescharacteristic
129C4×D191—21no—
130C4×D191—21no—
131C4×D191—81no—
132C4×D191—81no—
133C4×D191—81no—
134C191⋊C8—21no—
135C191⋊C8—21no—
136C23×C191—21no—
137C23×C191—21no—
138D4×C191—21no—
139D4×C191—21no—
140D4×C191—21no—
141D4×C191#4112yes—
142C2×C4×C191—21no—
143C2×C4×C191—21no—
144C2×C4×C191—81no—
145C2×C4×C191—81no—
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—22no—
160C2×D191—21no—
161C2×D191—21no—
162C2×D191—41no—
163C2×D191—41no—
164C2×D191—41no—
165C2×D191—41no—
166C2×D191—41no—
167C2×D191—84no—
168C4×C191—21no—
169C4×C191—21no—
170C4×C191—41no—
171C4×C191—41no—
172C4×C191C2×#4111yescharacteristic
173C4×C191C2×#4111yescharacteristic
174Dic191—21no—
175Dic191—21no—
176Dic191—21no—
177Dic191—41no—
178Dic191—41no—
179C2×C191—42no—
180C2×C191—81no—
181C2×C191#52511yescharacteristic
182C2×C191#57611yescharacteristic
183C2×C191#57611yescharacteristic
184D191—41no—
185D191—42no—
186D191—81no—
187C191#312211yescharacteristic, complemented, Sylow
188#3122—1911nomaximal, Sylow
189#540—1911no—
190#518—1911no—
191#482—1911no—
192#482—1911no—
193#478—1911no—
194#478—1911no—
195#459—1911no—
196#459—1911no—
197#447—1911no—
198#447—1911no—
199#442—1911no—
200#442—1911no—
201C4×D8—1911no—
202C4×D8D19111yescharacteristic, complemented
203#433—1911no—
204C22×D4—1911no—
205C2×D8—1911no—
206C2×D8—1911no—
207C2×D8—1911no—
208C2×D8C2×D19111yescharacteristic
209#127—1911no—
210#125—1911no—
211#123—3821no—
212#123—3821no—
213#121—3821no—
214#121—3821no—
215#121—1911no—
216#121—1911no—
217C4×D4—3821no—
218C4×D4—3821no—
219C4×D4—1911no—
220C4×D4—1911no—
221C4×D4—1911no—
222C4×D4—1911no—
223C4×D4C2×D19111yescharacteristic
224C4×D4C2×D19111yescharacteristic, complemented
225#117—1911no—
226#117—1911no—
227C2×C22⋊C4—3821no—
228C2×C22⋊C4—3821no—
229#107—1911no—
230#107C2×D19111yescharacteristic, complemented
231#106—1911no—
232#106—1911no—
233C4⋊C8—1911no—
234C4⋊C8—1911no—
235#102—1911no—
236#102—1911no—
237#102—1911no—
238#102—1911no—
239#102—1911no—
240#102—1911no—
241#102C2×D19111yescharacteristic
242#102C2×D19111yescharacteristic, complemented
243C22⋊C8—1911no—
244C22⋊C8—1911no—
245#97—1911no—
246C4×C8C2×D19111yescharacteristic, complemented
247C24—3821no—
248C2×D4—3821no—
249C2×D4—3822no—
250C2×D4—3822no—
251C2×D4—3821no—
252C2×D4—3821no—
253C2×D4—3821no—
254C2×D4—3821no—
255C2×D4—1911no—
256C2×D4—1911no—
257C2×D4C22×D19111yescharacteristic
258C2×D4C22×D19111yescharacteristic
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—3821no—
262C22×C4—3821no—
263C22×C4—3821no—
264C22×C4—3821no—
265C22×C4—1911no—
266D8—22no—
267D8—3822no—
268D8—3822no—
269D8—3822no—
270C2×C8—1911no—
271C2×C8—1911no—
272C2×C8C22×D19111yescharacteristic
273C2×C8C22×D19111yescharacteristic
274C4⋊C4—3821no—
275C4⋊C4—3821no—
276C4⋊C4—1911no—
277C4⋊C4—1911no—
278C4⋊C4—1911no—
279C4⋊C4—1911no—
280C4⋊C4C22×D19111yescharacteristic
281C4⋊C4C22×D19111yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—3821no—
285C22⋊C4—3821no—
286C22⋊C4—3821no—
287C22⋊C4—3821no—
288C22⋊C4—3821no—
289C22⋊C4—3821no—
290C22⋊C4—3821no—
291C22⋊C4—1911no—
292C22⋊C4—1911no—
293C42—3821no—
294C42—1911no—
295C42C22×D19111yescharacteristic
296C23—21no—
297C23—21no—
298C23—3824no—
299C23—3821no—
300C23—3821no—
301C23—1911no—
302C23—15281no—
303C23—15281no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—3824no—
308D4—3821no—
309D4—3821no—
310D4—3821no—
311D4—1912no—
312D4—15281no—
313D4—15281no—
314D4—15281no—
315D4—15281no—
316D4#1569028712yes—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—3821no—
322C2×C4—3821no—
323C2×C4—3821no—
324C2×C4—3821no—
325C2×C4—1911no—
326C2×C4—1911no—
327C2×C4—1911no—
328C2×C4—15281no—
329C2×C4—15281no—
330C2×C4—15281no—
331C2×C4—15281no—
332C2×C4D4×D19111yescharacteristic
333C2×C4D4×D19111yescharacteristic
334C2×C4C23×D19111yescharacteristic
335C8—21no—
336C8—21no—
337C8—3821no—
338C8—3821no—
339C22—22no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—3821no—
346C22—3821no—
347C22—3821no—
348C22—3822no—
349C22—15284no—
350C22—7641no—
351C22—7641no—
352C22—7641no—
353C22—7641no—
354C22—7641no—
355C22C2×D4×D19111yescharacteristic
356C4—21no—
357C4—21no—
358C4—41no—
359C4—41no—
360C4—3821no—
361C4—3821no—
362C4—3821no—
363C4—7641no—
364C4—7641no—
365C4#41×D19111yescharacteristic
366C4C2×#1569028711yescharacteristic
367C2—42no—
368C2—81no—
369C2—15281no—
370C2—7641no—
371C2—7642no—
372C2#2713317211yescharacteristic
373C2#2713346411yescharacteristic
374C2#2713346511yescharacteristic
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
FittingC4×D8×C191C2
socleC22×C191C22×D4
hypercenterC4×D8D191
hypocenterC191#3122
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #27133264C2semidirect
2. #27133135C2semidirect
3. #27132990C2semidirect
4. #27132985C2semidirect
5. #27132966C2semidirect
6. #27132961C2semidirect
7. #27132857C2semidirect
8. #27132856C2semidirect
9. #27132798C2semidirect
10. #27132795C2semidirect
11. #27132773C2semidirect
12. #27132773C2semidirect
13. C4×D1528C2semidirect
14. #27132722C2semidirect
15. C4×D8×C191C2semidirect
20. #20259318C22semidirect
21. #20259313C22semidirect
29. C4×D764C22semidirect
38. #20259256C22semidirect
39. #20259253C22semidirect
40. #20259253C22semidirect
41. Dic191⋊C8C22semidirect
42. Dic191⋊C8C22semidirect
44. #20259244C22semidirect
46. #20259243C22semidirect
48. #20259242C22semidirect
51. #20259233C22semidirect
54. C4×D4×C191C22semidirect
55. #107×C191C22semidirect
57. #102×C191C22semidirect
58. C4×C8×C191C22semidirect
187. C191#3122semidirect
202. C4×D8D191semidirect
224. C4×D4C2×D191semidirect
230. #107C2×D191semidirect
242. #102C2×D191semidirect
246. C4×C8C2×D191semidirect

Maximal subgroups

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

subgroupindex
#271332642
#271331352
#271329902
#271329852
#271329662
#271329612
#271328572
#271328562
#271327982
#271327952
#271327732
C4×D15282
#271327222
C4×D8×C1912
#3122191