Finite Group Databasebeta

← #37583957

Subgroups — #37583957

Order 24448.

370 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#27133267C211yesmaximal, characteristic, complemented
2#27133264C211yesmaximal, characteristic, complemented
3#27132965C211yesmaximal, characteristic, complemented
4#27132964C211yesmaximal, characteristic, complemented
5#27132963C211yesmaximal, characteristic, complemented
6#27132961C211yesmaximal, characteristic, complemented
7#27132915C211yesmaximal, characteristic, complemented
8#27132913C211yesmaximal, characteristic, complemented
9#27132898C211yesmaximal, characteristic, complemented
10#27132896C211yesmaximal, characteristic, complemented
11#27132856C211yesmaximal, characteristic, complemented
12#27132856C211yesmaximal, characteristic, complemented
13#27132855C211yesmaximal, characteristic, complemented
14#27132688C211yesmaximal, characteristic, complemented
15#459×C191C211yesmaximal, characteristic, complemented
16C2×#15690272C2211yescharacteristic
17C2×#15690272C2211yescharacteristic
18C2×#15690270C2211yescharacteristic
19C2×C8×D191C2211yescharacteristic
20#20259318C2211yescharacteristic
21#20259314C2211yescharacteristic
22#20259313C2211yescharacteristic
23#20259305—21no—
24#20259304—21no—
25#20259303—21no—
26#20259303—21no—
27#20259297C2211yescharacteristic
28#20259296—21no—
29#20259295—21no—
30#20259294—21no—
31#20259294—21no—
32#20259293C2211yescharacteristic
33#20259293C2211yescharacteristic
34#20259293C2211yescharacteristic
35C4×D764C2211yescharacteristic
36D4×Dic191C2211yescharacteristic
37D4×Dic191C2211yescharacteristic
38#20259279C2211yescharacteristic
39#20259256C2211yescharacteristic
40#20259255C2211yescharacteristic
41#20259254C2211yescharacteristic
42#20259253C2211yescharacteristic
43C4⋊(C191⋊C8)C2211yescharacteristic
44Dic191⋊C8C2211yescharacteristic
45Dic191⋊C8C2211yescharacteristic
46#20259244C2211yescharacteristic
47#20259244C2211yescharacteristic
48#20259243C2211yescharacteristic
49#20259243C2211yescharacteristic
50#20259243C2211yescharacteristic
51#20259243C2211yescharacteristic
52C2×D8×C191C2211yescharacteristic
53C2×D8×C191C2211yescharacteristic
54#127×C191C2211yescharacteristic
55C4×D4×C191C2211yescharacteristic
56C4⋊C8×C191C2211yescharacteristic
57#102×C191C2211yescharacteristic
58#102×C191C2211yescharacteristic
59C2×D764—21no—
60C2×D764C2311yescharacteristic
61C2×C22⋊D191—21no—
62C2×C22⋊D191—21no—
63C2×C22⋊D191—21no—
64C2×C22⋊D191—21no—
65C2×C22⋊D191—21no—
66C22×Dic191—21no—
67C22×Dic191—21no—
68C2×C4×D191—21no—
69C2×C4×D191C2311yescharacteristic
70#15690272—41no—
71#15690272—41no—
72#15690270—41no—
73C2×C191⋊C8C2311yescharacteristic
74C2×C191⋊C8C2311yescharacteristic
75C8×D191—41no—
76C4⋊Dic191—21no—
77C4⋊Dic191C2311yescharacteristic
78C4⋊Dic191C2311yescharacteristic
79C4⋊Dic191C2311yescharacteristic
80Dic191⋊C4—21no—
81Dic191⋊C4—21no—
82Dic191⋊C4—21no—
83Dic191⋊C4D411yescharacteristic
84Dic191⋊C4D411yescharacteristic
85C22⋊Dic191—21no—
86C22⋊Dic191—21no—
87C22⋊Dic191—21no—
88C22⋊Dic191—21no—
89C22⋊Dic191—21no—
90(C2×D191)⋊C4—21no—
91(C2×D191)⋊C4—21no—
92(C2×D191)⋊C4D411yescharacteristic
93(C2×D191)⋊C4D411yescharacteristic
94C4×Dic191C2311yescharacteristic
95C2×D4×C191—21no—
96C2×D4×C191—21no—
97C2×D4×C191C2311yescharacteristic
98C2×D4×C191C2311yescharacteristic
99C2×D4×C191C2311yescharacteristic
100C22×C4×C191—21no—
101D8×C191—41no—
102D8×C191—41no—
103C2×C8×C191C2311yescharacteristic
104C2×C8×C191C2311yescharacteristic
105C4⋊C4×C191C2311yescharacteristic
106C22⋊C4×C191—21no—
107C42×C191C2311yescharacteristic
108C22×D191—21no—
109C22×D191C2×D411yescharacteristic
110D764—21no—
111D764—21no—
112D764—81no—
113C22⋊D191—81no—
114C22⋊D191—81no—
115C22⋊D191—81no—
116C22⋊D191—81no—
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—
129C191⋊C8—21no—
130C191⋊C8—21no—
131C23×C191—21no—
132C23×C191—21no—
133C23×C191—21no—
134D4×C191—21no—
135D4×C191—21no—
136D4×C191—21no—
137D4×C191—21no—
138D4×C191—21no—
139D4×C191—21no—
140D4×C191—81no—
141D4×C191—81no—
142C2×C4×C191—21no—
143C2×C4×C191—81no—
144C2×C4×C191C2×D411yescharacteristic
145C2×C4×C191C2×D411yescharacteristic
146C2×C4×C191C2411yescharacteristic
147C8×C191—21no—
148C8×C191—21no—
149C22×C191—41no—
150C22×C191—41no—
151C22×C191—41no—
152C22×C191—41no—
153C22×C191—41no—
154C22×C191—41no—
155C22×C191—41no—
156C22×C191—41no—
157C22×C191—41no—
158C22×C191C22×D411yescharacteristic
159C2×D191—21no—
160C2×D191—21no—
161C2×D191—21no—
162C2×D191—41no—
163C2×D191—41no—
164C2×D191—41no—
165C4×C191—21no—
166C4×C191—21no—
167C4×C191—41no—
168C4×C191H(5,𝔽2)11yescharacteristic
169C4×C1912−1+411yescharacteristic
170Dic191—21no—
171Dic191—21no—
172Dic191—21no—
173Dic191—41no—
174Dic191—41no—
175Dic191—41no—
176C2×C191—81no—
177C2×C191—81no—
178C2×C191—81no—
179C2×C191#53711yescharacteristic
180C2×C191#57611yescharacteristic
181C2×C191#57611yescharacteristic
182D191—41no—
183D191—81no—
184C191#325911yescharacteristic, complemented, Sylow
185#3259—1911nomaximal, Sylow
186#540—1911no—
187#540—1911no—
188#478—1911no—
189#478—1911no—
190#478—1911no—
191#478—1911no—
192#469—1911no—
193#469—1911no—
194#466—1911no—
195#466—1911no—
196#459—1911no—
197#459—1911no—
198#459—1911no—
199#459D19111yescharacteristic, complemented
200#424—1911no—
201C2×D8—1911no—
202C2×D8—1911no—
203C2×D8C2×D19111yescharacteristic
204C2×D8C2×D19111yescharacteristic
205C2×M16—1911no—
206C22×C8—1911no—
207#127—1911no—
208#127C2×D19111yescharacteristic
209#125—1911no—
210#125—1911no—
211#123—3821no—
212#123—3821no—
213#123—3821no—
214#123—3821no—
215#121—3821no—
216#121—3821no—
217#121—3821no—
218#121—3821no—
219#121—1911no—
220#121—1911no—
221#121—1911no—
222#121—1911no—
223C4×D4—1911no—
224C4×D4—1911no—
225C4×D4—1911no—
226C4×D4C2×D19111yescharacteristic
227#117—1911no—
228#107—1911no—
229#107—1911no—
230#106—1911no—
231#106—1911no—
232C4⋊C8—1911no—
233C4⋊C8—1911no—
234C4⋊C8—1911no—
235C4⋊C8C2×D19111yescharacteristic
236#102—1911no—
237#102—1911no—
238#102—1911no—
239#102—1911no—
240#102—1911no—
241#102—1911no—
242#102C2×D19111yescharacteristic
243#102C2×D19111yescharacteristic
244C2×D4—21no—
245C2×D4—21no—
246C2×D4—3821no—
247C2×D4—3821no—
248C2×D4—3821no—
249C2×D4—3821no—
250C2×D4—3821no—
251C2×D4—3821no—
252C2×D4—1911no—
253C2×D4C22×D19111yescharacteristic
254C2×D4C22×D19111yescharacteristic
255C2×D4C22×D19111yescharacteristic
256C22×C4—21no—
257C22×C4—3821no—
258C22×C4—3821no—
259C22×C4—3821no—
260C22×C4—1911no—
261D8—41no—
262D8—41no—
263D8—7641no—
264D8—7641no—
265M16—7641no—
266C2×C8—1911no—
267C2×C8—1911no—
268C2×C8—7641no—
269C2×C8C22×D19111yescharacteristic
270C2×C8C22×D19111yescharacteristic
271C4⋊C4—3821no—
272C4⋊C4—3821no—
273C4⋊C4—3821no—
274C4⋊C4—3821no—
275C4⋊C4—1911no—
276C4⋊C4—1911no—
277C4⋊C4—1911no—
278C4⋊C4—1911no—
279C4⋊C4—1911no—
280C4⋊C4C22×D19111yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—3821no—
283C22⋊C4—3821no—
284C22⋊C4—3821no—
285C22⋊C4—3821no—
286C22⋊C4—3821no—
287C22⋊C4—3821no—
288C22⋊C4—3821no—
289C22⋊C4—1911no—
290C22⋊C4—1911no—
291C42—1911no—
292C42C22×D19111yescharacteristic
293C23—21no—
294C23—21no—
295C23—21no—
296C23—3821no—
297C23—1911no—
298D4—21no—
299D4—21no—
300D4—21no—
301D4—21no—
302D4—21no—
303D4—21no—
304D4—81no—
305D4—81no—
306D4—3821no—
307D4—3821no—
308D4—15281no—
309D4—15281no—
310D4—15281no—
311D4—15281no—
312D4—15281no—
313D4—15281no—
314C2×C4—21no—
315C2×C4—81no—
316C2×C4—3821no—
317C2×C4—3821no—
318C2×C4—3821no—
319C2×C4—3821no—
320C2×C4—3821no—
321C2×C4—1911no—
322C2×C4—1911no—
323C2×C4—1911no—
324C2×C4—15281no—
325C2×C4—15281no—
326C2×C4—15281no—
327C2×C4D4×D19111yescharacteristic
328C2×C4D4×D19111yescharacteristic
329C2×C4C23×D19111yescharacteristic
330C8—21no—
331C8—21no—
332C8—3821no—
333C8—3821no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—3821no—
344C22—3821no—
345C22—3821no—
346C22—7641no—
347C22—7641no—
348C22—7641no—
349C22C2×D4×D19111yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—3821no—
354C4—3821no—
355C4—3821no—
356C4—7641no—
357C4—7641no—
358C4—7641no—
359C4#2025936711yescharacteristic
360C4#2025936911yescharacteristic
361C2—81no—
362C2—81no—
363C2—81no—
364C2—15281no—
365C2—7641no—
366C2#2713324211yescharacteristic
367C2#2713346411yescharacteristic
368C2#2713346711yescharacteristic
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#459×C191C2
socleC22×C191C22×D4
hypercenter#459D191
hypocenterC191#3259
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #27133267C2semidirect
2. #27133264C2semidirect
3. #27132965C2semidirect
4. #27132964C2semidirect
5. #27132963C2semidirect
6. #27132961C2semidirect
7. #27132915C2semidirect
8. #27132913C2semidirect
9. #27132898C2semidirect
10. #27132896C2semidirect
11. #27132856C2semidirect
12. #27132856C2semidirect
13. #27132855C2semidirect
14. #27132688C2semidirect
15. #459×C191C2semidirect
184. C191#3259semidirect
199. #459D191semidirect

Maximal subgroups

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

subgroupindex
#271332672
#271332642
#271329652
#271329642
#271329632
#271329612
#271329152
#271329132
#271328982
#271328962
#271328562
#271328552
#271326882
#459×C1912
#3259191