Finite Group Databasebeta

← #37582064

Subgroups — #37582064

Order 24448.

504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#20259348C211yesmaximal, characteristic, complemented
2C2×#20259344C211yesmaximal, characteristic, complemented
3#27133230C211yesmaximal, characteristic, complemented
4#27133144C211yesmaximal, characteristic, complemented
5#27132884C212yesmaximal, complemented
6#27132877C212yesmaximal, complemented
7#27132862C212yesmaximal, complemented
8#27132857C212yesmaximal, complemented
9#27132689C211yesmaximal, characteristic, complemented
10#27132662C211yesmaximal, characteristic, complemented
11C2×#102×C191C211yesmaximal, characteristic, complemented
12C2×#15690287C2211yescharacteristic
13C2×#15690287C2211yescharacteristic
14#20259348—24no—
15#20259344—24no—
16C2×Dic764C2211yescharacteristic, complemented
17C2×#15690276C2211yescharacteristic, complemented
18C2×#15690276C2211yescharacteristic, complemented
19C2×#15690275C2212yes—
20C2×D1528C2211yescharacteristic, complemented
21C2×#15690272C2212yes—
22C2×#15690271C2211yescharacteristic
23#20259318C2212yes—
24#20259309C2212yes—
25#20259293—21no—
26#20259293—21no—
27#20259291—22no—
28#20259287C2212yescomplemented
29#20259284C2212yescomplemented
30C4×C22⋊D191—22no—
31#20259281C2211yescharacteristic
32#20259280—21no—
33C4⋊C4×D191—21no—
34Dic191⋊C8C2212yescomplemented
35Dic191⋊C8C2212yescomplemented
36#20259245C2212yescomplemented
37#20259242C2212yescomplemented
38C22×D4×C191C2211yescharacteristic
39C22×C8×C191C2211yescharacteristic
40C2×C4⋊C4×C191C2211yescharacteristic
41#102×C191C2212yes—
42#102×C191C2212yes—
43#15690287—22no—
44#15690287—22no—
45#15690287—22no—
46#15690287D414yescomplemented
47C2×Dic382C2311yescharacteristic
48C2×Dic382C2311yescharacteristic
49C2×D764C2311yescharacteristic
50C2×D764C2311yescharacteristic
51C2×C22⋊D191—22no—
52C2×C22⋊D191—22no—
53C2×C22⋊D191—21no—
54C2×C22⋊D191—21no—
55C2×C4×D191—22no—
56C2×C4×D191—21no—
57C2×C4×D191—21no—
58Dic764—22no—
59#15690276—22no—
60#15690276—22no—
61#15690275—24no—
62D1528—22no—
63#15690272—24no—
64#15690271—22no—
65C2×C191⋊C8C2312yes—
66C4⋊Dic191D411yescharacteristic
67C4⋊Dic191D411yescharacteristic
68Dic191⋊C4—22no—
69C22⋊Dic191—22no—
70C22⋊Dic191—22no—
71C22⋊Dic191D412yes—
72(C2×D191)⋊C4—22no—
73C4×Dic191—22no—
74C4×Dic191C2312yes—
75C24×C191—21no—
76C2×D4×C191—22no—
77C2×D4×C191—21no—
78C2×D4×C191—22no—
79C2×D4×C191C2312yes—
80C22×C4×C191—21no—
81C22×C4×C191C2311yescharacteristic
82C2×C8×C191—22no—
83C2×C8×C191C2311yescharacteristic
84C2×C8×C191C2311yescharacteristic
85C4⋊C4×C191—21no—
86C4⋊C4×C191C2312yes—
87C22×D191—21no—
88C22×D191—21no—
89Dic382—21no—
90Dic382—21no—
91Dic382—21no—
92Dic382C2×D412yes—
93D764—21no—
94D764—21no—
95D764—21no—
96D764C2×D412yes—
97C22⋊D191—24no—
98C22⋊D191—42no—
99C22⋊D191—82no—
100C22⋊D191—82no—
101C2×Dic191—21no—
102C2×Dic191—21no—
103C2×Dic191C2×D412yes—
104C2×Dic191C2×D412yes—
105C4×D191—24no—
106C4×D191—42no—
107C4×D191—82no—
108C191⋊C8—22no—
109C23×C191—22no—
110C23×C191—42no—
111C23×C191—81no—
112C23×C191—81no—
113C23×C191C2×D411yescharacteristic
114D4×C191—22no—
115D4×C191—22no—
116D4×C191—42no—
117C2×C4×C191—22no—
118C2×C4×C191—81no—
119C2×C4×C191C2×D411yescharacteristic
120C2×C4×C191C2×D412yes—
121C2×C4×C191#4112yes—
122C2×C4×C191C2411yescharacteristic
123C8×C191—21no—
124C8×C191—21no—
125C22×C191—21no—
126C22×C191—21no—
127C22×C191—42no—
128C22×C191—42no—
129C22×C191—42no—
130C22×C191—84no—
131C22×C191#12112yes—
132C22×C191C22×D411yescharacteristic
133C2×D191—22no—
134C2×D191—41no—
135C2×D191—41no—
136C2×D191—41no—
137C2×D191—41no—
138C2×D191—41no—
139C4×C191—42no—
140C4×C191#12112yes—
141C4×C191C22×D411yescharacteristic
142C4×C191C2×#4111yescharacteristic
143Dic191—22no—
144Dic191—22no—
145Dic191—22no—
146Dic191—41no—
147C2×C191—22no—
148C2×C191—82no—
149C2×C191C2×#12111yescharacteristic
150C2×C191#57611yescharacteristic
151C2×C191#57711yescharacteristic
152D191—42no—
153D191—81no—
154C191#304511yescharacteristic, complemented, Sylow
155#3045—1911nomaximal, Sylow
156C2×AGL(1,ℤ/8)—1911no—
157C2×#135—1911no—
158#535—1911no—
159#520—1911no—
160#464—1912no—
161#463—1912no—
162#460—1912no—
163#459—1912no—
164#424—1911no—
165#417—1911no—
166C2×#102D19111yescharacteristic, complemented
167C2×#41—1911no—
168C2×#41—1911no—
169C22×D4C2×D19111yescharacteristic
170AGL(1,ℤ/8)—3824no—
171#135—3824no—
172C2×Q16—1911no—
173C2×SD16—1912no—
174C2×SD16—1911no—
175C2×SD16—1911no—
176C2×D8—1912no—
177C2×D8—1911no—
178C2×M16—1911no—
179C22×C8C2×D19111yescharacteristic
180#127—1912no—
181#124—1912no—
182#121—3821no—
183#121—3821no—
184#120—3822no—
185C4×Q8—1912no—
186C4×D4—3822no—
187C4×D4—1912no—
188#117—3821no—
189#117—1911no—
190C2×C4⋊C4—3821no—
191C2×C4⋊C4C2×D19111yescharacteristic
192C4⋊C8—1912no—
193C4⋊C8—1912no—
194#103—1912no—
195#102—1912no—
196#102C2×D19112yes—
197#102C2×D19112yes—
198C24—21no—
199#41—3822no—
200#41—3822no—
201#41—3822no—
202#41—1914no—
203C2×Q8—1911no—
204C2×Q8—1911no—
205C2×D4—22no—
206C2×D4—21no—
207C2×D4—22no—
208C2×D4—3821no—
209C2×D4—3821no—
210C2×D4—3822no—
211C2×D4—3822no—
212C2×D4—1911no—
213C2×D4—1911no—
214C2×D4C22×D19112yes—
215C22×C4—21no—
216C22×C4—3822no—
217C22×C4—3821no—
218C22×C4—3821no—
219C22×C4C22×D19111yescharacteristic
220Q16—3822no—
221SD16—3822no—
222SD16—3822no—
223SD16—3824no—
224D8—3822no—
225D8—3824no—
226M16—3822no—
227C2×C8—22no—
228C2×C8—1912no—
229C2×C8C22×D19111yescharacteristic
230C2×C8C22×D19111yescharacteristic
231C4⋊C4—21no—
232C4⋊C4—3822no—
233C4⋊C4—1911no—
234C4⋊C4—1911no—
235C4⋊C4C22×D19112yes—
236C22⋊C4—3822no—
237C22⋊C4—3822no—
238C22⋊C4—3822no—
239C22⋊C4—1912no—
240C42—3822no—
241C42—1912no—
242C23—22no—
243C23—42no—
244C23—81no—
245C23—81no—
246C23—3821no—
247C23—3821no—
248C23D4×D19111yescharacteristic
249Q8—3821no—
250Q8—3821no—
251Q8—3821no—
252Q8—1912no—
253D4—22no—
254D4—22no—
255D4—42no—
256D4—3824no—
257D4—3821no—
258D4—3821no—
259D4—3821no—
260D4—1912no—
261D4—15282no—
262D4—15282no—
263D4—7642no—
264C2×C4—22no—
265C2×C4—81no—
266C2×C4—3821no—
267C2×C4—3824no—
268C2×C4—3821no—
269C2×C4—1912no—
270C2×C4—1912no—
271C2×C4—15282no—
272C2×C4—7642no—
273C2×C4D4×D19112yes—
274C2×C4D4×D19111yescharacteristic
275C2×C4#1569028712yes—
276C2×C4C23×D19111yescharacteristic
277C8—21no—
278C8—21no—
279C8—3822no—
280C22—21no—
281C22—21no—
282C22—42no—
283C22—42no—
284C22—42no—
285C22—84no—
286C22—3822no—
287C22—7641no—
288C22—7641no—
289C22—7641no—
290C22—7641no—
291C22—7641no—
292C22#2025929512yes—
293C22C2×D4×D19111yescharacteristic
294C4—42no—
295C4—3822no—
296C4—3822no—
297C4—3822no—
298C4—7641no—
299C4#2025929512yes—
300C4C2×D4×D19111yescharacteristic
301C4C2×#1569028711yescharacteristic
302C2—22no—
303C2—82no—
304C2—15281no—
305C2—7642no—
306C2C2×#2025929511yescharacteristic
307C2#2713346411yescharacteristic
308C2#2713346911yescharacteristic
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
FittingC2×#102×C191C2
socleC22×C191C22×D4
hypercenterC2×#102D191
hypocenterC191#3045
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. C2×#20259348C2semidirect
2. C2×#20259344C2semidirect
3. #27133230C2semidirect
4. #27133144C2semidirect
5. #27132884C2semidirect
6. #27132877C2semidirect
7. #27132862C2semidirect
8. #27132857C2semidirect
9. #27132689C2semidirect
10. #27132662C2semidirect
11. C2×#102×C191C2semidirect
16. C2×Dic764C22semidirect
17. C2×#15690276C22semidirect
18. C2×#15690276C22semidirect
20. C2×D1528C22semidirect
28. #20259287C22semidirect
29. #20259284C22semidirect
34. Dic191⋊C8C22semidirect
35. Dic191⋊C8C22semidirect
36. #20259245C22semidirect
37. #20259242C22semidirect
46. #15690287D4semidirect
154. C191#3045semidirect
166. C2×#102D191semidirect

Maximal subgroups

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

subgroupindex
C2×#202593482
C2×#202593442
#271332302
#271331442
#271328842
#271328772
#271328622
#271328572
#271326892
#271326622
C2×#102×C1912
#3045191