Finite Group Databasebeta

← #34055628

Subgroups — #34055628

Order 19072.

488 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 125 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
1#23750180C211yesmaximal, characteristic, complemented
2#127×D149C211yesmaximal, characteristic
3#23749999C211yesmaximal, characteristic, complemented
4#23749972C211yesmaximal, characteristic, complemented
5#23749971C211yesmaximal, characteristic, complemented
6#23749823C214yesmaximal, complemented
7#23749774C214yesmaximal, complemented
8#23749676C211yesmaximal, characteristic, complemented
9#492×C149C211yesmaximal, characteristic, complemented
10C2×D4×D149—21no—
11C2×D4×D149—21no—
12C2×D4×D149C2212yes—
13C2×#14558723C2214yescomplemented
14#18011911C2211yescharacteristic, complemented
15#18011908C2211yescharacteristic
16#18011907—21no—
17#18011907—21no—
18#18011907C2212yes—
19#18011902—21no—
20#18011891—21no—
21#18011887C2212yes—
22Q8×Dic149C2212yescomplemented
23#18011876—21no—
24#18011869—21no—
25C42×D149C2211yescharacteristic
26#18011840C2212yescomplemented
27#18011833C2214yescomplemented
28#18011832C2214yescomplemented
29#18011823C2212yes—
30C4×#11924746C2211yescharacteristic, complemented
31C2×SD16×C149C2214yescomplemented
32C4⋊Q8×C149C2211yescharacteristic, complemented
33#127×C149C2211yescharacteristic
34C4×C8×C149C2211yescharacteristic, complemented
35C23×D149—22no—
36C2×Dic298—21no—
37C2×D596—21no—
38C2×D596—21no—
39C2×D596C2312yes—
40C2×C22⋊D149—22no—
41C2×C22⋊D149—22no—
42C2×C22⋊D149—22no—
43D4×D149—44no—
44D4×D149—44no—
45D4×D149—44no—
46C2×C4×D149D411yescharacteristic
47C2×C4×D149D411yescharacteristic
48C2×C4×D149C2311yescharacteristic
49#14558723—44no—
50C2×#11924746C2312yes—
51C4⋊Dic149—22no—
52C4⋊Dic149—21no—
53C4⋊Dic149C2312yes—
54#14558715—22no—
55#14558713—22no—
56C4×Dic149—22no—
57C4×Dic149D411yescharacteristic
58C4×Dic149D411yescharacteristic
59C4×Dic149C2311yescharacteristic
60C2×Q8×C149C2312yes—
61C2×D4×C149—21no—
62C2×D4×C149—21no—
63C2×D4×C149C2312yes—
64SD16×C149—44no—
65C2×C8×C149C2312yes—
66C4⋊C4×C149—21no—
67C4⋊C4×C149—21no—
68C42×C149C2311yescharacteristic
69C22×D149—22no—
70C22×D149—44no—
71C22×D149—44no—
72C22×D149—44no—
73C22×D149C2×D411yescharacteristic
74Dic298—42no—
75D596—24no—
76D596—42no—
77D596—42no—
78C22⋊D149—44no—
79C22⋊D149—44no—
80C22⋊D149—44no—
81C2×Dic149—22no—
82C2×Dic149C2×D411yescharacteristic
83C2×Dic149C2×D411yescharacteristic
84C2×Dic149C2×D411yescharacteristic
85C4×D149—22no—
86C4×D149—22no—
87C4×D149SD1614yescomplemented
88#11924746—22no—
89C23×C149—22no—
90Q8×C149—24no—
91D4×C149—24no—
92D4×C149—42no—
93D4×C149—42no—
94C2×C4×C149—22no—
95C2×C4×C149C2×D411yescharacteristic
96C2×C4×C149C2×D411yescharacteristic
97C2×C4×C149C2411yescharacteristic
98C8×C149—22no—
99C22×C149—42no—
100C22×C149—42no—
101C22×C149—42no—
102C22×C149C22×D411yescharacteristic
103C2×D149—21no—
104C2×D149—21no—
105C2×D149—42no—
106C2×D149—42no—
107C2×D149—42no—
108C2×D149—88no—
109C2×D149C2×SD1612yes—
110C4×C149—42no—
111C4×C149C2×SD1612yes—
112C4×C149AGL(1,ℤ/8)12yes—
113C4×C149H(5,𝔽2)12yes—
114Dic149—21no—
115Dic149—21no—
116Dic149—42no—
117Dic149C2×SD1612yes—
118C2×C149—82no—
119C2×C149#53511yescharacteristic
120C2×C149C22×SD1611yescharacteristic
121C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
122D149—22no—
123D149—82no—
124C149#320811yescharacteristic, complemented, Sylow
125#3208—1491nomaximal, Sylow
126#533—1491no—
127C2×#127—1491no—
128#492—1491no—
129#492D14911yescharacteristic, complemented
130#486—1491no—
131#486—1491no—
132#460—1494no—
133#450—1494no—
134#431—1491no—
135C22×D4—2981no—
136C22×D4—2981no—
137C22×D4—1492no—
138C2×SD16—1494no—
139C2×SD16C2×D14914yescomplemented
140C4⋊Q8—1491no—
141C4⋊Q8C2×D14911yescharacteristic, complemented
142#127—2981no—
143#127—2981no—
144#127—1492no—
145#127—1491no—
146#127C2×D14911yescharacteristic
147#125—2981no—
148C22⋊Q8—2981no—
149C22⋊Q8—1492no—
150C4×Q8—2981no—
151C4×Q8—1492no—
152#117—2981no—
153C2×C42—1491no—
154C4⋊C8—1492no—
155#102—1494no—
156#102—1494no—
157C22⋊C8—1492no—
158C4×C8—1491no—
159C4×C8C2×D14911yescharacteristic, complemented
160C24—2982no—
161C2×Q8—2981no—
162C2×Q8C22×D14912yes—
163C2×D4—21no—
164C2×D4—21no—
165C2×D4—2982no—
166C2×D4—2982no—
167C2×D4—2982no—
168C2×D4—2981no—
169C2×D4—2981no—
170C2×D4—5964no—
171C2×D4—5964no—
172C2×D4—5964no—
173C2×D4—1492no—
174C2×D4C22×D14912yes—
175C22×C4—1491no—
176C22×C4—1491no—
177C22×C4—1491no—
178SD16—44no—
179SD16—5964no—
180C2×C8—1492no—
181C2×C8C22×D14912yes—
182C4⋊C4—21no—
183C4⋊C4—21no—
184C4⋊C4—2982no—
185C4⋊C4—2982no—
186C4⋊C4—2981no—
187C4⋊C4—1492no—
188C22⋊C4—2982no—
189C42—2982no—
190C42—1491no—
191C42—1491no—
192C42—1491no—
193C42C22×D14911yescharacteristic
194C23—22no—
195C23—2982no—
196C23—5964no—
197C23—5964no—
198C23—5964no—
199C23—1491no—
200Q8—24no—
201Q8—5962no—
202D4—24no—
203D4—42no—
204D4—42no—
205D4—2984no—
206D4—5964no—
207D4—5964no—
208D4—5964no—
209D4—5962no—
210D4—5962no—
211C2×C4—22no—
212C2×C4—2982no—
213C2×C4—2982no—
214C2×C4—2982no—
215C2×C4—1491no—
216C2×C4—1491no—
217C2×C4—1491no—
218C2×C4—1494no—
219C2×C4D4×D14911yescharacteristic
220C2×C4D4×D14911yescharacteristic
221C2×C4C23×D14911yescharacteristic
222C8—22no—
223C8—2982no—
224C22—42no—
225C22—42no—
226C22—42no—
227C22—2981no—
228C22—2981no—
229C22—5962no—
230C22—5962no—
231C22—5962no—
232C22—1492no—
233C22—11928no—
234C22C2×D4×D14911yescharacteristic
235C4—42no—
236C4—2981no—
237C4—2981no—
238C4—5962no—
239C4—1492no—
240C4SD16×D14912yes—
241C4#1801193812yes—
242C4#1801195612yes—
243C2—82no—
244C2—2982no—
245C2—11922no—
246C2#2375018811yescharacteristic
247C2C2×SD16×D14911yescharacteristic
248C2C2×#1801193811yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#492×C149C2
socleC22×C149C22×D4
prime radical#127×D149C2
hypercenter#492D149
hypocenterC149#3208
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. #23750180C2semidirect
3. #23749999C2semidirect
4. #23749972C2semidirect
5. #23749971C2semidirect
6. #23749823C2semidirect
7. #23749774C2semidirect
8. #23749676C2semidirect
9. #492×C149C2semidirect
13. C2×#14558723C22semidirect
14. #18011911C22semidirect
22. Q8×Dic149C22semidirect
26. #18011840C22semidirect
27. #18011833C22semidirect
28. #18011832C22semidirect
30. C4×#11924746C22semidirect
31. C2×SD16×C149C22semidirect
32. C4⋊Q8×C149C22semidirect
34. C4×C8×C149C22semidirect
87. C4×D149SD16semidirect
124. C149#3208semidirect
129. #492D149semidirect
139. C2×SD16C2×D149semidirect
141. C4⋊Q8C2×D149semidirect
159. C4×C8C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237501802
#127×D1492
#237499992
#237499722
#237499712
#237498232
#237497742
#237496762
#492×C1492
#3208149