Finite Group Databasebeta

← #34056300

Subgroups — #34056300

Order 19072.

520 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 121 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×#18011938C212yesmaximal, complemented
2#23750268C212yesmaximal, complemented
3#23749868C212yesmaximal, complemented
4#23749837C212yesmaximal, complemented
5#23749786C212yesmaximal, complemented
6#23749757C212yesmaximal, complemented
7C4×D1192C211yesmaximal, characteristic, complemented
8#23749704C211yesmaximal, characteristic, complemented
9#495×C149C211yesmaximal, characteristic, complemented
10C2×#14558737C2212yes—
11C2×D4×D149C2212yescomplemented
12#18011938—28no—
13C2×#14558723C2212yescomplemented
14C2×D1192C2211yescharacteristic
15C2×#14558721C2212yes—
16C2×#14558719C2212yescomplemented
17#18011893—22no—
18#18011887C2212yescomplemented
19#18011884—22no—
20#18011882C2212yes—
21#18011881—22no—
22C4×D596C2211yescharacteristic
23C4×D596C2212yescomplemented
24C22⋊C4×D149—22no—
25#18011845C2211yescharacteristic, complemented
26C4⋊#11924746C2211yescharacteristic, complemented
27#18011835C2212yescomplemented
28#18011833C2212yescomplemented
29#18011832C2212yescomplemented
30#18011823C2212yescomplemented
31C2×Q16×C149C2211yescharacteristic, complemented
32C2×SD16×C149C2212yescomplemented
33C2×D8×C149C2211yescharacteristic
34#124×C149C2212yescomplemented
35C4×C8×C149C2211yescharacteristic, complemented
36C23×D149—22no—
37#14558737—24no—
38#14558737—42no—
39C2×D596—22no—
40C2×D596D411yescharacteristic
41C2×D596C2312yes—
42C2×C22⋊D149—22no—
43C2×C22⋊D149—22no—
44D4×D149—24no—
45D4×D149—42no—
46C2×C4×D149—22no—
47C2×C4×D149—22no—
48C2×C4×D149C2312yes—
49#14558723—24no—
50D1192D414yescomplemented
51#14558721—24no—
52#14558719—24no—
53C2×#11924746C2312yes—
54C4⋊Dic149D411yescharacteristic
55C4⋊Dic149C2312yes—
56#14558715—22no—
57C22⋊Dic149—22no—
58#14558713—22no—
59#14558713—22no—
60#14558713D412yes—
61C2×Q8×C149C2312yes—
62C2×D4×C149C2312yes—
63Q16×C149—41no—
64SD16×C149—24no—
65D8×C149—41no—
66C2×C8×C149C2311yescharacteristic
67C2×C8×C149C2311yescharacteristic
68C22⋊C4×C149—22no—
69C22⋊C4×C149—22no—
70C42×C149C2311yescharacteristic
71C22×D149—22no—
72C22×D149—44no—
73C22×D149—44no—
74C22×D149—82no—
75C22×D149C2×D412yes—
76D596—22no—
77D596—41no—
78D596—44no—
79D596C2×D414yes—
80C22⋊D149—44no—
81C22⋊D149—82no—
82C2×Dic149—22no—
83C2×Dic149C2×D412yes—
84C4×D149—22no—
85C4×D149—22no—
86C4×D149—44no—
87C4×D149—82no—
88#11924746—22no—
89C23×C149—22no—
90Q8×C149—22no—
91Q8×C149—22no—
92D4×C149—22no—
93D4×C149—22no—
94C2×C4×C149—22no—
95C2×C4×C149C2×D411yescharacteristic
96C2×C4×C149C2×D411yescharacteristic
97C2×C4×C149C2411yescharacteristic
98C8×C149—21no—
99C8×C149C2×D412yes—
100C22×C149—42no—
101C22×C149—42no—
102C22×C149—42no—
103C22×C149C22×D411yescharacteristic
104C2×D149—22no—
105C2×D149—24no—
106C2×D149—22no—
107C2×D149—22no—
108C2×D149—42no—
109C2×D149—42no—
110C2×D149—88no—
111C4×C149—21no—
112C4×C149—21no—
113C4×C149—42no—
114C4×C149C22×D411yescharacteristic
115C4×C149H(5,𝔽2)11yescharacteristic
116Dic149—22no—
117Dic149—42no—
118C2×C149—82no—
119C2×C149D4211yescharacteristic
120C2×C149#57511yescharacteristic
121C2×C149#57611yescharacteristic
122D149—42no—
123D149—44no—
124C149#327311yescharacteristic, complemented, Sylow
125#3273—1491nomaximal, Sylow
126C2×AGL(1,ℤ/8)—1492no—
127#546—1492no—
128#495D14911yescharacteristic, complemented
129#468—1492no—
130#463—1492no—
131#452—1492no—
132#447—1492no—
133C4×D8—1491no—
134#436—1491no—
135C2×#41—1492no—
136C22×D4—1492no—
137AGL(1,ℤ/8)—2988no—
138C2×Q16C2×D14911yescharacteristic, complemented
139C2×SD16—1492no—
140C2×SD16C2×D14912yescomplemented
141C2×D8—1492no—
142C2×D8—1491no—
143C2×D8C2×D14911yescharacteristic
144C2×M16—1492no—
145#124C2×D14912yescomplemented
146#123—2982no—
147C22⋊Q8—1492no—
148#121—2982no—
149#121—1492no—
150#120—2982no—
151C4×D4—1492no—
152C4×D4—1491no—
153C2×C22⋊C4—2982no—
154#107—1491no—
155C4⋊C8—1491no—
156#103—1492no—
157#102—1492no—
158#102—1492no—
159C22⋊C8—1492no—
160C4×C8C2×D14911yescharacteristic, complemented
161C24—2982no—
162#41—2984no—
163#41—5962no—
164C2×Q8C22×D14912yes—
165C2×D4—2982no—
166C2×D4—2984no—
167C2×D4—2982no—
168C2×D4—2982no—
169C2×D4—5962no—
170C2×D4—1491no—
171C2×D4—1492no—
172C2×D4C22×D14912yes—
173C22×C4—2982no—
174C22×C4—2982no—
175C22×C4—1492no—
176Q16—41no—
177SD16—24no—
178SD16—2984no—
179D8—41no—
180D8—2984no—
181D8—1494no—
182M16—2984no—
183C2×C8—1492no—
184C2×C8C22×D14911yescharacteristic
185C2×C8C22×D14911yescharacteristic
186C4⋊C4—2982no—
187C4⋊C4—1492no—
188C4⋊C4—1491no—
189C22⋊C4—22no—
190C22⋊C4—22no—
191C22⋊C4—2982no—
192C22⋊C4—2982no—
193C22⋊C4—2982no—
194C22⋊C4—1492no—
195C42C22×D14911yescharacteristic
196C23—22no—
197C23—2982no—
198C23—5964no—
199C23—5964no—
200C23—1492no—
201C23—11922no—
202Q8—22no—
203Q8—22no—
204D4—22no—
205D4—22no—
206D4—2982no—
207D4—5961no—
208D4—5964no—
209D4—5964no—
210D4—1494no—
211D4—11922no—
212C2×C4—22no—
213C2×C4—2982no—
214C2×C4—2982no—
215C2×C4—2982no—
216C2×C4—5964no—
217C2×C4—1492no—
218C2×C4—11922no—
219C2×C4D4×D14911yescharacteristic
220C2×C4D4×D14911yescharacteristic
221C2×C4C23×D14911yescharacteristic
222C8—21no—
223C8—2982no—
224C8D4×D14912yes—
225C22—42no—
226C22—42no—
227C22—42no—
228C22—2982no—
229C22—2982no—
230C22—2982no—
231C22—2984no—
232C22—5962no—
233C22—5962no—
234C22—11928no—
235C22C2×D4×D14911yescharacteristic
236C4—21no—
237C4—21no—
238C4—42no—
239C4—2982no—
240C4—5962no—
241C4C2×D4×D14911yescharacteristic
242C4#1801195611yescharacteristic
243C2—82no—
244C2—5962no—
245C2—5964no—
246C2#2375026011yescharacteristic
247C2#2375042211yescharacteristic
248C2#2375042711yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#495×C149C2
socleC22×C149C22×D4
hypercenter#495D149
hypocenterC149#3273
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. C2×#18011938C2semidirect
2. #23750268C2semidirect
3. #23749868C2semidirect
4. #23749837C2semidirect
5. #23749786C2semidirect
6. #23749757C2semidirect
7. C4×D1192C2semidirect
8. #23749704C2semidirect
9. #495×C149C2semidirect
11. C2×D4×D149C22semidirect
13. C2×#14558723C22semidirect
16. C2×#14558719C22semidirect
18. #18011887C22semidirect
23. C4×D596C22semidirect
25. #18011845C22semidirect
26. C4⋊#11924746C22semidirect
27. #18011835C22semidirect
28. #18011833C22semidirect
29. #18011832C22semidirect
30. #18011823C22semidirect
31. C2×Q16×C149C22semidirect
32. C2×SD16×C149C22semidirect
34. #124×C149C22semidirect
35. C4×C8×C149C22semidirect
50. D1192D4semidirect
124. C149#3273semidirect
128. #495D149semidirect
138. C2×Q16C2×D149semidirect
140. C2×SD16C2×D149semidirect
145. #124C2×D149semidirect
160. C4×C8C2×D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119382
#237502682
#237498682
#237498372
#237497862
#237497572
C4×D11922
#237497042
#495×C1492
#3273149