Finite Group Databasebeta

← #34055551

Subgroups — #34055551

Order 19072.

442 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 109 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#23750191C212yesmaximal, complemented
2#23749952C212yesmaximal, complemented
3#23749947C212yesmaximal, complemented
4#23749876C212yesmaximal, complemented
5#23749861C211yesmaximal, characteristic, complemented
6#23749760C212yesmaximal, complemented
7#23749757C212yesmaximal, complemented
8#23749591C211yesmaximal, characteristic, complemented
9#466×C149C211yesmaximal, characteristic, complemented
10C2×#14558736C2211yescharacteristic
11C2×D4×D149C2212yescomplemented
12C2×D1192C2211yescharacteristic
13C2×#14558721C2212yes—
14C2×#14558720C2211yescharacteristic, complemented
15#18011907—22no—
16#18011897—22no—
17#18011886C2212yes—
18#18011885C2212yescomplemented
19#18011882C2212yes—
20#18011881—22no—
21#18011879—22no—
22#18011869C2212yescomplemented
23#18011845C2211yescharacteristic, complemented
24#18011842C2212yescomplemented
25#18011833C2212yescomplemented
26#18011832C2212yescomplemented
27#18011831C2212yescomplemented
28#18011823C2212yescomplemented
29#18011823C2212yescomplemented
30C2×D8×C149C2211yescharacteristic
31C22×C8×C149C2211yescharacteristic, complemented
32#121×C149C2212yescomplemented
33#107×C149C2211yescharacteristic, complemented
34#102×C149C2212yescomplemented
35C23×D149—22no—
36#14558736—41no—
37#14558736—41no—
38C2×Dic298D411yescharacteristic
39C2×D596—22no—
40C2×D596D411yescharacteristic
41C2×D596C2312yes—
42C2×C22⋊D149—22no—
43C2×C22⋊D149—22no—
44C2×C22⋊D149—22no—
45C2×C22⋊D149D412yes—
46D4×D149—42no—
47D4×D149—42no—
48C2×C4×D149C2312yes—
49D1192—41no—
50#14558721—42no—
51#14558720—41no—
52C2×#11924746C2312yes—
53C4⋊Dic149C2312yes—
54C22⋊Dic149—22no—
55#14558713—22no—
56#14558713—22no—
57#14558713—22no—
58C4×Dic149—22no—
59C2×D4×C149—22no—
60C2×D4×C149C2312yes—
61C22×C4×C149C2311yescharacteristic
62D8×C149—41no—
63C2×C8×C149—41no—
64C2×C8×C149C2311yescharacteristic
65C2×C8×C149C2311yescharacteristic
66C4⋊C4×C149C2312yes—
67C22⋊C4×C149—22no—
68C22×D149—22no—
69C22×D149—44no—
70C22×D149—82no—
71C22×D149—82no—
72C22×D149C2×D412yes—
73Dic298—41no—
74D596—22no—
75D596—22no—
76D596—41no—
77D596—82no—
78C22⋊D149—42no—
79C22⋊D149—44no—
80C22⋊D149—82no—
81C22⋊D149—82no—
82C2×Dic149—22no—
83C2×Dic149C2×D412yes—
84C4×D149—22no—
85C4×D149—22no—
86#11924746—22no—
87C23×C149—22no—
88C23×C149C2×D411yescharacteristic
89D4×C149—22no—
90D4×C149—22no—
91D4×C149—82no—
92C2×C4×C149—21no—
93C2×C4×C149—21no—
94C2×C4×C149—22no—
95C2×C4×C149C2×D411yescharacteristic
96C2×C4×C149C2411yescharacteristic
97C8×C149—21no—
98C8×C149—21no—
99C22×C149—21no—
100C22×C149—21no—
101C22×C149—21no—
102C22×C149—42no—
103C22×C149—42no—
104C22×C149—42no—
105C22×C149C22×D411yescharacteristic
106C2×D149—22no—
107C2×D149—22no—
108C2×D149—22no—
109C2×D149—42no—
110C2×D149—42no—
111C2×D149—42no—
112C2×D149—88no—
113C4×C149—21no—
114C4×C149—42no—
115C4×C149H(5,𝔽2)11yescharacteristic
116C4×C149H(5,𝔽2)11yescharacteristic
117Dic149—22no—
118Dic149—42no—
119C2×C149—41no—
120C2×C149—82no—
121C2×C149#53411yescharacteristic
122C2×C149#57611yescharacteristic
123C2×C149#57611yescharacteristic
124D149—42no—
125D149—82no—
126C149#319911yescharacteristic, complemented, Sylow
127#3199—1491nomaximal, Sylow
128#535—1492no—
129#482—1492no—
130#482—1492no—
131#469—1492no—
132#466—1491no—
133#466D14911yescharacteristic, complemented
134#447—1492no—
135#447—1492no—
136#408—1491no—
137C2×#41—1491no—
138C22×D4—1492no—
139C2×D8—1492no—
140C2×D8—1491no—
141C2×D8C2×D14911yescharacteristic
142C2×M16—1491no—
143C22×C8C2×D14911yescharacteristic, complemented
144#127—2982no—
145#124—2982no—
146#121—1492no—
147#121—1492no—
148#121—1492no—
149#121C2×D14912yescomplemented
150#120—2982no—
151#120—2982no—
152#117—1492no—
153#107—1491no—
154#107C2×D14911yescharacteristic, complemented
155#106—1492no—
156#102—1492no—
157#102—1492no—
158#102—1492no—
159#102C2×D14912yescomplemented
160C22⋊C8—1492no—
161C22⋊C8—1492no—
162C24—2982no—
163#41—5961no—
164#41—5961no—
165C2×Q8—1491no—
166C2×D4—22no—
167C2×D4—2982no—
168C2×D4—2982no—
169C2×D4—2982no—
170C2×D4—2982no—
171C2×D4—5962no—
172C2×D4—5962no—
173C2×D4—1492no—
174C2×D4—1491no—
175C2×D4—1492no—
176C2×D4C22×D14912yes—
177C22×C4—1492no—
178C22×C4C22×D14911yescharacteristic
179D8—41no—
180D8—5961no—
181D8—5962no—
182M16—5961no—
183C2×C8—41no—
184C2×C8—1492no—
185C2×C8C22×D14911yescharacteristic
186C2×C8C22×D14911yescharacteristic
187C4⋊C4—1492no—
188C4⋊C4C22×D14912yes—
189C22⋊C4—22no—
190C22⋊C4—2982no—
191C22⋊C4—2982no—
192C22⋊C4—2982no—
193C22⋊C4—2982no—
194C42—2982no—
195C23—22no—
196C23—2982no—
197C23—5964no—
198C23—1492no—
199C23—11922no—
200C23—11922no—
201C23D4×D14911yescharacteristic
202Q8—5961no—
203D4—22no—
204D4—22no—
205D4—82no—
206D4—2982no—
207D4—2982no—
208D4—5961no—
209D4—5962no—
210D4—5964no—
211D4—11922no—
212D4—11922no—
213D4—11922no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—22no—
217C2×C4—2982no—
218C2×C4—2982no—
219C2×C4—2982no—
220C2×C4—1492no—
221C2×C4D4×D14911yescharacteristic
222C2×C4C23×D14911yescharacteristic
223C8—21no—
224C8—21no—
225C8—2982no—
226C22—21no—
227C22—21no—
228C22—21no—
229C22—42no—
230C22—42no—
231C22—42no—
232C22—2982no—
233C22—2982no—
234C22—2982no—
235C22—5962no—
236C22—5962no—
237C22—5962no—
238C22—11928no—
239C22C2×D4×D14911yescharacteristic
240C4—21no—
241C4—42no—
242C4—2982no—
243C4—5962no—
244C4#1801195611yescharacteristic
245C4#1801195711yescharacteristic
246C2—41no—
247C2—82no—
248C2—5962no—
249C2—11922no—
250C2#2375018311yescharacteristic
251C2#2375042611yescharacteristic
252C2#2375042711yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#466×C149C2
socleC22×C149C22×D4
hypercenter#466D149
hypocenterC149#3199
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #23750191C2semidirect
2. #23749952C2semidirect
3. #23749947C2semidirect
4. #23749876C2semidirect
5. #23749861C2semidirect
6. #23749760C2semidirect
7. #23749757C2semidirect
8. #23749591C2semidirect
9. #466×C149C2semidirect
11. C2×D4×D149C22semidirect
14. C2×#14558720C22semidirect
18. #18011885C22semidirect
22. #18011869C22semidirect
23. #18011845C22semidirect
24. #18011842C22semidirect
25. #18011833C22semidirect
26. #18011832C22semidirect
27. #18011831C22semidirect
28. #18011823C22semidirect
29. #18011823C22semidirect
31. C22×C8×C149C22semidirect
32. #121×C149C22semidirect
33. #107×C149C22semidirect
34. #102×C149C22semidirect
126. C149#3199semidirect
133. #466D149semidirect
143. C22×C8C2×D149semidirect
149. #121C2×D149semidirect
154. #107C2×D149semidirect
159. #102C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237501912
#237499522
#237499472
#237498762
#237498612
#237497602
#237497572
#237495912
#466×C1492
#3199149