Finite Group Databasebeta

← #34055438

Subgroups — #34055438

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
1#121×D149C212yesmaximal, complemented
2#23749940C212yesmaximal, complemented
3#23749937C212yesmaximal, complemented
4#23749861C211yesmaximal, characteristic, complemented
5#23749859C212yesmaximal, complemented
6#23749760C212yesmaximal, complemented
7#23749757C212yesmaximal, complemented
8C2×#18011823C211yesmaximal, characteristic, complemented
9#466×C149C211yesmaximal, characteristic, complemented
10C2×D4×D149—22no—
11C2×D4×D149C2212yescomplemented
12C22×C4×D149C2211yescharacteristic
13C2×D1192C2211yescharacteristic, complemented
14C2×#14558721C2212yescomplemented
15C22×#11924746C2211yescharacteristic, complemented
16#18011886C2212yes—
17#18011885C2212yescomplemented
18#18011884—22no—
19#18011883—22no—
20#18011882C2212yes—
21C4⋊C4×D149C2212yescomplemented
22C22⋊C4×D149—22no—
23#18011845C2211yescharacteristic, complemented
24#18011844C2212yescomplemented
25#18011833C2212yescomplemented
26#18011832C2212yescomplemented
27#18011831C2212yescomplemented
28#18011823C2212yescomplemented
29#18011823C2212yescomplemented
30C2×D8×C149C2211yescharacteristic, complemented
31C22×C8×C149C2211yescharacteristic, complemented
32#121×C149C2212yescomplemented
33#107×C149C2211yescharacteristic, complemented
34#102×C149C2212yescomplemented
35C23×D149—22no—
36C23×D149D411yescharacteristic
37C2×D596—22no—
38C2×D596C2312yes—
39C2×C22⋊D149—22no—
40C2×C22⋊D149—22no—
41C2×C22⋊D149—22no—
42D4×D149—42no—
43D4×D149—42no—
44D4×D149—48no—
45C22×Dic149D411yescharacteristic
46C2×C4×D149—22no—
47C2×C4×D149—41no—
48C2×C4×D149—41no—
49C2×C4×D149D412yes—
50C2×C4×D149C2312yes—
51D1192—41no—
52#14558721—42no—
53C2×#11924746—41no—
54C2×#11924746C2312yes—
55C4⋊Dic149C2312yes—
56#14558715—22no—
57C22⋊Dic149—22no—
58#14558713—22no—
59#14558713—22no—
60C2×D4×C149—22no—
61C2×D4×C149C2312yes—
62C22×C4×C149C2311yescharacteristic
63D8×C149—41no—
64C2×C8×C149—41no—
65C2×C8×C149C2311yescharacteristic
66C2×C8×C149C2311yescharacteristic
67C4⋊C4×C149C2312yes—
68C22⋊C4×C149—22no—
69C22×D149—22no—
70C22×D149—41no—
71C22×D149—41no—
72C22×D149—44no—
73C22×D149—44no—
74C22×D149—44no—
75C22×D149D814yescomplemented
76C22×D149C2×D412yes—
77D596—22no—
78D596—22no—
79D596—44no—
80C22⋊D149—44no—
81C22⋊D149—44no—
82C22⋊D149—44no—
83C2×Dic149—22no—
84C2×Dic149—41no—
85C2×Dic149C2×D412yes—
86C4×D149—22no—
87C4×D149—22no—
88C4×D149—42no—
89C4×D149—44no—
90#11924746—22no—
91C23×C149—22no—
92C23×C149C2×D411yescharacteristic
93D4×C149—22no—
94D4×C149—22no—
95D4×C149—44no—
96C2×C4×C149—21no—
97C2×C4×C149—21no—
98C2×C4×C149—22no—
99C2×C4×C149C2×D411yescharacteristic
100C2×C4×C149C2411yescharacteristic
101C8×C149—21no—
102C8×C149—21no—
103C22×C149—21no—
104C22×C149—21no—
105C22×C149—42no—
106C22×C149—42no—
107C22×C149—42no—
108C22×C149C2×D812yes—
109C22×C149C22×D411yescharacteristic
110C2×D149—22no—
111C2×D149—22no—
112C2×D149—44no—
113C2×D149—42no—
114C2×D149—42no—
115C2×D149—42no—
116C2×D149—88no—
117C2×D149C2×D814yes—
118C4×C149—21no—
119C4×C149—42no—
120C4×C149H(5,𝔽2)11yescharacteristic
121C4×C149H(5,𝔽2)11yescharacteristic
122Dic149—22no—
123Dic149—42no—
124C2×C149—22no—
125C2×C149—82no—
126C2×C149#53411yescharacteristic
127C2×C149C22×D811yescharacteristic
128C2×C149#57511yescharacteristic
129D149—24no—
130D149—82no—
131C149#318611yescharacteristic, complemented, Sylow
132#3186—1491nomaximal, Sylow
133C2×#121—1492no—
134#480—1492no—
135#480—1492no—
136#466—1491no—
137#466—1492no—
138#466D14911yescharacteristic, complemented
139#447—1492no—
140#447—1492no—
141C2×C22⋊C8—1491no—
142C22×D4—2982no—
143C22×D4—1492no—
144C23×C4—1491no—
145C2×D8—1492no—
146C2×D8—1491no—
147C2×D8C2×D14911yescharacteristic, complemented
148C22×C8—1491no—
149C22×C8C2×D14911yescharacteristic, complemented
150#121—2982no—
151#121—2982no—
152#121—1492no—
153#121—1492no—
154#121—1492no—
155#121C2×D14912yescomplemented
156C2×C4⋊C4—1492no—
157C2×C22⋊C4—2982no—
158#107—1491no—
159#107—1492no—
160#107C2×D14911yescharacteristic, complemented
161#102—1492no—
162#102—1492no—
163#102—1492no—
164#102C2×D14912yescomplemented
165C22⋊C8—1492no—
166C22⋊C8—1492no—
167C24—2982no—
168C24—1491no—
169C2×D4—22no—
170C2×D4—2982no—
171C2×D4—2982no—
172C2×D4—2982no—
173C2×D4—2982no—
174C2×D4—5962no—
175C2×D4—5962no—
176C2×D4—5968no—
177C2×D4—1492no—
178C2×D4C22×D14912yes—
179C22×C4—2982no—
180C22×C4—5961no—
181C22×C4—5961no—
182C22×C4—1492no—
183C22×C4—1491no—
184C22×C4—1492no—
185C22×C4C22×D14911yescharacteristic
186D8—41no—
187D8—5961no—
188D8—5962no—
189C2×C8—41no—
190C2×C8—5961no—
191C2×C8—1492no—
192C2×C8C22×D14911yescharacteristic
193C2×C8C22×D14911yescharacteristic
194C4⋊C4—2982no—
195C4⋊C4—1492no—
196C4⋊C4C22×D14912yes—
197C22⋊C4—22no—
198C22⋊C4—2982no—
199C22⋊C4—2982no—
200C22⋊C4—2982no—
201C23—22no—
202C23—2982no—
203C23—5961no—
204C23—5961no—
205C23—5964no—
206C23—5964no—
207C23—5964no—
208C23—1492no—
209C23—1494no—
210C23D4×D14911yescharacteristic
211D4—22no—
212D4—22no—
213D4—44no—
214D4—2982no—
215D4—2982no—
216D4—5964no—
217D4—5964no—
218D4—5964no—
219D4—5964no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—22no—
223C2×C4—2982no—
224C2×C4—2982no—
225C2×C4—2982no—
226C2×C4—5962no—
227C2×C4—5964no—
228C2×C4—5961no—
229C2×C4—1492no—
230C2×C4D4×D14911yescharacteristic
231C2×C4C23×D14911yescharacteristic
232C8—21no—
233C8—21no—
234C8—2982no—
235C22—21no—
236C22—21no—
237C22—42no—
238C22—42no—
239C22—42no—
240C22—2982no—
241C22—2982no—
242C22—5964no—
243C22—5962no—
244C22—5962no—
245C22—5962no—
246C22—1494no—
247C22—11928no—
248C22D8×D14912yes—
249C22C2×D4×D14911yescharacteristic
250C4—21no—
251C4—42no—
252C4—2982no—
253C4—5962no—
254C4#1801195611yescharacteristic
255C4#1801195711yescharacteristic
256C2—22no—
257C2—82no—
258C2—2984no—
259C2—11922no—
260C2#2375018311yescharacteristic
261C2C2×D8×D14911yescharacteristic
262C2#2375042211yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#466×C149C2
socleC22×C149C22×D4
hypercenter#466D149
hypocenterC149#3186
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. #121×D149C2semidirect
2. #23749940C2semidirect
3. #23749937C2semidirect
4. #23749861C2semidirect
5. #23749859C2semidirect
6. #23749760C2semidirect
7. #23749757C2semidirect
8. C2×#18011823C2semidirect
9. #466×C149C2semidirect
11. C2×D4×D149C22semidirect
13. C2×D1192C22semidirect
14. C2×#14558721C22semidirect
15. C22×#11924746C22semidirect
17. #18011885C22semidirect
21. C4⋊C4×D149C22semidirect
23. #18011845C22semidirect
24. #18011844C22semidirect
25. #18011833C22semidirect
26. #18011832C22semidirect
27. #18011831C22semidirect
28. #18011823C22semidirect
29. #18011823C22semidirect
30. C2×D8×C149C22semidirect
31. C22×C8×C149C22semidirect
32. #121×C149C22semidirect
33. #107×C149C22semidirect
34. #102×C149C22semidirect
75. C22×D149D8semidirect
131. C149#3186semidirect
138. #466D149semidirect
147. C2×D8C2×D149semidirect
149. C22×C8C2×D149semidirect
155. #121C2×D149semidirect
160. #107C2×D149semidirect
164. #102C2×D149semidirect

Maximal subgroups

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

subgroupindex
#121×D1492
#237499402
#237499372
#237498612
#237498592
#237497602
#237497572
C2×#180118232
#466×C1492
#3186149