Finite Group Databasebeta

← #34055063

Subgroups — #34055063

Order 19072.

484 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 129 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#23750178C211yesmaximal, characteristic, complemented
2C2×#18011907C211yesmaximal, characteristic
3#23749988C214yesmaximal, complemented
4#23749970C214yesmaximal, complemented
5#23749631C211yesmaximal, characteristic, complemented
6#23749630C211yesmaximal, characteristic, complemented
7#23749629C211yesmaximal, characteristic, complemented
8M16×Dic149C211yesmaximal, characteristic, complemented
9#418×C149C211yesmaximal, characteristic, complemented
10C22×D596C2211yescharacteristic
11C22×C22⋊D149—22no—
12C2×#14558720C2211yescharacteristic
13#18011910C2212yescomplemented
14#18011907—22no—
15#18011907C2212yes—
16#18011907C2212yes—
17#18011902C2212yescomplemented
18#18011888—22no—
19C4×Dic298—22no—
20#18011870C2211yescharacteristic
21C2×C4×Dic149C2211yescharacteristic
22#18011833C2214yescomplemented
23#18011832C2214yescomplemented
24#18011831C2214yescomplemented
25#18011821C2212yescomplemented
26C8×Dic149C2212yescomplemented
27C22×D4×C149C2211yescharacteristic
28C2×M16×C149C2211yescharacteristic
29#117×C149C2211yescharacteristic
30#102×C149C2214yescomplemented
31C23×D149—21no—
32C2×Dic298—22no—
33C2×D596—21no—
34C2×D596—22no—
35C2×D596—22no—
36C2×D596C2312yes—
37C2×C22⋊D149—24no—
38C2×C22⋊D149—24no—
39C2×C22⋊D149—48no—
40C22×Dic149D412yes—
41#14558720—22no—
42C2×#11924746C2312yes—
43C4⋊Dic149—22no—
44C4⋊Dic149C2312yes—
45#14558715—22no—
46#14558715—22no—
47C22⋊Dic149—21no—
48C4×Dic149—21no—
49C4×Dic149D412yes—
50C4×Dic149C2311yescharacteristic
51C4×Dic149C2311yescharacteristic
52C24×C149—21no—
53C2×D4×C149—21no—
54C2×D4×C149—22no—
55C2×D4×C149—22no—
56C2×D4×C149C2312yes—
57C22×C4×C149C2311yescharacteristic
58M16×C149—22no—
59C2×C8×C149C2312yes—
60C4⋊C4×C149C2312yes—
61C22⋊C4×C149—21no—
62C42×C149—21no—
63C22×D149—22no—
64C22×D149—44no—
65C22×D149—42no—
66Dic298—44no—
67D596—22no—
68D596—22no—
69D596—42no—
70C22⋊D149—48no—
71C22⋊D149—48no—
72C2×Dic149—24no—
73C2×Dic149—22no—
74C2×Dic149C2×D412yes—
75C2×Dic149C2×D412yes—
76#11924746—22no—
77C23×C149—22no—
78C23×C149—44no—
79C23×C149—42no—
80C23×C149C2×D411yescharacteristic
81D4×C149—22no—
82D4×C149—22no—
83D4×C149—42no—
84C2×C4×C149—22no—
85C2×C4×C149C2×D411yescharacteristic
86C2×C4×C149#4112yes—
87C2×C4×C149#4112yes—
88C2×C4×C149C2411yescharacteristic
89C8×C149—22no—
90C22×C149—22no—
91C22×C149—42no—
92C22×C149—44no—
93C22×C149—84no—
94C22×C149#12412yes—
95C22×C149C22×D411yescharacteristic
96C2×D149—42no—
97C2×D149—44no—
98C2×D149—84no—
99C4×C149—42no—
100C4×C149#12412yes—
101C4×C149C2×#4111yescharacteristic
102C4×C149C2×#4111yescharacteristic
103Dic149—22no—
104Dic149—42no—
105Dic149AGL(1,ℤ/8)14yes—
106C2×C149—22no—
107C2×C149—82no—
108C2×C149C2×#12411yescharacteristic
109C2×C149C2×AGL(1,ℤ/8)12yes—
110D149—82no—
111C149#313811yescharacteristic, complemented, Sylow
112#3138—1491nomaximal, Sylow
113#533—1491no—
114C2×#127—1491no—
115#490—1494no—
116#486—1494no—
117#418—1491no—
118#418—1491no—
119#418—1491no—
120#418D14911yescharacteristic, complemented
121C4×M16—1491no—
122C22×D4—2982no—
123C22×D4—1491no—
124C22×D4C2×D14911yescharacteristic
125C2×M16—1491no—
126C2×M16C2×D14911yescharacteristic
127C4⋊Q8—1492no—
128#127—2982no—
129#127—1492no—
130#127—1492no—
131#125—1492no—
132C22⋊Q8—2982no—
133C4×Q8—2982no—
134#117—1491no—
135#117C2×D14911yescharacteristic
136C2×C42—1491no—
137#102—1494no—
138#102—1494no—
139#102—1494no—
140#102C2×D14914yescomplemented
141#97—1492no—
142C4×C8—1492no—
143C24—21no—
144C24—2981no—
145C2×Q8—2982no—
146C2×D4—21no—
147C2×D4—22no—
148C2×D4—22no—
149C2×D4—2984no—
150C2×D4—2984no—
151C2×D4—2981no—
152C2×D4—2982no—
153C2×D4—2982no—
154C2×D4—5968no—
155C2×D4—1492no—
156C2×D4C22×D14912yes—
157C22×C4—1492no—
158C22×C4C22×D14911yescharacteristic
159M16—22no—
160M16—2982no—
161C2×C8—1492no—
162C2×C8C22×D14912yes—
163C4⋊C4—2982no—
164C4⋊C4—2982no—
165C4⋊C4—2982no—
166C4⋊C4—1492no—
167C4⋊C4C22×D14912yes—
168C22⋊C4—21no—
169C22⋊C4—2981no—
170C42—21no—
171C42—2981no—
172C42—1492no—
173C42—1491no—
174C42—1491no—
175C23—22no—
176C23—44no—
177C23—42no—
178C23—2982no—
179C23—5964no—
180C23—5962no—
181C23D4×D14911yescharacteristic
182Q8—5964no—
183D4—22no—
184D4—22no—
185D4—42no—
186D4—2982no—
187D4—2982no—
188D4—5968no—
189D4—5968no—
190D4—5962no—
191C2×C4—22no—
192C2×C4—2984no—
193C2×C4—2982no—
194C2×C4—1492no—
195C2×C4—1492no—
196C2×C4D4×D14911yescharacteristic
197C2×C4#1455873512yes—
198C2×C4#1455873612yes—
199C2×C4C23×D14911yescharacteristic
200C8—22no—
201C8—2982no—
202C22—22no—
203C22—44no—
204C22—42no—
205C22—84no—
206C22—5964no—
207C22—5962no—
208C22—11924no—
209C22#1801189712yes—
210C22C2×D4×D14911yescharacteristic
211C4—42no—
212C4—2982no—
213C4—5962no—
214C4—1494no—
215C4#1801189712yes—
216C4C2×#1455873511yescharacteristic
217C4C2×#1455873611yescharacteristic
218C2—22no—
219C2—82no—
220C2—11922no—
221C2C2×#1801189711yescharacteristic
222C2AGL(1,ℤ/8)×D14912yes—
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#418×C149C2
socleC22×C149C22×D4
prime radicalC2×#18011907C2
hypercenter#418D149
hypocenterC149#3138
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. #23750178C2semidirect
3. #23749988C2semidirect
4. #23749970C2semidirect
5. #23749631C2semidirect
6. #23749630C2semidirect
7. #23749629C2semidirect
8. M16×Dic149C2semidirect
9. #418×C149C2semidirect
13. #18011910C22semidirect
17. #18011902C22semidirect
22. #18011833C22semidirect
23. #18011832C22semidirect
24. #18011831C22semidirect
25. #18011821C22semidirect
26. C8×Dic149C22semidirect
30. #102×C149C22semidirect
111. C149#3138semidirect
120. #418D149semidirect
140. #102C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237501782
C2×#180119072
#237499882
#237499702
#237496312
#237496302
#237496292
M16×Dic1492
#418×C1492
#3138149