Finite Group Databasebeta

← #34055038

Subgroups — #34055038

Order 19072.

392 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 117 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#23750181C211yesmaximal, characteristic, complemented
2#23750176C211yesmaximal, characteristic
3#23749993C211yesmaximal, characteristic, complemented
4#23749991C211yesmaximal, characteristic, complemented
5#23749990C211yesmaximal, characteristic, complemented
6#23749986C214yesmaximal, complemented
7#23749620C214yesmaximal, complemented
8#97×D149C211yesmaximal, characteristic, complemented
9#491×C149C211yesmaximal, characteristic, complemented
10C2×#14558737C2212yes—
11C2×C8×D149C2212yes—
12#18011910C2212yes—
13#18011908C2211yescharacteristic
14#18011903C2211yescharacteristic
15#18011900C2212yes—
16#18011889—22no—
17#18011886—22no—
18#18011876—22no—
19#18011873—22no—
20#18011869C2212yes—
21C42×D149C2211yescharacteristic
22#18011835C2214yes—
23#18011833C2214yes—
24#18011831C2214yes—
25#18011822C2211yescharacteristic
26#18011821C2212yes—
27C4⋊Q8×C149C2211yescharacteristic
28#125×C149C2211yescharacteristic
29#103×C149C2214yes—
30#97×C149C2211yescharacteristic
31#14558737—28no—
32C2×Dic298—22no—
33C2×D596—22no—
34C2×D596—22no—
35C2×D596C2312yes—
36C2×C4×D149—22no—
37C2×C4×D149D412yes—
38C2×C4×D149C2311yescharacteristic
39C2×#11924746C2312yes—
40C8×D149—24no—
41C4⋊Dic149C2312yes—
42#14558715—22no—
43#14558715—22no—
44#14558713—22no—
45#14558713—24no—
46C4×Dic149—22no—
47C4×Dic149D412yes—
48C4×Dic149C2311yescharacteristic
49C2×Q8×C149C2312yes—
50C2×C8×C149C2312yes—
51C4⋊C4×C149—22no—
52C4⋊C4×C149—22no—
53C4⋊C4×C149C2312yes—
54C42×C149C2311yescharacteristic
55C22×D149—22no—
56C22×D149C2×D411yescharacteristic
57Dic298—44no—
58D596—24no—
59D596—44no—
60D596—44no—
61C2×Dic149—22no—
62C2×Dic149C2×D412yes—
63C2×Dic149C2×D411yescharacteristic
64C4×D149—42no—
65C4×D149—44no—
66C4×D149#4114yes—
67#11924746—22no—
68Q8×C149—24no—
69C2×C4×C149—22no—
70C2×C4×C149—22no—
71C2×C4×C149C2×D412yes—
72C2×C4×C149C2411yescharacteristic
73C8×C149—22no—
74C22×C149C22×D411yescharacteristic
75C2×D149—22no—
76C2×D149—42no—
77C2×D149—44no—
78C2×D149#12412yes—
79C4×C149—22no—
80C4×C149—42no—
81C4×C149—42no—
82C4×C149C2×#4112yes—
83Dic149—22no—
84Dic149—42no—
85Dic149#12412yes—
86C2×C149C2×#12411yescharacteristic
87C2×C149#57512yes—
88D149—22no—
89D149—82no—
90C149#313511yescharacteristic, complemented, Sylow
91#3135—1491nomaximal, Sylow
92#533—1491no—
93#532—1491no—
94#491—1491no—
95#491D14911yescharacteristic, complemented
96#490—1491no—
97#490—1491no—
98#489—1494no—
99#416—1494no—
100C2×#97—1491no—
101C2×#41—1492no—
102C22×C8—1492no—
103C4⋊Q8—1492no—
104C4⋊Q8C2×D14911yescharacteristic
105#127—1491no—
106#125—1491no—
107#125C2×D14911yescharacteristic
108#124—1492no—
109C22⋊Q8—2982no—
110#121—2982no—
111C4×Q8—2982no—
112C4×D4—2982no—
113#117—1492no—
114C2×C42—1491no—
115#103—1494no—
116#103C2×D14914yes—
117#102—1494no—
118#102—1494no—
119#97—1492no—
120#97—1491no—
121#97C2×D14911yescharacteristic
122#41—2988no—
123C2×Q8—2982no—
124C2×Q8C22×D14912yes—
125C2×D4—2982no—
126C2×D4—2982no—
127C2×D4—1492no—
128C22×C4—2982no—
129C22×C4—1492no—
130C22×C4—1491no—
131C2×C8—2984no—
132C2×C8—1492no—
133C2×C8C22×D14912yes—
134C4⋊C4—22no—
135C4⋊C4—22no—
136C4⋊C4—2982no—
137C4⋊C4—2982no—
138C4⋊C4—1492no—
139C4⋊C4C22×D14912yes—
140C22⋊C4—2982no—
141C22⋊C4—2984no—
142C42—2982no—
143C42—1492no—
144C42—1491no—
145C42C22×D14911yescharacteristic
146C23—2982no—
147C23—1491no—
148Q8—24no—
149Q8—5964no—
150D4—2984no—
151D4—5964no—
152D4—5964no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—2982no—
156C2×C4—5962no—
157C2×C4—5964no—
158C2×C4—1492no—
159C2×C4—1491no—
160C2×C4—1494no—
161C2×C4D4×D14912yes—
162C2×C4C23×D14911yescharacteristic
163C8—22no—
164C8—2982no—
165C22—2982no—
166C22—5964no—
167C22—5962no—
168C22—1492no—
169C22C2×D4×D14911yescharacteristic
170C4—22no—
171C4—42no—
172C4—42no—
173C4—2982no—
174C4—5962no—
175C4—1492no—
176C4#41×D14912yes—
177C2—2982no—
178C2—11922no—
179C2#124×D14911yescharacteristic
180C2#2375042412yes—
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#491×C149C2
socleC22×C149C22×D4
prime radical#23750176C2
hypercenter#491D149
hypocenterC149#3135
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
1. #23750181C2semidirect
3. #23749993C2semidirect
4. #23749991C2semidirect
5. #23749990C2semidirect
6. #23749986C2semidirect
7. #23749620C2semidirect
8. #97×D149C2semidirect
9. #491×C149C2semidirect
90. C149#3135semidirect
95. #491D149semidirect

Maximal subgroups

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

subgroupindex
#237501812
#237501762
#237499932
#237499912
#237499902
#237499862
#237496202
#97×D1492
#491×C1492
#3135149