Finite Group Databasebeta

← #34045844

Subgroups — #34045844

Order 19072.

282 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 71 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#23749629C212yesmaximal
2#23749526C211yesmaximal, characteristic
3#23749394C211yesmaximal, characteristic, complemented
4#23749384C212yesmaximal, complemented
5#544×C149C211yesmaximal, characteristic, complemented
6C22×D596C2211yescharacteristic
7C2×#14558720C2212yes—
8C2×#14558713—22no—
9C2×C4×Dic149C2211yescharacteristic
10#18011831—22no—
11#18011831—22no—
12C4⋊Q8×C149—22no—
13#125×C149—22no—
14C22⋊Q8×C149—22no—
15#117×C149C2212yes—
16C2×C4⋊C4×C149C2211yescharacteristic
17C23×D149—21no—
18C2×D596—22no—
19C2×D596—22no—
20C2×D596—21no—
21C2×D596Q812yescomplemented
22C22×Dic149—21no—
23#14558720—22no—
24#14558720—22no—
25C2×#11924746—22no—
26#14558713—44no—
27C4×Dic149—22no—
28C2×Q8×C149—22no—
29C22×C4×C149D412yes—
30C22×C4×C149C2311yescharacteristic
31C4⋊C4×C149—22no—
32C4⋊C4×C149—24no—
33C4⋊C4×C149—22no—
34C4⋊C4×C149D412yes—
35C4⋊C4×C149D412yes—
36C22⋊C4×C149—22no—
37C42×C149—22no—
38C22×D149—22no—
39C22×D149—42no—
40C22×D149—42no—
41C22×D149—41no—
42C22×D149—41no—
43D596—24no—
44D596—42no—
45C2×Dic149—22no—
46C2×Dic149—41no—
47C2×Dic149—41no—
48#11924746—42no—
49C23×C149C2×D411yescharacteristic
50Q8×C149—82no—
51C2×C4×C149—22no—
52C2×C4×C149—22no—
53C2×C4×C149—22no—
54C2×C4×C149—42no—
55C2×C4×C149C2×D412yes—
56C2×C4×C149C2×Q811yescharacteristic
57C2×C4×C149#4112yes—
58C2×C4×C149#4111yescharacteristic
59C22×C149—21no—
60C22×C149—21no—
61C22×C149#12011yescharacteristic
62C22×C149C22⋊Q811yescharacteristic
63C22×C149#12411yescharacteristic
64C2×D149—44no—
65C2×D149—42no—
66C2×D149—82no—
67C2×D149—81no—
68C2×D149—81no—
69C4×C149—42no—
70C4×C149—42no—
71C4×C149—42no—
72C4×C149C22⋊Q812yes—
73C4×C149#12412yes—
74Dic149—42no—
75C2×C149—21no—
76C2×C149—21no—
77C2×C149#39311yescharacteristic
78C2×C149#45311yescharacteristic
79C2×C149#45411yescharacteristic
80D149—82no—
81C149#202711yescharacteristic, complemented, Sylow
82#2027—1491nomaximal, Sylow
83#544D14911yescharacteristic, complemented
84#418—1492no—
85#390—1491no—
86#343—1491no—
87#339—1492no—
88C22×D4—1491no—
89C2×M16—1492no—
90C4⋊Q8—22no—
91#125—22no—
92C22⋊Q8—22no—
93#117C2×D14912yes—
94C2×C4⋊C4C2×D14911yescharacteristic
95C2×C22⋊C4—2982no—
96C2×C42—1491no—
97#102—2982no—
98#102—2982no—
99C24—2981no—
100C2×Q8—22no—
101C2×D4—2982no—
102C2×D4—2982no—
103C2×D4—2981no—
104C2×D4—1492no—
105C22×C4—2981no—
106C22×C4C22⋊D14912yes—
107C22×C4C22×D14911yescharacteristic
108M16—2982no—
109M16—2982no—
110C2×C8—2982no—
111C4⋊C4—22no—
112C4⋊C4—24no—
113C4⋊C4—22no—
114C4⋊C4C22⋊D14912yes—
115C4⋊C4C22⋊D14912yes—
116C22⋊C4—22no—
117C22⋊C4—5964no—
118C42—22no—
119C42—2982no—
120C23—2982no—
121C23—5962no—
122C23—5962no—
123C23—5961no—
124C23—5961no—
125C23C2×C22⋊D14911yescharacteristic
126Q8—82no—
127D4—2984no—
128D4—5962no—
129C2×C4—22no—
130C2×C4—22no—
131C2×C4—22no—
132C2×C4—42no—
133C2×C4—2982no—
134C2×C4—5961no—
135C2×C4—5961no—
136C2×C4C2×C22⋊D14912yes—
137C2×C4Q8×D14911yescharacteristic
138C2×C4#1455873712yes—
139C2×C4#1455873711yescharacteristic
140C8—5962no—
141C22—21no—
142C22—21no—
143C22—5964no—
144C22—5962no—
145C22—11922no—
146C22—11921no—
147C22—11921no—
148C22#1801188011yescharacteristic
149C22#1801188711yescharacteristic
150C22#1801190011yescharacteristic
151C4—42no—
152C4—42no—
153C4—42no—
154C4—5962no—
155C4#1801188712yes—
156C4#1801190012yes—
157C2—21no—
158C2—21no—
159C2—11922no—
160C2#2374953611yescharacteristic
161C2#2374979311yescharacteristic
162C2#2374979811yescharacteristic
subgroupG/H
centerC22#18011880
commutator, cosocleC22×C4×C149C23
FrattiniC22×C4C22×D149
Fitting#544×C149C2
socleC22×C149#120
prime radicalC22×D596C22
hypercenter#544D149
hypocenterC149#2027
LCSG ▷ C22×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #544

Complements

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

NH ≅ G/Ntype
3. #23749394C2semidirect
4. #23749384C2semidirect
5. #544×C149C2semidirect
21. C2×D596Q8semidirect
81. C149#2027semidirect
83. #544D149semidirect

Maximal subgroups

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

subgroupindex
#237496292
#237495262
#237493942
#237493842
#544×C1492
#2027149