Finite Group Databasebeta

← #34054509

Subgroups — #34054509

Order 19072.

384 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 141 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
1C4×#14558736C211yesmaximal, characteristic
2#23749929C214yesmaximal, complemented
3#23749922C214yesmaximal, complemented
4#23749665C212yesmaximal, complemented
5#23749649C211yesmaximal, characteristic, complemented
6#23749624C212yesmaximal
7C2×#125×C149C211yesmaximal, characteristic, complemented
8C2×#14558736C2211yescharacteristic
9C2×#14558720C2212yes—
10C4×Dic298C2212yes—
11C4×D596C2212yes—
12C4×C22⋊D149—22no—
13#18011870C2211yescharacteristic
14#18011868—21no—
15C42×D149—21no—
16#18011844C2214yes—
17#18011842C2214yes—
18C4⋊#11924746C2214yes—
19#18011834C2214yes—
20#18011831C2214yes—
21#125×C149—21no—
22#125×C149—21no—
23#125×C149C2214yes—
24C2×C4⋊C4×C149—22no—
25C2×C4⋊C4×C149C2212yes—
26C2×C42×C149C2211yescharacteristic
27#14558736—22no—
28#14558736Q814yes—
29C2×Dic298C2311yescharacteristic
30C2×D596C2311yescharacteristic
31C2×C22⋊D149—21no—
32C2×C4×D149—21no—
33C2×C4×D149—22no—
34#14558720—24no—
35C2×#11924746C2314yes—
36C4⋊Dic149C2312yes—
37#14558715—22no—
38C22⋊Dic149—21no—
39#14558713—22no—
40C4×Dic149—21no—
41C4×Dic149—22no—
42C22×C4×C149—22no—
43C22×C4×C149D412yes—
44C22×C4×C149C2311yescharacteristic
45C4⋊C4×C149—24no—
46C4⋊C4×C149—24no—
47C4⋊C4×C149—22no—
48C4⋊C4×C149C2314yes—
49C42×C149D411yescharacteristic
50C42×C149D411yescharacteristic
51C42×C149C2312yes—
52C22×D149—21no—
53Dic298—21no—
54Dic298C2×Q812yes—
55D596—21no—
56D596C2×Q812yes—
57C22⋊D149—24no—
58C2×Dic149—21no—
59C2×Dic149—22no—
60C4×D149—24no—
61C4×D149—44no—
62#11924746—24no—
63C23×C149C2×D411yescharacteristic
64C2×C4×C149—24no—
65C2×C4×C149—42no—
66C2×C4×C149—44no—
67C2×C4×C149C2×D412yes—
68C2×C4×C149C2×D412yes—
69C2×C4×C149C2×D411yescharacteristic
70C2×C4×C149C2×Q812yes—
71C2×C4×C149#4112yes—
72C2×C4×C149C2411yescharacteristic
73C22×C149—22no—
74C22×C149C22⋊Q812yes—
75C22×C149C22×D411yescharacteristic
76C2×D149—22no—
77C2×D149—42no—
78C4×C149—22no—
79C4×C149—22no—
80C4×C149—44no—
81C4×C149C22⋊Q812yes—
82C4×C149C22×Q811yescharacteristic
83C4×C149C2×#4111yescharacteristic
84Dic149—22no—
85Dic149—42no—
86C2×C149—22no—
87C2×C149C2×C22⋊Q811yescharacteristic
88C2×C149#57512yes—
89D149—42no—
90C149#308011yescharacteristic, complemented, Sylow
91#3080—1491nomaximal, Sylow
92C2×#125D14911yescharacteristic, complemented
93C4×#41—1491no—
94#479—1494no—
95#478—1494no—
96#428—1492no—
97#423—1491no—
98#417—1492no—
99C2×#41—1491no—
100C2×M16—1492no—
101#125—21no—
102#125—21no—
103#125C2×D14914yes—
104C4×Q8—1492no—
105C4×D4—2982no—
106C4×D4—1492no—
107#117—2981no—
108#117—1491no—
109C2×C4⋊C4—22no—
110C2×C4⋊C4C2×D14912yes—
111C2×C42—2981no—
112C2×C42C2×D14911yescharacteristic
113#107—1494no—
114#106—1494no—
115C4⋊C8—1494no—
116#103—1494no—
117#102—1494no—
118#41—2982no—
119#41—1494no—
120C2×Q8—1491no—
121C2×D4—2981no—
122C2×D4—1491no—
123C22×C4—22no—
124C22×C4—2981no—
125C22×C4—2982no—
126C22×C4C22⋊D14912yes—
127C22×C4C22×D14911yescharacteristic
128M16—2984no—
129C2×C8—1494no—
130C4⋊C4—24no—
131C4⋊C4—24no—
132C4⋊C4—22no—
133C4⋊C4—2982no—
134C4⋊C4—1492no—
135C4⋊C4C22×D14914yes—
136C22⋊C4—2981no—
137C22⋊C4—2982no—
138C42—2981no—
139C42—2982no—
140C42C22⋊D14911yescharacteristic
141C42C22⋊D14911yescharacteristic
142C42C22×D14912yes—
143C23—2981no—
144C23C2×C22⋊D14911yescharacteristic
145Q8—2981no—
146Q8—1492no—
147D4—2984no—
148D4—2981no—
149D4—1492no—
150C2×C4—24no—
151C2×C4—42no—
152C2×C4—44no—
153C2×C4—2981no—
154C2×C4—2984no—
155C2×C4—2982no—
156C2×C4—5964no—
157C2×C4C2×C22⋊D14912yes—
158C2×C4C2×C22⋊D14912yes—
159C2×C4C2×C22⋊D14911yescharacteristic
160C2×C4Q8×D14912yes—
161C2×C4#1455873712yes—
162C2×C4C23×D14911yescharacteristic
163C8—2984no—
164C22—22no—
165C22—2982no—
166C22—5962no—
167C22#1801188712yes—
168C22C22×C22⋊D14911yescharacteristic
169C4—22no—
170C4—22no—
171C4—44no—
172C4—2982no—
173C4—5962no—
174C4#1801188712yes—
175C4C2×Q8×D14911yescharacteristic
176C4C2×#1455873711yescharacteristic
177C2—22no—
178C2—5962no—
179C2C2×#1801188711yescharacteristic
180C2#2375042312yes—
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC2×#125×C149C2
socleC22×C149C22×D4
prime radicalC2×#14558736C22
hypercenterC2×#125D149
hypocenterC149#3080
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
2. #23749929C2semidirect
3. #23749922C2semidirect
4. #23749665C2semidirect
5. #23749649C2semidirect
7. C2×#125×C149C2semidirect
90. C149#3080semidirect
92. C2×#125D149semidirect

Maximal subgroups

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

subgroupindex
C4×#145587362
#237499292
#237499222
#237496652
#237496492
#237496242
C2×#125×C1492
#3080149