Finite Group Databasebeta

← #34045795

Subgroups — #34045795

Order 19072.

350 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 69 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#23750425C211yesmaximal, characteristic, complemented
2#23750423C212yesmaximal, complemented
3#23749591C212yesmaximal, complemented
4#23749383C211yesmaximal, characteristic, complemented
5#408×C149C211yesmaximal, characteristic, complemented
6C2×#14558736C2212yes—
7#18011944—22no—
8#18011942—22no—
9#18011941—22no—
10#18011939—22no—
11#18011937—22no—
12#18011936—22no—
13#18011933—22no—
14#18011931—24no—
15C2×#14558720C2212yes—
16#18011823—24no—
17C2×#41×C149C2211yescharacteristic
18C2×M16×C149C2211yescharacteristic
19C22×C8×C149C2211yescharacteristic
20C22⋊C8×C149—22no—
21#14558736—22no—
22#14558736—22no—
23#14558736—22no—
24#14558736—22no—
25C2×Dic298D412yes—
26C2×D596D412yes—
27C2×C22⋊D149—22no—
28C2×C4×D149—22no—
29Dic596—22no—
30#14558726—24no—
31#14558725—24no—
32#14558724—24no—
33#14558723—24no—
34D1192—22no—
35#14558721—24no—
36#14558720—22no—
37#14558720—22no—
38C2×#11924746D414yes—
39#41×C149—22no—
40#41×C149—22no—
41C2×Q8×C149D411yescharacteristic
42C2×D4×C149—21no—
43C2×D4×C149D411yescharacteristic
44C22×C4×C149—21no—
45C22×C4×C149C2311yescharacteristic
46M16×C149—22no—
47C2×C8×C149—21no—
48C2×C8×C149—22no—
49C2×C8×C149D412yes—
50C22×D149—22no—
51Dic298—22no—
52Dic298—22no—
53D596—22no—
54D596—22no—
55C22⋊D149—42no—
56C22⋊D149—42no—
57C2×Dic149—22no—
58C4×D149—42no—
59C4×D149—42no—
60#11924746—24no—
61C23×C149—21no—
62C23×C149#4111yescharacteristic
63Q8×C149—22no—
64D4×C149—22no—
65D4×C149—42no—
66C2×C4×C149—21no—
67C2×C4×C149—41no—
68C2×C4×C149—41no—
69C2×C4×C149C2×D412yes—
70C2×C4×C149C2×D412yes—
71C2×C4×C149C2×D411yescharacteristic
72C2×C4×C149C2×D411yescharacteristic
73C8×C149—22no—
74C8×C149—41no—
75C22×C149—41no—
76C22×C149—42no—
77C22×C149—41no—
78C22×C149#12112yes—
79C22×C149#12111yescharacteristic
80C2×D149—44no—
81C2×D149—42no—
82C4×C149—41no—
83C4×C149#12011yescharacteristic
84C4×C149#12012yes—
85C4×C149#12711yescharacteristic
86Dic149—42no—
87C2×C149—22no—
88C2×C149—21no—
89C2×C149—81no—
90C2×C149#39211yescharacteristic
91D149—82no—
92C149#201711yescharacteristic, complemented, Sylow
93#2017—1491nomaximal, Sylow
94#575—1492no—
95#575—1491no—
96#408—1492no—
97#408D14911yescharacteristic, complemented
98#338—1491no—
99C2×#41—1492no—
100C2×#41C2×D14911yescharacteristic
101#137—2982no—
102#137—2982no—
103#137—2982no—
104AGL(1,ℤ/8)—2982no—
105AGL(1,ℤ/8)—2982no—
106AGL(1,ℤ/8)—2982no—
107#135—2984no—
108#135—2982no—
109C2×M16—1492no—
110C2×M16C2×D14911yescharacteristic
111C22×C8C2×D14911yescharacteristic
112C22⋊C8—22no—
113C22⋊C8—2984no—
114#41—22no—
115#41—22no—
116#41—2982no—
117#41—2982no—
118#41—2982no—
119#41—2982no—
120C2×Q8—1492no—
121C2×Q8D59611yescharacteristic
122C2×D4—21no—
123C2×D4—2982no—
124C2×D4—1492no—
125C2×D4D59611yescharacteristic
126C22×C4—21no—
127C22×C4—2982no—
128C22×C4C22×D14911yescharacteristic
129Q16—2982no—
130Q16—2984no—
131SD16—2984no—
132SD16—2984no—
133SD16—2984no—
134D8—2982no—
135D8—2984no—
136M16—22no—
137M16—2982no—
138M16—2982no—
139C2×C8—22no—
140C2×C8—21no—
141C2×C8—1494no—
142C2×C8C22⋊D14912yes—
143C23—21no—
144C23—2982no—
145C23#1455873611yescharacteristic
146Q8—22no—
147Q8—2982no—
148Q8—2982no—
149D4—22no—
150D4—42no—
151D4—2982no—
152D4—2982no—
153D4—5962no—
154D4—5962no—
155C2×C4—21no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—2982no—
159C2×C4—5962no—
160C2×C4—5962no—
161C2×C4D4×D14912yes—
162C2×C4D4×D14912yes—
163C2×C4C2×C22⋊D14911yescharacteristic
164C2×C4C2×D59611yescharacteristic
165C8—22no—
166C8—41no—
167C8—2984no—
168C22—41no—
169C22—42no—
170C22—41no—
171C22—5964no—
172C22—5962no—
173C22#1801188412yes—
174C22#1801188511yescharacteristic
175C4—41no—
176C4—5962no—
177C4#1801187911yescharacteristic
178C4#1801188112yes—
179C4#1801190711yescharacteristic
180C2—21no—
181C2—22no—
182C2—81no—
183C2—11922no—
184C2#2374953411yescharacteristic
subgroupG/H
centerC4#18011907
commutator, cosocleC22×C4×C149C23
FrattiniC22×C4C22×D149
Fitting#408×C149C2
socleC2×C149#392
hypercenter#408D149
hypocenterC149#2017
LCSG ▷ C22×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C4 ◁ C22×C4 ◁ #408

Complements

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

NH ≅ G/Ntype
1. #23750425C2semidirect
2. #23750423C2semidirect
3. #23749591C2semidirect
4. #23749383C2semidirect
5. #408×C149C2semidirect
92. C149#2017semidirect
97. #408D149semidirect

Maximal subgroups

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

subgroupindex
#237504252
#237504232
#237495912
#237493832
#408×C1492
#2017149