Finite Group Databasebeta

← #34045794

Subgroups — #34045794

Order 19072.

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

normal subgroups only

This group has 350 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#23750423C212yesmaximal, complemented
2#23749593C211yesmaximal, characteristic, complemented
3#23749592C212yesmaximal, complemented
4#23749383C211yesmaximal, characteristic, complemented
5#575×C149C211yesmaximal, characteristic, complemented
6C2×#14558736C2211yescharacteristic
7#18011942—22no—
8#18011941—22no—
9#18011937—22no—
10#18011936—22no—
11#18011931—24no—
12C2×#14558720C2212yes—
13C22×#11924746C2211yescharacteristic
14C22⋊#11924746—24no—
15#18011823—22no—
16C2×#41×C149C2212yes—
17#137×C149—22no—
18AGL(1,ℤ/8)×C149—22no—
19#135×C149—22no—
20C2×M16×C149C2211yescharacteristic
21#14558736—22no—
22#14558736—22no—
23C2×Dic298D411yescharacteristic
24C2×D596D411yescharacteristic
25C2×C22⋊D149—21no—
26C2×C4×D149—21no—
27#14558726—24no—
28#14558724—24no—
29#14558723—24no—
30#14558721—24no—
31#14558720—22no—
32#14558720—22no—
33C2×#11924746—21no—
34C2×#11924746—22no—
35C2×#11924746D414yes—
36#41×C149—22no—
37#41×C149—22no—
38#41×C149—22no—
39#41×C149—22no—
40C2×Q8×C149D412yes—
41C2×D4×C149—22no—
42C2×D4×C149D412yes—
43C22×C4×C149—22no—
44C22×C4×C149C2311yescharacteristic
45Q16×C149—22no—
46SD16×C149—24no—
47D8×C149—22no—
48M16×C149—22no—
49C2×C8×C149D412yes—
50C22×D149—21no—
51Dic298—22no—
52D596—22no—
53C22⋊D149—42no—
54C2×Dic149—21no—
55C4×D149—41no—
56C4×D149—41no—
57#11924746—24no—
58#11924746—41no—
59C23×C149—22no—
60C23×C149#4111yescharacteristic
61Q8×C149—22no—
62Q8×C149—22no—
63D4×C149—22no—
64D4×C149—22no—
65D4×C149—42no—
66D4×C149—42no—
67C2×C4×C149—22no—
68C2×C4×C149—42no—
69C2×C4×C149—42no—
70C2×C4×C149C2×D411yescharacteristic
71C2×C4×C149C2×D412yes—
72C2×C4×C149C2×D412yes—
73C2×C4×C149C2×D411yescharacteristic
74C8×C149—22no—
75C22×C149—41no—
76C22×C149—44no—
77C22×C149—42no—
78C22×C149#12111yescharacteristic
79C22×C149#12112yes—
80C2×D149—42no—
81C2×D149—41no—
82C4×C149—42no—
83C4×C149#12012yes—
84C4×C149#12011yescharacteristic
85C4×C149#12711yescharacteristic
86Dic149—41no—
87C2×C149—21no—
88C2×C149—22no—
89C2×C149—82no—
90C2×C149#39211yescharacteristic
91D149—81no—
92C149#201711yescharacteristic, complemented, Sylow
93#2017—1491nomaximal, Sylow
94#575—1492no—
95#575D14911yescharacteristic, complemented
96#408—1492no—
97#408—1491no—
98#338—1491no—
99C2×#41—1491no—
100C2×#41C2×D14912yes—
101#137—22no—
102#137—2982no—
103#137—2982no—
104AGL(1,ℤ/8)—22no—
105AGL(1,ℤ/8)—2982no—
106AGL(1,ℤ/8)—2982no—
107#135—22no—
108#135—2984no—
109C2×M16—1492no—
110C2×M16C2×D14911yescharacteristic
111C22×C8—1491no—
112C22⋊C8—2984no—
113C22⋊C8—2982no—
114#41—22no—
115#41—22no—
116#41—22no—
117#41—22no—
118#41—2982no—
119#41—2982no—
120C2×Q8—1491no—
121C2×Q8C22⋊D14912yes—
122C2×D4—22no—
123C2×D4—2981no—
124C2×D4—1491no—
125C2×D4C22⋊D14912yes—
126C22×C4—22no—
127C22×C4—2981no—
128C22×C4C22×D14911yescharacteristic
129Q16—22no—
130Q16—2984no—
131SD16—24no—
132SD16—2984no—
133SD16—2984no—
134D8—22no—
135D8—2984no—
136M16—22no—
137M16—2982no—
138M16—2982no—
139C2×C8—2982no—
140C2×C8—2981no—
141C2×C8—1494no—
142C2×C8C22⋊D14912yes—
143C23—22no—
144C23—2981no—
145C23#1455873511yescharacteristic
146Q8—22no—
147Q8—22no—
148Q8—2982no—
149D4—22no—
150D4—22no—
151D4—42no—
152D4—42no—
153D4—2982no—
154D4—5962no—
155C2×C4—22no—
156C2×C4—42no—
157C2×C4—42no—
158C2×C4—2981no—
159C2×C4—5961no—
160C2×C4—5961no—
161C2×C4D4×D14912yes—
162C2×C4D4×D14911yescharacteristic
163C2×C4C2×C22⋊D14911yescharacteristic
164C2×C4C2×C22⋊D14912yes—
165C8—22no—
166C8—2984no—
167C8—5961no—
168C22—41no—
169C22—44no—
170C22—42no—
171C22—5962no—
172C22—5961no—
173C22#1801188211yescharacteristic
174C22#1801188312yes—
175C4—42no—
176C4—5961no—
177C4#1801187912yes—
178C4#1801188011yescharacteristic
179C4#1801190711yescharacteristic
180C2—22no—
181C2—21no—
182C2—82no—
183C2—11921no—
184C2#2374953311yescharacteristic
subgroupG/H
centerC4#18011907
commutator, cosocleC22×C4×C149C23
FrattiniC22×C4C22×D149
Fitting#575×C149C2
socleC2×C149#392
hypercenter#575D149
hypocenterC149#2017
LCSG ▷ C22×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C4 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. #23750423C2semidirect
2. #23749593C2semidirect
3. #23749592C2semidirect
4. #23749383C2semidirect
5. #575×C149C2semidirect
92. C149#2017semidirect
95. #575D149semidirect

Maximal subgroups

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

subgroupindex
#237504232
#237495932
#237495922
#237493832
#575×C1492
#2017149