Finite Group Databasebeta

← #34070214

Subgroups — #34070214

Order 19328.

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#23753012C211yesmaximal, characteristic, complemented
2#23753010C212yesmaximal, complemented
3#23752178C212yesmaximal, complemented
4C151⋊#338C211yesmaximal, characteristic, complemented
5#408×C151C211yesmaximal, characteristic, complemented
6C2×#14559004C2212yes—
7#18012772—22no—
8#18012770—22no—
9#18012769—22no—
10#18012767—22no—
11#18012765—22no—
12#18012764—22no—
13#18012761—22no—
14#18012759—24no—
15C2×#14558988C2212yes—
16(C2×D151)⋊C8—24no—
17C2×#41×C151C2211yescharacteristic
18C2×M16×C151C2211yescharacteristic
19C22×C8×C151C2211yescharacteristic
20C22⋊C8×C151—22no—
21#14559004—22no—
22#14559004—22no—
23#14559004—22no—
24#14559004—22no—
25C2×Dic302D412yes—
26C2×D604D412yes—
27C2×C22⋊D151—22no—
28C2×C4×D151—22no—
29Dic604—22no—
30#14558994—24no—
31#14558993—24no—
32#14558992—24no—
33#14558991—24no—
34D1208—22no—
35#14558989—24no—
36#14558988—22no—
37#14558988—22no—
38C2×C151⋊C8D414yes—
39#41×C151—22no—
40#41×C151—22no—
41C2×Q8×C151D411yescharacteristic
42C2×D4×C151—21no—
43C2×D4×C151D411yescharacteristic
44C22×C4×C151—21no—
45C22×C4×C151C2311yescharacteristic
46M16×C151—22no—
47C2×C8×C151—21no—
48C2×C8×C151—22no—
49C2×C8×C151D412yes—
50C22×D151—22no—
51Dic302—22no—
52Dic302—22no—
53D604—22no—
54D604—22no—
55C22⋊D151—42no—
56C22⋊D151—42no—
57C2×Dic151—22no—
58C4×D151—42no—
59C4×D151—42no—
60C151⋊C8—24no—
61C23×C151—21no—
62C23×C151#4111yescharacteristic
63Q8×C151—22no—
64D4×C151—22no—
65D4×C151—42no—
66C2×C4×C151—21no—
67C2×C4×C151—41no—
68C2×C4×C151—41no—
69C2×C4×C151C2×D412yes—
70C2×C4×C151C2×D412yes—
71C2×C4×C151C2×D411yescharacteristic
72C2×C4×C151C2×D411yescharacteristic
73C8×C151—22no—
74C8×C151—41no—
75C22×C151—41no—
76C22×C151—42no—
77C22×C151—41no—
78C22×C151#12112yes—
79C22×C151#12111yescharacteristic
80C2×D151—44no—
81C2×D151—42no—
82C4×C151—41no—
83C4×C151#12011yescharacteristic
84C4×C151#12012yes—
85C4×C151#12711yescharacteristic
86Dic151—42no—
87C2×C151—22no—
88C2×C151—21no—
89C2×C151—81no—
90C2×C151#39211yescharacteristic
91D151—82no—
92C151#201711yescharacteristic, complemented, Sylow
93#2017—1511nomaximal, Sylow
94#575—1512no—
95#575—1511no—
96#408—1512no—
97#408D15111yescharacteristic, complemented
98#338—1511no—
99C2×#41—1512no—
100C2×#41C2×D15111yescharacteristic
101#137—3022no—
102#137—3022no—
103#137—3022no—
104AGL(1,ℤ/8)—3022no—
105AGL(1,ℤ/8)—3022no—
106AGL(1,ℤ/8)—3022no—
107#135—3024no—
108#135—3022no—
109C2×M16—1512no—
110C2×M16C2×D15111yescharacteristic
111C22×C8C2×D15111yescharacteristic
112C22⋊C8—22no—
113C22⋊C8—3024no—
114#41—22no—
115#41—22no—
116#41—3022no—
117#41—3022no—
118#41—3022no—
119#41—3022no—
120C2×Q8—1512no—
121C2×Q8D60411yescharacteristic
122C2×D4—21no—
123C2×D4—3022no—
124C2×D4—1512no—
125C2×D4D60411yescharacteristic
126C22×C4—21no—
127C22×C4—3022no—
128C22×C4C22×D15111yescharacteristic
129Q16—3022no—
130Q16—3024no—
131SD16—3024no—
132SD16—3024no—
133SD16—3024no—
134D8—3022no—
135D8—3024no—
136M16—22no—
137M16—3022no—
138M16—3022no—
139C2×C8—22no—
140C2×C8—21no—
141C2×C8—1514no—
142C2×C8C22⋊D15112yes—
143C23—21no—
144C23—3022no—
145C23#1455900411yescharacteristic
146Q8—22no—
147Q8—3022no—
148Q8—3022no—
149D4—22no—
150D4—42no—
151D4—3022no—
152D4—3022no—
153D4—6042no—
154D4—6042no—
155C2×C4—21no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—3022no—
159C2×C4—6042no—
160C2×C4—6042no—
161C2×C4D4×D15112yes—
162C2×C4D4×D15112yes—
163C2×C4C2×C22⋊D15111yescharacteristic
164C2×C4C2×D60411yescharacteristic
165C8—22no—
166C8—41no—
167C8—3024no—
168C22—41no—
169C22—42no—
170C22—41no—
171C22—6044no—
172C22—6042no—
173C22#1801271212yes—
174C22#1801271311yescharacteristic
175C4—41no—
176C4—6042no—
177C4#1801270711yescharacteristic
178C4#1801270912yes—
179C4#1801273511yescharacteristic
180C2—21no—
181C2—22no—
182C2—81no—
183C2—12082no—
184C2#2375212111yescharacteristic
subgroupG/H
centerC4#18012735
commutator, cosocleC22×C4×C151C23
FrattiniC22×C4C22×D151
Fitting#408×C151C2
socleC2×C151#392
hypercenter#408D151
hypocenterC151#2017
LCSG ▷ C22×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C4 ◁ C22×C4 ◁ #408

Complements

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

NH ≅ G/Ntype
1. #23753012C2semidirect
2. #23753010C2semidirect
3. #23752178C2semidirect
4. C151⋊#338C2semidirect
5. #408×C151C2semidirect
92. C151#2017semidirect
97. #408D151semidirect

Maximal subgroups

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

subgroupindex
#237530122
#237530102
#237521782
C151⋊#3382
#408×C1512
#2017151