Finite Group Databasebeta

← #34070213

Subgroups — #34070213

Order 19328.

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#23753010C212yesmaximal, complemented
2#23752180C211yesmaximal, characteristic, complemented
3#23752179C212yesmaximal, complemented
4C151⋊#338C211yesmaximal, characteristic, complemented
5#575×C151C211yesmaximal, characteristic, complemented
6C2×#14559004C2211yescharacteristic
7#18012770—22no—
8#18012769—22no—
9#18012765—22no—
10#18012764—22no—
11#18012759—24no—
12C2×#14558988C2212yes—
13C22×C151⋊C8C2211yescharacteristic
14C22⋊(C151⋊C8)—24no—
15(C2×D151)⋊C8—22no—
16C2×#41×C151C2212yes—
17#137×C151—22no—
18AGL(1,ℤ/8)×C151—22no—
19#135×C151—22no—
20C2×M16×C151C2211yescharacteristic
21#14559004—22no—
22#14559004—22no—
23C2×Dic302D411yescharacteristic
24C2×D604D411yescharacteristic
25C2×C22⋊D151—21no—
26C2×C4×D151—21no—
27#14558994—24no—
28#14558992—24no—
29#14558991—24no—
30#14558989—24no—
31#14558988—22no—
32#14558988—22no—
33C2×C151⋊C8—21no—
34C2×C151⋊C8—22no—
35C2×C151⋊C8D414yes—
36#41×C151—22no—
37#41×C151—22no—
38#41×C151—22no—
39#41×C151—22no—
40C2×Q8×C151D412yes—
41C2×D4×C151—22no—
42C2×D4×C151D412yes—
43C22×C4×C151—22no—
44C22×C4×C151C2311yescharacteristic
45Q16×C151—22no—
46SD16×C151—24no—
47D8×C151—22no—
48M16×C151—22no—
49C2×C8×C151D412yes—
50C22×D151—21no—
51Dic302—22no—
52D604—22no—
53C22⋊D151—42no—
54C2×Dic151—21no—
55C4×D151—41no—
56C4×D151—41no—
57C151⋊C8—24no—
58C151⋊C8—41no—
59C23×C151—22no—
60C23×C151#4111yescharacteristic
61Q8×C151—22no—
62Q8×C151—22no—
63D4×C151—22no—
64D4×C151—22no—
65D4×C151—42no—
66D4×C151—42no—
67C2×C4×C151—22no—
68C2×C4×C151—42no—
69C2×C4×C151—42no—
70C2×C4×C151C2×D411yescharacteristic
71C2×C4×C151C2×D412yes—
72C2×C4×C151C2×D412yes—
73C2×C4×C151C2×D411yescharacteristic
74C8×C151—22no—
75C22×C151—41no—
76C22×C151—44no—
77C22×C151—42no—
78C22×C151#12111yescharacteristic
79C22×C151#12112yes—
80C2×D151—42no—
81C2×D151—41no—
82C4×C151—42no—
83C4×C151#12012yes—
84C4×C151#12011yescharacteristic
85C4×C151#12711yescharacteristic
86Dic151—41no—
87C2×C151—21no—
88C2×C151—22no—
89C2×C151—82no—
90C2×C151#39211yescharacteristic
91D151—81no—
92C151#201711yescharacteristic, complemented, Sylow
93#2017—1511nomaximal, Sylow
94#575—1512no—
95#575D15111yescharacteristic, complemented
96#408—1512no—
97#408—1511no—
98#338—1511no—
99C2×#41—1511no—
100C2×#41C2×D15112yes—
101#137—22no—
102#137—3022no—
103#137—3022no—
104AGL(1,ℤ/8)—22no—
105AGL(1,ℤ/8)—3022no—
106AGL(1,ℤ/8)—3022no—
107#135—22no—
108#135—3024no—
109C2×M16—1512no—
110C2×M16C2×D15111yescharacteristic
111C22×C8—1511no—
112C22⋊C8—3024no—
113C22⋊C8—3022no—
114#41—22no—
115#41—22no—
116#41—22no—
117#41—22no—
118#41—3022no—
119#41—3022no—
120C2×Q8—1511no—
121C2×Q8C22⋊D15112yes—
122C2×D4—22no—
123C2×D4—3021no—
124C2×D4—1511no—
125C2×D4C22⋊D15112yes—
126C22×C4—22no—
127C22×C4—3021no—
128C22×C4C22×D15111yescharacteristic
129Q16—22no—
130Q16—3024no—
131SD16—24no—
132SD16—3024no—
133SD16—3024no—
134D8—22no—
135D8—3024no—
136M16—22no—
137M16—3022no—
138M16—3022no—
139C2×C8—3022no—
140C2×C8—3021no—
141C2×C8—1514no—
142C2×C8C22⋊D15112yes—
143C23—22no—
144C23—3021no—
145C23#1455900311yescharacteristic
146Q8—22no—
147Q8—22no—
148Q8—3022no—
149D4—22no—
150D4—22no—
151D4—42no—
152D4—42no—
153D4—3022no—
154D4—6042no—
155C2×C4—22no—
156C2×C4—42no—
157C2×C4—42no—
158C2×C4—3021no—
159C2×C4—6041no—
160C2×C4—6041no—
161C2×C4D4×D15111yescharacteristic
162C2×C4D4×D15112yes—
163C2×C4C2×C22⋊D15112yes—
164C2×C4C2×C22⋊D15111yescharacteristic
165C8—22no—
166C8—3024no—
167C8—6041no—
168C22—41no—
169C22—44no—
170C22—42no—
171C22—6042no—
172C22—6041no—
173C22#1801271011yescharacteristic
174C22#1801271112yes—
175C4—42no—
176C4—6041no—
177C4#1801270712yes—
178C4#1801270811yescharacteristic
179C4#1801273511yescharacteristic
180C2—22no—
181C2—21no—
182C2—82no—
183C2—12081no—
184C2#2375212011yescharacteristic
subgroupG/H
centerC4#18012735
commutator, cosocleC22×C4×C151C23
FrattiniC22×C4C22×D151
Fitting#575×C151C2
socleC2×C151#392
hypercenter#575D151
hypocenterC151#2017
LCSG ▷ C22×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C4 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. #23753010C2semidirect
2. #23752180C2semidirect
3. #23752179C2semidirect
4. C151⋊#338C2semidirect
5. #575×C151C2semidirect
92. C151#2017semidirect
95. #575D151semidirect

Maximal subgroups

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

subgroupindex
#237530102
#237521802
#237521792
C151⋊#3382
#575×C1512
#2017151