Finite Group Databasebeta

← #34071136

Subgroups — #34071136

Order 19328.

236 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 45 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#23752394C211yesmaximal, characteristic, complemented
2#23752384C212yesmaximal, complemented
3#23752011C211yesmaximal, characteristic, complemented
4#23752009C212yesmaximal, complemented
5#555×C151C211yesmaximal, characteristic, complemented
6#18012787C2211yescharacteristic
7#18012770—21no—
8#18012765—22no—
9#18012667—22no—
10#18012667—21no—
11#18012658C2211yescharacteristic
12#18012658C2212yes—
13C4⋊Q8×C151C2211yescharacteristic
14#124×C151—21no—
15#124×C151C2212yes—
16#121×C151—22no—
17C4×D4×C151—21no—
18#117×C151—22no—
19#14559005—41no—
20#14559004—22no—
21#14559004—21no—
22Q8×D151—41no—
23#14558994—41no—
24#14558992—42no—
25#14558991—41no—
26#14558989—42no—
27#14558988—22no—
28#14558988—21no—
29C2×Q8×C151D411yescharacteristic
30C2×Q8×C151C2311yescharacteristic
31C2×D4×C151—21no—
32C2×D4×C151—21no—
33C2×D4×C151D412yes—
34C22×C4×C151—22no—
35C4⋊C4×C151—21no—
36C4⋊C4×C151—22no—
37C22⋊C4×C151—22no—
38C22⋊C4×C151—22no—
39C22⋊C4×C151—22no—
40C42×C151—21no—
41C42×C151D412yes—
42C42×C151D411yescharacteristic
43Dic302—22no—
44Dic302—21no—
45D604—22no—
46D604—21no—
47C22⋊D151—41no—
48C4×D151—42no—
49C4×D151—41no—
50C151⋊C8—42no—
51C151⋊C8—41no—
52C23×C151—22no—
53Q8×C151—41no—
54Q8×C151—41no—
55D4×C151—42no—
56D4×C151—42no—
57D4×C151—81no—
58C2×C4×C151—21no—
59C2×C4×C151—21no—
60C2×C4×C151—22no—
61C2×C4×C151—44no—
62C2×C4×C151C2×D411yescharacteristic
63C2×C4×C151C2×D412yes—
64C22×C151—42no—
65C22×C151—42no—
66C22×C151—42no—
67C22×C151#12011yescharacteristic
68C2×D151—41no—
69C4×C151—22no—
70C4×C151—22no—
71C4×C151—21no—
72C4×C151—42no—
73C4×C151—41no—
74Dic151—41no—
75C2×C151—21no—
76C2×C151—82no—
77C2×C151B(4,𝔽2)11yescharacteristic
78D151—81no—
79C151#220411yescharacteristic, complemented, Sylow
80#2204—1511nomaximal, Sylow
81#555D15111yescharacteristic, complemented
82#456—1511no—
83#454—1512no—
84#356—1511no—
85#355—1512no—
862−1+4—1511no—
87#137—3021no—
88AGL(1,ℤ/8)—3022no—
89C4⋊Q8C2×D15111yescharacteristic
90#124—21no—
91#124C2×D15112yes—
92#121—22no—
93C4×D4—21no—
94#117—22no—
95#104—3022no—
96#104—3021no—
97#101—1511no—
98#101—1512no—
99#41—3022no—
100#41—3021no—
101#41—6041no—
102C2×Q8—6041no—
103C2×Q8C22⋊D15111yescharacteristic
104C2×Q8C22×D15111yescharacteristic
105C2×D4—21no—
106C2×D4—21no—
107C2×D4C22⋊D15112yes—
108C22×C4—22no—
109Q16—6041no—
110SD16—6042no—
111SD16—6041no—
112D8—6042no—
113M16—3022no—
114M16—3021no—
115C4⋊C4—21no—
116C4⋊C4—22no—
117C22⋊C4—22no—
118C22⋊C4—22no—
119C22⋊C4—22no—
120C42—21no—
121C42C22⋊D15112yes—
122C42C22⋊D15111yescharacteristic
123C23—22no—
124Q8—41no—
125Q8—41no—
126Q8—3022no—
127Q8—3021no—
128D4—42no—
129D4—42no—
130D4—81no—
131D4—3022no—
132D4—3021no—
133D4—6041no—
134C2×C4—21no—
135C2×C4—22no—
136C2×C4—21no—
137C2×C4—44no—
138C2×C4—6042no—
139C2×C4—6041no—
140C2×C4C2×C22⋊D15111yescharacteristic
141C2×C4C2×C22⋊D15112yes—
142C8—6042no—
143C8—6041no—
144C22—42no—
145C22—42no—
146C22—42no—
147C22—6041no—
148C22#1801270811yescharacteristic
149C4—22no—
150C4—22no—
151C4—21no—
152C4—42no—
153C4—41no—
154C4—6041no—
155C2—21no—
156C2—82no—
157C2—12081no—
158C2#2375239911yescharacteristic
subgroupG/H
centerC2#23752399
commutator, cosocleC2×Q8×C151C23
FrattiniC2×Q8C22×D151
Fitting#555×C151C2
socleC2×C151B(4,𝔽2)
hypercenter#555D151
hypocenterC151#2204
LCSG ▷ C2×Q8×C151 ▷ C22×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #555

Complements

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

NH ≅ G/Ntype
1. #23752394C2semidirect
2. #23752384C2semidirect
3. #23752011C2semidirect
4. #23752009C2semidirect
5. #555×C151C2semidirect
79. C151#2204semidirect
81. #555D151semidirect

Maximal subgroups

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

subgroupindex
#237523942
#237523842
#237520112
#237520092
#555×C1512
#2204151