Finite Group Databasebeta

← #34071138

Subgroups — #34071138

Order 19328.

236 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 41 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#23752928C211yesmaximal, characteristic, complemented
2#23752394C211yesmaximal, characteristic, complemented
3#23752387C212yesmaximal, complemented
4#23752008C212yesmaximal, complemented
5#356×C151C211yesmaximal, characteristic, complemented
6#18012787C2211yescharacteristic
7#18012770—21no—
8#18012767—22no—
9#18012728—21no—
10#18012728C2212yes—
11#18012714—22no—
12C4×D604—21no—
13#18012697—22no—
14#18012667—21no—
15#18012665—22no—
16#18012658C2211yescharacteristic
17C4⋊Q8×C151C2211yescharacteristic
18#101×C151C2212yes—
19#14559005—41no—
20#14559004—22no—
21#14559004—21no—
22Q8×D151—41no—
23C2×D604—21no—
24C2×D604—21no—
25C2×D604D412yes—
26C2×C4×D151—22no—
27#14558994—41no—
28#14558993—42no—
29#14558991—41no—
30D1208—42no—
31#14558988—21no—
32C4⋊Dic151—21no—
33(C2×D151)⋊C4—22no—
34(C2×D151)⋊C4—22no—
35(C2×D151)⋊C4—22no—
36C4×Dic151—21no—
37C4×Dic151D412yes—
38C2×Q8×C151D411yescharacteristic
39C2×Q8×C151C2311yescharacteristic
40M16×C151—22no—
41C4⋊C4×C151—22no—
42C42×C151D411yescharacteristic
43C22×D151—22no—
44Dic302—22no—
45Dic302—21no—
46D604—22no—
47D604—21no—
48D604—42no—
49D604—42no—
50D604—81no—
51C22⋊D151—41no—
52C2×Dic151—22no—
53C4×D151—44no—
54C4×D151—42no—
55C4×D151—41no—
56C151⋊C8—41no—
57Q8×C151—41no—
58Q8×C151—41no—
59C2×C4×C151—21no—
60C2×C4×C151—21no—
61C2×C4×C151C2×D412yes—
62C2×C4×C151C2×D411yescharacteristic
63C8×C151—42no—
64C22×C151#12011yescharacteristic
65C2×D151—42no—
66C2×D151—42no—
67C2×D151—41no—
68C2×D151—42no—
69C4×C151—22no—
70C4×C151—22no—
71C4×C151—21no—
72C4×C151—41no—
73Dic151—42no—
74Dic151—41no—
75C2×C151—21no—
76C2×C151B(4,𝔽2)11yescharacteristic
77D151—81no—
78D151—82no—
79C151#220411yescharacteristic, complemented, Sylow
80#2204—1511nomaximal, Sylow
81#555—1511no—
82#456—1511no—
83#454—1512no—
84#356D15111yescharacteristic, complemented
85#355—1512no—
862−1+4—1511no—
87#137—3021no—
88AGL(1,ℤ/8)—3022no—
89C4⋊Q8C2×D15111yescharacteristic
90#124—3021no—
91#124—1512no—
92#121—3022no—
93C4×D4—3021no—
94#117—3022no—
95#104—3022no—
96#104—3021no—
97#101—1511no—
98#101C2×D15112yes—
99#41—3022no—
100#41—3021no—
101#41—6041no—
102C2×Q8—6041no—
103C2×Q8D60411yescharacteristic
104C2×Q8C22×D15111yescharacteristic
105C2×D4—3021no—
106C2×D4—3021no—
107C2×D4—1512no—
108C22×C4—3022no—
109Q16—6041no—
110SD16—6042no—
111SD16—6041no—
112D8—6042no—
113M16—22no—
114M16—3021no—
115C4⋊C4—22no—
116C4⋊C4—3021no—
117C22⋊C4—3022no—
118C22⋊C4—3022no—
119C22⋊C4—3022no—
120C42—3021no—
121C42—1512no—
122C42D60411yescharacteristic
123C23—3022no—
124Q8—41no—
125Q8—41no—
126Q8—3022no—
127Q8—3021no—
128D4—3022no—
129D4—3021no—
130D4—6042no—
131D4—6042no—
132D4—6041no—
133D4—12081no—
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—3022no—
137C2×C4—6044no—
138C2×C4—6042no—
139C2×C4—6041no—
140C2×C4D4×D15112yes—
141C2×C4C2×D60411yescharacteristic
142C8—42no—
143C8—6041no—
144C22—6042no—
145C22—6042no—
146C22—6041no—
147C22—6042no—
148C22#1801270911yescharacteristic
149C4—22no—
150C4—22no—
151C4—21no—
152C4—41no—
153C4—6042no—
154C4—6041no—
155C2—21no—
156C2—12082no—
157C2—12081no—
158C2#2375240011yescharacteristic
subgroupG/H
centerC2#23752400
commutator, cosocleC2×Q8×C151C23
FrattiniC2×Q8C22×D151
Fitting#356×C151C2
socleC2×C151B(4,𝔽2)
hypercenter#356D151
hypocenterC151#2204
LCSG ▷ C2×Q8×C151 ▷ C22×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #356

Complements

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

NH ≅ G/Ntype
1. #23752928C2semidirect
2. #23752394C2semidirect
3. #23752387C2semidirect
4. #23752008C2semidirect
5. #356×C151C2semidirect
79. C151#2204semidirect
84. #356D151semidirect

Maximal subgroups

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

subgroupindex
#237529282
#237523942
#237523872
#237520082
#356×C1512
#2204151