Finite Group Databasebeta

← #34071135

Subgroups — #34071135

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#23752385C212yesmaximal, complemented
3#23752011C211yesmaximal, characteristic, complemented
4#23752008C212yesmaximal, complemented
5#456×C151C211yesmaximal, characteristic, complemented
6#18012764—22no—
7#18012728—21no—
8#18012728C2212yes—
9#18012714—22no—
10C4×D604—21no—
11#18012697—22no—
12#18012666—22no—
13#18012658C2212yes—
142−1+4×C151C2211yescharacteristic
15#137×C151—21no—
16C4⋊Q8×C151C2211yescharacteristic
17#104×C151—21no—
18#101×C151C2211yescharacteristic
19C2×D604—21no—
20C2×D604—21no—
21C2×D604D412yes—
22C2×C4×D151—22no—
23#14558991—42no—
24#14558989—42no—
25#14558988—22no—
26C4⋊Dic151—21no—
27(C2×D151)⋊C4—22no—
28(C2×D151)⋊C4—22no—
29(C2×D151)⋊C4—22no—
30C4×Dic151—21no—
31C4×Dic151D412yes—
32#41×C151—22no—
33#41×C151—21no—
34#41×C151—41no—
35C2×Q8×C151—41no—
36C2×Q8×C151D411yescharacteristic
37C2×Q8×C151C2311yescharacteristic
38Q16×C151—41no—
39SD16×C151—41no—
40M16×C151—21no—
41C4⋊C4×C151—22no—
42C42×C151D411yescharacteristic
43C22×D151—22no—
44D604—42no—
45D604—42no—
46D604—81no—
47C2×Dic151—22no—
48C4×D151—44no—
49C151⋊C8—42no—
50Q8×C151—22no—
51Q8×C151—21no—
52Q8×C151—41no—
53Q8×C151—41no—
54D4×C151—22no—
55D4×C151—21no—
56D4×C151—41no—
57C2×C4×C151—21no—
58C2×C4×C151—21no—
59C2×C4×C151—41no—
60C2×C4×C151—42no—
61C2×C4×C151C2×D412yes—
62C2×C4×C151C2×D411yescharacteristic
63C8×C151—41no—
64C22×C151—41no—
65C22×C151#12011yescharacteristic
66C2×D151—42no—
67C2×D151—42no—
68C2×D151—42no—
69C4×C151—22no—
70C4×C151—21no—
71C4×C151—22no—
72C4×C151—41no—
73C4×C151—41no—
74Dic151—42no—
75C2×C151—21no—
76C2×C151—81no—
77C2×C151B(4,𝔽2)11yescharacteristic
78D151—82no—
79C151#220411yescharacteristic, complemented, Sylow
80#2204—1511nomaximal, Sylow
81#555—1511no—
82#456D15111yescharacteristic, complemented
83#454—1512no—
84#356—1511no—
85#355—1512no—
862−1+4C2×D15111yescharacteristic
87#137—21no—
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—21no—
96#104—3022no—
97#101—1512no—
98#101C2×D15111yescharacteristic
99#41—22no—
100#41—21no—
101#41—41no—
102C2×Q8—41no—
103C2×Q8C22⋊D15111yescharacteristic
104C2×Q8C22×D15111yescharacteristic
105C2×D4—3021no—
106C2×D4—3021no—
107C2×D4—1512no—
108C22×C4—3022no—
109Q16—41no—
110SD16—41no—
111SD16—6042no—
112D8—6042no—
113M16—21no—
114M16—3022no—
115C4⋊C4—22no—
116C4⋊C4—3021no—
117C22⋊C4—3022no—
118C22⋊C4—3022no—
119C22⋊C4—3022no—
120C42—3021no—
121C42—1512no—
122C42C22⋊D15111yescharacteristic
123C23—3022no—
124Q8—22no—
125Q8—21no—
126Q8—41no—
127Q8—41no—
128D4—22no—
129D4—21no—
130D4—41no—
131D4—6042no—
132D4—6042no—
133D4—12081no—
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—41no—
137C2×C4—42no—
138C2×C4—3022no—
139C2×C4—6044no—
140C2×C4D4×D15112yes—
141C2×C4C2×C22⋊D15111yescharacteristic
142C8—41no—
143C8—6042no—
144C22—41no—
145C22—6042no—
146C22—6042no—
147C22—6042no—
148C22#1801270711yescharacteristic
149C4—22no—
150C4—21no—
151C4—22no—
152C4—41no—
153C4—41no—
154C4—6042no—
155C2—21no—
156C2—81no—
157C2—12082no—
158C2#2375239811yescharacteristic
subgroupG/H
centerC2#23752398
commutator, cosocleC2×Q8×C151C23
FrattiniC2×Q8C22×D151
Fitting#456×C151C2
socleC2×C151B(4,𝔽2)
hypercenter#456D151
hypocenterC151#2204
LCSG ▷ C2×Q8×C151 ▷ C22×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #456

Complements

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

NH ≅ G/Ntype
1. #23752928C2semidirect
2. #23752385C2semidirect
3. #23752011C2semidirect
4. #23752008C2semidirect
5. #456×C151C2semidirect
79. C151#2204semidirect
82. #456D151semidirect

Maximal subgroups

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

subgroupindex
#237529282
#237523852
#237520112
#237520082
#456×C1512
#2204151