Finite Group Databasebeta

← #34100354

Subgroups — #34100354

Order 20096.

252 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 79 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#23758039C211yesmaximal, characteristic
2#23757321C211yesmaximal, characteristic, complemented
3#23757255C211yesmaximal, characteristic
4#23757241C211yesmaximal, characteristic
5#23757037C211yesmaximal, characteristic, complemented
6#23757037C211yesmaximal, characteristic, complemented
7#430×C157C211yesmaximal, characteristic, complemented
8C2×#14578954C2211yescharacteristic
9#19097779—22no—
10#19097777—22no—
11C2×#14578938C2211yescharacteristic
12C2×#14578938C2211yescharacteristic
13M16×D157—22no—
14C22×#11929434C2211yescharacteristic
15#19097706—22no—
16#19097689C412yes—
17#19097687C412yes—
18#19097683—22no—
19C2×M16×C157C2211yescharacteristic
20C2×M16×C157C2211yescharacteristic
21C2×M16×C157C2211yescharacteristic
22#108×C157—22no—
23#14578954—21no—
24#14578954—21no—
25#14578954—21no—
26#14578954—21no—
27C2×Dic314C2×C411yescharacteristic
28C2×D628C2×C411yescharacteristic
29C2×C22⋊D157Q812yes—
30C2×C4×D157D412yes—
31#14578938—21no—
32#14578938—21no—
33#14578938C2×C412yes—
34#14578938D412yes—
35#14578937—24no—
36C2×#11929434—21no—
37C2×#11929434—21no—
38C2×#11929434—21no—
39C2×#11929434—21no—
40C2×#11929434—21no—
41C8×D157—24no—
42C22×C4×C157C2311yescharacteristic
43M16×C157—21no—
44M16×C157—21no—
45M16×C157—21no—
46M16×C157—21no—
47M16×C157C2×C412yes—
48M16×C157D412yes—
49C2×C8×C157—21no—
50C2×C8×C157—21no—
51C2×C8×C157—21no—
52C22×D157C4⋊C412yes—
53Dic314—21no—
54Dic314—21no—
55D628—21no—
56D628—21no—
57C22⋊D157—22no—
58C22⋊D157—22no—
59C2×Dic157C4⋊C412yes—
60C4×D157—22no—
61C4×D157—22no—
62#11929434—22no—
63#11929434—22no—
64#11929434—41no—
65C23×C157C2×Q811yescharacteristic
66C2×C4×C157C22×C411yescharacteristic
67C2×C4×C157C2×D411yescharacteristic
68C2×C4×C157C2×D411yescharacteristic
69C2×C4×C157C2×D411yescharacteristic
70C2×C4×C157#4111yescharacteristic
71C2×C4×C157#4111yescharacteristic
72C8×C157—22no—
73C8×C157—22no—
74C8×C157—41no—
75C22×C157—41no—
76C22×C157C2×C4⋊C411yescharacteristic
77C22×C157C22⋊Q811yescharacteristic
78C22×C157C22⋊Q811yescharacteristic
79C2×D157—22no—
80C2×D157—42no—
81C4×C157C4×D411yescharacteristic
82C4×C157C4×D411yescharacteristic
83C4×C157#12011yescharacteristic
84C4×C157#12311yescharacteristic
85Dic157—22no—
86C2×C157—21no—
87C2×C157—21no—
88C2×C157—21no—
89C2×C157#38511yescharacteristic
90D157—42no—
91C157#185811yescharacteristic, complemented, Sylow
92#1858—1571nomaximal, Sylow
93#568—1571no—
94#430—1571no—
95#430D15711yescharacteristic, complemented
96#413—1571no—
97#408—1571no—
98#341—1571no—
99#341—1571no—
100C2×#41—1571no—
101#131—3142no—
102#131—3142no—
103C2×M16—3142no—
104C2×M16—1571no—
105C2×M16—1571no—
106C2×M16C2×D15711yescharacteristic
107C2×M16C2×D15711yescharacteristic
108C2×M16C2×D15711yescharacteristic
109C22×C8—1571no—
110#108—22no—
111#108—3142no—
112#101—1572no—
113#100—1572no—
114C22⋊C8—3142no—
115#41—3141no—
116#41—3141no—
117#41—3141no—
118#41—3141no—
119C2×Q8—1571no—
120C2×D4—1572no—
121C2×D4—1571no—
122C22×C4—1572no—
123C22×C4C22×D15711yescharacteristic
124M16—21no—
125M16—21no—
126M16—21no—
127M16—21no—
128M16—3144no—
129M16—3141no—
130M16—3141no—
131M16—1572no—
132M16—1572no—
133M16C4×D15712yes—
134M16C22⋊D15712yes—
135C2×C8—21no—
136C2×C8—21no—
137C2×C8—21no—
138C2×C8—3144no—
139C2×C8—3141no—
140C2×C8—3141no—
141C2×C8—3141no—
142C2×C8—3141no—
143C2×C8—3141no—
144C23—1572no—
145C23Q8×D15711yescharacteristic
146Q8—3141no—
147Q8—3141no—
148D4—3142no—
149D4—3142no—
150D4—3141no—
151D4—3141no—
152C2×C4—3142no—
153C2×C4—3142no—
154C2×C4—1572no—
155C2×C4C2×C4×D15711yescharacteristic
156C2×C4D4×D15711yescharacteristic
157C2×C4D4×D15711yescharacteristic
158C2×C4C2×C22⋊D15711yescharacteristic
159C2×C4#1457895411yescharacteristic
160C2×C4#1457895511yescharacteristic
161C8—22no—
162C8—22no—
163C8—41no—
164C8—3142no—
165C8—3142no—
166C8—6281no—
167C22—41no—
168C22—3142no—
169C22—6282no—
170C22C4⋊C4×D15711yescharacteristic
171C22#1909774711yescharacteristic
172C22#1909774911yescharacteristic
173C4—3142no—
174C4C4×C22⋊D15711yescharacteristic
175C4#1909773311yescharacteristic
176C4#1909773911yescharacteristic
177C4#1909775611yescharacteristic
178C2—21no—
179C2—21no—
180C2—21no—
181C2—6282no—
182C2#2375714411yescharacteristic
subgroupG/H
centerC4#19097739
commutatorC2×C4×C157C22×C4
FrattiniC22×C4C22×D157
Fitting#430×C157C2
socleC2×C157#385
prime radicalC2×#14578954C22
cosocleC22×C4×C157C23
hypercenter#430D157
hypocenterC157#1858
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C4 ◁ C22×C4 ◁ #430

Complements

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

NH ≅ G/Ntype
2. #23757321C2semidirect
5. #23757037C2semidirect
6. #23757037C2semidirect
7. #430×C157C2semidirect
91. C157#1858semidirect
95. #430D157semidirect

Maximal subgroups

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

subgroupindex
#237580392
#237573212
#237572552
#237572412
#237570372
#430×C1572
#1858157