Finite Group Databasebeta

← #23762558

Subgroups — #23762558

Order 10112.

188 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 61 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#19098915C211yesmaximal, characteristic
2#19098858C211yesmaximal, characteristic
3#19098858C211yesmaximal, characteristic
4#19098309C211yesmaximal, characteristic
5Q8⋊(C79⋊C8)C211yesmaximal, characteristic
6Q8⋊(C79⋊C8)C211yesmaximal, characteristic
7#557×C79C211yesmaximal, characteristic
8#14579161C2211yescharacteristic
9#14579094—21no—
10#14579094—21no—
11C4⋊(C79⋊C8)C2211yescharacteristic
12C4⋊(C79⋊C8)C2211yescharacteristic
13#14579085—21no—
14#14579085—21no—
15#14579084—22no—
16C4×C79⋊C8C2211yescharacteristic
17C4⋊Q8×C79—21no—
18C4⋊Q8×C79C2211yescharacteristic
19#125×C79—22no—
20#125×C79—21no—
21C4×Q8×C79—21no—
22C4×Q8×C79—21no—
23C4×Q8×C79C2211yescharacteristic
24C4×Q8×C79C2211yescharacteristic
25C2×Dic158—21no—
26C2×C79⋊C8—21no—
27C2×C79⋊C8—21no—
28C2×C79⋊C8—21no—
29C4⋊Dic79—21no—
30C4⋊Dic79—21no—
31C2×Q8×C79—21no—
32C2×Q8×C79D411yescharacteristic
33C2×Q8×C79D411yescharacteristic
34C4⋊C4×C79—22no—
35C4⋊C4×C79—22no—
36C4⋊C4×C79—22no—
37C4⋊C4×C79—21no—
38C4⋊C4×C79—21no—
39C4⋊C4×C79—21no—
40C4⋊C4×C79D411yescharacteristic
41C4⋊C4×C79D411yescharacteristic
42C4⋊C4×C79D412yes—
43C42×C79—22no—
44C42×C79—21no—
45C42×C79—21no—
46C42×C79C2311yescharacteristic
47Q8×C79—21no—
48Q8×C79—21no—
49Q8×C79—21no—
50Q8×C79—41no—
51Q8×C79—41no—
52Q8×C79Q1612yes—
53C2×C4×C79—21no—
54C2×C4×C79—21no—
55C2×C4×C79—21no—
56C2×C4×C79—21no—
57C2×C4×C79—22no—
58C2×C4×C79C2×D411yescharacteristic
59C2×C4×C79C2×D411yescharacteristic
60C2×C4×C79C2×D411yescharacteristic
61C2×Dic79—41no—
62Dic158—42no—
63C79⋊C8—41no—
64C79⋊C8—41no—
65C79⋊C8—41no—
66C22×C79#12011yescharacteristic
67C4×C79—22no—
68C4×C79—21no—
69C4×C79—41no—
70C4×C79—42no—
71C4×C79—41no—
72C4×C79—41no—
73C4×C79C2×Q1611yescharacteristic
74C4×C79#13511yescharacteristic
75C4×C79#13711yescharacteristic
76C4×C79#13711yescharacteristic
77Dic79—81no—
78C2×C79#45111yescharacteristic
79C2×C79#45211yescharacteristic
80C2×C79#45411yescharacteristic
81#1636—791nomaximal, Sylow
82C79#163611yescharacteristic, complemented, Sylow
83#557D7911yescharacteristic
84#487—791no—
85#477—791no—
86#477—791no—
87#332—791no—
88Q8⋊C8—791no—
89Q8⋊C8—791no—
90C4⋊Q8—21no—
91C4⋊Q8—791no—
92C4⋊Q8C2×D7911yescharacteristic
93#125—22no—
94#125—21no—
95C4×Q8—21no—
96C4×Q8—21no—
97C4×Q8C2×D7911yescharacteristic
98C4×Q8C2×D7911yescharacteristic
99#107—1581no—
100#107—1581no—
101C4⋊C8—791no—
102C4⋊C8—791no—
103#103—1581no—
104#103—1581no—
105#103—1582no—
106C4×C8—791no—
107C2×Q8—21no—
108C2×Q8—1581no—
109C2×Q8C22⋊D7911yescharacteristic
110C2×Q8C22⋊D7911yescharacteristic
111C2×C8—1581no—
112C2×C8—1581no—
113C2×C8—1581no—
114C4⋊C4—22no—
115C4⋊C4—22no—
116C4⋊C4—22no—
117C4⋊C4—21no—
118C4⋊C4—21no—
119C4⋊C4—21no—
120C4⋊C4—1581no—
121C4⋊C4—1581no—
122C4⋊C4C22⋊D7912yes—
123C4⋊C4C22⋊D7911yescharacteristic
124C4⋊C4C22⋊D7911yescharacteristic
125C42—22no—
126C42—21no—
127C42—21no—
128C42C22×D7911yescharacteristic
129Q8—21no—
130Q8—21no—
131Q8—21no—
132Q8—41no—
133Q8—41no—
134Q8—3162no—
135Q8#1192961412yes—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—22no—
141C2×C4—3161no—
142C2×C4C2×C22⋊D7911yescharacteristic
143C2×C4C2×C22⋊D7911yescharacteristic
144C2×C4C2×C22⋊D7911yescharacteristic
145C8—3161no—
146C8—3161no—
147C8—3161no—
148C22#1457913011yescharacteristic
149C4—22no—
150C4—21no—
151C4—41no—
152C4—42no—
153C4—41no—
154C4—41no—
155C4—6321no—
156C4C2×#1192961411yescharacteristic
157C4#1457918111yescharacteristic
158C4#1457919111yescharacteristic
159C4#1457919211yescharacteristic
160C2#1909871911yescharacteristic
161C2#1909872511yescharacteristic
162C2#1909873611yescharacteristic
subgroupG/H
centerC22#14579130
commutator, cosocleC42×C79C23
FrattiniC42C22×D79
Fitting#557×C79C2
socle, prime radicalC22×C79#120
hypercenter#557D79
hypocenterC79#1636
LCSG ▷ C42×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #557

Complements

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

NH ≅ G/Ntype
82. C79#1636semidirect