Finite Group Databasebeta

← #23764743

Subgroups — #23764743

Order 10112.

246 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 73 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#19099191C211yesmaximal, characteristic
2#19098603C211yesmaximal, characteristic
3#19098432C211yesmaximal, characteristic
4#19098331C211yesmaximal, characteristic
5#19098324C211yesmaximal, characteristic
6#19098322C211yesmaximal, characteristic
7#428×C79C211yesmaximal, characteristic
8C2×#11929608C2211yescharacteristic
9#14579161—21no—
10#14579160—21no—
11#14579153—21no—
12#14579152—21no—
13#14579138—22no—
14#14579120C2211yescharacteristic
15C2×C4⋊Dic79C2211yescharacteristic
16C2×Dic79⋊C4—22no—
17C2×C4×Dic79C2211yescharacteristic
18#14579094—21no—
19#14579092—21no—
20C2×M16×C79C2211yescharacteristic
21#117×C79C2211yescharacteristic
22C2×C4⋊C4×C79C2211yescharacteristic
23#107×C79—21no—
24#106×C79—21no—
25C2×Dic158—22no—
26C22×Dic79—21no—
27C22×Dic79D412yes—
28#11929608—21no—
29#11929608Q812yescomplemented
30C2×C79⋊C8—21no—
31C4⋊Dic79—22no—
32C4⋊Dic79—21no—
33C4⋊Dic79—21no—
34C4⋊Dic79D411yescharacteristic
35C4⋊Dic79D411yescharacteristic
36Dic79⋊C4—22no—
37Dic79⋊C4—22no—
38Dic79⋊C4—44no—
39C22⋊Dic79—21no—
40C4×Dic79—21no—
41C4×Dic79—21no—
42C4×Dic79Q812yescomplemented
43C22×C4×C79—21no—
44C22×C4×C79C2311yescharacteristic
45M16×C79—21no—
46M16×C79Q812yescomplemented
47C2×C8×C79—21no—
48C4⋊C4×C79—21no—
49C4⋊C4×C79—21no—
50C4⋊C4×C79D411yescharacteristic
51C4⋊C4×C79D411yescharacteristic
52C22⋊C4×C79—21no—
53C42×C79—21no—
54C23×C79C2×D411yescharacteristic
55C2×C4×C79—21no—
56C2×C4×C79—21no—
57C2×C4×C79—42no—
58C2×C4×C79—41no—
59C2×C4×C79C2×D411yescharacteristic
60C2×C4×C79C2×D411yescharacteristic
61C2×C4×C79C2×Q811yescharacteristic
62C2×C4×C79C2×Q811yescharacteristic
63C2×C4×C79C2×Q811yescharacteristic
64C2×C4×C79#4111yescharacteristic
65C2×Dic79—22no—
66C2×Dic79—22no—
67C2×Dic79—22no—
68C2×Dic79—21no—
69C2×Dic79—21no—
70C2×Dic79—22no—
71C2×Dic79—42no—
72Dic158—82no—
73C8×C79—22no—
74C79⋊C8—22no—
75C22×C79—21no—
76C22×C79—21no—
77C22×C79#12011yescharacteristic
78C22×C79C22⋊Q811yescharacteristic
79C22×C79C4⋊Q811yescharacteristic
80C4×C79—41no—
81C4×C79—41no—
82C4×C79—81no—
83C4×C79C22⋊Q811yescharacteristic
84C4×C79C22⋊Q811yescharacteristic
85C4×C79C4⋊Q811yescharacteristic
86C4×C79C4⋊Q811yescharacteristic
87Dic79—24no—
88Dic79—41no—
89Dic79—42no—
90Dic79—41no—
91C2×C79—21no—
92C2×C79—21no—
93C2×C79#39511yescharacteristic
94C2×C79#45311yescharacteristic
95C2×C79#45611yescharacteristic
96#2060—791nomaximal, Sylow
97C79#206011yescharacteristic, complemented, Sylow
98#544—791no—
99#428—791no—
100#428D7911yescharacteristic
101#384—791no—
102#343—791no—
103#339—791no—
104#339—791no—
105C2×M16—791no—
106C2×M16C2×D7911yescharacteristic
107C4⋊Q8—1581no—
108C4⋊Q8—1581no—
109#125—1581no—
110#125—1581no—
111C22⋊Q8—1582no—
112#117—791no—
113#117C2×D7911yescharacteristic
114C2×C4⋊C4—791no—
115C2×C4⋊C4—1582no—
116C2×C4⋊C4C2×D7911yescharacteristic
117C2×C42—791no—
118#107—21no—
119#107—1581no—
120#106—21no—
121#106—1581no—
122C2×Q8—1582no—
123C22×C4—21no—
124C22×C4—792no—
125C22×C4—1581no—
126C22×C4C22×D7911yescharacteristic
127M16—21no—
128M16—792no—
129M16—1581no—
130M16Dic15812yescomplemented
131C2×C8—21no—
132C2×C8—1581no—
133C4⋊C4—21no—
134C4⋊C4—21no—
135C4⋊C4—3164no—
136C4⋊C4—791no—
137C4⋊C4—791no—
138C4⋊C4—1582no—
139C4⋊C4—1582no—
140C4⋊C4—1582no—
141C4⋊C4—1581no—
142C4⋊C4—1581no—
143C4⋊C4C22⋊D7911yescharacteristic
144C4⋊C4C22⋊D7911yescharacteristic
145C22⋊C4—21no—
146C22⋊C4—1581no—
147C42—21no—
148C42—792no—
149C42—1581no—
150C42—1581no—
151C23D4×D7911yescharacteristic
152Q8—6322no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—42no—
156C2×C4—41no—
157C2×C4—3162no—
158C2×C4—1581no—
159C2×C4—1581no—
160C2×C4—1582no—
161C2×C4—1582no—
162C2×C4—1582no—
163C2×C4—1582no—
164C2×C4D4×D7911yescharacteristic
165C2×C4C2×C22⋊D7911yescharacteristic
166C2×C4Q8×D7911yescharacteristic
167C2×C4Q8×D7911yescharacteristic
168C2×C4C2×Dic15811yescharacteristic
169C2×C4#1192962411yescharacteristic
170C8—22no—
171C8—1582no—
172C22—21no—
173C22—21no—
174C22#1457912911yescharacteristic
175C22#1457913911yescharacteristic
176C22#1457916011yescharacteristic
177C4—41no—
178C4—41no—
179C4—81no—
180C4—3162no—
181C4—3161no—
182C4—3161no—
183C4—1584no—
184C4#1457913911yescharacteristic
185C4#1457914011yescharacteristic
186C4#1457915911yescharacteristic
187C4#1457916011yescharacteristic
188C2—21no—
189C2—21no—
190C2#1909848311yescharacteristic
191C2#1909872911yescharacteristic
192C2#1909874411yescharacteristic
subgroupG/H
centerC22#14579129
commutator, cosocleC22×C4×C79C23
FrattiniC22×C4C22×D79
Fitting#428×C79C2
socleC22×C79#120
prime radicalC23×C79C2×D4
hypercenter#428D79
hypocenterC79#2060
LCSG ▷ C22×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
29. #11929608Q8semidirect
42. C4×Dic79Q8semidirect
46. M16×C79Q8semidirect
97. C79#2060semidirect
130. M16Dic158semidirect