Finite Group Databasebeta

← #23764749

Subgroups — #23764749

Order 10112.

230 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 75 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#19098606C211yesmaximal, characteristic
3#19098605C211yesmaximal, characteristic
4#19098429C211yesmaximal, characteristic
5#19098331C211yesmaximal, characteristic
6#19098323C211yesmaximal, characteristic
7#339×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×C4⋊Dic79C2211yescharacteristic
17#14579095—21no—
18#14579094—21no—
19#14579093—21no—
20#14579092—21no—
21C79⋊#95—22no—
22C2×M16×C79C2211yescharacteristic
23#117×C79C2211yescharacteristic
24C2×C42×C79C2211yescharacteristic
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⋊Dic79—21no—
35C4⋊Dic79—21no—
36C4⋊Dic79D411yescharacteristic
37C4⋊Dic79D411yescharacteristic
38Dic79⋊C4—22no—
39Dic79⋊C4—22no—
40C22⋊Dic79—21no—
41C4×Dic79—21no—
42C22×C4×C79—21no—
43C22×C4×C79C2311yescharacteristic
44M16×C79—21no—
45M16×C79Q812yescomplemented
46C2×C8×C79—21no—
47C4⋊C4×C79D411yescharacteristic
48C4⋊C4×C79D411yescharacteristic
49C22⋊C4×C79—21no—
50C42×C79—21no—
51C42×C79—21no—
52C42×C79Q812yescomplemented
53C23×C79C2×D411yescharacteristic
54C2×C4×C79—21no—
55C2×C4×C79—21no—
56C2×C4×C79—22no—
57C2×C4×C79—41no—
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—21no—
66C2×Dic79—21no—
67C2×Dic79—22no—
68C2×Dic79—42no—
69C2×Dic79—42no—
70C2×Dic79—41no—
71Dic158—82no—
72C8×C79—22no—
73C79⋊C8—22no—
74C22×C79—21no—
75C22×C79—21no—
76C22×C79#12011yescharacteristic
77C22×C79C22⋊Q811yescharacteristic
78C22×C79C4⋊Q811yescharacteristic
79C4×C79—42no—
80C4×C79—41no—
81C4×C79—41no—
82C4×C79C22⋊Q811yescharacteristic
83C4×C79C22⋊Q811yescharacteristic
84C4×C79C4⋊Q811yescharacteristic
85C4×C79C4⋊Q811yescharacteristic
86Dic79—41no—
87Dic79—41no—
88Dic79—42no—
89Dic79—81no—
90C2×C79—21no—
91C2×C79—21no—
92C2×C79#39511yescharacteristic
93C2×C79#45411yescharacteristic
94C2×C79#45511yescharacteristic
95#2061—791nomaximal, Sylow
96C79#206111yescharacteristic, complemented, Sylow
97#544—791no—
98#428—791no—
99#428—791no—
100#382—791no—
101#343—791no—
102#339—791no—
103#339D7911yescharacteristic
104C2×M16—791no—
105C2×M16C2×D7911yescharacteristic
106C4⋊Q8—1581no—
107C4⋊Q8—1581no—
108#125—1581no—
109#125—1581no—
110C22⋊Q8—1582no—
111#117—791no—
112#117C2×D7911yescharacteristic
113C2×C4⋊C4—791no—
114C2×C4⋊C4—791no—
115C2×C42C2×D7911yescharacteristic
116#107—1581no—
117#107—1581no—
118#106—1581no—
119#106—1581no—
120#95—1582no—
121C2×Q8—1582no—
122C22×C4—21no—
123C22×C4—792no—
124C22×C4—1581no—
125C22×C4C22×D7911yescharacteristic
126M16—21no—
127M16—792no—
128M16—1581no—
129M16Dic15812yescomplemented
130C2×C8—21no—
131C2×C8—1581no—
132C4⋊C4—791no—
133C4⋊C4—791no—
134C4⋊C4—1582no—
135C4⋊C4—1582no—
136C4⋊C4—1582no—
137C4⋊C4—1581no—
138C4⋊C4—1581no—
139C4⋊C4—1581no—
140C4⋊C4—1581no—
141C4⋊C4D31611yescharacteristic
142C4⋊C4D31611yescharacteristic
143C22⋊C4—21no—
144C22⋊C4—1581no—
145C42—21no—
146C42—21no—
147C42—1581no—
148C42Dic15812yescomplemented
149C23D4×D7911yescharacteristic
150Q8—6322no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—22no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—3162no—
157C2×C4—3162no—
158C2×C4—3161no—
159C2×C4—1581no—
160C2×C4—1581no—
161C2×C4—1582no—
162C2×C4D4×D7911yescharacteristic
163C2×C4C2×D31611yescharacteristic
164C2×C4Q8×D7911yescharacteristic
165C2×C4C2×Dic15811yescharacteristic
166C2×C4C2×Dic15811yescharacteristic
167C2×C4#1192962311yescharacteristic
168C8—22no—
169C8—1582no—
170C22—21no—
171C22—21no—
172C22#1457913111yescharacteristic
173C22#1457913811yescharacteristic
174C22#1457916011yescharacteristic
175C4—42no—
176C4—41no—
177C4—41no—
178C4—3161no—
179C4—3162no—
180C4—3161no—
181C4—6321no—
182C4#1457913811yescharacteristic
183C4#1457914111yescharacteristic
184C4#1457916011yescharacteristic
185C4#1457916111yescharacteristic
186C2—21no—
187C2—21no—
188C2#1909848411yescharacteristic
189C2#1909873711yescharacteristic
190C2#1909874211yescharacteristic
subgroupG/H
centerC22#14579131
commutator, cosocleC22×C4×C79C23
FrattiniC22×C4C22×D79
Fitting#339×C79C2
socleC22×C79#120
prime radicalC23×C79C2×D4
hypercenter#339D79
hypocenterC79#2061
LCSG ▷ C22×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
29. #11929608Q8semidirect
45. M16×C79Q8semidirect
52. C42×C79Q8semidirect
96. C79#2061semidirect
129. M16Dic158semidirect
148. C42Dic158semidirect