Finite Group Databasebeta

← #23764559

Subgroups — #23764559

Order 10112.

246 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 69 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#19098572C211yesmaximal, characteristic
3#19098470C211yesmaximal, characteristic
4#19098331C211yesmaximal, characteristic
5#19098324C211yesmaximal, characteristic
6#19098322C211yesmaximal, characteristic
7#419×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#14579085—21no—
18#14579085—21no—
19C79⋊#95—22no—
20C22×Q8×C79C2211yescharacteristic
21C2×M16×C79C2211yescharacteristic
22#117×C79C2211yescharacteristic
23#103×C79—21no—
24#103×C79—21no—
25C2×Dic158—22no—
26C22×Dic79—21no—
27C22×Dic79D412yes—
28#11929608—21no—
29#11929608—21no—
30C2×C79⋊C8—21no—
31C4⋊Dic79—22no—
32C4⋊Dic79—21no—
33C4⋊Dic79—21no—
34C4⋊Dic79D411yescharacteristic
35C4⋊Dic79D411yescharacteristic
36Dic79⋊C4—22no—
37Dic79⋊C4—22no—
38C22⋊Dic79—21no—
39C4×Dic79—21no—
40C4×Dic79—21no—
41C4×Dic79—21no—
42C2×Q8×C79—21no—
43C2×Q8×C79—21no—
44C2×Q8×C79—21no—
45C2×Q8×C79—21no—
46C2×Q8×C79—21no—
47C2×Q8×C79Q812yescomplemented
48C22×C4×C79—21no—
49C22×C4×C79C2311yescharacteristic
50M16×C79—21no—
51M16×C79—21no—
52C2×C8×C79—21no—
53C4⋊C4×C79D411yescharacteristic
54C4⋊C4×C79D411yescharacteristic
55C22⋊C4×C79—21no—
56C42×C79—21no—
57C23×C79C2×D411yescharacteristic
58Q8×C79—22no—
59Q8×C79—22no—
60Q8×C79—41no—
61Q8×C79—41no—
62C2×C4×C79—21no—
63C2×C4×C79—21no—
64C2×C4×C79—22no—
65C2×C4×C79—41no—
66C2×C4×C79—41no—
67C2×C4×C79C2×D411yescharacteristic
68C2×C4×C79C2×D411yescharacteristic
69C2×C4×C79C2×Q811yescharacteristic
70C2×C4×C79#4111yescharacteristic
71C2×C4×C79#4111yescharacteristic
72C2×C4×C79#4111yescharacteristic
73C2×Dic79—22no—
74C2×Dic79—21no—
75C2×Dic79—21no—
76C2×Dic79—22no—
77C2×Dic79—41no—
78C2×Dic79—41no—
79C2×Dic79—42no—
80Dic158—82no—
81C8×C79—41no—
82C79⋊C8—41no—
83C22×C79—21no—
84C22×C79—21no—
85C22×C79#12011yescharacteristic
86C22×C79C22⋊Q811yescharacteristic
87C22×C79#12411yescharacteristic
88C4×C79—42no—
89C4×C79—41no—
90C4×C79—41no—
91C4×C79C22⋊Q811yescharacteristic
92C4×C79C22⋊Q811yescharacteristic
93C4×C79#12411yescharacteristic
94C4×C79#12411yescharacteristic
95Dic79—42no—
96Dic79—41no—
97Dic79—42no—
98Dic79—41no—
99C2×C79—21no—
100C2×C79—21no—
101C2×C79#39311yescharacteristic
102C2×C79#45511yescharacteristic
103C2×C79#45611yescharacteristic
104#2028—791nomaximal, Sylow
105C79#202811yescharacteristic, complemented, Sylow
106#544—791no—
107#419—791no—
108#419D7911yescharacteristic
109#391—791no—
110#343—791no—
111#339—791no—
112#339—791no—
113C22×Q8C2×D7911yescharacteristic
114C2×M16—791no—
115C2×M16C2×D7911yescharacteristic
116C4⋊Q8—1581no—
117C4⋊Q8—1581no—
118#125—1581no—
119#125—1581no—
120C22⋊Q8—1582no—
121#117—791no—
122#117C2×D7911yescharacteristic
123C2×C4⋊C4—791no—
124C2×C42—791no—
125#103—21no—
126#103—21no—
127#103—1581no—
128#103—1581no—
129#95—1582no—
130C2×Q8—21no—
131C2×Q8—21no—
132C2×Q8—21no—
133C2×Q8—21no—
134C2×Q8—21no—
135C2×Q8—1582no—
136C2×Q8Dic15812yescomplemented
137C22×C4—21no—
138C22×C4—792no—
139C22×C4—1581no—
140C22×C4C22×D7911yescharacteristic
141M16—21no—
142M16—21no—
143M16—1581no—
144M16—1581no—
145C2×C8—21no—
146C2×C8—1581no—
147C4⋊C4—791no—
148C4⋊C4—791no—
149C4⋊C4—1582no—
150C4⋊C4—1582no—
151C4⋊C4—1582no—
152C4⋊C4—1581no—
153C4⋊C4—1581no—
154C4⋊C4C22⋊D7911yescharacteristic
155C4⋊C4C22⋊D7911yescharacteristic
156C22⋊C4—21no—
157C22⋊C4—1581no—
158C42—21no—
159C42—1581no—
160C42—1581no—
161C42—1581no—
162C23D4×D7911yescharacteristic
163Q8—22no—
164Q8—22no—
165Q8—41no—
166Q8—41no—
167Q8—6322no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—22no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—3161no—
174C2×C4—3161no—
175C2×C4—3162no—
176C2×C4—1582no—
177C2×C4—1581no—
178C2×C4—1581no—
179C2×C4—1582no—
180C2×C4D4×D7911yescharacteristic
181C2×C4C2×C22⋊D7911yescharacteristic
182C2×C4C2×Dic15811yescharacteristic
183C2×C4#1192962311yescharacteristic
184C2×C4#1192962311yescharacteristic
185C2×C4#1192962411yescharacteristic
186C8—41no—
187C8—3161no—
188C22—21no—
189C22—21no—
190C22#1457912911yescharacteristic
191C22#1457913811yescharacteristic
192C22#1457914711yescharacteristic
193C4—42no—
194C4—41no—
195C4—41no—
196C4—3162no—
197C4—3162no—
198C4—3161no—
199C4—3161no—
200C4#1457913811yescharacteristic
201C4#1457914011yescharacteristic
202C4#1457914711yescharacteristic
203C4#1457914811yescharacteristic
204C2—21no—
205C2—21no—
206C2#1909847511yescharacteristic
207C2#1909873911yescharacteristic
208C2#1909874411yescharacteristic
subgroupG/H
centerC22#14579129
commutator, cosocleC22×C4×C79C23
FrattiniC22×C4C22×D79
Fitting#419×C79C2
socleC22×C79#120
prime radicalC23×C79C2×D4
hypercenter#419D79
hypocenterC79#2028
LCSG ▷ C22×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
47. C2×Q8×C79Q8semidirect
105. C79#2028semidirect
136. C2×Q8Dic158semidirect