Finite Group Databasebeta

← #23776291

Subgroups — #23776291

Order 10112.

324 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 131 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#19099289C212yesmaximal
2#19098967C211yesmaximal, characteristic
3#19098965C211yesmaximal, characteristic
4#19098964C211yesmaximal, characteristic
5#19098870C212yesmaximal
6#19098868C212yesmaximal
7#19098846C212yesmaximal
8C8×Dic158C211yesmaximal, characteristic
9Q16×Dic79C211yesmaximal, characteristic
10Q16×Dic79C211yesmaximal, characteristic
11C4×Q16×C79C211yesmaximal, characteristic
12#14579160—22no—
13#14579160C2212yes—
14#14579153—22no—
15#14579153C2212yes—
16#14579152—22no—
17#14579152C2212yes—
18Q8×Dic79C2212yes—
19Q8×Dic79C2212yes—
20C4×Dic158—22no—
21C4×Dic158C2211yescharacteristic
22#14579095C2211yescharacteristic
23#14579095C2211yescharacteristic
24#14579094C2212yes—
25#14579093C2212yes—
26#14579092C2212yes—
27C4⋊(C79⋊C8)C2211yescharacteristic
28Dic79⋊C8C2211yescharacteristic
29Dic79⋊C8C2211yescharacteristic
30#14579085C2212yes—
31#14579085C2212yes—
32C8×Dic79C2211yescharacteristic
33C8×Dic79C2211yescharacteristic
34C2×Q16×C79C2211yescharacteristic
35C4×Q8×C79C2212yes—
36#107×C79C2211yescharacteristic
37#103×C79C2212yes—
38C4×C8×C79C2211yescharacteristic
39C2×Dic158—22no—
40C2×Dic158D411yescharacteristic
41C2×C79⋊C8C2311yescharacteristic
42C2×C79⋊C8C2311yescharacteristic
43C4⋊Dic79—22no—
44C4⋊Dic79—22no—
45C4⋊Dic79—22no—
46C4⋊Dic79D411yescharacteristic
47C4⋊Dic79C2312yes—
48C4⋊Dic79C2312yes—
49Dic79⋊C4—22no—
50Dic79⋊C4—22no—
51Dic79⋊C4—22no—
52Dic79⋊C4—22no—
53Dic79⋊C4D411yescharacteristic
54Dic79⋊C4D411yescharacteristic
55C4×Dic79—22no—
56C4×Dic79—22no—
57C4×Dic79C2311yescharacteristic
58C4×Dic79C2311yescharacteristic
59C2×Q8×C79C2312yes—
60Q16×C79Q814yescomplemented
61C2×C8×C79C2311yescharacteristic
62C2×C8×C79C2311yescharacteristic
63C4⋊C4×C79—22no—
64C4⋊C4×C79C2312yes—
65C42×C79—22no—
66C42×C79C2311yescharacteristic
67Q8×C79—22no—
68Q8×C79C2×Q814yes—
69C2×C4×C79—22no—
70C2×C4×C79—22no—
71C2×C4×C79C2×D411yescharacteristic
72C2×C4×C79C2×D411yescharacteristic
73C2×C4×C79C2411yescharacteristic
74C2×Dic79—22no—
75C2×Dic79—22no—
76C2×Dic79C2×D411yescharacteristic
77C2×Dic79C2×D411yescharacteristic
78C2×Dic79C2×D411yescharacteristic
79C2×Dic79C2×D411yescharacteristic
80Dic158—22no—
81Dic158—44no—
82C8×C79—21no—
83C8×C79C2×Q812yes—
84C79⋊C8—21no—
85C79⋊C8—21no—
86C22×C79C22×D411yescharacteristic
87C4×C79—24no—
88C4×C79—21no—
89C4×C79—21no—
90C4×C79—42no—
91C4×C79C22×Q811yescharacteristic
92C4×C792−1+411yescharacteristic
93Dic79—21no—
94Dic79—21no—
95Dic79—21no—
96Dic79—42no—
97Dic79—42no—
98Dic79#13512yes—
99C2×C79D4×Q811yescharacteristic
100C2×C79C2×#13511yescharacteristic
101C2×C79#57811yescharacteristic
102#3383—791nomaximal, Sylow
103C79#338311yescharacteristic, complemented, Sylow
104#557—792no—
105#500—791no—
106#499—791no—
107#499—791no—
108#479—792no—
109#479—792no—
110#475—792no—
111C8×Q8—791no—
112C4×Q16—791no—
113C4×Q16—791no—
114C4×Q16D7911yescharacteristic
115C2×Q16C2×D7911yescharacteristic
116C4⋊Q8—792no—
117C4⋊Q8—1582no—
118#125—792no—
119#125—792no—
120#125—1582no—
121#125—1582no—
122C4×Q8—791no—
123C4×Q8—792no—
124C4×Q8—792no—
125C4×Q8—1582no—
126C4×Q8C2×D7912yes—
127#107—791no—
128#107—791no—
129#107—792no—
130#107C2×D7911yescharacteristic
131#106—792no—
132#106—792no—
133C4⋊C8—791no—
134C4⋊C8—791no—
135C4⋊C8—791no—
136#103—792no—
137#103—792no—
138#103C2×D7912yes—
139C4×C8—791no—
140C4×C8—791no—
141C4×C8C2×D7911yescharacteristic
142C2×Q8—791no—
143C2×Q8—1582no—
144C2×Q8C22×D7912yes—
145Q16Dic15814yescomplemented
146C2×C8—791no—
147C2×C8—791no—
148C2×C8C22×D7911yescharacteristic
149C2×C8C22×D7911yescharacteristic
150C4⋊C4—22no—
151C4⋊C4—791no—
152C4⋊C4—791no—
153C4⋊C4—791no—
154C4⋊C4—792no—
155C4⋊C4—792no—
156C4⋊C4—1582no—
157C4⋊C4—1582no—
158C4⋊C4—1582no—
159C4⋊C4—1582no—
160C4⋊C4—1582no—
161C4⋊C4—1582no—
162C4⋊C4—1582no—
163C4⋊C4C22×D7912yes—
164C42—22no—
165C42—791no—
166C42—791no—
167C42—1582no—
168C42—1582no—
169C42C22×D7911yescharacteristic
170Q8—22no—
171Q8—3164no—
172Q8—1582no—
173Q8C2×Dic15814yes—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—791no—
177C2×C4—791no—
178C2×C4—791no—
179C2×C4—791no—
180C2×C4—1582no—
181C2×C4—1582no—
182C2×C4D4×D7911yescharacteristic
183C2×C4D4×D7911yescharacteristic
184C2×C4C23×D7911yescharacteristic
185C8—21no—
186C8—1581no—
187C8—1581no—
188C8C2×Dic15812yes—
189C22C2×D4×D7911yescharacteristic
190C4—24no—
191C4—21no—
192C4—21no—
193C4—42no—
194C4—3162no—
195C4—3162no—
196C4—792no—
197C4—1581no—
198C4—1581no—
199C4—1581no—
200C4C22×Dic15811yescharacteristic
201C4#1457920811yescharacteristic
202C2D4×Dic15811yescharacteristic
203C2#135×D7911yescharacteristic
204C2#1909937611yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
FittingC4×Q16×C79C2
socle, prime radicalC22×C79C22×D4
hypercenterC4×Q16D79
hypocenterC79#3383
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
60. Q16×C79Q8semidirect
103. C79#3383semidirect
145. Q16Dic158semidirect