Finite Group Databasebeta

← #34191413

Subgroups — #34191413

Order 20224.

364 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 89 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#23766705C211yesmaximal, characteristic
2#23764381C211yesmaximal, characteristic
3#23761900C212yesmaximal
4#23761302C212yesmaximal
5C79×#1274C211yesmaximal, characteristic
6#19099120C2211yescharacteristic
7#19098587C2211yescharacteristic
8#19098505—22no—
9#19098497—22no—
10C4×Dic79⋊C4—22no—
11C4×C4⋊Dic79C2212yes—
12#19098323—22no—
13#19098301—22no—
14#19098301—22no—
15#431×C79C2212yes—
16#376×C79C2211yescharacteristic
17C2×#11929608—21no—
18#14579161Q812yes—
19#14579153—21no—
20#14579140—22no—
21C4×Dic158—22no—
22#14579120—21no—
23C2×C4⋊Dic79—22no—
24C2×Dic79⋊C4—22no—
25C2×Dic79⋊C4—22no—
26C2×C4×Dic79—22no—
27C4⋊(C79⋊C8)—22no—
28C79⋊#95—22no—
29C79⋊#95—22no—
30C79⋊#95D412yes—
31C79⋊#95D412yes—
32C2×C42×C79D412yes—
33C2×C42×C79C2311yescharacteristic
34C4⋊C8×C79—22no—
35C22⋊C8×C79—22no—
36C4×C8×C79—22no—
37#95×C79—22no—
38C2×Dic158—22no—
39C22×Dic79—22no—
40C22×Dic79—22no—
41#11929608—42no—
42C2×C79⋊C8—41no—
43C4⋊Dic79—22no—
44C4⋊Dic79—22no—
45C4⋊Dic79—44no—
46Dic79⋊C4—44no—
47Dic79⋊C4—44no—
48Dic79⋊C4—42no—
49C22⋊Dic79—41no—
50C4×Dic79—41no—
51C4×Dic79—42no—
52C4×Dic79—42no—
53C22×C4×C79—22no—
54C22×C4×C79C2×D412yes—
55C22×C4×C79C2×D411yescharacteristic
56C2×C8×C79—42no—
57C42×C79—22no—
58C42×C79—22no—
59C42×C79C2×Q811yescharacteristic
60C42×C79#4111yescharacteristic
61C42×C79#4112yes—
62C23×C79#12011yescharacteristic
63C2×C4×C79—42no—
64C2×C4×C79—42no—
65C2×C4×C79—42no—
66C2×C4×C79—42no—
67C2×C4×C79C22⋊Q812yes—
68C2×C4×C79C22⋊Q811yescharacteristic
69C2×C4×C79#12412yes—
70C2×C4×C79#12411yescharacteristic
71C2×C4×C79#13512yes—
72C2×C4×C79#13712yes—
73C2×Dic79—24no—
74C2×Dic79—42no—
75C2×Dic79—42no—
76C2×Dic79—42no—
77C2×Dic79—42no—
78C2×Dic79—42no—
79C2×Dic79—42no—
80Dic158—82no—
81C8×C79—82no—
82C79⋊C8—81no—
83C22×C79—22no—
84C22×C79#39311yescharacteristic
85C22×C79#45212yes—
86C4×C79—22no—
87C4×C79—22no—
88C4×C79—82no—
89C4×C79#47912yes—
90C4×C79#48811yescharacteristic
91C4×C79#49111yescharacteristic
92Dic79—44no—
93Dic79—82no—
94Dic79—82no—
95#10373—791nomaximal, Sylow
96C2×C79—22no—
97C2×C79#202611yescharacteristic
98C2×C79#203112yes—
99#2402—791no—
100#1995—791no—
101#1503—792no—
102#1303—792no—
103#1274D7911yescharacteristic
104C79#1037311yescharacteristic, complemented, Sylow
105#533—791no—
106#431C2×D7912yes—
107#423—791no—
108#400—1582no—
109#398—1582no—
110C4×C4⋊C4—792no—
111C4×C4⋊C4—1582no—
112#376C2×D7911yescharacteristic
113#339—1582no—
114#328—1582no—
115#328—1582no—
116C2×M16—1581no—
117C4⋊Q8—792no—
118#125—1581no—
119C22⋊Q8—1582no—
120C4×Q8—1582no—
121#117—1581no—
122C2×C4⋊C4—1582no—
123C2×C4⋊C4—1582no—
124C2×C4⋊C4—1582no—
125C2×C42—1582no—
126C2×C42D31612yes—
127C2×C42C22×D7911yescharacteristic
128C4⋊C8—22no—
129C4⋊C8—1582no—
130C22⋊C8—22no—
131C4×C8—22no—
132#95—22no—
133#95—792no—
134#95—792no—
135#95—1582no—
136#95—1582no—
137C2×Q8—1582no—
138C22×C4—22no—
139C22×C4—1582no—
140C22×C4—1582no—
141C22×C4D4×D7912yes—
142C22×C4C2×D31611yescharacteristic
143M16—3162no—
144C2×C8—42no—
145C2×C8—3161no—
146C4⋊C4—3164no—
147C4⋊C4—3164no—
148C4⋊C4—3164no—
149C4⋊C4—3162no—
150C4⋊C4—1582no—
151C4⋊C4—1582no—
152C22⋊C4—3161no—
153C42—22no—
154C42—22no—
155C42—3161no—
156C42—3162no—
157C42—3162no—
158C42Q8×D7911yescharacteristic
159C42#1192962311yescharacteristic
160C42#1192962412yes—
161C23#1457913111yescharacteristic
162Q8—6322no—
163C2×C4—42no—
164C2×C4—42no—
165C2×C4—42no—
166C2×C4—42no—
167C2×C4—3162no—
168C2×C4—3162no—
169C2×C4—3162no—
170C2×C4—3162no—
171C2×C4—3162no—
172C2×C4—3162no—
173C2×C4—1584no—
174C2×C4#1457913912yes—
175C2×C4#1457914111yescharacteristic
176C2×C4#1457914712yes—
177C2×C4#1457914911yescharacteristic
178C2×C4#1457918312yes—
179C2×C4#1457919412yes—
180C8—82no—
181C8—6321no—
182C22—22no—
183C22#1909847611yescharacteristic
184C22#1909872712yes—
185C4—22no—
186C4—22no—
187C4—82no—
188C4—3164no—
189C4—6322no—
190C4—6322no—
191C4#1909887112yes—
192C4#1909891811yescharacteristic
193C4#1909893211yescharacteristic
194C2—22no—
195C2#2376455211yescharacteristic
196C2#2376457112yes—
subgroupG/H
centerC2×C4#14579149
commutator, cosocleC2×C42×C79C23
FrattiniC2×C42C22×D79
FittingC79×#1274C2
socleC22×C79#393
prime radicalC23×C79#120
hypercenter#1274D79
hypocenterC79#10373
LCSG ▷ C2×C42×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1274

Complements

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

NH ≅ G/Ntype
104. C79#10373semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#237667052
#237643812
#237619002
#237613022
C79×#12742
#1037379