Finite Group Databasebeta

← #34175850

Subgroups — #34175850

Order 20224.

214 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 37 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#23764567C211yesmaximal, characteristic
2#23761330C211yesmaximal, characteristic
3C79×#1306C211yesmaximal, characteristic
4#19099189C411yescharacteristic
5#19098426—21no—
6#19098330C411yescharacteristic
7#19098329—21no—
8#19098287—21no—
9#407×C79—21no—
10#381×C79C2211yescharacteristic
11#14579140—41no—
12#14579138—42no—
13C2×C22⋊Dic79—21no—
14C2×C22⋊Dic79—21no—
15C22⋊(C79⋊C8)—41no—
16C79⋊#95—42no—
17C23×C4×C79D411yescharacteristic
18C2×M16×C79—41no—
19C2×C22⋊C4×C79C2×C411yescharacteristic
20C2×C22⋊C4×C79D411yescharacteristic
21C22⋊C8×C79—22no—
22C22⋊C8×C79—41no—
23#95×C79—41no—
24C2×Dic158—41no—
25C22×Dic79—22no—
26C22×Dic79—41no—
27C2×C79⋊C8—81no—
28C4⋊Dic79—41no—
29Dic79⋊C4—42no—
30C22⋊Dic79—41no—
31C22⋊Dic79—41no—
32C22⋊Dic79—41no—
33C22⋊Dic79—41no—
34C24×C79C22⋊C411yescharacteristic
35C22×C4×C79—21no—
36C22×C4×C79—21no—
37C22×C4×C79—21no—
38C22×C4×C79—21no—
39C22×C4×C79—41no—
40C22×C4×C79—41no—
41C22×C4×C79SD1611yescharacteristic
42C22×C4×C79Q1611yescharacteristic
43M16×C79—81no—
44M16×C79—81no—
45C2×C8×C79—42no—
46C22⋊C4×C79—41no—
47C22⋊C4×C79—41no—
48C23×C79—21no—
49C23×C79—21no—
50C23×C79—81no—
51C23×C79#9911yescharacteristic
52C23×C79#10311yescharacteristic
53C23×C79#10411yescharacteristic
54C2×C4×C79—21no—
55C2×C4×C79—21no—
56C2×C4×C79—41no—
57C2×C4×C79—41no—
58C2×C4×C79—41no—
59C2×C4×C79—41no—
60C2×C4×C79—41no—
61C2×C4×C79—41no—
62C2×C4×C79—81no—
63C2×C4×C79—81no—
64C2×C4×C79—81no—
65C2×Dic79—42no—
66C2×Dic79—82no—
67C2×Dic79—81no—
68C2×Dic79—82no—
69Dic158—161no—
70C8×C79—82no—
71C79⋊C8—161no—
72C22×C79—21no—
73C22×C79—21no—
74C22×C79—41no—
75C22×C79—41no—
76C22×C79—41no—
77C22×C79—42no—
78C22×C79—81no—
79C22×C79#32811yescharacteristic
80C22×C79AΣL(1,𝔽16)11yescharacteristic
81C22×C79#35411yescharacteristic
82C4×C79—41no—
83C4×C79—41no—
84C4×C79—81no—
85C4×C79—81no—
86Dic79—82no—
87Dic79—161no—
88#7427—791nomaximal, Sylow
89C2×C79—21no—
90C2×C79—21no—
91C2×C79—21no—
92C2×C79—41no—
93C2×C79—41no—
94C2×C79#135111yescharacteristic
95#2030—791no—
96#1317—791no—
97#1306D7911yescharacteristic
98C79#742711yescharacteristic, complemented, Sylow
99#543—791no—
100#407—21no—
101#381—1581no—
102#381C2×D7911yescharacteristic
103#342—791no—
104#342—1581no—
105#323—1581no—
106C23×C4C22⋊D7911yescharacteristic
107C2×M16—41no—
108C22⋊Q8—3162no—
109C22⋊Q8—3161no—
110C2×C22⋊C4—1581no—
111C2×C22⋊C4—1581no—
112C2×C22⋊C4C4×D7911yescharacteristic
113C2×C22⋊C4D31611yescharacteristic
114C22⋊C8—22no—
115C22⋊C8—41no—
116C22⋊C8—3161no—
117#95—41no—
118#95—3162no—
119C24(C2×D79)⋊C411yescharacteristic
120C2×Q8—3161no—
121C22×C4—21no—
122C22×C4—21no—
123C22×C4—21no—
124C22×C4—21no—
125C22×C4—41no—
126C22×C4—41no—
127C22×C4—3161no—
128C22×C4—1582no—
129C22×C4#1192961211yescharacteristic
130C22×C4#1192961411yescharacteristic
131M16—81no—
132M16—81no—
133C2×C8—42no—
134C2×C8—6321no—
135C4⋊C4—3162no—
136C4⋊C4—3161no—
137C22⋊C4—41no—
138C22⋊C4—41no—
139C22⋊C4—3161no—
140C22⋊C4—3161no—
141C22⋊C4—3161no—
142C22⋊C4—3161no—
143C23—21no—
144C23—21no—
145C23—81no—
146C23#1457907511yescharacteristic
147C23#1457908411yescharacteristic
148C23#1457908911yescharacteristic
149Q8—12641no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—81no—
159C2×C4—81no—
160C2×C4—81no—
161C2×C4—3162no—
162C2×C4—6322no—
163C2×C4—6321no—
164C2×C4—6322no—
165C8—82no—
166C8—12641no—
167C22—21no—
168C22—21no—
169C22—41no—
170C22—41no—
171C22—41no—
172C22—42no—
173C22—81no—
174C22#1909829911yescharacteristic
175C22#1909834911yescharacteristic
176C22#1909835711yescharacteristic
177C4—41no—
178C4—41no—
179C4—81no—
180C4—81no—
181C4—6322no—
182C4—12641no—
183C2—21no—
184C2—21no—
185C2—21no—
186C2—41no—
187C2—41no—
188C2#2376142011yescharacteristic
subgroupG/H
centerC2#23761420
commutatorC2×C22⋊C4×C79C2×C4
Frattini#381C2×D79
FittingC79×#1306C2
socleC2×C79#1351
prime radicalC24×C79C22⋊C4
cosocle#381×C79C22
hypercenter#1306D79
hypocenterC79#7427
LCSG ▷ C2×C22⋊C4×C79 ▷ C24×C79 ▷ C22×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2 ◁ C23 ◁ C24 ◁ #381 ◁ #1306

Complements

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

NH ≅ G/Ntype
98. C79#7427semidirect

Maximal subgroups

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

subgroupindex
#237645672
#237613302
C79×#13062
#742779