Finite Group Databasebeta

← #34191517

Subgroups — #34191517

Order 20224.

406 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 73 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#23769070C211yesmaximal, characteristic
2#23763497C212yesmaximal
3#23763475C211yesmaximal, characteristic
4#23761254C212yesmaximal
5C79×#1306C211yesmaximal, characteristic
6C2×#14579120C2211yescharacteristic
7#19098486—22no—
8#19098460—22no—
9#19098446—22no—
10#19098426C2211yescharacteristic
11C4×C22⋊Dic79C2212yes—
12#19098329—22no—
13#19098324—22no—
14#19098324—22no—
15#407×C79C2212yes—
16#381×C79C2211yescharacteristic
17#14579120—22no—
18#14579120—22no—
19C2×C4⋊Dic79—22no—
20C2×C4⋊Dic79Q812yes—
21C2×Dic79⋊C4—22no—
22C2×Dic79⋊C4—22no—
23C2×C22⋊Dic79—22no—
24C2×C22⋊Dic79—21no—
25C2×C22⋊Dic79—21no—
26C2×C4×Dic79—21no—
27C2×C4×Dic79D412yes—
28C2×C4×Dic79D412yes—
29C79⋊#95—22no—
30C79⋊#95—22no—
31C79⋊#95—22no—
32C23×C4×C79C2311yescharacteristic
33C2×M16×C79—22no—
34C2×C22⋊C4×C79D412yes—
35C22⋊C8×C79—22no—
36C22⋊C8×C79—22no—
37#95×C79—22no—
38C22×Dic79—22no—
39C22×Dic79—22no—
40C22×Dic79—22no—
41C22×Dic79—41no—
42C4⋊Dic79—24no—
43C4⋊Dic79—44no—
44Dic79⋊C4—44no—
45Dic79⋊C4—82no—
46C22⋊Dic79—42no—
47C22⋊Dic79—44no—
48C22⋊Dic79—41no—
49C22⋊Dic79—41no—
50C4×Dic79—42no—
51C4×Dic79—42no—
52C4×Dic79—42no—
53C24×C79C2×D411yescharacteristic
54C22×C4×C79—22no—
55C22×C4×C79—42no—
56C22×C4×C79C2×D412yes—
57C22×C4×C79C2×Q811yescharacteristic
58C22×C4×C79#4112yes—
59C22×C4×C79#4111yescharacteristic
60M16×C79—42no—
61M16×C79—42no—
62C2×C8×C79—42no—
63C22⋊C4×C79—42no—
64C23×C79—22no—
65C23×C79—42no—
66C23×C79#12011yescharacteristic
67C23×C79C22⋊Q811yescharacteristic
68C23×C79#12411yescharacteristic
69C2×C4×C79—22no—
70C2×C4×C79—22no—
71C2×C4×C79—41no—
72C2×C4×C79—41no—
73C2×C4×C79—42no—
74C2×C4×C79—42no—
75C2×C4×C79—42no—
76C2×C4×C79—42no—
77C2×C4×C79C22⋊Q812yes—
78C2×C4×C79#12412yes—
79C2×Dic79—24no—
80C2×Dic79—42no—
81C2×Dic79—42no—
82C2×Dic79—42no—
83C2×Dic79—42no—
84C2×Dic79—42no—
85C2×Dic79—42no—
86C2×Dic79—82no—
87C2×Dic79—81no—
88C2×Dic79—82no—
89C8×C79—82no—
90C22×C79—22no—
91C22×C79—21no—
92C22×C79—21no—
93C22×C79—22no—
94C22×C79—22no—
95C22×C79—82no—
96C22×C79#39311yescharacteristic
97C22×C79#45812yes—
98C4×C79—22no—
99C4×C79—22no—
100C4×C79—82no—
101Dic79—44no—
102Dic79—82no—
103Dic79—82no—
104Dic79—161no—
105#10389—791nomaximal, Sylow
106C2×C79—22no—
107C2×C79—41no—
108C2×C79—41no—
109C2×C79#203011yescharacteristic
110C2×C79#203112yes—
111#2608—791no—
112#1826—792no—
113#1820—791no—
114#1306D7911yescharacteristic
115#1284—792no—
116C79#1038911yescharacteristic, complemented, Sylow
117C2×#117—791no—
118#407C2×D7912yes—
119#396—1582no—
120#389—1582no—
121#387—1582no—
122#381—791no—
123#381C2×D7911yescharacteristic
124C4×C22⋊C4—792no—
125#342—1582no—
126#339—1582no—
127#339—1582no—
128C23×C4C22×D7911yescharacteristic
129C2×M16—22no—
130#117—1582no—
131#117—1582no—
132C2×C4⋊C4—792no—
133C2×C4⋊C4—1582no—
134C2×C4⋊C4—1582no—
135C2×C4⋊C4—1582no—
136C2×C22⋊C4—1581no—
137C2×C22⋊C4—1581no—
138C2×C22⋊C4—1582no—
139C2×C22⋊C4D31612yes—
140C2×C42—792no—
141C2×C42—792no—
142C2×C42—1581no—
143C22⋊C8—22no—
144C22⋊C8—22no—
145#95—22no—
146#95—1582no—
147#95—1582no—
148#95—1582no—
149C24C2×D31611yescharacteristic
150C22×C4—22no—
151C22×C4—42no—
152C22×C4—3161no—
153C22×C4—1582no—
154C22×C4—1582no—
155C22×C4—1582no—
156C22×C4D4×D7912yes—
157C22×C4Q8×D7911yescharacteristic
158C22×C4#1192962311yescharacteristic
159C22×C4#1192962412yes—
160M16—42no—
161M16—42no—
162C2×C8—42no—
163C4⋊C4—3164no—
164C4⋊C4—3164no—
165C4⋊C4—6322no—
166C4⋊C4—1584no—
167C22⋊C4—42no—
168C22⋊C4—3161no—
169C22⋊C4—3161no—
170C22⋊C4—3164no—
171C22⋊C4—3162no—
172C42—3162no—
173C42—3162no—
174C42—3162no—
175C23—22no—
176C23—42no—
177C23#1457913111yescharacteristic
178C23#1457914111yescharacteristic
179C23#1457914911yescharacteristic
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—3162no—
189C2×C4—3162no—
190C2×C4—3162no—
191C2×C4—3162no—
192C2×C4—3162no—
193C2×C4—3162no—
194C2×C4—6322no—
195C2×C4—6321no—
196C2×C4—6322no—
197C2×C4—1584no—
198C2×C4#1457913912yes—
199C2×C4#1457914712yes—
200C8—82no—
201C22—22no—
202C22—21no—
203C22—21no—
204C22—22no—
205C22—22no—
206C22—82no—
207C22#1909847611yescharacteristic
208C22#1909875412yes—
209C4—22no—
210C4—22no—
211C4—82no—
212C4—3164no—
213C4—6322no—
214C4—6322no—
215C4—12641no—
216C2—22no—
217C2—41no—
218C2—41no—
219C2#2376456811yescharacteristic
220C2#2376457512yes—
subgroupG/H
centerC22#19098476
commutator, cosocleC23×C4×C79C23
FrattiniC23×C4C22×D79
FittingC79×#1306C2
socleC22×C79#393
prime radicalC24×C79C2×D4
hypercenter#1306D79
hypocenterC79#10389
LCSG ▷ C23×C4×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1306

Complements

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

NH ≅ G/Ntype
116. C79#10389semidirect

Maximal subgroups

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

subgroupindex
#237690702
#237634972
#237634752
#237612542
C79×#13062
#1038979