Finite Group Databasebeta

← #34191513

Subgroups — #34191513

Order 20224.

406 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 77 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#23763500C212yesmaximal
2#23763475C211yesmaximal, characteristic
3#23761308C211yesmaximal, characteristic
4#23761253C212yesmaximal
5C79×#2608C211yesmaximal, characteristic
6C2×#14579120C2211yescharacteristic
7#19098527C2212yes—
8#19098426C2211yescharacteristic
9#19098329—22no—
10#19098323—22no—
11#19098323—22no—
12#396×C79—22no—
13#389×C79—22no—
14#387×C79—22no—
15#381×C79C2211yescharacteristic
16C4×C22⋊C4×C79C2212yes—
17C2×#11929608—22no—
18#14579120—22no—
19#14579120—22no—
20C2×C4⋊Dic79Q812yes—
21C2×C22⋊Dic79—21no—
22C2×C22⋊Dic79—21no—
23C2×C4×Dic79—21no—
24C22⋊(C79⋊C8)—22no—
25C22⋊(C79⋊C8)—22no—
26C79⋊#95—22no—
27C23×C4×C79C2311yescharacteristic
28C2×C4⋊C4×C79—22no—
29C2×C4⋊C4×C79—22no—
30C2×C4⋊C4×C79—22no—
31C2×C22⋊C4×C79—22no—
32C2×C22⋊C4×C79D412yes—
33C2×C42×C79D412yes—
34C2×C42×C79D412yes—
35#95×C79—22no—
36#95×C79—22no—
37#95×C79—22no—
38C22×Dic79—22no—
39C22×Dic79—41no—
40#11929608—42no—
41#11929608—42no—
42C2×C79⋊C8—42no—
43C4⋊Dic79—24no—
44C22⋊Dic79—42no—
45C22⋊Dic79—41no—
46C22⋊Dic79—41no—
47C4×Dic79—42no—
48C24×C79C2×D411yescharacteristic
49C22×C4×C79—22no—
50C22×C4×C79—22no—
51C22×C4×C79—22no—
52C22×C4×C79—42no—
53C22×C4×C79C2×D412yes—
54C22×C4×C79C2×Q811yescharacteristic
55C22×C4×C79#4112yes—
56C22×C4×C79#4111yescharacteristic
57C4⋊C4×C79—44no—
58C4⋊C4×C79—44no—
59C4⋊C4×C79—82no—
60C22⋊C4×C79—44no—
61C22⋊C4×C79—42no—
62C42×C79—42no—
63C42×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—24no—
72C2×C4×C79—41no—
73C2×C4×C79—42no—
74C2×C4×C79—41no—
75C2×C4×C79—42no—
76C2×C4×C79—42no—
77C2×C4×C79—42no—
78C2×C4×C79—42no—
79C2×C4×C79—42no—
80C2×C4×C79—42no—
81C2×C4×C79—42no—
82C2×C4×C79—42no—
83C2×C4×C79C22⋊Q812yes—
84C2×C4×C79#12412yes—
85C2×Dic79—42no—
86C2×Dic79—82no—
87C2×Dic79—81no—
88C2×Dic79—82no—
89C79⋊C8—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—44no—
101C4×C79—82no—
102C4×C79—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#2608D7911yescharacteristic
112#1826—792no—
113#1820—791no—
114#1306—791no—
115#1284—792no—
116C79#1038911yescharacteristic, complemented, Sylow
117C2×#117—791no—
118#407—792no—
119#396—22no—
120#389—22no—
121#387—22no—
122#381—791no—
123#381C2×D7911yescharacteristic
124C4×C22⋊C4C2×D7912yes—
125#342—1582no—
126#339—1582no—
127#339—1582no—
128C23×C4C22×D7911yescharacteristic
129C2×M16—1582no—
130#117—1582no—
131#117—1582no—
132C2×C4⋊C4—22no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—22no—
135C2×C4⋊C4—792no—
136C2×C22⋊C4—22no—
137C2×C22⋊C4—1581no—
138C2×C22⋊C4—1581no—
139C2×C22⋊C4C22⋊D7912yes—
140C2×C42—1581no—
141C2×C42C22⋊D7912yes—
142C2×C42C22⋊D7912yes—
143C22⋊C8—1582no—
144C22⋊C8—1582no—
145#95—22no—
146#95—22no—
147#95—22no—
148#95—1582no—
149C24C2×C22⋊D7911yescharacteristic
150C22×C4—22no—
151C22×C4—22no—
152C22×C4—22no—
153C22×C4—42no—
154C22×C4—3161no—
155C22×C4—1582no—
156C22×C4C2×C22⋊D7912yes—
157C22×C4Q8×D7911yescharacteristic
158C22×C4#1192962512yes—
159C22×C4#1192962511yescharacteristic
160M16—3162no—
161M16—3162no—
162C2×C8—3162no—
163C4⋊C4—44no—
164C4⋊C4—44no—
165C4⋊C4—82no—
166C4⋊C4—1584no—
167C22⋊C4—44no—
168C22⋊C4—42no—
169C22⋊C4—3161no—
170C22⋊C4—3161no—
171C22⋊C4—3162no—
172C42—42no—
173C42—42no—
174C42—3162no—
175C23—22no—
176C23—42no—
177C23#1457913011yescharacteristic
178C23#1457913711yescharacteristic
179C23#1457915011yescharacteristic
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—24no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—42no—
190C2×C4—42no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—3162no—
195C2×C4—6322no—
196C2×C4—6321no—
197C2×C4—6322no—
198C2×C4#1457913712yes—
199C2×C4#1457915012yes—
200C8—6322no—
201C22—22no—
202C22—21no—
203C22—21no—
204C22—22no—
205C22—22no—
206C22—82no—
207C22#1909847411yescharacteristic
208C22#1909875312yes—
209C4—22no—
210C4—22no—
211C4—44no—
212C4—82no—
213C4—82no—
214C4—6322no—
215C4—12641no—
216C2—22no—
217C2—41no—
218C2—41no—
219C2#2376456611yescharacteristic
220C2#2376456912yes—
subgroupG/H
centerC22#19098474
commutator, cosocleC23×C4×C79C23
FrattiniC23×C4C22×D79
FittingC79×#2608C2
socleC22×C79#393
prime radicalC24×C79C2×D4
hypercenter#2608D79
hypocenterC79#10389
LCSG ▷ C23×C4×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2608

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
#237635002
#237634752
#237613082
#237612532
C79×#26082
#1038979