Finite Group Databasebeta

← #34191532

Subgroups — #34191532

Order 20224.

526 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 75 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#23771664C211yesmaximal, characteristic
2#23763474C212yesmaximal
3C79⋊#1304C211yesmaximal, characteristic
4C79⋊#1304C212yesmaximal
5C79×#1819C211yesmaximal, characteristic
6#19098499—22no—
7#19098486—24no—
8#19098419C2212yes—
9#19098419C2212yes—
10#19098330—24no—
11C22×C22⋊C4×C79C2211yescharacteristic
12#379×C79C2211yescharacteristic
13#379×C79C2211yescharacteristic
14#342×C79—22no—
15C2×C4⋊Dic79—22no—
16C2×Dic79⋊C4—24no—
17C2×C22⋊Dic79—22no—
18C2×C22⋊Dic79—22no—
19C2×C22⋊Dic79—22no—
20C2×C22⋊Dic79—22no—
21C2×C22⋊Dic79—22no—
22C2×C22⋊Dic79D414yes—
23C79⋊#95—22no—
24C25×C79C2311yescharacteristic
25C23×C4×C79Q812yes—
26C2×C22⋊C4×C79—21no—
27C2×C22⋊C4×C79—22no—
28C2×C22⋊C4×C79—22no—
29C2×C22⋊C4×C79—21no—
30C2×C22⋊C4×C79—21no—
31C2×C22⋊C4×C79—22no—
32C2×C22⋊C4×C79—22no—
33C2×C22⋊C4×C79D412yes—
34C22×Dic79—24no—
35C22×Dic79—42no—
36C4⋊Dic79—82no—
37Dic79⋊C4—84no—
38C22⋊Dic79—44no—
39C22⋊Dic79—44no—
40C22⋊Dic79—82no—
41C22⋊Dic79—82no—
42C22⋊Dic79—82no—
43C22⋊Dic79—82no—
44C24×C79—42no—
45C24×C79—82no—
46C24×C79C2×D412yes—
47C24×C79C2×D411yescharacteristic
48C24×C79C2×Q811yescharacteristic
49C24×C79#4112yes—
50C24×C79#4111yescharacteristic
51C22×C4×C79—22no—
52C22×C4×C79—22no—
53C22×C4×C79—22no—
54C22×C4×C79—22no—
55C22×C4×C79—41no—
56C22×C4×C79—82no—
57C22⋊C4×C79—41no—
58C22⋊C4×C79—42no—
59C22⋊C4×C79—41no—
60C22⋊C4×C79—42no—
61C22⋊C4×C79—42no—
62C22⋊C4×C79—82no—
63C22⋊C4×C79—82no—
64C23×C79—24no—
65C23×C79—22no—
66C23×C79—42no—
67C23×C79—41no—
68C23×C79—42no—
69C23×C79—42no—
70C23×C79—42no—
71C23×C79—42no—
72C23×C79—42no—
73C23×C79—42no—
74C23×C79—42no—
75C23×C79—41no—
76C23×C79—88no—
77C23×C79#12011yescharacteristic
78C23×C79C22⋊Q812yes—
79C23×C79C22⋊Q811yescharacteristic
80C23×C79#12412yes—
81C23×C79#12411yescharacteristic
82C2×C4×C79—44no—
83C2×C4×C79—42no—
84C2×C4×C79—42no—
85C2×C4×C79—82no—
86C2×C4×C79—82no—
87C2×C4×C79—82no—
88C2×C4×C79—81no—
89C2×C4×C79—82no—
90C2×Dic79—44no—
91C2×Dic79—44no—
92C2×Dic79—44no—
93C2×Dic79—82no—
94C2×Dic79—82no—
95C2×Dic79—82no—
96C22×C79—22no—
97C22×C79—21no—
98C22×C79—22no—
99C22×C79—21no—
100C22×C79—22no—
101C22×C79—22no—
102C22×C79—22no—
103C22×C79—22no—
104C22×C79—22no—
105C22×C79—22no—
106C22×C79—22no—
107C22×C79—44no—
108C22×C79—84no—
109C22×C79—82no—
110C22×C79—82no—
111C22×C79—84no—
112C22×C79#39311yescharacteristic
113C22×C79#45812yes—
114C4×C79—82no—
115C4×C79—82no—
116C4×C79—161no—
117Dic79—84no—
118Dic79—162no—
119#10393—791nomaximal, Sylow
120C2×C79—22no—
121C2×C79—42no—
122C2×C79—41no—
123C2×C79—42no—
124C2×C79—41no—
125C2×C79#203011yescharacteristic
126C2×C79#203212yes—
127#2842—791no—
128#1819—792no—
129#1819D7911yescharacteristic
130#1304—792no—
131#1304—791no—
132C79#1039311yescharacteristic, complemented, Sylow
133C22×C22⋊C4C2×D7911yescharacteristic
134#399—1582no—
135#396—1584no—
136#379—792no—
137#379—792no—
138#379C2×D7911yescharacteristic
139#379C2×D7911yescharacteristic
140#342—22no—
141#342—1584no—
142C25C22×D7911yescharacteristic
143C23×C4Dic15812yes—
144C2×C4⋊C4—1584no—
145C2×C4⋊C4—1582no—
146C2×C22⋊C4—22no—
147C2×C22⋊C4—21no—
148C2×C22⋊C4—22no—
149C2×C22⋊C4—21no—
150C2×C22⋊C4—21no—
151C2×C22⋊C4—22no—
152C2×C22⋊C4—22no—
153C2×C22⋊C4—794no—
154C2×C22⋊C4—1582no—
155C2×C22⋊C4—1582no—
156C2×C22⋊C4—1582no—
157C2×C22⋊C4—1582no—
158C2×C22⋊C4—1582no—
159C2×C22⋊C4C22⋊D7912yes—
160#95—1582no—
161C24—42no—
162C24—82no—
163C24D4×D7912yes—
164C24C2×C22⋊D7911yescharacteristic
165C24C2×Dic15811yescharacteristic
166C24#1192962312yes—
167C24#1192962411yescharacteristic
168C22×C4—22no—
169C22×C4—22no—
170C22×C4—22no—
171C22×C4—22no—
172C22×C4—41no—
173C22×C4—82no—
174C22×C4—3162no—
175C22×C4—1584no—
176C4⋊C4—6324no—
177C4⋊C4—6322no—
178C22⋊C4—41no—
179C22⋊C4—42no—
180C22⋊C4—41no—
181C22⋊C4—42no—
182C22⋊C4—42no—
183C22⋊C4—82no—
184C22⋊C4—82no—
185C22⋊C4—3164no—
186C22⋊C4—3164no—
187C22⋊C4—6322no—
188C22⋊C4—6322no—
189C22⋊C4—6322no—
190C22⋊C4—6322no—
191C23—22no—
192C23—24no—
193C23—42no—
194C23—41no—
195C23—42no—
196C23—42no—
197C23—42no—
198C23—42no—
199C23—42no—
200C23—42no—
201C23—42no—
202C23—41no—
203C23—88no—
204C23#1457912911yescharacteristic
205C23#1457913812yes—
206C23#1457914011yescharacteristic
207C23#1457914712yes—
208C23#1457914811yescharacteristic
209C2×C4—44no—
210C2×C4—42no—
211C2×C4—42no—
212C2×C4—82no—
213C2×C4—82no—
214C2×C4—82no—
215C2×C4—81no—
216C2×C4—82no—
217C2×C4—3164no—
218C2×C4—3164no—
219C2×C4—3164no—
220C2×C4—6322no—
221C2×C4—6322no—
222C2×C4—6322no—
223C22—22no—
224C22—21no—
225C22—22no—
226C22—22no—
227C22—21no—
228C22—22no—
229C22—22no—
230C22—22no—
231C22—22no—
232C22—22no—
233C22—22no—
234C22—44no—
235C22—82no—
236C22—84no—
237C22—84no—
238C22—82no—
239C22#1909847511yescharacteristic
240C22#1909875212yes—
241C4—82no—
242C4—82no—
243C4—161no—
244C4—6324no—
245C4—12642no—
246C2—22no—
247C2—41no—
248C2—42no—
249C2—42no—
250C2—41no—
251C2#2376456711yescharacteristic
252C2#2376457712yes—
subgroupG/H
centerC22#19098475
commutator, prime radical, cosocleC25×C79C23
FrattiniC25C22×D79
FittingC79×#1819C2
socleC22×C79#393
hypercenter#1819D79
hypocenterC79#10393
LCSG ▷ C25×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ C25 ◁ #1819

Complements

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

NH ≅ G/Ntype
132. C79#10393semidirect

Maximal subgroups

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

subgroupindex
#237716642
#237634742
C79⋊#13042
C79×#18192
#1039379