Finite Group Databasebeta

← #34181782

Subgroups — #34181782

Order 20224.

538 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 538 conjugacy classes of subgroups — too many to draw. Only its 91 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#23765998C211yesmaximal, characteristic
2#23763474C211yesmaximal, characteristic
3C79⋊#1304C212yesmaximal
4C79⋊#1304C212yesmaximal
5C79×#1819C211yesmaximal, characteristic
6#19098456—22no—
7#19098456—22no—
8#19098423C412yescomplemented
9#19098419C2212yes—
10#19098419C2211yescharacteristic
11#19098419C2211yescharacteristic
12C4×C22⋊Dic79C412yescomplemented
13#19098330—22no—
14C22×C22⋊C4×C79C2211yescharacteristic
15#379×C79C2212yes—
16#342×C79—22no—
17C2×C4⋊Dic79—22no—
18C2×C22⋊Dic79—22no—
19C2×C22⋊Dic79—21no—
20C2×C22⋊Dic79—21no—
21C2×C22⋊Dic79—21no—
22C2×C22⋊Dic79—21no—
23C2×C22⋊Dic79—22no—
24C2×C22⋊Dic79—22no—
25C2×C22⋊Dic79C2×C412yes—
26C2×C22⋊Dic79C2×C412yes—
27C2×C4×Dic79—22no—
28C79⋊#95—22no—
29C79⋊#95—22no—
30C25×C79C2311yescharacteristic
31C23×C4×C79C2×C411yescharacteristic
32C23×C4×C79C2×C411yescharacteristic
33C2×C22⋊C4×C79—22no—
34C2×C22⋊C4×C79—22no—
35C2×C22⋊C4×C79—22no—
36C2×C22⋊C4×C79—22no—
37C2×C22⋊C4×C79—22no—
38C2×C22⋊C4×C79D412yes—
39C2×C22⋊C4×C79D412yes—
40C22×Dic79—22no—
41C22×Dic79—22no—
42C22×Dic79—42no—
43C4⋊Dic79—82no—
44C22⋊Dic79—42no—
45C22⋊Dic79—42no—
46C22⋊Dic79—44no—
47C22⋊Dic79—81no—
48C22⋊Dic79—81no—
49C22⋊Dic79—81no—
50C22⋊Dic79—81no—
51C22⋊Dic79—82no—
52C22⋊Dic79—82no—
53C4×Dic79—82no—
54C24×C79—42no—
55C24×C79—81no—
56C24×C79—81no—
57C24×C79C22×C411yescharacteristic
58C24×C79C2×D411yescharacteristic
59C24×C79C2×D411yescharacteristic
60C24×C79#4112yes—
61C24×C79#4112yes—
62C22×C4×C79—21no—
63C22×C4×C79—21no—
64C22×C4×C79—21no—
65C22×C4×C79—21no—
66C22×C4×C79—42no—
67C22×C4×C79—81no—
68C22×C4×C79—81no—
69C22×C4×C79C22⋊C412yes—
70C22×C4×C79C22⋊C412yes—
71C22⋊C4×C79—24no—
72C22⋊C4×C79—24no—
73C22⋊C4×C79—44no—
74C22⋊C4×C79—82no—
75C22⋊C4×C79—82no—
76C23×C79—22no—
77C23×C79—22no—
78C23×C79—22no—
79C23×C79—41no—
80C23×C79—41no—
81C23×C79—41no—
82C23×C79—41no—
83C23×C79—41no—
84C23×C79—41no—
85C23×C79—42no—
86C23×C79—42no—
87C23×C79—42no—
88C23×C79—42no—
89C23×C79—42no—
90C23×C79—42no—
91C23×C79—88no—
92C23×C79C2×C22⋊C411yescharacteristic
93C23×C79#11711yescharacteristic
94C23×C79#11711yescharacteristic
95C23×C79#12312yes—
96C23×C79#12312yes—
97C2×C4×C79—22no—
98C2×C4×C79—22no—
99C2×C4×C79—42no—
100C2×C4×C79—42no—
101C2×C4×C79—81no—
102C2×C4×C79—81no—
103C2×C4×C79—81no—
104C2×C4×C79—81no—
105C2×C4×C79—82no—
106C2×C4×C79—82no—
107C2×C4×C79—82no—
108C2×Dic79—42no—
109C2×Dic79—42no—
110C2×Dic79—42no—
111C2×Dic79—42no—
112C2×Dic79—42no—
113C2×Dic79—42no—
114C2×Dic79—82no—
115C2×Dic79—82no—
116C2×Dic79—82no—
117C22×C79—21no—
118C22×C79—21no—
119C22×C79—22no—
120C22×C79—21no—
121C22×C79—21no—
122C22×C79—22no—
123C22×C79—21no—
124C22×C79—21no—
125C22×C79—21no—
126C22×C79—21no—
127C22×C79—22no—
128C22×C79—22no—
129C22×C79—22no—
130C22×C79—22no—
131C22×C79—44no—
132C22×C79—82no—
133C22×C79—82no—
134C22×C79—84no—
135C22×C79—84no—
136C22×C79#38111yescharacteristic
137C22×C79#41012yes—
138C4×C79—42no—
139C4×C79—42no—
140C4×C79—162no—
141Dic79—82no—
142Dic79—82no—
143Dic79—162no—
144#8750—791nomaximal, Sylow
145C2×C79—22no—
146C2×C79—42no—
147C2×C79—42no—
148C2×C79—41no—
149C2×C79—41no—
150C2×C79#182011yescharacteristic
151C2×C79#182811yescharacteristic
152C2×C79#182811yescharacteristic
153#2312—791no—
154#1819—791no—
155#1819D7911yescharacteristic
156#1304—792no—
157#1304—792no—
158C79#875011yescharacteristic, complemented, Sylow
159C22×C22⋊C4C2×D7911yescharacteristic
160#388—1582no—
161#388—1582no—
162#380—792no—
163#379—791no—
164#379—791no—
165#379—792no—
166#379C2×D7912yes—
167C4×C22⋊C4—792no—
168#342—22no—
169#342—1582no—
170C25C22×D7911yescharacteristic
171C23×C4C4×D7911yescharacteristic
172C23×C4C4×D7911yescharacteristic
173C2×C4⋊C4—1582no—
174C2×C22⋊C4—22no—
175C2×C22⋊C4—22no—
176C2×C22⋊C4—22no—
177C2×C22⋊C4—22no—
178C2×C22⋊C4—22no—
179C2×C22⋊C4—792no—
180C2×C22⋊C4—792no—
181C2×C22⋊C4—1582no—
182C2×C22⋊C4—1582no—
183C2×C22⋊C4—1582no—
184C2×C22⋊C4—1581no—
185C2×C22⋊C4—1581no—
186C2×C22⋊C4—1581no—
187C2×C22⋊C4—1581no—
188C2×C22⋊C4D31612yes—
189C2×C22⋊C4C22⋊D7912yes—
190C2×C42—1582no—
191#95—1582no—
192#95—1582no—
193C24—42no—
194C24—81no—
195C24—81no—
196C24C2×C4×D7911yescharacteristic
197C24C2×C22⋊D7911yescharacteristic
198C24C2×D31611yescharacteristic
199C24#1192962312yes—
200C24#1192962312yes—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—42no—
206C22×C4—81no—
207C22×C4—81no—
208C22×C4—3162no—
209C22×C4—1582no—
210C22×C4—1582no—
211C22×C4(C2×D79)⋊C412yes—
212C22×C4(C2×D79)⋊C412yes—
213C4⋊C4—6322no—
214C22⋊C4—24no—
215C22⋊C4—24no—
216C22⋊C4—44no—
217C22⋊C4—82no—
218C22⋊C4—82no—
219C22⋊C4—3162no—
220C22⋊C4—3162no—
221C22⋊C4—3164no—
222C22⋊C4—6321no—
223C22⋊C4—6321no—
224C22⋊C4—6321no—
225C22⋊C4—6321no—
226C22⋊C4—6322no—
227C22⋊C4—6322no—
228C42—6322no—
229C23—22no—
230C23—22no—
231C23—22no—
232C23—41no—
233C23—41no—
234C23—42no—
235C23—42no—
236C23—41no—
237C23—41no—
238C23—41no—
239C23—41no—
240C23—42no—
241C23—42no—
242C23—42no—
243C23—42no—
244C23—88no—
245C23C2×(C2×D79)⋊C411yescharacteristic
246C23#1457911711yescharacteristic
247C23#1457911711yescharacteristic
248C23#1457914212yes—
249C23#1457914512yes—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—81no—
255C2×C4—81no—
256C2×C4—81no—
257C2×C4—81no—
258C2×C4—82no—
259C2×C4—82no—
260C2×C4—82no—
261C2×C4—3162no—
262C2×C4—3162no—
263C2×C4—3162no—
264C2×C4—3162no—
265C2×C4—3162no—
266C2×C4—3162no—
267C2×C4—6322no—
268C2×C4—6322no—
269C2×C4—6322no—
270C22—21no—
271C22—21no—
272C22—22no—
273C22—22no—
274C22—21no—
275C22—21no—
276C22—21no—
277C22—21no—
278C22—21no—
279C22—21no—
280C22—22no—
281C22—22no—
282C22—22no—
283C22—22no—
284C22—44no—
285C22—82no—
286C22—82no—
287C22—84no—
288C22—84no—
289C22#1909842411yescharacteristic
290C22#1909853612yes—
291C4—42no—
292C4—42no—
293C4—162no—
294C4—6322no—
295C4—6322no—
296C4—12642no—
297C2—22no—
298C2—42no—
299C2—42no—
300C2—41no—
301C2—41no—
302C2#2376347511yescharacteristic
303C2#2376350611yescharacteristic
304C2#2376350611yescharacteristic
subgroupG/H
centerC22#19098424
commutatorC24×C79C22×C4
FrattiniC25C22×D79
FittingC79×#1819C2
socleC22×C79#381
prime radical, cosocleC25×C79C23
hypercenter#1819D79
hypocenterC79#8750
LCSG ▷ C24×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ C25 ◁ #1819

Complements

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

NH ≅ G/Ntype
8. #19098423C4semidirect
12. C4×C22⋊Dic79C4semidirect
158. C79#8750semidirect

Maximal subgroups

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

subgroupindex
#237659982
#237634742
C79⋊#13042
C79×#18192
#875079