Finite Group Databasebeta

← #34182939

Subgroups — #34182939

Order 20224.

510 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 123 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
1C4×#14579159C211yesmaximal, characteristic
2#23761794C212yesmaximal
3#23761724C211yesmaximal, characteristic
4#23761232C212yesmaximal
5C79×#2983C211yesmaximal, characteristic
6C2×#14579159C411yescharacteristic
7C2×C4×Dic158C2211yescharacteristic
8#19098616C2212yes—
9#19098470C411yescharacteristic
10#19098468C411yescharacteristic
11#19098458—22no—
12#19098432C411yescharacteristic
13C4×Dic79⋊C4—22no—
14C42×Dic79C2211yescharacteristic
15#19098293—24no—
16#19098289—22no—
17C2×C4×Q8×C79C2211yescharacteristic
18#446×C79—24no—
19#432×C79—22no—
20#431×C79C2212yes—
21C22×Dic158C2×C411yescharacteristic
22#14579159—22no—
23#14579159—22no—
24C4×Dic158—22no—
25C4×Dic158—22no—
26C2×C4⋊Dic79C2×C411yescharacteristic
27C2×Dic79⋊C4—22no—
28C2×Dic79⋊C4—22no—
29C2×Dic79⋊C4—21no—
30C2×C4×Dic79—21no—
31C2×C4×Dic79—21no—
32C2×C4×Dic79—21no—
33C2×C4×Dic79C2×C411yescharacteristic
34C2×C4×Dic79C2×C411yescharacteristic
35C4⋊(C79⋊C8)—22no—
36C22⋊(C79⋊C8)—22no—
37C4×C79⋊C8—22no—
38C79⋊#95—22no—
39C79⋊#95—22no—
40C22×Q8×C79C2×C411yescharacteristic
41C4×Q8×C79—22no—
42C4×Q8×C79—22no—
43C2×C4⋊C4×C79C2×C411yescharacteristic
44C2×C4⋊C4×C79D412yes—
45C2×C42×C79D412yes—
46C2×C42×C79C2311yescharacteristic
47C4⋊C8×C79—24no—
48C4⋊C8×C79D414yes—
49C22⋊C8×C79—22no—
50#97×C79—24no—
51C4×C8×C79—22no—
52C2×Dic158—22no—
53C2×Dic158—21no—
54C2×Dic158—22no—
55C2×Dic158M1612yes—
56C22×Dic79—21no—
57C22×Dic79—21no—
58C22×Dic79—21no—
59C22×Dic79—21no—
60C2×C79⋊C8—42no—
61C4⋊Dic79—22no—
62Dic79⋊C4—28no—
63Dic79⋊C4—44no—
64Dic79⋊C4—42no—
65C4×Dic79—24no—
66C4×Dic79—21no—
67C4×Dic79—22no—
68C4×Dic79—42no—
69C4×Dic79—41no—
70C4×Dic79—41no—
71C4×Dic79M1612yes—
72C2×Q8×C79—22no—
73C2×Q8×C79—21no—
74C2×Q8×C79—21no—
75C2×Q8×C79—22no—
76C22×C4×C79C22⋊C412yes—
77C22×C4×C79C22⋊C412yes—
78C22×C4×C79C22×C411yescharacteristic
79C22×C4×C79C2×D411yescharacteristic
80C22×C4×C79C2×D411yescharacteristic
81C2×C8×C79—24no—
82C4⋊C4×C79—22no—
83C4⋊C4×C79—24no—
84C42×C79—22no—
85C42×C79—22no—
86C42×C79C2×D412yes—
87C42×C79#4112yes—
88C23×C79C2×C22⋊C411yescharacteristic
89Q8×C79—42no—
90Q8×C79—42no—
91C2×C4×C79—22no—
92C2×C4×C79—22no—
93C2×C4×C79—22no—
94C2×C4×C79—22no—
95C2×C4×C79—22no—
96C2×C4×C79—41no—
97C2×C4×C79—42no—
98C2×C4×C79C4×D412yes—
99C2×C4×C79#12011yescharacteristic
100C2×C4×C79#12112yes—
101C2×C4×C79#12311yescharacteristic
102C2×C4×C79C2×M1611yescharacteristic
103C2×C4×C79C2×M1611yescharacteristic
104C2×C4×C79#13112yes—
105C2×Dic79—22no—
106C2×Dic79—22no—
107C2×Dic79—22no—
108C2×Dic79—22no—
109C2×Dic79—22no—
110C2×Dic79—41no—
111C2×Dic79—41no—
112C2×Dic79—41no—
113C2×Dic79—41no—
114C2×Dic79—42no—
115C2×Dic79—41no—
116Dic158—24no—
117Dic158—42no—
118C8×C79—44no—
119C79⋊C8—82no—
120C22×C79—21no—
121C22×C79—21no—
122C22×C79#38611yescharacteristic
123C22×C79#40711yescharacteristic
124C22×C79#40811yescharacteristic
125C4×C79—22no—
126C4×C79—21no—
127C4×C79—42no—
128C4×C79—42no—
129C4×C79#43512yes—
130C4×C79#43612yes—
131C4×C79#45612yes—
132Dic79—24no—
133Dic79—42no—
134Dic79—42no—
135Dic79—81no—
136#8962—791nomaximal, Sylow
137C2×C79—21no—
138C2×C79—21no—
139C2×C79#187011yescharacteristic
140C2×C79#188411yescharacteristic
141C2×C79#188611yescharacteristic
142#2983D7911yescharacteristic
143C4×C4⋊Q8—791no—
144#1479—792no—
145#1461—791no—
146#1276—792no—
147C79#896211yescharacteristic, complemented, Sylow
148C2×C4⋊Q8—791no—
149C2×C4×Q8—791no—
150C2×C4×Q8C2×D7911yescharacteristic
151#446—24no—
152#432—22no—
153#431—792no—
154#431C2×D7912yes—
155#391—791no—
156#391—791no—
157#389—1582no—
158#384—791no—
159C4×C4⋊C4—1582no—
160C43—791no—
161Q8⋊C8—1584no—
162#324—1582no—
163C22×Q8—791no—
164C22×Q8C4×D7911yescharacteristic
165C4⋊Q8—1582no—
166C4⋊Q8—1582no—
167C4×Q8—22no—
168C4×Q8—22no—
169C4×Q8—1582no—
170C4×Q8—1582no—
171C2×C4⋊C4—791no—
172C2×C4⋊C4—1582no—
173C2×C4⋊C4—1581no—
174C2×C4⋊C4—1582no—
175C2×C4⋊C4C4×D7911yescharacteristic
176C2×C4⋊C4D31612yes—
177C2×C42—791no—
178C2×C42—791no—
179C2×C42—1581no—
180C2×C42—1581no—
181C2×C42—1581no—
182C2×C42C22⋊D7912yes—
183C2×C42C22×D7911yescharacteristic
184C4⋊C8—24no—
185C4⋊C8—1582no—
186C4⋊C8C22⋊D7914yes—
187C22⋊C8—22no—
188C22⋊C8—1582no—
189#97—24no—
190C4×C8—22no—
191C4×C8—1582no—
192#95—1582no—
193#95—1582no—
194C2×Q8—22no—
195C2×Q8—21no—
196C2×Q8—21no—
197C2×Q8—22no—
198C2×Q8—792no—
199C2×Q8—1582no—
200C2×Q8—1582no—
201C2×Q8—1581no—
202C22×C4—1581no—
203C22×C4—1581no—
204C22×C4—1581no—
205C22×C4—1581no—
206C22×C4(C2×D79)⋊C412yes—
207C22×C4(C2×D79)⋊C412yes—
208C22×C4C2×C4×D7911yescharacteristic
209C22×C4C2×C22⋊D7911yescharacteristic
210C22×C4C2×D31611yescharacteristic
211C2×C8—24no—
212C2×C8—3162no—
213C4⋊C4—22no—
214C4⋊C4—24no—
215C4⋊C4—3164no—
216C4⋊C4—3162no—
217C4⋊C4—1588no—
218C4⋊C4—1582no—
219C42—22no—
220C42—22no—
221C42—3162no—
222C42—3161no—
223C42—3161no—
224C42—792no—
225C42—1584no—
226C42—1582no—
227C42—1581no—
228C42C2×C22⋊D7912yes—
229C42#1192962412yes—
230C23C2×(C2×D79)⋊C411yescharacteristic
231Q8—42no—
232Q8—42no—
233Q8—3162no—
234Q8—1584no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—41no—
241C2×C4—42no—
242C2×C4—3161no—
243C2×C4—3161no—
244C2×C4—3161no—
245C2×C4—3161no—
246C2×C4—3162no—
247C2×C4—3161no—
248C2×C4—1582no—
249C2×C4—1582no—
250C2×C4—1582no—
251C2×C4—1582no—
252C2×C4—1582no—
253C2×C4C4×C22⋊D7912yes—
254C2×C4#1457913011yescharacteristic
255C2×C4#1457913512yes—
256C2×C4#1457914411yescharacteristic
257C2×C4M16×D7911yescharacteristic
258C2×C4M16×D7911yescharacteristic
259C2×C4#1457916912yes—
260C8—44no—
261C8—6322no—
262C22—21no—
263C22—21no—
264C22#1909844211yescharacteristic
265C22#1909852611yescharacteristic
266C22#1909853111yescharacteristic
267C4—22no—
268C4—21no—
269C4—42no—
270C4—42no—
271C4—3162no—
272C4—3162no—
273C4—6321no—
274C4—1584no—
275C4#1909863212yes—
276C4#1909863912yes—
277C4#1909874612yes—
278C2—21no—
279C2—21no—
280C2#2376369711yescharacteristic
281C2#2376378311yescharacteristic
282C2#2376379311yescharacteristic
subgroupG/H
centerC2×C4#14579130
commutatorC22×C4×C79C22×C4
FrattiniC2×C42C22×D79
FittingC79×#2983C2
socleC22×C79#386
prime radicalC23×C79C2×C22⋊C4
cosocleC2×C42×C79C23
hypercenter#2983D79
hypocenterC79#8962
LCSG ▷ C22×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2983

Complements

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

NH ≅ G/Ntype
147. C79#8962semidirect

Maximal subgroups

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

subgroupindex
C4×#145791592
#237617942
#237617242
#237612322
C79×#29832
#896279