Finite Group Databasebeta

← #34185951

Subgroups — #34185951

Order 20224.

468 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 103 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#23772485C211yesmaximal, characteristic
2#23768385C211yesmaximal, characteristic
3#23762125C212yesmaximal
4#23761255C212yesmaximal
5C79×#1467C211yesmaximal, characteristic
6C2×#14579161C2211yescharacteristic
7C2×#14579159C412yes—
8#19098694—24no—
9#19098620—21no—
10#19098620C2212yes—
11#19098616—21no—
12#19098493—21no—
13#19098493—21no—
14#19098468C412yes—
15#19098461—21no—
16#19098461—21no—
17C4×C4⋊Dic79C2211yescharacteristic
18#19098311—24no—
19C2×C4×Q8×C79C2211yescharacteristic
20#432×C79C2212yes—
21#324×C79—21no—
22#324×C79—21no—
23C22×Dic158C2×C412yes—
24#14579161—22no—
25#14579161—22no—
26#14579159—44no—
27C2×C4⋊Dic79—21no—
28C2×C4⋊Dic79—21no—
29C2×C4⋊Dic79—21no—
30C2×Dic79⋊C4—22no—
31C2×Dic79⋊C4—22no—
32C2×C4×Dic79C2×C412yes—
33C4⋊(C79⋊C8)—22no—
34C4⋊(C79⋊C8)—22no—
35C4⋊(C79⋊C8)D414yes—
36C22⋊(C79⋊C8)—22no—
37#14579072—22no—
38#14579072—22no—
39C4×C79⋊C8—22no—
40C79⋊#95—22no—
41C79⋊#95—22no—
42C79⋊#95—21no—
43C22×Q8×C79C2×C411yescharacteristic
44C4×Q8×C79—22no—
45C4×Q8×C79—22no—
46C2×C4⋊C4×C79C2×C411yescharacteristic
47C2×C4⋊C4×C79D411yescharacteristic
48C2×C4⋊C4×C79D411yescharacteristic
49C2×C42×C79D411yescharacteristic
50C2×C42×C79D411yescharacteristic
51C2×C42×C79C2311yescharacteristic
52C4⋊C8×C79—22no—
53C22⋊C8×C79—22no—
54#97×C79—22no—
55C2×Dic158—24no—
56C2×Dic158—42no—
57C2×Dic158—42no—
58C22×Dic79—22no—
59C22×Dic79—22no—
60C2×C79⋊C8—24no—
61C4⋊Dic79—24no—
62C4⋊Dic79—41no—
63C4⋊Dic79—42no—
64C4⋊Dic79—41no—
65Dic79⋊C4—44no—
66Dic79⋊C4—44no—
67C4×Dic79—42no—
68C2×Q8×C79—22no—
69C2×Q8×C79—22no—
70C2×Q8×C79—41no—
71C22×C4×C79C22⋊C411yescharacteristic
72C22×C4×C79C22⋊C411yescharacteristic
73C22×C4×C79C22⋊C411yescharacteristic
74C22×C4×C79C22⋊C411yescharacteristic
75C22×C4×C79C22×C411yescharacteristic
76C22×C4×C79C2×D411yescharacteristic
77C22×C4×C79C2×D411yescharacteristic
78C2×C8×C79—42no—
79C4⋊C4×C79—22no—
80C4⋊C4×C79—22no—
81C4⋊C4×C79—22no—
82C42×C79—21no—
83C42×C79—21no—
84C42×C79—21no—
85C42×C79—21no—
86C42×C79C2×D412yes—
87C42×C79#4112yes—
88C23×C79C2×C22⋊C411yescharacteristic
89Q8×C79—44no—
90C2×C4×C79—21no—
91C2×C4×C79—21no—
92C2×C4×C79—21no—
93C2×C4×C79—21no—
94C2×C4×C79—22no—
95C2×C4×C79—21no—
96C2×C4×C79—21no—
97C2×C4×C79—21no—
98C2×C4×C79—21no—
99C2×C4×C79—21no—
100C2×C4×C79—41no—
101C2×C4×C79—41no—
102C2×C4×C79—41no—
103C2×C4×C79#10012yes—
104C2×C4×C79C4×D412yes—
105C2×C4×C79#12011yescharacteristic
106C2×C4×C79#12112yes—
107C2×C4×C79#12311yescharacteristic
108C2×Dic79—24no—
109C2×Dic79—42no—
110C2×Dic79—42no—
111C2×Dic79—42no—
112C2×Dic79—42no—
113C2×Dic79—42no—
114Dic158—84no—
115C8×C79—82no—
116C79⋊C8—44no—
117C22×C79—21no—
118C22×C79—21no—
119C22×C79#38611yescharacteristic
120C22×C79C2×#10011yescharacteristic
121C22×C79#41311yescharacteristic
122C4×C79—21no—
123C4×C79—22no—
124C4×C79—22no—
125C4×C79—22no—
126C4×C79—41no—
127C4×C79—41no—
128C4×C79—41no—
129C4×C79#45612yes—
130Dic79—44no—
131Dic79—82no—
132#9452—791nomaximal, Sylow
133C2×C79—21no—
134C2×C79—21no—
135C2×C79#188611yescharacteristic
136C2×C79#190011yescharacteristic
137C2×C79#190911yescharacteristic
138#2983—791no—
139#2546—791no—
140#1558—792no—
141#1467D7911yescharacteristic
142#1285—792no—
143C79#945211yescharacteristic, complemented, Sylow
144C2×C4⋊Q8—792no—
145C2×C4⋊Q8—791no—
146C2×C4×Q8C2×D7911yescharacteristic
147#446—1584no—
148#432—792no—
149#432—1581no—
150#432C2×D7912yes—
151#431—1581no—
152#398—1581no—
153#398—1581no—
154#391—792no—
155#389—1581no—
156#389—1581no—
157C4×C4⋊C4—791no—
158#333—1584no—
159#324—21no—
160#324—21no—
161C22×Q8—792no—
162C22×Q8C4×D7911yescharacteristic
163C4⋊Q8—3164no—
164C4⋊Q8—1582no—
165C4⋊Q8—1582no—
166C4×Q8—22no—
167C4×Q8—22no—
168C2×C4⋊C4—1582no—
169C2×C4⋊C4—1582no—
170C2×C4⋊C4—1581no—
171C2×C4⋊C4—1581no—
172C2×C4⋊C4—1581no—
173C2×C4⋊C4C4×D7911yescharacteristic
174C2×C4⋊C4C22⋊D7911yescharacteristic
175C2×C4⋊C4C22⋊D7911yescharacteristic
176C2×C42—792no—
177C2×C42D31611yescharacteristic
178C2×C42D31611yescharacteristic
179C2×C42C22×D7911yescharacteristic
180C4⋊C8—22no—
181C4⋊C8—794no—
182C4⋊C8—1582no—
183C4⋊C8—1582no—
184C22⋊C8—22no—
185C22⋊C8—1582no—
186#97—22no—
187#97—1582no—
188#97—1582no—
189C4×C8—1582no—
190#95—1582no—
191#95—1582no—
192#95—1581no—
193C2×Q8—22no—
194C2×Q8—22no—
195C2×Q8—41no—
196C2×Q8—3162no—
197C2×Q8—3162no—
198C2×Q8—1584no—
199C22×C4—1582no—
200C22×C4—1582no—
201C22×C4(C2×D79)⋊C411yescharacteristic
202C22×C4(C2×D79)⋊C411yescharacteristic
203C22×C4(C2×D79)⋊C411yescharacteristic
204C22×C4(C2×D79)⋊C411yescharacteristic
205C22×C4C2×C4×D7911yescharacteristic
206C22×C4C2×C22⋊D7911yescharacteristic
207C22×C4C2×D31611yescharacteristic
208C2×C8—42no—
209C2×C8—1584no—
210C4⋊C4—22no—
211C4⋊C4—22no—
212C4⋊C4—22no—
213C4⋊C4—3164no—
214C4⋊C4—3164no—
215C4⋊C4—3161no—
216C4⋊C4—3162no—
217C4⋊C4—3161no—
218C4⋊C4—1584no—
219C42—21no—
220C42—21no—
221C42—21no—
222C42—21no—
223C42—3162no—
224C42D4×D7912yes—
225C42#1192962312yes—
226C23C2×(C2×D79)⋊C411yescharacteristic
227Q8—44no—
228Q8—6324no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—3162no—
243C2×C4—3162no—
244C2×C4—3162no—
245C2×C4—3162no—
246C2×C4—3162no—
247C2×C4—1584no—
248C2×C4#1457907712yes—
249C2×C4(C22⋊D79)⋊C412yes—
250C2×C4#1457913111yescharacteristic
251C2×C4#1457913312yes—
252C2×C4#1457914511yescharacteristic
253C8—82no—
254C8—3164no—
255C22—21no—
256C22—21no—
257C22#1909844011yescharacteristic
258C22C2×#1457907711yescharacteristic
259C22#1909854511yescharacteristic
260C4—21no—
261C4—22no—
262C4—22no—
263C4—22no—
264C4—41no—
265C4—41no—
266C4—41no—
267C4—3164no—
268C4—6322no—
269C4#1909874812yes—
270C2—21no—
271C2—21no—
272C2#2376379111yescharacteristic
273C2#2376386111yescharacteristic
274C2#2376392011yescharacteristic
subgroupG/H
centerC22#19098440
commutatorC22×C4×C79C22×C4
FrattiniC2×C42C22×D79
FittingC79×#1467C2
socleC22×C79#386
prime radicalC23×C79C2×C22⋊C4
cosocleC2×C42×C79C23
hypercenter#1467D79
hypocenterC79#9452
LCSG ▷ C22×C4×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1467

Complements

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

NH ≅ G/Ntype
143. C79#9452semidirect

Maximal subgroups

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

subgroupindex
#237724852
#237683852
#237621252
#237612552
C79×#14672
#945279