Finite Group Databasebeta

← #34185973

Subgroups — #34185973

Order 20224.

432 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 107 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#23768612C211yesmaximal, characteristic
2#23762118C212yesmaximal
3#23761744C211yesmaximal, characteristic
4#23761257C212yesmaximal
5C79×#2983C211yesmaximal, characteristic
6C2×#14579161C2211yescharacteristic
7#19098620C2212yes—
8#19098502—21no—
9#19098502—21no—
10#19098470C412yes—
11#19098469—21no—
12#19098469—21no—
13#19098428C412yes—
14C4×C4⋊Dic79C2211yescharacteristic
15#19098310—24no—
16#19098289—21no—
17#19098289—21no—
18C2×C4×Q8×C79C2211yescharacteristic
19#446×C79—24no—
20#432×C79—21no—
21#432×C79C2212yes—
22#431×C79—21no—
23C22×Dic158—21no—
24#14579161—22no—
25#14579161—22no—
26C2×C4⋊Dic79—21no—
27C2×C4⋊Dic79—21no—
28C2×C4⋊Dic79C2×C412yes—
29C2×C4×Dic79C2×C412yes—
30C4⋊(C79⋊C8)—22no—
31C22⋊(C79⋊C8)—22no—
32#14579072—22no—
33C79⋊#95—22no—
34C79⋊#95—22no—
35C79⋊#95—22no—
36C79⋊#95—22no—
37C79⋊#95—21no—
38C22×Q8×C79C2×C411yescharacteristic
39C4×Q8×C79—22no—
40C4×Q8×C79—22no—
41C2×C4⋊C4×C79C2×C411yescharacteristic
42C2×C4⋊C4×C79D411yescharacteristic
43C2×C4⋊C4×C79D411yescharacteristic
44C2×C42×C79D411yescharacteristic
45C2×C42×C79D411yescharacteristic
46C2×C42×C79C2311yescharacteristic
47C4⋊C8×C79—22no—
48C4⋊C8×C79—22no—
49C4⋊C8×C79D414yes—
50C22⋊C8×C79—22no—
51#97×C79—22no—
52#97×C79—22no—
53C4×C8×C79—22no—
54C2×Dic158—44no—
55C2×Dic158—41no—
56C2×Dic158—41no—
57C22×Dic79—22no—
58C22×Dic79—22no—
59C2×C79⋊C8—42no—
60C4⋊Dic79—24no—
61C4⋊Dic79—42no—
62C4⋊Dic79—42no—
63C4×Dic79—42no—
64C2×Q8×C79—22no—
65C2×Q8×C79—22no—
66C2×Q8×C79—41no—
67C22×C4×C79C22⋊C411yescharacteristic
68C22×C4×C79C22⋊C411yescharacteristic
69C22×C4×C79C22⋊C411yescharacteristic
70C22×C4×C79C22⋊C411yescharacteristic
71C22×C4×C79C22×C411yescharacteristic
72C22×C4×C79C2×D411yescharacteristic
73C22×C4×C79C2×D411yescharacteristic
74C2×C8×C79—24no—
75C4⋊C4×C79—22no—
76C4⋊C4×C79—22no—
77C4⋊C4×C79—22no—
78C42×C79—21no—
79C42×C79—21no—
80C42×C79—21no—
81C42×C79—21no—
82C42×C79C2×D412yes—
83C42×C79#4112yes—
84C23×C79C2×C22⋊C411yescharacteristic
85Q8×C79—44no—
86C2×C4×C79—21no—
87C2×C4×C79—21no—
88C2×C4×C79—21no—
89C2×C4×C79—21no—
90C2×C4×C79—22no—
91C2×C4×C79—21no—
92C2×C4×C79—21no—
93C2×C4×C79—21no—
94C2×C4×C79—21no—
95C2×C4×C79—21no—
96C2×C4×C79—41no—
97C2×C4×C79—41no—
98C2×C4×C79—41no—
99C2×C4×C79#10112yes—
100C2×C4×C79C4×D412yes—
101C2×C4×C79#12011yescharacteristic
102C2×C4×C79#12112yes—
103C2×C4×C79#12311yescharacteristic
104C2×Dic79—42no—
105C2×Dic79—42no—
106C2×Dic79—44no—
107C2×Dic79—42no—
108C2×Dic79—42no—
109Dic158—82no—
110Dic158—82no—
111C8×C79—44no—
112C79⋊C8—82no—
113C22×C79—21no—
114C22×C79—21no—
115C22×C79#38611yescharacteristic
116C22×C79C2×#10111yescharacteristic
117C22×C79#41311yescharacteristic
118C4×C79—21no—
119C4×C79—22no—
120C4×C79—22no—
121C4×C79—22no—
122C4×C79—41no—
123C4×C79—41no—
124C4×C79—41no—
125C4×C79#45412yes—
126Dic79—82no—
127Dic79—82no—
128#9456—791nomaximal, Sylow
129C2×C79—21no—
130C2×C79—21no—
131C2×C79#188811yescharacteristic
132C2×C79#190111yescharacteristic
133C2×C79#190911yescharacteristic
134#2983D7911yescharacteristic
135#2568—791no—
136#1556—792no—
137#1467—791no—
138#1285—792no—
139C79#945611yescharacteristic, complemented, Sylow
140C2×C4⋊Q8—791no—
141C2×C4×Q8C2×D7911yescharacteristic
142#446—24no—
143#432—21no—
144#432—792no—
145#432C2×D7912yes—
146#431—21no—
147#400—1581no—
148#400—1581no—
149#391—792no—
150#391—1581no—
151#391—1581no—
152#382—792no—
153C4×C4⋊C4—791no—
154#332—1584no—
155#324—1581no—
156#324—1581no—
157C22×Q8—1581no—
158C22×Q8C4×D7911yescharacteristic
159C4⋊Q8—1582no—
160C4⋊Q8—1582no—
161C4×Q8—22no—
162C4×Q8—22no—
163C2×C4⋊C4—792no—
164C2×C4⋊C4—1581no—
165C2×C4⋊C4—1581no—
166C2×C4⋊C4C4×D7911yescharacteristic
167C2×C4⋊C4D31611yescharacteristic
168C2×C4⋊C4D31611yescharacteristic
169C2×C42—792no—
170C2×C42C22⋊D7911yescharacteristic
171C2×C42C22⋊D7911yescharacteristic
172C2×C42C22×D7911yescharacteristic
173C4⋊C8—22no—
174C4⋊C8—22no—
175C4⋊C8—1582no—
176C4⋊C8C22⋊D7914yes—
177C22⋊C8—22no—
178C22⋊C8—1582no—
179#97—22no—
180#97—22no—
181#97—1582no—
182C4×C8—22no—
183#95—1582no—
184#95—1582no—
185#95—1582no—
186#95—1582no—
187#95—1581no—
188C2×Q8—22no—
189C2×Q8—22no—
190C2×Q8—41no—
191C2×Q8—3164no—
192C2×Q8—3161no—
193C2×Q8—3161no—
194C22×C4—1582no—
195C22×C4—1582no—
196C22×C4(C2×D79)⋊C411yescharacteristic
197C22×C4(C2×D79)⋊C411yescharacteristic
198C22×C4(C2×D79)⋊C411yescharacteristic
199C22×C4(C2×D79)⋊C411yescharacteristic
200C22×C4C2×C4×D7911yescharacteristic
201C22×C4C2×C22⋊D7911yescharacteristic
202C22×C4C2×D31611yescharacteristic
203C2×C8—24no—
204C2×C8—3162no—
205C4⋊C4—22no—
206C4⋊C4—22no—
207C4⋊C4—22no—
208C4⋊C4—3162no—
209C4⋊C4—3162no—
210C4⋊C4—1584no—
211C42—21no—
212C42—21no—
213C42—21no—
214C42—21no—
215C42—3162no—
216C42C2×C22⋊D7912yes—
217C42#1192962412yes—
218C23C2×(C2×D79)⋊C411yescharacteristic
219Q8—44no—
220Q8—6322no—
221Q8—6322no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—3162no—
236C2×C4—3164no—
237C2×C4—3162no—
238C2×C4—3162no—
239C2×C4—3162no—
240C2×C4#1457907912yes—
241C2×C4C4×C22⋊D7912yes—
242C2×C4#1457913011yescharacteristic
243C2×C4#1457913512yes—
244C2×C4#1457914411yescharacteristic
245C8—44no—
246C8—6322no—
247C22—21no—
248C22—21no—
249C22#1909844211yescharacteristic
250C22C2×#1457907911yescharacteristic
251C22#1909854511yescharacteristic
252C4—21no—
253C4—22no—
254C4—22no—
255C4—22no—
256C4—41no—
257C4—41no—
258C4—41no—
259C4—6322no—
260C4—6322no—
261C4#1909873612yes—
262C2—21no—
263C2—21no—
264C2#2376380311yescharacteristic
265C2#2376386811yescharacteristic
266C2#2376392211yescharacteristic
subgroupG/H
centerC22#19098442
commutatorC22×C4×C79C22×C4
FrattiniC2×C42C22×D79
FittingC79×#2983C2
socleC22×C79#386
prime radicalC23×C79C2×C22⋊C4
cosocleC2×C42×C79C23
hypercenter#2983D79
hypocenterC79#9456
LCSG ▷ C22×C4×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2983

Complements

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

NH ≅ G/Ntype
139. C79#9456semidirect

Maximal subgroups

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

subgroupindex
#237686122
#237621182
#237617442
#237612572
C79×#29832
#945679