Finite Group Databasebeta

← #34189230

Subgroups — #34189230

Order 20224.

468 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 83 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#23774745C211yesmaximal, characteristic
2#23773530C212yesmaximal
3#23762014C212yesmaximal
4#23761270C211yesmaximal, characteristic
5C79×#1985C211yesmaximal, characteristic
6#19099120C2212yes—
7#19098893—22no—
8#19098859—22no—
9#19098848—22no—
10#19098804—22no—
11#19098774—22no—
12#19098773—22no—
13#19098719—22no—
14#19098668—24no—
15#19098620C2212yes—
16#19098304—24no—
17C2×C4×Q8×C79C2211yescharacteristic
18C2×C4⋊C8×C79C2211yescharacteristic
19C2×#97×C79C2211yescharacteristic
20#336×C79—22no—
21C2×Dic316—22no—
22C2×#11929614—24no—
23#14579161D412yes—
24#14579161D412yes—
25#14579153—22no—
26#14579140—22no—
27#14579140—22no—
28C4×Dic158—22no—
29C4×Dic158—22no—
30#14579120—22no—
31#14579095—22no—
32#14579092—24no—
33C4⋊(C79⋊C8)—22no—
34#14579086—24no—
35#14579085—24no—
36#14579084—24no—
37C22⋊(C79⋊C8)—22no—
38#14579072D414yes—
39C22×Q8×C79D411yescharacteristic
40C22×C8×C79—21no—
41C22×C8×C79D412yes—
42C4×Q8×C79—22no—
43C4×Q8×C79—22no—
44C2×C4⋊C4×C79—21no—
45C2×C4⋊C4×C79D411yescharacteristic
46C2×C42×C79—21no—
47C2×C42×C79C2311yescharacteristic
48C4⋊C8×C79—22no—
49#97×C79—22no—
50C2×Dic158—22no—
51C2×Dic158—22no—
52Dic316—82no—
53#11929614—48no—
54C2×C79⋊C8—24no—
55C4⋊Dic79—22no—
56C4⋊Dic79—22no—
57C4⋊Dic79—22no—
58C4⋊Dic79—22no—
59Dic79⋊C4—42no—
60Dic79⋊C4—42no—
61C22⋊Dic79—42no—
62C4×Dic79—42no—
63C2×Q8×C79—22no—
64C2×Q8×C79—42no—
65C22×C4×C79—21no—
66C22×C4×C79—21no—
67C22×C4×C79C2×D411yescharacteristic
68C22×C4×C79C2×D411yescharacteristic
69C22×C4×C79#4111yescharacteristic
70C2×C8×C79—22no—
71C2×C8×C79—22no—
72C2×C8×C79—42no—
73C2×C8×C79—41no—
74C2×C8×C79—41no—
75C4⋊C4×C79—22no—
76C4⋊C4×C79—42no—
77C42×C79—41no—
78C42×C79—41no—
79C42×C79C2×D412yes—
80C42×C79C2×D412yes—
81C23×C79#12111yescharacteristic
82Q8×C79—24no—
83Q8×C79—42no—
84C2×C4×C79—22no—
85C2×C4×C79—21no—
86C2×C4×C79—21no—
87C2×C4×C79—22no—
88C2×C4×C79—41no—
89C2×C4×C79—41no—
90C2×C4×C79—41no—
91C2×C4×C79—41no—
92C2×C4×C79—42no—
93C2×C4×C79#12011yescharacteristic
94C2×C4×C79#12012yes—
95C2×C4×C79#12112yes—
96C2×C4×C79#12711yescharacteristic
97C2×Dic79—42no—
98C2×Dic79—42no—
99Dic158—44no—
100Dic158—42no—
101Dic158—42no—
102C8×C79—42no—
103C8×C79—42no—
104C79⋊C8—44no—
105C22×C79—21no—
106C22×C79—21no—
107C22×C79#39211yescharacteristic
108C22×C79#47312yes—
109C4×C79—21no—
110C4×C79—22no—
111C4×C79—22no—
112C4×C79—42no—
113C4×C79—81no—
114C4×C79#45511yescharacteristic
115C4×C79#45611yescharacteristic
116Dic79—82no—
117Dic79—82no—
118#10031—791nomaximal, Sylow
119C2×C79—22no—
120C2×C79#200711yescharacteristic
121C2×C79#201011yescharacteristic
122C2×C79#202011yescharacteristic
123#3249—791no—
124#3113—792no—
125#1985D7911yescharacteristic
126#1531—792no—
127#1290—791no—
128C79#1003111yescharacteristic, complemented, Sylow
129#533—792no—
130C2×C4×Q8C2×D7911yescharacteristic
131#483—1582no—
132#477—1582no—
133#475—1582no—
134#467—1582no—
135#462—1582no—
136#462—1582no—
137#451—1582no—
138#441—1584no—
139#432—792no—
140C2×C4⋊C8C2×D7911yescharacteristic
141C2×#97C2×D7911yescharacteristic
142#336—22no—
143#330—1584no—
144C22×Q8D31611yescharacteristic
145C2×Q16—1582no—
146C2×Q16—1584no—
147C22×C8—21no—
148C22×C8C22⋊D7912yes—
149C4⋊Q8—792no—
150C4⋊Q8—792no—
151#125—1582no—
152C22⋊Q8—1582no—
153C22⋊Q8—1582no—
154C4×Q8—22no—
155C4×Q8—22no—
156C4×Q8—1582no—
157C4×Q8—1582no—
158#117—1582no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4D31611yescharacteristic
161C2×C42—21no—
162C2×C42C22×D7911yescharacteristic
163#107—1582no—
164#106—1584no—
165C4⋊C8—22no—
166C4⋊C8—1582no—
167#103—1584no—
168#103—1584no—
169#103—1584no—
170C22⋊C8—1582no—
171#97—22no—
172#97—794no—
173C2×Q8—22no—
174C2×Q8—42no—
175C2×Q8—1582no—
176C2×Q8—1582no—
177C22×C4—21no—
178C22×C4—21no—
179C22×C4C2×C22⋊D7911yescharacteristic
180C22×C4C2×D31611yescharacteristic
181C22×C4#1192962411yescharacteristic
182Q16—3168no—
183Q16—6322no—
184C2×C8—22no—
185C2×C8—22no—
186C2×C8—41no—
187C2×C8—41no—
188C2×C8—42no—
189C2×C8—1584no—
190C4⋊C4—22no—
191C4⋊C4—42no—
192C4⋊C4—3162no—
193C4⋊C4—3162no—
194C4⋊C4—1582no—
195C4⋊C4—1582no—
196C4⋊C4—1582no—
197C4⋊C4—1582no—
198C22⋊C4—3162no—
199C42—41no—
200C42—41no—
201C42—3162no—
202C42D4×D7912yes—
203C42D4×D7912yes—
204C23#1457913511yescharacteristic
205Q8—24no—
206Q8—42no—
207Q8—3164no—
208Q8—3162no—
209Q8—3162no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4—42no—
219C2×C4—3162no—
220C2×C4—3162no—
221C2×C4#1457912911yescharacteristic
222C2×C4#1457913112yes—
223C2×C4#1457913412yes—
224C2×C4#1457915711yescharacteristic
225C8—42no—
226C8—42no—
227C8—3164no—
228C22—21no—
229C22—21no—
230C22#1909847211yescharacteristic
231C22#1909883812yes—
232C4—22no—
233C4—21no—
234C4—22no—
235C4—42no—
236C4—81no—
237C4—6322no—
238C4—6322no—
239C4#1909874011yescharacteristic
240C4#1909874511yescharacteristic
241C2—22no—
242C2#2376444611yescharacteristic
243C2#2376446711yescharacteristic
244C2#2376452111yescharacteristic
subgroupG/H
centerC22#19098472
commutator, cosocleC2×C42×C79C23
FrattiniC2×C42C22×D79
FittingC79×#1985C2
socleC22×C79#392
prime radicalC23×C79#121
hypercenter#1985D79
hypocenterC79#10031
LCSG ▷ C2×C42×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1985

Complements

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

NH ≅ G/Ntype
128. C79#10031semidirect

Maximal subgroups

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

subgroupindex
#237747452
#237735302
#237620142
#237612702
C79×#19852
#1003179