Finite Group Databasebeta

← #34197774

Subgroups — #34197774

Order 20224.

270 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 71 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#23772330C211yesmaximal, characteristic
2#23765213C212yesmaximal
3#23761352C212yesmaximal
4#23761351C211yesmaximal, characteristic
5C79×#1327C211yesmaximal, characteristic
6#19099120C411yescharacteristic
7#19098690—22no—
8#19098687—22no—
9#19098591C411yescharacteristic
10#19098591C2211yescharacteristic
11#19098521C411yescharacteristic
12#19098521C2211yescharacteristic
13C2×C4×C79⋊C8C411yescharacteristic
14#19098383—22no—
15#19098345C2212yes—
16#19098340—22no—
17#423×C79C2211yescharacteristic
18#349×C79C2212yes—
19C22×C79⋊C8C2×C411yescharacteristic
20C22×C79⋊C8C2×C411yescharacteristic
21#14579161—21no—
22#14579153—21no—
23#14579140—22no—
24C4×Dic158—22no—
25#14579120C2×C411yescharacteristic
26#14579120C2×C411yescharacteristic
27#14579101—22no—
28Dic79⋊C8—22no—
29Dic79⋊C8—22no—
30#14579071—21no—
31#14579071D412yes—
32C4×C79⋊C8—21no—
33C4×C79⋊C8—21no—
34C8×Dic79—21no—
35C8×Dic79D412yes—
36C2×M16×C79C2×C411yescharacteristic
37C2×M16×C79C2311yescharacteristic
38C2×C42×C79C2×C411yescharacteristic
39M32×C79—22no—
40C4⋊C8×C79—22no—
41C2×Dic158—22no—
42C2×C79⋊C8—22no—
43C2×C79⋊C8—21no—
44C2×C79⋊C8—41no—
45C2×C79⋊C8C22⋊C411yescharacteristic
46C2×C79⋊C8C22⋊C411yescharacteristic
47C4⋊Dic79—22no—
48C4⋊Dic79—21no—
49C4⋊Dic79—21no—
50Dic79⋊C4—24no—
51C22⋊Dic79—21no—
52C22⋊Dic79M1612yes—
53C4×Dic79—21no—
54C4×Dic79C22⋊C412yes—
55C79⋊C16—42no—
56C22×C4×C79—21no—
57C22×C4×C79C22×C411yescharacteristic
58M16×C79—41no—
59M16×C79—41no—
60C2×C8×C79—21no—
61C2×C8×C79C2×D412yes—
62C42×C79—21no—
63C42×C79M1611yescharacteristic
64C42×C79M1611yescharacteristic
65C16×C79—42no—
66C23×C79C2×M1611yescharacteristic
67C2×C4×C79—21no—
68C2×C4×C79—21no—
69C2×C4×C79—21no—
70C2×C4×C79—21no—
71C2×C4×C79—42no—
72C2×C4×C79C2×C22⋊C411yescharacteristic
73C2×C4×C79C2×M1611yescharacteristic
74C2×Dic79—22no—
75C2×Dic79—22no—
76Dic158—44no—
77C8×C79—22no—
78C8×C79—41no—
79C79⋊C8—21no—
80C79⋊C8—41no—
81C79⋊C8#10112yes—
82C22×C79—21no—
83C22×C79—41no—
84C22×C79#40711yescharacteristic
85C4×C79—22no—
86C4×C79—21no—
87C4×C79—41no—
88C4×C79#41011yescharacteristic
89C4×C79C2×#10111yescharacteristic
90Dic79—42no—
91Dic79—42no—
92#11539—791nomaximal, Sylow
93C2×C79—21no—
94C2×C79—41no—
95C2×C79#146711yescharacteristic
96#2960—791no—
97#2166—792no—
98#1328—792no—
99#1327—791no—
100#1327D7911yescharacteristic
101C79#1153911yescharacteristic, complemented, Sylow
102#533—791no—
103#446—1582no—
104C8×Q8—1582no—
105#424—791no—
106#424—791no—
107#423C2×D7911yescharacteristic
108#405—791no—
109#405—791no—
110C2×C4×C8—791no—
111#364—1582no—
112#349—792no—
113#349C2×D7912yes—
114#347—1582no—
115C2×M16C4×D7911yescharacteristic
116C2×M16C22×D7911yescharacteristic
117C22×C8—791no—
118C22×C8—791no—
119C4⋊Q8—1581no—
120#125—1581no—
121C22⋊Q8—1582no—
122C4×Q8—1582no—
123#117—791no—
124#117—791no—
125C2×C42C4×D7911yescharacteristic
126M32—22no—
127M32—1582no—
128C4⋊C8—22no—
129C4⋊C8—1582no—
130C4⋊C8—1582no—
131#97—792no—
132#97—1581no—
133C4×C8—792no—
134C4×C8—1581no—
135C4×C8—1581no—
136C4×C8—1581no—
137C2×Q8—1582no—
138C22×C4—21no—
139C22×C4C2×C4×D7911yescharacteristic
140M16—41no—
141M16—41no—
142C2×C8—21no—
143C2×C8—3161no—
144C2×C8—791no—
145C2×C8—791no—
146C2×C8—1581no—
147C2×C8—1582no—
148C2×C8D4×D7912yes—
149C4⋊C4—1584no—
150C4⋊C4—1582no—
151C4⋊C4—1581no—
152C4⋊C4—1581no—
153C22⋊C4—792no—
154C22⋊C4—1581no—
155C42—21no—
156C42—792no—
157C42—1581no—
158C42#1192960711yescharacteristic
159C42#1192960711yescharacteristic
160C16—42no—
161C16—3162no—
162C23M16×D7911yescharacteristic
163Q8—3164no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—42no—
169C2×C4—1582no—
170C2×C4—1582no—
171C2×C4C22⋊C4×D7911yescharacteristic
172C2×C4C2×#1192960711yescharacteristic
173C8—22no—
174C8—41no—
175C8—3161no—
176C8—792no—
177C8—1581no—
178C22—21no—
179C22—41no—
180C22#1909852511yescharacteristic
181C4—22no—
182C4—21no—
183C4—41no—
184C4—3162no—
185C4—3162no—
186C4#1909853511yescharacteristic
187C4#101×D7911yescharacteristic
188C2—21no—
189C2—41no—
190C2#2376174211yescharacteristic
subgroupG/H
centerC4#19098535
commutatorC22×C4×C79C22×C4
FrattiniC2×M16C22×D79
FittingC79×#1327C2
socleC2×C79#1467
prime radicalC23×C79C2×M16
cosocleC2×M16×C79C23
hypercenter#1327D79
hypocenterC79#11539
LCSG ▷ C22×C4×C79 ▷ C22×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #1327

Complements

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

NH ≅ G/Ntype
101. C79#11539semidirect

Maximal subgroups

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

subgroupindex
#237723302
#237652132
#237613522
#237613512
C79×#13272
#1153979