Finite Group Databasebeta

← #34197776

Subgroups — #34197776

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#23772333C211yesmaximal, characteristic
2#23765213C212yesmaximal
3#23761353C211yesmaximal, characteristic
4#23761350C212yesmaximal
5C79×#1328C211yesmaximal, characteristic
6#19099116C411yescharacteristic
7#19098692—22no—
8#19098687—22no—
9#19098589C411yescharacteristic
10#19098586C2211yescharacteristic
11#19098521C2211yescharacteristic
12#19098519C411yescharacteristic
13C2×C8×Dic79C411yescharacteristic
14#19098383—22no—
15#19098345C2212yes—
16#19098340—22no—
17#424×C79C2211yescharacteristic
18#349×C79C2212yes—
19C2×#11929608C2×C411yescharacteristic
20C22×C79⋊C8C2×C411yescharacteristic
21#14579160—21no—
22#14579152—21no—
23#14579138—22no—
24C4×Dic158—22no—
25#14579120C2×C411yescharacteristic
26C2×C4×Dic79C2×C411yescharacteristic
27#14579101—22no—
28Dic79⋊C8—22no—
29Dic79⋊C8—22no—
30#14579072—21no—
31#14579071D412yes—
32C4×C79⋊C8—21no—
33C8×Dic79—21no—
34C8×Dic79—21no—
35C8×Dic79D412yes—
36C2×M16×C79C2311yescharacteristic
37C22×C8×C79C2×C411yescharacteristic
38#117×C79C2×C411yescharacteristic
39M32×C79—22no—
40C4⋊C8×C79—22no—
41C2×Dic158—22no—
42C22×Dic79—21no—
43#11929608—41no—
44C2×C79⋊C8—22no—
45C2×C79⋊C8—21no—
46C2×C79⋊C8C22⋊C411yescharacteristic
47C2×C79⋊C8C22⋊C411yescharacteristic
48C4⋊Dic79—22no—
49C4⋊Dic79—21no—
50Dic79⋊C4—22no—
51Dic79⋊C4—22no—
52C22⋊Dic79—21no—
53C4×Dic79—21no—
54C4×Dic79C22⋊C412yes—
55C4×Dic79M1611yescharacteristic
56C4×Dic79M1611yescharacteristic
57C79⋊C16—42no—
58C22×C4×C79C22×C411yescharacteristic
59M16×C79—41no—
60C2×C8×C79—21no—
61C2×C8×C79—41no—
62C2×C8×C79C2×D412yes—
63C4⋊C4×C79—21no—
64C22⋊C4×C79M1612yes—
65C42×C79—21no—
66C16×C79—42no—
67C23×C79C2×M1611yescharacteristic
68C2×C4×C79—21no—
69C2×C4×C79—21no—
70C2×C4×C79—22no—
71C2×C4×C79C2×C22⋊C411yescharacteristic
72C2×C4×C79C2×M1611yescharacteristic
73C2×Dic79—21no—
74C2×Dic79—21no—
75C2×Dic79—22no—
76C2×Dic79—42no—
77Dic158—44no—
78C8×C79—22no—
79C8×C79—41no—
80C79⋊C8—21no—
81C79⋊C8—41no—
82C79⋊C8#10112yes—
83C22×C79—21no—
84C22×C79—41no—
85C22×C79#40711yescharacteristic
86C4×C79—21no—
87C4×C79—42no—
88C4×C79#41011yescharacteristic
89C4×C79C2×#10111yescharacteristic
90Dic79—22no—
91Dic79—42no—
92Dic79—41no—
93#11539—791nomaximal, Sylow
94C2×C79—21no—
95C2×C79—41no—
96C2×C79#146711yescharacteristic
97#2960—791no—
98#2166—792no—
99#1328—791no—
100#1328D7911yescharacteristic
101#1327—792no—
102C79#1153911yescharacteristic, complemented, Sylow
103#533—791no—
104#446—1582no—
105C8×Q8—1582no—
106#424—791no—
107#424C2×D7911yescharacteristic
108#423—791no—
109#405—791no—
110#405—791no—
111C2×C4×C8—791no—
112#364—1582no—
113#349—792no—
114#349C2×D7912yes—
115#347—1582no—
116C2×M16—791no—
117C2×M16C22×D7911yescharacteristic
118C22×C8—791no—
119C22×C8C4×D7911yescharacteristic
120C4⋊Q8—1581no—
121#125—1581no—
122C22⋊Q8—1582no—
123C4×Q8—1582no—
124#117—791no—
125#117C4×D7911yescharacteristic
126C2×C42—791no—
127M32—22no—
128M32—1582no—
129C4⋊C8—22no—
130C4⋊C8—1582no—
131C4⋊C8—1582no—
132#97—792no—
133#97—1581no—
134C4×C8—792no—
135C4×C8—1581no—
136C4×C8—1581no—
137C4×C8—1581no—
138C2×Q8—1582no—
139C22×C4—1581no—
140C22×C4C2×C4×D7911yescharacteristic
141M16—41no—
142M16—3161no—
143C2×C8—21no—
144C2×C8—41no—
145C2×C8—791no—
146C2×C8—791no—
147C2×C8—1581no—
148C2×C8—1582no—
149C2×C8D4×D7912yes—
150C4⋊C4—21no—
151C4⋊C4—1582no—
152C4⋊C4—1582no—
153C4⋊C4—1582no—
154C4⋊C4—1581no—
155C22⋊C4—1581no—
156C22⋊C4#1192960712yes—
157C42—21no—
158C42—792no—
159C42—791no—
160C42—791no—
161C42—1581no—
162C16—42no—
163C16—3162no—
164C23C2×#1192960711yescharacteristic
165Q8—3164no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—22no—
169C2×C4—3162no—
170C2×C4—1581no—
171C2×C4—1582no—
172C2×C4—1581no—
173C2×C4C22⋊C4×D7911yescharacteristic
174C2×C4M16×D7911yescharacteristic
175C8—22no—
176C8—41no—
177C8—3161no—
178C8—792no—
179C8—1581no—
180C22—21no—
181C22—41no—
182C22#1909852511yescharacteristic
183C4—21no—
184C4—42no—
185C4—3161no—
186C4—3162no—
187C4—1582no—
188C4#1909853511yescharacteristic
189C4#101×D7911yescharacteristic
190C2—21no—
191C2—41no—
192C2#2376174211yescharacteristic
subgroupG/H
centerC4#19098535
commutatorC22×C4×C79C22×C4
FrattiniC2×M16C22×D79
FittingC79×#1328C2
socleC2×C79#1467
prime radicalC23×C79C2×M16
cosocleC2×M16×C79C23
hypercenter#1328D79
hypocenterC79#11539
LCSG ▷ C22×C4×C79 ▷ C22×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #1328

Complements

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

NH ≅ G/Ntype
102. C79#11539semidirect

Maximal subgroups

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

subgroupindex
#237723332
#237652132
#237613532
#237613502
C79×#13282
#1153979