Finite Group Databasebeta

← #34209128

Subgroups — #34209128

Order 20224.

200 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 57 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
1C2×#19098402C211yesmaximal, characteristic, complemented
2C2×#19098396C211yesmaximal, characteristic, complemented
3#23765492C211yesmaximal, characteristic, complemented
4#23765487C211yesmaximal, characteristic
5#23761580C211yesmaximal, characteristic, complemented
6#23761577C211yesmaximal, characteristic, complemented
7C79×#1423C211yesmaximal, characteristic, complemented
8C2×Dic632C2211yescharacteristic
9C2×D1264C2211yescharacteristic
10C2×C16×D79C2211yescharacteristic
11#19098805—21no—
12#19098800—21no—
13#19098402—22no—
14#19098396—22no—
15C2×C79⋊C32C2211yescharacteristic
16#19098366—21no—
17#19098363—21no—
18C2×C32×C79C2211yescharacteristic
19#366×C79C2211yescharacteristic
20#366×C79C2211yescharacteristic
21C2×Dic316—21no—
22C2×D632—21no—
23C2×C8×D79D411yescharacteristic
24#14579141—41no—
25#14579136—41no—
26Dic632—21no—
27Dic632—21no—
28D1264—21no—
29D1264—21no—
30C2×C79⋊C16D411yescharacteristic
31C16×D79—21no—
32C16×D79—21no—
33#14579084—41no—
34#14579081—41no—
35C79⋊C32—21no—
36C2×C16×C79C2311yescharacteristic
37#107×C79—21no—
38#107×C79—21no—
39C32×C79D412yescomplemented
40C2×Dic158—41no—
41C2×D316—41no—
42C2×D316—81no—
43C2×C4×D79D811yescharacteristic
44Dic316—41no—
45Dic316—41no—
46D632—41no—
47D632—41no—
48C2×C79⋊C8D811yescharacteristic
49C8×D79—21no—
50C8×D79—21no—
51C4⋊Dic79—81no—
52(C2×D79)⋊C4—81no—
53(C2×D79)⋊C4—81no—
54C79⋊C16—21no—
55C2×C8×C79C2×D411yescharacteristic
56C4⋊C4×C79—41no—
57C4⋊C4×C79—41no—
58C16×C79C2×D411yescharacteristic
59C16×C79#4111yescharacteristic
60C22×D79—81no—
61C22×D79D1611yescharacteristic
62C2×C4×C79—81no—
63C2×C4×C79—81no—
64C2×C4×C79C2×D811yescharacteristic
65C2×Dic79—81no—
66C2×Dic79D1611yescharacteristic
67D316—81no—
68D316—81no—
69D316—162no—
70C4×D79—21no—
71C4×D79—21no—
72Dic158—81no—
73Dic158—81no—
74C8×C79#12111yescharacteristic
75C8×C79#13511yescharacteristic
76C79⋊C8—21no—
77C22×C79C2×D1611yescharacteristic
78C2×D79—21no—
79C2×D79—21no—
80C2×D79—21no—
81C2×D79—161no—
82C2×D79—161no—
83C2×D79—161no—
84C4×C79—161no—
85C4×C79—161no—
86C4×C79#46611yescharacteristic
87C4×C79#50811yescharacteristic
88Dic79—21no—
89Dic79—161no—
90#13699—791nomaximal, Sylow
91C2×C79#221511yescharacteristic
92C2×C79#226311yescharacteristic
93C2×C79#226411yescharacteristic
94D79—41no—
95D79—321no—
96C2×SD64—791no—
97C2×M64—791no—
98#2216—791no—
99#2215—791no—
100#1423D7911yescharacteristic, complemented
101#1416—791no—
102#1415—791no—
103C79#1369911yescharacteristic, complemented, Sylow
104C2×Q32—791no—
105C2×D16—791no—
106C22×C16—791no—
107#467—1581no—
108#466—1581no—
109SD64—1582no—
110M64—1582no—
111C2×C32—791no—
112C2×C32C2×D7911yescharacteristic
113#366C2×D7911yescharacteristic
114#366C2×D7911yescharacteristic
115#358—1581no—
116#357—1581no—
117C2×Q16—1581no—
118C2×D8—1581no—
119C22×C8—791no—
120C22⋊Q8—3161no—
121#121—3161no—
122Q32—1581no—
123Q32—1581no—
124D16—1581no—
125D16—1581no—
126C2×C16—791no—
127C2×C16—1581no—
128C2×C16—1581no—
129C2×C16C22×D7911yescharacteristic
130#107—21no—
131#107—21no—
132#103—3161no—
133#102—3161no—
134C32—1581no—
135C32D31612yescomplemented
136C2×Q8—3161no—
137C2×D4—3161no—
138C2×D4—6321no—
139C22×C4—791no—
140Q16—3161no—
141Q16—3161no—
142D8—3161no—
143D8—3161no—
144C2×C8—791no—
145C2×C8—1581no—
146C2×C8—1581no—
147C2×C8D4×D7911yescharacteristic
148C4⋊C4—41no—
149C4⋊C4—41no—
150C4⋊C4—6321no—
151C22⋊C4—6321no—
152C22⋊C4—6321no—
153C16—1581no—
154C16C2×D31611yescharacteristic
155C16#1192962511yescharacteristic
156C23—791no—
157C23—6321no—
158Q8—6321no—
159Q8—6321no—
160D4—6321no—
161D4—6321no—
162D4—12642no—
163C2×C4—81no—
164C2×C4—81no—
165C2×C4—791no—
166C2×C4—6321no—
167C2×C4—1581no—
168C2×C4—1581no—
169C2×C4D8×D7911yescharacteristic
170C8—1581no—
171C8#1457913611yescharacteristic
172C8#1457918411yescharacteristic
173C22—1581no—
174C22—1581no—
175C22—1581no—
176C22—12641no—
177C22—12641no—
178C22—12641no—
179C22D16×D7911yescharacteristic
180C4—161no—
181C4—161no—
182C4—1581no—
183C4—12641no—
184C4#1909880011yescharacteristic
185C4#1909899611yescharacteristic
186C2—3161no—
187C2—25281no—
188C2#2376548711yescharacteristic
189C2#2376571111yescharacteristic
190C2#2376571911yescharacteristic
subgroupG/H
centerC22D16×D79
commutator, cosocleC2×C16×C79C23
FrattiniC2×C16C22×D79
FittingC79×#1423C2
socleC22×C79C2×D16
prime radical#23765487C2
hypercenter#1423D79
hypocenterC79#13699
LCSG ▷ C2×C16×C79 ▷ C8×C79 ▷ C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #1423

Complements

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

NH ≅ G/Ntype
1. C2×#19098402C2semidirect
2. C2×#19098396C2semidirect
3. #23765492C2semidirect
5. #23761580C2semidirect
6. #23761577C2semidirect
7. C79×#1423C2semidirect
39. C32×C79D4semidirect
100. #1423D79semidirect
103. C79#13699semidirect
135. C32D316semidirect

Maximal subgroups

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

subgroupindex
C2×#190984022
C2×#190983962
#237654922
#237654872
#237615802
#237615772
C79×#14232
#1369979