Finite Group Databasebeta

← #34209126

Subgroups — #34209126

Order 20224.

200 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 55 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×#19098401C211yesmaximal, characteristic, complemented
2C2×#19098396C211yesmaximal, characteristic, complemented
3#23765492C211yesmaximal, characteristic, complemented
4#23765483C211yesmaximal, characteristic
5#23761599C211yesmaximal, characteristic, complemented
6#23761582C211yesmaximal, characteristic, complemented
7C79×#1415C211yesmaximal, characteristic, complemented
8C2×Dic632C2211yescharacteristic
9C2×C16×D79C2211yescharacteristic
10#19098805—21no—
11#19098796—21no—
12#19098401—22no—
13#19098396—22no—
14C2×C79⋊C32C2211yescharacteristic
15#19098389C2211yescharacteristic
16#19098366—21no—
17#19098364—21no—
18C2×D16×C79C2211yescharacteristic
19C2×C32×C79C2211yescharacteristic
20#366×C79C2211yescharacteristic
21C2×Dic316—21no—
22C2×C8×D79D411yescharacteristic
23#14579141—41no—
24#14579132—41no—
25Dic632—21no—
26Dic632—21no—
27C2×C79⋊C16D411yescharacteristic
28C16×D79—21no—
29C16×D79—21no—
30#14579095—21no—
31#14579084—41no—
32#14579082—41no—
33C79⋊C32D412yescomplemented
34C2×D8×C79—21no—
35D16×C79—21no—
36D16×C79—21no—
37C2×C16×C79C2311yescharacteristic
38#107×C79—21no—
39C32×C79—21no—
40C2×Dic158—41no—
41C2×C22⋊D79—81no—
42C2×C4×D79D811yescharacteristic
43Dic316—41no—
44Dic316—41no—
45C2×C79⋊C8D811yescharacteristic
46C8×D79—21no—
47C8×D79—21no—
48C4⋊Dic79—41no—
49C4⋊Dic79—81no—
50C22⋊Dic79—81no—
51(C2×D79)⋊C4—81no—
52C79⋊C16—21no—
53C2×D4×C79—41no—
54D8×C79—41no—
55D8×C79—41no—
56C2×C8×C79C2×D411yescharacteristic
57C4⋊C4×C79—41no—
58C16×C79C2×D411yescharacteristic
59C16×C79#4111yescharacteristic
60C23×C79—81no—
61C22×D79D1611yescharacteristic
62D4×C79—81no—
63D4×C79—81no—
64C2×C4×C79—81no—
65C2×C4×C79C2×D811yescharacteristic
66C22⋊D79—162no—
67C2×Dic79—81no—
68C2×Dic79—81no—
69C2×Dic79D1611yescharacteristic
70C4×D79—21no—
71C4×D79—21no—
72Dic158—81no—
73Dic158—81no—
74C8×C79#12111yescharacteristic
75C8×C79#13511yescharacteristic
76C79⋊C8—21no—
77C22×C79—161no—
78C22×C79—161no—
79C22×C79—161no—
80C22×C79C2×D1611yescharacteristic
81C2×D79—21no—
82C2×D79—21no—
83C2×D79—21no—
84C4×C79—161no—
85C4×C79#46611yescharacteristic
86C4×C79#50811yescharacteristic
87Dic79—21no—
88Dic79—161no—
89Dic79—161no—
90#13699—791nomaximal, Sylow
91C2×C79—321no—
92C2×C79#221511yescharacteristic
93C2×C79#226311yescharacteristic
94C2×C79#226411yescharacteristic
95D79—41no—
96C2×SD64—791no—
97C2×M64—791no—
98#2216—791no—
99#2215—791no—
100#1423—791no—
101#1416—791no—
102#1415D7911yescharacteristic, complemented
103C79#1369911yescharacteristic, complemented, Sylow
104C2×Q32—791no—
105C2×D16C2×D7911yescharacteristic
106C22×C16—791no—
107#467—1581no—
108#466—1581no—
109SD64—1582no—
110M64—1582no—
111C2×C32—791no—
112C2×C32C2×D7911yescharacteristic
113#366—791no—
114#366C2×D7911yescharacteristic
115#358—1581no—
116#357—1581no—
117C2×Q16—1581no—
118C2×D8—21no—
119C22×C8—791no—
120C22⋊Q8—3161no—
121#121—3161no—
122Q32—1581no—
123Q32—1581no—
124D16—21no—
125D16—21no—
126C2×C16—791no—
127C2×C16—1581no—
128C2×C16—1581no—
129C2×C16C22×D7911yescharacteristic
130#107—21no—
131#107—1581no—
132#103—3161no—
133#102—3161no—
134C32—21no—
135C32—792no—
136C2×Q8—3161no—
137C2×D4—41no—
138C2×D4—6321no—
139C22×C4—791no—
140Q16—3161no—
141Q16—3161no—
142D8—41no—
143D8—41no—
144C2×C8—791no—
145C2×C8—1581no—
146C2×C8—1581no—
147C2×C8D4×D7911yescharacteristic
148C4⋊C4—41no—
149C4⋊C4—3161no—
150C4⋊C4—6321no—
151C22⋊C4—6321no—
152C22⋊C4—6321no—
153C16—1581no—
154C16D4×D7911yescharacteristic
155C16#1192962411yescharacteristic
156C23—81no—
157C23—791no—
158Q8—6321no—
159Q8—6321no—
160D4—81no—
161D4—81no—
162D4—12642no—
163C2×C4—81no—
164C2×C4—791no—
165C2×C4—6321no—
166C2×C4—6321no—
167C2×C4—1581no—
168C2×C4—1581no—
169C2×C4D8×D7911yescharacteristic
170C8—1581no—
171C8#1457913411yescharacteristic
172C8#1457918211yescharacteristic
173C22—161no—
174C22—161no—
175C22—161no—
176C22—1581no—
177C22—1581no—
178C22—1581no—
179C22D16×D7911yescharacteristic
180C4—161no—
181C4—1581no—
182C4—12641no—
183C4—12641no—
184C4#1909879811yescharacteristic
185C4#1909899411yescharacteristic
186C2—321no—
187C2—3161no—
188C2#2376548511yescharacteristic
189C2#2376571111yescharacteristic
190C2#2376571611yescharacteristic
subgroupG/H
centerC22D16×D79
commutator, cosocleC2×C16×C79C23
FrattiniC2×C16C22×D79
FittingC79×#1415C2
socleC22×C79C2×D16
prime radical#23765483C2
hypercenter#1415D79
hypocenterC79#13699
LCSG ▷ C2×C16×C79 ▷ C8×C79 ▷ C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #1415

Complements

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

NH ≅ G/Ntype
1. C2×#19098401C2semidirect
2. C2×#19098396C2semidirect
3. #23765492C2semidirect
5. #23761599C2semidirect
6. #23761582C2semidirect
7. C79×#1415C2semidirect
33. C79⋊C32D4semidirect
102. #1415D79semidirect
103. C79#13699semidirect

Maximal subgroups

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

subgroupindex
C2×#190984012
C2×#190983962
#237654922
#237654832
#237615992
#237615822
C79×#14152
#1369979