Finite Group Databasebeta

← #34209053

Subgroups — #34209053

Order 20224.

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

normal subgroups only

This group has 220 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×#19098401C211yesmaximal, characteristic, complemented
3#23765648C211yesmaximal, characteristic
4#23765258C211yesmaximal, characteristic, complemented
5Dic79⋊C32C211yesmaximal, characteristic, complemented
6#23761577C211yesmaximal, characteristic, complemented
7C79×#1415C211yesmaximal, characteristic, complemented
8C2×Dic632C2211yescharacteristic
9C2×D1264C2211yescharacteristic
10C2×#14579102—21no—
11#19098938—21no—
12#19098657—21no—
13#19098402—22no—
14#19098401—22no—
15C2×C79⋊C32C2211yescharacteristic
16#19098366—21no—
17C16×Dic79C2211yescharacteristic
18C2×D16×C79C2211yescharacteristic
19C2×C32×C79C2211yescharacteristic
20#366×C79C2211yescharacteristic
21C2×Dic316—21no—
22C2×D632—21no—
23C2×#11929609—41no—
24#14579157—41no—
25#14579126—41no—
26Dic632—21no—
27Dic632D412yescomplemented
28D1264—21no—
29D1264—21no—
30#14579102—42no—
31C2×C79⋊C16D411yescharacteristic
32#14579084—41no—
33C8×Dic79D411yescharacteristic
34C79⋊C32—21no—
35C2×D8×C79—21no—
36D16×C79—21no—
37D16×C79—21no—
38C2×C16×C79C2311yescharacteristic
39#107×C79—21no—
40C32×C79—21no—
41C2×Dic158—41no—
42C2×D316—41no—
43C2×C22⋊D79—81no—
44C2×C22⋊D79—81no—
45Dic316—22no—
46Dic316—41no—
47D632—41no—
48D632—41no—
49#11929609—82no—
50C2×C79⋊C8D811yescharacteristic
51Dic79⋊C4—81no—
52C4×Dic79—81no—
53C4×Dic79D811yescharacteristic
54C79⋊C16—21no—
55C2×D4×C79—41no—
56D8×C79—41no—
57D8×C79—41no—
58C2×C8×C79C2×D411yescharacteristic
59C4⋊C4×C79—41no—
60C16×C79C2×D411yescharacteristic
61C16×C79#4111yescharacteristic
62C23×C79—81no—
63C22×D79—81no—
64D4×C79—81no—
65D4×C79—81no—
66C2×C4×C79—81no—
67C2×C4×C79C2×D811yescharacteristic
68C22⋊D79—162no—
69C22⋊D79—162no—
70C2×Dic79—81no—
71C2×Dic79D1611yescharacteristic
72C2×Dic79D1611yescharacteristic
73D316—81no—
74D316—81no—
75Dic158—42no—
76Dic158—81no—
77C8×C79#12111yescharacteristic
78C8×C79AGL(1,ℤ/8)11yescharacteristic
79C79⋊C8—21no—
80C22×C79—161no—
81C22×C79—161no—
82C22×C79—161no—
83C22×C79C2×D1611yescharacteristic
84C2×D79—161no—
85C2×D79—161no—
86C2×D79—161no—
87C4×C79—161no—
88C4×C79#45911yescharacteristic
89C4×C79#50911yescharacteristic
90Dic79—21no—
91Dic79—82no—
92Dic79SD6412yescomplemented
93#13686—791nomaximal, Sylow
94C2×C79—321no—
95C2×C79#220611yescharacteristic
96C2×C79C2×SD6411yescharacteristic
97C2×C79#226311yescharacteristic
98D79—321no—
99C2×SD64—791no—
100C2×SD64—791no—
101#2246—791no—
102C4×Q32—791no—
103C4⋊C32—791no—
104#1415—791no—
105#1415D7911yescharacteristic, complemented
106C79#1368611yescharacteristic, complemented, Sylow
107C2×Q32—791no—
108C2×D16—791no—
109C2×D16—1581no—
110C2×D16C2×D7911yescharacteristic
111#493—1581no—
112C4×Q16—1581no—
113SD64—1582no—
114SD64—1582no—
115C2×C32—791no—
116C2×C32C2×D7911yescharacteristic
117#366C2×D7911yescharacteristic
118#358—1581no—
119C4×C16—791no—
120C2×Q16—1581no—
121C2×D8—21no—
122C2×D8—3161no—
123C2×D8—1581no—
124#127—3161no—
125C4×Q8—3161no—
126Q32—792no—
127Q32—1581no—
128D16—21no—
129D16—21no—
130D16—3162no—
131D16—1581no—
132D16—1581no—
133C2×C16—791no—
134C2×C16C22×D7911yescharacteristic
135#107—21no—
136#103—3161no—
137C4×C8—791no—
138C32—21no—
139C32—1581no—
140C2×Q8—3161no—
141C2×D4—41no—
142C2×D4—3161no—
143C2×D4—6321no—
144C2×D4—6321no—
145Q16—3161no—
146Q16—1582no—
147D8—41no—
148D8—41no—
149D8—3161no—
150D8—3161no—
151D8—6322no—
152C2×C8—791no—
153C2×C8D4×D7911yescharacteristic
154C4⋊C4—41no—
155C4⋊C4—6321no—
156C42—791no—
157C42—6321no—
158C16—1581no—
159C16D4×D7911yescharacteristic
160C16#1192962411yescharacteristic
161C23—81no—
162C23—6321no—
163Q8—3162no—
164Q8—6321no—
165D4—81no—
166D4—81no—
167D4—6321no—
168D4—6321no—
169D4—12642no—
170D4—12642no—
171C2×C4—81no—
172C2×C4—791no—
173C2×C4—791no—
174C2×C4—6321no—
175C2×C4D8×D7911yescharacteristic
176C8—1581no—
177C8#1457913411yescharacteristic
178C8#1457918811yescharacteristic
179C22—161no—
180C22—161no—
181C22—161no—
182C22—12641no—
183C22—12641no—
184C22—12641no—
185C22D16×D7911yescharacteristic
186C4—161no—
187C4—792no—
188C4—6322no—
189C4—1581no—
190C4#1909875711yescharacteristic
191C4#1909900011yescharacteristic
192C2—321no—
193C2—25281no—
194C2#2376543411yescharacteristic
195C2SD64×D7911yescharacteristic
196C2#2376571111yescharacteristic
subgroupG/H
centerC22D16×D79
commutator, cosocleC2×C16×C79C23
FrattiniC2×C16C22×D79
FittingC79×#1415C2
socleC22×C79C2×D16
prime radical#23765648C2
hypercenter#1415D79
hypocenterC79#13686
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×#19098402C2semidirect
2. C2×#19098401C2semidirect
4. #23765258C2semidirect
5. Dic79⋊C32C2semidirect
6. #23761577C2semidirect
7. C79×#1415C2semidirect
27. Dic632D4semidirect
92. Dic79SD64semidirect
105. #1415D79semidirect
106. C79#13686semidirect

Maximal subgroups

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

subgroupindex
C2×#190984022
C2×#190984012
#237656482
#237652582
Dic79⋊C322
#237615772
C79×#14152
#1368679