Finite Group Databasebeta

← #34199784

Subgroups — #34199784

Order 20224.

292 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 79 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#23774050C211yesmaximal, characteristic
2#23765216C211yesmaximal, characteristic, complemented
3#23761462C212yesmaximal, complemented
4#23761436C212yesmaximal, complemented
5C79×#2153C211yesmaximal, characteristic, complemented
6#19099168C412yes—
7#19098965C2211yescharacteristic
8#19098940C2211yescharacteristic
9#19098928C412yes—
10#19098816—21no—
11#19098799—21no—
12#19098676—21no—
13C4×D632—21no—
14#19098384C2212yes—
15#19098345—21no—
16#19098341—21no—
17C2×M32×C79—21no—
18#405×C79C2211yescharacteristic
19#364×C79—21no—
20#364×C79C2212yes—
21C2×D632—21no—
22C2×D632—21no—
23#14579158C2×C412yes—
24#14579153C2×C412yes—
25#14579146—42no—
26#14579135—22no—
27#14579134—42no—
28C4×D316—22no—
29#14579101—22no—
30#14579095—21no—
31#14579093—21no—
32#14579083—22no—
33#14579083—22no—
34C2×M16×C79D411yescharacteristic
35C22×C8×C79D411yescharacteristic
36#117×C79C2×C411yescharacteristic
37M32×C79—22no—
38M32×C79—41no—
39C2×C16×C79—41no—
40#97×C79C2×C411yescharacteristic
41#97×C79D411yescharacteristic
42C4×C8×C79D411yescharacteristic
43C4×C8×C79C2311yescharacteristic
44C2×D316—22no—
45C2×D316—42no—
46C2×C22⋊D79—42no—
47C2×C4×D79—42no—
48D632—42no—
49D632—41no—
50D632—41no—
51C4⋊Dic79—22no—
52Dic79⋊C4—42no—
53(C2×D79)⋊C4—42no—
54(C2×D79)⋊C4—42no—
55C79⋊C16—42no—
56C22×C4×C79C22⋊C411yescharacteristic
57M16×C79—22no—
58C2×C8×C79—21no—
59C2×C8×C79—21no—
60C2×C8×C79C22⋊C411yescharacteristic
61C2×C8×C79C22⋊C411yescharacteristic
62C2×C8×C79C2×D411yescharacteristic
63C2×C8×C79C2×D411yescharacteristic
64C4⋊C4×C79—21no—
65C22⋊C4×C79—21no—
66C42×C79C22⋊C411yescharacteristic
67C42×C79C22×C411yescharacteristic
68C16×C79—42no—
69C23×C79#10011yescharacteristic
70C22×D79—42no—
71C2×C4×C79—21no—
72C2×C4×C79—21no—
73C2×C4×C79—21no—
74C2×C4×C79—21no—
75C2×C4×C79#10011yescharacteristic
76C2×C4×C79C2×C22⋊C411yescharacteristic
77C22⋊D79—162no—
78C2×Dic79—42no—
79D316—42no—
80D316—42no—
81D316—162no—
82C4×D79—162no—
83C8×C79—21no—
84C8×C79—21no—
85C8×C79#13512yes—
86C8×C79AGL(1,ℤ/8)11yescharacteristic
87C8×C79#13711yescharacteristic
88C22×C79—21no—
89C22×C79—41no—
90C22×C79C2×#10011yescharacteristic
91C2×D79—82no—
92C2×D79—82no—
93C2×D79—82no—
94C4×C79—21no—
95C4×C79—41no—
96C4×C79—41no—
97C4×C79#41611yescharacteristic
98C4×C79#41711yescharacteristic
99Dic79—82no—
100#11989—791nomaximal, Sylow
101C2×C79—21no—
102C2×C79—41no—
103C2×C79#155111yescharacteristic
104D79—162no—
105#3176—791no—
106#2166—791no—
107#2153D7911yescharacteristic, complemented
108#1366—792no—
109#1357—792no—
110C79#1198911yescharacteristic, complemented, Sylow
111#540—792no—
112C2×M32—21no—
113#499—791no—
114#493—791no—
115#490—792no—
116#469—1581no—
117#466—1581no—
118#442—1581no—
119C4×D8—1581no—
120#405C2×D7911yescharacteristic
121#364—21no—
122#364—792no—
123#364C2×D7912yes—
124#349—1581no—
125#347—1581no—
126C2×D8—1581no—
127C2×D8—1581no—
128C2×M16D31611yescharacteristic
129C22×C8C22⋊D7911yescharacteristic
130#127—792no—
131#125—792no—
132#123—3162no—
133#121—3162no—
134#121—1582no—
135C4×D4—1582no—
136#117C4×D7911yescharacteristic
137M32—22no—
138M32—41no—
139M32—1582no—
140C2×C16—41no—
141#107—1581no—
142#106—1581no—
143#102—1582no—
144#102—1582no—
145#97C4×D7911yescharacteristic
146#97D31611yescharacteristic
147C4×C8C22⋊D7911yescharacteristic
148C4×C8C22×D7911yescharacteristic
149C2×D4—3162no—
150C2×D4—3162no—
151C2×D4—1582no—
152C22×C4—3162no—
153C22×C4(C2×D79)⋊C411yescharacteristic
154D8—3162no—
155D8—3161no—
156D8—3161no—
157M16—22no—
158C2×C8—21no—
159C2×C8—21no—
160C2×C8(C2×D79)⋊C411yescharacteristic
161C2×C8(C2×D79)⋊C411yescharacteristic
162C2×C8C2×C22⋊D7911yescharacteristic
163C2×C8C2×D31611yescharacteristic
164C4⋊C4—21no—
165C4⋊C4—3162no—
166C4⋊C4—1582no—
167C22⋊C4—21no—
168C22⋊C4—3162no—
169C22⋊C4—3162no—
170C42(C2×D79)⋊C411yescharacteristic
171C42C2×C4×D7911yescharacteristic
172C16—42no—
173C16—3162no—
174C23—3162no—
175C23#1457907711yescharacteristic
176D4—3162no—
177D4—3162no—
178D4—12642no—
179D4—12642no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—3162no—
185C2×C4—12642no—
186C2×C4#1457907711yescharacteristic
187C2×C4C2×(C2×D79)⋊C411yescharacteristic
188C8—21no—
189C8—21no—
190C8#1457918312yes—
191C8#1457918711yescharacteristic
192C8#1457919211yescharacteristic
193C22—21no—
194C22—41no—
195C22—6322no—
196C22—6322no—
197C22—6322no—
198C22C2×#1457907711yescharacteristic
199C4—21no—
200C4—41no—
201C4—41no—
202C4—6322no—
203C4#1909856011yescharacteristic
204C4#1909856211yescharacteristic
205C2—21no—
206C2—41no—
207C2—12642no—
208C2#2376209311yescharacteristic
subgroupG/H
centerC2#23762093
commutatorC42×C79C22×C4
FrattiniC4×C8C22×D79
FittingC79×#2153C2
socleC2×C79#1551
prime radical#23774050C2
cosocleC4×C8×C79C23
hypercenter#2153D79
hypocenterC79#11989
LCSG ▷ C42×C79 ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2 ◁ C2×C4 ◁ #405 ◁ #2153

Complements

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

NH ≅ G/Ntype
2. #23765216C2semidirect
3. #23761462C2semidirect
4. #23761436C2semidirect
5. C79×#2153C2semidirect
107. #2153D79semidirect
110. C79#11989semidirect

Maximal subgroups

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

subgroupindex
#237740502
#237652162
#237614622
#237614362
C79×#21532
#1198979