Finite Group Databasebeta

← #37508036

Subgroups — #37508036

Order 22912.

246 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 53 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#26039020C211yesmaximal, characteristic
2#26038757C212yesmaximal, complemented
3#26038172C212yesmaximal, complemented
4#26038165C211yesmaximal, characteristic, complemented
5#400×C179C211yesmaximal, characteristic, complemented
6C2×#15668259—21no—
7#19153093—22no—
8#19153088—22no—
9#19153087—21no—
10#19153087C2212yes—
11#19153044—22no—
12#19153033—22no—
13C22⋊(C179⋊C8)C2212yes—
14C2×C4⋊C4×C179C2211yescharacteristic
15C2×C4⋊C4×C179C2211yescharacteristic
16#95×C179—21no—
17#95×C179—21no—
18#95×C179C2211yescharacteristic
19#15668259—42no—
20#15668259—42no—
21C2×Dic358—21no—
22C2×D716—21no—
23C2×D716—21no—
24C2×D716D412yes—
25C2×C22⋊D179—22no—
26C2×C4×D179—22no—
27C2×C179⋊C8—22no—
28C4⋊Dic179—21no—
29C4⋊Dic179D412yes—
30(C2×D179)⋊C4—22no—
31(C2×D179)⋊C4—22no—
32C22×C4×C179—21no—
33C22×C4×C179—21no—
34C22×C4×C179D411yescharacteristic
35C22×C4×C179D411yescharacteristic
36C22×C4×C179C2311yescharacteristic
37C4⋊C4×C179—22no—
38C4⋊C4×C179—22no—
39C22×D179—22no—
40Dic358—42no—
41D716—42no—
42D716—42no—
43D716—81no—
44C22⋊D179—42no—
45C22⋊D179—42no—
46C2×Dic179—22no—
47C4×D179—44no—
48C179⋊C8—42no—
49C23×C179C2×D411yescharacteristic
50C2×C4×C179—21no—
51C2×C4×C179—21no—
52C2×C4×C179—21no—
53C2×C4×C179—41no—
54C2×C4×C179—41no—
55C2×C4×C179—41no—
56C2×C4×C179—41no—
57C2×C4×C179—42no—
58C2×C4×C179—41no—
59C2×C4×C179—41no—
60C2×C4×C179SD1612yes—
61C2×C4×C179C2×D412yes—
62C22×C179—21no—
63C22×C179—21no—
64C22×C179#12011yescharacteristic
65C22×C179C2×SD1611yescharacteristic
66C22×C179AGL(1,ℤ/8)11yescharacteristic
67C2×D179—42no—
68C2×D179—42no—
69C2×D179—42no—
70C4×C179—22no—
71C4×C179—22no—
72C4×C179—41no—
73C4×C179—81no—
74C4×C179—81no—
75Dic179—42no—
76C2×C179—21no—
77C2×C179—21no—
78C2×C179#45011yescharacteristic
79C2×C179#45411yescharacteristic
80C2×C179#45811yescharacteristic
81D179—82no—
82C179#161611yescharacteristic, complemented, Sylow
83#1616—1791nomaximal, Sylow
84#537—1791no—
85#481—1792no—
86#400D17911yescharacteristic, complemented
87#327—1792no—
88#324—1791no—
89C2×#41—3581no—
90C22⋊Q8—3582no—
91#121—3582no—
92#121—3581no—
93#121—1792no—
94C2×C4⋊C4C2×D17911yescharacteristic
95C2×C4⋊C4C2×D17911yescharacteristic
96#106—3582no—
97#102—3582no—
98C22⋊C8—1792no—
99#95—21no—
100#95—21no—
101#95C2×D17911yescharacteristic
102#41—7162no—
103#41—7162no—
104C2×Q8—3581no—
105C2×D4—3581no—
106C2×D4—3581no—
107C2×D4—3582no—
108C2×D4—1792no—
109C22×C4—21no—
110C22×C4—21no—
111C22×C4—3582no—
112C22×C4C22⋊D17911yescharacteristic
113C22×C4C22⋊D17911yescharacteristic
114C22×C4C22×D17911yescharacteristic
115C2×C8—3582no—
116C4⋊C4—22no—
117C4⋊C4—22no—
118C4⋊C4—3581no—
119C4⋊C4—1792no—
120C22⋊C4—3582no—
121C22⋊C4—3582no—
122C23—3582no—
123C23C2×C22⋊D17911yescharacteristic
124Q8—7162no—
125D4—14321no—
126D4—7162no—
127D4—7162no—
128D4—7162no—
129D4—7162no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—21no—
133C2×C4—41no—
134C2×C4—41no—
135C2×C4—41no—
136C2×C4—41no—
137C2×C4—42no—
138C2×C4—41no—
139C2×C4—41no—
140C2×C4—3582no—
141C2×C4—7164no—
142C2×C4#1566824612yes—
143C2×C4D4×D17912yes—
144C8—7162no—
145C22—21no—
146C22—21no—
147C22—7162no—
148C22—7162no—
149C22—7162no—
150C22#1915308111yescharacteristic
151C22C2×#1566824611yescharacteristic
152C22#1915313811yescharacteristic
153C4—22no—
154C4—22no—
155C4—41no—
156C4—81no—
157C4—81no—
158C4—7162no—
159C2—21no—
160C2—21no—
161C2—14322no—
162C2#2603858911yescharacteristic
163C2#2603861111yescharacteristic
164C2#2603862811yescharacteristic
subgroupG/H
centerC22#19153081
commutator, cosocleC22×C4×C179C23
FrattiniC22×C4C22×D179
Fitting#400×C179C2
socleC22×C179#120
prime radical#26039020C2
hypercenter#400D179
hypocenterC179#1616
LCSG ▷ C22×C4×C179 ▷ C22×C179 ▷ C179
UCSC1 ◁ C22 ◁ C22×C4 ◁ #400

Complements

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

NH ≅ G/Ntype
2. #26038757C2semidirect
3. #26038172C2semidirect
4. #26038165C2semidirect
5. #400×C179C2semidirect
82. C179#1616semidirect
86. #400D179semidirect

Maximal subgroups

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

subgroupindex
#260390202
#260387572
#260381722
#260381652
#400×C1792
#1616179