Finite Group Databasebeta

← #37508039

Subgroups — #37508039

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#26038758C212yesmaximal, complemented
3#26038378C211yesmaximal, characteristic, complemented
4#26038174C212yesmaximal, complemented
5#324×C179C211yesmaximal, characteristic, complemented
6C2×#15668259—21no—
7#19153093—22no—
8#19153088—22no—
9#19153087—21no—
10#19153087C2212yes—
11C2×C4⋊Dic179C2211yescharacteristic
12#19153045—22no—
13#19153035—22no—
14C179⋊#95—21no—
15C179⋊#95—21no—
16C179⋊#95C2211yescharacteristic
17C2×C4⋊C4×C179C2211yescharacteristic
18C22⋊C8×C179C2212yes—
19#15668259—42no—
20#15668259—42no—
21C2×Dic358—21no—
22C2×D716—21no—
23C2×D716—21no—
24C2×D716D412yes—
25C2×C22⋊D179—22no—
26C22×Dic179—21no—
27C22×Dic179—21no—
28C2×C4×D179—22no—
29C4⋊Dic179—21no—
30C4⋊Dic179—22no—
31C4⋊Dic179D412yes—
32(C2×D179)⋊C4—22no—
33(C2×D179)⋊C4—22no—
34C22×C4×C179D411yescharacteristic
35C22×C4×C179D411yescharacteristic
36C22×C4×C179C2311yescharacteristic
37C2×C8×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—
47C2×Dic179—41no—
48C2×Dic179—41no—
49C2×Dic179—42no—
50C2×Dic179—41no—
51C2×Dic179—41no—
52C4×D179—44no—
53C23×C179C2×D411yescharacteristic
54C2×C4×C179—21no—
55C2×C4×C179—21no—
56C2×C4×C179—21no—
57C2×C4×C179—41no—
58C2×C4×C179—41no—
59C2×C4×C179SD1612yes—
60C2×C4×C179C2×D412yes—
61C8×C179—42no—
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—
73Dic179—42no—
74Dic179—81no—
75Dic179—81no—
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#400—1791no—
87#327—1792no—
88#324D17911yescharacteristic, complemented
89C2×#41—3581no—
90C22⋊Q8—3582no—
91#121—3582no—
92#121—3581no—
93#121—1792no—
94C2×C4⋊C4—1791no—
95C2×C4⋊C4C2×D17911yescharacteristic
96#106—3582no—
97#102—3582no—
98C22⋊C8C2×D17912yes—
99#95—3581no—
100#95—3581no—
101#95—1791no—
102#41—7162no—
103#41—7162no—
104C2×Q8—3581no—
105C2×D4—3581no—
106C2×D4—3581no—
107C2×D4—3582no—
108C2×D4—1792no—
109C22×C4—3582no—
110C22×C4—3581no—
111C22×C4—3581no—
112C22×C4D71611yescharacteristic
113C22×C4D71611yescharacteristic
114C22×C4C22×D17911yescharacteristic
115C2×C8—22no—
116C4⋊C4—22no—
117C4⋊C4—3581no—
118C4⋊C4—3582no—
119C4⋊C4—1792no—
120C22⋊C4—3582no—
121C22⋊C4—3582no—
122C23—3582no—
123C23C2×D71611yescharacteristic
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—3582no—
136C2×C4—7164no—
137C2×C4—7161no—
138C2×C4—7161no—
139C2×C4—7162no—
140C2×C4—7161no—
141C2×C4—7161no—
142C2×C4#1566824812yes—
143C2×C4D4×D17912yes—
144C8—42no—
145C22—21no—
146C22—21no—
147C22—7162no—
148C22—7162no—
149C22—7162no—
150C22#1915308311yescharacteristic
151C22C2×#1566824811yescharacteristic
152C22#1915314111yescharacteristic
153C4—22no—
154C4—22no—
155C4—41no—
156C4—14321no—
157C4—14321no—
158C4—7162no—
159C2—21no—
160C2—21no—
161C2—14322no—
162C2#2603859211yescharacteristic
163C2#2603861411yescharacteristic
164C2#2603863011yescharacteristic
subgroupG/H
centerC22#19153083
commutator, cosocleC22×C4×C179C23
FrattiniC22×C4C22×D179
Fitting#324×C179C2
socleC22×C179#120
prime radical#26039020C2
hypercenter#324D179
hypocenterC179#1616
LCSG ▷ C22×C4×C179 ▷ C22×C179 ▷ C179
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #26038758C2semidirect
3. #26038378C2semidirect
4. #26038174C2semidirect
5. #324×C179C2semidirect
82. C179#1616semidirect
88. #324D179semidirect

Maximal subgroups

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

subgroupindex
#260390202
#260387582
#260383782
#260381742
#324×C1792
#1616179