Finite Group Databasebeta

← #37510068

Subgroups — #37510068

Order 22912.

394 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 71 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#26039239C211yesmaximal, characteristic, complemented
2#26038951C212yesmaximal, complemented
3#26038457C212yesmaximal, complemented
4#26038402C211yesmaximal, characteristic, complemented
5H(3,ℤ/4)×C179C211yesmaximal, characteristic, complemented
6C2×#15668259C2212yes—
7C22×C4×D179C2211yescharacteristic
8#19153146—22no—
9#19153141—22no—
10#19153135—22no—
11C2×#15668243C2211yescharacteristic
12#19153097—22no—
13#19153093—22no—
14#19153088—22no—
15#19153083—22no—
16C4×D716—24no—
17#19153041—24no—
18(C2×D179)⋊C8—22no—
19C2×M16×C179C2211yescharacteristic
20#117×C179C2212yes—
21C23×D179D411yescharacteristic
22#15668259—22no—
23#15668259—22no—
24#15668259—22no—
25#15668259—22no—
26C2×Dic358D412yescomplemented
27C2×D716—24no—
28C2×D716D412yescomplemented
29C2×C22⋊D179—22no—
30C22×Dic179D411yescharacteristic
31C2×C4×D179—22no—
32C2×C4×D179—21no—
33C2×C4×D179—22no—
34C2×C4×D179—22no—
35C2×C4×D179—21no—
36Dic716—22no—
37#15668248—24no—
38D1432—22no—
39#15668243—22no—
40C2×C179⋊C8—21no—
41C4⋊Dic179—24no—
42(C2×D179)⋊C4—24no—
43(C2×D179)⋊C4—24no—
44C22×C4×C179C2311yescharacteristic
45M16×C179—22no—
46C2×C8×C179D412yescomplemented
47C4⋊C4×C179—22no—
48C22⋊C4×C179—22no—
49C42×C179D414yescomplemented
50C22×D179—22no—
51C22×D179—21no—
52C22×D179—22no—
53C22×D179—42no—
54Dic358—22no—
55Dic358—22no—
56D716—22no—
57D716—22no—
58D716—48no—
59C22⋊D179—42no—
60C22⋊D179—42no—
61C2×Dic179—22no—
62C2×Dic179—22no—
63C2×Dic179—21no—
64C4×D179—41no—
65C4×D179—42no—
66C4×D179—42no—
67C4×D179—41no—
68C4×D179—42no—
69C179⋊C8—41no—
70C23×C179C2×D411yescharacteristic
71C2×C4×C179—24no—
72C2×C4×C179C2×D412yes—
73C2×C4×C179C2×D411yescharacteristic
74C2×C4×C179C2×D412yes—
75C2×C4×C179#4111yescharacteristic
76C8×C179—22no—
77C22×C179—41no—
78C22×C179#12012yes—
79C22×C179#12111yescharacteristic
80C2×D179—24no—
81C2×D179—22no—
82C2×D179—42no—
83C2×D179—41no—
84C2×D179—41no—
85C2×D179—44no—
86C2×D179—42no—
87C4×C179—44no—
88C4×C179#12011yescharacteristic
89C4×C179#12112yes—
90C4×C179#12711yescharacteristic
91Dic179—41no—
92Dic179—42no—
93C2×C179—22no—
94C2×C179—21no—
95C2×C179#39211yescharacteristic
96D179—42no—
97D179—82no—
98C179#201011yescharacteristic, complemented, Sylow
99#2010—1791nomaximal, Sylow
100#575—1791no—
101#525—1792no—
102#421—1792no—
103#407—1791no—
104H(3,ℤ/4)D17911yescharacteristic, complemented
105C2×#41—1792no—
106C23×C4—1791no—
107#137—3582no—
108AGL(1,ℤ/8)—3582no—
109#135—3582no—
110C2×M16—1791no—
111C2×M16C2×D17911yescharacteristic
112#123—3582no—
113C22⋊Q8—3582no—
114#121—3582no—
115#120—3582no—
116C4×D4—3584no—
117#117C2×D17912yes—
118#104—3584no—
119C22⋊C8—3582no—
120C24—1791no—
121#41—3582no—
122#41—3582no—
123#41—3582no—
124#41—3582no—
125C2×Q8—1792no—
126C2×D4—3584no—
127C2×D4—3582no—
128C2×D4—1792no—
129C22×C4—3582no—
130C22×C4—3581no—
131C22×C4—3582no—
132C22×C4—3582no—
133C22×C4—3581no—
134C22×C4—1791no—
135C22×C4C22×D17911yescharacteristic
136Q16—3582no—
137SD16—3584no—
138D8—3582no—
139M16—22no—
140M16—3582no—
141C2×C8—3581no—
142C2×C8D71612yescomplemented
143C4⋊C4—22no—
144C4⋊C4—3584no—
145C22⋊C4—22no—
146C22⋊C4—3584no—
147C22⋊C4—3584no—
148C42D71614yescomplemented
149C23—3582no—
150C23—3581no—
151C23—3582no—
152C23—7162no—
153C23D4×D17911yescharacteristic
154Q8—3582no—
155Q8—3582no—
156D4—3582no—
157D4—3582no—
158D4—7168no—
159D4—7162no—
160D4—7162no—
161C2×C4—24no—
162C2×C4—3582no—
163C2×C4—3582no—
164C2×C4—3581no—
165C2×C4—7161no—
166C2×C4—7162no—
167C2×C4—7162no—
168C2×C4—7161no—
169C2×C4—7162no—
170C2×C4D4×D17912yes—
171C2×C4C2×D71611yescharacteristic
172C2×C4C2×D71612yes—
173C2×C4#1566826011yescharacteristic
174C8—22no—
175C8—7161no—
176C22—41no—
177C22—3584no—
178C22—3582no—
179C22—7164no—
180C22—7162no—
181C22—7161no—
182C22—7162no—
183C22—7161no—
184C22#1915308312yes—
185C22#1915308811yescharacteristic
186C4—44no—
187C4—7161no—
188C4—7162no—
189C4#1915308311yescharacteristic
190C4#1915308812yes—
191C4#1915311011yescharacteristic
192C2—22no—
193C2—21no—
194C2—14322no—
195C2—7162no—
196C2#2603834911yescharacteristic
subgroupG/H
centerC4#19153110
commutator, cosocleC22×C4×C179C23
FrattiniC22×C4C22×D179
FittingH(3,ℤ/4)×C179C2
socleC2×C179#392
hypercenterH(3,ℤ/4)D179
hypocenterC179#2010
LCSG ▷ C22×C4×C179 ▷ C2×C179 ▷ C179
UCSC1 ◁ C4 ◁ C22×C4 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
1. #26039239C2semidirect
2. #26038951C2semidirect
3. #26038457C2semidirect
4. #26038402C2semidirect
5. H(3,ℤ/4)×C179C2semidirect
26. C2×Dic358D4semidirect
28. C2×D716D4semidirect
46. C2×C8×C179D4semidirect
49. C42×C179D4semidirect
98. C179#2010semidirect
104. H(3,ℤ/4)D179semidirect
142. C2×C8D716semidirect
148. C42D716semidirect

Maximal subgroups

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

subgroupindex
#260392392
#260389512
#260384572
#260384022
H(3,ℤ/4)×C1792
#2010179