Finite Group Databasebeta

← #26038947

Subgroups — #26038947

Order 11456.

330 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 107 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×#15668258C211yesmaximal, characteristic, complemented
2C22×C4×D179C211yesmaximal, characteristic, complemented
3#19153096C211yesmaximal, characteristic, complemented
4#19153091C212yesmaximal, complemented
5#19153086C212yesmaximal, complemented
6#19153083C211yesmaximal, characteristic, complemented
7#19153081C211yesmaximal, characteristic, complemented
8#19153075C212yesmaximal, complemented
9(C22⋊D179)⋊C4C212yesmaximal, complemented
10#19153069C211yesmaximal, characteristic, complemented
11#123×C179C211yesmaximal, characteristic, complemented
12C23×D179C2211yescharacteristic
13#15668258—24no—
14C2×Dic358C2211yescharacteristic, complemented
15C2×D716C2212yes—
16C2×C22⋊D179C2211yescharacteristic
17C2×C22⋊D179C2212yes—
18C2×C22⋊D179C2211yescharacteristic, complemented
19C22×Dic179C2211yescharacteristic
20C22×Dic179C2211yescharacteristic, complemented
21C2×C4×D179—24no—
22C2×C4×D179C2212yes—
23C2×C4×D179C2212yes—
24C2×C4×D179C2211yescharacteristic, complemented
25Dic179⋊C4C2212yescomplemented
26Dic179⋊C4C2212yescomplemented
27C22⋊Dic179C2211yescharacteristic
28(C2×D179)⋊C4C2212yes—
29(C2×D179)⋊C4C2212yes—
30(C2×D179)⋊C4C2212yescomplemented
31C4×Dic179C2212yescomplemented
32C2×D4×C179C2211yescharacteristic
33C22×C4×C179C2211yescharacteristic
34C4⋊C4×C179C2212yescomplemented
35C22⋊C4×C179C2211yescharacteristic
36C22⋊C4×C179C2212yescomplemented
37C22×D179—22no—
38C22×D179—24no—
39C22×D179C2311yescharacteristic
40C22×D179C2312yes—
41Dic358—22no—
42D716—24no—
43C22⋊D179—22no—
44C22⋊D179—24no—
45C22⋊D179—22no—
46C2×Dic179—22no—
47C2×Dic179D414yescomplemented
48C2×Dic179C2312yes—
49C2×Dic179C2311yescharacteristic
50C2×Dic179C2311yescharacteristic
51C2×Dic179C2311yescharacteristic
52C4×D179—24no—
53C4×D179—24no—
54C4×D179—22no—
55C23×C179C2311yescharacteristic
56C23×C179C2311yescharacteristic
57D4×C179—22no—
58C2×C4×C179—22no—
59C2×C4×C179C2312yes—
60C2×C4×C179C2311yescharacteristic
61C2×C4×C179C2312yes—
62C22×C179—22no—
63C22×C179—21no—
64C22×C179—22no—
65C22×C179C2×D412yes—
66C22×C179C2411yescharacteristic
67C2×D179—28no—
68C2×D179—22no—
69C2×D179—22no—
70C2×D179—21no—
71C2×D179—22no—
72C2×D179#4114yescomplemented
73C4×C179—22no—
74C4×C179—21no—
75C4×C179—22no—
76Dic179—21no—
77Dic179—22no—
78Dic179C2×D412yes—
79Dic179C2×D412yes—
80C2×C179—22no—
81C2×C179—41no—
82C2×C179C22×D411yescharacteristic
83C2×C179C2×#4112yes—
84D179—24no—
85D179—41no—
86C179#52511yescharacteristic, complemented, Sylow
87#525—1791nomaximal, Sylow
88C2×#41—1791no—
89C23×C4—1791no—
90#123—1791no—
91#123D17911yescharacteristic, complemented
92C22⋊Q8—1792no—
93#121—1792no—
94#120—1791no—
95#120—1791no—
96C4×D4—1792no—
97C4×D4—1792no—
98#117—1791no—
99C24—1791no—
100#41—3584no—
101C2×Q8—1791no—
102C2×D4—1792no—
103C2×D4—1791no—
104C2×D4—1791no—
105C2×D4—1792no—
106C2×D4C2×D17911yescharacteristic
107C22×C4—3584no—
108C22×C4—1791no—
109C22×C4—1792no—
110C22×C4—1792no—
111C22×C4—1791no—
112C22×C4—1791no—
113C22×C4C2×D17911yescharacteristic
114C4⋊C4—1792no—
115C4⋊C4—1792no—
116C4⋊C4C2×D17912yescomplemented
117C22⋊C4—1791no—
118C22⋊C4—1792no—
119C22⋊C4—1792no—
120C22⋊C4—1792no—
121C22⋊C4C2×D17911yescharacteristic
122C22⋊C4C2×D17912yescomplemented
123C42—1792no—
124C23—3584no—
125C23—3582no—
126C23—1791no—
127C23—1792no—
128C23C22×D17911yescharacteristic
129C23C22×D17911yescharacteristic
130Q8—3582no—
131D4—22no—
132D4—3584no—
133D4—3584no—
134D4—3582no—
135D4—3582no—
136C2×C4—22no—
137C2×C4—3584no—
138C2×C4—3584no—
139C2×C4—3582no—
140C2×C4—3582no—
141C2×C4—1792no—
142C2×C4—1791no—
143C2×C4—1794no—
144C2×C4—1791no—
145C2×C4—1791no—
146C2×C4C22×D17912yes—
147C2×C4C22×D17911yescharacteristic
148C2×C4C22×D17912yes—
149C22—22no—
150C22—22no—
151C22—21no—
152C22—3588no—
153C22—3582no—
154C22—3582no—
155C22—3582no—
156C22—3581no—
157C22—1794no—
158C22D4×D17912yes—
159C22C23×D17911yescharacteristic
160C4—22no—
161C4—22no—
162C4—21no—
163C4—3582no—
164C4—3581no—
165C4—1792no—
166C4—1792no—
167C2—22no—
168C2—41no—
169C2—3584no—
170C2—7161no—
171C2C2×D4×D17911yescharacteristic
172C2#41×D17912yes—
subgroupG/H
center, FrattiniC22C23×D179
commutator, socle, cosocleC22×C179C24
Fitting#123×C179C2
hypercenter#123D179
hypocenterC179#525
LCSG ▷ C22×C179 ▷ C179
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. C2×#15668258C2semidirect
2. C22×C4×D179C2semidirect
3. #19153096C2semidirect
4. #19153091C2semidirect
5. #19153086C2semidirect
6. #19153083C2semidirect
7. #19153081C2semidirect
8. #19153075C2semidirect
9. (C22⋊D179)⋊C4C2semidirect
10. #19153069C2semidirect
11. #123×C179C2semidirect
14. C2×Dic358C22semidirect
18. C2×C22⋊D179C22semidirect
20. C22×Dic179C22semidirect
24. C2×C4×D179C22semidirect
25. Dic179⋊C4C22semidirect
26. Dic179⋊C4C22semidirect
30. (C2×D179)⋊C4C22semidirect
31. C4×Dic179C22semidirect
34. C4⋊C4×C179C22semidirect
36. C22⋊C4×C179C22semidirect
47. C2×Dic179D4semidirect
72. C2×D179#41semidirect
86. C179#525semidirect
91. #123D179semidirect
116. C4⋊C4C2×D179semidirect
122. C22⋊C4C2×D179semidirect

Maximal subgroups

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

subgroupindex
C2×#156682582
C22×C4×D1792
#191530962
#191530912
#191530862
#191530832
#191530812
#191530752
(C22⋊D179)⋊C42
#191530692
#123×C1792
#525179