Finite Group Databasebeta

← #28350865

Subgroups — #28350865

Order 13696.

1258 conjugacy classes of subgroups; only the 455 normal subgroups are shown.

normal subgroups only

This group has 1258 conjugacy classes of subgroups — too many to draw. Only its 455 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#20293369C213yesmaximal, complemented
2#20293339C216yesmaximal, complemented
3#20293259C216yesmaximal, complemented
4#20293195C216yesmaximal, complemented
5#20293192C216yesmaximal, complemented
6#20293176C213yesmaximal, complemented
7H(3,𝔽4)×C107C211yesmaximal, characteristic, complemented
8C2×#13133819C2213yescomplemented
9C2×#13133817C2213yescomplemented
10C22×C22⋊D107C2216yescomplemented
11C2×D4×D107C2216yescomplemented
12#16812107C2213yescomplemented
13#16812106C2212yescomplemented
14#16812105C2213yes—
15#16812105C2216yescomplemented
16#16812098C2216yescomplemented
17#16812097C2213yescomplemented
18#16812095C22112yescomplemented
19#16812082C22112yescomplemented
20#16812082C22112yescomplemented
21#16812081C22112yescomplemented
22#16812079C2216yescomplemented
23#16812079C22112yescomplemented
24#16812078C2212yescomplemented
25#16812077C2216yescomplemented
26(C22⋊D107)⋊C4C22112yescomplemented
27#16812066C2216yescomplemented
28#16812065C2216yescomplemented
29C42×D107C2211yescharacteristic, complemented
30#124×C107C2213yescomplemented
31#124×C107C2216yescomplemented
32#120×C107C2216yescomplemented
33C23×D107C2316yes—
34#13133819—46no—
35#13133817—46no—
36C2×Dic214C2313yes—
37C2×D428C2313yes—
38C2×D428C2316yes—
39C2×D428C2316yes—
40C2×C22⋊D107—412no—
41C2×C22⋊D107C23112yes—
42C2×C22⋊D107C23112yes—
43C2×C22⋊D107C2316yes—
44D4×D107—412no—
45C22×Dic107C2316yes—
46C2×C4×D107C2313yes—
47C2×C4×D107C2316yes—
48Dic107⋊C4C23112yes—
49C22⋊Dic107C2316yes—
50(C2×D107)⋊C4C23112yes—
51(C2×D107)⋊C4C23112yes—
52C4×Dic107C2313yes—
53C4×Dic107C2316yes—
54C24×C107C2312yes—
55C2×Q8×C107C2313yes—
56C2×D4×C107C2313yes—
57C2×D4×C107C2316yes—
58C22⋊C4×C107C2316yes—
59C22⋊C4×C107C23112yes—
60C42×C107C2311yescharacteristic
61C42×C107C2312yes—
62C23×C107—46no—
63C23×C107C2416yes—
64C22×D107—412no—
65C22×D107—46no—
66C22×D107C2416yes—
67C22×D107C2411yescharacteristic
68Q8×C107—43no—
69D4×C107—46no—
70D4×C107—43no—
71C2×C4×C107C2413yes—
72C2×C4×C107C2416yes—
73C22⋊D107—224no—
74C22⋊D107—412no—
75C22⋊D107—46no—
76C2×Dic107—212no—
77C2×Dic107C2416yes—
78C2×Dic107C2413yes—
79D428—46no—
80D428—43no—
81D428—46no—
82C4×D107—212no—
83C4×D107—26no—
84Dic214—43no—
85C22×C107—26no—
86C22×C107—212no—
87C22×C107—84no—
88C22×C107C2511yescharacteristic
89C2×D107—23no—
90C2×D107—26no—
91C2×D107—212no—
92C2×D107—812no—
93C4×C107—23no—
94C4×C107—26no—
95Dic107—26no—
96Dic107H(5,𝔽2)16yes—
97C2×C107—46no—
98C2×C107C2×H(5,𝔽2)13yes—
99D107—41no—
100D107—46no—
101#3549—1071nomaximal, Sylow
102C107#354911yescharacteristic, complemented, Sylow
103H(3,𝔽4)—1073no—
104H(3,𝔽4)D10711yescharacteristic, complemented
105#555—1076no—
106D42—1076no—
107#535—1076no—
108#535—1076no—
109#532—1073no—
110C2×#41—1073no—
111C2×#41—1073no—
112C22×D4—1076no—
113C22×D4—1076no—
114C4⋊Q8—1073no—
115#127—1073no—
116#127—1076no—
117#127—1072no—
118#124—1076no—
119#124—10712no—
120#124—1073no—
121#124C2×D10713yescomplemented
122#124C2×D10716yescomplemented
123#121—10712no—
124#121—10712no—
125#121—10712no—
126#120—1072no—
127#120—1076no—
128#120—1076no—
129#120—10712no—
130#120C2×D10716yescomplemented
131C4×D4—10712no—
132#117—1076no—
133#117—1076no—
134C2×C42—1071no—
135C24—1076no—
136C24C22×D10712yes—
137#41—4286no—
138#41—4286no—
139C2×Q8—1073no—
140C2×Q8C22×D10713yes—
141C2×D4—10712no—
142C2×D4—1076no—
143C2×D4—10712no—
144C2×D4—1073no—
145C2×D4—1076no—
146C2×D4—1076no—
147C2×D4—42812no—
148C2×D4—42812no—
149C2×D4C22×D10713yes—
150C2×D4C22×D10716yes—
151C22×C4—1076no—
152C22×C4—1073no—
153C22×C4—1076no—
154C4⋊C4—10712no—
155C22⋊C4—1076no—
156C22⋊C4—10712no—
157C22⋊C4—10712no—
158C22⋊C4C22×D10716yes—
159C22⋊C4C22×D107112yes—
160C42—1073no—
161C42—1076no—
162C42C22×D10711yescharacteristic
163C42C22×D10712yes—
164C23—46no—
165C23—1076no—
166C23—1071no—
167C23—4286no—
168C23—42812no—
169C23C23×D10716yes—
170Q8—43no—
171Q8—4283no—
172D4—46no—
173D4—43no—
174D4—4286no—
175D4—4286no—
176D4—4283no—
177D4—42812no—
178D4—4286no—
179D4—21424no—
180C2×C4—1073no—
181C2×C4—1076no—
182C2×C4—21412no—
183C2×C4—2146no—
184C2×C4—21412no—
185C2×C4C23×D10713yes—
186C2×C4C23×D10716yes—
187C22—26no—
188C22—212no—
189C22—84no—
190C22—85612no—
191C22—2143no—
192C22—2146no—
193C22—21412no—
194C22C24×D10711yescharacteristic
195C4—26no—
196C4—23no—
197C4—1076no—
198C4—2146no—
199C2—46no—
200C2—4286no—
201C2—4281no—
202C2H(5,𝔽2)×D10713yes—
subgroupG/H
center, FrattiniC22C24×D107
commutator, socle, cosocleC22×C107C25
FittingH(3,𝔽4)×C107C2
hypercenterH(3,𝔽4)D107
hypocenterC107#3549
LCSG ▷ C22×C107 ▷ C107
UCSC1 ◁ C22 ◁ H(3,𝔽4)

Complements

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

NH ≅ G/Ntype
1. #20293369C2semidirect
2. #20293339C2semidirect
3. #20293259C2semidirect
4. #20293195C2semidirect
5. #20293192C2semidirect
6. #20293176C2semidirect
7. H(3,𝔽4)×C107C2semidirect
8. C2×#13133819C22semidirect
9. C2×#13133817C22semidirect
10. C22×C22⋊D107C22semidirect
11. C2×D4×D107C22semidirect
12. #16812107C22semidirect
13. #16812106C22semidirect
15. #16812105C22semidirect
16. #16812098C22semidirect
17. #16812097C22semidirect
18. #16812095C22semidirect
19. #16812082C22semidirect
20. #16812082C22semidirect
21. #16812081C22semidirect
22. #16812079C22semidirect
23. #16812079C22semidirect
24. #16812078C22semidirect
25. #16812077C22semidirect
26. (C22⋊D107)⋊C4C22semidirect
27. #16812066C22semidirect
28. #16812065C22semidirect
29. C42×D107C22semidirect
30. #124×C107C22semidirect
31. #124×C107C22semidirect
32. #120×C107C22semidirect
102. C107#3549semidirect
104. H(3,𝔽4)D107semidirect
121. #124C2×D107semidirect
122. #124C2×D107semidirect
130. #120C2×D107semidirect

Maximal subgroups

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

subgroupindex
#202933692
#202933392
#202932592
#202931952
#202931922
#202931762
H(3,𝔽4)×C1072
#3549107