Finite Group Databasebeta

← #28350601

Subgroups — #28350601

Order 13696.

1058 conjugacy classes of subgroups; only the 451 normal subgroups are shown.

normal subgroups only

This group has 1058 conjugacy classes of subgroups — too many to draw. Only its 451 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#20293377C213yesmaximal, complemented
2#20293371C216yesmaximal, complemented
3#20293366C216yesmaximal, complemented
4#20293176C213yesmaximal, complemented
5#20293156C216yesmaximal, complemented
6#20293133C216yesmaximal, complemented
7H(3,𝔽4)×C107C211yesmaximal, characteristic, complemented
8C2×#13133819C2211yescharacteristic, complemented
9C2×#13133817C2213yes—
10C23×Dic107C2212yescomplemented
11#16812107C2213yescomplemented
12#16812105C2213yes—
13#16812102C22112yescomplemented
14#16812101C2216yescomplemented
15#16812097C2213yescomplemented
16#16812093C2216yescomplemented
17#16812091C22112yescomplemented
18#16812090C2216yes—
19#16812086C22112yescomplemented
20#16812085C2216yescomplemented
21#16812082C22112yescomplemented
22#16812081C22112yes—
23#16812080C2216yes—
24#16812078C2216yescomplemented
25Q8×Dic107C2212yescomplemented
26D4×Dic107C2216yes—
27(C22⋊D107)⋊C4C22112yescomplemented
28#16812065C2216yescomplemented
29C42×D107C2213yescomplemented
30#124×C107C2213yes—
31#124×C107C2216yes—
32#120×C107C2216yes—
33#13133819—42no—
34#13133817—46no—
35C2×Dic214C2313yes—
36C2×D428C2313yes—
37C2×C22⋊D107C23112yes—
38C2×C22⋊D107C2316yes—
39C22×Dic107—44no—
40C22×Dic107C2316yes—
41C22×Dic107C2316yes—
42C2×C4×D107C2313yes—
43C2×C4×D107C2316yes—
44C4⋊Dic107C2316yes—
45C4⋊Dic107C2316yes—
46Dic107⋊C4C23112yes—
47Dic107⋊C4C23112yes—
48C22⋊Dic107C2316yes—
49C22⋊Dic107C23112yes—
50(C2×D107)⋊C4C23112yes—
51C4×Dic107C2316yes—
52C4×Dic107C2313yes—
53C24×C107C2312yes—
54C2×Q8×C107C2312yes—
55C2×Q8×C107C2311yescharacteristic
56C2×D4×C107C2316yes—
57C2×D4×C107C2313yes—
58C22⋊C4×C107C2316yes—
59C22⋊C4×C107C23112yes—
60C42×C107C2313yes—
61C23×C107—44no—
62C23×C107—42no—
63C23×C107C2416yes—
64C22×D107C2413yes—
65Q8×C107—42no—
66Q8×C107—41no—
67D4×C107—46no—
68D4×C107—43no—
69C2×C4×C107C2416yes—
70C2×C4×C107C2413yes—
71C22⋊D107—412no—
72C22⋊D107—46no—
73C2×Dic107—212no—
74C2×Dic107—46no—
75C2×Dic107C2416yes—
76C2×Dic107C2416yes—
77C2×Dic107C2411yescharacteristic
78D428—43no—
79C4×D107—26no—
80C4×D107—46no—
81Dic214—43no—
82C22×C107—26no—
83C22×C107—212no—
84C22×C107—48no—
85C22×C107C2511yescharacteristic
86C2×D107—23no—
87C2×D107—26no—
88C4×C107—23no—
89C4×C107—26no—
90Dic107—26no—
91Dic107—26no—
92Dic107H(5,𝔽2)12yes—
93C2×C107—46no—
94C2×C107C2×H(5,𝔽2)11yescharacteristic
95C2×C107#58512yes—
96D107—43no—
97#3529—1071nomaximal, Sylow
98C107#352911yescharacteristic, complemented, Sylow
99#563—1073no—
100#562—1076no—
101H(3,𝔽4)D10711yescharacteristic, complemented
102#560—1076no—
103#532—1073no—
104#529—1076no—
105#525—1076no—
106C2×#41—1071no—
107C2×#41—1073no—
108C23×C4—1072no—
109C4⋊Q8—1073no—
110#127—1073no—
111#126—10712no—
112#125—1076no—
113#124—1073no—
114#124C2×D10716yes—
115#124C2×D10713yes—
116#123—1076no—
117#123—1076no—
118#123—10712no—
119C22⋊Q8—1076no—
120C22⋊Q8—10712no—
121#121—10712no—
122#121—1076no—
123#121—10712no—
124#120—1076no—
125#120C2×D10716yes—
126C4×Q8—1072no—
127C4×D4—1076no—
128C4×D4—10712no—
129#117—1076no—
130C2×C42—1073no—
131C24C22×D10712yes—
132#41—4286no—
133#41—4282no—
134C2×Q8—1073no—
135C2×Q8C22×D10712yes—
136C2×Q8C22×D10711yescharacteristic
137C2×D4—10712no—
138C2×D4—1076no—
139C2×D4—1073no—
140C2×D4C22×D10716yes—
141C2×D4C22×D10713yes—
142C22×C4—1076no—
143C22×C4—1076no—
144C22×C4—1076no—
145C22×C4—1073no—
146C22×C4—4284no—
147C4⋊C4—10712no—
148C4⋊C4—10712no—
149C4⋊C4—1076no—
150C4⋊C4—1076no—
151C22⋊C4—1076no—
152C22⋊C4—10712no—
153C22⋊C4—10712no—
154C22⋊C4C22×D10716yes—
155C22⋊C4C22×D107112yes—
156C42—1076no—
157C42—1073no—
158C42C22×D10713yes—
159C23—42no—
160C23—44no—
161C23—1073no—
162C23C23×D10716yes—
163Q8—41no—
164Q8—42no—
165Q8—4283no—
166D4—43no—
167D4—46no—
168D4—4283no—
169D4—4286no—
170D4—42812no—
171C2×C4—1071no—
172C2×C4—1076no—
173C2×C4—1076no—
174C2×C4—4286no—
175C2×C4—4286no—
176C2×C4—2146no—
177C2×C4—21412no—
178C2×C4C23×D10716yes—
179C2×C4C23×D10713yes—
180C22—26no—
181C22—212no—
182C22—48no—
183C22—2143no—
184C22—2146no—
185C22C24×D10711yescharacteristic
186C4—23no—
187C4—26no—
188C4—1072no—
189C4—2146no—
190C4—2146no—
191C2—46no—
192C2—4283no—
193C2H(5,𝔽2)×D10711yescharacteristic
194C2#2029346212yes—
subgroupG/H
center, FrattiniC22C24×D107
commutator, socle, cosocleC22×C107C25
FittingH(3,𝔽4)×C107C2
hypercenterH(3,𝔽4)D107
hypocenterC107#3529
LCSG ▷ C22×C107 ▷ C107
UCSC1 ◁ C22 ◁ H(3,𝔽4)

Complements

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

NH ≅ G/Ntype
1. #20293377C2semidirect
2. #20293371C2semidirect
3. #20293366C2semidirect
4. #20293176C2semidirect
5. #20293156C2semidirect
6. #20293133C2semidirect
7. H(3,𝔽4)×C107C2semidirect
8. C2×#13133819C22semidirect
10. C23×Dic107C22semidirect
11. #16812107C22semidirect
13. #16812102C22semidirect
14. #16812101C22semidirect
15. #16812097C22semidirect
16. #16812093C22semidirect
17. #16812091C22semidirect
19. #16812086C22semidirect
20. #16812085C22semidirect
21. #16812082C22semidirect
24. #16812078C22semidirect
25. Q8×Dic107C22semidirect
27. (C22⋊D107)⋊C4C22semidirect
28. #16812065C22semidirect
29. C42×D107C22semidirect
98. C107#3529semidirect
101. H(3,𝔽4)D107semidirect

Maximal subgroups

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

subgroupindex
#202933772
#202933712
#202933662
#202931762
#202931562
#202931332
H(3,𝔽4)×C1072
#3529107