Finite Group Databasebeta

← #20295832

Subgroups — #20295832

Order 6976.

258 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 99 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#16812747C211yesmaximal, characteristic, complemented
2#16812744C211yesmaximal, characteristic, complemented
3#16812730C211yesmaximal, characteristic, complemented
4#16812728C212yesmaximal, complemented
5#16812726C212yesmaximal, complemented
6#16812725C211yesmaximal, characteristic, complemented
7#16812721C211yesmaximal, characteristic, complemented
8#16812720C212yesmaximal, complemented
9SD16×D109C212yesmaximal, complemented
10#16812705C211yesmaximal, characteristic, complemented
11C2×SD16×C109C211yesmaximal, characteristic, complemented
12#13182030—21no—
13#13182030C2212yescomplemented
14#13182029—22no—
15#13182029C2211yescharacteristic
16#13182029C2211yescharacteristic
17#13182029C2211yescharacteristic, complemented
18#13182028—21no—
19#13182028C2212yes—
20Q8×D109—21no—
21Q8×D109C2212yescomplemented
22C2×C22⋊D109—22no—
23D4×D109—21no—
24D4×D109C2212yes—
25Dic436C2211yescharacteristic, complemented
26#13182019C2212yescomplemented
27#13182018C2211yescharacteristic, complemented
28#13182018C2211yescharacteristic, complemented
29#13182017C2212yescomplemented
30#13182016C2212yescomplemented
31D872C2211yescharacteristic, complemented
32#13182014C2212yescomplemented
33#13182013C2211yescharacteristic, complemented
34#13182012C2212yescomplemented
35C8×D109C2212yescomplemented
36C2×Q8×C109C2211yescharacteristic, complemented
37C2×D4×C109C2211yescharacteristic
38SD16×C109C2212yescomplemented
39SD16×C109C2212yescomplemented
40C2×C8×C109C2211yescharacteristic, complemented
41C23×C109—21no—
42C22×D109—22no—
43Q8×C109—21no—
44Q8×C109C2312yes—
45D4×C109—21no—
46D4×C109C2312yes—
47C2×C4×C109—21no—
48C2×C4×C109C2311yescharacteristic
49C22⋊D109—21no—
50C22⋊D109—21no—
51C22⋊D109—22no—
52C22⋊D109—22no—
53C22⋊D109D412yes—
54C2×Dic109—22no—
55D436—22no—
56D436D411yescharacteristic
57D436C2311yescharacteristic
58D436C2311yescharacteristic
59C4×D109—22no—
60C4×D109—21no—
61C4×D109—21no—
62C4×D109—22no—
63C4×D109C2312yes—
64Dic218—22no—
65Dic218D411yescharacteristic
66Dic218C2311yescharacteristic
67Dic218C2311yescharacteristic
68C8×C109C2311yescharacteristic
69C8×C109C2311yescharacteristic
70#11724784C2312yes—
71C22×C109—22no—
72C22×C109—81no—
73C22×C109C2×D411yescharacteristic
74C2×D109—21no—
75C2×D109—21no—
76C2×D109—82no—
77C2×D109C2×D412yes—
78C4×C109—22no—
79C4×C109C2×D411yescharacteristic
80C4×C109C2411yescharacteristic
81Dic109—21no—
82Dic109—21no—
83Dic109C2×D412yes—
84C2×C109—21no—
85C2×C109—42no—
86C2×C109C22×D411yescharacteristic
87D109—22no—
88D109—41no—
89D109—41no—
90C109#57711yescharacteristic, complemented, Sylow
91#577—1091nomaximal, Sylow
922−1+4—1091no—
93H(5,𝔽2)—1091no—
94#137—1091no—
95#137—1092no—
96AGL(1,ℤ/8)—1091no—
97AGL(1,ℤ/8)—1092no—
98#135—1092no—
99#135—1091no—
100C2×SD16—1092no—
101C2×SD16D10911yescharacteristic, complemented
102#131—1091no—
103#41—1091no—
104#41—1092no—
105#41—1092no—
106#41—1091no—
107#41—1091no—
108#41—2182no—
109#41—2181no—
110#41—2181no—
111C2×Q8—1092no—
112C2×Q8—2181no—
113C2×Q8C2×D10911yescharacteristic, complemented
114C2×D4—1092no—
115C2×D4—2181no—
116C2×D4—2182no—
117C2×D4C2×D10911yescharacteristic
118Q16—1092no—
119Q16—1091no—
120SD16—1092no—
121SD16—1092no—
122SD16—1091no—
123SD16—1091no—
124SD16C2×D10912yescomplemented
125SD16C2×D10912yescomplemented
126D8—1092no—
127D8—1091no—
128M16—1091no—
129M16—1092no—
130C2×C8—1092no—
131C2×C8C2×D10911yescharacteristic, complemented
132C23—21no—
133C23—2182no—
134Q8—21no—
135Q8—1091no—
136Q8—1091no—
137Q8—1091no—
138Q8—2182no—
139Q8C22×D10912yes—
140D4—21no—
141D4—1092no—
142D4—1091no—
143D4—1091no—
144D4—1091no—
145D4—2182no—
146D4—2182no—
147D4—2182no—
148D4—2181no—
149D4—2181no—
150D4C22×D10912yes—
151C2×C4—21no—
152C2×C4—1092no—
153C2×C4—2182no—
154C2×C4—2182no—
155C2×C4—2182no—
156C2×C4—2181no—
157C2×C4—2181no—
158C2×C4C22×D10911yescharacteristic
159C8—1092no—
160C8C22×D10911yescharacteristic
161C8C22×D10911yescharacteristic
162C22—22no—
163C22—81no—
164C22—8722no—
165C22—1092no—
166C22—2181no—
167C22—2181no—
168C22D4×D10911yescharacteristic
169C4—22no—
170C4—1092no—
171C4—2181no—
172C4—2181no—
173C4D4×D10911yescharacteristic
174C4C23×D10911yescharacteristic
175C2—21no—
176C2—42no—
177C2—4361no—
178C2—4361no—
179C2—2182no—
180C2C2×D4×D10911yescharacteristic
subgroupG/H
centerC2C2×D4×D109
commutatorC4×C109C24
FrattiniC4C23×D109
FittingC2×SD16×C109C2
socleC2×C109C22×D4
hypercenterC2×SD16D109
hypocenterC109#577
LCSG ▷ C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. #16812747C2semidirect
2. #16812744C2semidirect
3. #16812730C2semidirect
4. #16812728C2semidirect
5. #16812726C2semidirect
6. #16812725C2semidirect
7. #16812721C2semidirect
8. #16812720C2semidirect
9. SD16×D109C2semidirect
10. #16812705C2semidirect
11. C2×SD16×C109C2semidirect
13. #13182030C22semidirect
17. #13182029C22semidirect
21. Q8×D109C22semidirect
25. Dic436C22semidirect
26. #13182019C22semidirect
27. #13182018C22semidirect
28. #13182018C22semidirect
29. #13182017C22semidirect
30. #13182016C22semidirect
31. D872C22semidirect
32. #13182014C22semidirect
33. #13182013C22semidirect
34. #13182012C22semidirect
35. C8×D109C22semidirect
36. C2×Q8×C109C22semidirect
38. SD16×C109C22semidirect
39. SD16×C109C22semidirect
40. C2×C8×C109C22semidirect
90. C109#577semidirect
101. C2×SD16D109semidirect
113. C2×Q8C2×D109semidirect
124. SD16C2×D109semidirect
125. SD16C2×D109semidirect
131. C2×C8C2×D109semidirect