Finite Group Databasebeta

← #21445031

Subgroups — #21445031

Order 7808.

208 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 55 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#16840472C211yesmaximal, characteristic
2#16840114C211yesmaximal, characteristic, complemented
3#16840039C211yesmaximal, characteristic
4#16839510C211yesmaximal, characteristic, complemented
5Q8⋊#92418C211yesmaximal, characteristic, complemented
6#16839489C211yesmaximal, characteristic
7C61×#462C211yesmaximal, characteristic, complemented
8#14519777C2211yescharacteristic
9#14519769—21no—
10#14519755—22no—
11#14519753—21no—
12C4×D244—21no—
13C4×D244C2211yescharacteristic
14C4⋊C4×D61—21no—
15#14519710—21no—
16C4⋊#92418C2211yescharacteristic
17#14519700—22no—
18#14519697—21no—
19C4×#92418C2211yescharacteristic
20C2×Q16×C61—21no—
21C4⋊Q8×C61C2211yescharacteristic
22C4×Q8×C61C2211yescharacteristic
23C4⋊C8×C61C2211yescharacteristic
24#103×C61—21no—
25C2×Q8×C61—21no—
26C2×Q8×C61D411yescharacteristic
27C2×D244D411yescharacteristic
28C2×C4×D61—21no—
29C2×C4×D61—22no—
30C2×Dic122D412yes—
31Q16×C61—42no—
32C2×C8×C61—21no—
33C4⋊C4×C61—21no—
34C4⋊C4×C61—21no—
35C4⋊C4×C61—21no—
36C4⋊C4×C61D411yescharacteristic
37C42×C61—21no—
38C42×C61C2311yescharacteristic
39#11758198—22no—
40#11758198—21no—
41C4⋊Dic61—21no—
42C4⋊Dic61—21no—
43C4⋊Dic61D411yescharacteristic
44#11758196—22no—
45#11758196—22no—
46C2×#92418—21no—
47C2×#92418—21no—
48C22×D61—21no—
49Q8×C61—21no—
50Q8×C61—21no—
51Q8×C61—41no—
52Q8×C61—41no—
53C2×C4×C61—21no—
54C2×C4×C61—21no—
55C2×C4×C61—41no—
56C2×C4×C61C2×D411yescharacteristic
57C2×C4×C61C2×D411yescharacteristic
58C2×C4×C61C2×D411yescharacteristic
59C2×Dic61—21no—
60C2×Dic61—22no—
61D244—21no—
62D244Q1612yescomplemented
63C4×D61—41no—
64C4×D61—41no—
65C4×D61—82no—
66Dic122—42no—
67C8×C61—41no—
68#92418—41no—
69#92418—41no—
70C22×C61#12011yescharacteristic
71C2×D61—22no—
72C2×D61—41no—
73C2×D61—41no—
74C4×C61—21no—
75C4×C61—41no—
76C4×C61—41no—
77C4×C61—81no—
78C4×C61C2×Q1611yescharacteristic
79C4×C61#13511yescharacteristic
80C4×C61AGL(1,ℤ/8)11yescharacteristic
81C4×C61#13711yescharacteristic
82Dic61—41no—
83Dic61—42no—
84#1644—611nomaximal, Sylow
85C2×C61#44911yescharacteristic
86C2×C61#45111yescharacteristic
87C2×C61#45511yescharacteristic
88D61—42no—
89#554—611no—
90#487—611no—
91#474—611no—
92#462D6111yescharacteristic, complemented
93#333—611no—
94Q8⋊C8—611no—
95D4⋊C8—611no—
96C61#164411yescharacteristic, complemented, Sylow
97C2×Q16—21no—
98C4⋊Q8—611no—
99C4⋊Q8C2×D6111yescharacteristic
100#125—1221no—
101C22⋊Q8—1222no—
102C22⋊Q8—1221no—
103C4×Q8C2×D6111yescharacteristic
104C4×D4—611no—
105C4×D4—1221no—
106C2×C4⋊C4—1221no—
107#107—1221no—
108C4⋊C8—611no—
109C4⋊C8C2×D6111yescharacteristic
110#103—21no—
111#103—1222no—
112#102—1221no—
113C4×C8—611no—
114C2×Q8—21no—
115C2×Q8—612no—
116C2×Q8C22⋊D6111yescharacteristic
117C2×D4—611no—
118C22×C4—1222no—
119C22×C4—1221no—
120Q16—42no—
121C2×C8—21no—
122C2×C8—1221no—
123C2×C8—1221no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—611no—
128C4⋊C4—1222no—
129C4⋊C4—1222no—
130C4⋊C4—1221no—
131C4⋊C4—1221no—
132C4⋊C4C22⋊D6111yescharacteristic
133C22⋊C4—1222no—
134C22⋊C4—1221no—
135C42—21no—
136C42C22×D6111yescharacteristic
137C23—1221no—
138Q8—21no—
139Q8—21no—
140Q8—41no—
141Q8—41no—
142Q8—2442no—
143D4—612no—
144D4—1221no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—41no—
148C2×C4—1221no—
149C2×C4—1222no—
150C2×C4—4882no—
151C2×C4—2441no—
152C2×C4—2441no—
153C2×C4D4×D6111yescharacteristic
154C2×C4D4×D6111yescharacteristic
155C2×C4C2×C22⋊D6111yescharacteristic
156C8—41no—
157C8—2441no—
158C8—2441no—
159C22—1222no—
160C22—2441no—
161C22—2441no—
162C22#1451974511yescharacteristic
163C4—21no—
164C4—41no—
165C4—41no—
166C4—81no—
167C4—2442no—
168C4—2441no—
169C4Q16×D6111yescharacteristic
170C4#1451979711yescharacteristic
171C4#1451980311yescharacteristic
172C4#1451980911yescharacteristic
173C2—2442no—
174C2#1683990511yescharacteristic
175C2#1683991611yescharacteristic
176C2#1683993811yescharacteristic
subgroupG/H
centerC22#14519745
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×#462C2
socleC22×C61#120
hypercenter#462D61
hypocenterC61#1644
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
2. #16840114C2semidirect
4. #16839510C2semidirect
5. Q8⋊#92418C2semidirect
7. C61×#462C2semidirect
62. D244Q16semidirect
92. #462D61semidirect
96. C61#1644semidirect