Finite Group Databasebeta

← #21444948

Subgroups — #21444948

Order 7808.

256 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 57 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#16840434C211yesmaximal, characteristic
2#16840135C211yesmaximal, characteristic, complemented
3#16840057C211yesmaximal, characteristic, complemented
4#16840053C211yesmaximal, characteristic, complemented
5#16839505C211yesmaximal, characteristic, complemented
6#16839491C211yesmaximal, characteristic, complemented
7C61×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×#11758226—21no—
9C2×#11758190—22no—
10#14519777C2211yescharacteristic
11#14519774—21no—
12#14519774C2211yescharacteristic
13#14519752—22no—
14#14519752—21no—
15C4×D244—21no—
16C4×D244C2211yescharacteristic
17#14519710—21no—
18#14519709—21no—
19C4⋊#92418C2211yescharacteristic
20#14519701—21no—
21#14519699—21no—
22C4×Q8×C61C2211yescharacteristic
23C4⋊C8×C61C2211yescharacteristic
24C4×C8×C61C2211yescharacteristic
25C2×Q8×C61D411yescharacteristic
26#11758226—42no—
27#11758226—42no—
28C2×D244—22no—
29C2×D244—21no—
30C2×D244—21no—
31C2×D244—22no—
32C2×D244D411yescharacteristic
33C2×D244D412yes—
34C2×C4×D61—22no—
35C2×C4×D61—21no—
36C2×Dic122—21no—
37C2×C8×C61—21no—
38C2×C8×C61—21no—
39C4⋊C4×C61—21no—
40C4⋊C4×C61D411yescharacteristic
41C42×C61—21no—
42C42×C61C2311yescharacteristic
43#11758198—22no—
44#11758198—21no—
45C4⋊Dic61—21no—
46C4⋊Dic61—21no—
47C4⋊Dic61D411yescharacteristic
48C2×#92418—21no—
49#11758190—44no—
50C22×D61—21no—
51C22×D61—22no—
52Q8×C61—21no—
53Q8×C61SD1612yescomplemented
54C2×C4×C61—21no—
55C2×C4×C61—21no—
56C2×C4×C61C2×D411yescharacteristic
57C2×C4×C61C2×D411yescharacteristic
58C2×C4×C61C2×D411yescharacteristic
59C2×Dic61—21no—
60C2×Dic61—41no—
61D244—21no—
62D244—21no—
63D244—42no—
64D244—44no—
65D244—41no—
66D244—41no—
67D244—41no—
68D244—41no—
69D244—82no—
70C4×D61—44no—
71C4×D61—41no—
72C4×D61—41no—
73Dic122—42no—
74C8×C61—22no—
75C8×C61—41no—
76#92418—41no—
77C22×C61#12011yescharacteristic
78C2×D61—42no—
79C2×D61—41no—
80C2×D61—41no—
81C2×D61—42no—
82C2×D61—42no—
83C2×D61—41no—
84C4×C61—22no—
85C4×C61—21no—
86C4×C61—41no—
87C4×C61C2×SD1611yescharacteristic
88C4×C61#13511yescharacteristic
89C4×C61AGL(1,ℤ/8)11yescharacteristic
90C4×C61#13711yescharacteristic
91Dic61—41no—
92Dic61—81no—
93#1631—611nomaximal, Sylow
94C2×C61#45011yescharacteristic
95C2×C61#45211yescharacteristic
96C2×C61#45311yescharacteristic
97D61—81no—
98D61—82no—
99#550—611no—
100#492—611no—
101#477—611no—
102#476—611no—
103#331—611no—
104Q8⋊C8D6111yescharacteristic, complemented
105D4⋊C8—611no—
106C61#163111yescharacteristic, complemented, Sylow
107C2×#41—1221no—
108C2×SD16—1222no—
109C4⋊Q8—611no—
110#127—611no—
111#127—1221no—
112#121—1222no—
113#121—1221no—
114C4×Q8C2×D6111yescharacteristic
115C4×D4—611no—
116C4×D4—1221no—
117#107—1221no—
118#106—1221no—
119C4⋊C8—611no—
120C4⋊C8C2×D6111yescharacteristic
121#103—1221no—
122#102—1221no—
123C4×C8C2×D6111yescharacteristic
124#41—2442no—
125#41—2442no—
126C2×Q8—1221no—
127C2×Q8D24411yescharacteristic
128C2×D4—611no—
129C2×D4—612no—
130C2×D4—1222no—
131C2×D4—1222no—
132C2×D4—1221no—
133C2×D4—1221no—
134C22×C4—1222no—
135C22×C4—1221no—
136SD16—2444no—
137C2×C8—21no—
138C2×C8—21no—
139C2×C8—1221no—
140C4⋊C4—21no—
141C4⋊C4—611no—
142C4⋊C4—1221no—
143C4⋊C4—1221no—
144C4⋊C4D24411yescharacteristic
145C22⋊C4—1222no—
146C22⋊C4—1221no—
147C42—21no—
148C42C22×D6111yescharacteristic
149C23—1221no—
150C23—1222no—
151Q8—21no—
152Q8—2442no—
153Q8#1175819012yescomplemented
154D4—1221no—
155D4—1221no—
156D4—4882no—
157D4—2442no—
158D4—2444no—
159D4—2441no—
160D4—2441no—
161D4—2441no—
162D4—2441no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—1221no—
166C2×C4—2444no—
167C2×C4—2441no—
168C2×C4—2441no—
169C2×C4—2441no—
170C2×C4C2×D24411yescharacteristic
171C2×C4D4×D6111yescharacteristic
172C2×C4D4×D6111yescharacteristic
173C8—22no—
174C8—41no—
175C8—2441no—
176C22—2442no—
177C22—2441no—
178C22—2441no—
179C22—2442no—
180C22—2441no—
181C22—2442no—
182C22#1451974711yescharacteristic
183C4—22no—
184C4—21no—
185C4—41no—
186C4—4881no—
187C4—2441no—
188C4C2×#1175819011yescharacteristic
189C4#1451979811yescharacteristic
190C4#1451980511yescharacteristic
191C4#1451980911yescharacteristic
192C2—4881no—
193C2—4882no—
194C2#1683991511yescharacteristic
195C2#1683992711yescharacteristic
196C2#1683993111yescharacteristic
subgroupG/H
centerC22#14519747
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×Q8⋊C8C2
socleC22×C61#120
hypercenterQ8⋊C8D61
hypocenterC61#1631
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
2. #16840135C2semidirect
3. #16840057C2semidirect
4. #16840053C2semidirect
5. #16839505C2semidirect
6. #16839491C2semidirect
7. C61×Q8⋊C8C2semidirect
53. Q8×C61SD16semidirect
104. Q8⋊C8D61semidirect
106. C61#1631semidirect
153. Q8#11758190semidirect