Finite Group Databasebeta

← #21444944

Subgroups — #21444944

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#16840136C211yesmaximal, characteristic, complemented
3#16840049C211yesmaximal, characteristic, complemented
4#16839505C211yesmaximal, characteristic, complemented
5Q8⋊#92418C211yesmaximal, characteristic, complemented
6#16839489C211yesmaximal, characteristic, complemented
7C61×#477C211yesmaximal, characteristic, complemented
8C2×#11758226—21no—
9C2×#11758201—22no—
10#14519774—21no—
11#14519774C2211yescharacteristic
12#14519752—22no—
13#14519752—21no—
14C4×D244—21no—
15C4×D244C2211yescharacteristic
16#14519708—21no—
17C4⋊#92418C2211yescharacteristic
18#14519697—21no—
19C4×#92418C2211yescharacteristic
20C4⋊Q8×C61C2211yescharacteristic
21C4×Q8×C61C2211yescharacteristic
22#107×C61—21no—
23C4⋊C8×C61C2211yescharacteristic
24#103×C61—21no—
25C2×Q8×C61—21no—
26C2×Q8×C61D411yescharacteristic
27#11758226—42no—
28#11758226—42no—
29C2×D244—22no—
30C2×D244—21no—
31C2×D244—21no—
32C2×D244—22no—
33C2×D244D411yescharacteristic
34C2×D244D412yes—
35C2×C4×D61—22no—
36C2×C4×D61—21no—
37C2×C8×C61—21no—
38C4⋊C4×C61—21no—
39C4⋊C4×C61—21no—
40C4⋊C4×C61—21no—
41C4⋊C4×C61D411yescharacteristic
42C42×C61—21no—
43C42×C61C2311yescharacteristic
44#11758201—44no—
45#11758198—22no—
46#11758198—21no—
47C4⋊Dic61D411yescharacteristic
48C2×#92418—21no—
49C2×#92418—21no—
50C22×D61—21no—
51C22×D61—22no—
52Q8×C61—21no—
53Q8×C61—42no—
54Q8×C61SD1612yescomplemented
55C2×C4×C61—21no—
56C2×C4×C61—21no—
57C2×C4×C61—41no—
58C2×C4×C61C2×D411yescharacteristic
59C2×C4×C61C2×D411yescharacteristic
60C2×C4×C61C2×D411yescharacteristic
61C2×Dic61—21no—
62D244—21no—
63D244—21no—
64D244—42no—
65D244—44no—
66D244—41no—
67D244—41no—
68D244—41no—
69D244—41no—
70D244—82no—
71C4×D61—44no—
72C4×D61—41no—
73C4×D61—41no—
74C8×C61—41no—
75#92418—22no—
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×C61—81no—
88C4×C61C2×SD1611yescharacteristic
89C4×C61#13511yescharacteristic
90C4×C61AGL(1,ℤ/8)11yescharacteristic
91C4×C61#13711yescharacteristic
92Dic61—41no—
93#1631—611nomaximal, Sylow
94C2×C61#45011yescharacteristic
95C2×C61#45211yescharacteristic
96C2×C61#45311yescharacteristic
97D61—81no—
98D61—82no—
99#550—611no—
100#492—611no—
101#477D6111yescharacteristic, complemented
102#476—611no—
103#331—611no—
104Q8⋊C8—611no—
105D4⋊C8—611no—
106C61#163111yescharacteristic, complemented, Sylow
107C2×#41—1221no—
108C2×SD16—1222no—
109C4⋊Q8C2×D6111yescharacteristic
110#127—611no—
111#127—1221no—
112#121—1222no—
113#121—1221no—
114C4×Q8C2×D6111yescharacteristic
115C4×D4—611no—
116C4×D4—1221no—
117#107—21no—
118#106—1221no—
119C4⋊C8—611no—
120C4⋊C8C2×D6111yescharacteristic
121#103—21no—
122#102—1221no—
123C4×C8—611no—
124#41—2442no—
125#41—2442no—
126C2×Q8—21no—
127C2×Q8C22⋊D6111yescharacteristic
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—1221no—
139C2×C8—1221no—
140C4⋊C4—21no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—611no—
144C4⋊C4C22⋊D6111yescharacteristic
145C22⋊C4—1222no—
146C22⋊C4—1221no—
147C42—21no—
148C42C22×D6111yescharacteristic
149C23—1221no—
150C23—1222no—
151Q8—21no—
152Q8—42no—
153Q8#1175820112yescomplemented
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—41no—
166C2×C4—1221no—
167C2×C4—2444no—
168C2×C4—2441no—
169C2×C4—2441no—
170C2×C4D4×D6111yescharacteristic
171C2×C4D4×D6111yescharacteristic
172C2×C4C2×C22⋊D6111yescharacteristic
173C8—41no—
174C8—1222no—
175C8—2441no—
176C22—2442no—
177C22—2441no—
178C22—2441no—
179C22—2442no—
180C22—2441no—
181C22—2442no—
182C22#1451974511yescharacteristic
183C4—22no—
184C4—21no—
185C4—41no—
186C4—81no—
187C4—2441no—
188C4C2×#1175820111yescharacteristic
189C4#1451980011yescharacteristic
190C4#1451980211yescharacteristic
191C4#1451980911yescharacteristic
192C2—4881no—
193C2—4882no—
194C2#1683991211yescharacteristic
195C2#1683992311yescharacteristic
196C2#1683992811yescharacteristic
subgroupG/H
centerC22#14519745
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×#477C2
socleC22×C61#120
hypercenter#477D61
hypocenterC61#1631
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
2. #16840136C2semidirect
3. #16840049C2semidirect
4. #16839505C2semidirect
5. Q8⋊#92418C2semidirect
6. #16839489C2semidirect
7. C61×#477C2semidirect
54. Q8×C61SD16semidirect
101. #477D61semidirect
106. C61#1631semidirect
153. Q8#11758201semidirect