Finite Group Databasebeta

← #21444943

Subgroups — #21444943

Order 7808.

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

normal subgroups only

This group has 256 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#16840432C211yesmaximal, characteristic
2#16840054C211yesmaximal, characteristic, complemented
3#16840049C211yesmaximal, characteristic, complemented
4#16839506C211yesmaximal, characteristic, complemented
5#16839494C211yesmaximal, characteristic, complemented
6#16839491C211yesmaximal, characteristic, complemented
7C61×#492C211yesmaximal, characteristic, complemented
8C2×#11758224—21no—
9#14519773—21no—
10#14519749—22no—
11#14519748—21no—
12C4×Dic122C2211yescharacteristic
13C4×D244C2211yescharacteristic
14D4×Dic61—21no—
15#14519710—21no—
16#14519708—21no—
17C4⋊#92418C2211yescharacteristic
18C4⋊#92418C2211yescharacteristic
19#14519700—21no—
20#14519697—21no—
21C2×SD16×C61—22no—
22C4⋊Q8×C61C2211yescharacteristic
23#127×C61C2211yescharacteristic
24C4×C8×C61C2211yescharacteristic
25C2×Q8×C61—21no—
26C2×D4×C61—21no—
27C2×D4×C61—21no—
28C2×D4×C61D412yes—
29C2×C22⋊D61—22no—
30C2×C22⋊D61—22no—
31C22×Dic61—22no—
32#11758224—42no—
33#11758224—42no—
34C2×D244D411yescharacteristic
35C2×C4×D61—21no—
36C2×Dic122D411yescharacteristic
37SD16×C61—44no—
38C2×C8×C61—21no—
39C4⋊C4×C61—21no—
40C4⋊C4×C61—21no—
41C42×C61C2311yescharacteristic
42C22⋊Dic61—22no—
43#11758198—21no—
44C4⋊Dic61D411yescharacteristic
45C4⋊Dic61D411yescharacteristic
46#11758196—21no—
47C4×Dic61—21no—
48C2×#92418—21no—
49C2×#92418—21no—
50C23×C61—22no—
51C22×D61—21no—
52Q8×C61—42no—
53D4×C61—42no—
54D4×C61—41no—
55D4×C61—41no—
56D4×C61—41no—
57D4×C61—41no—
58C2×C4×C61—41no—
59C2×C4×C61C2×D411yescharacteristic
60C2×C4×C61C2×D411yescharacteristic
61C2×C4×C61C2×D411yescharacteristic
62C22⋊D61—44no—
63C22⋊D61—82no—
64C2×Dic61—21no—
65C2×Dic61—21no—
66C2×Dic61—21no—
67C2×Dic61—44no—
68D244—21no—
69D244—21no—
70C4×D61—41no—
71C4×D61—41no—
72Dic122—21no—
73Dic122SD1612yescomplemented
74C8×C61—22no—
75#92418—41no—
76#92418—41no—
77C22×C61—42no—
78C22×C61—42no—
79C22×C61—42no—
80C22×C61#12011yescharacteristic
81C2×D61—41no—
82C2×D61—41no—
83C2×D61—41no—
84C4×C61—21no—
85C4×C61—81no—
86C4×C61C2×SD1611yescharacteristic
87C4×C61#13511yescharacteristic
88C4×C61AGL(1,ℤ/8)11yescharacteristic
89C4×C61#13711yescharacteristic
90Dic61—22no—
91Dic61—41no—
92Dic61—41no—
93#1631—611nomaximal, Sylow
94C2×C61—82no—
95C2×C61#45011yescharacteristic
96C2×C61#45211yescharacteristic
97C2×C61#45311yescharacteristic
98D61—81no—
99#550—611no—
100#492D6111yescharacteristic, complemented
101#477—611no—
102#476—611no—
103#331—611no—
104Q8⋊C8—611no—
105D4⋊C8—611no—
106C61#163111yescharacteristic, complemented, Sylow
107C2×#41—1221no—
108C2×SD16—22no—
109C4⋊Q8C2×D6111yescharacteristic
110#127—1221no—
111#127C2×D6111yescharacteristic
112#121—1221no—
113#121—1222no—
114C4×Q8—611no—
115C4×D4—611no—
116C4×D4—1221no—
117#107—1221no—
118#106—1221no—
119C4⋊C8—611no—
120C4⋊C8—611no—
121#103—1221no—
122#102—1221no—
123C4×C8C2×D6111yescharacteristic
124#41—2442no—
125#41—2442no—
126C2×Q8—21no—
127C2×Q8—611no—
128C2×D4—21no—
129C2×D4—21no—
130C2×D4—611no—
131C2×D4—1222no—
132C2×D4—1222no—
133C2×D4C22⋊D6112yes—
134C22×C4—1222no—
135C22×C4—1221no—
136SD16—44no—
137C2×C8—21no—
138C2×C8—1221no—
139C2×C8—1221no—
140C4⋊C4—21no—
141C4⋊C4—21no—
142C4⋊C4—611no—
143C4⋊C4—611no—
144C4⋊C4—1221no—
145C22⋊C4—1222no—
146C22⋊C4—1221no—
147C42—1221no—
148C42C22×D6111yescharacteristic
149C23—22no—
150C23—1221no—
151Q8—42no—
152Q8—612no—
153Q8—1221no—
154D4—42no—
155D4—41no—
156D4—41no—
157D4—41no—
158D4—41no—
159D4—1221no—
160D4—1221no—
161D4—4882no—
162D4—2444no—
163C2×C4—41no—
164C2×C4—1221no—
165C2×C4—1221no—
166C2×C4—1221no—
167C2×C4—2444no—
168C2×C4—2441no—
169C2×C4—2441no—
170C2×C4D4×D6111yescharacteristic
171C2×C4D4×D6111yescharacteristic
172C2×C4C2×C22⋊D6111yescharacteristic
173C8—22no—
174C8—2441no—
175C8—2441no—
176C22—42no—
177C22—42no—
178C22—42no—
179C22—2441no—
180C22—2441no—
181C22—2441no—
182C22#1451974511yescharacteristic
183C4—21no—
184C4—81no—
185C4—1222no—
186C4—2441no—
187C4—2441no—
188C4SD16×D6111yescharacteristic
189C4#1451979811yescharacteristic
190C4#1451980411yescharacteristic
191C4#1451980611yescharacteristic
192C2—82no—
193C2—4881no—
194C2#1683991111yescharacteristic
195C2#1683992111yescharacteristic
196C2#1683992911yescharacteristic
subgroupG/H
centerC22#14519745
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×#492C2
socleC22×C61#120
hypercenter#492D61
hypocenterC61#1631
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
2. #16840054C2semidirect
3. #16840049C2semidirect
4. #16839506C2semidirect
5. #16839494C2semidirect
6. #16839491C2semidirect
7. C61×#492C2semidirect
73. Dic122SD16semidirect
100. #492D61semidirect
106. C61#1631semidirect