Finite Group Databasebeta

← #21445100

Subgroups — #21445100

Order 7808.

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

normal subgroups only

This group has 240 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#16840415C211yesmaximal, characteristic
2#16840039C211yesmaximal, characteristic, complemented
3#16839964C211yesmaximal, characteristic, complemented
4#16839508C211yesmaximal, characteristic, complemented
5#16839491C211yesmaximal, characteristic, complemented
6#16839491C211yesmaximal, characteristic, complemented
7C61×#498C211yesmaximal, characteristic, complemented
8C2×#11758226—21no—
9C2×#11758201—21no—
10#14519762—22no—
11#14519753—21no—
12#14519752—21no—
13C4×D244C2211yescharacteristic
14C4×D244C2211yescharacteristic
15C4⋊C4×D61—21no—
16#14519710—21no—
17C4⋊#92418C2211yescharacteristic
18C4⋊#92418C2211yescharacteristic
19#14519701—21no—
20#14519697—21no—
21C4⋊Q8×C61C2211yescharacteristic
22C4⋊Q8×C61C2211yescharacteristic
23#106×C61—22no—
24C4×C8×C61C2211yescharacteristic
25C2×Q8×C61—21no—
26C2×Q8×C61—21no—
27#11758226—42no—
28#11758226—42no—
29C2×D244—22no—
30C2×D244D411yescharacteristic
31C2×D244D411yescharacteristic
32C2×C4×D61—22no—
33C2×C4×D61—21no—
34C2×C4×D61—21no—
35C2×C8×C61—21no—
36C4⋊C4×C61—21no—
37C4⋊C4×C61—21no—
38C4⋊C4×C61—21no—
39C4⋊C4×C61D412yes—
40C42×C61C2311yescharacteristic
41#11758201—42no—
42#11758198—22no—
43#11758198—21no—
44#11758198—21no—
45C4⋊Dic61D411yescharacteristic
46C4⋊Dic61D411yescharacteristic
47#11758196—22no—
48C2×#92418—21no—
49C2×#92418—21no—
50C22×D61—21no—
51C22×D61—21no—
52Q8×C61—41no—
53Q8×C61—41no—
54Q8×C61—41no—
55Q8×C61—41no—
56C2×C4×C61—22no—
57C2×C4×C61—41no—
58C2×C4×C61C2×D411yescharacteristic
59C2×C4×C61C2×D411yescharacteristic
60C2×C4×C61C2×D411yescharacteristic
61C2×Dic61—21no—
62C2×Dic61—21no—
63D244—21no—
64D244—21no—
65D244—21no—
66D244—44no—
67D244SD1612yescomplemented
68C4×D61—44no—
69C4×D61—41no—
70C4×D61—41no—
71C4×D61—41no—
72C4×D61—41no—
73C8×C61—22no—
74#92418—41no—
75#92418—41no—
76C22×C61#12011yescharacteristic
77C2×D61—22no—
78C2×D61—41no—
79C2×D61—41no—
80C2×D61—41no—
81C2×D61—41no—
82C2×D61—41no—
83C4×C61—21no—
84C4×C61—42no—
85C4×C61—81no—
86C4×C61C2×SD1611yescharacteristic
87C4×C61#13511yescharacteristic
88C4×C61AGL(1,ℤ/8)11yescharacteristic
89C4×C61AGL(1,ℤ/8)11yescharacteristic
90Dic61—41no—
91Dic61—41no—
92#1654—611nomaximal, Sylow
93C2×C61#44911yescharacteristic
94C2×C61#45011yescharacteristic
95C2×C61#45611yescharacteristic
96D61—42no—
97D61—81no—
98#547—611no—
99#498D6111yescharacteristic, complemented
100#474—611no—
101#461—611no—
102#332—611no—
103D4⋊C8—611no—
104D4⋊C8—611no—
105C61#165411yescharacteristic, complemented, Sylow
106C2×#41—1221no—
107C2×SD16—1221no—
108C4⋊Q8C2×D6111yescharacteristic
109C4⋊Q8C2×D6111yescharacteristic
110#123—1222no—
111C22⋊Q8—1221no—
112#121—1221no—
113C4×D4—611no—
114C4×D4—611no—
115C2×C4⋊C4—1221no—
116#107—1221no—
117#106—22no—
118C4⋊C8—611no—
119C4⋊C8—611no—
120#103—1221no—
121#102—1221no—
122C4×C8C2×D6111yescharacteristic
123#41—2442no—
124#41—2442no—
125C2×Q8—21no—
126C2×Q8—21no—
127C2×D4—611no—
128C2×D4—611no—
129C2×D4—1222no—
130C22×C4—1222no—
131C22×C4—1221no—
132C22×C4—1221no—
133SD16—2442no—
134C2×C8—21no—
135C2×C8—1221no—
136C2×C8—1221no—
137C4⋊C4—21no—
138C4⋊C4—21no—
139C4⋊C4—21no—
140C4⋊C4—611no—
141C4⋊C4—611no—
142C4⋊C4—1222no—
143C4⋊C4C22⋊D6112yes—
144C22⋊C4—1222no—
145C22⋊C4—1221no—
146C22⋊C4—1221no—
147C42C22×D6111yescharacteristic
148C23—1221no—
149C23—1221no—
150Q8—41no—
151Q8—41no—
152Q8—41no—
153Q8—41no—
154D4—612no—
155D4—1221no—
156D4—1221no—
157D4—1221no—
158D4—2444no—
159C2×C4—22no—
160C2×C4—41no—
161C2×C4—1221no—
162C2×C4—1221no—
163C2×C4—2444no—
164C2×C4—2441no—
165C2×C4—2441no—
166C2×C4—2441no—
167C2×C4—2441no—
168C2×C4D4×D6111yescharacteristic
169C2×C4D4×D6111yescharacteristic
170C2×C4C2×C22⋊D6111yescharacteristic
171C8—22no—
172C8—2441no—
173C8—2441no—
174C22—1222no—
175C22—2441no—
176C22—2441no—
177C22—2441no—
178C22—2441no—
179C22—2441no—
180C22#1451974511yescharacteristic
181C4—21no—
182C4—42no—
183C4—81no—
184C4—2441no—
185C4—2441no—
186C4SD16×D6111yescharacteristic
187C4#1451979811yescharacteristic
188C4#1451980411yescharacteristic
189C4#1451980411yescharacteristic
190C2—4881no—
191C2—2442no—
192C2#1683990611yescharacteristic
193C2#1683991111yescharacteristic
194C2#1683994411yescharacteristic
subgroupG/H
centerC22#14519745
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×#498C2
socleC22×C61#120
hypercenter#498D61
hypocenterC61#1654
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #498

Complements

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

NH ≅ G/Ntype
2. #16840039C2semidirect
3. #16839964C2semidirect
4. #16839508C2semidirect
5. #16839491C2semidirect
6. #16839491C2semidirect
7. C61×#498C2semidirect
67. D244SD16semidirect
99. #498D61semidirect
105. C61#1654semidirect