Finite Group Databasebeta

← #21445021

Subgroups — #21445021

Order 7808.

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

normal subgroups only

This group has 250 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#16840433C211yesmaximal, characteristic
2#16840109C211yesmaximal, characteristic, complemented
3#16840048C211yesmaximal, characteristic, complemented
4#16839967C211yesmaximal, characteristic, complemented
5#16839505C211yesmaximal, characteristic, complemented
6#16839494C211yesmaximal, characteristic, complemented
7C61×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×#11758222—21no—
9C2×#11758200—21no—
10#14519777C2211yescharacteristic
11#14519774C2211yescharacteristic
12#14519773—21no—
13#14519751—21no—
14#14519750—22no—
15C4×Dic122C2211yescharacteristic
16#14519739—21no—
17#14519709—21no—
18C4⋊#92418C2211yescharacteristic
19#14519702—21no—
20#14519700—21no—
21#14519699—22no—
22C4×D4×C61C2211yescharacteristic
23C4⋊C8×C61C2211yescharacteristic
24C4×C8×C61C2211yescharacteristic
25C2×D4×C61D411yescharacteristic
26C22×C4×C61—21no—
27C2×C22⋊D61—22no—
28C2×C22⋊D61—22no—
29#11758222—42no—
30#11758222—42no—
31C2×D244—21no—
32C2×D244—21no—
33C2×D244D412yes—
34C2×C4×D61—22no—
35C2×Dic122—21no—
36C2×Dic122D411yescharacteristic
37C2×C8×C61—21no—
38C2×C8×C61—21no—
39C4⋊C4×C61D411yescharacteristic
40C22⋊C4×C61—21no—
41C42×C61C2311yescharacteristic
42#11758200—42no—
43#11758198—22no—
44C4⋊Dic61—21no—
45C4⋊Dic61—21no—
46C4⋊Dic61D411yescharacteristic
47#11758196—21no—
48C4×Dic61—21no—
49C2×#92418—21no—
50C23×C61—21no—
51C22×D61—22no—
52D4×C61—21no—
53D4×C61—21no—
54C2×C4×C61—21no—
55C2×C4×C61—41no—
56C2×C4×C61—41no—
57C2×C4×C61C2×D411yescharacteristic
58C2×C4×C61C2×D411yescharacteristic
59C2×C4×C61C2×D411yescharacteristic
60C22⋊D61—44no—
61C22⋊D61—82no—
62C2×Dic61—21no—
63C2×Dic61—21no—
64C2×Dic61—41no—
65D244—42no—
66D244—41no—
67D244—41no—
68D244—41no—
69D244—41no—
70C4×D61—44no—
71Dic122—21no—
72Dic122—41no—
73Dic122—41no—
74Dic122SD1612yescomplemented
75C8×C61—41no—
76C8×C61—41no—
77#92418—41no—
78C22×C61—41no—
79C22×C61—41no—
80C22×C61—41no—
81C22×C61#12011yescharacteristic
82C2×D61—42no—
83C2×D61—42no—
84C2×D61—42no—
85C4×C61—21no—
86C4×C61—41no—
87C4×C61C2×SD1611yescharacteristic
88C4×C61#13511yescharacteristic
89C4×C61AGL(1,ℤ/8)11yescharacteristic
90C4×C61AGL(1,ℤ/8)11yescharacteristic
91Dic61—22no—
92Dic61—41no—
93Dic61—81no—
94#1642—611nomaximal, Sylow
95C2×C61—81no—
96C2×C61#44911yescharacteristic
97C2×C61#45011yescharacteristic
98C2×C61#45511yescharacteristic
99D61—82no—
100#550—611no—
101#486—611no—
102#475—611no—
103#461—611no—
104#331—611no—
105Q8⋊C8—611no—
106D4⋊C8D6111yescharacteristic, complemented
107C61#164211yescharacteristic, complemented, Sylow
108C2×#41—1221no—
109C2×SD16—1221no—
110C4⋊Q8—611no—
111#127—611no—
112#127—1221no—
113#121—1222no—
114#121—1221no—
115C4×Q8—611no—
116C4×D4—1221no—
117C4×D4C2×D6111yescharacteristic
118#106—1221no—
119C4⋊C8—611no—
120C4⋊C8C2×D6111yescharacteristic
121#103—1221no—
122#103—1221no—
123#102—1222no—
124C4×C8C2×D6111yescharacteristic
125#41—2442no—
126#41—2442no—
127C2×Q8—611no—
128C2×Q8—1221no—
129C2×D4—612no—
130C2×D4—1222no—
131C2×D4—1222no—
132C2×D4—1221no—
133C2×D4—1221no—
134C2×D4D24411yescharacteristic
135C22×C4—21no—
136C22×C4—1222no—
137SD16—2442no—
138C2×C8—21no—
139C2×C8—21no—
140C2×C8—1221no—
141C4⋊C4—611no—
142C4⋊C4—1221no—
143C4⋊C4—1221no—
144C4⋊C4—1221no—
145C4⋊C4D24411yescharacteristic
146C22⋊C4—21no—
147C22⋊C4—1222no—
148C42—1221no—
149C42C22×D6111yescharacteristic
150C23—21no—
151C23—1222no—
152Q8—612no—
153Q8—1221no—
154Q8—2441no—
155Q8—2441no—
156D4—21no—
157D4—21no—
158D4—4882no—
159D4—2442no—
160D4—2444no—
161D4—2441no—
162D4—2441no—
163D4—2441no—
164D4—2441no—
165C2×C4—21no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—1221no—
169C2×C4—1221no—
170C2×C4—2444no—
171C2×C4—2441no—
172C2×C4C2×D24411yescharacteristic
173C2×C4D4×D6111yescharacteristic
174C2×C4D4×D6111yescharacteristic
175C8—41no—
176C8—41no—
177C8—2441no—
178C22—41no—
179C22—41no—
180C22—41no—
181C22—2442no—
182C22—2442no—
183C22—2442no—
184C22#1451974711yescharacteristic
185C4—21no—
186C4—41no—
187C4—1222no—
188C4—4881no—
189C4—2441no—
190C4SD16×D6111yescharacteristic
191C4#1451979911yescharacteristic
192C4#1451980111yescharacteristic
193C4#1451980511yescharacteristic
194C2—81no—
195C2—4882no—
196C2#1683990911yescharacteristic
197C2#1683991411yescharacteristic
198C2#1683994111yescharacteristic
subgroupG/H
centerC22#14519747
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×D4⋊C8C2
socleC22×C61#120
hypercenterD4⋊C8D61
hypocenterC61#1642
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #16840109C2semidirect
3. #16840048C2semidirect
4. #16839967C2semidirect
5. #16839505C2semidirect
6. #16839494C2semidirect
7. C61×D4⋊C8C2semidirect
74. Dic122SD16semidirect
106. D4⋊C8D61semidirect
107. C61#1642semidirect