Finite Group Databasebeta

← #21444937

Subgroups — #21444937

Order 7808.

314 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 59 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
1D4×D244C211yesmaximal, characteristic
2#16840135C211yesmaximal, characteristic, complemented
3#16840053C211yesmaximal, characteristic, complemented
4#16840052C211yesmaximal, characteristic, complemented
5#16839505C211yesmaximal, characteristic, complemented
6#16839491C211yesmaximal, characteristic, complemented
7C61×D4⋊C8C211yesmaximal, characteristic, complemented
8C22×D244—21no—
9C2×D4×D61—21no—
10C2×#11758190—22no—
11#14519777C2211yescharacteristic, complemented
12#14519774C2211yescharacteristic
13#14519752—21no—
14#14519751—21no—
15#14519747—22no—
16C4×D244C2211yescharacteristic
17#14519709—21no—
18#14519708—21no—
19C4⋊#92418C2211yescharacteristic, complemented
20#14519699—21no—
21#14519698—21no—
22C4×D4×C61C2211yescharacteristic
23C4⋊C8×C61C2211yescharacteristic, complemented
24C4×C8×C61C2211yescharacteristic, complemented
25C23×D61—22no—
26C2×D4×C61D411yescharacteristic
27C22×C4×C61—21no—
28C2×C22⋊D61—22no—
29D4×D61—42no—
30D4×D61—42no—
31C2×D244—22no—
32C2×D244—21no—
33C2×D244—21no—
34C2×D244—42no—
35C2×D244—42no—
36C2×D244D411yescharacteristic
37C2×D244D412yes—
38C2×C4×D61—21no—
39C2×Dic122—21no—
40C2×C8×C61—21no—
41C2×C8×C61—21no—
42C4⋊C4×C61D411yescharacteristic
43C22⋊C4×C61—21no—
44C42×C61C2311yescharacteristic
45#11758198—22no—
46#11758198—21no—
47C4⋊Dic61—21no—
48C4⋊Dic61—21no—
49C4⋊Dic61D411yescharacteristic
50C2×#92418—21no—
51#11758190—44no—
52C23×C61—21no—
53C22×D61—21no—
54C22×D61—22no—
55C22×D61—44no—
56C22×D61—44no—
57C22×D61—82no—
58D4×C61—21no—
59D4×C61SD1612yescomplemented
60C2×C4×C61—21no—
61C2×C4×C61—41no—
62C2×C4×C61—41no—
63C2×C4×C61C2×D411yescharacteristic
64C2×C4×C61C2×D411yescharacteristic
65C2×C4×C61C2×D411yescharacteristic
66C22⋊D61—44no—
67C2×Dic61—21no—
68C2×Dic61—41no—
69D244—21no—
70D244—42no—
71D244—44no—
72D244—41no—
73D244—41no—
74D244—41no—
75D244—41no—
76D244SD1612yescomplemented
77C4×D61—41no—
78C4×D61—41no—
79Dic122—42no—
80C8×C61—22no—
81C8×C61—41no—
82#92418—41no—
83C22×C61—22no—
84C22×C61—41no—
85C22×C61—41no—
86C22×C61#12011yescharacteristic
87C2×D61—22no—
88C2×D61—41no—
89C2×D61—41no—
90C2×D61—42no—
91C2×D61—42no—
92C2×D61—42no—
93C2×D61—88no—
94C4×C61—21no—
95C4×C61—41no—
96C4×C61C2×SD1611yescharacteristic
97C4×C61C2×SD1611yescharacteristic
98C4×C61AGL(1,ℤ/8)11yescharacteristic
99C4×C61AGL(1,ℤ/8)11yescharacteristic
100Dic61—41no—
101Dic61—81no—
102#1629—611nomaximal, Sylow
103C2×C61—42no—
104C2×C61#45011yescharacteristic
105C2×C61#45011yescharacteristic
106C2×C61#45311yescharacteristic
107D61—42no—
108D61—82no—
109D42—611no—
110#492—611no—
111#476—611no—
112#476—611no—
113#331—611no—
114D4⋊C8—611no—
115D4⋊C8D6111yescharacteristic, complemented
116C61#162911yescharacteristic, complemented, Sylow
117C22×D4—1221no—
118C22×D4—1221no—
119C2×SD16—1222no—
120C4⋊Q8—611no—
121#127—611no—
122#121—1221no—
123#121—1221no—
124#120—1222no—
125C4×D4—611no—
126C4×D4C2×D6111yescharacteristic
127#106—1221no—
128#106—1221no—
129C4⋊C8—611no—
130C4⋊C8C2×D6111yescharacteristic, complemented
131#102—1221no—
132#102—1221no—
133C4×C8C2×D6111yescharacteristic, complemented
134C24—1222no—
135C2×Q8—1221no—
136C2×D4—611no—
137C2×D4—612no—
138C2×D4—1222no—
139C2×D4—1222no—
140C2×D4—1221no—
141C2×D4—1221no—
142C2×D4—2442no—
143C2×D4—2442no—
144C2×D4—2442no—
145C2×D4—2442no—
146C2×D4D24411yescharacteristic
147C22×C4—21no—
148C22×C4—1221no—
149SD16—2444no—
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—1221no—
153C4⋊C4—611no—
154C4⋊C4—1221no—
155C4⋊C4—1221no—
156C4⋊C4D24411yescharacteristic
157C22⋊C4—21no—
158C22⋊C4—1222no—
159C22⋊C4—1221no—
160C42C22×D6111yescharacteristic
161C23—21no—
162C23—1221no—
163C23—1222no—
164C23—4882no—
165C23—2444no—
166C23—2444no—
167Q8—2442no—
168D4—21no—
169D4—612no—
170D4—1221no—
171D4—2442no—
172D4—2444no—
173D4—2444no—
174D4—2441no—
175D4—2441no—
176D4—2441no—
177D4—2441no—
178D4#1175819012yescomplemented
179C2×C4—21no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—1221no—
183C2×C4—2441no—
184C2×C4—2441no—
185C2×C4—2441no—
186C2×C4C2×D24411yescharacteristic
187C2×C4D4×D6111yescharacteristic
188C2×C4D4×D6111yescharacteristic
189C8—22no—
190C8—41no—
191C8—2441no—
192C22—22no—
193C22—41no—
194C22—41no—
195C22—1222no—
196C22—4888no—
197C22—2442no—
198C22—2442no—
199C22—2442no—
200C22—2441no—
201C22—2441no—
202C22#1451974711yescharacteristic
203C4—21no—
204C4—41no—
205C4—4881no—
206C4—2441no—
207C4SD16×D6111yescharacteristic
208C4C2×#1175819011yescharacteristic
209C4#1451980111yescharacteristic
210C4#1451980511yescharacteristic
211C2—42no—
212C2—4882no—
213C2—2442no—
214C2#1683991411yescharacteristic
215C2#1683991511yescharacteristic
216C2#1683993111yescharacteristic
subgroupG/H
centerC22#14519747
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×D4⋊C8C2
socleC22×C61#120
hypercenterD4⋊C8D61
hypocenterC61#1629
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. #16840135C2semidirect
3. #16840053C2semidirect
4. #16840052C2semidirect
5. #16839505C2semidirect
6. #16839491C2semidirect
7. C61×D4⋊C8C2semidirect
11. #14519777C22semidirect
19. C4⋊#92418C22semidirect
23. C4⋊C8×C61C22semidirect
24. C4×C8×C61C22semidirect
59. D4×C61SD16semidirect
76. D244SD16semidirect
115. D4⋊C8D61semidirect
116. C61#1629semidirect
130. C4⋊C8C2×D61semidirect
133. C4×C8C2×D61semidirect
178. D4#11758190semidirect