Finite Group Databasebeta

← #21444882

Subgroups — #21444882

Order 7808.

278 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 278 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, complemented
2#16840138C211yesmaximal, characteristic, complemented
3#16839954C211yesmaximal, characteristic, complemented
4#16839505C211yesmaximal, characteristic, complemented
5Q8⋊#92418C211yesmaximal, characteristic, complemented
6#16839489C211yesmaximal, characteristic, complemented
7C61×#460C211yesmaximal, characteristic, complemented
8C2×#11758226—21no—
9C2×#11758199—21no—
10C2×#11758199—22no—
11#14519774—21no—
12#14519774C2211yescharacteristic
13#14519752—22no—
14#14519752—21no—
15C4×D244—21no—
16C4×D244C2211yescharacteristic
17C4⋊#92418C2211yescharacteristic
18#14519698—21no—
19C4×#92418C2211yescharacteristic
20C2×SD16×C61—21no—
21#127×C61C2211yescharacteristic
22C4×Q8×C61C2211yescharacteristic
23C4⋊C8×C61C2211yescharacteristic
24#102×C61—21no—
25C2×Q8×C61D411yescharacteristic
26C2×D4×C61—21no—
27C2×D4×C61—21no—
28C2×D4×C61—21no—
29#11758226—42no—
30#11758226—42no—
31C2×D244—22no—
32C2×D244—21no—
33C2×D244—21no—
34C2×D244—22no—
35C2×D244D411yescharacteristic
36C2×D244D412yes—
37C2×C4×D61—22no—
38C2×C4×D61—21no—
39SD16×C61—42no—
40C2×C8×C61—21no—
41C4⋊C4×C61—21no—
42C4⋊C4×C61D411yescharacteristic
43C42×C61—21no—
44C42×C61C2311yescharacteristic
45#11758199—44no—
46#11758199—42no—
47#11758198—22no—
48#11758198—21no—
49C4⋊Dic61D411yescharacteristic
50C2×#92418—21no—
51C2×#92418—21no—
52C23×C61—41no—
53C22×D61—21no—
54C22×D61—22no—
55Q8×C61—21no—
56Q8×C61D812yescomplemented
57D4×C61—42no—
58D4×C61—41no—
59D4×C61—41no—
60D4×C61—41no—
61D4×C61—41no—
62C2×C4×C61—21no—
63C2×C4×C61—21no—
64C2×C4×C61C2×D411yescharacteristic
65C2×C4×C61C2×D411yescharacteristic
66C2×C4×C61C2×D411yescharacteristic
67C2×Dic61—21no—
68D244—21no—
69D244—21no—
70D244—42no—
71D244—44no—
72D244—41no—
73D244—41no—
74D244—41no—
75D244—41no—
76D244—82no—
77C4×D61—44no—
78C4×D61—41no—
79C4×D61—41no—
80C8×C61—41no—
81#92418—22no—
82#92418—41no—
83C22×C61—81no—
84C22×C61—81no—
85C22×C61—81no—
86C22×C61#12011yescharacteristic
87C2×D61—42no—
88C2×D61—41no—
89C2×D61—41no—
90C2×D61—42no—
91C2×D61—42no—
92C2×D61—41no—
93C4×C61—22no—
94C4×C61—21no—
95C4×C61—41no—
96C4×C61C2×D811yescharacteristic
97C4×C61#13511yescharacteristic
98C4×C61AGL(1,ℤ/8)11yescharacteristic
99C4×C61AGL(1,ℤ/8)11yescharacteristic
100Dic61—41no—
101#1621—611nomaximal, Sylow
102C2×C61—161no—
103C2×C61#44711yescharacteristic
104C2×C61#44911yescharacteristic
105C2×C61#45311yescharacteristic
106D61—81no—
107D61—82no—
108#550—611no—
109#493—611no—
110#460D6111yescharacteristic, complemented
111#459—611no—
112#331—611no—
113Q8⋊C8—611no—
114D4⋊C8—611no—
115C61#162111yescharacteristic, complemented, Sylow
116C2×#41—1221no—
117C2×SD16—21no—
118C2×D8—1221no—
119C2×D8—1222no—
120#127—611no—
121#127—1221no—
122#127C2×D6111yescharacteristic
123#121—1222no—
124#121—1221no—
125C4×Q8C2×D6111yescharacteristic
126C4×D4—611no—
127C4×D4—1221no—
128C4⋊C8—611no—
129C4⋊C8C2×D6111yescharacteristic
130#102—21no—
131#102—1221no—
132C4×C8—611no—
133#41—2442no—
134#41—2442no—
135C2×Q8C22⋊D6111yescharacteristic
136C2×D4—21no—
137C2×D4—21no—
138C2×D4—21no—
139C2×D4—611no—
140C2×D4—612no—
141C2×D4—1222no—
142C2×D4—1222no—
143C2×D4—1221no—
144C2×D4—1221no—
145C22×C4—1222no—
146C22×C4—1221no—
147SD16—42no—
148D8—2444no—
149D8—2442no—
150C2×C8—21no—
151C2×C8—1221no—
152C2×C8—1221no—
153C4⋊C4—21no—
154C4⋊C4—611no—
155C4⋊C4C22⋊D6111yescharacteristic
156C22⋊C4—1222no—
157C22⋊C4—1221no—
158C42—21no—
159C42C22×D6111yescharacteristic
160C23—41no—
161C23—1221no—
162C23—1222no—
163Q8—21no—
164Q8#1175819912yescomplemented
165D4—42no—
166D4—41no—
167D4—41no—
168D4—41no—
169D4—41no—
170D4—1221no—
171D4—1221no—
172D4—4882no—
173D4—2442no—
174D4—2444no—
175D4—2441no—
176D4—2441no—
177D4—2441no—
178D4—2441no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—1221no—
182C2×C4—2444no—
183C2×C4—2441no—
184C2×C4—2441no—
185C2×C4D4×D6111yescharacteristic
186C2×C4D4×D6111yescharacteristic
187C2×C4C2×C22⋊D6111yescharacteristic
188C8—41no—
189C8—1222no—
190C8—2441no—
191C22—81no—
192C22—81no—
193C22—81no—
194C22—2442no—
195C22—2441no—
196C22—2441no—
197C22—2442no—
198C22—2441no—
199C22—2442no—
200C22#1451974511yescharacteristic
201C4—22no—
202C4—21no—
203C4—41no—
204C4—2441no—
205C4C2×#1175819911yescharacteristic
206C4#1451979811yescharacteristic
207C4#1451980211yescharacteristic
208C4#1451980411yescharacteristic
209C2—161no—
210C2—4881no—
211C2—4882no—
212C2#1683989511yescharacteristic
213C2#1683990611yescharacteristic
214C2#1683992811yescharacteristic
subgroupG/H
centerC22#14519745
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×#460C2
socleC22×C61#120
hypercenter#460D61
hypocenterC61#1621
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. #16840434C2semidirect
2. #16840138C2semidirect
3. #16839954C2semidirect
4. #16839505C2semidirect
5. Q8⋊#92418C2semidirect
6. #16839489C2semidirect
7. C61×#460C2semidirect
56. Q8×C61D8semidirect
110. #460D61semidirect
115. C61#1621semidirect
164. Q8#11758199semidirect