Finite Group Databasebeta

← #21455299

Subgroups — #21455299

Order 7808.

584 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 157 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
1C2×#14519802C212yesmaximal, complemented
2C2×#14519774C211yesmaximal, characteristic, complemented
3#16839962C214yesmaximal, complemented
4#16839957C214yesmaximal, complemented
5#16839786C211yesmaximal, characteristic, complemented
6#16839766C212yesmaximal, complemented
7C4×#41×C61C211yesmaximal, characteristic, complemented
8C22×D244—22no—
9C22×D244C2212yes—
10#14519802—28no—
11C2×#11758201C2214yescomplemented
12C2×#11758199C2214yescomplemented
13C2×#11758194C2212yes—
14#14519774—21no—
15#14519774—21no—
16#14519774C2214yes—
17C4⋊#92418C2214yescomplemented
18#14519697C2218yescomplemented
19C2×#41×C61C2211yescharacteristic
20C4×Q8×C61C2212yescomplemented
21C4×D4×C61—22no—
22C4×D4×C61C2212yescomplemented
23#117×C61—21no—
24#117×C61C2211yescharacteristic
25C2×C42×C61—21no—
26C2×C42×C61C2211yescharacteristic
27C23×D61—22no—
28#41×C61—22no—
29#41×C61D414yescomplemented
30C2×Q8×C61C2311yescharacteristic
31C2×D4×C61—21no—
32C2×D4×C61C2311yescharacteristic
33C22×C4×C61—21no—
34C22×C4×C61—22no—
35C22×C4×C61D412yes—
36C22×C4×C61C2311yescharacteristic
37C2×D244—24no—
38C2×D244—24no—
39C2×D244—24no—
40C2×D244—24no—
41C2×D244—22no—
42C2×D244—48no—
43C2×D244C2314yes—
44C4⋊C4×C61—22no—
45C4⋊C4×C61C2312yes—
46C22⋊C4×C61—21no—
47C22⋊C4×C61—22no—
48C42×C61—21no—
49C42×C61—22no—
50C42×C61D411yescharacteristic
51C42×C61D411yescharacteristic
52C42×C61C2312yes—
53#11758201—28no—
54#11758199—28no—
55#11758194—24no—
56C2×#92418C2314yes—
57C23×C61—21no—
58C23×C61C2×D411yescharacteristic
59C22×D61—24no—
60C22×D61—48no—
61C22×D61—44no—
62Q8×C61—21no—
63Q8×C61C2×D412yescomplemented
64D4×C61—24no—
65D4×C61—21no—
66D4×C61C2×D412yescomplemented
67C2×C4×C61—21no—
68C2×C4×C61—24no—
69C2×C4×C61—24no—
70C2×C4×C61—22no—
71C2×C4×C61—44no—
72C2×C4×C61C2×D412yes—
73C2×C4×C61C2×D411yescharacteristic
74C2×C4×C61C2×D412yes—
75C2×C4×C61C2×D412yes—
76C2×C4×C61#4112yes—
77C2×C4×C61C2411yescharacteristic
78D244—24no—
79D244—24no—
80D244—48no—
81D244—44no—
82D244—48no—
83#92418—24no—
84C22×C61—22no—
85C22×C61—22no—
86C22×C61—42no—
87C22×C61#12112yes—
88C22×C61C22×D411yescharacteristic
89C2×D61—44no—
90C2×D61—48no—
91C2×D61—88no—
92C4×C61—22no—
93C4×C61—22no—
94C4×C61—42no—
95C4×C61#12112yes—
96C4×C61AGL(1,ℤ/8)14yescomplemented
97C4×C61C22×D411yescharacteristic
98C4×C61C2×#4111yescharacteristic
99#3038—611nomaximal, Sylow
100C2×C61—22no—
101C2×C61—42no—
102C2×C61C2×#12111yescharacteristic
103C2×C61C2×AGL(1,ℤ/8)12yes—
104D61—84no—
105C2×AGL(1,ℤ/8)—612no—
106C2×#127—611no—
107C4×#41D6111yescharacteristic, complemented
108#460—614no—
109#459—614no—
110#423—611no—
111#418—612no—
112C61#303811yescharacteristic, complemented, Sylow
113C2×#41C2×D6111yescharacteristic
114C22×D4—612no—
115C22×D4—1222no—
116AGL(1,ℤ/8)—1228no—
117C2×SD16—614no—
118C2×D8—614no—
119C2×M16—612no—
120#127—614no—
121#127—1221no—
122#127—1221no—
123C4×Q8C2×D6112yescomplemented
124C4×D4—22no—
125C4×D4C2×D6112yescomplemented
126#117—21no—
127#117C2×D6111yescharacteristic
128C2×C42—21no—
129C2×C42C2×D6111yescharacteristic
130C4⋊C8—614no—
131#102—618no—
132C24—1222no—
133#41—22no—
134#41D24414yescomplemented
135C2×Q8C22×D6111yescharacteristic
136C2×D4—21no—
137C2×D4—614no—
138C2×D4—1224no—
139C2×D4—1224no—
140C2×D4—1224no—
141C2×D4—1224no—
142C2×D4—1222no—
143C2×D4—2448no—
144C2×D4C22×D6111yescharacteristic
145C22×C4—21no—
146C22×C4—22no—
147C22×C4C22⋊D6112yes—
148C22×C4C22×D6111yescharacteristic
149SD16—1228no—
150D8—1228no—
151M16—1224no—
152C2×C8—614no—
153C4⋊C4—22no—
154C4⋊C4C22×D6112yes—
155C22⋊C4—21no—
156C22⋊C4—22no—
157C42—21no—
158C42—22no—
159C42C22⋊D6111yescharacteristic
160C42C22⋊D6111yescharacteristic
161C42C22×D6112yes—
162C23—21no—
163C23—1224no—
164C23—2448no—
165C23—2444no—
166C23C2×C22⋊D6111yescharacteristic
167Q8—21no—
168Q8C2×D24412yescomplemented
169D4—24no—
170D4—21no—
171D4—1224no—
172D4—1224no—
173D4—2448no—
174D4—2444no—
175D4—2448no—
176D4C2×D24412yescomplemented
177C2×C4—21no—
178C2×C4—24no—
179C2×C4—24no—
180C2×C4—22no—
181C2×C4—44no—
182C2×C4C2×D24412yes—
183C2×C4#1175822212yes—
184C2×C4C2×C22⋊D6112yes—
185C2×C4C2×C22⋊D6111yescharacteristic
186C2×C4C2×C22⋊D6112yes—
187C2×C4C23×D6111yescharacteristic
188C8—1224no—
189C22—22no—
190C22—22no—
191C22—42no—
192C22—4888no—
193C22—2444no—
194C22—2448no—
195C22#1451975112yes—
196C22C22×C22⋊D6111yescharacteristic
197C4—22no—
198C4—22no—
199C4—42no—
200C4#1451975112yes—
201C4#1451980214yescomplemented
202C4C22×D24411yescharacteristic
203C4C2×#1175822211yescharacteristic
204C2—22no—
205C2—42no—
206C2—4884no—
207C2C2×#1451975111yescharacteristic
208C2C2×#1451980212yes—
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC4×#41×C61C2
socleC22×C61C22×D4
hypercenterC4×#41D61
hypocenterC61#3038
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
1. C2×#14519802C2semidirect
2. C2×#14519774C2semidirect
3. #16839962C2semidirect
4. #16839957C2semidirect
5. #16839786C2semidirect
6. #16839766C2semidirect
7. C4×#41×C61C2semidirect
11. C2×#11758201C22semidirect
12. C2×#11758199C22semidirect
17. C4⋊#92418C22semidirect
18. #14519697C22semidirect
20. C4×Q8×C61C22semidirect
22. C4×D4×C61C22semidirect
29. #41×C61D4semidirect
63. Q8×C61C2×D4semidirect
66. D4×C61C2×D4semidirect
96. C4×C61AGL(1,ℤ/8)semidirect
107. C4×#41D61semidirect
112. C61#3038semidirect
123. C4×Q8C2×D61semidirect
125. C4×D4C2×D61semidirect
134. #41D244semidirect
168. Q8C2×D244semidirect
176. D4C2×D244semidirect
201. C4#14519802semidirect