Finite Group Databasebeta

← #21433576

Subgroups — #21433576

Order 7552.

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×#14273752C212yesmaximal, complemented
2C2×#14273724C211yesmaximal, characteristic, complemented
3#16837602C214yesmaximal, complemented
4#16837597C214yesmaximal, complemented
5#16837426C211yesmaximal, characteristic, complemented
6#16837406C212yesmaximal, complemented
7C4×#41×C59C211yesmaximal, characteristic, complemented
8C22×D236—22no—
9C22×D236C2212yes—
10#14273752—28no—
11C2×#11745671C2214yescomplemented
12C2×#11745669C2214yescomplemented
13C2×#11745664C2212yes—
14#14273724—21no—
15#14273724—21no—
16#14273724C2214yes—
17C4⋊(C59⋊C8)C2214yescomplemented
18#14273647C2218yescomplemented
19C2×#41×C59C2211yescharacteristic
20C4×Q8×C59C2212yescomplemented
21C4×D4×C59—22no—
22C4×D4×C59C2212yescomplemented
23#117×C59—21no—
24#117×C59C2211yescharacteristic
25C2×C42×C59—21no—
26C2×C42×C59C2211yescharacteristic
27C23×D59—22no—
28#41×C59—22no—
29#41×C59D414yescomplemented
30C2×Q8×C59C2311yescharacteristic
31C2×D4×C59—21no—
32C2×D4×C59C2311yescharacteristic
33C22×C4×C59—21no—
34C22×C4×C59—22no—
35C22×C4×C59D412yes—
36C22×C4×C59C2311yescharacteristic
37C2×D236—24no—
38C2×D236—24no—
39C2×D236—22no—
40C2×D236—24no—
41C2×D236—24no—
42C2×D236—48no—
43C2×D236C2314yes—
44C4⋊C4×C59—22no—
45C4⋊C4×C59C2312yes—
46C22⋊C4×C59—21no—
47C22⋊C4×C59—22no—
48C42×C59—21no—
49C42×C59—22no—
50C42×C59D411yescharacteristic
51C42×C59D411yescharacteristic
52C42×C59C2312yes—
53#11745671—28no—
54#11745669—28no—
55#11745664—24no—
56C2×C59⋊C8C2314yes—
57C23×C59—21no—
58C23×C59C2×D411yescharacteristic
59C22×D59—24no—
60C22×D59—48no—
61C22×D59—44no—
62Q8×C59—21no—
63Q8×C59C2×D412yescomplemented
64D4×C59—24no—
65D4×C59—21no—
66D4×C59C2×D412yescomplemented
67C2×C4×C59—21no—
68C2×C4×C59—24no—
69C2×C4×C59—24no—
70C2×C4×C59—22no—
71C2×C4×C59—44no—
72C2×C4×C59C2×D412yes—
73C2×C4×C59C2×D412yes—
74C2×C4×C59C2×D411yescharacteristic
75C2×C4×C59C2×D412yes—
76C2×C4×C59#4112yes—
77C2×C4×C59C2411yescharacteristic
78D236—24no—
79D236—24no—
80D236—48no—
81D236—44no—
82D236—48no—
83C59⋊C8—24no—
84C22×C59—22no—
85C22×C59—22no—
86C22×C59—42no—
87C22×C59#12112yes—
88C22×C59C22×D411yescharacteristic
89C2×D59—44no—
90C2×D59—48no—
91C2×D59—88no—
92C4×C59—22no—
93C4×C59—22no—
94C4×C59—42no—
95C4×C59#12112yes—
96C4×C59AGL(1,ℤ/8)14yescomplemented
97C4×C59C22×D411yescharacteristic
98C4×C59C2×#4111yescharacteristic
99#3038—591nomaximal, Sylow
100C2×C59—22no—
101C2×C59—42no—
102C2×C59C2×#12111yescharacteristic
103C2×C59C2×AGL(1,ℤ/8)12yes—
104D59—84no—
105C2×AGL(1,ℤ/8)—592no—
106C2×#127—591no—
107C4×#41D5911yescharacteristic, complemented
108#460—594no—
109#459—594no—
110#423—591no—
111#418—592no—
112C59#303811yescharacteristic, complemented, Sylow
113C2×#41C2×D5911yescharacteristic
114C22×D4—592no—
115C22×D4—1182no—
116AGL(1,ℤ/8)—1188no—
117C2×SD16—594no—
118C2×D8—594no—
119C2×M16—592no—
120#127—594no—
121#127—1181no—
122#127—1181no—
123C4×Q8C2×D5912yescomplemented
124C4×D4—22no—
125C4×D4C2×D5912yescomplemented
126#117—21no—
127#117C2×D5911yescharacteristic
128C2×C42—21no—
129C2×C42C2×D5911yescharacteristic
130C4⋊C8—594no—
131#102—598no—
132C24—1182no—
133#41—22no—
134#41D23614yescomplemented
135C2×Q8C22×D5911yescharacteristic
136C2×D4—21no—
137C2×D4—594no—
138C2×D4—1184no—
139C2×D4—1184no—
140C2×D4—1184no—
141C2×D4—1184no—
142C2×D4—1182no—
143C2×D4—2368no—
144C2×D4C22×D5911yescharacteristic
145C22×C4—21no—
146C22×C4—22no—
147C22×C4C22⋊D5912yes—
148C22×C4C22×D5911yescharacteristic
149SD16—1188no—
150D8—1188no—
151M16—1184no—
152C2×C8—594no—
153C4⋊C4—22no—
154C4⋊C4C22×D5912yes—
155C22⋊C4—21no—
156C22⋊C4—22no—
157C42—21no—
158C42—22no—
159C42C22⋊D5911yescharacteristic
160C42C22⋊D5911yescharacteristic
161C42C22×D5912yes—
162C23—21no—
163C23—1184no—
164C23—2368no—
165C23—2364no—
166C23C2×C22⋊D5911yescharacteristic
167Q8—21no—
168Q8C2×D23612yescomplemented
169D4—24no—
170D4—21no—
171D4—1184no—
172D4—1184no—
173D4—2368no—
174D4—2364no—
175D4—2368no—
176D4C2×D23612yescomplemented
177C2×C4—21no—
178C2×C4—24no—
179C2×C4—24no—
180C2×C4—22no—
181C2×C4—44no—
182C2×C4C2×D23612yes—
183C2×C4#1174568512yes—
184C2×C4C2×C22⋊D5912yes—
185C2×C4C2×C22⋊D5911yescharacteristic
186C2×C4C2×C22⋊D5912yes—
187C2×C4C23×D5911yescharacteristic
188C8—1184no—
189C22—22no—
190C22—22no—
191C22—42no—
192C22—4728no—
193C22—2364no—
194C22—2368no—
195C22#1427370112yes—
196C22C22×C22⋊D5911yescharacteristic
197C4—22no—
198C4—22no—
199C4—42no—
200C4#1427370112yes—
201C4#1427375214yescomplemented
202C4C22×D23611yescharacteristic
203C4C2×#1174568511yescharacteristic
204C2—22no—
205C2—42no—
206C2—4724no—
207C2C2×#1427370111yescharacteristic
208C2C2×#1427375212yes—
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC4×#41×C59C2
socleC22×C59C22×D4
hypercenterC4×#41D59
hypocenterC59#3038
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
1. C2×#14273752C2semidirect
2. C2×#14273724C2semidirect
3. #16837602C2semidirect
4. #16837597C2semidirect
5. #16837426C2semidirect
6. #16837406C2semidirect
7. C4×#41×C59C2semidirect
11. C2×#11745671C22semidirect
12. C2×#11745669C22semidirect
17. C4⋊(C59⋊C8)C22semidirect
18. #14273647C22semidirect
20. C4×Q8×C59C22semidirect
22. C4×D4×C59C22semidirect
29. #41×C59D4semidirect
63. Q8×C59C2×D4semidirect
66. D4×C59C2×D4semidirect
96. C4×C59AGL(1,ℤ/8)semidirect
107. C4×#41D59semidirect
112. C59#3038semidirect
123. C4×Q8C2×D59semidirect
125. C4×D4C2×D59semidirect
134. #41D236semidirect
168. Q8C2×D236semidirect
176. D4C2×D236semidirect
201. C4#14273752semidirect