Finite Group Databasebeta

← #21423328

Subgroups — #21423328

Order 7552.

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

normal subgroups only

This group has 240 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#16838055C211yesmaximal, characteristic
2#16837679C211yesmaximal, characteristic, complemented
3#16837604C211yesmaximal, characteristic, complemented
4#16837148C211yesmaximal, characteristic, complemented
5#16837131C211yesmaximal, characteristic, complemented
6#16837131C211yesmaximal, characteristic, complemented
7C59×#500C211yesmaximal, characteristic, complemented
8C2×#11745689—21no—
9C2×#11745671—21no—
10#14273712—22no—
11#14273703—21no—
12#14273702—21no—
13C4×D236C2211yescharacteristic
14C4×D236C2211yescharacteristic
15C4⋊C4×D59—21no—
16#14273660—21no—
17C4⋊(C59⋊C8)C2211yescharacteristic
18C4⋊(C59⋊C8)C2211yescharacteristic
19#14273651—21no—
20#14273647—21no—
21C4⋊Q8×C59C2211yescharacteristic
22C4⋊Q8×C59C2211yescharacteristic
23#107×C59—22no—
24C4×C8×C59C2211yescharacteristic
25C2×Q8×C59—21no—
26C2×Q8×C59—21no—
27#11745689—42no—
28#11745689—42no—
29C2×D236—22no—
30C2×D236D411yescharacteristic
31C2×D236D411yescharacteristic
32C2×C4×D59—22no—
33C2×C4×D59—21no—
34C2×C4×D59—21no—
35C2×C8×C59—21no—
36C4⋊C4×C59—21no—
37C4⋊C4×C59—21no—
38C4⋊C4×C59—21no—
39C4⋊C4×C59D412yes—
40C42×C59C2311yescharacteristic
41#11745671—42no—
42(C2×D59)⋊C4—22no—
43(C2×D59)⋊C4—21no—
44(C2×D59)⋊C4—21no—
45C4⋊Dic59D411yescharacteristic
46C4⋊Dic59D411yescharacteristic
47Dic59⋊C4—22no—
48C2×C59⋊C8—21no—
49C2×C59⋊C8—21no—
50C22×D59—21no—
51C22×D59—21no—
52Q8×C59—41no—
53Q8×C59—41no—
54Q8×C59—41no—
55Q8×C59—41no—
56C2×C4×C59—22no—
57C2×C4×C59—41no—
58C2×C4×C59C2×D411yescharacteristic
59C2×C4×C59C2×D411yescharacteristic
60C2×C4×C59C2×D411yescharacteristic
61C2×Dic59—21no—
62C2×Dic59—21no—
63D236—21no—
64D236—21no—
65D236—21no—
66D236—44no—
67D236D812yes—
68C4×D59—44no—
69C4×D59—41no—
70C4×D59—41no—
71C4×D59—41no—
72C4×D59—41no—
73C8×C59—22no—
74C59⋊C8—41no—
75C59⋊C8—41no—
76C22×C59#12011yescharacteristic
77C2×D59—22no—
78C2×D59—41no—
79C2×D59—41no—
80C2×D59—41no—
81C2×D59—41no—
82C2×D59—41no—
83C4×C59—21no—
84C4×C59—42no—
85C4×C59—81no—
86C4×C59C2×D811yescharacteristic
87C4×C59#13511yescharacteristic
88C4×C59AGL(1,ℤ/8)11yescharacteristic
89C4×C59#13711yescharacteristic
90Dic59—41no—
91Dic59—41no—
92#1647—591nomaximal, Sylow
93C2×C59#44711yescharacteristic
94C2×C59#45211yescharacteristic
95C2×C59#45611yescharacteristic
96D59—42no—
97D59—81no—
98#547—591no—
99#500D5911yescharacteristic, complemented
100#474—591no—
101#461—591no—
102#332—591no—
103D4⋊C8—591no—
104D4⋊C8—591no—
105C59#164711yescharacteristic, complemented, Sylow
106C2×#41—1181no—
107C2×SD16—1181no—
108C4⋊Q8C2×D5911yescharacteristic
109C4⋊Q8C2×D5911yescharacteristic
110#123—1182no—
111C22⋊Q8—1181no—
112#121—1181no—
113C4×D4—591no—
114C4×D4—591no—
115C2×C4⋊C4—1181no—
116#107—22no—
117#107—1181no—
118C4⋊C8—591no—
119C4⋊C8—591no—
120#103—1181no—
121#102—1181no—
122C4×C8C2×D5911yescharacteristic
123#41—2362no—
124#41—2362no—
125C2×Q8—21no—
126C2×Q8—21no—
127C2×D4—591no—
128C2×D4—591no—
129C2×D4—1182no—
130C22×C4—1182no—
131C22×C4—1181no—
132C22×C4—1181no—
133SD16—2362no—
134C2×C8—21no—
135C2×C8—1181no—
136C2×C8—1181no—
137C4⋊C4—21no—
138C4⋊C4—21no—
139C4⋊C4—21no—
140C4⋊C4—591no—
141C4⋊C4—591no—
142C4⋊C4—1182no—
143C4⋊C4C22⋊D5912yes—
144C22⋊C4—1182no—
145C22⋊C4—1181no—
146C22⋊C4—1181no—
147C42C22×D5911yescharacteristic
148C23—1181no—
149C23—1181no—
150Q8—41no—
151Q8—41no—
152Q8—41no—
153Q8—41no—
154D4—592no—
155D4—1181no—
156D4—1181no—
157D4—1181no—
158D4—2364no—
159C2×C4—22no—
160C2×C4—41no—
161C2×C4—1181no—
162C2×C4—1181no—
163C2×C4—2364no—
164C2×C4—2361no—
165C2×C4—2361no—
166C2×C4—2361no—
167C2×C4—2361no—
168C2×C4D4×D5911yescharacteristic
169C2×C4D4×D5911yescharacteristic
170C2×C4C2×C22⋊D5911yescharacteristic
171C8—22no—
172C8—2361no—
173C8—2361no—
174C22—1182no—
175C22—2361no—
176C22—2361no—
177C22—2361no—
178C22—2361no—
179C22—2361no—
180C22#1427369511yescharacteristic
181C4—21no—
182C4—42no—
183C4—81no—
184C4—2361no—
185C4—2361no—
186C4D8×D5911yescharacteristic
187C4#1427375011yescharacteristic
188C4#1427375111yescharacteristic
189C4#1427375911yescharacteristic
190C2—4721no—
191C2—2362no—
192C2#1683753411yescharacteristic
193C2#1683756311yescharacteristic
194C2#1683758411yescharacteristic
subgroupG/H
centerC22#14273695
commutatorC42×C59C23
FrattiniC42C22×D59
FittingC59×#500C2
socleC22×C59#120
hypercenter#500D59
hypocenterC59#1647
LCSG ▷ C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #500

Complements

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

NH ≅ G/Ntype
2. #16837679C2semidirect
3. #16837604C2semidirect
4. #16837148C2semidirect
5. #16837131C2semidirect
6. #16837131C2semidirect
7. C59×#500C2semidirect
99. #500D59semidirect
105. C59#1647semidirect