Finite Group Databasebeta

← #21422817

Subgroups — #21422817

Order 7552.

246 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 65 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#16837953C211yesmaximal, characteristic
2#16837458C211yesmaximal, characteristic, complemented
3#16837424C211yesmaximal, characteristic, complemented
4#16837148C211yesmaximal, characteristic, complemented
5#16837145C211yesmaximal, characteristic, complemented
6#16837145C211yesmaximal, characteristic, complemented
7C59×#332C211yesmaximal, characteristic, complemented
8C2×#11745689—21no—
9C2×#11745659—21no—
10#14273724C2211yescharacteristic
11#14273716—21no—
12#14273702—21no—
13#14273702C412yes—
14#14273689—21no—
15#14273689C412yes—
16C42×D59C2211yescharacteristic
17C4⋊(C59⋊C8)C2211yescharacteristic
18C4⋊(C59⋊C8)C2211yescharacteristic
19Dic59⋊C8—21no—
20(C2×D59)⋊C8—21no—
21#14273637—21no—
22C4⋊Q8×C59C2211yescharacteristic
23C4⋊C8×C59C2211yescharacteristic
24C4⋊C8×C59C2211yescharacteristic
25C2×Q8×C59—21no—
26#11745689—42no—
27#11745689—42no—
28C2×D236—22no—
29C2×D236—21no—
30C2×D236—21no—
31C2×D236C2×C412yes—
32C2×C4×D59—22no—
33C2×C4×D59C2×C411yescharacteristic
34C2×C4×D59D411yescharacteristic
35C2×C4×D59D411yescharacteristic
36C2×C8×C59—21no—
37C2×C8×C59—21no—
38C4⋊C4×C59—21no—
39C4⋊C4×C59C2×C412yes—
40C42×C59C2311yescharacteristic
41(C2×D59)⋊C4—22no—
42(C2×D59)⋊C4—22no—
43C4×Dic59C2×C411yescharacteristic
44C4×Dic59D411yescharacteristic
45C4×Dic59D411yescharacteristic
46C2×C59⋊C8—21no—
47C2×C59⋊C8—21no—
48#11745659—42no—
49C22×D59—22no—
50C22×D59C22⋊C411yescharacteristic
51Q8×C59—41no—
52Q8×C59—41no—
53C2×C4×C59—22no—
54C2×C4×C59C22×C411yescharacteristic
55C2×C4×C59C2×D411yescharacteristic
56C2×C4×C59C2×D411yescharacteristic
57C2×Dic59C22⋊C411yescharacteristic
58C2×Dic59C22⋊C411yescharacteristic
59C2×Dic59C22⋊C411yescharacteristic
60D236—42no—
61D236—44no—
62D236—41no—
63D236—41no—
64D236—41no—
65D236—41no—
66C4×D59—21no—
67C4×D59—21no—
68C4×D59—21no—
69C4×D59—21no—
70C4×D59—41no—
71C4×D59—44no—
72C8×C59—41no—
73C8×C59—41no—
74C59⋊C8—41no—
75C59⋊C8—41no—
76C22×C59C2×C22⋊C411yescharacteristic
77C2×D59—21no—
78C2×D59—21no—
79C2×D59—21no—
80C2×D59—42no—
81C2×D59—42no—
82C2×D59—42no—
83C4×C59—21no—
84C4×C59—42no—
85C4×C59AGL(1,ℤ/8)11yescharacteristic
86C4×C59AGL(1,ℤ/8)11yescharacteristic
87C4×C59AGL(1,ℤ/8)11yescharacteristic
88C4×C59#13711yescharacteristic
89Dic59—21no—
90Dic59—21no—
91Dic59—21no—
92#1557—591nomaximal, Sylow
93C2×C59#41311yescharacteristic
94C2×C59#41711yescharacteristic
95C2×C59#41811yescharacteristic
96D59—41no—
97D59—82no—
98#532—591no—
99#432—591no—
100#423—591no—
101#332—591no—
102#332D5911yescharacteristic, complemented
103#331—591no—
104#331—591no—
105C59#155711yescharacteristic, complemented, Sylow
106C2×#41—1181no—
107C2×M16—1181no—
108C4⋊Q8C2×D5911yescharacteristic
109#127—591no—
110#124—1181no—
111#121—592no—
112#121—1181no—
113C4×D4—592no—
114C4×D4—1181no—
115C2×C42—591no—
116C4⋊C8—591no—
117C4⋊C8—591no—
118C4⋊C8—1181no—
119C4⋊C8C2×D5911yescharacteristic
120C4⋊C8C2×D5911yescharacteristic
121C22⋊C8—1181no—
122#97—1181no—
123#41—2362no—
124#41—2362no—
125C2×Q8—21no—
126C2×D4—592no—
127C2×D4—1182no—
128C2×D4—1181no—
129C2×D4—1181no—
130C22×C4—591no—
131C22×C4—591no—
132C22×C4—591no—
133C22×C4—1182no—
134M16—2362no—
135C2×C8—21no—
136C2×C8—21no—
137C2×C8—1181no—
138C2×C8—1181no—
139C4⋊C4—21no—
140C4⋊C4C4×D5912yes—
141C22⋊C4—1182no—
142C22⋊C4—1182no—
143C42—591no—
144C42—591no—
145C42—591no—
146C42C22×D5911yescharacteristic
147C23—591no—
148C23—1182no—
149Q8—41no—
150Q8—41no—
151D4—2362no—
152D4—2364no—
153D4—2361no—
154D4—2361no—
155D4—2361no—
156D4—2361no—
157C2×C4—22no—
158C2×C4—591no—
159C2×C4—591no—
160C2×C4—591no—
161C2×C4—1181no—
162C2×C4—1181no—
163C2×C4—1181no—
164C2×C4—1181no—
165C2×C4—2361no—
166C2×C4—2364no—
167C2×C4C2×C4×D5911yescharacteristic
168C2×C4D4×D5911yescharacteristic
169C2×C4D4×D5911yescharacteristic
170C8—41no—
171C8—41no—
172C8—2361no—
173C8—2361no—
174C22—1181no—
175C22—1181no—
176C22—1181no—
177C22—2362no—
178C22—2362no—
179C22—2362no—
180C22C22⋊C4×D5911yescharacteristic
181C4—21no—
182C4—42no—
183C4—1181no—
184C4—1181no—
185C4—1181no—
186C4#1427375111yescharacteristic
187C4#1427375411yescharacteristic
188C4#1427375411yescharacteristic
189C4#1427375911yescharacteristic
190C2—4722no—
191C2—2361no—
192C2#1683738511yescharacteristic
193C2#1683740211yescharacteristic
194C2#1683740511yescharacteristic
subgroupG/H
centerC22C22⋊C4×D59
commutatorC2×C4×C59C22×C4
FrattiniC42C22×D59
FittingC59×#332C2
socleC22×C59C2×C22⋊C4
hypercenter#332D59
hypocenterC59#1557
LCSG ▷ C2×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #16837458C2semidirect
3. #16837424C2semidirect
4. #16837148C2semidirect
5. #16837145C2semidirect
6. #16837145C2semidirect
7. C59×#332C2semidirect
102. #332D59semidirect
105. C59#1557semidirect