Finite Group Databasebeta

← #21423290

Subgroups — #21423290

Order 7552.

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

normal subgroups only

This group has 250 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#16838072C211yesmaximal, characteristic
2#16837748C211yesmaximal, characteristic, complemented
3#16837683C211yesmaximal, characteristic, complemented
4#16837613C211yesmaximal, characteristic, complemented
5#16837132C211yesmaximal, characteristic, complemented
6#16837129C211yesmaximal, characteristic, complemented
7C59×#331C211yesmaximal, characteristic, complemented
8C2×#11745687—21no—
9C2×Dic236—21no—
10#14273727C2211yescharacteristic
11#14273723—21no—
12#14273699—22no—
13#14273698—21no—
14C4×Dic118C2211yescharacteristic
15C4×D236C2211yescharacteristic
16D4×Dic59—21no—
17#14273661—21no—
18#14273652—21no—
19#14273649—21no—
20#14273648—22no—
21C4×C59⋊C8C2211yescharacteristic
22#127×C59C2211yescharacteristic
23C4⋊C8×C59C2211yescharacteristic
24C4⋊C8×C59C2211yescharacteristic
25C2×D4×C59—21no—
26C2×D4×C59—21no—
27C2×D4×C59D412yes—
28C2×C22⋊D59—22no—
29C2×C22⋊D59—22no—
30C22×Dic59—22no—
31#11745687—42no—
32#11745687—42no—
33C2×D236D411yescharacteristic
34C2×C4×D59—21no—
35C2×Dic118—21no—
36C2×Dic118D411yescharacteristic
37C2×C8×C59—21no—
38C2×C8×C59—21no—
39C42×C59C2311yescharacteristic
40C22⋊Dic59—22no—
41(C2×D59)⋊C4—21no—
42C4⋊Dic59—21no—
43C4⋊Dic59—21no—
44C4⋊Dic59D411yescharacteristic
45C4⋊Dic59D411yescharacteristic
46Dic59⋊C4—21no—
47C4×Dic59—21no—
48C2×C59⋊C8—21no—
49Dic236—42no—
50C23×C59—22no—
51C22×D59—21no—
52D4×C59—42no—
53D4×C59—41no—
54D4×C59—41no—
55D4×C59—41no—
56D4×C59—41no—
57C2×C4×C59C2×D411yescharacteristic
58C2×C4×C59C2×D411yescharacteristic
59C2×C4×C59C2×D411yescharacteristic
60C22⋊D59—44no—
61C22⋊D59—82no—
62C2×Dic59—21no—
63C2×Dic59—21no—
64C2×Dic59—21no—
65C2×Dic59—44no—
66C2×Dic59—41no—
67D236—21no—
68D236—21no—
69C4×D59—41no—
70C4×D59—41no—
71Dic118—21no—
72Dic118—41no—
73Dic118—41no—
74Dic118D812yes—
75C8×C59—41no—
76C8×C59—41no—
77C59⋊C8—41no—
78C22×C59—42no—
79C22×C59—42no—
80C22×C59—42no—
81C22×C59#12011yescharacteristic
82C2×D59—41no—
83C2×D59—41no—
84C2×D59—41no—
85C4×C59—21no—
86C4×C59C2×D811yescharacteristic
87C4×C59#13511yescharacteristic
88C4×C59AGL(1,ℤ/8)11yescharacteristic
89C4×C59#13711yescharacteristic
90Dic59—22no—
91Dic59—41no—
92Dic59—41no—
93Dic59—81no—
94#1641—591nomaximal, Sylow
95C2×C59—82no—
96C2×C59#44711yescharacteristic
97C2×C59#45211yescharacteristic
98C2×C59#45511yescharacteristic
99D59—81no—
100#550—591no—
101#486—591no—
102#474—591no—
103#462—591no—
104#331D5911yescharacteristic, complemented
105Q8⋊C8—591no—
106D4⋊C8—591no—
107C59#164111yescharacteristic, complemented, Sylow
108C2×#41—1181no—
109C2×Q16—1181no—
110C4⋊Q8—591no—
111#127—1181no—
112#127C2×D5911yescharacteristic
113#121—1181no—
114#121—1182no—
115C4×Q8—591no—
116C4×D4—591no—
117C4×D4—1181no—
118#107—1181no—
119C4⋊C8C2×D5911yescharacteristic
120C4⋊C8C2×D5911yescharacteristic
121#103—1181no—
122#102—1181no—
123#102—1182no—
124C4×C8—591no—
125#41—2362no—
126#41—2362no—
127C2×Q8—591no—
128C2×Q8—1181no—
129C2×D4—21no—
130C2×D4—21no—
131C2×D4—591no—
132C2×D4—1182no—
133C2×D4—1182no—
134C2×D4D23612yes—
135C22×C4—1182no—
136C22×C4—1181no—
137Q16—2362no—
138C2×C8—21no—
139C2×C8—21no—
140C2×C8—1181no—
141C4⋊C4—591no—
142C4⋊C4—591no—
143C4⋊C4—1181no—
144C4⋊C4—1181no—
145C4⋊C4—1181no—
146C22⋊C4—1182no—
147C22⋊C4—1181no—
148C42—1181no—
149C42C22×D5911yescharacteristic
150C23—22no—
151C23—1181no—
152Q8—592no—
153Q8—1181no—
154Q8—2361no—
155Q8—2361no—
156D4—42no—
157D4—41no—
158D4—41no—
159D4—41no—
160D4—41no—
161D4—1181no—
162D4—1181no—
163D4—4722no—
164D4—2364no—
165C2×C4—1181no—
166C2×C4—1181no—
167C2×C4—1181no—
168C2×C4—2364no—
169C2×C4—2361no—
170C2×C4—2361no—
171C2×C4—2361no—
172C2×C4C2×D23611yescharacteristic
173C2×C4D4×D5911yescharacteristic
174C2×C4D4×D5911yescharacteristic
175C8—41no—
176C8—41no—
177C8—2361no—
178C22—42no—
179C22—42no—
180C22—42no—
181C22—2361no—
182C22—2361no—
183C22—2361no—
184C22#1427369711yescharacteristic
185C4—21no—
186C4—1182no—
187C4—4721no—
188C4—2361no—
189C4—2361no—
190C4D8×D5911yescharacteristic
191C4#1427374611yescharacteristic
192C4#1427375411yescharacteristic
193C4#1427375611yescharacteristic
194C2—82no—
195C2—4721no—
196C2#1683753711yescharacteristic
197C2#1683756511yescharacteristic
198C2#1683758211yescharacteristic
subgroupG/H
centerC22#14273697
commutatorC42×C59C23
FrattiniC42C22×D59
FittingC59×#331C2
socleC22×C59#120
hypercenter#331D59
hypocenterC59#1641
LCSG ▷ C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #16837748C2semidirect
3. #16837683C2semidirect
4. #16837613C2semidirect
5. #16837132C2semidirect
6. #16837129C2semidirect
7. C59×#331C2semidirect
104. #331D59semidirect
107. C59#1641semidirect