Finite Group Databasebeta

← #21424337

Subgroups — #21424337

Order 7552.

262 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 79 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#16838168C211yesmaximal, characteristic
2#16837450C211yesmaximal, characteristic, complemented
3#16837426C211yesmaximal, characteristic, complemented
4#16837420C211yesmaximal, characteristic
5C2×#14273655C211yesmaximal, characteristic
6#16837172C211yesmaximal, characteristic, complemented
7C59×#339C211yesmaximal, characteristic, complemented
8C2×#11745685C2211yescharacteristic
9#14273735—22no—
10#14273733—22no—
11C2×#11745664C2211yescharacteristic
12C2×#11745664C2211yescharacteristic
13C2×#11745664C2211yescharacteristic
14M16×D59—22no—
15#14273662—22no—
16C4⋊(C59⋊C8)—22no—
17#14273655—22no—
18#14273655C412yescomplemented
19#14273655C412yescomplemented
20C2×M16×C59C2211yescharacteristic
21#117×C59C2211yescharacteristic
22C2×C42×C59C2211yescharacteristic
23C22×C4×C59—21no—
24C22×C4×C59C2311yescharacteristic
25C2×C22⋊D59—21no—
26#11745685—21no—
27#11745685—21no—
28#11745685C2×C412yes—
29#11745685D412yes—
30C2×D236Q811yescharacteristic
31C2×C4×D59—21no—
32C2×Dic118Q811yescharacteristic
33M16×C59—21no—
34M16×C59D412yes—
35C2×C8×C59—21no—
36C4⋊C4×C59—21no—
37C22⋊C4×C59—21no—
38C42×C59—21no—
39C42×C59—21no—
40C42×C59C2×C411yescharacteristic
41C42×C59C2×C411yescharacteristic
42#11745664—21no—
43#11745664—21no—
44#11745664—21no—
45#11745664—21no—
46#11745664—21no—
47#11745664C2×C412yes—
48C2×C59⋊C8—21no—
49C2×C59⋊C8—21no—
50C2×C59⋊C8D412yes—
51#11745659—24no—
52C8×D59—24no—
53C23×C59#4111yescharacteristic
54C22×D59—21no—
55C2×C4×C59—21no—
56C2×C4×C59—21no—
57C2×C4×C59—42no—
58C2×C4×C59—41no—
59C2×C4×C59C22×C411yescharacteristic
60C2×C4×C59C2×D411yescharacteristic
61C2×C4×C59C2×D411yescharacteristic
62C2×C4×C59C2×D411yescharacteristic
63C2×C4×C59C2×Q811yescharacteristic
64C2×C4×C59#4111yescharacteristic
65C22⋊D59—22no—
66C22⋊D59—22no—
67C2×Dic59—21no—
68D236—21no—
69D236C4⋊C412yes—
70C4×D59—22no—
71C4×D59—22no—
72Dic118—21no—
73Dic118C4⋊C412yes—
74C8×C59—22no—
75C59⋊C8—22no—
76C59⋊C8—22no—
77C59⋊C8—41no—
78C22×C59—41no—
79C22×C59C4×D411yescharacteristic
80C22×C59C22⋊Q811yescharacteristic
81C22×C59#12311yescharacteristic
82C2×D59—22no—
83C2×D59—81no—
84C4×C59—22no—
85C4×C59—41no—
86C4×C59—81no—
87C4×C59C2×C4⋊C411yescharacteristic
88C4×C59C4×D411yescharacteristic
89C4×C59#12011yescharacteristic
90C4×C59C22⋊Q811yescharacteristic
91Dic59—22no—
92#1861—591nomaximal, Sylow
93C2×C59—21no—
94C2×C59—21no—
95C2×C59—21no—
96C2×C59#38511yescharacteristic
97D59—42no—
98#568—591no—
99#430—591no—
100#423—591no—
101#421—591no—
102C2×#104—591no—
103#344—591no—
104#339D5911yescharacteristic, complemented
105C59#186111yescharacteristic, complemented, Sylow
106C2×#41—591no—
107#131—1182no—
108#131—1182no—
109C2×M16—591no—
110C2×M16—591no—
111C2×M16—591no—
112C2×M16—1182no—
113C2×M16C2×D5911yescharacteristic
114#117C2×D5911yescharacteristic
115C2×C42C2×D5911yescharacteristic
116#108—1182no—
117C4⋊C8—1182no—
118#104—592no—
119#104—592no—
120#104—1182no—
121#41—592no—
122#41—592no—
123#41—1181no—
124#41—1181no—
125C2×Q8—591no—
126C2×D4—591no—
127C2×D4—1181no—
128C22×C4—21no—
129C22×C4—1181no—
130C22×C4C22×D5911yescharacteristic
131M16—21no—
132M16—592no—
133M16—1184no—
134M16—1181no—
135M16—1181no—
136M16—1181no—
137M16—1181no—
138M16—1181no—
139M16D23612yes—
140C2×C8—21no—
141C2×C8—592no—
142C2×C8—1184no—
143C2×C8—1181no—
144C2×C8—1181no—
145C4⋊C4—21no—
146C22⋊C4—21no—
147C42—21no—
148C42—21no—
149C42C4×D5911yescharacteristic
150C42C4×D5911yescharacteristic
151C23—1181no—
152C23#1174568711yescharacteristic
153Q8—592no—
154Q8—1181no—
155D4—592no—
156D4—1182no—
157D4—1182no—
158D4—1181no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—42no—
162C2×C4—41no—
163C2×C4—1181no—
164C2×C4—1182no—
165C2×C4—1182no—
166C2×C4C2×C4×D5911yescharacteristic
167C2×C4C2×D23611yescharacteristic
168C2×C4#1174568511yescharacteristic
169C2×C4D4×D5911yescharacteristic
170C2×C4D4×D5911yescharacteristic
171C2×C4Q8×D5911yescharacteristic
172C8—22no—
173C8—1182no—
174C8—1182no—
175C8—2361no—
176C22—41no—
177C22—1182no—
178C22—4721no—
179C22(C22⋊D59)⋊C411yescharacteristic
180C22#1427370711yescharacteristic
181C22#1427370911yescharacteristic
182C4—22no—
183C4—41no—
184C4—81no—
185C4—1182no—
186C4C4⋊C4×D5911yescharacteristic
187C4C4×D23611yescharacteristic
188C4#1427369711yescharacteristic
189C4#1427370511yescharacteristic
190C2—21no—
191C2—21no—
192C2—21no—
193C2—2362no—
194C2#1683727611yescharacteristic
subgroupG/H
centerC4#14273697
commutatorC2×C4×C59C22×C4
FrattiniC22×C4C22×D59
FittingC59×#339C2
socleC2×C59#385
hypercenter#339D59
hypocenterC59#1861
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
2. #16837450C2semidirect
3. #16837426C2semidirect
6. #16837172C2semidirect
7. C59×#339C2semidirect
18. #14273655C4semidirect
19. #14273655C4semidirect
104. #339D59semidirect
105. C59#1861semidirect