Finite Group Databasebeta

← #21424766

Subgroups — #21424766

Order 7552.

216 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 71 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#16837451C211yesmaximal, characteristic, complemented
2#16837420C211yesmaximal, characteristic
3C2×#14273655C211yesmaximal, characteristic
4#16837384C211yesmaximal, characteristic
5C4×#11745664C211yesmaximal, characteristic, complemented
6#16837172C211yesmaximal, characteristic, complemented
7C59×#339C211yesmaximal, characteristic, complemented
8C2×#11745685C2211yescharacteristic
9C2×#11745664C2211yescharacteristic
10C2×#11745664C2211yescharacteristic
11C2×#11745664C2211yescharacteristic
12#14273663—22no—
13#14273655—21no—
14#14273655—21no—
15#14273655—22no—
16#14273645C412yescomplemented
17#14273643C412yescomplemented
18#14273638—21no—
19C4×C59⋊C8—21no—
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#11745685—21no—
29#11745685—21no—
30C2×D236C2×C411yescharacteristic
31C2×C4×D59—21no—
32C2×Dic118C2×C411yescharacteristic
33M16×C59—21no—
34M16×C59C2×C412yes—
35C2×C8×C59—21no—
36C4⋊C4×C59—21no—
37C22⋊C4×C59—21no—
38C42×C59—21no—
39C42×C59—21no—
40C42×C59D411yescharacteristic
41C42×C59D411yescharacteristic
42#11745664—21no—
43#11745664—21no—
44#11745664—21no—
45#11745664—21no—
46#11745664C2×C412yes—
47#11745664D412yes—
48C2×C59⋊C8—21no—
49C2×C59⋊C8—21no—
50C2×C59⋊C8—21no—
51C23×C59#4111yescharacteristic
52C22×D59—21no—
53C2×C4×C59—21no—
54C2×C4×C59—21no—
55C2×C4×C59—42no—
56C2×C4×C59—41no—
57C2×C4×C59C22×C411yescharacteristic
58C2×C4×C59C2×D411yescharacteristic
59C2×C4×C59C2×D411yescharacteristic
60C2×C4×C59#4111yescharacteristic
61C2×C4×C59#4111yescharacteristic
62C2×C4×C59#4111yescharacteristic
63C22⋊D59—41no—
64C22⋊D59—41no—
65C2×Dic59—21no—
66D236—21no—
67D236—21no—
68C4×D59—41no—
69C4×D59—41no—
70Dic118—21no—
71Dic118—21no—
72C8×C59—22no—
73C59⋊C8—22no—
74C59⋊C8—22no—
75C59⋊C8—41no—
76C22×C59—41no—
77C22×C59#11711yescharacteristic
78C22×C59#12311yescharacteristic
79C22×C59#12411yescharacteristic
80C2×D59—41no—
81C2×D59—81no—
82C4×C59—22no—
83C4×C59—41no—
84C4×C59—81no—
85C4×C59C4×D411yescharacteristic
86C4×C59C4×D411yescharacteristic
87C4×C59#12111yescharacteristic
88C4×C59#12611yescharacteristic
89Dic59—41no—
90#1932—591nomaximal, Sylow
91C2×C59—21no—
92C2×C59—21no—
93C2×C59—21no—
94C2×C59#38811yescharacteristic
95D59—81no—
96#430—591no—
97#421—591no—
98C2×#104—591no—
99#413—591no—
100C4×M16—591no—
101#344—591no—
102#339D5911yescharacteristic, complemented
103C59#193211yescharacteristic, complemented, Sylow
104C2×#41—591no—
105C2×M16—591no—
106C2×M16—591no—
107C2×M16—591no—
108C2×M16C2×D5911yescharacteristic
109#117C2×D5911yescharacteristic
110C2×C42C2×D5911yescharacteristic
111#108—1182no—
112#104—1182no—
113#104—1181no—
114#104—1181no—
115#101—592no—
116#100—592no—
117#97—1181no—
118C4×C8—1181no—
119#41—1181no—
120#41—1181no—
121#41—1181no—
122#41—1181no—
123C2×Q8—591no—
124C2×D4—591no—
125C2×D4—1181no—
126C22×C4—21no—
127C22×C4—1181no—
128C22×C4C22×D5911yescharacteristic
129M16—21no—
130M16—592no—
131M16—592no—
132M16—1181no—
133M16—1181no—
134M16—1181no—
135M16—1181no—
136M16C4×D5912yes—
137C2×C8—21no—
138C2×C8—1181no—
139C2×C8—1181no—
140C2×C8—1181no—
141C4⋊C4—21no—
142C22⋊C4—21no—
143C42—21no—
144C42—21no—
145C42D23611yescharacteristic
146C42D23611yescharacteristic
147C23—1181no—
148C23#1174568711yescharacteristic
149Q8—1181no—
150Q8—1181no—
151D4—1181no—
152D4—1181no—
153D4—2361no—
154D4—2361no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—42no—
158C2×C4—41no—
159C2×C4—1181no—
160C2×C4—2361no—
161C2×C4—2361no—
162C2×C4C2×C4×D5911yescharacteristic
163C2×C4C2×D23611yescharacteristic
164C2×C4#1174568511yescharacteristic
165C2×C4D4×D5911yescharacteristic
166C2×C4#1174568711yescharacteristic
167C2×C4#1174568911yescharacteristic
168C8—22no—
169C8—1182no—
170C8—1182no—
171C8—2361no—
172C22—41no—
173C22—4721no—
174C22—2361no—
175C22#1427368511yescharacteristic
176C22#1427371111yescharacteristic
177C22#1427371311yescharacteristic
178C4—22no—
179C4—41no—
180C4—81no—
181C4—2361no—
182C4(C22⋊D59)⋊C411yescharacteristic
183C4C4×D23611yescharacteristic
184C4#1427370211yescharacteristic
185C4#1427372211yescharacteristic
186C2—21no—
187C2—21no—
188C2—21no—
189C2—4721no—
190C2#1683729411yescharacteristic
subgroupG/H
centerC4#14273702
commutatorC2×C4×C59C22×C4
FrattiniC22×C4C22×D59
FittingC59×#339C2
socleC2×C59#388
hypercenter#339D59
hypocenterC59#1932
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
1. #16837451C2semidirect
5. C4×#11745664C2semidirect
6. #16837172C2semidirect
7. C59×#339C2semidirect
16. #14273645C4semidirect
17. #14273643C4semidirect
102. #339D59semidirect
103. C59#1932semidirect