Finite Group Databasebeta

← #21424477

Subgroups — #21424477

Order 7552.

332 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 85 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#16838169C211yesmaximal, characteristic, complemented
2#16837948C211yesmaximal, characteristic
3#16837420C212yesmaximal, complemented
4#16837161C212yesmaximal, complemented
5C59×#410C211yesmaximal, characteristic, complemented
6C2×#11745685C2211yescharacteristic
7#14273734—24no—
8C2×#11745664—22no—
9C2×#11745664C2212yes—
10#14273725C411yescharacteristic, complemented
11#14273723C411yescharacteristic, complemented
12#14273716C411yescharacteristic, complemented
13#14273714C411yescharacteristic, complemented
14#14273699—22no—
15C4×C22⋊D59—22no—
16C2×C4×Dic59C2211yescharacteristic
17#14273655—24no—
18C2×#41×C59C2211yescharacteristic
19#117×C59C2212yes—
20#99×C59—22no—
21#41×C59—22no—
22#41×C59—22no—
23C2×Q8×C59C2×C411yescharacteristic
24C2×D4×C59C2×C411yescharacteristic
25C2×D4×C59D412yes—
26C22×C4×C59D412yes—
27C22×C4×C59C2311yescharacteristic
28C2×C22⋊D59—22no—
29C2×C22⋊D59—21no—
30C22×Dic59—21no—
31#11745685—22no—
32#11745685—22no—
33C2×D236C2×C411yescharacteristic
34C2×C4×D59—21no—
35C2×Dic118C2×C411yescharacteristic
36C4⋊C4×C59—22no—
37C22⋊C4×C59—22no—
38C42×C59—22no—
39C22⋊Dic59—22no—
40(C2×D59)⋊C4—22no—
41Dic59⋊C4—22no—
42C4×Dic59—21no—
43C4×Dic59C2×C411yescharacteristic
44C4×Dic59C2×C411yescharacteristic
45#11745664—24no—
46#11745664—22no—
47#11745664D414yescomplemented
48C2×C59⋊C8—24no—
49C2×C59⋊C8—22no—
50C23×C59C22⋊C412yes—
51C23×C59C2×D411yescharacteristic
52C22×D59—21no—
53Q8×C59—22no—
54D4×C59—24no—
55D4×C59—22no—
56C2×C4×C59—22no—
57C2×C4×C59—22no—
58C2×C4×C59—42no—
59C2×C4×C59C22⋊C412yes—
60C2×C4×C59C22×C411yescharacteristic
61C2×C4×C59C2×D411yescharacteristic
62C2×C4×C59C2×D412yes—
63C2×C4×C59#4112yes—
64C22⋊D59—44no—
65C22⋊D59—42no—
66C2×Dic59—21no—
67C2×Dic59—21no—
68C2×Dic59—21no—
69C2×Dic59—42no—
70D236—22no—
71C4×D59—41no—
72C4×D59—41no—
73Dic118—22no—
74C59⋊C8—24no—
75C22×C59—22no—
76C22×C59—41no—
77C22×C59—42no—
78C22×C59C2×C22⋊C411yescharacteristic
79C22×C59#12112yes—
80C2×D59—42no—
81C2×D59—41no—
82C4×C59—22no—
83C4×C59—82no—
84C4×C59C4×D412yes—
85C4×C59#12011yescharacteristic
86C4×C59#12311yescharacteristic
87Dic59—22no—
88Dic59—41no—
89Dic59—41no—
90#1884—591nomaximal, Sylow
91C2×C59—21no—
92C2×C59—22no—
93C2×C59—42no—
94C2×C59#38611yescharacteristic
95D59—81no—
96#568—591no—
97#532—591no—
98#421—592no—
99#410D5911yescharacteristic, complemented
100#339—592no—
101C59#188411yescharacteristic, complemented, Sylow
102C2×#41—591no—
103C2×#41C2×D5911yescharacteristic
104#131—1184no—
105C2×M16—592no—
106C2×M16—1182no—
107C4⋊Q8—591no—
108#127—591no—
109#124—591no—
110#124—591no—
111#121—1182no—
112C4×D4—1182no—
113#117C2×D5912yes—
114C2×C42—591no—
115#104—1184no—
116#99—22no—
117#41—22no—
118#41—22no—
119#41—1182no—
120#41—1182no—
121C2×Q8—591no—
122C2×Q8C4×D5911yescharacteristic
123C2×D4—591no—
124C2×D4—1182no—
125C2×D4—1181no—
126C2×D4C4×D5911yescharacteristic
127C2×D4C22⋊D5912yes—
128C22×C4—1181no—
129C22×C4—1181no—
130C22×C4D23612yes—
131C22×C4C22×D5911yescharacteristic
132M16—594no—
133M16—1184no—
134M16—1182no—
135C2×C8—1184no—
136C2×C8—1182no—
137C4⋊C4—22no—
138C4⋊C4—1182no—
139C22⋊C4—22no—
140C22⋊C4—1182no—
141C22⋊C4—1182no—
142C42—22no—
143C42—591no—
144C42—591no—
145C42—1181no—
146C23—1181no—
147C23(C2×D59)⋊C412yes—
148C23C2×C22⋊D5911yescharacteristic
149Q8—22no—
150Q8—1182no—
151D4—24no—
152D4—22no—
153D4—1182no—
154D4—2364no—
155D4—2362no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—42no—
159C2×C4—1181no—
160C2×C4—1181no—
161C2×C4—1181no—
162C2×C4—2362no—
163C2×C4—2361no—
164C2×C4—2361no—
165C2×C4(C2×D59)⋊C412yes—
166C2×C4C2×C4×D5911yescharacteristic
167C2×C4C2×D23611yescharacteristic
168C2×C4D4×D5912yes—
169C2×C4#1174568712yes—
170C8—1184no—
171C22—22no—
172C22—41no—
173C22—42no—
174C22—2362no—
175C22—2361no—
176C22C2×(C2×D59)⋊C411yescharacteristic
177C22#1427369912yes—
178C4—22no—
179C4—82no—
180C4—1182no—
181C4—2361no—
182C4—2361no—
183C4(C22⋊D59)⋊C412yes—
184C4#1427369711yescharacteristic
185C4#1427371111yescharacteristic
186C2—22no—
187C2—21no—
188C2—42no—
189C2—4721no—
190C2#1683727911yescharacteristic
subgroupG/H
centerC4#14273697
commutatorC2×C4×C59C22×C4
FrattiniC22×C4C22×D59
FittingC59×#410C2
socleC2×C59#386
hypercenter#410D59
hypocenterC59#1884
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C4 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
1. #16838169C2semidirect
3. #16837420C2semidirect
4. #16837161C2semidirect
5. C59×#410C2semidirect
10. #14273725C4semidirect
11. #14273723C4semidirect
12. #14273716C4semidirect
13. #14273714C4semidirect
47. #11745664D4semidirect
99. #410D59semidirect
101. C59#1884semidirect