Finite Group Databasebeta

← #21424568

Subgroups — #21424568

Order 7552.

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

normal subgroups only

This group has 304 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
1C2×#14273760C211yesmaximal, characteristic
2#16838168C211yesmaximal, characteristic
3#16837420C211yesmaximal, characteristic
4#16837410C211yesmaximal, characteristic, complemented
5C2×#14273645C211yesmaximal, characteristic, complemented
6C59⋊#338C211yesmaximal, characteristic, complemented
7C59×#344C211yesmaximal, characteristic, complemented
8C2×#11745685C2211yescharacteristic
9C22×Dic118C2211yescharacteristic
10#14273760—22no—
11#14273760—22no—
12C2×Dic236C412yescomplemented
13C2×#11745660C412yescomplemented
14#14273735—22no—
15#14273733—22no—
16C2×#11745664C2211yescharacteristic
17C2×#11745664C2211yescharacteristic
18M16×D59—22no—
19#14273655—22no—
20#14273650—22no—
21#14273645—22no—
22C2×M16×C59C2211yescharacteristic
23C2×M16×C59C2211yescharacteristic
24#117×C59C2211yescharacteristic
25C22×C4×C59C2311yescharacteristic
26C2×C22⋊D59—21no—
27C22×Dic59—21no—
28#11745685—21no—
29#11745685—21no—
30#11745685D412yes—
31#11745685D412yes—
32C2×D236C2×C411yescharacteristic
33C2×C4×D59—21no—
34C2×Dic118—21no—
35C2×Dic118—21no—
36C2×Dic118—21no—
37C2×Dic118—21no—
38C2×Dic118—21no—
39C2×Dic118C2×C412yes—
40C2×Dic118C2×C411yescharacteristic
41M16×C59—21no—
42M16×C59—21no—
43M16×C59—21no—
44M16×C59D412yes—
45C2×C8×C59—21no—
46C2×C8×C59C2×C412yes—
47C4⋊C4×C59—21no—
48C22⋊C4×C59—21no—
49C42×C59—21no—
50#11745664—21no—
51#11745664—21no—
52#11745664—21no—
53#11745664—21no—
54C2×C59⋊C8—21no—
55C2×C59⋊C8D412yes—
56Dic236—24no—
57#11745660—24no—
58#11745659—24no—
59C8×D59—24no—
60C23×C59#4111yescharacteristic
61C22×D59—21no—
62C2×C4×C59—41no—
63C2×C4×C59C22×C411yescharacteristic
64C2×C4×C59C2×D411yescharacteristic
65C2×C4×C59C2×D411yescharacteristic
66C2×C4×C59C2×D411yescharacteristic
67C2×C4×C59C2×D411yescharacteristic
68C2×C4×C59#4111yescharacteristic
69C22⋊D59—22no—
70C22⋊D59—22no—
71C2×Dic59—21no—
72C2×Dic59—22no—
73C2×Dic59—41no—
74C2×Dic59—41no—
75D236—21no—
76D236C22⋊C412yes—
77C4×D59—22no—
78C4×D59—22no—
79Dic118—21no—
80Dic118—22no—
81Dic118—22no—
82Dic118—41no—
83Dic118—41no—
84Dic118C22⋊C412yes—
85C8×C59—22no—
86C8×C59—22no—
87C59⋊C8—22no—
88C59⋊C8—41no—
89C22×C59—41no—
90C22×C59C4×D411yescharacteristic
91C22×C59#12111yescharacteristic
92C22×C59#12311yescharacteristic
93C2×D59—22no—
94C2×D59—81no—
95C4×C59—81no—
96C4×C59C2×C22⋊C411yescharacteristic
97C4×C59C4×D411yescharacteristic
98C4×C59#12011yescharacteristic
99C4×C59#12111yescharacteristic
100Dic59—22no—
101Dic59—42no—
102#1902—591nomaximal, Sylow
103C2×C59—21no—
104C2×C59—21no—
105C2×C59—21no—
106C2×C59#38611yescharacteristic
107D59—42no—
108C2×#137—591no—
109#568—591no—
110#421—591no—
111#419—591no—
112C2×#101—591no—
113#344D5911yescharacteristic, complemented
114#338—591no—
115C59#190211yescharacteristic, complemented, Sylow
116C2×#41—591no—
117C22×Q8—591no—
118#137—1182no—
119#137—1182no—
120C2×Q16—592no—
121C2×SD16—592no—
122#131—1182no—
123#131—1182no—
124C2×M16—591no—
125C2×M16—591no—
126C2×M16—1182no—
127C2×M16C2×D5911yescharacteristic
128C2×M16C2×D5911yescharacteristic
129#117C2×D5911yescharacteristic
130#104—1182no—
131#103—1182no—
132#101—1182no—
133#41—592no—
134#41—592no—
135#41—1181no—
136#41—1181no—
137C2×Q8—591no—
138C2×Q8—592no—
139C2×Q8—1181no—
140C2×Q8—1181no—
141C2×Q8—1181no—
142C2×Q8—1181no—
143C2×Q8—1181no—
144C2×D4—591no—
145C2×D4—1181no—
146C22×C4—1181no—
147C22×C4—1181no—
148C22×C4C22×D5911yescharacteristic
149Q16—1184no—
150SD16—1184no—
151M16—21no—
152M16—21no—
153M16—21no—
154M16—1184no—
155M16—1181no—
156M16—1181no—
157M16—1181no—
158M16—1181no—
159M16D23612yes—
160C2×C8—21no—
161C2×C8—592no—
162C2×C8—1184no—
163C2×C8—1181no—
164C2×C8C4×D5912yes—
165C4⋊C4—21no—
166C22⋊C4—21no—
167C42—21no—
168C23—1181no—
169C23#1174568511yescharacteristic
170Q8—592no—
171Q8—1181no—
172Q8—1182no—
173Q8—1182no—
174Q8—2361no—
175Q8—2361no—
176D4—592no—
177D4—1182no—
178D4—1182no—
179D4—1181no—
180C2×C4—41no—
181C2×C4—1181no—
182C2×C4—1182no—
183C2×C4—1182no—
184C2×C4—1182no—
185C2×C4—2361no—
186C2×C4—2361no—
187C2×C4C2×C4×D5911yescharacteristic
188C2×C4C2×D23611yescharacteristic
189C2×C4D4×D5911yescharacteristic
190C2×C4D4×D5911yescharacteristic
191C2×C4D4×D5911yescharacteristic
192C2×C4#1174568911yescharacteristic
193C8—22no—
194C8—22no—
195C8—1182no—
196C8—2361no—
197C22—41no—
198C22—1182no—
199C22—4721no—
200C22C4×D23611yescharacteristic
201C22#1427370011yescharacteristic
202C22#1427371211yescharacteristic
203C4—81no—
204C4—1182no—
205C4—2362no—
206C4C22⋊C4×D5911yescharacteristic
207C4#1427368911yescharacteristic
208C4#1427369711yescharacteristic
209C4#1427370211yescharacteristic
210C2—21no—
211C2—21no—
212C2—21no—
213C2—2362no—
214C2#1683728011yescharacteristic
subgroupG/H
centerC2#16837280
commutatorC2×C4×C59C22×C4
FrattiniC22×C4C22×D59
FittingC59×#344C2
socleC2×C59#386
hypercenter#344D59
hypocenterC59#1902
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C22×C4 ◁ #344

Complements

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

NH ≅ G/Ntype
4. #16837410C2semidirect
5. C2×#14273645C2semidirect
6. C59⋊#338C2semidirect
7. C59×#344C2semidirect
12. C2×Dic236C4semidirect
13. C2×#11745660C4semidirect
113. #344D59semidirect
115. C59#1902semidirect