Finite Group Databasebeta

← #21424630

Subgroups — #21424630

Order 7552.

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

normal subgroups only

This group has 314 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#16837973C211yesmaximal, characteristic
2#16837879C211yesmaximal, characteristic, complemented
3#16837419C211yesmaximal, characteristic
4C2×#14273645C211yesmaximal, characteristic, complemented
5#16837159C211yesmaximal, characteristic, complemented
6#16837158C211yesmaximal, characteristic, complemented
7C59×#421C211yesmaximal, characteristic
8C22×Dic118C2211yescharacteristic
9C2×#11745664C2211yescharacteristic
10#14273725C412yescomplemented
11#14273714C412yescomplemented
12#14273708—22no—
13#14273706—22no—
14C4×Dic118—22no—
15#14273692—22no—
16#14273686C2211yescharacteristic
17#14273686C2211yescharacteristic
18#14273683—22no—
19#14273654—22no—
20#14273645—22no—
21C2×#41×C59C2211yescharacteristic
22C2×M16×C59C2211yescharacteristic
23#117×C59C2211yescharacteristic
24#104×C59—22no—
25#41×C59—21no—
26#41×C59—21no—
27#41×C59—21no—
28#41×C59—21no—
29C2×Q8×C59C2×C411yescharacteristic
30C2×D4×C59—21no—
31C2×D4×C59C2×C411yescharacteristic
32C22×C4×C59—21no—
33C22×C4×C59C2311yescharacteristic
34C22×Dic59D412yes—
35C2×Dic118—21no—
36C2×Dic118—21no—
37C2×Dic118—21no—
38C2×Dic118—21no—
39C2×Dic118C2×C412yes—
40C2×Dic118D412yes—
41M16×C59—21no—
42M16×C59—21no—
43C2×C8×C59—21no—
44C4⋊C4×C59—21no—
45C22⋊C4×C59—21no—
46C42×C59D412yes—
47C22⋊Dic59—21no—
48C22⋊Dic59—21no—
49C22⋊Dic59—24no—
50C4⋊Dic59—21no—
51C4⋊Dic59—21no—
52Dic59⋊C4—24no—
53Dic59⋊C4—24no—
54C4×Dic59—24no—
55C4×Dic59C2×C412yes—
56C4×Dic59D412yes—
57#11745664—21no—
58#11745664—21no—
59C2×C59⋊C8—21no—
60C23×C59—21no—
61C23×C59C2×D411yescharacteristic
62Q8×C59—21no—
63Q8×C59—21no—
64D4×C59—21no—
65D4×C59—21no—
66D4×C59—41no—
67D4×C59—41no—
68C2×C4×C59—21no—
69C2×C4×C59—22no—
70C2×C4×C59—41no—
71C2×C4×C59—41no—
72C2×C4×C59C22×C411yescharacteristic
73C2×C4×C59C2×D411yescharacteristic
74C2×C4×C59C2×D411yescharacteristic
75C2×C4×C59C2×D411yescharacteristic
76C2×C4×C59#4111yescharacteristic
77C2×C4×C59#4111yescharacteristic
78C2×Dic59—22no—
79C2×Dic59—22no—
80C2×Dic59—22no—
81C2×Dic59—22no—
82C2×Dic59C22⋊C414yes—
83Dic118—22no—
84Dic118—22no—
85Dic118—22no—
86Dic118—22no—
87C8×C59—41no—
88C59⋊C8—41no—
89C22×C59—41no—
90C22×C59—42no—
91C22×C59—41no—
92C22×C59C2×C22⋊C411yescharacteristic
93C22×C59#12011yescharacteristic
94C22×C59#12311yescharacteristic
95C4×C59—42no—
96C4×C59—41no—
97C4×C59C4×D411yescharacteristic
98C4×C59C4×D411yescharacteristic
99C4×C59#12111yescharacteristic
100C4×C59#12111yescharacteristic
101Dic59—24no—
102Dic59—42no—
103Dic59—42no—
104#1912—591nomaximal, Sylow
105C2×C59—21no—
106C2×C59—21no—
107C2×C59—21no—
108C2×C59—81no—
109C2×C59#38611yescharacteristic
110#536—591no—
111#519—591no—
112#421—591no—
113#421D5911yescharacteristic
114C2×#101—591no—
115H(3,ℤ/4)—591no—
116H(3,ℤ/4)—591no—
117C59#191211yescharacteristic, complemented, Sylow
118C2×#41C2×D5911yescharacteristic
119C22×Q8—591no—
120C2×M16—591no—
121C2×M16C2×D5911yescharacteristic
122C4⋊Q8—592no—
123#124—592no—
124#123—1182no—
125C22⋊Q8—1182no—
126C4×Q8—1182no—
127C4×Q8—1182no—
128#117—591no—
129#117—591no—
130#117—1182no—
131#117C2×D5911yescharacteristic
132#104—22no—
133#104—1182no—
134#101—1182no—
135#41—21no—
136#41—21no—
137#41—21no—
138#41—21no—
139C2×Q8—592no—
140C2×Q8—592no—
141C2×Q8—1181no—
142C2×Q8—1181no—
143C2×Q8—1181no—
144C2×Q8—1181no—
145C2×Q8C4×D5911yescharacteristic
146C2×D4—21no—
147C2×D4C4×D5911yescharacteristic
148C22×C4—21no—
149C22×C4—592no—
150C22×C4C22×D5911yescharacteristic
151M16—21no—
152M16—21no—
153M16—1181no—
154M16—1181no—
155C2×C8—21no—
156C2×C8—1181no—
157C4⋊C4—21no—
158C4⋊C4—1184no—
159C4⋊C4—1184no—
160C4⋊C4—1181no—
161C4⋊C4—1181no—
162C22⋊C4—21no—
163C22⋊C4—1184no—
164C22⋊C4—1181no—
165C22⋊C4—1181no—
166C42—592no—
167C42—592no—
168C42—1184no—
169C42C22⋊D5912yes—
170C23—21no—
171C23D4×D5911yescharacteristic
172Q8—21no—
173Q8—21no—
174Q8—1182no—
175Q8—1182no—
176Q8—1182no—
177Q8—1182no—
178D4—21no—
179D4—21no—
180D4—41no—
181D4—41no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—594no—
187C2×C4—1182no—
188C2×C4—1182no—
189C2×C4—1182no—
190C2×C4—1182no—
191C2×C4C2×C4×D5911yescharacteristic
192C2×C4#1174568511yescharacteristic
193C2×C4D4×D5911yescharacteristic
194C2×C4D4×D5911yescharacteristic
195C2×C4#1174568711yescharacteristic
196C2×C4C2×C22⋊D5911yescharacteristic
197C8—41no—
198C8—2361no—
199C22—41no—
200C22—42no—
201C22—41no—
202C22C22⋊C4×D5911yescharacteristic
203C22#1427369511yescharacteristic
204C22#1427370911yescharacteristic
205C4—42no—
206C4—41no—
207C4—1184no—
208C4—2362no—
209C4—2362no—
210C4(C22⋊D59)⋊C411yescharacteristic
211C4C4×C22⋊D5911yescharacteristic
212C4#1427369811yescharacteristic
213C4#1427370011yescharacteristic
214C2—21no—
215C2—21no—
216C2—21no—
217C2—81no—
218C2#1683727811yescharacteristic
subgroupG/H
centerC2#16837278
commutatorC2×C4×C59C22×C4
FrattiniC22×C4C22×D59
FittingC59×#421C2
socleC2×C59#386
hypercenter#421D59
hypocenterC59#1912
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
2. #16837879C2semidirect
4. C2×#14273645C2semidirect
5. #16837159C2semidirect
6. #16837158C2semidirect
10. #14273725C4semidirect
11. #14273714C4semidirect
117. C59#1912semidirect