Finite Group Databasebeta

← #21424591

Subgroups — #21424591

Order 7552.

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

normal subgroups only

This group has 310 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#16837879C211yesmaximal, characteristic, complemented
3#16837420C211yesmaximal, characteristic
4#16837410C211yesmaximal, characteristic, complemented
5#16837375C211yesmaximal, characteristic
6#16837173C211yesmaximal, characteristic, complemented
7C59×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
8C2×#11745685C2211yescharacteristic
9C22×Dic118C2211yescharacteristic
10#14273760—22no—
11#14273760—22no—
12C2×Dic236C412yescomplemented
13C2×#11745660C412yescomplemented
14C2×#11745664C2211yescharacteristic
15C4×Dic118—22no—
16#14273692—22no—
17#14273686C2211yescharacteristic
18#14273683—22no—
19#14273655—22no—
20#14273650—22no—
21#14273641—22no—
22C2×M16×C59C2211yescharacteristic
23#117×C59C2211yescharacteristic
24#117×C59C2211yescharacteristic
25C22×C4×C59C2311yescharacteristic
26C2×C22⋊D59—21no—
27C22×Dic59—21no—
28#11745685—21no—
29#11745685—21no—
30#11745685—21no—
31#11745685—21no—
32C2×D236C2×C411yescharacteristic
33C2×C4×D59—21no—
34C2×Dic118—21no—
35C2×Dic118—21no—
36C2×Dic118—21no—
37C2×Dic118C2×C411yescharacteristic
38C2×Dic118C2×C412yes—
39C2×Dic118D412yes—
40C2×Dic118D412yes—
41M16×C59—21no—
42M16×C59—21no—
43C2×C8×C59C2×C412yes—
44C4⋊C4×C59—21no—
45C4⋊C4×C59—21no—
46C22⋊C4×C59—21no—
47C22⋊C4×C59—21no—
48C42×C59—21no—
49C42×C59D412yes—
50C22⋊Dic59D412yes—
51C4⋊Dic59—21no—
52Dic59⋊C4—24no—
53C4×Dic59—24no—
54C4×Dic59—21no—
55#11745664—21no—
56#11745664—21no—
57C2×C59⋊C8—21no—
58Dic236—24no—
59#11745660—24no—
60C23×C59C2×D411yescharacteristic
61C22×D59—21no—
62C2×C4×C59—22no—
63C2×C4×C59—41no—
64C2×C4×C59C22×C411yescharacteristic
65C2×C4×C59C2×D411yescharacteristic
66C2×C4×C59C2×D411yescharacteristic
67C2×C4×C59C2×D411yescharacteristic
68C2×C4×C59#4111yescharacteristic
69C2×C4×C59#4111yescharacteristic
70C22⋊D59—41no—
71C22⋊D59—41no—
72C2×Dic59—22no—
73C2×Dic59—22no—
74C2×Dic59—22no—
75C2×Dic59—21no—
76C2×Dic59—22no—
77D236—21no—
78D236—21no—
79C4×D59—41no—
80C4×D59—41no—
81Dic118—22no—
82Dic118—22no—
83Dic118—22no—
84Dic118—21no—
85Dic118—21no—
86Dic118C22⋊C414yes—
87C8×C59—22no—
88C59⋊C8—41no—
89C22×C59—41no—
90C22×C59C4×D411yescharacteristic
91C22×C59#12011yescharacteristic
92C22×C59#12111yescharacteristic
93C2×D59—41no—
94C2×D59—81no—
95C4×C59—42no—
96C4×C59—81no—
97C4×C59C2×C22⋊C411yescharacteristic
98C4×C59C4×D411yescharacteristic
99C4×C59#12111yescharacteristic
100C4×C59#12311yescharacteristic
101Dic59—24no—
102Dic59—42no—
103Dic59—41no—
104#1905—591nomaximal, Sylow
105C2×C59—21no—
106C2×C59—21no—
107C2×C59—21no—
108C2×C59#38611yescharacteristic
109D59—81no—
110C2×#137—591no—
111#519—591no—
112#421—591no—
113#419—591no—
114#410—591no—
115#344—591no—
116H(3,ℤ/4)D5911yescharacteristic, complemented
117C59#190511yescharacteristic, complemented, Sylow
118C2×#41—591no—
119C22×Q8—591no—
120#137—1182no—
121#137—1182no—
122C2×Q16—592no—
123C2×SD16—592no—
124C2×M16—591no—
125C2×M16C2×D5911yescharacteristic
126C4×Q8—1182no—
127C4×Q8—1182no—
128#117—591no—
129#117—1182no—
130#117C2×D5911yescharacteristic
131#117C2×D5911yescharacteristic
132#104—1182no—
133#103—1182no—
134#99—1182no—
135#41—1181no—
136#41—1181no—
137#41—1181no—
138#41—1181no—
139C2×Q8—592no—
140C2×Q8—591no—
141C2×Q8—592no—
142C2×Q8—592no—
143C2×Q8—1181no—
144C2×Q8—1181no—
145C2×Q8—1181no—
146C2×D4—591no—
147C2×D4—1181no—
148C22×C4—1181no—
149C22×C4—1181no—
150C22×C4C22×D5911yescharacteristic
151Q16—1184no—
152SD16—1184no—
153M16—21no—
154M16—21no—
155M16—1181no—
156M16—1181no—
157C2×C8—1181no—
158C2×C8C4×D5912yes—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—1184no—
162C4⋊C4—1181no—
163C22⋊C4—21no—
164C22⋊C4—21no—
165C22⋊C4—592no—
166C42—21no—
167C42—1184no—
168C42—1181no—
169C42D23612yes—
170C23—1181no—
171C23D4×D5911yescharacteristic
172Q8—594no—
173Q8—1182no—
174Q8—1182no—
175Q8—1182no—
176Q8—1181no—
177Q8—1181no—
178D4—1181no—
179D4—1181no—
180D4—2361no—
181D4—2361no—
182C2×C4—22no—
183C2×C4—41no—
184C2×C4—1182no—
185C2×C4—1182no—
186C2×C4—1182no—
187C2×C4—1181no—
188C2×C4—1182no—
189C2×C4—2361no—
190C2×C4—2361no—
191C2×C4C2×C4×D5911yescharacteristic
192C2×C4C2×D23611yescharacteristic
193C2×C4#1174568511yescharacteristic
194C2×C4D4×D5911yescharacteristic
195C2×C4D4×D5911yescharacteristic
196C2×C4#1174568911yescharacteristic
197C8—22no—
198C8—2361no—
199C22—41no—
200C22—4721no—
201C22—2361no—
202C22#1427368911yescharacteristic
203C22#1427369711yescharacteristic
204C22#1427370011yescharacteristic
205C4—42no—
206C4—81no—
207C4—1184no—
208C4—2362no—
209C4—2361no—
210C4C22⋊C4×D5911yescharacteristic
211C4C4×D23611yescharacteristic
212C4#1427370211yescharacteristic
213C4#1427371211yescharacteristic
214C2—21no—
215C2—21no—
216C2—21no—
217C2—4721no—
218C2#1683728011yescharacteristic
subgroupG/H
centerC2#16837280
commutatorC2×C4×C59C22×C4
FrattiniC22×C4C22×D59
FittingC59×H(3,ℤ/4)C2
socleC2×C59#386
hypercenterH(3,ℤ/4)D59
hypocenterC59#1905
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C22×C4 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
2. #16837879C2semidirect
4. #16837410C2semidirect
6. #16837173C2semidirect
7. C59×H(3,ℤ/4)C2semidirect
12. C2×Dic236C4semidirect
13. C2×#11745660C4semidirect
116. H(3,ℤ/4)D59semidirect
117. C59#1905semidirect