Finite Group Databasebeta

← #21425371

Subgroups — #21425371

Order 7552.

274 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 65 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×#14273755C211yesmaximal, characteristic
2#16837418C211yesmaximal, characteristic, complemented
3#16837408C211yesmaximal, characteristic, complemented
4#16837384C211yesmaximal, characteristic, complemented
5C2×#14273643C211yesmaximal, characteristic, complemented
6#16837174C211yesmaximal, characteristic, complemented
7C59×#430C211yesmaximal, characteristic, complemented
8C2×#11745685C2211yescharacteristic
9C22×D236C2211yescharacteristic
10#14273755—22no—
11#14273755—22no—
12C2×#11745660—21no—
13C2×D472—21no—
14C2×#11745664C2211yescharacteristic
15#14273686C2211yescharacteristic
16#14273653—22no—
17#14273649—22no—
18#14273645—21no—
19#14273643—21no—
20#14273643—22no—
21C2×M16×C59C2211yescharacteristic
22C2×M16×C59C2211yescharacteristic
23C2×M16×C59C2211yescharacteristic
24#108×C59—22no—
25C23×D59—21no—
26C22×C4×C59C2311yescharacteristic
27C2×C22⋊D59—21no—
28#11745685—21no—
29#11745685—21no—
30#11745685—21no—
31#11745685—21no—
32C2×D236—21no—
33C2×D236—21no—
34C2×D236—21no—
35C2×D236—21no—
36C2×D236—21no—
37C2×D236D411yescharacteristic
38C2×D236D412yes—
39C2×C4×D59—21no—
40C2×Dic118D411yescharacteristic
41M16×C59—21no—
42M16×C59—21no—
43M16×C59—21no—
44M16×C59—21no—
45M16×C59D412yes—
46M16×C59D412yes—
47C2×C8×C59—21no—
48C2×C8×C59—21no—
49C2×C8×C59—21no—
50C22⋊Dic59—21no—
51C4⋊Dic59—21no—
52C4×Dic59—21no—
53#11745664—21no—
54#11745664—21no—
55C2×C59⋊C8—21no—
56D472—24no—
57#11745660—24no—
58C23×C59#4111yescharacteristic
59C22×D59—22no—
60C22×D59—21no—
61C22×D59—41no—
62C22×D59—41no—
63C22×D59—82no—
64C2×C4×C59C2×D411yescharacteristic
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—21no—
73C2×Dic59—41no—
74D236—22no—
75D236—21no—
76D236—21no—
77D236—22no—
78D236—41no—
79D236—41no—
80C4×D59—41no—
81C4×D59—41no—
82Dic118—21no—
83Dic118—21no—
84C8×C59—22no—
85C8×C59—22no—
86C8×C59—41no—
87C59⋊C8—41no—
88C22×C59—41no—
89C22×C59#12111yescharacteristic
90C22×C59#12311yescharacteristic
91C22×C59#12411yescharacteristic
92C2×D59—41no—
93C2×D59—42no—
94C2×D59—82no—
95C2×D59—82no—
96C2×D59—81no—
97C2×D59—82no—
98C4×C59#12011yescharacteristic
99C4×C59#12111yescharacteristic
100C4×C59#12111yescharacteristic
101C4×C59#12311yescharacteristic
102Dic59—41no—
103Dic59—81no—
104#2048—591nomaximal, Sylow
105C2×C59—21no—
106C2×C59—21no—
107C2×C59—21no—
108C2×C59#39411yescharacteristic
109D59—81no—
110D59—82no—
111C2×AGL(1,ℤ/8)—591no—
112#430D5911yescharacteristic, complemented
113#421—591no—
114#418—591no—
115#413—591no—
116C2×#100—591no—
117#344—591no—
118C59#204811yescharacteristic, complemented, Sylow
119C2×#41—591no—
120C22×D4—591no—
121AGL(1,ℤ/8)—1182no—
122AGL(1,ℤ/8)—1182no—
123C2×SD16—1181no—
124C2×D8—1181no—
125C2×M16—591no—
126C2×M16C2×D5911yescharacteristic
127C2×M16C2×D5911yescharacteristic
128C2×M16C2×D5911yescharacteristic
129#117—591no—
130#108—22no—
131#104—1182no—
132#102—1182no—
133#101—1181no—
134#100—1181no—
135#100—1182no—
136C24—1181no—
137#41—1181no—
138#41—1181no—
139#41—1181no—
140#41—1181no—
141C2×Q8—591no—
142C2×D4—591no—
143C2×D4—592no—
144C2×D4—1181no—
145C2×D4—1181no—
146C2×D4—1181no—
147C2×D4—1181no—
148C2×D4—1181no—
149C2×D4—1181no—
150C22×C4—1181no—
151C22×C4C22×D5911yescharacteristic
152SD16—1184no—
153D8—1184no—
154M16—21no—
155M16—21no—
156M16—21no—
157M16—21no—
158M16—1181no—
159M16—1181no—
160M16D23612yes—
161M16C22⋊D5912yes—
162C2×C8—21no—
163C2×C8—21no—
164C2×C8—21no—
165C2×C8—1181no—
166C4⋊C4—1181no—
167C22⋊C4—1181no—
168C42—1181no—
169C23—1182no—
170C23—1181no—
171C23—4722no—
172C23—2361no—
173C23—2361no—
174C23#1174568911yescharacteristic
175Q8—1181no—
176Q8—1181no—
177D4—1181no—
178D4—1182no—
179D4—1181no—
180D4—1182no—
181D4—2361no—
182D4—2361no—
183D4—2361no—
184D4—2361no—
185C2×C4—1181no—
186C2×C4—2361no—
187C2×C4—2361no—
188C2×C4—2361no—
189C2×C4C2×D23611yescharacteristic
190C2×C4#1174568511yescharacteristic
191C2×C4D4×D5911yescharacteristic
192C2×C4D4×D5911yescharacteristic
193C2×C4#1174568911yescharacteristic
194C2×C4C2×C22⋊D5911yescharacteristic
195C8—22no—
196C8—22no—
197C8—41no—
198C8—2361no—
199C22—41no—
200C22—4722no—
201C22—4721no—
202C22—4722no—
203C22—4722no—
204C22—2361no—
205C22—2362no—
206C22#1427370211yescharacteristic
207C22#1427371211yescharacteristic
208C22#1427371611yescharacteristic
209C4—4721no—
210C4—2361no—
211C4#1427369511yescharacteristic
212C4#1427370111yescharacteristic
213C4#1427370211yescharacteristic
214C4#1427371211yescharacteristic
215C2—21no—
216C2—21no—
217C2—21no—
218C2—4722no—
219C2—4721no—
220C2#1683731911yescharacteristic
subgroupG/H
centerC2#16837319
commutatorC22×C4×C59C23
FrattiniC22×C4C22×D59
FittingC59×#430C2
socleC2×C59#394
hypercenter#430D59
hypocenterC59#2048
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C22×C4 ◁ #430

Complements

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

NH ≅ G/Ntype
2. #16837418C2semidirect
3. #16837408C2semidirect
4. #16837384C2semidirect
5. C2×#14273643C2semidirect
6. #16837174C2semidirect
7. C59×#430C2semidirect
112. #430D59semidirect
118. C59#2048semidirect