Finite Group Databasebeta

← #21425378

Subgroups — #21425378

Order 7552.

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

normal subgroups only

This group has 254 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×#14273760C211yesmaximal, characteristic
2#16837418C211yesmaximal, characteristic
3#16837412C211yesmaximal, characteristic, complemented
4#16837384C211yesmaximal, characteristic
5C2×#14273645C211yesmaximal, characteristic, complemented
6#16837174C211yesmaximal, characteristic, complemented
7C59×#430C211yesmaximal, characteristic, complemented
8C2×#11745685C2211yescharacteristic
9C22×Dic118C2211yescharacteristic
10#14273760—22no—
11#14273760—22no—
12C2×Dic236—21no—
13C2×#11745660—21no—
14C2×#11745664C2211yescharacteristic
15#14273686C2211yescharacteristic
16#14273653—22no—
17#14273652—22no—
18#14273645—21no—
19#14273645—22no—
20#14273643—21no—
21C2×M16×C59C2211yescharacteristic
22C2×M16×C59C2211yescharacteristic
23C2×M16×C59C2211yescharacteristic
24#108×C59—22no—
25C22×C4×C59C2311yescharacteristic
26C2×C22⋊D59—21no—
27C22×Dic59—21no—
28#11745685—21no—
29#11745685—21no—
30#11745685—21no—
31#11745685—21no—
32C2×D236D411yescharacteristic
33C2×C4×D59—21no—
34C2×Dic118—21no—
35C2×Dic118—21no—
36C2×Dic118—21no—
37C2×Dic118—21no—
38C2×Dic118—21no—
39C2×Dic118D411yescharacteristic
40C2×Dic118D412yes—
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—
56Dic236—24no—
57#11745660—24no—
58C23×C59#4111yescharacteristic
59C22×D59—21no—
60C2×C4×C59C2×D411yescharacteristic
61C2×C4×C59C2×D411yescharacteristic
62C2×C4×C59C2×D411yescharacteristic
63C2×C4×C59C2×D411yescharacteristic
64C2×C4×C59#4111yescharacteristic
65C2×C4×C59#4111yescharacteristic
66C22⋊D59—41no—
67C22⋊D59—41no—
68C2×Dic59—22no—
69C2×Dic59—21no—
70C2×Dic59—41no—
71C2×Dic59—41no—
72C2×Dic59—41no—
73D236—21no—
74D236—21no—
75C4×D59—41no—
76C4×D59—41no—
77Dic118—22no—
78Dic118—21no—
79Dic118—21no—
80Dic118—22no—
81Dic118—41no—
82Dic118—41no—
83C8×C59—22no—
84C8×C59—22no—
85C8×C59—41no—
86C59⋊C8—41no—
87C22×C59—41no—
88C22×C59#12111yescharacteristic
89C22×C59#12311yescharacteristic
90C22×C59#12411yescharacteristic
91C2×D59—41no—
92C2×D59—81no—
93C4×C59#12011yescharacteristic
94C4×C59#12111yescharacteristic
95C4×C59#12111yescharacteristic
96C4×C59#12311yescharacteristic
97Dic59—42no—
98Dic59—41no—
99Dic59—81no—
100#2049—591nomaximal, Sylow
101C2×C59—21no—
102C2×C59—21no—
103C2×C59—21no—
104C2×C59#39411yescharacteristic
105D59—81no—
106C2×#137—591no—
107#430D5911yescharacteristic, complemented
108#421—591no—
109#419—591no—
110#413—591no—
111C2×#101—591no—
112#344—591no—
113C59#204911yescharacteristic, complemented, Sylow
114C2×#41—591no—
115C22×Q8—591no—
116#137—1182no—
117#137—1182no—
118C2×Q16—1181no—
119C2×SD16—1181no—
120C2×M16—591no—
121C2×M16C2×D5911yescharacteristic
122C2×M16C2×D5911yescharacteristic
123C2×M16C2×D5911yescharacteristic
124#117—591no—
125#108—22no—
126#104—1182no—
127#103—1182no—
128#101—1181no—
129#101—1182no—
130#100—1181no—
131#41—1181no—
132#41—1181no—
133#41—1181no—
134#41—1181no—
135C2×Q8—591no—
136C2×Q8—592no—
137C2×Q8—1181no—
138C2×Q8—1181no—
139C2×Q8—1181no—
140C2×Q8—1181no—
141C2×Q8—1181no—
142C2×D4—591no—
143C2×D4—1181no—
144C22×C4—1181no—
145C22×C4—1181no—
146C22×C4C22×D5911yescharacteristic
147Q16—1184no—
148SD16—1184no—
149M16—21no—
150M16—21no—
151M16—21no—
152M16—21no—
153M16—1181no—
154M16—1181no—
155M16D23612yes—
156M16C22⋊D5912yes—
157C2×C8—21no—
158C2×C8—21no—
159C2×C8—21no—
160C2×C8—1181no—
161C4⋊C4—1181no—
162C22⋊C4—1181no—
163C42—1181no—
164C23—1181no—
165C23#1174568911yescharacteristic
166Q8—1182no—
167Q8—1181no—
168Q8—1181no—
169Q8—1182no—
170Q8—2361no—
171Q8—2361no—
172D4—1181no—
173D4—1181no—
174D4—2361no—
175D4—2361no—
176C2×C4—1182no—
177C2×C4—1181no—
178C2×C4—2361no—
179C2×C4—2361no—
180C2×C4—2361no—
181C2×C4—2361no—
182C2×C4—2361no—
183C2×C4C2×D23611yescharacteristic
184C2×C4#1174568511yescharacteristic
185C2×C4D4×D5911yescharacteristic
186C2×C4D4×D5911yescharacteristic
187C2×C4#1174568911yescharacteristic
188C2×C4C2×C22⋊D5911yescharacteristic
189C8—22no—
190C8—22no—
191C8—41no—
192C8—2361no—
193C22—41no—
194C22—4721no—
195C22—2361no—
196C22#1427370211yescharacteristic
197C22#1427371211yescharacteristic
198C22#1427371611yescharacteristic
199C4—4721no—
200C4—2361no—
201C4—2362no—
202C4#1427369511yescharacteristic
203C4#1427370111yescharacteristic
204C4#1427370211yescharacteristic
205C4#1427371211yescharacteristic
206C2—21no—
207C2—21no—
208C2—21no—
209C2—4721no—
210C2#1683731911yescharacteristic
subgroupG/H
centerC2#16837319
commutatorC22×C4×C59C23
FrattiniC22×C4C22×D59
FittingC59×#430C2
socleC2×C59#394
hypercenter#430D59
hypocenterC59#2049
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
3. #16837412C2semidirect
5. C2×#14273645C2semidirect
6. #16837174C2semidirect
7. C59×#430C2semidirect
107. #430D59semidirect
113. C59#2049semidirect