Finite Group Databasebeta

← #21434753

Subgroups — #21434753

Order 7552.

338 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 115 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#16838010C212yesmaximal
2#16837802C211yesmaximal, characteristic, complemented
3#16837780C211yesmaximal, characteristic, complemented
4#16837769C212yesmaximal, complemented
5#16837661C211yesmaximal, characteristic
6#16837657C211yesmaximal, characteristic
7#16837642C212yesmaximal
8#16837510C211yesmaximal, characteristic, complemented
9C4×#11745672C212yesmaximal, complemented
10#16837359C211yesmaximal, characteristic
11C59×#441C211yesmaximal, characteristic, complemented
12C2×Dic236C2211yescharacteristic
13C2×#11745672C2212yes—
14C2×#11745659C2211yescharacteristic
15C2×C8×D59C2211yescharacteristic
16#14273725C2212yes—
17#14273722—22no—
18#14273721—22no—
19#14273719—22no—
20#14273718C2212yes—
21#14273717—22no—
22#14273707C2212yes—
23#14273703C2212yes—
24C4×Dic118C2212yes—
25#14273684C2211yescharacteristic
26#14273660C2212yes—
27#14273659C2211yescharacteristic
28#14273652C2212yes—
29#14273651C2212yes—
30#14273650C2212yes—
31#14273637C2211yescharacteristic
32C4×C59⋊C8C2211yescharacteristic
33C8×Dic59C2211yescharacteristic
34C2×Q16×C59C2211yescharacteristic
35C4×Q8×C59C2212yes—
36#106×C59C2211yescharacteristic
37#103×C59C2212yes—
38#97×C59C2211yescharacteristic
39C2×Q8×C59C2312yes—
40C2×C4×D59C2311yescharacteristic
41C2×Dic118C2312yes—
42Q16×C59—22no—
43C2×C8×C59C2311yescharacteristic
44C2×C8×C59C2311yescharacteristic
45C4⋊C4×C59—22no—
46C4⋊C4×C59C2312yes—
47C42×C59—22no—
48C42×C59C2311yescharacteristic
49#11745672—24no—
50(C2×D59)⋊C4—22no—
51(C2×D59)⋊C4—22no—
52(C2×D59)⋊C4D412yes—
53C4⋊Dic59—22no—
54C4⋊Dic59—22no—
55C4⋊Dic59C2312yes—
56Dic59⋊C4—22no—
57Dic59⋊C4—22no—
58Dic59⋊C4—22no—
59Dic59⋊C4—22no—
60Dic59⋊C4—22no—
61Dic59⋊C4D412yes—
62C4×Dic59—22no—
63C4×Dic59C2311yescharacteristic
64C2×C59⋊C8C2311yescharacteristic
65C2×C59⋊C8C2311yescharacteristic
66Dic236—22no—
67#11745659—22no—
68C8×D59—22no—
69C22×D59C2×D411yescharacteristic
70Q8×C59—22no—
71Q8×C59—22no—
72C2×C4×C59—22no—
73C2×C4×C59—22no—
74C2×C4×C59C2×D412yes—
75C2×C4×C59C2411yescharacteristic
76C2×Dic59—22no—
77C2×Dic59—22no—
78C2×Dic59C2×D412yes—
79C2×Dic59C2×D411yescharacteristic
80C4×D59—21no—
81C4×D59—21no—
82Dic118—22no—
83Dic118—22no—
84C8×C59—21no—
85C8×C59#4112yes—
86C59⋊C8—21no—
87C59⋊C8#4112yes—
88C22×C59C22×D411yescharacteristic
89C2×D59—21no—
90C2×D59—22no—
91C4×C59—22no—
92C4×C59—42no—
93C4×C59—42no—
94C4×C59C2×#4111yescharacteristic
95C4×C59C2×#4111yescharacteristic
96Dic59—21no—
97Dic59—22no—
98Dic59—42no—
99Dic59—42no—
100#3177—591nomaximal, Sylow
101C2×C59#53211yescharacteristic
102C2×C59#57812yes—
103D59—41no—
104#541—592no—
105#499—591no—
106#494—591no—
107#491—592no—
108#470—591no—
109#470—591no—
110#467—592no—
111#441—591no—
112#441D5911yescharacteristic, complemented
113C4×Q16—592no—
114#405—591no—
115C59#317711yescharacteristic, complemented, Sylow
116C2×Q16—592no—
117C2×Q16—591no—
118C2×Q16C2×D5911yescharacteristic
119C2×M16—591no—
120C22×C8—591no—
121C4⋊Q8—592no—
122#126—1182no—
123#126—1182no—
124#125—592no—
125#125—1182no—
126#125—1182no—
127C22⋊Q8—592no—
128C22⋊Q8—592no—
129C4×Q8—592no—
130C4×Q8C2×D5912yes—
131#117—591no—
132#107—592no—
133#106—591no—
134#106C2×D5911yescharacteristic
135#103—592no—
136#103—592no—
137#103—592no—
138#103C2×D5912yes—
139#97—591no—
140#97C2×D5911yescharacteristic
141C4×C8—591no—
142C4×C8—591no—
143C2×Q8—592no—
144C2×Q8C22×D5912yes—
145C22×C4—591no—
146Q16—22no—
147Q16—1184no—
148Q16—1182no—
149M16—1182no—
150C2×C8—591no—
151C2×C8—591no—
152C2×C8—1182no—
153C2×C8C22×D5911yescharacteristic
154C2×C8C22×D5911yescharacteristic
155C4⋊C4—22no—
156C4⋊C4—592no—
157C4⋊C4—592no—
158C4⋊C4—1182no—
159C4⋊C4—1182no—
160C4⋊C4—1182no—
161C4⋊C4—1182no—
162C4⋊C4—1182no—
163C4⋊C4—1182no—
164C4⋊C4—1182no—
165C4⋊C4C22×D5912yes—
166C22⋊C4—592no—
167C22⋊C4—1182no—
168C22⋊C4—1182no—
169C42—22no—
170C42—591no—
171C42—1182no—
172C42C22×D5911yescharacteristic
173C23—591no—
174Q8—22no—
175Q8—22no—
176Q8—1182no—
177Q8—1182no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—592no—
181C2×C4—591no—
182C2×C4—1181no—
183C2×C4—1181no—
184C2×C4—1182no—
185C2×C4—1182no—
186C2×C4D4×D5912yes—
187C2×C4C23×D5911yescharacteristic
188C8—21no—
189C8—592no—
190C8—1181no—
191C8#1174568512yes—
192C22—1181no—
193C22—1182no—
194C22C2×D4×D5911yescharacteristic
195C4—22no—
196C4—42no—
197C4—42no—
198C4—1181no—
199C4—1182no—
200C4—2362no—
201C4—2362no—
202C4#41×D5911yescharacteristic
203C4C2×#1174568511yescharacteristic
204C2—2361no—
205C2#1683794911yescharacteristic
206C2#1683821812yes—
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#441C2
socleC22×C59C22×D4
hypercenter#441D59
hypocenterC59#3177
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
2. #16837802C2semidirect
3. #16837780C2semidirect
4. #16837769C2semidirect
8. #16837510C2semidirect
9. C4×#11745672C2semidirect
11. C59×#441C2semidirect
112. #441D59semidirect
115. C59#3177semidirect