Finite Group Databasebeta

← #21424371

Subgroups — #21424371

Order 7552.

270 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 93 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×#14273662C211yesmaximal, characteristic, complemented
2#16837428C211yesmaximal, characteristic, complemented
3C2×#14273654C211yesmaximal, characteristic
4#16837398C211yesmaximal, characteristic
5#16837163C211yesmaximal, characteristic, complemented
6#16837156C211yesmaximal, characteristic, complemented
7C2×#131×C59C211yesmaximal, characteristic
8C2×#11745664C2211yescharacteristic
9C22×C59⋊C8C2211yescharacteristic
10#14273686C2211yescharacteristic
11C2×C4×Dic59C2211yescharacteristic
12#14273662—22no—
13Dic59⋊C8—21no—
14Dic59⋊C8—21no—
15#14273654—22no—
16#14273651C411yescharacteristic, complemented
17#14273651C411yescharacteristic, complemented
18#14273648C411yescharacteristic, complemented
19#14273648C411yescharacteristic, complemented
20C2×#41×C59C2211yescharacteristic
21#131×C59—22no—
22#131×C59—22no—
23C2×M16×C59—21no—
24C2×M16×C59C2211yescharacteristic
25C22×C8×C59—21no—
26C22×C8×C59C2211yescharacteristic
27#41×C59—21no—
28#41×C59—21no—
29#41×C59D412yes—
30#41×C59Q812yes—
31C2×Q8×C59C2×C411yescharacteristic
32C2×D4×C59—21no—
33C2×D4×C59C2×C411yescharacteristic
34C22×C4×C59—21no—
35C22×C4×C59C2311yescharacteristic
36C22×Dic59—21no—
37M16×C59—24no—
38M16×C59—21no—
39M16×C59D412yes—
40C2×C8×C59—24no—
41C2×C8×C59—21no—
42C2×C8×C59—21no—
43C2×C8×C59—21no—
44C2×C8×C59D411yescharacteristic
45C2×C8×C59D411yescharacteristic
46C22⋊Dic59—21no—
47C4⋊Dic59C2×C411yescharacteristic
48C4⋊Dic59C2×C411yescharacteristic
49C4×Dic59—21no—
50C4×Dic59—21no—
51C4×Dic59—21no—
52#11745664—21no—
53#11745664—21no—
54C2×C59⋊C8—21no—
55C2×C59⋊C8—21no—
56C2×C59⋊C8—21no—
57C2×C59⋊C8C2×C411yescharacteristic
58C2×C59⋊C8C2×C411yescharacteristic
59C23×C59—21no—
60C23×C59#4111yescharacteristic
61Q8×C59—21no—
62Q8×C59C4⋊C412yes—
63D4×C59—22no—
64D4×C59—22no—
65D4×C59—21no—
66D4×C59C4⋊C412yes—
67C2×C4×C59—21no—
68C2×C4×C59—22no—
69C2×C4×C59—22no—
70C2×C4×C59C22×C411yescharacteristic
71C2×C4×C59C2×D411yescharacteristic
72C2×C4×C59C2×D411yescharacteristic
73C2×C4×C59C2×D411yescharacteristic
74C2×C4×C59C2×Q811yescharacteristic
75C2×C4×C59#4111yescharacteristic
76C2×Dic59—22no—
77C2×Dic59—21no—
78C2×Dic59—21no—
79C2×Dic59—41no—
80C2×Dic59—41no—
81C8×C59—21no—
82C8×C59—22no—
83C8×C59—21no—
84C59⋊C8—21no—
85C59⋊C8—21no—
86C59⋊C8—41no—
87C22×C59—21no—
88C22×C59—21no—
89C22×C59—22no—
90C22×C59—41no—
91C22×C59—41no—
92C22×C59C4×D411yescharacteristic
93C22×C59C22⋊Q811yescharacteristic
94C22×C59#12311yescharacteristic
95C4×C59—22no—
96C4×C59C2×C4⋊C411yescharacteristic
97C4×C59C4×D411yescharacteristic
98C4×C59#12011yescharacteristic
99C4×C59C22⋊Q811yescharacteristic
100Dic59—42no—
101Dic59—41no—
102Dic59—41no—
103#1866—591nomaximal, Sylow
104C2×C59—21no—
105C2×C59—21no—
106C2×C59—42no—
107C2×C59#38511yescharacteristic
108C2×C59#44311yescharacteristic
109C2×C59#44411yescharacteristic
110C2×#131D5911yescharacteristic
111C2×#108—591no—
112#424—591no—
113C2×#104—591no—
114#416—591no—
115#339—591no—
116#336—591no—
117C59#186611yescharacteristic, complemented, Sylow
118C2×#41C2×D5911yescharacteristic
119#131—22no—
120#131—22no—
121C2×M16—21no—
122C2×M16—591no—
123C2×M16C2×D5911yescharacteristic
124C22×C8—21no—
125C22×C8—591no—
126C22×C8C2×D5911yescharacteristic
127#117—591no—
128C2×C42—591no—
129#108—1182no—
130C4⋊C8—1181no—
131C4⋊C8—1181no—
132#104—1182no—
133#103—591no—
134#103—591no—
135#102—591no—
136#102—591no—
137#41—21no—
138#41—21no—
139#41Dic11812yes—
140#41C22⋊D5912yes—
141C2×Q8C4×D5911yescharacteristic
142C2×D4—21no—
143C2×D4C4×D5911yescharacteristic
144C22×C4—21no—
145C22×C4—1181no—
146C22×C4C22×D5911yescharacteristic
147M16—24no—
148M16—21no—
149M16—1181no—
150M16—1181no—
151M16C22⋊D5912yes—
152C2×C8—24no—
153C2×C8—21no—
154C2×C8—21no—
155C2×C8—21no—
156C2×C8—591no—
157C2×C8—591no—
158C2×C8—1181no—
159C2×C8—1181no—
160C2×C8—1181no—
161C2×C8C22⋊D5911yescharacteristic
162C2×C8C22⋊D5911yescharacteristic
163C4⋊C4—591no—
164C4⋊C4—591no—
165C22⋊C4—1181no—
166C42—1181no—
167C42—1181no—
168C42—1181no—
169C23—21no—
170C23#1174568511yescharacteristic
171Q8—21no—
172Q8Dic59⋊C412yes—
173D4—22no—
174D4—22no—
175D4—21no—
176D4Dic59⋊C412yes—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—1182no—
181C2×C4—1181no—
182C2×C4—1181no—
183C2×C4—2361no—
184C2×C4—2361no—
185C2×C4C2×Dic11811yescharacteristic
186C2×C4C2×C4×D5911yescharacteristic
187C2×C4#1174568511yescharacteristic
188C2×C4C2×C22⋊D5911yescharacteristic
189C2×C4C2×C22⋊D5911yescharacteristic
190C2×C4C2×C22⋊D5911yescharacteristic
191C8—21no—
192C8—22no—
193C8—21no—
194C8—1181no—
195C8—1181no—
196C8—2361no—
197C22—21no—
198C22—21no—
199C22—22no—
200C22—41no—
201C22—41no—
202C22C4×C22⋊D5911yescharacteristic
203C22#1427370611yescharacteristic
204C22#1427371011yescharacteristic
205C4—22no—
206C4—2362no—
207C4—2361no—
208C4—2361no—
209C4C2×Dic59⋊C411yescharacteristic
210C4C4×C22⋊D5911yescharacteristic
211C4#1427369611yescharacteristic
212C4#1427370611yescharacteristic
213C2—21no—
214C2—21no—
215C2—42no—
216C2#1683727511yescharacteristic
217C2#1683751711yescharacteristic
218C2#1683752211yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D59
commutatorC2×C4×C59C22×C4
FrattiniC22×C4C22×D59
FittingC2×#131×C59C2
socleC22×C59C4×D4
hypercenterC2×#131D59
hypocenterC59#1866
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×#131

Complements

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

NH ≅ G/Ntype
1. C2×#14273662C2semidirect
2. #16837428C2semidirect
5. #16837163C2semidirect
6. #16837156C2semidirect
16. #14273651C4semidirect
17. #14273651C4semidirect
18. #14273648C4semidirect
19. #14273648C4semidirect
117. C59#1866semidirect