Finite Group Databasebeta

← #21424328

Subgroups — #21424328

Order 7552.

286 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 83 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#16837883C211yesmaximal, characteristic
2#16837442C211yesmaximal, characteristic, complemented
3C2×#14273655C211yesmaximal, characteristic
4#16837401C211yesmaximal, characteristic
5#16837171C211yesmaximal, characteristic, complemented
6#16837162C211yesmaximal, characteristic, complemented
7C59×#382C211yesmaximal, characteristic, complemented
8C2×#11745685C2211yescharacteristic
9C2×#11745664C2211yescharacteristic
10C2×#11745664C2211yescharacteristic
11#14273692—21no—
12#14273689—21no—
13C4×C22⋊D59—22no—
14#14273686C2211yescharacteristic
15#14273685—21no—
16C4⋊C4×D59—21no—
17#14273660—21no—
18#14273658—21no—
19#14273655C414yescomplemented
20#14273650—21no—
21#14273647—21no—
22C2×C4⋊C4×C59C2211yescharacteristic
23C2×C4⋊C4×C59C2211yescharacteristic
24C2×C42×C59C2211yescharacteristic
25#95×C59—22no—
26C22×C4×C59—21no—
27C22×C4×C59—21no—
28C22×C4×C59D412yes—
29C22×C4×C59C2311yescharacteristic
30C2×C22⋊D59—21no—
31#11745685—21no—
32#11745685—21no—
33#11745685C2×C412yes—
34#11745685Q812yes—
35C2×D236D411yescharacteristic
36C2×C4×D59—21no—
37C2×C4×D59—22no—
38C2×Dic118D411yescharacteristic
39C4⋊C4×C59—21no—
40C4⋊C4×C59—21no—
41C4⋊C4×C59—21no—
42C4⋊C4×C59—21no—
43C42×C59—21no—
44C42×C59C2×C412yescomplemented
45C22⋊Dic59—21no—
46(C2×D59)⋊C4—22no—
47C4⋊Dic59D411yescharacteristic
48C4⋊Dic59D411yescharacteristic
49Dic59⋊C4—22no—
50C4×Dic59—22no—
51C4×Dic59—21no—
52#11745664—21no—
53#11745664—21no—
54#11745664—21no—
55#11745664C2×C412yescomplemented
56C2×C59⋊C8—21no—
57C2×C59⋊C8—21no—
58C23×C59C2×D411yescharacteristic
59C22×D59—21no—
60C2×C4×C59—22no—
61C2×C4×C59—22no—
62C2×C4×C59—41no—
63C2×C4×C59—41no—
64C2×C4×C59—42no—
65C2×C4×C59—42no—
66C2×C4×C59—41no—
67C2×C4×C59C22×C411yescharacteristic
68C2×C4×C59C2×D411yescharacteristic
69C2×C4×C59C2×D411yescharacteristic
70C2×C4×C59C2×Q811yescharacteristic
71C2×C4×C59#4111yescharacteristic
72C2×C4×C59#4111yescharacteristic
73C22⋊D59—22no—
74C22⋊D59—22no—
75C2×Dic59—21no—
76C2×Dic59—21no—
77C2×Dic59—21no—
78D236—21no—
79D236C4⋊C412yes—
80C4×D59—22no—
81C4×D59—22no—
82C4×D59—82no—
83Dic118—21no—
84Dic118C4⋊C412yes—
85C59⋊C8—22no—
86C59⋊C8—41no—
87C22×C59—21no—
88C22×C59—21no—
89C22×C59C4×D411yescharacteristic
90C22×C59#12011yescharacteristic
91C22×C59C22⋊Q811yescharacteristic
92C2×D59—22no—
93C2×D59—41no—
94C2×D59—41no—
95C4×C59—42no—
96C4×C59—42no—
97C4×C59—81no—
98C4×C59C2×C4⋊C411yescharacteristic
99C4×C59C4×D411yescharacteristic
100C4×C59C22⋊Q811yescharacteristic
101C4×C59#12311yescharacteristic
102Dic59—22no—
103Dic59—41no—
104Dic59—41no—
105#1860—591nomaximal, Sylow
106C2×C59—21no—
107C2×C59—21no—
108C2×C59#38511yescharacteristic
109C2×C59#45411yescharacteristic
110C2×C59#45511yescharacteristic
111D59—42no—
112#520—591no—
113#428—591no—
114C2×#104—591no—
115#417—591no—
116#382D5911yescharacteristic, complemented
117#343—591no—
118#339—591no—
119C59#186011yescharacteristic, complemented, Sylow
120C2×#41—591no—
121C2×M16—591no—
122C2×M16—591no—
123C4×Q8—1181no—
124C4×D4—1181no—
125C4×D4—1182no—
126#117—591no—
127#117—1181no—
128C2×C4⋊C4—1181no—
129C2×C4⋊C4C2×D5911yescharacteristic
130C2×C4⋊C4C2×D5911yescharacteristic
131C2×C42C2×D5911yescharacteristic
132#107—1181no—
133#106—1181no—
134#104—594no—
135#103—1181no—
136#102—1181no—
137#95—22no—
138#41—592no—
139#41—592no—
140#41—1181no—
141#41—1181no—
142C2×Q8—591no—
143C2×D4—591no—
144C2×D4—1181no—
145C22×C4—21no—
146C22×C4—21no—
147C22×C4—1182no—
148C22×C4—1181no—
149C22×C4C22⋊D5912yes—
150C22×C4C22×D5911yescharacteristic
151M16—592no—
152M16—1181no—
153M16—1181no—
154M16—1181no—
155C2×C8—1181no—
156C2×C8—1181no—
157C4⋊C4—21no—
158C4⋊C4—21no—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—591no—
162C4⋊C4—591no—
163C4⋊C4—1182no—
164C22⋊C4—1182no—
165C22⋊C4—1181no—
166C42—21no—
167C42—1182no—
168C42—1181no—
169C42C4×D5912yescomplemented
170C23—1181no—
171C23C2×C22⋊D5911yescharacteristic
172Q8—592no—
173Q8—1181no—
174D4—592no—
175D4—1182no—
176D4—1182no—
177D4—1181no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—42no—
183C2×C4—42no—
184C2×C4—41no—
185C2×C4—1181no—
186C2×C4—1182no—
187C2×C4—1182no—
188C2×C4—1181no—
189C2×C4—1181no—
190C2×C4—4722no—
191C2×C4C2×C4×D5911yescharacteristic
192C2×C4#1174568511yescharacteristic
193C2×C4D4×D5911yescharacteristic
194C2×C4D4×D5911yescharacteristic
195C2×C4Q8×D5911yescharacteristic
196C2×C4#1174568911yescharacteristic
197C8—1182no—
198C8—2361no—
199C22—21no—
200C22—21no—
201C22—1182no—
202C22—2361no—
203C22—2361no—
204C22C4×C22⋊D5911yescharacteristic
205C22#1427369511yescharacteristic
206C22#1427370311yescharacteristic
207C4—42no—
208C4—42no—
209C4—81no—
210C4—1182no—
211C4—2361no—
212C4—2361no—
213C4C4⋊C4×D5911yescharacteristic
214C4#1427368911yescharacteristic
215C4#1427370511yescharacteristic
216C4#1427371211yescharacteristic
217C2—21no—
218C2—21no—
219C2—2362no—
220C2#1683727311yescharacteristic
221C2#1683757411yescharacteristic
222C2#1683757911yescharacteristic
subgroupG/H
centerC22#14273695
commutatorC2×C4×C59C22×C4
FrattiniC22×C4C22×D59
FittingC59×#382C2
socleC22×C59#120
hypercenter#382D59
hypocenterC59#1860
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #382

Complements

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

NH ≅ G/Ntype
2. #16837442C2semidirect
5. #16837171C2semidirect
6. #16837162C2semidirect
7. C59×#382C2semidirect
19. #14273655C4semidirect
44. C42×C59C2×C4semidirect
55. #11745664C2×C4semidirect
116. #382D59semidirect
119. C59#1860semidirect
169. C42C4×D59semidirect