Finite Group Databasebeta

← #21429121

Subgroups — #21429121

Order 7552.

556 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 181 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×#14273726C212yesmaximal
2C2×#14273725C212yesmaximal
3#16837323C212yesmaximal
4#16837322C211yesmaximal, characteristic
5#16837299C212yesmaximal
6#16837297C212yesmaximal
7#16837271C211yesmaximal, characteristic
8#16837253C212yesmaximal
9C59×#395C211yesmaximal, characteristic
10C22×Dic118C2212yes—
11C22×Dic118C2211yescharacteristic
12#14273726—28no—
13#14273725—28no—
14C2×C4⋊Dic59C2212yes—
15C2×C4⋊Dic59C2211yescharacteristic
16C2×Dic59⋊C4C2212yes—
17C2×Dic59⋊C4C2212yes—
18C2×Dic59⋊C4C2212yes—
19C2×Dic59⋊C4C2212yes—
20C2×Dic59⋊C4C2212yes—
21C2×Dic59⋊C4C2212yes—
22C2×C4×Dic59C2212yes—
23C2×C4×Dic59C2212yes—
24C2×C4×Dic59C2211yescharacteristic
25C59⋊#95C2212yes—
26C59⋊#95C2211yescharacteristic
27C59⋊#95C2212yes—
28C22×Q8×C59C2211yescharacteristic
29C2×C4⋊C4×C59C2212yes—
30C2×C4⋊C4×C59C2211yescharacteristic
31#95×C59C2212yes—
32#95×C59C2211yescharacteristic
33C2×Q8×C59—24no—
34C2×Q8×C59—41no—
35C22×C4×C59C2311yescharacteristic
36C22×C4×C59C2311yescharacteristic
37C22×C4×C59C2312yes—
38C22×C4×C59C2311yescharacteristic
39C22×C4×C59C2312yes—
40C22×Dic59C2312yes—
41C22×Dic59C2312yes—
42C22×Dic59C2312yes—
43C22×Dic59C2312yes—
44C2×Dic118—24no—
45C2×Dic118—24no—
46C2×Dic118—24no—
47C2×Dic118—41no—
48C2×Dic118—42no—
49C4⋊C4×C59—24no—
50C4⋊C4×C59—41no—
51C4⋊Dic59—24no—
52C4⋊Dic59—41no—
53Dic59⋊C4—24no—
54Dic59⋊C4—24no—
55Dic59⋊C4—24no—
56Dic59⋊C4—24no—
57Dic59⋊C4D418yes—
58Dic59⋊C4Q818yescomplemented
59C4×Dic59—24no—
60C4×Dic59—24no—
61C4×Dic59Q814yescomplemented
62C23×C59C2411yescharacteristic
63Q8×C59—44no—
64C2×C4×C59—22no—
65C2×C4×C59—22no—
66C2×C4×C59—21no—
67C2×C4×C59—22no—
68C2×C4×C59—21no—
69C2×C4×C59—22no—
70C2×C4×C59—22no—
71C2×C4×C59—22no—
72C2×C4×C59—21no—
73C2×C4×C59—21no—
74C2×C4×C59C2×D414yes—
75C2×C4×C59C2×Q812yes—
76C2×C4×C59C2×Q814yes—
77C2×Dic59—22no—
78C2×Dic59—22no—
79C2×Dic59—22no—
80C2×Dic59—22no—
81C2×Dic59—22no—
82C2×Dic59—22no—
83C2×Dic59—22no—
84C2×Dic59C2×D414yes—
85C2×Dic59C2×D414yes—
86C2×Dic59C2×Q814yes—
87C2×Dic59C2×Q814yes—
88C2×Dic59C2×Q814yes—
89Dic118—44no—
90Dic118—48no—
91C22×C59C22×D412yes—
92C22×C59C22×Q811yescharacteristic
93C22×C59C22×Q812yes—
94C22×C59H(5,𝔽2)11yescharacteristic
95C22×C592−1+411yescharacteristic
96C4×C59—22no—
97C4×C59—24no—
98C4×C59—24no—
99C4×C59—41no—
100C4×C59—41no—
101Dic59—24no—
102Dic59—24no—
103Dic59—42no—
104Dic59C4⋊Q818yescomplemented
105#2551—591nomaximal, Sylow
106C2×C59C2×C4⋊Q812yes—
107C2×C59#54411yescharacteristic
108C2×C59D4211yescharacteristic
109C2×C59D4×Q812yes—
110C2×C59Q8211yescharacteristic
111C2×C4⋊Q8—592no—
112C2×C4⋊Q8—592no—
113#395—591no—
114#395—592no—
115#395D5911yescharacteristic
116#389—592no—
117#389—592no—
118#384—591no—
119C4×C4⋊C4—592no—
120C59#255111yescharacteristic, complemented, Sylow
121C22×Q8—591no—
122C22×Q8—592no—
123C22×Q8C2×D5911yescharacteristic
124C4⋊Q8—1188no—
125C4⋊Q8—1188no—
126C2×C4⋊C4—592no—
127C2×C4⋊C4—592no—
128C2×C4⋊C4—592no—
129C2×C4⋊C4—592no—
130C2×C4⋊C4—592no—
131C2×C4⋊C4—592no—
132C2×C4⋊C4—592no—
133C2×C4⋊C4—591no—
134C2×C4⋊C4C2×D5912yes—
135C2×C4⋊C4C2×D5911yescharacteristic
136C2×C42—591no—
137C2×C42—592no—
138C2×C42—592no—
139#95—592no—
140#95—591no—
141#95—592no—
142#95C2×D5912yes—
143#95C2×D5911yescharacteristic
144C2×Q8—24no—
145C2×Q8—41no—
146C2×Q8—1184no—
147C2×Q8—1184no—
148C2×Q8—1184no—
149C2×Q8—2362no—
150C2×Q8—2361no—
151C22×C4—592no—
152C22×C4—592no—
153C22×C4—592no—
154C22×C4—592no—
155C22×C4C22×D5911yescharacteristic
156C22×C4C22×D5911yescharacteristic
157C22×C4C22×D5912yes—
158C22×C4C22×D5911yescharacteristic
159C22×C4C22×D5912yes—
160C4⋊C4—24no—
161C4⋊C4—41no—
162C4⋊C4—598no—
163C4⋊C4—598no—
164C4⋊C4—1184no—
165C4⋊C4—1184no—
166C4⋊C4—1184no—
167C4⋊C4—1184no—
168C4⋊C4—1184no—
169C4⋊C4—2361no—
170C42—594no—
171C42—1184no—
172C42—1184no—
173C23C23×D5911yescharacteristic
174Q8—44no—
175Q8—2368no—
176Q8—2364no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—21no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—594no—
188C2×C4—594no—
189C2×C4—594no—
190C2×C4—594no—
191C2×C4—594no—
192C2×C4—1182no—
193C2×C4—1182no—
194C2×C4—1182no—
195C2×C4—1182no—
196C2×C4—1182no—
197C2×C4—1182no—
198C2×C4—1182no—
199C2×C4D4×D5914yes—
200C2×C4Q8×D5912yes—
201C2×C4Q8×D5914yes—
202C22C2×D4×D5912yes—
203C22C2×Q8×D5911yescharacteristic
204C22C2×Q8×D5912yes—
205C22#1427377211yescharacteristic
206C22#1427377411yescharacteristic
207C4—22no—
208C4—24no—
209C4—24no—
210C4—41no—
211C4—41no—
212C4—598no—
213C4—1184no—
214C4—1184no—
215C4—2362no—
216C2C4⋊Q8×D5912yes—
217C2#1683803111yescharacteristic
218C2#1683803411yescharacteristic
219C2#1683806512yes—
220C2#1683813211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#395C2
hypercenter#395D59
hypocenterC59#2551
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
58. Dic59⋊C4Q8semidirect
61. C4×Dic59Q8semidirect
104. Dic59C4⋊Q8semidirect
120. C59#2551semidirect