Finite Group Databasebeta

← #21424367

Subgroups — #21424367

Order 7552.

298 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 103 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×C4×Dic118C211yesmaximal, characteristic
2C2×#14273659C211yesmaximal, characteristic
3C2×#14273652C211yesmaximal, characteristic
4C2×#14273652C211yesmaximal, characteristic
5#16837300C211yesmaximal, characteristic
6#16837165C211yesmaximal, characteristic
7C59×#336C211yesmaximal, characteristic
8C22×Dic118C2211yescharacteristic
9C4×Dic118—22no—
10C4×Dic118—22no—
11C2×C4⋊Dic59C2211yescharacteristic
12C2×C4⋊Dic59C2211yescharacteristic
13C2×C4⋊Dic59C2211yescharacteristic
14C2×Dic59⋊C4—21no—
15C2×Dic59⋊C4—21no—
16C2×C4×Dic59—21no—
17#14273659—22no—
18#14273652—22no—
19#14273652C414yescomplemented
20C59⋊#95—21no—
21C22×C8×C59C2211yescharacteristic
22C22×C8×C59C2211yescharacteristic
23C2×C42×C59C2211yescharacteristic
24C22×C4×C59D411yescharacteristic
25C22×C4×C59D411yescharacteristic
26C22×C4×C59C2311yescharacteristic
27C22×Dic59—21no—
28C22×Dic59—21no—
29C22×Dic59—21no—
30C22×Dic59—21no—
31C2×Dic118—21no—
32C2×Dic118—21no—
33C2×Dic118—21no—
34C2×Dic118C2×C412yes—
35C2×Dic118D412yes—
36C2×Dic118Q812yes—
37C2×C8×C59—21no—
38C2×C8×C59—21no—
39C2×C8×C59—21no—
40C2×C8×C59—21no—
41C2×C8×C59—21no—
42C2×C8×C59C2×C412yes—
43C42×C59—21no—
44C42×C59—21no—
45C4⋊Dic59—21no—
46C4⋊Dic59—21no—
47C4⋊Dic59—21no—
48C4⋊Dic59—21no—
49C4⋊Dic59C2×C412yes—
50C4⋊Dic59D412yes—
51Dic59⋊C4—24no—
52Dic59⋊C4—42no—
53C4×Dic59—24no—
54C23×C59C2×D411yescharacteristic
55C2×C4×C59—21no—
56C2×C4×C59—21no—
57C2×C4×C59—21no—
58C2×C4×C59—21no—
59C2×C4×C59—21no—
60C2×C4×C59SD1612yes—
61C2×C4×C59C22×C411yescharacteristic
62C2×C4×C59C2×D411yescharacteristic
63C2×C4×C59C2×D411yescharacteristic
64C2×C4×C59C2×Q811yescharacteristic
65C2×C4×C59#4111yescharacteristic
66C2×C4×C59#4111yescharacteristic
67C2×Dic59—22no—
68C2×Dic59—22no—
69C2×Dic59—22no—
70C2×Dic59—22no—
71C2×Dic59—22no—
72C2×Dic59—41no—
73C2×Dic59—41no—
74C2×Dic59—41no—
75C2×Dic59—41no—
76C2×Dic59—41no—
77C2×Dic59—41no—
78C2×Dic59—41no—
79Dic118—22no—
80Dic118—22no—
81Dic118—22no—
82Dic118C4⋊C414yescomplemented
83C8×C59—22no—
84C8×C59—41no—
85C22×C59C4×D411yescharacteristic
86C22×C59#12011yescharacteristic
87C22×C59C22⋊Q811yescharacteristic
88C22×C59C2×SD1611yescharacteristic
89C22×C59#13511yescharacteristic
90C22×C59#13711yescharacteristic
91C22×C59#13711yescharacteristic
92C4×C59—22no—
93C4×C59—41no—
94C4×C59C2×C4⋊C411yescharacteristic
95C4×C59C4×D411yescharacteristic
96C4×C59C22⋊Q811yescharacteristic
97C4×C59#12311yescharacteristic
98Dic59—24no—
99Dic59—42no—
100Dic59—42no—
101Dic59—81no—
102#1865—591nomaximal, Sylow
103C2×C59#38511yescharacteristic
104C2×C59C4×SD1611yescharacteristic
105C2×C59#44111yescharacteristic
106C2×C59#44811yescharacteristic
107C2×C59#45211yescharacteristic
108C2×C59#47511yescharacteristic
109C2×C59#47911yescharacteristic
110C2×C4×Q8—591no—
111C2×#106—591no—
112C2×#103—591no—
113C2×#103—591no—
114#389—591no—
115#340—591no—
116#336D5911yescharacteristic
117C59#186511yescharacteristic, complemented, Sylow
118C22×Q8—591no—
119C22×C8C2×D5911yescharacteristic
120C22×C8C2×D5911yescharacteristic
121C4×Q8—1182no—
122C4×Q8—1182no—
123C2×C4⋊C4—591no—
124C2×C4⋊C4—591no—
125C2×C4⋊C4—591no—
126C2×C4⋊C4—1181no—
127C2×C4⋊C4—1181no—
128C2×C42—1181no—
129C2×C42C2×D5911yescharacteristic
130#106—1182no—
131#103—594no—
132#103—1182no—
133#95—1181no—
134C2×Q8—592no—
135C2×Q8—592no—
136C2×Q8—592no—
137C2×Q8—1181no—
138C2×Q8—1181no—
139C2×Q8—1181no—
140C22×C4—1181no—
141C22×C4—1181no—
142C22×C4—1181no—
143C22×C4—1181no—
144C22×C4D23611yescharacteristic
145C22×C4D23611yescharacteristic
146C22×C4C22×D5911yescharacteristic
147C2×C8—21no—
148C2×C8—21no—
149C2×C8—21no—
150C2×C8—21no—
151C2×C8—21no—
152C2×C8C4×D5912yes—
153C4⋊C4—592no—
154C4⋊C4—592no—
155C4⋊C4—1184no—
156C4⋊C4—1181no—
157C4⋊C4—1181no—
158C4⋊C4—1181no—
159C4⋊C4—1181no—
160C4⋊C4—2362no—
161C42—21no—
162C42—21no—
163C42—1184no—
164C23C2×D23611yescharacteristic
165Q8—594no—
166Q8—1182no—
167Q8—1182no—
168Q8—1182no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—1182no—
175C2×C4—1182no—
176C2×C4—1182no—
177C2×C4—1182no—
178C2×C4—1182no—
179C2×C4—2361no—
180C2×C4—2361no—
181C2×C4—2361no—
182C2×C4—2361no—
183C2×C4—2361no—
184C2×C4—2361no—
185C2×C4—2361no—
186C2×C4#1174566012yes—
187C2×C4C2×C4×D5911yescharacteristic
188C2×C4#1174568511yescharacteristic
189C2×C4D4×D5911yescharacteristic
190C2×C4D4×D5911yescharacteristic
191C2×C4#1174568711yescharacteristic
192C2×C4Q8×D5911yescharacteristic
193C8—22no—
194C8—41no—
195C22C4×D23611yescharacteristic
196C22#1427369711yescharacteristic
197C22#1427370711yescharacteristic
198C22C2×#1174566011yescharacteristic
199C22#1427374911yescharacteristic
200C22#1427376011yescharacteristic
201C22#1427376011yescharacteristic
202C4—22no—
203C4—41no—
204C4—1184no—
205C4—4721no—
206C4—2362no—
207C4—2362no—
208C4C4⋊C4×D5911yescharacteristic
209C4(C22⋊D59)⋊C411yescharacteristic
210C4#1427370511yescharacteristic
211C4#1427370911yescharacteristic
212C2#1683727611yescharacteristic
213C2C4×#1174566011yescharacteristic
214C2#1683751011yescharacteristic
215C2#1683754311yescharacteristic
216C2#1683756611yescharacteristic
217C2#1683768811yescharacteristic
218C2#1683771011yescharacteristic
subgroupG/H
centerC23C2×D236
commutatorC2×C4×C59C22×C4
FrattiniC22×C4C22×D59
FittingC59×#336C2
socleC23×C59C2×D4
hypercenter#336D59
hypocenterC59#1865
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #336

Complements

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

NH ≅ G/Ntype
19. #14273652C4semidirect
82. Dic118C4⋊C4semidirect
117. C59#1865semidirect