Finite Group Databasebeta

← #21436986

Subgroups — #21436986

Order 7552.

324 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 125 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#16838131C211yesmaximal, characteristic
2#16838127C211yesmaximal, characteristic
3#16837805C211yesmaximal, characteristic
4#16837802C212yesmaximal
5#16837712C212yesmaximal
6#16837707C212yesmaximal
7#16837688C211yesmaximal, characteristic
8#16837526C211yesmaximal, characteristic
9C4×#11745672C211yesmaximal, characteristic
10#16837494C212yesmaximal
11C59×#475C211yesmaximal, characteristic
12C2×#11745672C2211yescharacteristic
13#14273727—21no—
14#14273727C2211yescharacteristic
15#14273725—21no—
16#14273718—22no—
17#14273718C2212yes—
18#14273718C2212yes—
19#14273717—22no—
20Q8×Dic59—21no—
21Q8×Dic59C2212yes—
22C4×Dic118—21no—
23C4×Dic118C2211yescharacteristic
24C4×Dic118C2211yescharacteristic
25#14273692C2212yes—
26#14273660C2212yes—
27#14273660C2212yes—
28#14273660C2211yescharacteristic
29#14273659C2212yes—
30Dic59⋊C8C2212yes—
31#14273652C2212yes—
32#14273651C2211yescharacteristic
33#14273650C2211yescharacteristic
34C4×C59⋊C8C2211yescharacteristic
35C8×Dic59C2212yes—
36C4⋊Q8×C59C2211yescharacteristic
37C4×Q8×C59C2211yescharacteristic
38#106×C59C2212yes—
39C4⋊C8×C59C2211yescharacteristic
40#103×C59C2212yes—
41C2×Q8×C59—21no—
42C2×Q8×C59C2311yescharacteristic
43C2×Dic118—21no—
44C2×Dic118D411yescharacteristic
45C2×Dic118C2311yescharacteristic
46C2×C8×C59C2312yes—
47C4⋊C4×C59—21no—
48C4⋊C4×C59—21no—
49C4⋊C4×C59C2312yes—
50C4⋊C4×C59C2311yescharacteristic
51C42×C59—21no—
52C42×C59C2311yescharacteristic
53#11745672Q814yescomplemented
54C4⋊Dic59—21no—
55C4⋊Dic59—22no—
56C4⋊Dic59—22no—
57C4⋊Dic59—22no—
58C4⋊Dic59D411yescharacteristic
59C4⋊Dic59C2311yescharacteristic
60C4⋊Dic59C2312yes—
61Dic59⋊C4—21no—
62Dic59⋊C4—22no—
63Dic59⋊C4—22no—
64Dic59⋊C4—22no—
65Dic59⋊C4D412yes—
66C4×Dic59—21no—
67C4×Dic59—22no—
68C4×Dic59—22no—
69C4×Dic59C2312yes—
70C2×C59⋊C8C2311yescharacteristic
71C2×C59⋊C8C2311yescharacteristic
72Q8×C59—21no—
73Q8×C59—42no—
74Q8×C59C2×Q812yes—
75C2×C4×C59—21no—
76C2×C4×C59—22no—
77C2×C4×C59—21no—
78C2×C4×C59C2×D411yescharacteristic
79C2×C4×C59C2×D411yescharacteristic
80C2×C4×C59C2411yescharacteristic
81C2×Dic59—21no—
82C2×Dic59—21no—
83C2×Dic59—22no—
84C2×Dic59C2×D412yes—
85C2×Dic59C2×D412yes—
86Dic118—22no—
87Dic118—21no—
88Dic118—42no—
89Dic118C2×Q812yes—
90C8×C59—22no—
91C59⋊C8—21no—
92C59⋊C8C2×Q812yes—
93C22×C59C22×D411yescharacteristic
94C4×C59—22no—
95C4×C59—21no—
96C4×C59—42no—
97C4×C59—41no—
98C4×C59#13512yes—
99C4×C59C22×Q811yescharacteristic
100C4×C592−1+411yescharacteristic
101Dic59—22no—
102Dic59—22no—
103Dic59—22no—
104Dic59—42no—
105Dic59—41no—
106#3383—591nomaximal, Sylow
107C2×C59D4×Q811yescharacteristic
108C2×C59C2×#13511yescharacteristic
109C2×C59#57811yescharacteristic
110#557—591no—
111#557—591no—
112#500—591no—
113#499—592no—
114#479—592no—
115#479—592no—
116#475—591no—
117#475D5911yescharacteristic
118C8×Q8—591no—
119C4×Q16—591no—
120C4×Q16—592no—
121C59#338311yescharacteristic, complemented, Sylow
122C2×Q16—591no—
123C4⋊Q8—591no—
124C4⋊Q8—1181no—
125C4⋊Q8—1181no—
126C4⋊Q8C2×D5911yescharacteristic
127#125—592no—
128#125—592no—
129#125—1182no—
130#125—1182no—
131C4×Q8—591no—
132C4×Q8—592no—
133C4×Q8—592no—
134C4×Q8—591no—
135C4×Q8—1181no—
136C4×Q8—1181no—
137C4×Q8C2×D5911yescharacteristic
138#107—591no—
139#107—592no—
140#107—592no—
141#106—592no—
142#106C2×D5912yes—
143C4⋊C8—592no—
144C4⋊C8C2×D5911yescharacteristic
145#103—591no—
146#103—592no—
147#103—591no—
148#103C2×D5912yes—
149C4×C8—592no—
150C4×C8—591no—
151C2×Q8—21no—
152C2×Q8—591no—
153C2×Q8—591no—
154C2×Q8—1181no—
155C2×Q8C22×D5911yescharacteristic
156Q16—594no—
157C2×C8—591no—
158C2×C8—591no—
159C2×C8C22×D5912yes—
160C4⋊C4—21no—
161C4⋊C4—21no—
162C4⋊C4—591no—
163C4⋊C4—592no—
164C4⋊C4—591no—
165C4⋊C4—592no—
166C4⋊C4—1182no—
167C4⋊C4—1182no—
168C4⋊C4—1182no—
169C4⋊C4—1182no—
170C4⋊C4—1182no—
171C4⋊C4—1182no—
172C4⋊C4—1181no—
173C4⋊C4—1181no—
174C4⋊C4C22×D5911yescharacteristic
175C4⋊C4C22×D5912yes—
176C42—21no—
177C42—592no—
178C42—1182no—
179C42—1182no—
180C42—1181no—
181C42C22×D5911yescharacteristic
182Q8—21no—
183Q8—42no—
184Q8—592no—
185Q8—1182no—
186Q8—1181no—
187Q8—2362no—
188Q8Q8×D5912yes—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—592no—
193C2×C4—592no—
194C2×C4—1181no—
195C2×C4—1181no—
196C2×C4—1182no—
197C2×C4D4×D5911yescharacteristic
198C2×C4D4×D5911yescharacteristic
199C2×C4C23×D5911yescharacteristic
200C8—22no—
201C8—592no—
202C8—1181no—
203C22C2×D4×D5911yescharacteristic
204C4—21no—
205C4—22no—
206C4—42no—
207C4—41no—
208C4—1182no—
209C4—1182no—
210C4—1182no—
211C4—2362no—
212C4—2361no—
213C4#1427374812yes—
214C4C2×Q8×D5911yescharacteristic
215C4#1427377411yescharacteristic
216C2#1683806511yescharacteristic
217C2C2×#1427374811yescharacteristic
218C2#1683821811yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#475C2
socleC22×C59C22×D4
hypercenter#475D59
hypocenterC59#3383
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
53. #11745672Q8semidirect
121. C59#3383semidirect