Finite Group Databasebeta

← #21425340

Subgroups — #21425340

Order 7552.

298 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 87 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×#14273725C211yesmaximal, characteristic
2C2×#14273652C211yesmaximal, characteristic
3C2×#14273651C211yesmaximal, characteristic
4C2×#14273650C211yesmaximal, characteristic
5#16837298C211yesmaximal, characteristic
6#16837156C211yesmaximal, characteristic
7C2×#103×C59C211yesmaximal, characteristic
8C22×Dic118C2211yescharacteristic
9C22×C59⋊C8C2211yescharacteristic
10#14273725—22no—
11#14273725—22no—
12C2×C4⋊Dic59C2211yescharacteristic
13C2×Dic59⋊C4—21no—
14C2×Dic59⋊C4—21no—
15C2×Dic59⋊C4—21no—
16C2×C4×Dic59C2211yescharacteristic
17#14273652—22no—
18#14273651—22no—
19#14273650—22no—
20C59⋊#95—21no—
21C22×Q8×C59C2211yescharacteristic
22C22×C8×C59C2211yescharacteristic
23C2×C4⋊C4×C59C2211yescharacteristic
24#103×C59—22no—
25C2×Q8×C59—21no—
26C2×Q8×C59—21no—
27C2×Q8×C59—21no—
28C2×Q8×C59—21no—
29C2×Q8×C59—21no—
30C2×Q8×C59D412yes—
31C22×C4×C59—21no—
32C22×C4×C59—21no—
33C22×C4×C59C2311yescharacteristic
34C22×Dic59—21no—
35C22×Dic59—21no—
36C22×Dic59D411yescharacteristic
37C22×Dic59D411yescharacteristic
38C2×Dic118—21no—
39C2×Dic118—21no—
40C2×Dic118—21no—
41C2×Dic118—21no—
42C2×Dic118—21no—
43C2×Dic118D412yes—
44C2×C8×C59—21no—
45C2×C8×C59—21no—
46C2×C8×C59—21no—
47C4⋊C4×C59—21no—
48C4⋊C4×C59—21no—
49C4⋊Dic59—21no—
50C4⋊Dic59D412yes—
51Dic59⋊C4—24no—
52Dic59⋊C4—24no—
53Dic59⋊C4—42no—
54C4×Dic59—21no—
55C4×Dic59—21no—
56C2×C59⋊C8—21no—
57C2×C59⋊C8—21no—
58C2×C59⋊C8—21no—
59C23×C59C2×D411yescharacteristic
60Q8×C59—22no—
61Q8×C59—22no—
62Q8×C59—41no—
63Q8×C59—41no—
64C2×C4×C59—22no—
65C2×C4×C59—41no—
66C2×C4×C59—41no—
67C2×C4×C59—41no—
68C2×C4×C59—41no—
69C2×C4×C59—41no—
70C2×C4×C59C2×D411yescharacteristic
71C2×C4×C59C2×D411yescharacteristic
72C2×C4×C59C2×D411yescharacteristic
73C2×C4×C59#4111yescharacteristic
74C2×C4×C59#4111yescharacteristic
75C2×C4×C59#4111yescharacteristic
76C2×Dic59—21no—
77C2×Dic59—21no—
78C2×Dic59—21no—
79C2×Dic59—21no—
80C2×Dic59—22no—
81C2×Dic59—22no—
82C2×Dic59—41no—
83C2×Dic59—41no—
84C2×Dic59—41no—
85C2×Dic59—41no—
86C2×Dic59SD1612yes—
87C2×Dic59Q1612yes—
88Dic118—22no—
89Dic118—22no—
90Dic118—41no—
91Dic118—41no—
92C8×C59—41no—
93C59⋊C8—41no—
94C22×C59#12011yescharacteristic
95C22×C59#12111yescharacteristic
96C22×C59#12411yescharacteristic
97C22×C59C2×SD1611yescharacteristic
98C22×C59C2×Q1611yescharacteristic
99C22×C59#13711yescharacteristic
100C22×C59#13711yescharacteristic
101C4×C59—42no—
102C4×C59—81no—
103C4×C59#12111yescharacteristic
104C4×C59#12111yescharacteristic
105C4×C59#12311yescharacteristic
106C4×C59#12311yescharacteristic
107Dic59—22no—
108Dic59—22no—
109Dic59—42no—
110Dic59—42no—
111#2043—591nomaximal, Sylow
112C2×C59#39411yescharacteristic
113C2×C59#44811yescharacteristic
114C2×C59#45111yescharacteristic
115C2×C59#46111yescharacteristic
116C2×C59#46211yescharacteristic
117C2×C59#48711yescharacteristic
118C2×C59#49111yescharacteristic
119C2×C4⋊Q8—591no—
120C2×#103—591no—
121C2×#103—591no—
122C2×#103—591no—
123C2×#103D5911yescharacteristic
124#389—591no—
125#336—591no—
126C59#204311yescharacteristic, complemented, Sylow
127C22×Q8—591no—
128C22×Q8C2×D5911yescharacteristic
129C22×C8—591no—
130C22×C8C2×D5911yescharacteristic
131C4⋊Q8—1182no—
132C4⋊Q8—1182no—
133C2×C4⋊C4—591no—
134C2×C4⋊C4—1181no—
135C2×C4⋊C4—1181no—
136C2×C4⋊C4—1181no—
137C2×C4⋊C4C2×D5911yescharacteristic
138C2×C42—591no—
139#103—22no—
140#103—1182no—
141#103—1182no—
142#103—1182no—
143#95—1181no—
144C2×Q8—21no—
145C2×Q8—21no—
146C2×Q8—21no—
147C2×Q8—21no—
148C2×Q8—21no—
149C2×Q8—592no—
150C2×Q8—1181no—
151C2×Q8—1181no—
152C2×Q8—1181no—
153C2×Q8—1181no—
154C2×Q8—1181no—
155C2×Q8C22⋊D5912yes—
156C22×C4—21no—
157C22×C4—21no—
158C22×C4—591no—
159C22×C4—591no—
160C22×C4—1181no—
161C22×C4—1181no—
162C22×C4C22×D5911yescharacteristic
163C2×C8—21no—
164C2×C8—21no—
165C2×C8—21no—
166C2×C8—1181no—
167C2×C8—1181no—
168C2×C8—1181no—
169C4⋊C4—21no—
170C4⋊C4—21no—
171C4⋊C4—592no—
172C4⋊C4—1184no—
173C4⋊C4—1184no—
174C4⋊C4—1181no—
175C4⋊C4—2362no—
176C42—1181no—
177C42—1181no—
178C23D4×D5911yescharacteristic
179Q8—22no—
180Q8—22no—
181Q8—41no—
182Q8—41no—
183Q8—1182no—
184Q8—1182no—
185Q8—2361no—
186Q8—2361no—
187C2×C4—22no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—592no—
194C2×C4—592no—
195C2×C4—1181no—
196C2×C4—1181no—
197C2×C4—1181no—
198C2×C4—1181no—
199C2×C4—1182no—
200C2×C4—1182no—
201C2×C4—2361no—
202C2×C4—2361no—
203C2×C4—2361no—
204C2×C4—2361no—
205C2×C4#1174568511yescharacteristic
206C2×C4#1174568511yescharacteristic
207C2×C4D4×D5911yescharacteristic
208C2×C4D4×D5911yescharacteristic
209C2×C4#1174568711yescharacteristic
210C2×C4C2×C22⋊D5911yescharacteristic
211C8—41no—
212C8—2361no—
213C22#1427369511yescharacteristic
214C22#1427370011yescharacteristic
215C22#1427371311yescharacteristic
216C22SD16×D5911yescharacteristic
217C22Q16×D5911yescharacteristic
218C22#1427375611yescharacteristic
219C22#1427375911yescharacteristic
220C4—42no—
221C4—81no—
222C4—1182no—
223C4—1182no—
224C4—2362no—
225C4—2362no—
226C4#1427369911yescharacteristic
227C4#1427370011yescharacteristic
228C4#1427370911yescharacteristic
229C4#1427371011yescharacteristic
230C2#1683731711yescharacteristic
231C2#1683753911yescharacteristic
232C2#1683755611yescharacteristic
233C2#1683760611yescharacteristic
234C2#1683761111yescharacteristic
235C2#1683775111yescharacteristic
236C2#1683776911yescharacteristic
subgroupG/H
centerC23D4×D59
commutatorC22×C4×C59C23
FrattiniC22×C4C22×D59
FittingC2×#103×C59C2
socleC23×C59C2×D4
hypercenterC2×#103D59
hypocenterC59#2043
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
126. C59#2043semidirect