Finite Group Databasebeta

← #21425417

Subgroups — #21425417

Order 7552.

288 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 85 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
1C22×#11745672C211yesmaximal, characteristic
2C2×Dic59⋊C8C211yesmaximal, characteristic
3C2×#14273652C211yesmaximal, characteristic
4#16837309C211yesmaximal, characteristic
5#16837307C211yesmaximal, characteristic
6#16837164C211yesmaximal, characteristic
7C2×#103×C59C211yesmaximal, characteristic
8C22×Dic118C2211yescharacteristic
9C2×#11745672—22no—
10C2×#11745672—22no—
11C2×#11745672—22no—
12C22×C59⋊C8C2211yescharacteristic
13C2×C4⋊Dic59C2211yescharacteristic
14C2×C4×Dic59C2211yescharacteristic
15Dic59⋊C8—22no—
16#14273652—22no—
17C59⋊#95—21no—
18C59⋊#95—21no—
19C59⋊#95—21no—
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—
49#11745672—28no—
50C4⋊Dic59—21no—
51C4⋊Dic59—21no—
52C4×Dic59—21no—
53C4×Dic59—21no—
54C2×C59⋊C8—21no—
55C2×C59⋊C8—21no—
56C2×C59⋊C8D412yes—
57C23×C59C2×D411yescharacteristic
58Q8×C59—22no—
59Q8×C59—22no—
60Q8×C59—41no—
61Q8×C59—41no—
62C2×C4×C59—22no—
63C2×C4×C59—41no—
64C2×C4×C59—41no—
65C2×C4×C59—41no—
66C2×C4×C59—41no—
67C2×C4×C59—41no—
68C2×C4×C59C2×D411yescharacteristic
69C2×C4×C59C2×D411yescharacteristic
70C2×C4×C59C2×D411yescharacteristic
71C2×C4×C59#4111yescharacteristic
72C2×C4×C59#4111yescharacteristic
73C2×C4×C59#4111yescharacteristic
74C2×Dic59—21no—
75C2×Dic59—21no—
76C2×Dic59—21no—
77C2×Dic59—22no—
78C2×Dic59—21no—
79C2×Dic59—21no—
80C2×Dic59—41no—
81C2×Dic59—41no—
82C2×Dic59—41no—
83C2×Dic59—41no—
84C2×Dic59—41no—
85C2×Dic59Q1612yescomplemented
86Dic118—22no—
87Dic118—22no—
88Dic118—41no—
89Dic118—41no—
90C8×C59—41no—
91C59⋊C8—22no—
92C22×C59#12111yescharacteristic
93C22×C59#12111yescharacteristic
94C22×C59#12111yescharacteristic
95C22×C59C2×Q1611yescharacteristic
96C22×C59#13511yescharacteristic
97C22×C59#13711yescharacteristic
98C22×C59#13711yescharacteristic
99C4×C59—42no—
100C4×C59—81no—
101C4×C59#12011yescharacteristic
102C4×C59#12311yescharacteristic
103C4×C59#12311yescharacteristic
104C4×C59#12411yescharacteristic
105Dic59—22no—
106Dic59—42no—
107Dic59—41no—
108Dic59—81no—
109#2056—591nomaximal, Sylow
110C2×C59#39411yescharacteristic
111C2×C59#46211yescharacteristic
112C2×C59#46211yescharacteristic
113C2×C59#46411yescharacteristic
114C2×C59#46411yescharacteristic
115C2×C59#46711yescharacteristic
116C2×C59#47011yescharacteristic
117C22×Q16—591no—
118C2×C4⋊C8—591no—
119C2×#103—591no—
120C2×#103D5911yescharacteristic
121#391—591no—
122#391—591no—
123#340—591no—
124C59#205611yescharacteristic, complemented, Sylow
125C22×Q8—591no—
126C22×Q8C2×D5911yescharacteristic
127C2×Q16—1182no—
128C2×Q16—1182no—
129C2×Q16—1182no—
130C22×C8—591no—
131C22×C8C2×D5911yescharacteristic
132C2×C4⋊C4—591no—
133C2×C4⋊C4C2×D5911yescharacteristic
134C2×C42—591no—
135C4⋊C8—1182no—
136#103—22no—
137#103—1182no—
138#95—1181no—
139#95—1181no—
140#95—1181no—
141#95—1181no—
142C2×Q8—21no—
143C2×Q8—21no—
144C2×Q8—21no—
145C2×Q8—21no—
146C2×Q8—21no—
147C2×Q8—592no—
148C2×Q8—1181no—
149C2×Q8—1181no—
150C2×Q8—1181no—
151C2×Q8—1181no—
152C2×Q8—1181no—
153C2×Q8C22⋊D5912yes—
154C22×C4—21no—
155C22×C4—21no—
156C22×C4—591no—
157C22×C4—591no—
158C22×C4—1181no—
159C22×C4—1181no—
160C22×C4C22×D5911yescharacteristic
161Q16—1188no—
162C2×C8—21no—
163C2×C8—21no—
164C2×C8—21no—
165C2×C8—592no—
166C2×C8—1181no—
167C2×C8—1181no—
168C4⋊C4—21no—
169C4⋊C4—21no—
170C4⋊C4—1181no—
171C4⋊C4—1181no—
172C42—1181no—
173C42—1181no—
174C23D4×D5911yescharacteristic
175Q8—22no—
176Q8—22no—
177Q8—41no—
178Q8—41no—
179Q8—1182no—
180Q8—1182no—
181Q8—2361no—
182Q8—2361no—
183C2×C4—22no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—592no—
190C2×C4—1181no—
191C2×C4—1181no—
192C2×C4—1181no—
193C2×C4—1182no—
194C2×C4—1181no—
195C2×C4—1181no—
196C2×C4—2361no—
197C2×C4—2361no—
198C2×C4—2361no—
199C2×C4—2361no—
200C2×C4—2361no—
201C2×C4#1174568511yescharacteristic
202C2×C4#1174568511yescharacteristic
203C2×C4D4×D5911yescharacteristic
204C2×C4D4×D5911yescharacteristic
205C2×C4#1174568711yescharacteristic
206C2×C4C2×C22⋊D5911yescharacteristic
207C8—41no—
208C8—1182no—
209C22#1427369911yescharacteristic
210C22#1427370011yescharacteristic
211C22#1427370011yescharacteristic
212C22Q16×D5911yescharacteristic
213C22#1427374811yescharacteristic
214C22#1427375611yescharacteristic
215C22#1427375911yescharacteristic
216C4—42no—
217C4—81no—
218C4—1182no—
219C4—4721no—
220C4—2361no—
221C4—2362no—
222C4#1427369511yescharacteristic
223C4#1427370911yescharacteristic
224C4#1427371011yescharacteristic
225C4#1427371311yescharacteristic
226C2#1683731711yescharacteristic
227C2#1683761011yescharacteristic
228C2#1683761111yescharacteristic
229C2#1683762211yescharacteristic
230C2#1683762711yescharacteristic
231C2#1683764211yescharacteristic
232C2#1683765911yescharacteristic
subgroupG/H
centerC23D4×D59
commutatorC22×C4×C59C23
FrattiniC22×C4C22×D59
FittingC2×#103×C59C2
socleC23×C59C2×D4
hypercenterC2×#103D59
hypocenterC59#2056
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
85. C2×Dic59Q16semidirect
124. C59#2056semidirect