Finite Group Databasebeta

← #21425477

Subgroups — #21425477

Order 7552.

248 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 89 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×#14273658C211yesmaximal, characteristic
2C2×C4⋊(C59⋊C8)C211yesmaximal, characteristic
3C2×#14273651C211yesmaximal, characteristic
4C2×#14273651C211yesmaximal, characteristic
5#16837300C211yesmaximal, characteristic
6#16837164C211yesmaximal, characteristic
7C59×#391C211yesmaximal, characteristic
8C22×C59⋊C8C2211yescharacteristic
9C22×C59⋊C8C2211yescharacteristic
10C2×C4⋊Dic59C2211yescharacteristic
11C2×C4⋊Dic59C2211yescharacteristic
12C2×Dic59⋊C4—21no—
13#14273658—22no—
14C4⋊(C59⋊C8)—22no—
15#14273651—22no—
16#14273651—22no—
17C59⋊#95—21no—
18C22×Q8×C59C2211yescharacteristic
19C2×C4⋊C4×C59C2211yescharacteristic
20C2×C42×C59C2211yescharacteristic
21#95×C59—21no—
22#95×C59—21no—
23C2×Q8×C59—21no—
24C2×Q8×C59—21no—
25C2×Q8×C59—21no—
26C2×Q8×C59—21no—
27C2×Q8×C59—21no—
28C2×Q8×C59Q812yes—
29C22×C4×C59—21no—
30C22×C4×C59—21no—
31C22×C4×C59D411yescharacteristic
32C22×C4×C59D411yescharacteristic
33C22×C4×C59C2311yescharacteristic
34C22×Dic59—21no—
35C22×Dic59—21no—
36C4⋊C4×C59—21no—
37C4⋊C4×C59—21no—
38C42×C59—21no—
39C42×C59—21no—
40C4⋊Dic59—21no—
41C4⋊Dic59—21no—
42C4⋊Dic59—21no—
43C4⋊Dic59D412yes—
44Dic59⋊C4—42no—
45C2×C59⋊C8—21no—
46C2×C59⋊C8—21no—
47C2×C59⋊C8—21no—
48C2×C59⋊C8—21no—
49C2×C59⋊C8—21no—
50C2×C59⋊C8D412yes—
51C23×C59C2×D411yescharacteristic
52Q8×C59—22no—
53Q8×C59—22no—
54Q8×C59—41no—
55Q8×C59—41no—
56C2×C4×C59—21no—
57C2×C4×C59—21no—
58C2×C4×C59—21no—
59C2×C4×C59—22no—
60C2×C4×C59—21no—
61C2×C4×C59—21no—
62C2×C4×C59—41no—
63C2×C4×C59—41no—
64C2×C4×C59—41no—
65C2×C4×C59—41no—
66C2×C4×C59—41no—
67C2×C4×C59SD1612yes—
68C2×C4×C59C2×D411yescharacteristic
69C2×C4×C59C2×D411yescharacteristic
70C2×C4×C59C2×Q811yescharacteristic
71C2×C4×C59#4111yescharacteristic
72C2×C4×C59#4111yescharacteristic
73C2×C4×C59#4111yescharacteristic
74C2×Dic59—22no—
75C2×Dic59—41no—
76C2×Dic59—41no—
77C2×Dic59—41no—
78C2×Dic59—41no—
79C2×Dic59—41no—
80C59⋊C8—22no—
81C59⋊C8—41no—
82C22×C59#12111yescharacteristic
83C22×C59#12111yescharacteristic
84C22×C59C22⋊Q811yescharacteristic
85C22×C59C2×SD1611yescharacteristic
86C22×C59#13511yescharacteristic
87C22×C59#13711yescharacteristic
88C22×C59#13711yescharacteristic
89C4×C59—22no—
90C4×C59—42no—
91C4×C59—41no—
92C4×C59—81no—
93C4×C59#12111yescharacteristic
94C4×C59C22⋊Q811yescharacteristic
95C4×C59C22⋊Q811yescharacteristic
96C4×C59#12611yescharacteristic
97Dic59—42no—
98Dic59—81no—
99#2066—591nomaximal, Sylow
100C2×C59#39611yescharacteristic
101C2×C59#46111yescharacteristic
102C2×C59#46411yescharacteristic
103C2×C59#46511yescharacteristic
104C2×C59#47011yescharacteristic
105C2×C59#47511yescharacteristic
106C2×C59#47911yescharacteristic
107C2×#106—591no—
108C2×C4⋊C8—591no—
109C2×#103—591no—
110C2×#103—591no—
111#391D5911yescharacteristic
112#389—591no—
113#340—591no—
114C59#206611yescharacteristic, complemented, Sylow
115C22×Q8C2×D5911yescharacteristic
116C22×C8—591no—
117C22×C8—591no—
118C2×C4⋊C4—591no—
119C2×C4⋊C4—591no—
120C2×C4⋊C4—1181no—
121C2×C4⋊C4C2×D5911yescharacteristic
122C2×C42C2×D5911yescharacteristic
123#106—1182no—
124C4⋊C8—1182no—
125#103—1182no—
126#103—1182no—
127#95—21no—
128#95—21no—
129#95—1181no—
130C2×Q8—21no—
131C2×Q8—21no—
132C2×Q8—21no—
133C2×Q8—21no—
134C2×Q8—21no—
135C2×Q8Dic11812yes—
136C22×C4—21no—
137C22×C4—21no—
138C22×C4—1181no—
139C22×C4—1181no—
140C22×C4C22⋊D5911yescharacteristic
141C22×C4C22⋊D5911yescharacteristic
142C22×C4C22×D5911yescharacteristic
143C2×C8—592no—
144C2×C8—1181no—
145C2×C8—1181no—
146C2×C8—1181no—
147C2×C8—1181no—
148C2×C8—1181no—
149C4⋊C4—21no—
150C4⋊C4—21no—
151C4⋊C4—592no—
152C4⋊C4—1181no—
153C4⋊C4—1181no—
154C4⋊C4—1181no—
155C4⋊C4—2362no—
156C42—21no—
157C42—21no—
158C23C2×C22⋊D5911yescharacteristic
159Q8—22no—
160Q8—22no—
161Q8—41no—
162Q8—41no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—1182no—
175C2×C4—2361no—
176C2×C4—2361no—
177C2×C4—2361no—
178C2×C4—2361no—
179C2×C4—2361no—
180C2×C4#1174567112yes—
181C2×C4C2×Dic11811yescharacteristic
182C2×C4#1174568511yescharacteristic
183C2×C4D4×D5911yescharacteristic
184C2×C4D4×D5911yescharacteristic
185C2×C4#1174568711yescharacteristic
186C2×C4#1174568711yescharacteristic
187C8—1182no—
188C8—2361no—
189C22#1427369811yescharacteristic
190C22#1427369911yescharacteristic
191C22#1427370611yescharacteristic
192C22C2×#1174567111yescharacteristic
193C22#1427374711yescharacteristic
194C22#1427375711yescharacteristic
195C22#1427375811yescharacteristic
196C4—22no—
197C4—41no—
198C4—42no—
199C4—81no—
200C4—4721no—
201C4—2362no—
202C4#1427370011yescharacteristic
203C4#1427370411yescharacteristic
204C4#1427370411yescharacteristic
205C4#1427372011yescharacteristic
206C2#1683732511yescharacteristic
207C2#1683760411yescharacteristic
208C2#1683762111yescharacteristic
209C2#1683763311yescharacteristic
210C2#1683765811yescharacteristic
211C2#1683768711yescharacteristic
212C2#1683770911yescharacteristic
subgroupG/H
centerC23C2×C22⋊D59
commutatorC22×C4×C59C23
FrattiniC22×C4C22×D59
FittingC59×#391C2
socleC23×C59C2×D4
hypercenter#391D59
hypocenterC59#2066
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #391

Complements

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

NH ≅ G/Ntype
114. C59#2066semidirect