Finite Group Databasebeta

← #21425488

Subgroups — #21425488

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×#14273660C211yesmaximal, characteristic
2C2×C4⋊(C59⋊C8)C211yesmaximal, characteristic
3C2×#14273650C211yesmaximal, characteristic
4C2×#14273650C211yesmaximal, characteristic
5#16837308C211yesmaximal, characteristic
6#16837164C211yesmaximal, characteristic
7C59×#389C211yesmaximal, characteristic
8C22×Dic118C2211yescharacteristic
9C22×C59⋊C8C2211yescharacteristic
10C22×C59⋊C8C2211yescharacteristic
11C2×C4⋊Dic59C2211yescharacteristic
12#14273660—22no—
13C4⋊(C59⋊C8)—22no—
14#14273650—22no—
15#14273650—22no—
16C59⋊#95—21no—
17C59⋊#95—21no—
18C2×C4⋊C4×C59—21no—
19C2×C4⋊C4×C59C2211yescharacteristic
20C2×C4⋊C4×C59C2211yescharacteristic
21C2×C42×C59C2211yescharacteristic
22#95×C59—21no—
23C22×C4×C59—21no—
24C22×C4×C59—21no—
25C22×C4×C59D411yescharacteristic
26C22×C4×C59D411yescharacteristic
27C22×C4×C59C2311yescharacteristic
28C22×Dic59—21no—
29C22×Dic59—21no—
30C2×Dic118—21no—
31C2×Dic118—21no—
32C2×Dic118—21no—
33C2×Dic118—21no—
34C2×Dic118—21no—
35C2×Dic118Q812yes—
36C4⋊C4×C59—21no—
37C4⋊C4×C59—21no—
38C4⋊C4×C59—21no—
39C4⋊C4×C59—42no—
40C4⋊C4×C59D412yes—
41C42×C59—21no—
42C42×C59—21no—
43C4⋊Dic59—21no—
44C4⋊Dic59—21no—
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
52C2×C4×C59—21no—
53C2×C4×C59—21no—
54C2×C4×C59—21no—
55C2×C4×C59—22no—
56C2×C4×C59—21no—
57C2×C4×C59—21no—
58C2×C4×C59—41no—
59C2×C4×C59—41no—
60C2×C4×C59—41no—
61C2×C4×C59—41no—
62C2×C4×C59—41no—
63C2×C4×C59Q1612yes—
64C2×C4×C59C2×D411yescharacteristic
65C2×C4×C59C2×D411yescharacteristic
66C2×C4×C59C2×Q811yescharacteristic
67C2×C4×C59#4111yescharacteristic
68C2×C4×C59#4111yescharacteristic
69C2×C4×C59#4111yescharacteristic
70C2×Dic59—22no—
71C2×Dic59—41no—
72C2×Dic59—41no—
73C2×Dic59—41no—
74C2×Dic59—41no—
75C2×Dic59—41no—
76Dic118—22no—
77Dic118—22no—
78Dic118—41no—
79Dic118—41no—
80C59⋊C8—22no—
81C59⋊C8—41no—
82C22×C59#12111yescharacteristic
83C22×C59#12111yescharacteristic
84C22×C59C22⋊Q811yescharacteristic
85C22×C59C2×Q1611yescharacteristic
86C22×C59#13511yescharacteristic
87C22×C59AGL(1,ℤ/8)11yescharacteristic
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#2068—591nomaximal, Sylow
100C2×C59#39611yescharacteristic
101C2×C59#46211yescharacteristic
102C2×C59#46311yescharacteristic
103C2×C59#46711yescharacteristic
104C2×C59#46811yescharacteristic
105C2×C59#47711yescharacteristic
106C2×C59#47911yescharacteristic
107C2×#107—591no—
108C2×C4⋊C8—591no—
109C2×#103—591no—
110C2×#103—591no—
111#391—591no—
112#389D5911yescharacteristic
113#340—591no—
114C59#206811yescharacteristic, complemented, Sylow
115C22×Q8—591no—
116C22×C8—591no—
117C22×C8—591no—
118C2×C4⋊C4—21no—
119C2×C4⋊C4—591no—
120C2×C4⋊C4C2×D5911yescharacteristic
121C2×C4⋊C4C2×D5911yescharacteristic
122C2×C42C2×D5911yescharacteristic
123#107—1182no—
124C4⋊C8—1182no—
125#103—1182no—
126#103—1182no—
127#95—21no—
128#95—1181no—
129#95—1181no—
130C2×Q8—592no—
131C2×Q8—1181no—
132C2×Q8—1181no—
133C2×Q8—1181no—
134C2×Q8—1181no—
135C2×Q8—1181no—
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—21no—
152C4⋊C4—42no—
153C4⋊C4—1181no—
154C4⋊C4—1181no—
155C4⋊C4D23612yes—
156C42—21no—
157C42—21no—
158C23C2×C22⋊D5911yescharacteristic
159Q8—1182no—
160Q8—1182no—
161Q8—2361no—
162Q8—2361no—
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#1174567212yes—
181C2×C4C2×D23611yescharacteristic
182C2×C4#1174568511yescharacteristic
183C2×C4D4×D5911yescharacteristic
184C2×C4#1174568711yescharacteristic
185C2×C4Q8×D5911yescharacteristic
186C2×C4#1174568911yescharacteristic
187C8—1182no—
188C8—2361no—
189C22#1427369911yescharacteristic
190C22#1427370111yescharacteristic
191C22#1427370311yescharacteristic
192C22C2×#1174567211yescharacteristic
193C22#1427374711yescharacteristic
194C22#1427375311yescharacteristic
195C22#1427375711yescharacteristic
196C4—22no—
197C4—41no—
198C4—42no—
199C4—81no—
200C4—4721no—
201C4—2362no—
202C4#1427370211yescharacteristic
203C4#1427370511yescharacteristic
204C4#1427370711yescharacteristic
205C4#1427372211yescharacteristic
206C2#1683732411yescharacteristic
207C2#1683761211yescharacteristic
208C2#1683761711yescharacteristic
209C2#1683764111yescharacteristic
210C2#1683764611yescharacteristic
211C2#1683769411yescharacteristic
212C2#1683770611yescharacteristic
subgroupG/H
centerC23C2×C22⋊D59
commutatorC22×C4×C59C23
FrattiniC22×C4C22×D59
FittingC59×#389C2
socleC23×C59C2×D4
hypercenter#389D59
hypocenterC59#2068
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
114. C59#2068semidirect