Finite Group Databasebeta

← #21425464

Subgroups — #21425464

Order 7552.

208 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 65 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×#14273662C211yesmaximal, characteristic
2#16837442C211yesmaximal, characteristic
3#16837430C211yesmaximal, characteristic
4#16837412C211yesmaximal, characteristic
5C2×#14273650C211yesmaximal, characteristic
6C2×#14273645C211yesmaximal, characteristic
7C59×#343C211yesmaximal, characteristic
8C22×Dic118C2211yescharacteristic
9C2×#11745664C2211yescharacteristic
10C22×C59⋊C8C2211yescharacteristic
11#14273686C2211yescharacteristic
12#14273662—22no—
13#14273660—21no—
14#14273658—21no—
15Dic59⋊C8—22no—
16#14273652—21no—
17#14273652—21no—
18#14273650—22no—
19#14273645—22no—
20C2×M16×C59C2211yescharacteristic
21C2×M16×C59C2211yescharacteristic
22C2×C4⋊C4×C59C2211yescharacteristic
23C22×C4×C59—21no—
24C22×C4×C59C2311yescharacteristic
25C22×Dic59—21no—
26C2×Dic118—21no—
27C2×Dic118—21no—
28C2×Dic118—21no—
29C2×Dic118—21no—
30C2×Dic118—21no—
31C2×Dic118Q812yes—
32M16×C59—21no—
33M16×C59—21no—
34M16×C59—21no—
35M16×C59—21no—
36C2×C8×C59—21no—
37C2×C8×C59—21no—
38C4⋊C4×C59—21no—
39C4⋊C4×C59—21no—
40C22⋊Dic59—21no—
41C4⋊Dic59D411yescharacteristic
42C4⋊Dic59D411yescharacteristic
43C4×Dic59—21no—
44#11745664—21no—
45#11745664D412yes—
46C2×C59⋊C8—21no—
47C2×C59⋊C8—21no—
48C2×C59⋊C8—21no—
49C2×C59⋊C8D412yes—
50C23×C59#4111yescharacteristic
51C2×C4×C59—41no—
52C2×C4×C59—81no—
53C2×C4×C59C2×D411yescharacteristic
54C2×C4×C59C2×D411yescharacteristic
55C2×C4×C59C2×D411yescharacteristic
56C2×C4×C59C2×Q811yescharacteristic
57C2×C4×C59#4111yescharacteristic
58C2×C4×C59#4111yescharacteristic
59C2×Dic59—21no—
60C2×Dic59—21no—
61C2×Dic59—22no—
62C2×Dic59—41no—
63C2×Dic59—41no—
64Dic118—22no—
65Dic118—22no—
66Dic118—41no—
67Dic118—41no—
68C8×C59—41no—
69C8×C59—41no—
70C59⋊C8—22no—
71C59⋊C8—22no—
72C22×C59—21no—
73C22×C59—21no—
74C22×C59#12111yescharacteristic
75C22×C59C22⋊Q811yescharacteristic
76C22×C59#12611yescharacteristic
77C4×C59—81no—
78C4×C59#12111yescharacteristic
79C4×C59#12111yescharacteristic
80C4×C59C22⋊Q811yescharacteristic
81C4×C59C22⋊Q811yescharacteristic
82Dic59—42no—
83Dic59—41no—
84Dic59—41no—
85#2064—591nomaximal, Sylow
86C2×C59—21no—
87C2×C59—21no—
88C2×C59#39611yescharacteristic
89C2×C59#47111yescharacteristic
90C2×C59#47311yescharacteristic
91C2×#108—591no—
92#428—591no—
93#424—591no—
94#419—591no—
95C2×#103—591no—
96C2×#101—591no—
97#343D5911yescharacteristic
98C59#206411yescharacteristic, complemented, Sylow
99C22×Q8—591no—
100C2×M16—591no—
101C2×M16C2×D5911yescharacteristic
102C2×M16C2×D5911yescharacteristic
103C22×C8—591no—
104#117—591no—
105C2×C4⋊C4C2×D5911yescharacteristic
106#108—1182no—
107#107—1181no—
108#106—1181no—
109C4⋊C8—1182no—
110#103—1182no—
111#103—1181no—
112#103—1181no—
113#101—1182no—
114C2×Q8—592no—
115C2×Q8—1181no—
116C2×Q8—1181no—
117C2×Q8—1181no—
118C2×Q8—1181no—
119C2×Q8—1181no—
120C22×C4—21no—
121C22×C4—1181no—
122C22×C4C22×D5911yescharacteristic
123M16—21no—
124M16—21no—
125M16—21no—
126M16—21no—
127M16—592no—
128M16—1181no—
129C2×C8—21no—
130C2×C8—21no—
131C2×C8—592no—
132C2×C8—1181no—
133C2×C8—1181no—
134C2×C8—1181no—
135C4⋊C4—21no—
136C4⋊C4—21no—
137C4⋊C4—591no—
138C4⋊C4—591no—
139C22⋊C4—1181no—
140C42—1181no—
141C23#1174568511yescharacteristic
142Q8—1182no—
143Q8—1182no—
144Q8—2361no—
145Q8—2361no—
146C2×C4—41no—
147C2×C4—81no—
148C2×C4—1181no—
149C2×C4—1181no—
150C2×C4—1182no—
151C2×C4—2361no—
152C2×C4—2361no—
153C2×C4#1174568511yescharacteristic
154C2×C4#1174568511yescharacteristic
155C2×C4D4×D5911yescharacteristic
156C2×C4D4×D5911yescharacteristic
157C2×C4D4×D5911yescharacteristic
158C2×C4Q8×D5911yescharacteristic
159C8—41no—
160C8—41no—
161C8—1182no—
162C8—1182no—
163C22—21no—
164C22—21no—
165C22#1427370011yescharacteristic
166C22#1427370511yescharacteristic
167C22#1427372111yescharacteristic
168C4—81no—
169C4—2361no—
170C4—2361no—
171C4—2362no—
172C4#1427370011yescharacteristic
173C4#1427370011yescharacteristic
174C4#1427370511yescharacteristic
175C4#1427370511yescharacteristic
176C2—21no—
177C2—21no—
178C2#1683732611yescharacteristic
179C2#1683766411yescharacteristic
180C2#1683767611yescharacteristic
subgroupG/H
centerC22#14273700
commutatorC22×C4×C59C23
FrattiniC22×C4C22×D59
FittingC59×#343C2
socleC22×C59#121
hypercenter#343D59
hypocenterC59#2064
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
98. C59#2064semidirect