Finite Group Databasebeta

← #21425087

Subgroups — #21425087

Order 7552.

228 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 83 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×#14273718C211yesmaximal, characteristic
2#16837425C211yesmaximal, characteristic
3M16×Dic59C211yesmaximal, characteristic
4#16837171C211yesmaximal, characteristic
5#16837170C211yesmaximal, characteristic
6#16837170C211yesmaximal, characteristic
7C59×#343C211yesmaximal, characteristic
8C2×#11745664C2211yescharacteristic
9C2×#11745664C2211yescharacteristic
10#14273718—21no—
11#14273718—21no—
12#14273718—21no—
13#14273718—21no—
14C2×C4⋊Dic59C412yes—
15C2×C4⋊Dic59C2211yescharacteristic
16C2×Dic59⋊C4C412yes—
17C2×C4×Dic59C2211yescharacteristic
18Dic59⋊C8—21no—
19Dic59⋊C8—21no—
20#14273637—21no—
21C8×Dic59—21no—
22C2×M16×C59C2211yescharacteristic
23C2×M16×C59C2211yescharacteristic
24C2×C4⋊C4×C59C2211yescharacteristic
25C22×C4×C59C2×C412yes—
26C22×C4×C59C2311yescharacteristic
27C22×Dic59C2×C412yes—
28C22×Dic59C2×C411yescharacteristic
29C22×Dic59C2×C411yescharacteristic
30M16×C59—21no—
31M16×C59—21no—
32M16×C59—21no—
33M16×C59Q812yes—
34C2×C8×C59—21no—
35C2×C8×C59—21no—
36C4⋊C4×C59—21no—
37C4⋊C4×C59—21no—
38C4⋊Dic59—21no—
39C4⋊Dic59—21no—
40C4⋊Dic59—22no—
41C4⋊Dic59—22no—
42Dic59⋊C4—22no—
43Dic59⋊C4—22no—
44C4×Dic59D411yescharacteristic
45C4×Dic59D411yescharacteristic
46C4×Dic59D411yescharacteristic
47C4×Dic59D411yescharacteristic
48#11745664—21no—
49#11745664—21no—
50#11745664—21no—
51#11745664Q812yes—
52C2×C59⋊C8—21no—
53C2×C59⋊C8—21no—
54C23×C59C22×C411yescharacteristic
55C2×C4×C59—22no—
56C2×C4×C59—42no—
57C2×C4×C59C2×D411yescharacteristic
58C2×C4×C59C2×D411yescharacteristic
59C2×C4×C59C2×Q811yescharacteristic
60C2×C4×C59C2×Q811yescharacteristic
61C2×C4×C59#4111yescharacteristic
62C2×C4×C59#4111yescharacteristic
63C2×Dic59—22no—
64C2×Dic59—41no—
65C2×Dic59—41no—
66C2×Dic59—42no—
67C2×Dic59C22⋊C411yescharacteristic
68C2×Dic59C22⋊C411yescharacteristic
69C2×Dic59C22⋊C411yescharacteristic
70C2×Dic59C22⋊C411yescharacteristic
71C8×C59—22no—
72C8×C59—41no—
73C59⋊C8—22no—
74C59⋊C8—41no—
75C22×C59—21no—
76C22×C59—21no—
77C22×C59C2×C22⋊C411yescharacteristic
78C22×C59C4×Q811yescharacteristic
79C22×C59C4×Q811yescharacteristic
80C4×C59—42no—
81C4×C59C22⋊Q811yescharacteristic
82C4×C59C22⋊Q811yescharacteristic
83C4×C59#12411yescharacteristic
84C4×C59C4⋊Q811yescharacteristic
85Dic59—21no—
86Dic59—21no—
87Dic59—21no—
88Dic59—21no—
89Dic59—42no—
90#1998—591nomaximal, Sylow
91C2×C59—21no—
92C2×C59—21no—
93C2×C59#39111yescharacteristic
94C2×C59#41311yescharacteristic
95C2×C59#41311yescharacteristic
96C2×#125—591no—
97#423—591no—
98C4×M16—591no—
99#343—591no—
100#343—591no—
101#343—591no—
102#343D5911yescharacteristic
103C59#199811yescharacteristic, complemented, Sylow
104C2×M16—591no—
105C2×M16—591no—
106C2×M16C2×D5911yescharacteristic
107C2×M16C2×D5911yescharacteristic
108#125—1181no—
109#125—1181no—
110#125—1181no—
111#125—1181no—
112C2×C4⋊C4—592no—
113C2×C4⋊C4—592no—
114C2×C4⋊C4—591no—
115C2×C4⋊C4C2×D5911yescharacteristic
116C2×C42—591no—
117C4⋊C8—1181no—
118C4⋊C8—1181no—
119#97—1181no—
120C4×C8—1181no—
121C22×C4—591no—
122C22×C4—591no—
123C22×C4—592no—
124C22×C4C4×D5912yes—
125C22×C4C22×D5911yescharacteristic
126M16—21no—
127M16—21no—
128M16—21no—
129M16—592no—
130M16—1181no—
131M16—1181no—
132M16—1181no—
133M16Dic11812yes—
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—1181no—
137C2×C8—1181no—
138C4⋊C4—21no—
139C4⋊C4—21no—
140C4⋊C4—1182no—
141C4⋊C4—1182no—
142C4⋊C4—1182no—
143C4⋊C4—1182no—
144C4⋊C4—1181no—
145C4⋊C4—1181no—
146C42—591no—
147C42—591no—
148C42—591no—
149C42—591no—
150C23C2×C4×D5911yescharacteristic
151C2×C4—22no—
152C2×C4—42no—
153C2×C4—591no—
154C2×C4—591no—
155C2×C4—591no—
156C2×C4—591no—
157C2×C4—1182no—
158C2×C4—2361no—
159C2×C4—2361no—
160C2×C4—2362no—
161C2×C4C2×Dic11811yescharacteristic
162C2×C4#1174568511yescharacteristic
163C2×C4D4×D5911yescharacteristic
164C2×C4D4×D5911yescharacteristic
165C2×C4#1174568711yescharacteristic
166C2×C4Q8×D5911yescharacteristic
167C8—22no—
168C8—41no—
169C8—1182no—
170C8—2361no—
171C22—21no—
172C22—21no—
173C22C22⋊C4×D5911yescharacteristic
174C22#1427369211yescharacteristic
175C22C4×Dic11811yescharacteristic
176C4—42no—
177C4—1181no—
178C4—1181no—
179C4—1181no—
180C4—1181no—
181C4—2362no—
182C4#1427370411yescharacteristic
183C4#1427370511yescharacteristic
184C4#1427371311yescharacteristic
185C4#1427372611yescharacteristic
186C2—21no—
187C2—21no—
188C2#1683730611yescharacteristic
189C2#1683738311yescharacteristic
190C2#1683738511yescharacteristic
subgroupG/H
centerC22C22⋊C4×D59
commutatorC23×C59C22×C4
FrattiniC22×C4C22×D59
FittingC59×#343C2
socleC22×C59C2×C22⋊C4
hypercenter#343D59
hypocenterC59#1998
LCSG ▷ C23×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
103. C59#1998semidirect