Finite Group Databasebeta

← #21422507

Subgroups — #21422507

Order 7552.

234 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 77 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
1#16837936C211yesmaximal, characteristic
2C4×#11745664C211yesmaximal, characteristic, complemented
3#16837132C212yesmaximal, complemented
4#16837129C212yesmaximal, complemented
5C2×C4⋊C8×C59C211yesmaximal, characteristic, complemented
6C2×#11745664—21no—
7#14273721—21no—
8#14273719C411yescharacteristic
9#14273715C411yescharacteristic
10#14273710—21no—
11#14273706C411yescharacteristic
12#14273701C411yescharacteristic
13C4×Dic118C2211yescharacteristic
14C4×D236C2211yescharacteristic
15C4×C22⋊D59—21no—
16#14273684—21no—
17#14273638—21no—
18C4×C59⋊C8C2212yes—
19C22×C8×C59—21no—
20C2×C42×C59C2211yescharacteristic
21C4⋊C8×C59—21no—
22C4⋊C8×C59C2212yes—
23C22×C4×C59C2×C411yescharacteristic
24C22×C4×C59D411yescharacteristic
25C22×C4×C59D411yescharacteristic
26C2×C22⋊D59—21no—
27C2×D236C2×C411yescharacteristic
28C2×C4×D59—21no—
29C2×Dic118C2×C411yescharacteristic
30C2×C8×C59—22no—
31C2×C8×C59—42no—
32C42×C59C2×C411yescharacteristic
33C42×C59D411yescharacteristic
34C42×C59D411yescharacteristic
35C42×C59C2311yescharacteristic
36C22⋊Dic59—21no—
37(C2×D59)⋊C4—21no—
38(C2×D59)⋊C4—21no—
39(C2×D59)⋊C4—21no—
40(C2×D59)⋊C4—21no—
41C4⋊Dic59C2×C411yescharacteristic
42C4⋊Dic59C2×C411yescharacteristic
43Dic59⋊C4—21no—
44Dic59⋊C4—21no—
45Dic59⋊C4—21no—
46Dic59⋊C4—21no—
47C4×Dic59—21no—
48#11745664—24no—
49C2×C59⋊C8—22no—
50C23×C59C22⋊C411yescharacteristic
51C22×D59—21no—
52C2×C4×C59—22no—
53C2×C4×C59—22no—
54C2×C4×C59—21no—
55C2×C4×C59—21no—
56C2×C4×C59C22⋊C411yescharacteristic
57C2×C4×C59C22⋊C411yescharacteristic
58C2×C4×C59C22⋊C411yescharacteristic
59C2×C4×C59C22×C411yescharacteristic
60C2×C4×C59C2×D411yescharacteristic
61C2×C4×C59C2×D411yescharacteristic
62C22⋊D59—42no—
63C2×Dic59—21no—
64C2×Dic59—21no—
65C2×Dic59—21no—
66D236—22no—
67C4×D59—41no—
68C4×D59—41no—
69Dic118—22no—
70C8×C59—42no—
71C59⋊C8—24no—
72C22×C59—21no—
73C22×C59—21no—
74C22×C59#10412yes—
75C22×C59C2×C22⋊C411yescharacteristic
76C2×D59—41no—
77C2×D59—41no—
78C2×D59—41no—
79C4×C59—21no—
80C4×C59—21no—
81C4×C59—21no—
82C4×C59—21no—
83C4×C59#13112yes—
84C4×C59AGL(1,ℤ/8)11yescharacteristic
85C4×C59#13711yescharacteristic
86Dic59—41no—
87Dic59—41no—
88Dic59—41no—
89#1483—591nomaximal, Sylow
90C2×C59—22no—
91C2×C59#40811yescharacteristic
92C2×C59#41711yescharacteristic
93C2×C59C2×#10411yescharacteristic
94D59—81no—
95#529—591no—
96C2×C4⋊C8D5911yescharacteristic, complemented
97C4×M16—591no—
98Q8⋊C8—592no—
99D4⋊C8—592no—
100C59#148311yescharacteristic, complemented, Sylow
101C2×M16—1181no—
102C22×C8—21no—
103#126—1181no—
104#125—591no—
105#124—591no—
106#123—1181no—
107C22⋊Q8—591no—
108#121—591no—
109C4×Q8—591no—
110C4×D4—591no—
111C4×D4—1181no—
112#117—1181no—
113C2×C42C2×D5911yescharacteristic
114C4⋊C8—21no—
115C4⋊C8C2×D5912yes—
116#97—1181no—
117C4×C8—592no—
118C2×Q8—591no—
119C2×D4—591no—
120C2×D4—1181no—
121C22×C4—1181no—
122C22×C4C4×D5911yescharacteristic
123C22×C4D23611yescharacteristic
124C22×C4C22⋊D5911yescharacteristic
125M16—1184no—
126C2×C8—22no—
127C2×C8—42no—
128C2×C8—1182no—
129C4⋊C4—591no—
130C4⋊C4—591no—
131C4⋊C4—1181no—
132C4⋊C4—1181no—
133C4⋊C4—1181no—
134C4⋊C4—1181no—
135C22⋊C4—1181no—
136C22⋊C4—1181no—
137C22⋊C4—1181no—
138C22⋊C4—1181no—
139C22⋊C4—1181no—
140C42—1181no—
141C42C4×D5911yescharacteristic
142C42D23611yescharacteristic
143C42C22⋊D5911yescharacteristic
144C42C22×D5911yescharacteristic
145C23—1181no—
146C23(C2×D59)⋊C411yescharacteristic
147Q8—1182no—
148D4—1182no—
149D4—2362no—
150C2×C4—22no—
151C2×C4—22no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—1181no—
155C2×C4—1181no—
156C2×C4—1181no—
157C2×C4—2361no—
158C2×C4—2361no—
159C2×C4(C2×D59)⋊C411yescharacteristic
160C2×C4(C2×D59)⋊C411yescharacteristic
161C2×C4(C2×D59)⋊C411yescharacteristic
162C2×C4C2×C4×D5911yescharacteristic
163C2×C4C2×D23611yescharacteristic
164C2×C4C2×C22⋊D5911yescharacteristic
165C8—42no—
166C8—1184no—
167C22—21no—
168C22—21no—
169C22—2361no—
170C22—2361no—
171C22—2361no—
172C22#1427365312yes—
173C22C2×(C2×D59)⋊C411yescharacteristic
174C4—21no—
175C4—21no—
176C4—21no—
177C4—21no—
178C4—2361no—
179C4—2361no—
180C4—2361no—
181C4#1427373312yes—
182C4#1427375311yescharacteristic
183C4#1427375811yescharacteristic
184C2—22no—
185C2—4721no—
186C2#1683736811yescharacteristic
187C2#1683740111yescharacteristic
188C2C2×#1427365311yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D59
commutatorC2×C4×C59C22×C4
FrattiniC42C22×D59
FittingC2×C4⋊C8×C59C2
socleC22×C59C2×C22⋊C4
hypercenterC2×C4⋊C8D59
hypocenterC59#1483
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
2. C4×#11745664C2semidirect
3. #16837132C2semidirect
4. #16837129C2semidirect
5. C2×C4⋊C8×C59C2semidirect
96. C2×C4⋊C8D59semidirect
100. C59#1483semidirect