Finite Group Databasebeta

← #21425784

Subgroups — #21425784

Order 7552.

230 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 55 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#16837977C211yesmaximal, characteristic
2#101×D59C212yesmaximal, complemented
3#16837201C211yesmaximal, characteristic, complemented
4#16837198C212yesmaximal, complemented
5C59×#356C211yesmaximal, characteristic, complemented
6C2×#11745689C411yescharacteristic
7C2×Q8×D59C2211yescharacteristic
8M16×D59—22no—
9#14273725C411yescharacteristic
10#14273716C2211yescharacteristic
11#14273715C411yescharacteristic
12#14273712—22no—
13#14273705—22no—
14#14273684C411yescharacteristic
15#14273646C2212yes—
16#14273645—22no—
17C4⋊Q8×C59C2211yescharacteristic
18#101×C59C2212yes—
19C2×Q8×C59C2×C411yescharacteristic
20C2×Q8×C59C2311yescharacteristic
21#11745689—42no—
22Q8×D59—42no—
23C2×D236—21no—
24C2×D236C2×C411yescharacteristic
25C2×C4×D59—21no—
26C2×C4×D59C2×C411yescharacteristic
27C2×C4×D59D412yes—
28C2×Dic118C2×C411yescharacteristic
29C2×Dic118D412yes—
30M16×C59—22no—
31C4⋊C4×C59—22no—
32C42×C59C2×C411yescharacteristic
33(C2×D59)⋊C4—21no—
34(C2×D59)⋊C4—22no—
35(C2×D59)⋊C4—22no—
36Dic59⋊C4—21no—
37Dic59⋊C4—22no—
38C4×Dic59C2×C411yescharacteristic
39#11745664—22no—
40#11745659—42no—
41C8×D59—42no—
42C22×D59—21no—
43C22×D59C22⋊C411yescharacteristic
44Q8×C59—41no—
45Q8×C59—41no—
46C2×C4×C59—21no—
47C2×C4×C59—21no—
48C2×C4×C59C22×C411yescharacteristic
49C2×C4×C59C2×D412yes—
50C2×Dic59—21no—
51C2×Dic59C22⋊C412yes—
52C2×Dic59C22⋊C411yescharacteristic
53D236—41no—
54D236—42no—
55C4×D59—22no—
56C4×D59—22no—
57C4×D59—22no—
58C4×D59—42no—
59Dic118—41no—
60Dic118—42no—
61C8×C59—42no—
62C59⋊C8—42no—
63C22×C59C2×C22⋊C411yescharacteristic
64C2×D59—41no—
65C2×D59—42no—
66C2×D59—41no—
67C2×D59#9912yes—
68C4×C59—22no—
69C4×C59—21no—
70C4×C59—41no—
71C4×C59—41no—
72Dic59—21no—
73Dic59—22no—
74Dic59—41no—
75#2133—591nomaximal, Sylow
76C2×C59—21no—
77C2×C59C2×#9911yescharacteristic
78D59—22no—
79D59—81no—
80#536—591no—
81C2×#101—592no—
82#356—591no—
83#356D5911yescharacteristic, complemented
84#355—592no—
85C59#213311yescharacteristic, complemented, Sylow
86C2×#41—591no—
87C22×Q8—591no—
88C2×M16—1182no—
89C4⋊Q8—591no—
90C4⋊Q8C2×D5911yescharacteristic
91#124—591no—
92#124—591no—
93#123—1182no—
94C22⋊Q8—1182no—
95#117—591no—
96#101—592no—
97#101—1182no—
98#101C2×D5912yes—
99#41—2362no—
100C2×Q8—591no—
101C2×Q8—592no—
102C2×Q8—2362no—
103C2×Q8C4×D5911yescharacteristic
104C2×Q8C22×D5911yescharacteristic
105C2×D4—591no—
106C2×D4—1181no—
107C22×C4—591no—
108C22×C4—592no—
109C22×C4—1181no—
110M16—22no—
111M16—1182no—
112M16—2362no—
113C2×C8—2362no—
114C4⋊C4—22no—
115C4⋊C4—1181no—
116C4⋊C4—1182no—
117C22⋊C4—1182no—
118C22⋊C4—1181no—
119C22⋊C4—1182no—
120C42—591no—
121C42C4×D5911yescharacteristic
122C23—591no—
123C23—1181no—
124Q8—41no—
125Q8—41no—
126Q8—2362no—
127Q8—2361no—
128D4—2361no—
129D4—2362no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—592no—
133C2×C4—591no—
134C2×C4—1182no—
135C2×C4—1182no—
136C2×C4—1182no—
137C2×C4—1181no—
138C2×C4—2362no—
139C2×C4C2×C4×D5911yescharacteristic
140C2×C4D4×D5912yes—
141C8—42no—
142C8—2362no—
143C22—592no—
144C22—2361no—
145C22—2362no—
146C22—2361no—
147C22C22⋊C4×D5911yescharacteristic
148C4—22no—
149C4—21no—
150C4—41no—
151C4—41no—
152C4—1181no—
153C4—1182no—
154C4—2361no—
155C2—21no—
156C2—1182no—
157C2—4721no—
158C2#99×D5911yescharacteristic
subgroupG/H
centerC2#99×D59
commutatorC2×C4×C59C22×C4
FrattiniC2×Q8C22×D59
FittingC59×#356C2
socleC2×C59C2×#99
hypercenter#356D59
hypocenterC59#2133
LCSG ▷ C2×C4×C59 ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #356

Complements

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

NH ≅ G/Ntype
2. #101×D59C2semidirect
3. #16837201C2semidirect
4. #16837198C2semidirect
5. C59×#356C2semidirect
83. #356D59semidirect
85. C59#2133semidirect