Finite Group Databasebeta

← #21426073

Subgroups — #21426073

Order 7552.

206 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 47 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#16838215C211yesmaximal, characteristic
2#16837843C211yesmaximal, characteristic, complemented
3#16837674C211yesmaximal, characteristic, complemented
4#16837218C211yesmaximal, characteristic, complemented
5#16837210C211yesmaximal, characteristic, complemented
6#16837185C211yesmaximal, characteristic, complemented
7C2×Q32×C59C211yesmaximal, characteristic, complemented
8#14273775—21no—
9#14273759—22no—
10#14273758—21no—
11#14273758—21no—
12#14273750—21no—
13#14273749C2211yescharacteristic
14Q16×D59—21no—
15#14273733C2211yescharacteristic
16#14273673—21no—
17#14273670—21no—
18#14273667C2211yescharacteristic
19#14273663C2211yescharacteristic
20#14273646—21no—
21C2×Q16×C59C2211yescharacteristic
22C2×Q16×C59C2211yescharacteristic
23Q32×C59—22no—
24C2×C16×C59C2211yescharacteristic
25C2×Q8×C59—21no—
26C2×Q8×C59—21no—
27#11745689—22no—
28#11745689—41no—
29Q8×D59—22no—
30Q8×D59—41no—
31#11745685—21no—
32#11745685—42no—
33#11745685D411yescharacteristic
34Q16×C59—21no—
35Q16×C59—21no—
36Q16×C59—21no—
37Q16×C59D412yes—
38C2×C8×C59C2311yescharacteristic
39#11745672—22no—
40#11745672—41no—
41#11745671—22no—
42#11745671—41no—
43#11745664—21no—
44#11745664D411yescharacteristic
45Dic236D411yescharacteristic
46D472D411yescharacteristic
47#11745660—21no—
48#11745659—21no—
49C8×D59—21no—
50C16×C59—21no—
51C59⋊C16—21no—
52Q8×C59—22no—
53Q8×C59—41no—
54Q8×C59—41no—
55Q8×C59—41no—
56C2×C4×C59—41no—
57C2×C4×C59—41no—
58C2×C4×C59C2×D411yescharacteristic
59C22⋊D59—21no—
60C22⋊D59—41no—
61D236—21no—
62D236—42no—
63D236D811yescharacteristic
64C4×D59—21no—
65C4×D59—42no—
66C4×D59—42no—
67C4×D59—41no—
68Dic118—21no—
69Dic118—42no—
70Dic118D811yescharacteristic
71C8×C59C2×D411yescharacteristic
72C8×C59C2×D411yescharacteristic
73C59⋊C8—21no—
74C59⋊C8—41no—
75C22×C59AGL(1,ℤ/8)11yescharacteristic
76C2×D59—21no—
77C2×D59—41no—
78C4×C59—42no—
79C4×C59—81no—
80C4×C59#12011yescharacteristic
81C4×C59C2×D811yescharacteristic
82Dic59—21no—
83Dic59—41no—
84#2195—591nomaximal, Sylow
85C2×C59—21no—
86C2×C59#44711yescharacteristic
87D59—41no—
88D59—81no—
89#578—591no—
90#510—591no—
91C2×Q32D5911yescharacteristic, complemented
92#473—591no—
93#362—591no—
94#359—591no—
95#350—591no—
96C59#219511yescharacteristic, complemented, Sylow
972−1+4—1181no—
98#137—1181no—
99#137—1182no—
100#137—1181no—
101#135—591no—
102#135—1181no—
103C2×Q16—1181no—
104C2×Q16C2×D5911yescharacteristic
105C2×Q16C2×D5911yescharacteristic
106#131—591no—
107Q32—22no—
108Q32—1181no—
109SD32—1181no—
110M32—591no—
111C2×C16C2×D5911yescharacteristic
112#108—591no—
113#101—1181no—
114#41—591no—
115#41—1182no—
116#41—1181no—
117#41—2362no—
118#41—2361no—
119C2×Q8—21no—
120C2×Q8—21no—
121C2×Q8—1182no—
122C2×Q8—2361no—
123Q16—21no—
124Q16—21no—
125Q16—21no—
126Q16—591no—
127Q16—1182no—
128Q16—2361no—
129Q16C22⋊D5912yes—
130SD16—1182no—
131SD16—1181no—
132SD16—2361no—
133D8—591no—
134M16—591no—
135M16—1181no—
136M16—1181no—
137C2×C8—1181no—
138C2×C8C22×D5911yescharacteristic
139C16—21no—
140C16—1181no—
141Q8—22no—
142Q8—41no—
143Q8—41no—
144Q8—41no—
145Q8—591no—
146Q8—1181no—
147Q8—2362no—
148D4—591no—
149D4—1181no—
150D4—1181no—
151D4—2362no—
152D4—2361no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—1181no—
156C2×C4—2362no—
157C2×C4—2362no—
158C2×C4—2361no—
159C2×C4D4×D5911yescharacteristic
160C8—1181no—
161C8—2361no—
162C8D4×D5911yescharacteristic
163C8C2×C22⋊D5911yescharacteristic
164C22—1181no—
165C22—2361no—
166C22#1427375111yescharacteristic
167C4—42no—
168C4—81no—
169C4—1181no—
170C4—2361no—
171C4#1427369511yescharacteristic
172C4D8×D5911yescharacteristic
173C2—21no—
174C2—4721no—
175C2—2361no—
176C2#1683753411yescharacteristic
subgroupG/H
centerC2#16837534
commutatorC2×C8×C59C23
FrattiniC2×C8C22×D59
FittingC2×Q32×C59C2
socleC2×C59#447
hypercenterC2×Q32D59
hypocenterC59#2195
LCSG ▷ C2×C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q32

Complements

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

NH ≅ G/Ntype
2. #16837843C2semidirect
3. #16837674C2semidirect
4. #16837218C2semidirect
5. #16837210C2semidirect
6. #16837185C2semidirect
7. C2×Q32×C59C2semidirect
91. C2×Q32D59semidirect
96. C59#2195semidirect