Finite Group Databasebeta

← #21423284

Subgroups — #21423284

Order 7552.

212 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 53 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#16838137C211yesmaximal, characteristic
2#16837749C211yesmaximal, characteristic
3#16837688C211yesmaximal, characteristic, complemented
4#16837612C211yesmaximal, characteristic, complemented
5#16837145C211yesmaximal, characteristic
6#16837134C211yesmaximal, characteristic, complemented
7C59×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×#11745672—21no—
9#14273727C2211yescharacteristic
10#14273724C2211yescharacteristic
11#14273716—21no—
12#14273715—21no—
13#14273712—22no—
14C4×Dic118C2211yescharacteristic
15C4×D236—21no—
16#14273689—21no—
17#14273659—21no—
18C4⋊(C59⋊C8)C2211yescharacteristic
19#14273652—21no—
20#14273650—21no—
21#14273649—22no—
22C4×Q8×C59C2211yescharacteristic
23C4⋊C8×C59C2211yescharacteristic
24C4×C8×C59C2211yescharacteristic
25C2×Q8×C59D411yescharacteristic
26C2×D236—21no—
27C2×D236—21no—
28C2×D236D412yes—
29C2×C4×D59—22no—
30C2×Dic118—21no—
31C2×Dic118D411yescharacteristic
32C2×C8×C59—21no—
33C2×C8×C59—21no—
34C4⋊C4×C59—21no—
35C4⋊C4×C59D411yescharacteristic
36C42×C59—21no—
37C42×C59C2311yescharacteristic
38#11745672—42no—
39(C2×D59)⋊C4—22no—
40(C2×D59)⋊C4—22no—
41(C2×D59)⋊C4—22no—
42C4⋊Dic59—21no—
43C4⋊Dic59—21no—
44C4⋊Dic59D411yescharacteristic
45Dic59⋊C4—21no—
46C4×Dic59—21no—
47C2×C59⋊C8—21no—
48C22×D59—22no—
49Q8×C59—21no—
50Q8×C59—21no—
51C2×C4×C59—21no—
52C2×C4×C59—21no—
53C2×C4×C59C2×D411yescharacteristic
54C2×C4×C59C2×D411yescharacteristic
55C2×C4×C59C2×D411yescharacteristic
56C2×Dic59—21no—
57C2×Dic59—21no—
58C2×Dic59—41no—
59D236—42no—
60D236—41no—
61D236—41no—
62D236—41no—
63D236—41no—
64C4×D59—82no—
65Dic118—21no—
66Dic118—21no—
67Dic118—41no—
68Dic118—41no—
69C8×C59—41no—
70C8×C59—41no—
71C59⋊C8—41no—
72C22×C59#12011yescharacteristic
73C2×D59—42no—
74C2×D59—42no—
75C2×D59—42no—
76C4×C59—21no—
77C4×C59—41no—
78C4×C59—41no—
79C4×C59#13511yescharacteristic
80C4×C59#13511yescharacteristic
81C4×C59AGL(1,ℤ/8)11yescharacteristic
82C4×C59#13711yescharacteristic
83Dic59—41no—
84Dic59—41no—
85Dic59—81no—
86#1640—591nomaximal, Sylow
87C2×C59#44911yescharacteristic
88C2×C59#45211yescharacteristic
89C2×C59#45511yescharacteristic
90D59—82no—
91#559—591no—
92#486—591no—
93#475—591no—
94#462—591no—
95#331—591no—
96Q8⋊C8—591no—
97Q8⋊C8D5911yescharacteristic, complemented
98C59#164011yescharacteristic, complemented, Sylow
99C2×Q16—1181no—
100C4⋊Q8—591no—
101#127—591no—
102#124—1181no—
103#124—1181no—
104#123—1182no—
105C4×Q8—591no—
106C4×Q8C2×D5911yescharacteristic
107C4×D4—1181no—
108C4×D4—1181no—
109#106—1181no—
110C4⋊C8—591no—
111C4⋊C8C2×D5911yescharacteristic
112#103—1181no—
113#103—1181no—
114#102—1182no—
115C4×C8C2×D5911yescharacteristic
116C2×Q8—591no—
117C2×Q8—1181no—
118C2×Q8D23611yescharacteristic
119C2×D4—592no—
120C2×D4—1181no—
121C2×D4—1181no—
122C22×C4—1182no—
123Q16—2362no—
124C2×C8—21no—
125C2×C8—21no—
126C2×C8—1181no—
127C4⋊C4—21no—
128C4⋊C4—591no—
129C4⋊C4—1181no—
130C4⋊C4—1181no—
131C4⋊C4—1181no—
132C4⋊C4D23611yescharacteristic
133C22⋊C4—1182no—
134C22⋊C4—1182no—
135C22⋊C4—1182no—
136C42—21no—
137C42—1181no—
138C42C22×D5911yescharacteristic
139C23—1182no—
140Q8—21no—
141Q8—21no—
142Q8—1181no—
143Q8—1181no—
144Q8—2361no—
145Q8—2361no—
146D4—2362no—
147D4—2361no—
148D4—2361no—
149D4—2361no—
150D4—2361no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—1181no—
154C2×C4—1181no—
155C2×C4—4722no—
156C2×C4—2361no—
157C2×C4C2×D23611yescharacteristic
158C2×C4D4×D5911yescharacteristic
159C2×C4D4×D5911yescharacteristic
160C8—41no—
161C8—41no—
162C8—2361no—
163C22—2362no—
164C22—2362no—
165C22—2362no—
166C22#1427369711yescharacteristic
167C4—21no—
168C4—41no—
169C4—41no—
170C4—4721no—
171C4—2361no—
172C4—2361no—
173C4#1427374811yescharacteristic
174C4#1427374911yescharacteristic
175C4#1427375511yescharacteristic
176C4#1427375911yescharacteristic
177C2—4722no—
178C2#1683754911yescharacteristic
179C2#1683756711yescharacteristic
180C2#1683758111yescharacteristic
subgroupG/H
centerC22#14273697
commutatorC42×C59C23
FrattiniC42C22×D59
FittingC59×Q8⋊C8C2
socleC22×C59#120
hypercenterQ8⋊C8D59
hypocenterC59#1640
LCSG ▷ C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
3. #16837688C2semidirect
4. #16837612C2semidirect
6. #16837134C2semidirect
7. C59×Q8⋊C8C2semidirect
97. Q8⋊C8D59semidirect
98. C59#1640semidirect