Finite Group Databasebeta

← #21423240

Subgroups — #21423240

Order 7552.

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

normal subgroups only

This group has 218 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#16838117C211yesmaximal, characteristic
2#16837781C211yesmaximal, characteristic, complemented
3#16837689C211yesmaximal, characteristic, complemented
4#16837150C211yesmaximal, characteristic, complemented
5D4⋊(C59⋊C8)C211yesmaximal, characteristic, complemented
6#16837129C211yesmaximal, characteristic, complemented
7C59×#476C211yesmaximal, characteristic, complemented
8C2×#11745672—22no—
9#14273727C2211yescharacteristic
10#14273713—22no—
11#14273701—21no—
12#14273698—21no—
13C4×D236C2211yescharacteristic
14#14273686—21no—
15#14273685—21no—
16#14273658—21no—
17C4⋊(C59⋊C8)C2211yescharacteristic
18#14273647—21no—
19C4×C59⋊C8C2211yescharacteristic
20C4⋊Q8×C59C2211yescharacteristic
21C4×D4×C59C2211yescharacteristic
22#106×C59—21no—
23C4⋊C8×C59C2211yescharacteristic
24#102×C59—21no—
25C2×Q8×C59—21no—
26C2×D4×C59D411yescharacteristic
27C22×C4×C59—21no—
28C2×C22⋊D59—22no—
29C2×D236D411yescharacteristic
30C2×C4×D59—21no—
31C2×Dic118D412yes—
32C2×C8×C59—21no—
33C4⋊C4×C59—21no—
34C4⋊C4×C59—21no—
35C4⋊C4×C59D411yescharacteristic
36C22⋊C4×C59—21no—
37C42×C59C2311yescharacteristic
38C22⋊Dic59—22no—
39#11745672—44no—
40(C2×D59)⋊C4—22no—
41(C2×D59)⋊C4—21no—
42C4⋊Dic59—21no—
43C4⋊Dic59—21no—
44C4⋊Dic59D411yescharacteristic
45C4×Dic59—22no—
46C2×C59⋊C8—21no—
47C2×C59⋊C8—21no—
48C23×C59—21no—
49C22×D59—21no—
50Q8×C59—42no—
51D4×C59—21no—
52D4×C59—21no—
53C2×C4×C59—21no—
54C2×C4×C59—41no—
55C2×C4×C59—41no—
56C2×C4×C59—41no—
57C2×C4×C59C2×D411yescharacteristic
58C2×C4×C59C2×D411yescharacteristic
59C2×C4×C59C2×D411yescharacteristic
60C22⋊D59—82no—
61C2×Dic59—21no—
62C2×Dic59—22no—
63D236—21no—
64D236—21no—
65C4×D59—41no—
66C4×D59—41no—
67Dic118—42no—
68C8×C59—41no—
69C59⋊C8—22no—
70C59⋊C8—41no—
71C22×C59—41no—
72C22×C59—41no—
73C22×C59—41no—
74C22×C59#12011yescharacteristic
75C2×D59—41no—
76C2×D59—41no—
77C2×D59—41no—
78C4×C59—21no—
79C4×C59—41no—
80C4×C59—81no—
81C4×C59#13511yescharacteristic
82C4×C59#13511yescharacteristic
83C4×C59#13711yescharacteristic
84C4×C59#13711yescharacteristic
85Dic59—41no—
86Dic59—42no—
87#1634—591nomaximal, Sylow
88C2×C59—81no—
89C2×C59#45211yescharacteristic
90C2×C59#45211yescharacteristic
91C2×C59#45311yescharacteristic
92D59—81no—
93#555—591no—
94#494—591no—
95#476—591no—
96#476D5911yescharacteristic, complemented
97#333—591no—
98D4⋊C8—591no—
99D4⋊C8—591no—
100C59#163411yescharacteristic, complemented, Sylow
101C2×Q16—1182no—
102C4⋊Q8—591no—
103C4⋊Q8C2×D5911yescharacteristic
104#124—1182no—
105#121—1181no—
106#121—1181no—
107C4×D4—591no—
108C4×D4C2×D5911yescharacteristic
109#117—1181no—
110#117—1181no—
111#106—21no—
112#106—1181no—
113C4⋊C8—591no—
114C4⋊C8C2×D5911yescharacteristic
115#102—21no—
116#102—1181no—
117C4×C8—591no—
118C2×Q8—21no—
119C2×Q8—592no—
120C2×D4—591no—
121C2×D4—1182no—
122C2×D4C22⋊D5911yescharacteristic
123C22×C4—21no—
124C22×C4—1181no—
125Q16—2364no—
126C2×C8—21no—
127C2×C8—1181no—
128C2×C8—1181no—
129C4⋊C4—21no—
130C4⋊C4—21no—
131C4⋊C4—591no—
132C4⋊C4—1181no—
133C4⋊C4—1181no—
134C4⋊C4C22⋊D5911yescharacteristic
135C22⋊C4—21no—
136C22⋊C4—1182no—
137C22⋊C4—1182no—
138C22⋊C4—1181no—
139C42—1182no—
140C42C22×D5911yescharacteristic
141C23—21no—
142C23—1181no—
143Q8—42no—
144Q8—2362no—
145D4—21no—
146D4—21no—
147D4—1181no—
148D4—1181no—
149D4—4722no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—1181no—
155C2×C4—1182no—
156C2×C4—2361no—
157C2×C4—2361no—
158C2×C4D4×D5911yescharacteristic
159C2×C4D4×D5911yescharacteristic
160C2×C4C2×C22⋊D5911yescharacteristic
161C8—41no—
162C8—1182no—
163C8—2361no—
164C22—41no—
165C22—41no—
166C22—41no—
167C22—2361no—
168C22—2361no—
169C22—2361no—
170C22#1427369511yescharacteristic
171C4—21no—
172C4—41no—
173C4—81no—
174C4—2361no—
175C4—2362no—
176C4#1427374711yescharacteristic
177C4#1427374811yescharacteristic
178C4#1427375611yescharacteristic
179C4#1427375811yescharacteristic
180C2—81no—
181C2—4721no—
182C2#1683756111yescharacteristic
183C2#1683756211yescharacteristic
184C2#1683756811yescharacteristic
subgroupG/H
centerC22#14273695
commutatorC42×C59C23
FrattiniC42C22×D59
FittingC59×#476C2
socleC22×C59#120
hypercenter#476D59
hypocenterC59#1634
LCSG ▷ C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
2. #16837781C2semidirect
3. #16837689C2semidirect
4. #16837150C2semidirect
5. D4⋊(C59⋊C8)C2semidirect
6. #16837129C2semidirect
7. C59×#476C2semidirect
96. #476D59semidirect
100. C59#1634semidirect