Finite Group Databasebeta

← #21424739

Subgroups — #21424739

Order 7552.

254 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 99 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
1C2×#14273661C211yesmaximal, characteristic
2C2×#14273651C211yesmaximal, characteristic
3#16837309C211yesmaximal, characteristic
4C4⋊C4×Dic59C211yesmaximal, characteristic
5#16837164C211yesmaximal, characteristic
6#16837156C211yesmaximal, characteristic
7C2×#103×C59C211yesmaximal, characteristic
8C22×C59⋊C8C2211yescharacteristic
9C2×C4⋊Dic59C2211yescharacteristic
10C2×C4⋊Dic59C2211yescharacteristic
11C2×C4×Dic59—21no—
12C2×C4×Dic59C2211yescharacteristic
13#14273661—22no—
14#14273651—22no—
15C59⋊#95—21no—
16C59⋊#95—21no—
17C59⋊#95—21no—
18C22×Q8×C59C2211yescharacteristic
19C22×C8×C59C2211yescharacteristic
20C2×C4⋊C4×C59C2211yescharacteristic
21#103×C59C414yescomplemented
22C2×Q8×C59—21no—
23C2×Q8×C59—21no—
24C2×Q8×C59—21no—
25C2×Q8×C59—21no—
26C2×Q8×C59—21no—
27C2×Q8×C59C2×C412yes—
28C22×C4×C59—21no—
29C22×C4×C59—21no—
30C22×C4×C59C2311yescharacteristic
31C22×Dic59—21no—
32C22×Dic59—21no—
33C22×Dic59D411yescharacteristic
34C22×Dic59D411yescharacteristic
35C2×C8×C59—21no—
36C2×C8×C59—21no—
37C2×C8×C59C2×C412yes—
38C4⋊C4×C59—21no—
39C4⋊C4×C59C2×C412yes—
40C4⋊Dic59—21no—
41C4⋊Dic59—21no—
42C4⋊Dic59—21no—
43C4⋊Dic59D412yes—
44C4×Dic59—21no—
45C4×Dic59—21no—
46C4×Dic59—42no—
47C2×C59⋊C8—21no—
48C2×C59⋊C8—21no—
49C2×C59⋊C8—21no—
50C23×C59C2×D411yescharacteristic
51Q8×C59—22no—
52Q8×C59—22no—
53Q8×C59—41no—
54Q8×C59—41no—
55C2×C4×C59—22no—
56C2×C4×C59—22no—
57C2×C4×C59—41no—
58C2×C4×C59—41no—
59C2×C4×C59—41no—
60C2×C4×C59—41no—
61C2×C4×C59C22×C411yescharacteristic
62C2×C4×C59C2×D411yescharacteristic
63C2×C4×C59#4111yescharacteristic
64C2×C4×C59#4111yescharacteristic
65C2×C4×C59#4111yescharacteristic
66C2×C4×C59#4111yescharacteristic
67C2×Dic59—21no—
68C2×Dic59—21no—
69C2×Dic59—22no—
70C2×Dic59—21no—
71C2×Dic59—21no—
72C2×Dic59—21no—
73C2×Dic59—41no—
74C2×Dic59—41no—
75C2×Dic59—41no—
76C2×Dic59—41no—
77C2×Dic59—41no—
78C2×Dic59Q1612yes—
79C8×C59—22no—
80C59⋊C8—41no—
81C22×C59C4×D411yescharacteristic
82C22×C59#12111yescharacteristic
83C22×C59#12311yescharacteristic
84C22×C59C2×Q1611yescharacteristic
85C22×C59#13511yescharacteristic
86C22×C59AGL(1,ℤ/8)11yescharacteristic
87C22×C59#13711yescharacteristic
88C4×C59—42no—
89C4×C59—42no—
90C4×C59#11711yescharacteristic
91C4×C59C4×D411yescharacteristic
92C4×C59#12411yescharacteristic
93C4×C59#12611yescharacteristic
94Dic59—22no—
95Dic59—42no—
96Dic59—41no—
97Dic59—81no—
98#1928—591nomaximal, Sylow
99C2×C59#38811yescharacteristic
100C2×C59C4×Q1611yescharacteristic
101C2×C59#44011yescharacteristic
102C2×C59#46211yescharacteristic
103C2×C59#46311yescharacteristic
104C2×C59#48411yescharacteristic
105C2×C59#48511yescharacteristic
106C2×#107—591no—
107C2×#103—591no—
108C2×#103D5911yescharacteristic
109#391—591no—
110C4×C4⋊C4—591no—
111#340—591no—
112#336—591no—
113C59#192811yescharacteristic, complemented, Sylow
114C22×Q8C2×D5911yescharacteristic
115C22×C8—591no—
116C22×C8C2×D5911yescharacteristic
117C2×C4⋊C4—591no—
118C2×C4⋊C4—591no—
119C2×C4⋊C4C2×D5911yescharacteristic
120C2×C42—591no—
121C2×C42—1181no—
122#107—1182no—
123#103—1182no—
124#103Dic5914yescomplemented
125#95—1181no—
126#95—1181no—
127#95—1181no—
128C2×Q8—21no—
129C2×Q8—21no—
130C2×Q8—21no—
131C2×Q8—21no—
132C2×Q8—21no—
133C2×Q8C2×Dic5912yes—
134C22×C4—21no—
135C22×C4—21no—
136C22×C4—591no—
137C22×C4—591no—
138C22×C4—1181no—
139C22×C4—1181no—
140C22×C4C22×D5911yescharacteristic
141C2×C8—21no—
142C2×C8—21no—
143C2×C8—1181no—
144C2×C8—1181no—
145C2×C8—1181no—
146C2×C8C2×Dic5912yes—
147C4⋊C4—21no—
148C4⋊C4—592no—
149C4⋊C4—1181no—
150C4⋊C4—1181no—
151C4⋊C4—1181no—
152C4⋊C4C2×Dic5912yes—
153C42—1181no—
154C42—1181no—
155C42—2362no—
156C23D4×D5911yescharacteristic
157Q8—22no—
158Q8—22no—
159Q8—41no—
160Q8—41no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—592no—
168C2×C4—1181no—
169C2×C4—1181no—
170C2×C4—1182no—
171C2×C4—1181no—
172C2×C4—1181no—
173C2×C4—1181no—
174C2×C4—2361no—
175C2×C4—2361no—
176C2×C4—2361no—
177C2×C4—2361no—
178C2×C4—2361no—
179C2×C4#1174568511yescharacteristic
180C2×C4#1174568511yescharacteristic
181C2×C4D4×D5911yescharacteristic
182C2×C4#1174568711yescharacteristic
183C2×C4#1174568711yescharacteristic
184C2×C4C22×Dic5911yescharacteristic
185C8—22no—
186C8—2361no—
187C22D4×Dic5911yescharacteristic
188C22#1427370011yescharacteristic
189C22#1427370911yescharacteristic
190C22Q16×D5911yescharacteristic
191C22#1427375011yescharacteristic
192C22#1427375411yescharacteristic
193C22#1427375611yescharacteristic
194C4—42no—
195C4—42no—
196C4—1182no—
197C4—4721no—
198C4—2361no—
199C4—2362no—
200C4#1427368611yescharacteristic
201C4D4×Dic5911yescharacteristic
202C4#1427371311yescharacteristic
203C4#1427372011yescharacteristic
204C2#1683729511yescharacteristic
205C2Q16×Dic5911yescharacteristic
206C2#1683750311yescharacteristic
207C2#1683761111yescharacteristic
208C2#1683762011yescharacteristic
209C2#1683773611yescharacteristic
210C2#1683774211yescharacteristic
subgroupG/H
centerC23D4×D59
commutatorC2×C4×C59C22×C4
FrattiniC22×C4C22×D59
FittingC2×#103×C59C2
socleC23×C59C2×D4
hypercenterC2×#103D59
hypocenterC59#1928
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
21. #103×C59C4semidirect
113. C59#1928semidirect
124. #103Dic59semidirect