Finite Group Databasebeta

← #21425439

Subgroups — #21425439

Order 7552.

246 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 73 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#16838030C211yesmaximal, characteristic
2#16837442C211yesmaximal, characteristic
3#16837271C211yesmaximal, characteristic
4#16837170C211yesmaximal, characteristic
5#16837163C211yesmaximal, characteristic
6#16837161C211yesmaximal, characteristic
7C59×#428C211yesmaximal, characteristic
8C2×#11745664C2211yescharacteristic
9#14273727—21no—
10#14273726—21no—
11#14273719—21no—
12#14273718—21no—
13#14273704—22no—
14#14273686C2211yescharacteristic
15C2×C4⋊Dic59C2211yescharacteristic
16C2×Dic59⋊C4—22no—
17C2×C4×Dic59C2211yescharacteristic
18#14273660—21no—
19#14273658—21no—
20C2×M16×C59C2211yescharacteristic
21#117×C59C2211yescharacteristic
22C2×C4⋊C4×C59C2211yescharacteristic
23#107×C59—21no—
24#106×C59—21no—
25C22×C4×C59—21no—
26C22×C4×C59C2311yescharacteristic
27C22×Dic59—21no—
28C22×Dic59D412yes—
29C2×Dic118—22no—
30M16×C59—21no—
31M16×C59Q812yescomplemented
32C2×C8×C59—21no—
33C4⋊C4×C59—21no—
34C4⋊C4×C59—21no—
35C4⋊C4×C59D411yescharacteristic
36C4⋊C4×C59D411yescharacteristic
37C22⋊C4×C59—21no—
38C42×C59—21no—
39C22⋊Dic59—21no—
40C4⋊Dic59—22no—
41C4⋊Dic59—21no—
42C4⋊Dic59—21no—
43C4⋊Dic59D411yescharacteristic
44C4⋊Dic59D411yescharacteristic
45Dic59⋊C4—22no—
46Dic59⋊C4—22no—
47Dic59⋊C4—44no—
48C4×Dic59—21no—
49C4×Dic59—21no—
50C4×Dic59Q812yescomplemented
51#11745664—21no—
52#11745664Q812yescomplemented
53C2×C59⋊C8—21no—
54C23×C59C2×D411yescharacteristic
55C2×C4×C59—21no—
56C2×C4×C59—21no—
57C2×C4×C59—42no—
58C2×C4×C59—41no—
59C2×C4×C59C2×D411yescharacteristic
60C2×C4×C59C2×D411yescharacteristic
61C2×C4×C59C2×Q811yescharacteristic
62C2×C4×C59C2×Q811yescharacteristic
63C2×C4×C59C2×Q811yescharacteristic
64C2×C4×C59#4111yescharacteristic
65C2×Dic59—22no—
66C2×Dic59—22no—
67C2×Dic59—22no—
68C2×Dic59—21no—
69C2×Dic59—21no—
70C2×Dic59—22no—
71C2×Dic59—42no—
72Dic118—82no—
73C8×C59—22no—
74C59⋊C8—22no—
75C22×C59—21no—
76C22×C59—21no—
77C22×C59#12011yescharacteristic
78C22×C59C22⋊Q811yescharacteristic
79C22×C59C4⋊Q811yescharacteristic
80C4×C59—41no—
81C4×C59—41no—
82C4×C59—81no—
83C4×C59C22⋊Q811yescharacteristic
84C4×C59C22⋊Q811yescharacteristic
85C4×C59C4⋊Q811yescharacteristic
86C4×C59C4⋊Q811yescharacteristic
87Dic59—24no—
88Dic59—41no—
89Dic59—42no—
90Dic59—41no—
91#2060—591nomaximal, Sylow
92C2×C59—21no—
93C2×C59—21no—
94C2×C59#39511yescharacteristic
95C2×C59#45311yescharacteristic
96C2×C59#45611yescharacteristic
97#544—591no—
98#428—591no—
99#428D5911yescharacteristic
100#384—591no—
101#343—591no—
102#339—591no—
103#339—591no—
104C59#206011yescharacteristic, complemented, Sylow
105C2×M16—591no—
106C2×M16C2×D5911yescharacteristic
107C4⋊Q8—1181no—
108C4⋊Q8—1181no—
109#125—1181no—
110#125—1181no—
111C22⋊Q8—1182no—
112#117—591no—
113#117C2×D5911yescharacteristic
114C2×C4⋊C4—591no—
115C2×C4⋊C4—1182no—
116C2×C4⋊C4C2×D5911yescharacteristic
117C2×C42—591no—
118#107—21no—
119#107—1181no—
120#106—21no—
121#106—1181no—
122C2×Q8—1182no—
123C22×C4—21no—
124C22×C4—592no—
125C22×C4—1181no—
126C22×C4C22×D5911yescharacteristic
127M16—21no—
128M16—592no—
129M16—1181no—
130M16Dic11812yescomplemented
131C2×C8—21no—
132C2×C8—1181no—
133C4⋊C4—21no—
134C4⋊C4—21no—
135C4⋊C4—591no—
136C4⋊C4—591no—
137C4⋊C4—1182no—
138C4⋊C4—1182no—
139C4⋊C4—1182no—
140C4⋊C4—1181no—
141C4⋊C4—1181no—
142C4⋊C4—2364no—
143C4⋊C4C22⋊D5911yescharacteristic
144C4⋊C4C22⋊D5911yescharacteristic
145C22⋊C4—21no—
146C22⋊C4—1181no—
147C42—21no—
148C42—592no—
149C42—1181no—
150C42—1181no—
151C23D4×D5911yescharacteristic
152Q8—4722no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—42no—
156C2×C4—41no—
157C2×C4—1182no—
158C2×C4—1182no—
159C2×C4—1182no—
160C2×C4—1181no—
161C2×C4—1181no—
162C2×C4—1182no—
163C2×C4—2362no—
164C2×C4C2×Dic11811yescharacteristic
165C2×C4#1174568511yescharacteristic
166C2×C4D4×D5911yescharacteristic
167C2×C4Q8×D5911yescharacteristic
168C2×C4Q8×D5911yescharacteristic
169C2×C4C2×C22⋊D5911yescharacteristic
170C8—22no—
171C8—1182no—
172C22—21no—
173C22—21no—
174C22#1427369511yescharacteristic
175C22#1427370511yescharacteristic
176C22#1427372611yescharacteristic
177C4—41no—
178C4—41no—
179C4—81no—
180C4—1184no—
181C4—2362no—
182C4—2361no—
183C4—2361no—
184C4#1427370511yescharacteristic
185C4#1427370611yescharacteristic
186C4#1427372511yescharacteristic
187C4#1427372611yescharacteristic
188C2—21no—
189C2—21no—
190C2#1683732211yescharacteristic
191C2#1683756811yescharacteristic
192C2#1683758311yescharacteristic
subgroupG/H
centerC22#14273695
commutatorC22×C4×C59C23
FrattiniC22×C4C22×D59
FittingC59×#428C2
socleC22×C59#120
hypercenter#428D59
hypocenterC59#2060
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
31. M16×C59Q8semidirect
50. C4×Dic59Q8semidirect
52. #11745664Q8semidirect
104. C59#2060semidirect
130. M16Dic118semidirect