Finite Group Databasebeta

← #21425445

Subgroups — #21425445

Order 7552.

230 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 75 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#16837445C211yesmaximal, characteristic
3#16837444C211yesmaximal, characteristic
4#16837268C211yesmaximal, characteristic
5#16837170C211yesmaximal, characteristic
6#16837162C211yesmaximal, characteristic
7C59×#339C211yesmaximal, characteristic
8C2×#11745664C2211yescharacteristic
9#14273727—21no—
10#14273726—21no—
11#14273719—21no—
12#14273718—21no—
13#14273704—22no—
14#14273686C2211yescharacteristic
15C2×C4⋊Dic59C2211yescharacteristic
16C2×C4⋊Dic59C2211yescharacteristic
17#14273661—21no—
18#14273660—21no—
19#14273659—21no—
20#14273658—21no—
21C59⋊#95—22no—
22C2×M16×C59C2211yescharacteristic
23#117×C59C2211yescharacteristic
24C2×C42×C59C2211yescharacteristic
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×C59D411yescharacteristic
34C4⋊C4×C59D411yescharacteristic
35C22⋊C4×C59—21no—
36C42×C59—21no—
37C42×C59—21no—
38C42×C59Q812yescomplemented
39C22⋊Dic59—21no—
40C4⋊Dic59—22no—
41C4⋊Dic59—21no—
42C4⋊Dic59—21no—
43C4⋊Dic59—21no—
44C4⋊Dic59—21no—
45C4⋊Dic59D411yescharacteristic
46C4⋊Dic59D411yescharacteristic
47Dic59⋊C4—22no—
48Dic59⋊C4—22no—
49C4×Dic59—21no—
50#11745664—21no—
51#11745664Q812yescomplemented
52C2×C59⋊C8—21no—
53C23×C59C2×D411yescharacteristic
54C2×C4×C59—21no—
55C2×C4×C59—21no—
56C2×C4×C59—22no—
57C2×C4×C59—41no—
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—21no—
66C2×Dic59—21no—
67C2×Dic59—22no—
68C2×Dic59—42no—
69C2×Dic59—42no—
70C2×Dic59—41no—
71Dic118—82no—
72C8×C59—22no—
73C59⋊C8—22no—
74C22×C59—21no—
75C22×C59—21no—
76C22×C59#12011yescharacteristic
77C22×C59C22⋊Q811yescharacteristic
78C22×C59C4⋊Q811yescharacteristic
79C4×C59—42no—
80C4×C59—41no—
81C4×C59—41no—
82C4×C59C22⋊Q811yescharacteristic
83C4×C59C22⋊Q811yescharacteristic
84C4×C59C4⋊Q811yescharacteristic
85C4×C59C4⋊Q811yescharacteristic
86Dic59—41no—
87Dic59—41no—
88Dic59—42no—
89Dic59—81no—
90#2061—591nomaximal, Sylow
91C2×C59—21no—
92C2×C59—21no—
93C2×C59#39511yescharacteristic
94C2×C59#45411yescharacteristic
95C2×C59#45511yescharacteristic
96#544—591no—
97#428—591no—
98#428—591no—
99#382—591no—
100#343—591no—
101#339—591no—
102#339D5911yescharacteristic
103C59#206111yescharacteristic, complemented, Sylow
104C2×M16—591no—
105C2×M16C2×D5911yescharacteristic
106C4⋊Q8—1181no—
107C4⋊Q8—1181no—
108#125—1181no—
109#125—1181no—
110C22⋊Q8—1182no—
111#117—591no—
112#117C2×D5911yescharacteristic
113C2×C4⋊C4—591no—
114C2×C4⋊C4—591no—
115C2×C42C2×D5911yescharacteristic
116#107—1181no—
117#107—1181no—
118#106—1181no—
119#106—1181no—
120#95—1182no—
121C2×Q8—1182no—
122C22×C4—21no—
123C22×C4—592no—
124C22×C4—1181no—
125C22×C4C22×D5911yescharacteristic
126M16—21no—
127M16—592no—
128M16—1181no—
129M16Dic11812yescomplemented
130C2×C8—21no—
131C2×C8—1181no—
132C4⋊C4—591no—
133C4⋊C4—591no—
134C4⋊C4—1182no—
135C4⋊C4—1182no—
136C4⋊C4—1182no—
137C4⋊C4—1181no—
138C4⋊C4—1181no—
139C4⋊C4—1181no—
140C4⋊C4—1181no—
141C4⋊C4D23611yescharacteristic
142C4⋊C4D23611yescharacteristic
143C22⋊C4—21no—
144C22⋊C4—1181no—
145C42—21no—
146C42—21no—
147C42—1181no—
148C42Dic11812yescomplemented
149C23D4×D5911yescharacteristic
150Q8—4722no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—22no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—1181no—
157C2×C4—1181no—
158C2×C4—1182no—
159C2×C4—2362no—
160C2×C4—2361no—
161C2×C4—2362no—
162C2×C4C2×Dic11811yescharacteristic
163C2×C4C2×Dic11811yescharacteristic
164C2×C4C2×D23611yescharacteristic
165C2×C4D4×D5911yescharacteristic
166C2×C4#1174568711yescharacteristic
167C2×C4Q8×D5911yescharacteristic
168C8—22no—
169C8—1182no—
170C22—21no—
171C22—21no—
172C22#1427369711yescharacteristic
173C22#1427370411yescharacteristic
174C22#1427372611yescharacteristic
175C4—42no—
176C4—41no—
177C4—41no—
178C4—4721no—
179C4—2361no—
180C4—2362no—
181C4—2361no—
182C4#1427370411yescharacteristic
183C4#1427370711yescharacteristic
184C4#1427372611yescharacteristic
185C4#1427372711yescharacteristic
186C2—21no—
187C2—21no—
188C2#1683732311yescharacteristic
189C2#1683757611yescharacteristic
190C2#1683758111yescharacteristic
subgroupG/H
centerC22#14273697
commutatorC22×C4×C59C23
FrattiniC22×C4C22×D59
FittingC59×#339C2
socleC22×C59#120
hypercenter#339D59
hypocenterC59#2061
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
31. M16×C59Q8semidirect
38. C42×C59Q8semidirect
51. #11745664Q8semidirect
103. C59#2061semidirect
129. M16Dic118semidirect
148. C42Dic118semidirect