Finite Group Databasebeta

← #21424750

Subgroups — #21424750

Order 7552.

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

normal subgroups only

This group has 212 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#16837410C211yesmaximal, characteristic
2C2×#14273650C211yesmaximal, characteristic
3C2×#14273645C211yesmaximal, characteristic
4#16837358C211yesmaximal, characteristic
5#16837171C211yesmaximal, characteristic
6#16837166C211yesmaximal, characteristic
7C59×#428C211yesmaximal, characteristic
8C22×Dic118C2211yescharacteristic
9C2×#11745664C2211yescharacteristic
10C2×#11745664C2211yescharacteristic
11C22×C59⋊C8C2211yescharacteristic
12#14273650—21no—
13#14273650—21no—
14#14273650—21no—
15#14273650—21no—
16#14273645C414yescomplemented
17#14273638—21no—
18C4×C59⋊C8—21no—
19C2×M16×C59C2211yescharacteristic
20#117×C59C2211yescharacteristic
21C2×C4⋊C4×C59C2211yescharacteristic
22#107×C59—21no—
23#106×C59—21no—
24C22×C4×C59—21no—
25C22×C4×C59C2311yescharacteristic
26C22×Dic59—21no—
27C2×Dic118—21no—
28C2×Dic118—21no—
29C2×Dic118—21no—
30C2×Dic118—21no—
31C2×Dic118—21no—
32C2×Dic118C2×C412yes—
33M16×C59—21no—
34M16×C59C2×C412yes—
35C2×C8×C59—21no—
36C4⋊C4×C59—21no—
37C4⋊C4×C59—21no—
38C4⋊C4×C59D411yescharacteristic
39C4⋊C4×C59D411yescharacteristic
40C22⋊C4×C59—21no—
41C42×C59—21no—
42#11745664—21no—
43#11745664—21no—
44#11745664—21no—
45#11745664C2×C412yes—
46C2×C59⋊C8—21no—
47C2×C59⋊C8—21no—
48C2×C59⋊C8—21no—
49C2×C59⋊C8—21no—
50C2×C59⋊C8D411yescharacteristic
51C2×C59⋊C8D411yescharacteristic
52C23×C59#4111yescharacteristic
53C2×C4×C59—21no—
54C2×C4×C59—21no—
55C2×C4×C59—41no—
56C2×C4×C59—81no—
57C2×C4×C59C22×C411yescharacteristic
58C2×C4×C59C2×D411yescharacteristic
59C2×C4×C59C2×D411yescharacteristic
60C2×C4×C59#4111yescharacteristic
61C2×C4×C59#4111yescharacteristic
62C2×C4×C59#4111yescharacteristic
63C2×Dic59—22no—
64C2×Dic59—41no—
65C2×Dic59—41no—
66Dic118—22no—
67Dic118—22no—
68Dic118—41no—
69Dic118—41no—
70C8×C59—22no—
71C59⋊C8—22no—
72C59⋊C8—21no—
73C59⋊C8—21no—
74C59⋊C8—41no—
75C22×C59—21no—
76C22×C59—21no—
77C22×C59#11711yescharacteristic
78C22×C59#12111yescharacteristic
79C22×C59#12611yescharacteristic
80C4×C59—41no—
81C4×C59—41no—
82C4×C59—81no—
83C4×C59C4×D411yescharacteristic
84C4×C59C4×D411yescharacteristic
85C4×C59#12311yescharacteristic
86C4×C59#12411yescharacteristic
87Dic59—42no—
88#1930—591nomaximal, Sylow
89C2×C59—21no—
90C2×C59—21no—
91C2×C59#38811yescharacteristic
92C2×C59#47111yescharacteristic
93C2×C59#47311yescharacteristic
94#428D5911yescharacteristic
95#419—591no—
96C2×#103—591no—
97C2×#101—591no—
98#405—591no—
99#343—591no—
100#341—591no—
101C59#193011yescharacteristic, complemented, Sylow
102C22×Q8—591no—
103C2×M16—591no—
104C2×M16—591no—
105C2×M16C2×D5911yescharacteristic
106C22×C8—591no—
107#117C2×D5911yescharacteristic
108C2×C4⋊C4C2×D5911yescharacteristic
109#107—21no—
110#106—21no—
111#103—1181no—
112#103—1181no—
113#103—1181no—
114#103—1181no—
115#101—594no—
116#97—1181no—
117C4×C8—1181no—
118C2×Q8—592no—
119C2×Q8—1181no—
120C2×Q8—1181no—
121C2×Q8—1181no—
122C2×Q8—1181no—
123C2×Q8—1181no—
124C22×C4—21no—
125C22×C4—1181no—
126C22×C4C22×D5911yescharacteristic
127M16—21no—
128M16—592no—
129M16—1181no—
130M16—1181no—
131M16—1181no—
132M16C4×D5912yes—
133C2×C8—21no—
134C2×C8—591no—
135C2×C8—591no—
136C2×C8—1181no—
137C2×C8—1181no—
138C2×C8—1181no—
139C2×C8—1181no—
140C4⋊C4—21no—
141C4⋊C4—21no—
142C4⋊C4C22⋊D5911yescharacteristic
143C4⋊C4C22⋊D5911yescharacteristic
144C22⋊C4—21no—
145C42—21no—
146C23#1174568711yescharacteristic
147Q8—1182no—
148Q8—1182no—
149Q8—2361no—
150Q8—2361no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—41no—
154C2×C4—81no—
155C2×C4—1182no—
156C2×C4—2361no—
157C2×C4—2361no—
158C2×C4C2×C4×D5911yescharacteristic
159C2×C4#1174568511yescharacteristic
160C2×C4D4×D5911yescharacteristic
161C2×C4#1174568911yescharacteristic
162C2×C4#1174568911yescharacteristic
163C2×C4C2×C22⋊D5911yescharacteristic
164C8—22no—
165C8—1182no—
166C8—1181no—
167C8—1181no—
168C8—2361no—
169C22—21no—
170C22—21no—
171C22#1427368511yescharacteristic
172C22#1427369911yescharacteristic
173C22#1427372211yescharacteristic
174C4—41no—
175C4—41no—
176C4—81no—
177C4—2362no—
178C4C4×C22⋊D5911yescharacteristic
179C4#1427368911yescharacteristic
180C4#1427371211yescharacteristic
181C4#1427371611yescharacteristic
182C2—21no—
183C2—21no—
184C2#1683729211yescharacteristic
185C2#1683766311yescharacteristic
186C2#1683767511yescharacteristic
subgroupG/H
centerC22#14273699
commutatorC2×C4×C59C22×C4
FrattiniC22×C4C22×D59
FittingC59×#428C2
socleC22×C59#121
hypercenter#428D59
hypocenterC59#1930
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
16. #14273645C4semidirect
101. C59#1930semidirect