Finite Group Databasebeta

← #21424480

Subgroups — #21424480

Order 7552.

332 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 93 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#16838169C211yesmaximal, characteristic, complemented
2#16837419C212yesmaximal, complemented
3#16837376C211yesmaximal, characteristic, complemented
4#16837162C212yesmaximal, complemented
5C59×#532C211yesmaximal, characteristic
6#14273734—24no—
7C2×#11745664—22no—
8C2×#11745664C2212yes—
9#14273686C2212yes—
10#14273654—24no—
11#14273642—22no—
12C2×#41×C59C2211yescharacteristic
13C2×#41×C59C2211yescharacteristic
14C4⋊Q8×C59C411yescharacteristic, complemented
15#127×C59C411yescharacteristic, complemented
16#124×C59C411yescharacteristic, complemented
17#124×C59C411yescharacteristic, complemented
18#121×C59—22no—
19C4×D4×C59—22no—
20C2×C42×C59C2211yescharacteristic
21#41×C59—22no—
22#41×C59—22no—
23#41×C59—22no—
24#41×C59—22no—
25C2×Q8×C59C2×C411yescharacteristic
26C2×Q8×C59C2×C411yescharacteristic
27C2×D4×C59—22no—
28C2×D4×C59—21no—
29C2×D4×C59C2×C411yescharacteristic
30C2×D4×C59C2×C411yescharacteristic
31C2×D4×C59D412yes—
32C22×C4×C59—21no—
33C22×C4×C59—21no—
34C22×C4×C59D412yes—
35C22×C4×C59C2311yescharacteristic
36C4⋊C4×C59—22no—
37C22⋊C4×C59—22no—
38C22⋊C4×C59—22no—
39C42×C59—21no—
40C42×C59C2×C411yescharacteristic
41C42×C59C2×C411yescharacteristic
42C22⋊Dic59—22no—
43C4⋊Dic59—22no—
44C4×Dic59—22no—
45#11745664—24no—
46#11745664—22no—
47#11745664D414yescomplemented
48C2×C59⋊C8—24no—
49C2×C59⋊C8—22no—
50C23×C59—21no—
51C23×C59C22⋊C412yes—
52C23×C59C2×D411yescharacteristic
53Q8×C59—22no—
54Q8×C59—22no—
55D4×C59—24no—
56D4×C59—22no—
57D4×C59—22no—
58D4×C59—44no—
59D4×C59—42no—
60C2×C4×C59—21no—
61C2×C4×C59—22no—
62C2×C4×C59—22no—
63C2×C4×C59—21no—
64C2×C4×C59—21no—
65C2×C4×C59—42no—
66C2×C4×C59—41no—
67C2×C4×C59—41no—
68C2×C4×C59C22⋊C412yes—
69C2×C4×C59C22×C411yescharacteristic
70C2×C4×C59C2×D412yes—
71C2×C4×C59C2×D411yescharacteristic
72C2×C4×C59#4112yes—
73C2×Dic59—42no—
74C59⋊C8—24no—
75C22×C59—22no—
76C22×C59—41no—
77C22×C59—42no—
78C22×C59—42no—
79C22×C59—41no—
80C22×C59C2×C22⋊C411yescharacteristic
81C22×C59#12112yes—
82C4×C59—22no—
83C4×C59—22no—
84C4×C59—41no—
85C4×C59—41no—
86C4×C59C4×D412yes—
87C4×C59#12011yescharacteristic
88C4×C59#12311yescharacteristic
89Dic59—82no—
90#1884—591nomaximal, Sylow
91C2×C59—22no—
92C2×C59—21no—
93C2×C59—42no—
94C2×C59—81no—
95C2×C59#38611yescharacteristic
96#568—591no—
97#532D5911yescharacteristic
98#421—592no—
99#410—591no—
100#339—592no—
101C59#188411yescharacteristic, complemented, Sylow
102C2×#41C2×D5911yescharacteristic
103C2×#41C2×D5911yescharacteristic
104#131—1184no—
105C2×M16—592no—
106C2×M16—1182no—
107C4⋊Q8Dic5911yescharacteristic, complemented
108#127Dic5911yescharacteristic, complemented
109#124Dic5911yescharacteristic, complemented
110#124Dic5911yescharacteristic, complemented
111#121—22no—
112C4×D4—22no—
113#117—592no—
114C2×C42C2×D5911yescharacteristic
115#104—1184no—
116#99—1182no—
117#41—22no—
118#41—22no—
119#41—22no—
120#41—22no—
121C2×Q8C2×Dic5911yescharacteristic
122C2×Q8C2×Dic5911yescharacteristic
123C2×D4—22no—
124C2×D4—21no—
125C2×D4C2×Dic5911yescharacteristic
126C2×D4C2×Dic5911yescharacteristic
127C2×D4C22⋊D5912yes—
128C22×C4—21no—
129C22×C4—21no—
130C22×C4C22⋊D5912yes—
131C22×C4C22×D5911yescharacteristic
132M16—594no—
133M16—1184no—
134M16—1182no—
135C2×C8—1184no—
136C2×C8—1182no—
137C4⋊C4—22no—
138C4⋊C4—1182no—
139C22⋊C4—22no—
140C22⋊C4—22no—
141C22⋊C4—1182no—
142C42—21no—
143C42—1182no—
144C42C2×Dic5911yescharacteristic
145C42C2×Dic5911yescharacteristic
146C23—21no—
147C23C22⋊Dic5912yes—
148C23C2×C22⋊D5911yescharacteristic
149Q8—22no—
150Q8—22no—
151D4—24no—
152D4—22no—
153D4—22no—
154D4—44no—
155D4—42no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—42no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—2362no—
165C2×C4C22⋊Dic5912yes—
166C2×C4D4×D5912yes—
167C2×C4#1174568712yes—
168C2×C4C22×Dic5911yescharacteristic
169C2×C4C2×C22⋊D5911yescharacteristic
170C8—1184no—
171C22—22no—
172C22—41no—
173C22—42no—
174C22—42no—
175C22—41no—
176C22C2×C22⋊Dic5911yescharacteristic
177C22#1427369912yes—
178C4—22no—
179C4—22no—
180C4—41no—
181C4—41no—
182C4—4722no—
183C4D4×Dic5912yes—
184C4#1427369511yescharacteristic
185C4#1427370811yescharacteristic
186C2—21no—
187C2—22no—
188C2—42no—
189C2—81no—
190C2#1683728211yescharacteristic
subgroupG/H
centerC4#14273695
commutatorC2×C4×C59C22×C4
FrattiniC22×C4C22×D59
FittingC59×#532C2
socleC2×C59#386
hypercenter#532D59
hypocenterC59#1884
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C4 ◁ C22×C4 ◁ #532

Complements

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

NH ≅ G/Ntype
1. #16838169C2semidirect
2. #16837419C2semidirect
3. #16837376C2semidirect
4. #16837162C2semidirect
14. C4⋊Q8×C59C4semidirect
15. #127×C59C4semidirect
16. #124×C59C4semidirect
17. #124×C59C4semidirect
47. #11745664D4semidirect
101. C59#1884semidirect
107. C4⋊Q8Dic59semidirect
108. #127Dic59semidirect
109. #124Dic59semidirect
110. #124Dic59semidirect