Finite Group Databasebeta

← #24917749

Subgroups — #24917749

Order 10624.

382 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 121 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#19128178C211yesmaximal, characteristic, complemented
2#19128022C212yesmaximal, complemented
3#19128005C212yesmaximal, complemented
4#19127898C212yesmaximal, complemented
5#19127839C212yesmaximal, complemented
6#19127801C212yesmaximal, complemented
7C4×#13050578C212yesmaximal, complemented
8#19127762C211yesmaximal, characteristic, complemented
9#540×C83C211yesmaximal, characteristic
10C22×Dic166C2211yescharacteristic
11C2×#13050578C2212yes—
12C2×#13050578C2212yes—
13C4×Dic166C2212yes—
14C4×Dic166C2212yes—
15#14581757—22no—
16#14581751C2211yescharacteristic
17#14581748—22no—
18#14581725C2212yes—
19#14581723C2212yes—
20C4⋊(C83⋊C8)C2212yes—
21#14581715C2212yes—
22#14581715C2212yes—
23#14581713C2212yes—
24#14581713C2212yes—
25C22⋊(C83⋊C8)C2212yes—
26#14581703C2211yescharacteristic
27C4×C83⋊C8C2211yescharacteristic
28#127×C83C2211yescharacteristic
29#125×C83C2211yescharacteristic
30#123×C83—22no—
31#121×C83—22no—
32#121×C83C2212yes—
33C4×D4×C83C2212yes—
34#117×C83C2211yescharacteristic
35C2×Dic166—21no—
36C2×Dic166—24no—
37C2×Dic166C2312yes—
38C22×Dic83—21no—
39#13050578—24no—
40#13050578—24no—
41C2×C83⋊C8C2312yes—
42C2×C83⋊C8C2312yes—
43C4⋊Dic83C2312yes—
44Dic83⋊C4—22no—
45Dic83⋊C4—22no—
46C22⋊Dic83—21no—
47C4×Dic83—22no—
48C4×Dic83—22no—
49C4×Dic83—21no—
50C2×D4×C83—22no—
51C2×D4×C83—22no—
52C2×D4×C83C2312yes—
53C22×C4×C83—22no—
54C22×C4×C83C2311yescharacteristic
55C4⋊C4×C83—22no—
56C4⋊C4×C83D412yes—
57C4⋊C4×C83C2312yes—
58C22⋊C4×C83—22no—
59C22⋊C4×C83—22no—
60C22⋊C4×C83D412yes—
61C42×C83C2311yescharacteristic
62C42×C83C2311yescharacteristic
63C23×C83—22no—
64C23×C83C2×D411yescharacteristic
65D4×C83—22no—
66D4×C83—22no—
67D4×C83—82no—
68D4×C83—82no—
69C2×C4×C83—22no—
70C2×C4×C83—22no—
71C2×C4×C83—82no—
72C2×C4×C83C2×D412yes—
73C2×C4×C83C2×D412yes—
74C2×C4×C83C2×D411yescharacteristic
75C2×C4×C83C2411yescharacteristic
76C2×Dic83—24no—
77C2×Dic83—22no—
78C2×Dic83—22no—
79Dic166—24no—
80Dic166—22no—
81Dic166#4114yes—
82C83⋊C8—22no—
83C83⋊C8—22no—
84C22×C83—21no—
85C22×C83—22no—
86C22×C83—42no—
87C22×C83—42no—
88C22×C83—42no—
89C22×C83C22×D411yescharacteristic
90C4×C83—21no—
91C4×C83—22no—
92C4×C83—22no—
93C4×C83—42no—
94C4×C83C2×#4112yes—
95Dic83—24no—
96Dic83—42no—
97C2×C83—41no—
98C2×C83—82no—
99C2×C83#52511yescharacteristic
100C2×C83#57712yes—
101#3126—831nomaximal, Sylow
102C83#312611yescharacteristic, complemented, Sylow
103#540D8311yescharacteristic
104#519—831no—
105#482—832no—
106#479—832no—
107#460—832no—
108#448—832no—
109#440—832no—
110C4×SD16—832no—
111#433—831no—
112C22×Q8—831no—
113C2×SD16—832no—
114C2×SD16—832no—
115#127C2×D8311yescharacteristic
116#125C2×D8311yescharacteristic
117#123—22no—
118#121—22no—
119#121C2×D8312yes—
120C4×Q8—832no—
121C4×Q8—832no—
122C4×Q8—1662no—
123C4×D4C2×D8312yes—
124#117—831no—
125#117—1662no—
126#117C2×D8311yescharacteristic
127#107—832no—
128#106—832no—
129C4⋊C8—832no—
130#103—832no—
131#103—832no—
132#102—832no—
133#102—832no—
134C22⋊C8—832no—
135#97—831no—
136C4×C8—831no—
137C2×Q8—832no—
138C2×Q8—1664no—
139C2×Q8—1661no—
140C2×D4—22no—
141C2×D4—22no—
142C2×D4C22×D8312yes—
143C22×C4—22no—
144C22×C4—1661no—
145C22×C4C22×D8311yescharacteristic
146SD16—1664no—
147SD16—1664no—
148C2×C8—832no—
149C2×C8—832no—
150C4⋊C4—22no—
151C4⋊C4—832no—
152C4⋊C4—1662no—
153C4⋊C4—1662no—
154C4⋊C4C22⋊D8312yes—
155C4⋊C4C22×D8312yes—
156C22⋊C4—22no—
157C22⋊C4—22no—
158C22⋊C4—1661no—
159C22⋊C4C22⋊D8312yes—
160C42—1661no—
161C42—1662no—
162C42—1662no—
163C42C22×D8311yescharacteristic
164C42C22×D8311yescharacteristic
165C23—22no—
166C23C2×C22⋊D8311yescharacteristic
167Q8—834no—
168Q8—1664no—
169Q8—1662no—
170D4—22no—
171D4—22no—
172D4—82no—
173D4—82no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—82no—
177C2×C4—1662no—
178C2×C4—1664no—
179C2×C4—1662no—
180C2×C4C2×C22⋊D8312yes—
181C2×C4C2×C22⋊D8312yes—
182C2×C4C2×C22⋊D8311yescharacteristic
183C2×C4C23×D8311yescharacteristic
184C8—1662no—
185C8—1662no—
186C22—21no—
187C22—22no—
188C22—42no—
189C22—42no—
190C22—42no—
191C22C22×C22⋊D8311yescharacteristic
192C4—21no—
193C4—22no—
194C4—22no—
195C4—42no—
196C4—3322no—
197C4—1664no—
198C4#41×D8312yes—
199C2—41no—
200C2—82no—
201C2#1912820811yescharacteristic
202C2#1912851212yes—
subgroupG/H
centerC22C22×C22⋊D83
commutator, cosocleC2×C4×C83C24
FrattiniC2×C4C23×D83
Fitting, prime radical#540×C83C2
socleC22×C83C22×D4
hypercenter#540D83
hypocenterC83#3126
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #19128178C2semidirect
2. #19128022C2semidirect
3. #19128005C2semidirect
4. #19127898C2semidirect
5. #19127839C2semidirect
6. #19127801C2semidirect
7. C4×#13050578C2semidirect
8. #19127762C2semidirect
102. C83#3126semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#191281782
#191280222
#191280052
#191278982
#191278392
#191278012
C4×#130505782
#191277622
#540×C832
#312683