Finite Group Databasebeta

← #24907388

Subgroups — #24907388

Order 10624.

584 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 101 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
1C22×#13050589C211yesmaximal, characteristic
2C2×#14581710C212yesmaximal, complemented
3C2×#14581709C211yesmaximal, characteristic, complemented
4#19127664C212yesmaximal, complemented
5C2×#100×C83C211yesmaximal, characteristic, complemented
6C2×#13050589—24no—
7C2×#13050589—24no—
8C2×#13050589—22no—
9C2×#13050589—22no—
10C22×Dic166C2211yescharacteristic
11C22×C22⋊D83C412yes—
12C23×Dic83C412yes—
13C22×C4×D83C2211yescharacteristic
14C2×#13050574C2212yes—
15#14581710—24no—
16#14581709—22no—
17(C2×D83)⋊C8—24no—
18C22×D4×C83C2211yescharacteristic
19C2×M16×C83C2212yes—
20#100×C83—22no—
21C23×D83C2×C411yescharacteristic
22#13050589—216no—
23#13050589—216no—
24C2×Dic166—22no—
25C2×Dic166—21no—
26C2×Dic166—21no—
27C2×Dic166D414yes—
28C2×C22⋊D83—24no—
29C2×C22⋊D83—24no—
30C2×C22⋊D83—24no—
31C22×Dic83—24no—
32C22×Dic83—24no—
33C22×Dic83—24no—
34C22×Dic83C2×C411yescharacteristic
35C22×Dic83C2×C412yes—
36C2×C4×D83—22no—
37C2×C4×D83—21no—
38C2×C4×D83—21no—
39C2×C4×D83D414yes—
40#13050574—22no—
41#13050574—22no—
42C2×C83⋊C8—22no—
43C24×C83C2×C412yes—
44C2×D4×C83—22no—
45C2×D4×C83—22no—
46C2×D4×C83D412yes—
47C2×D4×C83D412yes—
48C22×C4×C83C2311yescharacteristic
49M16×C83—22no—
50M16×C83—22no—
51C2×C8×C83—22no—
52C23×C83—22no—
53C23×C83—22no—
54C23×C83—44no—
55C23×C83C22⋊C414yes—
56C23×C83C22×C411yescharacteristic
57C22×D83—21no—
58C22×D83—21no—
59C22×D83—42no—
60C22×D83C22⋊C412yes—
61D4×C83—24no—
62D4×C83—24no—
63C2×C4×C83C2×D412yes—
64C2×C4×C83C2×D412yes—
65C2×C4×C83C2×D411yescharacteristic
66C2×C4×C83C2×D411yescharacteristic
67C22⋊D83—216no—
68C2×Dic83—216no—
69C2×Dic83—21no—
70C2×Dic83—21no—
71C2×Dic83—22no—
72C2×Dic83—22no—
73C2×Dic83C22⋊C412yes—
74C2×Dic83C22⋊C414yes—
75C4×D83—24no—
76C4×D83—24no—
77Dic166—24no—
78Dic166—24no—
79C8×C83—42no—
80C83⋊C8—42no—
81C22×C83—22no—
82C22×C83—24no—
83C22×C83—44no—
84C22×C83—44no—
85C22×C83—44no—
86C22×C83C2×C22⋊C411yescharacteristic
87C22×C83C2×C22⋊C411yescharacteristic
88C22×C83C2×C22⋊C411yescharacteristic
89C2×D83—22no—
90C2×D83—24no—
91C2×D83—42no—
92C2×D83—42no—
93C4×C83#12012yes—
94C4×C83#12012yes—
95Dic83—24no—
96Dic83—22no—
97C2×C83—21no—
98C2×C83—21no—
99C2×C83—44no—
100C2×C83#37911yescharacteristic
101C2×C83#41312yes—
102D83—42no—
103#1785—831nomaximal, Sylow
104C83#178511yescharacteristic, complemented, Sylow
105C22×#41—831no—
106C2×#101—832no—
107C2×#100—831no—
108C2×#100D8311yescharacteristic, complemented
109#407—832no—
110C2×#41—1664no—
111C2×#41—1664no—
112C2×#41—1662no—
113C2×#41—1662no—
114C22×Q8—831no—
115C22×D4—832no—
116C22×D4C2×D8311yescharacteristic
117C23×C4—831no—
118C23×C4—832no—
119C2×M16—832no—
120C2×M16C2×D8312yes—
121#101—1664no—
122#100—22no—
123#100—1662no—
124C22⋊C8—1664no—
125C24—831no—
126C24C4×D8312yes—
127#41—16616no—
128#41—16616no—
129C2×Q8—834no—
130C2×Q8—1662no—
131C2×Q8—1661no—
132C2×Q8—1661no—
133C2×D4—22no—
134C2×D4—22no—
135C2×D4—1664no—
136C2×D4—1664no—
137C2×D4—1664no—
138C2×D4D33212yes—
139C2×D4C22⋊D8312yes—
140C22×C4—831no—
141C22×C4—832no—
142C22×C4—834no—
143C22×C4—1664no—
144C22×C4—1664no—
145C22×C4—1664no—
146C22×C4—1662no—
147C22×C4—1661no—
148C22×C4—1661no—
149C22×C4C22×D8311yescharacteristic
150M16—22no—
151M16—22no—
152M16—1662no—
153M16—1662no—
154C2×C8—22no—
155C2×C8—1662no—
156C23—22no—
157C23—22no—
158C23—44no—
159C23—3322no—
160C23—832no—
161C23—1661no—
162C23—1661no—
163C23(C2×D83)⋊C414yes—
164C23C2×C4×D8311yescharacteristic
165Q8—1664no—
166Q8—1664no—
167D4—24no—
168D4—24no—
169D4—16616no—
170C2×C4—834no—
171C2×C4—832no—
172C2×C4—16616no—
173C2×C4—1661no—
174C2×C4—1662no—
175C2×C4—1661no—
176C2×C4—1662no—
177C2×C4—1664no—
178C2×C4—1664no—
179C2×C4D4×D8312yes—
180C2×C4D4×D8312yes—
181C2×C4C2×C22⋊D8311yescharacteristic
182C2×C4C2×D33211yescharacteristic
183C8—42no—
184C8—3322no—
185C22—22no—
186C22—24no—
187C22—44no—
188C22—44no—
189C22—44no—
190C22—3322no—
191C22—3322no—
192C22—1662no—
193C22—1664no—
194C22C22⋊C4×D8311yescharacteristic
195C22C22⋊C4×D8311yescharacteristic
196C22C2×(C2×D83)⋊C411yescharacteristic
197C4—1662no—
198C4—1664no—
199C4#1458176012yes—
200C4#1458176212yes—
201C2—21no—
202C2—21no—
203C2—44no—
204C2—3322no—
205C2#1912755611yescharacteristic
206C2#1912768212yes—
subgroupG/H
centerC22C22⋊C4×D83
commutatorC23×C83C22×C4
FrattiniC22×C4C22×D83
FittingC2×#100×C83C2
socleC22×C83C2×C22⋊C4
prime radicalC22×#13050589C2
cosocleC22×C4×C83C23
hypercenterC2×#100D83
hypocenterC83#1785
LCSG ▷ C23×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
2. C2×#14581710C2semidirect
3. C2×#14581709C2semidirect
4. #19127664C2semidirect
5. C2×#100×C83C2semidirect
104. C83#1785semidirect
108. C2×#100D83semidirect

Maximal subgroups

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

subgroupindex
C22×#130505892
C2×#145817102
C2×#145817092
#191276642
C2×#100×C832
#178583