Finite Group Databasebeta

← #24917841

Subgroups — #24917841

Order 10624.

380 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 129 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#19128254C211yesmaximal, characteristic
2C2×#14581790C211yesmaximal, characteristic
3#19128068C214yesmaximal, complemented
4#19128050C214yesmaximal, complemented
5#19127711C211yesmaximal, characteristic
6#19127710C211yesmaximal, characteristic
7#19127709C211yesmaximal, characteristic
8M16×Dic83C211yesmaximal, characteristic
9#419×C83C211yesmaximal, characteristic
10C22×Dic166C2211yescharacteristic
11C2×#13050574C2211yescharacteristic
12#14581791C2212yes—
13#14581790—22no—
14#14581790C2212yes—
15#14581790C2212yes—
16#14581783C2212yes—
17#14581769—22no—
18C4×Dic166—22no—
19#14581751C2211yescharacteristic
20C2×Dic83⋊C4—22no—
21C2×C4×Dic83C2211yescharacteristic
22#14581717C2214yes—
23#14581716C2214yes—
24#14581715C2214yes—
25#14581702C2212yes—
26C8×Dic83C2212yes—
27C22×Q8×C83C2211yescharacteristic
28C2×M16×C83C2211yescharacteristic
29#117×C83C2211yescharacteristic
30#103×C83C2214yes—
31C2×Dic166—22no—
32C2×Dic166—22no—
33C2×Dic166—21no—
34C2×Dic166—22no—
35C2×Dic166C2312yes—
36C22×Dic83—21no—
37C22×Dic83D412yes—
38#13050574—22no—
39C2×C83⋊C8C2312yes—
40C4⋊Dic83—22no—
41C4⋊Dic83C2312yes—
42Dic83⋊C4—22no—
43Dic83⋊C4—22no—
44Dic83⋊C4—24no—
45Dic83⋊C4—24no—
46C22⋊Dic83—21no—
47C4×Dic83—21no—
48C4×Dic83D412yes—
49C4×Dic83C2311yescharacteristic
50C4×Dic83C2311yescharacteristic
51C2×Q8×C83—21no—
52C2×Q8×C83—22no—
53C2×Q8×C83—22no—
54C2×Q8×C83C2312yes—
55C22×C4×C83—21no—
56C22×C4×C83C2311yescharacteristic
57M16×C83—22no—
58C2×C8×C83C2312yes—
59C4⋊C4×C83C2312yes—
60C22⋊C4×C83—21no—
61C42×C83—21no—
62C23×C83C2×D411yescharacteristic
63Q8×C83—22no—
64Q8×C83—22no—
65Q8×C83—42no—
66C2×C4×C83—22no—
67C2×C4×C83—22no—
68C2×C4×C83—42no—
69C2×C4×C83C2×D411yescharacteristic
70C2×C4×C83#4112yes—
71C2×C4×C83#4112yes—
72C2×C4×C83C2411yescharacteristic
73C2×Dic83—24no—
74C2×Dic83—22no—
75C2×Dic83—22no—
76C2×Dic83—42no—
77C2×Dic83C2×D412yes—
78C2×Dic83C2×D412yes—
79Dic166—22no—
80Dic166—22no—
81Dic166—42no—
82Dic166—44no—
83C8×C83—22no—
84C83⋊C8—22no—
85C22×C83—22no—
86C22×C83#12412yes—
87C22×C83C22×D411yescharacteristic
88C4×C83—42no—
89C4×C83—42no—
90C4×C83#12412yes—
91C4×C83C2×#4111yescharacteristic
92C4×C83C2×#4111yescharacteristic
93Dic83—22no—
94Dic83—42no—
95Dic83—42no—
96Dic83#13714yes—
97C2×C83—22no—
98C2×C83C2×#12411yescharacteristic
99C2×C83C2×#13712yes—
100#3139—831nomaximal, Sylow
101C83#313911yescharacteristic, complemented, Sylow
102#533—831no—
103C2×C4⋊Q8—831no—
104#491—834no—
105#487—834no—
106#419—831no—
107#419—831no—
108#419—831no—
109#419D8311yescharacteristic
110C4×M16—831no—
111C22×Q8—831no—
112C22×Q8C2×D8311yescharacteristic
113C2×M16—831no—
114C2×M16C2×D8311yescharacteristic
115C4⋊Q8—832no—
116C4⋊Q8—832no—
117C4⋊Q8—832no—
118C4⋊Q8—1662no—
119#125—832no—
120C22⋊Q8—1662no—
121C4×Q8—1662no—
122#117—831no—
123#117C2×D8311yescharacteristic
124C2×C4⋊C4—1662no—
125C2×C42—831no—
126#103—834no—
127#103—834no—
128#103—834no—
129#103C2×D8314yes—
130#97—832no—
131C4×C8—832no—
132C2×Q8—21no—
133C2×Q8—22no—
134C2×Q8—22no—
135C2×Q8—832no—
136C2×Q8—1662no—
137C2×Q8—1662no—
138C2×Q8—1662no—
139C2×Q8—1661no—
140C2×Q8C22×D8312yes—
141C22×C4—21no—
142C22×C4—832no—
143C22×C4—1661no—
144C22×C4C22×D8311yescharacteristic
145M16—22no—
146M16—1662no—
147C2×C8—832no—
148C2×C8C22×D8312yes—
149C4⋊C4—832no—
150C4⋊C4—1664no—
151C4⋊C4—1664no—
152C4⋊C4—1662no—
153C4⋊C4—1662no—
154C4⋊C4—1662no—
155C4⋊C4C22×D8312yes—
156C22⋊C4—21no—
157C22⋊C4—1661no—
158C42—21no—
159C42—832no—
160C42—831no—
161C42—831no—
162C42—1661no—
163C23D4×D8311yescharacteristic
164Q8—22no—
165Q8—22no—
166Q8—42no—
167Q8—3324no—
168Q8—3322no—
169Q8—1662no—
170Q8—1662no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—42no—
174C2×C4—3322no—
175C2×C4—832no—
176C2×C4—832no—
177C2×C4—1662no—
178C2×C4—1662no—
179C2×C4—1664no—
180C2×C4D4×D8311yescharacteristic
181C2×C4#1305058912yes—
182C2×C4#1305059012yes—
183C2×C4C23×D8311yescharacteristic
184C8—22no—
185C8—1662no—
186C22—22no—
187C22#1458177812yes—
188C22C2×D4×D8311yescharacteristic
189C4—42no—
190C4—42no—
191C4—3322no—
192C4—3322no—
193C4—834no—
194C4—1662no—
195C4#1458177812yes—
196C4C2×#1305058911yescharacteristic
197C4C2×#1305059011yescharacteristic
198C2—22no—
199C2C2×#1458177811yescharacteristic
200C2#137×D8312yes—
subgroupG/H
centerC22C2×D4×D83
commutator, cosocleC2×C4×C83C24
FrattiniC2×C4C23×D83
Fitting#419×C83C2
socleC22×C83C22×D4
prime radicalC23×C83C2×D4
hypercenter#419D83
hypocenterC83#3139
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
3. #19128068C2semidirect
4. #19128050C2semidirect
101. C83#3139semidirect

Maximal subgroups

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

subgroupindex
#191282542
C2×#145817902
#191280682
#191280502
#191277112
#191277102
#191277092
M16×Dic832
#419×C832
#313983