Finite Group Databasebeta

← #24917593

Subgroups — #24917593

Order 10624.

380 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 133 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#19128258C211yesmaximal, characteristic
2#19128031C212yesmaximal
3#19127986C212yesmaximal, complemented
4#19127911C212yesmaximal, complemented
5#19127857C212yesmaximal
6#19127806C214yesmaximal, complemented
7#19127758C211yesmaximal, characteristic
8C2×C4×Q8×C83C211yesmaximal, characteristic
9C2×#13050580C2214yes—
10#14581792C2211yescharacteristic
11#14581792C2211yescharacteristic
12#14581784—21no—
13#14581771—21no—
14#14581771C2212yes—
15C4×Dic166—21no—
16C4×Dic166C2212yes—
17#14581751—21no—
18#14581723C2214yes—
19C4⋊(C83⋊C8)C2212yes—
20#14581716C2214yes—
21#14581715C2214yes—
22C22⋊(C83⋊C8)C2212yes—
23#14581703C2212yes—
24C22×Q8×C83C2211yescharacteristic
25C4×Q8×C83—21no—
26C4×Q8×C83—21no—
27C4×Q8×C83C2212yes—
28C4×Q8×C83C2212yes—
29C2×C4⋊C4×C83—21no—
30C2×C4⋊C4×C83C2211yescharacteristic
31C2×C42×C83—21no—
32C2×C42×C83C2211yescharacteristic
33C2×Dic166—21no—
34C2×Dic166C2312yes—
35#13050580—28no—
36C2×C83⋊C8C2314yes—
37C4⋊Dic83—21no—
38C4⋊Dic83—21no—
39C4⋊Dic83—21no—
40C4⋊Dic83C2312yes—
41Dic83⋊C4—22no—
42Dic83⋊C4—22no—
43C22⋊Dic83—22no—
44C4×Dic83—22no—
45C2×Q8×C83—24no—
46C2×Q8×C83—21no—
47C2×Q8×C83C2312yes—
48C22×C4×C83—21no—
49C22×C4×C83—21no—
50C22×C4×C83D411yescharacteristic
51C22×C4×C83D411yescharacteristic
52C22×C4×C83C2311yescharacteristic
53C4⋊C4×C83—22no—
54C4⋊C4×C83—22no—
55C4⋊C4×C83—21no—
56C4⋊C4×C83C2312yes—
57C42×C83—22no—
58C42×C83—22no—
59C42×C83D411yescharacteristic
60C42×C83D411yescharacteristic
61C42×C83C2311yescharacteristic
62C42×C83C2311yescharacteristic
63C23×C83C2×D411yescharacteristic
64Q8×C83—24no—
65Q8×C83—22no—
66Q8×C83#4114yes—
67C2×C4×C83—24no—
68C2×C4×C83—22no—
69C2×C4×C83—22no—
70C2×C4×C83—22no—
71C2×C4×C83—22no—
72C2×C4×C83—22no—
73C2×C4×C83—42no—
74C2×C4×C83C2×D411yescharacteristic
75C2×C4×C83C2×D411yescharacteristic
76C2×C4×C83C2×D411yescharacteristic
77C2×C4×C83C2×D411yescharacteristic
78C2×C4×C83C2×D411yescharacteristic
79C2×C4×C83C2411yescharacteristic
80C2×Dic83—22no—
81C2×Dic83—22no—
82Dic166—24no—
83Dic166—42no—
84C83⋊C8—24no—
85C22×C83—21no—
86C22×C83—21no—
87C22×C83#13712yes—
88C22×C83C22×D411yescharacteristic
89C4×C83—24no—
90C4×C83—21no—
91C4×C83—21no—
92C4×C83—21no—
93C4×C83—21no—
94C4×C83—42no—
95C4×C83#13712yes—
96C4×C83C2×#4112yes—
97Dic83—42no—
98Dic83—42no—
99C2×C83—22no—
100C2×C83#52511yescharacteristic
101C2×C83C2×#13711yescharacteristic
102C2×C83C2×#13711yescharacteristic
103#3113—831nomaximal, Sylow
104C83#311311yescharacteristic, complemented, Sylow
105#533—831no—
106C2×C4×Q8D8311yescharacteristic
107#483—832no—
108#475—832no—
109#462—832no—
110#451—832no—
111#441—834no—
112#432—831no—
113C22×Q8C2×D8311yescharacteristic
114C2×Q16—834no—
115C4⋊Q8—831no—
116C4⋊Q8—831no—
117#125—1661no—
118C22⋊Q8—832no—
119C22⋊Q8—1661no—
120C4×Q8—21no—
121C4×Q8—21no—
122C4×Q8—832no—
123C4×Q8—1661no—
124C4×Q8C2×D8312yes—
125C4×Q8C2×D8312yes—
126#117—1661no—
127C2×C4⋊C4—21no—
128C2×C4⋊C4C2×D8311yescharacteristic
129C2×C42—21no—
130C2×C42C2×D8311yescharacteristic
131#106—834no—
132C4⋊C8—832no—
133#103—834no—
134#103—834no—
135C22⋊C8—832no—
136#97—832no—
137C2×Q8—24no—
138C2×Q8—21no—
139C2×Q8—832no—
140C2×Q8—1661no—
141C2×Q8C22×D8312yes—
142C22×C4—21no—
143C22×C4—21no—
144C22×C4C22⋊D8311yescharacteristic
145C22×C4C22⋊D8311yescharacteristic
146C22×C4C22×D8311yescharacteristic
147Q16—1668no—
148C2×C8—834no—
149C4⋊C4—22no—
150C4⋊C4—22no—
151C4⋊C4—21no—
152C4⋊C4—832no—
153C4⋊C4—1661no—
154C4⋊C4—1661no—
155C4⋊C4—1662no—
156C4⋊C4—1662no—
157C4⋊C4—1661no—
158C4⋊C4C22×D8312yes—
159C22⋊C4—1662no—
160C42—22no—
161C42—22no—
162C42—1662no—
163C42C22⋊D8311yescharacteristic
164C42C22⋊D8311yescharacteristic
165C42C22×D8311yescharacteristic
166C42C22×D8311yescharacteristic
167C23C2×C22⋊D8311yescharacteristic
168Q8—24no—
169Q8—22no—
170Q8—3322no—
171Q8—1664no—
172Q8#1305059014yes—
173C2×C4—24no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—42no—
180C2×C4—1662no—
181C2×C4—1662no—
182C2×C4C2×C22⋊D8311yescharacteristic
183C2×C4C2×C22⋊D8311yescharacteristic
184C2×C4C2×C22⋊D8311yescharacteristic
185C2×C4C2×C22⋊D8311yescharacteristic
186C2×C4C2×C22⋊D8311yescharacteristic
187C2×C4C23×D8311yescharacteristic
188C8—1664no—
189C22—21no—
190C22—21no—
191C22#1458182212yes—
192C22C22×C22⋊D8311yescharacteristic
193C4—24no—
194C4—21no—
195C4—21no—
196C4—21no—
197C4—21no—
198C4—42no—
199C4—3322no—
200C4—3322no—
201C4#1458182312yes—
202C4C2×#1305059012yes—
203C2—22no—
204C2#1912821211yescharacteristic
205C2C2×#1458182211yescharacteristic
206C2C2×#1458182311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D83
commutator, cosocleC2×C4×C83C24
FrattiniC2×C4C23×D83
FittingC2×C4×Q8×C83C2
socleC22×C83C22×D4
prime radicalC23×C83C2×D4
hypercenterC2×C4×Q8D83
hypocenterC83#3113
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
3. #19127986C2semidirect
4. #19127911C2semidirect
6. #19127806C2semidirect
104. C83#3113semidirect

Maximal subgroups

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

subgroupindex
#191282582
#191280312
#191279862
#191279112
#191278572
#191278062
#191277582
C2×C4×Q8×C832
#311383