Finite Group Databasebeta

← #29599102

Subgroups — #29599102

Order 15616.

370 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 99 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#21456343C211yesmaximal, characteristic
2#21447539C212yesmaximal
3#21443926C212yesmaximal
4#21443903C211yesmaximal, characteristic
5C61×#1971C211yesmaximal, characteristic
6#16840319—21no—
7C2×#14519717C2212yes—
8#16840171—24no—
9#16839800—21no—
10#16839800C2212yes—
11#16839566—24no—
12C22×Q16×C61C2211yescharacteristic
13C2×#106×C61C2211yescharacteristic
14C2×#103×C61—21no—
15C2×#97×C61C2211yescharacteristic
16C61×#391—21no—
17#14519777—22no—
18#14519769—22no—
19#14519756—42no—
20C4×Dic122—42no—
21#14519736—22no—
22#14519717—22no—
23#14519717—22no—
24C2×#11758185—22no—
25#14519711—22no—
26#14519711D414yes—
27#14519709—22no—
28#14519709—22no—
29C22×Q8×C61—21no—
30C2×Q16×C61—22no—
31C2×Q16×C61—22no—
32C2×Q16×C61—21no—
33C2×Q16×C61Q812yescomplemented
34C22×C8×C61D411yescharacteristic
35C22×C8×C61C2311yescharacteristic
36C2×C4⋊C4×C61—21no—
37C2×C42×C61D411yescharacteristic
38#106×C61—22no—
39#103×C61—42no—
40#97×C61—22no—
41#95×C61—42no—
42C2×Q8×C61—22no—
43C2×Q8×C61—41no—
44C2×Q8×C61—41no—
45C2×Q8×C61—41no—
46C2×Q8×C61—41no—
47C2×Q8×C61—41no—
48C22×C4×C61—41no—
49C22×C4×C61—41no—
50C22×C4×C61D812yes—
51C22×C4×C61C2×D411yescharacteristic
52C2×Dic122—42no—
53Q16×C61—24no—
54Q16×C61—42no—
55C2×C8×C61—21no—
56C2×C8×C61—21no—
57C2×C8×C61SD1612yes—
58C2×C8×C61C2×D412yes—
59C2×C8×C61C2×Q811yescharacteristic
60C2×C8×C61#4112yes—
61C2×C8×C61#4111yescharacteristic
62C4⋊C4×C61—41no—
63C4⋊C4×C61—41no—
64C42×C61—21no—
65C42×C61—21no—
66C22⋊Dic61—42no—
67C4⋊Dic61—24no—
68C4⋊Dic61—42no—
69#11758196—44no—
70C4×Dic61—42no—
71#11758185—42no—
72C23×C61C2×D811yescharacteristic
73Q8×C61—42no—
74Q8×C61—42no—
75Q8×C61—81no—
76Q8×C61—81no—
77C2×C4×C61—22no—
78C2×C4×C61—42no—
79C2×C4×C61—42no—
80C2×C4×C61—81no—
81C2×C4×C61—81no—
82C2×C4×C61—82no—
83C2×C4×C61—81no—
84C2×C4×C61#12011yescharacteristic
85C2×C4×C61C22⋊Q811yescharacteristic
86C2×C4×C61#12411yescharacteristic
87C2×C4×C61C2×SD1611yescharacteristic
88C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
89C2×C4×C61#13711yescharacteristic
90C2×Dic61—44no—
91Dic122—84no—
92C8×C61—22no—
93C8×C61C22⋊Q812yes—
94C8×C61#12412yes—
95#13368—611nomaximal, Sylow
96C22×C61—22no—
97C22×C61#44711yescharacteristic
98C22×C61#47411yescharacteristic
99C22×C61#48611yescharacteristic
100C4×C61—42no—
101C4×C61—82no—
102C4×C61—161no—
103C4×C61#39311yescharacteristic
104C4×C61#44811yescharacteristic
105C4×C61#47611yescharacteristic
106C4×C61#48911yescharacteristic
107Dic61—84no—
108#3162—611no—
109#2141—612no—
110#1971D6111yescharacteristic
111#1386—612no—
112#1377—611no—
113C2×C61—21no—
114C2×C61—21no—
115C2×C61#202311yescharacteristic
116C2×C61#219112yes—
117C22×Q16C2×D6111yescharacteristic
118#533—1221no—
119C2×M32—612no—
120#501—1224no—
121#427—612no—
122#427—1221no—
123C2×#106C2×D6111yescharacteristic
124C2×#103—21no—
125C2×#97C2×D6111yescharacteristic
126#391—21no—
127#358—1224no—
128C61#1336811yescharacteristic, complemented, Sylow
129C22×Q8—21no—
130C2×Q16—21no—
131C2×Q16—22no—
132C2×Q16—22no—
133C2×Q16Dic12212yescomplemented
134C22×C8C22⋊D6111yescharacteristic
135C22×C8C22×D6111yescharacteristic
136C4⋊Q8—1222no—
137#125—1222no—
138C22⋊Q8—2442no—
139C4×Q8—2442no—
140#117—1222no—
141C2×C4⋊C4—21no—
142C2×C42C22⋊D6111yescharacteristic
143M32—1222no—
144M32—1222no—
145C2×C16—1222no—
146#107—614no—
147#107—1222no—
148#106—22no—
149#106—1222no—
150#106—1222no—
151#103—42no—
152#97—22no—
153#95—42no—
154C2×Q8—22no—
155C2×Q8—41no—
156C2×Q8—41no—
157C2×Q8—41no—
158C2×Q8—41no—
159C2×Q8—41no—
160C2×Q8—2442no—
161C22×C4—41no—
162C22×C4—41no—
163C22×C4#1175819912yes—
164C22×C4C2×C22⋊D6111yescharacteristic
165Q16—24no—
166Q16—42no—
167C2×C8—21no—
168C2×C8—21no—
169C2×C8#1175820012yes—
170C2×C8C2×Dic12211yescharacteristic
171C2×C8#1175822211yescharacteristic
172C2×C8D4×D6112yes—
173C2×C8#1175822412yes—
174C4⋊C4—41no—
175C4⋊C4—41no—
176C4⋊C4—1224no—
177C4⋊C4—2444no—
178C4⋊C4—2442no—
179C22⋊C4—2442no—
180C42—21no—
181C42—21no—
182C42—2442no—
183C16—2442no—
184C23C2×#1175819911yescharacteristic
185Q8—42no—
186Q8—42no—
187Q8—81no—
188Q8—81no—
189Q8—4884no—
190C2×C4—22no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—81no—
194C2×C4—81no—
195C2×C4—82no—
196C2×C4—81no—
197C2×C4—2444no—
198C2×C4#1451974511yescharacteristic
199C2×C4#1451975611yescharacteristic
200C2×C4#1451976411yescharacteristic
201C2×C4C2×#1175820011yescharacteristic
202C2×C4#1451980211yescharacteristic
203C2×C4#1451980711yescharacteristic
204C8—22no—
205C8#1451975412yes—
206C8#1451976312yes—
207C22—22no—
208C22#1683989511yescharacteristic
209C22#1684004211yescharacteristic
210C22#1684010811yescharacteristic
211C4—42no—
212C4—82no—
213C4—161no—
214C4—4884no—
215C4#1683967411yescharacteristic
216C4#1683990011yescharacteristic
217C4#1684005211yescharacteristic
218C4#1684012111yescharacteristic
219C2—21no—
220C2—21no—
221C2#2144695511yescharacteristic
222C2#2144776912yes—
subgroupG/H
centerC22#16839895
commutator, cosocleC22×C8×C61C23
FrattiniC22×C8C22×D61
FittingC61×#1971C2
socleC22×C61#447
prime radicalC23×C61C2×D8
hypercenter#1971D61
hypocenterC61#13368
LCSG ▷ C22×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#97 ◁ #1971

Complements

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

NH ≅ G/Ntype
33. C2×Q16×C61Q8semidirect
128. C61#13368semidirect
133. C2×Q16Dic122semidirect

Maximal subgroups

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

subgroupindex
#214563432
#214475392
#214439262
#214439032
C61×#19712
#1336861