Finite Group Databasebeta

← #29599099

Subgroups — #29599099

Order 15616.

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

normal subgroups only

This group has 370 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
1#21447538C212yesmaximal
2#21446690C211yesmaximal, characteristic
3#21443924C212yesmaximal
4#21443903C211yesmaximal, characteristic
5C61×#3162C211yesmaximal, characteristic
6C22×Dic244C2211yescharacteristic
7C2×#14519717C2212yes—
8C2×#14519709C2211yescharacteristic
9C2×#14519702—21no—
10#16839668—21no—
11#16839565—24no—
12C61×#533—21no—
13C61×#501—24no—
14C61×#427—21no—
15C61×#427C2212yes—
16C2×#97×C61C2211yescharacteristic
17C22×Dic122—21no—
18C2×Dic244—22no—
19C2×Dic244—22no—
20C2×Dic244—21no—
21C2×Dic244Q812yescomplemented
22C2×C4⋊Dic61—21no—
23#14519717—22no—
24#14519717—22no—
25C2×#11758185—22no—
26#14519709—22no—
27#14519702—42no—
28#14519684—42no—
29C22×C8×C61D411yescharacteristic
30C22×C8×C61C2311yescharacteristic
31C4⋊Q8×C61—22no—
32#125×C61—22no—
33C22⋊Q8×C61—42no—
34C4×Q8×C61—42no—
35#117×C61—22no—
36C2×C42×C61D411yescharacteristic
37#107×C61—22no—
38#107×C61D414yes—
39#106×C61—22no—
40#106×C61—22no—
41#97×C61—22no—
42C2×Q8×C61—42no—
43C22×C4×C61D812yes—
44C22×C4×C61C2×D411yescharacteristic
45C22×Dic61—41no—
46C22×Dic61—41no—
47C2×Dic122—22no—
48C2×Dic122—41no—
49C2×Dic122—41no—
50C2×Dic122—41no—
51C2×Dic122—41no—
52C2×Dic122—41no—
53C2×C8×C61—21no—
54C2×C8×C61—21no—
55C2×C8×C61SD1612yes—
56C2×C8×C61C2×D412yes—
57C2×C8×C61C2×Q811yescharacteristic
58C2×C8×C61#4112yes—
59C2×C8×C61#4111yescharacteristic
60C4⋊C4×C61—24no—
61C4⋊C4×C61—44no—
62C4⋊C4×C61—42no—
63C22⋊C4×C61—42no—
64C42×C61—21no—
65C42×C61—21no—
66C42×C61—42no—
67C4⋊Dic61—41no—
68C4⋊Dic61—41no—
69Dic244—24no—
70Dic244—42no—
71#11758185—42no—
72C23×C61C2×D811yescharacteristic
73Q8×C61—84no—
74C2×C4×C61—22no—
75C2×C4×C61—42no—
76C2×C4×C61—44no—
77C2×C4×C61#12011yescharacteristic
78C2×C4×C61C22⋊Q811yescharacteristic
79C2×C4×C61#12411yescharacteristic
80C2×C4×C61C2×SD1611yescharacteristic
81C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
82C2×C4×C61#13711yescharacteristic
83C2×Dic61—42no—
84C2×Dic61—81no—
85C2×Dic61—81no—
86C2×Dic61—82no—
87C2×Dic61—81no—
88Dic122—42no—
89Dic122—42no—
90Dic122—81no—
91Dic122—81no—
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—84no—
102C4×C61#39311yescharacteristic
103C4×C61#44811yescharacteristic
104C4×C61#47611yescharacteristic
105C4×C61#48911yescharacteristic
106Dic61—82no—
107Dic61—161no—
108#3162D6111yescharacteristic
109#2141—612no—
110#1971—611no—
111#1386—612no—
112#1377—611no—
113C2×C61—21no—
114C2×C61—21no—
115C2×C61#202311yescharacteristic
116C2×C61#219112yes—
117C22×Q16—611no—
118#533—21no—
119C2×M32—612no—
120#501—24no—
121#427—21no—
122#427C2×D6112yes—
123C2×#106—611no—
124C2×#103—1221no—
125C2×#97C2×D6111yescharacteristic
126#391—1221no—
127#358—1224no—
128C61#1336811yescharacteristic, complemented, Sylow
129C22×Q8—1221no—
130C2×Q16—612no—
131C2×Q16—1222no—
132C2×Q16—1221no—
133C2×Q16—1222no—
134C22×C8C22⋊D6111yescharacteristic
135C22×C8C22×D6111yescharacteristic
136C4⋊Q8—22no—
137#125—22no—
138C22⋊Q8—42no—
139C4×Q8—42no—
140#117—22no—
141C2×C4⋊C4—1221no—
142C2×C42C22⋊D6111yescharacteristic
143M32—1222no—
144M32—1222no—
145C2×C16—1222no—
146#107—22no—
147#107C22⋊D6114yes—
148#106—22no—
149#106—22no—
150#106—1222no—
151#103—2442no—
152#97—22no—
153#95—2442no—
154C2×Q8—42no—
155C2×Q8—1222no—
156C2×Q8—2441no—
157C2×Q8—2441no—
158C2×Q8—2441no—
159C2×Q8—2441no—
160C2×Q8—2441no—
161C22×C4—2441no—
162C22×C4—2441no—
163C22×C4#1175819912yes—
164C22×C4C2×C22⋊D6111yescharacteristic
165Q16—1224no—
166Q16—2442no—
167C2×C8—21no—
168C2×C8—21no—
169C2×C8#1175820112yes—
170C2×C8Q8×D6111yescharacteristic
171C2×C8#1175822612yes—
172C2×C8#1175822611yescharacteristic
173C2×C8C2×C22⋊D6112yes—
174C4⋊C4—24no—
175C4⋊C4—44no—
176C4⋊C4—42no—
177C4⋊C4—2441no—
178C4⋊C4—2441no—
179C22⋊C4—42no—
180C42—21no—
181C42—21no—
182C42—42no—
183C16—2442no—
184C23C2×#1175819911yescharacteristic
185Q8—84no—
186Q8—4881no—
187Q8—4881no—
188Q8—2442no—
189Q8—2442no—
190C2×C4—22no—
191C2×C4—42no—
192C2×C4—44no—
193C2×C4—4882no—
194C2×C4—4881no—
195C2×C4—4881no—
196C2×C4—4881no—
197C2×C4—2442no—
198C2×C4#1451974611yescharacteristic
199C2×C4#1451975311yescharacteristic
200C2×C4#1451976611yescharacteristic
201C2×C4C2×#1175820111yescharacteristic
202C2×C4#1451980311yescharacteristic
203C2×C4#1451980811yescharacteristic
204C8—22no—
205C8#1451975312yes—
206C8#1451976612yes—
207C22—22no—
208C22#1683989611yescharacteristic
209C22#1684003911yescharacteristic
210C22#1684011011yescharacteristic
211C4—42no—
212C4—84no—
213C4—9761no—
214C4—4882no—
215C4#1683967311yescharacteristic
216C4#1683990111yescharacteristic
217C4#1684004911yescharacteristic
218C4#1684012411yescharacteristic
219C2—21no—
220C2—21no—
221C2#2144695211yescharacteristic
222C2#2144777012yes—
subgroupG/H
centerC22#16839896
commutator, cosocleC22×C8×C61C23
FrattiniC22×C8C22×D61
FittingC61×#3162C2
socleC22×C61#447
prime radicalC23×C61C2×D8
hypercenter#3162D61
hypocenterC61#13368
LCSG ▷ C22×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#97 ◁ #3162

Complements

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

NH ≅ G/Ntype
21. C2×Dic244Q8semidirect
128. C61#13368semidirect

Maximal subgroups

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

subgroupindex
#214475382
#214466902
#214439242
#214439032
C61×#31622
#1336861