Finite Group Databasebeta

← #29599402

Subgroups — #29599402

Order 15616.

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

normal subgroups only

This group has 436 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
1C2×#16839578C212yesmaximal
2#21447539C212yesmaximal
3#21446567C211yesmaximal, characteristic
4#21443901C211yesmaximal, characteristic
5C2×C61×#494C211yesmaximal, characteristic
6C2×#14519717C2212yes—
7C2×#14519713C2211yescharacteristic
8#16839800C2211yescharacteristic
9#16839788—21no—
10#16839578—24no—
11#16839566—24no—
12#16839522—21no—
13C22×Q16×C61—21no—
14C22×Q16×C61C2212yes—
15C2×C4⋊Q8×C61—21no—
16C61×#494—24no—
17C2×C4×C8×C61C2211yescharacteristic
18C2×#11758194—21no—
19#14519736—21no—
20#14519717—22no—
21#14519717—22no—
22C2×#11758185—22no—
23#14519713—22no—
24#14519711D412yes—
25#14519709—21no—
26#14519706—42no—
27C22×Q8×C61—22no—
28C2×Q16×C61—24no—
29C2×Q16×C61—22no—
30C2×Q16×C61—22no—
31C2×Q16×C61—22no—
32C2×Q16×C61—22no—
33C2×Q16×C61—22no—
34C2×Q16×C61—42no—
35C2×Q16×C61—42no—
36C2×Q16×C61D414yes—
37C22×C8×C61D411yescharacteristic
38C22×C8×C61C2311yescharacteristic
39C4⋊Q8×C61—24no—
40C4⋊Q8×C61—42no—
41C2×C4⋊C4×C61—42no—
42C2×C42×C61D411yescharacteristic
43C4×C8×C61—22no—
44C2×Q8×C61—24no—
45C2×Q8×C61—42no—
46C2×Q8×C61—42no—
47C2×Q8×C61—42no—
48C2×Q8×C61—42no—
49C2×Q8×C61—42no—
50C22×C4×C61—21no—
51C22×C4×C61—42no—
52C22×C4×C61C2×D411yescharacteristic
53Q16×C61—24no—
54Q16×C61—24no—
55Q16×C61—48no—
56Q16×C61—42no—
57Q16×C61—42no—
58C2×C8×C61—21no—
59C2×C8×C61—21no—
60C2×C8×C61D812yes—
61C2×C8×C61C2×D411yescharacteristic
62C2×C8×C61C2×D412yes—
63C2×C8×C61#4112yes—
64C2×C8×C61#4111yescharacteristic
65C4⋊C4×C61—48no—
66C42×C61—21no—
67C42×C61SD1612yes—
68C22⋊Dic61—41no—
69C4⋊Dic61—22no—
70C4×Dic61—41no—
71#11758194—41no—
72#11758194—41no—
73C2×#92418—41no—
74#11758185—42no—
75C23×C61AGL(1,ℤ/8)11yescharacteristic
76Q8×C61—44no—
77Q8×C61—44no—
78Q8×C61—82no—
79Q8×C61—82no—
80C2×C4×C61—24no—
81C2×C4×C61—22no—
82C2×C4×C61—44no—
83C2×C4×C61—82no—
84C2×C4×C61—82no—
85C2×C4×C61#12011yescharacteristic
86C2×C4×C61#12111yescharacteristic
87C2×C4×C61#12411yescharacteristic
88C2×C4×C61C2×D811yescharacteristic
89C2×C4×C61C2×SD1611yescharacteristic
90C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
91C2×Dic61—42no—
92C8×C61—22no—
93C8×C61#12112yes—
94C8×C61#12312yes—
95#92418—81no—
96#13415—611nomaximal, Sylow
97C22×C61—22no—
98C22×C61#45011yescharacteristic
99C22×C61#45911yescharacteristic
100C22×C61#49011yescharacteristic
101C4×C61—24no—
102C4×C61—84no—
103C4×C61#39411yescharacteristic
104C4×C61#44711yescharacteristic
105C4×C61#46011yescharacteristic
106C4×C61#48611yescharacteristic
107Dic61—82no—
108C2×#494D6111yescharacteristic
109C2×#362—612no—
110#2141—612no—
111#1945—611no—
112#1376—611no—
113C2×C61—21no—
114C2×C61—21no—
115C2×C61#204111yescharacteristic
116C2×C61#221412yes—
117C22×Q16—21no—
118C22×Q16C2×D6112yes—
119C2×C4⋊Q8—21no—
120C2×M32—612no—
121#494—24no—
122C2×#108—611no—
123#427—611no—
124#424—1221no—
125C2×C4×C8C2×D6111yescharacteristic
126#362—1224no—
127#358—1224no—
128#339—1221no—
129C61#1341511yescharacteristic, complemented, Sylow
130C22×Q8—22no—
131C2×Q16—24no—
132C2×Q16—22no—
133C2×Q16—22no—
134C2×Q16—22no—
135C2×Q16—22no—
136C2×Q16—22no—
137C2×Q16—42no—
138C2×Q16—42no—
139C2×Q16C22⋊D6114yes—
140C2×M16—1221no—
141C22×C8C22⋊D6111yescharacteristic
142C22×C8C22×D6111yescharacteristic
143C4⋊Q8—24no—
144C4⋊Q8—42no—
145#117—1221no—
146C2×C4⋊C4—42no—
147C2×C42C22⋊D6111yescharacteristic
148M32—1222no—
149M32—1222no—
150C2×C16—1222no—
151#108—1222no—
152#107—612no—
153#106—1221no—
154C4⋊C8—2442no—
155C4×C8—22no—
156C2×Q8—24no—
157C2×Q8—42no—
158C2×Q8—42no—
159C2×Q8—42no—
160C2×Q8—42no—
161C2×Q8—42no—
162C22×C4—21no—
163C22×C4—42no—
164C22×C4C2×C22⋊D6111yescharacteristic
165Q16—24no—
166Q16—24no—
167Q16—48no—
168Q16—42no—
169Q16—42no—
170M16—2441no—
171M16—2441no—
172C2×C8—21no—
173C2×C8—21no—
174C2×C8—2441no—
175C2×C8#1175819912yes—
176C2×C8D4×D6111yescharacteristic
177C2×C8#1175822412yes—
178C2×C8#1175822411yescharacteristic
179C2×C8C2×C22⋊D6112yes—
180C4⋊C4—48no—
181C4⋊C4—1222no—
182C22⋊C4—2441no—
183C42—21no—
184C42—2441no—
185C42#1175820012yes—
186C16—2442no—
187C23#1451980311yescharacteristic
188Q8—44no—
189Q8—44no—
190Q8—82no—
191Q8—82no—
192C2×C4—24no—
193C2×C4—22no—
194C2×C4—44no—
195C2×C4—82no—
196C2×C4—82no—
197C2×C4—2442no—
198C2×C4#1451974611yescharacteristic
199C2×C4#1451974811yescharacteristic
200C2×C4#1451976411yescharacteristic
201C2×C4C2×#1175819911yescharacteristic
202C2×C4C2×#1175820011yescharacteristic
203C2×C4#1451980311yescharacteristic
204C8—22no—
205C8—4881no—
206C8#1451974912yes—
207C8#1451975812yes—
208C22—22no—
209C22#1683991311yescharacteristic
210C22#1683995411yescharacteristic
211C22#1684012611yescharacteristic
212C4—24no—
213C4—84no—
214C4—4882no—
215C4#1683967611yescharacteristic
216C4#1683989611yescharacteristic
217C4#1683995911yescharacteristic
218C4#1684010811yescharacteristic
219C2—21no—
220C2—21no—
221C2#2144705011yescharacteristic
222C2#2144789712yes—
subgroupG/H
centerC22#16839954
commutator, cosocleC22×C8×C61C23
FrattiniC22×C8C22×D61
FittingC2×C61×#494C2
socleC22×C61#459
prime radicalC23×C61AGL(1,ℤ/8)
hypercenterC2×#494D61
hypocenterC61#13415
LCSG ▷ C22×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×C8 ◁ C2×#494

Complements

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

NH ≅ G/Ntype
129. C61#13415semidirect

Maximal subgroups

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

subgroupindex
C2×#168395782
#214475392
#214465672
#214439012
C2×C61×#4942
#1341561