Finite Group Databasebeta

← #29567505

Subgroups — #29567505

Order 15616.

268 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 39 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#21443755C211yesmaximal, characteristic, complemented
2#21443706C211yesmaximal, characteristic, complemented
3C61×#2010C211yesmaximal, characteristic
4C2×C22⋊#92418—21no—
5#16839544—21no—
6C61×#575C411yescharacteristic
7C61×#525—21no—
8C61×#421—21no—
9C61×#407C2211yescharacteristic
10C61×H(3,ℤ/4)C411yescharacteristic
11C22×#92418—41no—
12#14519717—41no—
13C22⋊#92418—22no—
14C22⋊#92418—41no—
15C2×#41×C61—21no—
16C23×C4×C61D411yescharacteristic
17#137×C61—41no—
18AGL(1,ℤ/8)×C61—41no—
19#135×C61—41no—
20C2×M16×C61C2×C411yescharacteristic
21C2×M16×C61D411yescharacteristic
22#123×C61—41no—
23C22⋊Q8×C61—41no—
24#121×C61—41no—
25#120×C61—41no—
26C4×D4×C61—42no—
27#117×C61—21no—
28#104×C61—42no—
29C22⋊C8×C61—41no—
30C24×C61SD1611yescharacteristic
31#41×C61—41no—
32#41×C61—41no—
33#41×C61—41no—
34#41×C61—41no—
35C2×Q8×C61—21no—
36C2×D4×C61—21no—
37C2×D4×C61—42no—
38C2×D4×C61—41no—
39C22×C4×C61—21no—
40C22×C4×C61—21no—
41C22×C4×C61—41no—
42C22×C4×C61—41no—
43C22×C4×C61—41no—
44C22×C4×C61C22⋊C411yescharacteristic
45C22×C4×C61D811yescharacteristic
46Q16×C61—41no—
47SD16×C61—42no—
48D8×C61—41no—
49M16×C61—41no—
50M16×C61—41no—
51C2×C8×C61—21no—
52C2×C8×C61—21no—
53C4⋊C4×C61—41no—
54C4⋊C4×C61—42no—
55C22⋊C4×C61—42no—
56C22⋊C4×C61—42no—
57C22⋊C4×C61—41no—
58C42×C61—22no—
59C2×#92418—42no—
60C2×#92418—81no—
61C2×#92418—81no—
62#11758185—81no—
63C23×C61—21no—
64C23×C61—41no—
65C23×C61—42no—
66C23×C61—41no—
67C23×C61#10211yescharacteristic
68Q8×C61—41no—
69Q8×C61—41no—
70D4×C61—41no—
71D4×C61—41no—
72D4×C61—81no—
73D4×C61—84no—
74D4×C61—81no—
75C2×C4×C61—21no—
76C2×C4×C61—21no—
77C2×C4×C61—21no—
78C2×C4×C61—41no—
79C2×C4×C61—41no—
80C2×C4×C61—41no—
81C2×C4×C61—42no—
82C2×C4×C61—41no—
83C2×C4×C61—81no—
84C2×C4×C61—81no—
85C2×C4×C61—81no—
86C2×C4×C61#9911yescharacteristic
87C2×C4×C61#10411yescharacteristic
88C8×C61—41no—
89C8×C61—41no—
90#92418—82no—
91#7397—611nomaximal, Sylow
92C22×C61—22no—
93C22×C61—21no—
94C22×C61—41no—
95C22×C61—41no—
96C22×C61—42no—
97C22×C61—41no—
98C22×C61—81no—
99C22×C61—82no—
100C22×C61—81no—
101C22×C61#32711yescharacteristic
102C4×C61—21no—
103C4×C61—41no—
104C4×C61—82no—
105C4×C61—81no—
106C4×C61AΣL(1,𝔽16)11yescharacteristic
107C4×C61#35311yescharacteristic
108#2010D6111yescharacteristic
109#1320—611no—
110#1298—611no—
111C2×C61—21no—
112C2×C61—41no—
113C2×C61—42no—
114C2×C61—161no—
115C2×C61#134311yescharacteristic
116#575Dic6111yescharacteristic
117#525—21no—
118#421—21no—
119#407C2×D6111yescharacteristic
120C2×C22⋊C8—1221no—
121#349—1221no—
122H(3,ℤ/4)Dic6111yescharacteristic
123C61#739711yescharacteristic, complemented, Sylow
124C2×#41—21no—
125C23×C4C22⋊D6111yescharacteristic
126#137—41no—
127AGL(1,ℤ/8)—41no—
128#135—41no—
129C2×M16C2×Dic6111yescharacteristic
130C2×M16C22⋊D6111yescharacteristic
131C22×C8—2441no—
132#123—41no—
133C22⋊Q8—41no—
134#121—41no—
135#120—41no—
136C4×D4—42no—
137#117—21no—
138M32—2441no—
139#104—42no—
140C22⋊C8—41no—
141C22⋊C8—1222no—
142C22⋊C8—2441no—
143C24#1175820011yescharacteristic
144#41—41no—
145#41—41no—
146#41—41no—
147#41—41no—
148C2×Q8—21no—
149C2×D4—21no—
150C2×D4—42no—
151C2×D4—41no—
152C22×C4—21no—
153C22×C4—21no—
154C22×C4—41no—
155C22×C4—41no—
156C22×C4—41no—
157C22×C4#1175819911yescharacteristic
158C22×C4C22⋊Dic6111yescharacteristic
159Q16—41no—
160SD16—42no—
161D8—41no—
162M16—41no—
163M16—41no—
164C2×C8—21no—
165C2×C8—21no—
166C2×C8—4881no—
167C2×C8—4881no—
168C2×C8—2442no—
169C4⋊C4—41no—
170C4⋊C4—42no—
171C22⋊C4—42no—
172C22⋊C4—42no—
173C22⋊C4—41no—
174C42—22no—
175C16—4881no—
176C23—21no—
177C23—41no—
178C23—42no—
179C23—41no—
180C23#1451969811yescharacteristic
181Q8—41no—
182Q8—41no—
183D4—41no—
184D4—41no—
185D4—81no—
186D4—84no—
187D4—81no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—42no—
195C2×C4—41no—
196C2×C4—81no—
197C2×C4—81no—
198C2×C4—81no—
199C2×C4#1451969211yescharacteristic
200C2×C4#1451970411yescharacteristic
201C8—41no—
202C8—41no—
203C8—4882no—
204C22—22no—
205C22—21no—
206C22—41no—
207C22—41no—
208C22—42no—
209C22—41no—
210C22—81no—
211C22—82no—
212C22—81no—
213C22#1683949611yescharacteristic
214C4—21no—
215C4—41no—
216C4—82no—
217C4—81no—
218C4#1683954911yescharacteristic
219C4#1683955511yescharacteristic
220C2—21no—
221C2—41no—
222C2—42no—
223C2—161no—
224C2#2144381611yescharacteristic
subgroupG/H
centerC4#16839555
commutatorC2×M16×C61C2×C4
Frattini#407C2×D61
Fitting, prime radicalC61×#2010C2
socleC2×C61#1343
cosocleC61×#407C22
hypercenter#2010D61
hypocenterC61#7397
LCSG ▷ C2×M16×C61 ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ #407 ◁ #2010

Complements

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

NH ≅ G/Ntype
1. #21443755C2semidirect
2. #21443706C2semidirect
123. C61#7397semidirect

Maximal subgroups

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

subgroupindex
#214437552
#214437062
C61×#20102
#739761