Finite Group Databasebeta

← #29593400

Subgroups — #29593400

Order 15616.

280 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 59 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#21448036C211yesmaximal, characteristic, complemented
2#21448031C211yesmaximal, characteristic
3#21447394C211yesmaximal, characteristic, complemented
4#21443807C211yesmaximal, characteristic, complemented
5#21443804C211yesmaximal, characteristic
6#21443770C211yesmaximal, characteristic, complemented
7C61×#3256C211yesmaximal, characteristic
8#16839811C2211yescharacteristic
9#16839584—21no—
10#16839584—21no—
11#16839578—21no—
12#16839575—21no—
13#16839544C2211yescharacteristic
14#16839544C2211yescharacteristic
15#16839534—21no—
16#16839522—21no—
17#16839519C2211yescharacteristic
18C61×#529—21no—
19C61×#479—21no—
20C61×#478—21no—
21C61×#470C2211yescharacteristic
22C61×#469C2211yescharacteristic
23C61×#468—21no—
24C61×#464—21no—
25C61×#463—21no—
26C61×#423C2211yescharacteristic
27C2×#11758194—21no—
28#14519736—21no—
29#14519717—21no—
30#14519717—21no—
31#14519713—21no—
32#14519713—21no—
33C2×Q16×C61D411yescharacteristic
34C2×SD16×C61—21no—
35C2×D8×C61D411yescharacteristic
36C2×M16×C61D411yescharacteristic
37C2×M16×C61C2311yescharacteristic
38#126×C61—41no—
39#125×C61—21no—
40#124×C61—21no—
41#123×C61—41no—
42C22⋊Q8×C61—21no—
43#121×C61—21no—
44C4×Q8×C61—21no—
45C4×D4×C61—21no—
46C4×D4×C61—41no—
47#117×C61—41no—
48C2×C42×C61D411yescharacteristic
49#107×C61—21no—
50#106×C61D411yescharacteristic
51#106×C61D411yescharacteristic
52C4⋊C8×C61—21no—
53C4⋊C8×C61—21no—
54#103×C61—21no—
55#103×C61—21no—
56#102×C61—21no—
57#102×C61—21no—
58C2×Q8×C61—21no—
59C2×D4×C61—21no—
60C2×D4×C61—41no—
61C22×C4×C61—21no—
62C22×C4×C61—41no—
63C22×C4×C61C2×D411yescharacteristic
64Q16×C61—41no—
65SD16×C61—81no—
66D8×C61—41no—
67M16×C61—41no—
68M16×C61—41no—
69C2×C8×C61—21no—
70C2×C8×C61C2×D411yescharacteristic
71C2×C8×C61C2×D411yescharacteristic
72C4⋊C4×C61—21no—
73C4⋊C4×C61—21no—
74C4⋊C4×C61—41no—
75C4⋊C4×C61—41no—
76C4⋊C4×C61—41no—
77C4⋊C4×C61—41no—
78C22⋊C4×C61—41no—
79C22⋊C4×C61—41no—
80C22⋊C4×C61—41no—
81C22⋊C4×C61—41no—
82C22⋊C4×C61—41no—
83C42×C61—21no—
84C42×C61—41no—
85C42×C61SD1611yescharacteristic
86C42×C61SD1611yescharacteristic
87C22⋊Dic61—41no—
88C4⋊Dic61—41no—
89C4×Dic61—41no—
90#11758194—41no—
91#11758194—41no—
92C2×#92418—41no—
93#11758185—41no—
94#11758185—41no—
95C23×C61—41no—
96C23×C61AGL(1,ℤ/8)11yescharacteristic
97Q8×C61—41no—
98Q8×C61—41no—
99D4×C61—41no—
100D4×C61—41no—
101D4×C61—82no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—41no—
107C2×C4×C61—41no—
108C2×C4×C61—41no—
109C2×C4×C61—81no—
110C2×C4×C61—82no—
111C2×C4×C61#12011yescharacteristic
112C2×C4×C61C2×SD1611yescharacteristic
113C2×Dic61—81no—
114C8×C61—21no—
115C8×C61—21no—
116C8×C61—41no—
117#92418—81no—
118#12309—611nomaximal, Sylow
119C22×C61—21no—
120C22×C61—41no—
121C22×C61—81no—
122C22×C61—81no—
123C22×C61—81no—
124C22×C61#45011yescharacteristic
125C4×C61—21no—
126C4×C61—41no—
127C4×C61—41no—
128C4×C61—81no—
129C4×C61—81no—
130C4×C61—81no—
131C4×C61#45411yescharacteristic
132C4×C61#45811yescharacteristic
133Dic61—161no—
134#3256D6111yescharacteristic
135#2239—611no—
136#2238—611no—
137#2102—611no—
138#1340—611no—
139#1339—611no—
140#1327—611no—
141C2×C61—21no—
142C2×C61—41no—
143C2×C61—161no—
144C2×C61#161611yescharacteristic
145#529—21no—
146#479—21no—
147#478—21no—
148#470C2×D6111yescharacteristic
149#469C2×D6111yescharacteristic
150#468—21no—
151#464—21no—
152#463—21no—
153#430—611no—
154#423C2×D6111yescharacteristic
155#365—1221no—
156#365—1221no—
157#362—1221no—
158#361—1221no—
159#349—611no—
160#349—611no—
161#344—1221no—
162#339—1221no—
163H(3,ℤ/4)—611no—
164C61#1230911yescharacteristic, complemented, Sylow
165C2×Q16C22⋊D6111yescharacteristic
166C2×SD16—21no—
167C2×D8C22⋊D6111yescharacteristic
168C2×M16—1221no—
169C2×M16C22⋊D6111yescharacteristic
170C2×M16C22×D6111yescharacteristic
171#126—41no—
172#125—21no—
173#124—21no—
174#123—41no—
175C22⋊Q8—21no—
176#121—21no—
177C4×Q8—21no—
178C4×D4—21no—
179C4×D4—41no—
180#117—41no—
181#117—1221no—
182C2×C42C22⋊D6111yescharacteristic
183M32—1221no—
184M32—1221no—
185#108—1221no—
186#108—1221no—
187#107—21no—
188#106C22⋊D6111yescharacteristic
189#106C22⋊D6111yescharacteristic
190C4⋊C8—21no—
191C4⋊C8—21no—
192#103—21no—
193#103—21no—
194#102—21no—
195#102—21no—
196C2×Q8—21no—
197C2×D4—21no—
198C2×D4—41no—
199C22×C4—21no—
200C22×C4—41no—
201C22×C4C2×C22⋊D6111yescharacteristic
202Q16—41no—
203SD16—81no—
204D8—41no—
205M16—41no—
206M16—41no—
207M16—2441no—
208M16—2441no—
209C2×C8—21no—
210C2×C8—2441no—
211C2×C8C2×C22⋊D6111yescharacteristic
212C2×C8C2×C22⋊D6111yescharacteristic
213C4⋊C4—21no—
214C4⋊C4—21no—
215C4⋊C4—41no—
216C4⋊C4—41no—
217C4⋊C4—41no—
218C4⋊C4—41no—
219C4⋊C4—2441no—
220C22⋊C4—41no—
221C22⋊C4—41no—
222C22⋊C4—41no—
223C22⋊C4—41no—
224C22⋊C4—41no—
225C22⋊C4—2441no—
226C42—21no—
227C42—41no—
228C42—2441no—
229C42#1175820011yescharacteristic
230C42#1175820011yescharacteristic
231C16—2441no—
232C16—2441no—
233C23—41no—
234C23#1451980311yescharacteristic
235Q8—41no—
236Q8—41no—
237D4—41no—
238D4—41no—
239D4—82no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—81no—
248C2×C4—82no—
249C2×C4—4881no—
250C2×C4#1451974611yescharacteristic
251C2×C4C2×#1175820011yescharacteristic
252C8—21no—
253C8—21no—
254C8—41no—
255C8—4881no—
256C22—21no—
257C22—41no—
258C22—81no—
259C22—81no—
260C22—81no—
261C22#1683991311yescharacteristic
262C4—21no—
263C4—41no—
264C4—41no—
265C4—81no—
266C4—81no—
267C4—81no—
268C4—9761no—
269C4#1683993511yescharacteristic
270C4#1683995211yescharacteristic
271C2—21no—
272C2—41no—
273C2—161no—
274C2#2144485611yescharacteristic
subgroupG/H
centerC2#21444856
commutator, cosocleC2×M16×C61C23
FrattiniC2×M16C22×D61
FittingC61×#3256C2
socleC2×C61#1616
prime radicalC61×#469C22
hypercenter#3256D61
hypocenterC61#12309
LCSG ▷ C2×M16×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #3256

Complements

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

NH ≅ G/Ntype
1. #21448036C2semidirect
3. #21447394C2semidirect
4. #21443807C2semidirect
6. #21443770C2semidirect
164. C61#12309semidirect

Maximal subgroups

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

subgroupindex
#214480362
#214480312
#214473942
#214438072
#214438042
#214437702
C61×#32562
#1230961