Finite Group Databasebeta

← #29593381

Subgroups — #29593381

Order 15616.

274 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 55 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#21457290C211yesmaximal, characteristic
2#21448038C211yesmaximal, characteristic, complemented
3#21448033C211yesmaximal, characteristic
4#21443812C211yesmaximal, characteristic, complemented
5#21443809C211yesmaximal, characteristic
6#21443772C211yesmaximal, characteristic, complemented
7C61×#2103C211yesmaximal, characteristic, complemented
8#16840383—21no—
9#16840053—21no—
10#16840048—21no—
11#16840020C2211yescharacteristic
12#16840015C2211yescharacteristic
13#16839991—21no—
14#16839985—21no—
15#16839978—21no—
16#16839586—21no—
17#16839586—21no—
18#16839577—21no—
19#16839574—21no—
20#16839544C2211yescharacteristic
21#16839544C2211yescharacteristic
22C61×#430C2211yescharacteristic
23C61×#424C2211yescharacteristic
24C61×#344—21no—
25C61×#341—21no—
26C61×#338C2211yescharacteristic
27C2×Dic244D411yescharacteristic
28C2×#11758190—21no—
29C2×D488D411yescharacteristic
30#14519777—21no—
31#14519772—41no—
32#14519765—21no—
33#14519763—41no—
34#14519759—41no—
35#14519756—21no—
36#14519755—41no—
37#14519751—21no—
38C4×Dic122—21no—
39C4×D244—21no—
40#14519717—21no—
41#14519717—21no—
42#14519709—21no—
43#14519709D411yescharacteristic
44#14519709D411yescharacteristic
45#14519702—21no—
46#14519702—21no—
47#14519699—21no—
48#14519699—21no—
49C2×M16×C61—21no—
50C2×M16×C61—21no—
51C2×M16×C61C2311yescharacteristic
52C22×C8×C61D411yescharacteristic
53#117×C61D411yescharacteristic
54#108×C61—21no—
55#108×C61—21no—
56C4⋊C8×C61—21no—
57C4⋊C8×C61—21no—
58C22×C4×C61C2×D411yescharacteristic
59C2×C22⋊D61—41no—
60C2×D244—21no—
61C2×C4×D61—41no—
62C2×Dic122—21no—
63C2×Dic122—41no—
64M16×C61—41no—
65M16×C61—41no—
66M16×C61—41no—
67M16×C61—41no—
68M16×C61—41no—
69C2×C8×C61—21no—
70C2×C8×C61—41no—
71C2×C8×C61—41no—
72C2×C8×C61—41no—
73C2×C8×C61C2×D411yescharacteristic
74C2×C8×C61C2×D411yescharacteristic
75C4⋊C4×C61—21no—
76C22⋊C4×C61SD1611yescharacteristic
77C22⋊C4×C61SD1611yescharacteristic
78C42×C61—21no—
79C22⋊Dic61—41no—
80#11758198—41no—
81#11758198—41no—
82#11758198—41no—
83#11758198—41no—
84C4⋊Dic61—21no—
85C4⋊Dic61—21no—
86C4⋊Dic61—41no—
87#11758196—41no—
88#11758196—41no—
89C4×Dic61—41no—
90Dic244—41no—
91D488—41no—
92#11758190—81no—
93#11758185—41no—
94#11758185—41no—
95C23×C61C2×SD1611yescharacteristic
96C22×D61—41no—
97C2×C4×C61—21no—
98C2×C4×C61—21no—
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61#12011yescharacteristic
102C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
103C22⋊D61—161no—
104C2×Dic61—41no—
105C2×Dic61—41no—
106C2×Dic61—41no—
107D244—41no—
108D244—41no—
109C4×D61—161no—
110Dic122—41no—
111Dic122—41no—
112Dic122—161no—
113C8×C61—21no—
114C8×C61—21no—
115C8×C61—41no—
116C8×C61—81no—
117C8×C61—81no—
118#12306—611nomaximal, Sylow
119C22×C61—21no—
120C22×C61—41no—
121C22×C61#45011yescharacteristic
122C2×D61—81no—
123C2×D61—81no—
124C2×D61—81no—
125C4×C61—21no—
126C4×C61—41no—
127C4×C61—41no—
128C4×C61#45411yescharacteristic
129C4×C61#45811yescharacteristic
130Dic61—81no—
131Dic61—81no—
132Dic61—81no—
133#3263—611no—
134#2239—611no—
135#2238—611no—
136#2103D6111yescharacteristic, complemented
137#1342—611no—
138#1341—611no—
139#1328—611no—
140C2×C61—21no—
141C2×C61—41no—
142C2×C61#161611yescharacteristic
143D61—161no—
144#542—1221no—
145#476—1221no—
146#475—1221no—
147#470—611no—
148#469—611no—
149#465—1221no—
150#464—1221no—
151#463—1221no—
152#430C2×D6111yescharacteristic
153#424C2×D6111yescharacteristic
154#365—1221no—
155#365—1221no—
156#362—1221no—
157#361—1221no—
158#349—611no—
159#349—611no—
160#344—21no—
161#341—21no—
162#338C2×D6111yescharacteristic
163C61#1230611yescharacteristic, complemented, Sylow
164C2×Q16—611no—
165C2×SD16—1221no—
166C2×D8—611no—
167C2×M16—21no—
168C2×M16—21no—
169C2×M16C22×D6111yescharacteristic
170C22×C8C22⋊D6111yescharacteristic
171C4⋊Q8—1221no—
172#126—2441no—
173#124—1221no—
174#124—2441no—
175#123—2441no—
176C22⋊Q8—1221no—
177C22⋊Q8—2441no—
178#121—1221no—
179C4×Q8—1221no—
180C4×D4—1221no—
181#117C22⋊D6111yescharacteristic
182M32—1221no—
183M32—1221no—
184#108—21no—
185#108—21no—
186#106—611no—
187#106—611no—
188#106—1221no—
189C4⋊C8—21no—
190C4⋊C8—21no—
191#103—1221no—
192#103—1221no—
193#102—1221no—
194#102—1221no—
195C2×Q8—1221no—
196C2×Q8—2441no—
197C2×D4—1221no—
198C2×D4—2441no—
199C22×C4—2441no—
200C22×C4C2×C22⋊D6111yescharacteristic
201Q16—2441no—
202SD16—4881no—
203D8—2441no—
204M16—41no—
205M16—41no—
206M16—41no—
207M16—41no—
208M16—41no—
209C2×C8—21no—
210C2×C8—41no—
211C2×C8—41no—
212C2×C8—41no—
213C2×C8D4×D6111yescharacteristic
214C2×C8D4×D6111yescharacteristic
215C4⋊C4—21no—
216C4⋊C4—1221no—
217C4⋊C4—1221no—
218C4⋊C4—2441no—
219C4⋊C4—2441no—
220C4⋊C4—2441no—
221C22⋊C4—2441no—
222C22⋊C4—2441no—
223C22⋊C4—2441no—
224C22⋊C4—2441no—
225C22⋊C4—2441no—
226C22⋊C4#1175820111yescharacteristic
227C22⋊C4#1175820111yescharacteristic
228C42—21no—
229C42—2441no—
230C16—2441no—
231C16—2441no—
232C23—2441no—
233C23C2×#1175820111yescharacteristic
234Q8—9761no—
235Q8—2441no—
236Q8—2441no—
237D4—9761no—
238D4—2441no—
239D4—2441no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—9761no—
245C2×C4—2441no—
246C2×C4—2441no—
247C2×C4—2441no—
248C2×C4#1451974511yescharacteristic
249C2×C4#1451980211yescharacteristic
250C8—21no—
251C8—21no—
252C8—41no—
253C8—81no—
254C8—81no—
255C22—21no—
256C22—41no—
257C22—4881no—
258C22—4881no—
259C22—4881no—
260C22#1683991211yescharacteristic
261C4—21no—
262C4—41no—
263C4—41no—
264C4—4881no—
265C4—4881no—
266C4—4881no—
267C4#1683993411yescharacteristic
268C4#1683995111yescharacteristic
269C2—21no—
270C2—41no—
271C2—9761no—
272C2#2144485511yescharacteristic
subgroupG/H
centerC2#21444855
commutator, cosocleC2×M16×C61C23
FrattiniC2×M16C22×D61
FittingC61×#2103C2
socleC2×C61#1616
prime radical#16840015C22
hypercenter#2103D61
hypocenterC61#12306
LCSG ▷ C2×M16×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #2103

Complements

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

NH ≅ G/Ntype
2. #21448038C2semidirect
4. #21443812C2semidirect
6. #21443772C2semidirect
7. C61×#2103C2semidirect
136. #2103D61semidirect
163. C61#12306semidirect

Maximal subgroups

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

subgroupindex
#214572902
#214480382
#214480332
#214438122
#214438092
#214437722
C61×#21032
#1230661