Finite Group Databasebeta

← #29591337

Subgroups — #29591337

Order 15616.

354 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 91 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#21456399C211yesmaximal, characteristic
2#21447617C211yesmaximal, characteristic, complemented
3#335×D61C211yesmaximal, characteristic, complemented
4#21443874C211yesmaximal, characteristic, complemented
5#21443866C211yesmaximal, characteristic, complemented
6#21443864C211yesmaximal, characteristic, complemented
7C61×#1364C211yesmaximal, characteristic, complemented
8#16840313—21no—
9#16840139C2211yescharacteristic
10#16840110—21no—
11#16839999—21no—
12#16839999C412yes—
13#16839844—21no—
14#16839844C412yes—
15C4⋊C8×D61—21no—
16C4×C8×D61C2211yescharacteristic
17C4⋊#11758185C2211yescharacteristic
18#16839541—21no—
19C16×Dic61—21no—
20#16839515C2211yescharacteristic
21#16839514—21no—
22C61×#500C2211yescharacteristic
23C61×C4⋊C16C2211yescharacteristic
24C61×#335C2211yescharacteristic
25C2×#11758226—41no—
26C2×D488—21no—
27C2×D488C2×C412yes—
28C2×C8×D61—41no—
29C2×C8×D61C2×C411yescharacteristic
30C2×C8×D61D411yescharacteristic
31#14519774—21no—
32#14519766—41no—
33#14519752—22no—
34#14519752—41no—
35#14519739—22no—
36#14519739—41no—
37C42×D61D411yescharacteristic
38C2×#11758185—21no—
39C4⋊#92418—21no—
40#14519706—41no—
41#14519697—22no—
42#14519697—22no—
43C4×#92418D411yescharacteristic
44C8×Dic61C2×C411yescharacteristic
45C8×Dic61D411yescharacteristic
46C4⋊Q8×C61—21no—
47C2×C16×C61—21no—
48#107×C61—21no—
49#107×C61C2×C412yes—
50C4⋊C8×C61—21no—
51C4×C8×C61C2311yescharacteristic
52C2×Q8×C61—41no—
53#11758226—82no—
54#11758226—82no—
55C2×D244—22no—
56C2×D244—42no—
57C2×D244—41no—
58C2×D244—41no—
59C2×C4×D61—42no—
60C2×C4×D61C22⋊C411yescharacteristic
61C2×C4×D61D811yescharacteristic
62C2×C4×D61SD1611yescharacteristic
63C2×C8×C61—41no—
64C2×C8×C61C22×C411yescharacteristic
65C2×C8×C61C2×D411yescharacteristic
66C4⋊C4×C61—22no—
67C4⋊C4×C61—41no—
68C42×C61C2×D411yescharacteristic
69#11758198—42no—
70#11758198—42no—
71C4×Dic61C22⋊C411yescharacteristic
72C4×Dic61D811yescharacteristic
73C4×Dic61SD1611yescharacteristic
74C2×#92418—41no—
75C2×#92418C22⋊C411yescharacteristic
76C2×#92418C22⋊C411yescharacteristic
77D488—42no—
78D488—41no—
79D488—41no—
80C8×D61—21no—
81C8×D61—21no—
82C8×D61—41no—
83C8×D61—82no—
84C16×C61—41no—
85#11758185—41no—
86C22×D61—42no—
87C22×D61#10211yescharacteristic
88Q8×C61—81no—
89Q8×C61—81no—
90C2×C4×C61—42no—
91C2×C4×C61C2×C22⋊C411yescharacteristic
92C2×C4×C61C2×D811yescharacteristic
93C2×C4×C61C2×SD1611yescharacteristic
94C2×Dic61#10211yescharacteristic
95C2×Dic61#10211yescharacteristic
96C2×Dic61#10211yescharacteristic
97D244—42no—
98D244—42no—
99D244—82no—
100D244—84no—
101D244—81no—
102D244—81no—
103C4×D61—21no—
104C4×D61—21no—
105C4×D61—41no—
106C4×D61—84no—
107C4×D61D1612yes—
108C4×D61SD3212yes—
109C8×C61—21no—
110C8×C61—81no—
111C8×C61#13511yescharacteristic
112C8×C61#13511yescharacteristic
113#92418—21no—
114#92418—21no—
115#92418—81no—
116#11947—611nomaximal, Sylow
117C22×C61C2×#10211yescharacteristic
118C2×D61—21no—
119C2×D61—21no—
120C2×D61—82no—
121C2×D61—82no—
122C2×D61—82no—
123C2×D61#35712yes—
124C4×C61—21no—
125C4×C61—82no—
126C4×C61#41311yescharacteristic
127C4×C61#41611yescharacteristic
128C4×C61C2×D1611yescharacteristic
129C4×C61C2×SD3211yescharacteristic
130Dic61—21no—
131Dic61—21no—
132Dic61#35712yes—
133#3169—611no—
134#2162—611no—
135C2×#335—611no—
136#1364—611no—
137#1364D6111yescharacteristic, complemented
138#1361—611no—
139#1361—611no—
140C2×C61#154011yescharacteristic
141C2×C61C2×#35711yescharacteristic
142C2×C61#214811yescharacteristic
143D61—22no—
144D61—162no—
145#532—1221no—
146#500C2×D6111yescharacteristic
147#493—611no—
148#486—1221no—
149#466—612no—
150#466—1221no—
151C4×D8—612no—
152C4×D8—1221no—
153C2×C4⋊C8—1221no—
154C2×C4×C8—611no—
155C4⋊C16—611no—
156C4⋊C16C2×D6111yescharacteristic
157C22⋊C16—1221no—
158C4×C16—1221no—
159#335—611no—
160#335—1221no—
161#335C2×D6111yescharacteristic
162C61#1194711yescharacteristic, complemented, Sylow
163C2×#41—2441no—
164C2×D8—612no—
165C2×D8—1221no—
166C22×C8—611no—
167C22×C8—611no—
168C22×C8—2441no—
169C4⋊Q8—21no—
170#127—1221no—
171#124—2441no—
172#121—1222no—
173#121—2441no—
174C4×D4—1222no—
175C4×D4—2441no—
176C2×C42—611no—
177C2×C16—21no—
178C2×C16—1221no—
179#107—21no—
180#107C4×D6112yes—
181C4⋊C8—21no—
182C4⋊C8—1221no—
183C4⋊C8—2441no—
184#102—1222no—
185#102—1222no—
186C4×C8—611no—
187C4×C8—611no—
188C4×C8—611no—
189C4×C8C22×D6111yescharacteristic
190#41—4882no—
191#41—4882no—
192C2×Q8—41no—
193C2×D4—1222no—
194C2×D4—2442no—
195C2×D4—2441no—
196C2×D4—2441no—
197C22×C4—611no—
198C22×C4—611no—
199C22×C4—611no—
200C22×C4—2442no—
201D8—2442no—
202D8—2441no—
203D8—2441no—
204C2×C8—41no—
205C2×C8—611no—
206C2×C8—611no—
207C2×C8—1221no—
208C2×C8—1221no—
209C2×C8—4882no—
210C2×C8—2441no—
211C2×C8—2441no—
212C2×C8C2×C4×D6111yescharacteristic
213C2×C8D4×D6111yescharacteristic
214C4⋊C4—22no—
215C4⋊C4—41no—
216C22⋊C4—2442no—
217C22⋊C4—2442no—
218C42—611no—
219C42—611no—
220C42—611no—
221C42D4×D6111yescharacteristic
222C16—41no—
223C16—2441no—
224C23—611no—
225C23—2442no—
226Q8—81no—
227Q8—81no—
228D4—4882no—
229D4—4884no—
230D4—4881no—
231D4—4881no—
232D4—2442no—
233D4—2442no—
234C2×C4—42no—
235C2×C4—611no—
236C2×C4—612no—
237C2×C4—612no—
238C2×C4—611no—
239C2×C4—611no—
240C2×C4—1221no—
241C2×C4—1221no—
242C2×C4—4884no—
243C2×C4—2441no—
244C2×C4C22⋊C4×D6111yescharacteristic
245C2×C4D8×D6111yescharacteristic
246C2×C4SD16×D6111yescharacteristic
247C8—21no—
248C8—81no—
249C8—1221no—
250C8—1221no—
251C8—4881no—
252C8#1451979811yescharacteristic
253C8#1451980011yescharacteristic
254C22—612no—
255C22—1221no—
256C22—1221no—
257C22—4882no—
258C22—4882no—
259C22—4882no—
260C22#102×D6111yescharacteristic
261C4—21no—
262C4—82no—
263C4—612no—
264C4—1221no—
265C4—1221no—
266C4#1683974511yescharacteristic
267C4#1683975711yescharacteristic
268C4D16×D6111yescharacteristic
269C4SD32×D6111yescharacteristic
270C2—1222no—
271C2—9762no—
272C2#2144446711yescharacteristic
273C2#357×D6111yescharacteristic
274C2#2144756711yescharacteristic
subgroupG/H
centerC22#102×D61
commutatorC2×C8×C61C22×C4
FrattiniC4×C8C22×D61
FittingC61×#1364C2
socleC22×C61C2×#102
prime radical#21456399C2
cosocleC4×C8×C61C23
hypercenter#1364D61
hypocenterC61#11947
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1364

Complements

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

NH ≅ G/Ntype
2. #21447617C2semidirect
3. #335×D61C2semidirect
4. #21443874C2semidirect
5. #21443866C2semidirect
6. #21443864C2semidirect
7. C61×#1364C2semidirect
137. #1364D61semidirect
162. C61#11947semidirect

Maximal subgroups

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

subgroupindex
#214563992
#214476172
#335×D612
#214438742
#214438662
#214438642
C61×#13642
#1194761