Finite Group Databasebeta

← #29593547

Subgroups — #29593547

Order 15616.

362 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 71 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#21458794C211yesmaximal, characteristic
2#21448076C211yesmaximal, characteristic, complemented
3#21447861C211yesmaximal, characteristic, complemented
4#21443864C211yesmaximal, characteristic, complemented
5Q8⋊#11758185C211yesmaximal, characteristic, complemented
6#21443779C211yesmaximal, characteristic, complemented
7C61×#1670C211yesmaximal, characteristic, complemented
8#16840434—21no—
9C2×#14519720—22no—
10C2×#14519720—21no—
11#16840139—21no—
12#16840139C2211yescharacteristic
13#16839958—22no—
14#16839958—21no—
15C4×D488—21no—
16C4×D488C2211yescharacteristic
17C4⋊#11758185C2211yescharacteristic
18#16839566—21no—
19C4×#11758185C2211yescharacteristic
20C61×#494C2211yescharacteristic
21C61×#475—21no—
22C8×Q8×C61C2211yescharacteristic
23C61×#335C2211yescharacteristic
24C61×#332—21no—
25C2×#11758226—41no—
26C2×D488—21no—
27C2×D488—22no—
28C2×D488D411yescharacteristic
29C2×D488D412yes—
30#14519774—22no—
31#14519774—21no—
32#14519752—42no—
33#14519752—41no—
34C4×D244—22no—
35C4×D244—21no—
36#14519720—44no—
37#14519720—42no—
38C2×#11758185—21no—
39C2×#11758185—21no—
40#14519711D411yescharacteristic
41#14519699—22no—
42#14519699—21no—
43C2×Q16×C61—21no—
44C2×Q16×C61—21no—
45C4⋊Q8×C61—21no—
46C4×Q8×C61D411yescharacteristic
47#106×C61—41no—
48C4⋊C8×C61—21no—
49C4⋊C8×C61—21no—
50C4⋊C8×C61D411yescharacteristic
51#103×C61—41no—
52C4×C8×C61—21no—
53C4×C8×C61C2311yescharacteristic
54C2×Q8×C61—41no—
55C2×Q8×C61D811yescharacteristic
56#11758226—82no—
57#11758226—82no—
58C2×D244—21no—
59C2×D244—22no—
60C2×D244—42no—
61C2×D244—41no—
62C2×D244—42no—
63C2×D244—41no—
64C2×C4×D61—42no—
65C2×C4×D61—41no—
66Q16×C61—42no—
67Q16×C61—41no—
68Q16×C61—41no—
69C2×C8×C61—21no—
70C2×C8×C61—41no—
71C2×C8×C61C2×D411yescharacteristic
72C2×C8×C61C2×D411yescharacteristic
73C4⋊C4×C61—21no—
74C4⋊C4×C61—41no—
75C4⋊C4×C61—41no—
76C4⋊C4×C61D811yescharacteristic
77C42×C61—21no—
78C42×C61C2×D411yescharacteristic
79#11758198—42no—
80#11758198—41no—
81C4⋊Dic61—21no—
82D488—21no—
83D488—21no—
84D488—42no—
85D488—41no—
86D488—41no—
87D488—82no—
88#11758185—22no—
89#11758185—41no—
90C22×D61—42no—
91C22×D61—41no—
92Q8×C61—21no—
93Q8×C61—81no—
94Q8×C61—81no—
95Q8×C61SD3212yescomplemented
96C2×C4×C61—21no—
97C2×C4×C61—21no—
98C2×C4×C61—81no—
99C2×C4×C61#12011yescharacteristic
100C2×C4×C61C2×D811yescharacteristic
101C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
102C2×Dic61—41no—
103D244—41no—
104D244—42no—
105D244—42no—
106D244—41no—
107D244—84no—
108D244—81no—
109D244—81no—
110D244—161no—
111D244—162no—
112C4×D61—84no—
113C4×D61—81no—
114C4×D61—81no—
115C8×C61—21no—
116C8×C61—41no—
117C8×C61—81no—
118C8×C61#13511yescharacteristic
119C8×C61AGL(1,ℤ/8)11yescharacteristic
120#12332—611nomaximal, Sylow
121C22×C61#44711yescharacteristic
122C2×D61—81no—
123C2×D61—82no—
124C2×D61—82no—
125C2×D61—81no—
126C2×D61—82no—
127C2×D61—81no—
128C4×C61—22no—
129C4×C61—21no—
130C4×C61—41no—
131C4×C61—161no—
132C4×C61#44911yescharacteristic
133C4×C61#45311yescharacteristic
134C4×C61C2×SD3211yescharacteristic
135C4×C61#50911yescharacteristic
136Dic61—81no—
137#3391—611no—
138#2248—611no—
139#2208—611no—
140#1670D6111yescharacteristic, complemented
141#1361—611no—
142Q8⋊C16—611no—
143#1331—611no—
144C2×C61#162111yescharacteristic
145C2×C61#218711yescharacteristic
146C2×C61#219411yescharacteristic
147D61—161no—
148D61—162no—
149#550—1221no—
150C2×SD32—1221no—
151C2×SD32—1222no—
152#494C2×D6111yescharacteristic
153#493—611no—
154#493—1221no—
155#475—21no—
156#459—1222no—
157#459—1221no—
158C8×Q8C2×D6111yescharacteristic
159C4×D8—611no—
160C4×D8—1221no—
161C4⋊C16—611no—
162#358—1221no—
163C4×C16—611no—
164#335C2×D6111yescharacteristic
165#332—21no—
166C61#1233211yescharacteristic, complemented, Sylow
167C2×#41—2441no—
168C2×Q16—21no—
169C2×Q16—21no—
170C2×D8—611no—
171C2×D8—612no—
172C2×D8—1222no—
173C2×D8—1221no—
174C4⋊Q8—21no—
175#127—1222no—
176#127—1221no—
177#121—2442no—
178#121—2441no—
179C4×Q8C22⋊D6111yescharacteristic
180C4×D4—1222no—
181C4×D4—1221no—
182SD32—2444no—
183SD32—2442no—
184C2×C16—1221no—
185C2×C16—1221no—
186#107—611no—
187#106—41no—
188C4⋊C8—21no—
189C4⋊C8—21no—
190C4⋊C8C22⋊D6111yescharacteristic
191#103—41no—
192#102—1222no—
193#102—1221no—
194C4×C8—21no—
195C4×C8C22×D6111yescharacteristic
196#41—4882no—
197#41—4882no—
198C2×Q8—41no—
199C2×Q8#1175819911yescharacteristic
200C2×D4—1221no—
201C2×D4—1222no—
202C2×D4—2442no—
203C2×D4—2442no—
204C2×D4—2441no—
205C2×D4—2441no—
206C22×C4—2442no—
207C22×C4—2441no—
208Q16—42no—
209Q16—41no—
210Q16—41no—
211D8—1221no—
212D8—1221no—
213D8—4882no—
214D8—2442no—
215D8—2441no—
216D8—2441no—
217C2×C8—21no—
218C2×C8—41no—
219C2×C8D4×D6111yescharacteristic
220C2×C8D4×D6111yescharacteristic
221C4⋊C4—21no—
222C4⋊C4—41no—
223C4⋊C4—41no—
224C4⋊C4—1221no—
225C4⋊C4#1175819911yescharacteristic
226C22⋊C4—2442no—
227C22⋊C4—2441no—
228C42—21no—
229C42C2×C22⋊D6111yescharacteristic
230C16—1222no—
231C16—2441no—
232C23—2442no—
233C23—2441no—
234Q8—21no—
235Q8—81no—
236Q8—81no—
237Q8#1451972012yescomplemented
238D4—9761no—
239D4—9762no—
240D4—4884no—
241D4—4881no—
242D4—4881no—
243D4—2441no—
244D4—2442no—
245D4—2441no—
246D4—2442no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—81no—
250C2×C4—4884no—
251C2×C4—4881no—
252C2×C4—4881no—
253C2×C4—2441no—
254C2×C4#1451974511yescharacteristic
255C2×C4C2×#1175819911yescharacteristic
256C2×C4#1451980211yescharacteristic
257C8—21no—
258C8—41no—
259C8—81no—
260C8#1451979811yescharacteristic
261C8#1451980411yescharacteristic
262C22—4881no—
263C22—4882no—
264C22—4882no—
265C22—4881no—
266C22—4882no—
267C22—4881no—
268C22#1683989511yescharacteristic
269C4—22no—
270C4—21no—
271C4—41no—
272C4—161no—
273C4—4881no—
274C4#1683990611yescharacteristic
275C4#1683992811yescharacteristic
276C4C2×#1451972011yescharacteristic
277C4#1684019711yescharacteristic
278C2—9761no—
279C2—9762no—
280C2#2144488211yescharacteristic
281C2#2144774711yescharacteristic
282C2#2144778811yescharacteristic
subgroupG/H
centerC22#16839895
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1670C2
socleC22×C61#447
prime radical#21458794C2
hypercenter#1670D61
hypocenterC61#12332
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8 ◁ #1670

Complements

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

NH ≅ G/Ntype
2. #21448076C2semidirect
3. #21447861C2semidirect
4. #21443864C2semidirect
5. Q8⋊#11758185C2semidirect
6. #21443779C2semidirect
7. C61×#1670C2semidirect
95. Q8×C61SD32semidirect
140. #1670D61semidirect
166. C61#12332semidirect
237. Q8#14519720semidirect

Maximal subgroups

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

subgroupindex
#214587942
#214480762
#214478612
#214438642
Q8⋊#117581852
#214437792
C61×#16702
#1233261