Finite Group Databasebeta

← #29593548

Subgroups — #29593548

Order 15616.

362 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 67 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#21458793C211yesmaximal, characteristic
2#21448076C211yesmaximal, characteristic, complemented
3#21445186C211yesmaximal, characteristic, complemented
4#21443866C211yesmaximal, characteristic, complemented
5#21443797C211yesmaximal, characteristic, complemented
6#21443780C211yesmaximal, characteristic, complemented
7C61×#2208C211yesmaximal, characteristic, complemented
8#16840433—21no—
9C2×#14519720—22no—
10#16840139C2211yescharacteristic
11#16840137—21no—
12#16840044—21no—
13#16839957—21no—
14#16839956—22no—
15C8×Dic122C2211yescharacteristic
16#16839844—21no—
17C4×#11758185C2211yescharacteristic
18#16839515C2211yescharacteristic
19#16839508—21no—
20C2×SD32×C61—21no—
21C61×#494C2211yescharacteristic
22C4×D8×C61C2211yescharacteristic
23C61×C4⋊C16C2211yescharacteristic
24C61×#358—21no—
25C2×#11758222—41no—
26C2×D488—21no—
27C2×D488D412yes—
28C2×#11758199—22no—
29#14519774—21no—
30#14519773—22no—
31#14519751—41no—
32#14519750—42no—
33C4×Dic122D411yescharacteristic
34#14519739—22no—
35#14519720—44no—
36C2×#11758185—21no—
37#14519708—41no—
38C4⋊#92418—21no—
39C4⋊#92418D411yescharacteristic
40#14519706—21no—
41#14519700—41no—
42#14519697—22no—
43C8×Dic61—21no—
44C2×Q16×C61—21no—
45C2×Q16×C61—21no—
46C2×D8×C61D411yescharacteristic
47C4⋊Q8×C61—21no—
48C4×D4×C61—21no—
49SD32×C61—42no—
50C2×C16×C61—21no—
51#107×C61D411yescharacteristic
52#102×C61—21no—
53C4×C8×C61C2311yescharacteristic
54C2×Q8×C61—41no—
55C2×D4×C61—21no—
56C22×C4×C61—41no—
57C2×C22⋊D61—42no—
58C2×C22⋊D61—42no—
59#11758222—82no—
60#11758222—82no—
61C2×D244—22no—
62C2×D244—41no—
63C2×D244—41no—
64C2×C4×D61—42no—
65C2×Dic122D811yescharacteristic
66Q16×C61—42no—
67Q16×C61—41no—
68Q16×C61—41no—
69D8×C61—21no—
70D8×C61—21no—
71C2×C8×C61C2×D411yescharacteristic
72C2×C8×C61C2×D411yescharacteristic
73C4⋊C4×C61—21no—
74C4⋊C4×C61—41no—
75C4⋊C4×C61—41no—
76C22⋊C4×C61—41no—
77C42×C61C2×D411yescharacteristic
78#11758199—82no—
79#11758198—42no—
80C4⋊Dic61D811yescharacteristic
81#11758196—21no—
82C4×Dic61—21no—
83C2×#92418—21no—
84C2×#92418—41no—
85D488—42no—
86D488—41no—
87D488—41no—
88C16×C61—41no—
89#11758185—22no—
90C23×C61—41no—
91C22×D61—42no—
92Q8×C61—81no—
93Q8×C61—81no—
94D4×C61—41no—
95D4×C61—41no—
96C2×C4×C61—41no—
97C2×C4×C61—81no—
98C2×C4×C61—81no—
99C2×C4×C61—81no—
100C2×C4×C61#12011yescharacteristic
101C2×C4×C61C2×D811yescharacteristic
102C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
103C22⋊D61—84no—
104C22⋊D61—162no—
105C2×Dic61—21no—
106C2×Dic61—21no—
107D244—42no—
108D244—42no—
109D244—81no—
110D244—81no—
111D244—161no—
112C4×D61—84no—
113Dic122—21no—
114Dic122SD3212yescomplemented
115C8×C61—21no—
116C8×C61#13511yescharacteristic
117C8×C61AGL(1,ℤ/8)11yescharacteristic
118#92418—41no—
119#92418—81no—
120#12332—611nomaximal, Sylow
121C22×C61—81no—
122C22×C61—81no—
123C22×C61—81no—
124C22×C61#44711yescharacteristic
125C2×D61—82no—
126C2×D61—82no—
127C2×D61—82no—
128C4×C61—21no—
129C4×C61—81no—
130C4×C61—161no—
131C4×C61#44911yescharacteristic
132C4×C61#45311yescharacteristic
133C4×C61C2×SD3211yescharacteristic
134C4×C61#50911yescharacteristic
135Dic61—22no—
136Dic61—41no—
137#3391—611no—
138#2248—611no—
139#2208D6111yescharacteristic, complemented
140#1670—611no—
141#1361—611no—
142Q8⋊C16—611no—
143#1331—611no—
144C2×C61—161no—
145C2×C61#162111yescharacteristic
146C2×C61#218711yescharacteristic
147C2×C61#219411yescharacteristic
148D61—162no—
149#550—1221no—
150C2×SD32—21no—
151C2×SD32—1222no—
152#494C2×D6111yescharacteristic
153#493—611no—
154#493—1221no—
155#475—1221no—
156#459—1222no—
157#459—1221no—
158C8×Q8—611no—
159C4×D8—1221no—
160C4×D8C2×D6111yescharacteristic
161C4⋊C16C2×D6111yescharacteristic
162#358—21no—
163C4×C16—611no—
164#335—611no—
165#332—1221no—
166C61#1233211yescharacteristic, complemented, Sylow
167C2×#41—2441no—
168C2×Q16—21no—
169C2×Q16—21no—
170C2×D8—612no—
171C2×D8—1222no—
172C2×D8—1221no—
173C2×D8C22⋊D6111yescharacteristic
174C4⋊Q8—21no—
175#127—1222no—
176#127—1221no—
177#121—2442no—
178#121—2441no—
179C4×Q8—611no—
180C4×D4—21no—
181C4×D4—1222no—
182SD32—42no—
183SD32—2444no—
184C2×C16—21no—
185C2×C16—1221no—
186#107C22⋊D6111yescharacteristic
187#106—2441no—
188C4⋊C8—611no—
189C4⋊C8—1221no—
190C4⋊C8—1221no—
191#103—2441no—
192#102—21no—
193#102—1222no—
194C4×C8—1221no—
195C4×C8C22×D6111yescharacteristic
196#41—4882no—
197#41—4882no—
198C2×Q8—41no—
199C2×Q8—611no—
200C2×D4—21no—
201C2×D4—1222no—
202C2×D4—2442no—
203C2×D4—2442no—
204C2×D4—2441no—
205C2×D4—2441no—
206C22×C4—41no—
207C22×C4—2442no—
208Q16—42no—
209Q16—41no—
210Q16—41no—
211D8—21no—
212D8—21no—
213D8—4882no—
214D8—2442no—
215D8—2441no—
216D8—2441no—
217C2×C8—1221no—
218C2×C8—2441no—
219C2×C8D4×D6111yescharacteristic
220C2×C8C2×C22⋊D6111yescharacteristic
221C4⋊C4—21no—
222C4⋊C4—41no—
223C4⋊C4—41no—
224C4⋊C4—611no—
225C4⋊C4—1221no—
226C22⋊C4—41no—
227C22⋊C4—2442no—
228C42—1221no—
229C42D4×D6111yescharacteristic
230C16—41no—
231C16—1222no—
232C23—41no—
233C23—2442no—
234Q8—81no—
235Q8—81no—
236Q8—612no—
237Q8—1221no—
238D4—41no—
239D4—41no—
240D4—9761no—
241D4—9762no—
242D4—4884no—
243D4—4881no—
244D4—4881no—
245D4—2442no—
246D4—2442no—
247C2×C4—41no—
248C2×C4—81no—
249C2×C4—81no—
250C2×C4—81no—
251C2×C4—1221no—
252C2×C4—1221no—
253C2×C4—4884no—
254C2×C4#1451974511yescharacteristic
255C2×C4D8×D6111yescharacteristic
256C2×C4#1451980111yescharacteristic
257C8—21no—
258C8—4881no—
259C8—2441no—
260C8#1451979711yescharacteristic
261C8#1451980311yescharacteristic
262C22—81no—
263C22—81no—
264C22—81no—
265C22—4882no—
266C22—4882no—
267C22—4882no—
268C22#1683989411yescharacteristic
269C4—21no—
270C4—81no—
271C4—161no—
272C4—1222no—
273C4—2441no—
274C4#1683990511yescharacteristic
275C4#1683992811yescharacteristic
276C4SD32×D6111yescharacteristic
277C4#1684019911yescharacteristic
278C2—161no—
279C2—9762no—
280C2#2144488311yescharacteristic
281C2#2144774611yescharacteristic
282C2#2144778711yescharacteristic
subgroupG/H
centerC22#16839894
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#2208C2
socleC22×C61#447
prime radical#21458793C2
hypercenter#2208D61
hypocenterC61#12332
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2208

Complements

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

NH ≅ G/Ntype
2. #21448076C2semidirect
3. #21445186C2semidirect
4. #21443866C2semidirect
5. #21443797C2semidirect
6. #21443780C2semidirect
7. C61×#2208C2semidirect
114. Dic122SD32semidirect
139. #2208D61semidirect
166. C61#12332semidirect

Maximal subgroups

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

subgroupindex
#214587932
#214480762
#214451862
#214438662
#214437972
#214437802
C61×#22082
#1233261