Finite Group Databasebeta

← #29593737

Subgroups — #29593737

Order 15616.

296 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 69 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#21458684C211yesmaximal, characteristic
2#21448046C211yesmaximal, characteristic, complemented
3#21445186C211yesmaximal, characteristic, complemented
4#21443876C211yesmaximal, characteristic, complemented
5#21443797C211yesmaximal, characteristic, complemented
6#21443780C211yesmaximal, characteristic
7C61×#2208C211yesmaximal, characteristic
8#16840469—21no—
9#16840167C2211yescharacteristic
10#16840163—21no—
11#16840060—22no—
12#16840052—21no—
13#16840044—21no—
14C8×Dic122C2211yescharacteristic
15D8×Dic61—21no—
16#16839566—22no—
17C4×#11758185C2211yescharacteristic
18#16839515C2211yescharacteristic
19#16839508—21no—
20C2×SD32×C61—21no—
21C61×#494C2211yescharacteristic
22C4×D8×C61C2211yescharacteristic
23C61×C4⋊C16C2211yescharacteristic
24C61×#358—21no—
25#14519777—21no—
26#14519768—22no—
27#14519756—41no—
28#14519754—42no—
29C4×Dic122D411yescharacteristic
30D4×Dic61—22no—
31C2×C4⋊Dic61—41no—
32C2×#11758185—21no—
33#14519711—21no—
34#14519711D412yes—
35#14519708—22no—
36#14519708—41no—
37C4⋊#92418—21no—
38C4⋊#92418D411yescharacteristic
39#14519706—21no—
40#14519700—41no—
41#14519698—22no—
42C8×Dic61—21no—
43C2×Q16×C61—21no—
44C2×Q16×C61—21no—
45C2×D8×C61D411yescharacteristic
46C4⋊Q8×C61—21no—
47C4×D4×C61—21no—
48SD32×C61—42no—
49C2×C16×C61—21no—
50#107×C61D411yescharacteristic
51#102×C61—21no—
52C4×C8×C61C2311yescharacteristic
53C2×Q8×C61—41no—
54C2×D4×C61—21no—
55C22×C4×C61—41no—
56C22×Dic61—42no—
57C2×Dic122—41no—
58C2×Dic122D811yescharacteristic
59Q16×C61—42no—
60Q16×C61—41no—
61Q16×C61—41no—
62D8×C61—21no—
63D8×C61SD1612yes—
64C2×C8×C61C2×D411yescharacteristic
65C2×C8×C61C2×D411yescharacteristic
66C4⋊C4×C61—21no—
67C4⋊C4×C61—41no—
68C4⋊C4×C61—41no—
69C22⋊C4×C61—41no—
70C42×C61C2×D411yescharacteristic
71C22⋊Dic61—42no—
72C4⋊Dic61—22no—
73C4⋊Dic61—42no—
74C4⋊Dic61—41no—
75C4⋊Dic61D811yescharacteristic
76#11758196—21no—
77#11758196—42no—
78C4×Dic61—21no—
79C2×#92418—21no—
80C2×#92418—41no—
81C16×C61—41no—
82#11758185—41no—
83C23×C61—41no—
84Q8×C61—81no—
85Q8×C61—81no—
86D4×C61—22no—
87D4×C61—41no—
88C2×C4×C61—41no—
89C2×C4×C61—81no—
90C2×C4×C61—81no—
91C2×C4×C61—81no—
92C2×C4×C61#12011yescharacteristic
93C2×C4×C61C2×D811yescharacteristic
94C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
95C2×Dic61—21no—
96C2×Dic61—21no—
97C2×Dic61—42no—
98C2×Dic61—162no—
99Dic122—21no—
100Dic122—21no—
101Dic122—161no—
102C8×C61—21no—
103C8×C61C2×SD1611yescharacteristic
104C8×C61#13711yescharacteristic
105#92418—41no—
106#92418—81no—
107#12359—611nomaximal, Sylow
108C22×C61—42no—
109C22×C61—81no—
110C22×C61—81no—
111C22×C61#44711yescharacteristic
112C4×C61—21no—
113C4×C61—81no—
114C4×C61—161no—
115C4×C61#44811yescharacteristic
116C4×C61#45411yescharacteristic
117C4×C61#50811yescharacteristic
118C4×C61#51011yescharacteristic
119Dic61—41no—
120Dic61—41no—
121Dic61—82no—
122#3380—611no—
123#2241—611no—
124#2208D6111yescharacteristic
125#1670—611no—
126#1365—611no—
127Q8⋊C16—611no—
128#1331—611no—
129C2×C61—82no—
130C2×C61#162711yescharacteristic
131C2×C61#218911yescharacteristic
132C2×C61#219411yescharacteristic
133#554—1221no—
134C2×SD32—21no—
135#500—611no—
136#499—1221no—
137#494C2×D6111yescharacteristic
138#478—1222no—
139#476—1221no—
140#475—1221no—
141C8×Q8—611no—
142C4×D8—1221no—
143C4×D8C2×D6111yescharacteristic
144C4⋊C16C2×D6111yescharacteristic
145#358—21no—
146#358—1222no—
147C4×C16—611no—
148#335—611no—
149#332—1221no—
150C61#1235911yescharacteristic, complemented, Sylow
151C2×Q16—21no—
152C2×Q16—21no—
153C2×D8C22⋊D6111yescharacteristic
154C4⋊Q8—21no—
155C4⋊Q8—1221no—
156#125—1222no—
157C22⋊Q8—2442no—
158C22⋊Q8—2441no—
159C4×Q8—611no—
160C4×D4—21no—
161C4×D4—1222no—
162C2×C4⋊C4—2441no—
163SD32—42no—
164C2×C16—21no—
165C2×C16—1221no—
166#107—612no—
167#107—1221no—
168#107C22⋊D6111yescharacteristic
169#106—1222no—
170#106—2441no—
171C4⋊C8—611no—
172C4⋊C8—1221no—
173C4⋊C8—1221no—
174#103—2441no—
175#102—21no—
176#102—1222no—
177C4×C8—1221no—
178C4×C8C22×D6111yescharacteristic
179C2×Q8—41no—
180C2×Q8—611no—
181C2×Q8—2441no—
182C2×D4—21no—
183C22×C4—41no—
184C22×C4—2442no—
185Q16—42no—
186Q16—41no—
187Q16—41no—
188D8—21no—
189D8#1175820012yes—
190C2×C8—1221no—
191C2×C8—2441no—
192C2×C8D4×D6111yescharacteristic
193C2×C8C2×C22⋊D6111yescharacteristic
194C4⋊C4—21no—
195C4⋊C4—41no—
196C4⋊C4—41no—
197C4⋊C4—611no—
198C4⋊C4—1221no—
199C4⋊C4—1222no—
200C4⋊C4—2442no—
201C4⋊C4—2442no—
202C4⋊C4—2441no—
203C22⋊C4—41no—
204C22⋊C4—2442no—
205C42—1221no—
206C42D4×D6111yescharacteristic
207C16—41no—
208C16—2441no—
209C23—41no—
210Q8—81no—
211Q8—81no—
212Q8—1221no—
213Q8—1221no—
214Q8—9761no—
215D4—22no—
216D4—41no—
217C2×C4—41no—
218C2×C4—81no—
219C2×C4—81no—
220C2×C4—81no—
221C2×C4—1221no—
222C2×C4—1221no—
223C2×C4—9762no—
224C2×C4—2442no—
225C2×C4#1451974511yescharacteristic
226C2×C4D8×D6111yescharacteristic
227C2×C4#1451980111yescharacteristic
228C8—21no—
229C8—4881no—
230C8—2441no—
231C8C2×#1175820011yescharacteristic
232C8#1451980711yescharacteristic
233C22—42no—
234C22—81no—
235C22—81no—
236C22#1683989411yescharacteristic
237C4—21no—
238C4—81no—
239C4—161no—
240C4—4882no—
241C4—2441no—
242C4—2441no—
243C4#1683990011yescharacteristic
244C4#1683993311yescharacteristic
245C4#1684019311yescharacteristic
246C4#1684020111yescharacteristic
247C2—82no—
248C2#2144492111yescharacteristic
249C2#2144775611yescharacteristic
250C2#2144778711yescharacteristic
subgroupG/H
centerC22#16839894
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#2208C2
socleC22×C61#447
prime radicalC2×D8×C61D4
hypercenter#2208D61
hypocenterC61#12359
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. #21448046C2semidirect
3. #21445186C2semidirect
4. #21443876C2semidirect
5. #21443797C2semidirect
150. C61#12359semidirect

Maximal subgroups

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

subgroupindex
#214586842
#214480462
#214451862
#214438762
#214437972
#214437802
C61×#22082
#1235961