Finite Group Databasebeta

← #29593694

Subgroups — #29593694

Order 15616.

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

normal subgroups only

This group has 298 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#21458711C211yesmaximal, characteristic, complemented
2#21448042C211yesmaximal, characteristic
3#21447856C211yesmaximal, characteristic
4#21443875C211yesmaximal, characteristic, complemented
5Q8⋊#11758185C211yesmaximal, characteristic, complemented
6#21443782C211yesmaximal, characteristic, complemented
7C61×#1668C211yesmaximal, characteristic
8#16840490—21no—
9C2×#14519721—21no—
10#16840167C2211yescharacteristic
11#16840164—21no—
12#16840070—22no—
13#16840048—21no—
14C4×Dic244—21no—
15C4×Dic244C2211yescharacteristic
16C4⋊#11758185C2211yescharacteristic
17#16839563—22no—
18#16839563—21no—
19C4×#11758185C2211yescharacteristic
20C61×#493C2211yescharacteristic
21C61×#460—21no—
22C8×Q8×C61C2211yescharacteristic
23C61×#335C2211yescharacteristic
24C61×#331—21no—
25C2×Dic244D411yescharacteristic
26#14519777—21no—
27#14519775—41no—
28#14519769—22no—
29#14519767—42no—
30C4×Dic122—22no—
31C4×Dic122—21no—
32#14519742—41no—
33#14519721—42no—
34C2×#11758185—21no—
35C2×#11758185—21no—
36#14519711—21no—
37#14519711D412yes—
38#14519711D411yescharacteristic
39#14519709—22no—
40#14519702—22no—
41#14519702—21no—
42C2×SD16×C61—41no—
43C2×D8×C61—21no—
44C2×D8×C61—21no—
45#127×C61—21no—
46C4×Q8×C61D411yescharacteristic
47C4⋊C8×C61—21no—
48C4⋊C8×C61—21no—
49C4⋊C8×C61D411yescharacteristic
50#102×C61—41no—
51C4×C8×C61—21no—
52C4×C8×C61C2311yescharacteristic
53C2×Q8×C61D811yescharacteristic
54C2×D4×C61—41no—
55C2×D4×C61—41no—
56C2×D4×C61—41no—
57C2×Dic122—21no—
58C2×Dic122—41no—
59SD16×C61—82no—
60D8×C61—42no—
61D8×C61—41no—
62D8×C61—41no—
63C2×C8×C61—21no—
64C2×C8×C61—41no—
65C2×C8×C61C2×D411yescharacteristic
66C2×C8×C61C2×D411yescharacteristic
67C4⋊C4×C61—21no—
68C4⋊C4×C61D811yescharacteristic
69C42×C61—21no—
70C42×C61C2×D411yescharacteristic
71C4⋊Dic61—21no—
72C4⋊Dic61—22no—
73C4⋊Dic61—41no—
74#11758196—42no—
75#11758196—42no—
76#11758196—42no—
77#11758196—41no—
78C4×Dic61—42no—
79C4×Dic61—41no—
80Dic244—21no—
81Dic244SD1612yescomplemented
82#11758185—41no—
83#11758185—41no—
84C23×C61—81no—
85Q8×C61—21no—
86Q8×C61—21no—
87D4×C61—81no—
88D4×C61—81no—
89D4×C61—81no—
90D4×C61—81no—
91D4×C61—161no—
92C2×C4×C61—21no—
93C2×C4×C61—21no—
94C2×C4×C61#12011yescharacteristic
95C2×C4×C61C2×D811yescharacteristic
96C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
97C2×Dic61—41no—
98C2×Dic61—41no—
99C2×Dic61—42no—
100Dic122—22no—
101Dic122—41no—
102Dic122—81no—
103Dic122—81no—
104C8×C61—21no—
105C8×C61—41no—
106C8×C61—81no—
107C8×C61C2×SD1611yescharacteristic
108C8×C61#13711yescharacteristic
109#12353—611nomaximal, Sylow
110C22×C61—161no—
111C22×C61—161no—
112C22×C61—161no—
113C22×C61#44711yescharacteristic
114C4×C61—21no—
115C4×C61—41no—
116C4×C61—41no—
117C4×C61#44811yescharacteristic
118C4×C61#45411yescharacteristic
119C4×C61#50811yescharacteristic
120C4×C61#50911yescharacteristic
121Dic61—42no—
122Dic61—82no—
123Dic61—81no—
124#3383—611no—
125#2240—611no—
126#2207—611no—
127#1668D6111yescharacteristic
128#1364—611no—
129Q8⋊C16—611no—
130#1332—611no—
131C2×C61—321no—
132C2×C61#162711yescharacteristic
133C2×C61#218611yescharacteristic
134C2×C61#219311yescharacteristic
135#557—1221no—
136C2×SD32—1221no—
137#500—611no—
138#499—1221no—
139#493C2×D6111yescharacteristic
140#479—1222no—
141#475—1221no—
142#460—21no—
143C8×Q8C2×D6111yescharacteristic
144C4×Q16—611no—
145C4×Q16—1221no—
146C4⋊C16—611no—
147#357—1221no—
148#357—1222no—
149C4×C16—611no—
150#335C2×D6111yescharacteristic
151#331—21no—
152C61#1235311yescharacteristic, complemented, Sylow
153C2×Q16—611no—
154C2×SD16—41no—
155C2×D8—21no—
156C2×D8—21no—
157C4⋊Q8—1221no—
158C4⋊Q8—2441no—
159#127—21no—
160#125—1222no—
161#125—2442no—
162C4×Q8—1222no—
163C4×Q8—1221no—
164C4×Q8—2441no—
165C4×Q8C22⋊D6111yescharacteristic
166SD32—2442no—
167C2×C16—1221no—
168C2×C16—1221no—
169#107—611no—
170#107—612no—
171#107—1221no—
172#106—1222no—
173C4⋊C8—21no—
174C4⋊C8—21no—
175C4⋊C8C22⋊D6111yescharacteristic
176#103—1222no—
177#103—1221no—
178#102—41no—
179C4×C8—21no—
180C4×C8C22×D6111yescharacteristic
181C2×Q8—1221no—
182C2×Q8—2441no—
183C2×Q8#1175819911yescharacteristic
184C2×D4—41no—
185C2×D4—41no—
186C2×D4—41no—
187Q16—612no—
188Q16—1221no—
189SD16—82no—
190D8—42no—
191D8—41no—
192D8—41no—
193C2×C8—21no—
194C2×C8—41no—
195C2×C8D4×D6111yescharacteristic
196C2×C8D4×D6111yescharacteristic
197C4⋊C4—21no—
198C4⋊C4—1221no—
199C4⋊C4—1222no—
200C4⋊C4—2442no—
201C4⋊C4—2442no—
202C4⋊C4—2442no—
203C4⋊C4—2441no—
204C4⋊C4—2441no—
205C4⋊C4#1175819911yescharacteristic
206C42—21no—
207C42—2442no—
208C42—2441no—
209C42C2×C22⋊D6111yescharacteristic
210C16—2441no—
211C16—2441no—
212C23—81no—
213Q8—21no—
214Q8—21no—
215Q8—1222no—
216Q8—4881no—
217Q8—4881no—
218Q8—2441no—
219D4—81no—
220D4—81no—
221D4—81no—
222D4—81no—
223D4—161no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—2441no—
227C2×C4—2442no—
228C2×C4—2441no—
229C2×C4#1451974511yescharacteristic
230C2×C4C2×#1175819911yescharacteristic
231C2×C4#1451980211yescharacteristic
232C8—21no—
233C8—41no—
234C8—81no—
235C8SD16×D6111yescharacteristic
236C8#1451980611yescharacteristic
237C22—161no—
238C22—161no—
239C22—161no—
240C22#1683989511yescharacteristic
241C4—21no—
242C4—41no—
243C4—41no—
244C4—4882no—
245C4—4881no—
246C4—2442no—
247C4#1683989911yescharacteristic
248C4#1683993311yescharacteristic
249C4#1684019211yescharacteristic
250C4#1684019811yescharacteristic
251C2—321no—
252C2#2144492011yescharacteristic
253C2#2144774011yescharacteristic
254C2#2144778111yescharacteristic
subgroupG/H
centerC22#16839895
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1668C2
socleC22×C61#447
prime radicalC61×#493C22
hypercenter#1668D61
hypocenterC61#12353
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8 ◁ #1668

Complements

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

NH ≅ G/Ntype
1. #21458711C2semidirect
4. #21443875C2semidirect
5. Q8⋊#11758185C2semidirect
6. #21443782C2semidirect
81. Dic244SD16semidirect
152. C61#12353semidirect

Maximal subgroups

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

subgroupindex
#214587112
#214480422
#214478562
#214438752
Q8⋊#117581852
#214437822
C61×#16682
#1235361