Finite Group Databasebeta

← #29593897

Subgroups — #29593897

Order 15616.

294 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 65 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#21458805C211yesmaximal, characteristic
2#21448048C211yesmaximal, characteristic, complemented
3#21445210C211yesmaximal, characteristic, complemented
4#21443869C211yesmaximal, characteristic, complemented
5#21443797C211yesmaximal, characteristic, complemented
6#21443780C211yesmaximal, characteristic
7C61×#2224C211yesmaximal, characteristic
8#16840482—21no—
9#16840145—21no—
10#16840142C2211yescharacteristic
11#16839983—22no—
12#16839969—21no—
13#16839967—21no—
14C8×Dic122C2211yescharacteristic
15#16839856—21no—
16#16839565—22no—
17C4×#11758185C2211yescharacteristic
18#16839515C2211yescharacteristic
19#16839508—21no—
20C61×#500C2211yescharacteristic
21C4×D8×C61C2211yescharacteristic
22C61×#366—21no—
23C61×C4⋊C16C2211yescharacteristic
24C61×#357—21no—
25C2×Dic244—21no—
26C2×Dic244D412yes—
27C2×#11758202—41no—
28C2×#11758200—22no—
29#14519777—21no—
30#14519770—42no—
31#14519764—22no—
32#14519756—41no—
33C4×Dic122D411yescharacteristic
34#14519742—22no—
35#14519736—41no—
36C2×#11758185—21no—
37C4⋊#92418—21no—
38C4⋊#92418D411yescharacteristic
39#14519706—21no—
40#14519701—41no—
41#14519700—22no—
42C8×Dic61—21no—
43C2×D8×C61D411yescharacteristic
44C4⋊Q8×C61—21no—
45C4×D4×C61—21no—
46C2×C16×C61—21no—
47#107×C61—21no—
48#107×C61—21no—
49#107×C61D411yescharacteristic
50#102×C61—21no—
51C4×C8×C61C2311yescharacteristic
52C2×Q8×C61—41no—
53C2×D4×C61—21no—
54C22×C4×C61—41no—
55C2×Dic122—22no—
56C2×Dic122D811yescharacteristic
57D8×C61—21no—
58D8×C61—21no—
59C2×C8×C61C2×D411yescharacteristic
60C2×C8×C61C2×D411yescharacteristic
61C4⋊C4×C61—21no—
62C4⋊C4×C61—41no—
63C4⋊C4×C61—41no—
64C22⋊C4×C61—41no—
65C42×C61C2×D411yescharacteristic
66C22⋊Dic61—42no—
67C22⋊Dic61—42no—
68#11758202—82no—
69#11758200—82no—
70C4⋊Dic61—41no—
71C4⋊Dic61—41no—
72C4⋊Dic61D811yescharacteristic
73#11758196—21no—
74#11758196—42no—
75C4×Dic61—21no—
76C4×Dic61—42no—
77C2×#92418—21no—
78C2×#92418—41no—
79Dic244—42no—
80Dic244—41no—
81Dic244—41no—
82C16×C61—41no—
83#11758185—41no—
84C23×C61—41no—
85Q8×C61—81no—
86Q8×C61—81no—
87D4×C61—41no—
88D4×C61—41no—
89C2×C4×C61—41no—
90C2×C4×C61—81no—
91C2×C4×C61—81no—
92C2×C4×C61—81no—
93C2×C4×C61#12011yescharacteristic
94C2×C4×C61C2×D811yescharacteristic
95C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
96C2×Dic61—21no—
97C2×Dic61—21no—
98C2×Dic61—42no—
99Dic122—21no—
100Dic122—21no—
101Dic122—42no—
102Dic122—42no—
103C8×C61—21no—
104C8×C61#13511yescharacteristic
105C8×C61#13711yescharacteristic
106#92418—41no—
107#92418—81no—
108#12383—611nomaximal, Sylow
109C22×C61—81no—
110C22×C61—81no—
111C22×C61—81no—
112C22×C61#44711yescharacteristic
113C4×C61—21no—
114C4×C61—81no—
115C4×C61—161no—
116C4×C61#45211yescharacteristic
117C4×C61#45511yescharacteristic
118C4×C61#50811yescharacteristic
119C4×C61#50911yescharacteristic
120Dic61—41no—
121Dic61—41no—
122Dic61—82no—
123#3393—611no—
124#2241—611no—
125#2224D6111yescharacteristic
126#1674—611no—
127#1362—611no—
128Q8⋊C16—611no—
129#1331—611no—
130C2×C61—161no—
131C2×C61#164111yescharacteristic
132C2×C61#218611yescharacteristic
133C2×C61#219511yescharacteristic
134#556—1221no—
135#500C2×D6111yescharacteristic
136#495—1221no—
137#494—611no—
138#464—1222no—
139#462—1221no—
140#461—1221no—
141C8×Q8—611no—
142C4×Q16—1221no—
143C4×D8C2×D6111yescharacteristic
144#366—21no—
145C4⋊C16C2×D6111yescharacteristic
146#358—1222no—
147#357—21no—
148C4×C16—611no—
149#335—611no—
150#332—1221no—
151C61#1238311yescharacteristic, complemented, Sylow
152C2×Q16—612no—
153C2×Q16—1221no—
154C2×Q16—2441no—
155C2×SD16—1222no—
156C2×D8C22⋊D6111yescharacteristic
157C4⋊Q8—21no—
158C4⋊Q8—1221no—
159#126—2442no—
160#124—1222no—
161C22⋊Q8—2441no—
162C4×Q8—611no—
163C4×Q8—1222no—
164C4×D4—21no—
165#117—2441no—
166C2×C16—21no—
167C2×C16—1221no—
168#107—21no—
169#107—21no—
170#107C22⋊D6111yescharacteristic
171C4⋊C8—611no—
172C4⋊C8—1221no—
173C4⋊C8—1221no—
174#103—1222no—
175#103—2441no—
176#102—21no—
177C4×C8—1221no—
178C4×C8C22×D6111yescharacteristic
179C2×Q8—41no—
180C2×Q8—611no—
181C2×Q8—1222no—
182C2×D4—21no—
183C22×C4—41no—
184Q16—4882no—
185Q16—2442no—
186Q16—2441no—
187Q16—2441no—
188SD16—4882no—
189D8—21no—
190D8—21no—
191C2×C8—1221no—
192C2×C8—2441no—
193C2×C8D4×D6111yescharacteristic
194C2×C8C2×C22⋊D6111yescharacteristic
195C4⋊C4—21no—
196C4⋊C4—41no—
197C4⋊C4—41no—
198C4⋊C4—611no—
199C4⋊C4—1221no—
200C4⋊C4—2442no—
201C4⋊C4—2441no—
202C4⋊C4—2441no—
203C22⋊C4—41no—
204C22⋊C4—2442no—
205C22⋊C4—2442no—
206C42—1221no—
207C42—2442no—
208C42D4×D6111yescharacteristic
209C16—41no—
210C16—2441no—
211C23—41no—
212Q8—81no—
213Q8—81no—
214Q8—1221no—
215Q8—1221no—
216Q8—2442no—
217Q8—2442no—
218D4—41no—
219D4—41no—
220C2×C4—41no—
221C2×C4—81no—
222C2×C4—81no—
223C2×C4—81no—
224C2×C4—1221no—
225C2×C4—1221no—
226C2×C4—2442no—
227C2×C4#1451974511yescharacteristic
228C2×C4D8×D6111yescharacteristic
229C2×C4#1451980111yescharacteristic
230C8—21no—
231C8—4881no—
232C8—2441no—
233C8#1451979711yescharacteristic
234C8#1451980811yescharacteristic
235C22—81no—
236C22—81no—
237C22—81no—
238C22#1683989411yescharacteristic
239C4—21no—
240C4—81no—
241C4—161no—
242C4—4882no—
243C4—2441no—
244C4—2441no—
245C4#1683992211yescharacteristic
246C4#1683993811yescharacteristic
247C4#1684019111yescharacteristic
248C4#1684019611yescharacteristic
249C2—161no—
250C2#2144501111yescharacteristic
251C2#2144773911yescharacteristic
252C2#2144779411yescharacteristic
subgroupG/H
centerC22#16839894
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#2224C2
socleC22×C61#447
prime radicalC2×D8×C61D4
hypercenter#2224D61
hypocenterC61#12383
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2224

Complements

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

NH ≅ G/Ntype
2. #21448048C2semidirect
3. #21445210C2semidirect
4. #21443869C2semidirect
5. #21443797C2semidirect
151. C61#12383semidirect

Maximal subgroups

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

subgroupindex
#214588052
#214480482
#214452102
#214438692
#214437972
#214437802
C61×#22242
#1238361