Finite Group Databasebeta

← #29593573

Subgroups — #29593573

Order 15616.

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

normal subgroups only

This group has 312 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#21448072C211yesmaximal, characteristic, complemented
3#21447864C211yesmaximal, characteristic
4#21445190C211yesmaximal, characteristic, complemented
5#21443867C211yesmaximal, characteristic, complemented
6#21443799C211yesmaximal, characteristic, complemented
7C61×#1331C211yesmaximal, characteristic
8#16840482—21no—
9C2×Dic488—22no—
10C2×#14519721—21no—
11#16840145—21no—
12#16840142C2211yescharacteristic
13#16840142C2211yescharacteristic
14#16840048—21no—
15#16839983—22no—
16#16839967—21no—
17C8×Dic122C2211yescharacteristic
18#16839856—21no—
19C4⋊#11758185C2211yescharacteristic
20#16839565—21no—
21#16839507—21no—
22C4×D8×C61C2211yescharacteristic
23C4×C16×C61C2211yescharacteristic
24C61×#335C2211yescharacteristic
25C2×Dic244—21no—
26C2×Dic244—21no—
27C2×Dic244—21no—
28C2×Dic244D412yes—
29C2×#11758200—22no—
30#14519777—21no—
31#14519777—21no—
32#14519770—42no—
33#14519764—22no—
34#14519756—41no—
35C4×Dic122D411yescharacteristic
36#14519742—22no—
37#14519736—41no—
38Dic488—44no—
39#14519721—42no—
40C2×#11758185—21no—
41#14519709—41no—
42C4⋊#92418D411yescharacteristic
43#14519706—21no—
44#14519702—41no—
45#14519700—22no—
46C8×Dic61—21no—
47C2×D8×C61D411yescharacteristic
48C4×D4×C61—21no—
49C2×C16×C61—21no—
50#107×C61D411yescharacteristic
51C4⋊C8×C61—21no—
52#102×C61—21no—
53C4×C8×C61C2311yescharacteristic
54C2×D4×C61—21no—
55C22×C4×C61—41no—
56C2×Dic122—22no—
57C2×Dic122—41no—
58C2×Dic122D811yescharacteristic
59D8×C61—21no—
60D8×C61—21no—
61C2×C8×C61—41no—
62C2×C8×C61C2×D411yescharacteristic
63C2×C8×C61C2×D411yescharacteristic
64C4⋊C4×C61—21no—
65C22⋊C4×C61—41no—
66C42×C61C2×D411yescharacteristic
67C22⋊Dic61—42no—
68C22⋊Dic61—42no—
69#11758200—82no—
70C4⋊Dic61—41no—
71C4⋊Dic61—41no—
72C4⋊Dic61—41no—
73C4⋊Dic61—41no—
74C4⋊Dic61D811yescharacteristic
75#11758196—21no—
76#11758196—42no—
77C4×Dic61—21no—
78C4×Dic61—42no—
79C2×#92418—21no—
80Dic244—42no—
81Dic244—42no—
82Dic244—41no—
83Dic244—41no—
84Dic244—41no—
85Dic244—41no—
86C16×C61—22no—
87#11758185—41no—
88C23×C61—41no—
89D4×C61—41no—
90D4×C61—41no—
91C2×C4×C61—41no—
92C2×C4×C61—81no—
93C2×C4×C61—81no—
94C2×C4×C61#12011yescharacteristic
95C2×C4×C61C2×D811yescharacteristic
96C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
97C2×Dic61—21no—
98C2×Dic61—21no—
99C2×Dic61—42no—
100C2×Dic61—81no—
101Dic122—21no—
102Dic122—21no—
103Dic122—42no—
104Dic122—42no—
105Dic122—81no—
106Dic122—81no—
107C8×C61—21no—
108C8×C61—81no—
109C8×C61#13511yescharacteristic
110C8×C61AGL(1,ℤ/8)11yescharacteristic
111#92418—41no—
112#12335—611nomaximal, Sylow
113C22×C61—81no—
114C22×C61—81no—
115C22×C61—81no—
116C22×C61#44711yescharacteristic
117C4×C61—21no—
118C4×C61—81no—
119C4×C61#44911yescharacteristic
120C4×C61#45311yescharacteristic
121C4×C61#50811yescharacteristic
122C4×C61#51011yescharacteristic
123Dic61—41no—
124Dic61—41no—
125Dic61—82no—
126Dic61—161no—
127#3393—611no—
128#2247—611no—
129#2208—611no—
130#1670—611no—
131#1362—611no—
132Q8⋊C16—611no—
133#1331D6111yescharacteristic
134C2×C61—161no—
135C2×C61#162111yescharacteristic
136C2×C61#218911yescharacteristic
137C2×C61#219511yescharacteristic
138#556—1221no—
139C2×Q32—1222no—
140C2×SD32—1221no—
141#495—1221no—
142#494—611no—
143#494—611no—
144#475—1221no—
145#464—1222no—
146#461—1221no—
147C8×Q8—611no—
148C4×Q16—1221no—
149C4×D8C2×D6111yescharacteristic
150C4⋊C16—611no—
151#358—1221no—
152C4×C16C2×D6111yescharacteristic
153#335C2×D6111yescharacteristic
154#332—1221no—
155C61#1233511yescharacteristic, complemented, Sylow
156C2×Q16—612no—
157C2×Q16—1221no—
158C2×Q16—1221no—
159C2×Q16—1221no—
160C2×SD16—1222no—
161C2×D8D24411yescharacteristic
162C4⋊Q8—1221no—
163C4⋊Q8—1221no—
164#126—2442no—
165#124—1222no—
166C22⋊Q8—2441no—
167C4×Q8—611no—
168C4×Q8—1222no—
169C4×D4—21no—
170#117—2441no—
171Q32—2444no—
172SD32—2442no—
173C2×C16—21no—
174C2×C16—1221no—
175#107D24411yescharacteristic
176#106—2441no—
177C4⋊C8—21no—
178C4⋊C8—611no—
179C4⋊C8—1221no—
180#103—1222no—
181#103—2441no—
182#102—21no—
183C4×C8—1221no—
184C4×C8C22×D6111yescharacteristic
185C2×Q8—611no—
186C2×Q8—1222no—
187C2×Q8—2441no—
188C2×D4—21no—
189C22×C4—41no—
190Q16—2442no—
191Q16—2442no—
192Q16—2441no—
193Q16—2441no—
194Q16—2441no—
195Q16—2441no—
196SD16—4882no—
197D8—21no—
198D8—21no—
199C2×C8—41no—
200C2×C8—1221no—
201C2×C8C2×D24411yescharacteristic
202C2×C8D4×D6111yescharacteristic
203C4⋊C4—21no—
204C4⋊C4—611no—
205C4⋊C4—1221no—
206C4⋊C4—2442no—
207C4⋊C4—2441no—
208C4⋊C4—2441no—
209C4⋊C4—2441no—
210C4⋊C4—2441no—
211C22⋊C4—41no—
212C22⋊C4—2442no—
213C22⋊C4—2442no—
214C42—1221no—
215C42—2442no—
216C42D4×D6111yescharacteristic
217C16—22no—
218C16—2441no—
219C23—41no—
220Q8—1221no—
221Q8—1221no—
222Q8—4881no—
223Q8—4881no—
224Q8—2442no—
225Q8—2442no—
226D4—41no—
227D4—41no—
228C2×C4—41no—
229C2×C4—81no—
230C2×C4—81no—
231C2×C4—1221no—
232C2×C4—1221no—
233C2×C4—4881no—
234C2×C4—2442no—
235C2×C4#1451974711yescharacteristic
236C2×C4D8×D6111yescharacteristic
237C2×C4#1451980411yescharacteristic
238C8—21no—
239C8—81no—
240C8—2441no—
241C8#1451979911yescharacteristic
242C8#1451980511yescharacteristic
243C22—81no—
244C22—81no—
245C22—81no—
246C22#1683989711yescharacteristic
247C4—21no—
248C4—81no—
249C4—9761no—
250C4—4882no—
251C4—2441no—
252C4—2441no—
253C4#1683990911yescharacteristic
254C4#1683993111yescharacteristic
255C4#1684019111yescharacteristic
256C4#1684020111yescharacteristic
257C2—161no—
258C2#2144488711yescharacteristic
259C2#2144776011yescharacteristic
260C2#2144779811yescharacteristic
subgroupG/H
centerC22#16839897
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1331C2
socleC22×C61#447
prime radicalC2×D8×C61D4
hypercenter#1331D61
hypocenterC61#12335
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1331

Complements

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

NH ≅ G/Ntype
2. #21448072C2semidirect
4. #21445190C2semidirect
5. #21443867C2semidirect
6. #21443799C2semidirect
155. C61#12335semidirect

Maximal subgroups

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

subgroupindex
#214588052
#214480722
#214478642
#214451902
#214438672
#214437992
C61×#13312
#1233561