Finite Group Databasebeta

← #29593916

Subgroups — #29593916

Order 15616.

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

normal subgroups only

This group has 282 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#21458823C211yesmaximal, characteristic
2#21447968C211yesmaximal, characteristic
3#21445220C211yesmaximal, characteristic
4#21443868C211yesmaximal, characteristic
5#21443799C211yesmaximal, characteristic
6#21443784C211yesmaximal, characteristic
7C61×#2241C211yesmaximal, characteristic
8#16840487—21no—
9#16840140—21no—
10#16840054—21no—
11#16839970—22no—
12#16839969—21no—
13C8×Dic122C2211yescharacteristic
14C4×Dic244C2211yescharacteristic
15Q16×Dic61—21no—
16#16839587—21no—
17C4⋊#11758185C2211yescharacteristic
18#16839565—21no—
19#16839515C2211yescharacteristic
20#16839511—21no—
21C61×#500C2211yescharacteristic
22C61×#494C2211yescharacteristic
23C61×#358—22no—
24C4×C16×C61C2211yescharacteristic
25C2×Dic244D411yescharacteristic
26C2×#11758202—22no—
27#14519775—22no—
28#14519768—41no—
29#14519767—42no—
30Q8×Dic61—22no—
31C4×Dic122—21no—
32C4×Dic122D411yescharacteristic
33#14519742—41no—
34C2×#11758185—21no—
35#14519711D411yescharacteristic
36#14519710—41no—
37C4⋊#92418—21no—
38C4⋊#92418D411yescharacteristic
39#14519706—21no—
40#14519702—21no—
41#14519701—22no—
42#14519700—41no—
43C8×Dic61—21no—
44C2×Q16×C61—21no—
45C2×Q16×C61D412yes—
46C4⋊Q8×C61—21no—
47C4⋊Q8×C61—21no—
48C2×C16×C61—21no—
49#107×C61—21no—
50#107×C61—21no—
51C4×C8×C61C2311yescharacteristic
52C2×Q8×C61—22no—
53C2×Q8×C61—41no—
54C2×Dic122—21no—
55C2×Dic122D811yescharacteristic
56Q16×C61—42no—
57Q16×C61—41no—
58Q16×C61—41no—
59C2×C8×C61C2×D411yescharacteristic
60C2×C8×C61C2×D411yescharacteristic
61C4⋊C4×C61—41no—
62C4⋊C4×C61—41no—
63C4⋊C4×C61—41no—
64C4⋊C4×C61—41no—
65C42×C61C2×D411yescharacteristic
66#11758202—82no—
67C4⋊Dic61—21no—
68C4⋊Dic61—42no—
69C4⋊Dic61D811yescharacteristic
70#11758196—21no—
71#11758196—42no—
72#11758196—42no—
73#11758196—41no—
74C4×Dic61—21no—
75C4×Dic61—42no—
76C4×Dic61—41no—
77C2×#92418—21no—
78C2×#92418—41no—
79Dic244—21no—
80Dic244—21no—
81C16×C61—41no—
82#11758185—41no—
83Q8×C61—42no—
84Q8×C61—42no—
85Q8×C61—161no—
86C2×C4×C61—42no—
87C2×C4×C61—81no—
88C2×C4×C61#12011yescharacteristic
89C2×C4×C61C2×D811yescharacteristic
90C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
91C2×Dic61—21no—
92C2×Dic61—21no—
93C2×Dic61—41no—
94C2×Dic61—41no—
95Dic122—21no—
96Dic122—41no—
97Dic122—41no—
98Dic122Q3212yes—
99C8×C61—21no—
100C8×C61#13511yescharacteristic
101C8×C61#13711yescharacteristic
102#92418—41no—
103#92418—81no—
104#12386—611nomaximal, Sylow
105C22×C61#44711yescharacteristic
106C4×C61—21no—
107C4×C61—82no—
108C4×C61—161no—
109C4×C61#45211yescharacteristic
110C4×C61#45511yescharacteristic
111C4×C61C2×Q3211yescharacteristic
112C4×C61#51011yescharacteristic
113Dic61—22no—
114Dic61—41no—
115Dic61—81no—
116Dic61—81no—
117#3395—611no—
118#2241D6111yescharacteristic
119#2227—611no—
120#1676—611no—
121#1362—611no—
122Q8⋊C16—611no—
123#1332—611no—
124C2×C61#164111yescharacteristic
125C2×C61#218811yescharacteristic
126C2×C61#219311yescharacteristic
127#557—1221no—
128#500C2×D6111yescharacteristic
129#494—1221no—
130#494C2×D6111yescharacteristic
131#477—1221no—
132#462—1221no—
133#462—1222no—
134C8×Q8—611no—
135C4×Q16—611no—
136C4×Q16—1221no—
137#366—1221no—
138C4⋊C16—611no—
139#358—22no—
140#358—1221no—
141C4×C16C2×D6111yescharacteristic
142#335—611no—
143#333—1221no—
144C61#1238611yescharacteristic, complemented, Sylow
145C2×Q16—21no—
146C2×Q16—611no—
147C2×Q16—1222no—
148C2×Q16C22⋊D6112yes—
149C4⋊Q8—21no—
150C4⋊Q8—21no—
151C4⋊Q8—1222no—
152#125—2441no—
153#125—2442no—
154C4×Q8—611no—
155C4×Q8—1222no—
156C4×Q8—1221no—
157C4×Q8—2441no—
158C2×C16—21no—
159C2×C16—1221no—
160#107—21no—
161#107—21no—
162#107—611no—
163#107—2441no—
164C4⋊C8—611no—
165C4⋊C8—1221no—
166C4⋊C8—1221no—
167#103—1222no—
168#103—1221no—
169#103—2441no—
170C4×C8—1221no—
171C4×C8C22×D6111yescharacteristic
172C2×Q8—22no—
173C2×Q8—41no—
174C2×Q8—611no—
175C2×Q8—1221no—
176Q16—42no—
177Q16—41no—
178Q16—41no—
179Q16—1221no—
180Q16—1221no—
181Q16—4882no—
182C2×C8—1221no—
183C2×C8—2441no—
184C2×C8D4×D6111yescharacteristic
185C2×C8C2×C22⋊D6111yescharacteristic
186C4⋊C4—41no—
187C4⋊C4—41no—
188C4⋊C4—41no—
189C4⋊C4—41no—
190C4⋊C4—611no—
191C4⋊C4—1221no—
192C4⋊C4—1221no—
193C4⋊C4—2442no—
194C4⋊C4—2442no—
195C4⋊C4—2442no—
196C4⋊C4—2441no—
197C42—1221no—
198C42—2442no—
199C42—2441no—
200C42D4×D6111yescharacteristic
201C16—41no—
202C16—2441no—
203Q8—42no—
204Q8—42no—
205Q8—161no—
206Q8—612no—
207Q8—1221no—
208Q8—2441no—
209Q8—2441no—
210C2×C4—42no—
211C2×C4—81no—
212C2×C4—1221no—
213C2×C4—1221no—
214C2×C4—2441no—
215C2×C4—2441no—
216C2×C4#1451974511yescharacteristic
217C2×C4D8×D6111yescharacteristic
218C2×C4#1451980111yescharacteristic
219C8—21no—
220C8—4881no—
221C8—2441no—
222C8#1451979811yescharacteristic
223C8#1451980611yescharacteristic
224C22#1683989411yescharacteristic
225C4—21no—
226C4—82no—
227C4—161no—
228C4—1222no—
229C4—4881no—
230C4—4881no—
231C4—2441no—
232C4#1683992111yescharacteristic
233C4#1683993911yescharacteristic
234C4Q32×D6111yescharacteristic
235C4#1684020411yescharacteristic
236C2#2144500911yescharacteristic
237C2#2144775111yescharacteristic
238C2#2144778211yescharacteristic
subgroupG/H
centerC22#16839894
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#2241C2
socle, prime radicalC22×C61#447
hypercenter#2241D61
hypocenterC61#12386
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2241

Complements

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

NH ≅ G/Ntype
144. C61#12386semidirect

Maximal subgroups

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

subgroupindex
#214588232
#214479682
#214452202
#214438682
#214437992
#214437842
C61×#22412
#1238661