Finite Group Databasebeta

← #29593888

Subgroups — #29593888

Order 15616.

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

normal subgroups only

This group has 288 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#21447958C211yesmaximal, characteristic
3#21445210C211yesmaximal, characteristic
4#21443868C211yesmaximal, characteristic
5#21443799C211yesmaximal, characteristic
6#21443784C211yesmaximal, characteristic
7C61×#2241C211yesmaximal, characteristic
8#16840487—21no—
9#16840140—21no—
10#16839970—22no—
11#16839969—21no—
12#16839969—21no—
13C8×Dic122C2211yescharacteristic
14C4×Dic244C2211yescharacteristic
15Q16×Dic61—21no—
16#16839589—21no—
17C4⋊#11758185C2211yescharacteristic
18#16839565—21no—
19#16839515C2211yescharacteristic
20#16839508—21no—
21C61×#500C2211yescharacteristic
22C61×#494C2211yescharacteristic
23C61×#358—22no—
24C4×C16×C61C2211yescharacteristic
25C2×Dic244D411yescharacteristic
26C2×#11758202—22no—
27C2×#11758202—41no—
28#14519775—22no—
29#14519768—41no—
30#14519767—42no—
31Q8×Dic61—22no—
32C4×Dic122—21no—
33C4×Dic122D411yescharacteristic
34#14519742—41no—
35C2×#11758185—21no—
36#14519711D411yescharacteristic
37C4⋊#92418—21no—
38C4⋊#92418D411yescharacteristic
39#14519706—21no—
40#14519702—21no—
41#14519701—22no—
42#14519701—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—
67#11758202—82no—
68C4⋊Dic61—21no—
69C4⋊Dic61—42no—
70C4⋊Dic61D811yescharacteristic
71#11758196—21no—
72#11758196—42no—
73#11758196—42no—
74#11758196—41no—
75C4×Dic61—21no—
76C4×Dic61—42no—
77C4×Dic61—41no—
78C2×#92418—21no—
79C2×#92418—41no—
80Dic244—21no—
81Dic244—21no—
82C16×C61—41no—
83#11758185—41no—
84Q8×C61—42no—
85Q8×C61—42no—
86Q8×C61—81no—
87Q8×C61—81no—
88C2×C4×C61—42no—
89C2×C4×C61—81no—
90C2×C4×C61#12011yescharacteristic
91C2×C4×C61C2×D811yescharacteristic
92C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
93C2×Dic61—21no—
94C2×Dic61—21no—
95C2×Dic61—41no—
96C2×Dic61—41no—
97Dic122—21no—
98Dic122—41no—
99Dic122—41no—
100Dic122SD3212yes—
101C8×C61—21no—
102C8×C61#13511yescharacteristic
103C8×C61#13711yescharacteristic
104#92418—41no—
105#92418—81no—
106#12382—611nomaximal, Sylow
107C22×C61#44711yescharacteristic
108C4×C61—21no—
109C4×C61—82no—
110C4×C61—161no—
111C4×C61#45211yescharacteristic
112C4×C61#45511yescharacteristic
113C4×C61C2×SD3211yescharacteristic
114C4×C61#51011yescharacteristic
115Dic61—22no—
116Dic61—41no—
117Dic61—81no—
118Dic61—81no—
119#3395—611no—
120#2241D6111yescharacteristic
121#2225—611no—
122#1674—611no—
123#1362—611no—
124Q8⋊C16—611no—
125#1332—611no—
126C2×C61#164111yescharacteristic
127C2×C61#218511yescharacteristic
128C2×C61#219511yescharacteristic
129#557—1221no—
130#500C2×D6111yescharacteristic
131#494—1221no—
132#494C2×D6111yescharacteristic
133#462—1221no—
134#462—1222no—
135#462—1221no—
136C8×Q8—611no—
137C4×Q16—611no—
138C4×Q16—1221no—
139#367—1221no—
140C4⋊C16—611no—
141#358—22no—
142#358—1221no—
143C4×C16C2×D6111yescharacteristic
144#335—611no—
145#332—1221no—
146C61#1238211yescharacteristic, complemented, Sylow
147C2×Q16—21no—
148C2×Q16—611no—
149C2×Q16—1222no—
150C2×Q16—2441no—
151C2×Q16C22⋊D6112yes—
152C4⋊Q8—21no—
153C4⋊Q8—21no—
154C4⋊Q8—1222no—
155#125—2441no—
156#125—2442no—
157C4×Q8—611no—
158C4×Q8—1222no—
159C4×Q8—1221no—
160C4×Q8—2441no—
161C2×C16—21no—
162C2×C16—1221no—
163#107—21no—
164#107—21no—
165#107—611no—
166C4⋊C8—611no—
167C4⋊C8—1221no—
168C4⋊C8—1221no—
169#103—1222no—
170#103—1221no—
171#103—2441no—
172C4×C8—1221no—
173C4×C8C22×D6111yescharacteristic
174C2×Q8—22no—
175C2×Q8—41no—
176C2×Q8—611no—
177C2×Q8—1221no—
178Q16—42no—
179Q16—41no—
180Q16—41no—
181Q16—1221no—
182Q16—1221no—
183Q16—4882no—
184Q16—4882no—
185C2×C8—1221no—
186C2×C8—2441no—
187C2×C8D4×D6111yescharacteristic
188C2×C8C2×C22⋊D6111yescharacteristic
189C4⋊C4—41no—
190C4⋊C4—41no—
191C4⋊C4—41no—
192C4⋊C4—41no—
193C4⋊C4—611no—
194C4⋊C4—1221no—
195C4⋊C4—1221no—
196C4⋊C4—2442no—
197C4⋊C4—2442no—
198C4⋊C4—2442no—
199C4⋊C4—2441no—
200C42—1221no—
201C42—2442no—
202C42—2441no—
203C42D4×D6111yescharacteristic
204C16—41no—
205C16—2441no—
206Q8—42no—
207Q8—42no—
208Q8—81no—
209Q8—81no—
210Q8—612no—
211Q8—1221no—
212Q8—2441no—
213Q8—2441no—
214C2×C4—42no—
215C2×C4—81no—
216C2×C4—1221no—
217C2×C4—1221no—
218C2×C4—2441no—
219C2×C4—2441no—
220C2×C4#1451974511yescharacteristic
221C2×C4D8×D6111yescharacteristic
222C2×C4#1451980111yescharacteristic
223C8—21no—
224C8—4881no—
225C8—2441no—
226C8#1451979811yescharacteristic
227C8#1451980611yescharacteristic
228C22#1683989411yescharacteristic
229C4—21no—
230C4—82no—
231C4—161no—
232C4—1222no—
233C4—4881no—
234C4—4881no—
235C4—2441no—
236C4#1683992111yescharacteristic
237C4#1683993911yescharacteristic
238C4SD32×D6111yescharacteristic
239C4#1684020111yescharacteristic
240C2#2144500911yescharacteristic
241C2#2144773411yescharacteristic
242C2#2144779611yescharacteristic
subgroupG/H
centerC22#16839894
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#2241C2
socle, prime radicalC22×C61#447
hypercenter#2241D61
hypocenterC61#12382
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
146. C61#12382semidirect

Maximal subgroups

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

subgroupindex
#214588232
#214479582
#214452102
#214438682
#214437992
#214437842
C61×#22412
#1238261