Finite Group Databasebeta

← #29593890

Subgroups — #29593890

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#21458824C211yesmaximal, characteristic
2#21448048C211yesmaximal, characteristic
3#21445210C211yesmaximal, characteristic
4#21443869C211yesmaximal, characteristic
5#21443797C211yesmaximal, characteristic
6#21443783C211yesmaximal, characteristic
7C61×#2225C211yesmaximal, characteristic
8#16840490—21no—
9#16840142C2211yescharacteristic
10#16840140—21no—
11#16839972—21no—
12#16839971—22no—
13#16839969—21no—
14C8×Dic122C2211yescharacteristic
15#16839856—21no—
16#16839565—22no—
17C4×#11758185C2211yescharacteristic
18#16839515C2211yescharacteristic
19#16839508—21no—
20C61×#500C2211yescharacteristic
21C4×Q16×C61C2211yescharacteristic
22C61×#367—21no—
23C61×C4⋊C16C2211yescharacteristic
24C61×#358—21no—
25C2×Dic244—21no—
26C2×Dic244D412yes—
27C2×#11758202—22no—
28C2×#11758202—41no—
29#14519777—21no—
30#14519775—22no—
31#14519769—41no—
32#14519767—42no—
33C4×Dic122—41no—
34C4×Dic122D411yescharacteristic
35#14519742—22no—
36C2×#11758185—21no—
37C4⋊#92418—21no—
38C4⋊#92418D411yescharacteristic
39#14519706—21no—
40#14519701—41no—
41#14519700—22no—
42C8×Dic61—21no—
43C2×Q16×C61D411yescharacteristic
44C4⋊Q8×C61—21no—
45C4×Q8×C61—21no—
46C2×C16×C61—21no—
47#107×C61—21no—
48#107×C61—21no—
49#107×C61D411yescharacteristic
50#103×C61—21no—
51C4×C8×C61C2311yescharacteristic
52C2×Q8×C61—21no—
53C2×Q8×C61—41no—
54C2×Dic122—22no—
55C2×Dic122D811yescharacteristic
56Q16×C61—21no—
57Q16×C61—21no—
58C2×C8×C61C2×D411yescharacteristic
59C2×C8×C61C2×D411yescharacteristic
60C4⋊C4×C61—21no—
61C4⋊C4×C61—41no—
62C4⋊C4×C61—41no—
63C4⋊C4×C61—41no—
64C42×C61—41no—
65C42×C61C2×D411yescharacteristic
66#11758202—82no—
67#11758202—82no—
68C4⋊Dic61—41no—
69C4⋊Dic61—41no—
70C4⋊Dic61D811yescharacteristic
71#11758196—21no—
72#11758196—42no—
73#11758196—42no—
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—
84Q8×C61—41no—
85Q8×C61—41no—
86Q8×C61—81no—
87Q8×C61—81no—
88C2×C4×C61—41no—
89C2×C4×C61—41no—
90C2×C4×C61—81no—
91C2×C4×C61#12011yescharacteristic
92C2×C4×C61C2×D811yescharacteristic
93C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
94C2×Dic61—21no—
95C2×Dic61—21no—
96C2×Dic61—42no—
97Dic122—21no—
98Dic122—42no—
99Dic122—42no—
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—81no—
110C4×C61—81no—
111C4×C61—161no—
112C4×C61#45211yescharacteristic
113C4×C61#45511yescharacteristic
114C4×C61C2×SD3211yescharacteristic
115C4×C61#51011yescharacteristic
116Dic61—22no—
117Dic61—41no—
118Dic61—82no—
119#3395—611no—
120#2241—611no—
121#2225D6111yescharacteristic
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—611no—
132#494—1221no—
133#462—1222no—
134#462—1221no—
135#462—1221no—
136C8×Q8—611no—
137C4×Q16—1221no—
138C4×Q16C2×D6111yescharacteristic
139#367—21no—
140C4⋊C16C2×D6111yescharacteristic
141#358—21no—
142#358—1222no—
143C4×C16—611no—
144#335—611no—
145#332—1221no—
146C61#1238211yescharacteristic, complemented, Sylow
147C2×Q16—612no—
148C2×Q16—1222no—
149C2×Q16—1221no—
150C2×Q16—2441no—
151C2×Q16C22⋊D6111yescharacteristic
152C4⋊Q8—21no—
153C4⋊Q8—1222no—
154C4⋊Q8—1221no—
155#125—2441no—
156#125—2442no—
157C4×Q8—21no—
158C4×Q8—611no—
159C4×Q8—1222no—
160C4×Q8—2441no—
161C2×C16—21no—
162C2×C16—1221no—
163#107—21no—
164#107—21no—
165#107C22⋊D6111yescharacteristic
166C4⋊C8—611no—
167C4⋊C8—1221no—
168C4⋊C8—1221no—
169#103—21no—
170#103—1222no—
171#103—2441no—
172C4×C8—1221no—
173C4×C8C22×D6111yescharacteristic
174C2×Q8—21no—
175C2×Q8—41no—
176C2×Q8—611no—
177C2×Q8—1222no—
178Q16—21no—
179Q16—21no—
180Q16—4882no—
181Q16—4882no—
182Q16—2442no—
183Q16—2441no—
184Q16—2441no—
185C2×C8—1221no—
186C2×C8—2441no—
187C2×C8D4×D6111yescharacteristic
188C2×C8C2×C22⋊D6111yescharacteristic
189C4⋊C4—21no—
190C4⋊C4—41no—
191C4⋊C4—41no—
192C4⋊C4—41no—
193C4⋊C4—611no—
194C4⋊C4—1221no—
195C4⋊C4—2442no—
196C4⋊C4—2442no—
197C4⋊C4—2442no—
198C4⋊C4—2441no—
199C4⋊C4—2441no—
200C42—41no—
201C42—1221no—
202C42—2442no—
203C42D4×D6111yescharacteristic
204C16—41no—
205C16—2441no—
206Q8—41no—
207Q8—41no—
208Q8—81no—
209Q8—81no—
210Q8—612no—
211Q8—1221no—
212Q8—2442no—
213Q8—2442no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—81no—
217C2×C4—1221no—
218C2×C4—1221no—
219C2×C4—2442no—
220C2×C4#1451974511yescharacteristic
221C2×C4D8×D6111yescharacteristic
222C2×C4#1451980111yescharacteristic
223C8—21no—
224C8—4881no—
225C8—2441no—
226C8#1451979711yescharacteristic
227C8#1451980811yescharacteristic
228C22#1683989411yescharacteristic
229C4—21no—
230C4—81no—
231C4—81no—
232C4—161no—
233C4—1222no—
234C4—4882no—
235C4—2441no—
236C4#1683992211yescharacteristic
237C4#1683993811yescharacteristic
238C4SD32×D6111yescharacteristic
239C4#1684020111yescharacteristic
240C2#2144501111yescharacteristic
241C2#2144773411yescharacteristic
242C2#2144779411yescharacteristic
subgroupG/H
centerC22#16839894
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#2225C2
socle, prime radicalC22×C61#447
hypercenter#2225D61
hypocenterC61#12382
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2225

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
#214588242
#214480482
#214452102
#214438692
#214437972
#214437832
C61×#22252
#1238261