Finite Group Databasebeta

← #29584367

Subgroups — #29584367

Order 15616.

448 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 77 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#21456594C211yesmaximal, characteristic
2#21446285C212yesmaximal
3#21446001C211yesmaximal, characteristic
4#21444340C212yesmaximal
5C61×#1293C211yesmaximal, characteristic
6C22×#11758194C2211yescharacteristic
7C2×#14519756C2212yes—
8#16840098—22no—
9#16840003—21no—
10#16840003—21no—
11#16839920—22no—
12C2×#14519706—21no—
13C2×#14519695—22no—
14C4×C22⋊Dic61C2211yescharacteristic
15#16839530—22no—
16#16839516—21no—
17#16839500—22no—
18#16839500—22no—
19C61×#407C2212yes—
20C2×C22⋊C8×C61C2211yescharacteristic
21C22×Dic122D412yes—
22C2×Dic244—21no—
23C2×Dic244—21no—
24C2×#11758194—22no—
25C2×#11758194—42no—
26C22×#92418—21no—
27#14519756—22no—
28#14519756—22no—
29#14519756—22no—
30#14519756—22no—
31C2×C4⋊Dic61D412yes—
32C2×#11758196—22no—
33C2×C22⋊Dic61—22no—
34C2×C22⋊Dic61—21no—
35C2×C4×Dic61—21no—
36#14519711—21no—
37#14519711—21no—
38#14519706—42no—
39#14519702—22no—
40#14519702—22no—
41#14519695—44no—
42#14519684D411yescharacteristic
43#14519684D411yescharacteristic
44C23×C4×C61C2311yescharacteristic
45C2×M16×C61—22no—
46C22×C8×C61D411yescharacteristic
47C22×C8×C61D411yescharacteristic
48C22⋊C8×C61—22no—
49C22⋊C8×C61—22no—
50C22⋊C8×C61—22no—
51C24×C61#4111yescharacteristic
52C22×C4×C61—41no—
53C22×C4×C61—41no—
54C22×C4×C61C2×D412yes—
55C22×C4×C61C2×D411yescharacteristic
56C22×C4×C61C2×D411yescharacteristic
57C22×C4×C61#4112yes—
58C22×Dic61—21no—
59C22×Dic61—21no—
60C22×Dic61—22no—
61C22×Dic61—22no—
62C2×Dic122—22no—
63C2×Dic122—22no—
64C2×Dic122—42no—
65C2×Dic122—42no—
66M16×C61—42no—
67M16×C61—42no—
68C2×C8×C61—21no—
69C2×C8×C61—21no—
70C2×C8×C61—41no—
71C2×C8×C61—41no—
72C2×C8×C61—42no—
73C22⋊Dic61—42no—
74C22⋊Dic61—42no—
75C22⋊Dic61—42no—
76C4⋊Dic61—22no—
77C4⋊Dic61—22no—
78#11758196—42no—
79#11758196—42no—
80C4×Dic61—41no—
81C4×Dic61—41no—
82#11758194—24no—
83#11758194—42no—
84C2×#92418—22no—
85C2×#92418—41no—
86C2×#92418—41no—
87Dic244—81no—
88Dic244—81no—
89C23×C61—21no—
90C23×C61—21no—
91C23×C61—41no—
92C23×C61—41no—
93C23×C61#12111yescharacteristic
94C23×C61#12312yes—
95C2×C4×C61—21no—
96C2×C4×C61—22no—
97C2×C4×C61—21no—
98C2×C4×C61—22no—
99C2×C4×C61—41no—
100C2×C4×C61—42no—
101C2×C4×C61#12011yescharacteristic
102C2×C4×C61#12112yes—
103C2×C4×C61#12411yescharacteristic
104C2×Dic61—22no—
105C2×Dic61—41no—
106C2×Dic61—41no—
107C2×Dic61—41no—
108C2×Dic61—41no—
109C2×Dic61—44no—
110C2×Dic61—42no—
111C2×Dic61—42no—
112C2×Dic61—41no—
113C2×Dic61—82no—
114Dic122—42no—
115Dic122—42no—
116Dic122—82no—
117C8×C61—41no—
118C8×C61—41no—
119C8×C61—82no—
120#92418—42no—
121#10559—611nomaximal, Sylow
122C22×C61—21no—
123C22×C61—21no—
124C22×C61—22no—
125C22×C61—22no—
126C22×C61—22no—
127C22×C61—81no—
128C22×C61—81no—
129C22×C61#39411yescharacteristic
130C22×C61#47311yescharacteristic
131C22×C61#47311yescharacteristic
132C4×C61—22no—
133C4×C61—21no—
134C4×C61B(4,𝔽2)11yescharacteristic
135C4×C61#45811yescharacteristic
136Dic61—42no—
137Dic61—81no—
138Dic61—82no—
139Dic61—82no—
140#3189—611no—
141#1901—612no—
142#1851—611no—
143#1508—612no—
144#1293D6111yescharacteristic
145C2×C61—21no—
146C2×C61—21no—
147C2×C61—42no—
148C2×C61#204411yescharacteristic
149C2×C61#204711yescharacteristic
150C2×C61#205011yescharacteristic
151C22×M16—611no—
152C2×C22⋊Q8—612no—
153#484—1222no—
154#467—1221no—
155#467—1221no—
156#451—1222no—
157C2×C4⋊C8—1221no—
158C2×#101—1222no—
159#407C2×D6112yes—
160C2×C22⋊C8C2×D6111yescharacteristic
161C4×C22⋊C4—611no—
162#343—1222no—
163#336—1221no—
164#328—1222no—
165#328—1222no—
166C61#1055911yescharacteristic, complemented, Sylow
167C22×Q8—612no—
168C23×C4C22×D6111yescharacteristic
169C2×Q16—1221no—
170C2×Q16—1221no—
171C2×M16—22no—
172C2×M16—1222no—
173C2×M16—2442no—
174C22×C8—1221no—
175C22×C8D24411yescharacteristic
176C22×C8D24411yescharacteristic
177C22⋊Q8—1222no—
178C22⋊Q8—1222no—
179C22⋊Q8—1222no—
180C22⋊Q8—1222no—
181C2×C4⋊C4—612no—
182C2×C4⋊C4—1222no—
183C2×C22⋊C4—1222no—
184C2×C22⋊C4—1221no—
185C2×C42—1221no—
186#107—1221no—
187#107—1221no—
188C4⋊C8—2442no—
189#103—1222no—
190#103—1222no—
191#101—2444no—
192C22⋊C8—22no—
193C22⋊C8—22no—
194C22⋊C8—22no—
195#95—611no—
196#95—611no—
197C24#1175822611yescharacteristic
198C2×Q8—1222no—
199C2×Q8—1222no—
200C2×Q8—2442no—
201C2×Q8—2442no—
202C22×C4—41no—
203C22×C4—41no—
204C22×C4—1221no—
205C22×C4—1222no—
206C22×C4—1221no—
207C22×C4—1222no—
208C22×C4C2×D24411yescharacteristic
209C22×C4#1175822212yes—
210C22×C4D4×D6112yes—
211C22×C4D4×D6111yescharacteristic
212Q16—4881no—
213Q16—4881no—
214M16—42no—
215M16—42no—
216M16—1224no—
217M16—2442no—
218C2×C8—21no—
219C2×C8—21no—
220C2×C8—41no—
221C2×C8—41no—
222C2×C8—42no—
223C2×C8—1222no—
224C2×C8—2441no—
225C2×C8—2441no—
226C4⋊C4—1222no—
227C4⋊C4—1222no—
228C4⋊C4—2442no—
229C4⋊C4—2442no—
230C22⋊C4—2442no—
231C22⋊C4—2442no—
232C22⋊C4—2442no—
233C42—2441no—
234C42—2441no—
235C23—21no—
236C23—21no—
237C23—41no—
238C23—41no—
239C23#1451975211yescharacteristic
240C23#1451976212yes—
241Q8—4882no—
242Q8—2442no—
243Q8—2442no—
244C2×C4—21no—
245C2×C4—22no—
246C2×C4—21no—
247C2×C4—22no—
248C2×C4—42no—
249C2×C4—41no—
250C2×C4—1222no—
251C2×C4—4882no—
252C2×C4—2441no—
253C2×C4—2441no—
254C2×C4—2444no—
255C2×C4—2442no—
256C2×C4—2442no—
257C2×C4—2441no—
258C2×C4—2441no—
259C2×C4—2441no—
260C2×C4#1451974711yescharacteristic
261C2×C4#1451975012yes—
262C2×C4#1451976511yescharacteristic
263C8—41no—
264C8—41no—
265C8—82no—
266C8—2442no—
267C22—21no—
268C22—21no—
269C22—22no—
270C22—22no—
271C22—22no—
272C22—81no—
273C22—81no—
274C22#1683968011yescharacteristic
275C22#1684003811yescharacteristic
276C22#1684003811yescharacteristic
277C4—22no—
278C4—21no—
279C4—4881no—
280C4—4882no—
281C4—4882no—
282C4—2442no—
283C4#1683995011yescharacteristic
284C4#1683995311yescharacteristic
285C2—21no—
286C2—21no—
287C2—42no—
288C2#2144707111yescharacteristic
289C2#2144708811yescharacteristic
290C2#2144710711yescharacteristic
subgroupG/H
centerC22#16839680
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC61×#1293C2
socleC22×C61#394
prime radicalC24×C61#41
hypercenter#1293D61
hypocenterC61#10559
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1293

Complements

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

NH ≅ G/Ntype
166. C61#10559semidirect

Maximal subgroups

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

subgroupindex
#214565942
#214462852
#214460012
#214443402
C61×#12932
#1055961