Finite Group Databasebeta

← #29593320

Subgroups — #29593320

Order 15616.

290 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 59 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#21457280C211yesmaximal, characteristic
2#21448017C211yesmaximal, characteristic, complemented
3#21448005C211yesmaximal, characteristic
4#21447324C211yesmaximal, characteristic, complemented
5#21443838C211yesmaximal, characteristic, complemented
6#21443835C211yesmaximal, characteristic
7C61×#1323C211yesmaximal, characteristic, complemented
8#16840383—21no—
9#16840058—21no—
10#16840043—21no—
11#16840008—21no—
12#16840003C2211yescharacteristic
13#16839998C2211yescharacteristic
14#16839985—21no—
15#16839978—21no—
16#16839805—21no—
17C2×#14519711C2211yescharacteristic
18#16839590—21no—
19#16839590—21no—
20#16839567—21no—
21#16839564—21no—
22#16839530—21no—
23#16839527C2211yescharacteristic
24C61×#424C2211yescharacteristic
25C61×C22⋊C16C2211yescharacteristic
26C61×C22⋊C16C2211yescharacteristic
27C2×Dic244D411yescharacteristic
28C2×#11758190—21no—
29C2×D488D411yescharacteristic
30C2×#11758194—21no—
31#14519777—21no—
32#14519772—41no—
33#14519765—21no—
34#14519763—41no—
35#14519759—41no—
36#14519756—21no—
37#14519755—41no—
38#14519751—21no—
39C4×Dic122—21no—
40C4×D244—21no—
41C2×C4⋊Dic61—21no—
42#14519711—21no—
43#14519711—21no—
44#14519711—21no—
45#14519711D411yescharacteristic
46#14519711D411yescharacteristic
47#14519710—41no—
48#14519708—41no—
49#14519702—21no—
50#14519702—21no—
51#14519699—21no—
52#14519699—21no—
53C2×M16×C61D411yescharacteristic
54C22×C8×C61C2311yescharacteristic
55#117×C61D411yescharacteristic
56C2×C16×C61—21no—
57C2×C16×C61—21no—
58C4⋊C8×C61—21no—
59C4⋊C8×C61—21no—
60C22×C4×C61C2×D411yescharacteristic
61C2×C22⋊D61—41no—
62C22×Dic61—41no—
63C2×D244—21no—
64C2×C4×D61—41no—
65C2×Dic122—21no—
66C2×Dic122—41no—
67M16×C61—41no—
68C2×C8×C61—21no—
69C2×C8×C61—41no—
70C2×C8×C61C2×D411yescharacteristic
71C2×C8×C61C2×D411yescharacteristic
72C4⋊C4×C61D811yescharacteristic
73C4⋊C4×C61D811yescharacteristic
74C22⋊C4×C61—21no—
75C42×C61—21no—
76C22⋊Dic61—41no—
77#11758198—41no—
78#11758198—41no—
79#11758198—41no—
80#11758198—41no—
81C4⋊Dic61—21no—
82C4⋊Dic61—21no—
83C4⋊Dic61—41no—
84C4⋊Dic61—41no—
85C4⋊Dic61—41no—
86#11758196—41no—
87#11758196—41no—
88C4×Dic61—41no—
89#11758194—22no—
90#11758194—41no—
91C2×#92418—41no—
92Dic244—41no—
93D488—41no—
94#11758190—81no—
95C16×C61—41no—
96C16×C61—41no—
97C23×C61AGL(1,ℤ/8)11yescharacteristic
98C22×D61—41no—
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61#12011yescharacteristic
104C2×C4×C61C2×D811yescharacteristic
105C22⋊D61—161no—
106C2×Dic61—41no—
107C2×Dic61—41no—
108C2×Dic61—41no—
109C2×Dic61—81no—
110C2×Dic61—161no—
111D244—41no—
112D244—41no—
113C4×D61—161no—
114Dic122—41no—
115Dic122—41no—
116Dic122—161no—
117C8×C61—21no—
118C8×C61—21no—
119C8×C61—41no—
120#92418—42no—
121#12295—611nomaximal, Sylow
122C22×C61—21no—
123C22×C61—21no—
124C22×C61—21no—
125C22×C61#44711yescharacteristic
126C2×D61—81no—
127C2×D61—81no—
128C2×D61—81no—
129C4×C61—21no—
130C4×C61—41no—
131C4×C61—41no—
132C4×C61#45611yescharacteristic
133C4×C61#45811yescharacteristic
134Dic61—81no—
135Dic61—81no—
136Dic61—81no—
137Dic61—161no—
138#3262—611no—
139#2235—611no—
140#2233—611no—
141#2089—611no—
142#1350—611no—
143#1349—611no—
144#1323D6111yescharacteristic, complemented
145C2×C61—41no—
146C2×C61#161011yescharacteristic
147C2×C61#219311yescharacteristic
148C2×C61#219411yescharacteristic
149D61—161no—
150#542—1221no—
151#477—1221no—
152#474—1221no—
153#468—1221no—
154#467—611no—
155#466—611no—
156#464—1221no—
157#463—1221no—
158#428—1221no—
159C2×#107—611no—
160#424C2×D6111yescharacteristic
161#367—1221no—
162#367—1221no—
163#358—1221no—
164#357—1221no—
165C22⋊C16C2×D6111yescharacteristic
166C22⋊C16C2×D6111yescharacteristic
167#343—1221no—
168#341—611no—
169C61#1229511yescharacteristic, complemented, Sylow
170C2×Q16—611no—
171C2×SD16—1221no—
172C2×D8—611no—
173C2×M16—1221no—
174C2×M16D24411yescharacteristic
175C22×C8C22×D6111yescharacteristic
176C4⋊Q8—1221no—
177#126—2441no—
178#124—1221no—
179#124—2441no—
180#123—2441no—
181C22⋊Q8—1221no—
182C22⋊Q8—2441no—
183#121—1221no—
184C4×Q8—1221no—
185C4×D4—1221no—
186#117D24411yescharacteristic
187C2×C4⋊C4—1221no—
188C2×C16—21no—
189C2×C16—21no—
190#107—611no—
191#107—611no—
192#107—1221no—
193#107—1221no—
194#107—1221no—
195#107—2441no—
196#106—2441no—
197C4⋊C8—21no—
198C4⋊C8—21no—
199#103—1221no—
200#103—1221no—
201#102—1221no—
202#102—1221no—
203C2×Q8—1221no—
204C2×Q8—2441no—
205C2×D4—1221no—
206C2×D4—2441no—
207C22×C4—2441no—
208C22×C4—2441no—
209C22×C4C2×D24411yescharacteristic
210Q16—2441no—
211SD16—4881no—
212D8—2441no—
213M16—41no—
214M16—1222no—
215M16—2441no—
216C2×C8—21no—
217C2×C8—41no—
218C2×C8—2441no—
219C2×C8D4×D6111yescharacteristic
220C2×C8D4×D6111yescharacteristic
221C4⋊C4—1221no—
222C4⋊C4—1221no—
223C4⋊C4—2441no—
224C4⋊C4—2441no—
225C4⋊C4—2441no—
226C4⋊C4—2441no—
227C4⋊C4—2441no—
228C4⋊C4D48811yescharacteristic
229C4⋊C4D48811yescharacteristic
230C22⋊C4—21no—
231C22⋊C4—2441no—
232C22⋊C4—2441no—
233C22⋊C4—2441no—
234C22⋊C4—2441no—
235C22⋊C4—2441no—
236C42—21no—
237C42—2441no—
238C16—41no—
239C16—41no—
240C23—2441no—
241C23#1451980511yescharacteristic
242Q8—9761no—
243Q8—2441no—
244Q8—2441no—
245D4—9761no—
246D4—2441no—
247D4—2441no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—9761no—
253C2×C4—9761no—
254C2×C4—4881no—
255C2×C4—2441no—
256C2×C4—2441no—
257C2×C4—2441no—
258C2×C4#1451974711yescharacteristic
259C2×C4C2×D48811yescharacteristic
260C8—21no—
261C8—21no—
262C8—41no—
263C8—2442no—
264C22—21no—
265C22—21no—
266C22—21no—
267C22—4881no—
268C22—4881no—
269C22—4881no—
270C22#1683989811yescharacteristic
271C4—21no—
272C4—41no—
273C4—41no—
274C4—9761no—
275C4—4881no—
276C4—4881no—
277C4—4881no—
278C4#1683994711yescharacteristic
279C4#1683995311yescharacteristic
280C2—41no—
281C2—9761no—
282C2#2144482411yescharacteristic
283C2#2144778511yescharacteristic
284C2#2144779211yescharacteristic
subgroupG/H
centerC22#16839898
commutator, cosocleC22×C8×C61C23
FrattiniC22×C8C22×D61
FittingC61×#1323C2
socleC22×C61#447
prime radical#16839998C22
hypercenter#1323D61
hypocenterC61#12295
LCSG ▷ C22×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #424 ◁ #1323

Complements

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

NH ≅ G/Ntype
2. #21448017C2semidirect
4. #21447324C2semidirect
5. #21443838C2semidirect
7. C61×#1323C2semidirect
144. #1323D61semidirect
169. C61#12295semidirect

Maximal subgroups

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

subgroupindex
#214572802
#214480172
#214480052
#214473242
#214438382
#214438352
C61×#13232
#1229561