Finite Group Databasebeta

← #29594033

Subgroups — #29594033

Order 15616.

292 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 63 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#21458424C211yesmaximal, characteristic
2#21448105C211yesmaximal, characteristic, complemented
3#21447967C211yesmaximal, characteristic, complemented
4#21445332C211yesmaximal, characteristic, complemented
5#21443870C211yesmaximal, characteristic, complemented
6#21443787C211yesmaximal, characteristic, complemented
7C61×#1330C211yesmaximal, characteristic, complemented
8#16840458—21no—
9#16840167C2211yescharacteristic
10#16840164C2211yescharacteristic
11#16840087—21no—
12#16840076—21no—
13#16840063—21no—
14#16840015—21no—
15#16839967—21no—
16C4×D488C2211yescharacteristic
17#16839804—21no—
18#16839590—21no—
19#16839590—21no—
20#16839588—21no—
21#16839564—21no—
22#16839513C2211yescharacteristic
23#16839507—21no—
24C61×#436C2211yescharacteristic
25C61×C4⋊C16C2211yescharacteristic
26C61×#346C2211yescharacteristic
27C2×#11758200—41no—
28C2×D488D411yescharacteristic
29#14519777—21no—
30#14519772—41no—
31#14519769—21no—
32#14519759—41no—
33#14519751—21no—
34#14519751—21no—
35#14519749—41no—
36C4×D244—21no—
37#14519737—41no—
38#14519736—21no—
39C2×C4⋊Dic61—21no—
40#14519711—21no—
41#14519711—21no—
42#14519711—21no—
43#14519711D411yescharacteristic
44#14519711D411yescharacteristic
45#14519711D411yescharacteristic
46#14519709—21no—
47#14519709—21no—
48C4⋊#92418—21no—
49#14519700—41no—
50#14519699—21no—
51#14519699—21no—
52#14519699—21no—
53C2×M16×C61—21no—
54C4×D4×C61D411yescharacteristic
55C2×C16×C61—21no—
56C2×C16×C61—21no—
57C4⋊C8×C61D411yescharacteristic
58C22⋊C8×C61—21no—
59C4×C8×C61C2311yescharacteristic
60C2×D4×C61D811yescharacteristic
61C22×C4×C61—21no—
62C2×C22⋊D61—41no—
63C2×C22⋊D61—41no—
64C22×Dic61—41no—
65C2×D244—21no—
66C2×C4×D61—41no—
67C2×Dic122—41no—
68M16×C61—41no—
69M16×C61—41no—
70C2×C8×C61—21no—
71C2×C8×C61C2×D411yescharacteristic
72C2×C8×C61C2×D411yescharacteristic
73C4⋊C4×C61D811yescharacteristic
74C22⋊C4×C61—21no—
75C42×C61C2×D411yescharacteristic
76C22⋊Dic61—41no—
77#11758200—82no—
78#11758198—41no—
79#11758198—41no—
80#11758198—41no—
81C4⋊Dic61—21no—
82C4⋊Dic61—21no—
83C4⋊Dic61—21no—
84C4⋊Dic61—41no—
85C4⋊Dic61—41no—
86C4⋊Dic61—41no—
87#11758196—41no—
88#11758196—41no—
89C4×Dic61—41no—
90C2×#92418—41no—
91D488—21no—
92D488—21no—
93C16×C61—22no—
94C16×C61—41no—
95C23×C61—21no—
96C22×D61—41no—
97D4×C61—41no—
98C2×C4×C61—21no—
99C2×C4×C61—41no—
100C2×C4×C61—41no—
101C2×C4×C61#12011yescharacteristic
102C2×C4×C61C2×D811yescharacteristic
103C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
104C22⋊D61—82no—
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—81no—
115Dic122—81no—
116C8×C61—21no—
117C8×C61—41no—
118C8×C61#13511yescharacteristic
119C8×C61#13711yescharacteristic
120#92418—81no—
121#12402—611nomaximal, Sylow
122C22×C61—41no—
123C22×C61—41no—
124C22×C61—41no—
125C22×C61#44711yescharacteristic
126C2×D61—81no—
127C2×D61—81no—
128C2×D61—81no—
129C4×C61—21no—
130C4×C61—21no—
131C4×C61—41no—
132C4×C61#45211yescharacteristic
133C4×C61#45611yescharacteristic
134Dic61—81no—
135Dic61—81no—
136Dic61—81no—
137Dic61—161no—
138#3355—611no—
139#2255—611no—
140#2226—611no—
141#1693—611no—
142#1363—611no—
143#1333—611no—
144#1330D6111yescharacteristic, complemented
145C2×C61—81no—
146C2×C61#164711yescharacteristic
147C2×C61#219011yescharacteristic
148C2×C61#219411yescharacteristic
149D61—161no—
150#553—1221no—
151#500—611no—
152#499—611no—
153#482—1221no—
154#480—1221no—
155#478—1221no—
156#469—1221no—
157#461—1221no—
158C4×D8—611no—
159#436C2×D6111yescharacteristic
160#428—1221no—
161#367—1221no—
162#367—1221no—
163#366—1221no—
164C4⋊C16C2×D6111yescharacteristic
165#357—1221no—
166#346C2×D6111yescharacteristic
167#334—611no—
168#332—1221no—
169C61#1240211yescharacteristic, complemented, Sylow
170C2×SD16—2441no—
171C2×D8—611no—
172C2×M16—21no—
173C4⋊Q8—1221no—
174#126—2441no—
175#125—1221no—
176#123—2441no—
177#121—1221no—
178#121—1221no—
179#121—2441no—
180C4×D4—1221no—
181C4×D4—2441no—
182C4×D4D24411yescharacteristic
183#117—1221no—
184C2×C4⋊C4—1221no—
185C2×C16—21no—
186C2×C16—21no—
187#107—611no—
188#107—611no—
189#107—611no—
190#107—1221no—
191#107—1221no—
192#107—1221no—
193#106—1221no—
194#106—1221no—
195C4⋊C8—1221no—
196C4⋊C8D24411yescharacteristic
197#103—2441no—
198#102—1221no—
199#102—1221no—
200#102—1221no—
201C22⋊C8—21no—
202C4×C8C22×D6111yescharacteristic
203C2×Q8—2441no—
204C2×D4—1221no—
205C2×D4—2441no—
206C2×D4—2441no—
207C2×D4D48811yescharacteristic
208C22×C4—21no—
209C22×C4—2441no—
210C22×C4—2441no—
211SD16—4882no—
212D8—1221no—
213D8—1221no—
214M16—41no—
215M16—41no—
216C2×C8—21no—
217C2×C8—2441no—
218C2×C8D4×D6111yescharacteristic
219C2×C8D4×D6111yescharacteristic
220C4⋊C4—1221no—
221C4⋊C4—1221no—
222C4⋊C4—1221no—
223C4⋊C4—2441no—
224C4⋊C4—2441no—
225C4⋊C4—2441no—
226C4⋊C4—2441no—
227C4⋊C4—2441no—
228C4⋊C4D48811yescharacteristic
229C22⋊C4—21no—
230C22⋊C4—2441no—
231C22⋊C4—2441no—
232C22⋊C4—2441no—
233C22⋊C4—2441no—
234C42—2441no—
235C42C2×D24411yescharacteristic
236C16—22no—
237C16—41no—
238C23—21no—
239C23—2441no—
240Q8—4881no—
241Q8—4881no—
242D4—41no—
243D4—9761no—
244D4—4882no—
245D4—2441no—
246D4—2441no—
247C2×C4—21no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—9761no—
251C2×C4—9761no—
252C2×C4—4881no—
253C2×C4—2441no—
254C2×C4—2441no—
255C2×C4—2441no—
256C2×C4#1451974711yescharacteristic
257C2×C4C2×D48811yescharacteristic
258C2×C4#1451980511yescharacteristic
259C8—21no—
260C8—41no—
261C8—4881no—
262C8#1451979611yescharacteristic
263C8#1451980611yescharacteristic
264C22—41no—
265C22—41no—
266C22—41no—
267C22—4881no—
268C22—4881no—
269C22—4881no—
270C22#1683989811yescharacteristic
271C4—21no—
272C4—21no—
273C4—41no—
274C4—9761no—
275C4—4881no—
276C4—4881no—
277C4—4881no—
278C4#1683992511yescharacteristic
279C4#1683994611yescharacteristic
280C2—81no—
281C2—9761no—
282C2#2144505611yescharacteristic
283C2#2144776711yescharacteristic
284C2#2144779211yescharacteristic
subgroupG/H
centerC22#16839898
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1330C2
socleC22×C61#447
prime radical#21458424C2
hypercenter#1330D61
hypocenterC61#12402
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #436 ◁ #1330

Complements

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

NH ≅ G/Ntype
2. #21448105C2semidirect
3. #21447967C2semidirect
4. #21445332C2semidirect
5. #21443870C2semidirect
6. #21443787C2semidirect
7. C61×#1330C2semidirect
144. #1330D61semidirect
169. C61#12402semidirect

Maximal subgroups

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

subgroupindex
#214584242
#214481052
#214479672
#214453322
#214438702
#214437872
C61×#13302
#1240261