Finite Group Databasebeta

← #29594020

Subgroups — #29594020

Order 15616.

286 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 61 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#21458426C211yesmaximal, characteristic
2#21448105C211yesmaximal, characteristic, complemented
3#21447956C211yesmaximal, characteristic, complemented
4#21445343C211yesmaximal, characteristic, complemented
5#21443872C211yesmaximal, characteristic, complemented
6#21443778C211yesmaximal, characteristic, complemented
7C61×#1333C211yesmaximal, characteristic, complemented
8#16840462—21no—
9#16840167C2211yescharacteristic
10#16840164C2211yescharacteristic
11#16840084—21no—
12#16840074—21no—
13#16840062—21no—
14#16840053—21no—
15#16840012—21no—
16#16839841C2211yescharacteristic
17#16839803—21no—
18#16839590—21no—
19#16839588—21no—
20#16839587—21no—
21C4⋊#11758185C2211yescharacteristic
22#16839563—21no—
23#16839510—21no—
24C4×D8×C61C2211yescharacteristic
25C61×#346C2211yescharacteristic
26C61×#334C2211yescharacteristic
27C2×#11758189—21no—
28#14519777—21no—
29#14519770—41no—
30#14519769—21no—
31#14519760—41no—
32#14519750—41no—
33#14519748—21no—
34#14519748—21no—
35C4×D244D411yescharacteristic
36C4×C22⋊D61—41no—
37#14519735—21no—
38C4⋊C4×D61—21no—
39C2×#11758185—21no—
40#14519711—21no—
41#14519711—21no—
42#14519711D411yescharacteristic
43#14519711D411yescharacteristic
44#14519710—21no—
45#14519709—21no—
46#14519709—41no—
47#14519708—21no—
48C4⋊#92418D411yescharacteristic
49#14519699—41no—
50#14519698—21no—
51#14519698—21no—
52#14519689—21no—
53C2×D8×C61D411yescharacteristic
54C4×D4×C61—21no—
55C2×C16×C61—21no—
56#107×C61D411yescharacteristic
57C4⋊C8×C61—21no—
58#102×C61—21no—
59C4×C8×C61C2311yescharacteristic
60C2×D4×C61—21no—
61C22×C4×C61—41no—
62C2×C22⋊D61—41no—
63C2×C22⋊D61—41no—
64C2×D244D811yescharacteristic
65C2×C4×D61—21no—
66C2×C4×D61—41no—
67C2×Dic122—41no—
68D8×C61—21no—
69D8×C61—21no—
70C2×C8×C61—41no—
71C2×C8×C61C2×D411yescharacteristic
72C2×C8×C61C2×D411yescharacteristic
73C4⋊C4×C61—21no—
74C22⋊C4×C61—41no—
75C42×C61C2×D411yescharacteristic
76C22⋊Dic61—41no—
77C22⋊Dic61—41no—
78#11758198—21no—
79#11758198—41no—
80C4⋊Dic61—21no—
81C4⋊Dic61—21no—
82C4⋊Dic61—41no—
83C4⋊Dic61—41no—
84C4⋊Dic61D811yescharacteristic
85#11758196—41no—
86#11758196—41no—
87#11758196—41no—
88C4×Dic61—41no—
89C2×#92418—21no—
90#11758189—41no—
91#11758189—41no—
92C16×C61—22no—
93#11758185—41no—
94C23×C61—41no—
95C22×D61—21no—
96D4×C61—41no—
97D4×C61—41no—
98C2×C4×C61—41no—
99C2×C4×C61—161no—
100C2×C4×C61#12011yescharacteristic
101C2×C4×C61C2×D811yescharacteristic
102C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
103C22⋊D61—82no—
104C22⋊D61—161no—
105C2×Dic61—21no—
106C2×Dic61—41no—
107C2×Dic61—41no—
108C2×Dic61—81no—
109D244—41no—
110C4×D61—41no—
111C4×D61—41no—
112C4×D61—161no—
113Dic122—161no—
114C8×C61—21no—
115C8×C61—81no—
116C8×C61#13511yescharacteristic
117C8×C61#13711yescharacteristic
118#92418—41no—
119#12400—611nomaximal, Sylow
120C22×C61—81no—
121C22×C61—81no—
122C22×C61—81no—
123C22×C61#44711yescharacteristic
124C2×D61—41no—
125C2×D61—41no—
126C2×D61—41no—
127C4×C61—21no—
128C4×C61—21no—
129C4×C61—81no—
130C4×C61#45211yescharacteristic
131C4×C61#45611yescharacteristic
132Dic61—41no—
133Dic61—81no—
134Dic61—81no—
135Dic61—161no—
136#3355—611no—
137#2255—611no—
138#2224—611no—
139#1695—611no—
140#1363—611no—
141#1333D6111yescharacteristic, complemented
142#1330—611no—
143C2×C61—161no—
144C2×C61#164711yescharacteristic
145C2×C61#219111yescharacteristic
146C2×C61#219211yescharacteristic
147D61—81no—
148#553—1221no—
149#500—611no—
150#499—611no—
151#482—1221no—
152#480—1221no—
153#478—1221no—
154#476—1221no—
155#469—1221no—
156C4×D8C2×D6111yescharacteristic
157#436—611no—
158#428—1221no—
159#367—1221no—
160#366—1221no—
161#366—1221no—
162C4⋊C16—611no—
163#357—1221no—
164#346C2×D6111yescharacteristic
165#334C2×D6111yescharacteristic
166#333—1221no—
167C61#1240011yescharacteristic, complemented, Sylow
168C2×D8D24411yescharacteristic
169C2×M16—1221no—
170C4⋊Q8—1221no—
171#126—2441no—
172#125—1221no—
173#123—2441no—
174#121—1221no—
175#121—1221no—
176#121—2441no—
177C4×D4—21no—
178C4×D4—611no—
179C4×D4—2441no—
180#117—1221no—
181C2×C4⋊C4—1221no—
182C2×C16—21no—
183C2×C16—1221no—
184#107—611no—
185#107—611no—
186#107—1221no—
187#107—1221no—
188#107—1221no—
189#107D24411yescharacteristic
190#106—1221no—
191#106—1221no—
192#106—2441no—
193C4⋊C8—21no—
194C4⋊C8—611no—
195#102—21no—
196#102—1221no—
197#102—1221no—
198#102—2441no—
199C22⋊C8—1221no—
200C4×C8C22×D6111yescharacteristic
201C2×Q8—2441no—
202C2×D4—21no—
203C2×D4—611no—
204C2×D4—2441no—
205C2×D4—2441no—
206C22×C4—41no—
207C22×C4—1221no—
208C22×C4—2441no—
209D8—21no—
210D8—21no—
211M16—2441no—
212M16—2441no—
213C2×C8—41no—
214C2×C8—1221no—
215C2×C8C2×D24411yescharacteristic
216C2×C8D4×D6111yescharacteristic
217C4⋊C4—21no—
218C4⋊C4—611no—
219C4⋊C4—1221no—
220C4⋊C4—1221no—
221C4⋊C4—2441no—
222C4⋊C4—2441no—
223C4⋊C4—2441no—
224C4⋊C4—2441no—
225C4⋊C4—2441no—
226C22⋊C4—41no—
227C22⋊C4—1221no—
228C22⋊C4—2441no—
229C22⋊C4—2441no—
230C22⋊C4—2441no—
231C42—2441no—
232C42D4×D6111yescharacteristic
233C16—22no—
234C16—2441no—
235C23—41no—
236C23—1221no—
237Q8—9761no—
238D4—41no—
239D4—41no—
240D4—9761no—
241D4—4882no—
242D4—2441no—
243C2×C4—41no—
244C2×C4—161no—
245C2×C4—1221no—
246C2×C4—9761no—
247C2×C4—4881no—
248C2×C4—2441no—
249C2×C4—2441no—
250C2×C4—2441no—
251C2×C4—2441no—
252C2×C4#1451974711yescharacteristic
253C2×C4D8×D6111yescharacteristic
254C2×C4#1451980411yescharacteristic
255C8—21no—
256C8—81no—
257C8—2441no—
258C8#1451979911yescharacteristic
259C8#1451981011yescharacteristic
260C22—81no—
261C22—81no—
262C22—81no—
263C22—2441no—
264C22—2441no—
265C22—2441no—
266C22#1683989711yescharacteristic
267C4—21no—
268C4—21no—
269C4—81no—
270C4—9761no—
271C4—4881no—
272C4—4881no—
273C4—2441no—
274C4#1683992611yescharacteristic
275C4#1683994611yescharacteristic
276C2—161no—
277C2—4881no—
278C2#2144505711yescharacteristic
279C2#2144777111yescharacteristic
280C2#2144777911yescharacteristic
subgroupG/H
centerC22#16839897
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1333C2
socleC22×C61#447
prime radical#21458426C2
hypercenter#1333D61
hypocenterC61#12400
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1333

Complements

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

NH ≅ G/Ntype
2. #21448105C2semidirect
3. #21447956C2semidirect
4. #21445343C2semidirect
5. #21443872C2semidirect
6. #21443778C2semidirect
7. C61×#1333C2semidirect
141. #1333D61semidirect
167. C61#12400semidirect

Maximal subgroups

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

subgroupindex
#214584262
#214481052
#214479562
#214453432
#214438722
#214437782
C61×#13332
#1240061