Finite Group Databasebeta

← #29594034

Subgroups — #29594034

Order 15616.

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

normal subgroups only

This group has 292 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#21447966C211yesmaximal, characteristic, complemented
4#21445333C211yesmaximal, 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#16840012—21no—
15#16839968—21no—
16#16839841C2211yescharacteristic
17#16839803—21no—
18#16839590—21no—
19#16839589—21no—
20#16839588—21no—
21C4⋊#11758185C2211yescharacteristic
22#16839563—21no—
23#16839509—21no—
24C4×D8×C61C2211yescharacteristic
25C61×#346C2211yescharacteristic
26C61×#334C2211yescharacteristic
27C2×#11758190—41no—
28C2×#11758189—21no—
29#14519777—21no—
30#14519770—41no—
31#14519769—21no—
32#14519760—41no—
33#14519750—41no—
34#14519748—21no—
35#14519748—21no—
36C4×D244D411yescharacteristic
37C4×C22⋊D61—41no—
38#14519735—21no—
39C4⋊C4×D61—21no—
40C2×#11758185—21no—
41#14519711—21no—
42#14519711—21no—
43#14519711D411yescharacteristic
44#14519711D411yescharacteristic
45#14519710—21no—
46#14519709—21no—
47#14519708—21no—
48C4⋊#92418D411yescharacteristic
49#14519702—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#11758190—82no—
91#11758189—41no—
92#11758189—41no—
93C16×C61—22no—
94#11758185—41no—
95C23×C61—41no—
96C22×D61—21no—
97D4×C61—41no—
98D4×C61—41no—
99C2×C4×C61—41no—
100C2×C4×C61—161no—
101C2×C4×C61#12011yescharacteristic
102C2×C4×C61C2×D811yescharacteristic
103C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
104C22⋊D61—82no—
105C22⋊D61—161no—
106C2×Dic61—21no—
107C2×Dic61—41no—
108C2×Dic61—41no—
109C2×Dic61—81no—
110D244—41no—
111C4×D61—41no—
112C4×D61—41no—
113C4×D61—161no—
114Dic122—81no—
115Dic122—81no—
116C8×C61—21no—
117C8×C61—81no—
118C8×C61#13511yescharacteristic
119C8×C61#13711yescharacteristic
120#92418—41no—
121#12402—611nomaximal, Sylow
122C22×C61—81no—
123C22×C61—81no—
124C22×C61—81no—
125C22×C61#44711yescharacteristic
126C2×D61—41no—
127C2×D61—41no—
128C2×D61—41no—
129C4×C61—21no—
130C4×C61—21no—
131C4×C61—81no—
132C4×C61#45211yescharacteristic
133C4×C61#45611yescharacteristic
134Dic61—41no—
135Dic61—81no—
136Dic61—81no—
137Dic61—161no—
138#3355—611no—
139#2255—611no—
140#2226—611no—
141#1693—611no—
142#1363—611no—
143#1333D6111yescharacteristic, complemented
144#1330—611no—
145C2×C61—161no—
146C2×C61#164711yescharacteristic
147C2×C61#219011yescharacteristic
148C2×C61#219411yescharacteristic
149D61—81no—
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×D8C2×D6111yescharacteristic
159#436—611no—
160#428—1221no—
161#367—1221no—
162#367—1221no—
163#366—1221no—
164C4⋊C16—611no—
165#357—1221no—
166#346C2×D6111yescharacteristic
167#334C2×D6111yescharacteristic
168#332—1221no—
169C61#1240211yescharacteristic, complemented, Sylow
170C2×SD16—2441no—
171C2×D8D24411yescharacteristic
172C2×M16—1221no—
173C4⋊Q8—1221no—
174#126—2441no—
175#125—1221no—
176#123—2441no—
177#121—1221no—
178#121—1221no—
179#121—2441no—
180C4×D4—21no—
181C4×D4—611no—
182C4×D4—2441no—
183#117—1221no—
184C2×C4⋊C4—1221no—
185C2×C16—21no—
186C2×C16—1221no—
187#107—611no—
188#107—611no—
189#107—1221no—
190#107—1221no—
191#107—1221no—
192#107D24411yescharacteristic
193#106—1221no—
194#106—1221no—
195C4⋊C8—21no—
196C4⋊C8—611no—
197#103—2441no—
198#102—21no—
199#102—1221no—
200#102—1221no—
201C22⋊C8—1221no—
202C4×C8C22×D6111yescharacteristic
203C2×Q8—2441no—
204C2×D4—21no—
205C2×D4—611no—
206C2×D4—2441no—
207C2×D4—2441no—
208C22×C4—41no—
209C22×C4—1221no—
210C22×C4—2441no—
211SD16—4882no—
212D8—21no—
213D8—21no—
214M16—2441no—
215M16—2441no—
216C2×C8—41no—
217C2×C8—1221no—
218C2×C8C2×D24411yescharacteristic
219C2×C8D4×D6111yescharacteristic
220C4⋊C4—21no—
221C4⋊C4—611no—
222C4⋊C4—1221no—
223C4⋊C4—1221no—
224C4⋊C4—2441no—
225C4⋊C4—2441no—
226C4⋊C4—2441no—
227C4⋊C4—2441no—
228C4⋊C4—2441no—
229C22⋊C4—41no—
230C22⋊C4—1221no—
231C22⋊C4—2441no—
232C22⋊C4—2441no—
233C22⋊C4—2441no—
234C42—2441no—
235C42D4×D6111yescharacteristic
236C16—22no—
237C16—2441no—
238C23—41no—
239C23—1221no—
240Q8—4881no—
241Q8—4881no—
242D4—41no—
243D4—41no—
244D4—9761no—
245D4—4882no—
246D4—2441no—
247C2×C4—41no—
248C2×C4—161no—
249C2×C4—1221no—
250C2×C4—9761no—
251C2×C4—4881no—
252C2×C4—2441no—
253C2×C4—2441no—
254C2×C4—2441no—
255C2×C4—2441no—
256C2×C4#1451974711yescharacteristic
257C2×C4D8×D6111yescharacteristic
258C2×C4#1451980411yescharacteristic
259C8—21no—
260C8—81no—
261C8—2441no—
262C8#1451979911yescharacteristic
263C8#1451981011yescharacteristic
264C22—81no—
265C22—81no—
266C22—81no—
267C22—2441no—
268C22—2441no—
269C22—2441no—
270C22#1683989711yescharacteristic
271C4—21no—
272C4—21no—
273C4—81no—
274C4—9761no—
275C4—4881no—
276C4—4881no—
277C4—2441no—
278C4#1683992611yescharacteristic
279C4#1683994611yescharacteristic
280C2—161no—
281C2—4881no—
282C2#2144505711yescharacteristic
283C2#2144776611yescharacteristic
284C2#2144779311yescharacteristic
subgroupG/H
centerC22#16839897
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1333C2
socleC22×C61#447
prime radical#21458426C2
hypercenter#1333D61
hypocenterC61#12402
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. #21447966C2semidirect
4. #21445333C2semidirect
5. #21443872C2semidirect
6. #21443778C2semidirect
7. C61×#1333C2semidirect
143. #1333D61semidirect
169. C61#12402semidirect

Maximal subgroups

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

subgroupindex
#214584262
#214481052
#214479662
#214453332
#214438722
#214437782
C61×#13332
#1240261