Finite Group Databasebeta

← #29593954

Subgroups — #29593954

Order 15616.

290 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 67 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#21448055C211yesmaximal, characteristic
2#21447971C211yesmaximal, characteristic, complemented
3#21445337C211yesmaximal, characteristic, complemented
4#21443862C211yesmaximal, characteristic
5#21443801C211yesmaximal, characteristic, complemented
6#21443789C211yesmaximal, characteristic, complemented
7C61×#3402C211yesmaximal, characteristic
8#16840167C2211yescharacteristic
9#16839972—21no—
10#16839587—21no—
11C4⋊#11758185C2211yescharacteristic
12#16839566—21no—
13#16839566—21no—
14#16839563—21no—
15#16839538C2211yescharacteristic
16#16839513C2211yescharacteristic
17#16839507—21no—
18C61×#556—21no—
19C61×#497—21no—
20C61×#495C2211yescharacteristic
21C61×#464—21no—
22C61×#463—21no—
23C61×#462—21no—
24C61×#446C2211yescharacteristic
25C61×#440—21no—
26C4×Q16×C61C2211yescharacteristic
27C2×#11758202—41no—
28#14519777—21no—
29C2×#11758185—21no—
30C2×#11758185—21no—
31#14519711—21no—
32#14519711—21no—
33C4⋊#92418—21no—
34#14519700—41no—
35C2×Q16×C61—21no—
36C2×Q16×C61D411yescharacteristic
37C2×Q16×C61D411yescharacteristic
38C2×SD16×C61—21no—
39C2×SD16×C61—21no—
40C2×D8×C61D411yescharacteristic
41C4⋊Q8×C61—21no—
42#126×C61—41no—
43#126×C61—41no—
44#124×C61—21no—
45#124×C61—21no—
46C22⋊Q8×C61—41no—
47C4×Q8×C61—21no—
48C4×Q8×C61—21no—
49C4×Q8×C61D411yescharacteristic
50C4×D4×C61—21no—
51#117×C61—41no—
52#107×C61D411yescharacteristic
53C4⋊C8×C61—21no—
54C4⋊C8×C61D411yescharacteristic
55#103×C61—21no—
56#103×C61—21no—
57#102×C61—21no—
58#97×C61—21no—
59C4×C8×C61C2311yescharacteristic
60C2×Q8×C61—21no—
61C2×Q8×C61—21no—
62C2×Q8×C61D811yescharacteristic
63C2×D4×C61—21no—
64C22×C4×C61—41no—
65C2×Dic122—41no—
66Q16×C61—21no—
67Q16×C61—21no—
68Q16×C61—41no—
69Q16×C61—81no—
70SD16×C61—41no—
71SD16×C61—41no—
72SD16×C61—81no—
73D8×C61—41no—
74C2×C8×C61—21no—
75C2×C8×C61C2×D411yescharacteristic
76C2×C8×C61C2×D411yescharacteristic
77C4⋊C4×C61—21no—
78C4⋊C4×C61—21no—
79C4⋊C4×C61—41no—
80C4⋊C4×C61—41no—
81C4⋊C4×C61—41no—
82C4⋊C4×C61—41no—
83C4⋊C4×C61D811yescharacteristic
84C22⋊C4×C61—41no—
85C22⋊C4×C61—41no—
86C22⋊C4×C61—41no—
87C22⋊C4×C61—41no—
88C22⋊C4×C61—41no—
89C42×C61—21no—
90C42×C61—41no—
91C42×C61—41no—
92C42×C61C2×D411yescharacteristic
93#11758202—82no—
94C4⋊Dic61—41no—
95C4⋊Dic61—41no—
96C2×#92418—41no—
97#11758185—41no—
98#11758185—41no—
99C23×C61—41no—
100Q8×C61—41no—
101Q8×C61—41no—
102Q8×C61—41no—
103Q8×C61—41no—
104Q8×C61—41no—
105D4×C61—41no—
106D4×C61—41no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—41no—
110C2×C4×C61—41no—
111C2×C4×C61—41no—
112C2×C4×C61—82no—
113C2×C4×C61#12011yescharacteristic
114C2×C4×C61C2×D811yescharacteristic
115C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
116C2×Dic61—81no—
117Dic122—81no—
118Dic122—81no—
119C8×C61—21no—
120C8×C61—41no—
121C8×C61#13511yescharacteristic
122C8×C61#13711yescharacteristic
123#92418—81no—
124#12391—611nomaximal, Sylow
125C22×C61—81no—
126C22×C61—81no—
127C22×C61—81no—
128C22×C61#44711yescharacteristic
129C4×C61—21no—
130C4×C61—21no—
131C4×C61—41no—
132C4×C61—41no—
133C4×C61—81no—
134C4×C61—81no—
135C4×C61—81no—
136C4×C61#45211yescharacteristic
137C4×C61#45511yescharacteristic
138Dic61—161no—
139#3402D6111yescharacteristic
140#2243—611no—
141#2227—611no—
142#1694—611no—
143#1360—611no—
144#1338—611no—
145#1334—611no—
146C2×C61—161no—
147C2×C61#164111yescharacteristic
148C2×C61#219011yescharacteristic
149C2×C61#219511yescharacteristic
150#556—21no—
151#500—611no—
152#497—21no—
153#495C2×D6111yescharacteristic
154#464—21no—
155#463—21no—
156#462—21no—
157#462—1221no—
158#446C2×D6111yescharacteristic
159#440—21no—
160C4×Q16C2×D6111yescharacteristic
161#366—1221no—
162C4⋊C16—611no—
163#358—1221no—
164#358—1221no—
165#357—1221no—
166#346—611no—
167#334—611no—
168#332—1221no—
169C61#1239111yescharacteristic, complemented, Sylow
170C2×Q16—21no—
171C2×Q16—2441no—
172C2×Q16C22⋊D6111yescharacteristic
173C2×Q16C22⋊D6111yescharacteristic
174C2×SD16—21no—
175C2×SD16—21no—
176C2×D8C22⋊D6111yescharacteristic
177C4⋊Q8—21no—
178C4⋊Q8—1221no—
179#126—41no—
180#126—41no—
181#124—21no—
182#124—21no—
183C22⋊Q8—41no—
184C4×Q8—21no—
185C4×Q8—21no—
186C4×Q8C22⋊D6111yescharacteristic
187C4×D4—21no—
188#117—41no—
189C2×C16—1221no—
190C2×C16—1221no—
191#107—1221no—
192#107—1221no—
193#107C22⋊D6111yescharacteristic
194C4⋊C8—21no—
195C4⋊C8—1221no—
196C4⋊C8C22⋊D6111yescharacteristic
197#103—21no—
198#103—21no—
199#103—2441no—
200#102—21no—
201#97—21no—
202C4×C8C22×D6111yescharacteristic
203C2×Q8—21no—
204C2×Q8—21no—
205C2×Q8—2441no—
206C2×Q8#1175819911yescharacteristic
207C2×D4—21no—
208C22×C4—41no—
209Q16—21no—
210Q16—21no—
211Q16—41no—
212Q16—81no—
213Q16—4882no—
214SD16—41no—
215SD16—41no—
216SD16—81no—
217D8—41no—
218C2×C8—21no—
219C2×C8—2441no—
220C2×C8C2×C22⋊D6111yescharacteristic
221C2×C8C2×C22⋊D6111yescharacteristic
222C4⋊C4—21no—
223C4⋊C4—21no—
224C4⋊C4—41no—
225C4⋊C4—41no—
226C4⋊C4—41no—
227C4⋊C4—41no—
228C4⋊C4—2441no—
229C4⋊C4—2441no—
230C4⋊C4#1175819911yescharacteristic
231C22⋊C4—41no—
232C22⋊C4—41no—
233C22⋊C4—41no—
234C22⋊C4—41no—
235C22⋊C4—41no—
236C42—21no—
237C42—41no—
238C42—41no—
239C42C2×C22⋊D6111yescharacteristic
240C16—2441no—
241C16—2441no—
242C23—41no—
243Q8—41no—
244Q8—41no—
245Q8—41no—
246Q8—41no—
247Q8—41no—
248Q8—4881no—
249Q8—4881no—
250D4—41no—
251D4—41no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—82no—
258C2×C4—4881no—
259C2×C4#1451974611yescharacteristic
260C2×C4C2×#1175819911yescharacteristic
261C2×C4#1451980311yescharacteristic
262C8—21no—
263C8—41no—
264C8—4881no—
265C8#1451979711yescharacteristic
266C8#1451980711yescharacteristic
267C22—81no—
268C22—81no—
269C22—81no—
270C22#1683989611yescharacteristic
271C4—21no—
272C4—21no—
273C4—41no—
274C4—41no—
275C4—81no—
276C4—81no—
277C4—81no—
278C4—9761no—
279C4#1683992411yescharacteristic
280C4#1683994011yescharacteristic
281C2—161no—
282C2#2144501211yescharacteristic
283C2#2144776511yescharacteristic
284C2#2144779711yescharacteristic
subgroupG/H
centerC22#16839896
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#3402C2
socleC22×C61#447
prime radicalC2×D8×C61D4
hypercenter#3402D61
hypocenterC61#12391
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #446 ◁ #3402

Complements

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

NH ≅ G/Ntype
2. #21447971C2semidirect
3. #21445337C2semidirect
5. #21443801C2semidirect
6. #21443789C2semidirect
169. C61#12391semidirect

Maximal subgroups

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

subgroupindex
#214480552
#214479712
#214453372
#214438622
#214438012
#214437892
C61×#34022
#1239161