Finite Group Databasebeta

← #29593527

Subgroups — #29593527

Order 15616.

340 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 65 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#21458829C211yesmaximal, characteristic, complemented
2#21448068C211yesmaximal, characteristic
3#21445176C211yesmaximal, characteristic, complemented
4#21443866C211yesmaximal, characteristic, complemented
5#21443797C211yesmaximal, characteristic, complemented
6#21443783C211yesmaximal, characteristic, complemented
7C61×#2207C211yesmaximal, characteristic, complemented
8#16840497—21no—
9C2×#14519718—22no—
10#16840147—21no—
11#16840139C2211yescharacteristic
12#16839980—22no—
13#16839962—21no—
14#16839959—21no—
15C8×Dic122C2211yescharacteristic
16#16839844—21no—
17C4×#11758185C2211yescharacteristic
18#16839515C2211yescharacteristic
19#16839506—21no—
20C2×SD32×C61—21no—
21C61×#493C2211yescharacteristic
22C4×Q16×C61C2211yescharacteristic
23C61×C4⋊C16C2211yescharacteristic
24C61×#357—21no—
25C2×#11758200—41no—
26C2×#11758201—22no—
27C2×D488—21no—
28C2×D488D412yes—
29#14519774—21no—
30#14519766—22no—
31#14519765—41no—
32#14519762—42no—
33C4×Dic122D411yescharacteristic
34C4×D244—41no—
35#14519739—22no—
36#14519718—44no—
37C2×#11758185—21no—
38C4⋊#92418—21no—
39C4⋊#92418D411yescharacteristic
40#14519706—21no—
41#14519698—41no—
42#14519697—22no—
43C8×Dic61—21no—
44C2×Q16×C61D411yescharacteristic
45C2×D8×C61—21no—
46C2×D8×C61—21no—
47#127×C61—21no—
48C4×Q8×C61—21no—
49SD32×C61—42no—
50C2×C16×C61—21no—
51#107×C61D411yescharacteristic
52#103×C61—21no—
53C4×C8×C61C2311yescharacteristic
54C2×Q8×C61—21no—
55C2×D4×C61—41no—
56C2×D4×C61—41no—
57C2×D4×C61—41no—
58C2×D244—22no—
59C2×D244—41no—
60C2×D244—41no—
61C2×C4×D61—42no—
62C2×Dic122D811yescharacteristic
63Q16×C61—21no—
64Q16×C61—21no—
65D8×C61—42no—
66D8×C61—41no—
67D8×C61—41no—
68C2×C8×C61C2×D411yescharacteristic
69C2×C8×C61C2×D411yescharacteristic
70C4⋊C4×C61—21no—
71C4⋊C4×C61—41no—
72C42×C61—41no—
73C42×C61C2×D411yescharacteristic
74#11758201—82no—
75#11758200—82no—
76#11758198—42no—
77#11758198—42no—
78#11758198—42no—
79C4⋊Dic61D811yescharacteristic
80#11758196—21no—
81C4×Dic61—21no—
82C2×#92418—21no—
83C2×#92418—41no—
84D488—42no—
85D488—41no—
86D488—41no—
87C16×C61—41no—
88#11758185—22no—
89C23×C61—81no—
90C22×D61—42no—
91Q8×C61—41no—
92Q8×C61—41no—
93D4×C61—81no—
94D4×C61—81no—
95D4×C61—81no—
96D4×C61—81no—
97D4×C61—161no—
98C2×C4×C61—41no—
99C2×C4×C61—41no—
100C2×C4×C61#12011yescharacteristic
101C2×C4×C61C2×D811yescharacteristic
102C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
103C2×Dic61—21no—
104C2×Dic61—21no—
105D244—42no—
106D244—42no—
107D244—81no—
108D244—81no—
109D244—161no—
110C4×D61—162no—
111Dic122—21no—
112Dic122—21no—
113C8×C61—21no—
114C8×C61#13511yescharacteristic
115C8×C61AGL(1,ℤ/8)11yescharacteristic
116#92418—41no—
117#92418—81no—
118#12329—611nomaximal, Sylow
119C22×C61—161no—
120C22×C61—161no—
121C22×C61—161no—
122C22×C61#44711yescharacteristic
123C2×D61—82no—
124C2×D61—82no—
125C2×D61—82no—
126C4×C61—21no—
127C4×C61—81no—
128C4×C61—81no—
129C4×C61#44911yescharacteristic
130C4×C61#45311yescharacteristic
131C4×C61#50811yescharacteristic
132C4×C61#50911yescharacteristic
133Dic61—41no—
134Dic61—41no—
135#3396—611no—
136#2246—611no—
137#2207D6111yescharacteristic, complemented
138#1668—611no—
139#1361—611no—
140Q8⋊C16—611no—
141#1332—611no—
142C2×C61—321no—
143C2×C61#162111yescharacteristic
144C2×C61#218611yescharacteristic
145C2×C61#219211yescharacteristic
146D61—162no—
147#559—1221no—
148C2×SD32—21no—
149C2×D16—1222no—
150#495—1221no—
151#493—611no—
152#493C2×D6111yescharacteristic
153#463—1222no—
154#460—1221no—
155#460—1221no—
156C8×Q8—611no—
157C4×Q16C2×D6111yescharacteristic
158C4×D8—1221no—
159C4⋊C16C2×D6111yescharacteristic
160#357—21no—
161C4×C16—611no—
162#335—611no—
163#331—1221no—
164C61#1232911yescharacteristic, complemented, Sylow
165C2×Q16C22⋊D6111yescharacteristic
166C2×SD16—1222no—
167C2×SD16—2441no—
168C2×D8—21no—
169C2×D8—21no—
170C2×D8—612no—
171C2×D8—1221no—
172#127—21no—
173#127—1221no—
174#124—1222no—
175#124—2441no—
176#123—2442no—
177C4×Q8—21no—
178C4×Q8—611no—
179C4×D4—1222no—
180C4×D4—2441no—
181SD32—42no—
182D16—2444no—
183C2×C16—21no—
184C2×C16—1221no—
185#107C22⋊D6111yescharacteristic
186C4⋊C8—611no—
187C4⋊C8—1221no—
188C4⋊C8—1221no—
189#103—21no—
190#102—1222no—
191#102—2441no—
192C4×C8—1221no—
193C4×C8C22×D6111yescharacteristic
194C2×Q8—21no—
195C2×Q8—611no—
196C2×D4—41no—
197C2×D4—41no—
198C2×D4—41no—
199C2×D4—1222no—
200C2×D4—2441no—
201C2×D4—2441no—
202C22×C4—2442no—
203Q16—21no—
204Q16—21no—
205SD16—4882no—
206SD16—4882no—
207D8—42no—
208D8—41no—
209D8—41no—
210D8—2442no—
211D8—2441no—
212D8—2441no—
213C2×C8—1221no—
214C2×C8—2441no—
215C2×C8D4×D6111yescharacteristic
216C2×C8C2×C22⋊D6111yescharacteristic
217C4⋊C4—21no—
218C4⋊C4—41no—
219C4⋊C4—611no—
220C4⋊C4—1221no—
221C22⋊C4—2442no—
222C22⋊C4—2442no—
223C22⋊C4—2442no—
224C42—41no—
225C42—1221no—
226C42D4×D6111yescharacteristic
227C16—41no—
228C16—1222no—
229C23—81no—
230C23—2442no—
231Q8—41no—
232Q8—41no—
233Q8—1221no—
234Q8—1221no—
235D4—81no—
236D4—81no—
237D4—81no—
238D4—81no—
239D4—161no—
240D4—9761no—
241D4—4881no—
242D4—4881no—
243D4—2442no—
244D4—2442no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—1221no—
248C2×C4—1221no—
249C2×C4—9762no—
250C2×C4#1451974511yescharacteristic
251C2×C4D8×D6111yescharacteristic
252C2×C4#1451980111yescharacteristic
253C8—21no—
254C8—4881no—
255C8—2441no—
256C8#1451979711yescharacteristic
257C8#1451980311yescharacteristic
258C22—161no—
259C22—161no—
260C22—161no—
261C22—4882no—
262C22—4882no—
263C22—4882no—
264C22#1683989411yescharacteristic
265C4—21no—
266C4—81no—
267C4—81no—
268C4—2441no—
269C4—2441no—
270C4#1683990511yescharacteristic
271C4#1683992811yescharacteristic
272C4#1684019311yescharacteristic
273C4#1684019911yescharacteristic
274C2—321no—
275C2—9762no—
276C2#2144488311yescharacteristic
277C2#2144774111yescharacteristic
278C2#2144777311yescharacteristic
subgroupG/H
centerC22#16839894
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#2207C2
socleC22×C61#447
prime radical#21448068C2
hypercenter#2207D61
hypocenterC61#12329
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2207

Complements

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

NH ≅ G/Ntype
1. #21458829C2semidirect
3. #21445176C2semidirect
4. #21443866C2semidirect
5. #21443797C2semidirect
6. #21443783C2semidirect
7. C61×#2207C2semidirect
137. #2207D61semidirect
164. C61#12329semidirect

Maximal subgroups

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

subgroupindex
#214588292
#214480682
#214451762
#214438662
#214437972
#214437832
C61×#22072
#1232961