Finite Group Databasebeta

← #29593452

Subgroups — #29593452

Order 15616.

384 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 69 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#21457569C211yesmaximal, characteristic, complemented
2#21448076C211yesmaximal, characteristic, complemented
3#21447860C211yesmaximal, characteristic, complemented
4#21445175C211yesmaximal, characteristic
5#21443782C211yesmaximal, characteristic, complemented
6#21443773C211yesmaximal, characteristic, complemented
7C61×#1362C211yesmaximal, characteristic, complemented
8C2×Q16×D61—21no—
9#16840427—21no—
10C2×#14519722—21no—
11C2×#14519720—22no—
12#16840139C2211yescharacteristic
13#16840000—21no—
14#16839969—21no—
15#16839958—21no—
16#16839916—22no—
17C4×Dic244C2211yescharacteristic
18C8×D244C2211yescharacteristic
19#16839564—21no—
20C4×#11758185C2211yescharacteristic
21#16839505—21no—
22C61×#494C2211yescharacteristic
23C61×C4⋊C16C2211yescharacteristic
24C61×#335C2211yescharacteristic
25C2×Q8×D61—22no—
26C2×Dic244D411yescharacteristic
27C2×#11758202—22no—
28Q16×D61—42no—
29Q16×D61—42no—
30C2×D488—21no—
31C2×D488—21no—
32C2×D488—41no—
33C2×C8×D61—21no—
34#14519776—41no—
35#14519774—21no—
36#14519755—42no—
37#14519753—22no—
38C4×Dic122—21no—
39C4×D244D411yescharacteristic
40#14519739—41no—
41#14519722—42no—
42#14519720—44no—
43C2×#11758185—21no—
44#14519711D411yescharacteristic
45C4⋊#92418D411yescharacteristic
46#14519702—21no—
47#14519701—22no—
48#14519699—41no—
49#14519689—21no—
50C2×Q16×C61—21no—
51C2×Q16×C61D412yes—
52C4⋊Q8×C61—21no—
53C2×C16×C61—21no—
54C4⋊C8×C61—21no—
55C4×C8×C61C2311yescharacteristic
56C2×Q8×C61—22no—
57Q8×D61—44no—
58Q8×D61—82no—
59C2×D244—41no—
60C2×D244—41no—
61C2×D244—41no—
62C2×D244D811yescharacteristic
63C2×C4×D61—21no—
64C2×C4×D61—42no—
65C2×Dic122—21no—
66C2×Dic122—42no—
67Q16×C61—42no—
68Q16×C61—41no—
69Q16×C61—41no—
70C2×C8×C61—41no—
71C2×C8×C61C2×D411yescharacteristic
72C2×C8×C61C2×D411yescharacteristic
73C4⋊C4×C61—41no—
74C4⋊C4×C61—41no—
75C42×C61C2×D411yescharacteristic
76#11758202—44no—
77#11758198—21no—
78#11758198—42no—
79C4⋊Dic61—21no—
80C4⋊Dic61D811yescharacteristic
81#11758196—42no—
82#11758196—41no—
83C4×Dic61—41no—
84C2×#92418—21no—
85Dic244—21no—
86Dic244D812yescomplemented
87D488—42no—
88D488—41no—
89D488—41no—
90D488—82no—
91C8×D61—41no—
92C8×D61—41no—
93C16×C61—41no—
94#11758185—22no—
95C22×D61—21no—
96C22×D61—81no—
97Q8×C61—42no—
98Q8×C61—42no—
99C2×C4×C61—42no—
100C2×C4×C61#12011yescharacteristic
101C2×C4×C61C2×D811yescharacteristic
102C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
103C2×Dic61—21no—
104C2×Dic61—41no—
105C2×Dic61—41no—
106D244—21no—
107D244—81no—
108D244—81no—
109D244—81no—
110D244—81no—
111D244—161no—
112D244SD3212yescomplemented
113C4×D61—41no—
114C4×D61—41no—
115C4×D61—84no—
116Dic122—22no—
117Dic122—41no—
118Dic122—84no—
119C8×C61—21no—
120C8×C61—81no—
121C8×C61C2×D811yescharacteristic
122C8×C61AGL(1,ℤ/8)11yescharacteristic
123#92418—41no—
124#12318—611nomaximal, Sylow
125C22×C61#44711yescharacteristic
126C2×D61—22no—
127C2×D61—41no—
128C2×D61—41no—
129C2×D61—161no—
130C2×D61—161no—
131C2×D61—161no—
132C4×C61—21no—
133C4×C61—82no—
134C4×C61#44711yescharacteristic
135C4×C61#45311yescharacteristic
136C4×C61C2×SD3211yescharacteristic
137C4×C61#51011yescharacteristic
138Dic61—42no—
139Dic61—41no—
140Dic61—81no—
141D4×Q16—611no—
142#2248—611no—
143#2207—611no—
144#1667—611no—
145#1362D6111yescharacteristic, complemented
146#1332—611no—
147D4⋊C16—611no—
148C2×C61#161911yescharacteristic
149C2×C61#218511yescharacteristic
150C2×C61#219311yescharacteristic
151D61—42no—
152D61—321no—
153C22×Q16—1221no—
154D4×Q8—1221no—
155C2×SD32—1221no—
156C2×SD32—1222no—
157#494C2×D6111yescharacteristic
158#493—611no—
159#467—1221no—
160#462—1221no—
161#459—1221no—
162#451—1222no—
163C4×Q16—611no—
164C8×D4—611no—
165C4⋊C16C2×D6111yescharacteristic
166#357—1221no—
167C4×C16—611no—
168#335C2×D6111yescharacteristic
169#331—1221no—
170C61#1231811yescharacteristic, complemented, Sylow
171C22×Q8—1222no—
172C2×Q16—21no—
173C2×Q16—611no—
174C2×Q16—1222no—
175C2×Q16—2442no—
176C2×Q16—2442no—
177C2×Q16D24412yes—
178C2×D8—1221no—
179C2×D8—1221no—
180C2×D8—2441no—
181C22×C8—1221no—
182C4⋊Q8—21no—
183C4⋊Q8—2441no—
184#127—1221no—
185C22⋊Q8—1222no—
186C22⋊Q8—2442no—
187C4×Q8—1221no—
188C4×D4—611no—
189C4×D4—2441no—
190SD32—2442no—
191SD32—2444no—
192C2×C16—21no—
193C2×C16—1221no—
194#107—611no—
195C4⋊C8—21no—
196C4⋊C8—611no—
197#103—1222no—
198#103—1221no—
199#102—2441no—
200C22⋊C8—1221no—
201C4×C8C22×D6111yescharacteristic
202C2×Q8—22no—
203C2×Q8—1221no—
204C2×Q8—4882no—
205C2×Q8—2442no—
206C2×Q8—2444no—
207C2×D4—611no—
208C2×D4—2441no—
209C2×D4—2441no—
210C2×D4—2441no—
211C22×C4—1221no—
212C22×C4—2442no—
213Q16—42no—
214Q16—41no—
215Q16—41no—
216Q16—612no—
217Q16—1221no—
218Q16—2444no—
219D8—4882no—
220D8—2442no—
221D8—2441no—
222D8—2441no—
223C2×C8—41no—
224C2×C8—1221no—
225C2×C8—2441no—
226C2×C8—2441no—
227C2×C8C2×D24411yescharacteristic
228C2×C8D4×D6111yescharacteristic
229C4⋊C4—41no—
230C4⋊C4—41no—
231C4⋊C4—611no—
232C4⋊C4—1221no—
233C4⋊C4—2442no—
234C4⋊C4—2441no—
235C22⋊C4—1221no—
236C22⋊C4—2442no—
237C42—2441no—
238C42D4×D6111yescharacteristic
239C16—41no—
240C16—1222no—
241C23—1221no—
242C23—4881no—
243Q8—42no—
244Q8—42no—
245Q8—1222no—
246Q8—4884no—
247Q8—2441no—
248D4—612no—
249D4—1221no—
250D4—9761no—
251D4—4881no—
252D4—4881no—
253D4—4881no—
254D4—4881no—
255C2×C4—42no—
256C2×C4—1221no—
257C2×C4—4884no—
258C2×C4—2441no—
259C2×C4—2441no—
260C2×C4—2441no—
261C2×C4—2441no—
262C2×C4#1451974711yescharacteristic
263C2×C4D8×D6111yescharacteristic
264C2×C4#1451980411yescharacteristic
265C8—21no—
266C8—81no—
267C8—2441no—
268C8D8×D6111yescharacteristic
269C8#1451980411yescharacteristic
270C22—1222no—
271C22—9761no—
272C22—9761no—
273C22—9761no—
274C22—2441no—
275C22—2441no—
276C22#1683989711yescharacteristic
277C4—21no—
278C4—82no—
279C4—4881no—
280C4—2441no—
281C4—2442no—
282C4#1683989711yescharacteristic
283C4#1683993211yescharacteristic
284C4SD32×D6111yescharacteristic
285C4#1684020411yescharacteristic
286C2—19521no—
287C2—2442no—
288C2#2144487411yescharacteristic
289C2#2144773711yescharacteristic
290C2#2144778611yescharacteristic
subgroupG/H
centerC22#16839897
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1362C2
socleC22×C61#447
prime radical#21445175C2
hypercenter#1362D61
hypocenterC61#12318
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1362

Complements

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

NH ≅ G/Ntype
1. #21457569C2semidirect
2. #21448076C2semidirect
3. #21447860C2semidirect
5. #21443782C2semidirect
6. #21443773C2semidirect
7. C61×#1362C2semidirect
86. Dic244D8semidirect
112. D244SD32semidirect
145. #1362D61semidirect
170. C61#12318semidirect

Maximal subgroups

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

subgroupindex
#214575692
#214480762
#214478602
#214451752
#214437822
#214437732
C61×#13622
#1231861