Finite Group Databasebeta

← #29593448

Subgroups — #29593448

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#21447856C211yesmaximal, characteristic, complemented
3#21445171C211yesmaximal, characteristic
4#21443868C211yesmaximal, characteristic, complemented
5#21443784C211yesmaximal, characteristic, complemented
6#21443775C211yesmaximal, characteristic, complemented
7C61×#2248C211yesmaximal, characteristic, complemented
8C2×Q16×D61—21no—
9#16840427—21no—
10C2×#14519721—21no—
11#16840000—21no—
12#16839969—21no—
13#16839954—21no—
14#16839916—22no—
15C4×Dic244C2211yescharacteristic
16C8×D244C2211yescharacteristic
17C4⋊#11758185C2211yescharacteristic
18#16839563—21no—
19#16839515C2211yescharacteristic
20#16839506—21no—
21C2×SD32×C61—22no—
22C61×#494C2211yescharacteristic
23C61×#493C2211yescharacteristic
24C4×C16×C61C2211yescharacteristic
25C2×Q8×D61—22no—
26C2×Dic244D411yescharacteristic
27C2×#11758202—22no—
28Q16×D61—42no—
29Q16×D61—42no—
30C2×#11758199—41no—
31C2×C8×D61—21no—
32#14519776—41no—
33#14519755—42no—
34#14519753—22no—
35C4×Dic122—21no—
36C4×D244D411yescharacteristic
37#14519739—41no—
38#14519721—42no—
39C2×#11758185—21no—
40#14519711D411yescharacteristic
41C4⋊#92418—21no—
42C4⋊#92418D411yescharacteristic
43#14519702—21no—
44#14519701—22no—
45#14519698—41no—
46#14519689—21no—
47C2×Q16×C61—21no—
48C2×Q16×C61D412yes—
49C2×D8×C61—21no—
50C2×D8×C61—21no—
51C4⋊Q8×C61—21no—
52#127×C61—21no—
53SD32×C61—44no—
54C2×C16×C61—21no—
55C4×C8×C61C2311yescharacteristic
56C2×Q8×C61—22no—
57C2×D4×C61—41no—
58C2×D4×C61—41no—
59C2×D4×C61—41no—
60Q8×D61—44no—
61Q8×D61—82no—
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—
70D8×C61—42no—
71D8×C61—41no—
72D8×C61—41no—
73C2×C8×C61C2×D411yescharacteristic
74C2×C8×C61C2×D411yescharacteristic
75C4⋊C4×C61—41no—
76C4⋊C4×C61—41no—
77C42×C61C2×D411yescharacteristic
78#11758202—44no—
79#11758199—82no—
80#11758198—21no—
81#11758198—42no—
82C4⋊Dic61—21no—
83C4⋊Dic61D811yescharacteristic
84#11758196—42no—
85#11758196—41no—
86C4×Dic61—41no—
87C2×#92418—21no—
88C2×#92418—41no—
89Dic244—21no—
90Dic244D812yescomplemented
91C8×D61—41no—
92C8×D61—41no—
93C16×C61—22no—
94#11758185—41no—
95C23×C61—81no—
96C22×D61—21no—
97Q8×C61—42no—
98Q8×C61—42no—
99D4×C61—81no—
100D4×C61—81no—
101D4×C61—81no—
102D4×C61—81no—
103D4×C61—161no—
104C2×C4×C61—42no—
105C2×C4×C61#12011yescharacteristic
106C2×C4×C61C2×D811yescharacteristic
107C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
108C2×Dic61—21no—
109C2×Dic61—41no—
110C2×Dic61—41no—
111D244—21no—
112D244SD3212yescomplemented
113C4×D61—41no—
114C4×D61—41no—
115C4×D61—84no—
116Dic122—22no—
117Dic122—41no—
118Dic122—84no—
119C8×C61—21no—
120C8×C61C2×D811yescharacteristic
121C8×C61AGL(1,ℤ/8)11yescharacteristic
122#92418—41no—
123#92418—81no—
124#12318—611nomaximal, Sylow
125C22×C61—161no—
126C22×C61—161no—
127C22×C61—161no—
128C22×C61#44711yescharacteristic
129C2×D61—22no—
130C2×D61—41no—
131C2×D61—41no—
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#2248D6111yescharacteristic, complemented
143#2207—611no—
144#1667—611no—
145#1362—611no—
146#1332—611no—
147D4⋊C16—611no—
148C2×C61—321no—
149C2×C61#161911yescharacteristic
150C2×C61#218511yescharacteristic
151C2×C61#219311yescharacteristic
152D61—42no—
153C22×Q16—1221no—
154D4×Q8—1221no—
155C2×SD32—22no—
156C2×SD32—1221no—
157#494C2×D6111yescharacteristic
158#493C2×D6111yescharacteristic
159#467—1221no—
160#462—1221no—
161#459—1221no—
162#451—1222no—
163C4×Q16—611no—
164C8×D4—611no—
165C4⋊C16—611no—
166#357—1221no—
167C4×C16C2×D6111yescharacteristic
168#335—611no—
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×Q16C22⋊D6112yes—
178C2×D8—21no—
179C2×D8—21no—
180C2×D8—2441no—
181C22×C8—1221no—
182C4⋊Q8—21no—
183C4⋊Q8—2441no—
184#127—21no—
185C22⋊Q8—1222no—
186C22⋊Q8—2442no—
187C4×Q8—1221no—
188C4×D4—611no—
189C4×D4—2441no—
190SD32—44no—
191SD32—2442no—
192C2×C16—21no—
193C2×C16—1221no—
194#107—611no—
195C4⋊C8—611no—
196C4⋊C8—1221no—
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—41no—
208C2×D4—41no—
209C2×D4—41no—
210C2×D4—611no—
211C22×C4—1221no—
212C22×C4—2442no—
213Q16—42no—
214Q16—41no—
215Q16—41no—
216Q16—612no—
217Q16—1221no—
218Q16—2444no—
219D8—42no—
220D8—41no—
221D8—41no—
222D8—4882no—
223C2×C8—1221no—
224C2×C8—2441no—
225C2×C8—2441no—
226C2×C8—2441no—
227C2×C8D4×D6111yescharacteristic
228C2×C8C2×C22⋊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—22no—
240C16—2441no—
241C23—81no—
242C23—1221no—
243Q8—42no—
244Q8—42no—
245Q8—1222no—
246Q8—4884no—
247Q8—2441no—
248D4—81no—
249D4—81no—
250D4—81no—
251D4—81no—
252D4—161no—
253D4—612no—
254D4—1221no—
255C2×C4—42no—
256C2×C4—1221no—
257C2×C4—4884no—
258C2×C4—2441no—
259C2×C4—2441no—
260C2×C4—2441no—
261C2×C4—2441no—
262C2×C4#1451974511yescharacteristic
263C2×C4D8×D6111yescharacteristic
264C2×C4#1451980111yescharacteristic
265C8—21no—
266C8—4881no—
267C8—2441no—
268C8D8×D6111yescharacteristic
269C8#1451980111yescharacteristic
270C22—161no—
271C22—161no—
272C22—161no—
273C22—1222no—
274C22—2441no—
275C22—2441no—
276C22#1683989411yescharacteristic
277C4—21no—
278C4—82no—
279C4—4881no—
280C4—2441no—
281C4—2442no—
282C4#1683989411yescharacteristic
283C4#1683992911yescharacteristic
284C4SD32×D6111yescharacteristic
285C4#1684020111yescharacteristic
286C2—321no—
287C2—2442no—
288C2#2144487111yescharacteristic
289C2#2144773411yescharacteristic
290C2#2144778211yescharacteristic
subgroupG/H
centerC22#16839894
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#2248C2
socleC22×C61#447
prime radical#21445171C2
hypercenter#2248D61
hypocenterC61#12318
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2248

Complements

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

NH ≅ G/Ntype
1. #21457569C2semidirect
2. #21447856C2semidirect
4. #21443868C2semidirect
5. #21443784C2semidirect
6. #21443775C2semidirect
7. C61×#2248C2semidirect
90. Dic244D8semidirect
112. D244SD32semidirect
142. #2248D61semidirect
170. C61#12318semidirect

Maximal subgroups

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

subgroupindex
#214575692
#214478562
#214451712
#214438682
#214437842
#214437752
C61×#22482
#1231861