Finite Group Databasebeta

← #29593469

Subgroups — #29593469

Order 15616.

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

normal subgroups only

This group has 384 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#21457577C211yesmaximal, characteristic
2#21447866C211yesmaximal, characteristic, complemented
3#21445181C211yesmaximal, characteristic, complemented
4#21443865C211yesmaximal, characteristic, complemented
5#21443784C211yesmaximal, characteristic, complemented
6#21443775C211yesmaximal, characteristic, complemented
7C61×#2248C211yesmaximal, characteristic, complemented
8C2×#14519796—21no—
9#16840432—21no—
10C2×#14519723—21no—
11#16840039—21no—
12#16839995—21no—
13#16839959—21no—
14#16839904—22no—
15C4×Dic244C2211yescharacteristic
16C8×D244C2211yescharacteristic
17C4⋊#11758185C2211yescharacteristic
18#16839566—21no—
19#16839515C2211yescharacteristic
20#16839508—21no—
21C2×SD32×C61—22no—
22C61×#494C2211yescharacteristic
23C61×#493C2211yescharacteristic
24C4×C16×C61C2211yescharacteristic
25C2×#11758224—22no—
26#14519796—42no—
27#14519796—42no—
28C2×Dic244D411yescharacteristic
29C2×#11758200—22no—
30C2×C8×D61—21no—
31#14519773—41no—
32#14519749—42no—
33#14519748—22no—
34C4×Dic122—21no—
35C4×D244D411yescharacteristic
36D4×Dic61—41no—
37#14519723—42no—
38C2×#11758185—21no—
39#14519711D411yescharacteristic
40#14519710—41no—
41C4⋊#92418—21no—
42C4⋊#92418D411yescharacteristic
43#14519702—21no—
44#14519698—22no—
45#14519697—41no—
46#14519689—21no—
47C2×Q16×C61—21no—
48C2×Q16×C61—21no—
49C2×D8×C61—21no—
50C2×D8×C61D412yes—
51C4⋊Q8×C61—21no—
52#127×C61—21no—
53SD32×C61—44no—
54C2×C16×C61—21no—
55C4×C8×C61C2311yescharacteristic
56C2×Q8×C61—41no—
57C2×D4×C61—22no—
58C2×D4×C61—41no—
59C2×D4×C61—41no—
60C2×C22⋊D61—42no—
61C2×C22⋊D61—42no—
62C22×Dic61—42no—
63#11758224—44no—
64#11758224—82no—
65C2×D244D811yescharacteristic
66C2×C4×D61—21no—
67C2×Dic122—21no—
68Q16×C61—42no—
69Q16×C61—41no—
70Q16×C61—41no—
71D8×C61—42no—
72D8×C61—41no—
73D8×C61—41no—
74C2×C8×C61C2×D411yescharacteristic
75C2×C8×C61C2×D411yescharacteristic
76C4⋊C4×C61—41no—
77C4⋊C4×C61—41no—
78C42×C61C2×D411yescharacteristic
79C22⋊Dic61—42no—
80#11758200—44no—
81#11758198—21no—
82C4⋊Dic61—21no—
83C4⋊Dic61D811yescharacteristic
84#11758196—41no—
85C4×Dic61—41no—
86C2×#92418—21no—
87C2×#92418—41no—
88Dic244—21no—
89Dic244D812yes—
90C8×D61—41no—
91C8×D61—41no—
92C16×C61—22no—
93#11758185—41no—
94C23×C61—42no—
95C22×D61—21no—
96Q8×C61—81no—
97Q8×C61—81no—
98D4×C61—42no—
99D4×C61—42no—
100D4×C61—81no—
101D4×C61—81no—
102D4×C61—161no—
103C2×C4×C61—81no—
104C2×C4×C61#12011yescharacteristic
105C2×C4×C61C2×D811yescharacteristic
106C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
107C22⋊D61—84no—
108C22⋊D61—162no—
109C2×Dic61—21no—
110C2×Dic61—41no—
111C2×Dic61—41no—
112C2×Dic61—84no—
113D244—21no—
114D244—21no—
115C4×D61—41no—
116C4×D61—41no—
117Dic122—22no—
118Dic122—41no—
119C8×C61—21no—
120C8×C61C2×D811yescharacteristic
121C8×C61AGL(1,ℤ/8)11yescharacteristic
122#92418—41no—
123#92418—81no—
124#12321—611nomaximal, Sylow
125C22×C61—82no—
126C22×C61—82no—
127C22×C61—82no—
128C22×C61#44711yescharacteristic
129C2×D61—41no—
130C2×D61—41no—
131C2×D61—41no—
132C4×C61—21no—
133C4×C61—161no—
134C4×C61#44711yescharacteristic
135C4×C61#45311yescharacteristic
136C4×C61#50811yescharacteristic
137C4×C61#51011yescharacteristic
138Dic61—42no—
139Dic61—41no—
140Dic61—81no—
141#3287—611no—
142#2248D6111yescharacteristic, complemented
143#2209—611no—
144#1669—611no—
145#1361—611no—
146#1332—611no—
147D4⋊C16—611no—
148C2×C61—162no—
149C2×C61#161911yescharacteristic
150C2×C61#218911yescharacteristic
151C2×C61#219411yescharacteristic
152D61—81no—
153C2×#135—1221no—
154#550—1221no—
155C2×Q32—1221no—
156C2×SD32—22no—
157#494C2×D6111yescharacteristic
158#493C2×D6111yescharacteristic
159#474—1221no—
160#466—1221no—
161#460—1221no—
162#449—1222no—
163C4×Q16—611no—
164C8×D4—611no—
165C4⋊C16—611no—
166#358—1221no—
167C4×C16C2×D6111yescharacteristic
168#335—611no—
169#332—1221no—
170C61#1232111yescharacteristic, complemented, Sylow
171C2×#41—1222no—
172#135—2442no—
173#135—2442no—
174C2×Q16—21no—
175C2×Q16—21no—
176C2×Q16—611no—
177C2×SD16—1222no—
178C2×D8—21no—
179C2×D8C22⋊D6112yes—
180C22×C8—1221no—
181C4⋊Q8—21no—
182#127—21no—
183#127—2441no—
184#121—1222no—
185#121—2442no—
186C4×Q8—1221no—
187C4×D4—611no—
188C4×D4—2441no—
189Q32—2442no—
190SD32—44no—
191C2×C16—21no—
192C2×C16—1221no—
193#107—611no—
194#107—2441no—
195C4⋊C8—611no—
196C4⋊C8—1221no—
197#103—1221no—
198#102—1222no—
199#102—2441no—
200C22⋊C8—1221no—
201C4×C8C22×D6111yescharacteristic
202#41—4882no—
203#41—2444no—
204C2×Q8—41no—
205C2×Q8—1221no—
206C2×D4—22no—
207C2×D4—41no—
208C2×D4—41no—
209C2×D4—611no—
210C2×D4—2442no—
211C2×D4—2442no—
212C22×C4—1221no—
213C22×C4—2442no—
214Q16—42no—
215Q16—41no—
216Q16—41no—
217Q16—612no—
218Q16—1221no—
219SD16—2444no—
220D8—42no—
221D8—41no—
222D8—41no—
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—2441no—
234C22⋊C4—1221no—
235C22⋊C4—2442no—
236C42—2441no—
237C42D4×D6111yescharacteristic
238C16—22no—
239C16—2441no—
240C23—42no—
241C23—1221no—
242Q8—81no—
243Q8—81no—
244Q8—1222no—
245Q8—2441no—
246D4—42no—
247D4—42no—
248D4—81no—
249D4—81no—
250D4—161no—
251D4—1221no—
252D4—1221no—
253D4—9762no—
254D4—4884no—
255C2×C4—81no—
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—82no—
271C22—82no—
272C22—82no—
273C22—2441no—
274C22—2441no—
275C22—2441no—
276C22#1683989411yescharacteristic
277C4—21no—
278C4—161no—
279C4—4881no—
280C4—2441no—
281C4—2442no—
282C4#1683989411yescharacteristic
283C4#1683992911yescharacteristic
284C4#1684019311yescharacteristic
285C4#1684020111yescharacteristic
286C2—162no—
287C2—4881no—
288C2#2144487111yescharacteristic
289C2#2144775611yescharacteristic
290C2#2144778911yescharacteristic
subgroupG/H
centerC22#16839894
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#2248C2
socleC22×C61#447
prime radical#21457577C2
hypercenter#2248D61
hypocenterC61#12321
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
2. #21447866C2semidirect
3. #21445181C2semidirect
4. #21443865C2semidirect
5. #21443784C2semidirect
6. #21443775C2semidirect
7. C61×#2248C2semidirect
142. #2248D61semidirect
170. C61#12321semidirect

Maximal subgroups

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

subgroupindex
#214575772
#214478662
#214451812
#214438652
#214437842
#214437752
C61×#22482
#1232161