Finite Group Databasebeta

← #29593540

Subgroups — #29593540

Order 15616.

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

normal subgroups only

This group has 328 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#21458808C211yesmaximal, characteristic, complemented
2#21448074C211yesmaximal, characteristic, complemented
3#21447851C211yesmaximal, characteristic
4#21443867C211yesmaximal, characteristic, complemented
5Q8⋊#11758185C211yesmaximal, characteristic, complemented
6#21443779C211yesmaximal, characteristic, complemented
7C61×#1668C211yesmaximal, characteristic, complemented
8#16840485—21no—
9C2×#14519721—22no—
10C2×#14519718—21no—
11#16840146—21no—
12#16840142C2211yescharacteristic
13#16839985—22no—
14#16839968—21no—
15C4×Dic244—21no—
16C4×D488C2211yescharacteristic
17C4⋊#11758185C2211yescharacteristic
18#16839563—21no—
19C4×#11758185C2211yescharacteristic
20C61×#493C2211yescharacteristic
21C61×#460—21no—
22C8×Q8×C61C2211yescharacteristic
23C61×#335C2211yescharacteristic
24C61×#331—21no—
25C2×Dic244—21no—
26C2×Dic244D412yes—
27C2×#11758190—22no—
28C2×D488D411yescharacteristic
29#14519777—21no—
30#14519772—42no—
31#14519765—22no—
32#14519753—41no—
33C4×Dic122—22no—
34C4×D244—21no—
35#14519735—41no—
36#14519721—44no—
37#14519718—42no—
38C2×#11758185—21no—
39C2×#11758185—21no—
40#14519711D411yescharacteristic
41#14519702—22no—
42#14519699—21no—
43C2×SD16×C61—41no—
44C2×D8×C61—21no—
45C2×D8×C61—21no—
46#127×C61—21no—
47C4×Q8×C61D411yescharacteristic
48C4⋊C8×C61—21no—
49C4⋊C8×C61—21no—
50C4⋊C8×C61D411yescharacteristic
51#102×C61—41no—
52C4×C8×C61—21no—
53C4×C8×C61C2311yescharacteristic
54C2×Q8×C61D811yescharacteristic
55C2×D4×C61—41no—
56C2×D4×C61—41no—
57C2×D4×C61—41no—
58C2×D244—21no—
59C2×C4×D61—41no—
60C2×Dic122—22no—
61SD16×C61—82no—
62D8×C61—42no—
63D8×C61—41no—
64D8×C61—41no—
65C2×C8×C61—21no—
66C2×C8×C61—41no—
67C2×C8×C61C2×D411yescharacteristic
68C2×C8×C61C2×D411yescharacteristic
69C4⋊C4×C61—21no—
70C4⋊C4×C61D811yescharacteristic
71C42×C61—21no—
72C42×C61C2×D411yescharacteristic
73#11758198—42no—
74#11758198—42no—
75#11758198—41no—
76C4⋊Dic61—21no—
77C4⋊Dic61—41no—
78C4⋊Dic61—41no—
79#11758196—42no—
80C4×Dic61—42no—
81Dic244—42no—
82Dic244—41no—
83Dic244—41no—
84D488—21no—
85D488—21no—
86#11758190—82no—
87#11758185—22no—
88#11758185—41no—
89C23×C61—81no—
90C22×D61—41no—
91Q8×C61—21no—
92Q8×C61—21no—
93D4×C61—81no—
94D4×C61—81no—
95D4×C61—81no—
96D4×C61—81no—
97D4×C61—161no—
98C2×C4×C61—21no—
99C2×C4×C61—21no—
100C2×C4×C61#12011yescharacteristic
101C2×C4×C61C2×D811yescharacteristic
102C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
103C2×Dic61—41no—
104C2×Dic61—42no—
105D244—41no—
106D244—41no—
107C4×D61—81no—
108C4×D61—81no—
109Dic122—42no—
110Dic122—42no—
111C8×C61—21no—
112C8×C61—41no—
113C8×C61—81no—
114C8×C61#13511yescharacteristic
115C8×C61AGL(1,ℤ/8)11yescharacteristic
116#12331—611nomaximal, Sylow
117C22×C61—161no—
118C22×C61—161no—
119C22×C61—161no—
120C22×C61#44711yescharacteristic
121C2×D61—81no—
122C2×D61—81no—
123C2×D61—81no—
124C4×C61—21no—
125C4×C61—41no—
126C4×C61—41no—
127C4×C61#44911yescharacteristic
128C4×C61#45311yescharacteristic
129C4×C61#50811yescharacteristic
130C4×C61#50911yescharacteristic
131Dic61—82no—
132Dic61—81no—
133#3393—611no—
134#2248—611no—
135#2206—611no—
136#1668D6111yescharacteristic, complemented
137#1362—611no—
138Q8⋊C16—611no—
139#1331—611no—
140C2×C61—321no—
141C2×C61#162111yescharacteristic
142C2×C61#218611yescharacteristic
143C2×C61#219311yescharacteristic
144D61—161no—
145#556—1221no—
146C2×SD32—1222no—
147C2×D16—1221no—
148#495—1221no—
149#494—611no—
150#493C2×D6111yescharacteristic
151#464—1222no—
152#461—1221no—
153#460—21no—
154C8×Q8C2×D6111yescharacteristic
155C4×Q16—1221no—
156C4×D8—611no—
157C4⋊C16—611no—
158#357—1221no—
159C4×C16—611no—
160#335C2×D6111yescharacteristic
161#331—21no—
162C61#1233111yescharacteristic, complemented, Sylow
163C2×Q16—612no—
164C2×Q16—1221no—
165C2×SD16—41no—
166C2×SD16—1222no—
167C2×D8—21no—
168C2×D8—21no—
169C2×D8—611no—
170C4⋊Q8—1221no—
171#127—21no—
172#126—2442no—
173#124—1222no—
174C22⋊Q8—2441no—
175C4×Q8—1222no—
176C4×Q8C22⋊D6111yescharacteristic
177C4×D4—1221no—
178#117—2441no—
179SD32—2444no—
180D16—2442no—
181C2×C16—1221no—
182C2×C16—1221no—
183#107—611no—
184C4⋊C8—21no—
185C4⋊C8—21no—
186C4⋊C8C22⋊D6111yescharacteristic
187#103—1222no—
188#102—41no—
189#102—1221no—
190C4×C8—21no—
191C4×C8C22×D6111yescharacteristic
192C2×Q8—1222no—
193C2×Q8#1175819911yescharacteristic
194C2×D4—41no—
195C2×D4—41no—
196C2×D4—41no—
197C2×D4—1221no—
198C22×C4—2441no—
199Q16—2442no—
200Q16—2441no—
201Q16—2441no—
202SD16—82no—
203SD16—4882no—
204D8—42no—
205D8—41no—
206D8—41no—
207D8—1221no—
208D8—1221no—
209C2×C8—21no—
210C2×C8—41no—
211C2×C8D4×D6111yescharacteristic
212C2×C8D4×D6111yescharacteristic
213C4⋊C4—21no—
214C4⋊C4—1221no—
215C4⋊C4—2442no—
216C4⋊C4—2441no—
217C4⋊C4—2441no—
218C4⋊C4#1175819911yescharacteristic
219C22⋊C4—2442no—
220C22⋊C4—2442no—
221C22⋊C4—2441no—
222C42—21no—
223C42—2442no—
224C42C2×C22⋊D6111yescharacteristic
225C16—1222no—
226C16—2441no—
227C23—81no—
228C23—2441no—
229Q8—21no—
230Q8—21no—
231Q8—2442no—
232Q8—2442no—
233D4—81no—
234D4—81no—
235D4—81no—
236D4—81no—
237D4—161no—
238D4—2441no—
239D4—2441no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—4881no—
243C2×C4—4881no—
244C2×C4—2441no—
245C2×C4—2442no—
246C2×C4#1451974511yescharacteristic
247C2×C4C2×#1175819911yescharacteristic
248C2×C4#1451980211yescharacteristic
249C8—21no—
250C8—41no—
251C8—81no—
252C8#1451979811yescharacteristic
253C8#1451980411yescharacteristic
254C22—161no—
255C22—161no—
256C22—161no—
257C22—4881no—
258C22—4881no—
259C22—4881no—
260C22#1683989511yescharacteristic
261C4—21no—
262C4—41no—
263C4—41no—
264C4—4882no—
265C4—4881no—
266C4#1683990611yescharacteristic
267C4#1683992811yescharacteristic
268C4#1684019211yescharacteristic
269C4#1684019811yescharacteristic
270C2—321no—
271C2—9761no—
272C2#2144488211yescharacteristic
273C2#2144774011yescharacteristic
274C2#2144778111yescharacteristic
subgroupG/H
centerC22#16839895
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1668C2
socleC22×C61#447
prime radical#21447851C2
hypercenter#1668D61
hypocenterC61#12331
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8 ◁ #1668

Complements

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

NH ≅ G/Ntype
1. #21458808C2semidirect
2. #21448074C2semidirect
4. #21443867C2semidirect
5. Q8⋊#11758185C2semidirect
6. #21443779C2semidirect
7. C61×#1668C2semidirect
136. #1668D61semidirect
162. C61#12331semidirect

Maximal subgroups

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

subgroupindex
#214588082
#214480742
#214478512
#214438672
Q8⋊#117581852
#214437792
C61×#16682
#1233161