Finite Group Databasebeta

← #29593624

Subgroups — #29593624

Order 15616.

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

normal subgroups only

This group has 318 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#21458242C211yesmaximal, characteristic, complemented
2#21448042C211yesmaximal, characteristic, complemented
3#21447851C211yesmaximal, characteristic, complemented
4#21443878C211yesmaximal, characteristic, complemented
5#21443779C211yesmaximal, characteristic, complemented
6D4⋊#11758185C211yesmaximal, characteristic, complemented
7C61×#1667C211yesmaximal, characteristic, complemented
8#16840477—21no—
9C2×#14519718—21no—
10#16840167C2211yescharacteristic
11#16840087—22no—
12#16840053—21no—
13#16839998—21no—
14C4×D488C2211yescharacteristic
15#16839800—21no—
16C4⋊#11758185C2211yescharacteristic
17#16839563—22no—
18#16839563—21no—
19C4×#11758185C2211yescharacteristic
20C61×#493C2211yescharacteristic
21C61×#459—21no—
22C8×D4×C61C2211yescharacteristic
23C61×#335C2211yescharacteristic
24C61×#331—21no—
25C2×D488D411yescharacteristic
26#14519777—21no—
27#14519763—42no—
28#14519751—22no—
29#14519748—41no—
30C4×D244—21no—
31#14519736—22no—
32#14519735—41no—
33#14519718—42no—
34C2×#11758185—21no—
35C2×#11758185—21no—
36#14519711—21no—
37#14519711D411yescharacteristic
38#14519711D412yes—
39#14519709—22no—
40#14519699—22no—
41#14519699—21no—
42C2×D8×C61—21no—
43C2×D8×C61—21no—
44C2×D8×C61—41no—
45C22×C8×C61—21no—
46#127×C61—21no—
47C4×D4×C61D411yescharacteristic
48C4⋊C8×C61—21no—
49C4⋊C8×C61D411yescharacteristic
50#102×C61—41no—
51C22⋊C8×C61—21no—
52C4×C8×C61C2311yescharacteristic
53C2×D4×C61—41no—
54C2×D4×C61—41no—
55C2×D4×C61—41no—
56C2×D4×C61D811yescharacteristic
57C22×C4×C61—21no—
58C2×C22⋊D61—42no—
59C2×D244—21no—
60C2×C4×D61—41no—
61C2×Dic122—41no—
62D8×C61—42no—
63D8×C61—41no—
64D8×C61—41no—
65D8×C61—82no—
66C2×C8×C61—21no—
67C2×C8×C61—41no—
68C2×C8×C61—41no—
69C2×C8×C61—41no—
70C2×C8×C61C2×D411yescharacteristic
71C2×C8×C61C2×D411yescharacteristic
72C4⋊C4×C61D811yescharacteristic
73C22⋊C4×C61—21no—
74C42×C61C2×D411yescharacteristic
75C22⋊Dic61—42no—
76#11758198—42no—
77#11758198—41no—
78C4⋊Dic61—21no—
79C4⋊Dic61—22no—
80C4⋊Dic61—41no—
81C4×Dic61—42no—
82D488—21no—
83D488—21no—
84#11758185—41no—
85#11758185—41no—
86C23×C61—21no—
87C23×C61—81no—
88C22×D61—41no—
89D4×C61—21no—
90D4×C61—21no—
91D4×C61—81no—
92D4×C61—81no—
93D4×C61—81no—
94D4×C61—81no—
95D4×C61—161no—
96C2×C4×C61—21no—
97C2×C4×C61—41no—
98C2×C4×C61—41no—
99C2×C4×C61#12011yescharacteristic
100C2×C4×C61C2×D811yescharacteristic
101C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
102C22⋊D61—162no—
103C2×Dic61—41no—
104C2×Dic61—42no—
105D244—41no—
106D244—41no—
107C4×D61—81no—
108C4×D61—81no—
109Dic122—161no—
110C8×C61—21no—
111C8×C61—41no—
112C8×C61—81no—
113C8×C61#13511yescharacteristic
114C8×C61AGL(1,ℤ/8)11yescharacteristic
115#12343—611nomaximal, Sylow
116C22×C61—41no—
117C22×C61—41no—
118C22×C61—41no—
119C22×C61—161no—
120C22×C61—161no—
121C22×C61—161no—
122C22×C61#44711yescharacteristic
123C2×D61—81no—
124C2×D61—81no—
125C2×D61—81no—
126C4×C61—21no—
127C4×C61—41no—
128C4×C61#44911yescharacteristic
129C4×C61#45411yescharacteristic
130C4×C61#50811yescharacteristic
131C4×C61#50911yescharacteristic
132Dic61—81no—
133Dic61—82no—
134#3341—611no—
135#2240—611no—
136#2206—611no—
137#1667D6111yescharacteristic, complemented
138#1365—611no—
139#1331—611no—
140D4⋊C16—611no—
141C2×C61—81no—
142C2×C61—321no—
143C2×C61#162511yescharacteristic
144C2×C61#218611yescharacteristic
145C2×C61#219211yescharacteristic
146D61—161no—
147#555—1221no—
148C2×D16—1221no—
149#500—611no—
150#493C2×D6111yescharacteristic
151#482—1222no—
152#476—1221no—
153#466—1221no—
154#459—21no—
155C4×D8—611no—
156C8×D4C2×D6111yescharacteristic
157#427—1221no—
158C4⋊C16—611no—
159#357—1221no—
160#357—1222no—
161C4×C16—611no—
162#335C2×D6111yescharacteristic
163#331—21no—
164C61#1234311yescharacteristic, complemented, Sylow
165C2×D8—21no—
166C2×D8—21no—
167C2×D8—41no—
168C2×D8—611no—
169C22×C8—21no—
170C4⋊Q8—1221no—
171#127—21no—
172#124—2442no—
173#121—1222no—
174#121—2441no—
175C4×D4—1221no—
176C4×D4C22⋊D6111yescharacteristic
177#117—1222no—
178#117—2441no—
179D16—2442no—
180C2×C16—1221no—
181C2×C16—1221no—
182#107—611no—
183#107—612no—
184#107—1221no—
185#106—1222no—
186C4⋊C8—21no—
187C4⋊C8C22⋊D6111yescharacteristic
188#102—41no—
189#102—1222no—
190#102—1221no—
191C22⋊C8—21no—
192C4×C8C22×D6111yescharacteristic
193C2×Q8—2441no—
194C2×D4—41no—
195C2×D4—41no—
196C2×D4—41no—
197C2×D4—1221no—
198C2×D4—2442no—
199C2×D4#1175819911yescharacteristic
200C22×C4—21no—
201C22×C4—2441no—
202D8—42no—
203D8—41no—
204D8—41no—
205D8—82no—
206D8—1221no—
207D8—1221no—
208C2×C8—21no—
209C2×C8—41no—
210C2×C8—41no—
211C2×C8—41no—
212C2×C8D4×D6111yescharacteristic
213C2×C8D4×D6111yescharacteristic
214C4⋊C4—1221no—
215C4⋊C4—1222no—
216C4⋊C4—2441no—
217C4⋊C4#1175819911yescharacteristic
218C22⋊C4—21no—
219C22⋊C4—2442no—
220C22⋊C4—2442no—
221C22⋊C4—2441no—
222C42—2442no—
223C42C2×C22⋊D6111yescharacteristic
224C16—2441no—
225C16—2441no—
226C23—21no—
227C23—81no—
228C23—2441no—
229Q8—9761no—
230D4—21no—
231D4—21no—
232D4—81no—
233D4—81no—
234D4—81no—
235D4—81no—
236D4—161no—
237D4—9762no—
238D4—2441no—
239D4—2441no—
240C2×C4—21no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—4881no—
244C2×C4—4881no—
245C2×C4—2441no—
246C2×C4—2442no—
247C2×C4#1451974511yescharacteristic
248C2×C4C2×#1175819911yescharacteristic
249C2×C4#1451980211yescharacteristic
250C8—21no—
251C8—41no—
252C8—81no—
253C8#1451979611yescharacteristic
254C8#1451980111yescharacteristic
255C22—41no—
256C22—41no—
257C22—41no—
258C22—161no—
259C22—161no—
260C22—161no—
261C22—4881no—
262C22—4881no—
263C22—4881no—
264C22#1683989511yescharacteristic
265C4—21no—
266C4—41no—
267C4—4881no—
268C4—4882no—
269C4#1683990411yescharacteristic
270C4#1683993311yescharacteristic
271C4#1684019211yescharacteristic
272C4#1684019811yescharacteristic
273C2—81no—
274C2—321no—
275C2—9761no—
276C2#2144490611yescharacteristic
277C2#2144774011yescharacteristic
278C2#2144777411yescharacteristic
subgroupG/H
centerC22#16839895
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1667C2
socleC22×C61#447
hypercenter#1667D61
hypocenterC61#12343
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C8×D4 ◁ #1667

Complements

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

NH ≅ G/Ntype
1. #21458242C2semidirect
2. #21448042C2semidirect
3. #21447851C2semidirect
4. #21443878C2semidirect
5. #21443779C2semidirect
6. D4⋊#11758185C2semidirect
7. C61×#1667C2semidirect
137. #1667D61semidirect
164. C61#12343semidirect

Maximal subgroups

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

subgroupindex
#214582422
#214480422
#214478512
#214438782
#214437792
D4⋊#117581852
C61×#16672
#1234361