Finite Group Databasebeta

← #29593456

Subgroups — #29593456

Order 15616.

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

normal subgroups only

This group has 390 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#21457541C211yesmaximal, characteristic, complemented
2#21448074C211yesmaximal, characteristic, complemented
3#21447851C211yesmaximal, characteristic, complemented
4#21443867C211yesmaximal, characteristic, complemented
5#21443779C211yesmaximal, characteristic, complemented
6D4⋊#11758185C211yesmaximal, characteristic, complemented
7C61×#1667C211yesmaximal, characteristic, complemented
8C2×#14519799—21no—
9#16840417—21no—
10C2×#14519721—22no—
11C2×#14519718—21no—
12#16840142C2211yescharacteristic
13#16840003—21no—
14#16839968—21no—
15#16839926—22no—
16C4×D488C2211yescharacteristic
17C4⋊#11758185C2211yescharacteristic
18#16839563—21no—
19C4×#11758185C2211yescharacteristic
20C61×#493C2211yescharacteristic
21C61×#459—21no—
22C8×D4×C61C2211yescharacteristic
23C61×#335C2211yescharacteristic
24C61×#331—21no—
25C2×#11758222—22no—
26#14519799—42no—
27#14519799—42no—
28C2×Dic244—21no—
29C2×Dic244D412yes—
30C2×#11758190—22no—
31C2×D488D411yescharacteristic
32#14519777—21no—
33#14519759—42no—
34#14519756—22no—
35#14519748—41no—
36C4×D244—21no—
37C4⋊C4×D61—41no—
38#14519721—44no—
39#14519718—42no—
40C2×#11758185—21no—
41C2×#11758185—21no—
42#14519711D411yescharacteristic
43#14519702—22no—
44#14519699—21no—
45C2×D8×C61—21no—
46C2×D8×C61—21no—
47C2×D8×C61—41no—
48C22×C8×C61—21no—
49#127×C61—21no—
50C4×D4×C61D411yescharacteristic
51C4⋊C8×C61—21no—
52C4⋊C8×C61D411yescharacteristic
53#102×C61—41no—
54C22⋊C8×C61—21no—
55C4×C8×C61C2311yescharacteristic
56C2×D4×C61—41no—
57C2×D4×C61—41no—
58C2×D4×C61—41no—
59C2×D4×C61D811yescharacteristic
60C22×C4×C61—21no—
61C2×C22⋊D61—42no—
62#11758222—44no—
63#11758222—82no—
64C2×D244—21no—
65C2×C4×D61—42no—
66C2×C4×D61—41no—
67C2×Dic122—22no—
68D8×C61—42no—
69D8×C61—41no—
70D8×C61—41no—
71D8×C61—82no—
72C2×C8×C61—21no—
73C2×C8×C61—41no—
74C2×C8×C61—41no—
75C2×C8×C61—41no—
76C2×C8×C61C2×D411yescharacteristic
77C2×C8×C61C2×D411yescharacteristic
78C4⋊C4×C61D811yescharacteristic
79C22⋊C4×C61—21no—
80C42×C61C2×D411yescharacteristic
81C22⋊Dic61—42no—
82#11758198—41no—
83C4⋊Dic61—21no—
84C4⋊Dic61—41no—
85C4⋊Dic61—41no—
86#11758196—42no—
87Dic244—42no—
88Dic244—41no—
89Dic244—41no—
90D488—21no—
91D488D812yescomplemented
92#11758190—44no—
93#11758185—22no—
94#11758185—41no—
95C23×C61—21no—
96C23×C61—81no—
97C22×D61—41no—
98D4×C61—21no—
99D4×C61—21no—
100D4×C61—81no—
101D4×C61—81no—
102D4×C61—81no—
103D4×C61—81no—
104D4×C61—161no—
105C2×C4×C61—21no—
106C2×C4×C61—41no—
107C2×C4×C61—41no—
108C2×C4×C61#12011yescharacteristic
109C2×C4×C61C2×D811yescharacteristic
110C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
111C22⋊D61—84no—
112C2×Dic61—41no—
113C2×Dic61—42no—
114D244—22no—
115D244—41no—
116C4×D61—84no—
117C4×D61—81no—
118C4×D61—81no—
119Dic122—42no—
120Dic122—42no—
121C8×C61—21no—
122C8×C61—41no—
123C8×C61—81no—
124C8×C61C2×D811yescharacteristic
125C8×C61AGL(1,ℤ/8)11yescharacteristic
126#12319—611nomaximal, Sylow
127C22×C61—41no—
128C22×C61—41no—
129C22×C61—41no—
130C22×C61—161no—
131C22×C61—161no—
132C22×C61—161no—
133C22×C61#44711yescharacteristic
134C2×D61—42no—
135C2×D61—81no—
136C2×D61—81no—
137C4×C61—21no—
138C4×C61—41no—
139C4×C61#44711yescharacteristic
140C4×C61#45311yescharacteristic
141C4×C61#50811yescharacteristic
142C4×C61#50911yescharacteristic
143Dic61—82no—
144Dic61—81no—
145#3283—611no—
146#2248—611no—
147#2206—611no—
148#1667D6111yescharacteristic, complemented
149#1362—611no—
150#1331—611no—
151D4⋊C16—611no—
152C2×C61—81no—
153C2×C61—321no—
154C2×C61#161911yescharacteristic
155C2×C61#218611yescharacteristic
156C2×C61#219311yescharacteristic
157D61—82no—
158C2×#135—1221no—
159#547—1221no—
160C2×SD32—1222no—
161C2×D16—1221no—
162#494—611no—
163#493C2×D6111yescharacteristic
164#467—1221no—
165#461—1221no—
166#459—21no—
167#452—1222no—
168C4×D8—611no—
169C8×D4C2×D6111yescharacteristic
170C4⋊C16—611no—
171#357—1221no—
172C4×C16—611no—
173#335C2×D6111yescharacteristic
174#331—21no—
175C61#1231911yescharacteristic, complemented, Sylow
176C2×#41—1222no—
177#135—2442no—
178#135—2442no—
179C2×Q16—612no—
180C2×Q16—1221no—
181C2×SD16—1222no—
182C2×D8—21no—
183C2×D8—21no—
184C2×D8—41no—
185C2×D8—611no—
186C22×C8—21no—
187C4⋊Q8—1221no—
188#127—21no—
189#123—2442no—
190C22⋊Q8—1222no—
191#121—2441no—
192C4×D4—1221no—
193C4×D4C22⋊D6111yescharacteristic
194C2×C4⋊C4—2441no—
195SD32—2444no—
196D16—2442no—
197C2×C16—1221no—
198C2×C16—1221no—
199#107—611no—
200C4⋊C8—21no—
201C4⋊C8C22⋊D6111yescharacteristic
202#103—1222no—
203#102—41no—
204#102—1221no—
205C22⋊C8—21no—
206C4×C8C22×D6111yescharacteristic
207#41—4882no—
208#41—2444no—
209C2×Q8—1222no—
210C2×D4—41no—
211C2×D4—41no—
212C2×D4—41no—
213C2×D4—1221no—
214C2×D4—2442no—
215C2×D4#1175819911yescharacteristic
216C22×C4—21no—
217C22×C4—2442no—
218C22×C4—2441no—
219Q16—2442no—
220Q16—2441no—
221Q16—2441no—
222SD16—2444no—
223D8—42no—
224D8—41no—
225D8—41no—
226D8—82no—
227D8—612no—
228D8—1221no—
229C2×C8—21no—
230C2×C8—41no—
231C2×C8—41no—
232C2×C8—41no—
233C2×C8D4×D6111yescharacteristic
234C2×C8D4×D6111yescharacteristic
235C4⋊C4—1221no—
236C4⋊C4—2442no—
237C4⋊C4—2441no—
238C4⋊C4—2441no—
239C4⋊C4#1175819911yescharacteristic
240C22⋊C4—21no—
241C22⋊C4—2442no—
242C22⋊C4—2441no—
243C42C2×C22⋊D6111yescharacteristic
244C16—1222no—
245C16—2441no—
246C23—21no—
247C23—81no—
248C23—2441no—
249Q8—2442no—
250Q8—2442no—
251D4—21no—
252D4—21no—
253D4—81no—
254D4—81no—
255D4—81no—
256D4—81no—
257D4—161no—
258D4—1222no—
259D4—4884no—
260D4—2441no—
261C2×C4—21no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—4884no—
265C2×C4—4881no—
266C2×C4—4881no—
267C2×C4—2441no—
268C2×C4—2442no—
269C2×C4#1451974511yescharacteristic
270C2×C4C2×#1175819911yescharacteristic
271C2×C4#1451980211yescharacteristic
272C8—21no—
273C8—41no—
274C8—81no—
275C8D8×D6111yescharacteristic
276C8#1451980111yescharacteristic
277C22—41no—
278C22—41no—
279C22—41no—
280C22—161no—
281C22—161no—
282C22—161no—
283C22—4881no—
284C22—4881no—
285C22—2442no—
286C22#1683989511yescharacteristic
287C4—21no—
288C4—41no—
289C4—4882no—
290C4—4881no—
291C4#1683989411yescharacteristic
292C4#1683992811yescharacteristic
293C4#1684019211yescharacteristic
294C4#1684019811yescharacteristic
295C2—81no—
296C2—321no—
297C2—4882no—
298C2#2144487211yescharacteristic
299C2#2144774011yescharacteristic
300C2#2144778111yescharacteristic
subgroupG/H
centerC22#16839895
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1667C2
socleC22×C61#447
hypercenter#1667D61
hypocenterC61#12319
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. #21457541C2semidirect
2. #21448074C2semidirect
3. #21447851C2semidirect
4. #21443867C2semidirect
5. #21443779C2semidirect
6. D4⋊#11758185C2semidirect
7. C61×#1667C2semidirect
91. D488D8semidirect
148. #1667D61semidirect
175. C61#12319semidirect

Maximal subgroups

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

subgroupindex
#214575412
#214480742
#214478512
#214438672
#214437792
D4⋊#117581852
C61×#16672
#1231961