Finite Group Databasebeta

← #29593455

Subgroups — #29593455

Order 15616.

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

normal subgroups only

This group has 390 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#21457539C211yesmaximal, characteristic, complemented
2#21447851C211yesmaximal, characteristic, complemented
3#21445171C211yesmaximal, characteristic, complemented
4#21443868C211yesmaximal, characteristic, complemented
5#21443781C211yesmaximal, characteristic, complemented
6#21443775C211yesmaximal, characteristic, complemented
7C61×#2248C211yesmaximal, characteristic, complemented
8C2×#14519800—21no—
9#16840415—21no—
10C2×#14519718—21no—
11#16840000—21no—
12#16839964—21no—
13#16839954—21no—
14#16839923—22no—
15C4×D488C2211yescharacteristic
16C8×D244C2211yescharacteristic
17C4⋊#11758185C2211yescharacteristic
18#16839563—21no—
19#16839515C2211yescharacteristic
20#16839506—21no—
21C2×SD32×C61—22no—
22C61×#494C2211yescharacteristic
23C61×#493C2211yescharacteristic
24C4×C16×C61C2211yescharacteristic
25C2×#11758226—22no—
26#14519800—42no—
27#14519800—42no—
28C2×#11758201—22no—
29C2×D488D411yescharacteristic
30C2×#11758199—41no—
31C2×C8×D61—21no—
32#14519762—42no—
33#14519753—22no—
34#14519752—41no—
35C4×D244—21no—
36C4×D244D411yescharacteristic
37C4⋊C4×D61—41no—
38#14519718—42no—
39C2×#11758185—21no—
40#14519711D411yescharacteristic
41C4⋊#92418—21no—
42C4⋊#92418D411yescharacteristic
43#14519701—22no—
44#14519699—21no—
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—
60#11758226—44no—
61#11758226—82no—
62C2×D244—21no—
63C2×D244—42no—
64C2×D244D811yescharacteristic
65C2×C4×D61—21no—
66C2×C4×D61—42no—
67C2×C4×D61—41no—
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
79#11758201—44no—
80#11758199—82no—
81#11758198—21no—
82#11758198—42no—
83#11758198—41no—
84C4⋊Dic61—21no—
85C4⋊Dic61D811yescharacteristic
86#11758196—42no—
87C2×#92418—21no—
88C2×#92418—41no—
89D488—21no—
90D488D812yescomplemented
91C8×D61—41no—
92C8×D61—41no—
93C16×C61—22no—
94#11758185—41no—
95C23×C61—81no—
96C22×D61—21no—
97C22×D61—41no—
98Q8×C61—42no—
99Q8×C61—42no—
100D4×C61—81no—
101D4×C61—81no—
102D4×C61—81no—
103D4×C61—81no—
104D4×C61—161no—
105C2×C4×C61—42no—
106C2×C4×C61#12011yescharacteristic
107C2×C4×C61C2×D811yescharacteristic
108C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
109C2×Dic61—21no—
110C2×Dic61—41no—
111D244—22no—
112D244—21no—
113D244—21no—
114D244—41no—
115D244—84no—
116C4×D61—41no—
117C4×D61—41no—
118C4×D61—84no—
119C4×D61—81no—
120C4×D61—81no—
121C8×C61—21no—
122C8×C61C2×D811yescharacteristic
123C8×C61AGL(1,ℤ/8)11yescharacteristic
124#92418—41no—
125#92418—81no—
126#12319—611nomaximal, Sylow
127C22×C61—161no—
128C22×C61—161no—
129C22×C61—161no—
130C22×C61#44711yescharacteristic
131C2×D61—41no—
132C2×D61—42no—
133C2×D61—41no—
134C2×D61—41no—
135C2×D61—81no—
136C2×D61—81no—
137C4×C61—21no—
138C4×C61—82no—
139C4×C61#44711yescharacteristic
140C4×C61#45311yescharacteristic
141C4×C61#50811yescharacteristic
142C4×C61#50911yescharacteristic
143Dic61—41no—
144Dic61—81no—
145#3283—611no—
146#2248D6111yescharacteristic, complemented
147#2206—611no—
148#1667—611no—
149#1362—611no—
150#1331—611no—
151D4⋊C16—611no—
152C2×C61—321no—
153C2×C61#161911yescharacteristic
154C2×C61#218611yescharacteristic
155C2×C61#219311yescharacteristic
156D61—81no—
157D61—82no—
158C2×#135—1221no—
159#547—1221no—
160C2×SD32—22no—
161C2×D16—1221no—
162#494C2×D6111yescharacteristic
163#493C2×D6111yescharacteristic
164#467—1221no—
165#461—1221no—
166#459—1221no—
167#452—1222no—
168C4×D8—611no—
169C8×D4—611no—
170C4⋊C16—611no—
171#357—1221no—
172C4×C16C2×D6111yescharacteristic
173#335—611no—
174#331—1221no—
175C61#1231911yescharacteristic, complemented, Sylow
176C2×#41—1222no—
177#135—2442no—
178#135—2442no—
179C2×Q16—21no—
180C2×Q16C22⋊D6112yes—
181C2×SD16—1222no—
182C2×D8—21no—
183C2×D8—21no—
184C2×D8—611no—
185C2×D8—2441no—
186C22×C8—1221no—
187C4⋊Q8—21no—
188#127—21no—
189#123—2442no—
190C22⋊Q8—1222no—
191#121—2441no—
192C4×D4—611no—
193C4×D4—1221no—
194C2×C4⋊C4—2441no—
195SD32—44no—
196D16—2442no—
197C2×C16—21no—
198C2×C16—1221no—
199#107—611no—
200C4⋊C8—611no—
201C4⋊C8—1221no—
202#103—1222no—
203#102—1221no—
204#102—2441no—
205C22⋊C8—1221no—
206C4×C8C22×D6111yescharacteristic
207#41—4882no—
208#41—2444no—
209C2×Q8—22no—
210C2×D4—41no—
211C2×D4—41no—
212C2×D4—41no—
213C2×D4—611no—
214C2×D4—1221no—
215C2×D4—2442no—
216C22×C4—1221no—
217C22×C4—2442no—
218C22×C4—2441no—
219Q16—42no—
220Q16—41no—
221Q16—41no—
222SD16—2444no—
223D8—42no—
224D8—41no—
225D8—41no—
226D8—612no—
227D8—1221no—
228D8—4882no—
229C2×C8—1221no—
230C2×C8—2441no—
231C2×C8—2441no—
232C2×C8—2441no—
233C2×C8D4×D6111yescharacteristic
234C2×C8C2×C22⋊D6111yescharacteristic
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4—611no—
238C4⋊C4—1221no—
239C4⋊C4—2442no—
240C22⋊C4—1221no—
241C22⋊C4—2442no—
242C22⋊C4—2441no—
243C42D4×D6111yescharacteristic
244C16—22no—
245C16—2441no—
246C23—81no—
247C23—1221no—
248C23—2441no—
249Q8—42no—
250Q8—42no—
251D4—81no—
252D4—81no—
253D4—81no—
254D4—81no—
255D4—161no—
256D4—1221no—
257D4—1221no—
258D4—1222no—
259D4—4884no—
260D4—2441no—
261C2×C4—42no—
262C2×C4—1221no—
263C2×C4—4884no—
264C2×C4—4881no—
265C2×C4—4881no—
266C2×C4—2441no—
267C2×C4—2441no—
268C2×C4—2441no—
269C2×C4#1451974511yescharacteristic
270C2×C4D8×D6111yescharacteristic
271C2×C4#1451980111yescharacteristic
272C8—21no—
273C8—4881no—
274C8—2441no—
275C8D8×D6111yescharacteristic
276C8#1451980111yescharacteristic
277C22—161no—
278C22—161no—
279C22—161no—
280C22—4881no—
281C22—4881no—
282C22—2442no—
283C22—2441no—
284C22—2441no—
285C22—2441no—
286C22#1683989411yescharacteristic
287C4—21no—
288C4—82no—
289C4—4881no—
290C4—2441no—
291C4#1683989411yescharacteristic
292C4#1683992911yescharacteristic
293C4#1684019311yescharacteristic
294C4#1684019911yescharacteristic
295C2—321no—
296C2—4882no—
297C2—4881no—
298C2#2144487111yescharacteristic
299C2#2144774111yescharacteristic
300C2#2144778211yescharacteristic
subgroupG/H
centerC22#16839894
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#2248C2
socleC22×C61#447
hypercenter#2248D61
hypocenterC61#12319
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. #21457539C2semidirect
2. #21447851C2semidirect
3. #21445171C2semidirect
4. #21443868C2semidirect
5. #21443781C2semidirect
6. #21443775C2semidirect
7. C61×#2248C2semidirect
90. D488D8semidirect
146. #2248D61semidirect
175. C61#12319semidirect

Maximal subgroups

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

subgroupindex
#214575392
#214478512
#214451712
#214438682
#214437812
#214437752
C61×#22482
#1231961