Finite Group Databasebeta

← #29593518

Subgroups — #29593518

Order 15616.

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

normal subgroups only

This group has 378 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#21458792C211yesmaximal, characteristic, complemented
2#21447851C211yesmaximal, characteristic, complemented
3#21445176C211yesmaximal, characteristic, complemented
4#21443865C211yesmaximal, characteristic, complemented
5#21443799C211yesmaximal, characteristic, complemented
6#21443781C211yesmaximal, characteristic, complemented
7C61×#2246C211yesmaximal, characteristic, complemented
8#16840432—21no—
9C2×#14519718—21no—
10#16840137—21no—
11#16839959—21no—
12#16839955—22no—
13#16839954—21no—
14C8×Dic122C2211yescharacteristic
15C4×D488C2211yescharacteristic
16D8×Dic61—21no—
17C4⋊#11758185C2211yescharacteristic
18#16839563—21no—
19#16839515C2211yescharacteristic
20#16839506—21no—
21C2×D16×C61—22no—
22C61×#493C2211yescharacteristic
23C61×#493C2211yescharacteristic
24C4×C16×C61C2211yescharacteristic
25C2×#11758224—41no—
26C2×#11758200—41no—
27C2×D488D411yescharacteristic
28C2×#11758199—22no—
29#14519773—22no—
30#14519749—42no—
31#14519748—41no—
32C4×Dic122D411yescharacteristic
33C4×D244—21no—
34D4×Dic61—22no—
35#14519718—42no—
36C2×#11758185—21no—
37#14519711D411yescharacteristic
38C4⋊#92418—21no—
39C4⋊#92418D411yescharacteristic
40#14519706—21no—
41#14519699—21no—
42#14519698—22no—
43#14519698—41no—
44C8×Dic61—21no—
45C2×D8×C61—21no—
46C2×D8×C61—21no—
47C2×D8×C61—21no—
48C2×D8×C61D412yes—
49#127×C61—21no—
50#127×C61—21no—
51D16×C61—44no—
52C2×C16×C61—21no—
53C4×C8×C61C2311yescharacteristic
54C2×D4×C61—22no—
55C2×D4×C61—41no—
56C2×D4×C61—41no—
57C2×D4×C61—41no—
58C2×D4×C61—41no—
59C2×D4×C61—41no—
60C2×C22⋊D61—42no—
61C2×C22⋊D61—42no—
62C22×Dic61—42no—
63#11758224—82no—
64#11758224—82no—
65C2×D244—21no—
66C2×C4×D61—41no—
67C2×Dic122D811yescharacteristic
68D8×C61—42no—
69D8×C61—42no—
70D8×C61—41no—
71D8×C61—41no—
72D8×C61—41no—
73D8×C61—41no—
74C2×C8×C61C2×D411yescharacteristic
75C2×C8×C61C2×D411yescharacteristic
76C42×C61C2×D411yescharacteristic
77C22⋊Dic61—42no—
78#11758200—82no—
79#11758199—82no—
80#11758198—41no—
81C4⋊Dic61—21no—
82C4⋊Dic61D811yescharacteristic
83#11758196—21no—
84C4×Dic61—21no—
85C2×#92418—21no—
86C2×#92418—41no—
87D488—21no—
88D488—21no—
89C16×C61—22no—
90#11758185—41no—
91C23×C61—42no—
92C23×C61—81no—
93C22×D61—41no—
94D4×C61—42no—
95D4×C61—42no—
96D4×C61—81no—
97D4×C61—81no—
98D4×C61—81no—
99D4×C61—81no—
100D4×C61—81no—
101D4×C61—81no—
102D4×C61—161no—
103D4×C61—161no—
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—21no—
111C2×Dic61—41no—
112C2×Dic61—84no—
113D244—41no—
114D244—41no—
115C4×D61—81no—
116C4×D61—81no—
117Dic122—21no—
118Dic122D1612yescomplemented
119C8×C61—21no—
120C8×C61#13511yescharacteristic
121C8×C61AGL(1,ℤ/8)11yescharacteristic
122#92418—41no—
123#92418—81no—
124#12328—611nomaximal, Sylow
125C22×C61—82no—
126C22×C61—82no—
127C22×C61—82no—
128C22×C61—161no—
129C22×C61—161no—
130C22×C61—161no—
131C22×C61#44711yescharacteristic
132C2×D61—81no—
133C2×D61—81no—
134C2×D61—81no—
135C4×C61—21no—
136C4×C61#44911yescharacteristic
137C4×C61#45311yescharacteristic
138C4×C61C2×D1611yescharacteristic
139C4×C61#50911yescharacteristic
140Dic61—22no—
141Dic61—41no—
142Dic61—81no—
143#3391—611no—
144#2246D6111yescharacteristic, complemented
145#2206—611no—
146#1668—611no—
147#1361—611no—
148Q8⋊C16—611no—
149#1331—611no—
150C2×C61—162no—
151C2×C61—321no—
152C2×C61#162111yescharacteristic
153C2×C61#218411yescharacteristic
154C2×C61#219211yescharacteristic
155D61—161no—
156#550—1221no—
157C2×D16—22no—
158C2×D16—1221no—
159#493—1221no—
160#493C2×D6111yescharacteristic
161#493C2×D6111yescharacteristic
162#460—1221no—
163#459—1221no—
164#459—1222no—
165C8×Q8—611no—
166C4×D8—611no—
167C4×D8—1221no—
168C4⋊C16—611no—
169#357—1221no—
170C4×C16C2×D6111yescharacteristic
171#335—611no—
172#331—1221no—
173C61#1232811yescharacteristic, complemented, Sylow
174C2×#41—2441no—
175C2×SD16—2441no—
176C2×D8—21no—
177C2×D8—21no—
178C2×D8—21no—
179C2×D8—611no—
180C2×D8—1222no—
181C2×D8C22⋊D6112yes—
182#127—21no—
183#127—21no—
184#127—1222no—
185#121—2441no—
186#121—2442no—
187C4×Q8—611no—
188C4×D4—1222no—
189C4×D4—1221no—
190D16—44no—
191D16—2442no—
192C2×C16—21no—
193C2×C16—1221no—
194#107—611no—
195C4⋊C8—611no—
196C4⋊C8—1221no—
197C4⋊C8—1221no—
198#102—1222no—
199#102—1221no—
200#102—2441no—
201C4×C8—1221no—
202C4×C8C22×D6111yescharacteristic
203#41—4882no—
204#41—4882no—
205C2×Q8—611no—
206C2×D4—22no—
207C2×D4—41no—
208C2×D4—41no—
209C2×D4—41no—
210C2×D4—41no—
211C2×D4—41no—
212C2×D4—1221no—
213C2×D4—2442no—
214C2×D4—2442no—
215C22×C4—2442no—
216C22×C4—2441no—
217SD16—4882no—
218D8—42no—
219D8—42no—
220D8—41no—
221D8—41no—
222D8—41no—
223D8—41no—
224D8—1221no—
225D8—1221no—
226D8—4882no—
227C2×C8—1221no—
228C2×C8—2441no—
229C2×C8D4×D6111yescharacteristic
230C2×C8C2×C22⋊D6111yescharacteristic
231C4⋊C4—611no—
232C4⋊C4—1221no—
233C4⋊C4—1221no—
234C22⋊C4—2442no—
235C22⋊C4—2441no—
236C42—1221no—
237C42D4×D6111yescharacteristic
238C16—22no—
239C16—2441no—
240C23—42no—
241C23—81no—
242C23—2441no—
243Q8—612no—
244Q8—1221no—
245D4—42no—
246D4—42no—
247D4—81no—
248D4—81no—
249D4—81no—
250D4—81no—
251D4—81no—
252D4—81no—
253D4—161no—
254D4—161no—
255D4—9762no—
256D4—4884no—
257D4—2441no—
258D4—2441no—
259C2×C4—1221no—
260C2×C4—1221no—
261C2×C4—4884no—
262C2×C4—4881no—
263C2×C4—4881no—
264C2×C4—2441no—
265C2×C4#1451974511yescharacteristic
266C2×C4D8×D6111yescharacteristic
267C2×C4#1451980111yescharacteristic
268C8—21no—
269C8—4881no—
270C8—2441no—
271C8#1451979611yescharacteristic
272C8#1451980111yescharacteristic
273C22—82no—
274C22—82no—
275C22—82no—
276C22—161no—
277C22—161no—
278C22—161no—
279C22—4881no—
280C22—4881no—
281C22—4881no—
282C22#1683989411yescharacteristic
283C4—21no—
284C4—1222no—
285C4—4881no—
286C4—2441no—
287C4#1683990411yescharacteristic
288C4#1683992911yescharacteristic
289C4D16×D6111yescharacteristic
290C4#1684019611yescharacteristic
291C2—162no—
292C2—321no—
293C2—9761no—
294C2#2144488111yescharacteristic
295C2#2144772911yescharacteristic
296C2#2144777511yescharacteristic
subgroupG/H
centerC22#16839894
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#2246C2
socleC22×C61#447
hypercenter#2246D61
hypocenterC61#12328
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2246

Complements

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

NH ≅ G/Ntype
1. #21458792C2semidirect
2. #21447851C2semidirect
3. #21445176C2semidirect
4. #21443865C2semidirect
5. #21443799C2semidirect
6. #21443781C2semidirect
7. C61×#2246C2semidirect
118. Dic122D16semidirect
144. #2246D61semidirect
173. C61#12328semidirect

Maximal subgroups

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

subgroupindex
#214587922
#214478512
#214451762
#214438652
#214437992
#214437812
C61×#22462
#1232861