Finite Group Databasebeta

← #29593707

Subgroups — #29593707

Order 15616.

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

normal subgroups only

This group has 312 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#21458688C211yesmaximal, characteristic, complemented
2#21447851C211yesmaximal, characteristic
3#21445176C211yesmaximal, characteristic, complemented
4#21443877C211yesmaximal, characteristic, complemented
5#21443799C211yesmaximal, characteristic, complemented
6#21443781C211yesmaximal, characteristic, complemented
7C61×#2240C211yesmaximal, characteristic, complemented
8#16840473—21no—
9C2×#14519718—21no—
10#16840163—21no—
11#16840065—22no—
12#16840049—21no—
13#16839959—21no—
14C8×Dic122C2211yescharacteristic
15C4×D488C2211yescharacteristic
16#16839844—21no—
17C4⋊#11758185C2211yescharacteristic
18#16839563—21no—
19#16839515C2211yescharacteristic
20#16839506—21no—
21C61×#500C2211yescharacteristic
22C61×#493C2211yescharacteristic
23C61×#357—22no—
24C4×C16×C61C2211yescharacteristic
25C2×#11758200—41no—
26C2×D488D411yescharacteristic
27#14519768—22no—
28#14519757—41no—
29#14519753—42no—
30C4×Dic122D411yescharacteristic
31C4×D244—21no—
32#14519739—22no—
33C4⋊C4×D61—41no—
34#14519718—42no—
35C2×#11758185—21no—
36#14519711D411yescharacteristic
37#14519708—22no—
38C4⋊#92418—21no—
39C4⋊#92418D411yescharacteristic
40#14519706—21no—
41#14519699—21no—
42#14519698—41no—
43#14519697—22no—
44C8×Dic61—21no—
45C2×D8×C61—21no—
46C2×D8×C61—21no—
47C4⋊Q8×C61—21no—
48#127×C61—21no—
49C2×C16×C61—21no—
50#107×C61—21no—
51#107×C61D412yes—
52C4×C8×C61C2311yescharacteristic
53C2×Q8×C61—41no—
54C2×D4×C61—41no—
55C2×D4×C61—41no—
56C2×D4×C61—41no—
57C2×D244—21no—
58C2×C4×D61—41no—
59C2×C4×D61—42no—
60C2×Dic122D811yescharacteristic
61D8×C61—42no—
62D8×C61—41no—
63D8×C61—41no—
64C2×C8×C61C2×D411yescharacteristic
65C2×C8×C61C2×D411yescharacteristic
66C4⋊C4×C61—22no—
67C4⋊C4×C61—41no—
68C42×C61C2×D411yescharacteristic
69#11758200—82no—
70#11758198—42no—
71#11758198—41no—
72C4⋊Dic61—21no—
73C4⋊Dic61—42no—
74C4⋊Dic61D811yescharacteristic
75#11758196—21no—
76#11758196—42no—
77C4×Dic61—21no—
78C2×#92418—21no—
79C2×#92418—41no—
80D488—21no—
81D488SD1612yescomplemented
82C16×C61—41no—
83#11758185—41no—
84C23×C61—81no—
85C22×D61—41no—
86Q8×C61—161no—
87D4×C61—81no—
88D4×C61—81no—
89D4×C61—81no—
90D4×C61—81no—
91D4×C61—161no—
92C2×C4×C61—42no—
93C2×C4×C61#12011yescharacteristic
94C2×C4×C61C2×D811yescharacteristic
95C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
96C2×Dic61—21no—
97C2×Dic61—21no—
98C2×Dic61—41no—
99D244—22no—
100D244—41no—
101C4×D61—81no—
102C4×D61—81no—
103C4×D61—162no—
104Dic122—21no—
105Dic122—21no—
106C8×C61—21no—
107C8×C61C2×SD1611yescharacteristic
108C8×C61#13711yescharacteristic
109#92418—41no—
110#92418—81no—
111#12355—611nomaximal, Sylow
112C22×C61—161no—
113C22×C61—161no—
114C22×C61—161no—
115C22×C61#44711yescharacteristic
116C2×D61—42no—
117C2×D61—81no—
118C2×D61—81no—
119C4×C61—21no—
120C4×C61—82no—
121C4×C61#44811yescharacteristic
122C4×C61#45411yescharacteristic
123C4×C61#50811yescharacteristic
124C4×C61#50911yescharacteristic
125Dic61—41no—
126Dic61—41no—
127Dic61—81no—
128#3380—611no—
129#2240D6111yescharacteristic, complemented
130#2206—611no—
131#1668—611no—
132#1365—611no—
133Q8⋊C16—611no—
134#1331—611no—
135C2×C61—321no—
136C2×C61#162711yescharacteristic
137C2×C61#218611yescharacteristic
138C2×C61#219211yescharacteristic
139D61—82no—
140#554—1221no—
141C2×D16—1221no—
142#500C2×D6111yescharacteristic
143#499—1221no—
144#493C2×D6111yescharacteristic
145#478—1222no—
146#476—1221no—
147#460—1221no—
148C8×Q8—611no—
149C4×D8—611no—
150C4×D8—1221no—
151C4⋊C16—611no—
152#357—22no—
153#357—1221no—
154C4×C16C2×D6111yescharacteristic
155#335—611no—
156#331—1221no—
157C61#1235511yescharacteristic, complemented, Sylow
158C2×SD16—2441no—
159C2×D8—21no—
160C2×D8—21no—
161C2×D8—611no—
162C4⋊Q8—21no—
163#127—21no—
164#125—1222no—
165C22⋊Q8—2441no—
166C22⋊Q8—2442no—
167C4×Q8—611no—
168C4×D4—1222no—
169C4×D4—1221no—
170C2×C4⋊C4—2441no—
171D16—2442no—
172C2×C16—21no—
173C2×C16—1221no—
174#107—21no—
175#107—611no—
176#107C22⋊D6112yes—
177#106—1222no—
178C4⋊C8—611no—
179C4⋊C8—1221no—
180C4⋊C8—1221no—
181#102—1222no—
182#102—1221no—
183#102—2441no—
184C4×C8—1221no—
185C4×C8C22×D6111yescharacteristic
186C2×Q8—41no—
187C2×Q8—611no—
188C2×D4—41no—
189C2×D4—41no—
190C2×D4—41no—
191C2×D4—1221no—
192C22×C4—2442no—
193C22×C4—2441no—
194SD16—4882no—
195D8—42no—
196D8—41no—
197D8—41no—
198D8—612no—
199D8—1221no—
200C2×C8—1221no—
201C2×C8—2441no—
202C2×C8D4×D6111yescharacteristic
203C2×C8C2×C22⋊D6111yescharacteristic
204C4⋊C4—22no—
205C4⋊C4—41no—
206C4⋊C4—611no—
207C4⋊C4—1221no—
208C4⋊C4—1221no—
209C4⋊C4—2442no—
210C4⋊C4—2442no—
211C22⋊C4—2442no—
212C22⋊C4—2441no—
213C42—1221no—
214C42D4×D6111yescharacteristic
215C16—41no—
216C16—2441no—
217C23—81no—
218C23—2441no—
219Q8—161no—
220Q8—1221no—
221Q8—1221no—
222D4—81no—
223D4—81no—
224D4—81no—
225D4—81no—
226D4—161no—
227D4—1222no—
228D4—2441no—
229C2×C4—42no—
230C2×C4—1221no—
231C2×C4—1221no—
232C2×C4—9762no—
233C2×C4—4881no—
234C2×C4—4881no—
235C2×C4—2441no—
236C2×C4#1451974511yescharacteristic
237C2×C4D8×D6111yescharacteristic
238C2×C4#1451980111yescharacteristic
239C8—21no—
240C8—4881no—
241C8—2441no—
242C8SD16×D6111yescharacteristic
243C8#1451980611yescharacteristic
244C22—161no—
245C22—161no—
246C22—161no—
247C22—4881no—
248C22—4881no—
249C22—2442no—
250C22#1683989411yescharacteristic
251C4—21no—
252C4—82no—
253C4—4881no—
254C4—2441no—
255C4—2441no—
256C4#1683989911yescharacteristic
257C4#1683993411yescharacteristic
258C4#1684019311yescharacteristic
259C4#1684019911yescharacteristic
260C2—321no—
261C2—4882no—
262C2#2144491911yescharacteristic
263C2#2144774111yescharacteristic
264C2#2144777511yescharacteristic
subgroupG/H
centerC22#16839894
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#2240C2
socleC22×C61#447
prime radical#21447851C2
hypercenter#2240D61
hypocenterC61#12355
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2240

Complements

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

NH ≅ G/Ntype
1. #21458688C2semidirect
3. #21445176C2semidirect
4. #21443877C2semidirect
5. #21443799C2semidirect
6. #21443781C2semidirect
7. C61×#2240C2semidirect
81. D488SD16semidirect
129. #2240D61semidirect
157. C61#12355semidirect

Maximal subgroups

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

subgroupindex
#214586882
#214478512
#214451762
#214438772
#214437992
#214437812
C61×#22402
#1235561