Finite Group Databasebeta

← #29593881

Subgroups — #29593881

Order 15616.

306 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 65 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#21458833C211yesmaximal, characteristic
2#21447958C211yesmaximal, characteristic, complemented
3#21445210C211yesmaximal, characteristic, complemented
4#21443865C211yesmaximal, characteristic
5#21443799C211yesmaximal, characteristic, complemented
6#21443784C211yesmaximal, characteristic, complemented
7C61×#2240C211yesmaximal, characteristic
8#16840498—21no—
9#16840145—21no—
10#16839975—22no—
11#16839969—21no—
12#16839959—21no—
13C8×Dic122C2211yescharacteristic
14C4×Dic244C2211yescharacteristic
15D8×Dic61—21no—
16#16839589—21no—
17C4⋊#11758185C2211yescharacteristic
18#16839565—21no—
19#16839515C2211yescharacteristic
20#16839508—21no—
21C61×#500C2211yescharacteristic
22C61×#493C2211yescharacteristic
23C61×#357—22no—
24C4×C16×C61C2211yescharacteristic
25C2×Dic244D411yescharacteristic
26C2×#11758202—41no—
27C2×#11758200—22no—
28#14519764—22no—
29#14519764—41no—
30#14519758—42no—
31C4×Dic122—21no—
32C4×Dic122D411yescharacteristic
33D4×Dic61—22no—
34D4×Dic61—41no—
35C2×#11758185—21no—
36#14519711D411yescharacteristic
37C4⋊#92418—21no—
38C4⋊#92418D411yescharacteristic
39#14519706—21no—
40#14519702—21no—
41#14519701—41no—
42#14519698—22no—
43C8×Dic61—21no—
44C2×D8×C61—21no—
45C2×D8×C61D412yes—
46C4⋊Q8×C61—21no—
47#127×C61—21no—
48C2×C16×C61—21no—
49#107×C61—21no—
50#107×C61—21no—
51C4×C8×C61C2311yescharacteristic
52C2×Q8×C61—41no—
53C2×D4×C61—22no—
54C2×D4×C61—41no—
55C2×D4×C61—41no—
56C22×Dic61—42no—
57C2×Dic122—21no—
58C2×Dic122D811yescharacteristic
59D8×C61—42no—
60D8×C61—41no—
61D8×C61—41no—
62C2×C8×C61C2×D411yescharacteristic
63C2×C8×C61C2×D411yescharacteristic
64C4⋊C4×C61—41no—
65C4⋊C4×C61—41no—
66C42×C61C2×D411yescharacteristic
67C22⋊Dic61—42no—
68C22⋊Dic61—42no—
69C22⋊Dic61—42no—
70#11758202—82no—
71#11758200—82no—
72C4⋊Dic61—21no—
73C4⋊Dic61D811yescharacteristic
74#11758196—21no—
75#11758196—41no—
76C4×Dic61—21no—
77C4×Dic61—41no—
78C2×#92418—21no—
79C2×#92418—41no—
80Dic244—21no—
81Dic244—21no—
82C16×C61—41no—
83#11758185—41no—
84C23×C61—42no—
85Q8×C61—81no—
86Q8×C61—81no—
87D4×C61—42no—
88D4×C61—42no—
89D4×C61—81no—
90D4×C61—81no—
91D4×C61—161no—
92C2×C4×C61—81no—
93C2×C4×C61#12011yescharacteristic
94C2×C4×C61C2×D811yescharacteristic
95C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
96C2×Dic61—21no—
97C2×Dic61—21no—
98C2×Dic61—41no—
99C2×Dic61—41no—
100C2×Dic61—162no—
101Dic122—21no—
102Dic122—21no—
103Dic122—41no—
104Dic122—41no—
105C8×C61—21no—
106C8×C61#13511yescharacteristic
107C8×C61#13711yescharacteristic
108#92418—41no—
109#92418—81no—
110#12381—611nomaximal, Sylow
111C22×C61—82no—
112C22×C61—82no—
113C22×C61—82no—
114C22×C61#44711yescharacteristic
115C4×C61—21no—
116C4×C61—161no—
117C4×C61#45211yescharacteristic
118C4×C61#45511yescharacteristic
119C4×C61#50811yescharacteristic
120C4×C61#50911yescharacteristic
121Dic61—41no—
122Dic61—41no—
123Dic61—81no—
124Dic61—81no—
125#3396—611no—
126#2240D6111yescharacteristic
127#2225—611no—
128#1674—611no—
129#1361—611no—
130Q8⋊C16—611no—
131#1332—611no—
132C2×C61—162no—
133C2×C61#164111yescharacteristic
134C2×C61#218611yescharacteristic
135C2×C61#219411yescharacteristic
136#559—1221no—
137#500C2×D6111yescharacteristic
138#495—1221no—
139#493C2×D6111yescharacteristic
140#463—1222no—
141#462—1221no—
142#460—1221no—
143C8×Q8—611no—
144C4×Q16—611no—
145C4×D8—1221no—
146#367—1221no—
147C4⋊C16—611no—
148#358—1221no—
149#357—22no—
150C4×C16C2×D6111yescharacteristic
151#335—611no—
152#332—1221no—
153C61#1238111yescharacteristic, complemented, Sylow
154C2×Q16—611no—
155C2×Q16—2441no—
156C2×SD16—1222no—
157C2×D8—21no—
158C2×D8C22⋊D6112yes—
159C4⋊Q8—21no—
160#127—21no—
161#124—1222no—
162#124—2441no—
163#123—2442no—
164C4×Q8—611no—
165C4×Q8—1221no—
166C4×D4—1222no—
167C4×D4—2441no—
168C2×C16—21no—
169C2×C16—1221no—
170#107—21no—
171#107—21no—
172#107—611no—
173C4⋊C8—611no—
174C4⋊C8—1221no—
175C4⋊C8—1221no—
176#103—1221no—
177#103—2441no—
178#102—1222no—
179C4×C8—1221no—
180C4×C8C22×D6111yescharacteristic
181C2×Q8—41no—
182C2×Q8—611no—
183C2×Q8—1221no—
184C2×D4—22no—
185C2×D4—41no—
186C2×D4—41no—
187C22×C4—2442no—
188Q16—1221no—
189Q16—1221no—
190Q16—4882no—
191SD16—4882no—
192D8—42no—
193D8—41no—
194D8—41no—
195C2×C8—1221no—
196C2×C8—2441no—
197C2×C8D4×D6111yescharacteristic
198C2×C8C2×C22⋊D6111yescharacteristic
199C4⋊C4—41no—
200C4⋊C4—41no—
201C4⋊C4—611no—
202C4⋊C4—1221no—
203C4⋊C4—1221no—
204C4⋊C4—2441no—
205C22⋊C4—2442no—
206C22⋊C4—2442no—
207C22⋊C4—2442no—
208C42—1221no—
209C42—2441no—
210C42D4×D6111yescharacteristic
211C16—41no—
212C16—2441no—
213C23—42no—
214Q8—81no—
215Q8—81no—
216Q8—1221no—
217Q8—1221no—
218Q8—2441no—
219Q8—2441no—
220D4—42no—
221D4—42no—
222D4—81no—
223D4—81no—
224D4—161no—
225C2×C4—81no—
226C2×C4—1221no—
227C2×C4—1221no—
228C2×C4—9762no—
229C2×C4—2441no—
230C2×C4—2441no—
231C2×C4#1451974511yescharacteristic
232C2×C4D8×D6111yescharacteristic
233C2×C4#1451980111yescharacteristic
234C8—21no—
235C8—4881no—
236C8—2441no—
237C8#1451979811yescharacteristic
238C8#1451980611yescharacteristic
239C22—82no—
240C22—82no—
241C22—82no—
242C22#1683989411yescharacteristic
243C4—21no—
244C4—161no—
245C4—4881no—
246C4—4881no—
247C4—2441no—
248C4—2441no—
249C4#1683992111yescharacteristic
250C4#1683993911yescharacteristic
251C4#1684019111yescharacteristic
252C4#1684019611yescharacteristic
253C2—162no—
254C2#2144500911yescharacteristic
255C2#2144773911yescharacteristic
256C2#2144778911yescharacteristic
subgroupG/H
centerC22#16839894
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#2240C2
socleC22×C61#447
prime radicalC61×#493C22
hypercenter#2240D61
hypocenterC61#12381
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
2. #21447958C2semidirect
3. #21445210C2semidirect
5. #21443799C2semidirect
6. #21443784C2semidirect
153. C61#12381semidirect

Maximal subgroups

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

subgroupindex
#214588332
#214479582
#214452102
#214438652
#214437992
#214437842
C61×#22402
#1238161