Finite Group Databasebeta

← #29593698

Subgroups — #29593698

Order 15616.

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

normal subgroups only

This group has 298 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#21458711C211yesmaximal, characteristic, complemented
2#21448043C211yesmaximal, characteristic
3#21447860C211yesmaximal, characteristic
4#21445179C211yesmaximal, characteristic
5#21443873C211yesmaximal, characteristic, complemented
6#21443784C211yesmaximal, characteristic, complemented
7C61×Q8⋊C16C211yesmaximal, characteristic, complemented
8#16840490—21no—
9C2×#14519722—21no—
10#16840167C2211yescharacteristic
11#16840164—21no—
12#16840139C2211yescharacteristic
13#16840070—22no—
14#16840048—21no—
15#16839962—21no—
16C4×Dic244—21no—
17C4×Dic244C2211yescharacteristic
18#16839564—22no—
19#16839564—21no—
20#16839515C2211yescharacteristic
21#16839505—21no—
22C8×Q8×C61C2211yescharacteristic
23C61×C4⋊C16C2211yescharacteristic
24C4×C16×C61C2211yescharacteristic
25C2×Dic244D411yescharacteristic
26C2×#11758201—41no—
27C2×D488—21no—
28C2×D488—21no—
29#14519777—21no—
30#14519775—41no—
31#14519774—21no—
32#14519769—22no—
33#14519767—42no—
34C4×Dic122—22no—
35C4×Dic122—21no—
36#14519742—41no—
37#14519722—42no—
38#14519711—21no—
39#14519711D412yes—
40#14519711D411yescharacteristic
41#14519709—22no—
42C4⋊#92418—21no—
43#14519702—22no—
44#14519702—21no—
45#14519697—41no—
46C4×Q8×C61D411yescharacteristic
47C2×C16×C61—21no—
48C2×C16×C61—21no—
49C4⋊C8×C61—21no—
50C4⋊C8×C61D411yescharacteristic
51C4×C8×C61—21no—
52C4×C8×C61C2311yescharacteristic
53C2×Q8×C61D811yescharacteristic
54C2×D244—41no—
55C2×D244—41no—
56C2×D244—41no—
57C2×Dic122—21no—
58C2×Dic122—41no—
59C2×C8×C61—21no—
60C2×C8×C61C2×D411yescharacteristic
61C2×C8×C61C2×D411yescharacteristic
62C4⋊C4×C61—21no—
63C4⋊C4×C61D811yescharacteristic
64C42×C61—21no—
65C42×C61C2×D411yescharacteristic
66#11758201—82no—
67C4⋊Dic61—21no—
68C4⋊Dic61—22no—
69C4⋊Dic61—41no—
70#11758196—42no—
71#11758196—42no—
72#11758196—42no—
73#11758196—41no—
74C4×Dic61—42no—
75C4×Dic61—41no—
76C2×#92418—41no—
77Dic244—21no—
78Dic244SD1612yescomplemented
79D488—42no—
80D488—41no—
81D488—41no—
82C16×C61—41no—
83C16×C61—41no—
84C22×D61—81no—
85Q8×C61—21no—
86Q8×C61—21no—
87C2×C4×C61—21no—
88C2×C4×C61—21no—
89C2×C4×C61#12011yescharacteristic
90C2×C4×C61C2×D811yescharacteristic
91C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
92C2×Dic61—41no—
93C2×Dic61—41no—
94C2×Dic61—42no—
95D244—81no—
96D244—81no—
97D244—81no—
98D244—81no—
99D244—161no—
100Dic122—22no—
101Dic122—41no—
102Dic122—81no—
103Dic122—81no—
104C8×C61—21no—
105C8×C61—41no—
106C8×C61C2×SD1611yescharacteristic
107C8×C61#13711yescharacteristic
108#92418—81no—
109#12353—611nomaximal, Sylow
110C22×C61#44711yescharacteristic
111C2×D61—161no—
112C2×D61—161no—
113C2×D61—161no—
114C4×C61—21no—
115C4×C61—41no—
116C4×C61—41no—
117C4×C61#44811yescharacteristic
118C4×C61#45411yescharacteristic
119C4×C61#50811yescharacteristic
120C4×C61#50911yescharacteristic
121Dic61—42no—
122Dic61—82no—
123Dic61—81no—
124#3383—611no—
125#2240—611no—
126#2207—611no—
127#1668—611no—
128#1364—611no—
129Q8⋊C16D6111yescharacteristic, complemented
130#1332—611no—
131C2×C61#162711yescharacteristic
132C2×C61#218611yescharacteristic
133C2×C61#219311yescharacteristic
134D61—321no—
135#557—1221no—
136C2×SD32—1221no—
137#500—611no—
138#499—1221no—
139#493—611no—
140#479—1222no—
141#475—1221no—
142#460—1221no—
143C8×Q8C2×D6111yescharacteristic
144C4×Q16—611no—
145C4×Q16—1221no—
146C4⋊C16C2×D6111yescharacteristic
147#357—1221no—
148#357—1222no—
149C4×C16C2×D6111yescharacteristic
150#335—611no—
151#331—1221no—
152C61#1235311yescharacteristic, complemented, Sylow
153C2×Q16—611no—
154C2×SD16—2441no—
155C2×D8—1221no—
156C2×D8—1221no—
157C4⋊Q8—1221no—
158C4⋊Q8—2441no—
159#127—1221no—
160#125—1222no—
161#125—2442no—
162C4×Q8—1222no—
163C4×Q8—1221no—
164C4×Q8—2441no—
165C4×Q8D24411yescharacteristic
166SD32—2442no—
167C2×C16—21no—
168C2×C16—21no—
169#107—611no—
170#107—612no—
171#107—1221no—
172#106—1222no—
173C4⋊C8—21no—
174C4⋊C8—1221no—
175C4⋊C8D24411yescharacteristic
176#103—1222no—
177#103—1221no—
178#102—2441no—
179C4×C8—21no—
180C4×C8C22×D6111yescharacteristic
181C2×Q8—1221no—
182C2×Q8—2441no—
183C2×Q8D48811yescharacteristic
184C2×D4—2441no—
185C2×D4—2441no—
186C2×D4—2441no—
187Q16—612no—
188Q16—1221no—
189SD16—4882no—
190D8—2442no—
191D8—2441no—
192D8—2441no—
193C2×C8—21no—
194C2×C8—2441no—
195C2×C8D4×D6111yescharacteristic
196C2×C8D4×D6111yescharacteristic
197C4⋊C4—21no—
198C4⋊C4—1221no—
199C4⋊C4—1222no—
200C4⋊C4—2442no—
201C4⋊C4—2442no—
202C4⋊C4—2442no—
203C4⋊C4—2441no—
204C4⋊C4—2441no—
205C4⋊C4D48811yescharacteristic
206C42—21no—
207C42—2442no—
208C42—2441no—
209C42C2×D24411yescharacteristic
210C16—41no—
211C16—41no—
212C23—4881no—
213Q8—21no—
214Q8—21no—
215Q8—1222no—
216Q8—4881no—
217Q8—4881no—
218Q8—2441no—
219D4—9761no—
220D4—4881no—
221D4—4881no—
222D4—4881no—
223D4—4881no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—2441no—
227C2×C4—2442no—
228C2×C4—2441no—
229C2×C4#1451974711yescharacteristic
230C2×C4C2×D48811yescharacteristic
231C2×C4#1451980511yescharacteristic
232C8—21no—
233C8—41no—
234C8—4881no—
235C8SD16×D6111yescharacteristic
236C8#1451980911yescharacteristic
237C22—9761no—
238C22—9761no—
239C22—9761no—
240C22#1683989811yescharacteristic
241C4—21no—
242C4—41no—
243C4—41no—
244C4—4882no—
245C4—4881no—
246C4—2442no—
247C4#1683990211yescharacteristic
248C4#1683993611yescharacteristic
249C4#1684019411yescharacteristic
250C4#1684020011yescharacteristic
251C2—19521no—
252C2#2144492411yescharacteristic
253C2#2144774411yescharacteristic
254C2#2144778511yescharacteristic
subgroupG/H
centerC22#16839898
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×Q8⋊C16C2
socleC22×C61#447
prime radical#16840139C22
hypercenterQ8⋊C16D61
hypocenterC61#12353
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8 ◁ Q8⋊C16

Complements

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

NH ≅ G/Ntype
1. #21458711C2semidirect
5. #21443873C2semidirect
6. #21443784C2semidirect
7. C61×Q8⋊C16C2semidirect
78. Dic244SD16semidirect
129. Q8⋊C16D61semidirect
152. C61#12353semidirect

Maximal subgroups

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

subgroupindex
#214587112
#214480432
#214478602
#214451792
#214438732
#214437842
C61×Q8⋊C162
#1235361