Finite Group Databasebeta

← #29593567

Subgroups — #29593567

Order 15616.

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

normal subgroups only

This group has 312 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#21458809C211yesmaximal, characteristic
2#21447861C211yesmaximal, characteristic
3#21445186C211yesmaximal, characteristic, complemented
4#21443868C211yesmaximal, characteristic, complemented
5#21443799C211yesmaximal, characteristic, complemented
6#21443781C211yesmaximal, characteristic
7C61×#2247C211yesmaximal, characteristic, complemented
8#16840486—21no—
9C2×#14519720—21no—
10#16840147—21no—
11#16840044—21no—
12#16839986—22no—
13#16839964—21no—
14C8×Dic122C2211yescharacteristic
15Q16×Dic61—21no—
16C4×D488C2211yescharacteristic
17C4⋊#11758185C2211yescharacteristic
18#16839566—21no—
19#16839515C2211yescharacteristic
20#16839508—21no—
21C2×Q32×C61—22no—
22C61×#494C2211yescharacteristic
23C61×#494C2211yescharacteristic
24C4×C16×C61C2211yescharacteristic
25C2×#11758201—22no—
26C2×D488D411yescharacteristic
27#14519772—42no—
28#14519766—22no—
29#14519757—41no—
30Q8×Dic61—22no—
31C4×Dic122D411yescharacteristic
32C4×D244—21no—
33#14519735—41no—
34#14519720—42no—
35C2×#11758185—21no—
36#14519711D411yescharacteristic
37#14519708—41no—
38C4⋊#92418—21no—
39C4⋊#92418D411yescharacteristic
40#14519706—21no—
41#14519701—22no—
42#14519700—41no—
43#14519699—21no—
44C8×Dic61—21no—
45C2×Q16×C61—21no—
46C2×Q16×C61—21no—
47C2×Q16×C61—21no—
48C2×Q16×C61D412yes—
49C4⋊Q8×C61—21no—
50C4⋊Q8×C61—21no—
51Q32×C61—44no—
52C2×C16×C61—21no—
53C4×C8×C61C2311yescharacteristic
54C2×Q8×C61—22no—
55C2×Q8×C61—41no—
56C2×D244—21no—
57C2×C4×D61—41no—
58C2×Dic122D811yescharacteristic
59Q16×C61—42no—
60Q16×C61—42no—
61Q16×C61—41no—
62Q16×C61—41no—
63Q16×C61—41no—
64Q16×C61—41no—
65C2×C8×C61C2×D411yescharacteristic
66C2×C8×C61C2×D411yescharacteristic
67C4⋊C4×C61—41no—
68C4⋊C4×C61—41no—
69C4⋊C4×C61—41no—
70C4⋊C4×C61—41no—
71C42×C61C2×D411yescharacteristic
72#11758201—82no—
73#11758198—42no—
74#11758198—42no—
75#11758198—41no—
76C4⋊Dic61—21no—
77C4⋊Dic61—42no—
78C4⋊Dic61D811yescharacteristic
79#11758196—21no—
80C4×Dic61—21no—
81C4×Dic61—42no—
82C2×#92418—21no—
83C2×#92418—41no—
84D488—21no—
85D488—21no—
86C16×C61—22no—
87#11758185—41no—
88C22×D61—41no—
89Q8×C61—42no—
90Q8×C61—42no—
91Q8×C61—81no—
92Q8×C61—81no—
93C2×C4×C61—42no—
94C2×C4×C61—81no—
95C2×C4×C61#12011yescharacteristic
96C2×C4×C61C2×D811yescharacteristic
97C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
98C2×Dic61—21no—
99C2×Dic61—21no—
100C2×Dic61—41no—
101D244—41no—
102D244—41no—
103C4×D61—81no—
104C4×D61—81no—
105Dic122—21no—
106Dic122—21no—
107C8×C61—21no—
108C8×C61#13511yescharacteristic
109C8×C61AGL(1,ℤ/8)11yescharacteristic
110#92418—41no—
111#92418—81no—
112#12335—611nomaximal, Sylow
113C22×C61#44711yescharacteristic
114C2×D61—81no—
115C2×D61—81no—
116C2×D61—81no—
117C4×C61—21no—
118C4×C61—82no—
119C4×C61—161no—
120C4×C61#44911yescharacteristic
121C4×C61#45311yescharacteristic
122C4×C61#50811yescharacteristic
123C4×C61#51011yescharacteristic
124Dic61—41no—
125Dic61—41no—
126Dic61—81no—
127#3393—611no—
128#2247D6111yescharacteristic, complemented
129#2208—611no—
130#1670—611no—
131#1362—611no—
132Q8⋊C16—611no—
133#1331—611no—
134C2×C61#162111yescharacteristic
135C2×C61#218911yescharacteristic
136C2×C61#219511yescharacteristic
137D61—161no—
138#556—1221no—
139C2×Q32—22no—
140C2×SD32—1221no—
141#495—1221no—
142#494C2×D6111yescharacteristic
143#494C2×D6111yescharacteristic
144#475—1221no—
145#464—1222no—
146#461—1221no—
147C8×Q8—611no—
148C4×Q16—1221no—
149C4×D8—611no—
150C4⋊C16—611no—
151#358—1221no—
152C4×C16C2×D6111yescharacteristic
153#335—611no—
154#332—1221no—
155C61#1233511yescharacteristic, complemented, Sylow
156C2×Q16—21no—
157C2×Q16—21no—
158C2×Q16—21no—
159C2×Q16C22⋊D6112yes—
160C2×SD16—1222no—
161C2×D8—611no—
162C4⋊Q8—21no—
163C4⋊Q8—21no—
164#126—2442no—
165#124—1222no—
166C22⋊Q8—2441no—
167C4×Q8—611no—
168C4×Q8—1222no—
169C4×D4—1221no—
170#117—2441no—
171Q32—44no—
172SD32—2442no—
173C2×C16—21no—
174C2×C16—1221no—
175#107—611no—
176#106—2441no—
177C4⋊C8—611no—
178C4⋊C8—1221no—
179C4⋊C8—1221no—
180#103—1222no—
181#103—2441no—
182#102—1221no—
183C4×C8—1221no—
184C4×C8C22×D6111yescharacteristic
185C2×Q8—22no—
186C2×Q8—41no—
187C2×Q8—611no—
188C2×D4—1221no—
189C22×C4—2441no—
190Q16—42no—
191Q16—42no—
192Q16—41no—
193Q16—41no—
194Q16—41no—
195Q16—41no—
196SD16—4882no—
197D8—1221no—
198D8—1221no—
199C2×C8—1221no—
200C2×C8—2441no—
201C2×C8D4×D6111yescharacteristic
202C2×C8C2×C22⋊D6111yescharacteristic
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—41no—
207C4⋊C4—611no—
208C4⋊C4—1221no—
209C4⋊C4—1221no—
210C4⋊C4—2442no—
211C22⋊C4—2442no—
212C22⋊C4—2442no—
213C22⋊C4—2441no—
214C42—1221no—
215C42—2442no—
216C42D4×D6111yescharacteristic
217C16—22no—
218C16—2441no—
219C23—2441no—
220Q8—42no—
221Q8—42no—
222Q8—81no—
223Q8—81no—
224Q8—1221no—
225Q8—1221no—
226D4—2441no—
227D4—2441no—
228C2×C4—42no—
229C2×C4—81no—
230C2×C4—1221no—
231C2×C4—1221no—
232C2×C4—4881no—
233C2×C4—4881no—
234C2×C4—2441no—
235C2×C4#1451974511yescharacteristic
236C2×C4D8×D6111yescharacteristic
237C2×C4#1451980111yescharacteristic
238C8—21no—
239C8—4881no—
240C8—2441no—
241C8#1451979611yescharacteristic
242C8#1451980111yescharacteristic
243C22—4881no—
244C22—4881no—
245C22—4881no—
246C22#1683989411yescharacteristic
247C4—21no—
248C4—82no—
249C4—161no—
250C4—4881no—
251C4—2441no—
252C4—2441no—
253C4#1683990411yescharacteristic
254C4#1683992911yescharacteristic
255C4#1684019511yescharacteristic
256C4#1684020411yescharacteristic
257C2—9761no—
258C2#2144488111yescharacteristic
259C2#2144775811yescharacteristic
260C2#2144779611yescharacteristic
subgroupG/H
centerC22#16839894
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#2247C2
socleC22×C61#447
prime radicalC2×D488D4
hypercenter#2247D61
hypocenterC61#12335
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2247

Complements

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

NH ≅ G/Ntype
3. #21445186C2semidirect
4. #21443868C2semidirect
5. #21443799C2semidirect
7. C61×#2247C2semidirect
128. #2247D61semidirect
155. C61#12335semidirect

Maximal subgroups

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

subgroupindex
#214588092
#214478612
#214451862
#214438682
#214437992
#214437812
C61×#22472
#1233561