Finite Group Databasebeta

← #29593563

Subgroups — #29593563

Order 15616.

306 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 75 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#21448071C211yesmaximal, characteristic
2#21447869C211yesmaximal, characteristic
3#21445189C211yesmaximal, characteristic
4#21443868C211yesmaximal, characteristic
5Q8⋊#11758185C211yesmaximal, characteristic
6#21443783C211yesmaximal, characteristic
7C61×#3395C211yesmaximal, characteristic
8C2×#14519723—22no—
9C2×#14519723—21no—
10#16840142C2211yescharacteristic
11#16840047—21no—
12C4⋊#11758185C2211yescharacteristic
13#16839565—21no—
14C4×#11758185C2211yescharacteristic
15#16839515C2211yescharacteristic
16#16839509—21no—
17C61×#557—21no—
18C61×#494—21no—
19C61×#494C2211yescharacteristic
20C61×#462—22no—
21C61×#462—21no—
22C8×Q8×C61C2211yescharacteristic
23C4×Q16×C61—21no—
24C4×Q16×C61C2211yescharacteristic
25C2×Dic244—21no—
26C2×Dic244—21no—
27#14519777—21no—
28#14519723—44no—
29#14519723—42no—
30C2×#11758185—21no—
31C2×#11758185—21no—
32#14519708—41no—
33C4⋊#92418—21no—
34#14519701—41no—
35C2×Q16×C61—22no—
36C2×Q16×C61—21no—
37C2×Q16×C61D411yescharacteristic
38C2×Q16×C61D412yes—
39C4⋊Q8×C61—22no—
40C4⋊Q8×C61—21no—
41#125×C61—42no—
42#125×C61—41no—
43C4×Q8×C61—22no—
44C4×Q8×C61—21no—
45C4×Q8×C61—41no—
46C4×Q8×C61D411yescharacteristic
47#107×C61D411yescharacteristic
48C4⋊C8×C61—21no—
49C4⋊C8×C61D411yescharacteristic
50#103×C61—22no—
51#103×C61—21no—
52C4×C8×C61—21no—
53C4×C8×C61C2311yescharacteristic
54C2×Q8×C61—21no—
55C2×Q8×C61—22no—
56C2×Q8×C61D811yescharacteristic
57C2×Dic122—41no—
58Q16×C61—21no—
59Q16×C61—21no—
60Q16×C61—42no—
61Q16×C61—41no—
62Q16×C61—41no—
63Q16×C61—82no—
64C2×C8×C61—21no—
65C2×C8×C61C2×D411yescharacteristic
66C2×C8×C61C2×D411yescharacteristic
67C4⋊C4×C61—21no—
68C4⋊C4×C61—21no—
69C4⋊C4×C61—42no—
70C4⋊C4×C61—42no—
71C4⋊C4×C61—42no—
72C4⋊C4×C61—41no—
73C4⋊C4×C61—41no—
74C4⋊C4×C61—41no—
75C4⋊C4×C61D811yescharacteristic
76C42×C61—21no—
77C42×C61—42no—
78C42×C61—41no—
79C42×C61C2×D411yescharacteristic
80C4⋊Dic61—41no—
81C4⋊Dic61—41no—
82C2×#92418—41no—
83Dic244—42no—
84Dic244—41no—
85Dic244—41no—
86#11758185—22no—
87#11758185—41no—
88Q8×C61—21no—
89Q8×C61—41no—
90Q8×C61—42no—
91Q8×C61—42no—
92Q8×C61—41no—
93Q8×C61Q3212yescomplemented
94C2×C4×C61—21no—
95C2×C4×C61—21no—
96C2×C4×C61—41no—
97C2×C4×C61—42no—
98C2×C4×C61—41no—
99C2×C4×C61#12011yescharacteristic
100C2×C4×C61C2×D811yescharacteristic
101C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
102C2×Dic61—81no—
103Dic122—81no—
104Dic122—81no—
105C8×C61—21no—
106C8×C61—41no—
107C8×C61#13511yescharacteristic
108C8×C61AGL(1,ℤ/8)11yescharacteristic
109#92418—81no—
110#12334—611nomaximal, Sylow
111C22×C61#44711yescharacteristic
112C4×C61—22no—
113C4×C61—21no—
114C4×C61—41no—
115C4×C61—81no—
116C4×C61—82no—
117C4×C61—81no—
118C4×C61#44911yescharacteristic
119C4×C61#45311yescharacteristic
120C4×C61C2×Q3211yescharacteristic
121C4×C61#51011yescharacteristic
122Dic61—161no—
123#3395D6111yescharacteristic
124#2247—611no—
125#2209—611no—
126#1670—611no—
127#1362—611no—
128Q8⋊C16—611no—
129#1332—611no—
130C2×C61#162111yescharacteristic
131C2×C61#218811yescharacteristic
132C2×C61#219511yescharacteristic
133#557—21no—
134C2×Q32—1221no—
135C2×Q32—1222no—
136#494—21no—
137#494—611no—
138#494C2×D6111yescharacteristic
139#475—1221no—
140#462—22no—
141#462—21no—
142C8×Q8C2×D6111yescharacteristic
143C4×Q16—21no—
144C4×Q16C2×D6111yescharacteristic
145C4⋊C16—611no—
146#358—1221no—
147C4×C16—611no—
148#335—611no—
149#332—1221no—
150C61#1233411yescharacteristic, complemented, Sylow
151C2×Q16—22no—
152C2×Q16—21no—
153C2×Q16—1221no—
154C2×Q16—1221no—
155C2×Q16C22⋊D6111yescharacteristic
156C2×Q16C22⋊D6112yes—
157C4⋊Q8—22no—
158C4⋊Q8—21no—
159C4⋊Q8—1221no—
160#125—42no—
161#125—41no—
162C4×Q8—22no—
163C4×Q8—21no—
164C4×Q8—41no—
165C4×Q8C22⋊D6111yescharacteristic
166Q32—2444no—
167Q32—2442no—
168C2×C16—1221no—
169C2×C16—1221no—
170#107C22⋊D6111yescharacteristic
171#106—2441no—
172C4⋊C8—21no—
173C4⋊C8—1221no—
174C4⋊C8C22⋊D6111yescharacteristic
175#103—22no—
176#103—21no—
177#103—2441no—
178C4×C8—21no—
179C4×C8C22×D6111yescharacteristic
180C2×Q8—21no—
181C2×Q8—22no—
182C2×Q8—2441no—
183C2×Q8#1175819911yescharacteristic
184Q16—21no—
185Q16—21no—
186Q16—42no—
187Q16—41no—
188Q16—41no—
189Q16—82no—
190Q16—2442no—
191Q16—2441no—
192Q16—2441no—
193C2×C8—21no—
194C2×C8—2441no—
195C2×C8C2×C22⋊D6111yescharacteristic
196C2×C8C2×C22⋊D6111yescharacteristic
197C4⋊C4—21no—
198C4⋊C4—21no—
199C4⋊C4—42no—
200C4⋊C4—42no—
201C4⋊C4—42no—
202C4⋊C4—41no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—2441no—
206C4⋊C4—2441no—
207C4⋊C4#1175819911yescharacteristic
208C42—21no—
209C42—42no—
210C42—41no—
211C42C2×C22⋊D6111yescharacteristic
212C16—1222no—
213C16—2441no—
214Q8—21no—
215Q8—41no—
216Q8—42no—
217Q8—42no—
218Q8—41no—
219Q8—4881no—
220Q8—4881no—
221Q8#1451972312yescomplemented
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—41no—
225C2×C4—42no—
226C2×C4—41no—
227C2×C4—4881no—
228C2×C4#1451974611yescharacteristic
229C2×C4C2×#1175819911yescharacteristic
230C2×C4#1451980311yescharacteristic
231C8—21no—
232C8—41no—
233C8—4881no—
234C8#1451979711yescharacteristic
235C8#1451980211yescharacteristic
236C22#1683989611yescharacteristic
237C4—22no—
238C4—21no—
239C4—41no—
240C4—81no—
241C4—82no—
242C4—81no—
243C4—9761no—
244C4#1683990711yescharacteristic
245C4#1683993011yescharacteristic
246C4C2×#1451972311yescharacteristic
247C4#1684020311yescharacteristic
248C2#2144488411yescharacteristic
249C2#2144775311yescharacteristic
250C2#2144779711yescharacteristic
subgroupG/H
centerC22#16839896
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#3395C2
socle, prime radicalC22×C61#447
hypercenter#3395D61
hypocenterC61#12334
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8 ◁ #3395

Complements

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

NH ≅ G/Ntype
93. Q8×C61Q32semidirect
150. C61#12334semidirect
221. Q8#14519723semidirect

Maximal subgroups

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

subgroupindex
#214480712
#214478692
#214451892
#214438682
Q8⋊#117581852
#214437832
C61×#33952
#1233461