Finite Group Databasebeta

← #29593553

Subgroups — #29593553

Order 15616.

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

normal subgroups only

This group has 324 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#21447866C211yesmaximal, characteristic, complemented
3#21445186C211yesmaximal, characteristic, complemented
4#21443865C211yesmaximal, characteristic
5#21443799C211yesmaximal, characteristic, complemented
6#21443784C211yesmaximal, characteristic, complemented
7C61×#2248C211yesmaximal, characteristic
8#16840498—21no—
9C2×#14519723—21no—
10#16840145—21no—
11#16840044—21no—
12#16839975—22no—
13#16839959—21no—
14C8×Dic122C2211yescharacteristic
15C4×Dic244C2211yescharacteristic
16D8×Dic61—21no—
17C4⋊#11758185C2211yescharacteristic
18#16839566—21no—
19#16839515C2211yescharacteristic
20#16839508—21no—
21C2×SD32×C61—22no—
22C61×#494C2211yescharacteristic
23C61×#493C2211yescharacteristic
24C4×C16×C61C2211yescharacteristic
25C2×Dic244D411yescharacteristic
26C2×#11758200—22no—
27#14519764—22no—
28#14519764—41no—
29#14519758—42no—
30C4×Dic122—21no—
31C4×Dic122D411yescharacteristic
32D4×Dic61—22no—
33D4×Dic61—41no—
34#14519723—42no—
35C2×#11758185—21no—
36#14519711D411yescharacteristic
37#14519708—41no—
38C4⋊#92418—21no—
39C4⋊#92418D411yescharacteristic
40#14519706—21no—
41#14519702—21no—
42#14519700—41no—
43#14519698—22no—
44C8×Dic61—21no—
45C2×Q16×C61—21no—
46C2×Q16×C61—21no—
47C2×D8×C61—21no—
48C2×D8×C61D412yes—
49C4⋊Q8×C61—21no—
50#127×C61—21no—
51SD32×C61—44no—
52C2×C16×C61—21no—
53C4×C8×C61C2311yescharacteristic
54C2×Q8×C61—41no—
55C2×D4×C61—22no—
56C2×D4×C61—41no—
57C2×D4×C61—41no—
58C22×Dic61—42no—
59C2×Dic122—21no—
60C2×Dic122D811yescharacteristic
61Q16×C61—42no—
62Q16×C61—41no—
63Q16×C61—41no—
64D8×C61—42no—
65D8×C61—41no—
66D8×C61—41no—
67C2×C8×C61C2×D411yescharacteristic
68C2×C8×C61C2×D411yescharacteristic
69C4⋊C4×C61—41no—
70C4⋊C4×C61—41no—
71C42×C61C2×D411yescharacteristic
72C22⋊Dic61—42no—
73C22⋊Dic61—42no—
74C22⋊Dic61—42no—
75#11758200—82no—
76C4⋊Dic61—21no—
77C4⋊Dic61D811yescharacteristic
78#11758196—21no—
79#11758196—41no—
80C4×Dic61—21no—
81C4×Dic61—41no—
82C2×#92418—21no—
83C2×#92418—41no—
84Dic244—21no—
85Dic244—21no—
86C16×C61—22no—
87#11758185—41no—
88C23×C61—42no—
89Q8×C61—81no—
90Q8×C61—81no—
91D4×C61—42no—
92D4×C61—42no—
93D4×C61—81no—
94D4×C61—81no—
95D4×C61—161no—
96C2×C4×C61—81no—
97C2×C4×C61#12011yescharacteristic
98C2×C4×C61C2×D811yescharacteristic
99C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
100C2×Dic61—21no—
101C2×Dic61—21no—
102C2×Dic61—41no—
103C2×Dic61—41no—
104C2×Dic61—162no—
105Dic122—21no—
106Dic122—21no—
107Dic122—41no—
108Dic122—41no—
109C8×C61—21no—
110C8×C61#13511yescharacteristic
111C8×C61AGL(1,ℤ/8)11yescharacteristic
112#92418—41no—
113#92418—81no—
114#12333—611nomaximal, Sylow
115C22×C61—82no—
116C22×C61—82no—
117C22×C61—82no—
118C22×C61#44711yescharacteristic
119C4×C61—21no—
120C4×C61—161no—
121C4×C61#44911yescharacteristic
122C4×C61#45311yescharacteristic
123C4×C61#50811yescharacteristic
124C4×C61#51011yescharacteristic
125Dic61—41no—
126Dic61—41no—
127Dic61—81no—
128Dic61—81no—
129#3396—611no—
130#2248D6111yescharacteristic
131#2209—611no—
132#1670—611no—
133#1361—611no—
134Q8⋊C16—611no—
135#1332—611no—
136C2×C61—162no—
137C2×C61#162111yescharacteristic
138C2×C61#218911yescharacteristic
139C2×C61#219411yescharacteristic
140#559—1221no—
141C2×Q32—1221no—
142C2×SD32—22no—
143#495—1221no—
144#494C2×D6111yescharacteristic
145#493C2×D6111yescharacteristic
146#475—1221no—
147#463—1222no—
148#460—1221no—
149C8×Q8—611no—
150C4×Q16—611no—
151C4×D8—1221no—
152C4⋊C16—611no—
153#358—1221no—
154C4×C16C2×D6111yescharacteristic
155#335—611no—
156#332—1221no—
157C61#1233311yescharacteristic, complemented, Sylow
158C2×Q16—21no—
159C2×Q16—21no—
160C2×Q16—611no—
161C2×SD16—1222no—
162C2×D8—21no—
163C2×D8C22⋊D6112yes—
164C4⋊Q8—21no—
165#127—21no—
166#124—1222no—
167#124—2441no—
168#123—2442no—
169C4×Q8—611no—
170C4×Q8—1221no—
171C4×D4—1222no—
172C4×D4—2441no—
173Q32—2442no—
174SD32—44no—
175C2×C16—21no—
176C2×C16—1221no—
177#107—611no—
178#106—2441no—
179C4⋊C8—611no—
180C4⋊C8—1221no—
181C4⋊C8—1221no—
182#103—1221no—
183#103—2441no—
184#102—1222no—
185C4×C8—1221no—
186C4×C8C22×D6111yescharacteristic
187C2×Q8—41no—
188C2×Q8—611no—
189C2×Q8—1221no—
190C2×D4—22no—
191C2×D4—41no—
192C2×D4—41no—
193C22×C4—2442no—
194Q16—42no—
195Q16—41no—
196Q16—41no—
197Q16—1221no—
198Q16—1221no—
199SD16—4882no—
200D8—42no—
201D8—41no—
202D8—41no—
203C2×C8—1221no—
204C2×C8—2441no—
205C2×C8D4×D6111yescharacteristic
206C2×C8C2×C22⋊D6111yescharacteristic
207C4⋊C4—41no—
208C4⋊C4—41no—
209C4⋊C4—611no—
210C4⋊C4—1221no—
211C4⋊C4—1221no—
212C4⋊C4—2441no—
213C22⋊C4—2442no—
214C22⋊C4—2442no—
215C22⋊C4—2442no—
216C42—1221no—
217C42—2441no—
218C42D4×D6111yescharacteristic
219C16—22no—
220C16—2441no—
221C23—42no—
222Q8—81no—
223Q8—81no—
224Q8—1221no—
225Q8—1221no—
226Q8—2441no—
227Q8—2441no—
228D4—42no—
229D4—42no—
230D4—81no—
231D4—81no—
232D4—161no—
233C2×C4—81no—
234C2×C4—1221no—
235C2×C4—1221no—
236C2×C4—9762no—
237C2×C4—2441no—
238C2×C4—2441no—
239C2×C4#1451974511yescharacteristic
240C2×C4D8×D6111yescharacteristic
241C2×C4#1451980111yescharacteristic
242C8—21no—
243C8—4881no—
244C8—2441no—
245C8#1451979611yescharacteristic
246C8#1451980111yescharacteristic
247C22—82no—
248C22—82no—
249C22—82no—
250C22#1683989411yescharacteristic
251C4—21no—
252C4—161no—
253C4—4881no—
254C4—4881no—
255C4—2441no—
256C4—2441no—
257C4#1683990411yescharacteristic
258C4#1683992911yescharacteristic
259C4#1684019311yescharacteristic
260C4#1684020111yescharacteristic
261C2—162no—
262C2#2144488111yescharacteristic
263C2#2144775611yescharacteristic
264C2#2144778911yescharacteristic
subgroupG/H
centerC22#16839894
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#2248C2
socleC22×C61#447
prime radicalC61×#493C22
hypercenter#2248D61
hypocenterC61#12333
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2248

Complements

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

NH ≅ G/Ntype
2. #21447866C2semidirect
3. #21445186C2semidirect
5. #21443799C2semidirect
6. #21443784C2semidirect
157. C61#12333semidirect

Maximal subgroups

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

subgroupindex
#214588332
#214478662
#214451862
#214438652
#214437992
#214437842
C61×#22482
#1233361