Finite Group Databasebeta

← #30605704

Subgroups — #30605704

Order 15616.

350 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 80 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
1C2×#16840683C211yesmaximal, characteristic, complemented
2#21461379C211yesmaximal, characteristic, complemented
3#21460838C212yesmaximal, complemented
4#21460833C212yesmaximal, complemented
5#21456393C211yesmaximal, characteristic
6C22×#11758187—21no—
7#16840783—21no—
8#16840683—21no—
9#16840683C2212yes—
10#16840626C2212yes—
11#16840623—21no—
12#16840307—21no—
13#16840166C2211yescharacteristic
14#16840137C2211yescharacteristic
15#16840107—21no—
16#16839998C411yescharacteristic
17#16839996—21no—
18D8×Dic61C411yescharacteristic
19#16839844C411yescharacteristic
20#16839842—21no—
21C2×C8×Dic61C2211yescharacteristic
22C61×#466C411yescharacteristic
23C2×#11758187—22no—
24C2×#11758187—42no—
25C4⋊#92420—22no—
26C22⋊#92420—41no—
27#14519832—41no—
28C2×#11758224—41no—
29C2×D488C2×C411yescharacteristic
30C2×#11758199—21no—
31C22×#92418D411yescharacteristic
32#14519776—21no—
33#14519773—21no—
34#14519763—41no—
35#14519751—21no—
36#14519749—41no—
37D4×Dic61—21no—
38#14519739—21no—
39#14519737—41no—
40C2×C4×Dic61D411yescharacteristic
41#14519711C2×C411yescharacteristic
42#14519710—21no—
43#14519699—21no—
44#14519698—21no—
45#14519697—21no—
46C8×Dic61C2×C411yescharacteristic
47C8×Dic61D411yescharacteristic
48C8×Dic61D411yescharacteristic
49C8×Dic61C2311yescharacteristic
50C2×D8×C61C2×C411yescharacteristic
51C22×C8×C61C2×C411yescharacteristic
52#121×C61—21no—
53#107×C61C2×C411yescharacteristic
54#102×C61—21no—
55C2×D4×C61—21no—
56C2×D4×C61—41no—
57C22×C4×C61C22⋊C411yescharacteristic
58C2×C22⋊D61—41no—
59C2×C22⋊D61—41no—
60C2×C22⋊D61—41no—
61C22×Dic61—41no—
62C22×Dic61D811yescharacteristic
63C22×Dic61SD1611yescharacteristic
64#11758224—84no—
65C2×D244—21no—
66C2×C4×D61—41no—
67C2×Dic122—41no—
68C2×#92420—42no—
69D8×C61—41no—
70C2×C8×C61—41no—
71C2×C8×C61C22⋊C411yescharacteristic
72C2×C8×C61C22×C411yescharacteristic
73C4⋊C4×C61—21no—
74C22⋊C4×C61—41no—
75C22⋊Dic61—41no—
76#11758199—41no—
77#11758199—41no—
78#11758198—41no—
79#11758198—41no—
80C4⋊Dic61—21no—
81#11758196—41no—
82C4×Dic61C22⋊C411yescharacteristic
83C4×Dic61D811yescharacteristic
84C4×Dic61SD1611yescharacteristic
85C4×Dic61C2×D411yescharacteristic
86C2×#92418—21no—
87C2×#92418—21no—
88C2×#92418C22⋊C411yescharacteristic
89C2×#92418C2×D411yescharacteristic
90D488—41no—
91#11758187—42no—
92C23×C61—41no—
93C23×C61#10211yescharacteristic
94C22×D61—41no—
95D4×C61—41no—
96D4×C61—41no—
97D4×C61—82no—
98C2×C4×C61—21no—
99C2×C4×C61—21no—
100C2×C4×C61—41no—
101C2×C4×C61#10211yescharacteristic
102C2×C4×C61C2×C22⋊C411yescharacteristic
103C22⋊D61—82no—
104C22⋊D61—82no—
105C22⋊D61—82no—
106C2×Dic61—22no—
107C2×Dic61—22no—
108C2×Dic61—41no—
109C2×Dic61—82no—
110C2×Dic61#10211yescharacteristic
111C2×Dic61#10211yescharacteristic
112C2×Dic61C2×D811yescharacteristic
113C2×Dic61C2×SD1611yescharacteristic
114D244—41no—
115D244—41no—
116C4×D61—82no—
117Dic122—82no—
118#92420—82no—
119C8×C61—21no—
120C8×C61—21no—
121#92418—21no—
122#92418AGL(1,ℤ/8)11yescharacteristic
123#92418#13711yescharacteristic
124#11982—611nomaximal, Sylow
125C22×C61—21no—
126C22×C61—21no—
127C22×C61—81no—
128C22×C61—81no—
129C22×C61—81no—
130C22×C61#36112yes—
131C22×C61C2×#10211yescharacteristic
132C2×D61—81no—
133C2×D61—81no—
134C2×D61—81no—
135C4×C61—21no—
136C4×C61—81no—
137C4×C61#41311yescharacteristic
138C4×C61#41711yescharacteristic
139Dic61—21no—
140Dic61—21no—
141Dic61—21no—
142Dic61—81no—
143Dic61#50812yes—
144#3169—611no—
145C2×C4⋊C16—611no—
146#1568—611no—
147#1365—612no—
148#1361—612no—
149C2×C61—22no—
150C2×C61—161no—
151C2×C61#154711yescharacteristic
152C2×C61#213811yescharacteristic
153C2×C61C2×#36111yescharacteristic
154D61—161no—
155#532—1221no—
156C22×C16—1221no—
157#500—611no—
158#493—611no—
159#486—1221no—
160#466—611no—
161#466—1221no—
162#466#692311yescharacteristic
163C4×D8—611no—
164C4×D8—611no—
165C4×D8—1221no—
166#432—1221no—
167C2×C4×C8—611no—
168C4⋊C16—612no—
169C4⋊C16—1221no—
170#335—612no—
171#334—1221no—
172C61#1198211yescharacteristic, complemented, Sylow
173C2×#41—2441no—
174C2×D8—611no—
175C2×D8—1221no—
176C2×D8C2×#692311yescharacteristic
177C22×C8—611no—
178C22×C8C2×#692311yescharacteristic
179C4⋊Q8—1221no—
180#127—1221no—
181#124—2441no—
182#121—21no—
183#121—1221no—
184#121—2441no—
185C4×D4—1221no—
186C4×D4—1221no—
187C4×D4—2441no—
188C2×C42—611no—
189C2×C16—1222no—
190C2×C16—2442no—
191#107—611no—
192#107—1221no—
193#107C2×#692311yescharacteristic
194C4⋊C8—1222no—
195#102—21no—
196#102—1221no—
197#102—1221no—
198#102—1221no—
199C22⋊C8—2441no—
200#97—2441no—
201C4×C8—611no—
202C4×C8—611no—
203C4×C8—611no—
204C4×C8—611no—
205#41—4884no—
206C2×Q8—2441no—
207C2×D4—21no—
208C2×D4—41no—
209C2×D4—1221no—
210C2×D4—2441no—
211C2×D4—2441no—
212C2×D4—2441no—
213C22×C4—611no—
214C22×C4—611no—
215C22×C4—2441no—
216C22×C4—2441no—
217C22×C4C22⋊#692311yescharacteristic
218D8—41no—
219D8—2441no—
220D8—2441no—
221D8—2441no—
222C2×C8—41no—
223C2×C8—611no—
224C2×C8—611no—
225C2×C8—1221no—
226C2×C8—1221no—
227C2×C8—2442no—
228C2×C8C22⋊#692311yescharacteristic
229C2×C8C22×#692311yescharacteristic
230C4⋊C4—21no—
231C4⋊C4—1221no—
232C4⋊C4—2441no—
233C22⋊C4—41no—
234C22⋊C4—2441no—
235C22⋊C4—2441no—
236C22⋊C4—2441no—
237C42—611no—
238C42—611no—
239C42—611no—
240C42—611no—
241C16—2442no—
242C23—41no—
243C23—2441no—
244C23#1451983911yescharacteristic
245Q8—4882no—
246D4—41no—
247D4—41no—
248D4—82no—
249D4—4882no—
250D4—4882no—
251D4—4882no—
252D4—2441no—
253D4—2441no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—41no—
257C2×C4—611no—
258C2×C4—611no—
259C2×C4—611no—
260C2×C4—611no—
261C2×C4—1222no—
262C2×C4—1222no—
263C2×C4—4882no—
264C2×C4—4882no—
265C2×C4—2441no—
266C2×C4#1451983911yescharacteristic
267C2×C4C2×C22⋊#692311yescharacteristic
268C8—21no—
269C8—21no—
270C8—611no—
271C8—611no—
272C8—1221no—
273C8—4882no—
274C22—21no—
275C22—21no—
276C22—81no—
277C22—81no—
278C22—81no—
279C22—4881no—
280C22—4881no—
281C22—4881no—
282C22#1684068012yes—
283C22C2×#1451983911yescharacteristic
284C4—21no—
285C4—81no—
286C4—612no—
287C4—1221no—
288C4—1221no—
289C4—1221no—
290C4—4881no—
291C4#1684074911yescharacteristic
292C4#1684075311yescharacteristic
293C2—22no—
294C2—161no—
295C2—9761no—
296C2#2146133111yescharacteristic
297C2#2146212611yescharacteristic
298C2C2×#1684068011yescharacteristic
subgroupG/H
centerC22C2×#14519839
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#466C4
socleC22×C61C2×#102
prime radical#21456393C2
cosocleC8×Dic61C23
hypercenter#466#6923
hypocenterC61#11982
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #466

Complements

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

NH ≅ G/Ntype
1. C2×#16840683C2semidirect
2. #21461379C2semidirect
3. #21460838C2semidirect
4. #21460833C2semidirect
172. C61#11982semidirect

Maximal subgroups

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

subgroupindex
C2×#168406832
#214613792
#214608382
#214608332
#214563932
#1198261