Finite Group Databasebeta

← #30605616

Subgroups — #30605616

Order 15616.

354 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 86 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#21462178C211yesmaximal, characteristic, complemented
2D61⋊#335C211yesmaximal, characteristic, complemented
3#21460837C212yesmaximal, complemented
4#21460833C212yesmaximal, complemented
5#21456395C211yesmaximal, characteristic
6D61⋊(C4⋊C8)—21no—
7#16840683C2212yes—
8#16840657—21no—
9C4×#11758187—21no—
10#16840626C2212yes—
11#16840625—21no—
12#16840309—21no—
13#16840166C2211yescharacteristic
14#16840137C2211yescharacteristic
15#16840107—21no—
16#16839999C411yescharacteristic
17#16839997—21no—
18#16839995C411yescharacteristic
19C4×D488C411yescharacteristic
20C4×#11758199—21no—
21C4×C8×D61C2211yescharacteristic
22C4×D8×C61C411yescharacteristic
23C2×D61⋊C8—41no—
24C2×#11758187—22no—
25#14519844—41no—
26C4⋊#92420—22no—
27C2×#11758222—41no—
28C2×D488C2×C411yescharacteristic
29C2×#11758199—21no—
30C2×C8×D61C2×C411yescharacteristic
31C2×C8×D61D411yescharacteristic
32#14519776—21no—
33#14519773—21no—
34#14519763—41no—
35#14519752—21no—
36#14519750—41no—
37#14519748—21no—
38C4×D244—21no—
39C4×C22⋊D61—41no—
40C42×D61D411yescharacteristic
41#14519711C2×C411yescharacteristic
42#14519710—21no—
43#14519699—21no—
44#14519698—21no—
45#14519697—21no—
46C4×#92418D411yescharacteristic
47C8×Dic61D411yescharacteristic
48C8×Dic61C2311yescharacteristic
49C2×D8×C61C2×C411yescharacteristic
50C4×D4×C61—21no—
51#107×C61C2×C411yescharacteristic
52#102×C61—21no—
53C4×C8×C61C2×C411yescharacteristic
54C2×D4×C61—21no—
55C22×C4×C61—41no—
56C2×C22⋊D61—41no—
57C2×C22⋊D61—41no—
58C2×C22⋊D61—41no—
59#11758222—82no—
60#11758222—82no—
61C2×D244—21no—
62C2×D244—41no—
63C2×C4×D61—41no—
64C2×C4×D61C22⋊C411yescharacteristic
65C2×C4×D61D811yescharacteristic
66C2×C4×D61SD1611yescharacteristic
67C2×Dic122—41no—
68C2×#92420—42no—
69D61⋊C8—82no—
70D8×C61—41no—
71C2×C8×C61C22⋊C411yescharacteristic
72C2×C8×C61C22×C411yescharacteristic
73C4⋊C4×C61—21no—
74C22⋊C4×C61—41no—
75C42×C61C22⋊C411yescharacteristic
76C22⋊Dic61—41no—
77#11758199—42no—
78#11758198—41no—
79#11758198—41no—
80C4⋊Dic61—21no—
81#11758196—41no—
82C4×Dic61D811yescharacteristic
83C4×Dic61SD1611yescharacteristic
84C4×Dic61C2×D411yescharacteristic
85C2×#92418C22⋊C411yescharacteristic
86C2×#92418C2×D411yescharacteristic
87D488—41no—
88C8×D61—22no—
89C8×D61—41no—
90#11758187—42no—
91C23×C61—41no—
92C22×D61—41no—
93C22×D61#10211yescharacteristic
94D4×C61—41no—
95D4×C61—41no—
96C2×C4×C61—41no—
97C2×C4×C61—82no—
98C2×C4×C61#10211yescharacteristic
99C2×C4×C61#10211yescharacteristic
100C2×C4×C61C2×C22⋊C411yescharacteristic
101C22⋊D61—82no—
102C22⋊D61—82no—
103C22⋊D61—81no—
104C22⋊D61—81no—
105C2×Dic61—41no—
106C2×Dic61#10211yescharacteristic
107C2×Dic61C2×D811yescharacteristic
108C2×Dic61C2×SD1611yescharacteristic
109D244—41no—
110D244—41no—
111D244—82no—
112C4×D61—21no—
113C4×D61—21no—
114C4×D61—41no—
115C4×D61—82no—
116C4×D61D1612yes—
117C4×D61SD3212yes—
118Dic122—81no—
119Dic122—81no—
120#92420—82no—
121C8×C61—21no—
122C8×C61—21no—
123#92418—21no—
124#92418#13512yes—
125#11947—611nomaximal, Sylow
126C22×C61—81no—
127C22×C61—81no—
128C22×C61—81no—
129C22×C61C2×#10211yescharacteristic
130C2×D61—21no—
131C2×D61—21no—
132C2×D61—81no—
133C2×D61—81no—
134C2×D61—81no—
135C2×D61#35712yes—
136C4×C61—21no—
137C4×C61—81no—
138C4×C61#35712yes—
139C4×C61#41311yescharacteristic
140C4×C61#41611yescharacteristic
141Dic61—21no—
142Dic61—21no—
143Dic61—81no—
144Dic61C2×D1611yescharacteristic
145Dic61C2×SD3211yescharacteristic
146#3169—611no—
147#2162—611no—
148C2×#335—611no—
149#1364—612no—
150#1361—612no—
151C2×C61—161no—
152C2×C61#154011yescharacteristic
153C2×C61C2×#35711yescharacteristic
154C2×C61#214811yescharacteristic
155D61—22no—
156D61—161no—
157#532—1221no—
158#500—611no—
159#493—611no—
160#486—1221no—
161#466—611no—
162#466—611no—
163#466—1221no—
164C4×D8—611no—
165C4×D8—1221no—
166C4×D8#692311yescharacteristic
167C2×C4⋊C8—1221no—
168C2×C4×C8—611no—
169C4⋊C16—612no—
170C22⋊C16—1221no—
171C4×C16—1221no—
172#335—612no—
173#335—1221no—
174C61#1194711yescharacteristic, complemented, Sylow
175C2×#41—2441no—
176C2×D8—611no—
177C2×D8—1221no—
178C2×D8C2×#692311yescharacteristic
179C22×C8—611no—
180C22×C8—611no—
181C22×C8—2441no—
182C4⋊Q8—1221no—
183#127—1221no—
184#124—2441no—
185#121—1221no—
186#121—1221no—
187#121—2441no—
188C4×D4—21no—
189C4×D4—1221no—
190C4×D4—2441no—
191C2×C42—611no—
192C2×C16—1222no—
193#107—611no—
194#107—1221no—
195#107C2×#692311yescharacteristic
196C4⋊C8—1222no—
197C4⋊C8—2441no—
198#102—21no—
199#102—1221no—
200#102—1221no—
201#102—1221no—
202C4×C8—611no—
203C4×C8—611no—
204C4×C8—611no—
205C4×C8C2×#692311yescharacteristic
206#41—4882no—
207#41—4882no—
208C2×Q8—2441no—
209C2×D4—21no—
210C2×D4—1221no—
211C2×D4—2441no—
212C2×D4—2441no—
213C2×D4—2441no—
214C2×D4—2441no—
215C22×C4—41no—
216C22×C4—611no—
217C22×C4—611no—
218C22×C4—611no—
219C22×C4—2441no—
220D8—41no—
221D8—2441no—
222D8—2442no—
223C2×C8—611no—
224C2×C8—611no—
225C2×C8—1222no—
226C2×C8—4882no—
227C2×C8—2441no—
228C2×C8—2442no—
229C2×C8C22⋊#692311yescharacteristic
230C2×C8C22×#692311yescharacteristic
231C4⋊C4—21no—
232C4⋊C4—1221no—
233C4⋊C4—2441no—
234C22⋊C4—41no—
235C22⋊C4—2441no—
236C22⋊C4—2441no—
237C22⋊C4—2441no—
238C42—611no—
239C42—611no—
240C42—611no—
241C42C22⋊#692311yescharacteristic
242C16—2442no—
243C23—41no—
244C23—611no—
245C23—2441no—
246Q8—4881no—
247Q8—4881no—
248D4—41no—
249D4—41no—
250D4—4882no—
251D4—4881no—
252D4—4881no—
253D4—4882no—
254D4—4882no—
255D4—2441no—
256D4—2441no—
257C2×C4—41no—
258C2×C4—82no—
259C2×C4—611no—
260C2×C4—612no—
261C2×C4—612no—
262C2×C4—611no—
263C2×C4—611no—
264C2×C4—1221no—
265C2×C4—1221no—
266C2×C4—4882no—
267C2×C4—2441no—
268C2×C4—2441no—
269C2×C4#1451983911yescharacteristic
270C2×C4#1451983911yescharacteristic
271C2×C4C2×C22⋊#692311yescharacteristic
272C8—21no—
273C8—21no—
274C8—612no—
275C8—1221no—
276C8—4882no—
277C22—81no—
278C22—81no—
279C22—81no—
280C22—612no—
281C22—1221no—
282C22—1221no—
283C22—4881no—
284C22—4881no—
285C22—4881no—
286C22C2×#1451983911yescharacteristic
287C4—21no—
288C4—81no—
289C4—611no—
290C4—611no—
291C4—1221no—
292C4—1221no—
293C4—4881no—
294C4#1684067412yes—
295C4#1684074811yescharacteristic
296C4#1684075211yescharacteristic
297C2—161no—
298C2—1222no—
299C2—9761no—
300C2#2146131611yescharacteristic
301C2C2×#1684067411yescharacteristic
302C2#2146214611yescharacteristic
subgroupG/H
centerC2×C4#14519839
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC4×D8×C61C4
socleC22×C61C2×#102
prime radical#21456395C2
cosocleC8×Dic61C23
hypercenterC4×D8#6923
hypocenterC61#11947
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #21462178C2semidirect
2. D61⋊#335C2semidirect
3. #21460837C2semidirect
4. #21460833C2semidirect
174. C61#11947semidirect

Maximal subgroups

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

subgroupindex
#214621782
D61⋊#3352
#214608372
#214608332
#214563952
#1194761