Finite Group Databasebeta

← #30605626

Subgroups — #30605626

Order 15616.

350 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 78 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#21462182C211yesmaximal, characteristic, complemented
2D61⋊#335C211yesmaximal, characteristic, complemented
3#21460838C212yesmaximal, complemented
4#21460833C212yesmaximal, complemented
5#21456395C211yesmaximal, characteristic
6D61⋊(C4⋊C8)—21no—
7#16840683C2212yes—
8#16840657—21no—
9#16840650—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—84no—
60C2×D244—21no—
61C2×D244—41no—
62C2×C4×D61—41no—
63C2×C4×D61C22⋊C411yescharacteristic
64C2×C4×D61D811yescharacteristic
65C2×C4×D61SD1611yescharacteristic
66C2×Dic122—41no—
67C2×#92420—42no—
68D61⋊C8—82no—
69D8×C61—41no—
70C2×C8×C61C22⋊C411yescharacteristic
71C2×C8×C61C22×C411yescharacteristic
72C4⋊C4×C61—21no—
73C22⋊C4×C61—41no—
74C42×C61C22⋊C411yescharacteristic
75C22⋊Dic61—41no—
76#11758199—42no—
77#11758198—41no—
78#11758198—41no—
79C4⋊Dic61—21no—
80#11758196—41no—
81C4×Dic61D811yescharacteristic
82C4×Dic61SD1611yescharacteristic
83C4×Dic61C2×D411yescharacteristic
84C2×#92418C22⋊C411yescharacteristic
85C2×#92418C2×D411yescharacteristic
86D488—41no—
87C8×D61—22no—
88C8×D61—41no—
89#11758187—42no—
90C23×C61—41no—
91C22×D61—41no—
92C22×D61#10211yescharacteristic
93D4×C61—41no—
94D4×C61—41no—
95C2×C4×C61—41no—
96C2×C4×C61—82no—
97C2×C4×C61#10211yescharacteristic
98C2×C4×C61#10211yescharacteristic
99C2×C4×C61C2×C22⋊C411yescharacteristic
100C22⋊D61—82no—
101C22⋊D61—82no—
102C22⋊D61—81no—
103C22⋊D61—81no—
104C2×Dic61—41no—
105C2×Dic61#10211yescharacteristic
106C2×Dic61C2×D811yescharacteristic
107C2×Dic61C2×SD1611yescharacteristic
108D244—41no—
109D244—41no—
110D244—82no—
111C4×D61—22no—
112C4×D61—21no—
113C4×D61—21no—
114C4×D61—21no—
115C4×D61—21no—
116C4×D61—82no—
117Dic122—82no—
118#92420—82no—
119C8×C61—21no—
120C8×C61—21no—
121#92418—21no—
122#92418#13512yes—
123#11952—611nomaximal, Sylow
124C22×C61—81no—
125C22×C61—81no—
126C22×C61—81no—
127C22×C61C2×#10211yescharacteristic
128C2×D61—21no—
129C2×D61—21no—
130C2×D61—81no—
131C2×D61—81no—
132C2×D61—81no—
133C2×D61#36112yes—
134C4×C61—21no—
135C4×C61—21no—
136C4×C61—81no—
137C4×C61#41311yescharacteristic
138C4×C61#41611yescharacteristic
139Dic61—21no—
140Dic61—21no—
141Dic61—81no—
142Dic61#50911yescharacteristic
143Dic61#51011yescharacteristic
144#3169—611no—
145#2163—611no—
146C2×#335—611no—
147#1365—612no—
148#1361—612no—
149C2×C61—161no—
150C2×C61#154011yescharacteristic
151C2×C61#213911yescharacteristic
152C2×C61C2×#36111yescharacteristic
153D61—22no—
154D61—161no—
155#532—1221no—
156#500—611no—
157#493—611no—
158#486—1221no—
159#466—611no—
160#466—611no—
161#466—1221no—
162C4×D8—611no—
163C4×D8—1221no—
164C4×D8#692311yescharacteristic
165C2×C4⋊C8—1221no—
166C2×C4×C8—611no—
167C4⋊C16—612no—
168C22⋊C16—1221no—
169#346—1221no—
170#335—612no—
171#335—1221no—
172C61#1195211yescharacteristic, complemented, Sylow
173C2×#41—2441no—
174C2×D8—611no—
175C2×D8—1221no—
176C2×D8C2×#692311yescharacteristic
177C22×C8—611no—
178C22×C8—611no—
179C22×C8—2441no—
180C4⋊Q8—1221no—
181#127—1221no—
182#124—2441no—
183#121—1221no—
184#121—1221no—
185#121—2441no—
186C4×D4—21no—
187C4×D4—1221no—
188C4×D4—2441no—
189C2×C42—611no—
190C2×C16—1222no—
191#107—611no—
192#107—1221no—
193#107C2×#692311yescharacteristic
194C4⋊C8—1222no—
195C4⋊C8—2441no—
196#102—21no—
197#102—1221no—
198#102—1221no—
199#102—1221no—
200C4×C8—611no—
201C4×C8—611no—
202C4×C8—611no—
203C4×C8C2×#692311yescharacteristic
204#41—4884no—
205C2×Q8—2441no—
206C2×D4—21no—
207C2×D4—1221no—
208C2×D4—2441no—
209C2×D4—2441no—
210C2×D4—2441no—
211C2×D4—2441no—
212C22×C4—41no—
213C22×C4—611no—
214C22×C4—611no—
215C22×C4—611no—
216C22×C4—2441no—
217D8—41no—
218D8—2441no—
219D8—2442no—
220C2×C8—611no—
221C2×C8—611no—
222C2×C8—1222no—
223C2×C8—4882no—
224C2×C8—2441no—
225C2×C8—2442no—
226C2×C8C22⋊#692311yescharacteristic
227C2×C8C22×#692311yescharacteristic
228C4⋊C4—21no—
229C4⋊C4—1221no—
230C4⋊C4—2441no—
231C22⋊C4—41no—
232C22⋊C4—2441no—
233C22⋊C4—2441no—
234C22⋊C4—2441no—
235C42—611no—
236C42—611no—
237C42—611no—
238C42C22⋊#692311yescharacteristic
239C16—2442no—
240C23—41no—
241C23—611no—
242C23—2441no—
243Q8—4882no—
244D4—41no—
245D4—41no—
246D4—4882no—
247D4—4881no—
248D4—4881no—
249D4—4882no—
250D4—4882no—
251D4—2441no—
252D4—2441no—
253C2×C4—41no—
254C2×C4—82no—
255C2×C4—611no—
256C2×C4—611no—
257C2×C4—611no—
258C2×C4—1221no—
259C2×C4—1221no—
260C2×C4—1222no—
261C2×C4—1221no—
262C2×C4—1221no—
263C2×C4—4882no—
264C2×C4—2441no—
265C2×C4#1451983911yescharacteristic
266C2×C4#1451983911yescharacteristic
267C2×C4C2×C22⋊#692311yescharacteristic
268C8—21no—
269C8—21no—
270C8—612no—
271C8—1221no—
272C8—4882no—
273C22—81no—
274C22—81no—
275C22—81no—
276C22—612no—
277C22—1221no—
278C22—1221no—
279C22—4881no—
280C22—4881no—
281C22—4881no—
282C22C2×#1451983911yescharacteristic
283C4—21no—
284C4—21no—
285C4—81no—
286C4—611no—
287C4—611no—
288C4—1221no—
289C4—1221no—
290C4—4881no—
291C4#1684074811yescharacteristic
292C4#1684075211yescharacteristic
293C2—161no—
294C2—1222no—
295C2—9761no—
296C2#2146131611yescharacteristic
297C2#2146212711yescharacteristic
298C2D61⋊#36111yescharacteristic
subgroupG/H
centerC22C2×#14519839
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC4×D8×C61C4
socleC22×C61C2×#102
prime radical#21456395C2
cosocleC8×Dic61C23
hypercenterC4×D8#6923
hypocenterC61#11952
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #21462182C2semidirect
2. D61⋊#335C2semidirect
3. #21460838C2semidirect
4. #21460833C2semidirect
172. C61#11952semidirect

Maximal subgroups

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

subgroupindex
#214621822
D61⋊#3352
#214608382
#214608332
#214563952
#1195261