Finite Group Databasebeta

← #30604930

Subgroups — #30604930

Order 15616.

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

normal subgroups only

This group has 368 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
1#21462178C211yesmaximal, characteristic, complemented
2C4×#14519847C211yesmaximal, characteristic, complemented
3#21460810C212yesmaximal, complemented
4#21460809C212yesmaximal, complemented
5#21456395C211yesmaximal, characteristic
6C2×#14519847—21no—
7C4×#11758213—21no—
8#16840683—21no—
9#16840657C2212yes—
10C4×#11758187—21no—
11#16840638C2212yes—
12#16840309—21no—
13#16840166C411yescharacteristic
14#16840137C411yescharacteristic
15#16840107—21no—
16#16839999C2211yescharacteristic
17#16839997—21no—
18#16839995C2211yescharacteristic
19C4×D488C411yescharacteristic
20C4×#11758199—21no—
21C4×C8×D61C2211yescharacteristic
22C4×D8×C61C411yescharacteristic
23C2×#11758213—22no—
24C2×#11758187—22no—
25#14519847—24no—
26#14519832—41no—
27C4×#92420—41no—
28C2×#11758222—41no—
29C2×D488C2×C411yescharacteristic
30C2×#11758199—21no—
31C2×C8×D61D411yescharacteristic
32C2×C8×D61C2311yescharacteristic
33#14519776—21no—
34#14519773—21no—
35#14519763—41no—
36#14519752—21no—
37#14519750—41no—
38#14519748—21no—
39C4×D244—21no—
40C4×C22⋊D61—41no—
41C42×D61D411yescharacteristic
42#14519711C2×C411yescharacteristic
43#14519710—21no—
44#14519699—21no—
45#14519698—21no—
46#14519697—21no—
47C4×#92418D411yescharacteristic
48C8×Dic61C2×C411yescharacteristic
49C8×Dic61D411yescharacteristic
50C2×D8×C61C2×C411yescharacteristic
51C4×D4×C61—21no—
52#107×C61C2×C411yescharacteristic
53#102×C61—21no—
54C4×C8×C61C2×C411yescharacteristic
55C2×D4×C61—21no—
56C22×C4×C61—41no—
57C2×C22⋊D61—41no—
58C2×C22⋊D61—41no—
59C2×C22⋊D61—41no—
60#11758222—84no—
61C2×D244—21no—
62C2×D244—41no—
63C2×C4×D61—41no—
64C2×C4×D61SD1611yescharacteristic
65C2×C4×D61SD1611yescharacteristic
66C2×C4×D61C2×D411yescharacteristic
67C2×Dic122—41no—
68C2×#92420—42no—
69#11758213—24no—
70#11758213—42no—
71D8×C61—41no—
72C2×C8×C61C22⋊C411yescharacteristic
73C2×C8×C61C22×C411yescharacteristic
74C4⋊C4×C61—21no—
75C22⋊C4×C61—41no—
76C42×C61C22⋊C411yescharacteristic
77C22⋊Dic61—41no—
78#11758199—42no—
79#11758198—41no—
80#11758198—41no—
81C4⋊Dic61—21no—
82#11758196—41no—
83C4×Dic61C22⋊C411yescharacteristic
84C4×Dic61D811yescharacteristic
85C4×Dic61D811yescharacteristic
86C2×#92418C22⋊C411yescharacteristic
87C2×#92418C2×D411yescharacteristic
88D488—41no—
89C8×D61—22no—
90C8×D61—41no—
91#11758187—42no—
92C23×C61—41no—
93C22×D61—41no—
94C22×D61C2×SD1611yescharacteristic
95D4×C61—41no—
96D4×C61—41no—
97C2×C4×C61—41no—
98C2×C4×C61—82no—
99C2×C4×C61#10211yescharacteristic
100C2×C4×C61#10211yescharacteristic
101C2×C4×C61C2×C22⋊C411yescharacteristic
102C22⋊D61—82no—
103C22⋊D61—82no—
104C22⋊D61—82no—
105C2×Dic61—41no—
106C2×Dic61#10211yescharacteristic
107C2×Dic61#10211yescharacteristic
108C2×Dic61C2×D811yescharacteristic
109D244—41no—
110D244—41no—
111D244—82no—
112C4×D61—22no—
113C4×D61—21no—
114C4×D61—21no—
115C4×D61—22no—
116C4×D61—82no—
117Dic122—82no—
118#92420—44no—
119C8×C61—21no—
120C8×C61—21no—
121#92418—21no—
122#92418#10412yes—
123#11747—611nomaximal, Sylow
124C22×C61—81no—
125C22×C61—81no—
126C22×C61—81no—
127C22×C61C2×#10211yescharacteristic
128C2×D61—21no—
129C2×D61—21no—
130C2×D61—21no—
131C2×D61—81no—
132C2×D61—81no—
133C2×D61—81no—
134C4×C61—21no—
135C4×C61—81no—
136C4×C61#36112yes—
137C4×C61#41011yescharacteristic
138C4×C61C2×#10411yescharacteristic
139Dic61—21no—
140Dic61—21no—
141Dic61—81no—
142Dic61#35912yes—
143#3169—611no—
144#2162—611no—
145C4×#108—611no—
146#1349—612no—
147#1349—612no—
148C2×C61—161no—
149C2×C61#150211yescharacteristic
150C2×C61C2×#35911yescharacteristic
151C2×C61C2×#36111yescharacteristic
152D61—41no—
153D61—161no—
154#532—1221no—
155#500—611no—
156#493—611no—
157#486—1221no—
158#466—611no—
159#466—611no—
160#466—1221no—
161C4×D8—611no—
162C4×D8—1221no—
163C4×D8#692311yescharacteristic
164C2×#108—1221no—
165C4×M16—1221no—
166C2×C4×C8—611no—
167C4⋊C16—1221no—
168C22⋊C16—612no—
169C4×C16—1221no—
170#341—612no—
171C61#1174711yescharacteristic, complemented, Sylow
172C2×#41—2441no—
173C2×D8—611no—
174C2×D8—1221no—
175C2×D8C2×#692311yescharacteristic
176C2×M16—1222no—
177C22×C8—611no—
178C22×C8—611no—
179C4⋊Q8—1221no—
180#127—1221no—
181#124—2441no—
182#121—1221no—
183#121—1221no—
184#121—2441no—
185C4×D4—21no—
186C4×D4—1221no—
187C4×D4—2441no—
188C2×C42—611no—
189C2×C16—1222no—
190#108—1224no—
191#107—611no—
192#107—1221no—
193#107C2×#692311yescharacteristic
194#102—21no—
195#102—1221no—
196#102—1221no—
197#102—1221no—
198#97—2441no—
199C4×C8—611no—
200C4×C8—611no—
201C4×C8—611no—
202C4×C8—2441no—
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—
220M16—1224no—
221M16—2442no—
222C2×C8—611no—
223C2×C8—611no—
224C2×C8—1222no—
225C2×C8—2441no—
226C2×C8—2442no—
227C2×C8C22⋊#692311yescharacteristic
228C2×C8C22×#692311yescharacteristic
229C4⋊C4—21no—
230C4⋊C4—1221no—
231C4⋊C4—2441no—
232C22⋊C4—41no—
233C22⋊C4—2441no—
234C22⋊C4—2441no—
235C22⋊C4—2441no—
236C42—611no—
237C42—611no—
238C42—611no—
239C42C22⋊#692311yescharacteristic
240C16—2442no—
241C23—41no—
242C23—611no—
243C23—2441no—
244Q8—4882no—
245D4—41no—
246D4—41no—
247D4—4882no—
248D4—4882no—
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—1222no—
259C2×C4—1221no—
260C2×C4—1221no—
261C2×C4—1222no—
262C2×C4—4882no—
263C2×C4—2441no—
264C2×C4#1451983911yescharacteristic
265C2×C4#1451983911yescharacteristic
266C2×C4C2×C22⋊#692311yescharacteristic
267C8—21no—
268C8—21no—
269C8—612no—
270C8—1221no—
271C8—2444no—
272C22—81no—
273C22—81no—
274C22—81no—
275C22—1221no—
276C22—1221no—
277C22—1221no—
278C22—4881no—
279C22—4881no—
280C22—4881no—
281C22C2×#1451983911yescharacteristic
282C4—21no—
283C4—81no—
284C4—612no—
285C4—1221no—
286C4—1221no—
287C4—4881no—
288C4#1684068012yes—
289C4#1684074111yescharacteristic
290C4D61⋊#10411yescharacteristic
291C2—161no—
292C2—9761no—
293C2—2441no—
294C2#2146119811yescharacteristic
295C2D61⋊#35911yescharacteristic
296C2C2×#1684068011yescharacteristic
subgroupG/H
centerC2×C4#14519839
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC4×D8×C61C4
socleC22×C61C2×#102
prime radical#21456395C2
cosocleC2×C8×D61C23
hypercenterC4×D8#6923
hypocenterC61#11747
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. C4×#14519847C2semidirect
3. #21460810C2semidirect
4. #21460809C2semidirect
171. C61#11747semidirect

Maximal subgroups

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

subgroupindex
#214621782
C4×#145198472
#214608102
#214608092
#214563952
#1174761