Finite Group Databasebeta

← #30604378

Subgroups — #30604378

Order 15616.

402 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 106 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#21462152C211yesmaximal, characteristic, complemented
2C4×D61⋊C16C211yesmaximal, characteristic, complemented
3#21460770C212yesmaximal, complemented
4D4⋊#11758187C212yesmaximal, complemented
5#21454528C211yesmaximal, characteristic
6C2×#14519852—21no—
7C2×D61⋊C16—21no—
8#16840683—21no—
9C4⋊#11758187C2212yes—
10#16840648—21no—
11C4×#11758187C2212yes—
12C2×#14519785—21no—
13#16840309C411yescharacteristic
14#16839841C411yescharacteristic
15#16839838—21no—
16D4×#92418C2211yescharacteristic
17#16839827C2211yescharacteristic
18#16839825—21no—
19#16839784C411yescharacteristic
20#16839727—21no—
21C4×C8×D61C2211yescharacteristic
22C61×#436C411yescharacteristic
23#14519852—42no—
24D61⋊C16—24no—
25C2×#11758187—22no—
26C2×#11758187—22no—
27C2×#11758222—21no—
28#14519785—42no—
29#14519785—42no—
30C2×#11758189—21no—
31C2×#11758189—21no—
32C22×#92418—21no—
33C2×C8×D61—21no—
34C2×C8×D61D411yescharacteristic
35C2×C8×D61D411yescharacteristic
36#14519776C811yescharacteristic
37#14519773C811yescharacteristic
38#14519763—21no—
39#14519752C811yescharacteristic
40#14519750—21no—
41#14519748C811yescharacteristic
42C4×D244C2×C411yescharacteristic
43C4×C22⋊D61—21no—
44C42×D61C2×C411yescharacteristic
45C4⋊#92418C2×C411yescharacteristic
46#14519706—21no—
47C22⋊#92418—21no—
48#14519689—21no—
49#14519689—21no—
50C4×#92418C2311yescharacteristic
51C8×Dic61D411yescharacteristic
52C8×Dic61D411yescharacteristic
53C2×M16×C61—21no—
54C4×D4×C61C2×C411yescharacteristic
55C4⋊C8×C61C2×C411yescharacteristic
56C22⋊C8×C61—21no—
57C4×C8×C61C2×C411yescharacteristic
58C2×D4×C61C2×C811yescharacteristic
59C22×C4×C61—21no—
60C2×C22⋊D61—21no—
61C2×C22⋊D61—21no—
62C2×C22⋊D61—21no—
63#11758222—42no—
64#11758222—42no—
65C2×D244—21no—
66C2×D244C2×C811yescharacteristic
67C2×C4×D61—21no—
68C2×C4×D61C22⋊C411yescharacteristic
69C2×C4×D61C2×C811yescharacteristic
70C2×C4×D61M1611yescharacteristic
71C2×Dic122—21no—
72M16×C61—42no—
73C2×C8×C61—21no—
74C2×C8×C61C22⋊C411yescharacteristic
75C2×C8×C61C22⋊C411yescharacteristic
76C4⋊C4×C61C2×C811yescharacteristic
77C22⋊C4×C61—21no—
78C42×C61C22×C411yescharacteristic
79C22⋊Dic61—21no—
80#11758198—21no—
81#11758198—21no—
82C4⋊Dic61C2×C811yescharacteristic
83#11758196—21no—
84C4×Dic61C22⋊C411yescharacteristic
85C4×Dic61C2×C811yescharacteristic
86C4×Dic61M1611yescharacteristic
87C2×#92418—21no—
88C2×#92418—41no—
89C2×#92418—41no—
90C2×#92418C2×D411yescharacteristic
91C2×#92418C2×D411yescharacteristic
92#11758189—42no—
93#11758189—42no—
94C8×D61—22no—
95C8×D61—41no—
96C8×D61—41no—
97C8×D61D812yes—
98C8×D61SD1612yes—
99#11758187—24no—
100#11758187—42no—
101C23×C61—21no—
102C22×D61—21no—
103C22×D61C22⋊C811yescharacteristic
104D4×C61—22no—
105C2×C4×C61—21no—
106C2×C4×C61—41no—
107C2×C4×C61—41no—
108C2×C4×C61C2×C22⋊C411yescharacteristic
109C2×C4×C61C22×C811yescharacteristic
110C2×C4×C61C2×M1611yescharacteristic
111C22⋊D61—42no—
112C22⋊D61—42no—
113C22⋊D61—42no—
114C2×Dic61—21no—
115C2×Dic61C22⋊C811yescharacteristic
116C2×Dic61C22⋊C811yescharacteristic
117C2×Dic61C22⋊C811yescharacteristic
118D244—22no—
119D244—42no—
120C4×D61—22no—
121C4×D61—22no—
122C4×D61—41no—
123C4×D61—41no—
124C4×D61#10212yes—
125C4×D61#10412yes—
126Dic122—42no—
127C8×C61—21no—
128C8×C61—41no—
129C8×C61#10212yes—
130#92418—21no—
131#92418—41no—
132#92418C2×D811yescharacteristic
133#92418C2×SD1611yescharacteristic
134#11584—611nomaximal, Sylow
135C22×C61—41no—
136C22×C61—41no—
137C22×C61—41no—
138C22×C61C2×C22⋊C811yescharacteristic
139C2×D61—21no—
140C2×D61—21no—
141C2×D61—41no—
142C2×D61—41no—
143C2×D61—41no—
144C2×D61D4⋊C812yes—
145C4×C61—21no—
146C4×C61—41no—
147C4×C61C2×#10211yescharacteristic
148C4×C61C2×#10411yescharacteristic
149C4×C61#50412yes—
150Dic61—21no—
151Dic61—41no—
152Dic61D4⋊C812yes—
153Dic61#35012yes—
154#2931—611no—
155#2150—611no—
156C2×C4×C16—611no—
157D4⋊C16—612no—
158D4⋊C16—612no—
159C2×C61—81no—
160C2×C61C2×D4⋊C811yescharacteristic
161C2×C61#211311yescharacteristic
162C2×C61C2×#35011yescharacteristic
163D61—22no—
164D61—81no—
165C2×#131—1221no—
166#532—611no—
167C2×M32—1221no—
168C22×C16—1221no—
169#436—611no—
170#436—1221no—
171#436#692311yescharacteristic
172C8×D4—611no—
173C8×D4—611no—
174C8×D4—1221no—
175#423—611no—
176#408—1221no—
177C2×C4×C8—611no—
178C4⋊C16—612no—
179C4⋊C16—1221no—
180C4×C16—612no—
181C4×C16—1221no—
182C61#1158411yescharacteristic, complemented, Sylow
183C2×#41—1221no—
184#131—2442no—
185#131—2442no—
186C2×M16—21no—
187C2×M16—1221no—
188C2×M16—1221no—
189C22×C8—611no—
190C22×C8—611no—
191C22×C8—1221no—
192C22×C8—1221no—
193C4⋊Q8—611no—
194#127—611no—
195#124—1221no—
196#121—611no—
197#121—611no—
198#121—1221no—
199C4×D4—611no—
200C4×D4—1221no—
201C4×D4C2×#692311yescharacteristic
202C2×C42—611no—
203M32—2442no—
204C2×C16—1222no—
205C2×C16—1224no—
206C2×C16—1222no—
207C4⋊C8—611no—
208C4⋊C8—1221no—
209C4⋊C8C2×#692311yescharacteristic
210C22⋊C8—21no—
211C22⋊C8—1221no—
212C22⋊C8—1221no—
213C22⋊C8—1221no—
214C4×C8—611no—
215C4×C8—611no—
216C4×C8—611no—
217C4×C8C2×#692311yescharacteristic
218#41—2442no—
219#41—2442no—
220C2×Q8—1221no—
221C2×D4—611no—
222C2×D4—1221no—
223C2×D4—1221no—
224C2×D4—1221no—
225C2×D4—1221no—
226C2×D4D61⋊C811yescharacteristic
227C22×C4—21no—
228C22×C4—611no—
229C22×C4—611no—
230C22×C4—611no—
231C22×C4—1221no—
232M16—42no—
233M16—2442no—
234M16—2442no—
235C2×C8—21no—
236C2×C8—611no—
237C2×C8—612no—
238C2×C8—612no—
239C2×C8—611no—
240C2×C8—1222no—
241C2×C8—1221no—
242C2×C8—2441no—
243C2×C8—2441no—
244C2×C8—2441no—
245C2×C8—2441no—
246C2×C8C22⋊#692311yescharacteristic
247C2×C8C22⋊#692311yescharacteristic
248C4⋊C4—611no—
249C4⋊C4—1221no—
250C4⋊C4D61⋊C811yescharacteristic
251C22⋊C4—21no—
252C22⋊C4—1221no—
253C22⋊C4—1221no—
254C22⋊C4—1221no—
255C42—611no—
256C42—611no—
257C42—611no—
258C42C22×#692311yescharacteristic
259C16—1224no—
260C16—2442no—
261C23—21no—
262C23—611no—
263C23—1221no—
264Q8—2442no—
265D4—22no—
266D4—1222no—
267D4—2442no—
268D4—2442no—
269D4—2442no—
270D4—2442no—
271C2×C4—21no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—611no—
275C2×C4—611no—
276C2×C4—612no—
277C2×C4—612no—
278C2×C4—611no—
279C2×C4—1222no—
280C2×C4—1222no—
281C2×C4—1221no—
282C2×C4—2441no—
283C2×C4—2441no—
284C2×C4C2×C22⋊#692311yescharacteristic
285C2×C4C2×D61⋊C811yescharacteristic
286C2×C4D61⋊M1611yescharacteristic
287C8—21no—
288C8—41no—
289C8—611no—
290C8—611no—
291C8—1221no—
292C8—2441no—
293C8#1451983912yes—
294C22—41no—
295C22—41no—
296C22—41no—
297C22—612no—
298C22—1221no—
299C22—1221no—
300C22—2441no—
301C22—2441no—
302C22—2441no—
303C22D61⋊(C22⋊C8)11yescharacteristic
304C4—21no—
305C4—41no—
306C4—612no—
307C4—612no—
308C4—1221no—
309C4—2441no—
310C4C2×#1451983911yescharacteristic
311C4D61⋊#10411yescharacteristic
312C4#1684082112yes—
313C2—81no—
314C2—1222no—
315C2—4881no—
316C2D61⋊(D4⋊C8)11yescharacteristic
317C2#2146205011yescharacteristic
318C2D61⋊#35011yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC42C22×#6923
FittingC61×#436C4
socleC22×C61C2×C22⋊C8
prime radical#16840309C4
cosocleC4×#92418C23
hypercenter#436#6923
hypocenterC61#11584
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #436

Complements

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

NH ≅ G/Ntype
1. #21462152C2semidirect
2. C4×D61⋊C16C2semidirect
3. #21460770C2semidirect
4. D4⋊#11758187C2semidirect
182. C61#11584semidirect

Maximal subgroups

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

subgroupindex
#214621522
C4×D61⋊C162
#214607702
D4⋊#117581872
#214545282
#1158461