Finite Group Databasebeta

← #29593463

Subgroups — #29593463

Order 15616.

442 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 73 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
1D4×D488C211yesmaximal, characteristic
2#21448076C211yesmaximal, characteristic, complemented
3#21447861C211yesmaximal, characteristic, complemented
4#21443864C211yesmaximal, characteristic, complemented
5#21443779C211yesmaximal, characteristic, complemented
6D4⋊#11758185C211yesmaximal, characteristic, complemented
7C61×#1669C211yesmaximal, characteristic, complemented
8C22×D488—21no—
9D4×D244—21no—
10C2×#14519720—22no—
11C2×#14519720—21no—
12#16840139C2211yescharacteristic
13#16839998—21no—
14#16839958—21no—
15#16839898—22no—
16C4×D488C2211yescharacteristic
17C4⋊#11758185C2211yescharacteristic, complemented
18#16839566—21no—
19C4×#11758185C2211yescharacteristic, complemented
20C61×#494C2211yescharacteristic, complemented
21C61×#474—21no—
22C8×D4×C61C2211yescharacteristic
23C61×#335C2211yescharacteristic, complemented
24C61×#332—21no—
25C22×D244—22no—
26C2×D4×D61—41no—
27C2×D488—22no—
28C2×D488—21no—
29C2×D488—42no—
30C2×D488—42no—
31C2×D488D411yescharacteristic
32C2×D488D412yes—
33#14519774—21no—
34#14519752—41no—
35#14519751—22no—
36#14519747—42no—
37C4×D244—21no—
38#14519720—44no—
39#14519720—42no—
40C2×#11758185—21no—
41C2×#11758185—21no—
42#14519711D411yescharacteristic
43#14519699—22no—
44#14519699—21no—
45C2×Q16×C61—21no—
46C2×Q16×C61—21no—
47C22×C8×C61—21no—
48C4⋊Q8×C61—21no—
49C4×D4×C61D411yescharacteristic
50#107×C61—41no—
51C4⋊C8×C61—21no—
52C4⋊C8×C61D411yescharacteristic
53#102×C61—41no—
54C22⋊C8×C61—21no—
55C4×C8×C61C2311yescharacteristic
56C23×D61—42no—
57C2×Q8×C61—41no—
58C2×D4×C61D811yescharacteristic
59C22×C4×C61—21no—
60C2×C22⋊D61—42no—
61D4×D61—82no—
62D4×D61—82no—
63C2×D244—21no—
64C2×D244—22no—
65C2×D244—44no—
66C2×D244—42no—
67C2×D244—41no—
68C2×D244—41no—
69C2×D244—82no—
70C2×C4×D61—41no—
71Q16×C61—42no—
72Q16×C61—41no—
73Q16×C61—41no—
74C2×C8×C61—21no—
75C2×C8×C61—41no—
76C2×C8×C61—41no—
77C2×C8×C61—41no—
78C2×C8×C61C2×D411yescharacteristic
79C2×C8×C61C2×D411yescharacteristic
80C4⋊C4×C61—41no—
81C4⋊C4×C61—41no—
82C4⋊C4×C61D811yescharacteristic
83C22⋊C4×C61—21no—
84C42×C61C2×D411yescharacteristic
85#11758198—42no—
86#11758198—41no—
87C4⋊Dic61—21no—
88D488—21no—
89D488—42no—
90D488—44no—
91D488—41no—
92D488—41no—
93D488D812yes—
94#11758185—22no—
95#11758185—41no—
96C23×C61—21no—
97C22×D61—41no—
98C22×D61—42no—
99C22×D61—84no—
100C22×D61—84no—
101C22×D61—162no—
102Q8×C61—81no—
103Q8×C61—81no—
104D4×C61—21no—
105D4×C61SD3212yescomplemented
106C2×C4×C61—21no—
107C2×C4×C61—41no—
108C2×C4×C61—41no—
109C2×C4×C61—81no—
110C2×C4×C61#12011yescharacteristic
111C2×C4×C61C2×D811yescharacteristic
112C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
113C22⋊D61—84no—
114C2×Dic61—41no—
115D244—22no—
116D244—42no—
117D244—41no—
118D244—42no—
119D244—84no—
120D244—81no—
121D244—81no—
122D244—161no—
123C4×D61—81no—
124C4×D61—81no—
125C8×C61—21no—
126C8×C61—41no—
127C8×C61—81no—
128C8×C61C2×D811yescharacteristic
129C8×C61AGL(1,ℤ/8)11yescharacteristic
130#12320—611nomaximal, Sylow
131C22×C61—22no—
132C22×C61—41no—
133C22×C61—41no—
134C22×C61#44711yescharacteristic
135C2×D61—42no—
136C2×D61—81no—
137C2×D61—81no—
138C2×D61—82no—
139C2×D61—82no—
140C2×D61—82no—
141C2×D61—168no—
142C4×C61—21no—
143C4×C61—41no—
144C4×C61—161no—
145C4×C61#44711yescharacteristic
146C4×C61#45311yescharacteristic
147C4×C61C2×SD3211yescharacteristic
148C4×C61#50911yescharacteristic
149Dic61—81no—
150D4×D8—611no—
151#2248—611no—
152#2208—611no—
153#1669D6111yescharacteristic, complemented
154#1361—611no—
155#1331—611no—
156D4⋊C16—611no—
157C2×C61—42no—
158C2×C61#161911yescharacteristic
159C2×C61#218711yescharacteristic
160C2×C61#219411yescharacteristic
161D61—82no—
162D61—162no—
163C22×D8—1221no—
164D42—1221no—
165C2×SD32—1221no—
166C2×SD32—1222no—
167#494C2×D6111yescharacteristic, complemented
168#493—611no—
169#474—21no—
170#466—1221no—
171#459—1221no—
172#447—1222no—
173C4×D8—611no—
174C8×D4C2×D6111yescharacteristic
175C4⋊C16—611no—
176#358—1221no—
177C4×C16—611no—
178#335C2×D6111yescharacteristic, complemented
179#332—21no—
180C61#1232011yescharacteristic, complemented, Sylow
181C22×D4—1222no—
182C22×D4—2441no—
183C2×Q16—21no—
184C2×Q16—21no—
185C2×D8—611no—
186C2×D8—612no—
187C2×D8—1222no—
188C2×D8—1221no—
189C2×D8—2442no—
190C2×D8—2442no—
191C22×C8—21no—
192C4⋊Q8—21no—
193#127—1221no—
194#121—1222no—
195#121—2441no—
196#120—2442no—
197C4×D4—1221no—
198C4×D4C22⋊D6111yescharacteristic
199SD32—2444no—
200SD32—2442no—
201C2×C16—1221no—
202C2×C16—1221no—
203#107—41no—
204#107—611no—
205C4⋊C8—21no—
206C4⋊C8C22⋊D6111yescharacteristic
207#102—41no—
208#102—1222no—
209#102—1221no—
210C22⋊C8—21no—
211C4×C8C22×D6111yescharacteristic
212C24—2442no—
213C2×Q8—41no—
214C2×D4—1221no—
215C2×D4—1222no—
216C2×D4—4882no—
217C2×D4—4882no—
218C2×D4—4882no—
219C2×D4—2442no—
220C2×D4—2444no—
221C2×D4—2442no—
222C2×D4—2441no—
223C2×D4—2441no—
224C2×D4#1175819911yescharacteristic
225C22×C4—21no—
226C22×C4—2441no—
227Q16—42no—
228Q16—41no—
229Q16—41no—
230D8—612no—
231D8—1221no—
232D8—2442no—
233D8—2444no—
234D8—2441no—
235D8—2441no—
236C2×C8—21no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—41no—
240C2×C8D4×D6111yescharacteristic
241C2×C8D4×D6111yescharacteristic
242C4⋊C4—41no—
243C4⋊C4—41no—
244C4⋊C4—1221no—
245C4⋊C4#1175819911yescharacteristic
246C22⋊C4—21no—
247C22⋊C4—2442no—
248C22⋊C4—2441no—
249C42C2×C22⋊D6111yescharacteristic
250C16—1222no—
251C16—2441no—
252C23—21no—
253C23—9762no—
254C23—4884no—
255C23—4884no—
256C23—2442no—
257C23—2441no—
258Q8—81no—
259Q8—81no—
260D4—21no—
261D4—1222no—
262D4—9761no—
263D4—4884no—
264D4—4884no—
265D4—4881no—
266D4—4881no—
267D4—2442no—
268D4—2442no—
269D4—2441no—
270D4#1451972012yescomplemented
271C2×C4—21no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—81no—
275C2×C4—4881no—
276C2×C4—4881no—
277C2×C4—2441no—
278C2×C4#1451974511yescharacteristic
279C2×C4C2×#1175819911yescharacteristic
280C2×C4#1451980211yescharacteristic
281C8—21no—
282C8—41no—
283C8—81no—
284C8D8×D6111yescharacteristic
285C8#1451980111yescharacteristic
286C22—22no—
287C22—41no—
288C22—41no—
289C22—9768no—
290C22—4882no—
291C22—4882no—
292C22—4882no—
293C22—4881no—
294C22—4881no—
295C22—2442no—
296C22#1683989511yescharacteristic
297C4—21no—
298C4—41no—
299C4—161no—
300C4—4881no—
301C4#1683989411yescharacteristic
302C4#1683992811yescharacteristic
303C4C2×#1451972011yescharacteristic
304C4#1684019711yescharacteristic
305C2—42no—
306C2—9762no—
307C2—4882no—
308C2#2144487211yescharacteristic
309C2#2144774711yescharacteristic
310C2#2144778811yescharacteristic
subgroupG/H
centerC22#16839895
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1669C2
socleC22×C61#447
prime radicalD4×D488C2
hypercenter#1669D61
hypocenterC61#12320
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C8×D4 ◁ #1669

Complements

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

NH ≅ G/Ntype
2. #21448076C2semidirect
3. #21447861C2semidirect
4. #21443864C2semidirect
5. #21443779C2semidirect
6. D4⋊#11758185C2semidirect
7. C61×#1669C2semidirect
17. C4⋊#11758185C22semidirect
19. C4×#11758185C22semidirect
20. C61×#494C22semidirect
23. C61×#335C22semidirect
105. D4×C61SD32semidirect
153. #1669D61semidirect
167. #494C2×D61semidirect
178. #335C2×D61semidirect
180. C61#12320semidirect
270. D4#14519720semidirect

Maximal subgroups

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

subgroupindex
D4×D4882
#214480762
#214478612
#214438642
#214437792
D4⋊#117581852
C61×#16692
#1232061