Finite Group Databasebeta

← #29593468

Subgroups — #29593468

Order 15616.

442 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 71 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
1D8×D244C211yesmaximal, characteristic
2#21448075C211yesmaximal, characteristic, complemented
3#21447864C211yesmaximal, characteristic, complemented
4#21445185C211yesmaximal, characteristic, complemented
5#21443864C211yesmaximal, characteristic, complemented
6#21443775C211yesmaximal, characteristic, complemented
7C61×#1331C211yesmaximal, characteristic, complemented
8C2×D8×D61—21no—
9D4×D244—21no—
10C2×#14519722—22no—
11C2×#14519721—21no—
12#16840142C2211yescharacteristic, complemented
13#16840139C2211yescharacteristic
14#16840043—21no—
15#16839999—21no—
16#16839957—21no—
17#16839897—22no—
18C8×D244C2211yescharacteristic
19C4⋊#11758185C2211yescharacteristic, complemented
20#16839565—21no—
21#16839507—21no—
22C4×D8×C61C2211yescharacteristic
23C4×C16×C61C2211yescharacteristic, complemented
24C61×#335C2211yescharacteristic, complemented
25C22×D244—41no—
26C2×D4×D61—22no—
27C2×Dic244—21no—
28C2×Dic244—21no—
29C2×D488—21no—
30C2×D488D412yes—
31C2×#11758199—22no—
32D8×D61—42no—
33D8×D61—42no—
34C2×C8×D61—21no—
35#14519777—21no—
36#14519774—21no—
37#14519752—22no—
38#14519751—41no—
39#14519747—42no—
40C4×D244D411yescharacteristic
41#14519722—44no—
42#14519721—42no—
43C2×#11758185—21no—
44#14519711—41no—
45C4⋊#92418D411yescharacteristic
46#14519699—41no—
47#14519697—22no—
48#14519689—21no—
49C2×D8×C61D411yescharacteristic
50C4×D4×C61—21no—
51C2×C16×C61—21no—
52#107×C61D411yescharacteristic
53C4⋊C8×C61—21no—
54#102×C61—21no—
55C4×C8×C61C2311yescharacteristic
56C23×D61—42no—
57C2×D4×C61—21no—
58C22×C4×C61—41no—
59C2×C22⋊D61—42no—
60D4×D61—44no—
61D4×D61—82no—
62C2×D244—22no—
63C2×D244—42no—
64C2×D244—41no—
65C2×D244—41no—
66C2×D244—82no—
67C2×D244—82no—
68C2×D244D811yescharacteristic
69C2×C4×D61—21no—
70C2×Dic122—41no—
71D8×C61—21no—
72D8×C61D812yes—
73C2×C8×C61—41no—
74C2×C8×C61C2×D411yescharacteristic
75C2×C8×C61C2×D411yescharacteristic
76C4⋊C4×C61—21no—
77C22⋊C4×C61—41no—
78C42×C61C2×D411yescharacteristic
79#11758199—44no—
80#11758198—21no—
81#11758198—42no—
82C4⋊Dic61—41no—
83C4⋊Dic61—41no—
84C4⋊Dic61D811yescharacteristic
85C2×#92418—21no—
86Dic244—42no—
87Dic244—41no—
88Dic244—41no—
89D488—42no—
90D488—41no—
91D488—41no—
92C8×D61—41no—
93C8×D61—41no—
94C16×C61—22no—
95#11758185—41no—
96C23×C61—41no—
97C22×D61—21no—
98C22×D61—42no—
99C22×D61—84no—
100C22×D61—84no—
101C22×D61—162no—
102D4×C61—22no—
103D4×C61—41no—
104C2×C4×C61—41no—
105C2×C4×C61—81no—
106C2×C4×C61—81no—
107C2×C4×C61#12011yescharacteristic
108C2×C4×C61C2×D811yescharacteristic
109C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
110C22⋊D61—84no—
111C2×Dic61—21no—
112C2×Dic61—81no—
113D244—21no—
114D244—42no—
115D244—42no—
116D244—84no—
117D244—81no—
118D244—81no—
119D244—161no—
120D244SD3212yescomplemented
121C4×D61—41no—
122C4×D61—41no—
123Dic122—81no—
124Dic122—81no—
125C8×C61—21no—
126C8×C61—81no—
127C8×C61C2×D811yescharacteristic
128C8×C61AGL(1,ℤ/8)11yescharacteristic
129#92418—41no—
130#12320—611nomaximal, Sylow
131C22×C61—42no—
132C22×C61—81no—
133C22×C61—81no—
134C22×C61#44711yescharacteristic
135C2×D61—22no—
136C2×D61—41no—
137C2×D61—41no—
138C2×D61—82no—
139C2×D61—82no—
140C2×D61—82no—
141C2×D61—168no—
142C4×C61—21no—
143C4×C61—81no—
144C4×C61#44711yescharacteristic
145C4×C61#45311yescharacteristic
146C4×C61C2×SD3211yescharacteristic
147C4×C61#50911yescharacteristic
148Dic61—41no—
149Dic61—161no—
150D4×D8—611no—
151#2248—611no—
152#2208—611no—
153#1669—611no—
154#1361—611no—
155#1331D6111yescharacteristic, complemented
156D4⋊C16—611no—
157C2×C61—82no—
158C2×C61#161911yescharacteristic
159C2×C61#218711yescharacteristic
160C2×C61#219411yescharacteristic
161D61—42no—
162D61—162no—
163C22×D8—1221no—
164D42—1221no—
165C2×SD32—1222no—
166C2×SD32—1221no—
167#494—611no—
168#493—611no—
169#474—1221no—
170#466—1221no—
171#459—1221no—
172#447—1222no—
173C4×D8C2×D6111yescharacteristic
174C8×D4—611no—
175C4⋊C16—611no—
176#358—1221no—
177C4×C16C2×D6111yescharacteristic, complemented
178#335C2×D6111yescharacteristic, complemented
179#332—1221no—
180C61#1232011yescharacteristic, complemented, Sylow
181C22×D4—1222no—
182C22×D4—2441no—
183C2×Q16—1221no—
184C2×Q16—1221no—
185C2×D8—612no—
186C2×D8—1222no—
187C2×D8—1221no—
188C2×D8—2442no—
189C2×D8—2442no—
190C2×D8D24411yescharacteristic
191C22×C8—1221no—
192C4⋊Q8—1221no—
193#127—1221no—
194#121—1222no—
195#121—2441no—
196#120—2442no—
197C4×D4—21no—
198C4×D4—611no—
199SD32—2444no—
200SD32—2442no—
201C2×C16—21no—
202C2×C16—1221no—
203#107—2441no—
204#107D24411yescharacteristic
205C4⋊C8—21no—
206C4⋊C8—611no—
207#102—21no—
208#102—1222no—
209#102—2441no—
210C22⋊C8—1221no—
211C4×C8C22×D6111yescharacteristic
212C24—2442no—
213C2×Q8—2441no—
214C2×D4—21no—
215C2×D4—611no—
216C2×D4—1222no—
217C2×D4—4882no—
218C2×D4—4882no—
219C2×D4—4882no—
220C2×D4—2442no—
221C2×D4—2442no—
222C2×D4—2444no—
223C2×D4—2441no—
224C2×D4—2441no—
225C22×C4—41no—
226C22×C4—1221no—
227Q16—2442no—
228Q16—2441no—
229Q16—2441no—
230D8—21no—
231D8—2442no—
232D8—2444no—
233D8—2441no—
234D8—2441no—
235D8D48812yes—
236C2×C8—41no—
237C2×C8—1221no—
238C2×C8—2441no—
239C2×C8—2441no—
240C2×C8C2×D24411yescharacteristic
241C2×C8D4×D6111yescharacteristic
242C4⋊C4—21no—
243C4⋊C4—611no—
244C4⋊C4—2441no—
245C4⋊C4—2441no—
246C22⋊C4—41no—
247C22⋊C4—1221no—
248C22⋊C4—2442no—
249C42D4×D6111yescharacteristic
250C16—22no—
251C16—2441no—
252C23—41no—
253C23—1221no—
254C23—9762no—
255C23—4884no—
256C23—4884no—
257C23—2442no—
258Q8—4881no—
259Q8—4881no—
260D4—22no—
261D4—41no—
262D4—612no—
263D4—1221no—
264D4—9761no—
265D4—4884no—
266D4—4884no—
267D4—4881no—
268D4—4881no—
269D4—2442no—
270D4—2442no—
271C2×C4—41no—
272C2×C4—81no—
273C2×C4—81no—
274C2×C4—1221no—
275C2×C4—4881no—
276C2×C4—2441no—
277C2×C4—2441no—
278C2×C4#1451974711yescharacteristic
279C2×C4D8×D6111yescharacteristic
280C2×C4#1451980411yescharacteristic
281C8—21no—
282C8—81no—
283C8—2441no—
284C8C2×D48811yescharacteristic
285C8#1451980511yescharacteristic
286C22—42no—
287C22—81no—
288C22—81no—
289C22—1222no—
290C22—9768no—
291C22—4882no—
292C22—4882no—
293C22—4882no—
294C22—2441no—
295C22—2441no—
296C22#1683989711yescharacteristic
297C4—21no—
298C4—81no—
299C4—9761no—
300C4—2441no—
301C4#1683989811yescharacteristic
302C4#1683993111yescharacteristic
303C4SD32×D6111yescharacteristic
304C4#1684019611yescharacteristic
305C2—82no—
306C2—9762no—
307C2—2442no—
308C2#2144487511yescharacteristic
309C2#2144774911yescharacteristic
310C2#2144779111yescharacteristic
subgroupG/H
centerC22#16839897
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1331C2
socleC22×C61#447
prime radicalD8×D244C2
hypercenter#1331D61
hypocenterC61#12320
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1331

Complements

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

NH ≅ G/Ntype
2. #21448075C2semidirect
3. #21447864C2semidirect
4. #21445185C2semidirect
5. #21443864C2semidirect
6. #21443775C2semidirect
7. C61×#1331C2semidirect
12. #16840142C22semidirect
19. C4⋊#11758185C22semidirect
23. C4×C16×C61C22semidirect
24. C61×#335C22semidirect
120. D244SD32semidirect
155. #1331D61semidirect
177. C4×C16C2×D61semidirect
178. #335C2×D61semidirect
180. C61#12320semidirect

Maximal subgroups

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

subgroupindex
D8×D2442
#214480752
#214478642
#214451852
#214438642
#214437752
C61×#13312
#1232061