Finite Group Databasebeta

← #29593791

Subgroups — #29593791

Order 15616.

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

normal subgroups only

This group has 424 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#21448044C211yesmaximal, characteristic, complemented
3#21447953C211yesmaximal, characteristic, complemented
4#21443864C211yesmaximal, characteristic, complemented
5#21443779C211yesmaximal, characteristic, complemented
6D4⋊#11758185C211yesmaximal, characteristic, complemented
7C61×#1673C211yesmaximal, characteristic, complemented
8C22×D488—21no—
9D4×D244—21no—
10#16840139C2211yescharacteristic
11#16839998—21no—
12#16839958—21no—
13#16839898—22no—
14C4×D488C2211yescharacteristic
15#16839587—21no—
16C4⋊#11758185C2211yescharacteristic, complemented
17#16839562—21no—
18#16839562—22no—
19C4×#11758185C2211yescharacteristic, complemented
20C61×#500C2211yescharacteristic, complemented
21C61×#461—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—
38C2×#11758185—21no—
39C2×#11758185—21no—
40#14519711D411yescharacteristic
41#14519699—22no—
42#14519699—21no—
43C2×SD16×C61—41no—
44C22×C8×C61—21no—
45C4⋊Q8×C61—21no—
46C4×D4×C61D411yescharacteristic
47#107×C61—21no—
48#107×C61—21no—
49C4⋊C8×C61—21no—
50C4⋊C8×C61D411yescharacteristic
51#103×C61—41no—
52C22⋊C8×C61—21no—
53C4×C8×C61C2311yescharacteristic
54C23×D61—42no—
55C2×Q8×C61—41no—
56C2×D4×C61D811yescharacteristic
57C22×C4×C61—21no—
58C2×C22⋊D61—42no—
59D4×D61—82no—
60D4×D61—82no—
61C2×D244—21no—
62C2×D244—22no—
63C2×D244—44no—
64C2×D244—42no—
65C2×D244—41no—
66C2×D244—41no—
67C2×D244—82no—
68C2×C4×D61—41no—
69SD16×C61—82no—
70C2×C8×C61—21no—
71C2×C8×C61—41no—
72C2×C8×C61—41no—
73C2×C8×C61—41no—
74C2×C8×C61C2×D411yescharacteristic
75C2×C8×C61C2×D411yescharacteristic
76C4⋊C4×C61—41no—
77C4⋊C4×C61—41no—
78C4⋊C4×C61D811yescharacteristic
79C22⋊C4×C61—21no—
80C42×C61C2×D411yescharacteristic
81#11758198—42no—
82#11758198—41no—
83C4⋊Dic61—21no—
84D488—21no—
85D488—42no—
86D488—44no—
87D488—41no—
88D488—41no—
89D488SD1612yescomplemented
90#11758185—41no—
91#11758185—41no—
92C23×C61—21no—
93C22×D61—41no—
94C22×D61—42no—
95C22×D61—84no—
96C22×D61—84no—
97C22×D61—162no—
98Q8×C61—81no—
99Q8×C61—81no—
100D4×C61—21no—
101D4×C61D1612yes—
102C2×C4×C61—21no—
103C2×C4×C61—41no—
104C2×C4×C61—41no—
105C2×C4×C61—81no—
106C2×C4×C61#12011yescharacteristic
107C2×C4×C61C2×D811yescharacteristic
108C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
109C22⋊D61—84no—
110C2×Dic61—41no—
111D244—22no—
112D244—42no—
113D244—41no—
114D244—42no—
115D244—84no—
116D244—81no—
117D244—81no—
118D244—161no—
119C4×D61—81no—
120C4×D61—81no—
121C8×C61—21no—
122C8×C61—41no—
123C8×C61—81no—
124C8×C61C2×SD1611yescharacteristic
125C8×C61AGL(1,ℤ/8)11yescharacteristic
126#12368—611nomaximal, Sylow
127C22×C61—22no—
128C22×C61—41no—
129C22×C61—41no—
130C22×C61#44711yescharacteristic
131C2×D61—42no—
132C2×D61—81no—
133C2×D61—81no—
134C2×D61—82no—
135C2×D61—82no—
136C2×D61—82no—
137C2×D61—168no—
138C4×C61—21no—
139C4×C61—41no—
140C4×C61—161no—
141C4×C61#45011yescharacteristic
142C4×C61#45511yescharacteristic
143C4×C61C2×D1611yescharacteristic
144C4×C61#50911yescharacteristic
145Dic61—81no—
146D4×D8—611no—
147#2240—611no—
148#2224—611no—
149#1673D6111yescharacteristic, complemented
150#1361—611no—
151#1331—611no—
152D4⋊C16—611no—
153C2×C61—42no—
154C2×C61#163911yescharacteristic
155C2×C61#218411yescharacteristic
156C2×C61#219411yescharacteristic
157D61—82no—
158D61—162no—
159C22×D8—1221no—
160D42—1221no—
161#500C2×D6111yescharacteristic, complemented
162#493—611no—
163#466—1221no—
164#461—21no—
165#459—1221no—
166#447—1222no—
167C4×D8—611no—
168C8×D4C2×D6111yescharacteristic
169#366—1221no—
170C4⋊C16—611no—
171#357—1221no—
172#357—1222no—
173C4×C16—611no—
174#335C2×D6111yescharacteristic, complemented
175#332—21no—
176C61#1236811yescharacteristic, complemented, Sylow
177C22×D4—1222no—
178C22×D4—2441no—
179C2×SD16—41no—
180C2×D8—611no—
181C2×D8—612no—
182C2×D8—1222no—
183C2×D8—1221no—
184C2×D8—2442no—
185C2×D8—2442no—
186C22×C8—21no—
187C4⋊Q8—21no—
188#127—1221no—
189#121—1222no—
190#121—2441no—
191#120—2442no—
192C4×D4—1221no—
193C4×D4C22⋊D6111yescharacteristic
194C2×C16—1221no—
195C2×C16—1221no—
196#107—21no—
197#107—21no—
198#107—611no—
199C4⋊C8—21no—
200C4⋊C8C22⋊D6111yescharacteristic
201#103—41no—
202#102—1222no—
203#102—1221no—
204C22⋊C8—21no—
205C4×C8C22×D6111yescharacteristic
206C24—2442no—
207C2×Q8—41no—
208C2×D4—1221no—
209C2×D4—1222no—
210C2×D4—4882no—
211C2×D4—4882no—
212C2×D4—4882no—
213C2×D4—2442no—
214C2×D4—2444no—
215C2×D4—2442no—
216C2×D4—2441no—
217C2×D4—2441no—
218C2×D4#1175819911yescharacteristic
219C22×C4—21no—
220C22×C4—2441no—
221SD16—82no—
222D8—612no—
223D8—1221no—
224D8—2442no—
225D8—2444no—
226D8—2441no—
227D8—2441no—
228C2×C8—21no—
229C2×C8—41no—
230C2×C8—41no—
231C2×C8—41no—
232C2×C8D4×D6111yescharacteristic
233C2×C8D4×D6111yescharacteristic
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—1221no—
237C4⋊C4#1175819911yescharacteristic
238C22⋊C4—21no—
239C22⋊C4—2442no—
240C22⋊C4—2441no—
241C42C2×C22⋊D6111yescharacteristic
242C16—2441no—
243C16—2441no—
244C23—21no—
245C23—9762no—
246C23—4884no—
247C23—4884no—
248C23—2442no—
249C23—2441no—
250Q8—81no—
251Q8—81no—
252D4—21no—
253D4—1222no—
254D4—9761no—
255D4—4884no—
256D4—4884no—
257D4—4881no—
258D4—4881no—
259D4—2442no—
260D4—2441no—
261D4—2442no—
262D4#1451971812yes—
263C2×C4—21no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—81no—
267C2×C4—4881no—
268C2×C4—4881no—
269C2×C4—2441no—
270C2×C4#1451974511yescharacteristic
271C2×C4C2×#1175819911yescharacteristic
272C2×C4#1451980211yescharacteristic
273C8—21no—
274C8—41no—
275C8—81no—
276C8SD16×D6111yescharacteristic
277C8#1451980411yescharacteristic
278C22—22no—
279C22—41no—
280C22—41no—
281C22—9768no—
282C22—4882no—
283C22—4882no—
284C22—4882no—
285C22—4881no—
286C22—4881no—
287C22—2442no—
288C22#1683989511yescharacteristic
289C4—21no—
290C4—41no—
291C4—161no—
292C4—4881no—
293C4#1683991111yescharacteristic
294C4#1683993811yescharacteristic
295C4C2×#1451971811yescharacteristic
296C4#1684019711yescharacteristic
297C2—42no—
298C2—9762no—
299C2—4882no—
300C2#2144499611yescharacteristic
301C2#2144773011yescharacteristic
302C2#2144778811yescharacteristic
subgroupG/H
centerC22#16839895
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1673C2
socleC22×C61#447
prime radicalD4×D488C2
hypercenter#1673D61
hypocenterC61#12368
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C8×D4 ◁ #1673

Complements

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

NH ≅ G/Ntype
2. #21448044C2semidirect
3. #21447953C2semidirect
4. #21443864C2semidirect
5. #21443779C2semidirect
6. D4⋊#11758185C2semidirect
7. C61×#1673C2semidirect
16. C4⋊#11758185C22semidirect
19. C4×#11758185C22semidirect
20. C61×#500C22semidirect
23. C61×#335C22semidirect
89. D488SD16semidirect
149. #1673D61semidirect
161. #500C2×D61semidirect
174. #335C2×D61semidirect
176. C61#12368semidirect

Maximal subgroups

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

subgroupindex
D4×D4882
#214480442
#214479532
#214438642
#214437792
D4⋊#117581852
C61×#16732
#1236861