Finite Group Databasebeta

← #29593822

Subgroups — #29593822

Order 15616.

418 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 69 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#21457494C211yesmaximal, characteristic
2#21448042C211yesmaximal, characteristic, complemented
3#21447967C211yesmaximal, characteristic, complemented
4#21445219C211yesmaximal, characteristic, complemented
5#21443779C211yesmaximal, characteristic, complemented
6#21443773C211yesmaximal, characteristic, complemented
7C61×#1361C211yesmaximal, characteristic, complemented
8C2×D8×D61—21no—
9#16840397—21no—
10#16840167C2211yescharacteristic, complemented
11#16840053—21no—
12#16839995—21no—
13#16839954—21no—
14#16839894—22no—
15C4×D488C2211yescharacteristic
16C8×D244C2211yescharacteristic
17#16839590—21no—
18#16839564—21no—
19#16839563—22no—
20C4×#11758185C2211yescharacteristic, complemented
21#16839510—21no—
22C61×#493C2211yescharacteristic
23C61×C4⋊C16C2211yescharacteristic, complemented
24C61×#335C2211yescharacteristic, complemented
25C2×D4×D61—22no—
26C2×D4×D61—41no—
27C2×D488D411yescharacteristic
28C2×#11758199—22no—
29D8×D61—42no—
30D8×D61—42no—
31C2×C8×D61—21no—
32#14519777—21no—
33#14519748—22no—
34#14519748—41no—
35#14519745—42no—
36C4×D244—21no—
37C4×D244D411yescharacteristic
38C2×#11758185—21no—
39#14519711—21no—
40#14519711—21no—
41#14519711D411yescharacteristic
42#14519709—41no—
43C4⋊#92418D411yescharacteristic
44#14519699—21no—
45#14519699—41no—
46#14519698—22no—
47#14519689—21no—
48C2×D8×C61—21no—
49C2×D8×C61D412yes—
50#127×C61—21no—
51C2×C16×C61—21no—
52C4⋊C8×C61—21no—
53C4×C8×C61C2311yescharacteristic
54C23×D61—42no—
55C2×D4×C61—22no—
56C2×D4×C61—41no—
57C2×D4×C61—41no—
58C2×C22⋊D61—42no—
59C2×C22⋊D61—42no—
60D4×D61—44no—
61D4×D61—82no—
62D4×D61—82no—
63D4×D61—82no—
64C2×D244—21no—
65C2×D244D811yescharacteristic
66C2×C4×D61—21no—
67C2×C4×D61—41no—
68C2×Dic122—41no—
69D8×C61—42no—
70D8×C61—41no—
71D8×C61—41no—
72C2×C8×C61—41no—
73C2×C8×C61C2×D411yescharacteristic
74C2×C8×C61C2×D411yescharacteristic
75C42×C61C2×D411yescharacteristic
76C22⋊Dic61—42no—
77#11758199—44no—
78#11758198—21no—
79#11758198—41no—
80C4⋊Dic61—21no—
81C4⋊Dic61—41no—
82C4⋊Dic61—41no—
83C4⋊Dic61D811yescharacteristic
84C2×#92418—21no—
85D488—21no—
86D488SD1612yes—
87C8×D61—41no—
88C8×D61—41no—
89C16×C61—41no—
90#11758185—41no—
91C23×C61—42no—
92C22×D61—21no—
93C22×D61—41no—
94C22×D61—84no—
95C22×D61—84no—
96C22×D61—162no—
97D4×C61—42no—
98D4×C61—42no—
99D4×C61—81no—
100D4×C61—81no—
101D4×C61—161no—
102C2×C4×C61#12011yescharacteristic
103C2×C4×C61C2×D811yescharacteristic
104C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
105C22⋊D61—84no—
106C22⋊D61—84no—
107C2×Dic61—21no—
108C2×Dic61—41no—
109C2×Dic61—81no—
110D244—22no—
111D244—21no—
112D244—41no—
113D244SD3212yes—
114C4×D61—41no—
115C4×D61—41no—
116C4×D61—81no—
117C4×D61—81no—
118Dic122—161no—
119C8×C61—21no—
120C8×C61—81no—
121C8×C61C2×SD1611yescharacteristic
122C8×C61AGL(1,ℤ/8)11yescharacteristic
123#92418—41no—
124#12372—611nomaximal, Sylow
125C22×C61—82no—
126C22×C61—82no—
127C22×C61—82no—
128C22×C61#44711yescharacteristic
129C2×D61—22no—
130C2×D61—41no—
131C2×D61—41no—
132C2×D61—42no—
133C2×D61—81no—
134C2×D61—81no—
135C2×D61—168no—
136C4×C61—21no—
137C4×C61#45011yescharacteristic
138C4×C61#45511yescharacteristic
139C4×C61C2×SD3211yescharacteristic
140C4×C61#50911yescharacteristic
141Dic61—41no—
142Dic61—81no—
143Dic61—161no—
144D4×D8—611no—
145#2240—611no—
146#2226—611no—
147#1675—611no—
148#1361D6111yescharacteristic, complemented
149#1331—611no—
150D4⋊C16—611no—
151C2×C61—162no—
152C2×C61#163911yescharacteristic
153C2×C61#218711yescharacteristic
154C2×C61#219211yescharacteristic
155D61—42no—
156D61—82no—
157C22×D8—1221no—
158D42—1221no—
159#500—611no—
160#493C2×D6111yescharacteristic
161#476—1221no—
162#466—1221no—
163#459—1221no—
164#447—1222no—
165C4×D8—611no—
166C8×D4—611no—
167#367—1221no—
168C4⋊C16C2×D6111yescharacteristic, complemented
169#357—1221no—
170#357—1222no—
171C4×C16—611no—
172#335C2×D6111yescharacteristic, complemented
173#333—1221no—
174C61#1237211yescharacteristic, complemented, Sylow
175C22×D4—1222no—
176C22×D4—2441no—
177C2×D8—21no—
178C2×D8—611no—
179C2×D8—1222no—
180C2×D8—2442no—
181C2×D8—2442no—
182C2×D8D24412yes—
183C22×C8—1221no—
184C4⋊Q8—1221no—
185#127—21no—
186#121—1222no—
187#121—2441no—
188#120—2442no—
189C4×D4—611no—
190C4×D4—1221no—
191C2×C16—21no—
192C2×C16—1221no—
193#107—611no—
194#107—1221no—
195#107—1221no—
196#106—2441no—
197C4⋊C8—21no—
198C4⋊C8—611no—
199#102—1222no—
200#102—1221no—
201#102—2441no—
202C22⋊C8—1221no—
203C4×C8C22×D6111yescharacteristic
204C24—2442no—
205C2×Q8—2441no—
206C2×D4—22no—
207C2×D4—41no—
208C2×D4—41no—
209C2×D4—611no—
210C2×D4—1221no—
211C2×D4—4882no—
212C2×D4—4882no—
213C2×D4—4882no—
214C2×D4—2442no—
215C2×D4—2444no—
216C2×D4—2442no—
217C22×C4—1221no—
218C22×C4—2441no—
219D8—42no—
220D8—41no—
221D8—41no—
222D8—612no—
223D8—1221no—
224D8—2444no—
225C2×C8—41no—
226C2×C8—1221no—
227C2×C8—2441no—
228C2×C8—2441no—
229C2×C8C2×D24411yescharacteristic
230C2×C8D4×D6111yescharacteristic
231C4⋊C4—611no—
232C4⋊C4—1221no—
233C4⋊C4—2441no—
234C4⋊C4—2441no—
235C22⋊C4—1221no—
236C22⋊C4—2442no—
237C22⋊C4—2441no—
238C42D4×D6111yescharacteristic
239C16—41no—
240C16—2441no—
241C23—42no—
242C23—1221no—
243C23—9762no—
244C23—4884no—
245C23—4884no—
246C23—2441no—
247Q8—9761no—
248D4—42no—
249D4—42no—
250D4—81no—
251D4—81no—
252D4—161no—
253D4—612no—
254D4—1221no—
255D4—1222no—
256D4—4884no—
257D4—4884no—
258D4—2441no—
259C2×C4—1221no—
260C2×C4—4881no—
261C2×C4—4881no—
262C2×C4—4881no—
263C2×C4—2441no—
264C2×C4—2441no—
265C2×C4—2441no—
266C2×C4#1451974711yescharacteristic
267C2×C4D8×D6111yescharacteristic
268C2×C4#1451980411yescharacteristic
269C8—21no—
270C8—81no—
271C8—2441no—
272C8SD16×D6111yescharacteristic
273C8#1451980111yescharacteristic
274C22—82no—
275C22—82no—
276C22—82no—
277C22—1222no—
278C22—9768no—
279C22—4881no—
280C22—4881no—
281C22—2442no—
282C22—2441no—
283C22—2441no—
284C22#1683989711yescharacteristic
285C4—21no—
286C4—9761no—
287C4—4881no—
288C4—2441no—
289C4#1683991411yescharacteristic
290C4#1683994211yescharacteristic
291C4SD32×D6111yescharacteristic
292C4#1684019611yescharacteristic
293C2—162no—
294C2—4882no—
295C2—2442no—
296C2#2144499911yescharacteristic
297C2#2144774911yescharacteristic
298C2#2144777911yescharacteristic
subgroupG/H
centerC22#16839897
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1361C2
socleC22×C61#447
prime radical#21457494C2
hypercenter#1361D61
hypocenterC61#12372
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1361

Complements

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

NH ≅ G/Ntype
2. #21448042C2semidirect
3. #21447967C2semidirect
4. #21445219C2semidirect
5. #21443779C2semidirect
6. #21443773C2semidirect
7. C61×#1361C2semidirect
10. #16840167C22semidirect
20. C4×#11758185C22semidirect
23. C61×C4⋊C16C22semidirect
24. C61×#335C22semidirect
148. #1361D61semidirect
168. C4⋊C16C2×D61semidirect
172. #335C2×D61semidirect
174. C61#12372semidirect

Maximal subgroups

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

subgroupindex
#214574942
#214480422
#214479672
#214452192
#214437792
#214437732
C61×#13612
#1237261