Finite Group Databasebeta

← #29593831

Subgroups — #29593831

Order 15616.

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

normal subgroups only

This group has 360 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#21457578C211yesmaximal, characteristic
2#21448043C211yesmaximal, characteristic, complemented
3#21447971C211yesmaximal, characteristic, complemented
4#21445219C211yesmaximal, characteristic, complemented
5#21443864C211yesmaximal, characteristic, complemented
6#21443775C211yesmaximal, characteristic, complemented
7C61×#1332C211yesmaximal, characteristic, complemented
8C2×#14519800—21no—
9#16840434—21no—
10#16840167C2211yescharacteristic
11#16840139C2211yescharacteristic
12#16840053—21no—
13#16839999—21no—
14#16839962—21no—
15#16839910—22no—
16C8×D244C2211yescharacteristic
17#16839587—21no—
18C4⋊#11758185C2211yescharacteristic
19#16839566—21no—
20#16839564—22no—
21#16839510—21no—
22C4×Q16×C61C2211yescharacteristic
23C4×C16×C61C2211yescharacteristic
24C61×#335C2211yescharacteristic
25C2×#11758226—22no—
26#14519800—42no—
27#14519800—42no—
28C2×#11758201—22no—
29C2×D488—21no—
30C2×D488D412yes—
31C2×C8×D61—21no—
32#14519777—21no—
33#14519774—21no—
34#14519774—41no—
35#14519752—22no—
36#14519752—42no—
37C4×D244—41no—
38C4×D244D411yescharacteristic
39C2×#11758185—21no—
40#14519711—21no—
41#14519711—21no—
42#14519709—41no—
43C4⋊#92418D411yescharacteristic
44#14519699—41no—
45#14519697—22no—
46#14519689—21no—
47C2×Q16×C61D411yescharacteristic
48C4×Q8×C61—21no—
49C2×C16×C61—21no—
50#107×C61D411yescharacteristic
51C4⋊C8×C61—21no—
52#103×C61—21no—
53C4×C8×C61C2311yescharacteristic
54C2×Q8×C61—21no—
55#11758226—44no—
56#11758226—82no—
57C2×D244—22no—
58C2×D244—42no—
59C2×D244—41no—
60C2×D244—42no—
61C2×D244—41no—
62C2×D244D811yescharacteristic
63C2×C4×D61—21no—
64C2×C4×D61—42no—
65C2×Dic122—41no—
66Q16×C61—21no—
67Q16×C61SD1612yes—
68C2×C8×C61—41no—
69C2×C8×C61C2×D411yescharacteristic
70C2×C8×C61C2×D411yescharacteristic
71C4⋊C4×C61—21no—
72C4⋊C4×C61—41no—
73C42×C61—41no—
74C42×C61C2×D411yescharacteristic
75#11758201—44no—
76#11758198—21no—
77#11758198—42no—
78C4⋊Dic61—41no—
79C4⋊Dic61—41no—
80C4⋊Dic61D811yescharacteristic
81C2×#92418—21no—
82D488—42no—
83D488—41no—
84D488—41no—
85C8×D61—41no—
86C8×D61—41no—
87C16×C61—41no—
88#11758185—41no—
89C22×D61—21no—
90C22×D61—42no—
91Q8×C61—22no—
92Q8×C61—41no—
93C2×C4×C61—41no—
94C2×C4×C61—41no—
95C2×C4×C61#12011yescharacteristic
96C2×C4×C61C2×D811yescharacteristic
97C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
98C2×Dic61—21no—
99C2×Dic61—81no—
100D244—21no—
101D244—21no—
102D244—42no—
103D244—42no—
104D244—84no—
105D244—81no—
106D244—81no—
107D244—161no—
108D244—162no—
109C4×D61—41no—
110C4×D61—41no—
111C4×D61—84no—
112Dic122—161no—
113C8×C61—21no—
114C8×C61—81no—
115C8×C61C2×SD1611yescharacteristic
116C8×C61AGL(1,ℤ/8)11yescharacteristic
117#92418—41no—
118#12373—611nomaximal, Sylow
119C22×C61#44711yescharacteristic
120C2×D61—41no—
121C2×D61—41no—
122C2×D61—41no—
123C2×D61—82no—
124C2×D61—82no—
125C2×D61—82no—
126C4×C61—21no—
127C4×C61—42no—
128C4×C61—81no—
129C4×C61#45011yescharacteristic
130C4×C61#45511yescharacteristic
131C4×C61#50811yescharacteristic
132C4×C61#51011yescharacteristic
133Dic61—41no—
134Dic61—161no—
135#3287—611no—
136#2240—611no—
137#2227—611no—
138#1675—611no—
139#1361—611no—
140#1332D6111yescharacteristic, complemented
141D4⋊C16—611no—
142C2×C61#163911yescharacteristic
143C2×C61#218911yescharacteristic
144C2×C61#219211yescharacteristic
145D61—81no—
146D61—162no—
147C2×#135—1221no—
148#550—1221no—
149#500—611no—
150#493—611no—
151#476—1221no—
152#466—1221no—
153#460—1221no—
154#449—1222no—
155C4×Q16C2×D6111yescharacteristic
156C8×D4—611no—
157#366—1221no—
158C4⋊C16—611no—
159#358—1221no—
160#357—1222no—
161C4×C16C2×D6111yescharacteristic
162#335C2×D6111yescharacteristic
163#333—1221no—
164C61#1237311yescharacteristic, complemented, Sylow
165C2×#41—1222no—
166#135—2442no—
167#135—2442no—
168C2×Q16D24411yescharacteristic
169C2×SD16—1222no—
170C2×D8—612no—
171C2×D8—1221no—
172C22×C8—1221no—
173C4⋊Q8—1221no—
174#127—1221no—
175#127—2441no—
176#121—1222no—
177#121—2442no—
178C4×Q8—21no—
179C4×D4—611no—
180C4×D4—2441no—
181C2×C16—21no—
182C2×C16—1221no—
183#107—1221no—
184#107—1221no—
185#107D24411yescharacteristic
186#106—2441no—
187C4⋊C8—21no—
188C4⋊C8—611no—
189#103—21no—
190#102—1222no—
191#102—2441no—
192C22⋊C8—1221no—
193C4×C8C22×D6111yescharacteristic
194#41—4882no—
195#41—2444no—
196C2×Q8—21no—
197C2×Q8—2441no—
198C2×D4—611no—
199C2×D4—1222no—
200C2×D4—2442no—
201C2×D4—2442no—
202C2×D4—2441no—
203C2×D4—2441no—
204C22×C4—1221no—
205C22×C4—2442no—
206Q16—21no—
207Q16#1175819012yes—
208SD16—2444no—
209D8—2442no—
210D8—2441no—
211D8—2441no—
212C2×C8—41no—
213C2×C8—1221no—
214C2×C8—2441no—
215C2×C8—2441no—
216C2×C8C2×D24411yescharacteristic
217C2×C8D4×D6111yescharacteristic
218C4⋊C4—21no—
219C4⋊C4—41no—
220C4⋊C4—611no—
221C4⋊C4—2441no—
222C4⋊C4—2441no—
223C22⋊C4—1221no—
224C22⋊C4—2442no—
225C42—41no—
226C42D4×D6111yescharacteristic
227C16—41no—
228C16—2441no—
229C23—1221no—
230C23—2442no—
231Q8—22no—
232Q8—41no—
233Q8—9761no—
234D4—1221no—
235D4—1221no—
236D4—9761no—
237D4—9762no—
238D4—4884no—
239D4—4881no—
240D4—4881no—
241D4—2442no—
242D4—2442no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—1221no—
246C2×C4—4884no—
247C2×C4—4881no—
248C2×C4—2441no—
249C2×C4—2441no—
250C2×C4#1451974711yescharacteristic
251C2×C4D8×D6111yescharacteristic
252C2×C4#1451980411yescharacteristic
253C8—21no—
254C8—81no—
255C8—2441no—
256C8C2×#1175819011yescharacteristic
257C8#1451980511yescharacteristic
258C22—4882no—
259C22—4882no—
260C22—4882no—
261C22—2441no—
262C22—2441no—
263C22—2441no—
264C22#1683989711yescharacteristic
265C4—21no—
266C4—42no—
267C4—81no—
268C4—9761no—
269C4—2441no—
270C4#1683991511yescharacteristic
271C4#1683994111yescharacteristic
272C4#1684019311yescharacteristic
273C4#1684020411yescharacteristic
274C2—9762no—
275C2—4881no—
276C2#2144500111yescharacteristic
277C2#2144776211yescharacteristic
278C2#2144777711yescharacteristic
subgroupG/H
centerC22#16839897
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1332C2
socleC22×C61#447
prime radical#21457578C2
hypercenter#1332D61
hypocenterC61#12373
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1332

Complements

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

NH ≅ G/Ntype
2. #21448043C2semidirect
3. #21447971C2semidirect
4. #21445219C2semidirect
5. #21443864C2semidirect
6. #21443775C2semidirect
7. C61×#1332C2semidirect
140. #1332D61semidirect
164. C61#12373semidirect

Maximal subgroups

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

subgroupindex
#214575782
#214480432
#214479712
#214452192
#214438642
#214437752
C61×#13322
#1237361