Finite Group Databasebeta

← #29593798

Subgroups — #29593798

Order 15616.

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

normal subgroups only

This group has 366 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#21457579C211yesmaximal, characteristic
2#21448044C211yesmaximal, characteristic, complemented
3#21447958C211yesmaximal, characteristic, complemented
4#21443864C211yesmaximal, characteristic, complemented
5#21443782C211yesmaximal, characteristic, complemented
6D4⋊#11758185C211yesmaximal, characteristic, complemented
7C61×#1673C211yesmaximal, characteristic, complemented
8C2×#14519799—21no—
9#16840433—21no—
10#16840139C2211yescharacteristic
11#16839998—21no—
12#16839963—21no—
13#16839909—22no—
14C4×Dic244C2211yescharacteristic
15#16839589—21no—
16C4⋊#11758185C2211yescharacteristic
17#16839565—21no—
18#16839562—22no—
19C4×#11758185C2211yescharacteristic
20C61×#500C2211yescharacteristic
21C61×#461—21no—
22C8×D4×C61C2211yescharacteristic
23C61×#335C2211yescharacteristic
24C61×#332—21no—
25C2×#11758222—22no—
26#14519799—42no—
27#14519799—42no—
28C2×Dic244D411yescharacteristic
29C2×#11758190—22no—
30C2×D488—21no—
31C2×D488D412yes—
32#14519774—21no—
33#14519773—41no—
34#14519751—22no—
35#14519750—42no—
36C4×Dic122—21no—
37#14519739—41no—
38C2×#11758185—21no—
39C2×#11758185—21no—
40#14519711D411yescharacteristic
41#14519702—21no—
42#14519699—22no—
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
54C2×Q8×C61—41no—
55C2×D4×C61D811yescharacteristic
56C22×C4×C61—21no—
57C2×C22⋊D61—42no—
58C2×C22⋊D61—42no—
59#11758222—44no—
60#11758222—82no—
61C2×D244—22no—
62C2×D244—41no—
63C2×D244—41no—
64C2×C4×D61—42no—
65C2×Dic122—21no—
66SD16×C61—82no—
67C2×C8×C61—21no—
68C2×C8×C61—41no—
69C2×C8×C61—41no—
70C2×C8×C61—41no—
71C2×C8×C61C2×D411yescharacteristic
72C2×C8×C61C2×D411yescharacteristic
73C4⋊C4×C61—41no—
74C4⋊C4×C61—41no—
75C4⋊C4×C61D811yescharacteristic
76C22⋊C4×C61—21no—
77C42×C61C2×D411yescharacteristic
78#11758198—42no—
79C4⋊Dic61—21no—
80#11758196—41no—
81C4×Dic61—41no—
82Dic244—21no—
83Dic244SD1612yescomplemented
84D488—42no—
85D488—41no—
86D488—41no—
87#11758190—44no—
88#11758185—41no—
89#11758185—41no—
90C23×C61—21no—
91C22×D61—42no—
92Q8×C61—81no—
93Q8×C61—81no—
94D4×C61—21no—
95D4×C61—21no—
96C2×C4×C61—21no—
97C2×C4×C61—41no—
98C2×C4×C61—41no—
99C2×C4×C61—81no—
100C2×C4×C61#12011yescharacteristic
101C2×C4×C61C2×D811yescharacteristic
102C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
103C22⋊D61—84no—
104C22⋊D61—162no—
105C2×Dic61—41no—
106C2×Dic61—41no—
107D244—42no—
108D244—42no—
109D244—81no—
110D244—81no—
111D244—161no—
112C4×D61—84no—
113Dic122—22no—
114Dic122—41no—
115C8×C61—21no—
116C8×C61—41no—
117C8×C61—81no—
118C8×C61C2×SD1611yescharacteristic
119C8×C61AGL(1,ℤ/8)11yescharacteristic
120#12369—611nomaximal, Sylow
121C22×C61—41no—
122C22×C61—41no—
123C22×C61—41no—
124C22×C61#44711yescharacteristic
125C2×D61—82no—
126C2×D61—82no—
127C2×D61—82no—
128C4×C61—21no—
129C4×C61—41no—
130C4×C61—161no—
131C4×C61#45011yescharacteristic
132C4×C61#45511yescharacteristic
133C4×C61#50811yescharacteristic
134C4×C61#50911yescharacteristic
135Dic61—42no—
136Dic61—81no—
137#3287—611no—
138#2240—611no—
139#2225—611no—
140#1673D6111yescharacteristic, complemented
141#1361—611no—
142#1332—611no—
143D4⋊C16—611no—
144C2×C61—81no—
145C2×C61#163911yescharacteristic
146C2×C61#218611yescharacteristic
147C2×C61#219411yescharacteristic
148D61—162no—
149C2×#135—1221no—
150#550—1221no—
151#500C2×D6111yescharacteristic
152#493—611no—
153#466—1221no—
154#461—21no—
155#460—1221no—
156#449—1222no—
157C4×Q16—611no—
158C8×D4C2×D6111yescharacteristic
159#367—1221no—
160C4⋊C16—611no—
161#358—1221no—
162#357—1222no—
163C4×C16—611no—
164#335C2×D6111yescharacteristic
165#332—21no—
166C61#1236911yescharacteristic, complemented, Sylow
167C2×#41—1222no—
168#135—2442no—
169#135—2442no—
170C2×Q16—611no—
171C2×SD16—41no—
172C2×SD16—1222no—
173C2×D8—612no—
174C2×D8—1221no—
175C22×C8—21no—
176C4⋊Q8—21no—
177#127—1221no—
178#127—2441no—
179#121—1222no—
180#121—2442no—
181C4×Q8—1221no—
182C4×D4—2441no—
183C4×D4C22⋊D6111yescharacteristic
184C2×C16—1221no—
185C2×C16—1221no—
186#107—21no—
187#107—21no—
188#107—611no—
189C4⋊C8—21no—
190C4⋊C8C22⋊D6111yescharacteristic
191#103—41no—
192#103—1221no—
193#102—1222no—
194C22⋊C8—21no—
195C4×C8C22×D6111yescharacteristic
196#41—4882no—
197#41—2444no—
198C2×Q8—41no—
199C2×Q8—1221no—
200C2×D4—1222no—
201C2×D4—2442no—
202C2×D4—2442no—
203C2×D4—2441no—
204C2×D4—2441no—
205C2×D4#1175819911yescharacteristic
206C22×C4—21no—
207C22×C4—2442no—
208Q16—612no—
209Q16—1221no—
210SD16—82no—
211SD16—2444no—
212D8—2442no—
213D8—2441no—
214D8—2441no—
215C2×C8—21no—
216C2×C8—41no—
217C2×C8—41no—
218C2×C8—41no—
219C2×C8D4×D6111yescharacteristic
220C2×C8D4×D6111yescharacteristic
221C4⋊C4—41no—
222C4⋊C4—41no—
223C4⋊C4—1221no—
224C4⋊C4—2441no—
225C4⋊C4#1175819911yescharacteristic
226C22⋊C4—21no—
227C22⋊C4—2442no—
228C42—2441no—
229C42C2×C22⋊D6111yescharacteristic
230C16—2441no—
231C16—2441no—
232C23—21no—
233C23—2442no—
234Q8—81no—
235Q8—81no—
236Q8—1222no—
237Q8—2441no—
238D4—21no—
239D4—21no—
240D4—9761no—
241D4—9762no—
242D4—4884no—
243D4—4881no—
244D4—4881no—
245D4—2442no—
246D4—2442no—
247C2×C4—21no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—81no—
251C2×C4—4884no—
252C2×C4—2441no—
253C2×C4—2441no—
254C2×C4#1451974511yescharacteristic
255C2×C4C2×#1175819911yescharacteristic
256C2×C4#1451980211yescharacteristic
257C8—21no—
258C8—41no—
259C8—81no—
260C8SD16×D6111yescharacteristic
261C8#1451980411yescharacteristic
262C22—41no—
263C22—41no—
264C22—41no—
265C22—4882no—
266C22—4882no—
267C22—4882no—
268C22#1683989511yescharacteristic
269C4—21no—
270C4—41no—
271C4—161no—
272C4—4881no—
273C4—2442no—
274C4#1683991111yescharacteristic
275C4#1683993811yescharacteristic
276C4#1684019211yescharacteristic
277C4#1684019811yescharacteristic
278C2—81no—
279C2—9762no—
280C2#2144499611yescharacteristic
281C2#2144774011yescharacteristic
282C2#2144778811yescharacteristic
subgroupG/H
centerC22#16839895
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1673C2
socleC22×C61#447
prime radical#21457579C2
hypercenter#1673D61
hypocenterC61#12369
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. #21447958C2semidirect
4. #21443864C2semidirect
5. #21443782C2semidirect
6. D4⋊#11758185C2semidirect
7. C61×#1673C2semidirect
83. Dic244SD16semidirect
140. #1673D61semidirect
166. C61#12369semidirect

Maximal subgroups

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

subgroupindex
#214575792
#214480442
#214479582
#214438642
#214437822
D4⋊#117581852
C61×#16732
#1236961