Finite Group Databasebeta

← #29593364

Subgroups — #29593364

Order 15616.

322 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 55 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#21456731C211yesmaximal, characteristic
2#21448038C211yesmaximal, characteristic, complemented
3#21448033C211yesmaximal, characteristic, complemented
4#21443806C211yesmaximal, characteristic, complemented
5#21443803C211yesmaximal, characteristic, complemented
6#21443757C211yesmaximal, characteristic, complemented
7C61×#2098C211yesmaximal, characteristic, complemented
8#16840340—21no—
9#16840093—21no—
10#16840081—21no—
11#16840020C2211yescharacteristic
12#16840015C2211yescharacteristic
13#16839991—21no—
14#16839926—21no—
15#16839909—21no—
16#16839586—21no—
17#16839586—21no—
18#16839577—21no—
19#16839574—21no—
20#16839544C2211yescharacteristic
21#16839544C2211yescharacteristic
22C61×#430C2211yescharacteristic
23C61×#424—21no—
24C61×#421—21no—
25C61×#408C2211yescharacteristic
26C61×H(3,ℤ/4)C2211yescharacteristic
27C2×#11758222—21no—
28C2×Dic244D411yescharacteristic
29C2×#11758190—21no—
30C2×D488D411yescharacteristic
31#14519756—21no—
32#14519756—21no—
33#14519753—41no—
34#14519751—21no—
35#14519751—21no—
36#14519749—41no—
37#14519749—41no—
38#14519748—41no—
39C2×C4⋊Dic61—21no—
40#14519717—21no—
41#14519717—21no—
42#14519709—21no—
43#14519709D411yescharacteristic
44#14519709D411yescharacteristic
45#14519702—21no—
46#14519702—21no—
47#14519699—21no—
48#14519699—21no—
49C2×#41×C61D411yescharacteristic
50C2×M16×C61—21no—
51C2×M16×C61C2311yescharacteristic
52C22×C8×C61D411yescharacteristic
53#117×C61—21no—
54#108×C61—21no—
55#108×C61—21no—
56C4⋊C8×C61—42no—
57#104×C61—42no—
58C22⋊C8×C61—21no—
59C22⋊C8×C61—21no—
60#41×C61—41no—
61#41×C61—41no—
62C2×Q8×C61SD1611yescharacteristic
63C2×D4×C61—21no—
64C2×D4×C61SD1611yescharacteristic
65C22×C4×C61—21no—
66C22×C4×C61C2×D411yescharacteristic
67C2×C22⋊D61—41no—
68C2×C22⋊D61—41no—
69C2×C22⋊D61—41no—
70C22×Dic61—41no—
71#11758222—81no—
72#11758222—81no—
73C2×D244—21no—
74C2×C4×D61—41no—
75C2×Dic122—21no—
76M16×C61—41no—
77M16×C61—41no—
78M16×C61—41no—
79C2×C8×C61—21no—
80C2×C8×C61—41no—
81C2×C8×C61—41no—
82C2×C8×C61C2×D411yescharacteristic
83C2×C8×C61C2×D411yescharacteristic
84C4⋊C4×C61—41no—
85C22⋊C4×C61—41no—
86C42×C61—22no—
87C22⋊Dic61—41no—
88C22⋊Dic61—41no—
89#11758198—41no—
90#11758198—41no—
91C4⋊Dic61—21no—
92C4⋊Dic61—21no—
93C4⋊Dic61—41no—
94#11758196—41no—
95#11758196—41no—
96Dic244—41no—
97D488—41no—
98#11758190—81no—
99#11758185—41no—
100#11758185—41no—
101C23×C61—21no—
102C23×C61AGL(1,ℤ/8)11yescharacteristic
103C22×D61—41no—
104Q8×C61—41no—
105D4×C61—41no—
106D4×C61—81no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—41no—
111C2×C4×C61—41no—
112C2×C4×C61—42no—
113C2×C4×C61#12011yescharacteristic
114C2×C4×C61C2×SD1611yescharacteristic
115C22⋊D61—82no—
116C22⋊D61—161no—
117C22⋊D61—161no—
118C2×Dic61—41no—
119C2×Dic61—41no—
120C2×Dic61—41no—
121C2×Dic61—161no—
122D244—41no—
123D244—41no—
124C4×D61—82no—
125Dic122—41no—
126Dic122—41no—
127C8×C61—21no—
128C8×C61—21no—
129C8×C61—41no—
130C8×C61—81no—
131#12303—611nomaximal, Sylow
132C22×C61—21no—
133C22×C61—41no—
134C22×C61—41no—
135C22×C61—41no—
136C22×C61—41no—
137C22×C61#45011yescharacteristic
138C2×D61—81no—
139C2×D61—81no—
140C2×D61—81no—
141C4×C61—21no—
142C4×C61—41no—
143C4×C61—82no—
144C4×C61#45311yescharacteristic
145C4×C61#45811yescharacteristic
146Dic61—81no—
147Dic61—81no—
148Dic61—81no—
149#3204—611no—
150#2239—611no—
151#2238—611no—
152#2098D6111yescharacteristic, complemented
153#1340—611no—
154#1339—611no—
155#1321—611no—
156C2×C61—21no—
157C2×C61—41no—
158C2×C61—81no—
159C2×C61#161311yescharacteristic
160D61—161no—
161#537—1221no—
162#483—1221no—
163#481—1221no—
164#470—611no—
165#469—611no—
166#465—1221no—
167#452—1221no—
168#449—1221no—
169#430C2×D6111yescharacteristic
170#424—21no—
171#421—21no—
172#408C2×D6111yescharacteristic
173#365—1221no—
174#365—1221no—
175#362—1221no—
176#361—1221no—
177#349—611no—
178#349—611no—
179H(3,ℤ/4)C2×D6111yescharacteristic
180C61#1230311yescharacteristic, complemented, Sylow
181C2×#41—1221no—
182C2×#41C22⋊D6111yescharacteristic
183C2×Q16—611no—
184C2×SD16—1221no—
185C2×D8—611no—
186C2×M16—21no—
187C2×M16C22×D6111yescharacteristic
188C22×C8C22⋊D6111yescharacteristic
189C22⋊Q8—1221no—
190C22⋊Q8—1221no—
191C22⋊Q8—2441no—
192#121—1221no—
193#121—1221no—
194#121—2441no—
195#121—2441no—
196#121—2441no—
197#117—21no—
198C2×C4⋊C4—1221no—
199M32—1221no—
200M32—1221no—
201#108—21no—
202#108—21no—
203#106—611no—
204#106—611no—
205#106—1221no—
206C4⋊C8—42no—
207#104—42no—
208#103—1221no—
209#103—1221no—
210#102—1221no—
211#102—1221no—
212C22⋊C8—21no—
213C22⋊C8—21no—
214#41—41no—
215#41—41no—
216#41—4881no—
217#41—4881no—
218C2×Q8—1221no—
219C2×Q8#1175820111yescharacteristic
220C2×D4—21no—
221C2×D4—1221no—
222C2×D4—2441no—
223C2×D4—2441no—
224C2×D4—2441no—
225C2×D4#1175820111yescharacteristic
226C22×C4—21no—
227C22×C4—2441no—
228C22×C4—2441no—
229C22×C4C2×C22⋊D6111yescharacteristic
230Q16—2441no—
231SD16—4881no—
232D8—2441no—
233M16—41no—
234M16—41no—
235M16—41no—
236C2×C8—21no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8D4×D6111yescharacteristic
240C2×C8D4×D6111yescharacteristic
241C4⋊C4—41no—
242C4⋊C4—1221no—
243C4⋊C4—1221no—
244C4⋊C4—2441no—
245C4⋊C4—2441no—
246C4⋊C4—2441no—
247C22⋊C4—41no—
248C22⋊C4—2441no—
249C22⋊C4—2441no—
250C22⋊C4—2441no—
251C22⋊C4—2441no—
252C42—22no—
253C16—2441no—
254C16—2441no—
255C23—21no—
256C23—2441no—
257C23#1451980211yescharacteristic
258Q8—41no—
259Q8—2441no—
260Q8—2441no—
261D4—41no—
262D4—81no—
263D4—9761no—
264D4—9761no—
265D4—4882no—
266D4—2441no—
267D4—2441no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—42no—
274C2×C4—9761no—
275C2×C4—4882no—
276C2×C4—2441no—
277C2×C4—2441no—
278C2×C4—2441no—
279C2×C4#1451974511yescharacteristic
280C2×C4C2×#1175820111yescharacteristic
281C8—21no—
282C8—21no—
283C8—41no—
284C8—81no—
285C22—21no—
286C22—41no—
287C22—41no—
288C22—41no—
289C22—41no—
290C22—4881no—
291C22—4881no—
292C22—4881no—
293C22#1683991211yescharacteristic
294C4—21no—
295C4—41no—
296C4—82no—
297C4—4881no—
298C4—4881no—
299C4—4881no—
300C4#1683992911yescharacteristic
301C4#1683995111yescharacteristic
302C2—21no—
303C2—41no—
304C2—81no—
305C2—9761no—
306C2#2144483811yescharacteristic
subgroupG/H
centerC2#21444838
commutator, cosocleC2×M16×C61C23
FrattiniC2×M16C22×D61
FittingC61×#2098C2
socleC2×C61#1613
prime radical#21456731C2
hypercenter#2098D61
hypocenterC61#12303
LCSG ▷ C2×M16×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #2098

Complements

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

NH ≅ G/Ntype
2. #21448038C2semidirect
3. #21448033C2semidirect
4. #21443806C2semidirect
5. #21443803C2semidirect
6. #21443757C2semidirect
7. C61×#2098C2semidirect
152. #2098D61semidirect
180. C61#12303semidirect

Maximal subgroups

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

subgroupindex
#214567312
#214480382
#214480332
#214438062
#214438032
#214437572
C61×#20982
#1230361