Finite Group Databasebeta

← #29593358

Subgroups — #29593358

Order 15616.

310 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 53 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#21456711C211yesmaximal, characteristic
2#21448038C211yesmaximal, characteristic, complemented
3#21447371C211yesmaximal, characteristic
4#21443808C211yesmaximal, characteristic, complemented
5#21443807C211yesmaximal, characteristic, complemented
6#21443756C211yesmaximal, characteristic
7C61×#2239C211yesmaximal, characteristic, complemented
8#16840335—21no—
9#16840106—21no—
10#16840101—21no—
11#16840020C2211yescharacteristic
12#16840001—21no—
13#16839919—21no—
14#16839916—21no—
15#16839790—21no—
16#16839778—21no—
17#16839730C2211yescharacteristic
18#16839586—21no—
19#16839577—21no—
20#16839544C2211yescharacteristic
21#16839519C2211yescharacteristic
22C61×#470C2211yescharacteristic
23C61×#430C2211yescharacteristic
24C61×#365—21no—
25C61×#362—21no—
26C61×#349C2211yescharacteristic
27C2×#11758222D411yescharacteristic
28C2×Q8×D61—21no—
29C2×Dic244D411yescharacteristic
30C2×#11758202—21no—
31C22×#92418D411yescharacteristic
32#14519776—41no—
33#14519763—41no—
34#14519762—41no—
35#14519759—41no—
36#14519757—21no—
37#14519756—21no—
38#14519753—21no—
39#14519736—21no—
40#14519735—21no—
41#14519717—21no—
42#14519710—21no—
43#14519709D411yescharacteristic
44#14519706—42no—
45#14519703—42no—
46#14519702—21no—
47#14519701—21no—
48#14519700—21no—
49#14519689—21no—
50#14519689—21no—
51C2×Q16×C61D411yescharacteristic
52C2×M16×C61—21no—
53C2×M16×C61C2311yescharacteristic
54C22⋊Q8×C61—21no—
55M32×C61—21no—
56#108×C61—21no—
57#108×C61—21no—
58#106×C61D411yescharacteristic
59#103×C61—21no—
60C2×Q8×C61—21no—
61C22×C4×C61C2×D411yescharacteristic
62C2×C22⋊D61—21no—
63Q8×D61—81no—
64Q8×D61—81no—
65#11758222—41no—
66#11758222—41no—
67C2×D244SD1611yescharacteristic
68C2×C4×D61—21no—
69C2×C4×D61—41no—
70C2×Dic122—21no—
71C2×Dic122—41no—
72C2×Dic122SD1611yescharacteristic
73Q16×C61—41no—
74M16×C61—41no—
75M16×C61—41no—
76M16×C61—41no—
77C2×C8×C61—41no—
78C2×C8×C61C2×D411yescharacteristic
79C2×C8×C61C2×D411yescharacteristic
80C4⋊C4×C61—21no—
81C4⋊C4×C61—41no—
82C22⋊C4×C61—41no—
83C22⋊Dic61—41no—
84C22⋊Dic61—41no—
85#11758202—81no—
86#11758198—41no—
87#11758198—41no—
88#11758198—41no—
89C4⋊Dic61—21no—
90C4⋊Dic61—41no—
91C4⋊Dic61—41no—
92#11758196—41no—
93#11758196—41no—
94C4×Dic61—22no—
95C4×Dic61—41no—
96C2×#92418—21no—
97C2×#92418—41no—
98Dic244—41no—
99C16×C61—41no—
100#11758185—41no—
101C23×C61AGL(1,ℤ/8)11yescharacteristic
102C22×D61—21no—
103Q8×C61—41no—
104Q8×C61—41no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—41no—
108C2×C4×C61—41no—
109C2×C4×C61#12011yescharacteristic
110C2×C4×C61C2×SD1611yescharacteristic
111C22⋊D61—81no—
112C2×Dic61—21no—
113C2×Dic61—42no—
114C2×Dic61—41no—
115C2×Dic61—41no—
116D244—41no—
117C4×D61—41no—
118C4×D61—41no—
119C4×D61—82no—
120Dic122—41no—
121Dic122—41no—
122Dic122—41no—
123Dic122—82no—
124C8×C61—21no—
125C8×C61—21no—
126C8×C61—81no—
127#92418—41no—
128#12302—611nomaximal, Sylow
129C22×C61—21no—
130C22×C61—41no—
131C22×C61#45011yescharacteristic
132C2×D61—42no—
133C2×D61—41no—
134C4×C61—21no—
135C4×C61—81no—
136C4×C61—81no—
137C4×C61#45311yescharacteristic
138C4×C61#45811yescharacteristic
139Dic61—41no—
140Dic61—81no—
141Dic61—82no—
142Dic61—81no—
143#3202—611no—
144#2239—611no—
145#2239D6111yescharacteristic, complemented
146#2098—611no—
147#1340—611no—
148#1340—611no—
149#1321—611no—
150C2×C61—21no—
151C2×C61—41no—
152C2×C61#161311yescharacteristic
153D61—81no—
154#536—1221no—
155#485—1221no—
156#485—1221no—
157#470—611no—
158#470C2×D6111yescharacteristic
159#467—1221no—
160#451—1221no—
161#451—1221no—
162#430C2×D6111yescharacteristic
163#424—1221no—
164#421—1221no—
165#408—611no—
166#365—21no—
167#365—1221no—
168#362—21no—
169#362—1221no—
170#349—611no—
171#349C2×D6111yescharacteristic
172H(3,ℤ/4)—611no—
173C61#1230211yescharacteristic, complemented, Sylow
174C2×#41—611no—
175C22×Q8—1221no—
176C2×Q16—611no—
177C2×Q16—1221no—
178C2×Q16C22⋊D6111yescharacteristic
179C2×M16—21no—
180C2×M16C22×D6111yescharacteristic
181C22×C8—611no—
182C4⋊Q8—2441no—
183#124—2441no—
184#123—2441no—
185#123—2441no—
186C22⋊Q8—21no—
187C22⋊Q8—1221no—
188C22⋊Q8—1221no—
189C22⋊Q8—1221no—
190#117—1221no—
191#117—1221no—
192M32—21no—
193M32—1221no—
194#108—21no—
195#108—21no—
196#107—1221no—
197#106—611no—
198#106C22⋊D6111yescharacteristic
199C4⋊C8—2442no—
200#104—2442no—
201#103—21no—
202#103—1221no—
203#103—1221no—
204#103—1221no—
205C22⋊C8—1221no—
206C22⋊C8—1221no—
207#41—2441no—
208#41—2441no—
209C2×Q8—21no—
210C2×Q8—611no—
211C2×Q8—1221no—
212C2×Q8—4881no—
213C2×Q8—4881no—
214C2×Q8—2441no—
215C2×D4—611no—
216C2×D4—1221no—
217C22×C4—1221no—
218C22×C4—2441no—
219C22×C4D4×D6111yescharacteristic
220Q16—41no—
221Q16—4881no—
222Q16—2441no—
223M16—41no—
224M16—41no—
225M16—41no—
226C2×C8—41no—
227C2×C8—1221no—
228C2×C8—2441no—
229C2×C8D4×D6111yescharacteristic
230C2×C8C2×C22⋊D6111yescharacteristic
231C4⋊C4—21no—
232C4⋊C4—41no—
233C4⋊C4—1221no—
234C4⋊C4—2441no—
235C4⋊C4—2441no—
236C4⋊C4—2441no—
237C4⋊C4—2441no—
238C22⋊C4—41no—
239C22⋊C4—2441no—
240C22⋊C4—2441no—
241C22⋊C4—2441no—
242C22⋊C4—2441no—
243C22⋊C4—2441no—
244C42—1222no—
245C42—2441no—
246C16—41no—
247C16—2441no—
248C23—1221no—
249C23#1451980411yescharacteristic
250Q8—41no—
251Q8—41no—
252Q8—4882no—
253Q8—2441no—
254Q8—2441no—
255Q8—2441no—
256D4—4881no—
257D4—2441no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—1221no—
263C2×C4—4882no—
264C2×C4—2442no—
265C2×C4—2441no—
266C2×C4—2441no—
267C2×C4—2441no—
268C2×C4—2441no—
269C2×C4#1451974511yescharacteristic
270C2×C4SD16×D6111yescharacteristic
271C8—21no—
272C8—21no—
273C8—81no—
274C8—2441no—
275C22—21no—
276C22—41no—
277C22—2442no—
278C22—2441no—
279C22#1683991111yescharacteristic
280C4—21no—
281C4—81no—
282C4—81no—
283C4—4881no—
284C4—4882no—
285C4—4881no—
286C4—2441no—
287C4#1683992811yescharacteristic
288C4#1683995111yescharacteristic
289C2—21no—
290C2—41no—
291C2—4881no—
292C2#2144483711yescharacteristic
subgroupG/H
centerC2#21444837
commutator, cosocleC2×M16×C61C23
FrattiniC2×M16C22×D61
FittingC61×#2239C2
socleC2×C61#1613
prime radicalC2×#11758222D4
hypercenter#2239D61
hypocenterC61#12302
LCSG ▷ C2×M16×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #2239

Complements

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

NH ≅ G/Ntype
2. #21448038C2semidirect
4. #21443808C2semidirect
5. #21443807C2semidirect
7. C61×#2239C2semidirect
145. #2239D61semidirect
173. C61#12302semidirect

Maximal subgroups

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

subgroupindex
#214567112
#214480382
#214473712
#214438082
#214438072
#214437562
C61×#22392
#1230261