Finite Group Databasebeta

← #29594235

Subgroups — #29594235

Order 15616.

262 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 63 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#21448068C211yesmaximal, characteristic, complemented
2#21447650C211yesmaximal, characteristic, complemented
3#21445175C211yesmaximal, characteristic, complemented
4#21445171C211yesmaximal, characteristic, complemented
5#21443892C211yesmaximal, characteristic, complemented
6#21443866C211yesmaximal, characteristic, complemented
7C61×#1361C211yesmaximal, characteristic, complemented
8C2×#14519718—21no—
9C2×#14519718—21no—
10C2×#14519716—21no—
11#16840139C2211yescharacteristic
12#16839958—21no—
13#16839954—21no—
14C8×D244C2211yescharacteristic
15#16839541—21no—
16C4×#11758185C2211yescharacteristic
17#16839515C2211yescharacteristic
18#16839506—21no—
19#16839505—21no—
20C61×#493C2211yescharacteristic
21C61×C4⋊C16C2211yescharacteristic
22C61×#335C2211yescharacteristic
23C2×D488—21no—
24C2×D488—21no—
25C2×D488—41no—
26C2×#11758199—41no—
27C2×C8×D61—21no—
28#14519774—21no—
29C4×D244D411yescharacteristic
30#14519718—42no—
31#14519718—42no—
32#14519716—42no—
33C2×#11758185D411yescharacteristic
34C2×#11758185D411yescharacteristic
35C4⋊#92418—21no—
36C4⋊#92418D411yescharacteristic
37#14519699—41no—
38#14519698—41no—
39#14519689—21no—
40C2×D8×C61—21no—
41C2×D8×C61—21no—
42#127×C61—21no—
43C2×C16×C61—21no—
44C4⋊C8×C61—21no—
45C4×C8×C61C2311yescharacteristic
46C2×D4×C61—41no—
47C2×D4×C61—41no—
48C2×D4×C61—41no—
49C2×D244—41no—
50C2×D244—41no—
51C2×D244—41no—
52C2×D244D811yescharacteristic
53C2×C4×D61—21no—
54D8×C61—41no—
55D8×C61—41no—
56D8×C61—81no—
57C2×C8×C61—41no—
58C2×C8×C61C2×D411yescharacteristic
59C2×C8×C61#4111yescharacteristic
60C42×C61C2×D411yescharacteristic
61#11758199—82no—
62#11758198—21no—
63C4⋊Dic61D811yescharacteristic
64C2×#92418—21no—
65C2×#92418—41no—
66D488—41no—
67D488—41no—
68D488—81no—
69D488—82no—
70C8×D61—41no—
71C8×D61—41no—
72C16×C61—41no—
73#11758185—21no—
74#11758185D812yescomplemented
75C23×C61—81no—
76C22×D61—21no—
77C22×D61—81no—
78D4×C61—81no—
79D4×C61—81no—
80D4×C61—81no—
81D4×C61—81no—
82D4×C61—161no—
83C2×C4×C61#12111yescharacteristic
84C2×C4×C61C2×D811yescharacteristic
85C2×C4×C61#13511yescharacteristic
86C2×Dic61—21no—
87D244—21no—
88D244—21no—
89D244—81no—
90D244—81no—
91D244—81no—
92D244—81no—
93D244—161no—
94C4×D61—41no—
95C4×D61—41no—
96C8×C61—21no—
97C8×C61—81no—
98C8×C61C2×D811yescharacteristic
99C8×C61AGL(1,ℤ/8)11yescharacteristic
100#92418—41no—
101#92418—81no—
102#12433—611nomaximal, Sylow
103C22×C61—161no—
104C22×C61—161no—
105C22×C61—161no—
106C22×C61#46611yescharacteristic
107C2×D61—41no—
108C2×D61—41no—
109C2×D61—41no—
110C2×D61—161no—
111C2×D61—161no—
112C2×D61—161no—
113C4×C61—21no—
114C4×C61#45911yescharacteristic
115C4×C61#47211yescharacteristic
116C4×C61#50911yescharacteristic
117C4×C61#50911yescharacteristic
118Dic61—41no—
119#2246—611no—
120#2169—611no—
121#1667—611no—
122#1667—611no—
123#1372—611no—
124#1361—611no—
125#1361D6111yescharacteristic, complemented
126C2×C61—321no—
127C2×C61#166711yescharacteristic
128C2×C61#221811yescharacteristic
129C2×C61#222111yescharacteristic
130D61—81no—
131D61—321no—
132C2×D16—1221no—
133C2×D16—1221no—
134C2×M32—1221no—
135#493—611no—
136#493C2×D6111yescharacteristic
137#459—1221no—
138#459—1221no—
139C8×D4—611no—
140C4⋊C16C2×D6111yescharacteristic
141C22⋊C16—1221no—
142C4×C16—611no—
143#335—611no—
144#335C2×D6111yescharacteristic
145#331—1221no—
146#331—1221no—
147C61#1243311yescharacteristic, complemented, Sylow
148C2×D8—21no—
149C2×D8—21no—
150C2×D8—1221no—
151C2×D8—1221no—
152C2×D8—2441no—
153C2×D8—2441no—
154C22×C8—1221no—
155#127—21no—
156#127—1221no—
157C4×D4—611no—
158D16—2442no—
159D16—2442no—
160M32—2442no—
161C2×C16—21no—
162C2×C16—611no—
163C2×C16—611no—
164C4⋊C8—21no—
165C4⋊C8—611no—
166C4⋊C8—1221no—
167#102—2441no—
168#102—2441no—
169C22⋊C8—1221no—
170C4×C8C22×D6111yescharacteristic
171C2×D4—41no—
172C2×D4—41no—
173C2×D4—41no—
174C2×D4—611no—
175C2×D4—2441no—
176C2×D4—2441no—
177C2×D4—2441no—
178C22×C4—1221no—
179D8—41no—
180D8—41no—
181D8—81no—
182D8—4881no—
183D8—4882no—
184D8—4882no—
185D8—2441no—
186D8—2441no—
187C2×C8—41no—
188C2×C8—1221no—
189C2×C8—2441no—
190C2×C8—2441no—
191C2×C8—2441no—
192C2×C8#1175822211yescharacteristic
193C2×C8D4×D6111yescharacteristic
194C4⋊C4—611no—
195C22⋊C4—1221no—
196C42D4×D6111yescharacteristic
197C16—41no—
198C16—612no—
199C16—1221no—
200C23—81no—
201C23—1221no—
202C23—4881no—
203D4—81no—
204D4—81no—
205D4—81no—
206D4—81no—
207D4—161no—
208D4—1221no—
209D4—1221no—
210D4—9761no—
211D4—4881no—
212D4—4881no—
213D4—4881no—
214D4—4881no—
215C2×C4—1221no—
216C2×C4—2441no—
217C2×C4—2441no—
218C2×C4#1451975011yescharacteristic
219C2×C4D8×D6111yescharacteristic
220C2×C4#1451979811yescharacteristic
221C8—21no—
222C8—81no—
223C8—4881no—
224C8—2441no—
225C8D8×D6111yescharacteristic
226C8#1451980411yescharacteristic
227C22—161no—
228C22—161no—
229C22—161no—
230C22—9761no—
231C22—9761no—
232C22—9761no—
233C22—2441no—
234C22—2441no—
235C22—2441no—
236C22#1683999711yescharacteristic
237C4—21no—
238C4—2441no—
239C4#1683995611yescharacteristic
240C4#1684003111yescharacteristic
241C4#1684019611yescharacteristic
242C4#1684019911yescharacteristic
243C2—321no—
244C2—19521no—
245C2—4881no—
246C2#2144517311yescharacteristic
247C2#2144792111yescharacteristic
248C2#2144793811yescharacteristic
subgroupG/H
centerC22#16839997
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1361C2
socleC22×C61#466
hypercenter#1361D61
hypocenterC61#12433
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
1. #21448068C2semidirect
2. #21447650C2semidirect
3. #21445175C2semidirect
4. #21445171C2semidirect
5. #21443892C2semidirect
6. #21443866C2semidirect
7. C61×#1361C2semidirect
74. #11758185D8semidirect
125. #1361D61semidirect
147. C61#12433semidirect

Maximal subgroups

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

subgroupindex
#214480682
#214476502
#214451752
#214451712
#214438922
#214438662
C61×#13612
#1243361