Finite Group Databasebeta

← #29594217

Subgroups — #29594217

Order 15616.

268 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 71 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
2D4×#11758185C211yesmaximal, characteristic, complemented
3#21445174C211yesmaximal, characteristic, complemented
4#21443890C211yesmaximal, characteristic, complemented
5#21443865C211yesmaximal, characteristic, complemented
6#21443864C211yesmaximal, characteristic, complemented
7C61×#1667C211yesmaximal, characteristic, complemented
8C2×#14519718—21no—
9C2×#14519718—21no—
10C22×#11758185—21no—
11#16840139C2211yescharacteristic
12#16839957—21no—
13C4⋊#11758185C2211yescharacteristic
14C22⋊#11758185—21no—
15C4×#11758185C2211yescharacteristic
16#16839515C2211yescharacteristic
17#16839505—21no—
18C61×#493C2211yescharacteristic
19C61×#459—21no—
20C8×D4×C61C2211yescharacteristic
21C61×#335C2211yescharacteristic
22C61×#331—21no—
23C2×D488—21no—
24C2×D488—21no—
25C2×#11758199—41no—
26#14519774—21no—
27#14519718—42no—
28#14519718—42no—
29C2×#11758185—21no—
30C2×#11758185—42no—
31C2×#11758185D411yescharacteristic
32C2×#11758185D411yescharacteristic
33C4⋊#92418—21no—
34#14519697—41no—
35C2×D8×C61—21no—
36C2×D8×C61—21no—
37C2×D8×C61—41no—
38C22×C8×C61—21no—
39#127×C61—21no—
40C4×D4×C61D411yescharacteristic
41C4⋊C8×C61—21no—
42C4⋊C8×C61D411yescharacteristic
43#102×C61—41no—
44C22⋊C8×C61—21no—
45C4×C8×C61C2311yescharacteristic
46C2×D4×C61—41no—
47C2×D4×C61—41no—
48C2×D4×C61—41no—
49C2×D4×C61D811yescharacteristic
50C22×C4×C61—21no—
51C2×D244—41no—
52C2×D244—41no—
53C2×D244—41no—
54D8×C61—41no—
55D8×C61—41no—
56D8×C61—81no—
57D8×C61—82no—
58C2×C8×C61—21no—
59C2×C8×C61—41no—
60C2×C8×C61—41no—
61C2×C8×C61—41no—
62C2×C8×C61C2×D411yescharacteristic
63C2×C8×C61#4111yescharacteristic
64C4⋊C4×C61D811yescharacteristic
65C22⋊C4×C61—21no—
66C42×C61C2×D411yescharacteristic
67#11758199—82no—
68C2×#92418—41no—
69D488—41no—
70D488—41no—
71D488—81no—
72#11758185—21no—
73#11758185—41no—
74#11758185D812yescomplemented
75C23×C61—21no—
76C23×C61—81no—
77C22×D61—81no—
78D4×C61—21no—
79D4×C61—81no—
80D4×C61—81no—
81D4×C61—81no—
82D4×C61—81no—
83D4×C61—161no—
84D4×C61D1612yescomplemented
85C2×C4×C61—21no—
86C2×C4×C61—41no—
87C2×C4×C61—41no—
88C2×C4×C61#12111yescharacteristic
89C2×C4×C61C2×D811yescharacteristic
90C2×C4×C61#13511yescharacteristic
91D244—81no—
92D244—81no—
93D244—81no—
94D244—81no—
95D244—161no—
96C8×C61—21no—
97C8×C61—41no—
98C8×C61—81no—
99C8×C61C2×D811yescharacteristic
100C8×C61AGL(1,ℤ/8)11yescharacteristic
101#92418—81no—
102#12430—611nomaximal, Sylow
103C22×C61—22no—
104C22×C61—41no—
105C22×C61—41no—
106C22×C61—161no—
107C22×C61—161no—
108C22×C61—161no—
109C22×C61#46611yescharacteristic
110C2×D61—161no—
111C2×D61—161no—
112C2×D61—161no—
113C4×C61—21no—
114C4×C61—41no—
115C4×C61#45911yescharacteristic
116C4×C61#47211yescharacteristic
117C4×C61C2×D1611yescharacteristic
118C4×C61#50811yescharacteristic
119#2246—611no—
120D4×C16—611no—
121#1667—611no—
122#1667D6111yescharacteristic, complemented
123#1371—611no—
124#1361—611no—
125#1361—611no—
126C2×C61—42no—
127C2×C61—321no—
128C2×C61#166711yescharacteristic
129C2×C61#221511yescharacteristic
130C2×C61#222111yescharacteristic
131D61—321no—
132C2×D16—1221no—
133C2×D16—1221no—
134C22×C16—1221no—
135#493—611no—
136#493C2×D6111yescharacteristic
137#459—21no—
138#459—1221no—
139C8×D4C2×D6111yescharacteristic
140C4⋊C16—611no—
141C22⋊C16—1221no—
142C4×C16—611no—
143#335—611no—
144#335C2×D6111yescharacteristic
145#331—21no—
146#331—1221no—
147C61#1243011yescharacteristic, complemented, Sylow
148C2×D8—21no—
149C2×D8—21no—
150C2×D8—41no—
151C2×D8—1221no—
152C2×D8—1221no—
153C2×D8—2441no—
154C22×C8—21no—
155#127—21no—
156#127—1221no—
157C4×D4C22⋊D6111yescharacteristic
158D16—2442no—
159D16—2442no—
160C2×C16—611no—
161C2×C16—611no—
162C2×C16—1221no—
163C2×C16—2442no—
164C4⋊C8—21no—
165C4⋊C8—1221no—
166C4⋊C8C22⋊D6111yescharacteristic
167#102—41no—
168#102—2441no—
169C22⋊C8—21no—
170C4×C8C22×D6111yescharacteristic
171C2×D4—41no—
172C2×D4—41no—
173C2×D4—41no—
174C2×D4—2441no—
175C2×D4—2441no—
176C2×D4—2441no—
177C2×D4#1175819911yescharacteristic
178C22×C4—21no—
179D8—41no—
180D8—41no—
181D8—81no—
182D8—82no—
183D8—4881no—
184D8—4882no—
185D8—2441no—
186D8—2441no—
187C2×C8—21no—
188C2×C8—41no—
189C2×C8—41no—
190C2×C8—41no—
191C2×C8—2441no—
192C2×C8D4×D6111yescharacteristic
193C2×C8#1175822411yescharacteristic
194C4⋊C4#1175819911yescharacteristic
195C22⋊C4—21no—
196C42C2×C22⋊D6111yescharacteristic
197C16—612no—
198C16—1221no—
199C16—2441no—
200C23—21no—
201C23—81no—
202C23—4881no—
203D4—21no—
204D4—81no—
205D4—81no—
206D4—81no—
207D4—81no—
208D4—161no—
209D4—9761no—
210D4—4881no—
211D4—4881no—
212D4—4881no—
213D4—4881no—
214D4#1451971812yescomplemented
215C2×C4—21no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4#1451974911yescharacteristic
219C2×C4C2×#1175819911yescharacteristic
220C2×C4#1451979711yescharacteristic
221C8—21no—
222C8—41no—
223C8—81no—
224C8—4881no—
225C8D8×D6111yescharacteristic
226C8#1451980111yescharacteristic
227C22—22no—
228C22—41no—
229C22—41no—
230C22—161no—
231C22—161no—
232C22—161no—
233C22—9761no—
234C22—9761no—
235C22—9761no—
236C22#1683999611yescharacteristic
237C4—21no—
238C4—41no—
239C4#1683995511yescharacteristic
240C4#1684003011yescharacteristic
241C4C2×#1451971811yescharacteristic
242C4#1684019211yescharacteristic
243C2—42no—
244C2—321no—
245C2—19521no—
246C2#2144517211yescharacteristic
247C2#2144790311yescharacteristic
248C2#2144793711yescharacteristic
subgroupG/H
centerC22#16839996
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1667C2
socleC22×C61#466
hypercenter#1667D61
hypocenterC61#12430
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C8×D4 ◁ #1667

Complements

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

NH ≅ G/Ntype
1. #21448068C2semidirect
2. D4×#11758185C2semidirect
3. #21445174C2semidirect
4. #21443890C2semidirect
5. #21443865C2semidirect
6. #21443864C2semidirect
7. C61×#1667C2semidirect
74. #11758185D8semidirect
84. D4×C61D16semidirect
122. #1667D61semidirect
147. C61#12430semidirect
214. D4#14519718semidirect

Maximal subgroups

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

subgroupindex
#214480682
D4×#117581852
#214451742
#214438902
#214438652
#214438642
C61×#16672
#1243061