Finite Group Databasebeta

← #29592487

Subgroups — #29592487

Order 15616.

374 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 59 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#21457258C211yesmaximal, characteristic, complemented
2#21447731C212yesmaximal, complemented
3#21443833C212yesmaximal, complemented
4#21443761C211yesmaximal, characteristic, complemented
5C61×#2045C211yesmaximal, characteristic, complemented
6#16840367—21no—
7C2×#14519718—22no—
8#16840063—22no—
9#16840015—21no—
10#16839998C2212yes—
11#16839958—22no—
12#16839563—22no—
13C22⋊#11758185C2212yes—
14C22×D8×C61C2211yescharacteristic
15C61×#424C2211yescharacteristic
16C61×#418—21no—
17C2×#100×C61—21no—
18C61×#341C2211yescharacteristic
19C2×D488—21no—
20C2×D488D412yes—
21#14519774—21no—
22#14519769—21no—
23#14519762—42no—
24#14519751—22no—
25#14519750—42no—
26C4×D244—22no—
27#14519718—44no—
28C2×#11758185—22no—
29#14519711D412yes—
30#14519709—21no—
31#14519699—22no—
32#14519699—22no—
33C22×D4×C61—21no—
34C2×D8×C61—22no—
35C2×D8×C61—42no—
36C2×M16×C61—21no—
37C2×M16×C61D411yescharacteristic
38C22×C8×C61C2311yescharacteristic
39#117×C61D411yescharacteristic
40C4⋊C8×C61—22no—
41#102×C61—42no—
42#100×C61—42no—
43C24×C61—41no—
44C2×D4×C61—22no—
45C2×D4×C61—41no—
46C2×D4×C61—41no—
47C2×D4×C61—41no—
48C2×D4×C61—41no—
49C2×D4×C61—41no—
50C22×C4×C61C2×D411yescharacteristic
51C2×C22⋊D61—42no—
52C2×D244—22no—
53C2×D244—42no—
54C2×C4×D61—42no—
55D8×C61—24no—
56D8×C61—42no—
57M16×C61—41no—
58M16×C61—41no—
59M16×C61—41no—
60C2×C8×C61—21no—
61C2×C8×C61—41no—
62C2×C8×C61—41no—
63C2×C8×C61C2×D412yes—
64C4⋊C4×C61D812yes—
65C22⋊C4×C61—21no—
66C42×C61—21no—
67#11758198—42no—
68#11758198—42no—
69C4⋊Dic61—22no—
70#11758196—42no—
71D488—42no—
72D488—81no—
73#11758185—42no—
74C23×C61—42no—
75C23×C61—81no—
76C23×C61—81no—
77C23×C61—162no—
78C23×C61AGL(1,ℤ/8)11yescharacteristic
79C22×D61—42no—
80D4×C61—42no—
81D4×C61—42no—
82D4×C61—81no—
83D4×C61—81no—
84C2×C4×C61—21no—
85C2×C4×C61—21no—
86C2×C4×C61—22no—
87C2×C4×C61#12011yescharacteristic
88C2×C4×C61C2×D811yescharacteristic
89C22⋊D61—162no—
90C2×Dic61—42no—
91D244—42no—
92D244—42no—
93D244—162no—
94C4×D61—162no—
95C8×C61—22no—
96C8×C61—41no—
97C8×C61—81no—
98#12164—611nomaximal, Sylow
99C22×C61—21no—
100C22×C61—22no—
101C22×C61—82no—
102C22×C61—162no—
103C22×C61—162no—
104C22×C61—162no—
105C22×C61#44711yescharacteristic
106C2×D61—82no—
107C2×D61—82no—
108C2×D61—82no—
109C4×C61—21no—
110C4×C61—42no—
111C4×C61#45411yescharacteristic
112C4×C61B(4,𝔽2)11yescharacteristic
113Dic61—82no—
114#3259—611no—
115#2184—612no—
116#2045D6111yescharacteristic, complemented
117#1349—612no—
118#1323—611no—
119C2×C61—41no—
120C2×C61—162no—
121C2×C61#159811yescharacteristic
122C2×C61#219212yes—
123D61—162no—
124C22×D8C2×D6111yescharacteristic
125#540—1221no—
126C2×D16—1222no—
127#478—1222no—
128#469—1221no—
129#466—612no—
130#459—1222no—
131#424C2×D6111yescharacteristic
132#418—21no—
133C2×#100—21no—
134#357—1222no—
135C22⋊C16—612no—
136#341C2×D6111yescharacteristic
137C61#1216411yescharacteristic, complemented, Sylow
138C22×D4—21no—
139C2×D8—22no—
140C2×D8—42no—
141C2×D8—612no—
142C2×D8—1221no—
143C2×M16—21no—
144C2×M16C22⋊D6111yescharacteristic
145C22×C8C22×D6111yescharacteristic
146#127—1221no—
147#125—1221no—
148#123—2442no—
149#121—1222no—
150#121—2442no—
151C4×D4—1222no—
152#117C22⋊D6111yescharacteristic
153D16—2444no—
154C2×C16—1222no—
155#107—612no—
156#106—1221no—
157C4⋊C8—22no—
158#102—42no—
159#102—1222no—
160#102—1222no—
161#100—42no—
162C24—41no—
163C2×D4—22no—
164C2×D4—41no—
165C2×D4—41no—
166C2×D4—41no—
167C2×D4—41no—
168C2×D4—41no—
169C2×D4—1222no—
170C2×D4—2442no—
171C2×D4—2442no—
172C22×C4—2442no—
173C22×C4C2×C22⋊D6111yescharacteristic
174D8—24no—
175D8—42no—
176D8—4881no—
177D8—2442no—
178M16—41no—
179M16—41no—
180M16—41no—
181C2×C8—21no—
182C2×C8—41no—
183C2×C8—41no—
184C2×C8D4×D6112yes—
185C4⋊C4—1222no—
186C4⋊C4—2442no—
187C4⋊C4#1175819912yes—
188C22⋊C4—21no—
189C22⋊C4—2442no—
190C22⋊C4—2442no—
191C42—21no—
192C16—2442no—
193C23—42no—
194C23—81no—
195C23—81no—
196C23—162no—
197C23—2442no—
198C23#1451980211yescharacteristic
199D4—42no—
200D4—42no—
201D4—81no—
202D4—81no—
203D4—9762no—
204D4—9762no—
205D4—2442no—
206D4—2442no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—22no—
210C2×C4—9762no—
211C2×C4—2442no—
212C2×C4#1451974511yescharacteristic
213C2×C4C2×#1175819911yescharacteristic
214C8—22no—
215C8—41no—
216C8—81no—
217C22—22no—
218C22—21no—
219C22—82no—
220C22—162no—
221C22—162no—
222C22—162no—
223C22—4882no—
224C22—4882no—
225C22—4882no—
226C22#1683989511yescharacteristic
227C4—21no—
228C4—42no—
229C4—4882no—
230C4#1683993411yescharacteristic
231C4#1683994811yescharacteristic
232C2—41no—
233C2—162no—
234C2—9762no—
235C2#2144475311yescharacteristic
236C2#2144777412yes—
subgroupG/H
centerC22#16839895
commutator, cosocleC22×C8×C61C23
FrattiniC22×C8C22×D61
FittingC61×#2045C2
socleC22×C61#447
hypercenter#2045D61
hypocenterC61#12164
LCSG ▷ C22×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #424 ◁ #2045

Complements

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

NH ≅ G/Ntype
1. #21457258C2semidirect
2. #21447731C2semidirect
3. #21443833C2semidirect
4. #21443761C2semidirect
5. C61×#2045C2semidirect
116. #2045D61semidirect
137. C61#12164semidirect

Maximal subgroups

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

subgroupindex
#214572582
#214477312
#214438332
#214437612
C61×#20452
#1216461