Finite Group Databasebeta

← #29592492

Subgroups — #29592492

Order 15616.

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

normal subgroups only

This group has 350 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#21457273C211yesmaximal, characteristic, complemented
2#21447748C212yesmaximal
3#21443836C212yesmaximal, complemented
4#21443761C211yesmaximal, characteristic, complemented
5C61×#2045C211yesmaximal, characteristic
6#16840374—21no—
7C2×#14519721—22no—
8#16840070—22no—
9#16840020—21no—
10#16840003C2212yes—
11#16839973—22no—
12#16839563—22no—
13C22⋊#11758185C2212yes—
14C22×D8×C61C2211yescharacteristic
15C61×#424C2211yescharacteristic
16C61×#418—21no—
17C2×#100×C61—21no—
18C61×#341C2211yescharacteristic
19C2×Dic244—21no—
20C2×Dic244D412yes—
21#14519777—21no—
22#14519770—42no—
23#14519769—21no—
24#14519767—42no—
25#14519756—22no—
26C4×Dic122—22no—
27#14519721—44no—
28C2×#11758185—22no—
29#14519711D412yes—
30#14519709—21no—
31#14519702—22no—
32#14519702—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×Dic122—22no—
52D8×C61—24no—
53D8×C61—42no—
54M16×C61—41no—
55M16×C61—41no—
56M16×C61—41no—
57C2×C8×C61—21no—
58C2×C8×C61—41no—
59C2×C8×C61—41no—
60C2×C8×C61C2×D412yes—
61C4⋊C4×C61D812yes—
62C22⋊C4×C61—21no—
63C42×C61—21no—
64C22⋊Dic61—42no—
65C4⋊Dic61—22no—
66C4⋊Dic61—42no—
67#11758196—42no—
68#11758196—42no—
69#11758196—42no—
70C4×Dic61—42no—
71Dic244—42no—
72Dic244—81no—
73#11758185—42no—
74C23×C61—42no—
75C23×C61—81no—
76C23×C61—81no—
77C23×C61—162no—
78C23×C61AGL(1,ℤ/8)11yescharacteristic
79D4×C61—42no—
80D4×C61—42no—
81D4×C61—81no—
82D4×C61—81no—
83C2×C4×C61—21no—
84C2×C4×C61—21no—
85C2×C4×C61—22no—
86C2×C4×C61#12011yescharacteristic
87C2×C4×C61C2×D811yescharacteristic
88C2×Dic61—42no—
89C2×Dic61—42no—
90Dic122—42no—
91Dic122—42no—
92C8×C61—22no—
93C8×C61—41no—
94C8×C61—81no—
95#12165—611nomaximal, Sylow
96C22×C61—21no—
97C22×C61—22no—
98C22×C61—82no—
99C22×C61—162no—
100C22×C61—162no—
101C22×C61—162no—
102C22×C61#44711yescharacteristic
103C4×C61—21no—
104C4×C61—42no—
105C4×C61#45411yescharacteristic
106C4×C61B(4,𝔽2)11yescharacteristic
107Dic61—82no—
108Dic61—82no—
109#3261—611no—
110#2187—612no—
111#2045D6111yescharacteristic
112#1350—612no—
113#1323—611no—
114C2×C61—41no—
115C2×C61—162no—
116C2×C61#159811yescharacteristic
117C2×C61#219312yes—
118C22×D8C2×D6111yescharacteristic
119#541—1221no—
120C2×SD32—1222no—
121#479—1222no—
122#470—1221no—
123#467—612no—
124#462—1222no—
125#424C2×D6111yescharacteristic
126#418—21no—
127C2×#100—21no—
128#357—1222no—
129C22⋊C16—612no—
130#341C2×D6111yescharacteristic
131C61#1216511yescharacteristic, complemented, Sylow
132C22×D4—21no—
133C2×Q16—612no—
134C2×Q16—1221no—
135C2×D8—22no—
136C2×D8—42no—
137C2×M16—21no—
138C2×M16C22⋊D6111yescharacteristic
139C22×C8C22×D6111yescharacteristic
140C4⋊Q8—1221no—
141#126—2442no—
142#125—1221no—
143#125—2442no—
144C22⋊Q8—1222no—
145C4×Q8—1222no—
146#117C22⋊D6111yescharacteristic
147SD32—2444no—
148C2×C16—1222no—
149#107—612no—
150#106—1221no—
151C4⋊C8—22no—
152#103—1222no—
153#103—1222no—
154#102—42no—
155#100—42no—
156C24—41no—
157C2×Q8—1222no—
158C2×D4—22no—
159C2×D4—41no—
160C2×D4—41no—
161C2×D4—41no—
162C2×D4—41no—
163C2×D4—41no—
164C22×C4C2×C22⋊D6111yescharacteristic
165Q16—4881no—
166Q16—2442no—
167D8—24no—
168D8—42no—
169M16—41no—
170M16—41no—
171M16—41no—
172C2×C8—21no—
173C2×C8—41no—
174C2×C8—41no—
175C2×C8D4×D6112yes—
176C4⋊C4—1222no—
177C4⋊C4—2442no—
178C4⋊C4—2442no—
179C4⋊C4—2442no—
180C4⋊C4—2442no—
181C4⋊C4#1175819912yes—
182C22⋊C4—21no—
183C22⋊C4—2442no—
184C42—21no—
185C42—2442no—
186C16—2442no—
187C23—42no—
188C23—81no—
189C23—81no—
190C23—162no—
191C23#1451980211yescharacteristic
192Q8—2442no—
193Q8—2442no—
194D4—42no—
195D4—42no—
196D4—81no—
197D4—81no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—2442no—
202C2×C4—2442no—
203C2×C4#1451974511yescharacteristic
204C2×C4C2×#1175819911yescharacteristic
205C8—22no—
206C8—41no—
207C8—81no—
208C22—22no—
209C22—21no—
210C22—82no—
211C22—162no—
212C22—162no—
213C22—162no—
214C22#1683989511yescharacteristic
215C4—21no—
216C4—42no—
217C4—4882no—
218C4—4882no—
219C4#1683993411yescharacteristic
220C4#1683994811yescharacteristic
221C2—41no—
222C2—162no—
223C2#2144475311yescharacteristic
224C2#2144778112yes—
subgroupG/H
centerC22#16839895
commutator, cosocleC22×C8×C61C23
FrattiniC22×C8C22×D61
FittingC61×#2045C2
socleC22×C61#447
prime radicalC22×D8×C61C22
hypercenter#2045D61
hypocenterC61#12165
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. #21457273C2semidirect
3. #21443836C2semidirect
4. #21443761C2semidirect
131. C61#12165semidirect

Maximal subgroups

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

subgroupindex
#214572732
#214477482
#214438362
#214437612
C61×#20452
#1216561