Finite Group Databasebeta

← #29583112

Subgroups — #29583112

Order 15616.

438 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 97 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#21454182C211yesmaximal, characteristic, complemented
2#21446647C211yesmaximal, characteristic
3#21444380C212yesmaximal
4#21443678C212yesmaximal, complemented
5C61×#1276C211yesmaximal, characteristic, complemented
6#16840312C2211yescharacteristic
7C2×#14519769—21no—
8#16839786C2211yescharacteristic
9C2×#14519705—21no—
10C2×#14519705—21no—
11#16839660—24no—
12#16839632—21no—
13#16839628C2212yes—
14#16839497—24no—
15C61×#431C2212yes—
16C43×C61C2211yescharacteristic
17C2×#11758222—21no—
18C2×#11758194—21no—
19#14519777Q811yescharacteristic
20#14519774Q811yescharacteristic
21#14519769—42no—
22#14519769—42no—
23#14519765—21no—
24#14519751—22no—
25C4×D244—22no—
26C2×C4⋊Dic61—24no—
27C2×C4⋊Dic61—22no—
28C2×#11758196—24no—
29C4⋊#92418—22no—
30#14519705—42no—
31#14519705—42no—
32#14519684—22no—
33#14519684D414yes—
34C2×C42×C61—22no—
35C2×C42×C61D411yescharacteristic
36C2×C42×C61D411yescharacteristic
37C2×C42×C61C2311yescharacteristic
38C4⋊C8×C61—22no—
39C22⋊C8×C61—22no—
40C4×C8×C61—22no—
41C22×C4×C61—21no—
42C22×C4×C61—21no—
43C22×C4×C61C2×D412yes—
44C22×C4×C61C2×D411yescharacteristic
45C2×C22⋊D61—41no—
46C22×Dic61—24no—
47#11758222—41no—
48#11758222—41no—
49#11758222—41no—
50#11758222—41no—
51C2×D244—21no—
52C2×D244—22no—
53C2×C4×D61—41no—
54C2×Dic122—21no—
55C2×C8×C61—42no—
56C42×C61—21no—
57C42×C61—21no—
58C42×C61—44no—
59C42×C61D812yes—
60C42×C61SD1612yes—
61C42×C61C2×Q811yescharacteristic
62C42×C61#4112yes—
63C42×C61#4111yescharacteristic
64#11758198—42no—
65C4⋊Dic61—22no—
66C4⋊Dic61—48no—
67C4⋊Dic61—42no—
68C4⋊Dic61—42no—
69#11758196—48no—
70#11758194—41no—
71#11758194—41no—
72C2×#92418—41no—
73C23×C61#12011yescharacteristic
74C22×D61—41no—
75C2×C4×C61—24no—
76C2×C4×C61—22no—
77C2×C4×C61—22no—
78C2×C4×C61—42no—
79C2×C4×C61—42no—
80C2×C4×C61C22⋊Q812yes—
81C2×C4×C61C22⋊Q811yescharacteristic
82C2×C4×C61#12412yes—
83C2×C4×C61#12411yescharacteristic
84C2×C4×C61C2×D811yescharacteristic
85C2×C4×C61C2×SD1611yescharacteristic
86C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
87C2×C4×C61#13711yescharacteristic
88C22⋊D61—81no—
89C22⋊D61—81no—
90C2×Dic61—48no—
91C2×Dic61—41no—
92C2×Dic61—44no—
93D244—41no—
94D244—41no—
95D244—82no—
96C4×D61—81no—
97C4×D61—81no—
98Dic122—41no—
99Dic122—41no—
100C8×C61—82no—
101#92418—81no—
102#10364—611nomaximal, Sylow
103C22×C61—22no—
104C22×C61#39311yescharacteristic
105C22×C61#44711yescharacteristic
106C22×C61#44811yescharacteristic
107C2×D61—81no—
108C2×D61—82no—
109C4×C61—24no—
110C4×C61—22no—
111C4×C61—22no—
112C4×C61—42no—
113C4×C61#47411yescharacteristic
114C4×C61#47611yescharacteristic
115C4×C61#48611yescharacteristic
116C4×C61#48911yescharacteristic
117Dic61—84no—
118Dic61—81no—
119#2859—611no—
120#1962—611no—
121#1517—612no—
122#1286—612no—
123#1276D6111yescharacteristic, complemented
124C2×C61—21no—
125C2×C61—21no—
126C2×C61#202311yescharacteristic
127C2×C61#203112yes—
128D61—161no—
129#532—611no—
130C2×#125—1221no—
131#431C2×D6112yes—
132#423—611no—
133C2×#104—1221no—
134C2×#104—1221no—
135#389—1224no—
136#384—1221no—
137#382—612no—
138C43C2×D6111yescharacteristic
139#327—1224no—
140C61#1036411yescharacteristic, complemented, Sylow
141C2×#41—1221no—
142C2×M16—1221no—
143C4⋊Q8—611no—
144#127—611no—
145#125—2442no—
146#125—2442no—
147#124—1221no—
148#121—1222no—
149C4×D4—1222no—
150C2×C4⋊C4—1224no—
151C2×C4⋊C4—1224no—
152C2×C4⋊C4—1222no—
153C2×C42—22no—
154C2×C42D24411yescharacteristic
155C2×C42D24411yescharacteristic
156C2×C42C22×D6111yescharacteristic
157C4⋊C8—22no—
158C4⋊C8—1222no—
159#104—2442no—
160#104—2442no—
161C22⋊C8—22no—
162C4×C8—22no—
163#95—614no—
164#95—1222no—
165#41—2441no—
166#41—2441no—
167#41—2441no—
168#41—2441no—
169C2×Q8—1221no—
170C2×D4—1222no—
171C2×D4—1221no—
172C2×D4—2441no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—1224no—
176C22×C4—2441no—
177C22×C4C2×D24411yescharacteristic
178C22×C4D4×D6112yes—
179M16—2441no—
180M16—2441no—
181C2×C8—42no—
182C2×C8—2441no—
183C4⋊C4—1222no—
184C4⋊C4—2448no—
185C4⋊C4—2448no—
186C4⋊C4—2442no—
187C4⋊C4—2442no—
188C22⋊C4—2442no—
189C42—21no—
190C42—21no—
191C42—44no—
192C42#1175819012yes—
193C42D48812yes—
194C42#1175822212yes—
195C42#1175822411yescharacteristic
196C42Q8×D6111yescharacteristic
197C23—2441no—
198C23#1451974711yescharacteristic
199Q8—2441no—
200Q8—2441no—
201D4—4882no—
202D4—4881no—
203D4—4881no—
204D4—2441no—
205D4—2441no—
206C2×C4—24no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—42no—
210C2×C4—42no—
211C2×C4—4881no—
212C2×C4—4881no—
213C2×C4—2448no—
214C2×C4—2444no—
215C2×C4—2441no—
216C2×C4#1451975512yes—
217C2×C4#1451975711yescharacteristic
218C2×C4#1451976312yes—
219C2×C4#1451976511yescharacteristic
220C2×C4C2×D48811yescharacteristic
221C2×C4C2×#1175819011yescharacteristic
222C2×C4#1451980511yescharacteristic
223C2×C4#1451981011yescharacteristic
224C8—82no—
225C8—4881no—
226C22—22no—
227C22—4881no—
228C22—4882no—
229C22#1683967511yescharacteristic
230C22#1683989811yescharacteristic
231C22#1683990311yescharacteristic
232C4—24no—
233C4—22no—
234C4—22no—
235C4—42no—
236C4—4884no—
237C4—4881no—
238C4#1684004311yescharacteristic
239C4#1684005311yescharacteristic
240C4#1684010911yescharacteristic
241C4#1684012211yescharacteristic
242C2—21no—
243C2—21no—
244C2—9761no—
245C2#2144695611yescharacteristic
246C2#2144699212yes—
subgroupG/H
centerC22#16839675
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1276C2
socleC22×C61#393
prime radical#16840312C22
hypercenter#1276D61
hypocenterC61#10364
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1276

Complements

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

NH ≅ G/Ntype
1. #21454182C2semidirect
4. #21443678C2semidirect
5. C61×#1276C2semidirect
123. #1276D61semidirect
140. C61#10364semidirect

Maximal subgroups

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

subgroupindex
#214541822
#214466472
#214443802
#214436782
C61×#12762
#1036461