Finite Group Databasebeta

← #29584783

Subgroups — #29584783

Order 15616.

330 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 93 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#21446651C211yesmaximal, characteristic
2#21445973C211yesmaximal, characteristic, complemented
3#21444466C212yesmaximal
4#21443715C212yesmaximal, complemented
5C61×#1274C211yesmaximal, characteristic, complemented
6#16840312C2211yescharacteristic
7#16839786C2211yescharacteristic
8C2×C4⋊#92418—21no—
9C2×C4⋊#92418—21no—
10C2×C4⋊#92418C2212yes—
11C2×#14519705—21no—
12C2×#14519705—21no—
13#16839507—22no—
14#16839505—22no—
15C61×#431C2212yes—
16C61×#376C2211yescharacteristic
17C2×#11758222—21no—
18C2×#11758194—21no—
19C22×#92418—22no—
20#14519777D411yescharacteristic
21#14519774D411yescharacteristic
22#14519765—21no—
23#14519751—22no—
24C4×D244—22no—
25C4⋊#92418—22no—
26C4⋊#92418—22no—
27C4⋊#92418—22no—
28C4⋊#92418—42no—
29C4⋊#92418—42no—
30#14519705—42no—
31#14519705—42no—
32C2×C42×C61D411yescharacteristic
33C2×C42×C61D411yescharacteristic
34C2×C42×C61C2311yescharacteristic
35C4⋊C8×C61—22no—
36C22⋊C8×C61—22no—
37C4×C8×C61—22no—
38#95×C61—22no—
39C22×C4×C61—21no—
40C22×C4×C61—21no—
41C22×C4×C61C2×D411yescharacteristic
42C22×C4×C61#4112yes—
43C2×C22⋊D61—41no—
44#11758222—41no—
45#11758222—41no—
46#11758222—41no—
47#11758222—41no—
48C2×D244—21no—
49C2×D244—22no—
50C2×C4×D61—41no—
51C2×Dic122—21no—
52C2×C8×C61—42no—
53C42×C61—21no—
54C42×C61—21no—
55C42×C61D812yes—
56C42×C61SD1612yes—
57C42×C61C2×D411yescharacteristic
58C42×C61#4111yescharacteristic
59C42×C61#4112yes—
60#11758198—42no—
61C4⋊Dic61—22no—
62#11758194—41no—
63#11758194—41no—
64C2×#92418—42no—
65C2×#92418—41no—
66C2×#92418—42no—
67C2×#92418—42no—
68C23×C61#12311yescharacteristic
69C22×D61—41no—
70C2×C4×C61—22no—
71C2×C4×C61—22no—
72C2×C4×C61—42no—
73C2×C4×C61—42no—
74C2×C4×C61—42no—
75C2×C4×C61#12111yescharacteristic
76C2×C4×C61#12312yes—
77C2×C4×C61#12411yescharacteristic
78C2×C4×C61#12612yes—
79C2×C4×C61C2×D811yescharacteristic
80C2×C4×C61C2×SD1611yescharacteristic
81C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
82C2×C4×C61#13711yescharacteristic
83C22⋊D61—81no—
84C22⋊D61—81no—
85C2×Dic61—41no—
86D244—41no—
87D244—41no—
88D244—82no—
89C4×D61—81no—
90C4×D61—81no—
91Dic122—41no—
92Dic122—41no—
93C8×C61—82no—
94#92418—82no—
95#92418—81no—
96#10627—611nomaximal, Sylow
97C22×C61—22no—
98C22×C61#39711yescharacteristic
99C22×C61#48011yescharacteristic
100C22×C61#48111yescharacteristic
101C2×D61—81no—
102C2×D61—82no—
103C4×C61—22no—
104C4×C61—22no—
105C4×C61—42no—
106C4×C61—42no—
107C4×C61#45911yescharacteristic
108C4×C61#46111yescharacteristic
109C4×C61#48611yescharacteristic
110C4×C61#48911yescharacteristic
111Dic61—81no—
112#1963—611no—
113#1843—611no—
114#1540—612no—
115#1301—612no—
116#1274D6111yescharacteristic, complemented
117C2×C61—21no—
118C2×C61—21no—
119C2×C61#207111yescharacteristic
120C2×C61#208012yes—
121D61—161no—
122#532—611no—
123#431C2×D6112yes—
124#423—611no—
125C2×C4⋊C8—612no—
126C2×C4⋊C8—1221no—
127C2×C4⋊C8—1221no—
128C2×#104—1221no—
129C2×#104—1221no—
130#376C2×D6111yescharacteristic
131#332—1222no—
132#331—1222no—
133C61#1062711yescharacteristic, complemented, Sylow
134C2×#41—1221no—
135C2×M16—1221no—
136C22×C8—1222no—
137C4⋊Q8—611no—
138#127—611no—
139#124—1221no—
140#121—1222no—
141C4×D4—1222no—
142C2×C42D24411yescharacteristic
143C2×C42D24411yescharacteristic
144C2×C42C22×D6111yescharacteristic
145C4⋊C8—22no—
146C4⋊C8—1222no—
147C4⋊C8—1222no—
148C4⋊C8—1222no—
149C4⋊C8—2442no—
150C4⋊C8—2442no—
151#104—2442no—
152#104—2442no—
153C22⋊C8—22no—
154C4×C8—22no—
155#95—22no—
156#41—2441no—
157#41—2441no—
158#41—2441no—
159#41—2441no—
160C2×Q8—1221no—
161C2×D4—1221no—
162C2×D4—1222no—
163C2×D4—2441no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—2441no—
167C22×C4C2×D24411yescharacteristic
168C22×C4#1175822412yes—
169M16—2441no—
170M16—2441no—
171C2×C8—42no—
172C2×C8—2442no—
173C2×C8—2441no—
174C2×C8—2442no—
175C2×C8—2442no—
176C4⋊C4—1222no—
177C22⋊C4—2442no—
178C42—21no—
179C42—21no—
180C42#1175819012yes—
181C42D48812yes—
182C42#1175822212yes—
183C42D4×D6111yescharacteristic
184C42#1175822611yescharacteristic
185C23—2441no—
186C23#1451976111yescharacteristic
187Q8—2441no—
188Q8—2441no—
189D4—4882no—
190D4—4881no—
191D4—4881no—
192D4—2441no—
193D4—2441no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—42no—
197C2×C4—42no—
198C2×C4—42no—
199C2×C4—4881no—
200C2×C4—4881no—
201C2×C4—2441no—
202C2×C4#1451975211yescharacteristic
203C2×C4#1451975912yes—
204C2×C4#1451976511yescharacteristic
205C2×C4#1451977212yes—
206C2×C4C2×D48811yescharacteristic
207C2×C4C2×#1175819011yescharacteristic
208C2×C4#1451980511yescharacteristic
209C2×C4#1451981011yescharacteristic
210C8—82no—
211C8—4882no—
212C8—4881no—
213C22—22no—
214C22—4881no—
215C22—4882no—
216C22#1683968911yescharacteristic
217C22#1684007611yescharacteristic
218C22#1684008111yescharacteristic
219C4—22no—
220C4—22no—
221C4—42no—
222C4—42no—
223C4—4881no—
224C4#1683995811yescharacteristic
225C4#1683996811yescharacteristic
226C4#1684010911yescharacteristic
227C4#1684012211yescharacteristic
228C2—21no—
229C2—21no—
230C2—9761no—
231C2#2144722411yescharacteristic
232C2#2144727112yes—
subgroupG/H
centerC2×C4#14519765
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1274C2
socleC22×C61#397
prime radical#16840312C22
hypercenter#1274D61
hypocenterC61#10627
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1274

Complements

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

NH ≅ G/Ntype
2. #21445973C2semidirect
4. #21443715C2semidirect
5. C61×#1274C2semidirect
116. #1274D61semidirect
133. C61#10627semidirect

Maximal subgroups

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

subgroupindex
#214466512
#214459732
#214444662
#214437152
C61×#12742
#1062761