Finite Group Databasebeta

← #29583148

Subgroups — #29583148

Order 15616.

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

normal subgroups only

This group has 402 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#21444313C212yesmaximal
3#21443722C212yesmaximal, complemented
4#21443648C211yesmaximal, characteristic, complemented
5C61×#2402C211yesmaximal, characteristic, complemented
6#16840312C2211yescharacteristic
7#16839815C2212yes—
8#16839786C2211yescharacteristic
9C2×#14519705—22no—
10#16839495—22no—
11#16839495—22no—
12C61×#400—22no—
13C61×#398—22no—
14C4×C4⋊C4×C61—22no—
15C4×C4⋊C4×C61C2212yes—
16C61×#376C2211yescharacteristic
17C2×#11758222—21no—
18C2×#11758194—21no—
19#14519777Q811yescharacteristic
20#14519774Q811yescharacteristic
21#14519765—21no—
22#14519751—22no—
23C4×D244—22no—
24C4⋊#92418—22no—
25C4⋊#92418—22no—
26#14519705—44no—
27C22⋊#92418—22no—
28C4×#92418—22no—
29C2×C4⋊C4×C61—22no—
30C2×C4⋊C4×C61—22no—
31C2×C4⋊C4×C61—22no—
32C2×C42×C61—22no—
33C2×C42×C61D412yes—
34C2×C42×C61C2311yescharacteristic
35#95×C61—22no—
36#95×C61—22no—
37#95×C61—22no—
38#95×C61D412yes—
39#95×C61D412yes—
40C22×C4×C61—22no—
41C22×C4×C61—22no—
42C22×C4×C61—22no—
43C22×C4×C61C2×D412yes—
44C22×C4×C61C2×D411yescharacteristic
45C2×C22⋊D61—41no—
46#11758222—42no—
47#11758222—42no—
48C2×D244—21no—
49C2×D244—22no—
50C2×C4×D61—41no—
51C2×Dic122—21no—
52C4⋊C4×C61—44no—
53C4⋊C4×C61—44no—
54C4⋊C4×C61—44no—
55C42×C61—22no—
56C42×C61—22no—
57C42×C61—42no—
58C42×C61—42no—
59C42×C61C2×Q811yescharacteristic
60C42×C61#4112yes—
61C42×C61#4111yescharacteristic
62#11758198—42no—
63C4⋊Dic61—22no—
64#11758194—42no—
65C2×#92418—42no—
66C2×#92418—41no—
67C23×C61#12011yescharacteristic
68C22×D61—41no—
69C2×C4×C61—24no—
70C2×C4×C61—42no—
71C2×C4×C61—42no—
72C2×C4×C61—42no—
73C2×C4×C61—42no—
74C2×C4×C61—42no—
75C2×C4×C61—42no—
76C2×C4×C61—42no—
77C2×C4×C61—42no—
78C2×C4×C61—42no—
79C2×C4×C61C22⋊Q812yes—
80C2×C4×C61C22⋊Q811yescharacteristic
81C2×C4×C61#12412yes—
82C2×C4×C61#12411yescharacteristic
83C2×C4×C61#13512yes—
84C2×C4×C61AGL(1,ℤ/8)12yes—
85C22⋊D61—82no—
86C2×Dic61—41no—
87D244—42no—
88D244—82no—
89C4×D61—81no—
90C4×D61—81no—
91Dic122—42no—
92#92418—82no—
93#92418—81no—
94#10372—611nomaximal, Sylow
95C22×C61—22no—
96C22×C61#39311yescharacteristic
97C22×C61#44912yes—
98C2×D61—81no—
99C2×D61—82no—
100C4×C61—22no—
101C4×C61—22no—
102C4×C61—44no—
103C4×C61—82no—
104C4×C61—82no—
105C4×C61#47812yes—
106C4×C61#48811yescharacteristic
107C4×C61#49011yescharacteristic
108Dic61—81no—
109#2402D6111yescharacteristic, complemented
110#1963—611no—
111#1502—612no—
112#1303—612no—
113#1274—611no—
114C2×C61—22no—
115C2×C61#202511yescharacteristic
116C2×C61#203112yes—
117D61—161no—
118#532—611no—
119#431—612no—
120#423—611no—
121C2×#104—1222no—
122#400—22no—
123#398—22no—
124C4×C4⋊C4—22no—
125C4×C4⋊C4C2×D6112yes—
126#376C2×D6111yescharacteristic
127#327—1222no—
128#327—1222no—
129C61#1037211yescharacteristic, complemented, Sylow
130C2×#41—1221no—
131C2×M16—1221no—
132C4⋊Q8—611no—
133#127—611no—
134#124—1221no—
135#121—1222no—
136C4×D4—1222no—
137C2×C4⋊C4—22no—
138C2×C4⋊C4—22no—
139C2×C4⋊C4—22no—
140C2×C42—22no—
141C2×C42C22⋊D6112yes—
142C2×C42C22×D6111yescharacteristic
143C4⋊C8—1222no—
144C4⋊C8—1222no—
145#104—2444no—
146C22⋊C8—1222no—
147C4×C8—1222no—
148#95—22no—
149#95—22no—
150#95—22no—
151#95C22⋊D6112yes—
152#95C22⋊D6112yes—
153#41—2442no—
154#41—2442no—
155C2×Q8—1221no—
156C2×D4—1222no—
157C2×D4—1221no—
158C2×D4—2441no—
159C22×C4—22no—
160C22×C4—22no—
161C22×C4—22no—
162C22×C4—2441no—
163C22×C4C2×C22⋊D6112yes—
164C22×C4C2×C22⋊D6111yescharacteristic
165M16—2442no—
166C2×C8—2442no—
167C2×C8—2441no—
168C4⋊C4—44no—
169C4⋊C4—44no—
170C4⋊C4—44no—
171C4⋊C4—1222no—
172C22⋊C4—2442no—
173C42—22no—
174C42—22no—
175C42—42no—
176C42—42no—
177C42Q8×D6111yescharacteristic
178C42#1175822611yescharacteristic
179C42#1175822612yes—
180C23—2441no—
181C23#1451974611yescharacteristic
182Q8—2442no—
183D4—4882no—
184D4—4882no—
185D4—2442no—
186C2×C4—24no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—42no—
190C2×C4—42no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4—42no—
196C2×C4—4881no—
197C2×C4—4881no—
198C2×C4—2441no—
199C2×C4#1451975312yes—
200C2×C4#1451975311yescharacteristic
201C2×C4#1451976612yes—
202C2×C4#1451976611yescharacteristic
203C2×C4#1451979712yes—
204C2×C4#1451980212yes—
205C8—4882no—
206C8—4881no—
207C22—22no—
208C22—4881no—
209C22—4882no—
210C22#1683967311yescharacteristic
211C22#1683990712yes—
212C4—22no—
213C4—22no—
214C4—44no—
215C4—82no—
216C4—82no—
217C4—4881no—
218C4#1684005912yes—
219C4#1684011911yescharacteristic
220C4#1684012811yescharacteristic
221C2—22no—
222C2—9761no—
223C2#2144696211yescharacteristic
224C2#2144698812yes—
subgroupG/H
centerC2×C4#14519766
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#2402C2
socleC22×C61#393
prime radical#16840312C22
hypercenter#2402D61
hypocenterC61#10372
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2402

Complements

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

NH ≅ G/Ntype
3. #21443722C2semidirect
4. #21443648C2semidirect
5. C61×#2402C2semidirect
109. #2402D61semidirect
129. C61#10372semidirect

Maximal subgroups

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

subgroupindex
#214466512
#214443132
#214437222
#214436482
C61×#24022
#1037261