Finite Group Databasebeta

← #29584088

Subgroups — #29584088

Order 15616.

388 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 79 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#21457129C211yesmaximal, characteristic
2#21444512C212yesmaximal, complemented
3#21444326C212yesmaximal, complemented
4#21443689C211yesmaximal, characteristic, complemented
5C61×#1832C211yesmaximal, characteristic, complemented
6#16840312C2212yes—
7#16840043—22no—
8#16839998—22no—
9#16839958—22no—
10#16839819C2212yes—
11#16839510—22no—
12#16839505—22no—
13#16839495—24no—
14C2×C4⋊C8×C61C2211yescharacteristic
15C2×C4⋊C8×C61C2211yescharacteristic
16C61×#376C2211yescharacteristic
17C61×#336—22no—
18C2×#11758222—22no—
19C2×D488—22no—
20#14519777D412yes—
21#14519774D412yes—
22#14519765—22no—
23#14519751—22no—
24#14519751—22no—
25C4×D244—22no—
26C4×D244—22no—
27#14519711—22no—
28C4⋊#92418—22no—
29#14519699—24no—
30C22⋊#92418—22no—
31#14519688—22no—
32C22×C8×C61—21no—
33C22×C8×C61D412yes—
34C2×C42×C61—21no—
35C2×C42×C61C2311yescharacteristic
36C4⋊C8×C61—22no—
37C4⋊C8×C61—22no—
38#95×C61—21no—
39#95×C61D412yes—
40C22×C4×C61—22no—
41C22×C4×C61C2×D411yescharacteristic
42C22×C4×C61C2×D411yescharacteristic
43C22×C4×C61#4111yescharacteristic
44C2×C22⋊D61—42no—
45#11758222—84no—
46C2×D244—22no—
47C2×D244—22no—
48C2×D244—22no—
49C2×C4×D61—42no—
50C2×Dic122—22no—
51C2×C8×C61—22no—
52C2×C8×C61—42no—
53C2×C8×C61—42no—
54C2×C8×C61—41no—
55C42×C61—41no—
56C42×C61—41no—
57C42×C61C2×D412yes—
58C42×C61#4112yes—
59#11758198—42no—
60#11758198—42no—
61C4⋊Dic61—22no—
62C4⋊Dic61—22no—
63C2×#92418—42no—
64D488—82no—
65C23×C61#12111yescharacteristic
66C22×D61—42no—
67C2×C4×C61—22no—
68C2×C4×C61—21no—
69C2×C4×C61—21no—
70C2×C4×C61—41no—
71C2×C4×C61—42no—
72C2×C4×C61—42no—
73C2×C4×C61—42no—
74C2×C4×C61#12011yescharacteristic
75C2×C4×C61#12112yes—
76C2×C4×C61#12312yes—
77C2×C4×C61#12411yescharacteristic
78C22⋊D61—84no—
79C2×Dic61—42no—
80D244—42no—
81D244—42no—
82D244—82no—
83D244—82no—
84C4×D61—84no—
85Dic122—82no—
86C8×C61—42no—
87C8×C61—81no—
88#92418—82no—
89#10513—611nomaximal, Sylow
90C22×C61—21no—
91C22×C61—21no—
92C22×C61#39411yescharacteristic
93C22×C61#47212yes—
94C2×D61—82no—
95C2×D61—82no—
96C2×D61—82no—
97C4×C61—22no—
98C4×C61—21no—
99C4×C61—22no—
100C4×C61—82no—
101C4×C61#45411yescharacteristic
102C4×C61#45511yescharacteristic
103Dic61—82no—
104#3245—611no—
105#1832D6111yescharacteristic, complemented
106#1551—612no—
107#1505—612no—
108#1290—611no—
109C2×C61—22no—
110C2×C61#204011yescharacteristic
111C2×C61#204511yescharacteristic
112C2×C61#205311yescharacteristic
113D61—162no—
114#532—612no—
115#474—1222no—
116#466—1222no—
117#459—1222no—
118#432—612no—
119C2×C4⋊C8C2×D6111yescharacteristic
120C2×C4⋊C8C2×D6111yescharacteristic
121#376C2×D6111yescharacteristic
122#336—22no—
123#333—1222no—
124#331—1222no—
125#327—1224no—
126C61#1051311yescharacteristic, complemented, Sylow
127C2×#41—1222no—
128C2×D8—1222no—
129C22×C8—21no—
130C22×C8C22⋊D6112yes—
131C4⋊Q8—612no—
132#127—612no—
133#124—1222no—
134#121—1222no—
135#121—1222no—
136C4×D4—1222no—
137C4×D4—1222no—
138C2×C42—21no—
139C2×C42C22×D6111yescharacteristic
140#107—1222no—
141C4⋊C8—22no—
142C4⋊C8—22no—
143C4⋊C8—1222no—
144#102—1224no—
145C22⋊C8—1222no—
146#97—1222no—
147#95—21no—
148#95D24412yes—
149#41—4884no—
150C2×Q8—1222no—
151C2×D4—1222no—
152C2×D4—1222no—
153C2×D4—1222no—
154C2×D4—2442no—
155C22×C4—22no—
156C22×C4—2442no—
157C22×C4C2×D24411yescharacteristic
158C22×C4#1175822211yescharacteristic
159C22×C4C2×C22⋊D6111yescharacteristic
160D8—4882no—
161C2×C8—22no—
162C2×C8—42no—
163C2×C8—42no—
164C2×C8—41no—
165C2×C8—2442no—
166C4⋊C4—1222no—
167C4⋊C4—1222no—
168C22⋊C4—2442no—
169C22⋊C4—2442no—
170C42—41no—
171C42—41no—
172C42D4×D6112yes—
173C42#1175822612yes—
174C23—2442no—
175C23#1451975111yescharacteristic
176Q8—4882no—
177D4—4882no—
178D4—4882no—
179D4—4884no—
180D4—2442no—
181D4—2442no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—41no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—4884no—
190C2×C4—2442no—
191C2×C4#1451974511yescharacteristic
192C2×C4#1451975212yes—
193C2×C4#1451976212yes—
194C2×C4#1451976611yescharacteristic
195C8—42no—
196C8—81no—
197C8—4882no—
198C22—21no—
199C22—21no—
200C22—4882no—
201C22—4882no—
202C22—4882no—
203C22#1683967911yescharacteristic
204C22#1684003212yes—
205C4—21no—
206C4—22no—
207C4—22no—
208C4—82no—
209C4—4882no—
210C4#1683993411yescharacteristic
211C4#1683993911yescharacteristic
212C2—22no—
213C2—9762no—
214C2#2144704811yescharacteristic
215C2#2144707511yescharacteristic
216C2#2144712511yescharacteristic
subgroupG/H
centerC22#16839679
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1832C2
socleC22×C61#394
prime radical#21457129C2
hypercenter#1832D61
hypocenterC61#10513
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1832

Complements

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

NH ≅ G/Ntype
2. #21444512C2semidirect
3. #21444326C2semidirect
4. #21443689C2semidirect
5. C61×#1832C2semidirect
105. #1832D61semidirect
126. C61#10513semidirect

Maximal subgroups

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

subgroupindex
#214571292
#214445122
#214443262
#214436892
C61×#18322
#1051361