Finite Group Databasebeta

← #29574423

Subgroups — #29574423

Order 15616.

336 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 103 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#21454925C211yesmaximal, characteristic
2#21446801C211yesmaximal, characteristic
3#21444586C212yesmaximal
4#21443713C212yesmaximal
5C61×#1526C211yesmaximal, characteristic
6#16839893—22no—
7#16839893—22no—
8#16839823—22no—
9#16839819C2212yes—
10#16839786C2211yescharacteristic
11#16839608C2211yescharacteristic
12#16839521—22no—
13#16839515—22no—
14#16839513—22no—
15C61×#533C2211yescharacteristic
16C4×M16×C61C2212yes—
17C61×#330C411yescharacteristic, complemented
18C61×#330C412yescomplemented
19C61×#330C411yescharacteristic, complemented
20C2×#11758194—21no—
21C2×C4×Dic61—21no—
22C4⋊#92418—22no—
23C4⋊#92418—22no—
24C4⋊#92418—22no—
25C4⋊#92418D412yes—
26C4⋊#92418D412yes—
27C22⋊#92418—22no—
28#14519688—22no—
29#14519688—22no—
30C4×#92418—22no—
31#14519684—22no—
32C2×M16×C61—22no—
33C4⋊Q8×C61Q812yes—
34#125×C61C2×C411yescharacteristic
35#125×C61C2×C411yescharacteristic
36C22⋊Q8×C61—22no—
37C4×Q8×C61—22no—
38#117×C61D412yes—
39C2×C42×C61C2311yescharacteristic
40#97×C61C2×C412yes—
41#97×C61C2×C412yes—
42C4×C8×C61—22no—
43C2×Q8×C61—22no—
44C22×C4×C61C2×D411yescharacteristic
45C22×C4×C61#4112yes—
46C22×Dic61—41no—
47M16×C61—44no—
48C2×C8×C61—22no—
49C2×C8×C61—22no—
50C4⋊C4×C61—22no—
51C4⋊C4×C61—22no—
52C4⋊C4×C61—22no—
53C4⋊C4×C61C4⋊C412yes—
54C4⋊C4×C61C4⋊C412yes—
55C22⋊C4×C61—22no—
56C42×C61—22no—
57C42×C61C22×C411yescharacteristic
58C42×C61C2×D412yes—
59C42×C61C2×Q811yescharacteristic
60C4×Dic61—22no—
61C4×Dic61—41no—
62#11758194—42no—
63C2×#92418—22no—
64C2×#92418—22no—
65C2×#92418—41no—
66C23×C61#12311yescharacteristic
67Q8×C61—82no—
68C2×C4×C61—21no—
69C2×C4×C61—21no—
70C2×C4×C61—22no—
71C2×C4×C61—22no—
72C2×C4×C61—42no—
73C2×C4×C61C2×C4⋊C411yescharacteristic
74C2×C4×C61C4×D412yes—
75C2×C4×C61#12011yescharacteristic
76C2×C4×C61C22⋊Q812yes—
77C2×Dic61—42no—
78C2×Dic61—82no—
79C8×C61—24no—
80C8×C61—42no—
81#92418—42no—
82#92418—42no—
83#92418—81no—
84#8919—611nomaximal, Sylow
85C22×C61—21no—
86C22×C61—22no—
87C22×C61#38511yescharacteristic
88C4×C61—21no—
89C4×C61—22no—
90C4×C61—22no—
91C4×C61—42no—
92C4×C61—42no—
93C4×C61#45411yescharacteristic
94C4×C61#45611yescharacteristic
95Dic61—82no—
96#2987—611no—
97#1995—611no—
98#1569—612no—
99#1526D6111yescharacteristic
100#1300—612no—
101C2×C61—41no—
102C2×C61#185711yescharacteristic
103C2×C61#186112yes—
104#533C2×D6111yescharacteristic
105#446—1222no—
106#446—1222no—
107#433—1222no—
108#432—612no—
109#423—611no—
110C4×M16C2×D6112yes—
111#376—611no—
112#339—1222no—
113#335—1222no—
114#334—1222no—
115#330Dic6111yescharacteristic, complemented
116#330Dic6112yescomplemented
117#330Dic6111yescharacteristic, complemented
118C61#891911yescharacteristic, complemented, Sylow
119C2×M16—22no—
120C2×M16—1221no—
121C4⋊Q8Dic12212yes—
122#125C2×Dic6111yescharacteristic
123#125C2×Dic6111yescharacteristic
124C22⋊Q8—22no—
125C4×Q8—22no—
126#117D24412yes—
127C2×C42—1221no—
128C2×C42C22×D6111yescharacteristic
129C4⋊C8—612no—
130C4⋊C8—612no—
131C4⋊C8—1222no—
132C4⋊C8—1222no—
133C4⋊C8—1222no—
134C22⋊C8—1222no—
135#97—1222no—
136#97—1222no—
137#97C2×Dic6112yes—
138#97C2×Dic6112yes—
139C4×C8—22no—
140C4×C8—1222no—
141#95—1222no—
142C2×Q8—22no—
143C22×C4—2441no—
144C22×C4C2×D24411yescharacteristic
145C22×C4#1175822412yes—
146M16—44no—
147M16—2442no—
148C2×C8—22no—
149C2×C8—22no—
150C2×C8—1222no—
151C2×C8—1222no—
152C2×C8—2441no—
153C4⋊C4—22no—
154C4⋊C4—22no—
155C4⋊C4—22no—
156C4⋊C4C4⋊Dic6112yes—
157C4⋊C4C4⋊Dic6112yes—
158C22⋊C4—22no—
159C42—22no—
160C42—1222no—
161C42—2441no—
162C42C2×Dic12211yescharacteristic
163C42D4×D6112yes—
164C42C22×Dic6111yescharacteristic
165C23#1451976111yescharacteristic
166Q8—82no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—42no—
172C2×C4—4882no—
173C2×C4—2442no—
174C2×C4C2×C4⋊Dic6111yescharacteristic
175C2×C4D4×Dic6112yes—
176C2×C4#1451974711yescharacteristic
177C2×C4#1451975412yes—
178C8—24no—
179C8—42no—
180C8—4881no—
181C8—2442no—
182C8—2442no—
183C22—21no—
184C22—22no—
185C22#1683963711yescharacteristic
186C4—21no—
187C4—22no—
188C4—22no—
189C4—42no—
190C4—42no—
191C4—4882no—
192C4#1683993711yescharacteristic
193C4#1683994711yescharacteristic
194C2—41no—
195C2#2144603611yescharacteristic
196C2#2144606112yes—
subgroupG/H
centerC2×C4#14519747
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1526C2
socleC22×C61#385
prime radicalC23×C61#123
cosocleC2×C42×C61C23
hypercenter#1526D61
hypocenterC61#8919
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1526

Complements

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

NH ≅ G/Ntype
17. C61×#330C4semidirect
18. C61×#330C4semidirect
19. C61×#330C4semidirect
115. #330Dic61semidirect
116. #330Dic61semidirect
117. #330Dic61semidirect
118. C61#8919semidirect

Maximal subgroups

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

subgroupindex
#214549252
#214468012
#214445862
#214437132
C61×#15262
#891961