Finite Group Databasebeta

← #29574420

Subgroups — #29574420

Order 15616.

336 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 95 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#21444584C212yesmaximal
3#21444414C211yesmaximal, characteristic
4#21443712C212yesmaximal
5C61×#1995C211yesmaximal, characteristic
6#16839893—22no—
7#16839893—22no—
8#16839823—22no—
9#16839819C2212yes—
10C4×#11758194C2212yes—
11#16839514—22no—
12#16839512—22no—
13#16839504C411yescharacteristic, complemented
14#16839504C412yescomplemented
15#16839504C411yescharacteristic, complemented
16C61×#533C2211yescharacteristic
17C61×#423C2211yescharacteristic
18C61×#376C2211yescharacteristic
19C61×#339—22no—
20C2×#11758194—22no—
21C4⋊#92418—22no—
22C4⋊#92418—22no—
23C4⋊#92418D412yes—
24C4⋊#92418D412yes—
25C22⋊#92418—22no—
26#14519688—22no—
27#14519688—22no—
28#14519688C2×C412yes—
29#14519688C2×C412yes—
30C4×#92418—22no—
31C4×#92418—22no—
32C2×M16×C61—21no—
33C4⋊Q8×C61Q812yes—
34#125×C61C2×C411yescharacteristic
35#125×C61C2×C411yescharacteristic
36C22⋊Q8×C61—22no—
37C4×Q8×C61—22no—
38#117×C61D412yes—
39C2×C42×C61—21no—
40C2×C42×C61C2311yescharacteristic
41C4⋊C8×C61—22no—
42#95×C61—22no—
43C2×Q8×C61—22no—
44C22×C4×C61—41no—
45C22×C4×C61C2×D411yescharacteristic
46C22×C4×C61#4112yes—
47M16×C61—42no—
48C2×C8×C61—41no—
49C4⋊C4×C61—22no—
50C4⋊C4×C61—22no—
51C4⋊C4×C61—22no—
52C4⋊C4×C61C4⋊C412yes—
53C4⋊C4×C61C4⋊C412yes—
54C22⋊C4×C61—22no—
55C42×C61—22no—
56C42×C61—22no—
57C42×C61—41no—
58C42×C61C22×C411yescharacteristic
59C42×C61C2×D412yes—
60C42×C61C2×Q811yescharacteristic
61#11758194—44no—
62C2×#92418—22no—
63C2×#92418—22no—
64C2×#92418—22no—
65C2×#92418—22no—
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×C61—42no—
74C2×C4×C61—82no—
75C2×C4×C61C2×C4⋊C411yescharacteristic
76C2×C4×C61C4×D412yes—
77C2×C4×C61#12011yescharacteristic
78C2×C4×C61C22⋊Q812yes—
79C8×C61—81no—
80#92418—24no—
81#92418—42no—
82#92418—42no—
83#92418—42no—
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—82no—
94C4×C61#45411yescharacteristic
95C4×C61#45611yescharacteristic
96#2987—611no—
97#1995D6111yescharacteristic
98#1569—612no—
99#1526—611no—
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#423C2×D6111yescharacteristic
110C4×M16—612no—
111#376C2×D6111yescharacteristic
112#339—22no—
113#335—1222no—
114#334—1222no—
115#330—611no—
116#330—612no—
117#330—611no—
118C61#891911yescharacteristic, complemented, Sylow
119C2×M16—21no—
120C2×M16—1222no—
121C4⋊Q8Dic12212yes—
122#125C4×D6111yescharacteristic
123#125C4×D6111yescharacteristic
124C22⋊Q8—22no—
125C4×Q8—22no—
126#117C22⋊D6112yes—
127C2×C42—21no—
128C2×C42C22×D6111yescharacteristic
129C4⋊C8—22no—
130C4⋊C8—612no—
131C4⋊C8—612no—
132C4⋊C8—1222no—
133C4⋊C8—1222no—
134C22⋊C8—1222no—
135#97—612no—
136#97—612no—
137#97—1222no—
138#97—1222no—
139C4×C8—1222no—
140C4×C8—1222no—
141#95—22no—
142C2×Q8—22no—
143C22×C4—41no—
144C22×C4#1175822412yes—
145C22×C4C2×C22⋊D6111yescharacteristic
146M16—42no—
147M16—2444no—
148C2×C8—41no—
149C2×C8—1222no—
150C2×C8—1222no—
151C2×C8—1222no—
152C2×C8—1222no—
153C4⋊C4—22no—
154C4⋊C4—22no—
155C4⋊C4—22no—
156C4⋊C4#1175819612yes—
157C4⋊C4#1175819612yes—
158C22⋊C4—22no—
159C42—22no—
160C42—22no—
161C42—41no—
162C42C2×Dic12211yescharacteristic
163C42C2×C4×D6111yescharacteristic
164C42D4×D6112yes—
165C23#1451975811yescharacteristic
166Q8—82no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—42no—
172C2×C4—42no—
173C2×C4—82no—
174C2×C4C2×#1175819611yescharacteristic
175C2×C4#1451973712yes—
176C2×C4#1451974511yescharacteristic
177C2×C4#1451975412yes—
178C8—81no—
179C8—1224no—
180C8—2442no—
181C8—2442no—
182C8—2442no—
183C22—21no—
184C22—22no—
185C22#1683963411yescharacteristic
186C4—21no—
187C4—22no—
188C4—22no—
189C4—42no—
190C4—42no—
191C4—82no—
192C4#1683993411yescharacteristic
193C4#1683994411yescharacteristic
194C2—41no—
195C2#2144603311yescharacteristic
196C2#2144605712yes—
subgroupG/H
centerC2×C4#14519745
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1995C2
socleC22×C61#385
prime radicalC23×C61#123
cosocleC2×C42×C61C23
hypercenter#1995D61
hypocenterC61#8919
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1995

Complements

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

NH ≅ G/Ntype
13. #16839504C4semidirect
14. #16839504C4semidirect
15. #16839504C4semidirect
118. C61#8919semidirect

Maximal subgroups

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

subgroupindex
#214549252
#214445842
#214444142
#214437122
C61×#19952
#891961