Finite Group Databasebeta

← #29584206

Subgroups — #29584206

Order 15616.

358 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 85 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#21445990C211yesmaximal, characteristic
2#21444557C212yesmaximal
3#21444274C212yesmaximal
4#21443732C211yesmaximal, characteristic
5C61×#3255C211yesmaximal, characteristic
6C2×#14519712—22no—
7#16839786C2211yescharacteristic
8#16839786C2212yes—
9C2×C4×#92418C2211yescharacteristic
10#16839508—22no—
11#16839508—22no—
12Q8⋊#92418—24no—
13C61×#533C2212yes—
14C61×#475—22no—
15C61×#470—22no—
16C61×#462—22no—
17C61×#423C2211yescharacteristic
18C2×#11758194—21no—
19C2×#11758194—22no—
20C22×#92418—21no—
21#14519712—44no—
22C4⋊#92418—22no—
23C4⋊#92418—22no—
24C4⋊#92418—22no—
25C4×#92418—21no—
26C4×#92418D412yes—
27C2×Q16×C61—22no—
28C2×M16×C61D412yes—
29C4⋊Q8×C61D412yes—
30C4⋊Q8×C61D412yes—
31#125×C61—22no—
32C22⋊Q8×C61—22no—
33C22⋊Q8×C61—22no—
34C4×Q8×C61—22no—
35C4×Q8×C61—22no—
36#117×C61—22no—
37C2×C42×C61C2311yescharacteristic
38#106×C61—22no—
39C4⋊C8×C61—22no—
40#103×C61—24no—
41C2×Q8×C61—22no—
42C2×Q8×C61—22no—
43C22×C4×C61C2×D411yescharacteristic
44C22×C4×C61#4112yes—
45Q16×C61—82no—
46M16×C61—42no—
47C2×C8×C61—22no—
48C4⋊C4×C61—22no—
49C4⋊C4×C61—22no—
50C4⋊C4×C61—22no—
51C4⋊C4×C61—22no—
52C4⋊C4×C61—42no—
53C4⋊C4×C61—42no—
54C22⋊C4×C61—42no—
55C42×C61—42no—
56C42×C61C2×D412yes—
57C42×C61C2×D411yescharacteristic
58C42×C61#4111yescharacteristic
59#11758194—42no—
60#11758194—82no—
61C2×#92418—22no—
62C2×#92418—22no—
63C2×#92418—22no—
64C2×#92418—41no—
65C2×#92418—42no—
66C23×C61#12411yescharacteristic
67Q8×C61—42no—
68Q8×C61—42no—
69Q8×C61—42no—
70Q8×C61—42no—
71C2×C4×C61—21no—
72C2×C4×C61—21no—
73C2×C4×C61—22no—
74C2×C4×C61—22no—
75C2×C4×C61—42no—
76C2×C4×C61—42no—
77C2×C4×C61#12011yescharacteristic
78C2×C4×C61#12111yescharacteristic
79C2×C4×C61#12112yes—
80C2×C4×C61#12312yes—
81C8×C61—42no—
82#92418—24no—
83#92418—81no—
84#92418—82no—
85#10534—611nomaximal, Sylow
86C22×C61—22no—
87C22×C61—21no—
88C22×C61#39411yescharacteristic
89C4×C61—22no—
90C4×C61—21no—
91C4×C61—82no—
92C4×C61—82no—
93C4×C61#45311yescharacteristic
94C4×C61#45611yescharacteristic
95C4×C61#47112yes—
96C4×C61#47312yes—
97#3255D6111yescharacteristic
98#1848—611no—
99#1561—612no—
100#1493—612no—
101#1309—611no—
102C2×C61—41no—
103C2×C61#203911yescharacteristic
104C2×C61#205212yes—
105#533C2×D6112yes—
106#475—22no—
107#470—22no—
108#462—22no—
109C2×#108—1222no—
110#423—611no—
111#423—612no—
112#423C2×D6111yescharacteristic
113C2×C4×C8—611no—
114#332—1222no—
115#332—1222no—
116Q8⋊C8—1224no—
117C61#1053411yescharacteristic, complemented, Sylow
118C2×Q16—22no—
119C2×M16—1222no—
120C2×M16—1221no—
121C2×M16C22⋊D6112yes—
122C22×C8—1221no—
123C4⋊Q8C22⋊D6112yes—
124C4⋊Q8C22⋊D6112yes—
125#125—22no—
126C22⋊Q8—22no—
127C22⋊Q8—22no—
128C4×Q8—22no—
129C4×Q8—22no—
130#117—22no—
131C2×C42C22×D6111yescharacteristic
132#108—2444no—
133#106—22no—
134C4⋊C8—22no—
135C4⋊C8—1222no—
136C4⋊C8—1222no—
137C4⋊C8—1222no—
138#103—24no—
139C4×C8—612no—
140C4×C8—1221no—
141C2×Q8—22no—
142C2×Q8—22no—
143C22×C4#1175822412yes—
144C22×C4C2×C22⋊D6111yescharacteristic
145Q16—82no—
146M16—42no—
147M16—4882no—
148M16—2442no—
149C2×C8—22no—
150C2×C8—1222no—
151C2×C8—1222no—
152C2×C8—1222no—
153C2×C8—2441no—
154C2×C8—2442no—
155C4⋊C4—22no—
156C4⋊C4—22no—
157C4⋊C4—22no—
158C4⋊C4—22no—
159C4⋊C4—42no—
160C4⋊C4—42no—
161C22⋊C4—42no—
162C42—42no—
163C42D4×D6111yescharacteristic
164C42#1175822411yescharacteristic
165C42C2×C22⋊D6112yes—
166C23#1451976411yescharacteristic
167Q8—42no—
168Q8—42no—
169Q8—42no—
170Q8—42no—
171C2×C4—21no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—21no—
175C2×C4—42no—
176C2×C4—42no—
177C2×C4#1451974611yescharacteristic
178C2×C4#1451974811yescharacteristic
179C2×C4#1451974912yes—
180C2×C4#1451975812yes—
181C8—42no—
182C8—1224no—
183C8—4882no—
184C8—4881no—
185C22—21no—
186C22—22no—
187C22#1683967611yescharacteristic
188C4—21no—
189C4—22no—
190C4—82no—
191C4—82no—
192C4#1683993011yescharacteristic
193C4#1683994511yescharacteristic
194C4#1684002712yes—
195C4#1684003512yes—
196C2—41no—
197C2#2144704011yescharacteristic
198C2#2144711512yes—
subgroupG/H
centerC22#16839676
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#3255C2
socleC22×C61#394
prime radicalC23×C61#124
hypercenter#3255D61
hypocenterC61#10534
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3255

Complements

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

NH ≅ G/Ntype
117. C61#10534semidirect

Maximal subgroups

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

subgroupindex
#214459902
#214445572
#214442742
#214437322
C61×#32552
#1053461