Finite Group Databasebeta

← #29584210

Subgroups — #29584210

Order 15616.

358 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 81 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#21457213C211yesmaximal, characteristic
2#21445990C211yesmaximal, characteristic
3#21444556C212yesmaximal
4#21444273C212yesmaximal
5C61×#1309C211yesmaximal, characteristic
6#16840319C2212yes—
7#16840048—22no—
8#16840020—22no—
9#16839973—22no—
10C2×#14519712—22no—
11#16839786C2211yescharacteristic
12C2×C4×#92418C2211yescharacteristic
13#16839509—22no—
14#16839507—22no—
15#16839492—24no—
16C61×#423C2212yes—
17C61×#423C2211yescharacteristic
18C2×Dic244—22no—
19C2×#11758194—21no—
20C22×#92418—21no—
21#14519777D412yes—
22#14519777D412yes—
23#14519769—22no—
24#14519756—22no—
25#14519756—22no—
26C4×Dic122—22no—
27C4×Dic122—22no—
28#14519736—22no—
29#14519712—44no—
30#14519709—22no—
31C4⋊#92418—22no—
32#14519702—24no—
33C4×#92418—21no—
34C4×#92418D412yes—
35C2×M16×C61—22no—
36C2×M16×C61D412yes—
37C2×C42×C61C2311yescharacteristic
38C4⋊C8×C61—22no—
39C4⋊C8×C61—22no—
40C4⋊C8×C61—22no—
41C22×C4×C61C2×D411yescharacteristic
42C22×C4×C61#4112yes—
43C2×Dic122—22no—
44C2×Dic122—22no—
45M16×C61—42no—
46M16×C61—82no—
47C2×C8×C61—22no—
48C2×C8×C61—42no—
49C42×C61C2×D412yes—
50C42×C61C2×D411yescharacteristic
51C42×C61#4111yescharacteristic
52C22⋊Dic61—42no—
53C4⋊Dic61—22no—
54C4⋊Dic61—22no—
55C4⋊Dic61—22no—
56C4⋊Dic61—22no—
57#11758196—42no—
58#11758196—42no—
59C4×Dic61—42no—
60#11758194—42no—
61C2×#92418—22no—
62C2×#92418—22no—
63C2×#92418—22no—
64C2×#92418—41no—
65Dic244—82no—
66C23×C61#12411yescharacteristic
67C2×C4×C61—21no—
68C2×C4×C61—21no—
69C2×C4×C61—22no—
70C2×C4×C61—22no—
71C2×C4×C61#12011yescharacteristic
72C2×C4×C61#12111yescharacteristic
73C2×C4×C61#12112yes—
74C2×C4×C61#12312yes—
75C2×Dic61—42no—
76C2×Dic61—42no—
77Dic122—42no—
78Dic122—42no—
79Dic122—42no—
80Dic122—42no—
81C8×C61—42no—
82C8×C61—82no—
83#92418—24no—
84#92418—81no—
85#10534—611nomaximal, Sylow
86C22×C61—22no—
87C22×C61—21no—
88C22×C61#39411yescharacteristic
89C4×C61—22no—
90C4×C61—21no—
91C4×C61#45311yescharacteristic
92C4×C61#45611yescharacteristic
93C4×C61#47112yes—
94C4×C61#47312yes—
95Dic61—82no—
96Dic61—82no—
97#3255—611no—
98#1848—611no—
99#1561—612no—
100#1493—612no—
101#1309D6111yescharacteristic
102C2×C61—41no—
103C2×C61#203911yescharacteristic
104C2×C61#205212yes—
105#533—612no—
106#475—1222no—
107#470—1222no—
108#462—1222no—
109C2×#108—1222no—
110#423—611no—
111#423C2×D6112yes—
112#423C2×D6111yescharacteristic
113C2×C4×C8—611no—
114#332—1222no—
115#332—1222no—
116Q8⋊C8—1224no—
117C61#1053411yescharacteristic, complemented, Sylow
118C2×Q16—1222no—
119C2×M16—22no—
120C2×M16—1221no—
121C2×M16D24412yes—
122C22×C8—1221no—
123C4⋊Q8—612no—
124C4⋊Q8—612no—
125#125—1222no—
126C22⋊Q8—1222no—
127C22⋊Q8—1222no—
128C4×Q8—1222no—
129C4×Q8—1222no—
130#117—1222no—
131C2×C42C22×D6111yescharacteristic
132#108—2444no—
133#106—1222no—
134C4⋊C8—22no—
135C4⋊C8—22no—
136C4⋊C8—22no—
137C4⋊C8—1222no—
138#103—1224no—
139C4×C8—612no—
140C4×C8—1221no—
141C2×Q8—1222no—
142C2×Q8—1222no—
143C22×C4C2×D24411yescharacteristic
144C22×C4#1175822212yes—
145Q16—4882no—
146M16—42no—
147M16—82no—
148M16—2442no—
149C2×C8—22no—
150C2×C8—42no—
151C2×C8—1222no—
152C2×C8—1222no—
153C2×C8—1222no—
154C2×C8—2441no—
155C4⋊C4—1222no—
156C4⋊C4—1222no—
157C4⋊C4—1222no—
158C4⋊C4—1222no—
159C4⋊C4—2442no—
160C4⋊C4—2442no—
161C22⋊C4—2442no—
162C42—2442no—
163C42D4×D6112yes—
164C42D4×D6111yescharacteristic
165C42#1175822611yescharacteristic
166C23#1451976511yescharacteristic
167Q8—2442no—
168Q8—2442no—
169Q8—2442no—
170Q8—2442no—
171C2×C4—21no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—21no—
175C2×C4—2442no—
176C2×C4—2442no—
177C2×C4#1451974711yescharacteristic
178C2×C4#1451975012yes—
179C2×C4#1451975211yescharacteristic
180C2×C4#1451976212yes—
181C8—42no—
182C8—82no—
183C8—1224no—
184C8—4881no—
185C22—21no—
186C22—22no—
187C22#1683968011yescharacteristic
188C4—21no—
189C4—22no—
190C4—4882no—
191C4—4882no—
192C4#1683993211yescharacteristic
193C4#1683994711yescharacteristic
194C4#1684002412yes—
195C4#1684003612yes—
196C2—41no—
197C2#2144704411yescharacteristic
198C2#2144712112yes—
subgroupG/H
centerC22#16839680
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1309C2
socleC22×C61#394
prime radicalC23×C61#124
hypercenter#1309D61
hypocenterC61#10534
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1309

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
#214572132
#214459902
#214445562
#214442732
C61×#13092
#1053461