Finite Group Databasebeta

← #29584209

Subgroups — #29584209

Order 15616.

358 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 83 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#21444556C212yesmaximal
3#21444275C212yesmaximal
4#21443732C211yesmaximal, characteristic
5C61×#1848C211yesmaximal, characteristic
6#16840319C2212yes—
7#16840048—22no—
8#16840020—22no—
9#16839973—22no—
10#16839786C2212yes—
11#16839509—22no—
12#16839507—22no—
13#16839494—24no—
14C2×#108×C61—22no—
15C61×#423C2211yescharacteristic
16C61×#423C2211yescharacteristic
17C2×C4×C8×C61C2211yescharacteristic
18C2×Dic244—22no—
19C2×#11758194—22no—
20#14519777D412yes—
21#14519777D412yes—
22#14519769—22no—
23#14519756—22no—
24#14519756—22no—
25C4×Dic122—22no—
26C4×Dic122—22no—
27#14519736—22no—
28#14519709—22no—
29C4⋊#92418—22no—
30C4⋊#92418—22no—
31#14519702—24no—
32C2×M16×C61—21no—
33C2×M16×C61D412yes—
34C22×C8×C61—21no—
35C2×C42×C61C2311yescharacteristic
36#108×C61—44no—
37C4⋊C8×C61—22no—
38C4⋊C8×C61—22no—
39C4×C8×C61—21no—
40C4×C8×C61D412yes—
41C22×C4×C61C2×D411yescharacteristic
42C22×C4×C61#4112yes—
43C2×Dic122—22no—
44C2×Dic122—22no—
45M16×C61—42no—
46M16×C61—42no—
47C2×C8×C61—22no—
48C2×C8×C61—22no—
49C2×C8×C61—22no—
50C2×C8×C61—22no—
51C2×C8×C61—41no—
52C42×C61C2×D412yes—
53C42×C61C2×D411yescharacteristic
54C42×C61#4111yescharacteristic
55C22⋊Dic61—42no—
56C4⋊Dic61—22no—
57C4⋊Dic61—22no—
58C4⋊Dic61—22no—
59C4⋊Dic61—22no—
60#11758196—42no—
61#11758196—42no—
62C4×Dic61—42no—
63#11758194—82no—
64C2×#92418—42no—
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—24no—
82C8×C61—42no—
83C8×C61—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#45311yescharacteristic
92C4×C61#45611yescharacteristic
93C4×C61#47112yes—
94C4×C61#47312yes—
95Dic61—82no—
96Dic61—82no—
97#3255—611no—
98#1848D6111yescharacteristic
99#1561—612no—
100#1493—612no—
101#1309—611no—
102C2×C61—41no—
103C2×C61#203911yescharacteristic
104C2×C61#205212yes—
105#533—612no—
106#475—1222no—
107#470—1222no—
108#462—1222no—
109C2×#108—22no—
110#423—612no—
111#423C2×D6111yescharacteristic
112#423C2×D6111yescharacteristic
113C2×C4×C8C2×D6111yescharacteristic
114#332—1222no—
115#332—1222no—
116Q8⋊C8—1224no—
117C61#1053411yescharacteristic, complemented, Sylow
118C2×Q16—1222no—
119C2×M16—21no—
120C2×M16—1222no—
121C2×M16C22⋊D6112yes—
122C22×C8—21no—
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—44no—
133#106—1222no—
134C4⋊C8—22no—
135C4⋊C8—22no—
136C4⋊C8—1222no—
137C4⋊C8—1222no—
138#103—1224no—
139C4×C8—21no—
140C4×C8D24412yes—
141C2×Q8—1222no—
142C2×Q8—1222no—
143C22×C4#1175822612yes—
144C22×C4C2×C22⋊D6111yescharacteristic
145Q16—4882no—
146M16—42no—
147M16—42no—
148M16—4882no—
149C2×C8—22no—
150C2×C8—22no—
151C2×C8—22no—
152C2×C8—22no—
153C2×C8—41no—
154C2×C8—2442no—
155C4⋊C4—1222no—
156C4⋊C4—1222no—
157C4⋊C4—1222no—
158C4⋊C4—1222no—
159C4⋊C4—2442no—
160C4⋊C4—2442no—
161C22⋊C4—2442no—
162C42—2442no—
163C42C2×D24411yescharacteristic
164C42#1175822211yescharacteristic
165C42D4×D6112yes—
166C23#1451976611yescharacteristic
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#1451974511yescharacteristic
178C2×C4#1451975111yescharacteristic
179C2×C4#1451975212yes—
180C2×C4#1451976212yes—
181C8—24no—
182C8—42no—
183C8—81no—
184C8—4882no—
185C22—21no—
186C22—22no—
187C22#1683967911yescharacteristic
188C4—21no—
189C4—22no—
190C4—4882no—
191C4—4882no—
192C4#1683992911yescharacteristic
193C4#1683994411yescharacteristic
194C4#1684002612yes—
195C4#1684003812yes—
196C2—41no—
197C2#2144704311yescharacteristic
198C2#2144712012yes—
subgroupG/H
centerC22#16839679
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1848C2
socleC22×C61#394
prime radicalC23×C61#124
hypercenter#1848D61
hypocenterC61#10534
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1848

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
#214445562
#214442752
#214437322
C61×#18482
#1053461