Finite Group Databasebeta

← #29574960

Subgroups — #29574960

Order 15616.

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

normal subgroups only

This group has 416 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#21456164C211yesmaximal, characteristic
2#21454890C211yesmaximal, characteristic
3#21444293C212yesmaximal, complemented
4#21443719C212yesmaximal, complemented
5C61×#1543C211yesmaximal, characteristic
6#16840319C2211yescharacteristic
7#16840130—21no—
8#16840126—21no—
9#16840121C414yes—
10#16839834—24no—
11#16839819C2212yes—
12#16839758—22no—
13#16839729—22no—
14C2×#14519688C2211yescharacteristic
15#16839494—24no—
16C61×#532C2211yescharacteristic
17C61×#431C2212yes—
18C61×#333—21no—
19C61×#331—21no—
20C2×#11758194—22no—
21C22×#92418—21no—
22C22×#92418—22no—
23#14519777C2×C412yes—
24#14519769—21no—
25#14519756—22no—
26C4×Dic122—22no—
27#14519736—21no—
28C4⋊#92418D414yes—
29#14519701—24no—
30#14519698—24no—
31C22⋊#92418—24no—
32C22⋊#92418—22no—
33#14519688—21no—
34#14519688—22no—
35#14519688C2×C412yes—
36C2×#41×C61D412yes—
37C4⋊Q8×C61D411yescharacteristic
38#127×C61D411yescharacteristic
39#124×C61C2×C412yes—
40#121×C61—22no—
41C4×D4×C61—22no—
42C2×C42×C61C2311yescharacteristic
43C4⋊C8×C61—22no—
44C22⋊C8×C61—22no—
45C4×C8×C61—22no—
46#41×C61—42no—
47#41×C61—42no—
48C2×Q8×C61C22⋊C412yes—
49C2×D4×C61—22no—
50C2×D4×C61—22no—
51C2×D4×C61C22⋊C412yes—
52C22×C4×C61—22no—
53C22×C4×C61C2×D411yescharacteristic
54C22×C4×C61#4112yes—
55C2×Dic122—22no—
56C2×C8×C61—42no—
57C4⋊C4×C61—22no—
58C22⋊C4×C61—24no—
59C42×C61C22×C411yescharacteristic
60C42×C61C2×D411yescharacteristic
61C42×C61C2×D412yes—
62C22⋊Dic61—41no—
63C4⋊Dic61—22no—
64C4⋊Dic61—22no—
65#11758196—42no—
66C4×Dic61—41no—
67#11758194—82no—
68C2×#92418—22no—
69C2×#92418—24no—
70C2×#92418—42no—
71C2×#92418—82no—
72C23×C61—22no—
73C23×C61#12311yescharacteristic
74Q8×C61—42no—
75D4×C61—42no—
76D4×C61—82no—
77D4×C61—82no—
78C2×C4×C61—22no—
79C2×C4×C61—22no—
80C2×C4×C61—42no—
81C2×C4×C61—42no—
82C2×C4×C61—42no—
83C2×C4×C61C2×C22⋊C411yescharacteristic
84C2×C4×C61C4×D412yes—
85C2×C4×C61#12011yescharacteristic
86C2×C4×C61#12112yes—
87C2×Dic61—42no—
88Dic122—44no—
89C8×C61—82no—
90#92418—42no—
91#92418—44no—
92#9005—611nomaximal, Sylow
93C22×C61—22no—
94C22×C61—21no—
95C22×C61—44no—
96C22×C61—42no—
97C22×C61#38611yescharacteristic
98C4×C61—22no—
99C4×C61—22no—
100C4×C61—21no—
101C4×C61—42no—
102C4×C61#45512yes—
103Dic61—82no—
104#3135—611no—
105#2980—611no—
106#1543D6111yescharacteristic
107#1497—612no—
108#1302—612no—
109C2×C61—41no—
110C2×C61—82no—
111C2×C61#188112yes—
112C2×C61#188511yescharacteristic
113#533—611no—
114#532C2×D6111yescharacteristic
115#491—1221no—
116#490—1221no—
117#489—614no—
118#435—1224no—
119#432—612no—
120#431C2×D6112yes—
121#416—1222no—
122#408—1222no—
123C2×#97—611no—
124#333—21no—
125#331—21no—
126Q8⋊C8—1224no—
127C61#900511yescharacteristic, complemented, Sylow
128C2×#41D24412yes—
129C2×M16—1222no—
130C22×C8—1222no—
131C22×C8—1221no—
132C4⋊Q8—612no—
133C4⋊Q8C22⋊D6111yescharacteristic
134#127C22⋊D6111yescharacteristic
135#125—1221no—
136#124C4×D6112yes—
137C22⋊Q8—1222no—
138#121—22no—
139C4×Q8—1222no—
140C4×D4—22no—
141#117—1221no—
142C2×C42C22×D6111yescharacteristic
143C4⋊C8—22no—
144C4⋊C8—614no—
145#103—1224no—
146#102—1224no—
147C22⋊C8—22no—
148C22⋊C8—1224no—
149C22⋊C8—1222no—
150#97—612no—
151#97—1222no—
152#97—1221no—
153C4×C8—22no—
154#41—42no—
155#41—42no—
156C2×Q8—1222no—
157C2×Q8#1175819812yes—
158C2×D4—22no—
159C2×D4—22no—
160C2×D4#1175819812yes—
161C22×C4—22no—
162C22×C4C2×D24411yescharacteristic
163C22×C4#1175822412yes—
164M16—4882no—
165C2×C8—42no—
166C2×C8—1222no—
167C2×C8—1224no—
168C2×C8—4882no—
169C2×C8—2442no—
170C4⋊C4—22no—
171C4⋊C4—1222no—
172C4⋊C4—1222no—
173C4⋊C4—2442no—
174C22⋊C4—24no—
175C22⋊C4—2441no—
176C42—2441no—
177C42C2×C4×D6111yescharacteristic
178C42D4×D6112yes—
179C42C2×C22⋊D6111yescharacteristic
180C23—22no—
181C23#1451976111yescharacteristic
182Q8—42no—
183Q8—2444no—
184D4—42no—
185D4—82no—
186D4—82no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—42no—
190C2×C4—42no—
191C2×C4—42no—
192C2×C4—2442no—
193C2×C4C2×#1175819811yescharacteristic
194C2×C4#1451973712yes—
195C2×C4#1451974711yescharacteristic
196C2×C4#1451974912yes—
197C8—82no—
198C8—2442no—
199C8—2444no—
200C22—22no—
201C22—21no—
202C22—44no—
203C22—42no—
204C22#1683963911yescharacteristic
205C4—22no—
206C4—22no—
207C4—21no—
208C4—42no—
209C4—4882no—
210C4#1683994212yes—
211C2—41no—
212C2—82no—
213C2#2144617912yes—
214C2#2144620511yescharacteristic
subgroupG/H
centerC2×C4#14519747
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1543C2
socleC22×C61#386
prime radicalC61×#532C22
cosocleC2×C42×C61C23
hypercenter#1543D61
hypocenterC61#9005
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1543

Complements

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

NH ≅ G/Ntype
3. #21444293C2semidirect
4. #21443719C2semidirect
127. C61#9005semidirect

Maximal subgroups

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

subgroupindex
#214561642
#214548902
#214442932
#214437192
C61×#15432
#900561