Finite Group Databasebeta

← #29584182

Subgroups — #29584182

Order 15616.

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

normal subgroups only

This group has 402 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, complemented
2#21444554C212yesmaximal, complemented
3#21444270C212yesmaximal, complemented
4#21443732C211yesmaximal, characteristic, complemented
5C61×#3253C211yesmaximal, characteristic
6C2×#14519712—22no—
7#16839786C2211yescharacteristic
8#16839786C2212yes—
9C2×C4×#92418C2211yescharacteristic
10#16839511—22no—
11#16839506—22no—
12D4⋊#92418—24no—
13C61×#532C2212yes—
14C61×#476—22no—
15C61×#469—22no—
16C61×#459—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×#41×C61—22no—
28C2×D8×C61—22no—
29C2×M16×C61D412yes—
30C4⋊Q8×C61D412yes—
31#127×C61D412yes—
32#124×C61—22no—
33#121×C61—22no—
34#121×C61—22no—
35C4×D4×C61—22no—
36C4×D4×C61—22no—
37C2×C42×C61C2311yescharacteristic
38#106×C61—22no—
39C4⋊C8×C61—22no—
40#102×C61—24no—
41#41×C61—82no—
42#41×C61—82no—
43C2×Q8×C61—22no—
44C2×D4×C61—22no—
45C2×D4×C61—22no—
46C2×D4×C61—22no—
47C2×D4×C61—42no—
48C22×C4×C61—42no—
49C22×C4×C61C2×D411yescharacteristic
50C22×C4×C61#4112yes—
51D8×C61—82no—
52M16×C61—42no—
53C2×C8×C61—22no—
54C4⋊C4×C61—22no—
55C4⋊C4×C61—22no—
56C22⋊C4×C61—42no—
57C22⋊C4×C61—42no—
58C42×C61C2×D412yes—
59C42×C61C2×D411yescharacteristic
60C42×C61#4111yescharacteristic
61#11758194—42no—
62#11758194—82no—
63C2×#92418—22no—
64C2×#92418—22no—
65C2×#92418—22no—
66C2×#92418—41no—
67C2×#92418—42no—
68C23×C61—42no—
69C23×C61#12411yescharacteristic
70Q8×C61—82no—
71D4×C61—42no—
72D4×C61—42no—
73D4×C61—42no—
74D4×C61—42no—
75D4×C61—82no—
76D4×C61—84no—
77C2×C4×C61—21no—
78C2×C4×C61—21no—
79C2×C4×C61—22no—
80C2×C4×C61—22no—
81C2×C4×C61—42no—
82C2×C4×C61—82no—
83C2×C4×C61—82no—
84C2×C4×C61#12011yescharacteristic
85C2×C4×C61#12111yescharacteristic
86C2×C4×C61#12112yes—
87C2×C4×C61#12312yes—
88C8×C61—42no—
89#92418—24no—
90#92418—81no—
91#92418—82no—
92#10530—611nomaximal, Sylow
93C22×C61—22no—
94C22×C61—21no—
95C22×C61—82no—
96C22×C61—82no—
97C22×C61—82no—
98C22×C61#39411yescharacteristic
99C4×C61—22no—
100C4×C61—21no—
101C4×C61—82no—
102C4×C61#45311yescharacteristic
103C4×C61#45611yescharacteristic
104C4×C61#47112yes—
105C4×C61#47212yes—
106#3253D6111yescharacteristic
107#1848—611no—
108#1560—612no—
109#1492—612no—
110#1309—611no—
111C2×C61—41no—
112C2×C61—162no—
113C2×C61#203911yescharacteristic
114C2×C61#205112yes—
115#532C2×D6112yes—
116#476—22no—
117#469—22no—
118#459—22no—
119C2×#108—1222no—
120#423—611no—
121#423—612no—
122#423C2×D6111yescharacteristic
123C2×C4×C8—611no—
124#333—1222no—
125#331—1222no—
126D4⋊C8—1224no—
127C61#1053011yescharacteristic, complemented, Sylow
128C2×#41—22no—
129C2×D8—22no—
130C2×M16—1222no—
131C2×M16—1221no—
132C2×M16C22⋊D6112yes—
133C22×C8—1221no—
134C4⋊Q8C22⋊D6112yes—
135#127C22⋊D6112yes—
136#124—22no—
137#121—22no—
138#121—22no—
139C4×D4—22no—
140C4×D4—22no—
141C2×C42C22×D6111yescharacteristic
142#108—2444no—
143#106—22no—
144C4⋊C8—22no—
145C4⋊C8—1222no—
146C4⋊C8—1222no—
147C4⋊C8—1222no—
148#102—24no—
149C4×C8—612no—
150C4×C8—1221no—
151#41—82no—
152#41—82no—
153C2×Q8—22no—
154C2×D4—22no—
155C2×D4—22no—
156C2×D4—22no—
157C2×D4—42no—
158C22×C4—42no—
159C22×C4#1175822412yes—
160C22×C4C2×C22⋊D6111yescharacteristic
161D8—82no—
162M16—42no—
163M16—4882no—
164M16—2442no—
165C2×C8—22no—
166C2×C8—1222no—
167C2×C8—1222no—
168C2×C8—1222no—
169C2×C8—2441no—
170C2×C8—2442no—
171C4⋊C4—22no—
172C4⋊C4—22no—
173C22⋊C4—42no—
174C22⋊C4—42no—
175C42D4×D6111yescharacteristic
176C42#1175822411yescharacteristic
177C42C2×C22⋊D6112yes—
178C23—42no—
179C23#1451976411yescharacteristic
180Q8—82no—
181D4—42no—
182D4—42no—
183D4—42no—
184D4—42no—
185D4—82no—
186D4—84no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—21no—
191C2×C4—42no—
192C2×C4—82no—
193C2×C4—82no—
194C2×C4#1451974611yescharacteristic
195C2×C4#1451974811yescharacteristic
196C2×C4#1451974912yes—
197C2×C4#1451975812yes—
198C8—42no—
199C8—1224no—
200C8—4882no—
201C8—4881no—
202C22—21no—
203C22—22no—
204C22—82no—
205C22—82no—
206C22—82no—
207C22#1683967611yescharacteristic
208C4—21no—
209C4—22no—
210C4—82no—
211C4#1683993011yescharacteristic
212C4#1683994511yescharacteristic
213C4#1684002312yes—
214C4#1684003012yes—
215C2—41no—
216C2—162no—
217C2#2144704011yescharacteristic
218C2#2144710812yes—
subgroupG/H
centerC22#16839676
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
Fitting, prime radicalC61×#3253C2
socleC22×C61#394
hypercenter#3253D61
hypocenterC61#10530
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3253

Complements

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

NH ≅ G/Ntype
1. #21445990C2semidirect
2. #21444554C2semidirect
3. #21444270C2semidirect
4. #21443732C2semidirect
127. C61#10530semidirect

Maximal subgroups

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

subgroupindex
#214459902
#214445542
#214442702
#214437322
C61×#32532
#1053061