Finite Group Databasebeta

← #30594952

Subgroups — #30594952

Order 15616.

244 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 32 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#21460908C211yesmaximal, characteristic, complemented
2#21460742C211yesmaximal, characteristic, complemented
3#21446922C211yesmaximal, characteristic
4#16840741—21no—
5C22⋊#11758187—21no—
6#16840560—21no—
7#16839730C2211yescharacteristic
8#16839729—21no—
9#16839520C411yescharacteristic, complemented
10C61×#575C411yescharacteristic, complemented
11#14519856—41no—
12C2×#11758187—41no—
13#14519836—41no—
14#14519835—22no—
15C2×#11758222D411yescharacteristic
16#14519808—41no—
17#14519807—41no—
18#14519803—41no—
19#14519802—41no—
20#14519797—42no—
21C2×#11758194—21no—
22C22×#92418D411yescharacteristic
23C22⋊#92418—42no—
24#14519689—41no—
25C2×#41×C61—21no—
26#137×C61—41no—
27AGL(1,ℤ/8)×C61—41no—
28#135×C61—41no—
29C2×M16×C61C2×C411yescharacteristic
30#41×C61—41no—
31#41×C61—41no—
32#41×C61—41no—
33#41×C61—41no—
34C2×Q8×C61—21no—
35C2×D4×C61—21no—
36C2×D4×C61—41no—
37C22×C4×C61—41no—
38C22×C4×C61C22⋊C411yescharacteristic
39C2×C22⋊D61—21no—
40#11758222—41no—
41#11758222—41no—
42C2×D244D811yescharacteristic
43C2×C4×D61—21no—
44C2×Dic122SD1611yescharacteristic
45C22⋊#6923—42no—
46C4⋊#6923—81no—
47C4×#6923—81no—
48Q16×C61—41no—
49SD16×C61—42no—
50D8×C61—41no—
51M16×C61—41no—
52C2×C8×C61—21no—
53#11758202—42no—
54#11758201—42no—
55#11758200—42no—
56#11758199—42no—
57#11758194—41no—
58#11758194—41no—
59C2×#92418—22no—
60C2×#92418—21no—
61C2×#92418—41no—
62#11758187—81no—
63C23×C61—41no—
64C23×C61#10411yescharacteristic
65C22×D61—21no—
66C2×#6923—82no—
67Q8×C61—41no—
68Q8×C61—41no—
69D4×C61—41no—
70D4×C61—41no—
71D4×C61—81no—
72D4×C61—81no—
73C2×C4×C61—21no—
74C2×C4×C61—21no—
75C2×C4×C61—41no—
76C2×C4×C61—81no—
77C2×C4×C61—81no—
78C2×C4×C61#9911yescharacteristic
79C2×C4×C61#10211yescharacteristic
80C22⋊D61—81no—
81C2×Dic61—21no—
82D244—41no—
83C4×D61—41no—
84C4×D61—41no—
85Dic122—41no—
86C8×C61—41no—
87#92418—42no—
88#92418—41no—
89#7406—611nomaximal, Sylow
90C22×C61—21no—
91C22×C61—41no—
92C22×C61—82no—
93C22×C61—81no—
94C22×C61#32711yescharacteristic
95C2×D61—41no—
96C2×D61—81no—
97#6923—162no—
98C4×C61—21no—
99C4×C61—81no—
100C4×C61AΣL(1,𝔽16)11yescharacteristic
101C4×C61#35311yescharacteristic
102Dic61—41no—
103#2017—611no—
104#1391—611no—
105#1315—611no—
106C2×C61—21no—
107C2×C61—41no—
108C2×C61—161no—
109C2×C61#134311yescharacteristic
110D61—81no—
111#575—1221no—
112#575#692311yescharacteristic, complemented
113#410—1221no—
114#408—611no—
115#408—1221no—
116C22⋊C16—1221no—
117#338—611no—
118C61#740611yescharacteristic, complemented, Sylow
119C2×#41—21no—
120C2×#41—611no—
121#137—41no—
122#137—2441no—
123#137—2441no—
124AGL(1,ℤ/8)—41no—
125AGL(1,ℤ/8)—2441no—
126AGL(1,ℤ/8)—2441no—
127#135—41no—
128#135—2442no—
129C2×M16—1221no—
130C2×M16C2×#692311yescharacteristic
131C22×C8—611no—
132#117—2441no—
133C2×C16—2441no—
134#99—1222no—
135#99—2441no—
136C22⋊C8—2441no—
137C22⋊C8—2442no—
138#41—41no—
139#41—41no—
140#41—41no—
141#41—41no—
142#41—2441no—
143#41—2441no—
144C2×Q8—21no—
145C2×Q8—611no—
146C2×D4—21no—
147C2×D4—41no—
148C2×D4—611no—
149C2×D4—1221no—
150C22×C4—41no—
151C22×C4—1221no—
152C22×C4C22⋊#692311yescharacteristic
153Q16—41no—
154Q16—2442no—
155SD16—42no—
156SD16—2442no—
157SD16—2442no—
158D8—41no—
159D8—2442no—
160M16—41no—
161M16—2441no—
162M16—2441no—
163C2×C8—21no—
164C2×C8—1222no—
165C2×C8—1221no—
166C2×C8—2441no—
167C4⋊C4—4881no—
168C22⋊C4—2442no—
169C42—4881no—
170C16—4881no—
171C23—41no—
172C23—1221no—
173C23#1451984111yescharacteristic
174Q8—41no—
175Q8—41no—
176Q8—2441no—
177D4—41no—
178D4—41no—
179D4—81no—
180D4—81no—
181D4—4881no—
182D4—2441no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—41no—
186C2×C4—81no—
187C2×C4—81no—
188C2×C4—1221no—
189C2×C4—4882no—
190C2×C4—2441no—
191C2×C4—2441no—
192C2×C4#1451983511yescharacteristic
193C2×C4#1451983911yescharacteristic
194C8—41no—
195C8—2442no—
196C8—2441no—
197C22—21no—
198C22—41no—
199C22—82no—
200C22—81no—
201C22—4881no—
202C22—2441no—
203C22#1684061311yescharacteristic
204C4—21no—
205C4—81no—
206C4—9762no—
207C4—2441no—
208C4#1684066211yescharacteristic
209C4#1684066611yescharacteristic
210C2—21no—
211C2—41no—
212C2—161no—
213C2—4881no—
214C2#2146079711yescharacteristic
subgroupG/H
centerC4#16840666
commutatorC2×M16×C61C2×C4
FrattiniC2×M16C2×#6923
FittingC61×#575C4
socleC2×C61#1343
prime radical#21446922C2
cosocle#16839730C22
hypercenter#575#6923
hypocenterC61#7406
LCSG ▷ C2×M16×C61 ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16 ◁ #575

Complements

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

NH ≅ G/Ntype
1. #21460908C2semidirect
2. #21460742C2semidirect
9. #16839520C4semidirect
10. C61×#575C4semidirect
112. #575#6923semidirect
118. C61#7406semidirect

Maximal subgroups

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

subgroupindex
#214609082
#214607422
#214469222
#740661