Finite Group Databasebeta

← #30594954

Subgroups — #30594954

Order 15616.

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

normal subgroups only

This group has 240 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#21460911C211yesmaximal, characteristic, complemented
2#21460742C211yesmaximal, characteristic, complemented
3#21446922C211yesmaximal, characteristic
4#16840748—21no—
5C22⋊#11758187—21no—
6#16840560—21no—
7#16839730C2211yescharacteristic
8#16839729—21no—
9#16839520C411yescharacteristic
10C61×#575C411yescharacteristic
11D61⋊M16—41no—
12C2×#11758187—41no—
13#14519838—41no—
14#14519837—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×D244SD1611yescharacteristic
43C2×C4×D61—21no—
44C2×Dic122D811yescharacteristic
45#11758217—42no—
46#11758213—81no—
47D61⋊C8—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—
66Q8×C61—41no—
67Q8×C61—41no—
68D4×C61—41no—
69D4×C61—41no—
70D4×C61—81no—
71D4×C61—81no—
72C2×C4×C61—21no—
73C2×C4×C61—21no—
74C2×C4×C61—41no—
75C2×C4×C61—81no—
76C2×C4×C61—81no—
77C2×C4×C61#9911yescharacteristic
78C2×C4×C61#10211yescharacteristic
79C22⋊D61—81no—
80C2×Dic61—21no—
81D244—41no—
82C4×D61—41no—
83C4×D61—41no—
84Dic122—41no—
85#92420—82no—
86C8×C61—41no—
87#92418—42no—
88#92418—41no—
89#7407—611nomaximal, Sylow
90C22×C61—21no—
91C22×C61—41no—
92C22×C61—82no—
93C22×C61—81no—
94C22×C61#32711yescharacteristic
95C2×D61—41no—
96C2×D61—81no—
97C4×C61—21no—
98C4×C61—81no—
99C4×C61AΣL(1,𝔽16)11yescharacteristic
100C4×C61#35311yescharacteristic
101Dic61—41no—
102#2017—611no—
103#1392—611no—
104#1315—611no—
105C2×C61—21no—
106C2×C61—41no—
107C2×C61—161no—
108C2×C61#134311yescharacteristic
109D61—81no—
110#575—1221no—
111#575#692311yescharacteristic
112#413—1221no—
113#408—611no—
114#408—1221no—
115C22⋊C16—1221no—
116#338—611no—
117C61#740711yescharacteristic, complemented, Sylow
118C2×#41—21no—
119C2×#41—611no—
120#137—41no—
121#137—2441no—
122#137—2441no—
123AGL(1,ℤ/8)—41no—
124AGL(1,ℤ/8)—2441no—
125AGL(1,ℤ/8)—2441no—
126#135—41no—
127#135—2442no—
128C2×M16—1221no—
129C2×M16—2441no—
130C2×M16C2×#692311yescharacteristic
131C22×C8—611no—
132C2×C16—2441no—
133#101—2441no—
134#100—1222no—
135C22⋊C8—2441no—
136C22⋊C8—2442no—
137#41—41no—
138#41—41no—
139#41—41no—
140#41—41no—
141#41—2441no—
142#41—2441no—
143C2×Q8—21no—
144C2×Q8—611no—
145C2×D4—21no—
146C2×D4—41no—
147C2×D4—611no—
148C2×D4—1221no—
149C22×C4—41no—
150C22×C4—1221no—
151C22×C4C22⋊#692311yescharacteristic
152Q16—41no—
153Q16—2442no—
154SD16—42no—
155SD16—2442no—
156SD16—2442no—
157D8—41no—
158D8—2442no—
159M16—41no—
160M16—4881no—
161M16—2442no—
162M16—2441no—
163M16—2441no—
164C2×C8—21no—
165C2×C8—1222no—
166C2×C8—1221no—
167C2×C8—4881no—
168C2×C8—2441no—
169C16—4881no—
170C23—41no—
171C23—1221no—
172C23#1451984111yescharacteristic
173Q8—41no—
174Q8—41no—
175Q8—2441no—
176D4—41no—
177D4—41no—
178D4—81no—
179D4—81no—
180D4—4881no—
181D4—2441no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—41no—
185C2×C4—81no—
186C2×C4—81no—
187C2×C4—1221no—
188C2×C4—2441no—
189C2×C4—2441no—
190C2×C4#1451983511yescharacteristic
191C2×C4#1451983911yescharacteristic
192C8—41no—
193C8—4882no—
194C8—2442no—
195C8—2441no—
196C22—21no—
197C22—41no—
198C22—82no—
199C22—81no—
200C22—4881no—
201C22—2441no—
202C22#1684061311yescharacteristic
203C4—21no—
204C4—81no—
205C4—2441no—
206C4#1684066211yescharacteristic
207C4#1684066611yescharacteristic
208C2—21no—
209C2—41no—
210C2—161no—
211C2—4881no—
212C2#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#7407
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. #21460911C2semidirect
2. #21460742C2semidirect
117. C61#7407semidirect

Maximal subgroups

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

subgroupindex
#214609112
#214607422
#214469222
#740761