Finite Group Databasebeta

← #29594155

Subgroups — #29594155

Order 15616.

234 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 69 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#21447966C211yesmaximal, characteristic
2#21445413C211yesmaximal, characteristic, complemented
3D8×#92418C211yesmaximal, characteristic
4#21443882C211yesmaximal, characteristic, complemented
5#21443876C211yesmaximal, characteristic, complemented
6#21443868C211yesmaximal, characteristic, complemented
7C61×#2208C211yesmaximal, characteristic
8#16840167C2211yescharacteristic
9#16840158—21no—
10#16840114—21no—
11D4×#92418—21no—
12#16839589—21no—
13C4⋊#11758185C2211yescharacteristic
14#16839563—21no—
15#16839515C2211yescharacteristic
16D4⋊#92418—21no—
17C8×#92418C2211yescharacteristic
18C2×SD32×C61—21no—
19C61×#494C2211yescharacteristic
20C4×D8×C61C2211yescharacteristic
21C61×C4⋊C16C2211yescharacteristic
22C61×#358—21no—
23C22×#92418—41no—
24#14519777—21no—
25C2×#11758185—21no—
26#14519711—21no—
27#14519711—21no—
28#14519708—41no—
29#14519708—41no—
30C4⋊#92418—21no—
31#14519700—42no—
32C22⋊#92418—41no—
33C4×#92418D411yescharacteristic
34C4×#92418D411yescharacteristic
35C2×Q16×C61—21no—
36C2×Q16×C61—21no—
37C2×D8×C61D411yescharacteristic
38C4⋊Q8×C61—21no—
39C4×D4×C61—21no—
40SD32×C61—42no—
41C2×C16×C61—21no—
42#107×C61D411yescharacteristic
43#102×C61—21no—
44C4×C8×C61C2311yescharacteristic
45C2×Q8×C61—41no—
46C2×D4×C61—21no—
47C22×C4×C61—41no—
48C2×Dic122—41no—
49Q16×C61—41no—
50Q16×C61—41no—
51Q16×C61—81no—
52D8×C61—21no—
53D8×C61SD1612yes—
54C2×C8×C61C2×D411yescharacteristic
55C2×C8×C61#4111yescharacteristic
56C4⋊C4×C61—21no—
57C4⋊C4×C61—41no—
58C4⋊C4×C61—41no—
59C22⋊C4×C61—41no—
60C42×C61C2×D411yescharacteristic
61C4⋊Dic61—41no—
62C4⋊Dic61—41no—
63C2×#92418—21no—
64C2×#92418—41no—
65C2×#92418—82no—
66C2×#92418D811yescharacteristic
67C2×#92418D811yescharacteristic
68C16×C61—41no—
69#11758185—41no—
70C23×C61—41no—
71Q8×C61—81no—
72Q8×C61—81no—
73D4×C61—22no—
74D4×C61—41no—
75C2×C4×C61—41no—
76C2×C4×C61—81no—
77C2×C4×C61—81no—
78C2×C4×C61—81no—
79C2×C4×C61#12111yescharacteristic
80C2×C4×C61C2×D811yescharacteristic
81C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
82C2×Dic61—81no—
83Dic122—82no—
84C8×C61—21no—
85C8×C61C2×SD1611yescharacteristic
86C8×C61#13511yescharacteristic
87#92418—21no—
88#92418—41no—
89#92418—81no—
90#92418SD3212yescomplemented
91#12420—611nomaximal, Sylow
92C22×C61—42no—
93C22×C61—81no—
94C22×C61—81no—
95C22×C61#45911yescharacteristic
96C4×C61—21no—
97C4×C61—81no—
98C4×C61—161no—
99C4×C61#46511yescharacteristic
100C4×C61#47111yescharacteristic
101C4×C61C2×SD3211yescharacteristic
102C4×C61#51011yescharacteristic
103Dic61—161no—
104#2226—611no—
105#2208D6111yescharacteristic
106#1707—611no—
107C8×D8—611no—
108#1367—611no—
109#1365—611no—
110#1362—611no—
111C2×C61—82no—
112C2×C61#166511yescharacteristic
113C2×C61#220811yescharacteristic
114C2×C61#221211yescharacteristic
115C2×SD32—21no—
116#500—611no—
117#498—1221no—
118#494C2×D6111yescharacteristic
119#487—1221no—
120C4×D8C2×D6111yescharacteristic
121C8×D4—1221no—
122#367—1221no—
123C4⋊C16—611no—
124C4⋊C16C2×D6111yescharacteristic
125#358—21no—
126#357—1221no—
127#335—611no—
128D4⋊C8—1221no—
129C82—611no—
130C61#1242011yescharacteristic, complemented, Sylow
131C2×Q16—21no—
132C2×Q16—21no—
133C2×D8C22⋊D6111yescharacteristic
134C22×C8—2441no—
135C4⋊Q8—21no—
136C4⋊Q8—1221no—
137C4×D4—21no—
138SD32—42no—
139C2×C16—21no—
140C2×C16—1221no—
141#107—1221no—
142#107—1221no—
143#107C22⋊D6111yescharacteristic
144#106—2441no—
145#106—2441no—
146C4⋊C8—1221no—
147#103—2442no—
148#102—21no—
149C22⋊C8—2441no—
150C4×C8—611no—
151C4×C8—611no—
152C4×C8C22×D6111yescharacteristic
153C2×Q8—41no—
154C2×Q8—2441no—
155C2×D4—21no—
156C22×C4—41no—
157Q16—41no—
158Q16—41no—
159Q16—81no—
160D8—21no—
161D8#1175820012yes—
162C2×C8—611no—
163C2×C8—611no—
164C2×C8—1221no—
165C2×C8—4882no—
166C2×C8—2441no—
167C2×C8#1175822411yescharacteristic
168C2×C8C2×C22⋊D6111yescharacteristic
169C4⋊C4—21no—
170C4⋊C4—41no—
171C4⋊C4—41no—
172C4⋊C4—2441no—
173C4⋊C4—2441no—
174C22⋊C4—41no—
175C42D4×D6111yescharacteristic
176C16—41no—
177C16—2441no—
178C23—41no—
179Q8—81no—
180Q8—81no—
181Q8—4882no—
182D4—22no—
183D4—41no—
184C2×C4—41no—
185C2×C4—81no—
186C2×C4—81no—
187C2×C4—81no—
188C2×C4—4881no—
189C2×C4#1451974911yescharacteristic
190C2×C4D8×D6111yescharacteristic
191C2×C4#1451980111yescharacteristic
192C8—21no—
193C8—612no—
194C8—1221no—
195C8—4881no—
196C8—2441no—
197C8C2×#1175820011yescharacteristic
198C8#1451979711yescharacteristic
199C22—42no—
200C22—81no—
201C22—81no—
202C22#1683995511yescharacteristic
203C4—21no—
204C4—81no—
205C4—161no—
206C4—9761no—
207C4#1683998911yescharacteristic
208C4#1684002311yescharacteristic
209C4SD32×D6111yescharacteristic
210C4#1684020111yescharacteristic
211C2—82no—
212C2#2144515811yescharacteristic
213C2#2144786211yescharacteristic
214C2#2144789011yescharacteristic
subgroupG/H
centerC22#16839955
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#2208C2
socleC22×C61#459
prime radicalC2×D8×C61D4
hypercenter#2208D61
hypocenterC61#12420
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2208

Complements

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

NH ≅ G/Ntype
2. #21445413C2semidirect
4. #21443882C2semidirect
5. #21443876C2semidirect
6. #21443868C2semidirect
90. #92418SD32semidirect
130. C61#12420semidirect

Maximal subgroups

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

subgroupindex
#214479662
#214454132
D8×#924182
#214438822
#214438762
#214438682
C61×#22082
#1242061