Finite Group Databasebeta

← #29592008

Subgroups — #29592008

Order 15616.

220 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 75 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
1C4×#14519722C211yesmaximal, characteristic
2#21444715C211yesmaximal, characteristic, complemented
3#21444703C211yesmaximal, characteristic
4#21443782C211yesmaximal, characteristic, complemented
5#21443779C211yesmaximal, characteristic
6#21443735C211yesmaximal, characteristic, complemented
7C61×#1371C211yesmaximal, characteristic, complemented
8C2×#14519722C411yescharacteristic
9#16839889—21no—
10C4×Dic244C2211yescharacteristic
11C4×D488C2211yescharacteristic
12#16839839—21no—
13#16839590C411yescharacteristic
14#16839567C411yescharacteristic
15#16839564C411yescharacteristic
16C4×#11758185C2211yescharacteristic
17#16839492—21no—
18#16839489—21no—
19C8×#92418C2211yescharacteristic
20C4×C16×C61C2211yescharacteristic
21C61×#335C2211yescharacteristic
22C61×#335C2211yescharacteristic
23C2×Dic244C2×C411yescharacteristic
24C2×D488C2×C411yescharacteristic
25C2×#11758189—41no—
26C4×Dic122—21no—
27C4×D244—21no—
28#14519722—22no—
29C2×#11758185—21no—
30#14519711C2×C411yescharacteristic
31#14519711C2×C411yescharacteristic
32#14519706—41no—
33#14519702—21no—
34#14519699—21no—
35#14519689—41no—
36#14519687—41no—
37C4×#92418D411yescharacteristic
38C4×#92418D411yescharacteristic
39C2×C16×C61C2×C411yescharacteristic
40C2×C16×C61C2×C411yescharacteristic
41C4⋊C8×C61—21no—
42C4⋊C8×C61—21no—
43C4×C8×C61C2311yescharacteristic
44C2×D244—21no—
45C2×C4×D61—41no—
46C2×Dic122—21no—
47C2×C8×C61—41no—
48C2×C8×C61—41no—
49C2×C8×C61C22×C411yescharacteristic
50C2×C8×C61#4111yescharacteristic
51C42×C61C2×D411yescharacteristic
52#11758198—41no—
53C4⋊Dic61—21no—
54C4⋊Dic61—21no—
55#11758196—41no—
56C4×Dic61—41no—
57C2×#92418—21no—
58C2×#92418D811yescharacteristic
59C2×#92418D811yescharacteristic
60Dic244—21no—
61Dic244—21no—
62D488—21no—
63D488—21no—
64#11758189—82no—
65C16×C61—21no—
66C16×C61M1612yescomplemented
67#11758185—22no—
68C22×D61—41no—
69C2×C4×C61C4×D411yescharacteristic
70C2×C4×C61C2×D811yescharacteristic
71C2×C4×C61#13511yescharacteristic
72C2×Dic61—41no—
73C2×Dic61—41no—
74C2×Dic61—41no—
75D244—41no—
76D244—41no—
77C4×D61—81no—
78C4×D61—81no—
79Dic122—41no—
80Dic122—41no—
81C8×C61—21no—
82C8×C61—81no—
83C8×C61—81no—
84C8×C61C2×M1611yescharacteristic
85C8×C61#13111yescharacteristic
86#92418—21no—
87#92418—21no—
88#92418—41no—
89#12084—611nomaximal, Sylow
90C22×C61C4×D811yescharacteristic
91C2×D61—81no—
92C2×D61—81no—
93C2×D61—81no—
94C4×C61—21no—
95C4×C61#43611yescharacteristic
96C4×C61#44311yescharacteristic
97C4×C61#50911yescharacteristic
98C4×C61#51011yescharacteristic
99Dic61—81no—
100Dic61—81no—
101Dic61—81no—
102C4×SD32—611no—
103#1591—611no—
104#1589—611no—
105#1371D6111yescharacteristic, complemented
106#1332—611no—
107#1331—611no—
108#1311—611no—
109C2×C61#158911yescharacteristic
110C2×C61#217511yescharacteristic
111C2×C61#217911yescharacteristic
112D61—161no—
113C2×SD32—611no—
114#446—1221no—
115C4×Q16—611no—
116C4×D8—611no—
117#436—1221no—
118#367—611no—
119#358—611no—
120#357—611no—
121C4×C16—611no—
122C4×C16C2×D6111yescharacteristic
123#335C2×D6111yescharacteristic
124#335C2×D6111yescharacteristic
125Q8⋊C8—1221no—
126D4⋊C8—1221no—
127C82—611no—
128C61#1208411yescharacteristic, complemented, Sylow
129C2×Q16—611no—
130C2×D8—611no—
131C2×M16—2441no—
132C4×Q8—1221no—
133C4×D4—1221no—
134SD32—1222no—
135C2×C16—1221no—
136C2×C16C4×D6111yescharacteristic
137C2×C16C4×D6111yescharacteristic
138#107—611no—
139#107—611no—
140C4⋊C8—21no—
141C4⋊C8—21no—
142C4⋊C8—2441no—
143#103—1221no—
144#102—1221no—
145C22⋊C8—2441no—
146#97—2441no—
147C4×C8—611no—
148C4×C8—611no—
149C4×C8C22×D6111yescharacteristic
150C2×Q8—1221no—
151C2×D4—1221no—
152C22×C4—2441no—
153Q16—1221no—
154Q16—1221no—
155D8—1221no—
156D8—1221no—
157M16—4882no—
158C2×C8—41no—
159C2×C8—41no—
160C2×C8—611no—
161C2×C8—611no—
162C2×C8—1221no—
163C2×C8C2×C4×D6111yescharacteristic
164C2×C8#1175822611yescharacteristic
165C4⋊C4—1221no—
166C4⋊C4—1221no—
167C4⋊C4—2441no—
168C22⋊C4—2441no—
169C42—2441no—
170C42D4×D6111yescharacteristic
171C16—21no—
172C16—1222no—
173C16#1175818912yescomplemented
174C23—2441no—
175Q8—2441no—
176Q8—2441no—
177D4—2441no—
178D4—2441no—
179C2×C4—4881no—
180C2×C4—4881no—
181C2×C4—2441no—
182C2×C4—2441no—
183C2×C4—2441no—
184C2×C4#1451973911yescharacteristic
185C2×C4D8×D6111yescharacteristic
186C2×C4#1451980011yescharacteristic
187C8—21no—
188C8—81no—
189C8—81no—
190C8—1221no—
191C8—1221no—
192C8—2441no—
193C8C2×#1175818911yescharacteristic
194C8#1451978511yescharacteristic
195C22—4881no—
196C22—4881no—
197C22—4881no—
198C22#1683984411yescharacteristic
199C4—21no—
200C4—4881no—
201C4—4881no—
202C4—4881no—
203C4#1683983911yescharacteristic
204C4#1683987811yescharacteristic
205C4#1684019611yescharacteristic
206C4#1684020411yescharacteristic
207C2—9761no—
208C2#2144470311yescharacteristic
209C2#2144768211yescharacteristic
210C2#2144770411yescharacteristic
subgroupG/H
centerC2×C4D8×D61
commutatorC2×C8×C61C22×C4
FrattiniC4×C8C22×D61
FittingC61×#1371C2
socleC22×C61C4×D8
prime radicalC2×D488C2×C4
cosocleC4×C8×C61C23
hypercenter#1371D61
hypocenterC61#12084
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ #1371

Complements

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

NH ≅ G/Ntype
2. #21444715C2semidirect
4. #21443782C2semidirect
6. #21443735C2semidirect
7. C61×#1371C2semidirect
66. C16×C61M16semidirect
105. #1371D61semidirect
128. C61#12084semidirect
173. C16#11758189semidirect

Maximal subgroups

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

subgroupindex
C4×#145197222
#214447152
#214447032
#214437822
#214437792
#214437352
C61×#13712
#1208461