Finite Group Databasebeta

← #29592024

Subgroups — #29592024

Order 15616.

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

normal subgroups only

This group has 212 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#21447681C211yesmaximal, characteristic
2#21444734C211yesmaximal, characteristic
3#21443884C211yesmaximal, characteristic, complemented
4#21443789C211yesmaximal, characteristic, complemented
5#21443785C211yesmaximal, characteristic
6#21443740C211yesmaximal, characteristic, complemented
7C61×#1593C211yesmaximal, characteristic, complemented
8C2×#14519720C411yescharacteristic
9C4×D488C2211yescharacteristic
10#16839841—21no—
11#16839587C411yescharacteristic
12#16839566C411yescharacteristic
13#16839562C411yescharacteristic
14#16839538C2211yescharacteristic
15#16839538C2211yescharacteristic
16#16839513C2211yescharacteristic
17#16839491—21no—
18C61×#446—21no—
19C4×Q16×C61C2211yescharacteristic
20C61×#334C2211yescharacteristic
21C61×Q8⋊C8—21no—
22C61×#322C2211yescharacteristic
23C2×D488C2×C411yescharacteristic
24C2×#11758189—41no—
25C4×D244—21no—
26#14519720—22no—
27C2×#11758185—21no—
28C2×#11758185C2×C411yescharacteristic
29C2×#11758185C2×C411yescharacteristic
30#14519711C2×C411yescharacteristic
31C4⋊#92418—21no—
32#14519699—21no—
33#14519689—41no—
34C2×Q16×C61C2×C411yescharacteristic
35C4×Q8×C61—21no—
36#107×C61C2×C411yescharacteristic
37C4⋊C8×C61—21no—
38C4⋊C8×C61—41no—
39#103×C61—21no—
40#97×C61—41no—
41C4×C8×C61D411yescharacteristic
42C4×C8×C61D411yescharacteristic
43C4×C8×C61C2311yescharacteristic
44C2×Q8×C61—21no—
45C2×D244—21no—
46C2×C4×D61—41no—
47Q16×C61—21no—
48Q16×C61—21no—
49C2×C8×C61—21no—
50C2×C8×C61—21no—
51C2×C8×C61—41no—
52C2×C8×C61C22×C411yescharacteristic
53C2×C8×C61#4111yescharacteristic
54C4⋊C4×C61—21no—
55C4⋊C4×C61—41no—
56C42×C61—41no—
57C42×C61C2×D411yescharacteristic
58#11758198—41no—
59C4⋊Dic61—21no—
60C2×#92418—41no—
61D488—21no—
62D488—21no—
63#11758189—82no—
64#11758185—21no—
65#11758185—41no—
66#11758185M1612yescomplemented
67C22×D61—41no—
68Q8×C61—41no—
69Q8×C61—41no—
70C2×C4×C61—41no—
71C2×C4×C61—41no—
72C2×C4×C61C4×D411yescharacteristic
73C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
74C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
75C2×Dic61—41no—
76D244—41no—
77D244—41no—
78C4×D61—81no—
79C4×D61—81no—
80C8×C61—21no—
81C8×C61—41no—
82C8×C61—41no—
83C8×C61—81no—
84C8×C61C2×M1611yescharacteristic
85C8×C61#13111yescharacteristic
86#92418—81no—
87#12087—611nomaximal, Sylow
88C22×C61#44211yescharacteristic
89C2×D61—81no—
90C2×D61—81no—
91C2×D61—81no—
92C4×C61—21no—
93C4×C61—21no—
94C4×C61—81no—
95C4×C61—81no—
96C4×C61#43611yescharacteristic
97C4×C61#44411yescharacteristic
98Dic61—81no—
99#2175—611no—
100#1594—611no—
101#1593D6111yescharacteristic, complemented
102#1368—611no—
103#1334—611no—
104#1333—611no—
105#1313—611no—
106C2×C61#159411yescharacteristic
107C2×C61#218011yescharacteristic
108C2×C61AGL(1,ℤ/16)11yescharacteristic
109D61—161no—
110C2×SD32—611no—
111#446—21no—
112C4×Q16C2×D6111yescharacteristic
113C4×D8—611no—
114#436—1221no—
115#366—611no—
116#358—611no—
117#357—611no—
118#346—611no—
119#346—611no—
120#334—611no—
121#334C2×D6111yescharacteristic
122Q8⋊C8—21no—
123D4⋊C8—1221no—
124#322C2×D6111yescharacteristic
125C61#1208711yescharacteristic, complemented, Sylow
126C2×Q16C4×D6111yescharacteristic
127C2×D8—611no—
128C2×M16—2441no—
129C4×Q8—21no—
130C4×D4—1221no—
131SD32—1222no—
132C2×C16—611no—
133C2×C16—611no—
134C2×C16—1221no—
135#107—611no—
136#107C4×D6111yescharacteristic
137C4⋊C8—21no—
138C4⋊C8—41no—
139C4⋊C8—1221no—
140#103—21no—
141#102—1221no—
142C22⋊C8—2441no—
143#97—41no—
144C4×C8C22⋊D6111yescharacteristic
145C4×C8C22⋊D6111yescharacteristic
146C4×C8C22×D6111yescharacteristic
147C2×Q8—21no—
148C2×D4—1221no—
149C22×C4—2441no—
150Q16—21no—
151Q16—21no—
152D8—1221no—
153D8—1221no—
154M16—4882no—
155C2×C8—21no—
156C2×C8—21no—
157C2×C8—41no—
158C2×C8—2441no—
159C2×C8C2×C4×D6111yescharacteristic
160C2×C8#1175822211yescharacteristic
161C4⋊C4—21no—
162C4⋊C4—41no—
163C4⋊C4—1221no—
164C22⋊C4—2441no—
165C42—41no—
166C42C2×C22⋊D6111yescharacteristic
167C16—612no—
168C16—1221no—
169C16—2441no—
170C23—2441no—
171Q8—41no—
172Q8—41no—
173D4—2441no—
174D4—2441no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—4881no—
178C2×C4—4881no—
179C2×C4—2441no—
180C2×C4C4×C22⋊D6111yescharacteristic
181C2×C4#1451980211yescharacteristic
182C2×C4#1451980311yescharacteristic
183C8—21no—
184C8—41no—
185C8—41no—
186C8—81no—
187C8—4881no—
188C8M16×D6111yescharacteristic
189C8#1451978511yescharacteristic
190C22—4881no—
191C22—4881no—
192C22—4881no—
193C22#1683987211yescharacteristic
194C4—21no—
195C4—21no—
196C4—81no—
197C4—81no—
198C4—4881no—
199C4#1683983811yescharacteristic
200C4#1683988211yescharacteristic
201C2—9761no—
202C2#2144473111yescharacteristic
203C2#2144770811yescharacteristic
204C2#2144771711yescharacteristic
subgroupG/H
centerC22#16839872
commutatorC2×C8×C61C22×C4
FrattiniC4×C8C22×D61
FittingC61×#1593C2
socleC22×C61#442
prime radicalC2×D488C2×C4
cosocleC4×C8×C61C23
hypercenter#1593D61
hypocenterC61#12087
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #322 ◁ #1593

Complements

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

NH ≅ G/Ntype
3. #21443884C2semidirect
4. #21443789C2semidirect
6. #21443740C2semidirect
7. C61×#1593C2semidirect
66. #11758185M16semidirect
101. #1593D61semidirect
125. C61#12087semidirect

Maximal subgroups

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

subgroupindex
#214476812
#214447342
#214438842
#214437892
#214437852
#214437402
C61×#15932
#1208761