Finite Group Databasebeta

← #29594174

Subgroups — #29594174

Order 15616.

234 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 63 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#21447953C211yesmaximal, characteristic
2#21447865C211yesmaximal, characteristic
3#21445417C211yesmaximal, characteristic, complemented
4#21444613C211yesmaximal, characteristic
5#21443882C211yesmaximal, characteristic, complemented
6#21443867C211yesmaximal, characteristic, complemented
7C61×#1364C211yesmaximal, characteristic, complemented
8C2×#14519722—21no—
9#16840158—21no—
10#16840142C2211yescharacteristic
11#16840112—21no—
12C4×D488C2211yescharacteristic
13#16839827—21no—
14#16839587—21no—
15C4⋊#11758185C2211yescharacteristic
16#16839567—21no—
17#16839562—21no—
18#16839489—21no—
19C8×#92418C2211yescharacteristic
20C61×#500C2211yescharacteristic
21C61×C4⋊C16C2211yescharacteristic
22C61×#335C2211yescharacteristic
23C2×Dic244—21no—
24C2×Dic244—21no—
25C2×D488D411yescharacteristic
26C2×C8×D61—41no—
27#14519777—21no—
28C4×D244—21no—
29#14519722—42no—
30C2×#11758185—21no—
31#14519711D411yescharacteristic
32#14519708—42no—
33#14519701—41no—
34#14519701—41no—
35#14519699—21no—
36#14519689—41no—
37C4×#92418D411yescharacteristic
38C4×#92418D411yescharacteristic
39C4⋊Q8×C61—21no—
40C2×C16×C61—21no—
41#107×C61—21no—
42#107×C61—21no—
43C4⋊C8×C61—21no—
44C4×C8×C61C2311yescharacteristic
45C2×Q8×C61—41no—
46C2×D244—21no—
47C2×C4×D61—41no—
48C2×Dic122—41no—
49C2×C8×C61—41no—
50C2×C8×C61C2×D411yescharacteristic
51C2×C8×C61#4111yescharacteristic
52C4⋊C4×C61—41no—
53C4⋊C4×C61—41no—
54C42×C61C2×D411yescharacteristic
55#11758198—41no—
56C4⋊Dic61—21no—
57C4⋊Dic61—41no—
58C4⋊Dic61—41no—
59C2×#92418—21no—
60C2×#92418D811yescharacteristic
61C2×#92418D811yescharacteristic
62Dic244—41no—
63Dic244—41no—
64Dic244—81no—
65D488—21no—
66D488SD1612yes—
67C8×D61—82no—
68C16×C61—41no—
69#11758185—41no—
70C22×D61—41no—
71Q8×C61—81no—
72Q8×C61—81no—
73C2×C4×C61—81no—
74C2×C4×C61#12111yescharacteristic
75C2×C4×C61C2×D811yescharacteristic
76C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
77C2×Dic61—41no—
78C2×Dic61—81no—
79D244—22no—
80D244—41no—
81C4×D61—81no—
82C4×D61—81no—
83Dic122—81no—
84Dic122—81no—
85C8×C61—21no—
86C8×C61—81no—
87C8×C61C2×SD1611yescharacteristic
88C8×C61#13511yescharacteristic
89#92418—22no—
90#92418—21no—
91#92418—21no—
92#12422—611nomaximal, Sylow
93C22×C61#45911yescharacteristic
94C2×D61—42no—
95C2×D61—81no—
96C2×D61—81no—
97C4×C61—21no—
98C4×C61—161no—
99C4×C61#46511yescharacteristic
100C4×C61#47111yescharacteristic
101C4×C61#50811yescharacteristic
102C4×C61#50911yescharacteristic
103Dic61—81no—
104Dic61—161no—
105#2224—611no—
106#2208—611no—
107#1707—611no—
108C8×D8—611no—
109#1367—611no—
110#1364D6111yescharacteristic, complemented
111#1362—611no—
112C2×C61#166511yescharacteristic
113C2×C61#221011yescharacteristic
114C2×C61#221411yescharacteristic
115D61—82no—
116C2×SD32—1221no—
117#500C2×D6111yescharacteristic
118#498—1221no—
119#494—611no—
120#487—1221no—
121C4×D8—611no—
122C8×D4—1221no—
123#366—1221no—
124C4⋊C16—611no—
125C4⋊C16C2×D6111yescharacteristic
126#358—1221no—
127#357—1221no—
128#335C2×D6111yescharacteristic
129D4⋊C8—1221no—
130C82—611no—
131C61#1242211yescharacteristic, complemented, Sylow
132C2×Q16—1221no—
133C2×Q16—1221no—
134C2×D8—611no—
135C22×C8—2441no—
136C4⋊Q8—21no—
137C4⋊Q8—1221no—
138C4×D4—1221no—
139SD32—2442no—
140C2×C16—21no—
141C2×C16—1221no—
142#107—21no—
143#107—21no—
144#107—611no—
145#106—2442no—
146C4⋊C8—21no—
147#103—2441no—
148#103—2441no—
149#102—1221no—
150C22⋊C8—2441no—
151C4×C8—611no—
152C4×C8—611no—
153C4×C8C22×D6111yescharacteristic
154C2×Q8—41no—
155C2×Q8—2441no—
156C2×D4—1221no—
157C22×C4—2441no—
158Q16—4881no—
159Q16—2441no—
160Q16—2441no—
161D8—612no—
162D8—1221no—
163C2×C8—41no—
164C2×C8—611no—
165C2×C8—611no—
166C2×C8—1221no—
167C2×C8—4882no—
168C2×C8#1175822211yescharacteristic
169C2×C8D4×D6111yescharacteristic
170C4⋊C4—41no—
171C4⋊C4—41no—
172C4⋊C4—1221no—
173C4⋊C4—2441no—
174C4⋊C4—2441no—
175C22⋊C4—2441no—
176C42D4×D6111yescharacteristic
177C16—41no—
178C16—2441no—
179C23—2441no—
180Q8—81no—
181Q8—81no—
182Q8—4881no—
183Q8—4881no—
184D4—1222no—
185D4—2441no—
186C2×C4—81no—
187C2×C4—4881no—
188C2×C4—4881no—
189C2×C4—4881no—
190C2×C4—2441no—
191C2×C4#1451975011yescharacteristic
192C2×C4D8×D6111yescharacteristic
193C2×C4#1451980411yescharacteristic
194C8—21no—
195C8—81no—
196C8—1222no—
197C8—1221no—
198C8—1221no—
199C8SD16×D6111yescharacteristic
200C8#1451980011yescharacteristic
201C22—4881no—
202C22—4881no—
203C22—2442no—
204C22#1683995611yescharacteristic
205C4—21no—
206C4—161no—
207C4—9761no—
208C4—4881no—
209C4#1683999411yescharacteristic
210C4#1684002811yescharacteristic
211C4#1684019311yescharacteristic
212C4#1684019611yescharacteristic
213C2—4882no—
214C2#2144516311yescharacteristic
215C2#2144787311yescharacteristic
216C2#2144789911yescharacteristic
subgroupG/H
centerC22#16839956
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1364C2
socleC22×C61#459
prime radicalC2×D488D4
hypercenter#1364D61
hypocenterC61#12422
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1364

Complements

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

NH ≅ G/Ntype
3. #21445417C2semidirect
5. #21443882C2semidirect
6. #21443867C2semidirect
7. C61×#1364C2semidirect
110. #1364D61semidirect
131. C61#12422semidirect

Maximal subgroups

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

subgroupindex
#214479532
#214478652
#214454172
#214446132
#214438822
#214438672
C61×#13642
#1242261