Finite Group Databasebeta

← #29594172

Subgroups — #29594172

Order 15616.

234 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 67 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#21447957C211yesmaximal, characteristic
2#21447865C211yesmaximal, characteristic
3#21445416C211yesmaximal, characteristic, complemented
4C8×D488C211yesmaximal, characteristic
5#21443873C211yesmaximal, characteristic, complemented
6#21443869C211yesmaximal, characteristic, complemented
7C61×#1367C211yesmaximal, characteristic, complemented
8C2×#14519722—21no—
9#16840167C2211yescharacteristic
10#16840160—21no—
11#16840142C2211yescharacteristic
12#16840113—21no—
13C4×D488C2211yescharacteristic
14C8×D244—21no—
15#16839588—21no—
16#16839567—21no—
17#16839564—21no—
18#16839515C2211yescharacteristic
19#16839491—21no—
20C61×C4⋊C16C2211yescharacteristic
21C61×C4⋊C16C2211yescharacteristic
22C82×C61C2211yescharacteristic
23C2×Dic244—21no—
24C2×Dic244—21no—
25C2×D488D411yescharacteristic
26C2×C8×D61—41no—
27#14519777—21no—
28#14519777—21no—
29C4×D244—21no—
30#14519722—42no—
31#14519711—21no—
32#14519711—21no—
33#14519711D411yescharacteristic
34#14519709—42no—
35C4⋊#92418—21no—
36#14519702—41no—
37#14519702—41no—
38#14519699—21no—
39#14519689—41no—
40C2×C16×C61—21no—
41C2×C16×C61—21no—
42C4×C8×C61D411yescharacteristic
43C4×C8×C61D411yescharacteristic
44C4×C8×C61C2311yescharacteristic
45C2×D244—21no—
46C2×C4×D61—41no—
47C2×Dic122—41no—
48C2×Dic122—41no—
49C2×C8×C61—21no—
50C2×C8×C61D811yescharacteristic
51C2×C8×C61D811yescharacteristic
52C2×C8×C61C2×D411yescharacteristic
53C2×C8×C61#4111yescharacteristic
54C42×C61C2×D411yescharacteristic
55#11758198—41no—
56C4⋊Dic61—21no—
57C4⋊Dic61—41no—
58C4⋊Dic61—41no—
59C4⋊Dic61—41no—
60C4⋊Dic61—41no—
61C2×#92418—41no—
62Dic244—41no—
63Dic244—41no—
64Dic244—81no—
65D488—21no—
66D488SD1612yes—
67C8×D61—82no—
68C16×C61—41no—
69C16×C61—41no—
70C22×D61—41no—
71C2×C4×C61#12111yescharacteristic
72C2×C4×C61C2×D811yescharacteristic
73C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
74C2×Dic61—41no—
75C2×Dic61—81no—
76C2×Dic61—81no—
77D244—22no—
78D244—41no—
79C4×D61—81no—
80C4×D61—81no—
81Dic122—81no—
82Dic122—81no—
83Dic122—81no—
84Dic122—81no—
85C8×C61—22no—
86C8×C61—21no—
87C8×C61—21no—
88C8×C61—21no—
89C8×C61C2×SD1611yescharacteristic
90C8×C61#13511yescharacteristic
91#92418—81no—
92#12422—611nomaximal, Sylow
93C22×C61#45911yescharacteristic
94C2×D61—42no—
95C2×D61—81no—
96C2×D61—81no—
97C4×C61—21no—
98C4×C61#46511yescharacteristic
99C4×C61#47111yescharacteristic
100C4×C61#50811yescharacteristic
101C4×C61#50911yescharacteristic
102Dic61—81no—
103Dic61—161no—
104Dic61—161no—
105#2224—611no—
106#2208—611no—
107#1707—611no—
108C8×D8—611no—
109#1367D6111yescharacteristic, complemented
110#1364—611no—
111#1362—611no—
112C2×C61#166511yescharacteristic
113C2×C61#221011yescharacteristic
114C2×C61#221411yescharacteristic
115D61—82no—
116C2×SD32—1221no—
117#500—611no—
118#498—1221no—
119#494—611no—
120#487—1221no—
121C4×D8—611no—
122C8×D4—1221no—
123#366—1221no—
124C4⋊C16C2×D6111yescharacteristic
125C4⋊C16C2×D6111yescharacteristic
126#358—1221no—
127#357—1221no—
128#335—611no—
129D4⋊C8—1221no—
130C82C2×D6111yescharacteristic
131C61#1242211yescharacteristic, complemented, Sylow
132C2×Q16—1221no—
133C2×Q16—1221no—
134C2×D8—611no—
135C22×C8—2441no—
136C4⋊Q8—1221no—
137C4⋊Q8—1221no—
138C4×D4—1221no—
139SD32—2442no—
140C2×C16—21no—
141C2×C16—21no—
142#107—611no—
143#107—1221no—
144#107—1221no—
145#106—2442no—
146C4⋊C8—1221no—
147#103—2441no—
148#103—2441no—
149#102—1221no—
150C22⋊C8—2441no—
151C4×C8D24411yescharacteristic
152C4×C8D24411yescharacteristic
153C4×C8C22×D6111yescharacteristic
154C2×Q8—2441no—
155C2×Q8—2441no—
156C2×D4—1221no—
157C22×C4—2441no—
158Q16—4881no—
159Q16—2441no—
160Q16—2441no—
161D8—612no—
162D8—1221no—
163C2×C8—21no—
164C2×C8—4882no—
165C2×C8—2441no—
166C2×C8D48811yescharacteristic
167C2×C8D48811yescharacteristic
168C2×C8D4×D6111yescharacteristic
169C2×C8#1175822611yescharacteristic
170C4⋊C4—1221no—
171C4⋊C4—2441no—
172C4⋊C4—2441no—
173C4⋊C4—2441no—
174C4⋊C4—2441no—
175C22⋊C4—2441no—
176C42C2×D24411yescharacteristic
177C16—41no—
178C16—41no—
179C23—2441no—
180Q8—4881no—
181Q8—4881no—
182Q8—4881no—
183Q8—4881no—
184D4—1222no—
185D4—2441no—
186C2×C4—4881no—
187C2×C4—4881no—
188C2×C4—4881no—
189C2×C4—4881no—
190C2×C4—2441no—
191C2×C4#1451975211yescharacteristic
192C2×C4C2×D48811yescharacteristic
193C2×C4#1451980511yescharacteristic
194C8—22no—
195C8—21no—
196C8—21no—
197C8—21no—
198C8—4881no—
199C8SD16×D6111yescharacteristic
200C8#1451979811yescharacteristic
201C22—4881no—
202C22—4881no—
203C22—2442no—
204C22#1683995811yescharacteristic
205C4—21no—
206C4—9761no—
207C4—9761no—
208C4—4881no—
209C4#1683999211yescharacteristic
210C4#1684002611yescharacteristic
211C4#1684019411yescharacteristic
212C4#1684020011yescharacteristic
213C2—4882no—
214C2#2144516111yescharacteristic
215C2#2144787511yescharacteristic
216C2#2144790111yescharacteristic
subgroupG/H
centerC22#16839958
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1367C2
socleC22×C61#459
prime radicalC2×D488D4
hypercenter#1367D61
hypocenterC61#12422
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C82 ◁ #1367

Complements

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

NH ≅ G/Ntype
3. #21445416C2semidirect
5. #21443873C2semidirect
6. #21443869C2semidirect
7. C61×#1367C2semidirect
109. #1367D61semidirect
131. C61#12422semidirect

Maximal subgroups

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

subgroupindex
#214479572
#214478652
#214454162
C8×D4882
#214438732
#214438692
C61×#13672
#1242261