Finite Group Databasebeta

← #29594168

Subgroups — #29594168

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#21447953C211yesmaximal, characteristic
2#21447861C211yesmaximal, characteristic
3C8×D488C211yesmaximal, characteristic
4#21443883C211yesmaximal, characteristic, complemented
5#21443874C211yesmaximal, characteristic, complemented
6#21443868C211yesmaximal, characteristic, complemented
7C61×#1707C211yesmaximal, characteristic, complemented
8C2×#14519720—21no—
9C4×D488C2211yescharacteristic
10C8×D244—21no—
11#16839587—21no—
12C4⋊#11758185C2211yescharacteristic
13C4⋊#11758185C2211yescharacteristic
14#16839566—21no—
15#16839562—21no—
16#16839515C2211yescharacteristic
17#16839491—21no—
18C61×#500C2211yescharacteristic
19C61×#498—21no—
20C61×#494C2211yescharacteristic
21C61×#487—21no—
22C82×C61C2211yescharacteristic
23C2×D488D411yescharacteristic
24C2×C8×D61—41no—
25C4×D244—21no—
26#14519720—42no—
27C2×#11758185—21no—
28C2×#11758185—21no—
29#14519711D411yescharacteristic
30C4⋊#92418—21no—
31#14519699—21no—
32#14519689—41no—
33C2×Q16×C61—21no—
34C2×Q16×C61—21no—
35C4⋊Q8×C61—21no—
36C4⋊Q8×C61—21no—
37#107×C61—21no—
38#107×C61—21no—
39#106×C61—42no—
40#103×C61—41no—
41#103×C61—41no—
42C4×C8×C61D411yescharacteristic
43C4×C8×C61D411yescharacteristic
44C4×C8×C61C2311yescharacteristic
45C2×Q8×C61—41no—
46C2×Q8×C61—41no—
47C2×D244—21no—
48C2×C4×D61—41no—
49Q16×C61—41no—
50Q16×C61—41no—
51Q16×C61—81no—
52C2×C8×C61—21no—
53C2×C8×C61D811yescharacteristic
54C2×C8×C61D811yescharacteristic
55C2×C8×C61C2×D411yescharacteristic
56C2×C8×C61#4111yescharacteristic
57C4⋊C4×C61—41no—
58C4⋊C4×C61—41no—
59C4⋊C4×C61—41no—
60C4⋊C4×C61—41no—
61C42×C61C2×D411yescharacteristic
62#11758198—41no—
63C4⋊Dic61—21no—
64C2×#92418—41no—
65D488—21no—
66D488SD1612yes—
67C8×D61—82no—
68#11758185—41no—
69#11758185—41no—
70C22×D61—41no—
71Q8×C61—81no—
72Q8×C61—81no—
73Q8×C61—81no—
74Q8×C61—81no—
75C2×C4×C61—81no—
76C2×C4×C61—81no—
77C2×C4×C61#12111yescharacteristic
78C2×C4×C61C2×D811yescharacteristic
79C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
80C2×Dic61—41no—
81D244—22no—
82D244—41no—
83C4×D61—81no—
84C4×D61—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—161no—
99C4×C61—161no—
100C4×C61#46511yescharacteristic
101C4×C61#47111yescharacteristic
102C4×C61#50811yescharacteristic
103C4×C61#50911yescharacteristic
104Dic61—81no—
105#2224—611no—
106#2208—611no—
107#1707D6111yescharacteristic, complemented
108C8×D8—611no—
109#1367—611no—
110#1364—611no—
111#1362—611no—
112C2×C61#166511yescharacteristic
113C2×C61#221011yescharacteristic
114C2×C61#221411yescharacteristic
115D61—82no—
116C2×SD32—1221no—
117#500C2×D6111yescharacteristic
118#498—21no—
119#494C2×D6111yescharacteristic
120#487—21no—
121C4×D8—611no—
122C8×D4—1221no—
123#366—1221no—
124C4⋊C16—611no—
125C4⋊C16—611no—
126#358—1221no—
127#357—1221no—
128#335—611no—
129D4⋊C8—1221no—
130C82C2×D6111yescharacteristic
131C61#1242211yescharacteristic, complemented, Sylow
132C2×Q16—21no—
133C2×Q16—21no—
134C2×D8—611no—
135C22×C8—2441no—
136C4⋊Q8—21no—
137C4⋊Q8—21no—
138C4×D4—1221no—
139SD32—2442no—
140C2×C16—1221no—
141C2×C16—1221no—
142#107—21no—
143#107—21no—
144#107—611no—
145#106—42no—
146C4⋊C8—1221no—
147#103—41no—
148#103—41no—
149#102—1221no—
150C22⋊C8—2441no—
151C4×C8C22⋊D6111yescharacteristic
152C4×C8C22⋊D6111yescharacteristic
153C4×C8C22×D6111yescharacteristic
154C2×Q8—41no—
155C2×Q8—41no—
156C2×D4—1221no—
157C22×C4—2441no—
158Q16—41no—
159Q16—41no—
160Q16—81no—
161D8—612no—
162D8—1221no—
163C2×C8—21no—
164C2×C8—4882no—
165C2×C8—2441no—
166C2×C8#1175819911yescharacteristic
167C2×C8#1175819911yescharacteristic
168C2×C8D4×D6111yescharacteristic
169C2×C8#1175822411yescharacteristic
170C4⋊C4—41no—
171C4⋊C4—41no—
172C4⋊C4—41no—
173C4⋊C4—41no—
174C4⋊C4—1221no—
175C22⋊C4—2441no—
176C42C2×C22⋊D6111yescharacteristic
177C16—2441no—
178C16—2441no—
179C23—2441no—
180Q8—81no—
181Q8—81no—
182Q8—81no—
183Q8—81no—
184D4—1222no—
185D4—2441no—
186C2×C4—81no—
187C2×C4—81no—
188C2×C4—4881no—
189C2×C4—4881no—
190C2×C4—2441no—
191C2×C4#1451974811yescharacteristic
192C2×C4C2×#1175819911yescharacteristic
193C2×C4#1451980311yescharacteristic
194C8—22no—
195C8—21no—
196C8—21no—
197C8—21no—
198C8—4881no—
199C8SD16×D6111yescharacteristic
200C8#1451979811yescharacteristic
201C22—4881no—
202C22—4881no—
203C22—2442no—
204C22#1683995411yescharacteristic
205C4—21no—
206C4—161no—
207C4—161no—
208C4—4881no—
209C4#1683998811yescharacteristic
210C4#1684002211yescharacteristic
211C4#1684019211yescharacteristic
212C4#1684019711yescharacteristic
213C2—4882no—
214C2#2144515711yescharacteristic
215C2#2144787111yescharacteristic
216C2#2144789711yescharacteristic
subgroupG/H
centerC22#16839954
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1707C2
socleC22×C61#459
prime radicalC2×D488D4
hypercenter#1707D61
hypocenterC61#12422
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C82 ◁ #1707

Complements

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

NH ≅ G/Ntype
4. #21443883C2semidirect
5. #21443874C2semidirect
6. #21443868C2semidirect
7. C61×#1707C2semidirect
107. #1707D61semidirect
131. C61#12422semidirect

Maximal subgroups

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

subgroupindex
#214479532
#214478612
C8×D4882
#214438832
#214438742
#214438682
C61×#17072
#1242261