Finite Group Databasebeta

← #29594150

Subgroups — #29594150

Order 15616.

240 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 71 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#21447971C211yesmaximal, characteristic, complemented
2#21447859C211yesmaximal, characteristic
3#21445411C211yesmaximal, characteristic
4#21443883C211yesmaximal, characteristic, complemented
5#21443878C211yesmaximal, characteristic, complemented
6#21443864C211yesmaximal, characteristic
7C8×Q16×C61C211yesmaximal, characteristic, complemented
8C2×#14519720—21no—
9#16840167C2211yescharacteristic
10#16840139C2211yescharacteristic
11#16840135—21no—
12#16840109—21no—
13#16839587—21no—
14C4⋊#11758185C2211yescharacteristic
15C4⋊#11758185C2211yescharacteristic
16#16839566—21no—
17#16839562—21no—
18C8×Q8×C61—21no—
19C4×Q16×C61C2211yescharacteristic
20C61×#335C2211yescharacteristic
21C61×Q8⋊C8—21no—
22C82×C61C2211yescharacteristic
23C2×#11758190—42no—
24C2×D488—21no—
25C2×D488—21no—
26#14519777—21no—
27#14519774—21no—
28#14519720—42no—
29C2×#11758185—21no—
30C2×#11758185—21no—
31#14519711—21no—
32#14519711—21no—
33#14519699—41no—
34#14519699—41no—
35C2×Q16×C61D411yescharacteristic
36C4×Q8×C61—21no—
37#107×C61D411yescharacteristic
38C4⋊C8×C61—21no—
39C4⋊C8×C61—41no—
40#103×C61—21no—
41C4×C8×C61—41no—
42C4×C8×C61D411yescharacteristic
43C4×C8×C61D411yescharacteristic
44C4×C8×C61C2311yescharacteristic
45C2×Q8×C61—21no—
46C2×D244—41no—
47C2×D244—41no—
48C2×D244—41no—
49C2×Dic122—41no—
50Q16×C61—21no—
51Q16×C61SD1612yescomplemented
52C2×C8×C61—21no—
53C2×C8×C61—41no—
54C2×C8×C61D811yescharacteristic
55C2×C8×C61D811yescharacteristic
56C2×C8×C61C2×D411yescharacteristic
57C2×C8×C61#4111yescharacteristic
58C4⋊C4×C61—21no—
59C4⋊C4×C61—41no—
60C42×C61—41no—
61C42×C61C2×D411yescharacteristic
62C4⋊Dic61—41no—
63C4⋊Dic61—41no—
64D488—41no—
65D488—41no—
66D488—81no—
67#11758190—84no—
68#11758185—41no—
69#11758185—41no—
70C22×D61—81no—
71Q8×C61—22no—
72Q8×C61—41no—
73C2×C4×C61—41no—
74C2×C4×C61—41no—
75C2×C4×C61#12111yescharacteristic
76C2×C4×C61C2×D811yescharacteristic
77C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
78C2×Dic61—81no—
79D244—82no—
80D244—81no—
81D244—81no—
82D244—81no—
83D244—81no—
84Dic122—82no—
85C8×C61—22no—
86C8×C61—21no—
87C8×C61—21no—
88C8×C61—21no—
89C8×C61—81no—
90C8×C61C2×SD1611yescharacteristic
91C8×C61#13511yescharacteristic
92#12419—611nomaximal, Sylow
93C22×C61#45911yescharacteristic
94C2×D61—161no—
95C2×D61—161no—
96C2×D61—161no—
97C4×C61—21no—
98C4×C61—42no—
99C4×C61—81no—
100C4×C61#46511yescharacteristic
101C4×C61#47111yescharacteristic
102C4×C61#50811yescharacteristic
103C4×C61#51011yescharacteristic
104Dic61—161no—
105#2227—611no—
106#2207—611no—
107#1706—611no—
108C8×Q16D6111yescharacteristic, complemented
109#1367—611no—
110#1365—611no—
111#1361—611no—
112C2×C61#166511yescharacteristic
113C2×C61#221111yescharacteristic
114C2×C61#221311yescharacteristic
115D61—321no—
116C2×SD32—1221no—
117#500—611no—
118#493—611no—
119#492—1221no—
120#486—1221no—
121C8×Q8—21no—
122C4×Q16C2×D6111yescharacteristic
123#366—1221no—
124C4⋊C16—611no—
125C4⋊C16—611no—
126#358—1221no—
127#357—1221no—
128#335C2×D6111yescharacteristic
129Q8⋊C8—21no—
130C82C2×D6111yescharacteristic
131C61#1241911yescharacteristic, complemented, Sylow
132C2×Q16D24411yescharacteristic
133C2×SD16—2442no—
134C2×D8—1221no—
135C2×D8—1221no—
136C4⋊Q8—1221no—
137#127—1221no—
138C4×Q8—21no—
139SD32—2442no—
140C2×C16—1221no—
141C2×C16—1221no—
142#107—1221no—
143#107—1221no—
144#107D24411yescharacteristic
145C4⋊C8—21no—
146C4⋊C8—41no—
147#103—21no—
148#102—2441no—
149#102—2441no—
150C4×C8—41no—
151C4×C8C22⋊D6111yescharacteristic
152C4×C8C22⋊D6111yescharacteristic
153C4×C8C22×D6111yescharacteristic
154C2×Q8—21no—
155C2×Q8—2441no—
156C2×D4—2441no—
157C2×D4—2441no—
158C2×D4—2441no—
159Q16—21no—
160Q16#1175819012yescomplemented
161SD16—4884no—
162D8—4881no—
163D8—2441no—
164D8—2441no—
165C2×C8—21no—
166C2×C8—41no—
167C2×C8#1175819911yescharacteristic
168C2×C8#1175819911yescharacteristic
169C2×C8C2×D24411yescharacteristic
170C2×C8#1175822211yescharacteristic
171C4⋊C4—21no—
172C4⋊C4—41no—
173C4⋊C4—2441no—
174C4⋊C4—2441no—
175C42—41no—
176C42C2×C22⋊D6111yescharacteristic
177C16—2441no—
178C16—2441no—
179C23—4881no—
180Q8—22no—
181Q8—41no—
182Q8—4882no—
183D4—4882no—
184D4—4881no—
185D4—4881no—
186D4—4881no—
187D4—4881no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—4881no—
191C2×C4#1451975111yescharacteristic
192C2×C4C2×#1175819911yescharacteristic
193C2×C4#1451980211yescharacteristic
194C8—22no—
195C8—21no—
196C8—21no—
197C8—21no—
198C8—81no—
199C8C2×#1175819011yescharacteristic
200C8#1451979911yescharacteristic
201C22—9761no—
202C22—9761no—
203C22—9761no—
204C22#1683995711yescharacteristic
205C4—21no—
206C4—42no—
207C4—81no—
208C4—9761no—
209C4#1683999111yescharacteristic
210C4#1684002511yescharacteristic
211C4#1684019211yescharacteristic
212C4#1684020311yescharacteristic
213C2—19521no—
214C2#2144516011yescharacteristic
215C2#2144788111yescharacteristic
216C2#2144789511yescharacteristic
subgroupG/H
centerC22#16839957
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC8×Q16×C61C2
socleC22×C61#459
prime radical#16840139C22
hypercenterC8×Q16D61
hypocenterC61#12419
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C82 ◁ C8×Q16

Complements

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

NH ≅ G/Ntype
1. #21447971C2semidirect
4. #21443883C2semidirect
5. #21443878C2semidirect
7. C8×Q16×C61C2semidirect
51. Q16×C61SD16semidirect
108. C8×Q16D61semidirect
131. C61#12419semidirect
160. Q16#11758190semidirect

Maximal subgroups

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

subgroupindex
#214479712
#214478592
#214454112
#214438832
#214438782
#214438642
C8×Q16×C612
#1241961