Finite Group Databasebeta

← #29594156

Subgroups — #29594156

Order 15616.

234 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 65 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#21447967C211yesmaximal, characteristic
2#21447861C211yesmaximal, characteristic
3#21445413C211yesmaximal, characteristic, complemented
4#21444613C211yesmaximal, characteristic
5#21443882C211yesmaximal, characteristic, complemented
6#21443878C211yesmaximal, characteristic, complemented
7C61×#1362C211yesmaximal, characteristic, complemented
8C2×#14519720—21no—
9#16840167C2211yescharacteristic
10#16840158—21no—
11#16840114—21no—
12C4×D488C2211yescharacteristic
13#16839827—21no—
14#16839590—21no—
15C4⋊#11758185C2211yescharacteristic
16#16839566—21no—
17#16839564—21no—
18#16839489—21no—
19C8×#92418C2211yescharacteristic
20C61×#494C2211yescharacteristic
21C61×C4⋊C16C2211yescharacteristic
22C61×#335C2211yescharacteristic
23C2×D488D411yescharacteristic
24C2×C8×D61—41no—
25#14519777—21no—
26C4×D244—21no—
27#14519720—42no—
28C2×#11758185—21no—
29#14519711—21no—
30#14519711—21no—
31#14519711D411yescharacteristic
32#14519708—41no—
33#14519708—41no—
34#14519700—42no—
35#14519699—21no—
36#14519689—41no—
37C4×#92418D411yescharacteristic
38C4×#92418D411yescharacteristic
39C2×Q16×C61—21no—
40C2×Q16×C61—21no—
41C4⋊Q8×C61—21no—
42C2×C16×C61—21no—
43C4⋊C8×C61—21no—
44C4×C8×C61C2311yescharacteristic
45C2×Q8×C61—41no—
46C2×D244—21no—
47C2×C4×D61—41no—
48C2×Dic122—41no—
49Q16×C61—41no—
50Q16×C61—41no—
51Q16×C61—81no—
52C2×C8×C61—41no—
53C2×C8×C61C2×D411yescharacteristic
54C2×C8×C61#4111yescharacteristic
55C4⋊C4×C61—41no—
56C4⋊C4×C61—41no—
57C42×C61C2×D411yescharacteristic
58#11758198—41no—
59C4⋊Dic61—21no—
60C4⋊Dic61—41no—
61C4⋊Dic61—41no—
62C2×#92418—21no—
63C2×#92418D811yescharacteristic
64C2×#92418D811yescharacteristic
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—82no—
84C8×C61—21no—
85C8×C61—81no—
86C8×C61C2×SD1611yescharacteristic
87C8×C61#13511yescharacteristic
88#92418—21no—
89#92418—41no—
90#92418SD3212yescomplemented
91#12420—611nomaximal, Sylow
92C22×C61#45911yescharacteristic
93C2×D61—42no—
94C2×D61—81no—
95C2×D61—81no—
96C4×C61—21no—
97C4×C61—161no—
98C4×C61#46511yescharacteristic
99C4×C61#47111yescharacteristic
100C4×C61C2×SD3211yescharacteristic
101C4×C61#51011yescharacteristic
102Dic61—81no—
103Dic61—161no—
104#2226—611no—
105#2208—611no—
106#1707—611no—
107C8×D8—611no—
108#1367—611no—
109#1365—611no—
110#1362D6111yescharacteristic, complemented
111C2×C61#166511yescharacteristic
112C2×C61#220811yescharacteristic
113C2×C61#221211yescharacteristic
114D61—82no—
115C2×SD32—1221no—
116#500—611no—
117#498—1221no—
118#494C2×D6111yescharacteristic
119#487—1221no—
120C4×D8—611no—
121C8×D4—1221no—
122#367—1221no—
123C4⋊C16—611no—
124C4⋊C16C2×D6111yescharacteristic
125#358—1221no—
126#357—1221no—
127#335C2×D6111yescharacteristic
128D4⋊C8—1221no—
129C82—611no—
130C61#1242011yescharacteristic, complemented, Sylow
131C2×Q16—21no—
132C2×Q16—21no—
133C2×D8—611no—
134C22×C8—2441no—
135C4⋊Q8—21no—
136C4⋊Q8—1221no—
137C4×D4—1221no—
138SD32—2442no—
139C2×C16—21no—
140C2×C16—1221no—
141#107—611no—
142#107—1221no—
143#107—1221no—
144#106—2441no—
145#106—2441no—
146C4⋊C8—21no—
147#103—2442no—
148#102—1221no—
149C22⋊C8—2441no—
150C4×C8—611no—
151C4×C8—611no—
152C4×C8C22×D6111yescharacteristic
153C2×Q8—41no—
154C2×Q8—2441no—
155C2×D4—1221no—
156C22×C4—2441no—
157Q16—41no—
158Q16—41no—
159Q16—81no—
160D8—612no—
161D8—1221no—
162C2×C8—41no—
163C2×C8—611no—
164C2×C8—611no—
165C2×C8—1221no—
166C2×C8—4882no—
167C2×C8#1175822211yescharacteristic
168C2×C8D4×D6111yescharacteristic
169C4⋊C4—41no—
170C4⋊C4—41no—
171C4⋊C4—1221no—
172C4⋊C4—2441no—
173C4⋊C4—2441no—
174C22⋊C4—2441no—
175C42D4×D6111yescharacteristic
176C16—41no—
177C16—2441no—
178C23—2441no—
179Q8—81no—
180Q8—81no—
181Q8—4882no—
182D4—1222no—
183D4—2441no—
184C2×C4—81no—
185C2×C4—4881no—
186C2×C4—4881no—
187C2×C4—4881no—
188C2×C4—2441no—
189C2×C4#1451975011yescharacteristic
190C2×C4D8×D6111yescharacteristic
191C2×C4#1451980411yescharacteristic
192C8—21no—
193C8—81no—
194C8—612no—
195C8—1221no—
196C8—2441no—
197C8SD16×D6111yescharacteristic
198C8#1451979611yescharacteristic
199C22—4881no—
200C22—4881no—
201C22—2442no—
202C22#1683995611yescharacteristic
203C4—21no—
204C4—161no—
205C4—9761no—
206C4—4881no—
207C4#1683999011yescharacteristic
208C4#1684002411yescharacteristic
209C4SD32×D6111yescharacteristic
210C4#1684020411yescharacteristic
211C2—4882no—
212C2#2144515911yescharacteristic
213C2#2144786311yescharacteristic
214C2#2144789111yescharacteristic
subgroupG/H
centerC22#16839956
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1362C2
socleC22×C61#459
prime radicalC2×D488D4
hypercenter#1362D61
hypocenterC61#12420
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1362

Complements

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

NH ≅ G/Ntype
3. #21445413C2semidirect
5. #21443882C2semidirect
6. #21443878C2semidirect
7. C61×#1362C2semidirect
90. #92418SD32semidirect
110. #1362D61semidirect
130. C61#12420semidirect

Maximal subgroups

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

subgroupindex
#214479672
#214478612
#214454132
#214446132
#214438822
#214438782
C61×#13622
#1242061