Finite Group Databasebeta

← #29594211

Subgroups — #29594211

Order 15616.

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

normal subgroups only

This group has 240 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#21447870C211yesmaximal, characteristic, complemented
2#21447856C211yesmaximal, characteristic
3#21445424C211yesmaximal, characteristic
4#21444625C211yesmaximal, characteristic, complemented
5#21443888C211yesmaximal, characteristic, complemented
6#21443867C211yesmaximal, characteristic, complemented
7C61×#1361C211yesmaximal, characteristic
8C2×Dic488—21no—
9C2×#14519721—21no—
10#16840142C2211yescharacteristic
11#16840108—21no—
12#16840108—21no—
13#16839886—21no—
14C4×Dic244C2211yescharacteristic
15C4⋊#11758185C2211yescharacteristic
16#16839567—21no—
17#16839563—21no—
18#16839492—21no—
19C8×#92418C2211yescharacteristic
20C61×#493C2211yescharacteristic
21C61×C4⋊C16C2211yescharacteristic
22C61×#335C2211yescharacteristic
23C2×Dic244—21no—
24C2×Dic244—21no—
25C2×Dic244D411yescharacteristic
26#14519777—21no—
27C4×Dic122—21no—
28Dic488—42no—
29#14519721—42no—
30C2×#11758185—21no—
31#14519711D411yescharacteristic
32#14519706—41no—
33#14519702—21no—
34#14519698—42no—
35#14519698—41no—
36#14519698—41no—
37C4×#92418D411yescharacteristic
38C4×#92418D411yescharacteristic
39C8×Dic61—41no—
40C2×D8×C61—21no—
41C2×D8×C61—21no—
42#127×C61—21no—
43C2×C16×C61—21no—
44C4⋊C8×C61—21no—
45C4×C8×C61C2311yescharacteristic
46C2×D4×C61—41no—
47C2×D4×C61—41no—
48C2×D4×C61—41no—
49C2×Dic122—21no—
50C2×Dic122—41no—
51D8×C61—41no—
52D8×C61—41no—
53D8×C61—81no—
54C2×C8×C61—41no—
55C2×C8×C61C2×D411yescharacteristic
56C2×C8×C61#4111yescharacteristic
57C42×C61C2×D411yescharacteristic
58C4⋊Dic61—21no—
59C4⋊Dic61—41no—
60C4⋊Dic61—41no—
61#11758196—41no—
62C4×Dic61—41no—
63C2×#92418—21no—
64C2×#92418D811yescharacteristic
65C2×#92418D811yescharacteristic
66Dic244—21no—
67Dic244—41no—
68Dic244—41no—
69Dic244—81no—
70Dic244D812yes—
71C16×C61—41no—
72#11758185—41no—
73C23×C61—81no—
74D4×C61—82no—
75D4×C61—81no—
76D4×C61—81no—
77D4×C61—81no—
78D4×C61—81no—
79C2×C4×C61#12111yescharacteristic
80C2×C4×C61C2×D811yescharacteristic
81C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
82C2×Dic61—41no—
83C2×Dic61—41no—
84C2×Dic61—81no—
85Dic122—22no—
86Dic122—41no—
87Dic122—81no—
88Dic122—81no—
89C8×C61—21no—
90C8×C61—81no—
91C8×C61C2×D811yescharacteristic
92C8×C61#13511yescharacteristic
93#92418—21no—
94#92418—21no—
95#92418—41no—
96#12429—611nomaximal, Sylow
97C22×C61—161no—
98C22×C61—161no—
99C22×C61—161no—
100C22×C61#45911yescharacteristic
101C4×C61—21no—
102C4×C61#46611yescharacteristic
103C4×C61#47211yescharacteristic
104C4×C61#50811yescharacteristic
105C4×C61#51011yescharacteristic
106Dic61—42no—
107Dic61—81no—
108Dic61—161no—
109#2209—611no—
110#2207—611no—
111#1709—611no—
112C8×Q16—611no—
113#1370—611no—
114#1362—611no—
115#1361D6111yescharacteristic
116C2×C61—321no—
117C2×C61#166711yescharacteristic
118C2×C61#221111yescharacteristic
119C2×C61#221211yescharacteristic
120C2×Q32—1221no—
121C2×SD32—1221no—
122#494—611no—
123#493C2×D6111yescharacteristic
124#486—1221no—
125#486—1221no—
126C8×Q8—1221no—
127C4×Q16—611no—
128C4⋊C16—611no—
129C4⋊C16C2×D6111yescharacteristic
130#358—1221no—
131#357—1221no—
132#335C2×D6111yescharacteristic
133Q8⋊C8—1221no—
134C82—611no—
135C61#1242911yescharacteristic, complemented, Sylow
136C2×Q16—611no—
137C2×Q16—1221no—
138C2×Q16—1221no—
139C2×D8—21no—
140C2×D8—21no—
141C4⋊Q8—1221no—
142#127—21no—
143C4×Q8—1221no—
144Q32—2442no—
145SD32—2442no—
146C2×C16—21no—
147C2×C16—1221no—
148#107—611no—
149C4⋊C8—21no—
150C4⋊C8—2441no—
151#103—1221no—
152#102—2441no—
153#102—2441no—
154#102—2442no—
155C4×C8—611no—
156C4×C8—611no—
157C4×C8—2441no—
158C4×C8C22×D6111yescharacteristic
159C2×Q8—1221no—
160C2×Q8—2441no—
161C2×D4—41no—
162C2×D4—41no—
163C2×D4—41no—
164Q16—612no—
165Q16—1221no—
166Q16—4881no—
167Q16—2441no—
168Q16—2441no—
169D8—41no—
170D8—41no—
171D8—81no—
172C2×C8—41no—
173C2×C8—611no—
174C2×C8—611no—
175C2×C8—1221no—
176C2×C8#1175822211yescharacteristic
177C2×C8D4×D6111yescharacteristic
178C4⋊C4—1221no—
179C4⋊C4—2441no—
180C4⋊C4—2441no—
181C4⋊C4—2441no—
182C42—2441no—
183C42D4×D6111yescharacteristic
184C16—41no—
185C16—2441no—
186C23—81no—
187Q8—1222no—
188Q8—4881no—
189Q8—4881no—
190Q8—2441no—
191D4—82no—
192D4—81no—
193D4—81no—
194D4—81no—
195D4—81no—
196C2×C4—4881no—
197C2×C4—2441no—
198C2×C4—2441no—
199C2×C4#1451975011yescharacteristic
200C2×C4D8×D6111yescharacteristic
201C2×C4#1451980411yescharacteristic
202C8—21no—
203C8—81no—
204C8—1221no—
205C8—1221no—
206C8—2441no—
207C8D8×D6111yescharacteristic
208C8#1451979811yescharacteristic
209C22—161no—
210C22—161no—
211C22—161no—
212C22#1683995611yescharacteristic
213C4—21no—
214C4—9761no—
215C4—4881no—
216C4—2442no—
217C4#1683999711yescharacteristic
218C4#1684003111yescharacteristic
219C4#1684019111yescharacteristic
220C4#1684020111yescharacteristic
221C2—321no—
222C2#2144517311yescharacteristic
223C2#2144788011yescharacteristic
224C2#2144788711yescharacteristic
subgroupG/H
centerC22#16839956
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1361C2
socleC22×C61#459
prime radicalC61×#493C22
hypercenter#1361D61
hypocenterC61#12429
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1361

Complements

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

NH ≅ G/Ntype
1. #21447870C2semidirect
4. #21444625C2semidirect
5. #21443888C2semidirect
6. #21443867C2semidirect
135. C61#12429semidirect

Maximal subgroups

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

subgroupindex
#214478702
#214478562
#214454242
#214446252
#214438882
#214438672
C61×#13612
#1242961