Finite Group Databasebeta

← #29594213

Subgroups — #29594213

Order 15616.

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

normal subgroups only

This group has 240 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#21447870C211yesmaximal, characteristic, complemented
2#21447860C211yesmaximal, characteristic
3#21445425C211yesmaximal, characteristic
4C8×Dic244C211yesmaximal, characteristic, complemented
5#21443869C211yesmaximal, characteristic, complemented
6#21443866C211yesmaximal, characteristic
7C61×#1370C211yesmaximal, characteristic, complemented
8C2×Dic488—21no—
9C2×#14519722—21no—
10#16840142C2211yescharacteristic
11#16840139C2211yescharacteristic
12#16840109—21no—
13#16840109—21no—
14C8×Dic122—21no—
15C4×Dic244C2211yescharacteristic
16#16839567—21no—
17#16839564—21no—
18#16839515C2211yescharacteristic
19#16839494—21no—
20C61×C4⋊C16C2211yescharacteristic
21C61×C4⋊C16C2211yescharacteristic
22C82×C61C2211yescharacteristic
23C2×Dic244—21no—
24C2×Dic244—21no—
25C2×Dic244D411yescharacteristic
26C2×D488—21no—
27C2×D488—21no—
28#14519777—21no—
29#14519774—21no—
30C4×Dic122—21no—
31Dic488—42no—
32#14519722—42no—
33#14519711D411yescharacteristic
34C4⋊#92418—21no—
35#14519706—41no—
36#14519702—21no—
37#14519699—42no—
38#14519699—41no—
39#14519699—41no—
40C8×Dic61—41no—
41C2×C16×C61—21no—
42C2×C16×C61—21no—
43C4×C8×C61D411yescharacteristic
44C4×C8×C61D411yescharacteristic
45C4×C8×C61C2311yescharacteristic
46C2×D244—41no—
47C2×D244—41no—
48C2×D244—41no—
49C2×Dic122—21no—
50C2×Dic122—41no—
51C2×C8×C61—21no—
52C2×C8×C61D811yescharacteristic
53C2×C8×C61D811yescharacteristic
54C2×C8×C61C2×D411yescharacteristic
55C2×C8×C61#4111yescharacteristic
56C42×C61C2×D411yescharacteristic
57C4⋊Dic61—21no—
58C4⋊Dic61—41no—
59C4⋊Dic61—41no—
60#11758196—41no—
61C4×Dic61—41no—
62C2×#92418—41no—
63Dic244—21no—
64Dic244—41no—
65Dic244—41no—
66Dic244—81no—
67Dic244D812yes—
68D488—41no—
69D488—41no—
70D488—81no—
71C16×C61—41no—
72C16×C61—41no—
73C22×D61—81no—
74C2×C4×C61#12111yescharacteristic
75C2×C4×C61C2×D811yescharacteristic
76C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
77C2×Dic61—41no—
78C2×Dic61—41no—
79C2×Dic61—81no—
80D244—82no—
81D244—81no—
82D244—81no—
83D244—81no—
84D244—81no—
85Dic122—22no—
86Dic122—41no—
87Dic122—81no—
88Dic122—81no—
89C8×C61—21no—
90C8×C61—21no—
91C8×C61—21no—
92C8×C61—41no—
93C8×C61C2×D811yescharacteristic
94C8×C61#13511yescharacteristic
95#92418—81no—
96#12429—611nomaximal, Sylow
97C22×C61#45911yescharacteristic
98C2×D61—161no—
99C2×D61—161no—
100C2×D61—161no—
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#1370D6111yescharacteristic, complemented
114#1362—611no—
115#1361—611no—
116C2×C61#166711yescharacteristic
117C2×C61#221111yescharacteristic
118C2×C61#221211yescharacteristic
119D61—321no—
120C2×Q32—1221no—
121C2×SD32—1221no—
122#494—611no—
123#493—611no—
124#486—1221no—
125#486—1221no—
126C8×Q8—1221no—
127C4×Q16—611no—
128C4⋊C16C2×D6111yescharacteristic
129C4⋊C16C2×D6111yescharacteristic
130#358—1221no—
131#357—1221no—
132#335—611no—
133Q8⋊C8—1221no—
134C82C2×D6111yescharacteristic
135C61#1242911yescharacteristic, complemented, Sylow
136C2×Q16—611no—
137C2×Q16—1221no—
138C2×Q16—1221no—
139C2×D8—1221no—
140C2×D8—1221no—
141C4⋊Q8—1221no—
142#127—1221no—
143C4×Q8—1221no—
144Q32—2442no—
145SD32—2442no—
146C2×C16—21no—
147C2×C16—21no—
148#107—611no—
149C4⋊C8—1221no—
150C4⋊C8—2441no—
151#103—1221no—
152#102—2442no—
153#102—2441no—
154#102—2441no—
155C4×C8—2441no—
156C4×C8D24411yescharacteristic
157C4×C8D24411yescharacteristic
158C4×C8C22×D6111yescharacteristic
159C2×Q8—1221no—
160C2×Q8—2441no—
161C2×D4—2441no—
162C2×D4—2441no—
163C2×D4—2441no—
164Q16—612no—
165Q16—1221no—
166Q16—4881no—
167Q16—2441no—
168Q16—2441no—
169D8—4881no—
170D8—2441no—
171D8—2441no—
172C2×C8—21no—
173C2×C8—2441no—
174C2×C8D48811yescharacteristic
175C2×C8D48811yescharacteristic
176C2×C8D4×D6111yescharacteristic
177C2×C8#1175822611yescharacteristic
178C4⋊C4—1221no—
179C4⋊C4—2441no—
180C4⋊C4—2441no—
181C4⋊C4—2441no—
182C42—2441no—
183C42C2×D24411yescharacteristic
184C16—41no—
185C16—41no—
186C23—4881no—
187Q8—1222no—
188Q8—4881no—
189Q8—4881no—
190Q8—2441no—
191D4—4882no—
192D4—4881no—
193D4—4881no—
194D4—4881no—
195D4—4881no—
196C2×C4—4881no—
197C2×C4—2441no—
198C2×C4—2441no—
199C2×C4#1451975211yescharacteristic
200C2×C4C2×D48811yescharacteristic
201C2×C4#1451980511yescharacteristic
202C8—21no—
203C8—21no—
204C8—21no—
205C8—41no—
206C8—4881no—
207C8D8×D6111yescharacteristic
208C8#1451980011yescharacteristic
209C22—9761no—
210C22—9761no—
211C22—9761no—
212C22#1683995811yescharacteristic
213C4—21no—
214C4—9761no—
215C4—4881no—
216C4—2442no—
217C4#1683999911yescharacteristic
218C4#1684003311yescharacteristic
219C4#1684019411yescharacteristic
220C4#1684020511yescharacteristic
221C2—19521no—
222C2#2144517511yescharacteristic
223C2#2144788211yescharacteristic
224C2#2144788911yescharacteristic
subgroupG/H
centerC22#16839958
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1370C2
socleC22×C61#459
prime radical#16840139C22
hypercenter#1370D61
hypocenterC61#12429
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C82 ◁ #1370

Complements

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

NH ≅ G/Ntype
1. #21447870C2semidirect
4. C8×Dic244C2semidirect
5. #21443869C2semidirect
7. C61×#1370C2semidirect
113. #1370D61semidirect
135. C61#12429semidirect

Maximal subgroups

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

subgroupindex
#214478702
#214478602
#214454252
C8×Dic2442
#214438692
#214438662
C61×#13702
#1242961