Finite Group Databasebeta

← #29600701

Subgroups — #29600701

Order 15616.

278 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 55 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#21458969C211yesmaximal, characteristic, complemented
2C2×#16839600C211yesmaximal, characteristic, complemented
3#21447936C211yesmaximal, characteristic, complemented
4#21444013C211yesmaximal, characteristic, complemented
5#21444003C211yesmaximal, characteristic, complemented
6#21443962C211yesmaximal, characteristic, complemented
7C61×#2263C211yesmaximal, characteristic, complemented
8#16840576—21no—
9#16840202—21no—
10#16840201—22no—
11#16840191—21no—
12C2×Dic488C2211yescharacteristic
13Q32×D61—21no—
14#16840178C2211yescharacteristic
15#16840029—21no—
16#16839600—22no—
17C2×#14519683C2211yescharacteristic
18#16839592C2211yescharacteristic
19#16839575—21no—
20C61×#508C2211yescharacteristic
21C2×D16×C61C2211yescharacteristic
22C61×SD64—21no—
23C61×D32—21no—
24C61×M64C2211yescharacteristic
25#14519824—41no—
26#14519807—41no—
27#14519806—42no—
28#14519803—41no—
29#14519796—22no—
30C2×Dic244—21no—
31Q16×D61—22no—
32#14519783D411yescharacteristic
33Dic488—21no—
34Dic488D412yes—
35#14519723—22no—
36#14519721—22no—
37#14519717D411yescharacteristic
38#14519716—21no—
39C16×D61—21no—
40#14519713—21no—
41#14519694—41no—
42#14519683—21no—
43#135×C61—21no—
44C2×D8×C61—21no—
45Q32×C61D411yescharacteristic
46SD32×C61—21no—
47D16×C61—21no—
48D16×C61—21no—
49D16×C61D411yescharacteristic
50C2×C16×C61C2311yescharacteristic
51C32×C61—21no—
52#41×C61—41no—
53C2×D4×C61—41no—
54Q8×D61—42no—
55#11758224—42no—
56#11758224—82no—
57#11758222—81no—
58#11758222D811yescharacteristic
59C2×Dic122—41no—
60C2×Dic122—81no—
61Q16×C61—21no—
62SD16×C61—41no—
63D8×C61—21no—
64D8×C61—41no—
65D8×C61—41no—
66C2×C8×C61C2×D411yescharacteristic
67#11758202—42no—
68#11758200—42no—
69#11758200—81no—
70#11758199—81no—
71#11758194—41no—
72#11758194D811yescharacteristic
73Dic244—22no—
74Dic244—41no—
75#11758189—21no—
76C8×D61—21no—
77C16×C61C2×D411yescharacteristic
78C16×C61C2×D411yescharacteristic
79#11758185—21no—
80C23×C61—81no—
81Q8×C61—41no—
82D4×C61—41no—
83D4×C61—81no—
84D4×C61—81no—
85D4×C61—81no—
86C2×C4×C61—81no—
87C2×C4×C61C2×D811yescharacteristic
88C22⋊D61—21no—
89C22⋊D61—82no—
90C2×Dic61—82no—
91C2×Dic61—81no—
92D244D1611yescharacteristic
93C4×D61—21no—
94C4×D61—82no—
95Dic122—42no—
96Dic122—82no—
97Dic122—81no—
98Dic122D1611yescharacteristic
99C8×C61#12011yescharacteristic
100C8×C61AGL(1,ℤ/8)11yescharacteristic
101#92418—21no—
102#92418—81no—
103#13670—611nomaximal, Sylow
104C22×C61—81no—
105C22×C61—161no—
106C22×C61—321no—
107C22×C61#50911yescharacteristic
108C2×D61—21no—
109C4×C61—81no—
110C4×C61#44711yescharacteristic
111C4×C61C2×D1611yescharacteristic
112Dic61—21no—
113Dic61—82no—
114#3417—611no—
115#2263D6111yescharacteristic, complemented
116C2×SD64—611no—
117#2221—611no—
118#1420—611no—
119#1417—611no—
120#1401—611no—
121C2×C61—21no—
122C2×C61—161no—
123C2×C61—321no—
124C2×C61#218411yescharacteristic
125D61—41no—
126#578—1221no—
127#510—1221no—
128#510—1222no—
129#508—1221no—
130#508C2×D6111yescharacteristic
131C2×Q32—611no—
132C2×Q32—1221no—
133C2×D16C2×D6111yescharacteristic
134#504—611no—
135#472—1221no—
136SD64—21no—
137SD64—1222no—
138D32—21no—
139M64C2×D6111yescharacteristic
140C2×C32—611no—
141#368—611no—
142#361—1221no—
143C61#1367011yescharacteristic, complemented, Sylow
1442−1+4—2441no—
145#137—2441no—
146#137—2442no—
147AGL(1,ℤ/8)—2441no—
148#135—21no—
149#135—1222no—
150C2×Q16—1222no—
151C2×Q16—1221no—
152C2×D8—21no—
153#131—611no—
154Q32—612no—
155Q32—1222no—
156Q32—1221no—
157Q32C22⋊D6111yescharacteristic
158SD32—21no—
159SD32—1222no—
160D16—21no—
161D16—21no—
162D16C22⋊D6111yescharacteristic
163M32—611no—
164M32—1221no—
165C2×C16—1221no—
166C2×C16C22×D6111yescharacteristic
167#108—1221no—
168#100—2441no—
169C32—21no—
170C32—1221no—
171#41—41no—
172#41—611no—
173#41—4881no—
174#41—4882no—
175#41—2442no—
176C2×Q8—4881no—
177C2×Q8—2442no—
178C2×Q8—2441no—
179C2×D4—41no—
180Q16—21no—
181Q16—1222no—
182Q16—2442no—
183Q16—2441no—
184SD16—41no—
185SD16—4881no—
186SD16—2442no—
187D8—21no—
188D8—41no—
189D8—41no—
190D8—4881no—
191M16—611no—
192M16—1221no—
193M16—2441no—
194C2×C8—1221no—
195C2×C8D4×D6111yescharacteristic
196C16—1221no—
197C16D4×D6111yescharacteristic
198C16C2×C22⋊D6111yescharacteristic
199C23—81no—
200Q8—41no—
201Q8—611no—
202Q8—4882no—
203Q8—4881no—
204Q8—2442no—
205D4—41no—
206D4—81no—
207D4—81no—
208D4—81no—
209D4—611no—
210D4—1221no—
211D4—4882no—
212C2×C4—81no—
213C2×C4—1221no—
214C2×C4—4882no—
215C2×C4—4882no—
216C2×C4—4881no—
217C2×C4D8×D6111yescharacteristic
218C8—1221no—
219C8—4881no—
220C8#1451974511yescharacteristic
221C8#1451980111yescharacteristic
222C22—81no—
223C22—161no—
224C22—321no—
225C22—1221no—
226C22#1684019611yescharacteristic
227C4—81no—
228C4—1221no—
229C4—4882no—
230C4#1683989411yescharacteristic
231C4D16×D6111yescharacteristic
232C2—21no—
233C2—161no—
234C2—321no—
235C2—2441no—
236C2#2144772911yescharacteristic
subgroupG/H
centerC2#21447729
commutator, cosocleC2×C16×C61C23
FrattiniC2×C16C22×D61
FittingC61×#2263C2
socleC2×C61#2184
hypercenter#2263D61
hypocenterC61#13670
LCSG ▷ C2×C16×C61 ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #2263

Complements

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

NH ≅ G/Ntype
1. #21458969C2semidirect
2. C2×#16839600C2semidirect
3. #21447936C2semidirect
4. #21444013C2semidirect
5. #21444003C2semidirect
6. #21443962C2semidirect
7. C61×#2263C2semidirect
115. #2263D61semidirect
143. C61#13670semidirect

Maximal subgroups

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

subgroupindex
#214589692
C2×#168396002
#214479362
#214440132
#214440032
#214439622
C61×#22632
#1367061