Finite Group Databasebeta

← #29600660

Subgroups — #29600660

Order 15616.

298 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 59 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
1C2×#16840191C211yesmaximal, characteristic, complemented
2C2×#16839600C211yesmaximal, characteristic, complemented
3#21447902C211yesmaximal, characteristic, complemented
4#21444001C211yesmaximal, characteristic, complemented
5#21443997C211yesmaximal, characteristic, complemented
6#21443956C211yesmaximal, characteristic, complemented
7C2×C61×D32C211yesmaximal, characteristic, complemented
8C2×#14519796—21no—
9#16840191—22no—
10#16840191—22no—
11C2×Dic488C2211yescharacteristic
12C2×#14519721—21no—
13C2×C16×D61C2211yescharacteristic
14#16839995—21no—
15#16839600—22no—
16C2×#14519683C2211yescharacteristic
17#16839588C2211yescharacteristic
18#16839563—21no—
19C2×D16×C61C2211yescharacteristic
20C2×D16×C61C2211yescharacteristic
21C61×D32—22no—
22C2×C32×C61C2211yescharacteristic
23C2×#11758224—41no—
24#14519796—24no—
25#14519796—42no—
26C2×Dic244—21no—
27C2×#11758200—41no—
28C2×C8×D61D411yescharacteristic
29#14519748—41no—
30Dic488—21no—
31Dic488D412yescomplemented
32#14519721—24no—
33C2×#11758185D411yescharacteristic
34C16×D61—21no—
35C16×D61—21no—
36#14519711—21no—
37#14519698—41no—
38#14519683—21no—
39C2×D8×C61—21no—
40C2×D8×C61—21no—
41D16×C61—21no—
42D16×C61—21no—
43D16×C61—21no—
44D16×C61D412yescomplemented
45C2×C16×C61C2311yescharacteristic
46C32×C61—21no—
47C2×D4×C61—41no—
48C2×D4×C61—41no—
49C2×C22⋊D61—81no—
50C2×C22⋊D61—81no—
51C22×Dic61—81no—
52#11758224—44no—
53#11758224—82no—
54C2×C4×D61D811yescharacteristic
55C2×Dic122—41no—
56D8×C61—22no—
57D8×C61—41no—
58D8×C61—41no—
59D8×C61—41no—
60C2×C8×C61C2×D411yescharacteristic
61C22⋊Dic61—81no—
62#11758200—44no—
63C4⋊Dic61—41no—
64C2×#92418D811yescharacteristic
65Dic244—22no—
66Dic244—41no—
67C8×D61—21no—
68C8×D61—21no—
69C16×C61C2×D411yescharacteristic
70C16×C61C2×D411yescharacteristic
71#11758185—21no—
72C23×C61—81no—
73C23×C61—81no—
74C22×D61D1611yescharacteristic
75D4×C61—42no—
76D4×C61—81no—
77D4×C61—81no—
78D4×C61—81no—
79C2×C4×C61C2×D811yescharacteristic
80C22⋊D61—84no—
81C22⋊D61—162no—
82C2×Dic61—84no—
83C2×Dic61—81no—
84C2×Dic61—81no—
85C2×Dic61D1611yescharacteristic
86C4×D61—21no—
87C4×D61—21no—
88Dic122—42no—
89Dic122—81no—
90C8×C61#12011yescharacteristic
91C8×C61AGL(1,ℤ/8)11yescharacteristic
92#92418—21no—
93#13663—611nomaximal, Sylow
94C22×C61—82no—
95C22×C61—161no—
96C22×C61—161no—
97C22×C61—161no—
98C22×C61—161no—
99C22×C61—161no—
100C22×C61C2×D1611yescharacteristic
101C2×D61—21no—
102C2×D61—21no—
103C2×D61—21no—
104C4×C61#44711yescharacteristic
105C4×C61#50911yescharacteristic
106Dic61—21no—
107Dic61—82no—
108Dic61—161no—
109C2×#508—611no—
110C2×SD64—611no—
111C2×D32D6111yescharacteristic, complemented
112#2215—611no—
113#1416—611no—
114#1415—611no—
115C22⋊C32—611no—
116C2×C61—162no—
117C2×C61—321no—
118C2×C61#218411yescharacteristic
119C2×C61#226211yescharacteristic
120C2×C61#226311yescharacteristic
121D61—41no—
122C2×#135—1221no—
123#508—1222no—
124#508—1222no—
125C2×Q32—611no—
126C2×SD32—1221no—
127C2×D16C2×D6111yescharacteristic
128C2×D16C2×D6111yescharacteristic
129C22×C16—611no—
130#466—1221no—
131SD64—1222no—
132D32—22no—
133C2×C32—611no—
134C2×C32C2×D6111yescharacteristic
135#366—611no—
136#357—1221no—
137C61#1366311yescharacteristic, complemented, Sylow
138C2×#41—2441no—
139#135—1224no—
140#135—2442no—
141C2×Q16—1221no—
142C2×SD16—2441no—
143C2×D8—21no—
144C2×D8—21no—
145C22×C8—611no—
146#121—2441no—
147Q32—612no—
148Q32—1221no—
149SD32—1224no—
150D16—21no—
151D16—21no—
152D16—21no—
153D16C22⋊D6112yescomplemented
154C2×C16—611no—
155C2×C16—1221no—
156C2×C16—1221no—
157C2×C16C22×D6111yescharacteristic
158#107—1221no—
159#102—2441no—
160C32—21no—
161C32—1221no—
162#41—4882no—
163#41—2444no—
164C2×Q8—2441no—
165C2×D4—41no—
166C2×D4—41no—
167C2×D4—4881no—
168C2×D4—4881no—
169C22×C4—611no—
170C22×C4—4881no—
171Q16—1222no—
172Q16—2441no—
173SD16—2444no—
174D8—22no—
175D8—41no—
176D8—41no—
177D8—41no—
178C2×C8—611no—
179C2×C8—1221no—
180C2×C8—1221no—
181C2×C8D4×D6111yescharacteristic
182C4⋊C4—2441no—
183C22⋊C4—4881no—
184C16—1221no—
185C16D4×D6111yescharacteristic
186C16C2×C22⋊D6111yescharacteristic
187C23—81no—
188C23—81no—
189C23—611no—
190Q8—4881no—
191Q8—2442no—
192D4—42no—
193D4—81no—
194D4—81no—
195D4—81no—
196D4—9762no—
197D4—4884no—
198C2×C4—611no—
199C2×C4—1221no—
200C2×C4—1221no—
201C2×C4—4884no—
202C2×C4—4881no—
203C2×C4—4881no—
204C2×C4D8×D6111yescharacteristic
205C8—1221no—
206C8#1451974511yescharacteristic
207C8#1451980111yescharacteristic
208C22—82no—
209C22—161no—
210C22—161no—
211C22—161no—
212C22—161no—
213C22—161no—
214C22—1221no—
215C22—1221no—
216C22—1221no—
217C22D16×D6111yescharacteristic
218C4—1221no—
219C4—9761no—
220C4—4882no—
221C4#1683989411yescharacteristic
222C4#1684019611yescharacteristic
223C2—162no—
224C2—321no—
225C2—2441no—
226C2#2144772911yescharacteristic
227C2#2144812511yescharacteristic
228C2#2144813011yescharacteristic
subgroupG/H
centerC22D16×D61
commutator, cosocleC2×C16×C61C23
FrattiniC2×C16C22×D61
FittingC2×C61×D32C2
socleC22×C61C2×D16
hypercenterC2×D32D61
hypocenterC61#13663
LCSG ▷ C2×C16×C61 ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×D32

Complements

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

NH ≅ G/Ntype
1. C2×#16840191C2semidirect
2. C2×#16839600C2semidirect
3. #21447902C2semidirect
4. #21444001C2semidirect
5. #21443997C2semidirect
6. #21443956C2semidirect
7. C2×C61×D32C2semidirect
31. Dic488D4semidirect
44. D16×C61D4semidirect
111. C2×D32D61semidirect
137. C61#13663semidirect
153. D16C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168401912
C2×#168396002
#214479022
#214440012
#214439972
#214439562
C2×C61×D322
#1366361