Finite Group Databasebeta

← #29600666

Subgroups — #29600666

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×#16840195C211yesmaximal, characteristic, complemented
2C2×#16839599C211yesmaximal, characteristic, complemented
3C2×D1952C211yesmaximal, characteristic, complemented
4#21447906C211yesmaximal, characteristic, complemented
5#21443996C211yesmaximal, characteristic, complemented
6#21443956C211yesmaximal, characteristic, complemented
7C61×#1416C211yesmaximal, characteristic, complemented
8C2×#14519800—21no—
9#16840195—22no—
10#16840195—22no—
11C2×#14519720—21no—
12C2×D976C2211yescharacteristic
13C2×D976C2211yescharacteristic
14C2×C16×D61C2211yescharacteristic
15#16839999—21no—
16#16839599—22no—
17D1952—22no—
18C2×#14519683C2211yescharacteristic
19#16839562—21no—
20C2×Q32×C61C2211yescharacteristic
21C2×C32×C61C2211yescharacteristic
22C61×#366C2211yescharacteristic
23C2×#11758226—41no—
24#14519800—24no—
25#14519800—42no—
26C2×#11758201—41no—
27C2×D488—21no—
28C2×D488—21no—
29C2×C8×D61D411yescharacteristic
30#14519752—41no—
31#14519720—24no—
32D976—21no—
33D976—21no—
34D976—21no—
35D976D412yescomplemented
36C2×#11758185D411yescharacteristic
37C16×D61—21no—
38C16×D61—21no—
39#14519697—41no—
40#14519683—21no—
41C2×Q16×C61—21no—
42Q32×C61—21no—
43Q32×C61D412yescomplemented
44C2×C16×C61C2311yescharacteristic
45#107×C61—21no—
46C32×C61—21no—
47C2×Q8×C61—41no—
48#11758226—44no—
49#11758226—82no—
50C2×D244—41no—
51C2×D244—41no—
52C2×D244—81no—
53C2×D244—81no—
54C2×C4×D61—81no—
55C2×C4×D61D811yescharacteristic
56Q16×C61—22no—
57Q16×C61—41no—
58C2×C8×C61C2×D411yescharacteristic
59C4⋊C4×C61—41no—
60#11758201—44no—
61#11758198—81no—
62C2×#92418D811yescharacteristic
63D488—22no—
64D488—41no—
65D488—41no—
66D488—41no—
67C8×D61—21no—
68C8×D61—21no—
69C16×C61C2×D411yescharacteristic
70C16×C61C2×D411yescharacteristic
71#11758185—21no—
72C22×D61—81no—
73C22×D61—81no—
74C22×D61D1611yescharacteristic
75Q8×C61—42no—
76Q8×C61—81no—
77C2×C4×C61—81no—
78C2×C4×C61—81no—
79C2×C4×C61C2×D811yescharacteristic
80C2×Dic61D1611yescharacteristic
81D244—42no—
82D244—84no—
83D244—81no—
84D244—81no—
85D244—81no—
86D244—162no—
87C4×D61—21no—
88C4×D61—21no—
89C4×D61—84no—
90C8×C61#12011yescharacteristic
91C8×C61AGL(1,ℤ/8)11yescharacteristic
92#92418—21no—
93#13663—611nomaximal, Sylow
94C22×C61C2×D1611yescharacteristic
95C2×D61—21no—
96C2×D61—21no—
97C2×D61—21no—
98C2×D61—82no—
99C2×D61—161no—
100C2×D61—161no—
101C2×D61—161no—
102C2×D61—161no—
103C2×D61—161no—
104C4×C61—82no—
105C4×C61—161no—
106C4×C61#44711yescharacteristic
107C4×C61#50911yescharacteristic
108Dic61—21no—
109C2×#508—611no—
110C2×SD64—611no—
111C2×D32—611no—
112#2215—611no—
113#1416D6111yescharacteristic, complemented
114#1415—611no—
115C22⋊C32—611no—
116C2×C61#218411yescharacteristic
117C2×C61#226211yescharacteristic
118C2×C61#226311yescharacteristic
119D61—41no—
120D61—162no—
121D61—321no—
122C2×#135—1221no—
123#508—1222no—
124#508—1222no—
125C2×Q32C2×D6111yescharacteristic
126C2×SD32—1221no—
127C2×D16—611no—
128C2×D16—611no—
129C22×C16—611no—
130#466—1221no—
131SD64—1222no—
132D32—1222no—
133C2×C32—611no—
134C2×C32C2×D6111yescharacteristic
135#366C2×D6111yescharacteristic
136#357—1221no—
137C61#1366311yescharacteristic, complemented, Sylow
138C2×#41—2441no—
139#135—1224no—
140#135—2442no—
141C2×Q16—21no—
142C2×SD16—2441no—
143C2×D8—1221no—
144C2×D8—1221no—
145C22×C8—611no—
146#121—2441no—
147Q32—21no—
148Q32D24412yescomplemented
149SD32—1224no—
150D16—612no—
151D16—1221no—
152D16—1221no—
153D16—1221no—
154C2×C16—611no—
155C2×C16—1221no—
156C2×C16—1221no—
157C2×C16C22×D6111yescharacteristic
158#107—21no—
159#102—2441no—
160C32—21no—
161C32—1221no—
162#41—4882no—
163#41—2444no—
164C2×Q8—41no—
165C2×D4—4881no—
166C2×D4—4881no—
167C2×D4—2441no—
168C2×D4—2441no—
169C22×C4—611no—
170C22×C4—4881no—
171Q16—22no—
172Q16—41no—
173SD16—2444no—
174D8—1222no—
175D8—2441no—
176D8—2441no—
177D8—2441no—
178C2×C8—611no—
179C2×C8—1221no—
180C2×C8—1221no—
181C2×C8D4×D6111yescharacteristic
182C4⋊C4—41no—
183C22⋊C4—4881no—
184C16—1221no—
185C16C2×D24411yescharacteristic
186C16D4×D6111yescharacteristic
187C23—611no—
188C23—4881no—
189C23—4881no—
190Q8—42no—
191Q8—81no—
192D4—9762no—
193D4—4884no—
194D4—4881no—
195D4—4881no—
196D4—4881no—
197D4—2442no—
198C2×C4—81no—
199C2×C4—81no—
200C2×C4—611no—
201C2×C4—1221no—
202C2×C4—1221no—
203C2×C4—4884no—
204C2×C4D8×D6111yescharacteristic
205C8—1221no—
206C8#1451974711yescharacteristic
207C8#1451980411yescharacteristic
208C22—1221no—
209C22—1221no—
210C22—1221no—
211C22—9761no—
212C22—9761no—
213C22—9761no—
214C22—9761no—
215C22—9761no—
216C22—4882no—
217C22D16×D6111yescharacteristic
218C4—82no—
219C4—161no—
220C4—1221no—
221C4#1683989711yescharacteristic
222C4#1684019911yescharacteristic
223C2—19521no—
224C2—9762no—
225C2—2441no—
226C2#2144773211yescharacteristic
227C2#2144812911yescharacteristic
228C2#2144813311yescharacteristic
subgroupG/H
centerC22D16×D61
commutator, cosocleC2×C16×C61C23
FrattiniC2×C16C22×D61
FittingC61×#1416C2
socleC22×C61C2×D16
hypercenter#1416D61
hypocenterC61#13663
LCSG ▷ C2×C16×C61 ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #1416

Complements

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

NH ≅ G/Ntype
1. C2×#16840195C2semidirect
2. C2×#16839599C2semidirect
3. C2×D1952C2semidirect
4. #21447906C2semidirect
5. #21443996C2semidirect
6. #21443956C2semidirect
7. C61×#1416C2semidirect
35. D976D4semidirect
43. Q32×C61D4semidirect
113. #1416D61semidirect
137. C61#13663semidirect
148. Q32D244semidirect

Maximal subgroups

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

subgroupindex
C2×#168401952
C2×#168395992
C2×D19522
#214479062
#214439962
#214439562
C61×#14162
#1366361