Finite Group Databasebeta

← #30606016

Subgroups — #30606016

Order 15616.

240 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 64 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#21461451C211yesmaximal, characteristic, complemented
2#21461400C211yesmaximal, characteristic, complemented
3#21460853C211yesmaximal, characteristic, complemented
4#21460774C211yesmaximal, characteristic, complemented
5#21460774C211yesmaximal, characteristic, complemented
6#92420⋊C16C211yesmaximal, characteristic, complemented
7#21447665C211yesmaximal, characteristic
8#16840796—21no—
9#16840790—21no—
10#16840648C2211yescharacteristic
11#16840625C2211yescharacteristic
12#16840625C2211yescharacteristic
13#16840610—21no—
14#16840610—21no—
15C8×#92420C2211yescharacteristic
16C2×D976C411yescharacteristic
17#16839844C2211yescharacteristic
18#16839844C2211yescharacteristic
19#16839562C411yescharacteristic
20#16839562C411yescharacteristic
21C16×Dic61C2211yescharacteristic
22C61×#366C411yescharacteristic
23C2×#11758213—41no—
24C2×D61⋊C8—41no—
25C2×#11758187—21no—
26C4⋊#92420—21no—
27C4⋊#92420—21no—
28#14519834—41no—
29#14519834—41no—
30C4×#92420D411yescharacteristic
31C4×#92420D411yescharacteristic
32C2×D488C2×C411yescharacteristic
33C2×D488C2×C411yescharacteristic
34#14519739—21no—
35#14519739—21no—
36D976—22no—
37C2×#11758185C2×C411yescharacteristic
38#14519697—21no—
39#14519697—21no—
40C8×Dic61C2311yescharacteristic
41C2×C16×C61C2×C411yescharacteristic
42#107×C61C2×C411yescharacteristic
43#107×C61C2×C411yescharacteristic
44C2×D244—21no—
45C2×D244—21no—
46C2×C4×D61—41no—
47C2×C4×D61—41no—
48C2×#92420—21no—
49C2×#92420—41no—
50C2×#92420—41no—
51C2×#92420D811yescharacteristic
52C2×#92420D811yescharacteristic
53#11758213—82no—
54D61⋊C8—82no—
55C2×C8×C61C22×C411yescharacteristic
56C4⋊C4×C61—21no—
57C4⋊C4×C61—21no—
58#11758198—41no—
59#11758198—41no—
60C4×Dic61C2×D411yescharacteristic
61C2×#92418#4111yescharacteristic
62D488—21no—
63D488—21no—
64D488—21no—
65D488M1612yescomplemented
66#11758187—41no—
67C16×C61—21no—
68#11758185—21no—
69C22×D61—41no—
70C22×D61—41no—
71C2×C4×C61—41no—
72C2×C4×C61—41no—
73C2×C4×C61C4×D411yescharacteristic
74C2×Dic61C2×D811yescharacteristic
75C2×Dic61#13511yescharacteristic
76D244—22no—
77D244—41no—
78D244—41no—
79D244—41no—
80C4×D61—81no—
81C4×D61—81no—
82C4×D61—81no—
83C4×D61—81no—
84#92420—22no—
85#92420—21no—
86#92420—21no—
87#92420—81no—
88#92420—81no—
89C8×C61C2×M1611yescharacteristic
90C8×C61#13111yescharacteristic
91#92418—21no—
92#12073—611nomaximal, Sylow
93C22×C61C4×D811yescharacteristic
94C2×D61—42no—
95C2×D61—81no—
96C2×D61—81no—
97C2×D61—81no—
98C2×D61—81no—
99C2×D61—81no—
100C4×C61—81no—
101C4×C61—81no—
102C4×C61#43511yescharacteristic
103C4×C61#44411yescharacteristic
104Dic61—21no—
105Dic61#50911yescharacteristic
106Dic61#50911yescharacteristic
107C4×D16—611no—
108#1589—611no—
109C8×D8—611no—
110#1372—611no—
111#1331—611no—
112#1331—611no—
113#1312—611no—
114C2×C61#158111yescharacteristic
115C2×C61#217711yescharacteristic
116C2×C61#217811yescharacteristic
117D61—82no—
118D61—161no—
119C2×D16—611no—
120C4×D8—611no—
121C4×D8—611no—
122#436—1221no—
123C8×D4—1221no—
124#366#692311yescharacteristic
125#357—611no—
126#357—611no—
127C4×C16—611no—
128C4×C16—611no—
129#335—611no—
130#335—611no—
131D4⋊C8—1221no—
132D4⋊C8—1221no—
133C82—611no—
134C61#1207311yescharacteristic, complemented, Sylow
135C2×D8—611no—
136C2×D8—611no—
137C2×M16—2441no—
138C22×C8—2441no—
139C4×D4—1221no—
140C4×D4—1221no—
141D16—1222no—
142C2×C16—611no—
143C2×C16—1221no—
144C2×C16C2×#692311yescharacteristic
145#107C2×#692311yescharacteristic
146#107C2×#692311yescharacteristic
147C4⋊C8—1221no—
148C4⋊C8—1221no—
149#102—1221no—
150#102—1221no—
151C22⋊C8—2441no—
152C22⋊C8—2441no—
153C4×C8—611no—
154C4×C8—611no—
155C4×C8—611no—
156C2×D4—1221no—
157C2×D4—1221no—
158C22×C4—2441no—
159C22×C4—2441no—
160D8—612no—
161D8—1221no—
162D8—1221no—
163D8—1221no—
164M16—4882no—
165C2×C8—611no—
166C2×C8—611no—
167C2×C8—611no—
168C2×C8—1221no—
169C2×C8—4882no—
170C2×C8—2441no—
171C2×C8—2441no—
172C2×C8C22×#692311yescharacteristic
173C4⋊C4—21no—
174C4⋊C4—21no—
175C22⋊C4—2441no—
176C22⋊C4—2441no—
177C42—611no—
178C16—21no—
179C16—1221no—
180C16—2441no—
181C23—2441no—
182C23—2441no—
183D4—1222no—
184D4—2441no—
185D4—2441no—
186D4—2441no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—611no—
190C2×C4—611no—
191C2×C4—4881no—
192C2×C4—4881no—
193C2×C4—4881no—
194C2×C4—4881no—
195C2×C4D4×#692311yescharacteristic
196C8—1221no—
197C8—1221no—
198C8—1222no—
199C8—1221no—
200C8—4881no—
201C8—4881no—
202C8D61⋊M1611yescharacteristic
203C8#1451986511yescharacteristic
204C22—4881no—
205C22—4881no—
206C22—4881no—
207C22—4881no—
208C22—4881no—
209C22—2442no—
210C22D8×#692311yescharacteristic
211C4—81no—
212C4—81no—
213C4—611no—
214C4—611no—
215C4—1221no—
216C4#1684079211yescharacteristic
217C4#1684080811yescharacteristic
218C2—9761no—
219C2—4882no—
220C2#2146141911yescharacteristic
221C2#2146221711yescharacteristic
222C2#2146222011yescharacteristic
subgroupG/H
centerC22D8×#6923
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#366C4
socleC22×C61C4×D8
prime radicalC2×D976C4
cosocleC8×Dic61C23
hypercenter#366#6923
hypocenterC61#12073
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #366

Complements

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

NH ≅ G/Ntype
1. #21461451C2semidirect
2. #21461400C2semidirect
3. #21460853C2semidirect
4. #21460774C2semidirect
5. #21460774C2semidirect
6. #92420⋊C16C2semidirect
65. D488M16semidirect
134. C61#12073semidirect

Maximal subgroups

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

subgroupindex
#214614512
#214614002
#214608532
#214607742
#92420⋊C162
#214476652
#1207361