Finite Group Databasebeta

← #30606017

Subgroups — #30606017

Order 15616.

240 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 66 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#21461452C211yesmaximal, characteristic, complemented
2D8×#92420C211yesmaximal, characteristic, complemented
3#21460853C211yesmaximal, characteristic, complemented
4#21460773C211yesmaximal, characteristic, complemented
5#21460773C211yesmaximal, characteristic, complemented
6#92420⋊C16C211yesmaximal, characteristic, complemented
7D16×Dic61C211yesmaximal, characteristic
8#16840797—21no—
9D4×#92420—21no—
10#16840648C2211yescharacteristic
11#16840625C2211yescharacteristic
12#16840625C2211yescharacteristic
13D4⋊#92420—21no—
14D4⋊#92420—21no—
15C8×#92420C2211yescharacteristic
16D8×Dic61C2211yescharacteristic
17D8×Dic61C2211yescharacteristic
18#16839588C411yescharacteristic
19#16839563C411yescharacteristic
20#16839563C411yescharacteristic
21C16×Dic61C2211yescharacteristic
22C2×D16×C61C411yescharacteristic
23C2×#11758217—41no—
24C22×#92420—41no—
25C2×#11758187—21no—
26C4⋊#92420—21no—
27C4⋊#92420—21no—
28C22⋊#92420—41no—
29C22⋊#92420—41no—
30C4×#92420D411yescharacteristic
31C4×#92420D411yescharacteristic
32D4×Dic61—21no—
33D4×Dic61—21no—
34C2×#11758185C2×C411yescharacteristic
35#14519711C2×C411yescharacteristic
36#14519711C2×C411yescharacteristic
37#14519698—21no—
38#14519698—21no—
39C8×Dic61C2311yescharacteristic
40C2×D8×C61C2×C411yescharacteristic
41C2×D8×C61C2×C411yescharacteristic
42D16×C61—22no—
43C2×C16×C61C2×C411yescharacteristic
44C2×D4×C61—21no—
45C2×D4×C61—21no—
46C22×Dic61—41no—
47C22×Dic61—41no—
48#11758217—82no—
49C2×#92420—21no—
50C2×#92420—41no—
51C2×#92420—41no—
52C2×#92420—82no—
53C2×#92420D811yescharacteristic
54C2×#92420D811yescharacteristic
55D8×C61—21no—
56D8×C61—21no—
57D8×C61—21no—
58D8×C61M1612yescomplemented
59C2×C8×C61C22×C411yescharacteristic
60C22⋊Dic61—41no—
61C22⋊Dic61—41no—
62C4⋊Dic61—21no—
63C4⋊Dic61—21no—
64C4×Dic61C2×D411yescharacteristic
65C2×#92418#4111yescharacteristic
66#11758187—41no—
67C16×C61—21no—
68#11758185—21no—
69C23×C61—41no—
70C23×C61—41no—
71D4×C61—22no—
72D4×C61—41no—
73D4×C61—41no—
74D4×C61—41no—
75C2×C4×C61C4×D411yescharacteristic
76C2×Dic61—41no—
77C2×Dic61—41no—
78C2×Dic61—81no—
79C2×Dic61—81no—
80C2×Dic61—81no—
81C2×Dic61—81no—
82C2×Dic61C2×D811yescharacteristic
83C2×Dic61#13511yescharacteristic
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×C61—42no—
94C22×C61—81no—
95C22×C61—81no—
96C22×C61—81no—
97C22×C61—81no—
98C22×C61—81no—
99C22×C61C4×D811yescharacteristic
100C4×C61#43511yescharacteristic
101C4×C61#44411yescharacteristic
102Dic61—21no—
103Dic61—81no—
104Dic61—81no—
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—82no—
115C2×C61—161no—
116C2×C61#158111yescharacteristic
117C2×C61#217711yescharacteristic
118C2×C61#217811yescharacteristic
119C2×D16#692311yescharacteristic
120C4×D8—611no—
121C4×D8—611no—
122#436—1221no—
123C8×D4—1221no—
124#366—611no—
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×D8C2×#692311yescharacteristic
136C2×D8C2×#692311yescharacteristic
137C2×M16—2441no—
138C22×C8—2441no—
139C4×D4—1221no—
140C4×D4—1221no—
141D16—22no—
142C2×C16—611no—
143C2×C16—1221no—
144C2×C16C2×#692311yescharacteristic
145#107—611no—
146#107—611no—
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—21no—
157C2×D4—21no—
158C22×C4—2441no—
159C22×C4—2441no—
160D8—21no—
161D8—21no—
162D8—21no—
163D8#1175821712yescomplemented
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—1221no—
174C4⋊C4—1221no—
175C22⋊C4—2441no—
176C22⋊C4—2441no—
177C42—611no—
178C16—21no—
179C16—1221no—
180C16—2441no—
181C23—41no—
182C23—41no—
183D4—22no—
184D4—41no—
185D4—41no—
186D4—41no—
187C2×C4—611no—
188C2×C4—611no—
189C2×C4—4881no—
190C2×C4—4881no—
191C2×C4—4881no—
192C2×C4—4881no—
193C2×C4—2441no—
194C2×C4—2441no—
195C2×C4D4×#692311yescharacteristic
196C8—1221no—
197C8—1221no—
198C8—1222no—
199C8—1221no—
200C8—4881no—
201C8—4881no—
202C8C2×#1175821711yescharacteristic
203C8#1451986411yescharacteristic
204C22—42no—
205C22—81no—
206C22—81no—
207C22—81no—
208C22—81no—
209C22—81no—
210C22D8×#692311yescharacteristic
211C4—611no—
212C4—611no—
213C4—1221no—
214C4—4881no—
215C4—4881no—
216C4#1684079311yescharacteristic
217C4#1684080911yescharacteristic
218C2—82no—
219C2—161no—
220C2#2146142011yescharacteristic
221C2#2146221711yescharacteristic
222C2#2146221811yescharacteristic
subgroupG/H
centerC22D8×#6923
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
Fitting, prime radicalC2×D16×C61C4
socleC22×C61C4×D8
cosocleC8×Dic61C23
hypercenterC2×D16#6923
hypocenterC61#12073
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×D16

Complements

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

NH ≅ G/Ntype
1. #21461452C2semidirect
2. D8×#92420C2semidirect
3. #21460853C2semidirect
4. #21460773C2semidirect
5. #21460773C2semidirect
6. #92420⋊C16C2semidirect
58. D8×C61M16semidirect
134. C61#12073semidirect
163. D8#11758217semidirect

Maximal subgroups

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

subgroupindex
#214614522
D8×#924202
#214608532
#214607732
#92420⋊C162
D16×Dic612
#1207361