Finite Group Databasebeta

← #30606069

Subgroups — #30606069

Order 15616.

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

normal subgroups only

This group has 224 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#21461458C211yesmaximal, characteristic, complemented
2#21461452C211yesmaximal, characteristic
3#21460853C211yesmaximal, characteristic, complemented
4#21460776C211yesmaximal, characteristic, complemented
5#21460773C211yesmaximal, characteristic
6C16×#92420C211yesmaximal, characteristic, complemented
7#21447674C211yesmaximal, characteristic
8#16840812—21no—
9#16840797—21no—
10#16840648C2211yescharacteristic
11#16840625C2211yescharacteristic
12#16840625C2211yescharacteristic
13#16840612—21no—
14D4⋊#92420—21no—
15C8×#92420C2211yescharacteristic
16C2×#14519721C411yescharacteristic
17#16839856C2211yescharacteristic
18D8×Dic61C2211yescharacteristic
19#16839589C411yescharacteristic
20#16839567C411yescharacteristic
21C16×Dic61C2211yescharacteristic
22C61×#357C411yescharacteristic
23C2×#11758217—41no—
24C2×#11758187—21no—
25C4⋊#92420—21no—
26C4⋊#92420—21no—
27C4⋊#92420—41no—
28C22⋊#92420—41no—
29#14519832—41no—
30C4×#92420D411yescharacteristic
31C4×#92420D411yescharacteristic
32C2×Dic244C2×C411yescharacteristic
33#14519742—21no—
34D4×Dic61—21no—
35#14519721—22no—
36C2×#11758185C2×C411yescharacteristic
37#14519711C2×C411yescharacteristic
38#14519700—21no—
39#14519698—21no—
40C8×Dic61C2311yescharacteristic
41C2×D8×C61C2×C411yescharacteristic
42C2×C16×C61C2×C411yescharacteristic
43#107×C61C2×C411yescharacteristic
44C2×D4×C61—21no—
45C22×Dic61—41no—
46C2×Dic122—21no—
47#11758217—82no—
48C2×#92420—21no—
49C2×#92420—41no—
50C2×#92420—41no—
51C2×#92420D811yescharacteristic
52C2×#92420D811yescharacteristic
53D8×C61—21no—
54D8×C61—21no—
55C2×C8×C61C22×C411yescharacteristic
56C4⋊C4×C61—21no—
57C22⋊Dic61—41no—
58C4⋊Dic61—21no—
59#11758196—41no—
60C4×Dic61—41no—
61C4×Dic61C2×D411yescharacteristic
62C2×#92418#4111yescharacteristic
63Dic244—21no—
64Dic244—21no—
65#11758187—22no—
66C16×C61—21no—
67#11758185M1612yescomplemented
68C23×C61—41no—
69D4×C61—41no—
70D4×C61—41no—
71C2×C4×C61—41no—
72C2×C4×C61C4×D411yescharacteristic
73C2×Dic61—41no—
74C2×Dic61—41no—
75C2×Dic61—81no—
76C2×Dic61—81no—
77C2×Dic61C2×D811yescharacteristic
78C2×Dic61#13511yescharacteristic
79Dic122—41no—
80Dic122—41no—
81#92420—22no—
82#92420—21no—
83#92420—81no—
84#92420—81no—
85#92420SD3212yescomplemented
86C8×C61C2×M1611yescharacteristic
87C8×C61#13111yescharacteristic
88#92418—21no—
89#12082—611nomaximal, Sylow
90C22×C61—81no—
91C22×C61—81no—
92C22×C61—81no—
93C22×C61C4×D811yescharacteristic
94C4×C61—81no—
95C4×C61#43611yescharacteristic
96C4×C61#44311yescharacteristic
97Dic61—21no—
98Dic61—81no—
99Dic61—81no—
100Dic61C2×SD3211yescharacteristic
101Dic61#50811yescharacteristic
102C4×SD32—611no—
103#1591—611no—
104#1589—611no—
105#1372—611no—
106#1332—611no—
107#1331—611no—
108C8×C16—611no—
109C2×C61—161no—
110C2×C61#158911yescharacteristic
111C2×C61C4×SD3211yescharacteristic
112C2×C61#217811yescharacteristic
113C2×SD32—611no—
114#446—1221no—
115C4×Q16—611no—
116C4×D8—611no—
117#436—1221no—
118#367—611no—
119#358—611no—
120#357#692311yescharacteristic
121C4×C16—611no—
122C4×C16—611no—
123#335—611no—
124#335—611no—
125Q8⋊C8—1221no—
126D4⋊C8—1221no—
127C82—611no—
128C61#1208211yescharacteristic, complemented, Sylow
129C2×Q16—611no—
130C2×D8C2×#692311yescharacteristic
131C2×M16—2441no—
132C4×Q8—1221no—
133C4×D4—1221no—
134SD32—1222no—
135C2×C16—611no—
136C2×C16—1221no—
137C2×C16C2×#692311yescharacteristic
138#107—611no—
139#107C2×#692311yescharacteristic
140C4⋊C8—1221no—
141C4⋊C8—1221no—
142C4⋊C8—2441no—
143#103—1221no—
144#102—1221no—
145C22⋊C8—2441no—
146#97—2441no—
147C4×C8—611no—
148C4×C8—611no—
149C4×C8—611no—
150C2×Q8—1221no—
151C2×D4—21no—
152C22×C4—2441no—
153Q16—1221no—
154Q16—1221no—
155D8—21no—
156D8—21no—
157M16—4882no—
158C2×C8—611no—
159C2×C8—611no—
160C2×C8—611no—
161C2×C8—1221no—
162C2×C8—2441no—
163C2×C8—2441no—
164C2×C8C22×#692311yescharacteristic
165C4⋊C4—21no—
166C4⋊C4—1221no—
167C4⋊C4—2441no—
168C22⋊C4—2441no—
169C42—611no—
170C42—2441no—
171C16—21no—
172C16—612no—
173C16—1222no—
174C23—41no—
175Q8—2441no—
176Q8—2441no—
177D4—41no—
178D4—41no—
179C2×C4—41no—
180C2×C4—611no—
181C2×C4—611no—
182C2×C4—4881no—
183C2×C4—4881no—
184C2×C4—2441no—
185C2×C4—2441no—
186C2×C4D4×#692311yescharacteristic
187C8—612no—
188C8—1221no—
189C8—1222no—
190C8—1221no—
191C8—4881no—
192C8—4881no—
193C8D61⋊M1611yescharacteristic
194C8#1451986411yescharacteristic
195C22—81no—
196C22—81no—
197C22—81no—
198C22D8×#692311yescharacteristic
199C4—81no—
200C4—611no—
201C4—611no—
202C4—1221no—
203C4—4881no—
204C4—4881no—
205C4#1684079511yescharacteristic
206C4#1684080511yescharacteristic
207C2—161no—
208C2#2146145011yescharacteristic
209C2SD32×#692311yescharacteristic
210C2#2146221811yescharacteristic
subgroupG/H
centerC22D8×#6923
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#357C4
socleC22×C61C4×D8
prime radicalC2×D8×C61C2×C4
cosocleC8×Dic61C23
hypercenter#357#6923
hypocenterC61#12082
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #357

Complements

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

NH ≅ G/Ntype
1. #21461458C2semidirect
3. #21460853C2semidirect
4. #21460776C2semidirect
6. C16×#92420C2semidirect
67. #11758185M16semidirect
85. #92420SD32semidirect
128. C61#12082semidirect

Maximal subgroups

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

subgroupindex
#214614582
#214614522
#214608532
#214607762
#214607732
C16×#924202
#214476742
#1208261