Finite Group Databasebeta

← #30594480

Subgroups — #30594480

Order 15616.

248 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 56 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#21462050C211yesmaximal, characteristic
2#21461704C211yesmaximal, characteristic
3#21445864C211yesmaximal, characteristic
4C2×#14519852C411yescharacteristic, complemented
5C2×D61⋊C16C411yescharacteristic, complemented
6D61⋊#108—21no—
7#16840748—21no—
8#16840657—21no—
9C22⋊#11758187—21no—
10#16840631C412yescomplemented
11C2×#14519785C2211yescharacteristic
12#16839798—21no—
13#16839735—21no—
14#16839519C411yescharacteristic
15C61×H(3,ℤ/4)C411yescharacteristic
16D61⋊M16—22no—
17#14519852—41no—
18D61⋊C16—41no—
19C2×#11758187—21no—
20C2×#11758187—21no—
21#14519848—41no—
22#14519847—41no—
23#14519838—41no—
24#14519837—41no—
25C2×#11758222D411yescharacteristic
26#14519785—41no—
27#14519785—41no—
28C2×#11758189C2×C411yescharacteristic
29C2×#11758189Q811yescharacteristic
30C22×#92418D411yescharacteristic
31C2×C8×D61C2×C411yescharacteristic
32C2×C8×D61D411yescharacteristic
33#14519736—21no—
34#14519710—41no—
35#14519708—41no—
36#14519691—41no—
37#14519691—41no—
38C2×M16×C61C2×C411yescharacteristic
39#117×C61—21no—
40C22×C4×C61C22⋊C411yescharacteristic
41C2×C22⋊D61D811yescharacteristic
42C2×C22⋊D61SD1611yescharacteristic
43#11758222—41no—
44#11758222—41no—
45C2×D244Q1611yescharacteristic
46C2×C4×D61C22⋊C411yescharacteristic
47C2×C4×D61C4⋊C411yescharacteristic
48C2×Dic122SD1611yescharacteristic
49#11758217—42no—
50#11758213—42no—
51D61⋊C8—42no—
52M16×C61—41no—
53C2×C8×C61C4211yescharacteristic
54C2×C8×C61C4⋊C411yescharacteristic
55C4⋊C4×C61—41no—
56C22⋊C4×C61—41no—
57C42×C61—41no—
58C22⋊Dic61—41no—
59C4⋊Dic61—41no—
60C4×Dic61—41no—
61C2×#92418—21no—
62C2×#92418—21no—
63C2×#92418C22⋊C411yescharacteristic
64C2×#92418C4⋊C411yescharacteristic
65#11758189—41no—
66#11758189—41no—
67C8×D61—21no—
68C8×D61—21no—
69C8×D61—21no—
70C8×D61—21no—
71#11758187—41no—
72#11758187—41no—
73C23×C61#10211yescharacteristic
74C22×D61#10311yescharacteristic
75C22×D61#10711yescharacteristic
76C2×C4×C61—21no—
77C2×C4×C61—21no—
78C2×C4×C61—81no—
79C2×C4×C61#9511yescharacteristic
80C2×C4×C61#10311yescharacteristic
81C22⋊D61—41no—
82C22⋊D61—41no—
83C2×Dic61—81no—
84C2×Dic61#10211yescharacteristic
85C2×Dic61#10611yescharacteristic
86D244—41no—
87C4×D61—21no—
88C4×D61—21no—
89C4×D61—21no—
90C4×D61—21no—
91Dic122—41no—
92#92420—82no—
93C8×C61—21no—
94C8×C61—21no—
95#92418—21no—
96#92418#9911yescharacteristic
97#92418#9911yescharacteristic
98#7227—611nomaximal, Sylow
99C22×C61—21no—
100C22×C61—41no—
101C22×C61#34011yescharacteristic
102C2×D61—21no—
103C2×D61—21no—
104C2×D61—41no—
105C2×D61—41no—
106C4×C61—21no—
107C4×C61—161no—
108C4×C61H(3,ℤ/4)11yescharacteristic
109C4×C61#34211yescharacteristic
110Dic61—21no—
111Dic61—21no—
112Dic61—161no—
113#2113—611no—
114#1813—611no—
115#1812—611no—
116C2×C61—21no—
117C2×C61—41no—
118C2×C61#128911yescharacteristic
119D61—41no—
120D61—41no—
121C2×#131—611no—
122C2×M32—611no—
123C22×C16—611no—
124C2×#108—1221no—
125#427—1221no—
126#413—1221no—
127#410—1221no—
128C22⋊C16—1221no—
129C22⋊C16—1221no—
130#338—612no—
131H(3,ℤ/4)—611no—
132H(3,ℤ/4)#692311yescharacteristic
133C61#722711yescharacteristic, complemented, Sylow
134C2×#41—611no—
135#131—2441no—
136#131—2441no—
137C2×M16—611no—
138C2×M16—611no—
139C2×M16—1222no—
140C2×M16C2×#692311yescharacteristic
141C22×C8—611no—
142C22×C8—611no—
143C22×C8—611no—
144#117—21no—
145#117—1221no—
146M32—2441no—
147C2×C16—1221no—
148C2×C16—1221no—
149C2×C16—2441no—
150#108—2441no—
151#108—2441no—
152#107—2441no—
153#106—2441no—
154#101—2441no—
155#100—2441no—
156#99—2441no—
157#99—2441no—
158#41—2441no—
159#41—2441no—
160C2×Q8—611no—
161C2×D4—611no—
162C2×D4—611no—
163C2×D4—611no—
164C22×C4—611no—
165C22×C4—611no—
166C22×C4C22⋊#692311yescharacteristic
167M16—41no—
168M16—2441no—
169M16—2441no—
170M16—2442no—
171M16—2442no—
172C2×C8—611no—
173C2×C8—611no—
174C2×C8—1221no—
175C2×C8—1221no—
176C2×C8—1221no—
177C2×C8—1221no—
178C2×C8—1221no—
179C2×C8—1221no—
180C2×C8—2442no—
181C2×C8C4×#692311yescharacteristic
182C2×C8C4⋊#692311yescharacteristic
183C4⋊C4—41no—
184C4⋊C4—2441no—
185C22⋊C4—41no—
186C22⋊C4—2441no—
187C42—41no—
188C42—2441no—
189C16—2441no—
190C16—2441no—
191C23—611no—
192C23—611no—
193C23#1451983911yescharacteristic
194Q8—2441no—
195D4—2441no—
196D4—2441no—
197D4—2441no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—81no—
201C2×C4—611no—
202C2×C4—611no—
203C2×C4—1221no—
204C2×C4—1221no—
205C2×C4—1221no—
206C2×C4—1221no—
207C2×C4—4881no—
208C2×C4(C2×#6923)⋊C411yescharacteristic
209C2×C4#1451984011yescharacteristic
210C8—21no—
211C8—21no—
212C8—611no—
213C8—611no—
214C8—1221no—
215C8—4882no—
216C22—21no—
217C22—41no—
218C22—1221no—
219C22—1221no—
220C22—2441no—
221C22—2441no—
222C22#1684063511yescharacteristic
223C4—21no—
224C4—161no—
225C4—1221no—
226C4—1221no—
227C4—9761no—
228C4#1684062911yescharacteristic
229C4#1684063911yescharacteristic
230C2—21no—
231C2—41no—
232C2—2441no—
233C2—2441no—
234C2#2146068111yescharacteristic
subgroupG/H
centerC4#16840629
commutatorC2×C8×C61C42
FrattiniC2×M16C2×#6923
FittingC61×H(3,ℤ/4)C4
socleC2×C61#1289
prime radicalC2×#11758222D4
cosocleC2×#14519785C22
hypercenterH(3,ℤ/4)#6923
hypocenterC61#7227
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C8 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
4. C2×#14519852C4semidirect
5. C2×D61⋊C16C4semidirect
10. #16840631C4semidirect
133. C61#7227semidirect

Maximal subgroups

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

subgroupindex
#214620502
#214617042
#214458642
#722761