Finite Group Databasebeta

← #30594487

Subgroups — #30594487

Order 15616.

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

normal subgroups only

This group has 244 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#21445868C211yesmaximal, characteristic
4C2×#14519852C411yescharacteristic
5C2×D61⋊C16C411yescharacteristic
6D61⋊#108—21no—
7#16840748—21no—
8#16840657—21no—
9C22⋊#11758187—21no—
10#16840631C412yes—
11C2×#14519785C2211yescharacteristic
12C2×#14519712—21no—
13#16839744—21no—
14#16839520C411yescharacteristic
15C61×#338C411yescharacteristic
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×#11758194—21no—
29C2×#11758189C2×C411yescharacteristic
30C2×#11758189Q811yescharacteristic
31C22×#92418D411yescharacteristic
32C2×C8×D61C2×C411yescharacteristic
33C2×C8×D61D411yescharacteristic
34#14519712—41no—
35#14519712—41no—
36#14519695—41no—
37#14519693—41no—
38C2×M16×C61—21no—
39C2×M16×C61C2×C411yescharacteristic
40C22×C4×C61C22⋊C411yescharacteristic
41C2×C22⋊D61SD1611yescharacteristic
42C2×C22⋊D61Q1611yescharacteristic
43#11758222—41no—
44#11758222—41no—
45C2×D244SD1611yescharacteristic
46C2×C4×D61C22⋊C411yescharacteristic
47C2×C4×D61C4⋊C411yescharacteristic
48C2×Dic122D811yescharacteristic
49#11758217—42no—
50#11758213—42no—
51D61⋊C8—42no—
52M16×C61—41no—
53M16×C61—41no—
54M16×C61—41no—
55C2×C8×C61—41no—
56C2×C8×C61C4211yescharacteristic
57C2×C8×C61C4⋊C411yescharacteristic
58#11758194—41no—
59#11758194—41no—
60C2×#92418—21no—
61C2×#92418—21no—
62C2×#92418—41no—
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#10311yescharacteristic
74C22×D61#10311yescharacteristic
75C22×D61#10611yescharacteristic
76C2×C4×C61—21no—
77C2×C4×C61—21no—
78C2×C4×C61#9511yescharacteristic
79C2×C4×C61#10211yescharacteristic
80C22⋊D61—41no—
81C22⋊D61—41no—
82C2×Dic61#10211yescharacteristic
83C2×Dic61#10711yescharacteristic
84D244—41no—
85C4×D61—21no—
86C4×D61—21no—
87C4×D61—21no—
88C4×D61—21no—
89Dic122—41no—
90#92420—82no—
91C8×C61—21no—
92C8×C61—21no—
93C8×C61—81no—
94#92418—21no—
95#92418—81no—
96#92418#9911yescharacteristic
97#92418#9911yescharacteristic
98#7229—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×C61H(3,ℤ/4)11yescharacteristic
108C4×C61#34211yescharacteristic
109Dic61—21no—
110Dic61—21no—
111#2113—611no—
112#1813—611no—
113#1813—611no—
114C2×C61—21no—
115C2×C61—41no—
116C2×C61#128911yescharacteristic
117D61—41no—
118D61—41no—
119C2×#131—611no—
120C2×M32—611no—
121C22×C16—611no—
122C2×#108—1221no—
123C2×#108—1221no—
124#413—1221no—
125#413—1221no—
126C22⋊C16—1221no—
127C22⋊C16—1221no—
128#338—612no—
129#338—611no—
130#338#692311yescharacteristic
131C61#722911yescharacteristic, complemented, Sylow
132C2×#41—611no—
133#131—2441no—
134#131—2441no—
135C2×M16—21no—
136C2×M16—611no—
137C2×M16—611no—
138C2×M16—1222no—
139C2×M16—1221no—
140C2×M16C2×#692311yescharacteristic
141C22×C8—611no—
142C22×C8—611no—
143C22×C8—611no—
144M32—2441no—
145C2×C16—1221no—
146C2×C16—1221no—
147C2×C16—2441no—
148#108—2441no—
149#108—2441no—
150#108—2441no—
151#108—2441no—
152#101—2441no—
153#101—2441no—
154#100—2441no—
155#100—2441no—
156#41—2441no—
157#41—2441no—
158C2×Q8—611no—
159C2×D4—611no—
160C2×D4—611no—
161C2×D4—611no—
162C22×C4—611no—
163C22×C4—611no—
164C22×C4C22⋊#692311yescharacteristic
165M16—41no—
166M16—41no—
167M16—41no—
168M16—2441no—
169M16—2441no—
170M16—2441no—
171M16—2442no—
172M16—2442no—
173M16—2441no—
174C2×C8—41no—
175C2×C8—611no—
176C2×C8—611no—
177C2×C8—1221no—
178C2×C8—1221no—
179C2×C8—1221no—
180C2×C8—1221no—
181C2×C8—1221no—
182C2×C8—1221no—
183C2×C8—2441no—
184C2×C8—2442no—
185C2×C8C4×#692311yescharacteristic
186C2×C8C4⋊#692311yescharacteristic
187C16—2441no—
188C16—2441no—
189C23—611no—
190C23—611no—
191C23#1451984011yescharacteristic
192Q8—2441no—
193D4—2441no—
194D4—2441no—
195D4—2441no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—611no—
199C2×C4—611no—
200C2×C4—1221no—
201C2×C4—1221no—
202C2×C4—1221no—
203C2×C4—1221no—
204C2×C4(C2×#6923)⋊C411yescharacteristic
205C2×C4#1451983911yescharacteristic
206C8—21no—
207C8—21no—
208C8—81no—
209C8—611no—
210C8—611no—
211C8—1221no—
212C8—4881no—
213C8—4882no—
214C22—21no—
215C22—41no—
216C22—1221no—
217C22—1221no—
218C22—2441no—
219C22—2441no—
220C22#1684063511yescharacteristic
221C4—21no—
222C4—1221no—
223C4—1221no—
224C4#1684062911yescharacteristic
225C4#1684063911yescharacteristic
226C2—21no—
227C2—41no—
228C2—2441no—
229C2—2441no—
230C2#2146068111yescharacteristic
subgroupG/H
centerC4#16840629
commutatorC2×C8×C61C42
FrattiniC2×M16C2×#6923
FittingC61×#338C4
socleC2×C61#1289
prime radicalC2×#11758222D4
cosocleC2×#14519785C22
hypercenter#338#6923
hypocenterC61#7229
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C8 ◁ #338

Complements

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

NH ≅ G/Ntype
131. C61#7229semidirect

Maximal subgroups

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

subgroupindex
#214620502
#214617042
#214458682
#722961