Finite Group Databasebeta

← #30595159

Subgroups — #30595159

Order 15616.

302 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 302 conjugacy classes of subgroups — too many to draw. Only its 50 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
1C2×#16840668C211yesmaximal, characteristic
2C2×#16840618C211yesmaximal, characteristic
3#21446220C211yesmaximal, characteristic
4C2×#14519836—21no—
5C2×#14519832—21no—
6#16840668—21no—
7#16840668C412yescomplemented
8#16840618—21no—
9#16840618C412yescomplemented
10C2×#14519766C2211yescharacteristic
11#16840240C411yescharacteristic, complemented
12#16839768—21no—
13#16839523—21no—
14C2×#101×C61C411yescharacteristic, complemented
15C22×#92420—41no—
16C2×C22⋊#6923—41no—
17#14519836—22no—
18#14519836—41no—
19#14519832—22no—
20#14519832—41no—
21C22×D244D411yescharacteristic
22#14519766—41no—
23#14519766C2×C411yescharacteristic
24#14519766C2×C411yescharacteristic
25#14519766D411yescharacteristic
26#14519766Q811yescharacteristic
27Q8×Dic61—42no—
28#14519736—21no—
29#14519736—41no—
30C2×#11758198—41no—
31C2×C4×Dic61D411yescharacteristic
32#14519699—42no—
33C22×Q8×C61C2×C411yescharacteristic
34C2×M16×C61—21no—
35#101×C61—41no—
36C23×D61—21no—
37C22×#6923—81no—
38C2×Q8×C61—21no—
39C2×Q8×C61—41no—
40C2×Q8×C61—41no—
41C2×Q8×C61C4211yescharacteristic
42C2×Q8×C61C4⋊C411yescharacteristic
43C22×C4×C61—21no—
44C22×C4×C61C22⋊C411yescharacteristic
45C22×Dic61—21no—
46C2×D244—21no—
47C2×D244—41no—
48C2×D244—41no—
49C2×D244C22⋊C411yescharacteristic
50C2×D244C4⋊C411yescharacteristic
51C22⋊#6923—42no—
52C22⋊#6923—81no—
53C2×#92420—42no—
54C2×#92420—44no—
55M16×C61—41no—
56M16×C61—41no—
57C2×C8×C61—41no—
58C22⋊Dic61—41no—
59#11758198—41no—
60#11758198—41no—
61#11758198—41no—
62#11758198—41no—
63C4⋊Dic61—22no—
64C4⋊Dic61—42no—
65C4×Dic61—21no—
66C4×Dic61—41no—
67C4×Dic61—42no—
68C4×Dic61C22⋊C411yescharacteristic
69C4×Dic61C4⋊C411yescharacteristic
70C23×C61#9911yescharacteristic
71C22×D61—21no—
72C22×D61—21no—
73C22×D61—41no—
74C22×D61—41no—
75C22×D61—82no—
76C2×#6923—82no—
77C2×#6923—162no—
78Q8×C61—42no—
79Q8×C61—41no—
80Q8×C61—41no—
81C2×C4×C61—21no—
82C2×C4×C61—21no—
83C2×C4×C61—21no—
84C2×C4×C61—21no—
85C2×C4×C61—41no—
86C2×C4×C61—41no—
87C2×C4×C61#9511yescharacteristic
88C2×C4×C61#9911yescharacteristic
89C2×Dic61—21no—
90C2×Dic61—21no—
91C2×Dic61—42no—
92C2×Dic61—42no—
93D244—41no—
94D244—41no—
95D244—81no—
96#92420—44no—
97C8×C61—81no—
98#7489—611nomaximal, Sylow
99C22×C61—22no—
100C22×C61#34211yescharacteristic
101C22×C61AΣL(1,𝔽16)11yescharacteristic
102C22×C61#35211yescharacteristic
103C2×D61—41no—
104C2×D61—41no—
105C2×D61—82no—
106C2×D61—81no—
107C2×D61—81no—
108C2×D61—161no—
109#6923—162no—
110C4×C61—21no—
111C4×C61—21no—
112C4×C61—41no—
113C4×C61—41no—
114Dic61—41no—
115Dic61—41no—
116Dic61—82no—
117C2×#354—611no—
118#1888—611no—
119C2×#329—611no—
120C2×C61—21no—
121C2×C61—21no—
122C2×C61#139011yescharacteristic
123C2×C61#140412yes—
124D61—81no—
125D61—81no—
126C2×#124—611no—
127#519—611no—
128#418—1221no—
129C2×#101#692311yescharacteristic, complemented
130C2×#99—1221no—
131C2×#97—1221no—
132#354—612no—
133#354—1221no—
134#339—1221no—
135#329—612no—
136#329—1221no—
137C61#748911yescharacteristic, complemented, Sylow
138C22×Q8C2×#692311yescharacteristic
139C22×D4—611no—
140C2×M16—21no—
141C22×C8—2441no—
142#124—611no—
143#124—611no—
144#124—611no—
145#124—611no—
146#124—2441no—
147C4×Q8—2442no—
148#117—1221no—
149#117—2441no—
150C2×C22⋊C4—2441no—
151C2×C22⋊C4—2441no—
152C2×C42—611no—
153#102—2442no—
154#101—41no—
155#99—1222no—
156#99—2441no—
157#97—1222no—
158#97—2441no—
159C24—1221no—
160C2×Q8—21no—
161C2×Q8—41no—
162C2×Q8—41no—
163C2×Q8C4×#692311yescharacteristic
164C2×Q8C4⋊#692311yescharacteristic
165C2×D4—611no—
166C2×D4—611no—
167C2×D4—1221no—
168C2×D4—2441no—
169C2×D4—2441no—
170C22×C4—21no—
171C22×C4—1221no—
172C22×C4—4881no—
173C22×C4C22⋊#692311yescharacteristic
174M16—41no—
175M16—41no—
176C2×C8—41no—
177C2×C8—2442no—
178C2×C8—2444no—
179C4⋊C4—1222no—
180C4⋊C4—2442no—
181C22⋊C4—4881no—
182C22⋊C4—2441no—
183C22⋊C4—2441no—
184C22⋊C4—2441no—
185C22⋊C4—2441no—
186C22⋊C4—2442no—
187C22⋊C4—2441no—
188C42—611no—
189C42—611no—
190C42—1221no—
191C42—2441no—
192C42—2442no—
193C23—1221no—
194C23—1221no—
195C23—4882no—
196C23—2441no—
197C23—2441no—
198C23#1451983611yescharacteristic
199Q8—41no—
200Q8—41no—
201Q8—42no—
202D4—4881no—
203D4—2441no—
204D4—2441no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—1221no—
212C2×C4—1221no—
213C2×C4—9762no—
214C2×C4—4882no—
215C2×C4—2442no—
216C2×C4—2442no—
217C2×C4(C2×#6923)⋊C411yescharacteristic
218C2×C4#1451983511yescharacteristic
219C8—81no—
220C8—2444no—
221C22—22no—
222C22—9761no—
223C22—4881no—
224C22—4881no—
225C22—4882no—
226C22—2441no—
227C22—2441no—
228C22#1684064011yescharacteristic
229C22#1684066311yescharacteristic
230C22#1684066511yescharacteristic
231C4—21no—
232C4—21no—
233C4—41no—
234C4—41no—
235C4—9762no—
236C4—4882no—
237C4—2441no—
238C4—2441no—
239C2—21no—
240C2—21no—
241C2—4881no—
242C2—4881no—
243C2#2146090411yescharacteristic
244C2#2146094312yes—
subgroupG/H
centerC22#16840663
commutatorC2×Q8×C61C42
FrattiniC22×Q8C2×#6923
FittingC2×#101×C61C4
socleC22×C61AΣL(1,𝔽16)
prime radicalC22×D244D4
cosocleC2×#14519766C22
hypercenterC2×#101#6923
hypocenterC61#7489
LCSG ▷ C2×Q8×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C22×Q8 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
7. #16840668C4semidirect
9. #16840618C4semidirect
11. #16840240C4semidirect
14. C2×#101×C61C4semidirect
129. C2×#101#6923semidirect
137. C61#7489semidirect

Maximal subgroups

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

subgroupindex
C2×#168406682
C2×#168406182
#214462202
#748961