Finite Group Databasebeta

← #30594329

Subgroups — #30594329

Order 15616.

370 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 76 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#21462047C211yesmaximal, characteristic
2C2×(C2×#6923)⋊C8C211yesmaximal, characteristic
3#21447428C211yesmaximal, characteristic
4C22×D61⋊C8C411yescharacteristic
5C22×C4×#6923C411yescharacteristic
6C2×#14519852—21no—
7#16840657—21no—
8C22⋊#11758187C412yescomplemented
9(C2×#6923)⋊C8—21no—
10(C2×#6923)⋊C8—21no—
11C22×C8×D61C2211yescharacteristic
12C2×#14519716—21no—
13C22⋊#11758185C411yescharacteristic, complemented
14#16839541—21no—
15C61×C22⋊C16C411yescharacteristic, complemented
16C23×#6923—21no—
17C2×D61⋊C8—21no—
18C2×D61⋊C8—41no—
19C2×D61⋊C8—41no—
20C2×D61⋊C8C812yes—
21C22×#92420—21no—
22C2×C4×#6923—21no—
23C2×C4×#6923—41no—
24C2×C4×#6923—41no—
25C2×C4×#6923C812yes—
26#14519852—41no—
27#14519852—41no—
28C2×#11758187—22no—
29C22×C4×D61C2×C411yescharacteristic
30C22×#92418C2×C411yescharacteristic
31C2×C8×D61—41no—
32C2×C8×D61—41no—
33C2×C8×D61D411yescharacteristic
34C2×C8×D61D411yescharacteristic
35C2×C8×D61D411yescharacteristic
36C2×C8×D61Q811yescharacteristic
37#14519716—41no—
38#14519716—41no—
39C2×#11758185—21no—
40C22×C8×C61C2×C411yescharacteristic
41C2×C16×C61—21no—
42C23×D61M1611yescharacteristic
43C22×#6923—24no—
44C22×#6923—22no—
45C22×#6923—42no—
46C22×#6923—41no—
47C22×#6923—41no—
48C22×C4×C61C4211yescharacteristic
49C22×Dic61M1611yescharacteristic
50C2×C4×D61—21no—
51C2×C4×D61—21no—
52C2×C4×D61—21no—
53C2×C4×D61—21no—
54C2×C4×D61C22⋊C411yescharacteristic
55C2×C4×D61C4⋊C411yescharacteristic
56C2×C4×D61C2×C811yescharacteristic
57C2×C4×D61C2×C811yescharacteristic
58C2×#92420—22no—
59C2×#92420—42no—
60C4×#6923—42no—
61C4×#6923—41no—
62C4×#6923—41no—
63D61⋊C8—41no—
64D61⋊C8—41no—
65D61⋊C8—42no—
66C2×C8×C61—41no—
67C2×C8×C61C22⋊C411yescharacteristic
68C2×C8×C61C4⋊C411yescharacteristic
69C2×#92418—41no—
70C2×#92418C22⋊C411yescharacteristic
71C2×#92418C4⋊C411yescharacteristic
72C8×D61—21no—
73C8×D61—21no—
74C8×D61—21no—
75C8×D61—21no—
76C8×D61—41no—
77C8×D61—41no—
78#11758187—42no—
79C16×C61—41no—
80#11758185—41no—
81C23×C61#9711yescharacteristic
82C22×D61—21no—
83C22×D61—21no—
84C22×D61—21no—
85C22×D61—21no—
86C22×D61—22no—
87C22×D61C22⋊C811yescharacteristic
88C22×D61C4⋊C811yescharacteristic
89C2×#6923—24no—
90C2×#6923—44no—
91C2×#6923—44no—
92C2×#6923—42no—
93C2×#6923—42no—
94C2×C4×C61—21no—
95C2×C4×C61—21no—
96C2×C4×C61#9511yescharacteristic
97C2×C4×C61C4×C811yescharacteristic
98C2×Dic61—21no—
99C2×Dic61—21no—
100C2×Dic61C22⋊C811yescharacteristic
101C2×Dic61C4⋊C811yescharacteristic
102C4×D61—21no—
103C4×D61—21no—
104C4×D61—21no—
105C4×D61—21no—
106C4×D61—21no—
107C4×D61—21no—
108C4×D61#9911yescharacteristic
109C4×D61#9911yescharacteristic
110C4×D61#10011yescharacteristic
111C4×D61#10111yescharacteristic
112#92420—42no—
113C8×C61—21no—
114C8×C61—21no—
115#92418—21no—
116#92418—21no—
117#7184—611nomaximal, Sylow
118C22×C61—21no—
119C22×C61—21no—
120C22×C61#33611yescharacteristic
121C22×C61#34711yescharacteristic
122C22×C61#34711yescharacteristic
123C2×D61—22no—
124C2×D61—22no—
125C2×D61—22no—
126C2×D61—22no—
127C2×D61—21no—
128C2×D61—21no—
129C2×D61—21no—
130C2×D61—21no—
131C2×D61#32311yescharacteristic
132C2×D61#32411yescharacteristic
133C2×D61#36412yes—
134#6923—44no—
135C4×C61—21no—
136C4×C61#34211yescharacteristic
137C4×C61#34311yescharacteristic
138Dic61—21no—
139Dic61#32311yescharacteristic
140Dic61#32411yescharacteristic
141#2112—611no—
142#2112—611no—
143C2×#336—611no—
144C2×C61—21no—
145C2×C61—21no—
146C2×C61#128011yescharacteristic
147C2×C61#137511yescharacteristic
148C2×C61#137611yescharacteristic
149D61—21no—
150D61—21no—
151D61—22no—
152C23×C8—611no—
153C23×C8—611no—
154C22×C42—611no—
155C2×M32—1221no—
156C2×M32—1221no—
157C22⋊C16—612no—
158C22⋊C16—611no—
159C22⋊C16—1221no—
160C22⋊C16—1221no—
161C22⋊C16#692311yescharacteristic, complemented
162#336—1221no—
163#336—1221no—
164C61#718411yescharacteristic, complemented, Sylow
165C23×C4—611no—
166C23×C4—1221no—
167C22×C8—611no—
168C22×C8—611no—
169C22×C8—611no—
170C22×C8—611no—
171C22×C8—611no—
172C22×C8—612no—
173C22×C8—1221no—
174C22×C8—1221no—
175C22×C8—2441no—
176C22×C8—2441no—
177C22×C8—2441no—
178C22×C8—2441no—
179C22×C8C2×#692311yescharacteristic
180C2×C42—612no—
181C2×C42—1221no—
182C2×C42—2441no—
183C2×C42—2441no—
184M32—2441no—
185M32—2441no—
186M32—2441no—
187M32—2441no—
188C2×C16—21no—
189C2×C16—1222no—
190C2×C16—1221no—
191C24—611no—
192C22×C4—611no—
193C22×C4—611no—
194C22×C4—611no—
195C22×C4—611no—
196C22×C4—611no—
197C22×C4—1221no—
198C22×C4—1221no—
199C22×C4—1221no—
200C22×C4—1221no—
201C22×C4—1222no—
202C22×C4—1224no—
203C22×C4—2442no—
204C22×C4—2441no—
205C22×C4—2441no—
206C22×C4C4×#692311yescharacteristic
207C2×C8—41no—
208C2×C8—611no—
209C2×C8—611no—
210C2×C8—1221no—
211C2×C8—1221no—
212C2×C8—1221no—
213C2×C8—1221no—
214C2×C8—1222no—
215C2×C8—2441no—
216C2×C8—2441no—
217C2×C8—2441no—
218C2×C8—2441no—
219C2×C8—2441no—
220C2×C8—2442no—
221C2×C8—2442no—
222C2×C8C4⋊#692311yescharacteristic
223C2×C8C22⋊#692311yescharacteristic
224C42—2441no—
225C42—2441no—
226C42—2442no—
227C16—41no—
228C16—2441no—
229C16—2442no—
230C23—611no—
231C23—611no—
232C23—1221no—
233C23—1222no—
234C23—1221no—
235C23—1221no—
236C23—1221no—
237C23#1451983111yescharacteristic
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—611no—
241C2×C4—611no—
242C2×C4—611no—
243C2×C4—611no—
244C2×C4—611no—
245C2×C4—611no—
246C2×C4—1221no—
247C2×C4—1221no—
248C2×C4—1221no—
249C2×C4—1221no—
250C2×C4—1221no—
251C2×C4—1221no—
252C2×C4—1221no—
253C2×C4—1221no—
254C2×C4—1224no—
255C2×C4—2442no—
256C2×C4—2444no—
257C2×C4—2444no—
258C2×C4—2442no—
259C2×C4(C2×#6923)⋊C411yescharacteristic
260C2×C4C8×#692311yescharacteristic
261C8—21no—
262C8—21no—
263C8—1221no—
264C8—1221no—
265C8—2442no—
266C22—21no—
267C22—21no—
268C22—612no—
269C22—611no—
270C22—611no—
271C22—1222no—
272C22—1222no—
273C22—1222no—
274C22—1222no—
275C22—1221no—
276C22—1221no—
277C22—1221no—
278C22—1221no—
279C22(C2×#6923)⋊C811yescharacteristic
280C22#1684065211yescharacteristic
281C22#1684065311yescharacteristic
282C4—21no—
283C4—611no—
284C4—611no—
285C4—1221no—
286C4—2444no—
287C4#1684063911yescharacteristic
288C4#1684064111yescharacteristic
289C2—21no—
290C2—21no—
291C2—1221no—
292C2—1222no—
293C2—1221no—
294C2#2146065611yescharacteristic
295C2#2146085911yescharacteristic
296C2#2146086211yescharacteristic
subgroupG/H
centerC2×C4(C2×#6923)⋊C4
commutatorC2×C4×C61C4×C8
FrattiniC22×C8C2×#6923
FittingC61×C22⋊C16C4
socleC22×C61#336
prime radicalC23×D61M16
cosocleC22×C8×D61C22
hypercenterC22⋊C16#6923
hypocenterC61#7184
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C22⋊C16

Complements

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

NH ≅ G/Ntype
8. C22⋊#11758187C4semidirect
13. C22⋊#11758185C4semidirect
15. C61×C22⋊C16C4semidirect
161. C22⋊C16#6923semidirect
164. C61#7184semidirect

Maximal subgroups

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

subgroupindex
#214620472
C2×(C2×#6923)⋊C82
#214474282
#718461