Finite Group Databasebeta

← C2×#21445910 #29679800

Subgroups — C2×#21445910 #29679800

Order 15616.

1878 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4⋊Dic61C211yesmaximal, characteristic
2C2×#16839622C211yesmaximal, characteristic
3#21445910C218yesmaximal, direct product factor
4C2×#16839525C214yesmaximal, complemented
5C22×C22⋊C8×C61C211yesmaximal, characteristic
6C24×Dic61—21no—
7C22×C4⋊Dic61—21no—
8C22×C4⋊Dic61—22no—
9C22×C4⋊Dic61—24no—
10C22×C4⋊Dic61C418yescomplemented
11C22×C4⋊Dic61C2212yes—
12C22×C4⋊Dic61C2212yes—
13C22×C4⋊Dic61C2214yes—
14C22×C22⋊Dic61—21no—
15#16839622—22no—
16#16839622C2214yes—
17C2×#14519684—21no—
18#16839525C22116yescomplemented
19C24×C4×C61C2211yescharacteristic
20C23×C8×C61C2212yes—
21C2×C22⋊C8×C61—24no—
22C2×C22⋊C8×C61C2214yes—
23C23×Dic61—28no—
24C23×Dic61—24no—
25C23×Dic61—22no—
26C23×Dic61—22no—
27C23×Dic61—48no—
28C2×C4⋊Dic61—216no—
29C2×C4⋊Dic61—28no—
30C2×C4⋊Dic61—22no—
31C2×C4⋊Dic61—24no—
32C2×C4⋊Dic61—24no—
33C2×C4⋊Dic61—28no—
34C2×C4⋊Dic61—28no—
35C2×C4⋊Dic61—22no—
36C2×C4⋊Dic61C2×C418yes—
37C2×C4⋊Dic61C2×C4116yescomplemented
38C2×C4⋊Dic61C2314yes—
39C2×C4⋊Dic61C2314yes—
40C2×C22⋊Dic61—24no—
41C2×C22⋊Dic61—44no—
42#14519684—24no—
43C25×C61D411yescharacteristic
44C23×C4×C61—28no—
45C23×C4×C61C2×C414yes—
46C23×C4×C61D411yescharacteristic
47C23×C4×C61D412yes—
48C23×C4×C61D414yes—
49C23×C4×C61C2312yes—
50C23×C4×C61C2311yescharacteristic
51C22×C8×C61—24no—
52C22×C8×C61—28no—
53C22×C8×C61C2314yes—
54C22⋊C8×C61—28no—
55C24×C61—24no—
56C24×C61—24no—
57C24×C61C22⋊C414yes—
58C24×C61SD1614yes—
59C24×C61Q1614yes—
60C24×C61C2×D412yes—
61C24×C61C2×D411yescharacteristic
62C22×C4×C61—24no—
63C22×C4×C61—216no—
64C22×C4×C61—28no—
65C22×C4×C61—216no—
66C22×C4×C61—28no—
67C22×C4×C61C22⋊C414yes—
68C22×C4×C61C22⋊C418yes—
69C22×C4×C61C22×C414yes—
70C22×C4×C61C22×C412yes—
71C22×C4×C61C2×D412yes—
72C22×C4×C61C2×D414yes—
73C22×C4×C61C2×D411yescharacteristic
74C22×C4×C61C2×D412yes—
75C22×C4×C61#4118yes—
76C22×C4×C61C2411yescharacteristic
77C22×Dic61—28no—
78C22×Dic61—216no—
79C22×Dic61—24no—
80C22×Dic61—24no—
81C22×Dic61—416no—
82C22×Dic61—432no—
83C22×Dic61—48no—
84C22×Dic61—44no—
85C22×Dic61—44no—
86C22×Dic61—44no—
87C2×C8×C61—24no—
88C2×C8×C61—28no—
89C2×C8×C61—48no—
90C22⋊Dic61—48no—
91C4⋊Dic61—28no—
92C4⋊Dic61—216no—
93C4⋊Dic61—24no—
94C4⋊Dic61—28no—
95C4⋊Dic61—44no—
96C4⋊Dic61C22×C418yes—
97C23×C61—24no—
98C23×C61—24no—
99C23×C61—28no—
100C23×C61—28no—
101C23×C61—216no—
102C23×C61—216no—
103C23×C61#103116yes—
104C23×C61C2×C22⋊C414yes—
105C23×C61C2×C22⋊C412yes—
106C23×C61#12314yes—
107C23×C61C2×SD1614yes—
108C23×C61C2×SD1612yes—
109C23×C61C2×Q1614yes—
110C23×C61C2×Q1612yes—
111C23×C61AGL(1,ℤ/8)14yes—
112C23×C61C22×D411yescharacteristic
113C2×C4×C61—24no—
114C2×C4×C61—28no—
115C2×C4×C61—28no—
116C2×C4×C61—28no—
117C2×C4×C61—216no—
118C2×C4×C61C2×C22⋊C414yes—
119C2×C4×C61C2×C22⋊C412yes—
120C2×C4×C61#11718yes—
121C2×C4×C61#12318yes—
122C2×C4×C61#12314yes—
123C2×C4×C61C23×C411yescharacteristic
124C2×C4×C61C22×D411yescharacteristic
125C2×C4×C61C2×#4114yes—
126C2×Dic61—28no—
127C2×Dic61—432no—
128C2×Dic61—48no—
129C2×Dic61—416no—
130C2×Dic61—44no—
131C2×Dic61—44no—
132C2×Dic61—44no—
133C2×Dic61—88no—
134C8×C61—44no—
135C2×#1824—611nomaximal, Sylow
136C22×C61—28no—
137C22×C61—28no—
138C22×C61—232no—
139C22×C61—24no—
140C22×C61—24no—
141C22×C61#38114yes—
142C22×C61C2×#10318yes—
143C22×C61C2×#10314yes—
144C22×C61#41814yes—
145C22×C61#48118yes—
146C22×C61#48418yes—
147C22×C61C22×C22⋊C411yescharacteristic
148C22×C61C2×#12312yes—
149C22×C61C22×SD1611yescharacteristic
150C22×C61C22×Q1611yescharacteristic
151C22×C61C2×AGL(1,ℤ/8)12yes—
152C4×C61—24no—
153C4×C61#38114yes—
154C4×C61C2×#11712yes—
155C4×C61C2×#12312yes—
156Dic61—48no—
157Dic61—84no—
158C23×C4⋊C4—611no—
159C22×C22⋊C8D6111yescharacteristic
160C2×#380—611no—
161#1824—618no—
162C2×#340—614no—
163C2×C61—28no—
164C2×C61#182418yescomplemented
165C2×C61C2×#38111yescharacteristic
166C2×C61C22×#10311yescharacteristic
167C2×C61C2×#41811yescharacteristic
168C2×C61C2×#48112yes—
169C2×C61C2×#48412yes—
170C24×C4—1221no—
171C24×C4C2×D6111yescharacteristic
172C23×C8C2×D6112yes—
173C22×C4⋊C4—618no—
174C22×C4⋊C4—614no—
175C22×C4⋊C4—612no—
176C22×C4⋊C4—612no—
177C22×C4⋊C4—1222no—
178C22×C4⋊C4—1221no—
179C22×C4⋊C4—1224no—
180C22×C22⋊C4—1221no—
181C2×C22⋊C8—24no—
182C2×C22⋊C8C2×D6114yes—
183#380—614no—
184#380—1222no—
185C2×#95—1221no—
186#340—6116no—
187C61C2×#182411yescharacteristic, complemented, Sylow
188C25D24411yescharacteristic
189C23×C4—28no—
190C23×C4—1228no—
191C23×C4—1224no—
192C23×C4—1222no—
193C23×C4—1222no—
194C23×C4—2448no—
195C23×C4C4×D6114yes—
196C23×C4D24412yes—
197C23×C4D24411yescharacteristic
198C23×C4C22⋊D6114yes—
199C23×C4C22×D6112yes—
200C23×C4C22×D6111yescharacteristic
201C22×C8—28no—
202C22×C8—24no—
203C22×C8C22×D6114yes—
204C2×C4⋊C4—618no—
205C2×C4⋊C4—6116no—
206C2×C4⋊C4—614no—
207C2×C4⋊C4—614no—
208C2×C4⋊C4—1228no—
209C2×C4⋊C4—12216no—
210C2×C4⋊C4—1224no—
211C2×C4⋊C4—1222no—
212C2×C4⋊C4—1228no—
213C2×C4⋊C4—1224no—
214C2×C4⋊C4—1228no—
215C2×C4⋊C4—1222no—
216C2×C22⋊C4—1224no—
217C2×C22⋊C4—2444no—
218C22⋊C8—28no—
219#95—1224no—
220C24—24no—
221C24—24no—
222C24#1175819014yes—
223C24Dic24414yes—
224C24#1175819814yes—
225C24C2×D24412yes—
226C24C2×D24411yescharacteristic
227C22×C4—24no—
228C22×C4—28no—
229C22×C4—216no—
230C22×C4—216no—
231C22×C4—28no—
232C22×C4—1224no—
233C22×C4—12216no—
234C22×C4—1228no—
235C22×C4—1224no—
236C22×C4—2444no—
237C22×C4—2444no—
238C22×C4—2444no—
239C22×C4—24432no—
240C22×C4—24416no—
241C22×C4—2448no—
242C22×C4#1175819814yes—
243C22×C4#1175819818yes—
244C22×C4C2×C4×D6114yes—
245C22×C4C2×C4×D6112yes—
246C22×C4C2×D24412yes—
247C22×C4C2×D24411yescharacteristic
248C22×C4#1175822418yes—
249C22×C4C2×C22⋊D6114yes—
250C22×C4C2×C22⋊D6112yes—
251C22×C4C23×D6111yescharacteristic
252C2×C8—24no—
253C2×C8—28no—
254C2×C8—48no—
255C4⋊C4—618no—
256C4⋊C4—1224no—
257C4⋊C4—12216no—
258C4⋊C4—1228no—
259C4⋊C4—1228no—
260C4⋊C4—2444no—
261C22⋊C4—2448no—
262C23—24no—
263C23—28no—
264C23—24no—
265C23—216no—
266C23—216no—
267C23—28no—
268C23#14519702116yes—
269C23C2×#1175819814yes—
270C23C2×#1175819812yes—
271C23#1451976114yes—
272C23C2×#1175819014yes—
273C23C2×#1175819012yes—
274C23C2×Dic24414yes—
275C23C2×Dic24412yes—
276C23#1451980514yes—
277C23C22×D24411yescharacteristic
278C2×C4—24no—
279C2×C4—28no—
280C2×C4—28no—
281C2×C4—28no—
282C2×C4—216no—
283C2×C4—1228no—
284C2×C4—4888no—
285C2×C4—2444no—
286C2×C4—2444no—
287C2×C4—2444no—
288C2×C4—24432no—
289C2×C4—24416no—
290C2×C4—2448no—
291C2×C4C2×#1175819814yes—
292C2×C4C2×#1175819812yes—
293C2×C4#1451973318yes—
294C2×C4#1451975818yes—
295C2×C4#1451976114yes—
296C2×C4C22×C4×D6111yescharacteristic
297C2×C4C22×C22⋊D6111yescharacteristic
298C2×C4C2×#1175822414yes—
299C8—44no—
300C22—24no—
301C22—232no—
302C22—28no—
303C22—28no—
304C22—24no—
305C22#1683962314yes—
306C22C2×#1451970218yes—
307C22C2×#1451970214yes—
308C22#1683976814yes—
309C22#1684008118yes—
310C22#1684009818yes—
311C22C22×#1175819811yescharacteristic
312C22C2×#1451976112yes—
313C22C22×#1175819011yescharacteristic
314C22C22×Dic24411yescharacteristic
315C22C2×#1451980512yes—
316C4—24no—
317C4—4884no—
318C4—2448no—
319C4#1683962314yes—
320C4C2×#1451973312yes—
321C4C2×#1451975812yes—
322C2—28no—
323C2#2144591018yesdirect product factor
324C2C2×#1683962311yescharacteristic
325C2C22×#1451970211yescharacteristic
326C2C2×#1683976811yescharacteristic
327C2C2×#1684008112yes—
328C2C2×#1684009812yes—
subgroupG/H
centerC24C2×D244
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC22×C22⋊C8×C61C2
socleC24×C61C2×D4
prime radicalC25×C61D4
cosocleC22×C4×C61C24
hypercenterC22×C22⋊C8D61
hypocenterC61C2×#1824
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C24 ◁ C24×C4 ◁ C22×C22⋊C8

Complements

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

NH ≅ G/Ntype
3. #21445910C2direct (N × H)
4. C2×#16839525C2semidirect
10. C22×C4⋊Dic61C4semidirect
18. #16839525C22semidirect
37. C2×C4⋊Dic61C2×C4semidirect
164. C2×C61#1824semidirect
187. C61C2×#1824semidirect
323. C2#21445910direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C4⋊Dic612
C2×#168396222
#214459102
C2×#168395252
C22×C22⋊C8×C612
C2×#182461