Finite Group Databasebeta

← C2×#21445534 #29677411

Subgroups — C2×#21445534 #29677411

Order 15616.

2398 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C8×D61C211yesmaximal, characteristic
2C22×#14519735C212yesmaximal
3#21445534C218yesmaximal, direct product factor
4C2×#16839525C211yesmaximal, characteristic, complemented
5C2×#16839524C212yesmaximal, complemented
6C2×C61×#340C211yesmaximal, characteristic, complemented
7C23×C4×D61C2211yescharacteristic
8C23×#92418C2211yescharacteristic
9C22×C8×D61—28no—
10C22×C8×D61C418yescomplemented
11C22×C8×D61C2214yes—
12C2×#14519735—24no—
13C2×#14519735—28no—
14C2×#14519735C4116yescomplemented
15C2×#14519735C2218yes—
16C22×C4⋊Dic61C2212yes—
17C22×#11758198—22no—
18C22×C4×Dic61—22no—
19#16839525C2214yescomplemented
20#16839524C2218yescomplemented
21C23×C8×C61C2211yescharacteristic
22C22×C4⋊C4×C61C2212yes—
23C61×#340C2214yescomplemented
24C24×D61D411yescharacteristic
25C23×Dic61—22no—
26C23×Dic61D411yescharacteristic
27C22×C4×D61C2×C414yes—
28C22×C4×D61C2×C418yes—
29C22×C4×D61D412yes—
30C22×C4×D61D418yes—
31C22×C4×D61Q814yes—
32C22×C4×D61C2312yes—
33C22×#92418—24no—
34C22×#92418C2×C414yes—
35C22×#92418C2312yes—
36C2×C8×D61—232no—
37C2×C8×D61—216no—
38C2×C8×D61C2×C4116yescomplemented
39#14519735—232no—
40#14519735—216no—
41#14519735C2×C4132yescomplemented
42C2×C4⋊Dic61—22no—
43C2×C4⋊Dic61—24no—
44C2×C4⋊Dic61C2×C418yes—
45C2×C4⋊Dic61C2314yes—
46C2×#11758198—216no—
47C2×#11758198—28no—
48C2×C4×Dic61—216no—
49C2×C4×Dic61—28no—
50C23×C4×C61—22no—
51C23×C4×C61C2311yescharacteristic
52C22×C8×C61—24no—
53C22×C8×C61C2×C414yes—
54C22×C8×C61C2312yes—
55C2×C4⋊C4×C61—22no—
56C2×C4⋊C4×C61—24no—
57C2×C4⋊C4×C61C2×C418yes—
58C2×C4⋊C4×C61C2314yes—
59C24×C61C2×D411yescharacteristic
60C23×D61—22no—
61C23×D61—24no—
62C23×D61—22no—
63C23×D61C22⋊C418yes—
64C23×D61C4⋊C414yes—
65C23×D61C2×D412yes—
66C22×C4×C61—28no—
67C22×C4×C61—24no—
68C22×C4×C61—44no—
69C22×C4×C61—44no—
70C22×C4×C61C22×C412yes—
71C22×C4×C61C22×C414yes—
72C22×C4×C61C2×D411yescharacteristic
73C22×C4×C61C2×D414yes—
74C22×C4×C61C2×Q812yes—
75C22×C4×C61C2411yescharacteristic
76C22×Dic61—28no—
77C22×Dic61—24no—
78C22×Dic61—44no—
79C22×Dic61—44no—
80C22×Dic61C22⋊C418yes—
81C22×Dic61C4⋊C414yes—
82C22×Dic61C2×D412yes—
83C2×C4×D61C42116yes—
84C2×C4×D61C22⋊C4116yes—
85C2×C4×D61C22⋊C4116yes—
86C2×C4×D61C4⋊C418yes—
87C2×C4×D61C4⋊C4132yes—
88C2×C4×D61C22×C414yes—
89C2×C4×D61C22×C418yes—
90C2×C4×D61C2×D418yes—
91C2×C4×D61C2×Q814yes—
92C2×C8×C61—28no—
93C2×C8×C61—24no—
94C2×C8×C61C22×C414yes—
95C4⋊C4×C61—28no—
96C4⋊C4×C61—24no—
97C4⋊C4×C61C22×C418yes—
98#11758198—232no—
99C4⋊Dic61—28no—
100C4⋊Dic61—24no—
101C4⋊Dic61C22×C418yes—
102C4×Dic61—232no—
103C2×#92418—28no—
104C2×#92418—24no—
105C2×#92418C22×C414yes—
106C8×D61—232no—
107C23×C61C2×C22⋊C414yes—
108C23×C61C2×C4⋊C412yes—
109C23×C61#13512yes—
110C23×C61#13514yes—
111C23×C61#13512yes—
112C23×C61C22×D411yescharacteristic
113C22×D61—22no—
114C22×D61—24no—
115C22×D61—22no—
116C22×D61—216no—
117C22×D61—216no—
118C22×D61—28no—
119C22×D61—28no—
120C22×D61#95116yes—
121C22×D61C2×C22⋊C418yes—
122C22×D61C2×C4⋊C414yes—
123C2×C4×C61—28no—
124C2×C4×C61—44no—
125C2×C4×C61—44no—
126C2×C4×C61—416no—
127C2×C4×C61C2×C4214yes—
128C2×C4×C61C2×C22⋊C414yes—
129C2×C4×C61C2×C22⋊C414yes—
130C2×C4×C61C2×C4⋊C418yes—
131C2×C4×C61C2×C4⋊C412yes—
132C2×C4×C61C23×C411yescharacteristic
133C2×C4×C61C23×C412yes—
134C2×C4×C61C22×D412yes—
135C2×C4×C61C22×Q811yescharacteristic
136C2×Dic61—28no—
137C2×Dic61—44no—
138C2×Dic61—44no—
139C2×Dic61—416no—
140C2×Dic61#95116yes—
141C2×Dic61C2×C22⋊C418yes—
142C2×Dic61C2×C4⋊C414yes—
143C4×D61#95132yes—
144C4×D61C2×C4218yes—
145C4×D61C2×C22⋊C418yes—
146C4×D61C2×C4⋊C4116yes—
147C8×C61—24no—
148#92418—24no—
149C2×#1735—611nomaximal, Sylow
150C22×C61C2×#9514yes—
151C22×C61#41618yes—
152C22×C61#41618yes—
153C22×C61#42714yes—
154C22×C61#42714yes—
155C22×C61C22×C22⋊C412yes—
156C22×C61C22×C4⋊C411yescharacteristic
157C22×C61C2×#13511yescharacteristic
158C22×C61C2×#13512yes—
159C22×C61C2×#13511yescharacteristic
160C2×D61—28no—
161C2×D61—28no—
162C2×D61—24no—
163C2×D61—24no—
164C2×D61—232no—
165C2×D61C2×#9518yes—
166C4×C61—48no—
167C4×C61C2×#9514yes—
168C4×C61C22×C4211yescharacteristic
169C4×C61C22×C22⋊C411yescharacteristic
170C4×C61C22×C4⋊C412yes—
171Dic61—48no—
172Dic61C2×#9518yes—
173C24×C8—611no—
174C22×#117—612no—
175#1735—618no—
176C2×#340—611no—
177C2×#340—612no—
178C2×#340D6111yescharacteristic, complemented
179C2×C61#173518yescomplemented
180C2×C61C22×#9511yescharacteristic
181C2×C61C2×#41612yes—
182C2×C61C2×#41612yes—
183C2×C61C2×#42711yescharacteristic
184C2×C61C2×#42711yescharacteristic
185D61—28no—
186C24×C4—611no—
187C23×C8—611no—
188C23×C8—618no—
189C23×C8—614no—
190C23×C8—1228no—
191C23×C8C2×D6111yescharacteristic
192C2×#117—6116no—
193C2×#117—618no—
194C2×#117—1224no—
195C2×#117—1228no—
196C22×C4⋊C4—612no—
197C22×C4⋊C4C2×D6112yes—
198C22×C22⋊C4—1222no—
199C22×C42—1222no—
200#340—614no—
201#340—618no—
202#340C2×D6114yescomplemented
203C61C2×#173511yescharacteristic, complemented, Sylow
204C25—611no—
205C23×C4—22no—
206C23×C4—611no—
207C23×C4—618no—
208C23×C4—614no—
209C23×C4—612no—
210C23×C4—618no—
211C23×C4—614no—
212C23×C4—612no—
213C23×C4—1222no—
214C23×C4C22×D6111yescharacteristic
215C22×C8—24no—
216C22×C8—614no—
217C22×C8—612no—
218C22×C8—6116no—
219C22×C8—12216no—
220C22×C8—12232no—
221C22×C8—1224no—
222C22×C8C4×D6114yes—
223C22×C8C22×D6112yes—
224#117—6132no—
225#117—12216no—
226#117—12232no—
227C2×C4⋊C4—24no—
228C2×C4⋊C4—22no—
229C2×C4⋊C4—618no—
230C2×C4⋊C4—614no—
231C2×C4⋊C4—1224no—
232C2×C4⋊C4—1222no—
233C2×C4⋊C4C4×D6118yes—
234C2×C4⋊C4C22×D6114yes—
235C2×C22⋊C4—1228no—
236C2×C22⋊C4—12216no—
237C2×C42—1228no—
238C2×C42—12216no—
239C24—612no—
240C24—618no—
241C24—614no—
242C24—1222no—
243C24—1224no—
244C24—1222no—
245C24D4×D6111yescharacteristic
246C22×C4—24no—
247C22×C4—28no—
248C22×C4—44no—
249C22×C4—44no—
250C22×C4—612no—
251C22×C4—618no—
252C22×C4—614no—
253C22×C4—618no—
254C22×C4—614no—
255C22×C4—618no—
256C22×C4—614no—
257C22×C4—6116no—
258C22×C4—6116no—
259C22×C4—6116no—
260C22×C4—618no—
261C22×C4—6132no—
262C22×C4—1224no—
263C22×C4—1228no—
264C22×C4—2444no—
265C22×C4—2444no—
266C22×C4C2×C4×D6112yes—
267C22×C4C2×C4×D6114yes—
268C22×C4D4×D6114yes—
269C22×C4D4×D6111yescharacteristic
270C22×C4Q8×D6112yes—
271C22×C4C23×D6111yescharacteristic
272C2×C8—24no—
273C2×C8—28no—
274C2×C8—614no—
275C2×C8—12232no—
276C2×C8—1224no—
277C2×C8—1228no—
278C2×C8C2×C4×D6114yes—
279C4⋊C4—24no—
280C4⋊C4—28no—
281C4⋊C4—618no—
282C4⋊C4—1224no—
283C4⋊C4—1228no—
284C4⋊C4C2×C4×D6118yes—
285C22⋊C4—12232no—
286C42—12232no—
287C23—618no—
288C23—614no—
289C23—6116no—
290C23—12216no—
291C23—12216no—
292C23—1222no—
293C23—1224no—
294C23—1222no—
295C23—1228no—
296C23—1228no—
297C23C22⋊C4×D6114yes—
298C23C4⋊C4×D6112yes—
299C23#1451979612yes—
300C23#1451979814yes—
301C23#1451980012yes—
302C23C2×D4×D6111yescharacteristic
303C2×C4—28no—
304C2×C4—416no—
305C2×C4—44no—
306C2×C4—44no—
307C2×C4—618no—
308C2×C4—614no—
309C2×C4—6116no—
310C2×C4—618no—
311C2×C4—618no—
312C2×C4—6116no—
313C2×C4—6132no—
314C2×C4—1228no—
315C2×C4—24416no—
316C2×C4—2444no—
317C2×C4—2444no—
318C2×C4C42×D6114yes—
319C2×C4C22⋊C4×D6114yes—
320C2×C4C22⋊C4×D6114yes—
321C2×C4C4⋊C4×D6118yes—
322C2×C4C4⋊C4×D6112yes—
323C2×C4C22×C4×D6111yescharacteristic
324C2×C4C22×C4×D6112yes—
325C2×C4C2×D4×D6112yes—
326C2×C4C2×Q8×D6111yescharacteristic
327C8—24no—
328C8—1224no—
329C22—618no—
330C22—1224no—
331C22—1224no—
332C22—12232no—
333C22—1228no—
334C22—1228no—
335C22#95×D6114yes—
336C22#1683975518yes—
337C22#1683975718yes—
338C22#1683979714yes—
339C22#1683979914yes—
340C22C2×C22⋊C4×D6112yes—
341C22C2×C4⋊C4×D6111yescharacteristic
342C22C2×#1451979611yescharacteristic
343C22C2×#1451979812yes—
344C22C2×#1451980011yescharacteristic
345C4—48no—
346C4—618no—
347C4—2448no—
348C4#95×D6114yes—
349C4C2×C42×D6111yescharacteristic
350C4C2×C22⋊C4×D6111yescharacteristic
351C4C2×C4⋊C4×D6112yes—
352C2—1228no—
353C2#2144553418yesdirect product factor
354C2C2×#95×D6111yescharacteristic
355C2C2×#1683975512yes—
356C2C2×#1683975712yes—
357C2C2×#1683979711yescharacteristic
358C2C2×#1683979911yescharacteristic
subgroupG/H
centerC24D4×D61
commutatorC4×C61C22×C42
FrattiniC22×C4C23×D61
FittingC2×C61×#340C2
socleC24×C61C2×D4
prime radicalC24×D61D4
cosocleC22×C4×C61C24
hypercenterC2×#340D61
hypocenterC61C2×#1735
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
3. #21445534C2direct (N × H)
4. C2×#16839525C2semidirect
5. C2×#16839524C2semidirect
6. C2×C61×#340C2semidirect
10. C22×C8×D61C4semidirect
14. C2×#14519735C4semidirect
19. #16839525C22semidirect
20. #16839524C22semidirect
23. C61×#340C22semidirect
38. C2×C8×D61C2×C4semidirect
41. #14519735C2×C4semidirect
178. C2×#340D61semidirect
179. C2×C61#1735semidirect
202. #340C2×D61semidirect
203. C61C2×#1735semidirect
353. C2#21445534direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C8×D612
C22×#145197352
#214455342
C2×#168395252
C2×#168395242
C2×C61×#3402
C2×#173561