Finite Group Databasebeta

← C2×#21444839 #29652134

Subgroups — C2×#21444839 #29652134

Order 15616.

1524 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840078C212yesmaximal, complemented
2C2×#16839698C211yesmaximal, characteristic, complemented
3#21444839C218yesmaximal, direct product factor
4C2×#16839496C212yesmaximal, complemented
5C2×#16839486C211yesmaximal, characteristic, complemented
6C2×C61×#534C211yesmaximal, characteristic
7C22×C4⋊Dic61C2211yescharacteristic, complemented
8C22×#11758196—21no—
9C22×C22⋊Dic61—21no—
10#16840078—24no—
11#16840078C2218yescomplemented
12C2×#14519708—22no—
13C2×#14519698—22no—
14C2×C22⋊#92418C2212yescomplemented
15#16839698—22no—
16#16839698C2214yescomplemented
17C2×#14519684C2211yescharacteristic, complemented
18#16839496C2218yescomplemented
19#16839486C2214yescomplemented
20C23×D4×C61—21no—
21C61×#534—24no—
22C61×#534—22no—
23C61×#534C2214yes—
24C2×#123×C61—22no—
25C2×#121×C61—21no—
26C2×#121×C61C2212yes—
27C2×#120×C61—22no—
28C22×C22⋊C4×C61C2211yescharacteristic
29C23×Dic61—21no—
30C23×Dic61—21no—
31C22×#92418—22no—
32C2×C4⋊Dic61—22no—
33C2×C4⋊Dic61—22no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61C2312yescomplemented
36C2×#11758196—24no—
37C2×#11758196—44no—
38C2×C22⋊Dic61—24no—
39C2×C22⋊Dic61—44no—
40#14519708—28no—
41#14519698—28no—
42C22⋊#92418—22no—
43C22⋊#92418C2314yescomplemented
44#14519684—21no—
45#14519684C2312yescomplemented
46C25×C61—21no—
47C25×C61D411yescharacteristic
48C22×D4×C61—24no—
49C22×D4×C61—22no—
50C22×D4×C61—24no—
51C22×D4×C61—22no—
52C22×D4×C61—21no—
53C22×D4×C61—44no—
54C22×D4×C61—44no—
55C22×D4×C61D412yes—
56C23×C4×C61—21no—
57C23×C4×C61D411yescharacteristic
58C23×C4×C61C2311yescharacteristic
59#123×C61—28no—
60#123×C61—28no—
61#121×C61—24no—
62#121×C61—22no—
63#121×C61—22no—
64#121×C61—24no—
65#121×C61D414yes—
66#121×C61C2314yes—
67#120×C61—28no—
68#120×C61—28no—
69C2×C4⋊C4×C61—21no—
70C2×C4⋊C4×C61D412yes—
71C2×C22⋊C4×C61—22no—
72C2×C22⋊C4×C61—22no—
73C2×C22⋊C4×C61—22no—
74C2×C22⋊C4×C61—22no—
75C2×C22⋊C4×C61D412yes—
76C2×C22⋊C4×C61C2312yes—
77C24×C61—21no—
78C24×C61—21no—
79C24×C61—22no—
80C24×C61—24no—
81C24×C61—22no—
82C24×C61—42no—
83C24×C61—42no—
84C24×C61—44no—
85C24×C61—82no—
86C24×C61—82no—
87C24×C61SD1614yes—
88C24×C61C2×D411yescharacteristic
89C24×C61C2×D412yes—
90C2×D4×C61—28no—
91C2×D4×C61—24no—
92C2×D4×C61—24no—
93C2×D4×C61—24no—
94C2×D4×C61—22no—
95C2×D4×C61—44no—
96C2×D4×C61—48no—
97C2×D4×C61—416no—
98C2×D4×C61—48no—
99C2×D4×C61—48no—
100C2×D4×C61—44no—
101C2×D4×C61—44no—
102C2×D4×C61—82no—
103C2×D4×C61C2×D414yes—
104C22×C4×C61—24no—
105C22×C4×C61—21no—
106C22×C4×C61—22no—
107C22×C4×C61—21no—
108C22×C4×C61—42no—
109C22×C4×C61—44no—
110C22×C4×C61—42no—
111C22×C4×C61C2×D412yes—
112C22×C4×C61C2×D412yes—
113C22×C4×C61C2×D411yescharacteristic
114C22×C4×C61C2×D412yes—
115C22×C4×C61C2411yescharacteristic
116C22×Dic61—24no—
117C22×Dic61—22no—
118C22×Dic61—22no—
119C22×Dic61—42no—
120C22×Dic61—42no—
121C22×Dic61—42no—
122C22×Dic61—42no—
123C22×Dic61—41no—
124C22×Dic61—41no—
125C4⋊C4×C61—24no—
126C4⋊C4×C61—22no—
127C4⋊C4×C61C2×D414yes—
128C22⋊C4×C61—28no—
129C22⋊C4×C61—24no—
130C22⋊C4×C61—24no—
131C22⋊C4×C61—24no—
132C22⋊C4×C61—24no—
133C22⋊Dic61—48no—
134C4⋊Dic61—24no—
135C4⋊Dic61—42no—
136#11758196—48no—
137C2×#92418—24no—
138C2×#92418—44no—
139C23×C61—22no—
140C23×C61—22no—
141C23×C61—22no—
142C23×C61—24no—
143C23×C61—22no—
144C23×C61—24no—
145C23×C61—24no—
146C23×C61—42no—
147C23×C61—48no—
148C23×C61—42no—
149C23×C61—48no—
150C23×C61—42no—
151C23×C61—42no—
152C23×C61—44no—
153C23×C61—44no—
154C23×C61—44no—
155C23×C61—84no—
156C23×C61—81no—
157C23×C61—81no—
158C23×C61—84no—
159C23×C61—84no—
160C23×C61—816no—
161C23×C61#12011yescharacteristic
162C23×C61#12011yescharacteristic
163C23×C61C2×SD1612yes—
164C23×C61C2×SD1614yes—
165C23×C61AGL(1,ℤ/8)12yes—
166C23×C61C22×D411yescharacteristic
167D4×C61—44no—
168D4×C61—416no—
169D4×C61—44no—
170D4×C61—44no—
171D4×C61—48no—
172D4×C61—82no—
173D4×C61—84no—
174C2×C4×C61—24no—
175C2×C4×C61—22no—
176C2×C4×C61—24no—
177C2×C4×C61—42no—
178C2×C4×C61—41no—
179C2×C4×C61—41no—
180C2×C4×C61—48no—
181C2×C4×C61—44no—
182C2×C4×C61—42no—
183C2×C4×C61—42no—
184C2×C4×C61—81no—
185C2×C4×C61#12012yes—
186C2×C4×C61C22×D412yes—
187C2×Dic61—24no—
188C2×Dic61—48no—
189C2×Dic61—42no—
190C2×Dic61—42no—
191C2×Dic61—42no—
192C2×Dic61—42no—
193C2×Dic61—42no—
194C2×Dic61—82no—
195C2×Dic61—82no—
196#92418—44no—
197C2×#1613—611nomaximal, Sylow
198C22×C61—24no—
199C22×C61—24no—
200C22×C61—21no—
201C22×C61—21no—
202C22×C61—21no—
203C22×C61—21no—
204C22×C61—24no—
205C22×C61—44no—
206C22×C61—48no—
207C22×C61—42no—
208C22×C61—42no—
209C22×C61—44no—
210C22×C61—44no—
211C22×C61—44no—
212C22×C61—82no—
213C22×C61—84no—
214C22×C61—816no—
215C22×C61—88no—
216C22×C61#45012yes—
217C22×C61#45012yes—
218C22×C61#45312yes—
219C22×C61#45812yes—
220C22×C61C2×#12011yescharacteristic
221C22×C61C22×SD1611yescharacteristic
222C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
223C4×C61—22no—
224C4×C61—22no—
225C4×C61—44no—
226C4×C61—42no—
227Dic61—44no—
228Dic61—82no—
229C2×#534D6111yescharacteristic
230C2×#481—612no—
231C2×#399—611no—
232#1613—618no—
233C2×#327—612no—
234C2×#323—611no—
235C2×C61—21no—
236C2×C61—21no—
237C2×C61—22no—
238C2×C61—44no—
239C2×C61—84no—
240C2×C61#161314yescomplemented
241C2×C61C2×#45011yescharacteristic
242C2×C61C2×#45311yescharacteristic
243C2×C61C2×#45811yescharacteristic
244C23×D4—21no—
245#534—24no—
246#534—22no—
247#534C2×D6114yes—
248C2×#123—22no—
249C2×#121—21no—
250C2×#121C2×D6112yes—
251C2×#120—22no—
252C22×C4⋊C4—611no—
253C22×C4⋊C4—1221no—
254C22×C22⋊C4—1221no—
255C22×C22⋊C4C2×D6111yescharacteristic
256#481—618no—
257#481—1224no—
258C2×#106—1222no—
259C2×#102—1222no—
260C2×C22⋊C8—612no—
261#399—614no—
262#399—1222no—
263C2×#95—611no—
264#327—618no—
265#323—614no—
266C61C2×#161311yescharacteristic, complemented, Sylow
267C25—21no—
268C25C22⋊D6111yescharacteristic
269C22×D4—22no—
270C22×D4—24no—
271C22×D4—22no—
272C22×D4—24no—
273C22×D4—21no—
274C22×D4—44no—
275C22×D4—44no—
276C22×D4C22⋊D6112yes—
277C23×C4—21no—
278C23×C4—1221no—
279C23×C4—1221no—
280C23×C4C22⋊D6111yescharacteristic
281C23×C4C22×D6111yescharacteristic
282C22×C8—1222no—
283#123—28no—
284#123—28no—
285#121—24no—
286#121—24no—
287#121—22no—
288#121—22no—
289#121C22⋊D6114yes—
290#121C22×D6114yes—
291#120—28no—
292#120—28no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—612no—
295C2×C4⋊C4—1222no—
296C2×C4⋊C4—1222no—
297C2×C4⋊C4—1221no—
298C2×C4⋊C4—1224no—
299C2×C4⋊C4—2444no—
300C2×C4⋊C4C22⋊D6112yes—
301C2×C22⋊C4—22no—
302C2×C22⋊C4—22no—
303C2×C22⋊C4—22no—
304C2×C22⋊C4—22no—
305C2×C22⋊C4—1224no—
306C2×C22⋊C4—2444no—
307C2×C22⋊C4C22⋊D6112yes—
308C2×C22⋊C4C22×D6112yes—
309#106—1228no—
310#102—1228no—
311C22⋊C8—614no—
312C22⋊C8—1222no—
313#95—612no—
314#95—1221no—
315C24—21no—
316C24—21no—
317C24—22no—
318C24—24no—
319C24—22no—
320C24—42no—
321C24—42no—
322C24—44no—
323C24—82no—
324C24—82no—
325C24#1175820014yes—
326C24C2×C22⋊D6111yescharacteristic
327C24C2×C22⋊D6112yes—
328C2×D4—28no—
329C2×D4—24no—
330C2×D4—24no—
331C2×D4—24no—
332C2×D4—22no—
333C2×D4—44no—
334C2×D4—48no—
335C2×D4—416no—
336C2×D4—48no—
337C2×D4—48no—
338C2×D4—44no—
339C2×D4—44no—
340C2×D4—82no—
341C2×D4C2×C22⋊D6114yes—
342C22×C4—24no—
343C22×C4—21no—
344C22×C4—22no—
345C22×C4—21no—
346C22×C4—42no—
347C22×C4—44no—
348C22×C4—42no—
349C22×C4—1224no—
350C22×C4—1222no—
351C22×C4—1222no—
352C22×C4—2442no—
353C22×C4—2442no—
354C22×C4—2441no—
355C22×C4—2441no—
356C22×C4—2442no—
357C22×C4—2442no—
358C22×C4C2×C22⋊D6112yes—
359C22×C4C2×C22⋊D6112yes—
360C22×C4C2×C22⋊D6112yes—
361C22×C4C2×C22⋊D6111yescharacteristic
362C22×C4C23×D6111yescharacteristic
363C2×C8—1224no—
364C2×C8—2444no—
365C4⋊C4—24no—
366C4⋊C4—22no—
367C4⋊C4—1224no—
368C4⋊C4—2448no—
369C4⋊C4—2442no—
370C4⋊C4C2×C22⋊D6114yes—
371C22⋊C4—28no—
372C22⋊C4—24no—
373C22⋊C4—24no—
374C22⋊C4—24no—
375C22⋊C4—24no—
376C22⋊C4—2448no—
377C23—22no—
378C23—22no—
379C23—22no—
380C23—24no—
381C23—22no—
382C23—24no—
383C23—24no—
384C23—42no—
385C23—48no—
386C23—42no—
387C23—48no—
388C23—42no—
389C23—42no—
390C23—44no—
391C23—44no—
392C23—44no—
393C23—81no—
394C23—81no—
395C23—84no—
396C23—84no—
397C23—84no—
398C23—816no—
399C23#1451974611yescharacteristic
400C23#1451974611yescharacteristic
401C23C2×#1175820012yes—
402C23C2×#1175820014yes—
403C23#1451980312yes—
404C23C22×C22⋊D6111yescharacteristic
405D4—44no—
406D4—416no—
407D4—44no—
408D4—44no—
409D4—48no—
410D4—82no—
411D4—84no—
412C2×C4—24no—
413C2×C4—22no—
414C2×C4—24no—
415C2×C4—42no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—48no—
419C2×C4—44no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—81no—
423C2×C4—1224no—
424C2×C4—4882no—
425C2×C4—4882no—
426C2×C4—2442no—
427C2×C4—2442no—
428C2×C4—2442no—
429C2×C4—2442no—
430C2×C4—2448no—
431C2×C4—2442no—
432C2×C4#1451974612yes—
433C2×C4C22×C22⋊D6112yes—
434C8—2444no—
435C22—21no—
436C22—21no—
437C22—21no—
438C22—21no—
439C22—24no—
440C22—24no—
441C22—24no—
442C22—44no—
443C22—42no—
444C22—42no—
445C22—48no—
446C22—44no—
447C22—44no—
448C22—44no—
449C22—82no—
450C22—84no—
451C22—816no—
452C22—88no—
453C22#1683991312yes—
454C22#1683991312yes—
455C22#1683993012yes—
456C22#1683995212yes—
457C22C2×#1451974611yescharacteristic
458C22C22×#1175820011yescharacteristic
459C22C2×#1451980311yescharacteristic
460C4—22no—
461C4—22no—
462C4—42no—
463C4—44no—
464C4—4882no—
465C4—2444no—
466C2—21no—
467C2—21no—
468C2—22no—
469C2—44no—
470C2—84no—
471C2#2144483914yesdirect product factor
472C2C2×#1683991311yescharacteristic
473C2C2×#1683993011yescharacteristic
474C2C2×#1683995211yescharacteristic
subgroupG/H
centerC23#14519746
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
Fitting, prime radicalC2×C61×#534C2
socleC23×C61#120
hypercenterC2×#534D61
hypocenterC61C2×#1613
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#534

Complements

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

NH ≅ G/Ntype
1. C2×#16840078C2semidirect
2. C2×#16839698C2semidirect
3. #21444839C2direct (N × H)
4. C2×#16839496C2semidirect
5. C2×#16839486C2semidirect
7. C22×C4⋊Dic61C22semidirect
11. #16840078C22semidirect
14. C2×C22⋊#92418C22semidirect
16. #16839698C22semidirect
17. C2×#14519684C22semidirect
18. #16839496C22semidirect
19. #16839486C22semidirect
35. C2×C4⋊Dic61C23semidirect
43. C22⋊#92418C23semidirect
45. #14519684C23semidirect
240. C2×C61#1613semidirect
266. C61C2×#1613semidirect
471. C2#21444839direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168400782
C2×#168396982
#214448392
C2×#168394962
C2×#168394862
C2×C61×#5342
C2×#161361