Finite Group Databasebeta

← C2×#21447023 #29707486

Subgroups — C2×#21447023 #29707486

Order 15616.

1662 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519756C211yesmaximal, characteristic
2C22×#14519711C211yesmaximal, characteristic, complemented
3C22×#14519702C211yesmaximal, characteristic, complemented
4C22×#14519702C211yesmaximal, characteristic, complemented
5C2×#16839622C211yesmaximal, characteristic
6#21447023C218yesmaximal, direct product factor
7C2×#16839525C211yesmaximal, characteristic, complemented
8C22×C22⋊C8×C61C211yesmaximal, characteristic
9C23×Dic122C2211yescharacteristic
10C2×#14519756—24no—
11C2×#14519756—22no—
12C2×#14519756—24no—
13C2×#14519756C2214yes—
14C22×C4⋊Dic61C2211yescharacteristic
15C22×C4⋊Dic61C2211yescharacteristic
16C22×C4⋊Dic61C2211yescharacteristic
17C22×#11758196—21no—
18C22×C22⋊Dic61—21no—
19C22×C22⋊Dic61—21no—
20C2×#14519711—24no—
21C2×#14519711C2214yescomplemented
22C2×#14519702—24no—
23C2×#14519702—24no—
24C2×#14519702C2214yescomplemented
25C2×#14519702C2214yescomplemented
26#16839622—22no—
27#16839622C2214yes—
28C2×#14519684—21no—
29#16839525C2214yescomplemented
30C24×C4×C61C2211yescharacteristic
31C23×C8×C61C2211yescharacteristic
32C23×C8×C61C2211yescharacteristic
33C2×C22⋊C8×C61—24no—
34C2×C22⋊C8×C61C2214yes—
35C22×Dic122—22no—
36C22×Dic122—22no—
37C22×Dic122—22no—
38C22×Dic122—22no—
39C22×Dic122—21no—
40C22×Dic122—22no—
41C22×Dic122D414yes—
42C22×Dic122C2312yes—
43C23×Dic61—21no—
44C23×Dic61—21no—
45C23×Dic61—21no—
46C23×Dic61—21no—
47#14519756—216no—
48#14519756—28no—
49#14519756—28no—
50C2×C4⋊Dic61—21no—
51C2×C4⋊Dic61—22no—
52C2×C4⋊Dic61—22no—
53C2×C4⋊Dic61—22no—
54C2×C4⋊Dic61—22no—
55C2×C4⋊Dic61—22no—
56C2×C4⋊Dic61—21no—
57C2×C4⋊Dic61—21no—
58C2×C4⋊Dic61D414yes—
59C2×C4⋊Dic61C2312yes—
60C2×C4⋊Dic61C2312yes—
61C2×C4⋊Dic61C2312yes—
62C2×#11758196—28no—
63C2×#11758196—24no—
64C2×C22⋊Dic61—28no—
65C2×C22⋊Dic61—24no—
66C2×C22⋊Dic61—24no—
67C2×C22⋊Dic61—44no—
68#14519711—28no—
69#14519702—28no—
70#14519702—28no—
71#14519684—24no—
72C25×C61D411yescharacteristic
73C23×C4×C61—22no—
74C23×C4×C61—22no—
75C23×C4×C61—22no—
76C23×C4×C61—22no—
77C23×C4×C61—22no—
78C23×C4×C61—22no—
79C23×C4×C61D411yescharacteristic
80C23×C4×C61D412yes—
81C23×C4×C61C2312yes—
82C23×C4×C61C2311yescharacteristic
83C22×C8×C61—22no—
84C22×C8×C61—22no—
85C22×C8×C61—22no—
86C22×C8×C61—22no—
87C22×C8×C61—22no—
88C22×C8×C61D414yes—
89C22×C8×C61C2312yes—
90C22×C8×C61C2312yes—
91C22⋊C8×C61—28no—
92C24×C61—22no—
93C24×C61—22no—
94C24×C61—22no—
95C24×C61—22no—
96C24×C61—22no—
97C24×C61—22no—
98C24×C61Q1614yes—
99C24×C61C2×D412yes—
100C24×C61C2×D411yescharacteristic
101C22×C4×C61—22no—
102C22×C4×C61—22no—
103C22×C4×C61—22no—
104C22×C4×C61—24no—
105C22×C4×C61—24no—
106C22×C4×C61—24no—
107C22×C4×C61—22no—
108C22×C4×C61—22no—
109C22×C4×C61—22no—
110C22×C4×C61—22no—
111C22×C4×C61—22no—
112C22×C4×C61—22no—
113C22×C4×C61—44no—
114C22×C4×C61—44no—
115C22×C4×C61—44no—
116C22×C4×C61—44no—
117C22×C4×C61C2×D412yes—
118C22×C4×C61C2×D411yescharacteristic
119C22×C4×C61C2×D412yes—
120C22×C4×C61C2×D412yes—
121C22×C4×C61C2×D412yes—
122C22×C4×C61#4112yes—
123C22×C4×C61#4112yes—
124C22×C4×C61#4112yes—
125C22×C4×C61C2411yescharacteristic
126C22×Dic61—24no—
127C22×Dic61—24no—
128C22×Dic61—22no—
129C22×Dic61—22no—
130C22×Dic61—22no—
131C22×Dic61—22no—
132C22×Dic61—42no—
133C22×Dic61—42no—
134C22×Dic61—42no—
135C22×Dic61—42no—
136C22×Dic61—42no—
137C22×Dic61—42no—
138C22×Dic61—42no—
139C22×Dic61—42no—
140C22×Dic61—42no—
141C22×Dic61—42no—
142C2×Dic122—28no—
143C2×Dic122—28no—
144C2×Dic122—22no—
145C2×Dic122—22no—
146C2×Dic122—22no—
147C2×Dic122—22no—
148C2×Dic122—24no—
149C2×Dic122—22no—
150C2×Dic122—44no—
151C2×Dic122—42no—
152C2×Dic122—42no—
153C2×Dic122—44no—
154C2×Dic122C2×D414yes—
155C2×C8×C61—28no—
156C2×C8×C61—22no—
157C2×C8×C61—22no—
158C2×C8×C61—22no—
159C2×C8×C61—22no—
160C2×C8×C61—22no—
161C2×C8×C61—44no—
162C2×C8×C61C2×D414yes—
163C22⋊Dic61—216no—
164C22⋊Dic61—48no—
165C4⋊Dic61—24no—
166C4⋊Dic61—22no—
167C4⋊Dic61—22no—
168C4⋊Dic61—22no—
169C4⋊Dic61—22no—
170C4⋊Dic61—22no—
171C4⋊Dic61—42no—
172C4⋊Dic61—42no—
173C4⋊Dic61C2×D414yes—
174#11758196—216no—
175C23×C61—22no—
176C23×C61—22no—
177C23×C61—22no—
178C23×C61—22no—
179C23×C61—22no—
180C23×C61—22no—
181C23×C61—28no—
182C23×C61—28no—
183C23×C61—28no—
184C23×C61—44no—
185C23×C61—44no—
186C23×C61—44no—
187C23×C61—44no—
188C23×C61#12012yes—
189C23×C61#12112yes—
190C23×C61#12312yes—
191C23×C61C2×Q1614yes—
192C23×C61C2×Q1612yes—
193C23×C61#13512yes—
194C23×C61AGL(1,ℤ/8)12yes—
195C23×C61#13712yes—
196C23×C61C22×D411yescharacteristic
197C2×C4×C61—22no—
198C2×C4×C61—22no—
199C2×C4×C61—22no—
200C2×C4×C61—44no—
201C2×C4×C61—42no—
202C2×C4×C61—42no—
203C2×C4×C61—42no—
204C2×C4×C61—42no—
205C2×C4×C61—48no—
206C2×C4×C61#12012yes—
207C2×C4×C61#12114yes—
208C2×C4×C61#12114yes—
209C2×C4×C61#12112yes—
210C2×C4×C61#12314yes—
211C2×C4×C61#12312yes—
212C2×C4×C61#12414yes—
213C2×C4×C61C22×D411yescharacteristic
214C2×C4×C61C22×D411yescharacteristic
215C2×C4×C61C22×D411yescharacteristic
216C2×C4×C61C2×#4111yescharacteristic
217C2×C4×C61C2×#4111yescharacteristic
218C2×C4×C61C2×#4111yescharacteristic
219C2×Dic61—24no—
220C2×Dic61—24no—
221C2×Dic61—42no—
222C2×Dic61—42no—
223C2×Dic61—42no—
224C2×Dic61—42no—
225C2×Dic61—48no—
226C2×Dic61—48no—
227C2×Dic61—42no—
228C2×Dic61—42no—
229C2×Dic61—42no—
230C2×Dic61—42no—
231C2×Dic61—42no—
232C2×Dic61—42no—
233C2×Dic61—84no—
234C2×Dic61—84no—
235Dic122—24no—
236Dic122—24no—
237Dic122—42no—
238Dic122—42no—
239Dic122—48no—
240C8×C61—24no—
241C8×C61—42no—
242C2×#2036—611nomaximal, Sylow
243C22×C61—24no—
244C22×C61—24no—
245C22×C61—24no—
246C22×C61—42no—
247C22×C61—42no—
248C22×C61—42no—
249C22×C61—42no—
250C22×C61—416no—
251C22×C61#39414yes—
252C22×C61#44914yes—
253C22×C61#45114yes—
254C22×C61#46714yes—
255C22×C61#46814yes—
256C22×C61#48414yes—
257C22×C61#48514yes—
258C22×C61C2×#12011yescharacteristic
259C22×C61C2×#12111yescharacteristic
260C22×C61C2×#12311yescharacteristic
261C22×C61C22×Q1611yescharacteristic
262C22×C61C2×#13511yescharacteristic
263C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
264C22×C61C2×#13711yescharacteristic
265C4×C61—42no—
266C4×C61#39414yes—
267C4×C61C2×#12111yescharacteristic
268C4×C61C2×#12111yescharacteristic
269C4×C61C2×#12311yescharacteristic
270C4×C61C2×#12411yescharacteristic
271Dic61—44no—
272Dic61—44no—
273Dic61—82no—
274Dic61—82no—
275C22×C22⋊Q8—611no—
276C22×#107—611no—
277C22×#103—611no—
278C22×#103—611no—
279C22×C22⋊C8D6111yescharacteristic
280C2×#380—611no—
281#2036—618no—
282C2×#340—611no—
283C2×C61—44no—
284C2×C61#203618yescomplemented
285C2×C61C2×#39411yescharacteristic
286C2×C61C2×#45111yescharacteristic
287C2×C61C2×#44911yescharacteristic
288C2×C61C2×#46711yescharacteristic
289C2×C61C2×#46811yescharacteristic
290C2×C61C2×#48511yescharacteristic
291C2×C61C2×#48411yescharacteristic
292C23×Q8—611no—
293C24×C4C2×D6111yescharacteristic
294C23×C8C2×D6111yescharacteristic
295C23×C8C2×D6111yescharacteristic
296C2×C22⋊Q8—614no—
297C2×C22⋊Q8—1224no—
298C2×C22⋊Q8—1224no—
299C2×C22⋊Q8—1222no—
300C22×C4⋊C4—611no—
301C22×C4⋊C4—611no—
302C22×C4⋊C4—611no—
303C22×C4⋊C4—1221no—
304C22×C22⋊C4—1221no—
305C22×C22⋊C4—1221no—
306C2×#107—614no—
307C2×#107—1224no—
308C2×#103—614no—
309C2×#103—614no—
310C2×#103—1224no—
311C2×#103—1224no—
312C2×C22⋊C8—24no—
313C2×C22⋊C8C2×D6114yes—
314#380—614no—
315#380—1222no—
316C2×#95—1221no—
317#340—614no—
318C61C2×#203611yescharacteristic, complemented, Sylow
319C25D24411yescharacteristic
320C22×Q8—614no—
321C22×Q8—612no—
322C22×Q8—1221no—
323C22×Q8—1222no—
324C22×Q8—1222no—
325C22×Q8—1222no—
326C22×Q8—1222no—
327C22×Q8—1222no—
328C23×C4—22no—
329C23×C4—22no—
330C23×C4—22no—
331C23×C4—22no—
332C23×C4—22no—
333C23×C4—22no—
334C23×C4—1221no—
335C23×C4—1221no—
336C23×C4—1221no—
337C23×C4—1221no—
338C23×C4D24412yes—
339C23×C4D24411yescharacteristic
340C23×C4C22×D6112yes—
341C23×C4C22×D6111yescharacteristic
342C22×C8—22no—
343C22×C8—22no—
344C22×C8—22no—
345C22×C8—22no—
346C22×C8—22no—
347C22×C8C22⋊D6114yes—
348C22×C8C22×D6112yes—
349C22×C8C22×D6112yes—
350C22⋊Q8—1228no—
351C22⋊Q8—1228no—
352C22⋊Q8—12216no—
353C2×C4⋊C4—614no—
354C2×C4⋊C4—612no—
355C2×C4⋊C4—612no—
356C2×C4⋊C4—612no—
357C2×C4⋊C4—1228no—
358C2×C4⋊C4—1221no—
359C2×C4⋊C4—1224no—
360C2×C4⋊C4—1222no—
361C2×C4⋊C4—1222no—
362C2×C4⋊C4—1222no—
363C2×C4⋊C4—1222no—
364C2×C4⋊C4—1222no—
365C2×C4⋊C4—1221no—
366C2×C4⋊C4—1221no—
367C2×C22⋊C4—1228no—
368C2×C22⋊C4—1224no—
369C2×C22⋊C4—1224no—
370C2×C22⋊C4—2444no—
371#107—1228no—
372#103—1228no—
373#103—1228no—
374C22⋊C8—28no—
375#95—1224no—
376C24—22no—
377C24—22no—
378C24—22no—
379C24—22no—
380C24—22no—
381C24—22no—
382C24Dic24414yes—
383C24C2×D24412yes—
384C24C2×D24411yescharacteristic
385C2×Q8—614no—
386C2×Q8—1222no—
387C2×Q8—1224no—
388C2×Q8—1222no—
389C2×Q8—1222no—
390C2×Q8—1222no—
391C2×Q8—1222no—
392C2×Q8—1228no—
393C2×Q8—1228no—
394C2×Q8—2444no—
395C2×Q8—2442no—
396C2×Q8—2442no—
397C2×Q8—2444no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—24no—
408C22×C4—24no—
409C22×C4—24no—
410C22×C4—44no—
411C22×C4—44no—
412C22×C4—44no—
413C22×C4—44no—
414C22×C4—1222no—
415C22×C4—1222no—
416C22×C4—1224no—
417C22×C4—1224no—
418C22×C4—1222no—
419C22×C4—1222no—
420C22×C4—2442no—
421C22×C4—2442no—
422C22×C4—2442no—
423C22×C4—2442no—
424C22×C4—2442no—
425C22×C4—2442no—
426C22×C4—2442no—
427C22×C4—2442no—
428C22×C4—2442no—
429C22×C4—2442no—
430C22×C4C2×D24412yes—
431C22×C4C2×D24411yescharacteristic
432C22×C4#1175822212yes—
433C22×C4D4×D6112yes—
434C22×C4D4×D6112yes—
435C22×C4#1175822412yes—
436C22×C4#1175822412yes—
437C22×C4C2×C22⋊D6112yes—
438C22×C4C23×D6111yescharacteristic
439C2×C8—22no—
440C2×C8—22no—
441C2×C8—28no—
442C2×C8—22no—
443C2×C8—22no—
444C2×C8—22no—
445C2×C8—44no—
446C2×C8C2×C22⋊D6114yes—
447C4⋊C4—614no—
448C4⋊C4—12216no—
449C4⋊C4—1222no—
450C4⋊C4—1224no—
451C4⋊C4—1222no—
452C4⋊C4—1222no—
453C4⋊C4—1222no—
454C4⋊C4—1222no—
455C4⋊C4—2442no—
456C4⋊C4—2442no—
457C22⋊C4—12216no—
458C22⋊C4—2448no—
459C23—22no—
460C23—22no—
461C23—28no—
462C23—22no—
463C23—22no—
464C23—22no—
465C23—22no—
466C23—28no—
467C23—28no—
468C23—44no—
469C23—44no—
470C23—44no—
471C23—44no—
472C23#1451974712yes—
473C23#1451975112yes—
474C23#1451976112yes—
475C23C2×Dic24414yes—
476C23C2×Dic24412yes—
477C23#1451979912yes—
478C23#1451980512yes—
479C23#1451981012yes—
480C23C22×D24411yescharacteristic
481Q8—1224no—
482Q8—1224no—
483Q8—2442no—
484Q8—2442no—
485Q8—2448no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—44no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—48no—
495C2×C4—1224no—
496C2×C4—1224no—
497C2×C4—4884no—
498C2×C4—4884no—
499C2×C4—2442no—
500C2×C4—2442no—
501C2×C4—2442no—
502C2×C4—2442no—
503C2×C4—2442no—
504C2×C4—2442no—
505C2×C4—2442no—
506C2×C4—2442no—
507C2×C4—2442no—
508C2×C4—2442no—
509C2×C4—2448no—
510C2×C4—2448no—
511C2×C4#1451974712yes—
512C2×C4#1451974814yes—
513C2×C4#1451974914yes—
514C2×C4#1451975112yes—
515C2×C4#1451975914yes—
516C2×C4#1451976112yes—
517C2×C4#1451976314yes—
518C2×C4C2×D4×D6111yescharacteristic
519C2×C4C2×D4×D6111yescharacteristic
520C2×C4C22×C22⋊D6111yescharacteristic
521C2×C4C2×#1175822411yescharacteristic
522C2×C4C2×#1175822411yescharacteristic
523C2×C4C2×#1175822211yescharacteristic
524C8—24no—
525C8—42no—
526C22—24no—
527C22—24no—
528C22—24no—
529C22—42no—
530C22—42no—
531C22—42no—
532C22—416no—
533C22—42no—
534C22#1683967814yes—
535C22#1683990914yes—
536C22#1683992014yes—
537C22#1684000314yes—
538C22#1684000814yes—
539C22#1684009814yes—
540C22#1684010414yes—
541C22C2×#1451974711yescharacteristic
542C22C2×#1451975111yescharacteristic
543C22C2×#1451976111yescharacteristic
544C22C22×Dic24411yescharacteristic
545C22C2×#1451979911yescharacteristic
546C22C2×#1451980511yescharacteristic
547C22C2×#1451981011yescharacteristic
548C4—42no—
549C4—4882no—
550C4—4882no—
551C4—2444no—
552C4—2444no—
553C4#1683967814yes—
554C4C2×#1451974811yescharacteristic
555C4C2×#1451974911yescharacteristic
556C4C2×#1451975911yescharacteristic
557C4C2×#1451976311yescharacteristic
558C2—44no—
559C2#2144702318yesdirect product factor
560C2C2×#1683967811yescharacteristic
561C2C2×#1683992011yescharacteristic
562C2C2×#1683990911yescharacteristic
563C2C2×#1684000311yescharacteristic
564C2C2×#1684000811yescharacteristic
565C2C2×#1684010411yescharacteristic
566C2C2×#1684009811yescharacteristic
subgroupG/H
centerC24C2×D244
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC22×C22⋊C8×C61C2
socleC24×C61C2×D4
prime radicalC25×C61D4
hypercenterC22×C22⋊C8D61
hypocenterC61C2×#2036
LCSG ▷ C22×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
2. C22×#14519711C2semidirect
3. C22×#14519702C2semidirect
4. C22×#14519702C2semidirect
6. #21447023C2direct (N × H)
7. C2×#16839525C2semidirect
21. C2×#14519711C22semidirect
24. C2×#14519702C22semidirect
25. C2×#14519702C22semidirect
29. #16839525C22semidirect
284. C2×C61#2036semidirect
318. C61C2×#2036semidirect
559. C2#21447023direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197562
C22×#145197112
C22×#145197022
C2×#168396222
#214470232
C2×#168395252
C22×C22⋊C8×C612
C2×#203661