Finite Group Databasebeta

← C2×#21446275 #29681798

Subgroups — C2×#21446275 #29681798

Order 15616.

2066 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519760C211yesmaximal, characteristic
2C22×#14519736C211yesmaximal, characteristic, complemented
3C22×#14519691C212yesmaximal
4#21446275C218yesmaximal, direct product factor
5C2×#16839528C212yesmaximal, complemented
6C2×C61×#381C211yesmaximal, characteristic, complemented
7C23×C22⋊D61C2211yescharacteristic
8C2×#14519760—21no—
9C2×#14519760—21no—
10C2×#14519760—22no—
11C2×#14519760—22no—
12C2×#14519760—22no—
13C2×#14519760C414yescomplemented
14C2×#14519760C2214yes—
15C2×#14519736—28no—
16C2×#14519736—22no—
17C2×#14519736C2214yescomplemented
18C22×C4⋊Dic61—21no—
19C22×#11758196C412yescomplemented
20C22×C22⋊Dic61C2212yes—
21C22×C22⋊Dic61C2211yescharacteristic
22C22×#11758198C412yescomplemented
23C22×C4×Dic61—21no—
24C2×#14519691—28no—
25C2×#14519691C2218yes—
26#16839528C2218yescomplemented
27C24×C4×C61C2211yescharacteristic
28C22×C22⋊C4×C61C2212yes—
29C61×#381—22no—
30C61×#381C2214yescomplemented
31C2×#95×C61—22no—
32C24×D61C2×C411yescharacteristic
33C22×C22⋊D61—24no—
34C22×C22⋊D61—21no—
35C22×C22⋊D61—21no—
36C22×C22⋊D61—21no—
37C22×C22⋊D61—21no—
38C22×C22⋊D61—24no—
39C22×C22⋊D61C2×C412yes—
40C22×C22⋊D61C2312yes—
41C23×Dic61—22no—
42C23×Dic61C2×C411yescharacteristic
43C23×Dic61C2×C412yes—
44#14519760—24no—
45#14519760—24no—
46#14519760—28no—
47#14519760—24no—
48#14519760—24no—
49#14519760—28no—
50#14519736—216no—
51#14519736—216no—
52C2×C4⋊Dic61—28no—
53C2×C4⋊Dic61—24no—
54C2×#11758196—24no—
55C2×#11758196—22no—
56C2×#11758196—22no—
57C2×#11758196C2×C418yescomplemented
58C2×C22⋊Dic61—22no—
59C2×C22⋊Dic61—24no—
60C2×C22⋊Dic61—21no—
61C2×C22⋊Dic61—21no—
62C2×C22⋊Dic61—21no—
63C2×C22⋊Dic61—21no—
64C2×C22⋊Dic61C2×C412yes—
65C2×C22⋊Dic61D418yes—
66C2×C22⋊Dic61C2312yes—
67C2×C22⋊Dic61C2314yes—
68C2×#11758198—24no—
69C2×#11758198—22no—
70C2×#11758198—22no—
71C2×#11758198C2×C418yescomplemented
72C2×C4×Dic61—28no—
73C2×C4×Dic61—24no—
74#14519691—216no—
75C25×C61C2311yescharacteristic
76C23×C4×C61—24no—
77C23×C4×C61—24no—
78C23×C4×C61—22no—
79C23×C4×C61C2×C412yes—
80C23×C4×C61C2×C412yes—
81C23×C4×C61D411yescharacteristic
82C23×C4×C61D411yescharacteristic
83C23×C4×C61D412yes—
84C23×C4×C61D412yes—
85C23×C4×C61D412yes—
86C23×C4×C61C2312yes—
87C2×C22⋊C4×C61—24no—
88C2×C22⋊C4×C61—24no—
89C2×C22⋊C4×C61—22no—
90C2×C22⋊C4×C61C2314yes—
91#95×C61—28no—
92C24×C61—44no—
93C24×C61C22×C411yescharacteristic
94C24×C61C22×C411yescharacteristic
95C24×C61C2×D411yescharacteristic
96C24×C61C2×D411yescharacteristic
97C24×C61C2×D411yescharacteristic
98C24×C61C2×D411yescharacteristic
99C24×C61C2×D414yes—
100C24×C61#4114yes—
101C24×C61C2411yescharacteristic
102C23×D61—21no—
103C23×D61—21no—
104C23×D61—24no—
105C23×D61—44no—
106C23×D61C22×C412yes—
107C22×C4×C61—28no—
108C22×C4×C61—28no—
109C22×C4×C61—22no—
110C22×C4×C61—22no—
111C22×C4×C61—24no—
112C22×C4×C61—28no—
113C22×C4×C61—28no—
114C22×C4×C61—22no—
115C22×C4×C61—22no—
116C22×C4×C61—24no—
117C22×C4×C61—24no—
118C22×C4×C61—24no—
119C22×C4×C61—24no—
120C22×C4×C61—48no—
121C22×C4×C61—44no—
122C22×C4×C61C22⋊C414yes—
123C22×C4×C61C22⋊C412yes—
124C22×C4×C61C22⋊C412yes—
125C22×C4×C61C22⋊C412yes—
126C22×C4×C61C22⋊C412yes—
127C22×C4×C61C22⋊C414yes—
128C22×C4×C61C22×C414yes—
129C22×C4×C61C2×D412yes—
130C22×C4×C61C2×D412yes—
131C22×C4×C61C2×D414yes—
132C2×C22⋊D61—22no—
133C2×C22⋊D61—22no—
134C2×C22⋊D61—28no—
135C2×C22⋊D61—24no—
136C2×C22⋊D61—22no—
137C2×C22⋊D61—22no—
138C2×C22⋊D61—24no—
139C2×C22⋊D61—42no—
140C2×C22⋊D61—42no—
141C2×C22⋊D61—44no—
142C2×C22⋊D61—44no—
143C2×C22⋊D61—42no—
144C2×C22⋊D61—42no—
145C22×Dic61—21no—
146C22×Dic61—21no—
147C22×Dic61—22no—
148C22×Dic61—22no—
149C22×Dic61—24no—
150C22×Dic61—28no—
151C22×Dic61—24no—
152C22×Dic61—48no—
153C22×Dic61—44no—
154C22×Dic61C22×C412yes—
155C22×Dic61C22×C414yes—
156C22⋊C4×C61—24no—
157C22⋊C4×C61—24no—
158C22⋊C4×C61—44no—
159C22⋊Dic61—22no—
160C22⋊Dic61—22no—
161C22⋊Dic61—28no—
162C22⋊Dic61—24no—
163C22⋊Dic61—22no—
164C22⋊Dic61—22no—
165C22⋊Dic61C2×D418yes—
166#11758198—28no—
167#11758198—28no—
168C4⋊Dic61—216no—
169#11758196—28no—
170#11758196—28no—
171C4×Dic61—216no—
172C23×C61—24no—
173C23×C61—24no—
174C23×C61—24no—
175C23×C61—42no—
176C23×C61—42no—
177C23×C61—42no—
178C23×C61—48no—
179C23×C61—48no—
180C23×C61—42no—
181C23×C61C2×C22⋊C411yescharacteristic
182C23×C61C2×C22⋊C411yescharacteristic
183C23×C61C2×C22⋊C411yescharacteristic
184C23×C61C2×C22⋊C411yescharacteristic
185C23×C61C4×D414yes—
186C23×C61C4×D414yes—
187C23×C61#12012yes—
188C23×C61#12012yes—
189C23×C61#12114yes—
190C23×C61#12114yes—
191C23×C61#12312yes—
192C23×C61#12312yes—
193C23×C61C23×C411yescharacteristic
194C23×C61C22×D411yescharacteristic
195C23×C61C22×D411yescharacteristic
196C23×C61C22×D412yes—
197C23×C61C2×#4112yes—
198C22×D61—22no—
199C22×D61—24no—
200C22×D61—44no—
201C22×D61—42no—
202C22×D61—42no—
203C22×D61—44no—
204C22×D61—44no—
205C22×D61—88no—
206C2×C4×C61—28no—
207C2×C4×C61—22no—
208C2×C4×C61—22no—
209C2×C4×C61—28no—
210C2×C4×C61—22no—
211C2×C4×C61—22no—
212C2×C4×C61—28no—
213C2×C4×C61—24no—
214C2×C4×C61—24no—
215C2×C4×C61—28no—
216C2×C4×C61—24no—
217C2×C4×C61—24no—
218C2×C4×C61—48no—
219C2×C4×C61—44no—
220C2×C4×C61—88no—
221C2×C4×C61C2×C22⋊C414yes—
222C2×C4×C61C2×C22⋊C414yes—
223C22⋊D61—42no—
224C22⋊D61—44no—
225C22⋊D61—42no—
226C22⋊D61—44no—
227C22⋊D61—44no—
228C2×Dic61—22no—
229C2×Dic61—24no—
230C2×Dic61—24no—
231C2×Dic61—28no—
232C2×Dic61—48no—
233C2×Dic61—416no—
234C2×Dic61—44no—
235C2×Dic61—42no—
236C2×Dic61—42no—
237C2×Dic61—44no—
238C2×Dic61—44no—
239C2×#1899—611nomaximal, Sylow
240C22×C61—22no—
241C22×C61—22no—
242C22×C61—22no—
243C22×C61—22no—
244C22×C61—22no—
245C22×C61—22no—
246C22×C61—24no—
247C22×C61—28no—
248C22×C61—28no—
249C22×C61—24no—
250C22×C61—44no—
251C22×C61—42no—
252C22×C61—44no—
253C22×C61—42no—
254C22×C61—42no—
255C22×C61—42no—
256C22×C61#38612yes—
257C22×C61#38612yes—
258C22×C61#38612yes—
259C22×C61#38612yes—
260C22×C61#41014yes—
261C22×C61C22×C22⋊C411yescharacteristic
262C22×C61C2×C4×D412yes—
263C22×C61C2×#12011yescharacteristic
264C22×C61C2×#12112yes—
265C22×C61C2×#12311yescharacteristic
266C2×D61—44no—
267C2×D61—42no—
268C2×D61—84no—
269C2×D61—84no—
270C2×D61—84no—
271C4×C61—24no—
272C4×C61—24no—
273C4×C61—84no—
274Dic61—48no—
275Dic61—44no—
276Dic61—42no—
277C22×#123—611no—
278C22×#117—611no—
279C22×#99—612no—
280C2×#381D6111yescharacteristic, complemented
281#1899—618no—
282C2×#342—612no—
283C2×C61—21no—
284C2×C61—22no—
285C2×C61—22no—
286C2×C61—22no—
287C2×C61—21no—
288C2×C61—22no—
289C2×C61—22no—
290C2×C61#189914yescomplemented
291C2×C61C2×#38611yescharacteristic
292C2×C61C2×#41012yes—
293D61—82no—
294C23×D4—611no—
295C24×C4C2×D6111yescharacteristic
296C2×#123—614no—
297C2×#123—614no—
298C2×#123—1221no—
299C2×#123—1222no—
300C2×#123—1221no—
301C2×#123—1222no—
302C2×#123—1222no—
303C2×#117—614no—
304C2×#117—1228no—
305C2×#117—1222no—
306C22×C4⋊C4—612no—
307C22×C4⋊C4—1221no—
308C22×C22⋊C4—612no—
309C22×C22⋊C4—611no—
310C22×C22⋊C4—612no—
311C22×C22⋊C4C2×D6112yes—
312C22×C42—1221no—
313C2×#99—618no—
314C2×#99—1228no—
315#381—22no—
316#381C2×D6114yescomplemented
317C2×#95—22no—
318#342—618no—
319C61C2×#189911yescharacteristic, complemented, Sylow
320C25—611no—
321C25C22×D6111yescharacteristic
322C22×D4—612no—
323C22×D4—612no—
324C22×D4—1221no—
325C22×D4—1221no—
326C22×D4—1224no—
327C22×D4—1224no—
328C22×D4—1221no—
329C22×D4—1221no—
330C23×C4—24no—
331C23×C4—24no—
332C23×C4—22no—
333C23×C4—611no—
334C23×C4—612no—
335C23×C4—1222no—
336C23×C4C4×D6112yes—
337C23×C4C4×D6112yes—
338C23×C4D24411yescharacteristic
339C23×C4D24412yes—
340C23×C4D24411yescharacteristic
341C23×C4C22⋊D6112yes—
342C23×C4C22⋊D6112yes—
343C23×C4C22×D6112yes—
344#123—1224no—
345#123—1228no—
346#123—1224no—
347#123—1224no—
348#123—1224no—
349#123—1228no—
350#117—12216no—
351#117—12216no—
352C2×C4⋊C4—618no—
353C2×C4⋊C4—1228no—
354C2×C4⋊C4—1224no—
355C2×C4⋊C4—1222no—
356C2×C4⋊C4—1222no—
357C2×C4⋊C4—1224no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—618no—
362C2×C22⋊C4—614no—
363C2×C22⋊C4—612no—
364C2×C22⋊C4—612no—
365C2×C22⋊C4—618no—
366C2×C22⋊C4—1222no—
367C2×C22⋊C4—1221no—
368C2×C22⋊C4—1221no—
369C2×C22⋊C4—1224no—
370C2×C22⋊C4—1221no—
371C2×C22⋊C4—1221no—
372C2×C22⋊C4—1224no—
373C2×C22⋊C4—1222no—
374C2×C22⋊C4—1222no—
375C2×C22⋊C4C22×D6114yes—
376C2×C42—1228no—
377C2×C42—1224no—
378#99—12216no—
379#95—28no—
380C24—44no—
381C24—612no—
382C24—1224no—
383C24—1221no—
384C24—1221no—
385C24—2444no—
386C24C2×C4×D6111yescharacteristic
387C24C2×C4×D6111yescharacteristic
388C24C2×D24411yescharacteristic
389C24C2×D24411yescharacteristic
390C24D4×D6114yes—
391C24#1175822414yes—
392C24C2×C22⋊D6111yescharacteristic
393C24C2×C22⋊D6111yescharacteristic
394C24C23×D6111yescharacteristic
395C2×D4—1224no—
396C2×D4—1222no—
397C2×D4—1222no—
398C2×D4—1224no—
399C2×D4—1222no—
400C2×D4—1222no—
401C2×D4—1228no—
402C2×D4—2442no—
403C2×D4—2442no—
404C2×D4—2444no—
405C2×D4—2444no—
406C2×D4—2442no—
407C2×D4—2442no—
408C22×C4—24no—
409C22×C4—24no—
410C22×C4—28no—
411C22×C4—28no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—24no—
415C22×C4—28no—
416C22×C4—28no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—24no—
420C22×C4—24no—
421C22×C4—48no—
422C22×C4—44no—
423C22×C4—612no—
424C22×C4—614no—
425C22×C4—1224no—
426C22×C4—1222no—
427C22×C4—1221no—
428C22×C4—1222no—
429C22×C4—1221no—
430C22×C4—1224no—
431C22×C4—1228no—
432C22×C4—2448no—
433C22×C4—2444no—
434C22×C4#1175819814yes—
435C22×C4#1175819812yes—
436C22×C4#1175819814yes—
437C22×C4#1175819812yes—
438C22×C4#1175819812yes—
439C22×C4#1175819812yes—
440C22×C4C2×C4×D6114yes—
441C22×C4C2×D24412yes—
442C22×C4C2×D24412yes—
443C22×C4C2×C22⋊D6114yes—
444C4⋊C4—12216no—
445C4⋊C4—1228no—
446C4⋊C4—1228no—
447C22⋊C4—24no—
448C22⋊C4—24no—
449C22⋊C4—44no—
450C22⋊C4—618no—
451C22⋊C4—1224no—
452C22⋊C4—1222no—
453C22⋊C4—1222no—
454C22⋊C4—1222no—
455C22⋊C4—1222no—
456C22⋊C4—1228no—
457C22⋊C4—1228no—
458C22⋊C4—1228no—
459C42—12216no—
460C23—24no—
461C23—24no—
462C23—24no—
463C23—42no—
464C23—42no—
465C23—48no—
466C23—48no—
467C23—42no—
468C23—42no—
469C23—1224no—
470C23—1222no—
471C23—4888no—
472C23—2444no—
473C23—2444no—
474C23—2444no—
475C23—2442no—
476C23—2442no—
477C23C2×#1175819811yescharacteristic
478C23C2×#1175819811yescharacteristic
479C23C2×#1175819811yescharacteristic
480C23C2×#1175819811yescharacteristic
481C23#1451973714yes—
482C23#1451973714yes—
483C23#1451974712yes—
484C23#1451974712yes—
485C23#1451974914yes—
486C23#1451974914yes—
487C23#1451976112yes—
488C23#1451976112yes—
489C23C22×C4×D6111yescharacteristic
490C23C2×D4×D6112yes—
491C23C22×C22⋊D6111yescharacteristic
492C23C22×D24411yescharacteristic
493C23C2×#1175822412yes—
494D4—2442no—
495D4—2444no—
496D4—2442no—
497D4—2444no—
498D4—2444no—
499C2×C4—28no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—28no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—28no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—28no—
509C2×C4—24no—
510C2×C4—24no—
511C2×C4—48no—
512C2×C4—44no—
513C2×C4—88no—
514C2×C4—1224no—
515C2×C4—1222no—
516C2×C4—1224no—
517C2×C4—1228no—
518C2×C4—24416no—
519C2×C4—2448no—
520C2×C4—2444no—
521C2×C4—2444no—
522C2×C4—2442no—
523C2×C4—2442no—
524C2×C4—2444no—
525C2×C4C2×#1175819814yes—
526C2×C4C2×#1175819814yes—
527C22—28no—
528C22—24no—
529C22—28no—
530C22—24no—
531C22—22no—
532C22—22no—
533C22—22no—
534C22—22no—
535C22—22no—
536C22—22no—
537C22—42no—
538C22—42no—
539C22—44no—
540C22—42no—
541C22—44no—
542C22—42no—
543C22—4884no—
544C22—4884no—
545C22—4884no—
546C22—2442no—
547C22—2444no—
548C22#1683963912yes—
549C22#1683963912yes—
550C22#1683963912yes—
551C22#1683963912yes—
552C22#1683973514yes—
553C22C22×#1175819811yescharacteristic
554C22C2×#1451973712yes—
555C22C2×#1451974711yescharacteristic
556C22C2×#1451974912yes—
557C22C2×#1451976111yescharacteristic
558C4—24no—
559C4—24no—
560C4—84no—
561C4—2448no—
562C4—2442no—
563C4—2444no—
564C2—22no—
565C2—21no—
566C2—22no—
567C2—22no—
568C2—21no—
569C2—22no—
570C2—22no—
571C2—4882no—
572C2#2144627514yesdirect product factor
573C2C2×#1683963911yescharacteristic
574C2C2×#1683973512yes—
subgroupG/H
centerC23C2×#11758198
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC2×C61×#381C2
socleC23×C61C2×C22⋊C4
prime radicalC23×C22⋊D61C22
cosocleC24×C61C24
hypercenterC2×#381D61
hypocenterC61C2×#1899
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#381

Complements

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

NH ≅ G/Ntype
2. C22×#14519736C2semidirect
4. #21446275C2direct (N × H)
5. C2×#16839528C2semidirect
6. C2×C61×#381C2semidirect
13. C2×#14519760C4semidirect
17. C2×#14519736C22semidirect
19. C22×#11758196C4semidirect
22. C22×#11758198C4semidirect
26. #16839528C22semidirect
30. C61×#381C22semidirect
57. C2×#11758196C2×C4semidirect
71. C2×#11758198C2×C4semidirect
280. C2×#381D61semidirect
290. C2×C61#1899semidirect
316. #381C2×D61semidirect
319. C61C2×#1899semidirect
572. C2#21446275direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197602
C22×#145197362
C22×#145196912
#214462752
C2×#168395282
C2×C61×#3812
C2×#189961