Finite Group Databasebeta

← C2×#21447459 #29832733

Subgroups — C2×#21447459 #29832733

Order 15616.

1398 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840270C211yesmaximal, characteristic
2C2×#16839743C211yesmaximal, characteristic, complemented
3C2×#16839734C211yesmaximal, characteristic, complemented
4#21447459C218yesmaximal, direct product factor
5C2×#16839552C211yesmaximal, characteristic, complemented
6C2×#16839550C211yesmaximal, characteristic, complemented
7C2×#16839548C211yesmaximal, characteristic, complemented
8C2×C61×#352C211yesmaximal, characteristic, complemented
9C22×#11758224C2211yescharacteristic
10C23×C4×D61C411yescharacteristic, complemented
11C2×M16×D61—21no—
12#16840270—22no—
13#16840270—22no—
14#16840270C414yescomplemented
15#16840270C2214yes—
16C2×#14519760C411yescharacteristic, complemented
17C2×#14519755—21no—
18C2×#14519750—21no—
19C2×#14519747C411yescharacteristic, complemented
20C2×#14519745C2211yescharacteristic
21C2×#14519739—21no—
22C2×#14519737—21no—
23C2×#14519733—21no—
24C2×#14519733C411yescharacteristic, complemented
25#16839743—22no—
26#16839743C2214yescomplemented
27C2×#14519695—21no—
28C2×#14519694C2211yescharacteristic
29#16839734—22no—
30#16839734C2214yescomplemented
31C2×#14519692C2211yescharacteristic
32C2×#14519691—21no—
33#16839552C2214yescomplemented
34#16839550C2214yescomplemented
35#16839548C2214yescomplemented
36C2×#123×C61C2211yescharacteristic
37C2×#100×C61C2211yescharacteristic
38C2×#99×C61C2211yescharacteristic
39C61×#352C2214yescomplemented
40C24×D61C2×C411yescharacteristic
41C2×#11758224—41no—
42C2×#11758224—42no—
43C2×#11758224—41no—
44C2×#11758224C2×C412yes—
45C2×#11758224D412yes—
46C2×#11758224D412yes—
47C2×#11758224C2312yes—
48C22×Dic122D411yescharacteristic
49C22×D244—21no—
50C22×C22⋊D61—21no—
51C22×C22⋊D61C2×C411yescharacteristic
52C22×C22⋊D61D411yescharacteristic
53C23×Dic61C2×C411yescharacteristic
54C23×Dic61D411yescharacteristic
55C22×C4×D61—21no—
56C22×C4×D61—21no—
57C22×C4×D61—22no—
58C22×C4×D61—42no—
59C22×C4×D61—41no—
60C22×C4×D61—41no—
61C22×C4×D61C2×C414yescomplemented
62C22×C4×D61D411yescharacteristic
63C2×#11758194—21no—
64C2×#11758189—41no—
65M16×D61—24no—
66M16×D61—42no—
67C2×C8×D61—41no—
68#14519760—22no—
69#14519760C2×C414yescomplemented
70#14519755—24no—
71#14519755—24no—
72#14519750—24no—
73#14519750—24no—
74#14519747—22no—
75#14519747C2×C414yescomplemented
76#14519745—21no—
77#14519745—21no—
78#14519745C2×C412yes—
79#14519745C2312yes—
80#14519739—24no—
81#14519739—24no—
82#14519737—24no—
83#14519737—24no—
84#14519733—22no—
85#14519733—24no—
86#14519733—42no—
87#14519733C2×C414yescomplemented
88C2×#11758196—21no—
89C2×#11758196—21no—
90C2×#11758196—41no—
91C2×C22⋊Dic61—21no—
92C2×C22⋊Dic61C2×C411yescharacteristic
93C2×#11758198—21no—
94C2×#11758198—21no—
95C2×#11758198—21no—
96C2×C4×Dic61—21no—
97C2×C4×Dic61—41no—
98#14519695—24no—
99#14519694—21no—
100#14519694C2312yes—
101#14519692—21no—
102#14519692C2312yes—
103#14519691—24no—
104C22×D4×C61C2311yescharacteristic
105C23×C4×C61C2×C411yescharacteristic
106C2×M16×C61—21no—
107#123×C61—21no—
108#123×C61—21no—
109#123×C61C2×C412yes—
110#123×C61C2312yes—
111C2×C4⋊C4×C61—21no—
112C2×C22⋊C4×C61—21no—
113C2×C22⋊C4×C61—21no—
114C2×C22⋊C4×C61C2×C411yescharacteristic
115#100×C61—21no—
116#100×C61C2312yes—
117#99×C61—21no—
118#99×C61C2312yes—
119C24×C61C22×C411yescharacteristic
120C24×C61C2×D411yescharacteristic
121C23×D61—21no—
122C23×D61—21no—
123C23×D61—44no—
124C23×D61—41no—
125C23×D61—41no—
126C23×D61C22⋊C411yescharacteristic
127C23×D61C22×C412yes—
128C2×D4×C61—41no—
129C2×D4×C61—41no—
130C2×D4×C61C22×C411yescharacteristic
131C2×D4×C61C2×D411yescharacteristic
132C2×D4×C61C2×D411yescharacteristic
133C2×D4×C61C2411yescharacteristic
134C22×C4×C61—21no—
135C22×C4×C61—21no—
136C22×C4×C61—21no—
137C22×C4×C61—41no—
138C22×C4×C61—41no—
139C22×C4×C61—41no—
140C22×C4×C61C22×C412yes—
141C22×C4×C61C2×D411yescharacteristic
142C2×C22⋊D61—22no—
143C2×C22⋊D61—22no—
144C2×C22⋊D61—41no—
145C2×C22⋊D61—41no—
146C2×C22⋊D61—41no—
147C2×C22⋊D61—41no—
148C2×C22⋊D61—44no—
149C2×C22⋊D61C22⋊C412yes—
150C2×C22⋊D61C22⋊C412yes—
151C2×C22⋊D61C22×C412yes—
152C2×C22⋊D61C2×D412yes—
153C22×Dic61—22no—
154C22×Dic61—21no—
155C22×Dic61—21no—
156C22×Dic61—21no—
157C22×Dic61—21no—
158C22×Dic61—22no—
159C22×Dic61—21no—
160C22×Dic61—41no—
161C22×Dic61C22⋊C411yescharacteristic
162C22×Dic61C22⋊C412yes—
163C22×Dic61C22⋊C411yescharacteristic
164C22×Dic61C22⋊C412yes—
165C22×Dic61C22⋊C411yescharacteristic
166C22×Dic61C22×C412yes—
167C22×Dic61C2×D412yes—
168#11758224—42no—
169#11758224—42no—
170#11758224—42no—
171#11758224—42no—
172#11758224—42no—
173#11758224—42no—
174#11758224—42no—
175#11758224—42no—
176C2×D244—24no—
177C2×D244—44no—
178C2×C4×D61—21no—
179C2×C4×D61—22no—
180C2×C4×D61—21no—
181C2×C4×D61—24no—
182C2×C4×D61—24no—
183C2×C4×D61—42no—
184C2×C4×D61—42no—
185C2×C4×D61—44no—
186C2×C4×D61—44no—
187C2×C4×D61—42no—
188C2×C4×D61—41no—
189C2×C4×D61—41no—
190C2×C4×D61—44no—
191C2×C4×D61—44no—
192C2×C4×D61C22⋊C412yes—
193C2×C4×D61C2×D412yes—
194C2×Dic122—41no—
195C2×Dic122—41no—
196C2×Dic122C22⋊C412yes—
197C2×Dic122C2×D412yes—
198M16×C61—22no—
199M16×C61—41no—
200C2×C8×C61—41no—
201C4⋊C4×C61—22no—
202C4⋊C4×C61—22no—
203C22⋊C4×C61—22no—
204C22⋊C4×C61—21no—
205C22⋊C4×C61—22no—
206C22⋊C4×C61—22no—
207C22⋊C4×C61—41no—
208C22⋊C4×C61C22×C412yes—
209C22⋊Dic61—21no—
210C22⋊Dic61—22no—
211C22⋊Dic61—41no—
212C22⋊Dic61C22×C412yes—
213#11758198—24no—
214#11758198—22no—
215#11758198—22no—
216#11758198—24no—
217#11758196—24no—
218#11758196—24no—
219#11758196—44no—
220C4×Dic61—24no—
221C4×Dic61—44no—
222#11758194—22no—
223#11758194—41no—
224C2×#92418—41no—
225#11758189—44no—
226C8×D61—44no—
227C23×C61—21no—
228C23×C61—21no—
229C23×C61—21no—
230C23×C61—21no—
231C23×C61—42no—
232C23×C61—42no—
233C23×C61C2×C22⋊C411yescharacteristic
234C23×C61C2×C22⋊C411yescharacteristic
235C23×C61C2×C22⋊C411yescharacteristic
236C23×C61C23×C411yescharacteristic
237C23×C61C22×D411yescharacteristic
238C22×D61—24no—
239C22×D61—22no—
240C22×D61—21no—
241C22×D61—21no—
242C22×D61—44no—
243C22×D61—44no—
244C22×D61—42no—
245C22×D61—42no—
246C22×D61—48no—
247C22×D61—44no—
248C22×D61—41no—
249C22×D61—41no—
250C22×D61—42no—
251C22×D61—44no—
252C22×D61—42no—
253C22×D61C2×C22⋊C412yes—
254D4×C61—41no—
255D4×C61—41no—
256D4×C61—41no—
257D4×C61—41no—
258C2×C4×C61—21no—
259C2×C4×C61—21no—
260C2×C4×C61—22no—
261C2×C4×C61—22no—
262C2×C4×C61—42no—
263C2×C4×C61—42no—
264C2×C4×C61—41no—
265C2×C4×C61—41no—
266C2×C4×C61—42no—
267C2×C4×C61—42no—
268C2×C4×C61—82no—
269C2×C4×C61C2×C22⋊C411yescharacteristic
270C2×C4×C61C22×D411yescharacteristic
271C22⋊D61—42no—
272C22⋊D61—42no—
273C22⋊D61—42no—
274C22⋊D61—42no—
275C22⋊D61—44no—
276C22⋊D61—44no—
277C2×Dic61—21no—
278C2×Dic61—21no—
279C2×Dic61—21no—
280C2×Dic61—21no—
281C2×Dic61—22no—
282C2×Dic61—22no—
283C2×Dic61—22no—
284C2×Dic61—22no—
285C2×Dic61—22no—
286C2×Dic61—22no—
287C2×Dic61—22no—
288C2×Dic61—22no—
289C2×Dic61—22no—
290C2×Dic61—42no—
291C2×Dic61—42no—
292C2×Dic61—82no—
293C2×Dic61#9912yes—
294C2×Dic61#9911yescharacteristic
295C2×Dic61#9911yescharacteristic
296C2×Dic61C2×C22⋊C412yes—
297C2×Dic61C2×C22⋊C412yes—
298C2×Dic61C2×C22⋊C412yes—
299D244—48no—
300C4×D61—22no—
301C4×D61—22no—
302C4×D61—22no—
303C4×D61—22no—
304C4×D61—48no—
305C4×D61—44no—
306C4×D61—44no—
307Dic122—42no—
308Dic122—42no—
309C8×C61—42no—
310#92418—42no—
311C2×#2120—611nomaximal, Sylow
312C22×C61—22no—
313C22×C61—21no—
314C22×C61—21no—
315C22×C61—21no—
316C22×C61—21no—
317C22×C61—41no—
318C22×C61—41no—
319C22×C61—41no—
320C22×C61—41no—
321C22×C61—42no—
322C22×C61—42no—
323C22×C61—42no—
324C22×C61—81no—
325C22×C61C2×#9911yescharacteristic
326C22×C61C2×#9911yescharacteristic
327C22×C61C22×C22⋊C411yescharacteristic
328C2×D61—24no—
329C2×D61—22no—
330C2×D61—42no—
331C2×D61—44no—
332C2×D61—48no—
333C2×D61—44no—
334C2×D61—42no—
335C2×D61—42no—
336C2×D61—44no—
337C2×D61—42no—
338C2×D61—44no—
339C2×D61—81no—
340C4×C61—21no—
341C4×C61—21no—
342C4×C61—42no—
343C4×C61—42no—
344C4×C61—82no—
345Dic61—22no—
346Dic61—22no—
347Dic61—42no—
348Dic61—82no—
349Dic61C2×#9912yes—
350Dic61C2×#9912yes—
351C2×#525—611no—
352C2×#413—611no—
353C2×#410—611no—
354#2120—618no—
355C2×#352—611no—
356C2×#352D6111yescharacteristic, complemented
357C2×AΣL(1,𝔽16)—611no—
358C2×AΣL(1,𝔽16)—611no—
359C2×C61—21no—
360C2×C61—21no—
361C2×C61—41no—
362C2×C61—41no—
363C2×C61—41no—
364C2×C61—41no—
365C2×C61#212012yescomplemented
366C2×C61C22×#9911yescharacteristic
367D61—44no—
368D61—42no—
369C22×#41—611no—
370C24×C4—611no—
371C22×M16—1221no—
372#525—614no—
373#525—614no—
374#525—1222no—
375#525—1222no—
376C2×#123—611no—
377C2×#123C2×D6111yescharacteristic
378C2×C22⋊Q8—1221no—
379C2×#121—1221no—
380C2×#120—611no—
381C2×#120—611no—
382C2×C4×D4—1221no—
383C2×C4×D4—1221no—
384C2×#117—611no—
385C2×#117—1221no—
386#413—614no—
387#413—1222no—
388C2×#101—1221no—
389C2×#100—611no—
390C2×#100C2×D6111yescharacteristic
391#410—614no—
392#410—1222no—
393C2×#99—611no—
394C2×#99—1221no—
395C2×#99C2×D6111yescharacteristic
396#352—614no—
397#352C2×D6114yescomplemented
398AΣL(1,𝔽16)—614no—
399AΣL(1,𝔽16)—614no—
400C61C2×#212011yescharacteristic, complemented, Sylow
401C25—611no—
402C2×#41—612no—
403C2×#41—612no—
404C2×#41—612no—
405C2×#41—612no—
406C2×#41—2441no—
407C2×#41—2441no—
408C2×#41—2442no—
409C22×Q8—611no—
410C22×D4—611no—
411C22×D4—611no—
412C22×D4—1221no—
413C22×D4—1221no—
414C22×D4C22×D6111yescharacteristic
415C23×C4—611no—
416C23×C4—611no—
417C23×C4—611no—
418C23×C4—614no—
419C23×C4—1221no—
420C23×C4—1221no—
421C23×C4—1222no—
422C23×C4—2442no—
423C23×C4—2441no—
424C23×C4—2441no—
425C23×C4C4×D6111yescharacteristic
426C2×M16—21no—
427C2×M16—1224no—
428C2×M16—1221no—
429C2×M16—2441no—
430C2×M16—2442no—
431C22×C8—2441no—
432#123—21no—
433#123—21no—
434#123—614no—
435#123—1222no—
436#123C4×D6112yes—
437#123C22×D6112yes—
438C22⋊Q8—1224no—
439C22⋊Q8—1224no—
440#121—1224no—
441#121—1224no—
442#120—612no—
443#120—612no—
444#120—614no—
445#120—1222no—
446#120—1221no—
447#120—1221no—
448C4×D4—1224no—
449C4×D4—1224no—
450C4×D4—1224no—
451C4×D4—1224no—
452#117—614no—
453#117—1222no—
454#117—1224no—
455#117—2442no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—1221no—
458C2×C4⋊C4—1221no—
459C2×C4⋊C4—2441no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—611no—
463C2×C22⋊C4—1221no—
464C2×C22⋊C4—1221no—
465C2×C22⋊C4—1221no—
466C2×C22⋊C4—1221no—
467C2×C22⋊C4C4×D6111yescharacteristic
468C2×C42—1221no—
469C2×C42—2441no—
470#101—1224no—
471#100—21no—
472#100—612no—
473#100—1221no—
474#100C22×D6112yes—
475#99—21no—
476#99—612no—
477#99—1224no—
478#99—1221no—
479#99C22×D6112yes—
480C24—611no—
481C24—612no—
482C24—1221no—
483C24—1221no—
484C24—2441no—
485C24—2441no—
486C24—2444no—
487C24C2×C4×D6111yescharacteristic
488C24D4×D6111yescharacteristic
489#41—2442no—
490#41—2442no—
491#41—2442no—
492#41—2442no—
493#41—2442no—
494#41—2442no—
495#41—2442no—
496#41—2442no—
497C2×Q8—612no—
498C2×Q8—612no—
499C2×Q8—2441no—
500C2×Q8—2441no—
501C2×D4—41no—
502C2×D4—41no—
503C2×D4—612no—
504C2×D4—612no—
505C2×D4—612no—
506C2×D4—612no—
507C2×D4—1224no—
508C2×D4—1222no—
509C2×D4—1222no—
510C2×D4—2444no—
511C2×D4—2441no—
512C2×D4—2441no—
513C2×D4—2441no—
514C2×D4—2441no—
515C2×D4—2444no—
516C2×D4C2×C4×D6111yescharacteristic
517C2×D4D4×D6111yescharacteristic
518C2×D4D4×D6111yescharacteristic
519C2×D4C23×D6111yescharacteristic
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—41no—
524C22×C4—41no—
525C22×C4—41no—
526C22×C4—611no—
527C22×C4—612no—
528C22×C4—612no—
529C22×C4—612no—
530C22×C4—612no—
531C22×C4—611no—
532C22×C4—611no—
533C22×C4—612no—
534C22×C4—612no—
535C22×C4—1221no—
536C22×C4—1222no—
537C22×C4—1221no—
538C22×C4—1224no—
539C22×C4—1224no—
540C22×C4—1221no—
541C22×C4—1221no—
542C22×C4—1222no—
543C22×C4—1222no—
544C22×C4—1221no—
545C22×C4—1221no—
546C22×C4—1221no—
547C22×C4—2442no—
548C22×C4—2441no—
549C22×C4—2441no—
550C22×C4—2444no—
551C22×C4—2444no—
552C22×C4—2442no—
553C22×C4—2442no—
554C22×C4—2444no—
555C22×C4—2444no—
556C22×C4—2441no—
557C22×C4C2×C4×D6112yes—
558C22×C4D4×D6111yescharacteristic
559M16—22no—
560M16—41no—
561M16—1222no—
562M16—2444no—
563M16—2441no—
564C2×C8—41no—
565C2×C8—2444no—
566C2×C8—2441no—
567C4⋊C4—22no—
568C4⋊C4—22no—
569C4⋊C4—1224no—
570C4⋊C4—1224no—
571C4⋊C4—2444no—
572C22⋊C4—22no—
573C22⋊C4—22no—
574C22⋊C4—21no—
575C22⋊C4—22no—
576C22⋊C4—41no—
577C22⋊C4—612no—
578C22⋊C4—1224no—
579C22⋊C4—1224no—
580C22⋊C4—1221no—
581C22⋊C4—1222no—
582C22⋊C4—1222no—
583C22⋊C4—1222no—
584C22⋊C4—2441no—
585C22⋊C4C2×C4×D6112yes—
586C42—1224no—
587C42—2444no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—42no—
593C23—42no—
594C23—612no—
595C23—1224no—
596C23—1221no—
597C23—1222no—
598C23—1221no—
599C23—2442no—
600C23—2442no—
601C23—2442no—
602C23—2442no—
603C23—2444no—
604C23—2444no—
605C23—2444no—
606C23—2448no—
607C23—2444no—
608C23—2441no—
609C23—2441no—
610C23C22⋊C4×D6111yescharacteristic
611C23C22⋊C4×D6111yescharacteristic
612C23C22⋊C4×D6111yescharacteristic
613C23C22×C4×D6111yescharacteristic
614C23C2×D4×D6111yescharacteristic
615Q8—2442no—
616Q8—2442no—
617D4—41no—
618D4—41no—
619D4—41no—
620D4—41no—
621D4—2448no—
622D4—2442no—
623D4—2442no—
624D4—2442no—
625D4—2442no—
626D4—2444no—
627D4—2444no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—82no—
639C2×C4—612no—
640C2×C4—612no—
641C2×C4—611no—
642C2×C4—611no—
643C2×C4—612no—
644C2×C4—612no—
645C2×C4—1222no—
646C2×C4—1222no—
647C2×C4—1222no—
648C2×C4—1222no—
649C2×C4—1222no—
650C2×C4—1222no—
651C2×C4—1222no—
652C2×C4—1222no—
653C2×C4—1222no—
654C2×C4—1222no—
655C2×C4—1222no—
656C2×C4—1222no—
657C2×C4—1221no—
658C2×C4—1221no—
659C2×C4—1221no—
660C2×C4—1221no—
661C2×C4—1222no—
662C2×C4—4882no—
663C2×C4—2444no—
664C2×C4—2444no—
665C2×C4—2448no—
666C2×C4—2442no—
667C2×C4—2442no—
668C2×C4C22⋊C4×D6111yescharacteristic
669C2×C4C2×D4×D6111yescharacteristic
670C8—42no—
671C8—2442no—
672C22—22no—
673C22—21no—
674C22—21no—
675C22—21no—
676C22—21no—
677C22—41no—
678C22—41no—
679C22—41no—
680C22—41no—
681C22—42no—
682C22—42no—
683C22—42no—
684C22—81no—
685C22—1224no—
686C22—1222no—
687C22—4881no—
688C22—2442no—
689C22—2442no—
690C22—2444no—
691C22—2444no—
692C22—2444no—
693C22—2448no—
694C22—2442no—
695C22—2444no—
696C22—2442no—
697C22#99×D6111yescharacteristic
698C22#99×D6111yescharacteristic
699C22C2×C22⋊C4×D6111yescharacteristic
700C4—21no—
701C4—21no—
702C4—42no—
703C4—42no—
704C4—82no—
705C4—612no—
706C4—612no—
707C4—1222no—
708C4—1222no—
709C4—4882no—
710C4—2442no—
711C2—21no—
712C2—21no—
713C2—41no—
714C2—41no—
715C2—41no—
716C2—41no—
717C2—2442no—
718C2—2444no—
719C2#2144745912yesdirect product factor
720C2C2×#99×D6111yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC23×C61C23×C4
FrattiniC2×D4C23×D61
FittingC2×C61×#352C2
socleC22×C61C2×#99
prime radicalC2×#16840270C2
cosocleC2×D4×C61C24
hypercenterC2×#352D61
hypocenterC61C2×#2120
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#352

Complements

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

NH ≅ G/Ntype
2. C2×#16839743C2semidirect
3. C2×#16839734C2semidirect
4. #21447459C2direct (N × H)
5. C2×#16839552C2semidirect
6. C2×#16839550C2semidirect
7. C2×#16839548C2semidirect
8. C2×C61×#352C2semidirect
10. C23×C4×D61C4semidirect
14. #16840270C4semidirect
16. C2×#14519760C4semidirect
19. C2×#14519747C4semidirect
24. C2×#14519733C4semidirect
26. #16839743C22semidirect
30. #16839734C22semidirect
33. #16839552C22semidirect
34. #16839550C22semidirect
35. #16839548C22semidirect
39. C61×#352C22semidirect
61. C22×C4×D61C2×C4semidirect
69. #14519760C2×C4semidirect
75. #14519747C2×C4semidirect
87. #14519733C2×C4semidirect
356. C2×#352D61semidirect
365. C2×C61#2120semidirect
397. #352C2×D61semidirect
400. C61C2×#2120semidirect
719. C2#21447459direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168402702
C2×#168397432
C2×#168397342
#214474592
C2×#168395522
C2×#168395502
C2×#168395482
C2×C61×#3522
C2×#212061