Finite Group Databasebeta

← #29606384

Subgroups — #29606384

Order 15616.

2662 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519752C211yesmaximal, characteristic
2C22×#14519734C211yesmaximal, characteristic, complemented
3C2×#16839664C211yesmaximal, characteristic, complemented
4C2×#16839663C211yesmaximal, characteristic, complemented
5C2×#16839619C211yesmaximal, characteristic, complemented
6#21444063C214yesmaximal, complemented
7#21444059C214yesmaximal, complemented
8#21444048C211yesmaximal, characteristic, complemented
9C61×C4⋊#95C211yesmaximal, characteristic, complemented
10C23×D244C2211yescharacteristic
11C23×D244C2212yes—
12C23×C4×D61C2211yescharacteristic
13C2×#14519752—24no—
14C2×#14519752—24no—
15C2×#14519752C418yescomplemented
16C2×#14519734—24no—
17C2×#14519734—24no—
18C2×#14519734—24no—
19C22×C4⋊Dic61C2211yescharacteristic
20C22×#11758196C2212yes—
21C22×#11758198C2212yes—
22C22×#11758198C2212yes—
23C22×#11758198C2214yes—
24C22×#11758198C2214yes—
25C22×#11758198C2212yes—
26C22×C4×Dic61C2211yescharacteristic
27#16839664—24no—
28#16839663—24no—
29#16839619—24no—
30C2×#14519684C2212yes—
31C2×#14519684C2214yes—
32C22×C4⋊C4×C61C2211yescharacteristic
33C22×C4⋊C4×C61C2211yescharacteristic
34C22×C42×C61C2211yescharacteristic
35C2×#95×C61C2214yes—
36C24×D61C2312yes—
37C24×D61C2311yescharacteristic
38C22×D244—24no—
39C22×D244—24no—
40C22×D244—22no—
41C22×D244—22no—
42C22×D244—22no—
43C22×D244—22no—
44C22×D244—22no—
45C22×D244—22no—
46C22×D244—44no—
47C22×D244—44no—
48C22×D244C2×C414yes—
49C22×D244C2×C418yes—
50C23×Dic61C2312yes—
51C23×Dic61C2312yes—
52C23×Dic61C2311yescharacteristic
53C22×C4×D61—22no—
54C22×C4×D61—22no—
55C22×C4×D61—22no—
56C22×C4×D61—22no—
57C22×C4×D61C2×C414yes—
58C22×C4×D61D414yes—
59C22×C4×D61D414yes—
60#14519752—232no—
61#14519734—232no—
62C2×C4⋊Dic61—22no—
63C2×C4⋊Dic61—22no—
64C2×C4⋊Dic61—22no—
65C2×#11758196—24no—
66C2×#11758196—24no—
67C2×#11758196—24no—
68C2×#11758198—24no—
69C2×#11758198—24no—
70C2×#11758198—24no—
71C2×#11758198—24no—
72C2×#11758198—24no—
73C2×#11758198—24no—
74C2×#11758198—28no—
75C2×#11758198—28no—
76C2×#11758198—44no—
77C2×#11758198—44no—
78C2×#11758198—44no—
79C2×#11758198—44no—
80C2×#11758198—44no—
81C2×#11758198C2×C418yes—
82C2×C4×Dic61—22no—
83C2×C4×Dic61—22no—
84C2×C4×Dic61D414yescomplemented
85#14519684—24no—
86#14519684—44no—
87C23×C4×C61C2312yes—
88C23×C4×C61C2312yes—
89C23×C4×C61C2312yes—
90C23×C4×C61C2311yescharacteristic
91C2×C4⋊C4×C61—22no—
92C2×C4⋊C4×C61—22no—
93C2×C4⋊C4×C61—22no—
94C2×C4⋊C4×C61—22no—
95C2×C4⋊C4×C61—22no—
96C2×C4⋊C4×C61C2×C414yes—
97C2×C42×C61—22no—
98C2×C42×C61—22no—
99C2×C42×C61D414yescomplemented
100#95×C61—44no—
101C24×C61C2411yescharacteristic
102C23×D61—21no—
103C23×D61—21no—
104C23×D61—21no—
105C23×D61—21no—
106C23×D61—22no—
107C23×D61—22no—
108C23×D61—22no—
109C23×D61—22no—
110C23×D61—22no—
111C23×D61—22no—
112C23×D61—22no—
113C23×D61—22no—
114C23×D61—22no—
115C23×D61—22no—
116C23×D61—24no—
117C23×D61—24no—
118C23×D61—24no—
119C23×D61—24no—
120C23×D61C22×C414yes—
121C23×D61C22×C412yes—
122C23×D61C2×D412yes—
123C23×D61C2×D412yes—
124C22×C4×C61—22no—
125C22×C4×C61—22no—
126C22×C4×C61—22no—
127C22×C4×C61—22no—
128C22×C4×C61—24no—
129C22×C4×C61—24no—
130C22×C4×C61—22no—
131C22×C4×C61—22no—
132C22×C4×C61—22no—
133C22×C4×C61—22no—
134C22×C4×C61—22no—
135C22×C4×C61—22no—
136C22×C4×C61—22no—
137C22×C4×C61—24no—
138C22×C4×C61—24no—
139C22×C4×C61C22×C414yes—
140C22×C4×C61C22×C412yes—
141C22×C4×C61C2×D414yes—
142C22×C4×C61C2×D412yes—
143C22×C4×C61C2×D412yes—
144C22×C4×C61C2×D412yes—
145C22×C4×C61C2×D412yes—
146C22×C4×C61#4112yes—
147C22×C4×C61#4112yes—
148C22×Dic61—21no—
149C22×Dic61—21no—
150C22×Dic61—21no—
151C22×Dic61—21no—
152C22×Dic61—22no—
153C22×Dic61—22no—
154C22×Dic61—22no—
155C22×Dic61—22no—
156C22×Dic61—22no—
157C22×Dic61—22no—
158C22×Dic61—22no—
159C22×Dic61—22no—
160C22×Dic61—22no—
161C22×Dic61—24no—
162C22×Dic61—24no—
163C22×Dic61C22×C412yes—
164C22×Dic61C2×D414yes—
165C22×Dic61C2×D412yes—
166C22×Dic61C2×D412yes—
167C2×D244—216no—
168C2×D244—28no—
169C2×D244—28no—
170C2×D244—28no—
171C2×D244—416no—
172C2×D244—48no—
173C2×D244—416no—
174C2×D244—48no—
175C2×D244—44no—
176C2×D244—44no—
177C2×D244—44no—
178C2×D244—44no—
179C2×C4×D61—28no—
180C2×C4×D61—28no—
181C2×C4×D61—28no—
182C2×C4×D61—28no—
183C2×C4×D61—28no—
184C2×C4×D61—28no—
185C2×C4×D61C22⋊C4116yescomplemented
186C4⋊C4×C61—28no—
187C4⋊C4×C61—44no—
188C42×C61—28no—
189#11758198—216no—
190#11758198—216no—
191#11758198—416no—
192#11758198—416no—
193#11758198—48no—
194C4⋊Dic61—44no—
195#11758196—216no—
196C4×Dic61—28no—
197C23×C61C23×C411yescharacteristic
198C23×C61C22×D411yescharacteristic
199C23×C61C22×D411yescharacteristic
200C23×C61C22×D411yescharacteristic
201C23×C61C22×D411yescharacteristic
202C23×C61C2×#4111yescharacteristic
203C23×C61C2×#4111yescharacteristic
204C23×C61H(5,𝔽2)12yes—
205C23×C61H(5,𝔽2)12yes—
206C23×C61H(5,𝔽2)12yes—
207C23×C612−1+412yes—
208C22×D61—22no—
209C22×D61—22no—
210C22×D61—24no—
211C22×D61—24no—
212C22×D61—22no—
213C22×D61—22no—
214C22×D61—22no—
215C22×D61—22no—
216C22×D61—22no—
217C22×D61—24no—
218C22×D61—22no—
219C22×D61—22no—
220C22×D61—22no—
221C22×D61—24no—
222C22×D61—24no—
223C22×D61—24no—
224C22×D61—24no—
225C22×D61—28no—
226C22×D61—28no—
227C22×D61—42no—
228C22×D61—42no—
229C22×D61—42no—
230C22×D61—42no—
231C22×D61—42no—
232C22×D61—42no—
233C22×D61—42no—
234C22×D61—42no—
235C22×D61—42no—
236C22×D61—42no—
237C22×D61—42no—
238C22×D61—42no—
239C22×D61—44no—
240C22×D61—44no—
241C22×D61—44no—
242C22×D61—42no—
243C22×D61—42no—
244C22×D61—42no—
245C22×D61—42no—
246C22×D61—44no—
247C22×D61—44no—
248C22×D61—44no—
249C22×D61—44no—
250C22×D61—44no—
251C22×D61—44no—
252C22×D61—44no—
253C22×D61C2×C22⋊C414yes—
254C2×C4×C61—24no—
255C2×C4×C61—28no—
256C2×C4×C61—24no—
257C2×C4×C61—24no—
258C2×C4×C61—24no—
259C2×C4×C61—42no—
260C2×C4×C61—44no—
261C2×C4×C61—42no—
262C2×C4×C61—42no—
263C2×C4×C61—42no—
264C2×C4×C61—42no—
265C2×C4×C61—42no—
266C2×C4×C61—42no—
267C2×C4×C61—44no—
268C2×C4×C61—42no—
269C2×C4×C61—42no—
270C2×C4×C61—44no—
271C2×C4×C61C2×C22⋊C414yes—
272C2×C4×C61C4×D414yes—
273C2×C4×C61C4×D414yes—
274C2×C4×C61#12014yes—
275C2×C4×C61#12114yes—
276C2×C4×C61#12114yes—
277C2×C4×C61#12314yes—
278C2×Dic61—22no—
279C2×Dic61—22no—
280C2×Dic61—22no—
281C2×Dic61—22no—
282C2×Dic61—22no—
283C2×Dic61—22no—
284C2×Dic61—24no—
285C2×Dic61—24no—
286C2×Dic61—24no—
287C2×Dic61—42no—
288C2×Dic61—42no—
289C2×Dic61—42no—
290C2×Dic61—42no—
291C2×Dic61—42no—
292C2×Dic61—42no—
293C2×Dic61—44no—
294C2×Dic61—42no—
295C2×Dic61—44no—
296C2×Dic61C2×C22⋊C414yes—
297D244—432no—
298D244—416no—
299C4×D61—232no—
300#14257—611nomaximal, Sylow
301C22×C61C22×C22⋊C411yescharacteristic
302C22×C61C2×C4×D411yescharacteristic
303C22×C61C2×C4×D411yescharacteristic
304C22×C61#51812yes—
305C22×C61#52012yes—
306C22×C61C2×#12011yescharacteristic
307C22×C61C2×#12111yescharacteristic
308C22×C61C2×#12111yescharacteristic
309C22×C61C2×#12311yescharacteristic
310C22×C61#53511yescharacteristic
311C22×C61#53512yes—
312C22×C61#53512yes—
313C22×C61#53511yescharacteristic
314C22×C61#53511yescharacteristic
315C22×C61#53512yes—
316C22×C61#53611yescharacteristic
317C22×C61#53712yes—
318C22×C61#53712yes—
319C22×C61#53712yes—
320C22×C61#54012yes—
321C22×C61#54012yes—
322C22×C61#54212yes—
323C22×C61#54212yes—
324C2×D61—24no—
325C2×D61—24no—
326C2×D61—24no—
327C2×D61—44no—
328C2×D61—44no—
329C2×D61—44no—
330C2×D61—42no—
331C2×D61—42no—
332C2×D61—42no—
333C2×D61—42no—
334C2×D61—44no—
335C2×D61—44no—
336C2×D61—44no—
337C2×D61—48no—
338C2×D61—48no—
339C2×D61—44no—
340C2×D61—84no—
341C2×D61—82no—
342C2×D61—82no—
343C2×D61—82no—
344C2×D61—82no—
345C2×D61—84no—
346C4×C61—44no—
347C4×C61—44no—
348C4×C61—82no—
349C4×C61#38618yes—
350Dic61—24no—
351Dic61—44no—
352Dic61—82no—
353C22×#121—611no—
354C22×#117—611no—
355C2×#390—611no—
356C2×#390—611no—
357C2×#380—611no—
358#1439—614no—
359#1438—614no—
360C4⋊#95—611no—
361C4⋊#95D6111yescharacteristic, complemented
362C2×C61C2×#38611yescharacteristic
363C2×C61#230911yescharacteristic
364C2×C61#231111yescharacteristic
365C2×C61#232412yes—
366C2×C61#232412yes—
367C2×C61#261512yes—
368C2×C61#261911yescharacteristic
369C2×C61#261911yescharacteristic
370C2×C61#262011yescharacteristic
371C2×C61#262011yescharacteristic
372C2×C61#262412yes—
373D61—44no—
374D61—84no—
375C23×D4—611no—
376C23×D4—612no—
377C24×C4—611no—
378C2×#121—618no—
379C2×#121—1224no—
380C2×#121—1224no—
381C2×#117—1224no—
382C2×#117—1224no—
383C2×#117—1224no—
384C22×C4⋊C4—612no—
385C22×C4⋊C4—611no—
386C22×C4⋊C4C2×D6111yescharacteristic
387C22×C4⋊C4C2×D6111yescharacteristic
388C22×C22⋊C4—612no—
389C22×C22⋊C4—612no—
390C22×C22⋊C4—612no—
391C22×C22⋊C4—614no—
392C22×C22⋊C4—614no—
393C22×C42—611no—
394C22×C42C2×D6111yescharacteristic
395#390—1224no—
396#390—1224no—
397#380—1224no—
398C2×#95—612no—
399C2×#95—614no—
400C2×#95C2×D6114yes—
401C61#1425711yescharacteristic, complemented, Sylow
402C25—611no—
403C25—612no—
404C22×D4—614no—
405C22×D4—618no—
406C22×D4—1224no—
407C22×D4—1224no—
408C22×D4—1222no—
409C22×D4—1222no—
410C22×D4—1222no—
411C22×D4—1222no—
412C22×D4—1222no—
413C22×D4—1222no—
414C22×D4—2444no—
415C22×D4—2444no—
416C23×C4—611no—
417C23×C4—614no—
418C23×C4—614no—
419C23×C4—614no—
420C23×C4—612no—
421C23×C4—612no—
422C23×C4—1222no—
423C23×C4—1222no—
424C23×C4—1222no—
425C23×C4—1222no—
426C23×C4C22×D6112yes—
427C23×C4C22×D6112yes—
428C23×C4C22×D6112yes—
429C23×C4C22×D6111yescharacteristic
430#121—12232no—
431#117—12232no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—1224no—
438C2×C4⋊C4—1224no—
439C2×C4⋊C4—1224no—
440C2×C4⋊C4—1222no—
441C2×C4⋊C4—1222no—
442C2×C4⋊C4—1222no—
443C2×C4⋊C4C4×D6114yes—
444C2×C22⋊C4—618no—
445C2×C22⋊C4—1224no—
446C2×C22⋊C4—1224no—
447C2×C22⋊C4—1224no—
448C2×C22⋊C4—1224no—
449C2×C22⋊C4—1224no—
450C2×C22⋊C4—1228no—
451C2×C22⋊C4—1224no—
452C2×C22⋊C4—1228no—
453C2×C22⋊C4—2444no—
454C2×C22⋊C4—2444no—
455C2×C22⋊C4—2444no—
456C2×C22⋊C4—2444no—
457C2×C22⋊C4—2444no—
458C2×C42—22no—
459C2×C42—22no—
460C2×C42—614no—
461C2×C42—1222no—
462C2×C42—1222no—
463C2×C42D24414yescomplemented
464#95—44no—
465#95—1224no—
466#95—2444no—
467C24—612no—
468C24—612no—
469C24—612no—
470C24—614no—
471C24—1221no—
472C24—1221no—
473C24—1221no—
474C24—1221no—
475C24—1222no—
476C24—1222no—
477C24—1222no—
478C24—1222no—
479C24—1222no—
480C24—1222no—
481C24—1222no—
482C24—1222no—
483C24—1222no—
484C24—1222no—
485C24—1224no—
486C24—1224no—
487C24—1224no—
488C24—1224no—
489C24C23×D6111yescharacteristic
490C2×D4—12216no—
491C2×D4—1228no—
492C2×D4—1228no—
493C2×D4—1228no—
494C2×D4—24416no—
495C2×D4—2448no—
496C2×D4—24416no—
497C2×D4—2448no—
498C2×D4—2444no—
499C2×D4—2444no—
500C2×D4—2444no—
501C2×D4—2444no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—24no—
516C22×C4—24no—
517C22×C4—612no—
518C22×C4—612no—
519C22×C4—612no—
520C22×C4—6116no—
521C22×C4—614no—
522C22×C4—1221no—
523C22×C4—1221no—
524C22×C4—1221no—
525C22×C4—1221no—
526C22×C4—1228no—
527C22×C4—1228no—
528C22×C4—1228no—
529C22×C4—1228no—
530C22×C4—1228no—
531C22×C4—1228no—
532C22×C4—1222no—
533C22×C4—1222no—
534C22×C4—1222no—
535C22×C4—1222no—
536C22×C4—1222no—
537C22×C4—1222no—
538C22×C4—1222no—
539C22×C4—1222no—
540C22×C4—1222no—
541C22×C4—1224no—
542C22×C4—1224no—
543C22×C4C2×C4×D6114yes—
544C22×C4C2×C4×D6112yes—
545C22×C4C2×D24414yes—
546C22×C4C2×D24412yes—
547C22×C4#1175822212yes—
548C22×C4D4×D6112yes—
549C22×C4D4×D6112yes—
550C22×C4D4×D6112yes—
551C22×C4#1175822612yes—
552C4⋊C4—28no—
553C4⋊C4—44no—
554C4⋊C4—12216no—
555C4⋊C4—2444no—
556C22⋊C4—12216no—
557C22⋊C4—12216no—
558C22⋊C4—24416no—
559C22⋊C4—24416no—
560C22⋊C4—2448no—
561C42—28no—
562C42—1228no—
563C23—614no—
564C23—1222no—
565C23—1222no—
566C23—1224no—
567C23—1224no—
568C23—1222no—
569C23—1222no—
570C23—1222no—
571C23—1222no—
572C23—1222no—
573C23—1224no—
574C23—1222no—
575C23—1222no—
576C23—1222no—
577C23—1224no—
578C23—1224no—
579C23—1224no—
580C23—1224no—
581C23—1228no—
582C23—1228no—
583C23—2442no—
584C23—2442no—
585C23—2442no—
586C23—2442no—
587C23—2442no—
588C23—2444no—
589C23—2444no—
590C23—2442no—
591C23—2442no—
592C23—2444no—
593C23—2442no—
594C23—2444no—
595C23—2444no—
596C23—2444no—
597C23—2444no—
598C23—2444no—
599C23—2444no—
600C23—2444no—
601C23—2442no—
602C23—2442no—
603C23—2442no—
604C23—2442no—
605C23—2442no—
606C23—2442no—
607C23—2442no—
608C23—2442no—
609C23C22×C4×D6111yescharacteristic
610C23C2×D4×D6111yescharacteristic
611C23C2×D4×D6111yescharacteristic
612C23C2×D4×D6111yescharacteristic
613C23C22×D24411yescharacteristic
614C23C2×#1175822211yescharacteristic
615C23C2×#1175822611yescharacteristic
616C23#1451982212yes—
617C23#1451982312yes—
618C23#1451982312yes—
619C23#1451982512yes—
620D4—24432no—
621D4—24416no—
622C2×C4—24no—
623C2×C4—28no—
624C2×C4—24no—
625C2×C4—24no—
626C2×C4—24no—
627C2×C4—42no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4—44no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—44no—
637C2×C4—42no—
638C2×C4—44no—
639C2×C4—614no—
640C2×C4—1222no—
641C2×C4—1222no—
642C2×C4—1222no—
643C2×C4—1222no—
644C2×C4—1222no—
645C2×C4—1222no—
646C2×C4—12232no—
647C2×C4—1224no—
648C2×C4—1224no—
649C2×C4—1224no—
650C2×C4—2442no—
651C2×C4—2442no—
652C2×C4—2442no—
653C2×C4—2444no—
654C2×C4—2444no—
655C2×C4—2442no—
656C2×C4—2442no—
657C2×C4—2442no—
658C2×C4—2442no—
659C2×C4C22⋊C4×D6114yes—
660C2×C4#1451973914yes—
661C2×C4C4×D24414yes—
662C2×C4#1451974714yes—
663C2×C4#1451975014yes—
664C2×C4#1451975214yes—
665C2×C4#1451976214yes—
666C22—1224no—
667C22—1224no—
668C22—1224no—
669C22—4884no—
670C22—4882no—
671C22—4882no—
672C22—4882no—
673C22—4882no—
674C22—4884no—
675C22—2444no—
676C22—2448no—
677C22—2448no—
678C22—2444no—
679C22—2444no—
680C22—2444no—
681C22—2442no—
682C22—2442no—
683C22—2442no—
684C22—2444no—
685C22—2442no—
686C22—2444no—
687C22—2444no—
688C22C2×C22⋊C4×D6111yescharacteristic
689C22C2×#1451973911yescharacteristic
690C22C2×C4×D24411yescharacteristic
691C22#1684023412yes—
692C22#1684024412yes—
693C22C2×#1451974711yescharacteristic
694C22C2×#1451975011yescharacteristic
695C22C2×#1451975211yescharacteristic
696C22C2×#1451976211yescharacteristic
697C22#1684032511yescharacteristic
698C22#1684032812yes—
699C22#1684032812yes—
700C22#1684033011yescharacteristic
701C22#1684033011yescharacteristic
702C22#1684033112yes—
703C22#1684033711yescharacteristic
704C22#1684034212yes—
705C22#1684034212yes—
706C22#1684034312yes—
707C22#1684036312yes—
708C22#1684036812yes—
709C22#1684038412yes—
710C22#1684038612yes—
711C4—44no—
712C4—44no—
713C4—82no—
714C4—1224no—
715C4—4882no—
716C4—2444no—
717C4#1683964018yes—
718C2—4884no—
719C2—2444no—
720C2C2×#1683964011yescharacteristic
721C2#2144839811yescharacteristic
722C2#2144841011yescharacteristic
723C2#2144851012yes—
724C2#2144851312yes—
725C2#2145154512yes—
726C2#2145157211yescharacteristic
727C2#2145157411yescharacteristic
728C2#2145157911yescharacteristic
729C2#2145158311yescharacteristic
730C2#2145161312yes—
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×C4⋊#95C2
socle, cosocleC24×C61C24
prime radicalC22×#14519752C2
hypercenterC4⋊#95D61
hypocenterC61#14257
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
2. C22×#14519734C2semidirect
3. C2×#16839664C2semidirect
4. C2×#16839663C2semidirect
5. C2×#16839619C2semidirect
6. #21444063C2semidirect
7. #21444059C2semidirect
8. #21444048C2semidirect
9. C61×C4⋊#95C2semidirect
15. C2×#14519752C4semidirect
84. C2×C4×Dic61D4semidirect
99. C2×C42×C61D4semidirect
185. C2×C4×D61C22⋊C4semidirect
361. C4⋊#95D61semidirect
401. C61#14257semidirect
463. C2×C42D244semidirect

Maximal subgroups

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

subgroupindex
C22×#145197522
C22×#145197342
C2×#168396642
C2×#168396632
C2×#168396192
#214440632
#214440592
#214440482
C61×C4⋊#952
#1425761