Finite Group Databasebeta

← #29586847

Subgroups — #29586847

Order 15616.

1370 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#11758190C211yesmaximal, characteristic
2C2×#16839772C211yesmaximal, characteristic, complemented
3C2×#16839768C211yesmaximal, characteristic
4C22×#14519695C211yesmaximal, characteristic, complemented
5C22×#14519693C211yesmaximal, characteristic
6#21445515C211yesmaximal, characteristic, complemented
7C2×C61×#341C211yesmaximal, characteristic, complemented
8C23×Dic122C2211yescharacteristic
9C23×D244C2211yescharacteristic
10C22×#11758190—22no—
11C22×#11758190—22no—
12C22×#11758190—22no—
13C22×#11758190—22no—
14C22×#11758190—22no—
15C22×#11758190—22no—
16C22×#11758190C414yescomplemented
17C22×#11758194C2211yescharacteristic
18C2×#14519736C2211yescharacteristic
19#16839772—22no—
20#16839772—22no—
21#16839768—22no—
22#16839768—22no—
23C2×#14519702—22no—
24C2×#14519699—22no—
25C2×#14519695—22no—
26C2×#14519695—22no—
27C2×#14519695—22no—
28C2×#14519693—22no—
29C2×#14519693—22no—
30C2×#14519693—22no—
31#16839516—22no—
32C22×M16×C61C2211yescharacteristic
33C22×M16×C61C2211yescharacteristic
34C23×C8×C61C2211yescharacteristic
35C61×#341—22no—
36C24×D61—21no—
37C22×Dic122—21no—
38C22×Dic122—21no—
39C22×Dic122—21no—
40C22×Dic122—21no—
41C22×Dic122—21no—
42C22×Dic122—21no—
43C22×Dic122—21no—
44C22×Dic122—21no—
45C22×Dic122—21no—
46C22×Dic122—21no—
47C22×Dic122—21no—
48C22×Dic122C2×C412yes—
49C22×Dic122D412yes—
50C22×Dic122D412yes—
51C22×D244—21no—
52C22×D244—21no—
53C22×D244—21no—
54C22×D244—21no—
55C22×D244—21no—
56C22×D244—21no—
57C22×D244—21no—
58C22×D244—21no—
59C22×D244—21no—
60C22×D244—21no—
61C22×D244—21no—
62C22×D244C2×C412yes—
63C22×D244D412yes—
64C22×D244D412yes—
65C23×Dic61—21no—
66C2×#11758190—28no—
67C2×#11758190—28no—
68C2×#11758190—28no—
69C2×#11758190—28no—
70C2×#11758190—28no—
71C2×#11758190—28no—
72C2×#11758190—28no—
73C2×#11758194—21no—
74C2×#11758194—21no—
75C2×#11758194—21no—
76C2×#11758194—21no—
77C2×#11758194—21no—
78C2×#11758194D412yes—
79C22×#92418—21no—
80#14519736—21no—
81#14519736—21no—
82#14519736—21no—
83#14519736—21no—
84C2×C4⋊Dic61D412yes—
85C2×C22⋊Dic61—21no—
86C2×C4×Dic61—21no—
87#14519702—28no—
88#14519699—28no—
89#14519695—28no—
90#14519693—28no—
91C23×C4×C61C2311yescharacteristic
92C2×M16×C61—21no—
93C2×M16×C61—21no—
94C2×M16×C61—21no—
95C2×M16×C61—21no—
96C2×M16×C61—21no—
97C2×M16×C61—21no—
98C2×M16×C61—21no—
99C2×M16×C61—21no—
100C2×M16×C61—21no—
101C2×M16×C61—21no—
102C2×M16×C61D412yes—
103C2×M16×C61D412yes—
104C22×C8×C61—21no—
105C22×C8×C61—21no—
106C22×C8×C61—21no—
107C22×C8×C61—21no—
108C22×C8×C61—21no—
109C22×C8×C61—21no—
110C22×C8×C61C2×C412yes—
111C22×C8×C61D412yes—
112C22×C8×C61D412yes—
113C24×C61#4111yescharacteristic
114C23×D61—22no—
115C23×D61—22no—
116C23×D61—22no—
117C23×D61—41no—
118C23×D61—41no—
119C23×D61—41no—
120C23×D61—41no—
121C23×D61—84no—
122C22×C4×C61C22×C411yescharacteristic
123C22×C4×C61C2×D411yescharacteristic
124C22×C4×C61C2×D411yescharacteristic
125C22×C4×C61C2×D411yescharacteristic
126C22×C4×C61C2×D411yescharacteristic
127C22×C4×C61C2×D411yescharacteristic
128C22×C4×C61C2×D411yescharacteristic
129C22×C4×C61C2×D411yescharacteristic
130C22×C4×C61C2×D411yescharacteristic
131C22×C4×C61C2×D411yescharacteristic
132C22×C4×C61C2×D411yescharacteristic
133C22×C4×C61#4111yescharacteristic
134C22×C4×C61#4111yescharacteristic
135C22×C4×C61#4111yescharacteristic
136C22×Dic61—22no—
137C22×Dic61—22no—
138C22×Dic61—22no—
139C22×Dic61—22no—
140C22×Dic61—41no—
141C22×Dic61—41no—
142C22×Dic61—41no—
143C22×Dic61—41no—
144C2×D244—22no—
145C2×D244—22no—
146C2×D244—22no—
147C2×D244—22no—
148C2×D244—22no—
149C2×D244—22no—
150C2×D244—22no—
151C2×D244—22no—
152C2×D244—22no—
153C2×D244—22no—
154C2×D244—22no—
155C2×D244—22no—
156C2×D244—22no—
157C2×D244—22no—
158C2×D244—22no—
159C2×D244—41no—
160C2×D244—41no—
161C2×D244—41no—
162C2×D244—41no—
163C2×D244—41no—
164C2×D244—41no—
165C2×D244—41no—
166C2×D244—41no—
167C2×D244—41no—
168C2×D244—41no—
169C2×D244—41no—
170C2×D244—41no—
171C2×D244C22⋊C414yes—
172C2×Dic122—22no—
173C2×Dic122—22no—
174C2×Dic122—22no—
175C2×Dic122—22no—
176C2×Dic122—22no—
177C2×Dic122—22no—
178C2×Dic122—22no—
179C2×Dic122—22no—
180C2×Dic122—22no—
181C2×Dic122—22no—
182C2×Dic122—22no—
183C2×Dic122—22no—
184C2×Dic122—22no—
185C2×Dic122—22no—
186C2×Dic122—22no—
187C2×Dic122—41no—
188C2×Dic122—41no—
189C2×Dic122—41no—
190C2×Dic122—41no—
191C2×Dic122—41no—
192C2×Dic122—41no—
193C2×Dic122—41no—
194C2×Dic122—41no—
195C2×Dic122—41no—
196C2×Dic122—41no—
197C2×Dic122—41no—
198C2×Dic122—41no—
199C2×Dic122C22⋊C414yes—
200M16×C61—22no—
201M16×C61—22no—
202M16×C61—22no—
203M16×C61—22no—
204M16×C61—41no—
205M16×C61—41no—
206M16×C61—41no—
207M16×C61—41no—
208C2×C8×C61—22no—
209C2×C8×C61—22no—
210C2×C8×C61—22no—
211C2×C8×C61—22no—
212C2×C8×C61—22no—
213C2×C8×C61—22no—
214C2×C8×C61—22no—
215C2×C8×C61—22no—
216C2×C8×C61—41no—
217C2×C8×C61—41no—
218C2×C8×C61—41no—
219C2×C8×C61—41no—
220C2×C8×C61C22⋊C414yes—
221C22⋊Dic61—41no—
222C22⋊Dic61—41no—
223C4⋊Dic61—22no—
224C4⋊Dic61—22no—
225C4×Dic61—41no—
226C4×Dic61—41no—
227#11758194—22no—
228#11758194—22no—
229#11758194—41no—
230#11758194—41no—
231C2×#92418—22no—
232C2×#92418—41no—
233C2×#92418—41no—
234#11758190—232no—
235C23×C61—24no—
236C23×C61C4×D411yescharacteristic
237C23×C61#12111yescharacteristic
238C23×C61#12111yescharacteristic
239C23×C61#12111yescharacteristic
240C23×C61#12311yescharacteristic
241C23×C61#12311yescharacteristic
242C23×C61#12411yescharacteristic
243C22×D61—24no—
244C22×D61—42no—
245C22×D61—42no—
246C22×D61—42no—
247C22×D61—42no—
248C22×D61—42no—
249C22×D61—42no—
250C22×D61—84no—
251C22×D61—84no—
252C22×D61—84no—
253C22×D61—84no—
254C22×D61—84no—
255C22×D61—84no—
256C22×D61—84no—
257C2×C4×C61C2×C22⋊C411yescharacteristic
258C2×C4×C61C2×C22⋊C411yescharacteristic
259C2×C4×C61C2×C22⋊C411yescharacteristic
260C2×C4×C61C4×D411yescharacteristic
261C2×C4×C61C4×D411yescharacteristic
262C2×C4×C61C4×D411yescharacteristic
263C2×C4×C61#12011yescharacteristic
264C2×C4×C61#12011yescharacteristic
265C2×C4×C61#12011yescharacteristic
266C2×C4×C61#12011yescharacteristic
267C2×C4×C61#12011yescharacteristic
268C2×C4×C61#12011yescharacteristic
269C2×C4×C61#12011yescharacteristic
270C2×C4×C61#12011yescharacteristic
271C2×C4×C61#12111yescharacteristic
272C2×C4×C61#12111yescharacteristic
273C2×C4×C61#12111yescharacteristic
274C2×C4×C61#12111yescharacteristic
275C2×C4×C61#12111yescharacteristic
276C2×C4×C61#12111yescharacteristic
277C2×C4×C61#12111yescharacteristic
278C2×C4×C61#12111yescharacteristic
279C2×C4×C61#12111yescharacteristic
280C2×C4×C61#12311yescharacteristic
281C2×C4×C61#12311yescharacteristic
282C2×C4×C61#12411yescharacteristic
283C2×C4×C61#12711yescharacteristic
284C2×C4×C61#12711yescharacteristic
285C2×Dic61—24no—
286C2×Dic61—42no—
287C2×Dic61—42no—
288C2×Dic61—42no—
289C2×Dic61—42no—
290C2×Dic61—42no—
291C2×Dic61—42no—
292C2×Dic61—42no—
293C2×Dic61—44no—
294D244—24no—
295D244—24no—
296D244—42no—
297D244—42no—
298D244—42no—
299D244—42no—
300D244—42no—
301D244—42no—
302Dic122—24no—
303Dic122—24no—
304Dic122—42no—
305Dic122—42no—
306Dic122—42no—
307Dic122—42no—
308Dic122—42no—
309Dic122—42no—
310C8×C61—24no—
311C8×C61—42no—
312C8×C61—42no—
313#92418—42no—
314#11028—611nomaximal, Sylow
315C22×C61—22no—
316C22×C61—22no—
317C22×C61—22no—
318C22×C61—22no—
319C22×C61—22no—
320C22×C61—22no—
321C22×C61#38611yescharacteristic
322C22×C61#38611yescharacteristic
323C22×C61#39011yescharacteristic
324C22×C61#39211yescharacteristic
325C22×C61#39411yescharacteristic
326C22×C61#39411yescharacteristic
327C22×C61#39411yescharacteristic
328C22×C61#47114yes—
329C2×D61—44no—
330C2×D61—84no—
331C2×D61—84no—
332C2×D61—84no—
333C2×D61—84no—
334C2×D61—84no—
335C2×D61—84no—
336C2×D61—84no—
337C4×C61#37911yescharacteristic
338C4×C61#38611yescharacteristic
339C4×C61#38611yescharacteristic
340C4×C61#39011yescharacteristic
341C4×C61#39211yescharacteristic
342C4×C61#39211yescharacteristic
343C4×C61#39211yescharacteristic
344C4×C61#39411yescharacteristic
345Dic61—44no—
346Dic61—82no—
347C23×SD16—611no—
348C2×#419—611no—
349C2×#418—611no—
350C22×#101—611no—
351C22×#100—611no—
352C2×#341D6111yescharacteristic, complemented
353#1729—611no—
354C2×C61—21no—
355C2×C61—21no—
356C2×C61—21no—
357C2×C61—21no—
358C2×C61#143811yescharacteristic
359C2×C61#197712yes—
360C2×C61#201912yes—
361C2×C61#204612yes—
362D61—84no—
363C23×Q8—611no—
364C23×D4—611no—
365C22×SD16—614no—
366C22×SD16—1222no—
367C22×SD16—1222no—
368C22×SD16—1222no—
369C22×SD16—1222no—
370C22×SD16—1222no—
371C22×SD16—1222no—
372C22×M16—611no—
373C22×M16C2×D6111yescharacteristic
374C22×M16C2×D6111yescharacteristic
375C23×C8C2×D6111yescharacteristic
376C2×#117—611no—
377#419—1222no—
378#419—1222no—
379#418—1222no—
380#418—1222no—
381C2×#103—1222no—
382C2×#102—1222no—
383C2×#101—1222no—
384C2×#101—1222no—
385C2×#101—1222no—
386C2×#100—1222no—
387C2×#100—1222no—
388C2×#100—1222no—
389#341—22no—
390#336—1222no—
391C61#1102811yescharacteristic, complemented, Sylow
392C25—1221no—
393C22×Q8—612no—
394C22×Q8—612no—
395C22×Q8—612no—
396C22×Q8—1221no—
397C22×Q8—1221no—
398C22×Q8—1221no—
399C22×Q8—1221no—
400C22×Q8—1221no—
401C22×Q8—1221no—
402C22×Q8—1221no—
403C22×Q8—1221no—
404C22×Q8—1221no—
405C22×Q8—1221no—
406C22×Q8—1221no—
407C22×D4—612no—
408C22×D4—612no—
409C22×D4—612no—
410C22×D4—1221no—
411C22×D4—1221no—
412C22×D4—1221no—
413C22×D4—1221no—
414C22×D4—1221no—
415C22×D4—1221no—
416C22×D4—1221no—
417C22×D4—1221no—
418C22×D4—1221no—
419C22×D4—1221no—
420C22×D4—1221no—
421C23×C4—1221no—
422C23×C4C22×D6111yescharacteristic
423C2×SD16—1228no—
424C2×SD16—1228no—
425C2×SD16—1228no—
426C2×SD16—1228no—
427C2×SD16—1228no—
428C2×SD16—1228no—
429C2×SD16—1228no—
430C2×M16—21no—
431C2×M16—21no—
432C2×M16—21no—
433C2×M16—21no—
434C2×M16—21no—
435C2×M16—21no—
436C2×M16—21no—
437C2×M16—21no—
438C2×M16—21no—
439C2×M16—21no—
440C2×M16—612no—
441C2×M16—1221no—
442C2×M16—1221no—
443C2×M16—1221no—
444C2×M16—1221no—
445C2×M16—1221no—
446C2×M16D24412yes—
447C2×M16D24412yes—
448C22×C8—21no—
449C22×C8—21no—
450C22×C8—21no—
451C22×C8—21no—
452C22×C8—21no—
453C22×C8—21no—
454C22×C8—1221no—
455C22×C8C4×D6112yes—
456C22×C8D24412yes—
457C22×C8C22⋊D6112yes—
458#117—1221no—
459#117—1221no—
460#117—1221no—
461#117—1221no—
462C2×C4⋊C4—612no—
463C2×C22⋊C4—1221no—
464C2×C42—1221no—
465#103—1228no—
466#102—1228no—
467#101—1228no—
468#100—1228no—
469C24—1222no—
470C24—1222no—
471C24—1222no—
472C24—4884no—
473C24—2441no—
474C24—2441no—
475C24—2441no—
476C24—2441no—
477C24#1175822611yescharacteristic
478C2×Q8—614no—
479C2×Q8—1222no—
480C2×Q8—1222no—
481C2×Q8—1222no—
482C2×Q8—1222no—
483C2×Q8—1222no—
484C2×Q8—1222no—
485C2×Q8—1222no—
486C2×Q8—1222no—
487C2×Q8—1222no—
488C2×Q8—1222no—
489C2×Q8—1222no—
490C2×Q8—1222no—
491C2×Q8—1222no—
492C2×Q8—1222no—
493C2×Q8—1222no—
494C2×Q8—2441no—
495C2×Q8—2441no—
496C2×Q8—2441no—
497C2×Q8—2441no—
498C2×Q8—2441no—
499C2×Q8—2441no—
500C2×Q8—2441no—
501C2×Q8—2441no—
502C2×Q8—2441no—
503C2×Q8—2441no—
504C2×Q8—2441no—
505C2×Q8—2441no—
506C2×D4—614no—
507C2×D4—1222no—
508C2×D4—1222no—
509C2×D4—1222no—
510C2×D4—1222no—
511C2×D4—1222no—
512C2×D4—1222no—
513C2×D4—1222no—
514C2×D4—1222no—
515C2×D4—1222no—
516C2×D4—1222no—
517C2×D4—1222no—
518C2×D4—1222no—
519C2×D4—1222no—
520C2×D4—1222no—
521C2×D4—1222no—
522C2×D4—2441no—
523C2×D4—2441no—
524C2×D4—2441no—
525C2×D4—2441no—
526C2×D4—2441no—
527C2×D4—2441no—
528C2×D4—2441no—
529C2×D4—2441no—
530C2×D4—2441no—
531C2×D4—2441no—
532C2×D4—2441no—
533C2×D4—2441no—
534C22×C4—1222no—
535C22×C4—1222no—
536C22×C4—1222no—
537C22×C4—1222no—
538C22×C4—2441no—
539C22×C4—2441no—
540C22×C4—2441no—
541C22×C4—2441no—
542C22×C4C2×C4×D6111yescharacteristic
543C22×C4C2×D24411yescharacteristic
544C22×C4C2×D24411yescharacteristic
545C22×C4C2×D24411yescharacteristic
546C22×C4#1175822211yescharacteristic
547C22×C4#1175822211yescharacteristic
548C22×C4D4×D6111yescharacteristic
549C22×C4D4×D6111yescharacteristic
550C22×C4D4×D6111yescharacteristic
551C22×C4D4×D6111yescharacteristic
552C22×C4D4×D6111yescharacteristic
553C22×C4D4×D6111yescharacteristic
554C22×C4#1175822611yescharacteristic
555C22×C4C2×C22⋊D6111yescharacteristic
556SD16—12232no—
557M16—22no—
558M16—22no—
559M16—22no—
560M16—22no—
561M16—41no—
562M16—41no—
563M16—41no—
564M16—41no—
565M16—1222no—
566M16—1222no—
567M16—2441no—
568M16—2441no—
569C2×C8—22no—
570C2×C8—22no—
571C2×C8—22no—
572C2×C8—22no—
573C2×C8—22no—
574C2×C8—22no—
575C2×C8—22no—
576C2×C8—22no—
577C2×C8—41no—
578C2×C8—41no—
579C2×C8—41no—
580C2×C8—41no—
581C2×C8—1222no—
582C2×C8—2441no—
583C2×C8—2441no—
584C2×C8#1175819814yes—
585C4⋊C4—1222no—
586C4⋊C4—1222no—
587C22⋊C4—2441no—
588C22⋊C4—2441no—
589C42—2441no—
590C42—2441no—
591C23—24no—
592C23—1224no—
593C23—4884no—
594C23—4884no—
595C23—4884no—
596C23—4884no—
597C23—4884no—
598C23—4884no—
599C23—4884no—
600C23—2442no—
601C23—2442no—
602C23—2442no—
603C23—2442no—
604C23—2442no—
605C23—2442no—
606C23#1451973911yescharacteristic
607C23#1451975211yescharacteristic
608C23#1451975211yescharacteristic
609C23#1451975211yescharacteristic
610C23#1451976211yescharacteristic
611C23#1451976211yescharacteristic
612C23#1451976611yescharacteristic
613Q8—1224no—
614Q8—1224no—
615Q8—2442no—
616Q8—2442no—
617Q8—2442no—
618Q8—2442no—
619Q8—2442no—
620Q8—2442no—
621D4—1224no—
622D4—1224no—
623D4—2442no—
624D4—2442no—
625D4—2442no—
626D4—2442no—
627D4—2442no—
628D4—2442no—
629C2×C4—1224no—
630C2×C4—2444no—
631C2×C4—2442no—
632C2×C4—2442no—
633C2×C4—2442no—
634C2×C4—2442no—
635C2×C4—2442no—
636C2×C4—2442no—
637C2×C4—2442no—
638C2×C4C22⋊C4×D6111yescharacteristic
639C2×C4C22⋊C4×D6111yescharacteristic
640C2×C4C2×#1175819811yescharacteristic
641C2×C4#1451973911yescharacteristic
642C2×C4C4×D24411yescharacteristic
643C2×C4C4×D24411yescharacteristic
644C2×C4#1451974511yescharacteristic
645C2×C4#1451974511yescharacteristic
646C2×C4#1451974711yescharacteristic
647C2×C4#1451974711yescharacteristic
648C2×C4#1451974711yescharacteristic
649C2×C4#1451974711yescharacteristic
650C2×C4#1451974711yescharacteristic
651C2×C4#1451974711yescharacteristic
652C2×C4#1451975011yescharacteristic
653C2×C4#1451975011yescharacteristic
654C2×C4#1451975011yescharacteristic
655C2×C4#1451975011yescharacteristic
656C2×C4#1451975111yescharacteristic
657C2×C4#1451975111yescharacteristic
658C2×C4#1451975211yescharacteristic
659C2×C4#1451975211yescharacteristic
660C2×C4#1451975211yescharacteristic
661C2×C4#1451976211yescharacteristic
662C2×C4#1451976211yescharacteristic
663C2×C4#1451976511yescharacteristic
664C2×C4#1451977311yescharacteristic
665C2×C4#1451977411yescharacteristic
666C8—24no—
667C8—42no—
668C8—42no—
669C8—2442no—
670C22—22no—
671C22—22no—
672C22—22no—
673C22—22no—
674C22—22no—
675C22—22no—
676C22—4884no—
677C22—4884no—
678C22—4884no—
679C22—4884no—
680C22—4884no—
681C22—4884no—
682C22—4884no—
683C22—2444no—
684C22#1683964011yescharacteristic
685C22#1683964011yescharacteristic
686C22#1683966311yescharacteristic
687C22#1683967211yescharacteristic
688C22#1683967911yescharacteristic
689C22#1683967911yescharacteristic
690C22#1683968011yescharacteristic
691C22#1684002614yes—
692C4—4882no—
693C4—2444no—
694C4#1683961711yescharacteristic
695C4#1683964011yescharacteristic
696C4#1683964011yescharacteristic
697C4#1683966411yescharacteristic
698C4#1683967111yescharacteristic
699C4#1683967111yescharacteristic
700C4#1683967211yescharacteristic
701C4#1683968011yescharacteristic
702C2—21no—
703C2—21no—
704C2—21no—
705C2—21no—
706C2—4884no—
707C2#2144405911yescharacteristic
708C2#2144672012yes—
709C2#2144693612yes—
710C2#2144708312yes—
subgroupG/H
centerC23#14519752
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC2×C61×#341C2
socleC23×C61#121
prime radicalC23×D244C22
cosocleC23×C4×C61C23
hypercenterC2×#341D61
hypocenterC61#11028
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#341

Complements

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

NH ≅ G/Ntype
2. C2×#16839772C2semidirect
4. C22×#14519695C2semidirect
6. #21445515C2semidirect
7. C2×C61×#341C2semidirect
16. C22×#11758190C4semidirect
352. C2×#341D61semidirect
391. C61#11028semidirect

Maximal subgroups

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

subgroupindex
C23×#117581902
C2×#168397722
C2×#168397682
C22×#145196952
C22×#145196932
#214455152
C2×C61×#3412
#1102861