Finite Group Databasebeta

← #29586370

Subgroups — #29586370

Order 15616.

1054 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839766C211yesmaximal, characteristic
2C22×#14519697C211yesmaximal, characteristic
3C22×#14519693C211yesmaximal, characteristic
4C2×#16839718C211yesmaximal, characteristic, complemented
5C2×#16839531C211yesmaximal, characteristic, complemented
6C2×#16839526C211yesmaximal, characteristic, complemented
7C61×#1736C211yesmaximal, characteristic, complemented
8C23×D244C2211yescharacteristic
9C22×#11758194C2211yescharacteristic
10C22×#11758194C2211yescharacteristic
11C23×#92418C2211yescharacteristic
12#16839766—22no—
13#16839766C414yescomplemented
14C2×#14519697—21no—
15C2×#14519697—21no—
16C2×#14519697—22no—
17C2×#14519697—22no—
18C2×#14519697C414yescomplemented
19C2×#14519693—22no—
20C2×#14519693—22no—
21C2×#14519693C414yescomplemented
22#16839718—22no—
23#16839718—22no—
24C2×#14519688—21no—
25C2×C4×#92418—21no—
26#16839531—22no—
27#16839526—22no—
28C22×M16×C61C2211yescharacteristic
29C2×#117×C61C2211yescharacteristic
30C22×C4⋊C4×C61C2211yescharacteristic
31C61×#340—22no—
32C24×D61—21no—
33C22×D244—21no—
34C22×D244—21no—
35C22×D244—21no—
36C22×D244—21no—
37C22×D244—21no—
38C22×D244—21no—
39C22×D244—21no—
40C22×D244—21no—
41C22×D244—21no—
42C22×D244—21no—
43C22×D244—21no—
44C22×D244C2×C412yes—
45C22×D244C2×C412yes—
46C22×D244C2×C412yes—
47C2×#11758194—21no—
48C2×#11758194—21no—
49C2×#11758194—21no—
50C2×#11758194—21no—
51C2×#11758194—21no—
52C2×#11758194—21no—
53C2×#11758194—21no—
54C2×#11758194—21no—
55C2×#11758194C2×C412yes—
56C2×#11758194C2×C412yes—
57C2×#11758194D412yes—
58C2×#11758194D412yes—
59C22×#92418—21no—
60C22×#92418—21no—
61C22×#92418—21no—
62C22×#92418—21no—
63C22×#92418—21no—
64C22×#92418—21no—
65C22×#92418C2×C412yes—
66C22×#92418D411yescharacteristic
67C22×#92418D411yescharacteristic
68C22×#92418D412yes—
69#14519697—28no—
70#14519697—24no—
71#14519697—24no—
72#14519693—28no—
73#14519688—24no—
74C4×#92418—24no—
75C23×C4×C61—21no—
76C23×C4×C61C2311yescharacteristic
77C2×M16×C61—21no—
78C2×M16×C61—21no—
79C2×M16×C61—21no—
80C2×M16×C61—21no—
81C2×M16×C61—21no—
82C2×M16×C61C2×C412yes—
83C22×C8×C61—21no—
84#117×C61—21no—
85#117×C61—21no—
86#117×C61C2×C412yes—
87#117×C61D412yes—
88C2×C4⋊C4×C61—21no—
89C2×C4⋊C4×C61—21no—
90C2×C4⋊C4×C61—21no—
91C2×C4⋊C4×C61—21no—
92C2×C4⋊C4×C61—21no—
93C2×C4⋊C4×C61C2×C412yes—
94C2×C4⋊C4×C61D412yes—
95C2×C22⋊C4×C61—21no—
96C2×C42×C61—21no—
97C24×C61#4111yescharacteristic
98C23×D61—22no—
99C23×D61—22no—
100C23×D61—22no—
101C23×D61—41no—
102C23×D61—41no—
103C23×D61—41no—
104C23×D61—41no—
105C23×D61—82no—
106C23×D61—82no—
107C22×C4×C61—22no—
108C22×C4×C61—22no—
109C22×C4×C61—41no—
110C22×C4×C61—41no—
111C22×C4×C61—82no—
112C22×C4×C61C22×C411yescharacteristic
113C22×C4×C61C22×C411yescharacteristic
114C22×C4×C61C22×C411yescharacteristic
115C22×C4×C61C2×D411yescharacteristic
116C22×C4×C61C2×D411yescharacteristic
117C22×C4×C61C2×D411yescharacteristic
118C22×C4×C61C2×D411yescharacteristic
119C22×C4×C61C2×D411yescharacteristic
120C22×C4×C61C2×D411yescharacteristic
121C22×C4×C61#4111yescharacteristic
122C22×C4×C61#4111yescharacteristic
123C22×C4×C61#4111yescharacteristic
124C22×C4×C61#4111yescharacteristic
125C22×C4×C61#4111yescharacteristic
126C2×D244—22no—
127C2×D244—22no—
128C2×D244—22no—
129C2×D244—22no—
130C2×D244—22no—
131C2×D244—22no—
132C2×D244—22no—
133C2×D244—22no—
134C2×D244—22no—
135C2×D244—22no—
136C2×D244—22no—
137C2×D244—22no—
138C2×D244—22no—
139C2×D244—22no—
140C2×D244—22no—
141C2×D244—41no—
142C2×D244—41no—
143C2×D244—41no—
144C2×D244—41no—
145C2×D244—41no—
146C2×D244—41no—
147C2×D244—41no—
148C2×D244—41no—
149C2×D244—41no—
150C2×D244—41no—
151C2×D244—41no—
152C2×D244—41no—
153C2×D244C4214yes—
154M16×C61—22no—
155M16×C61—22no—
156M16×C61—41no—
157M16×C61—41no—
158C2×C8×C61—22no—
159C2×C8×C61—41no—
160C2×C8×C61—41no—
161C4⋊C4×C61—22no—
162C4⋊C4×C61—22no—
163C4⋊C4×C61—22no—
164C4⋊C4×C61—41no—
165C4⋊C4×C61—41no—
166C4⋊C4×C61C22⋊C414yes—
167C22⋊C4×C61—22no—
168C22⋊C4×C61—22no—
169C42×C61—22no—
170C42×C61—22no—
171#11758194—22no—
172#11758194—22no—
173#11758194—22no—
174#11758194—22no—
175#11758194—22no—
176#11758194—41no—
177#11758194—41no—
178#11758194C22⋊C414yes—
179C2×#92418—22no—
180C2×#92418—22no—
181C2×#92418—22no—
182C2×#92418—21no—
183C2×#92418—22no—
184C2×#92418—21no—
185C2×#92418—22no—
186C2×#92418—22no—
187C2×#92418—22no—
188C2×#92418—21no—
189C2×#92418—21no—
190C2×#92418—22no—
191C2×#92418—41no—
192C2×#92418—41no—
193C2×#92418C22⋊C412yes—
194C2×#92418C22⋊C412yes—
195C23×C61—22no—
196C23×C61—22no—
197C23×C61#11711yescharacteristic
198C23×C61C4×D411yescharacteristic
199C23×C61C4×D411yescharacteristic
200C23×C61#12111yescharacteristic
201C23×C61#12311yescharacteristic
202C23×C61#12411yescharacteristic
203C23×C61#12611yescharacteristic
204C22×D61—24no—
205C22×D61—42no—
206C22×D61—42no—
207C22×D61—42no—
208C22×D61—42no—
209C22×D61—42no—
210C22×D61—42no—
211C22×D61—84no—
212C22×D61—84no—
213C22×D61—82no—
214C22×D61—82no—
215C22×D61—82no—
216C22×D61—82no—
217C22×D61—84no—
218C22×D61—84no—
219C22×D61—82no—
220C22×D61—82no—
221C2×C4×C61—24no—
222C2×C4×C61—42no—
223C2×C4×C61—42no—
224C2×C4×C61—42no—
225C2×C4×C61—82no—
226C2×C4×C61—82no—
227C2×C4×C61—82no—
228C2×C4×C61C2×C4211yescharacteristic
229C2×C4×C61C2×C22⋊C411yescharacteristic
230C2×C4×C61C2×C22⋊C411yescharacteristic
231C2×C4×C61C2×C22⋊C411yescharacteristic
232C2×C4×C61#11711yescharacteristic
233C2×C4×C61#11711yescharacteristic
234C2×C4×C61C4×D411yescharacteristic
235C2×C4×C61C4×D411yescharacteristic
236C2×C4×C61C4×D411yescharacteristic
237C2×C4×C61C4×D411yescharacteristic
238C2×C4×C61C4×D411yescharacteristic
239C2×C4×C61C4×D411yescharacteristic
240C2×C4×C61C4×D411yescharacteristic
241C2×C4×C61C4×D411yescharacteristic
242C2×C4×C61C4×D411yescharacteristic
243C2×C4×C61C4×D411yescharacteristic
244C2×C4×C61#12011yescharacteristic
245C2×C4×C61#12111yescharacteristic
246C2×C4×C61#12111yescharacteristic
247C2×C4×C61#12111yescharacteristic
248C2×C4×C61#12111yescharacteristic
249C2×C4×C61#12111yescharacteristic
250C2×C4×C61#12311yescharacteristic
251C2×C4×C61#12311yescharacteristic
252C2×C4×C61#12411yescharacteristic
253C2×C4×C61#12411yescharacteristic
254C2×C4×C61#12611yescharacteristic
255C2×C4×C61#12711yescharacteristic
256D244—24no—
257D244—24no—
258D244—42no—
259D244—42no—
260D244—42no—
261D244—42no—
262D244—42no—
263D244—42no—
264C8×C61—42no—
265#92418—22no—
266#92418—22no—
267#92418—24no—
268#92418—42no—
269#10943—611nomaximal, Sylow
270C22×C61—22no—
271C22×C61—22no—
272C22×C61—22no—
273C22×C61—22no—
274C22×C61—21no—
275C22×C61—21no—
276C22×C61—21no—
277C22×C61—21no—
278C22×C61C4×C22⋊C411yescharacteristic
279C22×C61#38611yescharacteristic
280C22×C61#38811yescharacteristic
281C22×C61#38811yescharacteristic
282C22×C61#38811yescharacteristic
283C22×C61#38811yescharacteristic
284C22×C61#39011yescharacteristic
285C22×C61#47112yes—
286C22×C61#47212yes—
287C2×D61—44no—
288C2×D61—84no—
289C2×D61—84no—
290C2×D61—84no—
291C2×D61—84no—
292C2×D61—84no—
293C2×D61—82no—
294C2×D61—82no—
295C2×D61—84no—
296C4×C61—44no—
297C4×C61—82no—
298C4×C61C4×C22⋊C411yescharacteristic
299C4×C61C4×C22⋊C411yescharacteristic
300C4×C61#38611yescharacteristic
301C4×C61#38611yescharacteristic
302C4×C61#38811yescharacteristic
303C4×C61#38811yescharacteristic
304C4×C61#39011yescharacteristic
305C4×C61#39011yescharacteristic
306C2×#418—611no—
307C22×#102—611no—
308C22×#100—611no—
309C2×#405—611no—
310C2×#343—611no—
311C2×#341—611no—
312#1736D6111yescharacteristic, complemented
313C2×C61—21no—
314C2×C61—21no—
315C2×C61—21no—
316C2×C61—21no—
317C2×C61#143711yescharacteristic
318C2×C61#190712yes—
319C2×C61#193112yes—
320C2×C61#197711yescharacteristic
321C2×C61#197811yescharacteristic
322D61—84no—
323C23×D4—611no—
324C22×M16—611no—
325C22×M16—611no—
326C22×M16C2×D6111yescharacteristic
327C23×C8—611no—
328C2×#117C2×D6111yescharacteristic
329C22×C4⋊C4C2×D6111yescharacteristic
330#418—614no—
331#418—1222no—
332C2×#102—614no—
333C2×#102—1222no—
334C2×#102—1221no—
335C2×#102—1221no—
336C2×#102—1222no—
337C2×#100—614no—
338C2×#100—1222no—
339C2×#100—1222no—
340#405—1222no—
341#405—1222no—
342C2×#97—1221no—
343C2×C4×C8—1221no—
344#343—1222no—
345#341—1222no—
346#340—22no—
347C61#1094311yescharacteristic, complemented, Sylow
348C25—1221no—
349C22×D4—612no—
350C22×D4—612no—
351C22×D4—612no—
352C22×D4—1221no—
353C22×D4—1221no—
354C22×D4—1221no—
355C22×D4—1221no—
356C22×D4—1221no—
357C22×D4—1221no—
358C22×D4—1221no—
359C22×D4—1221no—
360C22×D4—1221no—
361C22×D4—1221no—
362C22×D4—1221no—
363C23×C4—21no—
364C23×C4C22×D6111yescharacteristic
365C2×M16—21no—
366C2×M16—21no—
367C2×M16—21no—
368C2×M16—21no—
369C2×M16—21no—
370C2×M16—612no—
371C2×M16—612no—
372C2×M16—612no—
373C2×M16—612no—
374C2×M16—1221no—
375C2×M16—1221no—
376C2×M16—1221no—
377C2×M16—1221no—
378C2×M16—1221no—
379C2×M16—1221no—
380C2×M16—1221no—
381C2×M16—1221no—
382C2×M16C4×D6112yes—
383C22×C8—21no—
384C22×C8—612no—
385C22×C8—612no—
386C22×C8—611no—
387C22×C8—611no—
388C22×C8—1221no—
389C22×C8—1221no—
390C22×C8—1221no—
391C22×C8—1221no—
392C22×C8—1221no—
393C22×C8—1221no—
394#117—21no—
395#117—21no—
396#117C4×D6112yes—
397#117D24412yes—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4C4×D6112yes—
404C2×C4⋊C4C22⋊D6112yes—
405C2×C22⋊C4—21no—
406C2×C42—21no—
407#102—1224no—
408#102—1224no—
409#102—1228no—
410#100—1228no—
411#97—1224no—
412C4×C8—1224no—
413C24—1222no—
414C24—1222no—
415C24—1222no—
416C24—4882no—
417C24—4882no—
418C24—2441no—
419C24—2441no—
420C24—2441no—
421C24—2441no—
422C24#1175822411yescharacteristic
423C2×D4—614no—
424C2×D4—1222no—
425C2×D4—1222no—
426C2×D4—1222no—
427C2×D4—1222no—
428C2×D4—1222no—
429C2×D4—1222no—
430C2×D4—1222no—
431C2×D4—1222no—
432C2×D4—1222no—
433C2×D4—1222no—
434C2×D4—1222no—
435C2×D4—1222no—
436C2×D4—1222no—
437C2×D4—1222no—
438C2×D4—1222no—
439C2×D4—2441no—
440C2×D4—2441no—
441C2×D4—2441no—
442C2×D4—2441no—
443C2×D4—2441no—
444C2×D4—2441no—
445C2×D4—2441no—
446C2×D4—2441no—
447C2×D4—2441no—
448C2×D4—2441no—
449C2×D4—2441no—
450C2×D4—2441no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4—82no—
456C22×C4C2×C4×D6111yescharacteristic
457C22×C4C2×C4×D6111yescharacteristic
458C22×C4C2×C4×D6111yescharacteristic
459C22×C4C2×D24411yescharacteristic
460C22×C4#1175822211yescharacteristic
461C22×C4#1175822211yescharacteristic
462C22×C4D4×D6111yescharacteristic
463C22×C4D4×D6111yescharacteristic
464C22×C4D4×D6111yescharacteristic
465C22×C4D4×D6111yescharacteristic
466C22×C4#1175822411yescharacteristic
467C22×C4#1175822611yescharacteristic
468C22×C4#1175822611yescharacteristic
469C22×C4C2×C22⋊D6111yescharacteristic
470M16—22no—
471M16—22no—
472M16—41no—
473M16—41no—
474M16—614no—
475M16—1222no—
476M16—1222no—
477M16—1222no—
478M16—1222no—
479M16—1222no—
480M16—2441no—
481M16—2441no—
482C2×C8—22no—
483C2×C8—41no—
484C2×C8—41no—
485C2×C8—612no—
486C2×C8—612no—
487C2×C8—1222no—
488C2×C8—1222no—
489C2×C8—1222no—
490C2×C8—1221no—
491C2×C8—1222no—
492C2×C8—1221no—
493C2×C8—1222no—
494C2×C8—1222no—
495C2×C8—1222no—
496C2×C8—1221no—
497C2×C8—1221no—
498C2×C8—1222no—
499C2×C8—2441no—
500C2×C8—2441no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—41no—
505C4⋊C4—41no—
506C4⋊C4#1175819814yes—
507C22⋊C4—22no—
508C22⋊C4—22no—
509C42—22no—
510C42—22no—
511C23—22no—
512C23—22no—
513C23—1224no—
514C23—4882no—
515C23—4882no—
516C23—4884no—
517C23—4884no—
518C23—4882no—
519C23—4882no—
520C23—4884no—
521C23—4884no—
522C23—4882no—
523C23—4882no—
524C23—2442no—
525C23—2442no—
526C23—2442no—
527C23—2442no—
528C23—2442no—
529C23—2442no—
530C23#1451973511yescharacteristic
531C23#1451973711yescharacteristic
532C23#1451973711yescharacteristic
533C23#1451974911yescharacteristic
534C23#1451976111yescharacteristic
535C23#1451976311yescharacteristic
536C23#1451977211yescharacteristic
537D4—1224no—
538D4—1224no—
539D4—2442no—
540D4—2442no—
541D4—2442no—
542D4—2442no—
543D4—2442no—
544D4—2442no—
545C2×C4—24no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—82no—
550C2×C4—82no—
551C2×C4—82no—
552C2×C4C42×D6111yescharacteristic
553C2×C4C22⋊C4×D6111yescharacteristic
554C2×C4C22⋊C4×D6111yescharacteristic
555C2×C4C2×#1175819811yescharacteristic
556C2×C4#1451973411yescharacteristic
557C2×C4#1451973511yescharacteristic
558C2×C4#1451973711yescharacteristic
559C2×C4#1451973711yescharacteristic
560C2×C4C4×C22⋊D6111yescharacteristic
561C2×C4C4×C22⋊D6111yescharacteristic
562C2×C4#1451973911yescharacteristic
563C2×C4#1451973911yescharacteristic
564C2×C4#1451973911yescharacteristic
565C2×C4#1451973911yescharacteristic
566C2×C4C4×D24411yescharacteristic
567C2×C4C4×D24411yescharacteristic
568C2×C4#1451974711yescharacteristic
569C2×C4#1451974911yescharacteristic
570C2×C4#1451975011yescharacteristic
571C2×C4#1451975011yescharacteristic
572C2×C4#1451975211yescharacteristic
573C2×C4#1451975211yescharacteristic
574C2×C4#1451976211yescharacteristic
575C2×C4#1451976211yescharacteristic
576C2×C4#1451976311yescharacteristic
577C2×C4#1451976611yescharacteristic
578C2×C4#1451977211yescharacteristic
579C2×C4#1451977311yescharacteristic
580C8—42no—
581C8—1222no—
582C8—1222no—
583C8—1224no—
584C8—2442no—
585C22—21no—
586C22—21no—
587C22—21no—
588C22—21no—
589C22—22no—
590C22—22no—
591C22—22no—
592C22—22no—
593C22—4884no—
594C22—4884no—
595C22—4884no—
596C22—4884no—
597C22—4882no—
598C22—4882no—
599C22—4884no—
600C22—4884no—
601C22—2444no—
602C22#1683960911yescharacteristic
603C22#1683963911yescharacteristic
604C22#1683965111yescharacteristic
605C22#1683965211yescharacteristic
606C22#1683965411yescharacteristic
607C22#1683965411yescharacteristic
608C22#1683966211yescharacteristic
609C22#1684002712yes—
610C22#1684003012yes—
611C4—44no—
612C4—82no—
613C4#1683960911yescharacteristic
614C4C4×#1175819811yescharacteristic
615C4#1683964011yescharacteristic
616C4#1683964011yescharacteristic
617C4#1683965111yescharacteristic
618C4#1683965211yescharacteristic
619C4#1683966211yescharacteristic
620C4#1683966311yescharacteristic
621C2—21no—
622C2—21no—
623C2—21no—
624C2—21no—
625C2—4884no—
626C2#2144405511yescharacteristic
627C2#2144632512yes—
628C2#2144648012yes—
629C2#2144672111yescharacteristic
630C2#2144672811yescharacteristic
subgroupG/H
centerC23#14519749
commutatorC2×C4×C61C2×C42
FrattiniC23×C4C22×D61
FittingC61×#1736C2
socleC23×C61#121
prime radicalC23×D244C22
cosocleC23×C4×C61C23
hypercenter#1736D61
hypocenterC61#10943
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
4. C2×#16839718C2semidirect
5. C2×#16839531C2semidirect
6. C2×#16839526C2semidirect
7. C61×#1736C2semidirect
13. #16839766C4semidirect
18. C2×#14519697C4semidirect
21. C2×#14519693C4semidirect
312. #1736D61semidirect
347. C61#10943semidirect

Maximal subgroups

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

subgroupindex
C2×#168397662
C22×#145196972
C22×#145196932
C2×#168397182
C2×#168395312
C2×#168395262
C61×#17362
#1094361