Finite Group Databasebeta

← #29586269

Subgroups — #29586269

Order 15616.

1074 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519705C211yesmaximal, characteristic
2C22×#14519703C211yesmaximal, characteristic
3#21448307C211yesmaximal, characteristic
4C2×#16839608C211yesmaximal, characteristic, complemented
5C2×#16839521C211yesmaximal, characteristic, complemented
6#21445512C211yesmaximal, characteristic, complemented
7C2×C61×#339C211yesmaximal, characteristic, complemented
8C22×#11758222C2211yescharacteristic
9C22×#11758194C2211yescharacteristic
10C22×C4×Dic61C2211yescharacteristic
11C22×C4×Dic61C2211yescharacteristic
12C2×#14519705—22no—
13C2×#14519705—22no—
14C2×#14519705C414yescomplemented
15C2×#14519703—22no—
16C2×#14519703—22no—
17C2×#14519703C414yescomplemented
18#16839667C412yescomplemented
19#16839663C412yescomplemented
20#16839639—22no—
21C4×#11758198—22no—
22#16839608—22no—
23#16839608—22no—
24C2×#14519684—22no—
25#16839521—22no—
26#16839516—22no—
27C22×M16×C61C2211yescharacteristic
28C2×#117×C61C2211yescharacteristic
29C22×C42×C61C2211yescharacteristic
30C61×#339—22no—
31C2×#11758222—21no—
32C2×#11758222—21no—
33C2×#11758222—21no—
34C2×#11758222—21no—
35C2×#11758222—21no—
36C2×#11758222—21no—
37C2×#11758222—21no—
38C2×#11758222—21no—
39C2×#11758222—21no—
40C2×#11758222—21no—
41C2×#11758222C2×C412yes—
42C2×#11758222C2×C412yes—
43C22×Dic122C2×C411yescharacteristic
44C22×D244C2×C411yescharacteristic
45C22×C22⋊D61—21no—
46C23×Dic61—21no—
47C23×Dic61D412yes—
48C22×C4×D61—21no—
49C2×#11758194—21no—
50C2×#11758194—21no—
51C2×#11758194—21no—
52C2×#11758194—21no—
53C2×#11758194—21no—
54C2×#11758194C2×C412yes—
55C22×#92418—21no—
56C2×#11758198—24no—
57C2×C4×Dic61—21no—
58C2×C4×Dic61—21no—
59C2×C4×Dic61—21no—
60C2×C4×Dic61—21no—
61C2×C4×Dic61—21no—
62C2×C4×Dic61—21no—
63C2×C4×Dic61—21no—
64C2×C4×Dic61C2×C412yes—
65C2×C4×Dic61C2×C412yes—
66C2×C4×Dic61D412yes—
67C2×C4×Dic61D412yes—
68C2×C4×Dic61D412yes—
69#14519705—28no—
70#14519703—28no—
71#14519684—28no—
72#14519684—24no—
73C23×C4×C61—21no—
74C23×C4×C61C2311yescharacteristic
75C2×M16×C61—21no—
76C2×M16×C61—21no—
77C2×M16×C61—21no—
78C2×M16×C61—21no—
79C2×M16×C61—21no—
80C2×M16×C61C2×C412yes—
81C22×C8×C61—21no—
82#117×C61—21no—
83#117×C61—21no—
84#117×C61—21no—
85#117×C61—21no—
86C2×C4⋊C4×C61C2×C412yes—
87C2×C22⋊C4×C61—21no—
88C2×C42×C61—21no—
89C2×C42×C61—21no—
90C2×C42×C61—21no—
91C2×C42×C61—21no—
92C2×C42×C61C2×C412yes—
93C2×C42×C61D412yes—
94C2×C42×C61D412yes—
95C24×C61C2×D411yescharacteristic
96C23×D61—21no—
97C22×C4×C61—22no—
98C22×C4×C61—22no—
99C22×C4×C61—22no—
100C22×C4×C61—22no—
101C22×C4×C61—44no—
102C22×C4×C61C22×C411yescharacteristic
103C22×C4×C61C22×C411yescharacteristic
104C22×C4×C61C22×C411yescharacteristic
105C22×C4×C61C2×D411yescharacteristic
106C22×C4×C61C2×D411yescharacteristic
107C22×C4×C61C2×D411yescharacteristic
108C22×C4×C61C2×D411yescharacteristic
109C22×C4×C61C2×D411yescharacteristic
110C22×C4×C61#4111yescharacteristic
111C22×C4×C61#4111yescharacteristic
112C22×C4×C61#4111yescharacteristic
113C22×C4×C61#4111yescharacteristic
114C22×C4×C61#4111yescharacteristic
115C22×C4×C61#4111yescharacteristic
116C2×C22⋊D61—22no—
117C2×C22⋊D61—22no—
118C2×C22⋊D61—41no—
119C2×C22⋊D61—41no—
120C2×C22⋊D61—41no—
121C2×C22⋊D61—41no—
122C22×Dic61—21no—
123C22×Dic61—22no—
124C22×Dic61—22no—
125C22×Dic61—22no—
126C22×Dic61—22no—
127C22×Dic61—22no—
128C22×Dic61—44no—
129C22×Dic61—44no—
130C22×Dic61C22⋊C414yes—
131#11758222—22no—
132#11758222—22no—
133#11758222—22no—
134#11758222—22no—
135#11758222—22no—
136#11758222—22no—
137#11758222—22no—
138#11758222—22no—
139#11758222—41no—
140#11758222—41no—
141#11758222—41no—
142#11758222—41no—
143#11758222—41no—
144#11758222—41no—
145#11758222—41no—
146#11758222—41no—
147C2×D244—21no—
148C2×D244—21no—
149C2×D244—21no—
150C2×D244—21no—
151C2×D244—21no—
152C2×D244C4212yes—
153C2×C4×D61—22no—
154C2×C4×D61—22no—
155C2×C4×D61—41no—
156C2×C4×D61—41no—
157C2×C4×D61—41no—
158C2×C4×D61—41no—
159C2×Dic122—21no—
160C2×Dic122—21no—
161C2×Dic122—21no—
162C2×Dic122—21no—
163C2×Dic122—21no—
164C2×Dic122C4212yes—
165M16×C61—22no—
166M16×C61—22no—
167M16×C61—41no—
168M16×C61—41no—
169C2×C8×C61—22no—
170C2×C8×C61—41no—
171C2×C8×C61—41no—
172C4⋊C4×C61—22no—
173C4⋊C4×C61—22no—
174C22⋊C4×C61—41no—
175C22⋊C4×C61—41no—
176C42×C61—22no—
177C42×C61—22no—
178C42×C61—22no—
179C42×C61—41no—
180C42×C61—41no—
181C42×C61C22⋊C414yescomplemented
182#11758198—48no—
183C4×Dic61—22no—
184C4×Dic61—22no—
185C4×Dic61—22no—
186C4×Dic61—22no—
187C4×Dic61—22no—
188C4×Dic61—22no—
189C4×Dic61—22no—
190C4×Dic61C22⋊C414yescomplemented
191#11758194—22no—
192#11758194—22no—
193#11758194—41no—
194#11758194—41no—
195C2×#92418—22no—
196C2×#92418—41no—
197C2×#92418—41no—
198C23×C61—24no—
199C23×C61C2×C22⋊C411yescharacteristic
200C23×C61C4×D411yescharacteristic
201C23×C61C4×D411yescharacteristic
202C23×C61#12011yescharacteristic
203C23×C61#12111yescharacteristic
204C23×C61#12111yescharacteristic
205C23×C61#12311yescharacteristic
206C22×D61—22no—
207C22×D61—41no—
208C22×D61—41no—
209C22×D61—44no—
210C2×C4×C61—24no—
211C2×C4×C61—44no—
212C2×C4×C61—44no—
213C2×C4×C61—44no—
214C2×C4×C61—42no—
215C2×C4×C61—44no—
216C2×C4×C61C2×C4211yescharacteristic
217C2×C4×C61C2×C22⋊C411yescharacteristic
218C2×C4×C61C2×C22⋊C411yescharacteristic
219C2×C4×C61#11711yescharacteristic
220C2×C4×C61#11711yescharacteristic
221C2×C4×C61#11711yescharacteristic
222C2×C4×C61C4×D411yescharacteristic
223C2×C4×C61C4×D411yescharacteristic
224C2×C4×C61C4×D411yescharacteristic
225C2×C4×C61C4×D411yescharacteristic
226C2×C4×C61C4×D411yescharacteristic
227C2×C4×C61C4×D411yescharacteristic
228C2×C4×C61C4×D411yescharacteristic
229C2×C4×C61C4×D411yescharacteristic
230C2×C4×C61C4×D411yescharacteristic
231C2×C4×C61C4×D411yescharacteristic
232C2×C4×C61#12111yescharacteristic
233C2×C4×C61#12111yescharacteristic
234C2×C4×C61#12111yescharacteristic
235C2×C4×C61#12111yescharacteristic
236C2×C4×C61#12311yescharacteristic
237C2×C4×C61#12311yescharacteristic
238C2×C4×C61#12411yescharacteristic
239C2×C4×C61#12411yescharacteristic
240C2×C4×C61#12411yescharacteristic
241C2×C4×C61#12611yescharacteristic
242C2×C4×C61#12611yescharacteristic
243C2×C4×C61#12711yescharacteristic
244C22⋊D61—42no—
245C22⋊D61—42no—
246C22⋊D61—42no—
247C22⋊D61—42no—
248C2×Dic61—22no—
249C2×Dic61—24no—
250C2×Dic61—24no—
251C2×Dic61—24no—
252C2×Dic61—24no—
253C2×Dic61—44no—
254C2×Dic61—44no—
255C2×Dic61—44no—
256C2×Dic61—44no—
257C2×Dic61—44no—
258C2×Dic61—41no—
259C2×Dic61—41no—
260D244—22no—
261D244—22no—
262D244—41no—
263D244—41no—
264C4×D61—42no—
265C4×D61—42no—
266C4×D61—42no—
267C4×D61—42no—
268Dic122—22no—
269Dic122—22no—
270Dic122—41no—
271Dic122—41no—
272C8×C61—42no—
273#92418—42no—
274#10924—611nomaximal, Sylow
275C22×C61—22no—
276C22×C61—22no—
277C22×C61—22no—
278C22×C61—22no—
279C22×C61—22no—
280C22×C61—22no—
281C22×C61C4×C22⋊C411yescharacteristic
282C22×C61#38611yescharacteristic
283C22×C61#38611yescharacteristic
284C22×C61#38611yescharacteristic
285C22×C61#38811yescharacteristic
286C22×C61#38811yescharacteristic
287C22×C61#39011yescharacteristic
288C22×C61#42114yes—
289C2×D61—42no—
290C2×D61—44no—
291C2×D61—82no—
292C2×D61—82no—
293C4×C61—44no—
294C4×C61—82no—
295C4×C61C4×C22⋊C411yescharacteristic
296C4×C61C4×C22⋊C411yescharacteristic
297C4×C61#38811yescharacteristic
298C4×C61#38811yescharacteristic
299C4×C61#38811yescharacteristic
300C4×C61#38811yescharacteristic
301C4×C61#39011yescharacteristic
302C4×C61#39011yescharacteristic
303Dic61—44no—
304Dic61—44no—
305Dic61—42no—
306C22×#104—611no—
307C22×#104—611no—
308#2297—611no—
309C2×#376—611no—
310C2×#339—611no—
311C2×#339D6111yescharacteristic, complemented
312#1728—611no—
313C2×C61—21no—
314C2×C61—21no—
315C2×C61—21no—
316C2×C61—21no—
317C2×C61#143711yescharacteristic
318C2×C61#175912yes—
319C2×C61#189712yes—
320C2×C61#196312yes—
321D61—82no—
322C22×#41—611no—
323C22×M16—611no—
324C22×M16C2×D6111yescharacteristic
325C2×#117C2×D6111yescharacteristic
326C22×C42—611no—
327C22×C42—611no—
328C22×C42C2×D6111yescharacteristic
329C2×#104—614no—
330C2×#104—614no—
331C2×#104—1222no—
332C2×#104—1222no—
333C2×#104—1222no—
334C2×#104—1222no—
335#391—612no—
336#390—612no—
337#386—1222no—
338C4×C22⋊C4—1222no—
339#376—1222no—
340#376—1222no—
341C2×#95—1222no—
342#339—22no—
343#339—1222no—
344#336—1222no—
345C61#1092411yescharacteristic, complemented, Sylow
346C2×#41—612no—
347C2×#41—612no—
348C2×#41—1221no—
349C2×#41—1221no—
350C2×#41—1221no—
351C2×#41—1221no—
352C2×#41—1221no—
353C2×#41—1221no—
354C2×#41—1221no—
355C2×#41—1221no—
356C2×#41—1221no—
357C2×#41—1221no—
358C22×Q8—611no—
359C22×D4—611no—
360C22×D4—1221no—
361C23×C4—21no—
362C23×C4—612no—
363C23×C4—1221no—
364C23×C4—1221no—
365C23×C4C22×D6111yescharacteristic
366C2×M16—21no—
367C2×M16—21no—
368C2×M16—21no—
369C2×M16—21no—
370C2×M16—21no—
371C2×M16—612no—
372C2×M16—1221no—
373C2×M16—1221no—
374C2×M16—1221no—
375C2×M16—1221no—
376C2×M16—1221no—
377C2×M16C4×D6112yes—
378C22×C8—21no—
379C22×C8—1221no—
380#117—21no—
381#117—21no—
382#117—21no—
383#117—21no—
384C2×C4⋊C4C4×D6112yes—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—1224no—
387C2×C42—21no—
388C2×C42—21no—
389C2×C42—21no—
390C2×C42—21no—
391C2×C42—612no—
392C2×C42—612no—
393C2×C42—612no—
394C2×C42—612no—
395C2×C42—612no—
396C2×C42—1221no—
397C2×C42—1221no—
398C2×C42—1221no—
399C2×C42—1221no—
400C2×C42—1221no—
401C2×C42—1221no—
402C2×C42—1221no—
403C2×C42C4×D6112yes—
404C2×C42D24412yes—
405C2×C42C22⋊D6112yes—
406#104—1228no—
407#104—1228no—
408#95—1224no—
409#95—1228no—
410C24—1221no—
411C24D4×D6111yescharacteristic
412#41—1222no—
413#41—1222no—
414#41—1222no—
415#41—1222no—
416#41—1222no—
417#41—1222no—
418#41—1222no—
419#41—1222no—
420#41—2441no—
421#41—2441no—
422#41—2441no—
423#41—2441no—
424#41—2441no—
425#41—2441no—
426#41—2441no—
427#41—2441no—
428C2×Q8—612no—
429C2×Q8—1221no—
430C2×Q8—1221no—
431C2×Q8—1221no—
432C2×Q8—1221no—
433C2×Q8—1221no—
434C2×D4—612no—
435C2×D4—1222no—
436C2×D4—1222no—
437C2×D4—1221no—
438C2×D4—1221no—
439C2×D4—1221no—
440C2×D4—1221no—
441C2×D4—1221no—
442C2×D4—2441no—
443C2×D4—2441no—
444C2×D4—2441no—
445C2×D4—2441no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—44no—
451C22×C4—614no—
452C22×C4—1221no—
453C22×C4—1222no—
454C22×C4—1222no—
455C22×C4—1222no—
456C22×C4—1222no—
457C22×C4—1222no—
458C22×C4—1222no—
459C22×C4—1222no—
460C22×C4—2444no—
461C22×C4—2444no—
462C22×C4—2441no—
463C22×C4—2441no—
464C22×C4—2441no—
465C22×C4—2441no—
466C22×C4C2×C4×D6111yescharacteristic
467C22×C4C2×C4×D6111yescharacteristic
468C22×C4C2×C4×D6111yescharacteristic
469C22×C4C2×D24411yescharacteristic
470C22×C4#1175822211yescharacteristic
471C22×C4#1175822211yescharacteristic
472C22×C4D4×D6111yescharacteristic
473C22×C4D4×D6111yescharacteristic
474C22×C4D4×D6111yescharacteristic
475C22×C4#1175822411yescharacteristic
476C22×C4#1175822411yescharacteristic
477C22×C4#1175822611yescharacteristic
478C22×C4#1175822611yescharacteristic
479C22×C4C2×C22⋊D6111yescharacteristic
480M16—22no—
481M16—22no—
482M16—41no—
483M16—41no—
484M16—1222no—
485M16—1222no—
486M16—2441no—
487M16—2441no—
488C2×C8—22no—
489C2×C8—41no—
490C2×C8—41no—
491C2×C8—1222no—
492C2×C8—2441no—
493C2×C8—2441no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C22⋊C4—41no—
497C22⋊C4—41no—
498C22⋊C4—2448no—
499C42—22no—
500C42—22no—
501C42—22no—
502C42—41no—
503C42—41no—
504C42—614no—
505C42—1222no—
506C42—1222no—
507C42—1222no—
508C42—1222no—
509C42—1222no—
510C42—1222no—
511C42—1222no—
512C42#1175819814yescomplemented
513C23—24no—
514C23—1222no—
515C23—2444no—
516C23—2441no—
517C23—2441no—
518C23C22⋊C4×D6111yescharacteristic
519C23#1451973711yescharacteristic
520C23#1451973911yescharacteristic
521C23#1451974711yescharacteristic
522C23#1451974911yescharacteristic
523C23#1451975011yescharacteristic
524C23#1451976211yescharacteristic
525Q8—1222no—
526Q8—1222no—
527Q8—2441no—
528Q8—2441no—
529D4—1222no—
530D4—1222no—
531D4—2442no—
532D4—2442no—
533D4—2442no—
534D4—2442no—
535D4—2441no—
536D4—2441no—
537C2×C4—24no—
538C2×C4—44no—
539C2×C4—44no—
540C2×C4—44no—
541C2×C4—44no—
542C2×C4—42no—
543C2×C4—1224no—
544C2×C4—1224no—
545C2×C4—1222no—
546C2×C4—1224no—
547C2×C4—1224no—
548C2×C4—2444no—
549C2×C4—2444no—
550C2×C4—2444no—
551C2×C4—2444no—
552C2×C4—2444no—
553C2×C4—2441no—
554C2×C4—2441no—
555C2×C4—2442no—
556C2×C4—2442no—
557C2×C4—2442no—
558C2×C4—2442no—
559C2×C4C42×D6111yescharacteristic
560C2×C4C22⋊C4×D6111yescharacteristic
561C2×C4C2×#1175819811yescharacteristic
562C2×C4#1451973411yescharacteristic
563C2×C4#1451973511yescharacteristic
564C2×C4#1451973511yescharacteristic
565C2×C4#1451973711yescharacteristic
566C2×C4#1451973711yescharacteristic
567C2×C4#1451973711yescharacteristic
568C2×C4C4×C22⋊D6111yescharacteristic
569C2×C4C4×C22⋊D6111yescharacteristic
570C2×C4#1451973911yescharacteristic
571C2×C4#1451973911yescharacteristic
572C2×C4#1451973911yescharacteristic
573C2×C4C4×D24411yescharacteristic
574C2×C4C4×D24411yescharacteristic
575C2×C4#1451974911yescharacteristic
576C2×C4#1451975011yescharacteristic
577C2×C4#1451975211yescharacteristic
578C2×C4#1451975211yescharacteristic
579C2×C4#1451976111yescharacteristic
580C2×C4#1451976211yescharacteristic
581C2×C4#1451976311yescharacteristic
582C2×C4#1451976311yescharacteristic
583C2×C4#1451976611yescharacteristic
584C2×C4#1451977211yescharacteristic
585C2×C4#1451977211yescharacteristic
586C2×C4#1451977311yescharacteristic
587C8—42no—
588C8—2442no—
589C22—22no—
590C22—22no—
591C22—22no—
592C22—22no—
593C22—22no—
594C22—22no—
595C22—4882no—
596C22—4882no—
597C22—2442no—
598C22—2444no—
599C22#1683960911yescharacteristic
600C22#1683963911yescharacteristic
601C22#1683964011yescharacteristic
602C22#1683964011yescharacteristic
603C22#1683965111yescharacteristic
604C22#1683965211yescharacteristic
605C22#1683966211yescharacteristic
606C22#1683977714yes—
607C4—44no—
608C4—82no—
609C4—2444no—
610C4—2444no—
611C4—2442no—
612C4#1683960911yescharacteristic
613C4C4×#1175819811yescharacteristic
614C4#1683965111yescharacteristic
615C4#1683965211yescharacteristic
616C4#1683965411yescharacteristic
617C4#1683965411yescharacteristic
618C4#1683966211yescharacteristic
619C4#1683966311yescharacteristic
620C2—21no—
621C2—21no—
622C2—21no—
623C2—21no—
624C2—4882no—
625C2#2144405511yescharacteristic
626C2#2144562812yes—
627C2#2144626612yes—
628C2#2144664912yes—
subgroupG/H
centerC22×C4D4×D61
commutatorC2×C4×C61C2×C42
FrattiniC23×C4C22×D61
FittingC2×C61×#339C2
socleC23×C61C2×C22⋊C4
prime radicalC22×#11758222C22
cosocleC23×C4×C61C23
hypercenterC2×#339D61
hypocenterC61#10924
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#339

Complements

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

NH ≅ G/Ntype
4. C2×#16839608C2semidirect
5. C2×#16839521C2semidirect
6. #21445512C2semidirect
7. C2×C61×#339C2semidirect
14. C2×#14519705C4semidirect
17. C2×#14519703C4semidirect
18. #16839667C4semidirect
19. #16839663C4semidirect
181. C42×C61C22⋊C4semidirect
190. C4×Dic61C22⋊C4semidirect
311. C2×#339D61semidirect
345. C61#10924semidirect
512. C42#11758198semidirect

Maximal subgroups

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

subgroupindex
C22×#145197052
C22×#145197032
#214483072
C2×#168396082
C2×#168395212
#214455122
C2×C61×#3392
#1092461