Finite Group Databasebeta

← #29587579

Subgroups — #29587579

Order 15616.

894 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839810C211yesmaximal, characteristic, complemented
2C2×#16839780C211yesmaximal, characteristic
3C22×#14519703C211yesmaximal, characteristic
4C2×#16839744C211yesmaximal, characteristic
5C2×#16839521C211yesmaximal, characteristic, complemented
6#21445512C211yesmaximal, characteristic, complemented
7C2×C61×#344C211yesmaximal, characteristic, complemented
8C22×#11758222C2211yescharacteristic
9C22×#11758194C2211yescharacteristic
10C22×#11758194C2211yescharacteristic
11C22×C4×Dic61C2211yescharacteristic
12#16839810—22no—
13#16839810—22no—
14C2×#14519712—22no—
15#16839780—22no—
16#16839780—22no—
17C2×#14519705—22no—
18C2×#14519703—22no—
19C2×#14519703—22no—
20C2×#14519703—22no—
21#16839744—22no—
22#16839744—22no—
23C2×#14519695C412yescomplemented
24C2×#14519693C412yescomplemented
25#16839521—22no—
26#16839516—22no—
27C22×M16×C61C2211yescharacteristic
28C22×M16×C61C2211yescharacteristic
29C2×#117×C61C2211yescharacteristic
30C61×#344—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×#11758222D412yes—
42C2×#11758222Q812yes—
43C22×Dic122C2×C411yescharacteristic
44C22×D244C2×C411yescharacteristic
45C22×C22⋊D61—21no—
46C23×Dic61—21no—
47C22×C4×D61—21no—
48C2×#11758194—21no—
49C2×#11758194—21no—
50C2×#11758194—21no—
51C2×#11758194—21no—
52C2×#11758194—21no—
53C2×#11758194—21no—
54C2×#11758194—21no—
55C2×#11758194—21no—
56C2×#11758194C2×C412yes—
57C2×#11758194D412yes—
58C2×#11758194D412yes—
59C2×#11758194D412yes—
60C22×#92418—21no—
61C22×#92418—21no—
62C2×C4×Dic61—21no—
63C2×C4×Dic61—21no—
64C2×C4×Dic61—21no—
65C2×C4×Dic61—21no—
66C2×C4×Dic61—21no—
67C2×C4×Dic61D412yes—
68#14519712—28no—
69#14519705—28no—
70#14519703—28no—
71#14519695—24no—
72#14519693—24no—
73C23×C4×C61C2311yescharacteristic
74C2×M16×C61—21no—
75C2×M16×C61—21no—
76C2×M16×C61—21no—
77C2×M16×C61—21no—
78C2×M16×C61—21no—
79C2×M16×C61—21no—
80C2×M16×C61—21no—
81C2×M16×C61—21no—
82C2×M16×C61—21no—
83C2×M16×C61—21no—
84C2×M16×C61C2×C412yes—
85C2×M16×C61D412yes—
86C22×C8×C61—21no—
87C22×C8×C61—21no—
88#117×C61—21no—
89#117×C61—21no—
90#117×C61—21no—
91#117×C61D412yes—
92C2×C4⋊C4×C61—21no—
93C2×C22⋊C4×C61—21no—
94C2×C42×C61—21no—
95C24×C61#4111yescharacteristic
96C23×D61—21no—
97C22×C4×C61—41no—
98C22×C4×C61C22×C411yescharacteristic
99C22×C4×C61C2×D411yescharacteristic
100C22×C4×C61C2×D411yescharacteristic
101C22×C4×C61C2×D411yescharacteristic
102C22×C4×C61C2×D411yescharacteristic
103C22×C4×C61C2×D411yescharacteristic
104C22×C4×C61C2×D411yescharacteristic
105C22×C4×C61C2×D411yescharacteristic
106C22×C4×C61C2×Q811yescharacteristic
107C22×C4×C61#4111yescharacteristic
108C22×C4×C61#4111yescharacteristic
109C22×C4×C61#4111yescharacteristic
110C22×C4×C61#4111yescharacteristic
111C22×C4×C61#4111yescharacteristic
112C2×C22⋊D61—22no—
113C2×C22⋊D61—22no—
114C2×C22⋊D61—41no—
115C2×C22⋊D61—41no—
116C2×C22⋊D61—41no—
117C2×C22⋊D61—41no—
118C22×Dic61—21no—
119C22×Dic61—22no—
120C22×Dic61—44no—
121C22×Dic61—41no—
122C22×Dic61—41no—
123#11758222—22no—
124#11758222—22no—
125#11758222—22no—
126#11758222—22no—
127#11758222—22no—
128#11758222—22no—
129#11758222—22no—
130#11758222—22no—
131#11758222—41no—
132#11758222—41no—
133#11758222—41no—
134#11758222—41no—
135#11758222—41no—
136#11758222—41no—
137#11758222—41no—
138#11758222—41no—
139C2×D244—21no—
140C2×D244—21no—
141C2×D244—21no—
142C2×D244—21no—
143C2×D244—21no—
144C2×D244C4⋊C412yes—
145C2×C4×D61—22no—
146C2×C4×D61—22no—
147C2×C4×D61—41no—
148C2×C4×D61—41no—
149C2×C4×D61—41no—
150C2×C4×D61—41no—
151C2×Dic122—21no—
152C2×Dic122—21no—
153C2×Dic122—21no—
154C2×Dic122—21no—
155C2×Dic122—21no—
156C2×Dic122C4⋊C412yes—
157M16×C61—22no—
158M16×C61—22no—
159M16×C61—22no—
160M16×C61—22no—
161M16×C61—41no—
162M16×C61—41no—
163M16×C61—41no—
164M16×C61—41no—
165C2×C8×C61—22no—
166C2×C8×C61—22no—
167C2×C8×C61—41no—
168C2×C8×C61—41no—
169C2×C8×C61—41no—
170C2×C8×C61—41no—
171C4⋊C4×C61—22no—
172C4⋊C4×C61—41no—
173C22⋊C4×C61—22no—
174C22⋊C4×C61—41no—
175C42×C61—22no—
176C42×C61—41no—
177C4×Dic61—22no—
178C4×Dic61—22no—
179C4×Dic61—41no—
180C4×Dic61—41no—
181#11758194—22no—
182#11758194—22no—
183#11758194—22no—
184#11758194—22no—
185#11758194—22no—
186#11758194—41no—
187#11758194—41no—
188#11758194C22⋊C414yes—
189C2×#92418—22no—
190C2×#92418—22no—
191C2×#92418—22no—
192C2×#92418—22no—
193C2×#92418—41no—
194C2×#92418—41no—
195C23×C61—42no—
196C23×C61#11711yescharacteristic
197C23×C61#12111yescharacteristic
198C23×C61C22⋊Q811yescharacteristic
199C23×C61#12311yescharacteristic
200C23×C61#12311yescharacteristic
201C23×C61#12411yescharacteristic
202C23×C61#12411yescharacteristic
203C22×D61—22no—
204C22×D61—41no—
205C22×D61—41no—
206C22×D61—82no—
207C2×C4×C61—42no—
208C2×C4×C61—82no—
209C2×C4×C61C2×C22⋊C411yescharacteristic
210C2×C4×C61C2×C4⋊C411yescharacteristic
211C2×C4×C61C4×D411yescharacteristic
212C2×C4×C61C4×D411yescharacteristic
213C2×C4×C61C4×D411yescharacteristic
214C2×C4×C61C4×D411yescharacteristic
215C2×C4×C61#12011yescharacteristic
216C2×C4×C61#12011yescharacteristic
217C2×C4×C61#12011yescharacteristic
218C2×C4×C61#12111yescharacteristic
219C2×C4×C61#12111yescharacteristic
220C2×C4×C61#12111yescharacteristic
221C2×C4×C61#12111yescharacteristic
222C2×C4×C61#12111yescharacteristic
223C2×C4×C61#12111yescharacteristic
224C2×C4×C61#12111yescharacteristic
225C2×C4×C61C22⋊Q811yescharacteristic
226C2×C4×C61C22⋊Q811yescharacteristic
227C2×C4×C61C22⋊Q811yescharacteristic
228C2×C4×C61C22⋊Q811yescharacteristic
229C2×C4×C61C22⋊Q811yescharacteristic
230C2×C4×C61#12311yescharacteristic
231C2×C4×C61#12311yescharacteristic
232C2×C4×C61#12311yescharacteristic
233C2×C4×C61#12411yescharacteristic
234C2×C4×C61#12611yescharacteristic
235C2×C4×C61#12611yescharacteristic
236C2×C4×C61#12711yescharacteristic
237C22⋊D61—42no—
238C22⋊D61—42no—
239C22⋊D61—42no—
240C22⋊D61—42no—
241C2×Dic61—24no—
242C2×Dic61—22no—
243C2×Dic61—42no—
244C2×Dic61—44no—
245C2×Dic61—44no—
246C2×Dic61—41no—
247C2×Dic61—41no—
248C2×Dic61—42no—
249D244—22no—
250D244—22no—
251D244—41no—
252D244—41no—
253C4×D61—42no—
254C4×D61—42no—
255C4×D61—42no—
256C4×D61—42no—
257Dic122—22no—
258Dic122—22no—
259Dic122—41no—
260Dic122—41no—
261C8×C61—42no—
262C8×C61—42no—
263#92418—24no—
264#92418—42no—
265#11146—611nomaximal, Sylow
266C22×C61—22no—
267C22×C61—22no—
268C22×C61—22no—
269C22×C61—41no—
270C22×C61—41no—
271C22×C61—41no—
272C22×C61—41no—
273C22×C61#38011yescharacteristic
274C22×C61#38811yescharacteristic
275C22×C61#38811yescharacteristic
276C22×C61#39311yescharacteristic
277C22×C61#39411yescharacteristic
278C22×C61#39411yescharacteristic
279C22×C61#39911yescharacteristic
280C2×D61—42no—
281C2×D61—82no—
282C2×D61—82no—
283C2×D61—82no—
284C4×C61—82no—
285C4×C61#38511yescharacteristic
286C4×C61#38511yescharacteristic
287C4×C61#38611yescharacteristic
288C4×C61#39011yescharacteristic
289C4×C61#39211yescharacteristic
290C4×C61#39611yescharacteristic
291C4×C61#39611yescharacteristic
292C4×C61#39711yescharacteristic
293Dic61—44no—
294Dic61—42no—
295C2×#430—611no—
296C2×#421—611no—
297C22×#104—611no—
298C2×#413—611no—
299C2×#344D6111yescharacteristic, complemented
300C2×#339—611no—
301#1728—611no—
302C2×C61—21no—
303C2×C61—21no—
304C2×C61—21no—
305C2×C61—21no—
306C2×C61—21no—
307C2×C61—21no—
308C2×C61#143911yescharacteristic
309C2×C61#193212yes—
310D61—82no—
311C22×#41—611no—
312C22×M16—611no—
313C22×M16—611no—
314C22×M16C2×D6111yescharacteristic
315C22×M16C2×D6111yescharacteristic
316C2×#117C2×D6111yescharacteristic
317C22×C42—611no—
318#430—1222no—
319#430—1222no—
320C2×#108—1222no—
321#421—1222no—
322#421—1222no—
323C2×#104—1222no—
324C2×#104—1222no—
325C2×#104—1222no—
326C2×#104—1222no—
327#413—1222no—
328#413—1222no—
329C2×#101—612no—
330C2×#100—612no—
331#344—22no—
332#339—1222no—
333#336—1222no—
334C61#1114611yescharacteristic, complemented, Sylow
335C2×#41—612no—
336C2×#41—612no—
337C2×#41—1221no—
338C2×#41—1221no—
339C2×#41—1221no—
340C2×#41—1221no—
341C2×#41—1221no—
342C2×#41—1221no—
343C2×#41—1221no—
344C2×#41—1221no—
345C2×#41—1221no—
346C2×#41—1221no—
347C22×Q8—611no—
348C22×D4—611no—
349C22×D4—1221no—
350C23×C4—1221no—
351C23×C4—1221no—
352C23×C4C22×D6111yescharacteristic
353C2×M16—21no—
354C2×M16—21no—
355C2×M16—21no—
356C2×M16—21no—
357C2×M16—21no—
358C2×M16—21no—
359C2×M16—21no—
360C2×M16—21no—
361C2×M16—21no—
362C2×M16—21no—
363C2×M16—612no—
364C2×M16—612no—
365C2×M16—612no—
366C2×M16—612no—
367C2×M16—1221no—
368C2×M16—1221no—
369C2×M16—1221no—
370C2×M16—1221no—
371C2×M16—1221no—
372C2×M16—1221no—
373C2×M16—1221no—
374C2×M16—1221no—
375C2×M16C4×D6112yes—
376C2×M16D24412yes—
377C22×C8—21no—
378C22×C8—21no—
379C22×C8—1221no—
380C22×C8—1221no—
381#117—21no—
382#117—21no—
383#117—21no—
384#117C22⋊D6112yes—
385C2×C4⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C42—21no—
388C2×C42—612no—
389C2×C42—1221no—
390C2×C42—1221no—
391C2×C42—1221no—
392C2×C42—1221no—
393C2×C42—1221no—
394#108—1228no—
395#104—1228no—
396#104—1228no—
397#101—1224no—
398#100—1224no—
399C24—1221no—
400C24#1175822211yescharacteristic
401#41—1222no—
402#41—1222no—
403#41—1222no—
404#41—1222no—
405#41—1222no—
406#41—1222no—
407#41—1222no—
408#41—1222no—
409#41—2441no—
410#41—2441no—
411#41—2441no—
412#41—2441no—
413#41—2441no—
414#41—2441no—
415#41—2441no—
416#41—2441no—
417C2×Q8—612no—
418C2×Q8—1221no—
419C2×Q8—1221no—
420C2×Q8—1221no—
421C2×Q8—1221no—
422C2×Q8—1221no—
423C2×D4—612no—
424C2×D4—1222no—
425C2×D4—1222no—
426C2×D4—1221no—
427C2×D4—1221no—
428C2×D4—1221no—
429C2×D4—1221no—
430C2×D4—1221no—
431C2×D4—2441no—
432C2×D4—2441no—
433C2×D4—2441no—
434C2×D4—2441no—
435C22×C4—41no—
436C22×C4—1221no—
437C22×C4—1222no—
438C22×C4—1222no—
439C22×C4—1222no—
440C22×C4—2444no—
441C22×C4—2441no—
442C22×C4—2441no—
443C22×C4—2441no—
444C22×C4—2441no—
445C22×C4—2441no—
446C22×C4—2441no—
447C22×C4C2×C4×D6111yescharacteristic
448C22×C4C2×D24411yescharacteristic
449C22×C4#1175822211yescharacteristic
450C22×C4#1175822211yescharacteristic
451C22×C4#1175822211yescharacteristic
452C22×C4D4×D6111yescharacteristic
453C22×C4D4×D6111yescharacteristic
454C22×C4D4×D6111yescharacteristic
455C22×C4D4×D6111yescharacteristic
456C22×C4D4×D6111yescharacteristic
457C22×C4#1175822411yescharacteristic
458C22×C4Q8×D6111yescharacteristic
459C22×C4#1175822611yescharacteristic
460C22×C4C2×C22⋊D6111yescharacteristic
461M16—22no—
462M16—22no—
463M16—22no—
464M16—22no—
465M16—41no—
466M16—41no—
467M16—41no—
468M16—41no—
469M16—614no—
470M16—1222no—
471M16—1222no—
472M16—1222no—
473M16—1222no—
474M16—1222no—
475M16—2441no—
476M16—2441no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—41no—
480C2×C8—41no—
481C2×C8—41no—
482C2×C8—41no—
483C2×C8—1222no—
484C2×C8—1222no—
485C2×C8—1222no—
486C2×C8—1222no—
487C2×C8—2441no—
488C2×C8—2441no—
489C4⋊C4—22no—
490C4⋊C4—41no—
491C22⋊C4—22no—
492C22⋊C4—41no—
493C42—22no—
494C42—41no—
495C42—1222no—
496C42—1222no—
497C42—2441no—
498C42—2441no—
499C23—42no—
500C23—1222no—
501C23—4882no—
502C23—2441no—
503C23—2441no—
504C23#1451973411yescharacteristic
505C23#1451975011yescharacteristic
506C23#1451975511yescharacteristic
507C23#1451976011yescharacteristic
508C23#1451976211yescharacteristic
509C23#1451976311yescharacteristic
510C23#1451976511yescharacteristic
511Q8—1222no—
512Q8—1222no—
513Q8—2441no—
514Q8—2441no—
515D4—1222no—
516D4—1222no—
517D4—2442no—
518D4—2442no—
519D4—2442no—
520D4—2442no—
521D4—2441no—
522D4—2441no—
523C2×C4—42no—
524C2×C4—82no—
525C2×C4—1224no—
526C2×C4—1222no—
527C2×C4—2442no—
528C2×C4—2444no—
529C2×C4—2444no—
530C2×C4—2442no—
531C2×C4—2441no—
532C2×C4—2441no—
533C2×C4—2442no—
534C2×C4—2442no—
535C2×C4—2442no—
536C2×C4—2442no—
537C2×C4C22⋊C4×D6111yescharacteristic
538C2×C4C4⋊C4×D6111yescharacteristic
539C2×C4#1451973711yescharacteristic
540C2×C4C4×C22⋊D6111yescharacteristic
541C2×C4#1451973911yescharacteristic
542C2×C4C4×D24411yescharacteristic
543C2×C4#1451974511yescharacteristic
544C2×C4#1451974711yescharacteristic
545C2×C4#1451974711yescharacteristic
546C2×C4#1451974911yescharacteristic
547C2×C4#1451975011yescharacteristic
548C2×C4#1451975011yescharacteristic
549C2×C4#1451975011yescharacteristic
550C2×C4#1451975011yescharacteristic
551C2×C4#1451975111yescharacteristic
552C2×C4#1451975211yescharacteristic
553C2×C4#1451975311yescharacteristic
554C2×C4#1451975511yescharacteristic
555C2×C4#1451975511yescharacteristic
556C2×C4#1451975511yescharacteristic
557C2×C4#1451975711yescharacteristic
558C2×C4#1451975911yescharacteristic
559C2×C4#1451976211yescharacteristic
560C2×C4#1451976211yescharacteristic
561C2×C4#1451976311yescharacteristic
562C2×C4#1451977111yescharacteristic
563C2×C4#1451977211yescharacteristic
564C2×C4#1451977311yescharacteristic
565C8—42no—
566C8—42no—
567C8—1224no—
568C8—2442no—
569C22—22no—
570C22—22no—
571C22—22no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—4882no—
577C22—4882no—
578C22—4882no—
579C22—2442no—
580C22#1683962111yescharacteristic
581C22#1683965111yescharacteristic
582C22#1683965311yescharacteristic
583C22#1683967511yescharacteristic
584C22#1683967711yescharacteristic
585C22#1683968011yescharacteristic
586C22#1683969711yescharacteristic
587C4—82no—
588C4—2444no—
589C4—2442no—
590C4#1683963311yescharacteristic
591C4#1683963611yescharacteristic
592C4#1683964011yescharacteristic
593C4#1683966211yescharacteristic
594C4#1683967111yescharacteristic
595C4#1683968411yescharacteristic
596C4#1683968611yescharacteristic
597C4#1683969111yescharacteristic
598C2—21no—
599C2—21no—
600C2—21no—
601C2—21no—
602C2—21no—
603C2—21no—
604C2—4882no—
605C2#2144406311yescharacteristic
606C2#2144648612yes—
subgroupG/H
centerC2×C4#14519750
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC2×C61×#344C2
socleC22×C61#388
prime radicalC22×#11758222C22
cosocleC23×C4×C61C23
hypercenterC2×#344D61
hypocenterC61#11146
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#344

Complements

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

NH ≅ G/Ntype
1. C2×#16839810C2semidirect
5. C2×#16839521C2semidirect
6. #21445512C2semidirect
7. C2×C61×#344C2semidirect
23. C2×#14519695C4semidirect
24. C2×#14519693C4semidirect
299. C2×#344D61semidirect
334. C61#11146semidirect

Maximal subgroups

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

subgroupindex
C2×#168398102
C2×#168397802
C22×#145197032
C2×#168397442
C2×#168395212
#214455122
C2×C61×#3442
#1114661