Finite Group Databasebeta

← #29587081

Subgroups — #29587081

Order 15616.

934 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519703C211yesmaximal, characteristic
2C2×#16839756C211yesmaximal, characteristic
3C2×#16839728C211yesmaximal, characteristic
4C2×#16839526C211yesmaximal, characteristic, complemented
5C2×#16839521C211yesmaximal, characteristic, complemented
6C2×#16839516C211yesmaximal, characteristic, complemented
7C2×C61×#424C211yesmaximal, characteristic, complemented
8C22×#11758222C2211yescharacteristic
9C22×#11758194C2211yescharacteristic
10C23×#92418C2211yescharacteristic
11C22×C4×Dic61C2211yescharacteristic
12C2×#14519703—22no—
13C2×#14519703—22no—
14C2×#14519703—22no—
15#16839756—22no—
16#16839756—22no—
17C2×#14519700C412yescomplemented
18C2×#14519697C412yescomplemented
19#16839728—22no—
20#16839728—22no—
21C2×#14519689—22no—
22#16839526—22no—
23#16839521—22no—
24#16839516—22no—
25C22×M16×C61C2211yescharacteristic
26C23×C8×C61C2211yescharacteristic
27C2×#117×C61C2211yescharacteristic
28C61×#424—22no—
29C61×#424—22no—
30C2×C4⋊C8×C61—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×#11758194D412yes—
54C22×#92418—21no—
55C22×#92418—21no—
56C22×#92418—21no—
57C22×#92418—21no—
58C22×#92418—21no—
59C22×#92418—21no—
60C22×#92418—21no—
61C22×#92418C2×C412yes—
62C2×C4×Dic61—21no—
63C2×C4×Dic61—21no—
64C2×C4×Dic61—21no—
65C2×C4×Dic61—21no—
66C2×C4×Dic61—21no—
67C2×C4×Dic61D412yes—
68#14519703—28no—
69#14519700—24no—
70#14519697—24no—
71#14519689—28no—
72C23×C4×C61C2311yescharacteristic
73C2×M16×C61—21no—
74C2×M16×C61—21no—
75C2×M16×C61—21no—
76C2×M16×C61—21no—
77C2×M16×C61—21no—
78C2×M16×C61D412yes—
79C22×C8×C61—21no—
80C22×C8×C61—21no—
81C22×C8×C61—21no—
82C22×C8×C61—21no—
83C22×C8×C61—21no—
84C22×C8×C61—21no—
85C22×C8×C61—21no—
86C22×C8×C61D412yes—
87#117×C61—21no—
88#117×C61—21no—
89#117×C61D412yes—
90#117×C61D412yes—
91C2×C4⋊C4×C61C2×C412yes—
92C2×C22⋊C4×C61—21no—
93C2×C42×C61—21no—
94C4⋊C8×C61—28no—
95C24×C61#4111yescharacteristic
96C23×D61—21no—
97C22×C4×C61—22no—
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—24no—
119C22×Dic61—21no—
120C22×Dic61—22no—
121C22×Dic61—42no—
122C22×Dic61—41no—
123C22×Dic61—41no—
124#11758222—22no—
125#11758222—22no—
126#11758222—22no—
127#11758222—22no—
128#11758222—22no—
129#11758222—22no—
130#11758222—22no—
131#11758222—22no—
132#11758222—41no—
133#11758222—41no—
134#11758222—41no—
135#11758222—41no—
136#11758222—41no—
137#11758222—41no—
138#11758222—41no—
139#11758222—41no—
140C2×D244—21no—
141C2×D244—21no—
142C2×D244—21no—
143C2×D244—21no—
144C2×D244—21no—
145C2×D244C4⋊C412yes—
146C2×C4×D61—22no—
147C2×C4×D61—22no—
148C2×C4×D61—41no—
149C2×C4×D61—41no—
150C2×C4×D61—41no—
151C2×C4×D61—41no—
152C2×Dic122—21no—
153C2×Dic122—21no—
154C2×Dic122—21no—
155C2×Dic122—21no—
156C2×Dic122—21no—
157C2×Dic122C4⋊C412yes—
158M16×C61—22no—
159M16×C61—22no—
160M16×C61—41no—
161M16×C61—41no—
162C2×C8×C61—22no—
163C2×C8×C61—22no—
164C2×C8×C61—22no—
165C2×C8×C61—22no—
166C2×C8×C61—41no—
167C2×C8×C61—41no—
168C2×C8×C61—41no—
169C2×C8×C61—41no—
170C2×C8×C61—41no—
171C2×C8×C61—41no—
172C4⋊C4×C61—22no—
173C4⋊C4×C61C22⋊C414yes—
174C22⋊C4×C61—22no—
175C22⋊C4×C61—22no—
176C42×C61—22no—
177C42×C61—22no—
178C4×Dic61—22no—
179C4×Dic61—22no—
180C4×Dic61—41no—
181C4×Dic61—41no—
182#11758194—22no—
183#11758194—22no—
184#11758194—41no—
185#11758194—41no—
186C2×#92418—22no—
187C2×#92418—22no—
188C2×#92418—22no—
189C2×#92418—22no—
190C2×#92418—41no—
191C2×#92418—41no—
192C2×#92418—41no—
193C2×#92418—41no—
194C2×#92418—41no—
195C2×#92418—41no—
196C23×C61—22no—
197C23×C61—22no—
198C23×C61C4×D411yescharacteristic
199C23×C61#12111yescharacteristic
200C23×C61C22⋊Q811yescharacteristic
201C23×C61#12311yescharacteristic
202C23×C61#12311yescharacteristic
203C23×C61#12311yescharacteristic
204C23×C61#12611yescharacteristic
205C22×D61—22no—
206C22×D61—41no—
207C22×D61—41no—
208C22×D61—42no—
209C22×D61—42no—
210C2×C4×C61—24no—
211C2×C4×C61—42no—
212C2×C4×C61—42no—
213C2×C4×C61C2×C22⋊C411yescharacteristic
214C2×C4×C61C2×C4⋊C411yescharacteristic
215C2×C4×C61#11711yescharacteristic
216C2×C4×C61C4×D411yescharacteristic
217C2×C4×C61C4×D411yescharacteristic
218C2×C4×C61C4×D411yescharacteristic
219C2×C4×C61#12011yescharacteristic
220C2×C4×C61#12011yescharacteristic
221C2×C4×C61#12011yescharacteristic
222C2×C4×C61#12111yescharacteristic
223C2×C4×C61#12111yescharacteristic
224C2×C4×C61#12111yescharacteristic
225C2×C4×C61#12111yescharacteristic
226C2×C4×C61#12111yescharacteristic
227C2×C4×C61#12111yescharacteristic
228C2×C4×C61#12111yescharacteristic
229C2×C4×C61C22⋊Q811yescharacteristic
230C2×C4×C61C22⋊Q811yescharacteristic
231C2×C4×C61C22⋊Q811yescharacteristic
232C2×C4×C61C22⋊Q811yescharacteristic
233C2×C4×C61C22⋊Q811yescharacteristic
234C2×C4×C61#12311yescharacteristic
235C2×C4×C61#12311yescharacteristic
236C2×C4×C61#12411yescharacteristic
237C2×C4×C61#12411yescharacteristic
238C2×C4×C61#12411yescharacteristic
239C2×C4×C61#12611yescharacteristic
240C2×C4×C61#12711yescharacteristic
241C22⋊D61—42no—
242C22⋊D61—42no—
243C22⋊D61—42no—
244C22⋊D61—42no—
245C2×Dic61—24no—
246C2×Dic61—22no—
247C2×Dic61—44no—
248C2×Dic61—44no—
249C2×Dic61—42no—
250C2×Dic61—41no—
251C2×Dic61—41no—
252C2×Dic61—42no—
253D244—22no—
254D244—22no—
255D244—41no—
256D244—41no—
257C4×D61—42no—
258C4×D61—42no—
259C4×D61—42no—
260C4×D61—42no—
261Dic122—22no—
262Dic122—22no—
263Dic122—41no—
264Dic122—41no—
265C8×C61—42no—
266C8×C61—42no—
267#92418—42no—
268#92418—42no—
269#11068—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×C61#38511yescharacteristic
279C22×C61#38611yescharacteristic
280C22×C61#38811yescharacteristic
281C22×C61#39411yescharacteristic
282C22×C61#39611yescharacteristic
283C22×C61#39711yescharacteristic
284C22×C61#39911yescharacteristic
285C22×C61#44312yes—
286C22×C61#44412yes—
287C2×D61—44no—
288C2×D61—42no—
289C2×D61—82no—
290C2×D61—81no—
291C2×D61—81no—
292C4×C61—44no—
293C4×C61#38011yescharacteristic
294C4×C61#38511yescharacteristic
295C4×C61#38811yescharacteristic
296C4×C61#39011yescharacteristic
297C4×C61#39211yescharacteristic
298C4×C61#39311yescharacteristic
299C4×C61#39411yescharacteristic
300C4×C61#39611yescharacteristic
301Dic61—44no—
302Dic61—42no—
303C2×#424D6111yescharacteristic, complemented
304C22×#104—611no—
305C2×#416—611no—
306C2×#408—611no—
307C2×#341—611no—
308C2×#339—611no—
309C2×#336—611no—
310C2×C61—21no—
311C2×C61—21no—
312C2×C61—21no—
313C2×C61—21no—
314C2×C61#143911yescharacteristic
315C2×C61#186612yes—
316C2×C61#187612yes—
317C2×C61#193711yescharacteristic
318C2×C61#193811yescharacteristic
319D61—82no—
320C22×#41—611no—
321C22×M16—611no—
322C22×M16C2×D6111yescharacteristic
323C23×C8—611no—
324C23×C8C2×D6111yescharacteristic
325C2×#117C2×D6111yescharacteristic
326C22×C42—611no—
327#424—22no—
328#424—22no—
329C2×C4⋊C8—22no—
330C2×#104—1222no—
331C2×#104—1222no—
332C2×#104—1222no—
333#416—1222no—
334#416—1222no—
335C2×#103—612no—
336C2×#102—612no—
337#408—1222no—
338#408—1222no—
339C2×C22⋊C8—1222no—
340#341—1222no—
341#339—1222no—
342#336—1222no—
343C61#1106811yescharacteristic, complemented, Sylow
344C2×#41—612no—
345C2×#41—612no—
346C2×#41—1221no—
347C2×#41—1221no—
348C2×#41—1221no—
349C2×#41—1221no—
350C2×#41—1221no—
351C2×#41—1221no—
352C2×#41—1221no—
353C2×#41—1221no—
354C2×#41—1221no—
355C2×#41—1221no—
356C22×Q8—611no—
357C22×D4—611no—
358C22×D4—1221no—
359C23×C4—1221no—
360C23×C4—1221no—
361C23×C4C22×D6111yescharacteristic
362C2×M16—21no—
363C2×M16—21no—
364C2×M16—21no—
365C2×M16—21no—
366C2×M16—21no—
367C2×M16—612no—
368C2×M16—1221no—
369C2×M16—1221no—
370C2×M16—1221no—
371C2×M16—1221no—
372C2×M16—1221no—
373C2×M16C22⋊D6112yes—
374C22×C8—21no—
375C22×C8—21no—
376C22×C8—21no—
377C22×C8—21no—
378C22×C8—21no—
379C22×C8—21no—
380C22×C8—21no—
381C22×C8—612no—
382C22×C8—1221no—
383C22×C8—1221no—
384C22×C8—1221no—
385C22×C8—1221no—
386C22×C8—1221no—
387C22×C8—1221no—
388C22×C8—1221no—
389C22×C8C22⋊D6112yes—
390#117—21no—
391#117—21no—
392#117D24412yes—
393#117C22⋊D6112yes—
394C2×C4⋊C4C4×D6112yes—
395C2×C22⋊C4—21no—
396C2×C42—21no—
397C2×C42—612no—
398C2×C42—1221no—
399C2×C42—1221no—
400C2×C42—1221no—
401C2×C42—1221no—
402C2×C42—1221no—
403C4⋊C8—28no—
404#104—1228no—
405#103—1224no—
406#102—1224no—
407C22⋊C8—1228no—
408C24—1221no—
409C24#1175822211yescharacteristic
410#41—1222no—
411#41—1222no—
412#41—1222no—
413#41—1222no—
414#41—1222no—
415#41—1222no—
416#41—1222no—
417#41—1222no—
418#41—2441no—
419#41—2441no—
420#41—2441no—
421#41—2441no—
422#41—2441no—
423#41—2441no—
424#41—2441no—
425#41—2441no—
426C2×Q8—612no—
427C2×Q8—1221no—
428C2×Q8—1221no—
429C2×Q8—1221no—
430C2×Q8—1221no—
431C2×Q8—1221no—
432C2×D4—612no—
433C2×D4—1222no—
434C2×D4—1222no—
435C2×D4—1221no—
436C2×D4—1221no—
437C2×D4—1221no—
438C2×D4—1221no—
439C2×D4—1221no—
440C2×D4—2441no—
441C2×D4—2441no—
442C2×D4—2441no—
443C2×D4—2441no—
444C22×C4—22no—
445C22×C4—1224no—
446C22×C4—1221no—
447C22×C4—1222no—
448C22×C4—1222no—
449C22×C4—1222no—
450C22×C4—2442no—
451C22×C4—2441no—
452C22×C4—2441no—
453C22×C4—2441no—
454C22×C4—2441no—
455C22×C4—2441no—
456C22×C4—2441no—
457C22×C4C2×C4×D6111yescharacteristic
458C22×C4C2×D24411yescharacteristic
459C22×C4#1175822211yescharacteristic
460C22×C4D4×D6111yescharacteristic
461C22×C4D4×D6111yescharacteristic
462C22×C4D4×D6111yescharacteristic
463C22×C4#1175822411yescharacteristic
464C22×C4Q8×D6111yescharacteristic
465C22×C4#1175822611yescharacteristic
466C22×C4#1175822611yescharacteristic
467C22×C4#1175822611yescharacteristic
468C22×C4C2×C22⋊D6111yescharacteristic
469C22×C4C2×C22⋊D6111yescharacteristic
470C22×C4C2×C22⋊D6111yescharacteristic
471M16—22no—
472M16—22no—
473M16—41no—
474M16—41no—
475M16—1222no—
476M16—1222no—
477M16—2441no—
478M16—2441no—
479C2×C8—22no—
480C2×C8—22no—
481C2×C8—22no—
482C2×C8—22no—
483C2×C8—41no—
484C2×C8—41no—
485C2×C8—41no—
486C2×C8—41no—
487C2×C8—41no—
488C2×C8—41no—
489C2×C8—1222no—
490C2×C8—1222no—
491C2×C8—1222no—
492C2×C8—1222no—
493C2×C8—2441no—
494C2×C8—2441no—
495C2×C8—2441no—
496C2×C8—2441no—
497C2×C8—2441no—
498C2×C8—2441no—
499C4⋊C4—22no—
500C4⋊C4#1175819814yes—
501C22⋊C4—22no—
502C22⋊C4—22no—
503C42—22no—
504C42—22no—
505C42—1222no—
506C42—1222no—
507C42—2441no—
508C42—2441no—
509C23—22no—
510C23—22no—
511C23—1222no—
512C23—2442no—
513C23—2442no—
514C23—2441no—
515C23—2441no—
516C23C4×C22⋊D6111yescharacteristic
517C23#1451975111yescharacteristic
518C23#1451975511yescharacteristic
519C23#1451976011yescharacteristic
520C23#1451976211yescharacteristic
521C23#1451976211yescharacteristic
522C23#1451977211yescharacteristic
523Q8—1222no—
524Q8—1222no—
525Q8—2441no—
526Q8—2441no—
527D4—1222no—
528D4—1222no—
529D4—2442no—
530D4—2442no—
531D4—2442no—
532D4—2442no—
533D4—2441no—
534D4—2441no—
535C2×C4—24no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—1224no—
539C2×C4—1222no—
540C2×C4—2444no—
541C2×C4—2442no—
542C2×C4—2444no—
543C2×C4—2441no—
544C2×C4—2441no—
545C2×C4—2442no—
546C2×C4—2442no—
547C2×C4—2442no—
548C2×C4—2442no—
549C2×C4—2442no—
550C2×C4C2×#1175819811yescharacteristic
551C2×C4C4⋊C4×D6111yescharacteristic
552C2×C4#1451973511yescharacteristic
553C2×C4C4×C22⋊D6111yescharacteristic
554C2×C4#1451973911yescharacteristic
555C2×C4#1451973911yescharacteristic
556C2×C4#1451974511yescharacteristic
557C2×C4#1451974511yescharacteristic
558C2×C4#1451974611yescharacteristic
559C2×C4#1451974811yescharacteristic
560C2×C4#1451974911yescharacteristic
561C2×C4#1451974911yescharacteristic
562C2×C4#1451975111yescharacteristic
563C2×C4#1451975211yescharacteristic
564C2×C4#1451975211yescharacteristic
565C2×C4#1451975211yescharacteristic
566C2×C4#1451975311yescharacteristic
567C2×C4#1451975311yescharacteristic
568C2×C4#1451975311yescharacteristic
569C2×C4#1451975511yescharacteristic
570C2×C4#1451975711yescharacteristic
571C2×C4#1451976211yescharacteristic
572C2×C4#1451976211yescharacteristic
573C2×C4#1451976611yescharacteristic
574C2×C4#1451976611yescharacteristic
575C2×C4#1451976611yescharacteristic
576C2×C4#1451977211yescharacteristic
577C2×C4#1451977311yescharacteristic
578C8—42no—
579C8—42no—
580C8—2442no—
581C8—2442no—
582C22—22no—
583C22—22no—
584C22—21no—
585C22—21no—
586C22—21no—
587C22—21no—
588C22—22no—
589C22—22no—
590C22—4882no—
591C22—4881no—
592C22—4881no—
593C22—2444no—
594C22—2442no—
595C22#1683963311yescharacteristic
596C22#1683964111yescharacteristic
597C22#1683965211yescharacteristic
598C22#1683967911yescharacteristic
599C22#1683968411yescharacteristic
600C22#1683968811yescharacteristic
601C22#1683969711yescharacteristic
602C22#1683987712yes—
603C22#1683988212yes—
604C4—44no—
605C4—2444no—
606C4—2442no—
607C4#1683961911yescharacteristic
608C4#1683963311yescharacteristic
609C4#1683965211yescharacteristic
610C4#1683966311yescharacteristic
611C4#1683967011yescharacteristic
612C4#1683967311yescharacteristic
613C4#1683967911yescharacteristic
614C4#1683968411yescharacteristic
615C2—21no—
616C2—21no—
617C2—21no—
618C2—21no—
619C2—4882no—
620C2#2144406111yescharacteristic
621C2#2144609312yes—
622C2#2144614612yes—
623C2#2144652211yescharacteristic
624C2#2144652911yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D61
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC2×C61×#424C2
socleC23×C61C4×D4
prime radicalC22×#11758222C22
cosocleC23×C4×C61C23
hypercenterC2×#424D61
hypocenterC61#11068
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C23×C8 ◁ C2×#424

Complements

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

NH ≅ G/Ntype
4. C2×#16839526C2semidirect
5. C2×#16839521C2semidirect
6. C2×#16839516C2semidirect
7. C2×C61×#424C2semidirect
17. C2×#14519700C4semidirect
18. C2×#14519697C4semidirect
303. C2×#424D61semidirect
343. C61#11068semidirect

Maximal subgroups

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

subgroupindex
C22×#145197032
C2×#168397562
C2×#168397282
C2×#168395262
C2×#168395212
C2×#168395162
C2×C61×#4242
#1106861