Finite Group Databasebeta

← #29587165

Subgroups — #29587165

Order 15616.

898 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
1C2×#16839786C211yesmaximal, characteristic, complemented
2C22×#14519705C211yesmaximal, characteristic
3#21454336C211yesmaximal, characteristic
4C2×#16839744C211yesmaximal, characteristic
5#21445558C211yesmaximal, characteristic, complemented
6C2×#16839520C211yesmaximal, characteristic, complemented
7C2×C61×#339C211yesmaximal, characteristic, complemented
8C22×#11758222C2211yescharacteristic
9C22×#11758194C2211yescharacteristic
10C22×#11758194C2211yescharacteristic
11C22×#11758194C2211yescharacteristic
12#16839786—22no—
13#16839786—22no—
14C2×C4⋊#92418—22no—
15C2×#14519705—22no—
16C2×#14519705—21no—
17C2×#14519705—21no—
18C2×#14519705C414yescomplemented
19#16839770—21no—
20#16839766—21no—
21#16839761—22no—
22#16839756—22no—
23#16839744—22no—
24#16839744—22no—
25C2×#14519695—21no—
26C2×#14519693—21no—
27#16839531—22no—
28#16839520—22no—
29C22×M16×C61C2211yescharacteristic
30C2×#117×C61C2211yescharacteristic
31C22×C42×C61C2211yescharacteristic
32C61×#339—21no—
33C61×#339—21no—
34C2×#11758222—21no—
35C2×#11758222—21no—
36C2×#11758222—21no—
37C2×#11758222—21no—
38C2×#11758222—21no—
39C2×#11758222—21no—
40C2×#11758222—21no—
41C2×#11758222—21no—
42C2×#11758222—21no—
43C2×#11758222—21no—
44C2×#11758222C2×C412yes—
45C2×#11758222Q812yes—
46C22×Dic122D411yescharacteristic
47C22×D244D411yescharacteristic
48C22×C22⋊D61—21no—
49C22×C4×D61—21no—
50C2×#11758194—21no—
51C2×#11758194—21no—
52C2×#11758194—21no—
53C2×#11758194—21no—
54C2×#11758194—21no—
55C2×#11758194—21no—
56C2×#11758194—21no—
57C2×#11758194—21no—
58C2×#11758194—21no—
59C2×#11758194—21no—
60C2×#11758194—21no—
61C2×#11758194—21no—
62C2×#11758194—21no—
63C2×#11758194—21no—
64C2×#11758194—21no—
65C2×#11758194—21no—
66C2×#11758194C2×C412yes—
67C2×#11758194D412yes—
68C22×#92418—21no—
69C22×#92418—21no—
70C22×#92418D412yes—
71C4⋊#92418—28no—
72#14519705—24no—
73#14519705—24no—
74#14519700—24no—
75#14519697—24no—
76#14519695—24no—
77#14519693—24no—
78C23×C4×C61—21no—
79C23×C4×C61C2311yescharacteristic
80C2×M16×C61—21no—
81C2×M16×C61—21no—
82C2×M16×C61—21no—
83C2×M16×C61—21no—
84C2×M16×C61—21no—
85C2×M16×C61D412yes—
86C22×C8×C61—21no—
87#117×C61—21no—
88#117×C61—21no—
89#117×C61—21no—
90#117×C61—21no—
91C2×C4⋊C4×C61D412yes—
92C2×C22⋊C4×C61—21no—
93C2×C42×C61—21no—
94C2×C42×C61—21no—
95C2×C42×C61—21no—
96C2×C42×C61—21no—
97C2×C42×C61C2×C412yes—
98C2×C42×C61D412yes—
99C2×C42×C61D411yescharacteristic
100C2×C42×C61D411yescharacteristic
101C24×C61#4111yescharacteristic
102C23×D61—21no—
103C22×C4×C61—21no—
104C22×C4×C61—22no—
105C22×C4×C61—21no—
106C22×C4×C61—22no—
107C22×C4×C61—22no—
108C22×C4×C61—44no—
109C22×C4×C61C22×C411yescharacteristic
110C22×C4×C61C2×D411yescharacteristic
111C22×C4×C61C2×D411yescharacteristic
112C22×C4×C61C2×D411yescharacteristic
113C22×C4×C61C2×D411yescharacteristic
114C22×C4×C61C2×D411yescharacteristic
115C22×C4×C61C2×D411yescharacteristic
116C22×C4×C61C2×D411yescharacteristic
117C22×C4×C61C2×Q811yescharacteristic
118C22×C4×C61#4111yescharacteristic
119C22×C4×C61#4111yescharacteristic
120C22×C4×C61#4111yescharacteristic
121C22×C4×C61#4111yescharacteristic
122C22×C4×C61#4111yescharacteristic
123C2×C22⋊D61—22no—
124C2×C22⋊D61—22no—
125C2×C22⋊D61—41no—
126C2×C22⋊D61—41no—
127C2×C22⋊D61—41no—
128C2×C22⋊D61—41no—
129C22×Dic61—21no—
130#11758222—22no—
131#11758222—22no—
132#11758222—22no—
133#11758222—22no—
134#11758222—22no—
135#11758222—22no—
136#11758222—22no—
137#11758222—22no—
138#11758222—41no—
139#11758222—41no—
140#11758222—41no—
141#11758222—41no—
142#11758222—41no—
143#11758222—41no—
144#11758222—41no—
145#11758222—41no—
146C2×D244—21no—
147C2×D244—21no—
148C2×D244—21no—
149C2×D244—21no—
150C2×D244—21no—
151C2×D244C4⋊C412yes—
152C2×C4×D61—22no—
153C2×C4×D61—22no—
154C2×C4×D61—41no—
155C2×C4×D61—41no—
156C2×C4×D61—41no—
157C2×C4×D61—41no—
158C2×Dic122—21no—
159C2×Dic122—21no—
160C2×Dic122—21no—
161C2×Dic122—21no—
162C2×Dic122—21no—
163C2×Dic122C4⋊C412yes—
164M16×C61—22no—
165M16×C61—22no—
166M16×C61—41no—
167M16×C61—41no—
168C2×C8×C61—22no—
169C2×C8×C61—41no—
170C2×C8×C61—41no—
171C4⋊C4×C61—22no—
172C4⋊C4×C61—22no—
173C22⋊C4×C61—41no—
174C22⋊C4×C61—41no—
175C42×C61—22no—
176C42×C61—22no—
177C42×C61—21no—
178C42×C61—21no—
179C42×C61—41no—
180C42×C61—41no—
181C42×C61C22⋊C412yes—
182C42×C61C22⋊C412yes—
183#11758194—22no—
184#11758194—22no—
185#11758194—22no—
186#11758194—22no—
187#11758194—41no—
188#11758194—41no—
189#11758194—41no—
190#11758194—41no—
191#11758194—41no—
192#11758194—41no—
193#11758194—41no—
194#11758194—41no—
195C2×#92418—22no—
196C2×#92418—22no—
197C2×#92418—22no—
198C2×#92418—22no—
199C2×#92418—22no—
200C2×#92418—41no—
201C2×#92418—41no—
202C2×#92418—41no—
203C2×#92418—41no—
204C23×C61—42no—
205C23×C61C4×D411yescharacteristic
206C23×C61#12111yescharacteristic
207C23×C61C22⋊Q811yescharacteristic
208C23×C61#12311yescharacteristic
209C23×C61#12311yescharacteristic
210C23×C61#12311yescharacteristic
211C23×C61#12611yescharacteristic
212C22×D61—22no—
213C22×D61—41no—
214C22×D61—41no—
215C22×D61—82no—
216C2×C4×C61—24no—
217C2×C4×C61—22no—
218C2×C4×C61—22no—
219C2×C4×C61—44no—
220C2×C4×C61—44no—
221C2×C4×C61—42no—
222C2×C4×C61—42no—
223C2×C4×C61—82no—
224C2×C4×C61C2×C22⋊C411yescharacteristic
225C2×C4×C61C2×C4⋊C411yescharacteristic
226C2×C4×C61#11711yescharacteristic
227C2×C4×C61C4×D411yescharacteristic
228C2×C4×C61C4×D411yescharacteristic
229C2×C4×C61C4×D411yescharacteristic
230C2×C4×C61#12011yescharacteristic
231C2×C4×C61#12011yescharacteristic
232C2×C4×C61#12011yescharacteristic
233C2×C4×C61#12111yescharacteristic
234C2×C4×C61#12111yescharacteristic
235C2×C4×C61#12111yescharacteristic
236C2×C4×C61#12111yescharacteristic
237C2×C4×C61#12111yescharacteristic
238C2×C4×C61#12111yescharacteristic
239C2×C4×C61#12111yescharacteristic
240C2×C4×C61C22⋊Q811yescharacteristic
241C2×C4×C61C22⋊Q811yescharacteristic
242C2×C4×C61C22⋊Q811yescharacteristic
243C2×C4×C61C22⋊Q811yescharacteristic
244C2×C4×C61C22⋊Q811yescharacteristic
245C2×C4×C61#12311yescharacteristic
246C2×C4×C61#12311yescharacteristic
247C2×C4×C61#12411yescharacteristic
248C2×C4×C61#12411yescharacteristic
249C2×C4×C61#12411yescharacteristic
250C2×C4×C61#12611yescharacteristic
251C2×C4×C61#12711yescharacteristic
252C22⋊D61—42no—
253C22⋊D61—42no—
254C22⋊D61—42no—
255C22⋊D61—42no—
256C2×Dic61—22no—
257C2×Dic61—41no—
258C2×Dic61—41no—
259D244—22no—
260D244—22no—
261D244—41no—
262D244—41no—
263C4×D61—42no—
264C4×D61—42no—
265C4×D61—42no—
266C4×D61—42no—
267Dic122—22no—
268Dic122—22no—
269Dic122—41no—
270Dic122—41no—
271C8×C61—42no—
272#92418—42no—
273#92418—42no—
274#92418—42no—
275#11082—611nomaximal, Sylow
276C22×C61—22no—
277C22×C61—22no—
278C22×C61—22no—
279C22×C61—41no—
280C22×C61—41no—
281C22×C61—41no—
282C22×C61—41no—
283C22×C61#38511yescharacteristic
284C22×C61#38611yescharacteristic
285C22×C61#38811yescharacteristic
286C22×C61#39411yescharacteristic
287C22×C61#39611yescharacteristic
288C22×C61#39711yescharacteristic
289C22×C61#39911yescharacteristic
290C2×D61—42no—
291C2×D61—82no—
292C2×D61—82no—
293C2×D61—82no—
294C4×C61—24no—
295C4×C61—42no—
296C4×C61—82no—
297C4×C61#38011yescharacteristic
298C4×C61#38511yescharacteristic
299C4×C61#38811yescharacteristic
300C4×C61#39011yescharacteristic
301C4×C61#39211yescharacteristic
302C4×C61#39311yescharacteristic
303C4×C61#39411yescharacteristic
304C4×C61#39611yescharacteristic
305Dic61—42no—
306C2×#423—611no—
307C22×#104—611no—
308#2896—611no—
309C2×#413—611no—
310#1742—611no—
311C2×#339D6111yescharacteristic, complemented
312C2×#338—611no—
313C2×C61—21no—
314C2×C61—21no—
315C2×C61—21no—
316C2×C61—21no—
317C2×C61—21no—
318C2×C61—21no—
319C2×C61#143911yescharacteristic
320C2×C61#205012yes—
321D61—82no—
322C22×#41—611no—
323C22×M16—611no—
324C22×M16—611no—
325C22×M16—611no—
326C22×M16C2×D6111yescharacteristic
327C2×#117C2×D6111yescharacteristic
328C22×C42C2×D6111yescharacteristic
329#423—1222no—
330#423—1222no—
331C2×C4⋊C8—1222no—
332C2×#104—614no—
333C2×#104—1222no—
334C2×#104—1221no—
335C2×#104—1221no—
336#419—1221no—
337#418—1221no—
338#417—1222no—
339#416—1222no—
340#413—1222no—
341#413—1222no—
342C2×#101—1221no—
343C2×#100—1221no—
344#343—1222no—
345#339—21no—
346#339—21no—
347#338—1222no—
348C61#1108211yescharacteristic, complemented, Sylow
349C2×#41—612no—
350C2×#41—612no—
351C2×#41—1221no—
352C2×#41—1221no—
353C2×#41—1221no—
354C2×#41—1221no—
355C2×#41—1221no—
356C2×#41—1221no—
357C2×#41—1221no—
358C2×#41—1221no—
359C2×#41—1221no—
360C2×#41—1221no—
361C22×Q8—611no—
362C22×D4—611no—
363C22×D4—1221no—
364C23×C4—21no—
365C23×C4—1221no—
366C23×C4C22×D6111yescharacteristic
367C2×M16—21no—
368C2×M16—21no—
369C2×M16—21no—
370C2×M16—21no—
371C2×M16—21no—
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×M16—1221no—
383C2×M16—1221no—
384C2×M16—1221no—
385C2×M16—1221no—
386C2×M16—1221no—
387C2×M16—1221no—
388C2×M16—1221no—
389C2×M16—1221no—
390C2×M16D24412yes—
391C22×C8—21no—
392C22×C8—612no—
393C22×C8—1221no—
394C22×C8—1221no—
395#117—21no—
396#117—21no—
397#117—21no—
398#117—21no—
399C2×C4⋊C4D24412yes—
400C2×C22⋊C4—21no—
401C2×C42—21no—
402C2×C42—21no—
403C2×C42—21no—
404C2×C42—21no—
405C2×C42C4×D6112yes—
406C2×C42D24412yes—
407C2×C42C22⋊D6111yescharacteristic
408C2×C42C22⋊D6111yescharacteristic
409C4⋊C8—1228no—
410#104—1224no—
411#104—1224no—
412#103—1224no—
413#102—1224no—
414#101—1224no—
415#100—1224no—
416C24—1221no—
417C24#1175822411yescharacteristic
418#41—1222no—
419#41—1222no—
420#41—1222no—
421#41—1222no—
422#41—1222no—
423#41—1222no—
424#41—1222no—
425#41—1222no—
426#41—2441no—
427#41—2441no—
428#41—2441no—
429#41—2441no—
430#41—2441no—
431#41—2441no—
432#41—2441no—
433#41—2441no—
434C2×Q8—612no—
435C2×Q8—1221no—
436C2×Q8—1221no—
437C2×Q8—1221no—
438C2×Q8—1221no—
439C2×Q8—1221no—
440C2×D4—612no—
441C2×D4—1222no—
442C2×D4—1222no—
443C2×D4—1221no—
444C2×D4—1221no—
445C2×D4—1221no—
446C2×D4—1221no—
447C2×D4—1221no—
448C2×D4—2441no—
449C2×D4—2441no—
450C2×D4—2441no—
451C2×D4—2441no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—44no—
458C22×C4—1221no—
459C22×C4—1222no—
460C22×C4—1222no—
461C22×C4—2441no—
462C22×C4—2441no—
463C22×C4—2441no—
464C22×C4—2441no—
465C22×C4C2×C4×D6111yescharacteristic
466C22×C4C2×D24411yescharacteristic
467C22×C4C2×D24411yescharacteristic
468C22×C4C2×D24411yescharacteristic
469C22×C4#1175822211yescharacteristic
470C22×C4#1175822211yescharacteristic
471C22×C4D4×D6111yescharacteristic
472C22×C4D4×D6111yescharacteristic
473C22×C4D4×D6111yescharacteristic
474C22×C4#1175822411yescharacteristic
475C22×C4#1175822411yescharacteristic
476C22×C4Q8×D6111yescharacteristic
477C22×C4#1175822611yescharacteristic
478C22×C4C2×C22⋊D6111yescharacteristic
479M16—22no—
480M16—22no—
481M16—41no—
482M16—41no—
483M16—1222no—
484M16—1222no—
485M16—1222no—
486M16—1222no—
487M16—2441no—
488M16—2441no—
489M16—2441no—
490M16—2441no—
491M16—2441no—
492M16—2441no—
493M16—2441no—
494M16—2441no—
495C2×C8—22no—
496C2×C8—41no—
497C2×C8—41no—
498C2×C8—1222no—
499C2×C8—1222no—
500C2×C8—1222no—
501C2×C8—1222no—
502C2×C8—1222no—
503C2×C8—2441no—
504C2×C8—2441no—
505C2×C8—2441no—
506C2×C8—2441no—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C22⋊C4—41no—
510C22⋊C4—41no—
511C42—22no—
512C42—22no—
513C42—21no—
514C42—21no—
515C42—41no—
516C42—41no—
517C42#1175819812yes—
518C42#1175819812yes—
519C23—42no—
520C23—1222no—
521C23—4882no—
522C23—2441no—
523C23—2441no—
524C23#1451973711yescharacteristic
525C23#1451974911yescharacteristic
526C23#1451975711yescharacteristic
527C23#1451975911yescharacteristic
528C23#1451976111yescharacteristic
529C23#1451976111yescharacteristic
530C23#1451977211yescharacteristic
531Q8—1222no—
532Q8—1222no—
533Q8—2441no—
534Q8—2441no—
535D4—1222no—
536D4—1222no—
537D4—2442no—
538D4—2442no—
539D4—2442no—
540D4—2442no—
541D4—2441no—
542D4—2441no—
543C2×C4—24no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—44no—
547C2×C4—44no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—82no—
551C2×C4—1222no—
552C2×C4—2441no—
553C2×C4—2441no—
554C2×C4—2442no—
555C2×C4—2442no—
556C2×C4—2442no—
557C2×C4—2442no—
558C2×C4C2×#1175819811yescharacteristic
559C2×C4C4⋊C4×D6111yescharacteristic
560C2×C4#1451973511yescharacteristic
561C2×C4#1451973711yescharacteristic
562C2×C4C4×D24411yescharacteristic
563C2×C4C4×D24411yescharacteristic
564C2×C4#1451974711yescharacteristic
565C2×C4#1451974711yescharacteristic
566C2×C4#1451974711yescharacteristic
567C2×C4#1451974811yescharacteristic
568C2×C4#1451974911yescharacteristic
569C2×C4#1451975111yescharacteristic
570C2×C4#1451975111yescharacteristic
571C2×C4#1451975211yescharacteristic
572C2×C4#1451975211yescharacteristic
573C2×C4#1451975211yescharacteristic
574C2×C4#1451975311yescharacteristic
575C2×C4#1451975511yescharacteristic
576C2×C4#1451975511yescharacteristic
577C2×C4#1451975711yescharacteristic
578C2×C4#1451975711yescharacteristic
579C2×C4#1451975911yescharacteristic
580C2×C4#1451976111yescharacteristic
581C2×C4#1451976311yescharacteristic
582C2×C4#1451976311yescharacteristic
583C2×C4#1451976511yescharacteristic
584C2×C4#1451977211yescharacteristic
585C2×C4#1451977411yescharacteristic
586C8—42no—
587C8—2442no—
588C8—2442no—
589C8—2442no—
590C22—22no—
591C22—22no—
592C22—22no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—4882no—
598C22—4882no—
599C22—4882no—
600C22—2442no—
601C22#1683963611yescharacteristic
602C22#1683963911yescharacteristic
603C22#1683965411yescharacteristic
604C22#1683967811yescharacteristic
605C22#1683968411yescharacteristic
606C22#1683968911yescharacteristic
607C22#1683969911yescharacteristic
608C4—24no—
609C4—42no—
610C4—82no—
611C4—2442no—
612C4#1683961911yescharacteristic
613C4#1683963611yescharacteristic
614C4#1683965411yescharacteristic
615C4#1683966411yescharacteristic
616C4#1683967211yescharacteristic
617C4#1683967511yescharacteristic
618C4#1683967811yescharacteristic
619C4#1683968411yescharacteristic
620C2—21no—
621C2—21no—
622C2—21no—
623C2—21no—
624C2—21no—
625C2—21no—
626C2—4882no—
627C2#2144406511yescharacteristic
628C2#2144710512yes—
subgroupG/H
centerC2×C4#14519763
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC2×C61×#339C2
socleC22×C61#394
prime radicalC22×#11758222C22
cosocleC23×C4×C61C23
hypercenterC2×#339D61
hypocenterC61#11082
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#339

Complements

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

NH ≅ G/Ntype
1. C2×#16839786C2semidirect
5. #21445558C2semidirect
6. C2×#16839520C2semidirect
7. C2×C61×#339C2semidirect
18. C2×#14519705C4semidirect
311. C2×#339D61semidirect
348. C61#11082semidirect

Maximal subgroups

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

subgroupindex
C2×#168397862
C22×#145197052
#214543362
C2×#168397442
#214455582
C2×#168395202
C2×C61×#3392
#1108261