Finite Group Databasebeta

← #29587161

Subgroups — #29587161

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
1C22×#14519705C211yesmaximal, characteristic
2#21454339C211yesmaximal, characteristic
3C2×#16839744C211yesmaximal, characteristic
4#21445557C211yesmaximal, characteristic, complemented
5C2×#16839522C211yesmaximal, characteristic, complemented
6C2×#16839520C211yesmaximal, characteristic, complemented
7C2×C61×#423C211yesmaximal, characteristic, complemented
8C22×#11758222C2211yescharacteristic
9C22×#11758194C2211yescharacteristic
10C22×#11758194C2211yescharacteristic
11C2×#14519736C2211yescharacteristic
12C2×#14519705—21no—
13C2×#14519705—21no—
14C2×#14519705—22no—
15C2×#14519705C414yescomplemented
16#16839772—21no—
17#16839768—21no—
18#16839764—22no—
19#16839759—22no—
20#16839744—22no—
21#16839744—22no—
22C2×#14519695—21no—
23C2×#14519693—21no—
24#16839530—22no—
25#16839522—21no—
26#16839522—21no—
27#16839520—22no—
28C22×M16×C61C2211yescharacteristic
29C22×M16×C61C2211yescharacteristic
30C22×C42×C61C2211yescharacteristic
31C61×#423—22no—
32C61×#423—22no—
33C2×C4⋊C8×C61—22no—
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×#11758194C2×C412yes—
61C2×#11758194D412yes—
62C22×#92418—21no—
63C22×#92418—21no—
64#14519736—21no—
65#14519736—21no—
66#14519736—21no—
67#14519736—21no—
68C2×C4⋊Dic61D412yes—
69C2×C22⋊Dic61—21no—
70C2×C4×Dic61—21no—
71#14519705—24no—
72#14519705—24no—
73#14519702—24no—
74#14519699—24no—
75#14519695—24no—
76#14519693—24no—
77C23×C4×C61—21no—
78C23×C4×C61C2311yescharacteristic
79C2×M16×C61—21no—
80C2×M16×C61—21no—
81C2×M16×C61—21no—
82C2×M16×C61—21no—
83C2×M16×C61—21no—
84C2×M16×C61—21no—
85C2×M16×C61—21no—
86C2×M16×C61—21no—
87C2×M16×C61—21no—
88C2×M16×C61—21no—
89C2×M16×C61—21no—
90C2×M16×C61D412yes—
91C22×C8×C61—21no—
92C22×C8×C61D412yes—
93C2×C42×C61—21no—
94C2×C42×C61—21no—
95C2×C42×C61—21no—
96C2×C42×C61C2×C412yes—
97C2×C42×C61D411yescharacteristic
98C2×C42×C61D411yescharacteristic
99C2×C42×C61D412yes—
100C4⋊C8×C61—28no—
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—44no—
108C22×C4×C61C22×C411yescharacteristic
109C22×C4×C61C2×D411yescharacteristic
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×Q811yescharacteristic
117C22×C4×C61#4111yescharacteristic
118C22×C4×C61#4111yescharacteristic
119C22×C4×C61#4111yescharacteristic
120C22×C4×C61#4111yescharacteristic
121C22×C4×C61#4111yescharacteristic
122C2×C22⋊D61—22no—
123C2×C22⋊D61—22no—
124C2×C22⋊D61—41no—
125C2×C22⋊D61—41no—
126C2×C22⋊D61—41no—
127C2×C22⋊D61—41no—
128C22×Dic61—21no—
129C22×Dic61—22no—
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—
168M16×C61—41no—
169M16×C61—41no—
170M16×C61—41no—
171M16×C61—41no—
172C2×C8×C61—22no—
173C2×C8×C61—22no—
174C2×C8×C61—22no—
175C2×C8×C61—22no—
176C2×C8×C61—41no—
177C2×C8×C61—41no—
178C42×C61—22no—
179C42×C61—22no—
180C42×C61—21no—
181C42×C61—21no—
182C42×C61C22⋊C412yes—
183C42×C61C22⋊C412yes—
184C22⋊Dic61—41no—
185C22⋊Dic61—41no—
186C4⋊Dic61—22no—
187C4⋊Dic61—22no—
188C4×Dic61—41no—
189C4×Dic61—41no—
190#11758194—22no—
191#11758194—22no—
192#11758194—22no—
193#11758194—22no—
194#11758194—41no—
195#11758194—41no—
196#11758194—41no—
197#11758194—41no—
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×C61C2×C22⋊C411yescharacteristic
223C2×C4×C61C2×C4⋊C411yescharacteristic
224C2×C4×C61#11711yescharacteristic
225C2×C4×C61C4×D411yescharacteristic
226C2×C4×C61C4×D411yescharacteristic
227C2×C4×C61C4×D411yescharacteristic
228C2×C4×C61#12011yescharacteristic
229C2×C4×C61#12011yescharacteristic
230C2×C4×C61#12011yescharacteristic
231C2×C4×C61#12111yescharacteristic
232C2×C4×C61#12111yescharacteristic
233C2×C4×C61#12111yescharacteristic
234C2×C4×C61#12111yescharacteristic
235C2×C4×C61#12111yescharacteristic
236C2×C4×C61#12111yescharacteristic
237C2×C4×C61#12111yescharacteristic
238C2×C4×C61C22⋊Q811yescharacteristic
239C2×C4×C61C22⋊Q811yescharacteristic
240C2×C4×C61C22⋊Q811yescharacteristic
241C2×C4×C61C22⋊Q811yescharacteristic
242C2×C4×C61C22⋊Q811yescharacteristic
243C2×C4×C61#12311yescharacteristic
244C2×C4×C61#12311yescharacteristic
245C2×C4×C61#12411yescharacteristic
246C2×C4×C61#12411yescharacteristic
247C2×C4×C61#12411yescharacteristic
248C2×C4×C61#12611yescharacteristic
249C2×C4×C61#12711yescharacteristic
250C22⋊D61—42no—
251C22⋊D61—42no—
252C22⋊D61—42no—
253C22⋊D61—42no—
254C2×Dic61—22no—
255C2×Dic61—41no—
256C2×Dic61—41no—
257C2×Dic61—42no—
258C2×Dic61—82no—
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—
272C8×C61—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#38011yescharacteristic
297C4×C61#38511yescharacteristic
298C4×C61#38811yescharacteristic
299C4×C61#39011yescharacteristic
300C4×C61#39211yescharacteristic
301C4×C61#39311yescharacteristic
302C4×C61#39411yescharacteristic
303C4×C61#39611yescharacteristic
304Dic61—42no—
305Dic61—82no—
306C2×#423D6111yescharacteristic, complemented
307C22×#104—611no—
308#2896—611no—
309C2×#413—611no—
310#1742—611no—
311C2×#339—611no—
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×M16C2×D6111yescharacteristic
326C22×M16C2×D6111yescharacteristic
327C2×#117—611no—
328C22×C42C2×D6111yescharacteristic
329#423—22no—
330#423—22no—
331C2×C4⋊C8—22no—
332C2×#104—614no—
333C2×#104—1221no—
334C2×#104—1221no—
335C2×#104—1222no—
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—1221no—
346#339—1221no—
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—21no—
373C2×M16—21no—
374C2×M16—21no—
375C2×M16—21no—
376C2×M16—21no—
377C2×M16—21no—
378C2×M16—612no—
379C2×M16—612no—
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×M16C22⋊D6112yes—
391C22×C8—21no—
392C22×C8—1221no—
393C22×C8—1221no—
394C22×C8C22⋊D6112yes—
395#117—1221no—
396#117—1221no—
397#117—1221no—
398#117—1221no—
399C2×C4⋊C4—612no—
400C2×C22⋊C4—1221no—
401C2×C42—21no—
402C2×C42—21no—
403C2×C42—21no—
404C2×C42—1221no—
405C2×C42C4×D6112yes—
406C2×C42D24411yescharacteristic
407C2×C42D24411yescharacteristic
408C2×C42C22⋊D6112yes—
409C4⋊C8—28no—
410#104—1224no—
411#104—1224no—
412#103—1224no—
413#102—1224no—
414#101—1224no—
415#100—1224no—
416C24—1221no—
417C24#1175822211yescharacteristic
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—44no—
457C22×C4—1221no—
458C22×C4—1222no—
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×C4#1175822211yescharacteristic
468C22×C4D4×D6111yescharacteristic
469C22×C4D4×D6111yescharacteristic
470C22×C4D4×D6111yescharacteristic
471C22×C4#1175822411yescharacteristic
472C22×C4Q8×D6111yescharacteristic
473C22×C4#1175822611yescharacteristic
474C22×C4#1175822611yescharacteristic
475C22×C4#1175822611yescharacteristic
476C22×C4C2×C22⋊D6111yescharacteristic
477C22×C4C2×C22⋊D6111yescharacteristic
478C22×C4C2×C22⋊D6111yescharacteristic
479M16—22no—
480M16—22no—
481M16—41no—
482M16—41no—
483M16—41no—
484M16—41no—
485M16—41no—
486M16—41no—
487M16—1222no—
488M16—1222no—
489M16—1222no—
490M16—1222no—
491M16—2441no—
492M16—2441no—
493M16—2441no—
494M16—2441no—
495C2×C8—22no—
496C2×C8—22no—
497C2×C8—22no—
498C2×C8—22no—
499C2×C8—41no—
500C2×C8—41no—
501C2×C8—1222no—
502C2×C8—1222no—
503C2×C8—2441no—
504C2×C8—2441no—
505C2×C8—2441no—
506C2×C8—2441no—
507C4⋊C4—1222no—
508C4⋊C4—1222no—
509C22⋊C4—2441no—
510C22⋊C4—2441no—
511C42—22no—
512C42—22no—
513C42—21no—
514C42—21no—
515C42—2441no—
516C42—2441no—
517C42#1175819812yes—
518C42#1175819812yes—
519C23—42no—
520C23—1222no—
521C23—4882no—
522C23—2441no—
523C23—2441no—
524C23C4×C22⋊D6111yescharacteristic
525C23#1451975111yescharacteristic
526C23#1451975511yescharacteristic
527C23#1451976011yescharacteristic
528C23#1451976211yescharacteristic
529C23#1451976211yescharacteristic
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—1222no—
550C2×C4—4882no—
551C2×C4—2442no—
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×C4C4×C22⋊D6111yescharacteristic
562C2×C4#1451973911yescharacteristic
563C2×C4#1451973911yescharacteristic
564C2×C4#1451974511yescharacteristic
565C2×C4#1451974511yescharacteristic
566C2×C4#1451974611yescharacteristic
567C2×C4#1451974811yescharacteristic
568C2×C4#1451974911yescharacteristic
569C2×C4#1451974911yescharacteristic
570C2×C4#1451975111yescharacteristic
571C2×C4#1451975211yescharacteristic
572C2×C4#1451975211yescharacteristic
573C2×C4#1451975211yescharacteristic
574C2×C4#1451975311yescharacteristic
575C2×C4#1451975311yescharacteristic
576C2×C4#1451975311yescharacteristic
577C2×C4#1451975511yescharacteristic
578C2×C4#1451975711yescharacteristic
579C2×C4#1451976211yescharacteristic
580C2×C4#1451976211yescharacteristic
581C2×C4#1451976611yescharacteristic
582C2×C4#1451976611yescharacteristic
583C2×C4#1451976611yescharacteristic
584C2×C4#1451977211yescharacteristic
585C2×C4#1451977311yescharacteristic
586C8—42no—
587C8—42no—
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#1683963311yescharacteristic
602C22#1683964111yescharacteristic
603C22#1683965211yescharacteristic
604C22#1683967911yescharacteristic
605C22#1683968411yescharacteristic
606C22#1683968811yescharacteristic
607C22#1683969711yescharacteristic
608C4—24no—
609C4—42no—
610C4—4882no—
611C4—2442no—
612C4#1683961911yescharacteristic
613C4#1683963311yescharacteristic
614C4#1683965211yescharacteristic
615C4#1683966311yescharacteristic
616C4#1683967011yescharacteristic
617C4#1683967311yescharacteristic
618C4#1683967911yescharacteristic
619C4#1683968411yescharacteristic
620C2—21no—
621C2—21no—
622C2—21no—
623C2—21no—
624C2—21no—
625C2—21no—
626C2—4882no—
627C2#2144406111yescharacteristic
628C2#2144710612yes—
subgroupG/H
centerC2×C4#14519766
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC2×C61×#423C2
socleC22×C61#394
prime radicalC22×#11758222C22
cosocleC23×C4×C61C23
hypercenterC2×#423D61
hypocenterC61#11082
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#423

Complements

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

NH ≅ G/Ntype
4. #21445557C2semidirect
5. C2×#16839522C2semidirect
6. C2×#16839520C2semidirect
7. C2×C61×#423C2semidirect
15. C2×#14519705C4semidirect
306. C2×#423D61semidirect
348. C61#11082semidirect

Maximal subgroups

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

subgroupindex
C22×#145197052
#214543392
C2×#168397442
#214455572
C2×#168395222
C2×#168395202
C2×C61×#4232
#1108261