Finite Group Databasebeta

← #29683722

Subgroups — #29683722

Order 15616.

1718 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840330C211yesmaximal, characteristic
2C2×#16839762C211yesmaximal, characteristic, complemented
3C2×#16839765C211yesmaximal, characteristic, complemented
4C2×#16839757C211yesmaximal, characteristic, complemented
5C2×#102×D61C211yesmaximal, characteristic, complemented
6C2×#16839716C211yesmaximal, characteristic, complemented
7#21448444C211yesmaximal, characteristic, complemented
8#21446642C211yesmaximal, characteristic, complemented
9#21446641C211yesmaximal, characteristic, complemented
10#21446636C211yesmaximal, characteristic, complemented
11#21446632C211yesmaximal, characteristic, complemented
12#21446627C211yesmaximal, characteristic, complemented
13#21446625C211yesmaximal, characteristic, complemented
14#21446623C211yesmaximal, characteristic, complemented
15C61×#1958C211yesmaximal, characteristic, complemented
16C22×#11758226C2211yescharacteristic
17C22×D4×D61C2211yescharacteristic
18C22×#11758189C2211yescharacteristic
19C22×C8×D61C2211yescharacteristic
20#16840330—24no—
21#16840330C418yescomplemented
22C2×#14519774C2211yescharacteristic
23C2×#14519773C2211yescharacteristic
24C2×#14519766C2211yescharacteristic
25C2×#14519750—22no—
26C2×#14519747—22no—
27C2×#14519735C2211yescharacteristic
28C2×#14519734C2211yescharacteristic
29C2×C4⋊C4×D61C2211yescharacteristic
30#16839765—24no—
31#16839762—24no—
32#16839757—24no—
33C2×#14519701C2211yescharacteristic, complemented
34C2×#14519701C2211yescharacteristic, complemented
35C2×#14519699C2211yescharacteristic
36C2×#14519699C2211yescharacteristic
37C2×#14519699C2211yescharacteristic, complemented
38C2×#14519699C2211yescharacteristic, complemented
39C2×#14519698C2211yescharacteristic
40C2×#14519698C2211yescharacteristic
41C2×#14519697C2211yescharacteristic
42C2×#14519697C2211yescharacteristic
43C2×#14519697C2211yescharacteristic, complemented
44C2×#14519697C2211yescharacteristic, complemented
45#102×D61—24no—
46#16839716—24no—
47C2×#14519688C2211yescharacteristic, complemented
48C2×#14519687C2211yescharacteristic, complemented
49C2×C8×Dic61C2211yescharacteristic, complemented
50#16839659—22no—
51#16839636—22no—
52#16839632C2211yescharacteristic, complemented
53#16839631C2211yescharacteristic, complemented
54#16839627C2211yescharacteristic, complemented
55C2×#124×C61C2211yescharacteristic
56C2×#103×C61C2211yescharacteristic, complemented
57C2×#103×C61C2211yescharacteristic, complemented
58C2×#102×C61C2211yescharacteristic
59C2×#102×C61C2211yescharacteristic
60C2×C4×C8×C61C2211yescharacteristic, complemented
61C61×#382C2211yescharacteristic, complemented
62C24×D61—21no—
63C2×#11758226—22no—
64C2×#11758226—22no—
65C2×#11758226—22no—
66C2×#11758226—22no—
67C2×#11758226—22no—
68C2×#11758226C2×C414yes—
69C22×D244—21no—
70C22×D244—22no—
71C22×D244C2311yescharacteristic
72C22×D244C2311yescharacteristic
73C22×C22⋊D61—21no—
74C22×C22⋊D61—22no—
75C2×D4×D61—22no—
76C2×D4×D61—22no—
77C2×D4×D61—22no—
78C2×D4×D61—22no—
79C2×D4×D61—22no—
80C2×D4×D61C2×C414yes—
81C22×C4×D61—21no—
82C22×C4×D61—21no—
83C22×C4×D61C2311yescharacteristic
84C2×#11758189—22no—
85C2×#11758189—22no—
86C2×#11758189D414yescomplemented
87C22×#92418C2311yescharacteristic
88C22×#92418C2311yescharacteristic
89C2×C8×D61—22no—
90C2×C8×D61—22no—
91C2×C8×D61D414yescomplemented
92#14519774—22no—
93#14519774C2×C414yescomplemented
94#14519773—22no—
95#14519773C2×C414yescomplemented
96#14519766—22no—
97#14519766C2×C414yescomplemented
98#14519750—216no—
99#14519747—216no—
100#14519735—22no—
101#14519735—22no—
102#14519734C2×C414yes—
103#14519734D414yes—
104C2×C4⋊Dic61—22no—
105C2×C4⋊Dic61C2311yescharacteristic
106C2×C4⋊Dic61C2311yescharacteristic
107C2×#11758196—21no—
108C2×#11758196—22no—
109C2×#11758196D412yes—
110C4⋊C4×D61—22no—
111C4⋊C4×D61—22no—
112C2×#11758198—22no—
113C2×#11758198—21no—
114C2×#11758198D412yes—
115C2×C4×Dic61—21no—
116C2×C4×Dic61C2311yescharacteristic
117#14519701—22no—
118#14519701—22no—
119#14519699—22no—
120#14519699—22no—
121#14519699—22no—
122#14519699—22no—
123#14519698—22no—
124#14519698—22no—
125#14519697—22no—
126#14519697—22no—
127#14519697—22no—
128#14519697—22no—
129#14519688—22no—
130#14519687—22no—
131C8×Dic61—22no—
132#14519684—22no—
133C22×Q8×C61C2311yescharacteristic
134C22×D4×C61C2311yescharacteristic
135C22×C8×C61C2311yescharacteristic
136C22×C8×C61C2311yescharacteristic
137#124×C61—22no—
138#124×C61C2×C414yescomplemented
139C2×C4⋊C4×C61C2311yescharacteristic
140C2×C4⋊C4×C61C2311yescharacteristic
141C2×C22⋊C4×C61—22no—
142C2×C42×C61C2311yescharacteristic
143#103×C61—22no—
144#103×C61—22no—
145#102×C61—22no—
146#102×C61—22no—
147C4×C8×C61—22no—
148#95×C61—22no—
149C24×C61—21no—
150C23×D61—21no—
151C23×D61—21no—
152C23×D61—24no—
153C23×D61—42no—
154C23×D61—42no—
155C23×D61—82no—
156C23×D61—82no—
157C23×D61C2×D411yescharacteristic
158C2×Q8×C61—21no—
159C2×Q8×C61—21no—
160C2×Q8×C61—21no—
161C2×Q8×C61—21no—
162C2×Q8×C61—21no—
163C2×Q8×C61C22×C412yes—
164C2×D4×C61—21no—
165C2×D4×C61—21no—
166C2×D4×C61—21no—
167C2×D4×C61—21no—
168C2×D4×C61—21no—
169C2×D4×C61C22×C412yes—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61C2×D412yes—
174C22×C4×C61C2411yescharacteristic
175C2×C22⋊D61—24no—
176C2×C22⋊D61—28no—
177C2×C22⋊D61—42no—
178C2×C22⋊D61—42no—
179C2×C22⋊D61—82no—
180C2×C22⋊D61—82no—
181C22×Dic61—21no—
182C22×Dic61—21no—
183C22×Dic61C2×D412yes—
184C22×Dic61C2×D411yescharacteristic
185#11758226—28no—
186#11758226—28no—
187#11758226—44no—
188#11758226—44no—
189D4×D61—28no—
190D4×D61—28no—
191D4×D61—44no—
192D4×D61—44no—
193C2×D244—21no—
194C2×D244—21no—
195C2×D244—21no—
196C2×D244—21no—
197C2×D244—21no—
198C2×D244—21no—
199C2×D244—21no—
200C2×D244—21no—
201C2×D244—24no—
202C2×D244—21no—
203C2×D244—21no—
204C2×D244—28no—
205C2×D244—42no—
206C2×D244—42no—
207C2×D244—82no—
208C2×D244—82no—
209C2×D244C22×C412yes—
210C2×D244C22×C412yes—
211C2×C4×D61—24no—
212C2×C4×D61—42no—
213C2×C4×D61—42no—
214C2×C4×D61—42no—
215C2×C4×D61—82no—
216C2×C4×D61C22×C412yes—
217C2×C4×D61C2×D412yes—
218C2×C4×D61C2×D412yes—
219C2×C4×D61C2×D412yes—
220C2×C4×D61#4112yes—
221C2×C4×D61#4112yes—
222C2×C8×C61—21no—
223C2×C8×C61—21no—
224C2×C8×C61—21no—
225C2×C8×C61—21no—
226C2×C8×C61C2×D412yes—
227C2×C8×C61C2×D412yes—
228C4⋊C4×C61—21no—
229C4⋊C4×C61—21no—
230C4⋊C4×C61—21no—
231C4⋊C4×C61—21no—
232C22⋊C4×C61—28no—
233C42×C61C22×C412yes—
234C42×C61C2×D412yes—
235#11758198—28no—
236#11758198—42no—
237#11758198C22⋊C418yes—
238C4⋊Dic61—21no—
239C4⋊Dic61—21no—
240C4⋊Dic61—21no—
241C4⋊Dic61—21no—
242C4⋊Dic61—82no—
243#11758196—42no—
244#11758196—82no—
245#11758196C22⋊C418yes—
246C4×Dic61—42no—
247C4×Dic61C22×C412yes—
248C4×Dic61C2×D412yes—
249C2×#92418—21no—
250C2×#92418—21no—
251C2×#92418—21no—
252C2×#92418—21no—
253C2×#92418C2×D412yes—
254C2×#92418C2×D412yes—
255#11758189—28no—
256C8×D61—28no—
257C23×C61—22no—
258C23×C61—41no—
259C23×C61—41no—
260C23×C61—42no—
261C23×C61—42no—
262C23×C61C22×D411yescharacteristic
263C22×D61—22no—
264C22×D61—22no—
265C22×D61—22no—
266C22×D61—22no—
267C22×D61—41no—
268C22×D61—41no—
269C22×D61—41no—
270C22×D61—41no—
271C22×D61—42no—
272C22×D61—42no—
273C22×D61—42no—
274C22×D61—42no—
275C22×D61—48no—
276C22×D61—88no—
277C22×D61—88no—
278C22×D61—84no—
279C22×D61—84no—
280C22×D61C2×C22⋊C412yes—
281C22×D61#12412yes—
282C22×D61#12712yes—
283Q8×C61—22no—
284Q8×C61—22no—
285Q8×C61—41no—
286Q8×C61—41no—
287D4×C61—22no—
288D4×C61—22no—
289D4×C61—41no—
290D4×C61—41no—
291C2×C4×C61—22no—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—41no—
295C2×C4×C61—41no—
296C2×C4×C61—41no—
297C2×C4×C61—41no—
298C2×C4×C61—42no—
299C2×C4×C61—42no—
300C2×C4×C61C2×C22⋊C414yes—
301C2×C4×C61C23×C411yescharacteristic
302C2×C4×C61C22×D411yescharacteristic
303C2×C4×C61C22×D411yescharacteristic
304C2×C4×C61C22×D411yescharacteristic
305C2×C4×C61C2×#4111yescharacteristic
306C2×C4×C61C2×#4111yescharacteristic
307C22⋊D61—48no—
308C22⋊D61—88no—
309C2×Dic61—22no—
310C2×Dic61—22no—
311C2×Dic61—41no—
312C2×Dic61—41no—
313C2×Dic61—42no—
314C2×Dic61—42no—
315C2×Dic61C2×C22⋊C414yes—
316C2×Dic61C2×C22⋊C412yes—
317C2×Dic61#12412yes—
318C2×Dic61#12712yes—
319D244—22no—
320D244—22no—
321D244—22no—
322D244—22no—
323D244—48no—
324D244—41no—
325D244—41no—
326D244—41no—
327D244—41no—
328D244—88no—
329C4×D61—48no—
330C4×D61—84no—
331C4×D61C4×D414yes—
332C4×D61C4×D414yes—
333C4×D61#12114yes—
334C4×D61#12114yes—
335C8×C61—22no—
336C8×C61—22no—
337#92418—22no—
338#92418—22no—
339#21206—611nomaximal, Sylow
340C22×C61—44no—
341C22×C61—42no—
342C22×C61—82no—
343C22×C61—81no—
344C22×C61—81no—
345C22×C61C22×C22⋊C411yescharacteristic
346C22×C61C2×#12411yescharacteristic
347C22×C61C2×#12711yescharacteristic
348C22×C61#57612yes—
349C22×C61#57712yes—
350C2×D61—24no—
351C2×D61—24no—
352C2×D61—22no—
353C2×D61—22no—
354C2×D61—44no—
355C2×D61—44no—
356C2×D61—42no—
357C2×D61—42no—
358C2×D61—816no—
359C2×D61—82no—
360C2×D61—82no—
361C2×D61—81no—
362C2×D61—81no—
363C2×D61—81no—
364C2×D61—81no—
365C2×D61#39014yes—
366C4×C61—24no—
367C4×C61—42no—
368C4×C61—81no—
369C4×C61—81no—
370C4×C61C2×C4×D411yescharacteristic
371C4×C61C2×C4×D411yescharacteristic
372C4×C61C2×#12111yescharacteristic
373C4×C61C2×#12111yescharacteristic
374Dic61—24no—
375Dic61—81no—
376Dic61—81no—
377Dic61#39014yes—
378C2×#535—611no—
379C2×#417—611no—
380C2×#418—611no—
381C2×#416—611no—
382C22×#102—611no—
383C2×#405—611no—
384#2317—611no—
385#1961—611no—
386#1961—611no—
387#1959—611no—
388#1959—611no—
389#1958—611no—
390#1958D6111yescharacteristic, complemented
391#1957—611no—
392#1957—611no—
393C2×C61—82no—
394C2×C61C2×#39011yescharacteristic
395C2×C61#289712yes—
396C2×C61#313612yes—
397C2×C61#315411yescharacteristic
398C2×C61#315511yescharacteristic
399D61—24no—
400D61—82no—
401D61—82no—
402C22×#41—611no—
403C23×D4—611no—
404C22×M16—611no—
405C23×C8—611no—
406#535—618no—
407#535—1224no—
408C2×#127—611no—
409C2×#127—611no—
410C2×#124—611no—
411C2×#124C2×D6111yescharacteristic
412C2×#121—1222no—
413C2×#120—1222no—
414C2×#117—611no—
415C2×#117—611no—
416C22×C4⋊C4—611no—
417#418—1224no—
418#417—1224no—
419#416—1224no—
420C2×#103—611no—
421C2×#103—611no—
422C2×#103C2×D6111yescharacteristic, complemented
423C2×#103C2×D6111yescharacteristic, complemented
424C2×#102—611no—
425C2×#102—611no—
426C2×#102—611no—
427C2×#102—611no—
428C2×#102—611no—
429C2×#102—611no—
430C2×#102—611no—
431C2×#102—611no—
432C2×#102—611no—
433C2×#102—611no—
434C2×#102—1224no—
435C2×#102C2×D6111yescharacteristic
436C2×#102C2×D6111yescharacteristic
437#405—1224no—
438C2×#97—611no—
439C2×#97—611no—
440C2×C4×C8—611no—
441C2×C4×C8C2×D6111yescharacteristic, complemented
442#389—1222no—
443#385—1222no—
444#384—611no—
445#384—611no—
446#382—611no—
447#382C2×D6111yescharacteristic, complemented
448C61#2120611yescharacteristic, complemented, Sylow
449C25—1221no—
450C2×#41—614no—
451C2×#41—1222no—
452C2×#41—1222no—
453C2×#41—1222no—
454C2×#41—1222no—
455C2×#41—1222no—
456C22×Q8C22×D6111yescharacteristic
457C22×D4—614no—
458C22×D4—611no—
459C22×D4—611no—
460C22×D4—1221no—
461C22×D4—1222no—
462C22×D4—1222no—
463C22×D4—1222no—
464C22×D4—1222no—
465C22×D4—1222no—
466C22×D4—1222no—
467C22×D4—1221no—
468C22×D4—1222no—
469C22×D4C22×D6111yescharacteristic
470C23×C4—611no—
471C23×C4—1221no—
472C23×C4—1221no—
473C2×M16—614no—
474C2×M16—1222no—
475C2×M16—1222no—
476C22×C8—611no—
477C22×C8—611no—
478C22×C8—614no—
479C22×C8—1222no—
480C22×C8—1222no—
481C22×C8C22×D6111yescharacteristic
482C22×C8C22×D6111yescharacteristic
483#127—614no—
484#127—614no—
485#127—1222no—
486#127—1222no—
487#124—22no—
488#124—614no—
489#124—1222no—
490#124C4×D6114yescomplemented
491#121—12216no—
492#120—12216no—
493#117—614no—
494#117—614no—
495#117—1222no—
496#117—1222no—
497C2×C4⋊C4—612no—
498C2×C4⋊C4—611no—
499C2×C4⋊C4—611no—
500C2×C4⋊C4—1222no—
501C2×C4⋊C4—1222no—
502C2×C4⋊C4—1222no—
503C2×C4⋊C4—1222no—
504C2×C4⋊C4—1221no—
505C2×C4⋊C4C22×D6111yescharacteristic
506C2×C4⋊C4C22×D6111yescharacteristic
507C2×C22⋊C4—22no—
508C2×C22⋊C4—612no—
509C2×C22⋊C4—1222no—
510C2×C22⋊C4—1221no—
511C2×C42—611no—
512C2×C42—1221no—
513C2×C42C22×D6111yescharacteristic
514#103—22no—
515#103—22no—
516#103—1222no—
517#103—1222no—
518#102—22no—
519#102—22no—
520#102—1222no—
521#102—1222no—
522#102—1222no—
523#102—1222no—
524#102—1222no—
525#102—1222no—
526#102—1222no—
527#102—1222no—
528#102—1222no—
529#102—1222no—
530#97—1222no—
531#97—1222no—
532C4×C8—22no—
533C4×C8—1222no—
534#95—22no—
535#95—1222no—
536C24—21no—
537C24—611no—
538C24—1224no—
539C24—1221no—
540C24—1221no—
541C24—4882no—
542C24—4882no—
543C24—2442no—
544C24—2442no—
545#41—1228no—
546#41—1228no—
547#41—2444no—
548#41—2444no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8C2×C4×D6112yes—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—612no—
561C2×D4—612no—
562C2×D4—1224no—
563C2×D4—1228no—
564C2×D4—1228no—
565C2×D4—1228no—
566C2×D4—1224no—
567C2×D4—1221no—
568C2×D4—1221no—
569C2×D4—1221no—
570C2×D4—1221no—
571C2×D4—1221no—
572C2×D4—1221no—
573C2×D4—1221no—
574C2×D4—1221no—
575C2×D4—1221no—
576C2×D4—1221no—
577C2×D4—1228no—
578C2×D4—4882no—
579C2×D4—4882no—
580C2×D4—4882no—
581C2×D4—4882no—
582C2×D4—2442no—
583C2×D4—2442no—
584C2×D4—2444no—
585C2×D4—2444no—
586C2×D4—2442no—
587C2×D4—2442no—
588C2×D4C2×C4×D6112yes—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—611no—
593C22×C4—612no—
594C22×C4—612no—
595C22×C4—612no—
596C22×C4—612no—
597C22×C4—612no—
598C22×C4—612no—
599C22×C4—612no—
600C22×C4—1224no—
601C22×C4—1221no—
602C22×C4—1221no—
603C22×C4—4882no—
604C22×C4—2442no—
605C22×C4—2442no—
606C22×C4—2442no—
607C22×C4D4×D6112yes—
608C22×C4C23×D6111yescharacteristic
609M16—1228no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—612no—
615C2×C8—612no—
616C2×C8—1228no—
617C2×C8—1221no—
618C2×C8—1221no—
619C2×C8—1221no—
620C2×C8—1221no—
621C2×C8D4×D6112yes—
622C2×C8D4×D6112yes—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—618no—
628C4⋊C4—1221no—
629C4⋊C4—1221no—
630C4⋊C4—1221no—
631C4⋊C4—1221no—
632C4⋊C4—4882no—
633C4⋊C4—4882no—
634C4⋊C4—2442no—
635C22⋊C4—28no—
636C22⋊C4—618no—
637C22⋊C4—1228no—
638C22⋊C4—2442no—
639C42—612no—
640C42—612no—
641C42—2442no—
642C42C2×C4×D6112yes—
643C42D4×D6112yes—
644C23—22no—
645C23—41no—
646C23—41no—
647C23—42no—
648C23—42no—
649C23—612no—
650C23—612no—
651C23—612no—
652C23—1222no—
653C23—1222no—
654C23—1222no—
655C23—1222no—
656C23—4888no—
657C23—4888no—
658C23—4884no—
659C23—4884no—
660C23—2448no—
661C23—2441no—
662C23—2441no—
663C23—2441no—
664C23—2441no—
665C23—2442no—
666C23—2442no—
667C23—2442no—
668C23—2442no—
669C23C2×D4×D6111yescharacteristic
670Q8—22no—
671Q8—22no—
672Q8—41no—
673Q8—41no—
674D4—22no—
675D4—22no—
676D4—41no—
677D4—41no—
678D4—1222no—
679D4—1222no—
680D4—1222no—
681D4—1222no—
682D4—4888no—
683D4—4888no—
684D4—2448no—
685D4—2448no—
686D4—2441no—
687D4—2441no—
688D4—2441no—
689D4—2441no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—612no—
700C2×C4—612no—
701C2×C4—612no—
702C2×C4—614no—
703C2×C4—614no—
704C2×C4—614no—
705C2×C4—614no—
706C2×C4—614no—
707C2×C4—1222no—
708C2×C4—1222no—
709C2×C4—4884no—
710C2×C4—2448no—
711C2×C4—2441no—
712C2×C4—2441no—
713C2×C4—2442no—
714C2×C4—2442no—
715C2×C4C22⋊C4×D6114yes—
716C2×C4C22×C4×D6111yescharacteristic
717C2×C4C2×D4×D6111yescharacteristic
718C2×C4C2×D4×D6111yescharacteristic
719C2×C4C2×D4×D6111yescharacteristic
720C2×C4#41×D6111yescharacteristic
721C2×C4#41×D6111yescharacteristic
722C8—22no—
723C8—22no—
724C8—1222no—
725C8—1222no—
726C22—44no—
727C22—42no—
728C22—82no—
729C22—81no—
730C22—81no—
731C22—614no—
732C22—1224no—
733C22—1224no—
734C22—1222no—
735C22—1222no—
736C22—48816no—
737C22—4882no—
738C22—4882no—
739C22—4881no—
740C22—4881no—
741C22—4881no—
742C22—4881no—
743C22—2444no—
744C22—2444no—
745C22—2442no—
746C22—2442no—
747C22C2×C22⋊C4×D6111yescharacteristic
748C22#124×D6111yescharacteristic
749C22#127×D6111yescharacteristic
750C22#1684056412yes—
751C22#1684056912yes—
752C4—24no—
753C4—42no—
754C4—81no—
755C4—81no—
756C4—614no—
757C4—1224no—
758C4—4881no—
759C4—4881no—
760C4C4×D4×D6111yescharacteristic
761C4C4×D4×D6111yescharacteristic
762C4#121×D6111yescharacteristic
763C4#121×D6111yescharacteristic
764C2—82no—
765C2—1224no—
766C2—4882no—
767C2—4882no—
768C2#390×D6111yescharacteristic
769C2#2145434112yes—
770C2#2145617212yes—
771C2#2145629011yescharacteristic
772C2#2145630111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1958C2
socleC23×C61C22×D4
prime radicalC2×#16840330C2
cosocleC22×C4×C61C24
hypercenter#1958D61
hypocenterC61#21206
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1958

Complements

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

NH ≅ G/Ntype
2. C2×#16839762C2semidirect
3. C2×#16839765C2semidirect
4. C2×#16839757C2semidirect
5. C2×#102×D61C2semidirect
6. C2×#16839716C2semidirect
7. #21448444C2semidirect
8. #21446642C2semidirect
9. #21446641C2semidirect
10. #21446636C2semidirect
11. #21446632C2semidirect
12. #21446627C2semidirect
13. #21446625C2semidirect
14. #21446623C2semidirect
15. C61×#1958C2semidirect
21. #16840330C4semidirect
33. C2×#14519701C22semidirect
34. C2×#14519701C22semidirect
37. C2×#14519699C22semidirect
38. C2×#14519699C22semidirect
43. C2×#14519697C22semidirect
44. C2×#14519697C22semidirect
47. C2×#14519688C22semidirect
48. C2×#14519687C22semidirect
49. C2×C8×Dic61C22semidirect
52. #16839632C22semidirect
53. #16839631C22semidirect
54. #16839627C22semidirect
56. C2×#103×C61C22semidirect
57. C2×#103×C61C22semidirect
60. C2×C4×C8×C61C22semidirect
61. C61×#382C22semidirect
86. C2×#11758189D4semidirect
91. C2×C8×D61D4semidirect
93. #14519774C2×C4semidirect
95. #14519773C2×C4semidirect
97. #14519766C2×C4semidirect
138. #124×C61C2×C4semidirect
390. #1958D61semidirect
422. C2×#103C2×D61semidirect
423. C2×#103C2×D61semidirect
441. C2×C4×C8C2×D61semidirect
447. #382C2×D61semidirect
448. C61#21206semidirect
490. #124C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168403302
C2×#168397622
C2×#168397652
C2×#168397572
C2×#102×D612
C2×#168397162
#214484442
#214466422
#214466412
#214466362
#214466322
#214466272
#214466252
#214466232
C61×#19582
#2120661