Finite Group Databasebeta

← C2×#21446864 #29706971

Subgroups — C2×#21446864 #29706971

Order 15616.

2038 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519808C211yesmaximal, characteristic, complemented
2C2×#16840340C211yesmaximal, characteristic
3C22×#14519704C211yesmaximal, characteristic, complemented
4C22×#14519703C211yesmaximal, characteristic, complemented
5C2×#16839669C211yesmaximal, characteristic, complemented
6#21446864C218yesmaximal, direct product factor
7C2×#16839530C211yesmaximal, characteristic, complemented
8C22×#137×C61C211yesmaximal, characteristic, complemented
9C22×#11758222C2211yescharacteristic
10C2×#14519808—24no—
11C2×#14519808—24no—
12C2×#14519808—22no—
13C2×#14519808C2214yescomplemented
14C22×#11758202—21no—
15C22×#11758201—21no—
16C22×#11758194C2211yescharacteristic
17#16840340—22no—
18#16840340—22no—
19#16840340—22no—
20#16840340C2214yes—
21C2×#14519756—21no—
22C2×#14519753—21no—
23C2×#14519751—21no—
24C2×#14519749—22no—
25C2×#14519748—21no—
26C22×C4⋊Dic61C2211yescharacteristic
27C22×C4×Dic61C2211yescharacteristic
28C2×#14519704—24no—
29C2×#14519704C2214yescomplemented
30C2×#14519703—24no—
31C2×#14519703C2214yescomplemented
32#16839669—22no—
33#16839669C2214yescomplemented
34C2×#14519684—22no—
35#16839530C2214yescomplemented
36C22×#41×C61C2211yescharacteristic
37C23×Q8×C61C2211yescharacteristic
38C2×#137×C61—22no—
39C2×#137×C61—24no—
40C2×#137×C61—24no—
41C2×#137×C61C2214yescomplemented
42C22×Q16×C61—21no—
43C22×SD16×C61—21no—
44C22×M16×C61C2211yescharacteristic
45C2×#11758222—21no—
46C2×#11758222—21no—
47C2×#11758222—22no—
48C2×#11758222—22no—
49C2×#11758222—22no—
50C2×#11758222—22no—
51C2×#11758222D412yes—
52C2×#11758222C2312yes—
53C22×Dic122D411yescharacteristic
54C22×D244D411yescharacteristic
55C22×C22⋊D61—21no—
56C22×C22⋊D61—22no—
57C23×Dic61—21no—
58C23×Dic61D412yes—
59C22×C4×D61—21no—
60#14519808—216no—
61#14519808—28no—
62#14519808—28no—
63C2×#11758202—28no—
64C2×#11758202—24no—
65C2×#11758201—28no—
66C2×#11758201—24no—
67C2×#11758194—22no—
68C2×#11758194—21no—
69C2×#11758194D414yescomplemented
70C2×#11758194C2312yes—
71C22×#92418—21no—
72#14519756—24no—
73#14519756—24no—
74#14519753—24no—
75#14519753—24no—
76#14519751—24no—
77#14519751—24no—
78#14519749—28no—
79#14519749—28no—
80#14519748—24no—
81#14519748—24no—
82C2×C4⋊Dic61—21no—
83C2×C4⋊Dic61—21no—
84C2×C4⋊Dic61—21no—
85C2×C4⋊Dic61—21no—
86C2×C4⋊Dic61D412yes—
87C2×C4⋊Dic61C2312yes—
88C2×#11758196—22no—
89C2×C22⋊Dic61—22no—
90C2×#11758198—22no—
91C2×C4×Dic61—22no—
92C2×C4×Dic61—22no—
93C2×C4×Dic61—21no—
94C2×C4×Dic61C2312yes—
95#14519704—28no—
96#14519703—28no—
97#14519684—28no—
98C2×#41×C61—21no—
99C2×#41×C61—21no—
100C2×#41×C61—22no—
101C2×#41×C61—22no—
102C2×#41×C61—22no—
103C2×#41×C61—22no—
104C2×#41×C61D412yes—
105C2×#41×C61C2312yes—
106C22×Q8×C61—21no—
107C22×Q8×C61—22no—
108C22×Q8×C61—21no—
109C22×Q8×C61—21no—
110C22×Q8×C61—22no—
111C22×Q8×C61—21no—
112C22×Q8×C61—21no—
113C22×Q8×C61—22no—
114C22×Q8×C61D411yescharacteristic
115C22×Q8×C61D414yescomplemented
116C22×Q8×C61C2312yes—
117C22×D4×C61—21no—
118C22×D4×C61D411yescharacteristic
119C23×C4×C61—21no—
120C23×C4×C61—21no—
121C23×C4×C61C2311yescharacteristic
122#137×C61—216no—
123#137×C61—28no—
124#137×C61—28no—
125C2×Q16×C61—28no—
126C2×Q16×C61—24no—
127C2×SD16×C61—28no—
128C2×SD16×C61—24no—
129C2×M16×C61—22no—
130C2×M16×C61—21no—
131C2×M16×C61D414yescomplemented
132C2×M16×C61C2312yes—
133C22×C8×C61—21no—
134C24×C61—21no—
135C24×C61C2×D411yescharacteristic
136C23×D61—21no—
137#41×C61—24no—
138#41×C61—24no—
139#41×C61—22no—
140#41×C61—22no—
141#41×C61—22no—
142#41×C61—22no—
143#41×C61—42no—
144#41×C61—42no—
145#41×C61—42no—
146#41×C61—42no—
147C2×Q8×C61—21no—
148C2×Q8×C61—24no—
149C2×Q8×C61—22no—
150C2×Q8×C61—24no—
151C2×Q8×C61—24no—
152C2×Q8×C61—22no—
153C2×Q8×C61—24no—
154C2×Q8×C61—24no—
155C2×Q8×C61—22no—
156C2×Q8×C61—22no—
157C2×Q8×C61—22no—
158C2×Q8×C61—22no—
159C2×Q8×C61—22no—
160C2×Q8×C61—41no—
161C2×Q8×C61—41no—
162C2×Q8×C61—42no—
163C2×Q8×C61—42no—
164C2×Q8×C61—42no—
165C2×Q8×C61—42no—
166C2×Q8×C61—42no—
167C2×Q8×C61C2×D412yes—
168C2×Q8×C61C2×D414yescomplemented
169C2×D4×C61—22no—
170C2×D4×C61—22no—
171C2×D4×C61—22no—
172C2×D4×C61—21no—
173C2×D4×C61—22no—
174C2×D4×C61—42no—
175C2×D4×C61—42no—
176C2×D4×C61C2×D412yes—
177C22×C4×C61—21no—
178C22×C4×C61—24no—
179C22×C4×C61—22no—
180C22×C4×C61—22no—
181C22×C4×C61—22no—
182C22×C4×C61—41no—
183C22×C4×C61—41no—
184C22×C4×C61—42no—
185C22×C4×C61—42no—
186C22×C4×C61—42no—
187C22×C4×C61C2×D412yes—
188C22×C4×C61C2×D411yescharacteristic
189C22×C4×C61C2×D411yescharacteristic
190C22×C4×C61C2×D411yescharacteristic
191C22×C4×C61C2×D411yescharacteristic
192C22×C4×C61C2×D411yescharacteristic
193C22×C4×C61C2×D412yes—
194C22×C4×C61C2×D412yes—
195C22×C4×C61#4112yes—
196C22×C4×C61C2411yescharacteristic
197C2×C22⋊D61—22no—
198C2×C22⋊D61—22no—
199C2×C22⋊D61—28no—
200C2×C22⋊D61—42no—
201C2×C22⋊D61—42no—
202C2×C22⋊D61—84no—
203C22×Dic61—24no—
204C22×Dic61—21no—
205C22×Dic61—22no—
206C22×Dic61—22no—
207C22×Dic61—22no—
208C22×Dic61—42no—
209C22×Dic61—42no—
210C22×Dic61—44no—
211C22×Dic61C2×D414yes—
212#11758222—24no—
213#11758222—24no—
214#11758222—22no—
215#11758222—22no—
216#11758222—22no—
217#11758222—22no—
218#11758222—42no—
219#11758222—42no—
220#11758222—42no—
221#11758222—42no—
222C2×D244—22no—
223C2×D244—22no—
224C2×D244—21no—
225C2×D244C2×D412yes—
226C2×C4×D61—22no—
227C2×C4×D61—22no—
228C2×C4×D61—42no—
229C2×C4×D61—42no—
230C2×Dic122—22no—
231C2×Dic122—22no—
232C2×Dic122—21no—
233C2×Dic122C2×D412yes—
234Q16×C61—216no—
235SD16×C61—216no—
236M16×C61—24no—
237M16×C61—22no—
238M16×C61C2×D414yescomplemented
239C2×C8×C61—24no—
240C2×C8×C61—22no—
241C22⋊Dic61—28no—
242#11758202—216no—
243#11758201—216no—
244#11758198—28no—
245C4⋊Dic61—22no—
246C4⋊Dic61—22no—
247C4⋊Dic61—22no—
248C4⋊Dic61—22no—
249#11758196—28no—
250C4×Dic61—22no—
251C4×Dic61—22no—
252C4×Dic61—42no—
253#11758194—24no—
254#11758194—22no—
255#11758194C2×D414yescomplemented
256C2×#92418—24no—
257C2×#92418—22no—
258C23×C61—22no—
259C23×C61—22no—
260C23×C61—22no—
261C23×C61—42no—
262C23×C61—42no—
263C23×C61—42no—
264C23×C61#12011yescharacteristic
265C23×C61#12011yescharacteristic
266C23×C61#12112yes—
267C23×C61#12712yes—
268C23×C61C22×D411yescharacteristic
269C22×D61—22no—
270C22×D61—42no—
271C22×D61—42no—
272C22×D61—42no—
273Q8×C61—24no—
274Q8×C61—24no—
275Q8×C61—22no—
276Q8×C61—22no—
277Q8×C61—42no—
278Q8×C61—42no—
279Q8×C61—44no—
280Q8×C61—44no—
281Q8×C61—42no—
282D4×C61—22no—
283D4×C61—22no—
284D4×C61—42no—
285D4×C61—42no—
286D4×C61—44no—
287D4×C61—42no—
288C2×C4×C61—22no—
289C2×C4×C61—24no—
290C2×C4×C61—42no—
291C2×C4×C61—42no—
292C2×C4×C61—42no—
293C2×C4×C61—44no—
294C2×C4×C61—44no—
295C2×C4×C61—42no—
296C2×C4×C61—42no—
297C2×C4×C61—44no—
298C2×C4×C61#12012yes—
299C2×C4×C61#12012yes—
300C2×C4×C61#12012yes—
301C2×C4×C61#12012yes—
302C2×C4×C61#12011yescharacteristic
303C2×C4×C61#12011yescharacteristic
304C2×C4×C61#12112yes—
305C2×C4×C61#12112yes—
306C2×C4×C61#12112yes—
307C2×C4×C61#12112yes—
308C2×C4×C61#12112yes—
309C2×C4×C61#12712yes—
310C2×C4×C61C22×D411yescharacteristic
311C2×C4×C61C22×D411yescharacteristic
312C2×C4×C61C22×D411yescharacteristic
313C2×C4×C61C22×D411yescharacteristic
314C2×C4×C61C22×D411yescharacteristic
315C2×C4×C61C2×#4111yescharacteristic
316C22⋊D61—42no—
317C22⋊D61—42no—
318C22⋊D61—44no—
319C22⋊D61—88no—
320C2×Dic61—24no—
321C2×Dic61—22no—
322C2×Dic61—24no—
323C2×Dic61—42no—
324C2×Dic61—48no—
325C2×Dic61—42no—
326C2×Dic61—42no—
327C2×Dic61—44no—
328C2×Dic61—44no—
329C2×Dic61—82no—
330D244—22no—
331D244—22no—
332D244—42no—
333C4×D61—42no—
334C4×D61—42no—
335C4×D61—44no—
336Dic122—22no—
337Dic122—22no—
338Dic122—42no—
339C8×C61—24no—
340#92418—24no—
341C2×#2007—611nomaximal, Sylow
342C22×C61—21no—
343C22×C61—21no—
344C22×C61—21no—
345C22×C61—21no—
346C22×C61—24no—
347C22×C61—24no—
348C22×C61—42no—
349C22×C61—42no—
350C22×C61—42no—
351C22×C61—84no—
352C22×C61#39212yes—
353C22×C61#39212yes—
354C22×C61#45512yes—
355C22×C61#45612yes—
356C22×C61C2×#12011yescharacteristic
357C22×C61C2×#12111yescharacteristic
358C22×C61C2×#12711yescharacteristic
359C2×D61—42no—
360C2×D61—42no—
361C2×D61—42no—
362C2×D61—84no—
363C4×C61—42no—
364C4×C61—44no—
365C4×C61#39212yes—
366C4×C61#39212yes—
367C4×C61C2×#12011yescharacteristic
368C4×C61C2×#12011yescharacteristic
369C4×C61C2×#12111yescharacteristic
370C4×C61C2×#12111yescharacteristic
371Dic61—44no—
372Dic61—42no—
373Dic61—44no—
374C22×#137—611no—
375C22×#137D6111yescharacteristic, complemented
376C2×#537—611no—
377C22×#104—611no—
378C22×#104—611no—
379C2×#391—611no—
380#2007—618no—
381C2×#343—611no—
382C2×C61—21no—
383C2×C61—21no—
384C2×C61—22no—
385C2×C61—82no—
386C2×C61#200714yescomplemented
387C2×C61C2×#39211yescharacteristic
388C2×C61C2×#45511yescharacteristic
389C2×C61C2×#45611yescharacteristic
390D61—82no—
391C22×#41—611no—
392C22×#41C2×D6111yescharacteristic
393C23×Q8C2×D6111yescharacteristic
394C2×#137—22no—
395C2×#137—24no—
396C2×#137—24no—
397C2×#137—614no—
398C2×#137—1224no—
399C2×#137—1222no—
400C2×#137—1224no—
401C2×#137C2×D6114yescomplemented
402C22×Q16—21no—
403C22×Q16—1221no—
404C22×SD16—21no—
405C22×SD16—1221no—
406C22×M16—611no—
407C22×M16C2×D6111yescharacteristic
408#537—614no—
409#537—1222no—
410#537—1222no—
411#537—1222no—
412C2×C22⋊Q8—1221no—
413C2×C22⋊Q8—1221no—
414C2×#121—1221no—
415C2×#121—1222no—
416C2×#121—1221no—
417C22×C4⋊C4—611no—
418C22×C42—611no—
419C2×#104—614no—
420C2×#104—614no—
421C2×#104—1224no—
422C2×#104—1224no—
423#391—614no—
424#391—1222no—
425C2×#95—1222no—
426#343—614no—
427C61C2×#200711yescharacteristic, complemented, Sylow
428C2×#41—21no—
429C2×#41—21no—
430C2×#41—22no—
431C2×#41—22no—
432C2×#41—22no—
433C2×#41—22no—
434C2×#41—612no—
435C2×#41—612no—
436C2×#41—1221no—
437C2×#41—1221no—
438C2×#41—1222no—
439C2×#41—1222no—
440C2×#41—1222no—
441C2×#41—1222no—
442C2×#41C22⋊D6112yes—
443C2×#41C22×D6112yes—
444C22×Q8—21no—
445C22×Q8—22no—
446C22×Q8—21no—
447C22×Q8—21no—
448C22×Q8—22no—
449C22×Q8—21no—
450C22×Q8—21no—
451C22×Q8—22no—
452C22×Q8—611no—
453C22×Q8C22⋊D6111yescharacteristic
454C22×Q8C22⋊D6114yescomplemented
455C22×Q8C22×D6112yes—
456C22×D4—21no—
457C22×D4—611no—
458C22×D4—1222no—
459C22×D4—1221no—
460C22×D4C22⋊D6111yescharacteristic
461C23×C4—21no—
462C23×C4—21no—
463C23×C4—612no—
464C23×C4—1221no—
465C23×C4—1221no—
466C23×C4C22×D6111yescharacteristic
467#137—216no—
468#137—28no—
469#137—28no—
470#137—1228no—
471#137—12216no—
472#137—1228no—
473C2×Q16—28no—
474C2×Q16—24no—
475C2×Q16—1224no—
476C2×Q16—1228no—
477C2×SD16—28no—
478C2×SD16—24no—
479C2×SD16—1224no—
480C2×SD16—1228no—
481C2×M16—21no—
482C2×M16—22no—
483C2×M16—614no—
484C2×M16—612no—
485C2×M16—1221no—
486C2×M16—1222no—
487C2×M16C22⋊D6114yescomplemented
488C2×M16C22×D6112yes—
489C22×C8—21no—
490C22×C8—1221no—
491C22⋊Q8—1224no—
492C22⋊Q8—1224no—
493C22⋊Q8—1224no—
494C22⋊Q8—1224no—
495#121—1224no—
496#121—1224no—
497#121—1228no—
498#121—1224no—
499#121—1228no—
500#121—1224no—
501C2×C4⋊C4—612no—
502C2×C4⋊C4—612no—
503C2×C4⋊C4—1222no—
504C2×C4⋊C4—1221no—
505C2×C4⋊C4—1221no—
506C2×C4⋊C4—1221no—
507C2×C4⋊C4—1221no—
508C2×C22⋊C4—1222no—
509C2×C22⋊C4—1222no—
510C2×C42—612no—
511C2×C42—1222no—
512C2×C42—1222no—
513C2×C42—1221no—
514#104—1228no—
515#104—1228no—
516#95—1228no—
517C24—21no—
518C24—1221no—
519C24D4×D6111yescharacteristic
520#41—22no—
521#41—22no—
522#41—22no—
523#41—22no—
524#41—24no—
525#41—24no—
526#41—42no—
527#41—42no—
528#41—42no—
529#41—42no—
530#41—1222no—
531#41—1222no—
532#41—1222no—
533#41—1222no—
534#41—1224no—
535#41—1224no—
536#41—2442no—
537#41—2442no—
538#41—2442no—
539#41—2442no—
540C2×Q8—22no—
541C2×Q8—21no—
542C2×Q8—24no—
543C2×Q8—22no—
544C2×Q8—22no—
545C2×Q8—22no—
546C2×Q8—22no—
547C2×Q8—24no—
548C2×Q8—24no—
549C2×Q8—24no—
550C2×Q8—22no—
551C2×Q8—24no—
552C2×Q8—22no—
553C2×Q8—41no—
554C2×Q8—41no—
555C2×Q8—42no—
556C2×Q8—42no—
557C2×Q8—42no—
558C2×Q8—42no—
559C2×Q8—42no—
560C2×Q8—612no—
561C2×Q8—1221no—
562C2×Q8—1222no—
563C2×Q8—1222no—
564C2×Q8C2×C22⋊D6112yes—
565C2×Q8C2×C22⋊D6114yescomplemented
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—21no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4—612no—
574C2×D4—1228no—
575C2×D4—1222no—
576C2×D4—1222no—
577C2×D4—1222no—
578C2×D4—1221no—
579C2×D4—1222no—
580C2×D4—4884no—
581C2×D4—2442no—
582C2×D4—2442no—
583C2×D4C2×C22⋊D6112yes—
584C22×C4—22no—
585C22×C4—21no—
586C22×C4—24no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—614no—
595C22×C4—1222no—
596C22×C4—1224no—
597C22×C4—1222no—
598C22×C4—1222no—
599C22×C4—1221no—
600C22×C4—1222no—
601C22×C4—1222no—
602C22×C4—2444no—
603C22×C4—2442no—
604C22×C4—2442no—
605C22×C4—2442no—
606C22×C4—2442no—
607C22×C4D4×D6111yescharacteristic
608C22×C4D4×D6111yescharacteristic
609C22×C4D4×D6112yes—
610C22×C4D4×D6111yescharacteristic
611C22×C4#1175822412yes—
612C22×C4C2×C22⋊D6112yes—
613C22×C4C2×C22⋊D6111yescharacteristic
614C22×C4C2×C22⋊D6111yescharacteristic
615C22×C4C2×C22⋊D6112yes—
616C22×C4C23×D6111yescharacteristic
617Q16—216no—
618Q16—12216no—
619SD16—216no—
620SD16—12216no—
621M16—22no—
622M16—24no—
623M16—614no—
624M16—1222no—
625M16—1224no—
626M16C2×C22⋊D6114yescomplemented
627C2×C8—22no—
628C2×C8—24no—
629C2×C8—1222no—
630C2×C8—1224no—
631C4⋊C4—1228no—
632C4⋊C4—1222no—
633C4⋊C4—1222no—
634C4⋊C4—1222no—
635C4⋊C4—1222no—
636C22⋊C4—1228no—
637C22⋊C4—1228no—
638C42—1222no—
639C42—1222no—
640C42—2442no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—1222no—
648C23—2442no—
649C23—2442no—
650C23—2442no—
651C23#1451974511yescharacteristic
652C23#1451974511yescharacteristic
653C23#1451974912yes—
654C23#1451977312yes—
655C23C2×D4×D6111yescharacteristic
656Q8—24no—
657Q8—24no—
658Q8—22no—
659Q8—22no—
660Q8—42no—
661Q8—42no—
662Q8—44no—
663Q8—44no—
664Q8—42no—
665Q8—1222no—
666Q8—1222no—
667Q8—2442no—
668D4—22no—
669D4—22no—
670D4—42no—
671D4—42no—
672D4—44no—
673D4—42no—
674D4—1222no—
675D4—1222no—
676D4—4888no—
677D4—2442no—
678D4—2442no—
679D4—2444no—
680D4—2442no—
681C2×C4—22no—
682C2×C4—24no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—44no—
687C2×C4—44no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—44no—
691C2×C4—1224no—
692C2×C4—1224no—
693C2×C4—1222no—
694C2×C4—4882no—
695C2×C4—2442no—
696C2×C4—2448no—
697C2×C4—2444no—
698C2×C4—2442no—
699C2×C4—2442no—
700C2×C4—2442no—
701C2×C4—2442no—
702C2×C4—2444no—
703C2×C4—2444no—
704C2×C4#1451974512yes—
705C2×C4#1451974512yes—
706C2×C4#1451974511yescharacteristic
707C2×C4#1451974511yescharacteristic
708C2×C4#1451974612yes—
709C2×C4#1451974612yes—
710C2×C4#1451974812yes—
711C2×C4#1451974812yes—
712C2×C4#1451974912yes—
713C2×C4#1451974912yes—
714C2×C4#1451974912yes—
715C2×C4#1451977312yes—
716C2×C4C2×D4×D6111yescharacteristic
717C2×C4C2×D4×D6111yescharacteristic
718C2×C4C22×C22⋊D6111yescharacteristic
719C2×C4C22×C22⋊D6111yescharacteristic
720C2×C4C22×C22⋊D6111yescharacteristic
721C2×C4C2×#1175822411yescharacteristic
722C8—24no—
723C8—1224no—
724C22—21no—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—24no—
729C22—24no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—84no—
734C22—4884no—
735C22—2442no—
736C22—2442no—
737C22—2442no—
738C22#1683967012yes—
739C22#1683967012yes—
740C22#1683993812yes—
741C22#1683994312yes—
742C22C2×#1451974511yescharacteristic
743C22C2×#1451974911yescharacteristic
744C22C2×#1451977311yescharacteristic
745C4—42no—
746C4—44no—
747C4—2444no—
748C4—2444no—
749C4—2442no—
750C4#1683967012yes—
751C4#1683967012yes—
752C4C2×#1451974511yescharacteristic
753C4C2×#1451974611yescharacteristic
754C4C2×#1451974811yescharacteristic
755C4C2×#1451974911yescharacteristic
756C2—21no—
757C2—21no—
758C2—22no—
759C2—82no—
760C2—4882no—
761C2#2144686414yesdirect product factor
762C2C2×#1683967011yescharacteristic
763C2C2×#1683993811yescharacteristic
764C2C2×#1683994311yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC22×#137×C61C2
socleC23×C61#120
prime radicalC2×#16840340C2
hypercenterC22×#137D61
hypocenterC61C2×#2007
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#137

Complements

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

NH ≅ G/Ntype
1. C22×#14519808C2semidirect
3. C22×#14519704C2semidirect
4. C22×#14519703C2semidirect
5. C2×#16839669C2semidirect
6. #21446864C2direct (N × H)
7. C2×#16839530C2semidirect
8. C22×#137×C61C2semidirect
13. C2×#14519808C22semidirect
29. C2×#14519704C22semidirect
31. C2×#14519703C22semidirect
33. #16839669C22semidirect
35. #16839530C22semidirect
41. C2×#137×C61C22semidirect
69. C2×#11758194D4semidirect
115. C22×Q8×C61D4semidirect
131. C2×M16×C61D4semidirect
168. C2×Q8×C61C2×D4semidirect
238. M16×C61C2×D4semidirect
255. #11758194C2×D4semidirect
375. C22×#137D61semidirect
386. C2×C61#2007semidirect
401. C2×#137C2×D61semidirect
427. C61C2×#2007semidirect
454. C22×Q8C22⋊D61semidirect
487. C2×M16C22⋊D61semidirect
565. C2×Q8C2×C22⋊D61semidirect
626. M16C2×C22⋊D61semidirect
761. C2#21446864direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198082
C2×#168403402
C22×#145197042
C22×#145197032
C2×#168396692
#214468642
C2×#168395302
C22×#137×C612
C2×#200761