Finite Group Databasebeta

← #29707254

Subgroups — #29707254

Order 15616.

2258 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459148C211yesmaximal, characteristic, complemented
2C2×#16840273C211yesmaximal, characteristic, complemented
3C2×#16839736C211yesmaximal, characteristic, complemented
4C2×#16839735C211yesmaximal, characteristic, complemented
5#21448202C211yesmaximal, characteristic, complemented
6#21446947C214yesmaximal, complemented
7#21446942C214yesmaximal, complemented
8#21445551C211yesmaximal, characteristic, complemented
9C2×C61×#525C211yesmaximal, characteristic, complemented
10C22×#11758222C2211yescharacteristic
11#16840340—22no—
12#16840336—21no—
13#16840333—21no—
14#16840329—21no—
15#16840326—21no—
16#16840321C2214yes—
17#16840308—22no—
18#16840273—24no—
19#16840273—24no—
20#16840273—22no—
21#16840269—22no—
22C2×#14519760C2212yes—
23C2×#14519756—21no—
24C2×#14519751—21no—
25C2×#14519746C2212yes—
26C2×C4×C22⋊D61—22no—
27C2×#14519736C2211yescharacteristic
28C2×#14519736C2211yescharacteristic
29C2×#14519736C2211yescharacteristic
30#16839736—24no—
31#16839735—24no—
32C2×#14519692C2214yes—
33C2×#14519691C2214yes—
34#16839625C2212yes—
35#16839622—22no—
36#16839618C2212yes—
37C4×C22⋊Dic61—22no—
38#16839528C2214yes—
39C22×#41×C61C2211yescharacteristic
40C24×C4×C61C2211yescharacteristic
41C61×#525—24no—
42C61×#525—24no—
43C2×#123×C61C2212yes—
44C2×C22⋊Q8×C61—21no—
45C2×#121×C61—21no—
46C2×#120×C61C2212yes—
47C2×C4×D4×C61—22no—
48C2×#117×C61C2211yescharacteristic
49C2×#11758222—22no—
50C2×#11758222—22no—
51C2×#11758222—21no—
52C2×#11758222—22no—
53C2×#11758222—21no—
54C2×#11758222—21no—
55C2×#11758222—21no—
56C2×#11758222—22no—
57C22×Dic122D411yescharacteristic, complemented
58C22×D244D411yescharacteristic, complemented
59C22×C22⋊D61—22no—
60C22×C22⋊D61C2312yes—
61C22×C4×D61D412yescomplemented
62#14519775—22no—
63#14519773—22no—
64#14519766—22no—
65#14519764—22no—
66#14519760—24no—
67#14519760—24no—
68#14519760—24no—
69#14519758—24no—
70#14519756—28no—
71#14519756—24no—
72#14519753—24no—
73#14519751—28no—
74#14519751—24no—
75#14519749—28no—
76#14519748—24no—
77#14519746—24no—
78#14519746—24no—
79#14519746—24no—
80#14519745—24no—
81C4×C22⋊D61—216no—
82C4×C22⋊D61—28no—
83#14519736—21no—
84#14519736—22no—
85#14519736—21no—
86#14519736—21no—
87#14519736—21no—
88#14519736—22no—
89#14519736—22no—
90#14519736D414yescomplemented
91C2×C4⋊Dic61—21no—
92C2×C4⋊Dic61—21no—
93C2×C4⋊Dic61D412yescomplemented
94C2×#11758196—22no—
95C2×C22⋊Dic61—22no—
96C2×C22⋊Dic61—24no—
97C2×C22⋊Dic61C2312yes—
98C2×C22⋊Dic61C2312yes—
99C2×C22⋊Dic61C2312yes—
100C2×#11758198—22no—
101C2×C4×Dic61—21no—
102C2×C4×Dic61—21no—
103C2×C4×Dic61D412yescomplemented
104#14519692—28no—
105#14519691—28no—
106#14519684—24no—
107C25×C61C2311yescharacteristic
108C2×#41×C61—22no—
109C2×#41×C61—21no—
110C2×#41×C61—21no—
111C2×#41×C61—21no—
112C2×#41×C61—21no—
113C2×#41×C61—22no—
114C2×#41×C61—22no—
115C2×#41×C61—22no—
116C22×Q8×C61D411yescharacteristic, complemented
117C22×D4×C61—22no—
118C22×D4×C61D411yescharacteristic, complemented
119C22×D4×C61C2312yes—
120C23×C4×C61—21no—
121C23×C4×C61—21no—
122C23×C4×C61—22no—
123C23×C4×C61—21no—
124C23×C4×C61—21no—
125C23×C4×C61—21no—
126C23×C4×C61—21no—
127C23×C4×C61—22no—
128C23×C4×C61—22no—
129C23×C4×C61D414yescomplemented
130C23×C4×C61D412yescomplemented
131C23×C4×C61C2311yescharacteristic
132C23×C4×C61C2311yescharacteristic
133#123×C61—24no—
134#123×C61—24no—
135C22⋊Q8×C61—28no—
136#121×C61—28no—
137#120×C61—24no—
138#120×C61—24no—
139C4×D4×C61—216no—
140#117×C61—22no—
141#117×C61D414yescomplemented
142C2×C4⋊C4×C61—21no—
143C2×C4⋊C4×C61—22no—
144C2×C22⋊C4×C61—22no—
145C2×C22⋊C4×C61—22no—
146C2×C22⋊C4×C61C2312yes—
147C2×C42×C61—21no—
148C24×C61—21no—
149C24×C61—21no—
150C24×C61—21no—
151C24×C61—21no—
152C24×C61—21no—
153C24×C61—21no—
154C24×C61—44no—
155C24×C61C2×D412yes—
156C24×C61C2×D412yes—
157C24×C61C2411yescharacteristic
158C23×D61C2×D412yes—
159#41×C61—42no—
160#41×C61—42no—
161#41×C61—42no—
162#41×C61—42no—
163#41×C61—42no—
164#41×C61—42no—
165#41×C61—42no—
166#41×C61—42no—
167C2×Q8×C61—22no—
168C2×Q8×C61—21no—
169C2×Q8×C61—21no—
170C2×Q8×C61—22no—
171C2×D4×C61—28no—
172C2×D4×C61—22no—
173C2×D4×C61—22no—
174C2×D4×C61—22no—
175C2×D4×C61—22no—
176C2×D4×C61—22no—
177C2×D4×C61—22no—
178C2×D4×C61—22no—
179C2×D4×C61—21no—
180C2×D4×C61—21no—
181C2×D4×C61—22no—
182C2×D4×C61—48no—
183C22×C4×C61—22no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61—24no—
191C22×C4×C61—24no—
192C22×C4×C61—24no—
193C22×C4×C61—24no—
194C22×C4×C61—24no—
195C22×C4×C61—22no—
196C22×C4×C61—22no—
197C22×C4×C61—24no—
198C22×C4×C61—24no—
199C22×C4×C61—24no—
200C22×C4×C61—41no—
201C22×C4×C61—41no—
202C22×C4×C61—41no—
203C22×C4×C61—41no—
204C22×C4×C61—42no—
205C22×C4×C61—42no—
206C22×C4×C61—42no—
207C22×C4×C61—42no—
208C22×C4×C61—42no—
209C22×C4×C61—42no—
210C22×C4×C61C2×D412yes—
211C22×C4×C61C2×D412yes—
212C22×C4×C61C2×D411yescharacteristic
213C22×C4×C61C2×D411yescharacteristic
214C22×C4×C61C2×D411yescharacteristic
215C22×C4×C61C2×D411yescharacteristic
216C22×C4×C61C2×D412yes—
217C22×C4×C61C2×D411yescharacteristic
218C22×C4×C61C2×D411yescharacteristic
219C22×C4×C61C2×D412yes—
220C22×C4×C61C2×D412yes—
221C22×C4×C61#4112yes—
222C2×C22⋊D61—28no—
223C2×C22⋊D61—22no—
224C2×C22⋊D61—22no—
225C2×C22⋊D61—22no—
226C2×C22⋊D61—22no—
227C2×C22⋊D61—22no—
228C2×C22⋊D61—22no—
229C2×C22⋊D61—28no—
230C2×C22⋊D61—48no—
231C22×Dic61—22no—
232C22×Dic61—22no—
233C22×Dic61C2×D412yes—
234C22×Dic61C2×D414yes—
235#11758222—42no—
236#11758222—42no—
237#11758222—42no—
238#11758222—42no—
239#11758222—42no—
240#11758222—42no—
241#11758222—42no—
242#11758222—42no—
243C2×D244—21no—
244C2×D244—22no—
245C2×D244—21no—
246C2×D244—22no—
247C2×C4×D61—24no—
248C2×C4×D61—22no—
249C2×C4×D61—22no—
250C2×C4×D61—24no—
251C2×Dic122—21no—
252C2×Dic122—22no—
253C2×Dic122—21no—
254C2×Dic122—22no—
255C4⋊C4×C61—28no—
256C4⋊C4×C61—24no—
257C22⋊C4×C61—28no—
258C22⋊C4×C61—28no—
259C22⋊C4×C61—22no—
260C22⋊C4×C61C2×D414yes—
261C42×C61—24no—
262C22⋊Dic61—28no—
263C22⋊Dic61—28no—
264C22⋊Dic61—22no—
265C22⋊Dic61—22no—
266C22⋊Dic61—22no—
267C22⋊Dic61—22no—
268C22⋊Dic61—22no—
269C22⋊Dic61—48no—
270C22⋊Dic61C2×D414yes—
271#11758198—28no—
272#11758198—28no—
273C4⋊Dic61—24no—
274C4⋊Dic61—22no—
275C4⋊Dic61—22no—
276C4⋊Dic61—42no—
277#11758196—28no—
278#11758196—28no—
279C4×Dic61—24no—
280C4×Dic61—22no—
281C4×Dic61—22no—
282C4×Dic61—42no—
283C23×C61—24no—
284C23×C61—24no—
285C23×C61—24no—
286C23×C61—22no—
287C23×C61—22no—
288C23×C61—22no—
289C23×C61—22no—
290C23×C61—22no—
291C23×C61—22no—
292C23×C61—44no—
293C23×C61—42no—
294C23×C61—42no—
295C23×C61—42no—
296C23×C61—42no—
297C23×C61—44no—
298C23×C61—44no—
299C23×C61—44no—
300C23×C61—44no—
301C23×C61—41no—
302C23×C61—41no—
303C23×C61—41no—
304C23×C61—41no—
305C23×C61C22×D411yescharacteristic
306C23×C61C22×D411yescharacteristic
307C23×C61C22×D411yescharacteristic
308C23×C61C22×D411yescharacteristic
309C23×C61C22×D411yescharacteristic
310C23×C61C22×D411yescharacteristic
311C23×C61C2×#4111yescharacteristic
312C22×D61—22no—
313C22×D61—22no—
314C22×D61—22no—
315C22×D61—44no—
316Q8×C61—42no—
317Q8×C61—42no—
318D4×C61—416no—
319D4×C61—42no—
320D4×C61—42no—
321D4×C61—42no—
322D4×C61—42no—
323D4×C61—42no—
324D4×C61—42no—
325C2×C4×C61—22no—
326C2×C4×C61—22no—
327C2×C4×C61—24no—
328C2×C4×C61—22no—
329C2×C4×C61—22no—
330C2×C4×C61—22no—
331C2×C4×C61—22no—
332C2×C4×C61—44no—
333C2×C4×C61—41no—
334C2×C4×C61—41no—
335C2×C4×C61—41no—
336C2×C4×C61—41no—
337C2×C4×C61—44no—
338C2×C4×C61—44no—
339C2×C4×C61—44no—
340C2×C4×C61—44no—
341C2×C4×C61—44no—
342C2×C4×C61—44no—
343C2×C4×C61#12011yescharacteristic
344C2×C4×C61#12012yes—
345C2×C4×C61#12011yescharacteristic
346C2×C4×C61#12012yes—
347C2×C4×C61#12011yescharacteristic
348C2×C4×C61#12011yescharacteristic
349C2×C4×C61#12012yes—
350C2×C4×C61#12012yes—
351C2×C4×C61#12112yes—
352C2×C4×C61#12112yes—
353C2×C4×C61#12112yes—
354C2×C4×C61#12112yes—
355C2×C4×C61#12112yes—
356C2×C4×C61#12112yes—
357C2×C4×C61#12712yes—
358C2×C4×C61#12712yes—
359C22⋊D61—416no—
360C22⋊D61—42no—
361C22⋊D61—42no—
362C22⋊D61—42no—
363C22⋊D61—42no—
364C22⋊D61—88no—
365C2×Dic61—24no—
366C2×Dic61—24no—
367C2×Dic61—22no—
368C2×Dic61—22no—
369C2×Dic61—22no—
370C2×Dic61—44no—
371C2×Dic61—44no—
372C2×Dic61—44no—
373C2×Dic61—42no—
374D244—42no—
375D244—42no—
376C4×D61—44no—
377C4×D61—44no—
378Dic122—42no—
379Dic122—42no—
380#23443—611nomaximal, Sylow
381C22×C61—22no—
382C22×C61—22no—
383C22×C61—22no—
384C22×C61—24no—
385C22×C61—24no—
386C22×C61—24no—
387C22×C61—41no—
388C22×C61—41no—
389C22×C61—41no—
390C22×C61—41no—
391C22×C61—42no—
392C22×C61—44no—
393C22×C61—42no—
394C22×C61—44no—
395C22×C61—42no—
396C22×C61—44no—
397C22×C61—44no—
398C22×C61—42no—
399C22×C61—44no—
400C22×C61—42no—
401C22×C61—44no—
402C22×C61—82no—
403C22×C61C2×#12011yescharacteristic
404C22×C61C2×#12011yescharacteristic
405C22×C61C2×#12011yescharacteristic
406C22×C61C2×#12111yescharacteristic
407C22×C61C2×#12111yescharacteristic
408C22×C61C2×#12111yescharacteristic
409C22×C61C2×#12711yescharacteristic
410C2×D61—44no—
411C2×D61—42no—
412C2×D61—44no—
413C2×D61—82no—
414C4×C61—44no—
415C4×C61—42no—
416C4×C61—42no—
417C4×C61#39212yes—
418C4×C61#39212yes—
419C4×C61#39212yes—
420C4×C61#39212yes—
421Dic61—44no—
422Dic61—42no—
423Dic61—44no—
424Dic61—82no—
425#3449—611no—
426C2×#525—611no—
427C2×#525D6111yescharacteristic, complemented
428C2×#410—611no—
429C2×#410—611no—
430#2280—611no—
431#2022—614no—
432#2021—614no—
433#1740—611no—
434C2×C61—21no—
435C2×C61—21no—
436C2×C61—21no—
437C2×C61—21no—
438C2×C61—21no—
439C2×C61—21no—
440C2×C61—44no—
441C2×C61—82no—
442C2×C61C2×#39211yescharacteristic
443C2×C61#302512yes—
444D61—82no—
445C22×#41—611no—
446C22×#41C2×D6111yescharacteristic
447C24×C4C2×D6111yescharacteristic
448#537—1222no—
449#536—1221no—
450#536—1221no—
451#535—1221no—
452#535—1221no—
453#534—614no—
454#532—1222no—
455#525—24no—
456#525—24no—
457#525—1224no—
458#525—1222no—
459#525—1224no—
460#525—1222no—
461C2×#123—612no—
462C2×#123C2×D6112yes—
463C2×C22⋊Q8—21no—
464C2×C22⋊Q8—1221no—
465C2×#121—21no—
466C2×#121—1221no—
467C2×#120—612no—
468C2×#120C2×D6112yes—
469C2×C4×D4—22no—
470C2×C4×D4—1222no—
471C2×#117—611no—
472C2×#117—611no—
473C2×#117—611no—
474C2×#117C2×D6111yescharacteristic
475#410—1224no—
476#410—1224no—
477C2×#99—614no—
478C2×#99—614no—
479#381—612no—
480#380—1222no—
481#379—612no—
482C4×C22⋊C4—1222no—
483#342—614no—
484C61#2344311yescharacteristic, complemented, Sylow
485C25C22×D6111yescharacteristic
486C2×#41—21no—
487C2×#41—21no—
488C2×#41—21no—
489C2×#41—21no—
490C2×#41—22no—
491C2×#41—22no—
492C2×#41—22no—
493C2×#41—22no—
494C2×#41—1222no—
495C2×#41—1221no—
496C2×#41—1221no—
497C2×#41—1222no—
498C2×#41—1222no—
499C2×#41—1221no—
500C2×#41—1221no—
501C2×#41—1222no—
502C22×Q8—611no—
503C22×Q8C22⋊D6111yescharacteristic, complemented
504C22×D4—22no—
505C22×D4—612no—
506C22×D4—611no—
507C22×D4—1222no—
508C22×D4C22⋊D6111yescharacteristic, complemented
509C22×D4C22×D6112yes—
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—22no—
513C23×C4—21no—
514C23×C4—21no—
515C23×C4—22no—
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—22no—
519C23×C4—612no—
520C23×C4C22⋊D6112yescomplemented
521C23×C4C22⋊D6114yescomplemented
522C23×C4C22×D6111yescharacteristic
523C23×C4C22×D6111yescharacteristic
524C4⋊Q8—1222no—
525#127—1222no—
526#124—1222no—
527#124—1222no—
528#123—24no—
529#123—24no—
530#123—1224no—
531#123—1224no—
532#123—1224no—
533#123—1224no—
534C22⋊Q8—28no—
535C22⋊Q8—1228no—
536C22⋊Q8—1224no—
537C22⋊Q8—1224no—
538#121—28no—
539#121—1228no—
540#121—1224no—
541#121—1228no—
542#121—1224no—
543#120—24no—
544#120—24no—
545#120—1224no—
546#120—1224no—
547#120—1224no—
548#120—1224no—
549C4×D4—216no—
550C4×D4—12216no—
551C4×D4—1228no—
552#117—22no—
553#117—614no—
554#117—1221no—
555#117—1221no—
556#117—1222no—
557#117—1221no—
558#117—1221no—
559#117—1222no—
560#117—1222no—
561#117C22⋊D6114yescomplemented
562C2×C4⋊C4—21no—
563C2×C4⋊C4—22no—
564C2×C4⋊C4—612no—
565C2×C4⋊C4—1222no—
566C2×C4⋊C4—1221no—
567C2×C4⋊C4—1221no—
568C2×C22⋊C4—22no—
569C2×C22⋊C4—22no—
570C2×C22⋊C4—612no—
571C2×C22⋊C4—612no—
572C2×C22⋊C4—612no—
573C2×C22⋊C4—1222no—
574C2×C22⋊C4—1222no—
575C2×C22⋊C4—1224no—
576C2×C22⋊C4C22×D6112yes—
577C2×C42—21no—
578C2×C42—612no—
579C2×C42—1221no—
580C2×C42—1221no—
581#99—1228no—
582#99—1228no—
583#95—1224no—
584C24—21no—
585C24—21no—
586C24—21no—
587C24—21no—
588C24—21no—
589C24—21no—
590C24—44no—
591C24—612no—
592C24C2×C22⋊D6112yes—
593C24C2×C22⋊D6112yes—
594C24C23×D6111yescharacteristic
595#41—42no—
596#41—42no—
597#41—42no—
598#41—42no—
599#41—42no—
600#41—42no—
601#41—42no—
602#41—42no—
603#41—2442no—
604#41—2442no—
605#41—2442no—
606#41—2442no—
607#41—2442no—
608#41—2442no—
609#41—2442no—
610#41—2442no—
611C2×Q8—21no—
612C2×Q8—21no—
613C2×Q8—22no—
614C2×Q8—22no—
615C2×Q8—1221no—
616C2×Q8—1222no—
617C2×Q8—1221no—
618C2×Q8—1222no—
619C2×D4—28no—
620C2×D4—22no—
621C2×D4—22no—
622C2×D4—22no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—22no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—22no—
629C2×D4—22no—
630C2×D4—48no—
631C2×D4—1228no—
632C2×D4—1228no—
633C2×D4—1222no—
634C2×D4—1222no—
635C2×D4—1222no—
636C2×D4—1222no—
637C2×D4—1222no—
638C2×D4—1222no—
639C2×D4—1221no—
640C2×D4—1222no—
641C2×D4—1221no—
642C2×D4—1222no—
643C2×D4—2448no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—22no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—24no—
652C22×C4—24no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—24no—
656C22×C4—24no—
657C22×C4—24no—
658C22×C4—24no—
659C22×C4—24no—
660C22×C4—24no—
661C22×C4—41no—
662C22×C4—41no—
663C22×C4—41no—
664C22×C4—41no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—42no—
668C22×C4—42no—
669C22×C4—42no—
670C22×C4—42no—
671C22×C4—612no—
672C22×C4—614no—
673C22×C4—1222no—
674C22×C4—1224no—
675C22×C4—1222no—
676C22×C4—1222no—
677C22×C4—1224no—
678C22×C4—1222no—
679C22×C4D4×D6111yescharacteristic
680C22×C4D4×D6111yescharacteristic
681C22×C4D4×D6111yescharacteristic
682C22×C4D4×D6112yes—
683C22×C4D4×D6111yescharacteristic
684C22×C4#1175822412yes—
685C22×C4C2×C22⋊D6112yes—
686C22×C4C2×C22⋊D6112yes—
687C22×C4C2×C22⋊D6111yescharacteristic
688C22×C4C2×C22⋊D6112yes—
689C22×C4C2×C22⋊D6111yescharacteristic
690C22×C4C2×C22⋊D6112yes—
691C4⋊C4—28no—
692C4⋊C4—24no—
693C4⋊C4—1228no—
694C4⋊C4—1228no—
695C4⋊C4—1222no—
696C4⋊C4—1222no—
697C4⋊C4—1224no—
698C4⋊C4—2442no—
699C22⋊C4—28no—
700C22⋊C4—28no—
701C22⋊C4—22no—
702C22⋊C4—614no—
703C22⋊C4—1228no—
704C22⋊C4—1228no—
705C22⋊C4—1228no—
706C22⋊C4—1228no—
707C22⋊C4—1222no—
708C22⋊C4—1222no—
709C22⋊C4—1222no—
710C22⋊C4—1222no—
711C22⋊C4—1222no—
712C22⋊C4—2448no—
713C22⋊C4C2×C22⋊D6114yes—
714C42—24no—
715C42—1222no—
716C42—1224no—
717C42—1222no—
718C42—2442no—
719C23—24no—
720C23—24no—
721C23—24no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—44no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—42no—
733C23—44no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—1222no—
742C23—1222no—
743C23—1222no—
744C23—2444no—
745C23C2×D4×D6111yescharacteristic
746C23C2×D4×D6111yescharacteristic
747C23C2×D4×D6111yescharacteristic
748C23C22×C22⋊D6111yescharacteristic
749C23C22×C22⋊D6111yescharacteristic
750C23C22×C22⋊D6111yescharacteristic
751C23C2×#1175822411yescharacteristic
752Q8—42no—
753Q8—42no—
754Q8—2442no—
755Q8—2442no—
756D4—416no—
757D4—42no—
758D4—42no—
759D4—42no—
760D4—42no—
761D4—42no—
762D4—42no—
763D4—4888no—
764D4—24416no—
765D4—2442no—
766D4—2442no—
767D4—2442no—
768D4—2442no—
769D4—2442no—
770D4—2442no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—24no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—44no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—1224no—
790C2×C4—1224no—
791C2×C4—1222no—
792C2×C4—1222no—
793C2×C4—1222no—
794C2×C4—2444no—
795C2×C4—2442no—
796C2×C4—2444no—
797C2×C4—2444no—
798C2×C4—2444no—
799C2×C4—2444no—
800C2×C4#1451974512yes—
801C2×C4#1451974511yescharacteristic
802C2×C4#1451974511yescharacteristic
803C2×C4#1451974512yes—
804C2×C4#1451974511yescharacteristic
805C2×C4#1451974511yescharacteristic
806C2×C4#1451974612yes—
807C2×C4#1451974612yes—
808C2×C4#1451974812yes—
809C2×C4#1451974812yes—
810C2×C4#1451974912yes—
811C2×C4#1451974912yes—
812C2×C4#1451974912yes—
813C2×C4#1451974912yes—
814C2×C4#1451977312yes—
815C2×C4#1451977312yes—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—24no—
820C22—24no—
821C22—24no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—42no—
827C22—44no—
828C22—42no—
829C22—42no—
830C22—44no—
831C22—44no—
832C22—44no—
833C22—42no—
834C22—44no—
835C22—42no—
836C22—44no—
837C22—82no—
838C22—4882no—
839C22—2444no—
840C22—2442no—
841C22—2444no—
842C22C2×#1451974511yescharacteristic
843C22C2×#1451974511yescharacteristic
844C22C2×#1451974611yescharacteristic
845C22C2×#1451974811yescharacteristic
846C22C2×#1451974911yescharacteristic
847C22C2×#1451974911yescharacteristic
848C22C2×#1451977311yescharacteristic
849C4—44no—
850C4—42no—
851C4—42no—
852C4—4882no—
853C4—2444no—
854C4—2442no—
855C4—2444no—
856C4#1683967012yes—
857C4#1683967012yes—
858C4#1683967012yes—
859C4#1683967012yes—
860C2—21no—
861C2—21no—
862C2—21no—
863C2—21no—
864C2—21no—
865C2—21no—
866C2—44no—
867C2—82no—
868C2—4882no—
869C2C2×#1683967011yescharacteristic
870C2#2145521012yes—
subgroupG/H
centerC2×C4#14519745
commutator, cosocleC24×C61C24
FrattiniC24C23×D61
FittingC2×C61×#525C2
socleC22×C61C2×#120
hypercenterC2×#525D61
hypocenterC61#23443
LCSG ▷ C24×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. #21459148C2semidirect
2. C2×#16840273C2semidirect
3. C2×#16839736C2semidirect
4. C2×#16839735C2semidirect
5. #21448202C2semidirect
6. #21446947C2semidirect
7. #21446942C2semidirect
8. #21445551C2semidirect
9. C2×C61×#525C2semidirect
57. C22×Dic122D4semidirect
58. C22×D244D4semidirect
61. C22×C4×D61D4semidirect
90. #14519736D4semidirect
93. C2×C4⋊Dic61D4semidirect
103. C2×C4×Dic61D4semidirect
116. C22×Q8×C61D4semidirect
118. C22×D4×C61D4semidirect
129. C23×C4×C61D4semidirect
130. C23×C4×C61D4semidirect
141. #117×C61D4semidirect
427. C2×#525D61semidirect
484. C61#23443semidirect
503. C22×Q8C22⋊D61semidirect
508. C22×D4C22⋊D61semidirect
520. C23×C4C22⋊D61semidirect
521. C23×C4C22⋊D61semidirect
561. #117C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
#214591482
C2×#168402732
C2×#168397362
C2×#168397352
#214482022
#214469472
#214469422
#214455512
C2×C61×#5252
#2344361