Finite Group Databasebeta

← #29602202

Subgroups — #29602202

Order 15616.

2690 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D61C211yesmaximal, characteristic
2C2×#16839639C212yesmaximal
3C2×#16839634C212yesmaximal, complemented
4C2×#16839621C211yesmaximal, characteristic, complemented
5C22×#14519684C211yesmaximal, characteristic, complemented
6#21444070C212yesmaximal, complemented
7#21444063C212yesmaximal, complemented
8#21444047C211yesmaximal, characteristic, complemented
9#21444044C211yesmaximal, characteristic, complemented
10#21444040C211yesmaximal, characteristic, complemented
11C61×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×C22⋊D61C2211yescharacteristic
13C24×Dic61C2212yes—
14C23×C4×D61C2211yescharacteristic
15C2×C4×C22⋊D61—28no—
16C2×C4×C22⋊D61C418yescomplemented
17C22×#11758196C2212yes—
18C22×#11758196C2212yes—
19C22×#11758196C2211yescharacteristic
20C22×C22⋊Dic61C2211yescharacteristic
21C22×#11758198C2212yes—
22C22×#11758198C2212yes—
23C22×#11758198C2211yescharacteristic
24C22×C4×Dic61C2211yescharacteristic
25#16839639—28no—
26#16839634—28no—
27#16839621—24no—
28C2×#14519684—24no—
29C2×#14519684C2212yes—
30C2×#14519684C2212yes—
31C2×#14519684C2212yes—
32C2×#14519684C2212yes—
33C2×#14519684C2211yescharacteristic
34C2×#14519684C2212yes—
35C2×#14519684C2211yescharacteristic
36C24×C4×C61C2211yescharacteristic
37C22×C22⋊C4×C61C2212yes—
38C2×#95×C61C2211yescharacteristic
39C2×#95×C61C2211yescharacteristic
40C2×#95×C61C2212yes—
41C24×D61C2311yescharacteristic
42C22×C22⋊D61—24no—
43C22×C22⋊D61—24no—
44C22×C22⋊D61C2×C414yes—
45C22×C22⋊D61D414yes—
46C22×C22⋊D61Q814yes—
47C23×Dic61—24no—
48C23×Dic61—24no—
49C23×Dic61—24no—
50C23×Dic61—24no—
51C23×Dic61—24no—
52C23×Dic61—42no—
53C23×Dic61—42no—
54C23×Dic61C2312yes—
55C23×Dic61C2312yes—
56C23×Dic61C2311yescharacteristic
57C23×Dic61C2311yescharacteristic
58C23×Dic61C2311yescharacteristic
59C22×C4×D61—22no—
60C22×C4×D61—22no—
61C22×C4×D61—24no—
62C22×C4×D61—42no—
63C22×C4×D61C2×C414yescomplemented
64C4×C22⋊D61—232no—
65C2×#11758196—24no—
66C2×#11758196—24no—
67C2×#11758196—24no—
68C2×#11758196—24no—
69C2×#11758196—24no—
70C2×#11758196—42no—
71C2×#11758196—42no—
72C2×#11758196C2×C414yescomplemented
73C2×C22⋊Dic61C2×C414yes—
74C2×C22⋊Dic61D418yes—
75C2×#11758198—24no—
76C2×#11758198—24no—
77C2×#11758198—24no—
78C2×#11758198—24no—
79C2×#11758198—24no—
80C2×#11758198—42no—
81C2×#11758198—42no—
82C2×#11758198C2×C414yescomplemented
83C2×C4×Dic61—24no—
84C2×C4×Dic61C2×C414yescomplemented
85#14519684—22no—
86#14519684—24no—
87#14519684—24no—
88#14519684—24no—
89#14519684—24no—
90#14519684—24no—
91#14519684D414yescomplemented
92C25×C61C2311yescharacteristic
93C23×C4×C61—24no—
94C23×C4×C61—22no—
95C23×C4×C61—22no—
96C23×C4×C61—42no—
97C23×C4×C61C2×C414yes—
98C23×C4×C61C2312yes—
99C23×C4×C61C2312yes—
100C23×C4×C61C2311yescharacteristic
101C23×C4×C61C2311yescharacteristic
102C2×C22⋊C4×C61—24no—
103C2×C22⋊C4×C61—24no—
104C2×C22⋊C4×C61—24no—
105#95×C61—22no—
106#95×C61—22no—
107#95×C61—42no—
108C24×C61—21no—
109C24×C61—22no—
110C24×C61—21no—
111C24×C61—21no—
112C24×C61—22no—
113C24×C61—21no—
114C24×C61C22×C412yes—
115C24×C61C2×D414yes—
116C24×C61C2×D412yes—
117C24×C61C2×Q812yes—
118C24×C61#4114yes—
119C24×C61C2411yescharacteristic
120C23×D61—22no—
121C23×D61—21no—
122C23×D61—21no—
123C23×D61—22no—
124C23×D61—22no—
125C23×D61—22no—
126C23×D61—21no—
127C23×D61—21no—
128C23×D61C22×C412yes—
129C23×D61C2×D412yes—
130C23×D61C2×Q812yes—
131C22×C4×C61—22no—
132C22×C4×C61—22no—
133C22×C4×C61—28no—
134C22×C4×C61—21no—
135C22×C4×C61—22no—
136C22×C4×C61—21no—
137C22×C4×C61—22no—
138C22×C4×C61—28no—
139C22×C4×C61—22no—
140C22×C4×C61—22no—
141C22×C4×C61—22no—
142C22×C4×C61—22no—
143C22×C4×C61—22no—
144C22×C4×C61—22no—
145C22×C4×C61—22no—
146C22×C4×C61—22no—
147C22×C4×C61—22no—
148C22×C4×C61—22no—
149C22×C4×C61—22no—
150C22×C4×C61—22no—
151C22×C4×C61—22no—
152C22×C4×C61—22no—
153C22×C4×C61—44no—
154C22×C4×C61—48no—
155C22×C4×C61—48no—
156C22×C4×C61C22×C412yes—
157C22×C4×C61C22×C412yes—
158C22×C4×C61C2×D412yes—
159C22×C4×C61#4112yes—
160C2×C22⋊D61—28no—
161C2×C22⋊D61—28no—
162C2×C22⋊D61—216no—
163C2×C22⋊D61—216no—
164C2×C22⋊D61C4⋊C4116yescomplemented
165C22×Dic61—21no—
166C22×Dic61—22no—
167C22×Dic61—21no—
168C22×Dic61—22no—
169C22×Dic61—22no—
170C22×Dic61—22no—
171C22×Dic61—21no—
172C22×Dic61—21no—
173C22×Dic61—216no—
174C22×Dic61—22no—
175C22×Dic61—22no—
176C22×Dic61—22no—
177C22×Dic61—22no—
178C22×Dic61—22no—
179C22×Dic61—22no—
180C22×Dic61—22no—
181C22×Dic61—22no—
182C22×Dic61—22no—
183C22×Dic61—22no—
184C22×Dic61—22no—
185C22×Dic61—22no—
186C22×Dic61—48no—
187C22×Dic61—48no—
188C22×Dic61—48no—
189C22×Dic61—48no—
190C22×Dic61—48no—
191C22×Dic61—48no—
192C22×Dic61C22×C412yes—
193C22×Dic61C22×C412yes—
194C22×Dic61C22×C412yes—
195C22×Dic61C2×D414yes—
196C22×Dic61C2×D414yes—
197C22×Dic61C2×D414yes—
198C22×Dic61C2×D412yes—
199C22×Dic61C2×Q812yes—
200C22×Dic61#4114yes—
201C2×C4×D61—28no—
202C2×C4×D61—28no—
203C2×C4×D61—44no—
204C2×C4×D61—48no—
205C2×C4×D61—48no—
206C22⋊C4×C61—48no—
207C22⋊Dic61C22⋊C4116yescomplemented
208#11758198—28no—
209#11758198—48no—
210#11758198—48no—
211#11758196—28no—
212#11758196—48no—
213#11758196—48no—
214C4×Dic61—28no—
215C23×C61—22no—
216C23×C61—22no—
217C23×C61—22no—
218C23×C61—22no—
219C23×C61—24no—
220C23×C61—24no—
221C23×C61—24no—
222C23×C61—24no—
223C23×C61—22no—
224C23×C61—24no—
225C23×C61—24no—
226C23×C61—24no—
227C23×C61—24no—
228C23×C61—24no—
229C23×C61—22no—
230C23×C61—22no—
231C23×C61—22no—
232C23×C61—24no—
233C23×C61C2×C22⋊C414yes—
234C23×C61C2×C4⋊C414yes—
235C23×C61#11714yes—
236C23×C61#12118yes—
237C23×C61C22⋊Q818yes—
238C23×C61C23×C411yescharacteristic
239C23×C61C22×D412yes—
240C23×C61C22×D411yescharacteristic
241C23×C61C22×D411yescharacteristic
242C23×C61C22×Q811yescharacteristic
243C23×C61C2×#4112yes—
244C23×C61C2×#4111yescharacteristic
245C23×C61C2×#4112yes—
246C23×C61H(5,𝔽2)12yes—
247C23×C61H(5,𝔽2)11yescharacteristic
248C23×C612−1+411yescharacteristic
249C22×D61—22no—
250C22×D61—22no—
251C22×D61—22no—
252C22×D61—22no—
253C22×D61—22no—
254C22×D61—22no—
255C22×D61—24no—
256C22×D61—24no—
257C22×D61—22no—
258C22×D61—24no—
259C22×D61—22no—
260C22×D61—22no—
261C22×D61—22no—
262C22×D61—24no—
263C22×D61—42no—
264C22×D61—42no—
265C22×D61—42no—
266C22×D61—42no—
267C22×D61—42no—
268C22×D61—42no—
269C22×D61—42no—
270C22×D61—42no—
271C22×D61C2×C4⋊C414yes—
272C2×C4×C61—22no—
273C2×C4×C61—22no—
274C2×C4×C61—24no—
275C2×C4×C61—24no—
276C2×C4×C61—22no—
277C2×C4×C61—22no—
278C2×C4×C61—22no—
279C2×C4×C61—416no—
280C2×C4×C61—42no—
281C2×C4×C61—42no—
282C2×C4×C61—42no—
283C2×C4×C61—42no—
284C2×C4×C61—42no—
285C2×C4×C61—42no—
286C2×C4×C61—42no—
287C2×C4×C61—42no—
288C2×C4×C61—42no—
289C2×C4×C61—42no—
290C2×C4×C61—42no—
291C2×C4×C61—42no—
292C2×C4×C61—42no—
293C2×C4×C61—42no—
294C2×C4×C61—42no—
295C2×C4×C61—42no—
296C2×C4×C61C4×D414yes—
297C22⋊D61—232no—
298C2×Dic61—22no—
299C2×Dic61—22no—
300C2×Dic61—22no—
301C2×Dic61—22no—
302C2×Dic61—22no—
303C2×Dic61—22no—
304C2×Dic61—24no—
305C2×Dic61—24no—
306C2×Dic61—24no—
307C2×Dic61—24no—
308C2×Dic61—24no—
309C2×Dic61—24no—
310C2×Dic61—24no—
311C2×Dic61—24no—
312C2×Dic61—24no—
313C2×Dic61—24no—
314C2×Dic61—24no—
315C2×Dic61—24no—
316C2×Dic61—432no—
317C2×Dic61—42no—
318C2×Dic61—42no—
319C2×Dic61—42no—
320C2×Dic61—42no—
321C2×Dic61—42no—
322C2×Dic61—42no—
323C2×Dic61—42no—
324C2×Dic61—42no—
325C2×Dic61C2×C22⋊C414yes—
326C2×Dic61C2×C22⋊C414yes—
327C2×Dic61C2×C4⋊C414yes—
328C4×D61—416no—
329#13899—611nomaximal, Sylow
330C22×C61—24no—
331C22×C61—24no—
332C22×C61—24no—
333C22×C61—24no—
334C22×C61—24no—
335C22×C61—28no—
336C22×C61—28no—
337C22×C61—28no—
338C22×C61—28no—
339C22×C61—24no—
340C22×C61#38018yescomplemented
341C22×C61C22×C22⋊C411yescharacteristic
342C22×C61C22×C4⋊C411yescharacteristic
343C22×C61C2×#11711yescharacteristic
344C22×C61C2×C4×D411yescharacteristic
345C22×C61C4×#4111yescharacteristic
346C22×C61#51811yescharacteristic
347C22×C61#52011yescharacteristic
348C22×C61C2×#12112yes—
349C22×C61C2×C22⋊Q812yes—
350C22×C61#52512yes—
351C22×C61#52912yes—
352C22×C61#53812yes—
353C22×C61#53912yes—
354C22×C61D4212yes—
355C22×C61D4211yescharacteristic
356C22×C61#54612yes—
357C22×C61#54612yes—
358C22×C61#54612yes—
359C22×C61#54712yes—
360C22×C61#54711yescharacteristic
361C22×C61D4×Q811yescharacteristic
362C22×C61#55412yes—
363C22×C61#55411yescharacteristic
364C2×D61—24no—
365C2×D61—24no—
366C2×D61—24no—
367C2×D61—42no—
368C2×D61—42no—
369C2×D61—42no—
370C2×D61—44no—
371C2×D61—44no—
372C2×D61—44no—
373C2×D61—44no—
374C2×D61—42no—
375C4×C61—24no—
376C4×C61—42no—
377C4×C61—82no—
378C4×C61—82no—
379Dic61—24no—
380Dic61—24no—
381Dic61—24no—
382Dic61—44no—
383Dic61—44no—
384C22×C4×D4—611no—
385C2×#386—612no—
386C2×#385—612no—
387C2×#380—611no—
388C22×#95—611no—
389#1441—612no—
390#1439—612no—
391C4⋊#95—611no—
392#1434—611no—
393C22⋊#95—611no—
394C22⋊#95D6111yescharacteristic, complemented
395C2×C61—28no—
396C2×C61C2×#38011yescharacteristic
397C2×C61#229011yescharacteristic
398C2×C61#231811yescharacteristic
399C2×C61D4×C22⋊C411yescharacteristic
400C2×C61#233911yescharacteristic
401C2×C61D4×C4⋊C411yescharacteristic
402C2×C61#234911yescharacteristic
403C2×C61#242412yes—
404C2×C61#242512yes—
405C2×C61#244912yes—
406C2×C61#245012yes—
407D61—44no—
408C23×D4—611no—
409C24×C4—611no—
410C24×C4—612no—
411C24×C4C2×D6111yescharacteristic
412C2×C4×D4—618no—
413C2×C4×D4—1228no—
414C22×C4⋊C4—611no—
415C22×C4⋊C4—612no—
416C22×C4⋊C4—612no—
417C22×C22⋊C4—611no—
418C22×C22⋊C4—611no—
419C22×C22⋊C4—612no—
420C22×C22⋊C4—612no—
421C22×C22⋊C4C2×D6112yes—
422C22×C42—611no—
423#386—1228no—
424#385—1228no—
425#380—1224no—
426C2×#95—611no—
427C2×#95—611no—
428C2×#95—612no—
429C2×#95—612no—
430C2×#95—612no—
431C2×#95—612no—
432C2×#95—612no—
433C2×#95—1224no—
434C2×#95C2×D6111yescharacteristic
435C2×#95C2×D6111yescharacteristic
436C2×#95C2×D6112yes—
437C61#1389911yescharacteristic, complemented, Sylow
438C25—611no—
439C25C22×D6111yescharacteristic
440C22×D4—614no—
441C22×D4—614no—
442C22×D4—614no—
443C22×D4—1224no—
444C22×D4—1224no—
445C23×C4—24no—
446C23×C4—22no—
447C23×C4—22no—
448C23×C4—42no—
449C23×C4—611no—
450C23×C4—611no—
451C23×C4—611no—
452C23×C4—612no—
453C23×C4—612no—
454C23×C4—614no—
455C23×C4—1224no—
456C23×C4—1224no—
457C23×C4—1224no—
458C23×C4—1224no—
459C23×C4—1222no—
460C23×C4—1222no—
461C23×C4—1224no—
462C23×C4—1224no—
463C23×C4—2442no—
464C23×C4—2442no—
465C23×C4—2442no—
466C23×C4C4×D6114yes—
467C23×C4C22×D6112yes—
468C23×C4C22×D6112yes—
469C23×C4C22×D6111yescharacteristic
470C23×C4C22×D6111yescharacteristic
471C4×D4—12232no—
472C2×C4⋊C4—614no—
473C2×C4⋊C4—1224no—
474C2×C4⋊C4—1224no—
475C2×C4⋊C4—1224no—
476C2×C4⋊C4—1224no—
477C2×C4⋊C4—1224no—
478C2×C4⋊C4—2442no—
479C2×C4⋊C4—2442no—
480C2×C22⋊C4—24no—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—614no—
484C2×C22⋊C4—618no—
485C2×C22⋊C4—614no—
486C2×C22⋊C4—1224no—
487C2×C22⋊C4—1224no—
488C2×C22⋊C4—1224no—
489C2×C22⋊C4—1224no—
490C2×C22⋊C4—1224no—
491C2×C22⋊C4—2442no—
492C2×C22⋊C4—2442no—
493C2×C42—614no—
494C2×C42—1224no—
495#95—22no—
496#95—22no—
497#95—42no—
498#95—614no—
499#95—1224no—
500#95—1224no—
501#95—1224no—
502#95—1224no—
503#95—1224no—
504#95—1222no—
505C24—21no—
506C24—22no—
507C24—21no—
508C24—22no—
509C24—21no—
510C24—21no—
511C24—612no—
512C24—612no—
513C24—612no—
514C24—1221no—
515C24—1222no—
516C24—1222no—
517C24—1221no—
518C24—1222no—
519C24—1222no—
520C24—1221no—
521C24—1221no—
522C24C2×C4×D6112yes—
523C24#1175822214yes—
524C24D4×D6114yes—
525C24D4×D6112yes—
526C24Q8×D6112yes—
527C24C23×D6111yescharacteristic
528C2×D4—6116no—
529C2×D4—1228no—
530C2×D4—1228no—
531C2×D4—12216no—
532C2×D4—12216no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—21no—
538C22×C4—22no—
539C22×C4—28no—
540C22×C4—28no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—44no—
556C22×C4—48no—
557C22×C4—48no—
558C22×C4—612no—
559C22×C4—612no—
560C22×C4—612no—
561C22×C4—612no—
562C22×C4—614no—
563C22×C4—614no—
564C22×C4—612no—
565C22×C4—614no—
566C22×C4—614no—
567C22×C4—1228no—
568C22×C4—1222no—
569C22×C4—1221no—
570C22×C4—1222no—
571C22×C4—1221no—
572C22×C4—1222no—
573C22×C4—1222no—
574C22×C4—1221no—
575C22×C4—1221no—
576C22×C4—12216no—
577C22×C4—1222no—
578C22×C4—1222no—
579C22×C4—1222no—
580C22×C4—1222no—
581C22×C4—1222no—
582C22×C4—1222no—
583C22×C4—1222no—
584C22×C4—1222no—
585C22×C4—1222no—
586C22×C4—1222no—
587C22×C4—1222no—
588C22×C4—1222no—
589C22×C4—1228no—
590C22×C4—2444no—
591C22×C4—2448no—
592C22×C4—2448no—
593C22×C4—2448no—
594C22×C4—2448no—
595C22×C4—2448no—
596C22×C4—2448no—
597C22×C4—2448no—
598C22×C4—2448no—
599C22×C4C2×C4×D6112yes—
600C22×C4C2×C4×D6112yes—
601C22×C4D4×D6112yes—
602C22×C4#1175822412yes—
603C4⋊C4—1228no—
604C4⋊C4—2448no—
605C4⋊C4—2448no—
606C22⋊C4—48no—
607C22⋊C4—6116no—
608C22⋊C4—1228no—
609C22⋊C4—2448no—
610C22⋊C4—2448no—
611C42—1228no—
612C23—24no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—24no—
619C23—24no—
620C23—24no—
621C23—24no—
622C23—24no—
623C23—22no—
624C23—24no—
625C23—24no—
626C23—24no—
627C23—24no—
628C23—22no—
629C23—22no—
630C23—614no—
631C23—1222no—
632C23—1224no—
633C23—1222no—
634C23—1222no—
635C23—1222no—
636C23—1222no—
637C23—1222no—
638C23—1222no—
639C23—1224no—
640C23—1224no—
641C23—1222no—
642C23—1224no—
643C23—1222no—
644C23—1222no—
645C23—2442no—
646C23—2442no—
647C23—2442no—
648C23—2442no—
649C23—2442no—
650C23—2442no—
651C23—2442no—
652C23—2442no—
653C23C22⋊C4×D6114yes—
654C23C4⋊C4×D6114yes—
655C23#1451973414yes—
656C23#1451975018yes—
657C23#1451975518yes—
658C23C22×C4×D6111yescharacteristic
659C23C2×D4×D6112yes—
660C23C2×D4×D6111yescharacteristic
661C23C2×D4×D6111yescharacteristic
662C23C2×Q8×D6111yescharacteristic
663C23#41×D6112yes—
664C23C2×#1175822411yescharacteristic
665C23C2×#1175822212yes—
666C23#1451982212yes—
667C23#1451982311yescharacteristic
668C23#1451982411yescharacteristic
669D4—12232no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—416no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—614no—
695C2×C4—614no—
696C2×C4—614no—
697C2×C4—1222no—
698C2×C4—1222no—
699C2×C4—1222no—
700C2×C4—1222no—
701C2×C4—1222no—
702C2×C4—1222no—
703C2×C4—1224no—
704C2×C4—1224no—
705C2×C4—1224no—
706C2×C4—1224no—
707C2×C4—1224no—
708C2×C4—1224no—
709C2×C4—1224no—
710C2×C4—1224no—
711C2×C4—1224no—
712C2×C4—1224no—
713C2×C4—1224no—
714C2×C4—1224no—
715C2×C4—24416no—
716C2×C4—24432no—
717C2×C4—2442no—
718C2×C4—2442no—
719C2×C4—2442no—
720C2×C4—2442no—
721C2×C4—2442no—
722C2×C4—2442no—
723C2×C4—2442no—
724C2×C4—2442no—
725C2×C4#1451973714yes—
726C22—24no—
727C22—24no—
728C22—24no—
729C22—28no—
730C22—28no—
731C22—28no—
732C22—28no—
733C22—24no—
734C22—24no—
735C22—24no—
736C22—1224no—
737C22—1224no—
738C22—1224no—
739C22—2442no—
740C22—2444no—
741C22—2444no—
742C22—2444no—
743C22—2444no—
744C22—2442no—
745C22—2442no—
746C22—2442no—
747C22#1683962118yescomplemented
748C22C2×C22⋊C4×D6111yescharacteristic
749C22C2×C4⋊C4×D6111yescharacteristic
750C22C2×#1451973411yescharacteristic
751C22C2×#1451973711yescharacteristic
752C22#1684023011yescharacteristic
753C22#1684023511yescharacteristic
754C22#1684024211yescharacteristic
755C22C2×#1451975012yes—
756C22C2×#1451975512yes—
757C22#1684027112yes—
758C22#1684029212yes—
759C22#1684034512yes—
760C22#1684035412yes—
761C22#1684039412yes—
762C22#1684039611yescharacteristic
763C22#1684039912yes—
764C22#1684040112yes—
765C22#1684040412yes—
766C22#1684041012yes—
767C22#1684041211yescharacteristic
768C22#1684042511yescharacteristic
769C22#1684046612yes—
770C22#1684047011yescharacteristic
771C4—24no—
772C4—42no—
773C4—82no—
774C4—82no—
775C4—1224no—
776C4—1224no—
777C4—1224no—
778C4—2444no—
779C4—2444no—
780C2—28no—
781C2—2444no—
782C2C2×#1683962111yescharacteristic
783C2#2144825811yescharacteristic
784C2#2144844611yescharacteristic
785C2#2144863511yescharacteristic
786C2#2144864311yescharacteristic
787C2#2144871511yescharacteristic
788C2#2144872311yescharacteristic
789C2#2144935712yes—
790C2#2144937212yes—
791C2#2144963012yes—
792C2#2144964512yes—
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×C22⋊#95C2
socle, cosocleC24×C61C24
prime radicalC23×C22⋊D61C22
hypercenterC22⋊#95D61
hypocenterC61#13899
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×#16839634C2semidirect
4. C2×#16839621C2semidirect
5. C22×#14519684C2semidirect
6. #21444070C2semidirect
7. #21444063C2semidirect
8. #21444047C2semidirect
9. #21444044C2semidirect
10. #21444040C2semidirect
11. C61×C22⋊#95C2semidirect
16. C2×C4×C22⋊D61C4semidirect
63. C22×C4×D61C2×C4semidirect
72. C2×#11758196C2×C4semidirect
82. C2×#11758198C2×C4semidirect
84. C2×C4×Dic61C2×C4semidirect
91. #14519684D4semidirect
164. C2×C22⋊D61C4⋊C4semidirect
207. C22⋊Dic61C22⋊C4semidirect
340. C22×C61#380semidirect
394. C22⋊#95D61semidirect
437. C61#13899semidirect
747. C22#16839621semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D612
C2×#168396392
C2×#168396342
C2×#168396212
C22×#145196842
#214440702
#214440632
#214440472
#214440442
#214440402
C61×C22⋊#952
#1389961