Finite Group Databasebeta

← #29607016

Subgroups — #29607016

Order 15616.

2174 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839670C211yesmaximal, characteristic
2C2×#16839665C211yesmaximal, characteristic, complemented
3C2×#16839662C212yesmaximal, complemented
4C2×#16839651C211yesmaximal, characteristic, complemented
5C2×#16839650C212yesmaximal, complemented
6#21444083C211yesmaximal, characteristic, complemented
7#21444065C211yesmaximal, characteristic, complemented
8#21444062C212yesmaximal, complemented
9#21444058C212yesmaximal, complemented
10#95×Dic61C211yesmaximal, characteristic, complemented
11C61×#1438C211yesmaximal, characteristic, complemented
12C23×C22⋊D61C2212yes—
13C22×C4⋊Dic61C2211yescharacteristic
14C22×#11758196C2211yescharacteristic
15C22×#11758196C2212yes—
16C22×C22⋊Dic61C2212yes—
17C22×C22⋊Dic61C2212yes—
18C22×C22⋊Dic61C2212yes—
19C22×#11758198C2211yescharacteristic
20C22×#11758198C2211yescharacteristic
21C22×#11758198C2211yescharacteristic
22C22×#11758198C2212yes—
23C22×C4×Dic61C2212yes—
24C22×C4×Dic61C2211yescharacteristic
25#16839670C418yescomplemented
26#16839665—24no—
27#16839662—28no—
28#16839651—24no—
29#16839650—28no—
30C2×#14519684C2212yes—
31C2×#14519684C2212yes—
32C2×#14519684C2211yescharacteristic
33C2×#14519684C2212yes—
34C2×#14519684C2211yescharacteristic
35C23×D4×C61C2211yescharacteristic
36C22×C22⋊C4×C61C2212yes—
37C22×C22⋊C4×C61C2212yes—
38C2×#95×C61C2211yescharacteristic
39C2×#95×C61C2211yescharacteristic
40C24×D61C2311yescharacteristic
41C22×C22⋊D61—24no—
42C22×C22⋊D61—24no—
43C22×C22⋊D61—42no—
44C22×C22⋊D61—42no—
45C22×C22⋊D61—42no—
46C22×C22⋊D61—42no—
47C22×C22⋊D61C2×C418yes—
48C23×Dic61C2312yes—
49C23×Dic61C2311yescharacteristic
50C23×Dic61C2311yescharacteristic
51C23×Dic61C2312yes—
52C23×Dic61C2311yescharacteristic
53C2×C4⋊Dic61—22no—
54C2×C4⋊Dic61—42no—
55C2×#11758196—24no—
56C2×#11758196—22no—
57C2×#11758196—24no—
58C2×#11758196—42no—
59C2×#11758196—42no—
60C2×C22⋊Dic61—24no—
61C2×C22⋊Dic61—24no—
62C2×C22⋊Dic61—24no—
63C2×C22⋊Dic61—24no—
64C2×C22⋊Dic61—24no—
65C2×C22⋊Dic61—24no—
66C2×C22⋊Dic61—42no—
67C2×C22⋊Dic61—42no—
68C2×C22⋊Dic61C2×C418yes—
69C2×#11758198—22no—
70C2×#11758198—22no—
71C2×#11758198—24no—
72C2×#11758198—22no—
73C2×#11758198—22no—
74C2×#11758198—24no—
75C2×#11758198—42no—
76C2×#11758198—42no—
77C2×#11758198—42no—
78C2×#11758198C2×C414yes—
79C2×C4×Dic61—42no—
80C2×C4×Dic61—42no—
81C2×C4×Dic61—42no—
82C2×C4×Dic61D418yescomplemented
83C2×C4×Dic61D414yescomplemented
84#14519684—24no—
85#14519684—24no—
86#14519684—22no—
87#14519684—24no—
88#14519684C2×C414yes—
89C25×C61C2312yes—
90C22×D4×C61—22no—
91C22×D4×C61—22no—
92C22×D4×C61—42no—
93C22×D4×C61—42no—
94C22×D4×C61C2×C414yes—
95C23×C4×C61C2311yescharacteristic
96C23×C4×C61C2311yescharacteristic
97C23×C4×C61C2312yes—
98C23×C4×C61C2311yescharacteristic
99C2×C22⋊C4×C61—24no—
100C2×C22⋊C4×C61—24no—
101C2×C22⋊C4×C61—42no—
102C2×C22⋊C4×C61—42no—
103C2×C22⋊C4×C61—42no—
104C2×C22⋊C4×C61—42no—
105#95×C61—22no—
106#95×C61—22no—
107C24×C61—22no—
108C24×C61—22no—
109C24×C61—22no—
110C24×C61—22no—
111C24×C61—22no—
112C24×C61—22no—
113C24×C61—22no—
114C24×C61—22no—
115C24×C61—22no—
116C24×C61—22no—
117C24×C61—22no—
118C24×C61—22no—
119C24×C61—22no—
120C24×C61—22no—
121C24×C61C22×C414yes—
122C24×C61C2411yescharacteristic
123C23×D61—22no—
124C23×D61—21no—
125C23×D61—22no—
126C23×D61—21no—
127C23×D61—21no—
128C23×D61—21no—
129C23×D61—22no—
130C23×D61—22no—
131C23×D61—21no—
132C23×D61—21no—
133C23×D61C22×C412yes—
134C2×D4×C61—28no—
135C2×D4×C61—48no—
136C2×D4×C61—44no—
137C2×D4×C61—44no—
138C2×D4×C61—48no—
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—21no—
148C22×C4×C61—21no—
149C22×C4×C61—22no—
150C22×C4×C61—22no—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—22no—
154C22×C4×C61—22no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61C22×C412yes—
158C22×C4×C61C2×D414yes—
159C22×C4×C61C2×D412yes—
160C22×C4×C61#4112yes—
161C2×C22⋊D61—216no—
162C2×C22⋊D61—48no—
163C2×C22⋊D61—48no—
164C2×C22⋊D61—48no—
165C2×C22⋊D61—48no—
166C2×C22⋊D61—48no—
167C2×C22⋊D61—48no—
168C22×Dic61—22no—
169C22×Dic61—22no—
170C22×Dic61—22no—
171C22×Dic61—22no—
172C22×Dic61—21no—
173C22×Dic61—22no—
174C22×Dic61—21no—
175C22×Dic61—21no—
176C22×Dic61—22no—
177C22×Dic61—22no—
178C22×Dic61—21no—
179C22×Dic61—22no—
180C22×Dic61—22no—
181C22×Dic61—21no—
182C22×Dic61—21no—
183C22×Dic61—22no—
184C22×Dic61—22no—
185C22×Dic61—22no—
186C22×Dic61—22no—
187C22×Dic61—22no—
188C22×Dic61—22no—
189C22×Dic61—22no—
190C22×Dic61C22×C412yes—
191C22×Dic61C22×C414yes—
192C22×Dic61C2×D412yes—
193C22×Dic61C2×D414yes—
194C22×Dic61C2×D414yes—
195C22×Dic61C2×D412yes—
196C22×Dic61#4114yes—
197C22⋊C4×C61—48no—
198C22⋊C4×C61—48no—
199C22⋊Dic61—216no—
200C22⋊Dic61—48no—
201C22⋊Dic61—48no—
202#11758198—28no—
203#11758198—44no—
204#11758198—48no—
205#11758198—44no—
206C4⋊Dic61—44no—
207#11758196—48no—
208#11758196—44no—
209C4×Dic61—48no—
210C4×Dic61—44no—
211C23×C61—24no—
212C23×C61—24no—
213C23×C61—24no—
214C23×C61—24no—
215C23×C61—24no—
216C23×C61—24no—
217C23×C61—24no—
218C23×C61—42no—
219C23×C61—42no—
220C23×C61—42no—
221C23×C61—42no—
222C23×C61—42no—
223C23×C61—42no—
224C23×C61—42no—
225C23×C61—42no—
226C23×C61—42no—
227C23×C61—42no—
228C23×C61—42no—
229C23×C61—42no—
230C23×C61—42no—
231C23×C61—42no—
232C23×C61—42no—
233C23×C61—42no—
234C23×C61—42no—
235C23×C61—42no—
236C23×C61—42no—
237C23×C61—42no—
238C23×C61—42no—
239C23×C61—42no—
240C23×C61—42no—
241C23×C61—42no—
242C23×C61—42no—
243C23×C61—42no—
244C23×C61—42no—
245C23×C61—42no—
246C23×C61C23×C411yescharacteristic
247C23×C61C22×D412yes—
248C23×C61C22×D411yescharacteristic
249C23×C61C2×#4112yes—
250C23×C61C2×#4111yescharacteristic
251C23×C61H(5,𝔽2)11yescharacteristic
252C23×C61H(5,𝔽2)12yes—
253C23×C61H(5,𝔽2)12yes—
254C23×C61H(5,𝔽2)11yescharacteristic
255C23×C61H(5,𝔽2)11yescharacteristic
256C23×C612−1+411yescharacteristic
257C22×D61—22no—
258C22×D61—24no—
259C22×D61—22no—
260C22×D61—24no—
261C22×D61—22no—
262C22×D61—41no—
263C22×D61—42no—
264C22×D61—41no—
265C22×D61—41no—
266C22×D61—42no—
267C22×D61—42no—
268C22×D61—42no—
269C22×D61—41no—
270C22×D61—41no—
271C22×D61—42no—
272C22×D61—41no—
273C22×D61—42no—
274C22×D61—42no—
275C22×D61—42no—
276C22×D61—42no—
277C22×D61—41no—
278C22×D61—42no—
279C22×D61—41no—
280D4×C61—416no—
281C2×C4×C61—24no—
282C2×C4×C61—22no—
283C2×C4×C61—22no—
284C2×C4×C61—24no—
285C2×C4×C61—24no—
286C2×C4×C61—24no—
287C2×C4×C61—24no—
288C2×C4×C61—42no—
289C2×C4×C61—42no—
290C2×C4×C61—42no—
291C2×C4×C61—42no—
292C2×C4×C61—41no—
293C2×C4×C61—41no—
294C2×C4×C61—41no—
295C2×C4×C61—42no—
296C2×C4×C61—42no—
297C2×C4×C61—42no—
298C2×C4×C61—41no—
299C2×C4×C61—41no—
300C2×C4×C61—41no—
301C2×C4×C61—42no—
302C2×C4×C61C4×D414yes—
303C22⋊D61—432no—
304C2×Dic61—24no—
305C2×Dic61—24no—
306C2×Dic61—22no—
307C2×Dic61—24no—
308C2×Dic61—24no—
309C2×Dic61—24no—
310C2×Dic61—24no—
311C2×Dic61—22no—
312C2×Dic61—24no—
313C2×Dic61—24no—
314C2×Dic61—22no—
315C2×Dic61—24no—
316C2×Dic61—22no—
317C2×Dic61—22no—
318C2×Dic61—22no—
319C2×Dic61—41no—
320C2×Dic61—42no—
321C2×Dic61—41no—
322C2×Dic61—42no—
323C2×Dic61—42no—
324C2×Dic61—42no—
325C2×Dic61—42no—
326C2×Dic61—42no—
327C2×Dic61—42no—
328C2×Dic61—42no—
329C2×Dic61—42no—
330C2×Dic61—42no—
331C2×Dic61C4×D418yes—
332C2×Dic61#12714yes—
333#14321—611nomaximal, Sylow
334C22×C61—44no—
335C22×C61—44no—
336C22×C61—44no—
337C22×C61—44no—
338C22×C61—44no—
339C22×C61—44no—
340C22×C61—44no—
341C22×C61—82no—
342C22×C61—82no—
343C22×C61—82no—
344C22×C61—82no—
345C22×C61—82no—
346C22×C61—82no—
347C22×C61—82no—
348C22×C61—82no—
349C22×C61C2×C4×D412yes—
350C22×C61C2×C4×D411yescharacteristic
351C22×C61#51811yescharacteristic
352C22×C61#51812yes—
353C22×C61#52011yescharacteristic
354C22×C61C2×#12711yescharacteristic
355C22×C61#53212yes—
356C22×C61#53211yescharacteristic
357C22×C61#53411yescharacteristic
358C22×C61#53412yes—
359C22×C61#53511yescharacteristic
360C22×C61#53512yes—
361C22×C61#53512yes—
362C22×C61#53511yescharacteristic
363C22×C61#53712yes—
364C22×C61#53711yescharacteristic
365C22×C61#53812yes—
366C22×C61#53812yes—
367C22×C61#53812yes—
368C22×C61#54012yes—
369C22×C61#54011yescharacteristic
370C22×C61#54212yes—
371C22×C61#54211yescharacteristic
372C2×D61—42no—
373C2×D61—44no—
374C2×D61—42no—
375C2×D61—44no—
376C2×D61—42no—
377C2×D61—81no—
378C2×D61—81no—
379C2×D61—82no—
380C2×D61—81no—
381C2×D61—82no—
382C2×D61—81no—
383C4×C61—24no—
384C4×C61—44no—
385C4×C61—81no—
386C4×C61—81no—
387Dic61—28no—
388Dic61—24no—
389Dic61—42no—
390Dic61—42no—
391Dic61—82no—
392C2×#392—611no—
393C2×#390—611no—
394C2×#390—612no—
395C2×#388—611no—
396C2×#388—612no—
397#1444—611no—
398#1439—611no—
399#1439—612no—
400#1438—612no—
401#1438D6111yescharacteristic, complemented
402C4×#95—611no—
403C2×C61—84no—
404C2×C61C4×#12711yescharacteristic
405C2×C61#232111yescharacteristic
406C2×C61#232112yes—
407C2×C61#232412yes—
408C2×C61#232411yescharacteristic
409C2×C61#265611yescharacteristic
410C2×C61#265711yescharacteristic
411C2×C61#266112yes—
412C2×C61#266111yescharacteristic
413C2×C61#266212yes—
414C2×C61#266211yescharacteristic
415D61—82no—
416C23×D4—612no—
417C23×D4C2×D6111yescharacteristic
418C22×C4⋊C4—611no—
419C22×C4⋊C4—612no—
420C22×C4⋊C4—611no—
421C22×C22⋊C4—612no—
422C22×C22⋊C4—611no—
423C22×C22⋊C4—612no—
424C22×C22⋊C4—611no—
425C22×C22⋊C4—612no—
426C22×C22⋊C4—611no—
427C22×C22⋊C4—612no—
428C22×C22⋊C4C2×D6112yes—
429C22×C22⋊C4C2×D6112yes—
430C22×C42—612no—
431C22×C42—611no—
432#392—618no—
433#390—1228no—
434#390—1224no—
435#388—1224no—
436#388—1228no—
437C2×#95—611no—
438C2×#95—612no—
439C2×#95—612no—
440C2×#95—611no—
441C2×#95—612no—
442C2×#95C2×D6111yescharacteristic
443C2×#95C2×D6111yescharacteristic
444C61#1432111yescharacteristic, complemented, Sylow
445C25—611no—
446C25C22×D6112yes—
447C22×D4—22no—
448C22×D4—22no—
449C22×D4—42no—
450C22×D4—42no—
451C22×D4—618no—
452C22×D4—1224no—
453C22×D4—1224no—
454C22×D4—2442no—
455C22×D4—2442no—
456C22×D4—2442no—
457C22×D4—2442no—
458C22×D4C4×D6114yes—
459C23×C4—611no—
460C23×C4—612no—
461C23×C4—611no—
462C23×C4—611no—
463C23×C4—612no—
464C23×C4C22×D6111yescharacteristic
465C23×C4C22×D6111yescharacteristic
466C23×C4C22×D6112yes—
467C23×C4C22×D6111yescharacteristic
468C2×C4⋊C4—1222no—
469C2×C4⋊C4—1224no—
470C2×C4⋊C4—1224no—
471C2×C4⋊C4—1222no—
472C2×C4⋊C4—2442no—
473C2×C4⋊C4—2442no—
474C2×C4⋊C4—2442no—
475C2×C22⋊C4—24no—
476C2×C22⋊C4—24no—
477C2×C22⋊C4—42no—
478C2×C22⋊C4—42no—
479C2×C22⋊C4—42no—
480C2×C22⋊C4—42no—
481C2×C22⋊C4—618no—
482C2×C22⋊C4—614no—
483C2×C22⋊C4—1224no—
484C2×C22⋊C4—1224no—
485C2×C22⋊C4—1222no—
486C2×C22⋊C4—1222no—
487C2×C22⋊C4—1222no—
488C2×C22⋊C4—1222no—
489C2×C22⋊C4—1224no—
490C2×C22⋊C4—1224no—
491C2×C22⋊C4—1224no—
492C2×C22⋊C4—1224no—
493C2×C22⋊C4—1224no—
494C2×C22⋊C4—1224no—
495C2×C22⋊C4—2442no—
496C2×C22⋊C4—2442no—
497C2×C22⋊C4—2442no—
498C2×C22⋊C4—2442no—
499C2×C22⋊C4—2442no—
500C2×C42—618no—
501C2×C42—614no—
502C2×C42—2442no—
503C2×C42—2442no—
504C2×C42—2442no—
505#95—22no—
506#95—22no—
507#95—614no—
508#95—1222no—
509#95—1224no—
510#95—1224no—
511#95—1224no—
512C24—22no—
513C24—22no—
514C24—22no—
515C24—22no—
516C24—22no—
517C24—22no—
518C24—22no—
519C24—22no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—612no—
527C24—1221no—
528C24—1222no—
529C24—1222no—
530C24—1221no—
531C24—1221no—
532C24—1222no—
533C24—1222no—
534C24—1221no—
535C24—1221no—
536C24—1221no—
537C24C2×C4×D6114yes—
538C24C23×D6111yescharacteristic
539C2×D4—28no—
540C2×D4—48no—
541C2×D4—44no—
542C2×D4—44no—
543C2×D4—48no—
544C2×D4—12216no—
545C2×D4—2448no—
546C2×D4—2448no—
547C2×D4—2448no—
548C2×D4—2448no—
549C2×D4—2448no—
550C2×D4—2448no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—614no—
570C22×C4—614no—
571C22×C4—614no—
572C22×C4—612no—
573C22×C4—614no—
574C22×C4—612no—
575C22×C4—612no—
576C22×C4—1221no—
577C22×C4—1222no—
578C22×C4—1222no—
579C22×C4—1222no—
580C22×C4—1222no—
581C22×C4—1222no—
582C22×C4—1221no—
583C22×C4—1222no—
584C22×C4—1221no—
585C22×C4—1222no—
586C22×C4—1222no—
587C22×C4—1221no—
588C22×C4—1222no—
589C22×C4—1221no—
590C22×C4—1221no—
591C22×C4—1222no—
592C22×C4—1222no—
593C22×C4—1222no—
594C22×C4—1222no—
595C22×C4—1222no—
596C22×C4—1222no—
597C22×C4—1222no—
598C22×C4C2×C4×D6112yes—
599C22×C4D4×D6114yes—
600C22×C4D4×D6112yes—
601C22×C4#1175822412yes—
602C4⋊C4—2444no—
603C4⋊C4—2444no—
604C4⋊C4—2448no—
605C22⋊C4—48no—
606C22⋊C4—48no—
607C22⋊C4—12216no—
608C22⋊C4—1228no—
609C22⋊C4—2448no—
610C22⋊C4—2444no—
611C22⋊C4—2444no—
612C22⋊C4—2448no—
613C22⋊C4—2448no—
614C42—2444no—
615C42—2448no—
616C23—24no—
617C23—24no—
618C23—24no—
619C23—24no—
620C23—24no—
621C23—24no—
622C23—24no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—1224no—
652C23—1222no—
653C23—1222no—
654C23—1224no—
655C23—1222no—
656C23—2441no—
657C23—2442no—
658C23—2441no—
659C23—2441no—
660C23—2442no—
661C23—2442no—
662C23—2441no—
663C23—2442no—
664C23—2441no—
665C23—2442no—
666C23—2441no—
667C23—2442no—
668C23—2442no—
669C23—2442no—
670C23—2442no—
671C23—2441no—
672C23—2442no—
673C23—2441no—
674C23C22×C4×D6111yescharacteristic
675C23C2×D4×D6112yes—
676C23C2×D4×D6111yescharacteristic
677C23#41×D6112yes—
678C23C2×#1175822411yescharacteristic
679C23#1451982211yescharacteristic
680C23#1451982212yes—
681C23#1451982212yes—
682C23#1451982211yescharacteristic
683C23#1451982311yescharacteristic
684C23#1451982411yescharacteristic
685D4—416no—
686D4—24432no—
687C2×C4—24no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—42no—
701C2×C4—41no—
702C2×C4—42no—
703C2×C4—41no—
704C2×C4—42no—
705C2×C4—41no—
706C2×C4—42no—
707C2×C4—41no—
708C2×C4—618no—
709C2×C4—614no—
710C2×C4—1224no—
711C2×C4—1224no—
712C2×C4—1222no—
713C2×C4—1224no—
714C2×C4—1224no—
715C2×C4—1224no—
716C2×C4—1224no—
717C2×C4—1222no—
718C2×C4—1224no—
719C2×C4—1224no—
720C2×C4—1224no—
721C2×C4—1222no—
722C2×C4—1222no—
723C2×C4—1222no—
724C2×C4—1222no—
725C2×C4—2442no—
726C2×C4—2442no—
727C2×C4—2442no—
728C2×C4—2442no—
729C2×C4—2442no—
730C2×C4—2442no—
731C2×C4—2442no—
732C2×C4—2441no—
733C2×C4—2442no—
734C2×C4—2441no—
735C2×C4—2442no—
736C2×C4—2442no—
737C2×C4#1451973714yes—
738C22—44no—
739C22—44no—
740C22—44no—
741C22—44no—
742C22—44no—
743C22—44no—
744C22—44no—
745C22—82no—
746C22—82no—
747C22—82no—
748C22—82no—
749C22—82no—
750C22—82no—
751C22—82no—
752C22—82no—
753C22—4881no—
754C22—4881no—
755C22—4882no—
756C22—4881no—
757C22—4882no—
758C22—4881no—
759C22—2442no—
760C22—2444no—
761C22—2444no—
762C22—2442no—
763C22—2442no—
764C22C4×D4×D6112yes—
765C22C2×#1451973711yescharacteristic
766C22#1684023411yescharacteristic
767C22#1684023512yes—
768C22#1684024111yescharacteristic
769C22#127×D6111yescharacteristic
770C22#1684030712yes—
771C22#1684031111yescharacteristic
772C22#1684032211yescharacteristic
773C22#1684032212yes—
774C22#1684032711yescharacteristic
775C22#1684032712yes—
776C22#1684032812yes—
777C22#1684032811yescharacteristic
778C22#1684034112yes—
779C22#1684034111yescharacteristic
780C22#1684034412yes—
781C22#1684034712yes—
782C22#1684034812yes—
783C22#1684036212yes—
784C22#1684036611yescharacteristic
785C22#1684038012yes—
786C22#1684038111yescharacteristic
787C4—24no—
788C4—44no—
789C4—81no—
790C4—81no—
791C4—1228no—
792C4—1224no—
793C4—4882no—
794C4—2442no—
795C4—2442no—
796C2—84no—
797C2—4882no—
798C2#2144838311yescharacteristic
799C2#2144847411yescharacteristic
800C2#2144847512yes—
801C2#2144850912yes—
802C2#2144851511yescharacteristic
803C2#2145192011yescharacteristic
804C2#2145192411yescharacteristic
805C2#2145194412yes—
806C2#2145195411yescharacteristic
807C2#2145195512yes—
808C2#2145196411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1438C2
socle, cosocleC24×C61C24
prime radicalC2×#16839670C2
hypercenter#1438D61
hypocenterC61#14321
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
2. C2×#16839665C2semidirect
3. C2×#16839662C2semidirect
4. C2×#16839651C2semidirect
5. C2×#16839650C2semidirect
6. #21444083C2semidirect
7. #21444065C2semidirect
8. #21444062C2semidirect
9. #21444058C2semidirect
10. #95×Dic61C2semidirect
11. C61×#1438C2semidirect
25. #16839670C4semidirect
82. C2×C4×Dic61D4semidirect
83. C2×C4×Dic61D4semidirect
401. #1438D61semidirect
444. C61#14321semidirect

Maximal subgroups

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

subgroupindex
C2×#168396702
C2×#168396652
C2×#168396622
C2×#168396512
C2×#168396502
#214440832
#214440652
#214440622
#214440582
#95×Dic612
C61×#14382
#1432161