Finite Group Databasebeta

← #29603136

Subgroups — #29603136

Order 15616.

2474 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519760C211yesmaximal, characteristic
2C2×#16839641C211yesmaximal, characteristic
3C2×#16839641C211yesmaximal, characteristic
4C2×#16839635C211yesmaximal, characteristic, complemented
5C2×#16839625C211yesmaximal, characteristic, complemented
6C2×C4×C22⋊Dic61C211yesmaximal, characteristic, complemented
7#21444085C212yesmaximal, complemented
8#21444063C212yesmaximal, complemented
9#21444055C212yesmaximal, complemented
10#21444047C212yesmaximal, complemented
11C22×#95×C61C211yesmaximal, characteristic, complemented
12C23×C22⋊D61C2211yescharacteristic
13C2×#14519760—24no—
14C2×#14519760—24no—
15C2×#14519760C418yescomplemented
16C22×#11758196C2212yes—
17C22×#11758196C2212yes—
18C22×C22⋊Dic61C2211yescharacteristic
19C22×C22⋊Dic61C2211yescharacteristic
20C22×C22⋊Dic61C2211yescharacteristic
21C22×#11758198C2211yescharacteristic
22C22×#11758198C2212yes—
23C22×#11758198C2212yes—
24C22×#11758198C2211yescharacteristic
25C22×C4×Dic61C2212yes—
26#16839641—24no—
27#16839641—24no—
28#16839635—24no—
29#16839625—24no—
30C4×C22⋊Dic61—24no—
31C2×#14519684C2212yes—
32C2×#14519684C2212yes—
33C2×#14519684C2212yes—
34C2×#14519684C2211yescharacteristic
35C2×#14519684C2212yes—
36C2×#14519684C2211yescharacteristic
37C2×#14519684C2212yes—
38C24×C4×C61C2211yescharacteristic
39C24×C4×C61C2211yescharacteristic
40C24×C4×C61C2211yescharacteristic
41C2×#95×C61—24no—
42C2×#95×C61C2212yes—
43C2×#95×C61C2212yes—
44C24×D61C2311yescharacteristic
45C22×C22⋊D61—22no—
46C22×C22⋊D61—22no—
47C22×C22⋊D61—22no—
48C22×C22⋊D61—22no—
49C22×C22⋊D61—22no—
50C22×C22⋊D61—22no—
51C22×C22⋊D61C2×C414yes—
52C23×Dic61C2311yescharacteristic
53C23×Dic61C2311yescharacteristic
54C23×Dic61C2311yescharacteristic
55C23×Dic61C2312yes—
56C23×Dic61C2312yes—
57#14519760—232no—
58C2×#11758196—24no—
59C2×#11758196—24no—
60C2×#11758196—24no—
61C2×#11758196—24no—
62C2×#11758196—42no—
63C2×#11758196C2×C418yescomplemented
64C2×C22⋊Dic61—22no—
65C2×C22⋊Dic61—22no—
66C2×C22⋊Dic61—22no—
67C2×C22⋊Dic61—22no—
68C2×C22⋊Dic61—22no—
69C2×C22⋊Dic61C2×C414yes—
70C2×C22⋊Dic61D414yes—
71C2×C22⋊Dic61D414yes—
72C2×C22⋊Dic61D414yes—
73C2×#11758198—24no—
74C2×#11758198—24no—
75C2×#11758198—22no—
76C2×#11758198—22no—
77C2×#11758198—24no—
78C2×#11758198—24no—
79C2×#11758198—24no—
80C2×#11758198—42no—
81C2×#11758198—42no—
82C2×#11758198C2×C418yescomplemented
83C2×C4×Dic61—24no—
84C2×C4×Dic61—24no—
85C2×C4×Dic61—42no—
86#14519684—22no—
87#14519684—22no—
88#14519684—24no—
89#14519684—24no—
90#14519684—24no—
91#14519684—24no—
92#14519684—24no—
93C25×C61C2311yescharacteristic
94C23×C4×C61—22no—
95C23×C4×C61—22no—
96C23×C4×C61—22no—
97C23×C4×C61—22no—
98C23×C4×C61—22no—
99C23×C4×C61—22no—
100C23×C4×C61—22no—
101C23×C4×C61—22no—
102C23×C4×C61—22no—
103C23×C4×C61—24no—
104C23×C4×C61—24no—
105C23×C4×C61—22no—
106C23×C4×C61—22no—
107C23×C4×C61—42no—
108C23×C4×C61—42no—
109C23×C4×C61C2×C414yes—
110C23×C4×C61D414yes—
111C23×C4×C61C2312yes—
112C23×C4×C61C2311yescharacteristic
113C23×C4×C61C2312yes—
114C23×C4×C61C2311yescharacteristic
115#95×C61—24no—
116#95×C61—24no—
117C24×C61—22no—
118C24×C61—22no—
119C24×C61—22no—
120C24×C61—22no—
121C24×C61C22×C412yes—
122C24×C61C2×D412yes—
123C24×C61C2×D412yes—
124C24×C61C2×D412yes—
125C24×C61C2×D412yes—
126C24×C61#4112yes—
127C24×C61#4112yes—
128C24×C61C2411yescharacteristic
129C23×D61—21no—
130C23×D61—21no—
131C23×D61—21no—
132C23×D61—21no—
133C23×D61—21no—
134C23×D61—21no—
135C23×D61—22no—
136C23×D61—22no—
137C23×D61—22no—
138C23×D61—22no—
139C23×D61C22×C412yes—
140C22×C4×C61—21no—
141C22×C4×C61—21no—
142C22×C4×C61—22no—
143C22×C4×C61—28no—
144C22×C4×C61—28no—
145C22×C4×C61—28no—
146C22×C4×C61—28no—
147C22×C4×C61—28no—
148C22×C4×C61—22no—
149C22×C4×C61—22no—
150C22×C4×C61—22no—
151C22×C4×C61—21no—
152C22×C4×C61—22no—
153C22×C4×C61—22no—
154C22×C4×C61—22no—
155C22×C4×C61—22no—
156C22×C4×C61—22no—
157C22×C4×C61—22no—
158C22×C4×C61—21no—
159C22×C4×C61—22no—
160C22×C4×C61—22no—
161C22×C4×C61—22no—
162C22×C4×C61—22no—
163C22×C4×C61—22no—
164C22×C4×C61—28no—
165C22×C4×C61—44no—
166C22×C4×C61—48no—
167C22×C4×C61—48no—
168C22×C4×C61—48no—
169C22×C4×C61—48no—
170C22×C4×C61—44no—
171C22×C4×C61—44no—
172C22×C4×C61—44no—
173C22×C4×C61—44no—
174C22×C4×C61—44no—
175C22×C4×C61—44no—
176C22×C4×C61C22×C414yes—
177C22×C4×C61C2×D412yes—
178C22×C4×C61C2×D412yes—
179C22×C4×C61#4114yes—
180C22×C4×C61#4114yes—
181C2×C22⋊D61—28no—
182C2×C22⋊D61—28no—
183C2×C22⋊D61—28no—
184C2×C22⋊D61—44no—
185C2×C22⋊D61—44no—
186C2×C22⋊D61—44no—
187C2×C22⋊D61—44no—
188C22×Dic61—22no—
189C22×Dic61—22no—
190C22×Dic61—22no—
191C22×Dic61—22no—
192C22×Dic61—21no—
193C22×Dic61—21no—
194C22×Dic61—21no—
195C22×Dic61—21no—
196C22×Dic61—22no—
197C22×Dic61—21no—
198C22×Dic61—21no—
199C22×Dic61—22no—
200C22×Dic61—22no—
201C22×Dic61—22no—
202C22×Dic61—22no—
203C22×Dic61—22no—
204C22×Dic61—21no—
205C22×Dic61—21no—
206C22×Dic61—21no—
207C22×Dic61—21no—
208C22×Dic61—21no—
209C22×Dic61—21no—
210C22×Dic61—22no—
211C22×Dic61—22no—
212C22×Dic61—22no—
213C22×Dic61—22no—
214C22×Dic61C22×C412yes—
215C22×Dic61C22×C414yes—
216C22×Dic61C2×D414yes—
217C22×Dic61C2×D414yes—
218C22×Dic61C2×D414yes—
219C22⋊Dic61—28no—
220C22⋊Dic61—44no—
221C22⋊Dic61C22⋊C4116yescomplemented
222#11758198—216no—
223#11758198—48no—
224#11758198—44no—
225#11758198—44no—
226#11758196—216no—
227#11758196—48no—
228C4×Dic61—48no—
229C23×C61—24no—
230C23×C61—24no—
231C23×C61—22no—
232C23×C61—22no—
233C23×C61—24no—
234C23×C61—22no—
235C23×C61—22no—
236C23×C61—24no—
237C23×C61—24no—
238C23×C61—24no—
239C23×C61—24no—
240C23×C61—24no—
241C23×C61—24no—
242C23×C61—24no—
243C23×C61—24no—
244C23×C61—24no—
245C23×C61C2×C22⋊C414yes—
246C23×C61C4×D414yes—
247C23×C61C4×D414yes—
248C23×C61#12114yes—
249C23×C61#12114yes—
250C23×C61#12414yes—
251C23×C61#12714yes—
252C23×C61C23×C411yescharacteristic
253C23×C61C22×D411yescharacteristic
254C23×C61C22×D411yescharacteristic
255C23×C61C22×D411yescharacteristic
256C23×C61C22×D411yescharacteristic
257C23×C61C2×#4111yescharacteristic
258C23×C61C2×#4111yescharacteristic
259C23×C61C2×#4112yes—
260C23×C61C2×#4112yes—
261C23×C61H(5,𝔽2)12yes—
262C23×C612−1+412yes—
263C22×D61—22no—
264C22×D61—22no—
265C22×D61—22no—
266C22×D61—24no—
267C22×D61—24no—
268C22×D61—41no—
269C22×D61—41no—
270C22×D61—41no—
271C22×D61—41no—
272C22×D61—41no—
273C22×D61—42no—
274C22×D61—41no—
275C22×D61—41no—
276C22×D61—41no—
277C22×D61—42no—
278C22×D61—42no—
279C22×D61—42no—
280C22×D61—42no—
281C22×D61—42no—
282C22×D61—42no—
283C22×D61—42no—
284C22×D61—42no—
285C22×D61—42no—
286C2×C4×C61—22no—
287C2×C4×C61—22no—
288C2×C4×C61—24no—
289C2×C4×C61—24no—
290C2×C4×C61—24no—
291C2×C4×C61—24no—
292C2×C4×C61—24no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—24no—
296C2×C4×C61—22no—
297C2×C4×C61—24no—
298C2×C4×C61—24no—
299C2×C4×C61—416no—
300C2×C4×C61—416no—
301C2×C4×C61—42no—
302C2×C4×C61—42no—
303C2×C4×C61—42no—
304C2×C4×C61—42no—
305C2×C4×C61—42no—
306C2×C4×C61—42no—
307C2×C4×C61—42no—
308C2×C4×C61—42no—
309C2×C4×C61—42no—
310C2×C4×C61—42no—
311C2×C4×C61—416no—
312C2×C4×C61#12314yescomplemented
313C22⋊D61—416no—
314C2×Dic61—24no—
315C2×Dic61—24no—
316C2×Dic61—24no—
317C2×Dic61—24no—
318C2×Dic61—24no—
319C2×Dic61—24no—
320C2×Dic61—22no—
321C2×Dic61—22no—
322C2×Dic61—22no—
323C2×Dic61—24no—
324C2×Dic61—24no—
325C2×Dic61—24no—
326C2×Dic61—41no—
327C2×Dic61—41no—
328C2×Dic61—41no—
329C2×Dic61—42no—
330C2×Dic61—41no—
331C2×Dic61—42no—
332C2×Dic61—42no—
333C2×Dic61—42no—
334C2×Dic61—41no—
335C2×Dic61—41no—
336C2×Dic61—41no—
337C2×Dic61—41no—
338C2×Dic61—41no—
339C2×Dic61—41no—
340C2×Dic61—42no—
341C2×Dic61—42no—
342C2×Dic61—42no—
343C2×Dic61—42no—
344C2×Dic61C2×C22⋊C418yes—
345#13996—611nomaximal, Sylow
346C22×C61—24no—
347C22×C61—28no—
348C22×C61—28no—
349C22×C61—24no—
350C22×C61—24no—
351C22×C61—28no—
352C22×C61—28no—
353C22×C61—24no—
354C22×C61—24no—
355C22×C61—24no—
356C22×C61#39018yes—
357C22×C61C22×C22⋊C411yescharacteristic
358C22×C61C2×C4×D411yescharacteristic
359C22×C61C2×C4×D411yescharacteristic
360C22×C61C4×#4112yes—
361C22×C61#52012yes—
362C22×C61C2×#12111yescharacteristic
363C22×C61C2×#12111yescharacteristic
364C22×C61C2×#12311yescharacteristic
365C22×C61#52511yescharacteristic
366C22×C61C2×#12411yescharacteristic
367C22×C61#52912yes—
368C22×C61C2×#12711yescharacteristic
369C22×C61#53411yescharacteristic
370C22×C61#53611yescharacteristic
371C22×C61#53912yes—
372C22×C61#54612yes—
373C22×C61#54612yes—
374C22×C61#54612yes—
375C22×C61#54712yes—
376C22×C61#54712yes—
377C22×C61#54712yes—
378C22×C61#55112yes—
379C22×C61#55212yes—
380C2×D61—42no—
381C2×D61—44no—
382C2×D61—44no—
383C2×D61—42no—
384C2×D61—42no—
385C2×D61—81no—
386C2×D61—81no—
387C2×D61—82no—
388C2×D61—82no—
389C2×D61—81no—
390C2×D61—81no—
391C4×C61—24no—
392C4×C61—42no—
393C4×C61—44no—
394C4×C61—44no—
395Dic61—28no—
396Dic61—44no—
397Dic61—42no—
398Dic61—81no—
399Dic61—81no—
400C22×#123—611no—
401C2×#386—611no—
402C2×#386—611no—
403C2×#385—611no—
404C2×#381—611no—
405C2×C4×C22⋊C4—611no—
406C22×#95D6111yescharacteristic, complemented
407#1445—612no—
408#1439—612no—
409#1437—612no—
410C4⋊#95—612no—
411C2×C61—28no—
412C2×C61C2×#39011yescharacteristic
413C2×C61C4×#12311yescharacteristic
414C2×C61#232211yescharacteristic
415C2×C61#233912yes—
416C2×C61#235912yes—
417C2×C61#241211yescharacteristic
418C2×C61#241311yescharacteristic
419C2×C61#242512yes—
420C2×C61#248812yes—
421C2×C61#250111yescharacteristic
422C2×C61#253911yescharacteristic
423D61—82no—
424C23×D4—611no—
425C24×C4C2×D6111yescharacteristic
426C24×C4C2×D6111yescharacteristic
427C24×C4C2×D6111yescharacteristic
428C2×#123—618no—
429C2×#123—1224no—
430C2×#123—1224no—
431C22×C4⋊C4—612no—
432C22×C4⋊C4—612no—
433C22×C22⋊C4—611no—
434C22×C22⋊C4—611no—
435C22×C22⋊C4—612no—
436C22×C22⋊C4—611no—
437C22×C22⋊C4—611no—
438C22×C22⋊C4—612no—
439C22×C22⋊C4—611no—
440C22×C42—612no—
441#386—1224no—
442#386—1224no—
443#385—1224no—
444#381—1224no—
445C4×C22⋊C4—1224no—
446C2×#95—24no—
447C2×#95—611no—
448C2×#95—612no—
449C2×#95—612no—
450C2×#95—612no—
451C2×#95—612no—
452C2×#95—612no—
453C2×#95—611no—
454C2×#95C2×D6112yes—
455C2×#95C2×D6112yes—
456C61#1399611yescharacteristic, complemented, Sylow
457C25—611no—
458C25C22×D6111yescharacteristic
459C22×D4—614no—
460C22×D4—1222no—
461C22×D4—1222no—
462C22×D4—1222no—
463C22×D4—1222no—
464C22×D4—1222no—
465C22×D4—1222no—
466C23×C4—22no—
467C23×C4—22no—
468C23×C4—22no—
469C23×C4—22no—
470C23×C4—22no—
471C23×C4—22no—
472C23×C4—22no—
473C23×C4—22no—
474C23×C4—22no—
475C23×C4—24no—
476C23×C4—24no—
477C23×C4—22no—
478C23×C4—22no—
479C23×C4—42no—
480C23×C4—42no—
481C23×C4—612no—
482C23×C4—612no—
483C23×C4—611no—
484C23×C4—611no—
485C23×C4—611no—
486C23×C4C4×D6114yes—
487C23×C4C22⋊D6114yes—
488C23×C4C22×D6112yes—
489C23×C4C22×D6112yes—
490C23×C4C22×D6111yescharacteristic
491C23×C4C22×D6111yescharacteristic
492#123—12232no—
493C2×C4⋊C4—618no—
494C2×C4⋊C4—1224no—
495C2×C4⋊C4—1224no—
496C2×C4⋊C4—1224no—
497C2×C4⋊C4—1224no—
498C2×C4⋊C4—2442no—
499C2×C22⋊C4—614no—
500C2×C22⋊C4—614no—
501C2×C22⋊C4—614no—
502C2×C22⋊C4—614no—
503C2×C22⋊C4—618no—
504C2×C22⋊C4—1224no—
505C2×C22⋊C4—1224no—
506C2×C22⋊C4—1222no—
507C2×C22⋊C4—1222no—
508C2×C22⋊C4—1224no—
509C2×C22⋊C4—1222no—
510C2×C22⋊C4—1222no—
511C2×C22⋊C4—1222no—
512C2×C22⋊C4—1224no—
513C2×C22⋊C4—1224no—
514C2×C22⋊C4—1222no—
515C2×C22⋊C4—1222no—
516C2×C22⋊C4—2442no—
517C2×C22⋊C4—2442no—
518C2×C42—1224no—
519C2×C42—1224no—
520C2×C42—2442no—
521#95—24no—
522#95—24no—
523#95—1224no—
524#95—1224no—
525#95—1224no—
526#95—1224no—
527#95—1224no—
528#95—1222no—
529#95—1222no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—612no—
535C24—1221no—
536C24—1221no—
537C24—1221no—
538C24—1221no—
539C24—1221no—
540C24—1222no—
541C24—1222no—
542C24—1221no—
543C24—1222no—
544C24—1222no—
545C24C2×C4×D6112yes—
546C24#1175822212yes—
547C24D4×D6112yes—
548C24D4×D6112yes—
549C24D4×D6112yes—
550C24#1175822412yes—
551C24C2×C22⋊D6112yes—
552C24C23×D6111yescharacteristic
553C2×D4—1228no—
554C2×D4—1228no—
555C2×D4—1228no—
556C2×D4—2444no—
557C2×D4—2444no—
558C2×D4—2444no—
559C2×D4—2444no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—22no—
563C22×C4—28no—
564C22×C4—22no—
565C22×C4—21no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—28no—
581C22×C4—28no—
582C22×C4—28no—
583C22×C4—28no—
584C22×C4—28no—
585C22×C4—44no—
586C22×C4—48no—
587C22×C4—48no—
588C22×C4—48no—
589C22×C4—48no—
590C22×C4—44no—
591C22×C4—44no—
592C22×C4—44no—
593C22×C4—44no—
594C22×C4—44no—
595C22×C4—44no—
596C22×C4—614no—
597C22×C4—614no—
598C22×C4—614no—
599C22×C4—612no—
600C22×C4—614no—
601C22×C4—1222no—
602C22×C4—1222no—
603C22×C4—1222no—
604C22×C4—1222no—
605C22×C4—1221no—
606C22×C4—1222no—
607C22×C4—1221no—
608C22×C4—1221no—
609C22×C4—1221no—
610C22×C4—1221no—
611C22×C4—1222no—
612C22×C4—1222no—
613C22×C4—1222no—
614C22×C4—1221no—
615C22×C4—1222no—
616C22×C4—1222no—
617C22×C4—1221no—
618C22×C4—1221no—
619C22×C4—1221no—
620C22×C4—1221no—
621C22×C4—1221no—
622C22×C4—1221no—
623C22×C4—1222no—
624C22×C4—1222no—
625C22×C4—1222no—
626C22×C4—1222no—
627C22×C4C2×C4×D6114yes—
628C22×C4#1175822214yes—
629C22×C4#1175822214yes—
630C22×C4C2×C22⋊D6112yes—
631C22×C4C2×C22⋊D6112yes—
632C4⋊C4—12216no—
633C4⋊C4—2448no—
634C22⋊C4—6116no—
635C22⋊C4—12216no—
636C22⋊C4—1228no—
637C22⋊C4—2448no—
638C22⋊C4—2444no—
639C22⋊C4—2444no—
640C22⋊C4—2444no—
641C42—2448no—
642C23—24no—
643C23—24no—
644C23—22no—
645C23—22no—
646C23—24no—
647C23—22no—
648C23—22no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—1222no—
659C23—1222no—
660C23—1222no—
661C23—1224no—
662C23—1224no—
663C23—2441no—
664C23—2441no—
665C23—2441no—
666C23—2441no—
667C23—2441no—
668C23—2442no—
669C23—2441no—
670C23—2441no—
671C23—2441no—
672C23—2442no—
673C23—2442no—
674C23—2442no—
675C23—2442no—
676C23—2442no—
677C23—2442no—
678C23—2442no—
679C23—2442no—
680C23—2442no—
681C23C22⋊C4×D6114yes—
682C23#1451973714yes—
683C23C4×C22⋊D6114yes—
684C23#1451974914yes—
685C23#1451975014yes—
686C23#1451976314yes—
687C23#1451977314yes—
688C23C22×C4×D6111yescharacteristic
689C23C2×D4×D6111yescharacteristic
690C23C2×D4×D6111yescharacteristic
691C23C2×D4×D6111yescharacteristic
692C23C22×C22⋊D6111yescharacteristic
693C23C2×#1175822411yescharacteristic
694C23C2×#1175822211yescharacteristic
695C23C2×#1175822212yes—
696C23C2×#1175822212yes—
697C23#1451982212yes—
698C23#1451982512yes—
699D4—24416no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—24no—
710C2×C4—22no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—416no—
714C2×C4—416no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—416no—
725C2×C4—42no—
726C2×C4—618no—
727C2×C4—1224no—
728C2×C4—1224no—
729C2×C4—1224no—
730C2×C4—1224no—
731C2×C4—1224no—
732C2×C4—1224no—
733C2×C4—1222no—
734C2×C4—1222no—
735C2×C4—1222no—
736C2×C4—1224no—
737C2×C4—1224no—
738C2×C4—1224no—
739C2×C4—2441no—
740C2×C4—2441no—
741C2×C4—2441no—
742C2×C4—2441no—
743C2×C4—2441no—
744C2×C4—2441no—
745C2×C4—2442no—
746C2×C4—2442no—
747C2×C4—2442no—
748C2×C4—2442no—
749C2×C4—2441no—
750C2×C4—2441no—
751C2×C4—2441no—
752C2×C4—2442no—
753C2×C4—2441no—
754C2×C4—2442no—
755C2×C4—2442no—
756C2×C4—2442no—
757C2×C4#1451976014yescomplemented
758C22—24no—
759C22—24no—
760C22—24no—
761C22—28no—
762C22—24no—
763C22—28no—
764C22—28no—
765C22—28no—
766C22—24no—
767C22—24no—
768C22—4881no—
769C22—4881no—
770C22—4882no—
771C22—4882no—
772C22—4881no—
773C22—4881no—
774C22—2442no—
775C22—2442no—
776C22—2444no—
777C22—2442no—
778C22—2444no—
779C22#1683966218yes—
780C22C2×C22⋊C4×D6111yescharacteristic
781C22C2×#1451973711yescharacteristic
782C22C2×C4×C22⋊D6111yescharacteristic
783C22C4×#1175822212yes—
784C22#1684024312yes—
785C22C2×#1451974911yescharacteristic
786C22C2×#1451975011yescharacteristic
787C22C2×#1451976011yescharacteristic
788C22#1684027311yescharacteristic
789C22C2×#1451976311yescharacteristic
790C22#1684029612yes—
791C22C2×#1451977311yescharacteristic
792C22#1684032111yescharacteristic
793C22#1684033611yescharacteristic
794C22#1684035912yes—
795C22#1684040212yes—
796C22#1684040212yes—
797C22#1684040212yes—
798C22#1684041312yes—
799C22#1684041312yes—
800C22#1684041312yes—
801C22#1684043812yes—
802C22#1684044712yes—
803C4—24no—
804C4—44no—
805C4—44no—
806C4—42no—
807C4—1228no—
808C4—4881no—
809C4—4881no—
810C4—2442no—
811C4—2444no—
812C2—28no—
813C2—4882no—
814C2C2×#1683966211yescharacteristic
815C2C4×#1451976011yescharacteristic
816C2#2144848811yescharacteristic
817C2#2144864612yes—
818C2#2144880712yes—
819C2#2144921511yescharacteristic
820C2#2144922611yescharacteristic
821C2#2144937012yes—
822C2#2145014512yes—
823C2#2145028611yescharacteristic
824C2#2145075011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC22×#95×C61C2
socle, cosocleC24×C61C24
prime radicalC23×C22⋊D61C22
hypercenterC22×#95D61
hypocenterC61#13996
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C22×#95

Complements

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

NH ≅ G/Ntype
4. C2×#16839635C2semidirect
5. C2×#16839625C2semidirect
6. C2×C4×C22⋊Dic61C2semidirect
7. #21444085C2semidirect
8. #21444063C2semidirect
9. #21444055C2semidirect
10. #21444047C2semidirect
11. C22×#95×C61C2semidirect
15. C2×#14519760C4semidirect
63. C2×#11758196C2×C4semidirect
82. C2×#11758198C2×C4semidirect
221. C22⋊Dic61C22⋊C4semidirect
312. C2×C4×C61#123semidirect
406. C22×#95D61semidirect
456. C61#13996semidirect
757. C2×C4#14519760semidirect

Maximal subgroups

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

subgroupindex
C22×#145197602
C2×#168396412
C2×#168396352
C2×#168396252
C2×C4×C22⋊Dic612
#214440852
#214440632
#214440552
#214440472
C22×#95×C612
#1399661