Finite Group Databasebeta

← #29602532

Subgroups — #29602532

Order 15616.

4470 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#11758226C211yesmaximal, characteristic
2C2×#16839669C211yesmaximal, characteristic, complemented
3C2×#16839664C211yesmaximal, characteristic, complemented
4C2×#16839663C211yesmaximal, characteristic, complemented
5C2×#16839619C211yesmaximal, characteristic, complemented
6C2×C4×#11758198C211yesmaximal, characteristic, complemented
7#21444059C214yesmaximal, complemented
8#21444040C214yesmaximal, complemented
9C2×C61×#391C211yesmaximal, characteristic, complemented
10C22×#11758226—24no—
11C22×#11758226—24no—
12C22×#11758226—24no—
13C22×#11758226—24no—
14C22×#11758226—24no—
15C22×#11758226—24no—
16C22×#11758226C418yescomplemented
17C23×D244C2212yes—
18C23×D244C2211yescharacteristic
19C23×C4×D61C2212yes—
20C23×C4×D61C2211yescharacteristic
21C22×C4⋊Dic61C2211yescharacteristic
22C22×#11758198C2212yes—
23C22×#11758198C2214yes—
24C22×#11758198C2214yes—
25C22×#11758198C2212yes—
26C22×C4×Dic61C2211yescharacteristic
27#16839669—24no—
28#16839664—24no—
29#16839663—24no—
30#16839619—24no—
31C4×#11758198—24no—
32C2×#14519684C2214yes—
33C2×#14519684C2212yes—
34C2×#14519684C2212yes—
35C23×Q8×C61C2211yescharacteristic
36C22×C4⋊C4×C61C2211yescharacteristic
37C22×C42×C61C2211yescharacteristic
38C61×#391—24no—
39C2×#95×C61C2214yes—
40C24×D61C2312yes—
41C24×D61C2311yescharacteristic
42C2×#11758226—232no—
43C2×#11758226—232no—
44C2×#11758226—232no—
45C2×#11758226—232no—
46C2×#11758226—232no—
47C2×#11758226—232no—
48C2×#11758226—232no—
49C22×D244—24no—
50C22×D244—24no—
51C22×D244—24no—
52C22×D244—24no—
53C22×D244—24no—
54C22×D244—22no—
55C22×D244—22no—
56C22×D244—22no—
57C22×D244—24no—
58C22×D244—22no—
59C22×D244C2×C418yes—
60C22×D244C2×C414yes—
61C22×D244D414yes—
62C22×D244D414yes—
63C23×Dic61C2312yes—
64C23×Dic61C2312yes—
65C23×Dic61C2311yescharacteristic
66C22×C4×D61—24no—
67C22×C4×D61—24no—
68C22×C4×D61—24no—
69C22×C4×D61—22no—
70C22×C4×D61—22no—
71C22×C4×D61—22no—
72C22×C4×D61—24no—
73C22×C4×D61—22no—
74C22×C4×D61—24no—
75C22×C4×D61—24no—
76C22×C4×D61C2×C418yes—
77C22×C4×D61C2×C414yes—
78C22×C4×D61D414yes—
79C22×C4×D61D414yes—
80C2×C4⋊Dic61—22no—
81C2×C4⋊Dic61—22no—
82C2×C4⋊Dic61—22no—
83C2×#11758198—24no—
84C2×#11758198—24no—
85C2×#11758198—24no—
86C2×#11758198—24no—
87C2×#11758198—28no—
88C2×#11758198—28no—
89C2×#11758198—28no—
90C2×#11758198—28no—
91C2×#11758198—44no—
92C2×#11758198—44no—
93C2×#11758198—44no—
94C2×C4×Dic61—22no—
95C2×C4×Dic61—22no—
96C2×C4×Dic61—22no—
97#14519684—28no—
98#14519684—24no—
99#14519684—24no—
100C22×Q8×C61—22no—
101C22×Q8×C61—22no—
102C22×Q8×C61—22no—
103C22×Q8×C61—22no—
104C22×Q8×C61C2×C414yes—
105C22×Q8×C61D414yes—
106C22×Q8×C61D414yes—
107C23×C4×C61C2312yes—
108C23×C4×C61C2312yes—
109C23×C4×C61C2312yes—
110C23×C4×C61C2311yescharacteristic
111C2×C4⋊C4×C61—22no—
112C2×C4⋊C4×C61—22no—
113C2×C4⋊C4×C61—22no—
114C2×C42×C61—22no—
115C2×C42×C61—22no—
116C2×C42×C61—22no—
117#95×C61—28no—
118C24×C61C2411yescharacteristic
119C23×D61—22no—
120C23×D61—22no—
121C23×D61—21no—
122C23×D61—21no—
123C23×D61—22no—
124C23×D61—21no—
125C23×D61—22no—
126C23×D61—21no—
127C23×D61—22no—
128C23×D61—22no—
129C23×D61—24no—
130C23×D61—24no—
131C23×D61—22no—
132C23×D61—24no—
133C23×D61—22no—
134C23×D61—24no—
135C23×D61C22×C414yes—
136C23×D61C22×C412yes—
137C23×D61C2×D414yes—
138C23×D61C2×D414yes—
139C23×D61C2×D412yes—
140C23×D61C2×D412yes—
141C2×Q8×C61—28no—
142C2×Q8×C61—28no—
143C2×Q8×C61—28no—
144C2×Q8×C61—28no—
145C2×Q8×C61—28no—
146C2×Q8×C61—28no—
147C2×Q8×C61C22⋊C4116yescomplemented
148C22×C4×C61—22no—
149C22×C4×C61—22no—
150C22×C4×C61—22no—
151C22×C4×C61—22no—
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—22no—
159C22×C4×C61—22no—
160C22×C4×C61—22no—
161C22×C4×C61—24no—
162C22×C4×C61—24no—
163C22×C4×C61C22×C414yes—
164C22×C4×C61C22×C412yes—
165C22×C4×C61C2×D414yes—
166C22×C4×C61C2×D414yes—
167C22×C4×C61C2×D412yes—
168C22×C4×C61C2×D412yes—
169C22×C4×C61C2×D412yes—
170C22×C4×C61C2×D412yes—
171C22×C4×C61C2×D412yes—
172C22×C4×C61C2×D412yes—
173C22×C4×C61#4114yescomplemented
174C22×Dic61—21no—
175C22×Dic61—21no—
176C22×Dic61—21no—
177C22×Dic61—21no—
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—22no—
187C22×Dic61—24no—
188C22×Dic61—24no—
189C22×Dic61C22×C412yes—
190C22×Dic61C2×D412yes—
191C22×Dic61C2×D412yes—
192C22×Dic61#4114yescomplemented
193#11758226—2256no—
194C2×D244—216no—
195C2×D244—216no—
196C2×D244—216no—
197C2×D244—216no—
198C2×D244—216no—
199C2×D244—216no—
200C2×D244—216no—
201C2×D244—28no—
202C2×D244—28no—
203C2×D244—28no—
204C2×D244—28no—
205C2×D244—28no—
206C2×D244—28no—
207C2×D244C22⋊C4116yescomplemented
208C2×C4×D61—216no—
209C2×C4×D61—216no—
210C2×C4×D61—216no—
211C2×C4×D61—216no—
212C2×C4×D61—216no—
213C2×C4×D61—216no—
214C2×C4×D61—28no—
215C2×C4×D61—28no—
216C2×C4×D61—28no—
217C2×C4×D61—28no—
218C2×C4×D61—28no—
219C2×C4×D61—28no—
220C2×C4×D61—216no—
221C2×C4×D61C22⋊C4116yescomplemented
222C4⋊C4×C61—44no—
223C42×C61—44no—
224#11758198—216no—
225#11758198—416no—
226#11758198—416no—
227#11758198—48no—
228C4⋊Dic61—44no—
229C4×Dic61—44no—
230C23×C61C23×C411yescharacteristic
231C23×C61C22×D411yescharacteristic
232C23×C61C22×D411yescharacteristic
233C23×C61C22×D411yescharacteristic
234C23×C61C22×D411yescharacteristic
235C23×C61C22×D411yescharacteristic
236C23×C61C22×D411yescharacteristic
237C23×C61C2×#4112yes—
238C23×C61C2×#4112yes—
239C23×C61H(5,𝔽2)12yes—
240C23×C612−1+412yes—
241C22×D61—24no—
242C22×D61—22no—
243C22×D61—24no—
244C22×D61—22no—
245C22×D61—28no—
246C22×D61—24no—
247C22×D61—24no—
248C22×D61—28no—
249C22×D61—24no—
250C22×D61—22no—
251C22×D61—24no—
252C22×D61—22no—
253C22×D61—24no—
254C22×D61—22no—
255C22×D61—24no—
256C22×D61—22no—
257C22×D61—24no—
258C22×D61—22no—
259C22×D61—22no—
260C22×D61—22no—
261C22×D61—22no—
262C22×D61—24no—
263C22×D61—28no—
264C22×D61—28no—
265C22×D61—28no—
266C22×D61—28no—
267C22×D61—44no—
268C22×D61—42no—
269C22×D61—42no—
270C22×D61—42no—
271C22×D61—42no—
272C22×D61—44no—
273C22×D61—42no—
274C22×D61—42no—
275C22×D61—42no—
276C22×D61—42no—
277C22×D61—42no—
278C22×D61—44no—
279C22×D61—42no—
280C22×D61—44no—
281C22×D61—42no—
282C22×D61—44no—
283C22×D61—42no—
284C22×D61—44no—
285C22×D61C2×C22⋊C418yes—
286C22×D61C2×C22⋊C414yes—
287Q8×C61—232no—
288C2×C4×C61—24no—
289C2×C4×C61—24no—
290C2×C4×C61—24no—
291C2×C4×C61—24no—
292C2×C4×C61—24no—
293C2×C4×C61—24no—
294C2×C4×C61—24no—
295C2×C4×C61—24no—
296C2×C4×C61—24no—
297C2×C4×C61—42no—
298C2×C4×C61—42no—
299C2×C4×C61—42no—
300C2×C4×C61—42no—
301C2×C4×C61—42no—
302C2×C4×C61—42no—
303C2×C4×C61—42no—
304C2×C4×C61—44no—
305C2×C4×C61—44no—
306C2×C4×C61C2×C22⋊C418yes—
307C2×C4×C61C2×C22⋊C414yes—
308C2×C4×C61C2×C22⋊C414yes—
309C2×C4×C61C2×C22⋊C414yes—
310C2×C4×C61#12014yes—
311C2×C4×C61#12014yes—
312C2×C4×C61#12014yes—
313C2×C4×C61#12014yes—
314C2×Dic61—22no—
315C2×Dic61—22no—
316C2×Dic61—22no—
317C2×Dic61—22no—
318C2×Dic61—22no—
319C2×Dic61—22no—
320C2×Dic61—24no—
321C2×Dic61—24no—
322C2×Dic61—24no—
323C2×Dic61—42no—
324C2×Dic61—42no—
325C2×Dic61—42no—
326C2×Dic61—42no—
327C2×Dic61—42no—
328C2×Dic61—42no—
329C2×Dic61—42no—
330C2×Dic61—44no—
331C2×Dic61—44no—
332C2×Dic61C2×C22⋊C414yes—
333D244—264no—
334D244—232no—
335C4×D61—264no—
336C4×D61—232no—
337#13937—611nomaximal, Sylow
338C22×C61C22×C22⋊C411yescharacteristic
339C22×C61C22×C22⋊C411yescharacteristic
340C22×C61C22×C22⋊C411yescharacteristic
341C22×C61C4×#4112yes—
342C22×C61#52012yes—
343C22×C61C2×#12011yescharacteristic
344C22×C61C2×#12011yescharacteristic
345C22×C61C2×#12011yescharacteristic
346C22×C61C2×#12011yescharacteristic
347C22×C61#52512yes—
348C22×C61#53211yescharacteristic
349C22×C61#53211yescharacteristic
350C22×C61#53511yescharacteristic
351C22×C61#53611yescharacteristic
352C22×C61#53712yes—
353C22×C61#54612yes—
354C22×C61#54612yes—
355C22×C61#54712yes—
356C22×C61#54712yes—
357C22×C61#54812yes—
358C22×C61#54812yes—
359C22×C61#55012yes—
360C22×C61#55012yes—
361C2×D61—24no—
362C2×D61—216no—
363C2×D61—28no—
364C2×D61—24no—
365C2×D61—24no—
366C2×D61—44no—
367C2×D61—44no—
368C2×D61—44no—
369C2×D61—48no—
370C2×D61—44no—
371C2×D61—48no—
372C2×D61—44no—
373C2×D61—48no—
374C2×D61—42no—
375C2×D61—44no—
376C2×D61—42no—
377C2×D61—44no—
378C2×D61—42no—
379C2×D61—44no—
380C2×D61—42no—
381C2×D61—44no—
382C2×D61—44no—
383C4×C61—28no—
384C4×C61—44no—
385C4×C61—82no—
386C4×C61#37918yes—
387Dic61—24no—
388Dic61—44no—
389Dic61—82no—
390C23×#41—611no—
391C2×#391—611no—
392C2×#391D6111yescharacteristic, complemented
393C2×#390—611no—
394C2×#390—611no—
395C2×#380—611no—
396C2×C4×C22⋊C4—611no—
397#1438—614no—
398C22⋊#95—614no—
399C2×C61C2×#37911yescharacteristic
400C2×C61#229711yescharacteristic
401C2×C61#231111yescharacteristic
402C2×C61#233912yes—
403C2×C61#234112yes—
404C2×C61#240712yes—
405C2×C61#240712yes—
406C2×C61#243111yescharacteristic
407C2×C61#243111yescharacteristic
408C2×C61#243211yescharacteristic
409C2×C61#243211yescharacteristic
410D61—44no—
411D61—48no—
412C22×#41—618no—
413C22×#41—1224no—
414C22×#41—1224no—
415C22×#41—1224no—
416C22×#41—1224no—
417C22×#41—1224no—
418C22×#41—1224no—
419C23×Q8C2×D6111yescharacteristic
420C23×D4—611no—
421C23×D4—612no—
422C24×C4—611no—
423C24×C4—612no—
424C22×C4⋊C4—611no—
425C22×C4⋊C4C2×D6111yescharacteristic
426C22×C22⋊C4—612no—
427C22×C22⋊C4—614no—
428C22×C22⋊C4—614no—
429C22×C22⋊C4—612no—
430C22×C42—611no—
431C22×C42C2×D6111yescharacteristic
432#391—24no—
433#391—1224no—
434#390—1224no—
435#390—1224no—
436#380—1224no—
437C4×C22⋊C4—1224no—
438C2×#95—612no—
439C2×#95—612no—
440C2×#95—614no—
441C2×#95C2×D6114yes—
442C61#1393711yescharacteristic, complemented, Sylow
443C25—611no—
444C25—612no—
445C2×#41—12232no—
446C2×#41—12232no—
447C2×#41—12232no—
448C2×#41—12232no—
449C2×#41—12232no—
450C2×#41—12232no—
451C2×#41—12232no—
452C22×Q8—22no—
453C22×Q8—22no—
454C22×Q8—22no—
455C22×Q8—22no—
456C22×Q8C4×D6114yes—
457C22×Q8D24414yes—
458C22×Q8C22⋊D6114yes—
459C22×D4—614no—
460C22×D4—618no—
461C22×D4—614no—
462C22×D4—614no—
463C22×D4—1224no—
464C22×D4—1224no—
465C22×D4—1224no—
466C22×D4—1224no—
467C22×D4—1224no—
468C22×D4—1222no—
469C22×D4—1222no—
470C22×D4—1222no—
471C22×D4—1224no—
472C22×D4—1222no—
473C23×C4—611no—
474C23×C4—614no—
475C23×C4—614no—
476C23×C4—614no—
477C23×C4—612no—
478C23×C4—618no—
479C23×C4—612no—
480C23×C4—1224no—
481C23×C4—1224no—
482C23×C4—1224no—
483C23×C4—1224no—
484C23×C4—1224no—
485C23×C4—1222no—
486C23×C4—1222no—
487C23×C4—1222no—
488C23×C4—1224no—
489C23×C4—1222no—
490C23×C4C22×D6112yes—
491C23×C4C22×D6112yes—
492C23×C4C22×D6112yes—
493C23×C4C22×D6111yescharacteristic
494C2×C4⋊C4—22no—
495C2×C4⋊C4—22no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—1222no—
498C2×C4⋊C4—1222no—
499C2×C4⋊C4—1222no—
500C2×C22⋊C4—1224no—
501C2×C22⋊C4—1224no—
502C2×C22⋊C4—1224no—
503C2×C22⋊C4—1228no—
504C2×C22⋊C4—1224no—
505C2×C22⋊C4—1228no—
506C2×C22⋊C4—1228no—
507C2×C22⋊C4—1228no—
508C2×C22⋊C4—2444no—
509C2×C22⋊C4—2444no—
510C2×C22⋊C4—2444no—
511C2×C42—22no—
512C2×C42—22no—
513C2×C42—22no—
514C2×C42—1222no—
515C2×C42—1222no—
516C2×C42—1222no—
517#95—28no—
518#95—1224no—
519#95—1224no—
520#95—1228no—
521C24—612no—
522C24—614no—
523C24—612no—
524C24—612no—
525C24—614no—
526C24—614no—
527C24—1222no—
528C24—1222no—
529C24—1221no—
530C24—1221no—
531C24—1222no—
532C24—1221no—
533C24—1222no—
534C24—1221no—
535C24—1222no—
536C24—1224no—
537C24—1222no—
538C24—1224no—
539C24—1222no—
540C24—1224no—
541C24—1222no—
542C24—1224no—
543C24C23×D6111yescharacteristic
544#41—122256no—
545C2×Q8—28no—
546C2×Q8—28no—
547C2×Q8—28no—
548C2×Q8—28no—
549C2×Q8—28no—
550C2×Q8—28no—
551C2×Q8#11758198116yescomplemented
552C2×D4—6116no—
553C2×D4—12216no—
554C2×D4—12216no—
555C2×D4—12216no—
556C2×D4—12216no—
557C2×D4—12216no—
558C2×D4—12216no—
559C2×D4—1228no—
560C2×D4—12216no—
561C2×D4—1228no—
562C2×D4—1228no—
563C2×D4—1228no—
564C2×D4—1228no—
565C2×D4—1228no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—24no—
580C22×C4—24no—
581C22×C4—612no—
582C22×C4—612no—
583C22×C4—612no—
584C22×C4—6116no—
585C22×C4—614no—
586C22×C4—12216no—
587C22×C4—12216no—
588C22×C4—12216no—
589C22×C4—12216no—
590C22×C4—12216no—
591C22×C4—12216no—
592C22×C4—1221no—
593C22×C4—1221no—
594C22×C4—1221no—
595C22×C4—1221no—
596C22×C4—1228no—
597C22×C4—12216no—
598C22×C4—1228no—
599C22×C4—1228no—
600C22×C4—1228no—
601C22×C4—1228no—
602C22×C4—1228no—
603C22×C4—1222no—
604C22×C4—1222no—
605C22×C4—1222no—
606C22×C4—1222no—
607C22×C4—1222no—
608C22×C4—1222no—
609C22×C4—1222no—
610C22×C4—1222no—
611C22×C4—1222no—
612C22×C4—1224no—
613C22×C4—1224no—
614C22×C4C2×C4×D6114yes—
615C22×C4C2×C4×D6112yes—
616C22×C4C2×D24414yes—
617C22×C4C2×D24412yes—
618C22×C4D4×D6112yes—
619C22×C4D4×D6112yes—
620C22×C4D4×D6112yes—
621C22×C4D4×D6112yes—
622C22×C4#1175822614yescomplemented
623C22×C4C2×C22⋊D6114yes—
624C22×C4C2×C22⋊D6112yes—
625C4⋊C4—44no—
626C4⋊C4—2444no—
627C22⋊C4—12216no—
628C22⋊C4—24416no—
629C22⋊C4—24416no—
630C22⋊C4—2448no—
631C42—44no—
632C42—2444no—
633C23—614no—
634C23—618no—
635C23—1224no—
636C23—1222no—
637C23—1224no—
638C23—1222no—
639C23—1224no—
640C23—1228no—
641C23—1228no—
642C23—1224no—
643C23—1224no—
644C23—1222no—
645C23—1224no—
646C23—1222no—
647C23—1224no—
648C23—1222no—
649C23—1224no—
650C23—1222no—
651C23—1224no—
652C23—1222no—
653C23—1222no—
654C23—1222no—
655C23—1222no—
656C23—1224no—
657C23—1228no—
658C23—1228no—
659C23—1228no—
660C23—1228no—
661C23—2444no—
662C23—2442no—
663C23—2442no—
664C23—2442no—
665C23—2442no—
666C23—2444no—
667C23—2442no—
668C23—2442no—
669C23—2442no—
670C23—2442no—
671C23—2442no—
672C23—2444no—
673C23—2442no—
674C23—2444no—
675C23—2442no—
676C23—2444no—
677C23—2442no—
678C23—2444no—
679C23C22×C4×D6111yescharacteristic
680C23C2×D4×D6111yescharacteristic
681C23C2×D4×D6111yescharacteristic
682C23C2×D4×D6111yescharacteristic
683C23C2×D4×D6111yescharacteristic
684C23C22×C22⋊D6111yescharacteristic
685C23C22×D24411yescharacteristic
686C23#41×D6112yes—
687C23C2×#1175822612yes—
688C23#1451982312yes—
689C23#1451982512yes—
690Q8—232no—
691D4—12264no—
692D4—12232no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—44no—
710C2×C4—44no—
711C2×C4—614no—
712C2×C4—12264no—
713C2×C4—1222no—
714C2×C4—1222no—
715C2×C4—1222no—
716C2×C4—1222no—
717C2×C4—1222no—
718C2×C4—1222no—
719C2×C4—12232no—
720C2×C4—1224no—
721C2×C4—1224no—
722C2×C4—1224no—
723C2×C4—2442no—
724C2×C4—2442no—
725C2×C4—2442no—
726C2×C4—2444no—
727C2×C4—2444no—
728C2×C4—2442no—
729C2×C4—2442no—
730C2×C4—2442no—
731C2×C4—2442no—
732C2×C4C22⋊C4×D6114yes—
733C2×C4C22⋊C4×D6114yes—
734C2×C4C2×#1175819818yes—
735C2×C4C2×#1175819814yes—
736C2×C4#1451974514yes—
737C2×C4#1451974514yes—
738C2×C4#1451974714yes—
739C2×C4#1451974714yes—
740C22—1224no—
741C22—12216no—
742C22—1224no—
743C22—1228no—
744C22—1224no—
745C22—2444no—
746C22—2444no—
747C22—2444no—
748C22—2448no—
749C22—2444no—
750C22—2448no—
751C22—2444no—
752C22—2448no—
753C22—2444no—
754C22—2442no—
755C22—2444no—
756C22—2442no—
757C22—2444no—
758C22—2442no—
759C22—2444no—
760C22—2442no—
761C22—2444no—
762C22C2×C22⋊C4×D6111yescharacteristic
763C22C2×C22⋊C4×D6111yescharacteristic
764C22C22×#1175819811yescharacteristic
765C22C4×#1175822612yes—
766C22#1684024412yes—
767C22C2×#1451974511yescharacteristic
768C22C2×#1451974511yescharacteristic
769C22C2×#1451974711yescharacteristic
770C22C2×#1451974711yescharacteristic
771C22#1684027512yes—
772C22#1684031111yescharacteristic
773C22#1684031311yescharacteristic
774C22#1684033011yescharacteristic
775C22#1684033711yescharacteristic
776C22#1684034212yes—
777C22#1684040312yes—
778C22#1684040512yes—
779C22#1684041412yes—
780C22#1684041512yes—
781C22#1684042312yes—
782C22#1684042412yes—
783C22#1684043112yes—
784C22#1684043412yes—
785C4—28no—
786C4—44no—
787C4—82no—
788C4—1224no—
789C4—4882no—
790C4—2444no—
791C4#1683961718yes—
792C2—2444no—
793C2—2448no—
794C2C2×#1683961711yescharacteristic
795C2#2144830811yescharacteristic
796C2#2144841011yescharacteristic
797C2#2144864812yes—
798C2#2144865712yes—
799C2#2144916612yes—
800C2#2144916712yes—
801C2#2144944011yescharacteristic
802C2#2144944111yescharacteristic
803C2#2144944411yescharacteristic
804C2#2144944611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C61×#391C2
socle, cosocleC24×C61C24
prime radicalC23×#11758226C2
hypercenterC2×#391D61
hypocenterC61#13937
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
2. C2×#16839669C2semidirect
3. C2×#16839664C2semidirect
4. C2×#16839663C2semidirect
5. C2×#16839619C2semidirect
6. C2×C4×#11758198C2semidirect
7. #21444059C2semidirect
8. #21444040C2semidirect
9. C2×C61×#391C2semidirect
16. C22×#11758226C4semidirect
147. C2×Q8×C61C22⋊C4semidirect
173. C22×C4×C61#41semidirect
192. C22×Dic61#41semidirect
207. C2×D244C22⋊C4semidirect
221. C2×C4×D61C22⋊C4semidirect
392. C2×#391D61semidirect
442. C61#13937semidirect
551. C2×Q8#11758198semidirect
622. C22×C4#11758226semidirect

Maximal subgroups

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

subgroupindex
C23×#117582262
C2×#168396692
C2×#168396642
C2×#168396632
C2×#168396192
C2×C4×#117581982
#214440592
#214440402
C2×C61×#3912
#1393761