Finite Group Databasebeta

← #29601414

Subgroups — #29601414

Order 15616.

4254 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊C4×D61C212yesmaximal
2C2×#16839617C211yesmaximal, characteristic
3C2×C4×#11758198C212yesmaximal, complemented
4C2×#16839609C212yesmaximal, complemented
5#21444056C211yesmaximal, characteristic, complemented
6#21444056C212yesmaximal, complemented
7#21444040C212yesmaximal, complemented
8#21444040C212yesmaximal, complemented
9C61×#1437C211yesmaximal, characteristic, complemented
10C25×D61C2211yescharacteristic
11C23×C4×D61C2212yes—
12C23×C4×D61C2212yes—
13C22×C22⋊Dic61C2212yes—
14C22×C22⋊Dic61C2211yescharacteristic
15C22×#11758198C2212yes—
16C22×#11758198C2212yes—
17C22×#11758198C2212yes—
18C22×#11758198C2212yes—
19C2×C22⋊C4×D61—28no—
20C2×C22⋊C4×D61—28no—
21C2×C22⋊C4×D61C4116yescomplemented
22C22×C4×Dic61C2211yescharacteristic, complemented
23C22×C4×Dic61C2212yescomplemented
24#16839617C418yescomplemented
25C4×#11758198—28no—
26#16839609—28no—
27C2×#14519684C2212yescomplemented
28C2×#14519684C2212yescomplemented
29C2×#14519684C2212yescomplemented
30C2×#14519684C2212yescomplemented
31C2×#14519684C2211yescharacteristic, complemented
32C22×C22⋊C4×C61C2212yes—
33C22×C22⋊C4×C61C2211yescharacteristic
34C22×C42×C61C2211yescharacteristic, complemented
35C2×#95×C61C2212yescomplemented
36C2×#95×C61C2211yescharacteristic, complemented
37C24×D61—24no—
38C24×D61—24no—
39C24×D61—24no—
40C24×D61—24no—
41C24×D61—41no—
42C24×D61—41no—
43C24×D61—42no—
44C24×D61C2×C418yes—
45C24×D61C2×C414yes—
46C24×D61C2312yes—
47C23×Dic61C2312yes—
48C23×Dic61C2312yes—
49C23×Dic61C2312yes—
50C22×C4×D61—24no—
51C22×C4×D61—24no—
52C22×C4×D61—24no—
53C22×C4×D61—24no—
54C22×C4×D61—24no—
55C22×C4×D61—24no—
56C22×C4×D61—24no—
57C22×C4×D61—24no—
58C22×C4×D61—42no—
59C22×C4×D61—42no—
60C22×C4×D61—42no—
61C22×C4×D61—42no—
62C22×C4×D61C2×C418yescomplemented
63C22×C4×D61C2×C418yescomplemented
64C2×C22⋊Dic61—24no—
65C2×C22⋊Dic61—24no—
66C2×C22⋊Dic61—42no—
67C2×C22⋊Dic61C2×C418yescomplemented
68C2×C22⋊Dic61C2×C414yescomplemented
69C2×#11758198—24no—
70C2×#11758198—24no—
71C2×#11758198—24no—
72C2×#11758198—24no—
73C2×#11758198—24no—
74C2×#11758198—24no—
75C2×#11758198C2×C418yes—
76C2×#11758198C2×C418yes—
77C2×#11758198C2×C418yescomplemented
78C2×#11758198C2×C418yescomplemented
79C2×#11758198D418yes—
80C2×#11758198D418yes—
81C22⋊C4×D61—264no—
82C2×C4×Dic61—24no—
83C2×C4×Dic61—24no—
84C2×C4×Dic61—24no—
85C2×C4×Dic61—41no—
86C2×C4×Dic61—42no—
87#14519684—24no—
88#14519684—24no—
89#14519684—24no—
90#14519684—41no—
91#14519684—42no—
92C25×C61C2311yescharacteristic
93C23×C4×C61C2311yescharacteristic
94C23×C4×C61C2311yescharacteristic
95C23×C4×C61C2312yes—
96C23×C4×C61C2312yes—
97C2×C22⋊C4×C61—24no—
98C2×C22⋊C4×C61—24no—
99C2×C22⋊C4×C61—41no—
100C2×C22⋊C4×C61—41no—
101C2×C22⋊C4×C61C2×C418yescomplemented
102C2×C22⋊C4×C61C2×C414yescomplemented
103C2×C42×C61—24no—
104C2×C42×C61—41no—
105#95×C61—24no—
106#95×C61—41no—
107C24×C61—22no—
108C24×C61—22no—
109C24×C61—22no—
110C24×C61—22no—
111C24×C61—21no—
112C24×C61—21no—
113C24×C61—22no—
114C24×C61C22×C414yes—
115C24×C61C22×C412yes—
116C24×C61C2411yescharacteristic
117C23×D61—22no—
118C23×D61—22no—
119C23×D61—22no—
120C23×D61—22no—
121C23×D61—22no—
122C23×D61—22no—
123C23×D61—22no—
124C23×D61—22no—
125C23×D61—216no—
126C23×D61—216no—
127C23×D61—216no—
128C23×D61—216no—
129C23×D61—216no—
130C23×D61—216no—
131C23×D61—48no—
132C23×D61—48no—
133C23×D61—44no—
134C23×D61—44no—
135C23×D61—44no—
136C23×D61—48no—
137C23×D61—44no—
138C23×D61—48no—
139C23×D61—48no—
140C23×D61—48no—
141C23×D61—48no—
142C23×D61—48no—
143C23×D61—44no—
144C23×D61—44no—
145C23×D61C42116yescomplemented
146C23×D61C22×C414yes—
147C23×D61C22×C414yes—
148C23×D61C22×C414yes—
149C23×D61C2×D414yes—
150C23×D61C2×D414yes—
151C23×D61#4114yes—
152C23×D61#4114yes—
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—22no—
162C22×C4×C61—22no—
163C22×C4×C61—22no—
164C22×C4×C61—22no—
165C22×C4×C61—22no—
166C22×C4×C61—22no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61C22×C414yes—
172C22×C4×C61C22×C412yes—
173C22×C4×C61C22×C412yes—
174C22×C4×C61C22×C414yes—
175C22×C4×C61C2×D414yes—
176C22×C4×C61C2×D414yes—
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—22no—
187C22×Dic61—22no—
188C22×Dic61—22no—
189C22×Dic61—22no—
190C22×Dic61—22no—
191C22×Dic61—22no—
192C22×Dic61—22no—
193C22×Dic61C22×C414yes—
194C22×Dic61C22×C414yes—
195C22×Dic61C22×C414yes—
196C22×Dic61C2×D414yes—
197C22×Dic61C2×D414yes—
198C2×C4×D61—216no—
199C2×C4×D61—216no—
200C2×C4×D61—216no—
201C2×C4×D61—216no—
202C2×C4×D61—48no—
203C2×C4×D61—48no—
204C2×C4×D61—48no—
205C2×C4×D61—48no—
206C2×C4×D61—48no—
207C2×C4×D61—48no—
208C2×C4×D61—48no—
209C2×C4×D61—48no—
210C2×C4×D61—48no—
211C2×C4×D61—48no—
212C22⋊C4×C61—216no—
213C22⋊C4×C61—44no—
214C42×C61—44no—
215C22⋊Dic61—216no—
216C22⋊Dic61—44no—
217#11758198—216no—
218#11758198—216no—
219#11758198—216no—
220#11758198C22⋊C4132yescomplemented
221C4×Dic61—44no—
222C4×Dic61—48no—
223C23×C61—24no—
224C23×C61—24no—
225C23×C61—24no—
226C23×C61—24no—
227C23×C61—24no—
228C23×C61—24no—
229C23×C61—22no—
230C23×C61—22no—
231C23×C61—24no—
232C23×C61—24no—
233C23×C61—41no—
234C23×C61—42no—
235C23×C61—41no—
236C23×C61—42no—
237C23×C61—42no—
238C23×C61—42no—
239C23×C61—42no—
240C23×C61—42no—
241C23×C61—41no—
242C23×C61—41no—
243C23×C61C2×C4214yes—
244C23×C61C23×C412yes—
245C23×C61C23×C411yescharacteristic
246C23×C61C22×D412yes—
247C23×C61C22×D412yes—
248C23×C61C2×#4112yes—
249C23×C61C2×#4112yes—
250C23×C61H(5,𝔽2)11yescharacteristic
251C23×C61H(5,𝔽2)11yescharacteristic
252C23×C61H(5,𝔽2)12yes—
253C22×D61—24no—
254C22×D61—24no—
255C22×D61—24no—
256C22×D61—24no—
257C22×D61—24no—
258C22×D61—24no—
259C22×D61—24no—
260C22×D61—24no—
261C22×D61—24no—
262C22×D61—24no—
263C22×D61—24no—
264C22×D61—24no—
265C22×D61—24no—
266C22×D61—24no—
267C22×D61—24no—
268C22×D61—24no—
269C22×D61—24no—
270C22×D61—24no—
271C22×D61—24no—
272C22×D61—24no—
273C22×D61—24no—
274C22×D61—24no—
275C22×D61—24no—
276C22×D61—24no—
277C22×D61—24no—
278C22×D61—24no—
279C22×D61—24no—
280C22×D61—24no—
281C22×D61—264no—
282C22×D61—416no—
283C22×D61—432no—
284C22×D61—432no—
285C22×D61—432no—
286C22×D61—432no—
287C22×D61—432no—
288C22×D61—416no—
289C22×D61—416no—
290C22×D61C2×C4218yes—
291C22×D61C2×C22⋊C418yes—
292C22×D61#11718yes—
293C22×D61C4×D418yes—
294C22×D61C4×D418yes—
295C22×D61C4×D418yes—
296C22×D61C4×D418yes—
297C2×C4×C61—24no—
298C2×C4×C61—24no—
299C2×C4×C61—24no—
300C2×C4×C61—24no—
301C2×C4×C61—24no—
302C2×C4×C61—24no—
303C2×C4×C61—24no—
304C2×C4×C61—24no—
305C2×C4×C61—24no—
306C2×C4×C61—24no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—24no—
310C2×C4×C61—41no—
311C2×C4×C61—41no—
312C2×C4×C61—42no—
313C2×C4×C61—42no—
314C2×C4×C61—42no—
315C2×C4×C61—42no—
316C2×C4×C61—42no—
317C2×C4×C61—42no—
318C2×C4×C61—41no—
319C2×C4×C61—41no—
320C2×C4×C61C2×C22⋊C418yescomplemented
321C2×Dic61—24no—
322C2×Dic61—24no—
323C2×Dic61—24no—
324C2×Dic61—24no—
325C2×Dic61—24no—
326C2×Dic61—24no—
327C2×Dic61—24no—
328C2×Dic61—24no—
329C2×Dic61—24no—
330C2×Dic61—24no—
331C2×Dic61—24no—
332C2×Dic61—24no—
333C2×Dic61—42no—
334C2×Dic61—42no—
335C2×Dic61—42no—
336C2×Dic61—42no—
337C2×Dic61—42no—
338C2×Dic61—42no—
339C2×Dic61—42no—
340C2×Dic61—42no—
341C2×Dic61C2×C22⋊C418yescomplemented
342C4×D61—432no—
343C4×D61—432no—
344C22⋊C42—611nomaximal, Sylow
345C22×C61—28no—
346C22×C61—24no—
347C22×C61—44no—
348C22×C61—44no—
349C22×C61—44no—
350C22×C61—44no—
351C22×C61—44no—
352C22×C61—42no—
353C22×C61—42no—
354C22×C61C22×C4211yescharacteristic
355C22×C61C22×C22⋊C412yes—
356C22×C61C2×#11712yes—
357C22×C61C2×C4×D412yes—
358C22×C61C2×C4×D412yes—
359C22×C61C2×C4×D412yes—
360C22×C61C2×C4×D412yes—
361C22×C61#51812yes—
362C22×C61#51812yes—
363C22×C61#51811yescharacteristic
364C22×C61#51811yescharacteristic
365C22×C61D4211yescharacteristic
366C22×C61D4212yes—
367C22×C61D4211yescharacteristic
368C22×C61#54612yes—
369C22×C61#54612yes—
370C22×C61#54612yes—
371C22×C61#54612yes—
372C22×C61#55112yes—
373C22×C61#55111yescharacteristic
374C22×C61#55111yescharacteristic
375C2×D61—28no—
376C2×D61—28no—
377C2×D61—28no—
378C2×D61—28no—
379C2×D61—28no—
380C2×D61—28no—
381C2×D61—28no—
382C2×D61—28no—
383C2×D61—28no—
384C2×D61—28no—
385C2×D61—28no—
386C2×D61—28no—
387C2×D61—28no—
388C2×D61—28no—
389C2×D61—464no—
390C2×D61C4×C22⋊C4116yescomplemented
391C4×C61—28no—
392C4×C61—44no—
393C4×C61—42no—
394C4×C61—42no—
395Dic61—28no—
396Dic61—44no—
397Dic61—44no—
398C23×C22⋊C4—612no—
399C2×#379—611no—
400C2×C4×C22⋊C4—612no—
401C2×C4×C22⋊C4—612no—
402#1437—611no—
403#1437—612no—
404#1437D6111yescharacteristic, complemented
405C22⋊#95—612no—
406C22⋊#95—612no—
407C2×C61—44no—
408C2×C61C2×C4×C22⋊C412yes—
409C2×C61#227311yescharacteristic
410C2×C61D4×C22⋊C412yes—
411C2×C61D4×C22⋊C412yes—
412C2×C61#234212yes—
413C2×C61#234212yes—
414C2×C61#235812yes—
415C2×C61#235811yescharacteristic
416C2×C61#235811yescharacteristic
417D61—216no—
418C26—611no—
419C24×C4—612no—
420C24×C4—612no—
421C22×C22⋊C4—612no—
422C22×C22⋊C4—612no—
423C22×C22⋊C4—612no—
424C22×C22⋊C4—612no—
425C22×C22⋊C4—612no—
426C22×C22⋊C4—611no—
427C22×C22⋊C4—6116no—
428C22×C22⋊C4—1228no—
429C22×C22⋊C4—1228no—
430C22×C22⋊C4C2×D6112yes—
431C22×C22⋊C4C2×D6111yescharacteristic
432C22×C42—611no—
433C22×C42—612no—
434C22×C42C2×D6111yescharacteristic, complemented
435#379—618no—
436C4×C22⋊C4—1228no—
437C4×C22⋊C4—1228no—
438C2×#95—612no—
439C2×#95—612no—
440C2×#95—612no—
441C2×#95—612no—
442C2×#95—611no—
443C2×#95C2×D6112yescomplemented
444C2×#95C2×D6111yescharacteristic, complemented
445C61C22⋊C4211yescharacteristic, complemented, Sylow
446C25—612no—
447C25—618no—
448C25—614no—
449C25—1224no—
450C25—1224no—
451C25—1224no—
452C25—1224no—
453C25—2441no—
454C25—2441no—
455C25—2442no—
456C25C22×D6111yescharacteristic
457C23×C4—612no—
458C23×C4—612no—
459C23×C4—612no—
460C23×C4—618no—
461C23×C4—618no—
462C23×C4—1224no—
463C23×C4—1224no—
464C23×C4—1224no—
465C23×C4—1224no—
466C23×C4—1224no—
467C23×C4—1224no—
468C23×C4—1224no—
469C23×C4—1224no—
470C23×C4—2442no—
471C23×C4—2442no—
472C23×C4—2442no—
473C23×C4—2442no—
474C23×C4C22×D6111yescharacteristic
475C23×C4C22×D6111yescharacteristic
476C23×C4C22×D6112yes—
477C23×C4C22×D6112yes—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—41no—
481C2×C22⋊C4—41no—
482C2×C22⋊C4—618no—
483C2×C22⋊C4—618no—
484C2×C22⋊C4—618no—
485C2×C22⋊C4—618no—
486C2×C22⋊C4—618no—
487C2×C22⋊C4—618no—
488C2×C22⋊C4—618no—
489C2×C22⋊C4—614no—
490C2×C22⋊C4—12264no—
491C2×C22⋊C4—1224no—
492C2×C22⋊C4—1224no—
493C2×C22⋊C4—1224no—
494C2×C22⋊C4—1224no—
495C2×C22⋊C4—1224no—
496C2×C22⋊C4—1224no—
497C2×C22⋊C4—1224no—
498C2×C22⋊C4—1224no—
499C2×C22⋊C4—2442no—
500C2×C22⋊C4C4×D6118yescomplemented
501C2×C22⋊C4C4×D6114yescomplemented
502C2×C42—24no—
503C2×C42—41no—
504C2×C42—1224no—
505C2×C42—1224no—
506C2×C42—1224no—
507C2×C42—2442no—
508C2×C42—2441no—
509#95—24no—
510#95—41no—
511#95—1224no—
512#95—1224no—
513#95—1224no—
514#95—2441no—
515#95—2442no—
516C24—22no—
517C24—22no—
518C24—22no—
519C24—22no—
520C24—21no—
521C24—21no—
522C24—22no—
523C24—614no—
524C24—614no—
525C24—614no—
526C24—614no—
527C24—614no—
528C24—614no—
529C24—614no—
530C24—6116no—
531C24—12216no—
532C24—12216no—
533C24—12216no—
534C24—12216no—
535C24—12216no—
536C24—12216no—
537C24—1222no—
538C24—1222no—
539C24—1222no—
540C24—1222no—
541C24—1222no—
542C24—1222no—
543C24—1222no—
544C24—1222no—
545C24—2448no—
546C24—2448no—
547C24—2444no—
548C24—2444no—
549C24—2444no—
550C24—2448no—
551C24—2444no—
552C24—2448no—
553C24—2448no—
554C24—2448no—
555C24—2448no—
556C24—2448no—
557C24—2444no—
558C24—2444no—
559C24C2×C4×D6114yes—
560C24C2×C4×D6112yes—
561C24C23×D6111yescharacteristic
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
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—21no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—22no—
580C22×C4—614no—
581C22×C4—614no—
582C22×C4—614no—
583C22×C4—614no—
584C22×C4—614no—
585C22×C4—12216no—
586C22×C4—12216no—
587C22×C4—12216no—
588C22×C4—1222no—
589C22×C4—1222no—
590C22×C4—1222no—
591C22×C4—1222no—
592C22×C4—1222no—
593C22×C4—1222no—
594C22×C4—1222no—
595C22×C4—1222no—
596C22×C4—1222no—
597C22×C4—1222no—
598C22×C4—1222no—
599C22×C4—1222no—
600C22×C4—1222no—
601C22×C4—1222no—
602C22×C4—1222no—
603C22×C4—1222no—
604C22×C4—12216no—
605C22×C4—2448no—
606C22×C4—2448no—
607C22×C4—2448no—
608C22×C4—2448no—
609C22×C4—2448no—
610C22×C4—2448no—
611C22×C4—2448no—
612C22×C4—2448no—
613C22×C4—2448no—
614C22×C4—2448no—
615C22×C4C2×C4×D6112yes—
616C22×C4C2×C4×D6112yes—
617C22×C4C2×C4×D6114yes—
618C22×C4C2×C4×D6114yes—
619C22×C4D4×D6114yes—
620C22×C4D4×D6114yes—
621C22⋊C4—216no—
622C22⋊C4—44no—
623C22⋊C4—6132no—
624C22⋊C4—12216no—
625C22⋊C4—12216no—
626C22⋊C4—12216no—
627C22⋊C4—12216no—
628C22⋊C4—2444no—
629C42—44no—
630C42—2448no—
631C42—2444no—
632C23—24no—
633C23—24no—
634C23—24no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—22no—
641C23—22no—
642C23—41no—
643C23—42no—
644C23—41no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—41no—
651C23—41no—
652C23—618no—
653C23—618no—
654C23—618no—
655C23—618no—
656C23—618no—
657C23—618no—
658C23—618no—
659C23—12264no—
660C23—1224no—
661C23—1224no—
662C23—1224no—
663C23—1224no—
664C23—1224no—
665C23—1224no—
666C23—1224no—
667C23—1224no—
668C23—1224no—
669C23—1224no—
670C23—1224no—
671C23—1224no—
672C23—1224no—
673C23—1224no—
674C23—1224no—
675C23—1224no—
676C23—1224no—
677C23—1224no—
678C23—1224no—
679C23—1224no—
680C23—1224no—
681C23—1224no—
682C23—1224no—
683C23—1224no—
684C23—1224no—
685C23—1224no—
686C23—1224no—
687C23—1224no—
688C23—24416no—
689C23—24432no—
690C23—24416no—
691C23—24416no—
692C23—24432no—
693C23—24432no—
694C23—24432no—
695C23—24432no—
696C23C42×D6114yes—
697C23C22×C4×D6112yes—
698C23C22×C4×D6111yescharacteristic
699C23C2×D4×D6112yes—
700C23C2×D4×D6112yes—
701C23#41×D6112yes—
702C23#41×D6112yes—
703C23#1451982211yescharacteristic
704C23#1451982211yescharacteristic
705C23#1451982312yes—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—41no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—618no—
730C2×C4—1224no—
731C2×C4—1224no—
732C2×C4—1224no—
733C2×C4—1224no—
734C2×C4—1224no—
735C2×C4—1224no—
736C2×C4—1224no—
737C2×C4—1224no—
738C2×C4—1224no—
739C2×C4—1224no—
740C2×C4—1224no—
741C2×C4—1224no—
742C2×C4—24432no—
743C2×C4—24432no—
744C2×C4—2442no—
745C2×C4—2442no—
746C2×C4—2442no—
747C2×C4—2442no—
748C2×C4—2442no—
749C2×C4—2442no—
750C2×C4—2442no—
751C2×C4—2442no—
752C2×C4C22⋊C4×D6118yescomplemented
753C22—28no—
754C22—24no—
755C22—44no—
756C22—42no—
757C22—42no—
758C22—44no—
759C22—44no—
760C22—44no—
761C22—44no—
762C22—6116no—
763C22—1228no—
764C22—1228no—
765C22—1228no—
766C22—1228no—
767C22—1228no—
768C22—1228no—
769C22—1228no—
770C22—1228no—
771C22—1228no—
772C22—1228no—
773C22—1228no—
774C22—1228no—
775C22—1228no—
776C22—1228no—
777C22—24464no—
778C22C2×C42×D6111yescharacteristic
779C22C2×C22⋊C4×D6112yes—
780C22#117×D6112yes—
781C22C4×D4×D6112yes—
782C22C4×D4×D6112yes—
783C22C4×D4×D6112yes—
784C22C4×D4×D6112yes—
785C22#1684023412yes—
786C22#1684023412yes—
787C22#1684023511yescharacteristic
788C22#1684023611yescharacteristic
789C22#1684039411yescharacteristic
790C22#1684039612yes—
791C22#1684039711yescharacteristic
792C22#1684040112yes—
793C22#1684040412yes—
794C22#1684040512yes—
795C22#1684040912yes—
796C22#1684043712yes—
797C22#1684044011yescharacteristic
798C22#1684044211yescharacteristic
799C4—28no—
800C4—42no—
801C4—42no—
802C4—44no—
803C4—1228no—
804C4—2444no—
805C4—2444no—
806C2—44no—
807C2—12216no—
808C2C4×C22⋊C4×D6112yes—
809C2#2144817111yescharacteristic
810C2#2144863712yes—
811C2#2144864012yes—
812C2#2144866312yes—
813C2#2144866712yes—
814C2#2144879712yes—
815C2#2144880011yescharacteristic
816C2#2144880211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC22×C61C22×C42
FittingC61×#1437C2
socle, cosocleC24×C61C24
prime radicalC25×D61C22
hypercenter#1437D61
hypocenterC61C22⋊C42
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
3. C2×C4×#11758198C2semidirect
4. C2×#16839609C2semidirect
5. #21444056C2semidirect
6. #21444056C2semidirect
7. #21444040C2semidirect
8. #21444040C2semidirect
9. C61×#1437C2semidirect
21. C2×C22⋊C4×D61C4semidirect
22. C22×C4×Dic61C22semidirect
23. C22×C4×Dic61C22semidirect
24. #16839617C4semidirect
27. C2×#14519684C22semidirect
28. C2×#14519684C22semidirect
29. C2×#14519684C22semidirect
30. C2×#14519684C22semidirect
31. C2×#14519684C22semidirect
34. C22×C42×C61C22semidirect
35. C2×#95×C61C22semidirect
36. C2×#95×C61C22semidirect
62. C22×C4×D61C2×C4semidirect
63. C22×C4×D61C2×C4semidirect
67. C2×C22⋊Dic61C2×C4semidirect
68. C2×C22⋊Dic61C2×C4semidirect
77. C2×#11758198C2×C4semidirect
78. C2×#11758198C2×C4semidirect
101. C2×C22⋊C4×C61C2×C4semidirect
102. C2×C22⋊C4×C61C2×C4semidirect
145. C23×D61C42semidirect
220. #11758198C22⋊C4semidirect
320. C2×C4×C61C2×C22⋊C4semidirect
341. C2×Dic61C2×C22⋊C4semidirect
390. C2×D61C4×C22⋊C4semidirect
404. #1437D61semidirect
434. C22×C42C2×D61semidirect
443. C2×#95C2×D61semidirect
444. C2×#95C2×D61semidirect
445. C61C22⋊C42semidirect
500. C2×C22⋊C4C4×D61semidirect
501. C2×C22⋊C4C4×D61semidirect
752. C2×C4C22⋊C4×D61semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊C4×D612
C2×#168396172
C2×C4×#117581982
C2×#168396092
#214440562
#214440402
C61×#14372
C22⋊C4261