Finite Group Databasebeta

← #29601159

Subgroups — #29601159

Order 15616.

3366 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519739C211yesmaximal, characteristic
2C22×C42×D61C211yesmaximal, characteristic, complemented
3C2×#16839640C212yesmaximal
4C2×#16839609C211yesmaximal, characteristic, complemented
5C2×#16839609C212yesmaximal, complemented
6#21444057C211yesmaximal, characteristic, complemented
7#21444055C211yesmaximal, characteristic, complemented
8#21444051C211yesmaximal, characteristic, complemented
9#21444040C212yesmaximal, complemented
10#95×Dic61C212yesmaximal, complemented
11C61×#1436C211yesmaximal, characteristic, complemented
12C23×D244C2211yescharacteristic
13C23×C4×D61C2212yes—
14C23×C4×D61C2211yescharacteristic
15C23×C4×D61C2211yescharacteristic
16C2×#14519739—24no—
17C2×#14519739—24no—
18C2×#14519739C418yescomplemented
19C22×#11758198C2211yescharacteristic
20C22×#11758198C2212yes—
21C22×#11758198C2212yes—
22C22×#11758198C2212yes—
23C22×#11758198C2211yescharacteristic
24C22×C4×Dic61C2211yescharacteristic
25C22×C4×Dic61C2212yes—
26C22×C4×Dic61C2211yescharacteristic
27C22×C4×Dic61C2212yes—
28C2×C42×D61—28no—
29C2×C42×D61—24no—
30#16839640C4116yescomplemented
31#16839609—28no—
32#16839609—24no—
33C2×#14519684C2212yes—
34C2×#14519684C2212yes—
35C2×#14519684C2212yes—
36C2×#14519684C2211yescharacteristic
37C2×#14519684C2212yes—
38C22×C4⋊C4×C61C2211yescharacteristic
39C22×C42×C61C2211yescharacteristic
40C2×#95×C61C2212yes—
41C2×#95×C61C2211yescharacteristic
42C2×#95×C61C2212yes—
43C24×D61C2311yescharacteristic
44C24×D61C2311yescharacteristic
45C22×D244—22no—
46C22×D244—22no—
47C22×D244—24no—
48C22×D244C2×C414yes—
49C22×D244C2×C418yes—
50C23×Dic61C2312yes—
51C23×Dic61C2311yescharacteristic
52C23×Dic61C2312yes—
53C23×Dic61C2311yescharacteristic
54C22×C4×D61—24no—
55C22×C4×D61—24no—
56C22×C4×D61—24no—
57C22×C4×D61—24no—
58C22×C4×D61—24no—
59C22×C4×D61—24no—
60C22×C4×D61—24no—
61C22×C4×D61—24no—
62C22×C4×D61—22no—
63C22×C4×D61—22no—
64C22×C4×D61—24no—
65C22×C4×D61—24no—
66C22×C4×D61C2×C414yes—
67C22×C4×D61C2×C414yescomplemented
68C22×C4×D61C2×C418yescomplemented
69C22×C4×D61D414yes—
70C22×C4×D61D414yes—
71#14519739—232no—
72C2×#11758198—22no—
73C2×#11758198—22no—
74C2×#11758198—24no—
75C2×#11758198—24no—
76C2×#11758198—22no—
77C2×#11758198—22no—
78C2×#11758198—24no—
79C2×#11758198—24no—
80C2×#11758198—24no—
81C2×#11758198—24no—
82C2×#11758198C2×C414yes—
83C2×#11758198C2×C414yescomplemented
84C2×#11758198C2×C418yescomplemented
85C2×#11758198C2×C418yescomplemented
86C2×#11758198C2×C418yescomplemented
87C2×C4×Dic61—22no—
88C2×C4×Dic61—24no—
89C2×C4×Dic61—24no—
90C2×C4×Dic61—24no—
91C2×C4×Dic61—22no—
92C2×C4×Dic61—22no—
93C2×C4×Dic61—24no—
94C2×C4×Dic61—24no—
95C2×C4×Dic61—24no—
96C2×C4×Dic61C2×C414yescomplemented
97C2×C4×Dic61D418yescomplemented
98C42×D61—232no—
99#14519684—22no—
100#14519684—24no—
101#14519684—24no—
102#14519684—24no—
103#14519684C2×C418yescomplemented
104C23×C4×C61C2312yes—
105C23×C4×C61C2311yescharacteristic
106C23×C4×C61C2311yescharacteristic
107C23×C4×C61C2311yescharacteristic
108C23×C4×C61C2312yes—
109C2×C4⋊C4×C61—22no—
110C2×C4⋊C4×C61—22no—
111C2×C4⋊C4×C61C2×C414yescomplemented
112C2×C42×C61—22no—
113C2×C42×C61—24no—
114#95×C61—24no—
115#95×C61—22no—
116#95×C61C2×C418yescomplemented
117C24×C61C2411yescharacteristic
118C23×D61—22no—
119C23×D61—22no—
120C23×D61—22no—
121C23×D61—22no—
122C23×D61—21no—
123C23×D61—21no—
124C23×D61—22no—
125C23×D61—22no—
126C23×D61—22no—
127C23×D61—22no—
128C23×D61—22no—
129C23×D61C22×C412yes—
130C23×D61C22×C414yes—
131C23×D61C22×C412yes—
132C23×D61C22×C414yes—
133C23×D61C2×D412yes—
134C23×D61C2×D412yes—
135C23×D61#4114yes—
136C22×C4×C61—22no—
137C22×C4×C61—22no—
138C22×C4×C61—22no—
139C22×C4×C61—21no—
140C22×C4×C61—21no—
141C22×C4×C61—22no—
142C22×C4×C61—22no—
143C22×C4×C61—22no—
144C22×C4×C61—22no—
145C22×C4×C61—22no—
146C22×C4×C61—21no—
147C22×C4×C61—21no—
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×C61C22×C412yes—
156C22×C4×C61C22×C414yes—
157C22×C4×C61C22×C414yes—
158C22×C4×C61C22×C412yes—
159C22×C4×C61C22×C412yes—
160C22×C4×C61C22×C414yes—
161C22×C4×C61C2×D412yes—
162C22×C4×C61C2×D412yes—
163C22×C4×C61C2×D414yes—
164C22×C4×C61#4114yes—
165C22×Dic61—22no—
166C22×Dic61—22no—
167C22×Dic61—22no—
168C22×Dic61—22no—
169C22×Dic61—22no—
170C22×Dic61—22no—
171C22×Dic61—21no—
172C22×Dic61—21no—
173C22×Dic61—22no—
174C22×Dic61—22no—
175C22×Dic61—22no—
176C22×Dic61—22no—
177C22×Dic61—22no—
178C22×Dic61—22no—
179C22×Dic61C22×C414yes—
180C22×Dic61C22×C412yes—
181C22×Dic61C22×C414yes—
182C22×Dic61C22×C412yes—
183C22×Dic61C2×D414yes—
184C22×Dic61C2×D412yes—
185C22×Dic61C2×D412yes—
186C22×Dic61C2×D414yes—
187C22×Dic61#4114yes—
188C22×Dic61#4114yes—
189C2×D244—28no—
190C2×D244—28no—
191C2×D244—216no—
192C2×D244—216no—
193C2×D244C42116yescomplemented
194C2×C4×D61—216no—
195C2×C4×D61—216no—
196C2×C4×D61—216no—
197C2×C4×D61—216no—
198C2×C4×D61—216no—
199C2×C4×D61—216no—
200C2×C4×D61—216no—
201C2×C4×D61—216no—
202C2×C4×D61—28no—
203C2×C4×D61—216no—
204C2×C4×D61—28no—
205C2×C4×D61—28no—
206C2×C4×D61—216no—
207C2×C4×D61—44no—
208C2×C4×D61—48no—
209C2×C4×D61—44no—
210C2×C4×D61C22⋊C4116yescomplemented
211C4⋊C4×C61—28no—
212C42×C61—28no—
213#11758198—28no—
214#11758198—216no—
215#11758198—28no—
216#11758198—216no—
217#11758198—216no—
218C4×Dic61—28no—
219C4×Dic61—28no—
220C4×Dic61—216no—
221C4×Dic61—48no—
222C23×C61C23×C411yescharacteristic
223C23×C61C23×C412yes—
224C23×C61C22×D411yescharacteristic
225C23×C61C22×D411yescharacteristic
226C23×C61C22×D412yes—
227C23×C61C2×#4112yes—
228C23×C61C2×#4112yes—
229C23×C61C2×#4112yes—
230C23×C61C2×#4112yes—
231C22×D61—24no—
232C22×D61—24no—
233C22×D61—24no—
234C22×D61—24no—
235C22×D61—24no—
236C22×D61—24no—
237C22×D61—22no—
238C22×D61—24no—
239C22×D61—22no—
240C22×D61—24no—
241C22×D61—24no—
242C22×D61—24no—
243C22×D61—24no—
244C22×D61—24no—
245C22×D61—22no—
246C22×D61—22no—
247C22×D61—22no—
248C22×D61—22no—
249C22×D61—24no—
250C22×D61—24no—
251C22×D61—24no—
252C22×D61—24no—
253C22×D61—24no—
254C22×D61—24no—
255C22×D61—24no—
256C22×D61—24no—
257C22×D61—41no—
258C22×D61—42no—
259C22×D61—41no—
260C22×D61—42no—
261C22×D61—42no—
262C22×D61—42no—
263C22×D61—42no—
264C22×D61—42no—
265C22×D61—41no—
266C22×D61—41no—
267C22×D61C2×C4214yes—
268C22×D61C2×C4214yescomplemented
269C22×D61C2×C22⋊C414yes—
270C22×D61#11714yes—
271C22×D61C4×D418yes—
272C22×D61C4×D418yes—
273C2×C4×C61—22no—
274C2×C4×C61—22no—
275C2×C4×C61—24no—
276C2×C4×C61—24no—
277C2×C4×C61—24no—
278C2×C4×C61—24no—
279C2×C4×C61—24no—
280C2×C4×C61—22no—
281C2×C4×C61—24no—
282C2×C4×C61—24no—
283C2×C4×C61—22no—
284C2×C4×C61—24no—
285C2×C4×C61—24no—
286C2×C4×C61—24no—
287C2×C4×C61—22no—
288C2×C4×C61—24no—
289C2×C4×C61—24no—
290C2×C4×C61—24no—
291C2×C4×C61—24no—
292C2×C4×C61—41no—
293C2×C4×C61—42no—
294C2×C4×C61—42no—
295C2×C4×C61—41no—
296C2×C4×C61—42no—
297C2×C4×C61—42no—
298C2×C4×C61—42no—
299C2×C4×C61C2×C4214yescomplemented
300C2×C4×C61C2×C22⋊C414yes—
301C2×C4×C61C4×D418yescomplemented
302C2×Dic61—24no—
303C2×Dic61—24no—
304C2×Dic61—24no—
305C2×Dic61—24no—
306C2×Dic61—24no—
307C2×Dic61—24no—
308C2×Dic61—22no—
309C2×Dic61—24no—
310C2×Dic61—24no—
311C2×Dic61—24no—
312C2×Dic61—24no—
313C2×Dic61—42no—
314C2×Dic61—42no—
315C2×Dic61—42no—
316C2×Dic61—42no—
317C2×Dic61—41no—
318C2×Dic61—41no—
319C2×Dic61—42no—
320C2×Dic61C2×C22⋊C414yes—
321C2×Dic61C4×D418yes—
322C2×Dic61C4×D418yescomplemented
323C2×Dic61#12014yes—
324C2×Dic61#12118yes—
325C2×Dic61#12314yes—
326D244—232no—
327C4×D61—264no—
328C4×D61—232no—
329C4×D61—416no—
330C4×#386—611nomaximal, Sylow
331C22×C61C22×C4211yescharacteristic
332C22×C61C22×C22⋊C411yescharacteristic
333C22×C61C2×#11711yescharacteristic
334C22×C61C2×C4×D412yes—
335C22×C61C2×C4×D412yes—
336C22×C61C2×C4×D412yes—
337C22×C61C2×C4×D412yes—
338C22×C61C2×C4×D412yes—
339C22×C61C4×#4112yes—
340C22×C61C4×#4112yes—
341C22×C61C4×#4112yes—
342C22×C61C2×#12011yescharacteristic
343C22×C61C2×#12112yes—
344C22×C61C2×#12311yescharacteristic
345C22×C61#52512yes—
346C22×C61#52512yes—
347C22×C61#52512yes—
348C22×C61#52912yes—
349C22×C61#52912yes—
350C22×C61#53211yescharacteristic
351C22×C61#53211yescharacteristic
352C2×D61—28no—
353C2×D61—24no—
354C2×D61—28no—
355C2×D61—24no—
356C2×D61—28no—
357C2×D61—28no—
358C2×D61—28no—
359C2×D61—28no—
360C2×D61—24no—
361C2×D61—28no—
362C2×D61—42no—
363C2×D61—44no—
364C2×D61—42no—
365C2×D61—44no—
366C2×D61—44no—
367C2×D61—44no—
368C2×D61—44no—
369C2×D61C4×C22⋊C418yescomplemented
370C4×C61—24no—
371C4×C61—24no—
372C4×C61—28no—
373C4×C61—42no—
374C4×C61—44no—
375Dic61—28no—
376Dic61—42no—
377Dic61—44no—
378Dic61#38618yescomplemented
379C22×C4×D4—611no—
380C23×C42—611no—
381C2×#386—612no—
382C2×C4×C22⋊C4—611no—
383C2×C4×C22⋊C4—612no—
384#1437—611no—
385#1437—611no—
386#1436—611no—
387#1436D6111yescharacteristic, complemented
388C22⋊#95—612no—
389C4×#95—612no—
390C2×C61C2×C4×C22⋊C411yescharacteristic
391C2×C61C42×D412yes—
392C2×C61C2×#38611yescharacteristic
393C2×C61#229012yes—
394C2×C61#229711yescharacteristic
395C2×C61C4×#12012yes—
396C2×C61C4×#12112yes—
397C2×C61C4×#12112yes—
398C2×C61C4×#12312yes—
399D61—28no—
400D61—44no—
401C23×D4—611no—
402C24×C4—611no—
403C24×C4—612no—
404C24×C4—611no—
405C2×C4×D4—618no—
406C2×C4×D4—1224no—
407C2×C4×D4—1224no—
408C22×C4⋊C4C2×D6111yescharacteristic
409C22×C22⋊C4—611no—
410C22×C22⋊C4—611no—
411C22×C22⋊C4—612no—
412C22×C22⋊C4—612no—
413C22×C22⋊C4—612no—
414C22×C42—612no—
415C22×C42—611no—
416C22×C42—611no—
417C22×C42—612no—
418C22×C42—1228no—
419C22×C42—1224no—
420C22×C42C2×D6111yescharacteristic
421#386—6116no—
422C4×C22⋊C4—1228no—
423C4×C22⋊C4—1224no—
424C2×#95—612no—
425C2×#95—612no—
426C2×#95—612no—
427C2×#95—612no—
428C2×#95—611no—
429C2×#95C2×D6112yes—
430C2×#95C2×D6111yescharacteristic
431C2×#95C2×D6112yes—
432C61C4×#38611yescharacteristic, complemented, Sylow
433C25—611no—
434C25—611no—
435C22×D4—614no—
436C22×D4—618no—
437C22×D4—1222no—
438C22×D4—1222no—
439C22×D4—1224no—
440C23×C4—611no—
441C23×C4—612no—
442C23×C4—614no—
443C23×C4—614no—
444C23×C4—614no—
445C23×C4—612no—
446C23×C4—611no—
447C23×C4—614no—
448C23×C4—618no—
449C23×C4—1224no—
450C23×C4—1224no—
451C23×C4—1224no—
452C23×C4—1224no—
453C23×C4—1222no—
454C23×C4—1222no—
455C23×C4—1224no—
456C23×C4—1224no—
457C23×C4—1224no—
458C23×C4—1224no—
459C23×C4—1224no—
460C23×C4—1224no—
461C23×C4C22×D6112yes—
462C23×C4C22×D6111yescharacteristic
463C23×C4C22×D6111yescharacteristic
464C23×C4C22×D6111yescharacteristic
465C23×C4C22×D6112yes—
466C4×D4—12232no—
467C2×C4⋊C4—22no—
468C2×C4⋊C4—22no—
469C2×C4⋊C4C4×D6114yescomplemented
470C2×C22⋊C4—614no—
471C2×C22⋊C4—614no—
472C2×C22⋊C4—618no—
473C2×C22⋊C4—618no—
474C2×C22⋊C4—618no—
475C2×C22⋊C4—1224no—
476C2×C22⋊C4—1224no—
477C2×C22⋊C4—1222no—
478C2×C22⋊C4—1222no—
479C2×C22⋊C4—1224no—
480C2×C22⋊C4—1224no—
481C2×C22⋊C4—1222no—
482C2×C22⋊C4—1222no—
483C2×C22⋊C4—1224no—
484C2×C22⋊C4—1224no—
485C2×C42—22no—
486C2×C42—24no—
487C2×C42—614no—
488C2×C42—618no—
489C2×C42—12232no—
490C2×C42—1222no—
491C2×C42—1222no—
492C2×C42—1224no—
493C2×C42—1224no—
494C2×C42—1224no—
495C2×C42—1222no—
496C2×C42—1224no—
497C2×C42—1224no—
498C2×C42—1224no—
499#95—24no—
500#95—22no—
501#95—618no—
502#95—1224no—
503#95—1224no—
504#95—1222no—
505#95—1224no—
506#95C4×D6118yescomplemented
507C24—612no—
508C24—614no—
509C24—612no—
510C24—612no—
511C24—614no—
512C24—614no—
513C24—612no—
514C24—1222no—
515C24—1222no—
516C24—1222no—
517C24—1222no—
518C24—1222no—
519C24—1221no—
520C24—1221no—
521C24—1222no—
522C24—1222no—
523C24—1222no—
524C24—1222no—
525C24C23×D6111yescharacteristic
526C2×D4—6116no—
527C2×D4—1228no—
528C2×D4—1228no—
529C2×D4—12216no—
530C2×D4—12216no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—612no—
551C22×C4—614no—
552C22×C4—612no—
553C22×C4—612no—
554C22×C4—614no—
555C22×C4—614no—
556C22×C4—614no—
557C22×C4—614no—
558C22×C4—6116no—
559C22×C4—614no—
560C22×C4—612no—
561C22×C4—1228no—
562C22×C4—12216no—
563C22×C4—12216no—
564C22×C4—12216no—
565C22×C4—1228no—
566C22×C4—1228no—
567C22×C4—12216no—
568C22×C4—12216no—
569C22×C4—12216no—
570C22×C4—12216no—
571C22×C4—12216no—
572C22×C4—12216no—
573C22×C4—1222no—
574C22×C4—1222no—
575C22×C4—1222no—
576C22×C4—1222no—
577C22×C4—12216no—
578C22×C4—1222no—
579C22×C4—1222no—
580C22×C4—1221no—
581C22×C4—1221no—
582C22×C4—1222no—
583C22×C4—1222no—
584C22×C4—1222no—
585C22×C4—1222no—
586C22×C4—1222no—
587C22×C4—1222no—
588C22×C4—2444no—
589C22×C4—2448no—
590C22×C4—2444no—
591C22×C4C2×C4×D6114yes—
592C22×C4C2×C4×D6112yes—
593C22×C4C2×C4×D6114yes—
594C22×C4C2×C4×D6112yes—
595C22×C4C2×C4×D6112yes—
596C22×C4C2×C4×D6114yes—
597C22×C4D4×D6112yes—
598C22×C4D4×D6112yes—
599C22×C4D4×D6114yes—
600C22×C4#1175822614yes—
601C4⋊C4—28no—
602C22⋊C4—12216no—
603C22⋊C4—1228no—
604C22⋊C4—12216no—
605C22⋊C4—1228no—
606C22⋊C4—12216no—
607C42—28no—
608C42—12216no—
609C42—1228no—
610C42—1228no—
611C42—2448no—
612C23—614no—
613C23—614no—
614C23—614no—
615C23—618no—
616C23—618no—
617C23—614no—
618C23—1224no—
619C23—1224no—
620C23—1224no—
621C23—1224no—
622C23—1224no—
623C23—1224no—
624C23—1222no—
625C23—1224no—
626C23—1222no—
627C23—1224no—
628C23—1224no—
629C23—1224no—
630C23—1224no—
631C23—1224no—
632C23—1222no—
633C23—1222no—
634C23—1222no—
635C23—1222no—
636C23—1224no—
637C23—1224no—
638C23—1224no—
639C23—1224no—
640C23—1224no—
641C23—1224no—
642C23—1224no—
643C23—1224no—
644C23—2441no—
645C23—2442no—
646C23—2441no—
647C23—2442no—
648C23—2442no—
649C23—2442no—
650C23—2442no—
651C23—2442no—
652C23—2441no—
653C23—2441no—
654C23C22×C4×D6111yescharacteristic
655C23C22×C4×D6112yes—
656C23C2×D4×D6111yescharacteristic
657C23C2×D4×D6111yescharacteristic
658C23C2×D4×D6112yes—
659C23#41×D6112yes—
660C23#41×D6112yes—
661C23#41×D6112yes—
662C23C2×#1175822612yes—
663D4—12232no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—22no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—22no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—22no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—41no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—41no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—614no—
691C2×C4—618no—
692C2×C4—614no—
693C2×C4—618no—
694C2×C4—614no—
695C2×C4—618no—
696C2×C4—12232no—
697C2×C4—12264no—
698C2×C4—1224no—
699C2×C4—1224no—
700C2×C4—1224no—
701C2×C4—1224no—
702C2×C4—1224no—
703C2×C4—1224no—
704C2×C4—1222no—
705C2×C4—1224no—
706C2×C4—1224no—
707C2×C4—1224no—
708C2×C4—1224no—
709C2×C4—24416no—
710C2×C4—2442no—
711C2×C4—2442no—
712C2×C4—2442no—
713C2×C4—2442no—
714C2×C4—2441no—
715C2×C4—2441no—
716C2×C4—2442no—
717C2×C4C42×D6114yescomplemented
718C2×C4C22⋊C4×D6114yes—
719C2×C4#1451973918yescomplemented
720C22—618no—
721C22—1224no—
722C22—1228no—
723C22—1224no—
724C22—1228no—
725C22—1228no—
726C22—1228no—
727C22—1228no—
728C22—1228no—
729C22—1224no—
730C22—1228no—
731C22—2442no—
732C22—2444no—
733C22—2442no—
734C22—2444no—
735C22—2444no—
736C22—2444no—
737C22—2444no—
738C22C2×C42×D6111yescharacteristic
739C22C2×C22⋊C4×D6111yescharacteristic
740C22#117×D6111yescharacteristic
741C22C4×D4×D6112yes—
742C22C4×D4×D6112yes—
743C22C4×D4×D6112yes—
744C22C4×D4×D6112yes—
745C22C2×#1451973912yes—
746C22#1684023012yes—
747C22C4×#1175822612yes—
748C22C4×#1175822612yes—
749C22#120×D6111yescharacteristic
750C22#121×D6112yes—
751C22#123×D6111yescharacteristic
752C22#1684027012yes—
753C22#1684027512yes—
754C22#1684027512yes—
755C22#1684029512yes—
756C22#1684029712yes—
757C22#1684031111yescharacteristic
758C22#1684031311yescharacteristic
759C4—24no—
760C4—28no—
761C4—24no—
762C4—42no—
763C4—44no—
764C4—618no—
765C4—1228no—
766C4—2442no—
767C4—2444no—
768C2—1228no—
769C2—2444no—
770C2C4×C22⋊C4×D6111yescharacteristic
771C2C4×#1451973912yes—
772C2#386×D6111yescharacteristic
773C2#2144825712yes—
774C2#2144830811yescharacteristic
775C2#2144832012yes—
776C2#2144832712yes—
777C2#2144833112yes—
778C2#2144834012yes—
subgroupG/H
center, FrattiniC24C23×D61
commutatorC22×C61C22×C42
FittingC61×#1436C2
socle, cosocleC24×C61C24
prime radicalC23×D244C22
hypercenter#1436D61
hypocenterC61C4×#386
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
2. C22×C42×D61C2semidirect
4. C2×#16839609C2semidirect
5. C2×#16839609C2semidirect
6. #21444057C2semidirect
7. #21444055C2semidirect
8. #21444051C2semidirect
9. #21444040C2semidirect
10. #95×Dic61C2semidirect
11. C61×#1436C2semidirect
18. C2×#14519739C4semidirect
30. #16839640C4semidirect
67. C22×C4×D61C2×C4semidirect
68. C22×C4×D61C2×C4semidirect
83. C2×#11758198C2×C4semidirect
84. C2×#11758198C2×C4semidirect
85. C2×#11758198C2×C4semidirect
86. C2×#11758198C2×C4semidirect
96. C2×C4×Dic61C2×C4semidirect
97. C2×C4×Dic61D4semidirect
103. #14519684C2×C4semidirect
111. C2×C4⋊C4×C61C2×C4semidirect
116. #95×C61C2×C4semidirect
193. C2×D244C42semidirect
210. C2×C4×D61C22⋊C4semidirect
268. C22×D61C2×C42semidirect
299. C2×C4×C61C2×C42semidirect
301. C2×C4×C61C4×D4semidirect
322. C2×Dic61C4×D4semidirect
369. C2×D61C4×C22⋊C4semidirect
378. Dic61#386semidirect
387. #1436D61semidirect
432. C61C4×#386semidirect
469. C2×C4⋊C4C4×D61semidirect
506. #95C4×D61semidirect
717. C2×C4C42×D61semidirect
719. C2×C4#14519739semidirect

Maximal subgroups

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

subgroupindex
C22×#145197392
C22×C42×D612
C2×#168396402
C2×#168396092
#214440572
#214440552
#214440512
#214440402
#95×Dic612
C61×#14362
C4×#38661