Finite Group Databasebeta

← #29602383

Subgroups — #29602383

Order 15616.

2458 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D61C211yesmaximal, characteristic
2C2×#16839662C212yesmaximal
3C2×#16839657C212yesmaximal, complemented
4C2×#16839621C211yesmaximal, characteristic, complemented
5#21444062C212yesmaximal, complemented
6#21444061C212yesmaximal, complemented
7#21444047C211yesmaximal, characteristic, complemented
8#21444042C211yesmaximal, characteristic, complemented
9#21444040C211yesmaximal, characteristic, complemented
10#95×Dic61C211yesmaximal, characteristic, complemented
11C2×C61×#380C211yesmaximal, characteristic, complemented
12C23×C22⋊D61C2211yescharacteristic
13C23×C4×D61C2211yescharacteristic
14C2×C4×C22⋊D61—28no—
15C2×C4×C22⋊D61C418yescomplemented
16C22×#11758196C2212yes—
17C22×#11758196C2212yes—
18C22×#11758196C2211yescharacteristic
19C22×C22⋊Dic61C2212yes—
20C22×C22⋊Dic61C2211yescharacteristic
21C22×#11758198C2212yes—
22C22×#11758198C2212yes—
23C22×#11758198C2211yescharacteristic
24C22×C4×Dic61C2212yes—
25C22×C4×Dic61C2211yescharacteristic
26#16839662—28no—
27#16839657—28no—
28#16839621—24no—
29C2×#14519684C2212yes—
30C2×#14519684C2212yes—
31C2×#14519684C2211yescharacteristic
32C2×#14519684C2212yes—
33C2×#14519684C2211yescharacteristic
34C2×#14519684C2212yes—
35C24×C4×C61C2211yescharacteristic
36C22×C4⋊C4×C61C2212yes—
37C22×C22⋊C4×C61C2212yes—
38C61×#380—24no—
39C2×#95×C61C2211yescharacteristic
40C2×#95×C61C2211yescharacteristic
41C24×D61C2311yescharacteristic
42C22×C22⋊D61—24no—
43C22×C22⋊D61—24no—
44C22×C22⋊D61C2×C414yes—
45C22×C22⋊D61D414yes—
46C22×C22⋊D61Q814yes—
47C23×Dic61C2312yes—
48C23×Dic61C2311yescharacteristic
49C23×Dic61C2312yes—
50C23×Dic61C2311yescharacteristic
51C23×Dic61C2311yescharacteristic
52C22×C4×D61—22no—
53C22×C4×D61—22no—
54C22×C4×D61—24no—
55C22×C4×D61—42no—
56C22×C4×D61C2×C414yes—
57C4×C22⋊D61—232no—
58C2×#11758196—24no—
59C2×#11758196—24no—
60C2×#11758196—24no—
61C2×#11758196—24no—
62C2×#11758196—24no—
63C2×#11758196—42no—
64C2×#11758196C2×C414yes—
65C2×#11758196D418yes—
66C2×C22⋊Dic61—24no—
67C2×C22⋊Dic61—24no—
68C2×C22⋊Dic61—24no—
69C2×C22⋊Dic61—42no—
70C2×C22⋊Dic61C2×C414yes—
71C2×#11758198—24no—
72C2×#11758198—24no—
73C2×#11758198—24no—
74C2×#11758198—24no—
75C2×#11758198—24no—
76C2×#11758198—42no—
77C2×#11758198—42no—
78C2×#11758198C2×C414yes—
79C2×C4×Dic61—24no—
80C2×C4×Dic61—24no—
81C2×C4×Dic61—24no—
82C2×C4×Dic61—24no—
83C2×C4×Dic61C2×C414yes—
84#14519684—22no—
85#14519684—24no—
86#14519684—22no—
87#14519684—24no—
88#14519684—24no—
89#14519684—42no—
90C25×C61C2311yescharacteristic
91C23×C4×C61—24no—
92C23×C4×C61—22no—
93C23×C4×C61—22no—
94C23×C4×C61—42no—
95C23×C4×C61C2×C414yes—
96C23×C4×C61C2312yes—
97C23×C4×C61C2312yes—
98C23×C4×C61C2311yescharacteristic
99C23×C4×C61C2311yescharacteristic
100C2×C4⋊C4×C61—24no—
101C2×C4⋊C4×C61—24no—
102C2×C4⋊C4×C61—42no—
103C2×C22⋊C4×C61—24no—
104C2×C22⋊C4×C61—24no—
105C2×C22⋊C4×C61—42no—
106#95×C61—22no—
107#95×C61D414yescomplemented
108C24×C61—22no—
109C24×C61—21no—
110C24×C61—22no—
111C24×C61—21no—
112C24×C61—22no—
113C24×C61—21no—
114C24×C61—22no—
115C24×C61—21no—
116C24×C61C22×C412yes—
117C24×C61C2×D412yes—
118C24×C61C2×Q812yes—
119C24×C61C2411yescharacteristic
120C23×D61—22no—
121C23×D61—21no—
122C23×D61—21no—
123C23×D61—22no—
124C23×D61—22no—
125C23×D61—22no—
126C23×D61—21no—
127C23×D61—21no—
128C23×D61C22×C412yes—
129C23×D61C2×D412yes—
130C23×D61C2×Q812yes—
131C22×C4×C61—22no—
132C22×C4×C61—21no—
133C22×C4×C61—21no—
134C22×C4×C61—22no—
135C22×C4×C61—22no—
136C22×C4×C61—22no—
137C22×C4×C61—22no—
138C22×C4×C61—22no—
139C22×C4×C61—22no—
140C22×C4×C61—22no—
141C22×C4×C61—22no—
142C22×C4×C61—28no—
143C22×C4×C61—28no—
144C22×C4×C61—22no—
145C22×C4×C61—22no—
146C22×C4×C61—22no—
147C22×C4×C61—22no—
148C22×C4×C61—22no—
149C22×C4×C61—22no—
150C22×C4×C61—22no—
151C22×C4×C61—44no—
152C22×C4×C61—48no—
153C22×C4×C61—48no—
154C22×C4×C61C22×C412yes—
155C22×C4×C61C22×C412yes—
156C22×C4×C61C2×D414yes—
157C22×C4×C61C2×D414yes—
158C22×C4×C61C2×D412yes—
159C22×C4×C61#4112yes—
160C2×C22⋊D61—28no—
161C2×C22⋊D61—28no—
162C2×C22⋊D61—216no—
163C2×C22⋊D61—216no—
164C2×C22⋊D61C4⋊C4116yescomplemented
165C22×Dic61—21no—
166C22×Dic61—21no—
167C22×Dic61—22no—
168C22×Dic61—22no—
169C22×Dic61—22no—
170C22×Dic61—22no—
171C22×Dic61—22no—
172C22×Dic61—22no—
173C22×Dic61—22no—
174C22×Dic61—21no—
175C22×Dic61—22no—
176C22×Dic61—21no—
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×Dic61C22×C412yes—
186C22×Dic61C22×C412yes—
187C22×Dic61C22×C412yes—
188C22×Dic61C2×D414yes—
189C22×Dic61C2×D414yes—
190C22×Dic61C2×D412yes—
191C22×Dic61C2×Q812yes—
192C22×Dic61#4114yes—
193C22×Dic61#4114yes—
194C2×C4×D61—28no—
195C2×C4×D61—28no—
196C2×C4×D61—44no—
197C2×C4×D61—48no—
198C2×C4×D61—48no—
199C4⋊C4×C61—48no—
200C22⋊C4×C61—48no—
201C22⋊Dic61—28no—
202C22⋊Dic61—48no—
203#11758198—28no—
204#11758198—48no—
205#11758198—48no—
206#11758196—48no—
207#11758196—48no—
208#11758196C22⋊C4116yescomplemented
209C4×Dic61—28no—
210C4×Dic61—48no—
211C23×C61—22no—
212C23×C61—22no—
213C23×C61—22no—
214C23×C61—22no—
215C23×C61—22no—
216C23×C61—22no—
217C23×C61—24no—
218C23×C61—24no—
219C23×C61—22no—
220C23×C61—24no—
221C23×C61—22no—
222C23×C61—22no—
223C23×C61—22no—
224C23×C61—24no—
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×C61C2×C4⋊C414yes—
234C23×C61C23×C411yescharacteristic
235C23×C61C22×D412yes—
236C23×C61C22×D411yescharacteristic
237C23×C61C22×D411yescharacteristic
238C23×C61C22×Q811yescharacteristic
239C23×C61C2×#4112yes—
240C23×C61C2×#4111yescharacteristic
241C23×C61C2×#4112yes—
242C23×C61H(5,𝔽2)12yes—
243C23×C61H(5,𝔽2)11yescharacteristic
244C23×C612−1+411yescharacteristic
245C22×D61—22no—
246C22×D61—22no—
247C22×D61—22no—
248C22×D61—22no—
249C22×D61—22no—
250C22×D61—22no—
251C22×D61—24no—
252C22×D61—24no—
253C22×D61—22no—
254C22×D61—24no—
255C22×D61—22no—
256C22×D61—22no—
257C22×D61—22no—
258C22×D61—24no—
259C22×D61—42no—
260C22×D61—42no—
261C22×D61—42no—
262C22×D61—42no—
263C22×D61—42no—
264C22×D61—42no—
265C22×D61—42no—
266C22×D61—42no—
267C22×D61C2×C4⋊C414yes—
268C2×C4×C61—22no—
269C2×C4×C61—22no—
270C2×C4×C61—22no—
271C2×C4×C61—22no—
272C2×C4×C61—24no—
273C2×C4×C61—24no—
274C2×C4×C61—24no—
275C2×C4×C61—24no—
276C2×C4×C61—24no—
277C2×C4×C61—24no—
278C2×C4×C61—24no—
279C2×C4×C61—416no—
280C2×C4×C61—42no—
281C2×C4×C61—42no—
282C2×C4×C61—42no—
283C2×C4×C61—42no—
284C2×C4×C61—42no—
285C2×C4×C61—42no—
286C2×C4×C61—42no—
287C2×C4×C61—42no—
288C2×C4×C61—42no—
289C2×C4×C61—42no—
290C2×C4×C61—42no—
291C2×C4×C61C2×C22⋊C414yes—
292C2×C4×C61C4×D414yes—
293C22⋊D61—232no—
294C2×Dic61—22no—
295C2×Dic61—22no—
296C2×Dic61—24no—
297C2×Dic61—24no—
298C2×Dic61—22no—
299C2×Dic61—22no—
300C2×Dic61—22no—
301C2×Dic61—24no—
302C2×Dic61—24no—
303C2×Dic61—24no—
304C2×Dic61—42no—
305C2×Dic61—42no—
306C2×Dic61—42no—
307C2×Dic61—42no—
308C2×Dic61—42no—
309C2×Dic61—42no—
310C2×Dic61—42no—
311C2×Dic61—42no—
312C2×Dic61—42no—
313C2×Dic61—42no—
314C2×Dic61—42no—
315C2×Dic61—42no—
316C2×Dic61—42no—
317C2×Dic61C2×C22⋊C414yes—
318C2×Dic61C2×C22⋊C414yes—
319C2×Dic61C2×C4⋊C414yes—
320C2×Dic61#11714yes—
321C2×Dic61#12118yes—
322C2×Dic61C22⋊Q818yes—
323C4×D61—416no—
324#13920—611nomaximal, Sylow
325C22×C61—24no—
326C22×C61—24no—
327C22×C61—24no—
328C22×C61—42no—
329C22×C61—42no—
330C22×C61—42no—
331C22×C61—44no—
332C22×C61—44no—
333C22×C61—44no—
334C22×C61—44no—
335C22×C61—42no—
336C22×C61C22×C22⋊C411yescharacteristic
337C22×C61C22×C4⋊C411yescharacteristic
338C22×C61C2×#11711yescharacteristic
339C22×C61C2×C4×D411yescharacteristic
340C22×C61C4×#4111yescharacteristic
341C22×C61#51811yescharacteristic
342C22×C61#52011yescharacteristic
343C22×C61C2×#12112yes—
344C22×C61C2×C22⋊Q812yes—
345C22×C61#52912yes—
346C22×C61#53212yes—
347C22×C61#54012yes—
348C22×C61#54212yes—
349C22×C61D4212yes—
350C22×C61D4211yescharacteristic
351C22×C61#54612yes—
352C22×C61#54612yes—
353C22×C61#54711yescharacteristic
354C22×C61#54812yes—
355C22×C61D4×Q811yescharacteristic
356C22×C61#55012yes—
357C22×C61#55412yes—
358C22×C61#55411yescharacteristic
359C2×D61—24no—
360C2×D61—24no—
361C2×D61—24no—
362C2×D61—42no—
363C2×D61—42no—
364C2×D61—42no—
365C2×D61—44no—
366C2×D61—44no—
367C2×D61—44no—
368C2×D61—44no—
369C2×D61—42no—
370C4×C61—24no—
371C4×C61—24no—
372C4×C61—44no—
373C4×C61—82no—
374Dic61—24no—
375Dic61—42no—
376Dic61—44no—
377Dic61—82no—
378Dic61#38018yescomplemented
379C22×C4×D4—611no—
380C2×#390—612no—
381C2×#389—612no—
382C2×#380—611no—
383C2×#380D6111yescharacteristic, complemented
384#1439—612no—
385#1439—612no—
386C4⋊#95—611no—
387C22⋊#95—611no—
388C22⋊#95—611no—
389C4×#95—611no—
390C2×C61—44no—
391C2×C61C2×#38011yescharacteristic
392C2×C61#229311yescharacteristic
393C2×C61#231911yescharacteristic
394C2×C61D4×C22⋊C411yescharacteristic
395C2×C61#234111yescharacteristic
396C2×C61D4×C4⋊C411yescharacteristic
397C2×C61#234911yescharacteristic
398C2×C61#242712yes—
399C2×C61#242812yes—
400C2×C61#245212yes—
401C2×C61#245412yes—
402D61—44no—
403C23×D4—611no—
404C24×C4—611no—
405C24×C4C2×D6111yescharacteristic
406C2×C4×D4—618no—
407C2×C4×D4—1228no—
408C22×C4⋊C4—611no—
409C22×C4⋊C4—612no—
410C22×C4⋊C4—612no—
411C22×C4⋊C4C2×D6112yes—
412C22×C22⋊C4—611no—
413C22×C22⋊C4—611no—
414C22×C22⋊C4—612no—
415C22×C22⋊C4—612no—
416C22×C22⋊C4—612no—
417C22×C22⋊C4C2×D6112yes—
418C22×C42—611no—
419C22×C42—612no—
420#390—1228no—
421#389—1228no—
422#380—24no—
423#380—1224no—
424C2×#95—611no—
425C2×#95—612no—
426C2×#95—611no—
427C2×#95—612no—
428C2×#95—612no—
429C2×#95—612no—
430C2×#95C2×D6111yescharacteristic
431C2×#95C2×D6111yescharacteristic
432C61#1392011yescharacteristic, complemented, Sylow
433C25—611no—
434C25C22×D6111yescharacteristic
435C22×D4—614no—
436C22×D4—614no—
437C22×D4—614no—
438C22×D4—1224no—
439C22×D4—1224no—
440C23×C4—22no—
441C23×C4—24no—
442C23×C4—22no—
443C23×C4—42no—
444C23×C4—611no—
445C23×C4—611no—
446C23×C4—611no—
447C23×C4—612no—
448C23×C4—614no—
449C23×C4—612no—
450C23×C4—1224no—
451C23×C4—1222no—
452C23×C4—1222no—
453C23×C4—2442no—
454C23×C4C4×D6114yes—
455C23×C4C22×D6112yes—
456C23×C4C22×D6112yes—
457C23×C4C22×D6111yescharacteristic
458C23×C4C22×D6111yescharacteristic
459C4×D4—12232no—
460C2×C4⋊C4—24no—
461C2×C4⋊C4—24no—
462C2×C4⋊C4—42no—
463C2×C4⋊C4—614no—
464C2×C4⋊C4—618no—
465C2×C4⋊C4—1224no—
466C2×C4⋊C4—1224no—
467C2×C4⋊C4—1224no—
468C2×C4⋊C4—1224no—
469C2×C4⋊C4—1224no—
470C2×C4⋊C4—2442no—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—42no—
474C2×C22⋊C4—614no—
475C2×C22⋊C4—614no—
476C2×C22⋊C4—1224no—
477C2×C22⋊C4—1224no—
478C2×C22⋊C4—1224no—
479C2×C22⋊C4—1224no—
480C2×C22⋊C4—1224no—
481C2×C22⋊C4—1224no—
482C2×C22⋊C4—1224no—
483C2×C22⋊C4—1224no—
484C2×C22⋊C4—2442no—
485C2×C22⋊C4—2442no—
486C2×C22⋊C4—2442no—
487C2×C42—614no—
488C2×C42—1224no—
489C2×C42—1224no—
490C2×C42—1224no—
491C2×C42—1224no—
492#95—22no—
493#95—1224no—
494#95—1224no—
495#95—1222no—
496#95—1224no—
497#95—1222no—
498#95—2442no—
499#95C22⋊D6114yescomplemented
500C24—22no—
501C24—21no—
502C24—22no—
503C24—22no—
504C24—21no—
505C24—21no—
506C24—22no—
507C24—21no—
508C24—612no—
509C24—612no—
510C24—612no—
511C24—1222no—
512C24—1221no—
513C24—1222no—
514C24—1222no—
515C24—1221no—
516C24—1221no—
517C24—1222no—
518C24—1221no—
519C24C2×C4×D6112yes—
520C24D4×D6112yes—
521C24Q8×D6112yes—
522C24C23×D6111yescharacteristic
523C2×D4—6116no—
524C2×D4—1228no—
525C2×D4—1228no—
526C2×D4—12216no—
527C2×D4—12216no—
528C22×C4—22no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—28no—
540C22×C4—28no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—44no—
549C22×C4—48no—
550C22×C4—48no—
551C22×C4—612no—
552C22×C4—614no—
553C22×C4—612no—
554C22×C4—612no—
555C22×C4—614no—
556C22×C4—612no—
557C22×C4—614no—
558C22×C4—612no—
559C22×C4—614no—
560C22×C4—1228no—
561C22×C4—1221no—
562C22×C4—1221no—
563C22×C4—1222no—
564C22×C4—1222no—
565C22×C4—1222no—
566C22×C4—1222no—
567C22×C4—1222no—
568C22×C4—1222no—
569C22×C4—1222no—
570C22×C4—1221no—
571C22×C4—1222no—
572C22×C4—1221no—
573C22×C4—1222no—
574C22×C4—1228no—
575C22×C4—1222no—
576C22×C4—1222no—
577C22×C4—1222no—
578C22×C4—1222no—
579C22×C4—1222no—
580C22×C4—1222no—
581C22×C4—1222no—
582C22×C4—2444no—
583C22×C4—2448no—
584C22×C4—2448no—
585C22×C4C2×C4×D6112yes—
586C22×C4C2×C4×D6112yes—
587C22×C4#1175822212yes—
588C22×C4D4×D6114yes—
589C22×C4C2×C22⋊D6114yes—
590C22×C4C2×C22⋊D6112yes—
591C4⋊C4—48no—
592C4⋊C4—6116no—
593C4⋊C4—2448no—
594C4⋊C4—2448no—
595C22⋊C4—48no—
596C22⋊C4—1228no—
597C22⋊C4—1228no—
598C22⋊C4—2448no—
599C22⋊C4—2448no—
600C22⋊C4—2448no—
601C42—1228no—
602C42—2448no—
603C23—22no—
604C23—24no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—24no—
612C23—24no—
613C23—22no—
614C23—24no—
615C23—22no—
616C23—22no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—614no—
626C23—1222no—
627C23—1224no—
628C23—1222no—
629C23—1222no—
630C23—1222no—
631C23—1222no—
632C23—1222no—
633C23—1222no—
634C23—1224no—
635C23—1224no—
636C23—1222no—
637C23—1224no—
638C23—1222no—
639C23—1222no—
640C23—2442no—
641C23—2442no—
642C23—2442no—
643C23—2442no—
644C23—2442no—
645C23—2442no—
646C23—2442no—
647C23—2442no—
648C23C4⋊C4×D6114yes—
649C23C22×C4×D6111yescharacteristic
650C23C2×D4×D6112yes—
651C23C2×D4×D6111yescharacteristic
652C23C22×C22⋊D6111yescharacteristic
653C23C2×Q8×D6111yescharacteristic
654C23#41×D6112yes—
655C23#41×D6112yes—
656C23C2×#1175822211yescharacteristic
657C23#1451982212yes—
658C23#1451982211yescharacteristic
659C23#1451982511yescharacteristic
660D4—12232no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—416no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—614no—
685C2×C4—614no—
686C2×C4—614no—
687C2×C4—618no—
688C2×C4—618no—
689C2×C4—614no—
690C2×C4—1222no—
691C2×C4—1222no—
692C2×C4—1224no—
693C2×C4—1224no—
694C2×C4—1222no—
695C2×C4—1222no—
696C2×C4—1222no—
697C2×C4—1224no—
698C2×C4—1224no—
699C2×C4—1224no—
700C2×C4—24416no—
701C2×C4—2442no—
702C2×C4—2442no—
703C2×C4—2442no—
704C2×C4—2442no—
705C2×C4—2442no—
706C2×C4—2442no—
707C2×C4—2442no—
708C2×C4—2442no—
709C2×C4—2442no—
710C2×C4—2442no—
711C2×C4—2442no—
712C2×C4—2442no—
713C2×C4—2442no—
714C2×C4C22⋊C4×D6114yes—
715C2×C4C4×C22⋊D6114yes—
716C22—24no—
717C22—24no—
718C22—24no—
719C22—42no—
720C22—42no—
721C22—44no—
722C22—44no—
723C22—42no—
724C22—44no—
725C22—42no—
726C22—44no—
727C22—1224no—
728C22—1224no—
729C22—1224no—
730C22—2442no—
731C22—2442no—
732C22—2444no—
733C22—2444no—
734C22—2442no—
735C22—2444no—
736C22—2442no—
737C22—2444no—
738C22C2×C22⋊C4×D6111yescharacteristic
739C22C2×C4⋊C4×D6111yescharacteristic
740C22#117×D6111yescharacteristic
741C22C2×C4×C22⋊D6111yescharacteristic
742C22#1684023011yescharacteristic
743C22#1684023511yescharacteristic
744C22#1684024311yescharacteristic
745C22#121×D6112yes—
746C22C22⋊Q8×D6112yes—
747C22#1684029012yes—
748C22#1684030812yes—
749C22#1684036212yes—
750C22#1684038212yes—
751C22D4×C22⋊D6111yescharacteristic
752C22D4×C22⋊D6112yes—
753C22#1684040112yes—
754C22#1684040212yes—
755C22#1684041311yescharacteristic
756C22#1684042212yes—
757C22Q8×C22⋊D6111yescharacteristic
758C22#1684043012yes—
759C22#1684046612yes—
760C22#1684046711yescharacteristic
761C4—24no—
762C4—24no—
763C4—44no—
764C4—82no—
765C4—618no—
766C4—1224no—
767C4—4882no—
768C4—2444no—
769C4—2442no—
770C2—44no—
771C2—2444no—
772C2#380×D6111yescharacteristic
773C2#2144827811yescharacteristic
774C2#2144846111yescharacteristic
775C2C22⋊C4×C22⋊D6111yescharacteristic
776C2#2144865611yescharacteristic
777C2C4⋊C4×C22⋊D6111yescharacteristic
778C2#2144872311yescharacteristic
779C2#2144939512yes—
780C2#2144940412yes—
781C2#2144966812yes—
782C2#2144969012yes—
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C61×#380C2
socle, cosocleC24×C61C24
prime radicalC23×C22⋊D61C22
hypercenterC2×#380D61
hypocenterC61#13920
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
3. C2×#16839657C2semidirect
4. C2×#16839621C2semidirect
5. #21444062C2semidirect
6. #21444061C2semidirect
7. #21444047C2semidirect
8. #21444042C2semidirect
9. #21444040C2semidirect
10. #95×Dic61C2semidirect
11. C2×C61×#380C2semidirect
15. C2×C4×C22⋊D61C4semidirect
107. #95×C61D4semidirect
164. C2×C22⋊D61C4⋊C4semidirect
208. #11758196C22⋊C4semidirect
378. Dic61#380semidirect
383. C2×#380D61semidirect
432. C61#13920semidirect
499. #95C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D612
C2×#168396622
C2×#168396572
C2×#168396212
#214440622
#214440612
#214440472
#214440422
#214440402
#95×Dic612
C2×C61×#3802
#1392061