Finite Group Databasebeta

← #29601747

Subgroups — #29601747

Order 15616.

2574 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D61C211yesmaximal, characteristic
2C2×C4×#11758196C211yesmaximal, characteristic, complemented
3C2×C4×#11758198C211yesmaximal, characteristic, complemented
4C2×C4×#11758198C211yesmaximal, characteristic, complemented
5C2×C4×C22⋊Dic61C211yesmaximal, characteristic, complemented
6C2×#16839608C211yesmaximal, characteristic, complemented
7#21444085C212yesmaximal, complemented
8#21444063C212yesmaximal, complemented
9#21444062C212yesmaximal, complemented
10#21444058C212yesmaximal
11C2×C4×C22⋊C4×C61C211yesmaximal, characteristic, complemented
12C23×C22⋊D61C2211yescharacteristic
13C23×C4×D61C2211yescharacteristic
14C2×C4×C22⋊D61—24no—
15C2×C4×C22⋊D61—24no—
16C2×C4×C22⋊D61C418yescomplemented
17C22×#11758196C2212yes—
18C22×#11758196C2211yescharacteristic
19C22×C22⋊Dic61C2212yes—
20C22×C22⋊Dic61C2211yescharacteristic
21C22×#11758198C2212yes—
22C22×#11758198C2212yes—
23C22×#11758198C2211yescharacteristic
24C22×C4×Dic61C2211yescharacteristic
25C22×C4×Dic61C2211yescharacteristic
26C22×C4×Dic61C2211yescharacteristic
27C4×#11758196—24no—
28C4×#11758198—24no—
29C4×#11758198—24no—
30C4×C22⋊Dic61—24no—
31#16839608—24no—
32C2×#14519684C2212yes—
33C2×#14519684C2212yes—
34C2×#14519684C2212yes—
35C2×#14519684C2212yes—
36C2×#14519684C2212yes—
37C2×#14519684C2212yes—
38C24×C4×C61C2211yescharacteristic
39C22×C22⋊C4×C61C2212yes—
40C22×C42×C61C2211yescharacteristic
41C22×C42×C61C2211yescharacteristic
42C4×C22⋊C4×C61—24no—
43C2×#95×C61C2212yes—
44C24×D61C2311yescharacteristic
45C22×C22⋊D61—24no—
46C22×C22⋊D61—24no—
47C22×C22⋊D61—22no—
48C22×C22⋊D61—22no—
49C22×C22⋊D61C2×C414yes—
50C23×Dic61C2311yescharacteristic
51C23×Dic61C2312yes—
52C23×Dic61C2312yes—
53C23×Dic61C2311yescharacteristic
54C23×Dic61C2311yescharacteristic
55C22×C4×D61—22no—
56C22×C4×D61—22no—
57C22×C4×D61—22no—
58C22×C4×D61—22no—
59C22×C4×D61—22no—
60C22×C4×D61—22no—
61C22×C4×D61C2×C414yes—
62C4×C22⋊D61—232no—
63C2×#11758196—24no—
64C2×#11758196—22no—
65C2×#11758196—22no—
66C2×#11758196—24no—
67C2×#11758196—24no—
68C2×#11758196C2×C414yes—
69C2×C22⋊Dic61—24no—
70C2×C22⋊Dic61—22no—
71C2×C22⋊Dic61—22no—
72C2×C22⋊Dic61—24no—
73C2×C22⋊Dic61—24no—
74C2×C22⋊Dic61C2×C414yes—
75C2×#11758198—24no—
76C2×#11758198—24no—
77C2×#11758198—24no—
78C2×#11758198—24no—
79C2×#11758198—22no—
80C2×#11758198—22no—
81C2×#11758198—24no—
82C2×#11758198—24no—
83C2×#11758198C2×C414yes—
84C2×C4×Dic61—22no—
85C2×C4×Dic61—22no—
86C2×C4×Dic61—22no—
87C2×C4×Dic61—22no—
88C2×C4×Dic61—22no—
89C2×C4×Dic61C2×C414yes—
90C2×C4×Dic61D414yes—
91C2×C4×Dic61D414yes—
92C2×C4×Dic61D414yescomplemented
93#14519684—24no—
94#14519684—24no—
95#14519684—24no—
96#14519684—24no—
97#14519684—24no—
98#14519684—24no—
99C25×C61C2311yescharacteristic
100C23×C4×C61—22no—
101C23×C4×C61—22no—
102C23×C4×C61—22no—
103C23×C4×C61—22no—
104C23×C4×C61—22no—
105C23×C4×C61—22no—
106C23×C4×C61C2×C414yes—
107C23×C4×C61C2311yescharacteristic
108C23×C4×C61C2312yes—
109C23×C4×C61C2312yes—
110C23×C4×C61C2311yescharacteristic
111C2×C22⋊C4×C61—24no—
112C2×C22⋊C4×C61—24no—
113C2×C22⋊C4×C61—24no—
114C2×C42×C61—22no—
115C2×C42×C61—22no—
116C2×C42×C61—22no—
117C2×C42×C61—22no—
118C2×C42×C61—22no—
119C2×C42×C61D414yescomplemented
120#95×C61—24no—
121C24×C61—21no—
122C24×C61—21no—
123C24×C61—21no—
124C24×C61—21no—
125C24×C61—22no—
126C24×C61—22no—
127C24×C61—21no—
128C24×C61—21no—
129C24×C61—22no—
130C24×C61C22×C412yes—
131C24×C61#4114yes—
132C24×C61C2411yescharacteristic
133C23×D61—21no—
134C23×D61—21no—
135C23×D61—21no—
136C23×D61—21no—
137C23×D61—21no—
138C23×D61—21no—
139C23×D61—22no—
140C23×D61—22no—
141C23×D61—22no—
142C23×D61C22×C412yes—
143C23×D61#4114yes—
144C22×C4×C61—21no—
145C22×C4×C61—22no—
146C22×C4×C61—22no—
147C22×C4×C61—22no—
148C22×C4×C61—22no—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61—22no—
153C22×C4×C61—22no—
154C22×C4×C61—22no—
155C22×C4×C61—22no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—22no—
159C22×C4×C61—22no—
160C22×C4×C61—22no—
161C22×C4×C61—22no—
162C22×C4×C61—28no—
163C22×C4×C61—28no—
164C22×C4×C61—28no—
165C22×C4×C61—44no—
166C22×C4×C61—44no—
167C22×C4×C61—44no—
168C22×C4×C61—44no—
169C22×C4×C61C22×C412yes—
170C22×C4×C61C22×C412yes—
171C22×C4×C61C2×D414yes—
172C22×C4×C61C2×D412yes—
173C22×C4×C61C2×D412yes—
174C22×C4×C61C2×D412yes—
175C22×C4×C61C2×D412yes—
176C22×C4×C61#4114yes—
177C22×C4×C61#4112yes—
178C22×C4×C61#4112yes—
179C2×C22⋊D61—216no—
180C2×C22⋊D61—216no—
181C2×C22⋊D61—28no—
182C2×C22⋊D61—28no—
183C2×C22⋊D61—28no—
184C22×Dic61—22no—
185C22×Dic61—22no—
186C22×Dic61—22no—
187C22×Dic61—22no—
188C22×Dic61—21no—
189C22×Dic61—21no—
190C22×Dic61—21no—
191C22×Dic61—21no—
192C22×Dic61—22no—
193C22×Dic61—22no—
194C22×Dic61—22no—
195C22×Dic61—22no—
196C22×Dic61—21no—
197C22×Dic61—21no—
198C22×Dic61—22no—
199C22×Dic61—22no—
200C22×Dic61—22no—
201C22×Dic61—22no—
202C22×Dic61—22no—
203C22×Dic61—22no—
204C22×Dic61—22no—
205C22×Dic61—22no—
206C22×Dic61C22×C412yes—
207C22×Dic61C22×C412yes—
208C22×Dic61C22×C412yes—
209C22×Dic61C2×D414yes—
210C22×Dic61C2×D412yes—
211C22×Dic61C2×D412yes—
212C22×Dic61C2×D412yes—
213C22×Dic61C2×D412yes—
214C22×Dic61#4114yes—
215C2×C4×D61—28no—
216C2×C4×D61—28no—
217C2×C4×D61—28no—
218C2×C4×D61—44no—
219C2×C4×D61—44no—
220C2×C4×D61—44no—
221C2×C4×D61—44no—
222C22⋊C4×C61—216no—
223C42×C61—28no—
224C42×C61—44no—
225C22⋊Dic61—216no—
226C22⋊Dic61—28no—
227#11758198—216no—
228#11758198—216no—
229#11758198—28no—
230#11758196—216no—
231#11758196—28no—
232C4×Dic61—28no—
233C4×Dic61—44no—
234C4×Dic61C22⋊C4116yescomplemented
235C23×C61—22no—
236C23×C61—22no—
237C23×C61—22no—
238C23×C61—22no—
239C23×C61—22no—
240C23×C61—22no—
241C23×C61—24no—
242C23×C61—24no—
243C23×C61—24no—
244C23×C61—24no—
245C23×C61—24no—
246C23×C61—24no—
247C23×C61—41no—
248C23×C61—41no—
249C23×C61—42no—
250C23×C61—42no—
251C23×C61—42no—
252C23×C61—41no—
253C23×C61—42no—
254C23×C61—42no—
255C23×C61—41no—
256C23×C61—42no—
257C23×C61#11714yes—
258C23×C61C23×C411yescharacteristic
259C23×C61C22×D411yescharacteristic
260C23×C61C22×D411yescharacteristic
261C23×C61C22×D411yescharacteristic
262C23×C61C22×D411yescharacteristic
263C23×C61C2×#4112yes—
264C23×C61C2×#4112yes—
265C23×C61C2×#4111yescharacteristic
266C23×C61C2×#4111yescharacteristic
267C23×C61C2×#4112yes—
268C23×C61C2×#4112yes—
269C22×D61—22no—
270C22×D61—22no—
271C22×D61—22no—
272C22×D61—22no—
273C22×D61—22no—
274C22×D61—22no—
275C22×D61—24no—
276C22×D61—24no—
277C22×D61—24no—
278C22×D61—24no—
279C22×D61—24no—
280C22×D61—24no—
281C22×D61—41no—
282C22×D61—41no—
283C22×D61—42no—
284C22×D61—42no—
285C22×D61—42no—
286C22×D61—41no—
287C22×D61—42no—
288C22×D61—42no—
289C22×D61—41no—
290C22×D61—42no—
291C22×D61#11714yes—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—24no—
296C2×C4×C61—24no—
297C2×C4×C61—24no—
298C2×C4×C61—24no—
299C2×C4×C61—24no—
300C2×C4×C61—24no—
301C2×C4×C61—41no—
302C2×C4×C61—41no—
303C2×C4×C61—42no—
304C2×C4×C61—42no—
305C2×C4×C61—42no—
306C2×C4×C61—42no—
307C2×C4×C61—41no—
308C2×C4×C61—42no—
309C2×C4×C61—42no—
310C2×C4×C61—42no—
311C2×C4×C61—41no—
312C2×C4×C61—42no—
313C2×C4×C61—416no—
314C2×C4×C61C2×C22⋊C414yes—
315C2×C4×C61C4×D414yes—
316C2×C4×C61C4×D414yes—
317C2×C4×C61#12114yes—
318C2×C4×C61#12114yes—
319C2×C4×C61#12414yes—
320C2×C4×C61#12714yes—
321C22⋊D61—232no—
322C2×Dic61—22no—
323C2×Dic61—22no—
324C2×Dic61—22no—
325C2×Dic61—22no—
326C2×Dic61—24no—
327C2×Dic61—24no—
328C2×Dic61—24no—
329C2×Dic61—24no—
330C2×Dic61—22no—
331C2×Dic61—22no—
332C2×Dic61—22no—
333C2×Dic61—24no—
334C2×Dic61—24no—
335C2×Dic61—24no—
336C2×Dic61—24no—
337C2×Dic61—24no—
338C2×Dic61—24no—
339C2×Dic61—41no—
340C2×Dic61—41no—
341C2×Dic61—42no—
342C2×Dic61—42no—
343C2×Dic61—42no—
344C2×Dic61—42no—
345C2×Dic61—41no—
346C2×Dic61—42no—
347C2×Dic61—42no—
348C2×Dic61—42no—
349C2×Dic61—41no—
350C2×Dic61—42no—
351C2×Dic61C2×C22⋊C414yes—
352C2×Dic61C2×C22⋊C414yes—
353C4×D61—416no—
354#13847—611nomaximal, Sylow
355C22×C61—24no—
356C22×C61—24no—
357C22×C61—24no—
358C22×C61—44no—
359C22×C61—44no—
360C22×C61—44no—
361C22×C61—44no—
362C22×C61—42no—
363C22×C61—42no—
364C22×C61—42no—
365C22×C61—42no—
366C22×C61C22×C22⋊C411yescharacteristic
367C22×C61C2×#11711yescharacteristic
368C22×C61C2×#11711yescharacteristic
369C22×C61C2×C4×D411yescharacteristic
370C22×C61C2×C4×D411yescharacteristic
371C22×C61C4×#4111yescharacteristic
372C22×C61C4×#4111yescharacteristic
373C22×C61C2×#12111yescharacteristic
374C22×C61C2×#12111yescharacteristic
375C22×C61#52512yes—
376C22×C61#52512yes—
377C22×C61#52512yes—
378C22×C61#52512yes—
379C22×C61#52512yes—
380C22×C61#52512yes—
381C22×C61#52512yes—
382C22×C61C2×#12411yescharacteristic
383C22×C61#52912yes—
384C22×C61#52912yes—
385C22×C61#52912yes—
386C22×C61#52912yes—
387C22×C61C2×#12711yescharacteristic
388C22×C61#53212yes—
389C2×D61—24no—
390C2×D61—24no—
391C2×D61—24no—
392C2×D61—44no—
393C2×D61—44no—
394C2×D61—44no—
395C2×D61—44no—
396C2×D61—42no—
397C2×D61—42no—
398C2×D61—42no—
399C2×D61—42no—
400C4×C61—44no—
401C4×C61—44no—
402C4×C61—42no—
403C4×C61#39018yes—
404Dic61—24no—
405Dic61—24no—
406Dic61—44no—
407Dic61—44no—
408Dic61—42no—
409C22×C4×D4—611no—
410C2×C4×C4⋊C4—611no—
411C2×C4×C22⋊C4—611no—
412C2×C4×C22⋊C4—611no—
413C2×C4×C22⋊C4—611no—
414C2×C4×C22⋊C4D6111yescharacteristic, complemented
415C2×#376—611no—
416#1445—612no—
417#1439—612no—
418#1439—612no—
419#1438—612no—
420C2×C61—44no—
421C2×C61#228011yescharacteristic
422C2×C61#229011yescharacteristic
423C2×C61#229011yescharacteristic
424C2×C61#229011yescharacteristic
425C2×C61#229011yescharacteristic
426C2×C61C2×#39011yescharacteristic
427C2×C61#229711yescharacteristic
428C2×C61#239212yes—
429C2×C61#239212yes—
430C2×C61#239712yes—
431C2×C61#239812yes—
432D61—44no—
433C23×D4—611no—
434C24×C4—611no—
435C24×C4C2×D6111yescharacteristic
436C2×C4×D4—618no—
437C2×C4×D4—1224no—
438C2×C4×D4—1224no—
439C22×C4⋊C4—611no—
440C22×C4⋊C4—612no—
441C22×C22⋊C4—611no—
442C22×C22⋊C4—611no—
443C22×C22⋊C4—612no—
444C22×C22⋊C4—612no—
445C22×C22⋊C4—612no—
446C22×C22⋊C4C2×D6112yes—
447C22×C42—611no—
448C22×C42—611no—
449C22×C42—611no—
450C22×C42C2×D6111yescharacteristic
451C22×C42C2×D6111yescharacteristic
452C4×C4⋊C4—1224no—
453C4×C22⋊C4—24no—
454C4×C22⋊C4—1224no—
455C4×C22⋊C4—1224no—
456C4×C22⋊C4—1224no—
457#376—1224no—
458C2×#95—612no—
459C2×#95—612no—
460C2×#95—612no—
461C2×#95—612no—
462C2×#95—612no—
463C2×#95—612no—
464C2×#95C2×D6112yes—
465C61#1384711yescharacteristic, complemented, Sylow
466C25—611no—
467C25C22×D6111yescharacteristic
468C22×D4—614no—
469C22×D4—1222no—
470C22×D4—1222no—
471C22×D4—1224no—
472C22×D4—1224no—
473C23×C4—22no—
474C23×C4—22no—
475C23×C4—22no—
476C23×C4—22no—
477C23×C4—22no—
478C23×C4—22no—
479C23×C4—611no—
480C23×C4—611no—
481C23×C4—612no—
482C23×C4—612no—
483C23×C4—611no—
484C23×C4—614no—
485C23×C4—1222no—
486C23×C4—1222no—
487C23×C4—1222no—
488C23×C4—1222no—
489C23×C4—1222no—
490C23×C4—1222no—
491C23×C4C4×D6114yes—
492C23×C4C22×D6111yescharacteristic
493C23×C4C22×D6112yes—
494C23×C4C22×D6112yes—
495C23×C4C22×D6111yescharacteristic
496C4×D4—12232no—
497C2×C4⋊C4—614no—
498C2×C4⋊C4—1222no—
499C2×C4⋊C4—1222no—
500C2×C4⋊C4—1224no—
501C2×C4⋊C4—1224no—
502C2×C4⋊C4—1224no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—614no—
507C2×C22⋊C4—614no—
508C2×C22⋊C4—1222no—
509C2×C22⋊C4—1222no—
510C2×C22⋊C4—1224no—
511C2×C22⋊C4—1224no—
512C2×C22⋊C4—1224no—
513C2×C22⋊C4—1224no—
514C2×C22⋊C4—1222no—
515C2×C22⋊C4—1222no—
516C2×C22⋊C4—1224no—
517C2×C22⋊C4—1224no—
518C2×C22⋊C4—1224no—
519C2×C22⋊C4—1224no—
520C2×C22⋊C4—1224no—
521C2×C42—22no—
522C2×C42—22no—
523C2×C42—22no—
524C2×C42—22no—
525C2×C42—22no—
526C2×C42—614no—
527C2×C42—614no—
528C2×C42—614no—
529C2×C42—614no—
530C2×C42—1222no—
531C2×C42—1222no—
532C2×C42—1222no—
533C2×C42—1222no—
534C2×C42—1222no—
535C2×C42C22⋊D6114yescomplemented
536#95—24no—
537#95—1224no—
538#95—1224no—
539#95—1224no—
540#95—1224no—
541#95—1224no—
542#95—1224no—
543C24—21no—
544C24—21no—
545C24—21no—
546C24—21no—
547C24—22no—
548C24—22no—
549C24—21no—
550C24—22no—
551C24—21no—
552C24—612no—
553C24—614no—
554C24—1221no—
555C24—1221no—
556C24—1221no—
557C24—1221no—
558C24—1222no—
559C24—1221no—
560C24—1222no—
561C24—1221no—
562C24—1222no—
563C24C2×C4×D6112yes—
564C24#1175822214yes—
565C24C23×D6111yescharacteristic
566C2×D4—1228no—
567C2×D4—1228no—
568C2×D4—12216no—
569C2×D4—12216no—
570C2×D4—1228no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—21no—
589C22×C4—28no—
590C22×C4—28no—
591C22×C4—28no—
592C22×C4—44no—
593C22×C4—44no—
594C22×C4—44no—
595C22×C4—44no—
596C22×C4—612no—
597C22×C4—612no—
598C22×C4—612no—
599C22×C4—612no—
600C22×C4—612no—
601C22×C4—612no—
602C22×C4—612no—
603C22×C4—614no—
604C22×C4—614no—
605C22×C4—1222no—
606C22×C4—1222no—
607C22×C4—1222no—
608C22×C4—1222no—
609C22×C4—1222no—
610C22×C4—1221no—
611C22×C4—1222no—
612C22×C4—1222no—
613C22×C4—1221no—
614C22×C4—1221no—
615C22×C4—1221no—
616C22×C4—1222no—
617C22×C4—1222no—
618C22×C4—1222no—
619C22×C4—1222no—
620C22×C4—1221no—
621C22×C4—1222no—
622C22×C4—1222no—
623C22×C4—1222no—
624C22×C4—1222no—
625C22×C4—1222no—
626C22×C4—1221no—
627C22×C4—1228no—
628C22×C4—1228no—
629C22×C4—1228no—
630C22×C4—2444no—
631C22×C4—2444no—
632C22×C4—2444no—
633C22×C4—2444no—
634C22×C4C2×C4×D6112yes—
635C22×C4C2×C4×D6112yes—
636C22×C4#1175822214yes—
637C22×C4#1175822212yes—
638C22×C4D4×D6112yes—
639C22×C4D4×D6112yes—
640C22×C4D4×D6112yes—
641C22×C4#1175822412yes—
642C22×C4C2×C22⋊D6114yes—
643C22×C4C2×C22⋊D6112yes—
644C4⋊C4—1228no—
645C4⋊C4—12216no—
646C22⋊C4—216no—
647C22⋊C4—1228no—
648C22⋊C4—12216no—
649C22⋊C4—12216no—
650C22⋊C4—1228no—
651C22⋊C4—12216no—
652C42—28no—
653C42—44no—
654C42—6116no—
655C42—1228no—
656C42—2444no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—41no—
670C23—41no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—41no—
675C23—42no—
676C23—42no—
677C23—41no—
678C23—42no—
679C23—614no—
680C23—1222no—
681C23—1222no—
682C23—1222no—
683C23—1222no—
684C23—1222no—
685C23—1222no—
686C23—1224no—
687C23—1224no—
688C23—1224no—
689C23—1224no—
690C23—1224no—
691C23—1224no—
692C23—2441no—
693C23—2441no—
694C23—2442no—
695C23—2442no—
696C23—2442no—
697C23—2441no—
698C23—2442no—
699C23—2442no—
700C23—2441no—
701C23—2442no—
702C23#1451973414yes—
703C23C22×C4×D6111yescharacteristic
704C23C2×D4×D6111yescharacteristic
705C23C2×D4×D6111yescharacteristic
706C23C2×D4×D6111yescharacteristic
707C23C22×C22⋊D6111yescharacteristic
708C23#41×D6112yes—
709C23#41×D6112yes—
710C23C2×#1175822411yescharacteristic
711C23C2×#1175822212yes—
712C23C2×#1175822211yescharacteristic
713C23C2×#1175822212yes—
714D4—12232no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—41no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—41no—
735C2×C4—42no—
736C2×C4—416no—
737C2×C4—614no—
738C2×C4—614no—
739C2×C4—1222no—
740C2×C4—1222no—
741C2×C4—1222no—
742C2×C4—1222no—
743C2×C4—1224no—
744C2×C4—1224no—
745C2×C4—1224no—
746C2×C4—1224no—
747C2×C4—1222no—
748C2×C4—1222no—
749C2×C4—1222no—
750C2×C4—1224no—
751C2×C4—1224no—
752C2×C4—1224no—
753C2×C4—1224no—
754C2×C4—1224no—
755C2×C4—1224no—
756C2×C4—2441no—
757C2×C4—2441no—
758C2×C4—2442no—
759C2×C4—2442no—
760C2×C4—2442no—
761C2×C4—2442no—
762C2×C4—2441no—
763C2×C4—2442no—
764C2×C4—2442no—
765C2×C4—2442no—
766C2×C4—2441no—
767C2×C4—2442no—
768C2×C4—24416no—
769C2×C4C22⋊C4×D6114yes—
770C2×C4#1451973714yes—
771C2×C4C4×C22⋊D6114yes—
772C2×C4#1451974914yes—
773C2×C4#1451975014yes—
774C2×C4#1451976314yes—
775C2×C4#1451977314yes—
776C22—24no—
777C22—24no—
778C22—24no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—44no—
783C22—44no—
784C22—42no—
785C22—44no—
786C22—44no—
787C22—1224no—
788C22—1224no—
789C22—1224no—
790C22—2442no—
791C22—2442no—
792C22—2442no—
793C22—2444no—
794C22—2444no—
795C22—2442no—
796C22—2444no—
797C22—2444no—
798C22C2×C22⋊C4×D6111yescharacteristic
799C22#117×D6111yescharacteristic
800C22C2×#1451973411yescharacteristic
801C22C2×#1451973711yescharacteristic
802C22C2×C4×C22⋊D6111yescharacteristic
803C22#1684023011yescharacteristic
804C22C4×#1175822211yescharacteristic
805C22C2×#1451974911yescharacteristic
806C22C2×#1451975011yescharacteristic
807C22#1684026912yes—
808C22#1684027112yes—
809C22#1684027112yes—
810C22#1684027112yes—
811C22#1684027112yes—
812C22#1684027112yes—
813C22#1684027312yes—
814C22C2×#1451976311yescharacteristic
815C22#1684029012yes—
816C22#1684029212yes—
817C22#1684029412yes—
818C22#1684029612yes—
819C22C2×#1451977311yescharacteristic
820C22#1684030912yes—
821C4—42no—
822C4—44no—
823C4—44no—
824C4—1224no—
825C4—1224no—
826C4—2442no—
827C4—2444no—
828C4—2444no—
829C4#1683966218yes—
830C2—44no—
831C2—2444no—
832C2#2144820011yescharacteristic
833C2#2144825611yescharacteristic
834C2#2144825811yescharacteristic
835C2#2144826211yescharacteristic
836C2#2144826511yescharacteristic
837C2C2×#1683966211yescharacteristic
838C2#2144830511yescharacteristic
839C2#2144906112yes—
840C2#2144906312yes—
841C2#2144909812yes—
842C2#2144910612yes—
subgroupG/H
centerC23×C4C22×D61
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC2×C4×C22⋊C4×C61C2
socle, cosocleC24×C61C24
prime radicalC23×C22⋊D61C22
hypercenterC2×C4×C22⋊C4D61
hypocenterC61#13847
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11758196C2semidirect
3. C2×C4×#11758198C2semidirect
4. C2×C4×#11758198C2semidirect
5. C2×C4×C22⋊Dic61C2semidirect
6. C2×#16839608C2semidirect
7. #21444085C2semidirect
8. #21444063C2semidirect
9. #21444062C2semidirect
11. C2×C4×C22⋊C4×C61C2semidirect
16. C2×C4×C22⋊D61C4semidirect
92. C2×C4×Dic61D4semidirect
119. C2×C42×C61D4semidirect
234. C4×Dic61C22⋊C4semidirect
414. C2×C4×C22⋊C4D61semidirect
465. C61#13847semidirect
535. C2×C42C22⋊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×C4×#117581962
C2×C4×#117581982
C2×C4×C22⋊Dic612
C2×#168396082
#214440852
#214440632
#214440622
#214440582
C2×C4×C22⋊C4×C612
#1384761