Finite Group Databasebeta

← #29603459

Subgroups — #29603459

Order 15616.

3166 conjugacy classes of subgroups.

The subgroup lattice has 1398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519749C211yesmaximal, characteristic
2C2×#16839642C211yesmaximal, characteristic, complemented
3C2×#16839641C211yesmaximal, characteristic, complemented
4C2×#16839641C211yesmaximal, characteristic, complemented
5C2×#16839639C211yesmaximal, characteristic, complemented
6C22×#14519684C211yesmaximal, characteristic, complemented
7#21444069C211yesmaximal, characteristic, complemented
8#21444066C211yesmaximal, characteristic, complemented
9#21444061C211yesmaximal, characteristic, complemented
10#21444058C211yesmaximal, characteristic, complemented
11#21444057C211yesmaximal, characteristic, complemented
12#21444052C211yesmaximal, characteristic, complemented
13#21444042C211yesmaximal, characteristic, complemented
14#21444041C211yesmaximal, characteristic, complemented
15C22×C4×D4×C61C211yesmaximal, characteristic, complemented
16C23×C22⋊D61C2211yescharacteristic
17C23×C22⋊D61C2211yescharacteristic
18C24×Dic61C2211yescharacteristic
19C24×Dic61C2211yescharacteristic
20C2×#14519749—24no—
21C2×#14519749—24no—
22C2×#14519749C418yescomplemented
23C22×#11758196C2211yescharacteristic
24C22×C22⋊Dic61C2211yescharacteristic
25C22×C22⋊Dic61C2211yescharacteristic
26C22×C22⋊Dic61C2211yescharacteristic
27C22×C22⋊Dic61C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×#11758198C2211yescharacteristic
32C22×#11758198C2211yescharacteristic
33#16839642—24no—
34#16839641—24no—
35#16839641—24no—
36#16839639—24no—
37C2×#14519684—24no—
38C2×#14519684C2211yescharacteristic
39C2×#14519684C2211yescharacteristic
40C2×#14519684C2211yescharacteristic
41C2×#14519684C2211yescharacteristic
42C2×#14519684C2211yescharacteristic
43C2×#14519684C2211yescharacteristic
44C2×#14519684C2211yescharacteristic
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50C2×#14519684C2211yescharacteristic
51C2×#14519684C2211yescharacteristic
52C23×D4×C61C2211yescharacteristic
53C24×C4×C61C2211yescharacteristic
54C24×C4×C61C2211yescharacteristic
55C2×C4×D4×C61—24no—
56C2×C4×D4×C61—24no—
57C2×C4×D4×C61—24no—
58C22×C4⋊C4×C61C2211yescharacteristic
59C22×C22⋊C4×C61C2211yescharacteristic
60C22×C22⋊C4×C61C2211yescharacteristic
61C22×C42×C61C2211yescharacteristic
62C24×D61C2311yescharacteristic
63C22×C22⋊D61—22no—
64C22×C22⋊D61—22no—
65C22×C22⋊D61—22no—
66C22×C22⋊D61—22no—
67C22×C22⋊D61—22no—
68C22×C22⋊D61—22no—
69C22×C22⋊D61—22no—
70C22×C22⋊D61—22no—
71C22×C22⋊D61—22no—
72C22×C22⋊D61—22no—
73C22×C22⋊D61—41no—
74C22×C22⋊D61—41no—
75C22×C22⋊D61C2×C414yescomplemented
76C22×C22⋊D61C2×C414yescomplemented
77C23×Dic61—22no—
78C23×Dic61—22no—
79C23×Dic61—22no—
80C23×Dic61—22no—
81C23×Dic61—22no—
82C23×Dic61—22no—
83C23×Dic61—22no—
84C23×Dic61—22no—
85C23×Dic61—22no—
86C23×Dic61—41no—
87C23×Dic61—41no—
88C23×Dic61—41no—
89C23×Dic61—41no—
90C23×Dic61C2×C414yescomplemented
91C23×Dic61C2311yescharacteristic
92C23×Dic61C2311yescharacteristic
93C23×Dic61C2311yescharacteristic
94C23×Dic61C2311yescharacteristic
95C23×Dic61C2311yescharacteristic
96C23×Dic61C2311yescharacteristic
97C23×Dic61C2311yescharacteristic
98#14519749—232no—
99C2×#11758196—22no—
100C2×#11758196—22no—
101C2×#11758196C2×C414yescomplemented
102C2×C22⋊Dic61—22no—
103C2×C22⋊Dic61—22no—
104C2×C22⋊Dic61—22no—
105C2×C22⋊Dic61—22no—
106C2×C22⋊Dic61—22no—
107C2×C22⋊Dic61—22no—
108C2×C22⋊Dic61—22no—
109C2×C22⋊Dic61—22no—
110C2×C22⋊Dic61—22no—
111C2×C22⋊Dic61—41no—
112C2×C22⋊Dic61—41no—
113C2×C22⋊Dic61C2×C414yescomplemented
114C2×#11758198—22no—
115C2×#11758198—22no—
116C2×#11758198—22no—
117C2×#11758198—22no—
118C2×#11758198—22no—
119C2×#11758198—22no—
120C2×#11758198—22no—
121C2×#11758198—22no—
122C2×#11758198—22no—
123C2×#11758198—22no—
124C2×#11758198—41no—
125C2×#11758198—41no—
126C2×#11758198—41no—
127C2×#11758198—41no—
128C2×#11758198C2×C414yescomplemented
129#14519684—22no—
130#14519684—22no—
131#14519684—22no—
132#14519684—22no—
133#14519684—22no—
134#14519684—22no—
135#14519684—22no—
136#14519684—22no—
137#14519684—22no—
138#14519684—22no—
139#14519684—22no—
140#14519684—41no—
141#14519684—41no—
142#14519684D414yescomplemented
143C25×C61C2311yescharacteristic
144C25×C61C2311yescharacteristic
145C22×D4×C61—22no—
146C22×D4×C61—22no—
147C22×D4×C61—22no—
148C22×D4×C61—22no—
149C22×D4×C61C2×C414yes—
150C22×D4×C61D414yes—
151C22×D4×C61D414yes—
152C23×C4×C61—22no—
153C23×C4×C61—22no—
154C23×C4×C61—22no—
155C23×C4×C61—22no—
156C23×C4×C61—22no—
157C23×C4×C61—22no—
158C23×C4×C61—22no—
159C23×C4×C61—22no—
160C23×C4×C61—22no—
161C23×C4×C61—41no—
162C23×C4×C61—41no—
163C23×C4×C61—41no—
164C23×C4×C61—41no—
165C23×C4×C61D414yescomplemented
166C23×C4×C61C2311yescharacteristic
167C23×C4×C61C2311yescharacteristic
168C23×C4×C61C2311yescharacteristic
169C23×C4×C61C2311yescharacteristic
170C23×C4×C61C2311yescharacteristic
171C4×D4×C61—232no—
172C2×C4⋊C4×C61—22no—
173C2×C4⋊C4×C61—22no—
174C2×C4⋊C4×C61—22no—
175C2×C22⋊C4×C61—22no—
176C2×C22⋊C4×C61—22no—
177C2×C22⋊C4×C61—22no—
178C2×C22⋊C4×C61—22no—
179C2×C22⋊C4×C61—22no—
180C2×C22⋊C4×C61D414yescomplemented
181C2×C42×C61—22no—
182C2×C42×C61—22no—
183C2×C42×C61—22no—
184C24×C61—21no—
185C24×C61—21no—
186C24×C61—21no—
187C24×C61—21no—
188C24×C61—21no—
189C24×C61—21no—
190C24×C61—21no—
191C24×C61—21no—
192C24×C61—21no—
193C24×C61—21no—
194C24×C61—21no—
195C24×C61—21no—
196C24×C61—21no—
197C24×C61—21no—
198C24×C61—21no—
199C24×C61—21no—
200C24×C61—21no—
201C24×C61—21no—
202C24×C61—21no—
203C24×C61—21no—
204C24×C61C22×C412yes—
205C24×C61C22×C412yes—
206C24×C61C2×D412yes—
207C24×C61C2×D412yes—
208C24×C61C2×D412yes—
209C24×C61C2×D412yes—
210C24×C61C2×D412yes—
211C24×C61C2×D412yes—
212C24×C61#4112yes—
213C24×C61#4112yes—
214C24×C61C2411yescharacteristic
215C23×D61—21no—
216C23×D61—21no—
217C23×D61—21no—
218C23×D61—21no—
219C23×D61—21no—
220C23×D61—21no—
221C23×D61—21no—
222C23×D61—21no—
223C23×D61—21no—
224C23×D61—21no—
225C23×D61—21no—
226C23×D61—21no—
227C23×D61—21no—
228C23×D61—21no—
229C23×D61C22×C412yes—
230C2×D4×C61—28no—
231C2×D4×C61—28no—
232C2×D4×C61—28no—
233C2×D4×C61—28no—
234C2×D4×C61—28no—
235C2×D4×C61—28no—
236C2×D4×C61C22⋊C4116yescomplemented
237C22×C4×C61—21no—
238C22×C4×C61—21no—
239C22×C4×C61—21no—
240C22×C4×C61—21no—
241C22×C4×C61—21no—
242C22×C4×C61—21no—
243C22×C4×C61—21no—
244C22×C4×C61—21no—
245C22×C4×C61—28no—
246C22×C4×C61—28no—
247C22×C4×C61—21no—
248C22×C4×C61—21no—
249C22×C4×C61—21no—
250C22×C4×C61—21no—
251C22×C4×C61—21no—
252C22×C4×C61—21no—
253C22×C4×C61—21no—
254C22×C4×C61—21no—
255C22×C4×C61—21no—
256C22×C4×C61—21no—
257C22×C4×C61—21no—
258C22×C4×C61—21no—
259C22×C4×C61—21no—
260C22×C4×C61—21no—
261C22×C4×C61—21no—
262C22×C4×C61—21no—
263C22×C4×C61—21no—
264C22×C4×C61—21no—
265C22×C4×C61—28no—
266C22×C4×C61—44no—
267C22×C4×C61—44no—
268C22×C4×C61—44no—
269C22×C4×C61—44no—
270C22×C4×C61—44no—
271C22×C4×C61—44no—
272C22×C4×C61—44no—
273C22×C4×C61—44no—
274C22×C4×C61—44no—
275C22×C4×C61—44no—
276C22×C4×C61—44no—
277C22×C4×C61C22×C412yes—
278C22×C4×C61C2×D412yes—
279C22×C4×C61C2×D412yes—
280C22×C4×C61C2×D412yes—
281C22×C4×C61C2×D412yes—
282C22×C4×C61C2×D412yes—
283C22×C4×C61C2×D412yes—
284C22×C4×C61C2×D412yes—
285C22×C4×C61#4112yes—
286C2×C22⋊D61—28no—
287C2×C22⋊D61—28no—
288C2×C22⋊D61—28no—
289C2×C22⋊D61—28no—
290C2×C22⋊D61—28no—
291C2×C22⋊D61—44no—
292C2×C22⋊D61—44no—
293C2×C22⋊D61—44no—
294C2×C22⋊D61—44no—
295C2×C22⋊D61—44no—
296C2×C22⋊D61—44no—
297C2×C22⋊D61—44no—
298C2×C22⋊D61—44no—
299C2×C22⋊D61—44no—
300C22×Dic61—21no—
301C22×Dic61—21no—
302C22×Dic61—21no—
303C22×Dic61—21no—
304C22×Dic61—28no—
305C22×Dic61—28no—
306C22×Dic61—21no—
307C22×Dic61—21no—
308C22×Dic61—21no—
309C22×Dic61—21no—
310C22×Dic61—21no—
311C22×Dic61—21no—
312C22×Dic61—21no—
313C22×Dic61—21no—
314C22×Dic61—21no—
315C22×Dic61—21no—
316C22×Dic61—21no—
317C22×Dic61—21no—
318C22×Dic61—21no—
319C22×Dic61—21no—
320C22×Dic61—21no—
321C22×Dic61—21no—
322C22×Dic61—21no—
323C22×Dic61—21no—
324C22×Dic61—21no—
325C22×Dic61—21no—
326C22×Dic61—21no—
327C22×Dic61—21no—
328C22×Dic61—21no—
329C22×Dic61—21no—
330C22×Dic61—28no—
331C22×Dic61—21no—
332C22×Dic61—21no—
333C22×Dic61—21no—
334C22×Dic61—21no—
335C22×Dic61—21no—
336C22×Dic61—21no—
337C22×Dic61—21no—
338C22×Dic61—21no—
339C22×Dic61—21no—
340C22×Dic61—21no—
341C22×Dic61—21no—
342C22×Dic61—21no—
343C22×Dic61—21no—
344C22×Dic61—21no—
345C22×Dic61—44no—
346C22×Dic61—44no—
347C22×Dic61—44no—
348C22×Dic61—44no—
349C22×Dic61—44no—
350C22×Dic61—44no—
351C22×Dic61—44no—
352C22×Dic61—44no—
353C22×Dic61—44no—
354C22×Dic61—44no—
355C22×Dic61—44no—
356C22×Dic61C22×C412yes—
357C22×Dic61C22×C412yes—
358C22×Dic61C22×C412yes—
359C22×Dic61C2×D412yes—
360C22×Dic61C2×D412yes—
361C22×Dic61#4112yes—
362C22×Dic61#4112yes—
363C4⋊C4×C61—28no—
364C22⋊C4×C61—28no—
365C22⋊C4×C61—28no—
366C42×C61—28no—
367C22⋊Dic61—28no—
368C22⋊Dic61—44no—
369C22⋊Dic61—44no—
370C22⋊Dic61—44no—
371#11758198—28no—
372#11758198—44no—
373#11758198—44no—
374#11758198—44no—
375#11758198—44no—
376#11758196—28no—
377C23×C61—22no—
378C23×C61—22no—
379C23×C61—22no—
380C23×C61—22no—
381C23×C61—22no—
382C23×C61—22no—
383C23×C61—22no—
384C23×C61—22no—
385C23×C61—22no—
386C23×C61—22no—
387C23×C61—22no—
388C23×C61—22no—
389C23×C61—22no—
390C23×C61—22no—
391C23×C61—22no—
392C23×C61—22no—
393C23×C61—22no—
394C23×C61—22no—
395C23×C61—22no—
396C23×C61—22no—
397C23×C61—22no—
398C23×C61—22no—
399C23×C61—22no—
400C23×C61—22no—
401C23×C61—22no—
402C23×C61—22no—
403C23×C61—22no—
404C23×C61—22no—
405C23×C61—22no—
406C23×C61—22no—
407C23×C61—22no—
408C23×C61—22no—
409C23×C61—22no—
410C23×C61—22no—
411C23×C61—22no—
412C23×C61—22no—
413C23×C61—22no—
414C23×C61—22no—
415C23×C61—22no—
416C23×C61—22no—
417C23×C61—22no—
418C23×C61—22no—
419C23×C61—22no—
420C23×C61—22no—
421C23×C61—22no—
422C23×C61—22no—
423C23×C61—41no—
424C23×C61—41no—
425C23×C61—41no—
426C23×C61—41no—
427C23×C61—41no—
428C23×C61—41no—
429C23×C61—41no—
430C23×C61—41no—
431C23×C61—41no—
432C23×C61—41no—
433C23×C61—41no—
434C23×C61—41no—
435C23×C61—41no—
436C23×C61—41no—
437C23×C61—41no—
438C23×C61—41no—
439C23×C61C2×C22⋊C414yes—
440C23×C61C2×C22⋊C414yes—
441C23×C61C4×D414yes—
442C23×C61C4×D414yes—
443C23×C61#12014yes—
444C23×C61#12114yes—
445C23×C61#12114yes—
446C23×C61#12314yes—
447C23×C61C23×C411yescharacteristic
448C23×C61C22×D411yescharacteristic
449C23×C61C22×D411yescharacteristic
450C23×C61C22×D411yescharacteristic
451C23×C61C22×D411yescharacteristic
452C23×C61C22×D411yescharacteristic
453C23×C61C2×#4111yescharacteristic
454C23×C61C2×#4111yescharacteristic
455C23×C61C2×#4111yescharacteristic
456C23×C61C2×#4111yescharacteristic
457C23×C61C2×#4111yescharacteristic
458C23×C61H(5,𝔽2)11yescharacteristic
459C23×C61H(5,𝔽2)11yescharacteristic
460C23×C61H(5,𝔽2)11yescharacteristic
461C23×C612−1+411yescharacteristic
462C22×D61—22no—
463C22×D61—22no—
464C22×D61—22no—
465C22×D61—22no—
466C22×D61—22no—
467C22×D61—22no—
468C22×D61—22no—
469C22×D61—41no—
470C22×D61—41no—
471C22×D61—41no—
472C22×D61—41no—
473C22×D61—41no—
474C22×D61—41no—
475C22×D61—41no—
476C22×D61—41no—
477C22×D61—41no—
478C22×D61—41no—
479C22×D61—41no—
480C22×D61—41no—
481C22×D61—41no—
482C22×D61—41no—
483C22×D61—41no—
484C22×D61—41no—
485C22×D61—41no—
486C22×D61—41no—
487C22×D61—41no—
488C22×D61—41no—
489C22×D61—41no—
490C22×D61—41no—
491C22×D61—41no—
492C22×D61—41no—
493C22×D61—41no—
494C22×D61—41no—
495C22×D61—41no—
496C22×D61—41no—
497D4×C61—232no—
498C2×C4×C61—22no—
499C2×C4×C61—22no—
500C2×C4×C61—22no—
501C2×C4×C61—22no—
502C2×C4×C61—22no—
503C2×C4×C61—22no—
504C2×C4×C61—22no—
505C2×C4×C61—22no—
506C2×C4×C61—22no—
507C2×C4×C61—22no—
508C2×C4×C61—22no—
509C2×C4×C61—22no—
510C2×C4×C61—22no—
511C2×C4×C61—22no—
512C2×C4×C61—22no—
513C2×C4×C61—22no—
514C2×C4×C61—22no—
515C2×C4×C61—22no—
516C2×C4×C61—22no—
517C2×C4×C61—22no—
518C2×C4×C61—22no—
519C2×C4×C61—416no—
520C2×C4×C61—416no—
521C2×C4×C61—41no—
522C2×C4×C61—41no—
523C2×C4×C61—41no—
524C2×C4×C61—41no—
525C2×C4×C61—41no—
526C2×C4×C61—41no—
527C2×C4×C61—41no—
528C2×C4×C61—41no—
529C2×C4×C61—41no—
530C2×C4×C61—41no—
531C2×C4×C61—41no—
532C2×C4×C61—41no—
533C2×C4×C61C2×C22⋊C414yes—
534C2×C4×C61#12114yescomplemented
535C22⋊D61—416no—
536C22⋊D61—416no—
537C2×Dic61—22no—
538C2×Dic61—22no—
539C2×Dic61—22no—
540C2×Dic61—22no—
541C2×Dic61—22no—
542C2×Dic61—22no—
543C2×Dic61—22no—
544C2×Dic61—22no—
545C2×Dic61—22no—
546C2×Dic61—22no—
547C2×Dic61—22no—
548C2×Dic61—22no—
549C2×Dic61—22no—
550C2×Dic61—22no—
551C2×Dic61—22no—
552C2×Dic61—22no—
553C2×Dic61—22no—
554C2×Dic61—22no—
555C2×Dic61—416no—
556C2×Dic61—416no—
557C2×Dic61—41no—
558C2×Dic61—41no—
559C2×Dic61—41no—
560C2×Dic61—41no—
561C2×Dic61—41no—
562C2×Dic61—41no—
563C2×Dic61—41no—
564C2×Dic61—41no—
565C2×Dic61—41no—
566C2×Dic61—41no—
567C2×Dic61—41no—
568C2×Dic61—41no—
569C2×Dic61—41no—
570C2×Dic61—41no—
571C2×Dic61—41no—
572C2×Dic61—41no—
573C2×Dic61—41no—
574C2×Dic61—41no—
575C2×Dic61—41no—
576C2×Dic61—41no—
577C2×Dic61—41no—
578C2×Dic61—41no—
579C2×Dic61—41no—
580C2×Dic61—41no—
581C2×Dic61—41no—
582C2×Dic61—41no—
583C2×Dic61—41no—
584C2×Dic61—41no—
585C2×Dic61—41no—
586C2×Dic61—41no—
587C2×Dic61C4×D414yescomplemented
588#14023—611nomaximal, Sylow
589C22×C61—24no—
590C22×C61—24no—
591C22×C61—24no—
592C22×C61—24no—
593C22×C61—24no—
594C22×C61—24no—
595C22×C61—24no—
596C22×C61—24no—
597C22×C61—24no—
598C22×C61—24no—
599C22×C61—24no—
600C22×C61—24no—
601C22×C61—24no—
602C22×C61—24no—
603C22×C61—24no—
604C22×C61—24no—
605C22×C61—24no—
606C22×C61—42no—
607C22×C61—42no—
608C22×C61—42no—
609C22×C61—42no—
610C22×C61—42no—
611C22×C61—42no—
612C22×C61—42no—
613C22×C61—42no—
614C22×C61—42no—
615C22×C61—42no—
616C22×C61—42no—
617C22×C61—42no—
618C22×C61#38618yescomplemented
619C22×C61C22×C22⋊C411yescharacteristic
620C22×C61C2×C4×D411yescharacteristic
621C22×C61C2×C4×D411yescharacteristic
622C22×C61C2×C4×D411yescharacteristic
623C22×C61C4×#4111yescharacteristic
624C22×C61#51811yescharacteristic
625C22×C61#52011yescharacteristic
626C22×C61C2×#12011yescharacteristic
627C22×C61C2×#12111yescharacteristic
628C22×C61C2×#12111yescharacteristic
629C22×C61C2×#12111yescharacteristic
630C22×C61C2×#12311yescharacteristic
631C22×C61#52511yescharacteristic
632C22×C61#52911yescharacteristic
633C22×C61#53211yescharacteristic
634C22×C61#53411yescharacteristic
635C22×C61#53711yescharacteristic
636C22×C61#53811yescharacteristic
637C22×C61#53911yescharacteristic
638C22×C61D4211yescharacteristic
639C22×C61D4211yescharacteristic
640C22×C61D4211yescharacteristic
641C22×C61#54611yescharacteristic
642C22×C61#54611yescharacteristic
643C22×C61#54611yescharacteristic
644C22×C61#54611yescharacteristic
645C22×C61#54611yescharacteristic
646C22×C61#54611yescharacteristic
647C22×C61#54711yescharacteristic
648C22×C61#54711yescharacteristic
649C22×C61#54711yescharacteristic
650C22×C61#54811yescharacteristic
651C22×C61#55311yescharacteristic
652C22×C61#55311yescharacteristic
653C22×C61#55311yescharacteristic
654C2×D61—42no—
655C2×D61—42no—
656C2×D61—42no—
657C2×D61—42no—
658C2×D61—42no—
659C2×D61—42no—
660C2×D61—42no—
661C2×D61—81no—
662C2×D61—81no—
663C2×D61—81no—
664C2×D61—81no—
665C2×D61—81no—
666C2×D61—81no—
667C2×D61—81no—
668C2×D61—81no—
669C4×C61—24no—
670C4×C61—24no—
671C4×C61—42no—
672C4×C61—42no—
673C4×C61—42no—
674Dic61—24no—
675Dic61—42no—
676Dic61—42no—
677Dic61—42no—
678Dic61—42no—
679Dic61—81no—
680Dic61—81no—
681C22×#121—611no—
682C22×C4×D4D6111yescharacteristic, complemented
683C2×#386—611no—
684C2×#386—611no—
685C2×#386—611no—
686C2×#386—611no—
687C22×#95—611no—
688#1441—611no—
689#1440—611no—
690#1439—611no—
691#1438—611no—
692#1437—611no—
693#1436—611no—
694C22⋊#95—611no—
695C22⋊#95—611no—
696C2×C61—28no—
697C2×C61—44no—
698C2×C61C2×#38611yescharacteristic
699C2×C61C4×#12111yescharacteristic
700C2×C61#232511yescharacteristic
701C2×C61D4×C22⋊C411yescharacteristic
702C2×C61#233911yescharacteristic
703C2×C61#236111yescharacteristic
704C2×C61#236411yescharacteristic
705C2×C61#241011yescharacteristic
706C2×C61#241611yescharacteristic
707C2×C61#242411yescharacteristic
708C2×C61#242511yescharacteristic
709C2×C61#243011yescharacteristic
710C2×C61#244311yescharacteristic
711C2×C61#244411yescharacteristic
712C2×C61#254311yescharacteristic
713D61—82no—
714C23×D4—611no—
715C23×D4—611no—
716C23×D4C2×D6111yescharacteristic
717C24×C4—611no—
718C24×C4—611no—
719C24×C4C2×D6111yescharacteristic
720C24×C4C2×D6111yescharacteristic
721C2×#121—618no—
722C2×#121—1224no—
723C2×#121—1224no—
724C2×C4×D4—24no—
725C2×C4×D4—24no—
726C2×C4×D4—24no—
727C22×C4⋊C4—611no—
728C22×C4⋊C4C2×D6111yescharacteristic
729C22×C22⋊C4—611no—
730C22×C22⋊C4—611no—
731C22×C22⋊C4—611no—
732C22×C22⋊C4—611no—
733C22×C22⋊C4—611no—
734C22×C22⋊C4—611no—
735C22×C22⋊C4—611no—
736C22×C22⋊C4—611no—
737C22×C22⋊C4—611no—
738C22×C22⋊C4C2×D6111yescharacteristic
739C22×C22⋊C4C2×D6111yescharacteristic
740C22×C42C2×D6111yescharacteristic
741#386—1224no—
742#386—1224no—
743#386—1224no—
744#386—1224no—
745C2×#95—611no—
746C2×#95—611no—
747C2×#95—611no—
748C2×#95—611no—
749C2×#95—611no—
750C2×#95—611no—
751C2×#95—611no—
752C2×#95—611no—
753C2×#95—611no—
754C2×#95—611no—
755C2×#95—611no—
756C2×#95—611no—
757C2×#95—611no—
758C2×#95—611no—
759C2×#95—1224no—
760C61#1402311yescharacteristic, complemented, Sylow
761C25—611no—
762C25C22×D6111yescharacteristic
763C25C22×D6111yescharacteristic
764C22×D4—22no—
765C22×D4—22no—
766C22×D4—22no—
767C22×D4—22no—
768C22×D4—614no—
769C22×D4—614no—
770C22×D4—1222no—
771C22×D4—1222no—
772C22×D4—1222no—
773C22×D4—1222no—
774C22×D4—1222no—
775C22×D4—1222no—
776C22×D4—1222no—
777C22×D4—1222no—
778C22×D4—1222no—
779C22×D4—1222no—
780C22×D4—2441no—
781C22×D4—2441no—
782C22×D4C4×D6114yes—
783C22×D4D24414yes—
784C22×D4C22⋊D6114yes—
785C23×C4—22no—
786C23×C4—22no—
787C23×C4—22no—
788C23×C4—22no—
789C23×C4—22no—
790C23×C4—22no—
791C23×C4—22no—
792C23×C4—22no—
793C23×C4—22no—
794C23×C4—41no—
795C23×C4—41no—
796C23×C4—41no—
797C23×C4—41no—
798C23×C4—611no—
799C23×C4—611no—
800C23×C4—611no—
801C23×C4—611no—
802C23×C4—611no—
803C23×C4—614no—
804C23×C4—611no—
805C23×C4—611no—
806C23×C4—1222no—
807C23×C4—1222no—
808C23×C4—1222no—
809C23×C4—1222no—
810C23×C4—1222no—
811C23×C4—1222no—
812C23×C4—1222no—
813C23×C4—1222no—
814C23×C4—1222no—
815C23×C4—2441no—
816C23×C4—2441no—
817C23×C4—2441no—
818C23×C4—2441no—
819C23×C4C22⋊D6114yescomplemented
820C23×C4C22×D6111yescharacteristic
821C23×C4C22×D6111yescharacteristic
822C23×C4C22×D6111yescharacteristic
823C23×C4C22×D6111yescharacteristic
824C23×C4C22×D6111yescharacteristic
825#121—12232no—
826C4×D4—232no—
827C2×C4⋊C4—22no—
828C2×C4⋊C4—22no—
829C2×C4⋊C4—22no—
830C2×C4⋊C4—614no—
831C2×C4⋊C4—1222no—
832C2×C4⋊C4—1222no—
833C2×C22⋊C4—22no—
834C2×C22⋊C4—22no—
835C2×C22⋊C4—22no—
836C2×C22⋊C4—22no—
837C2×C22⋊C4—22no—
838C2×C22⋊C4—614no—
839C2×C22⋊C4—614no—
840C2×C22⋊C4—1222no—
841C2×C22⋊C4—1222no—
842C2×C22⋊C4—1222no—
843C2×C22⋊C4—1222no—
844C2×C22⋊C4—1222no—
845C2×C22⋊C4—1222no—
846C2×C22⋊C4—1222no—
847C2×C22⋊C4—1222no—
848C2×C22⋊C4—1222no—
849C2×C22⋊C4—1222no—
850C2×C22⋊C4—1222no—
851C2×C22⋊C4—1222no—
852C2×C22⋊C4—1222no—
853C2×C22⋊C4—1222no—
854C2×C22⋊C4—1222no—
855C2×C22⋊C4—1222no—
856C2×C22⋊C4—1222no—
857C2×C22⋊C4—1222no—
858C2×C22⋊C4—1222no—
859C2×C22⋊C4—2441no—
860C2×C22⋊C4—2441no—
861C2×C22⋊C4—2441no—
862C2×C22⋊C4—2441no—
863C2×C22⋊C4—2441no—
864C2×C22⋊C4—2441no—
865C2×C22⋊C4C22⋊D6114yescomplemented
866C2×C42—22no—
867C2×C42—22no—
868C2×C42—22no—
869#95—614no—
870#95—1222no—
871#95—1222no—
872#95—1222no—
873#95—1222no—
874#95—1222no—
875#95—1222no—
876#95—1222no—
877#95—1222no—
878#95—1222no—
879#95—1222no—
880#95—1222no—
881#95—2441no—
882#95—2441no—
883C24—21no—
884C24—21no—
885C24—21no—
886C24—21no—
887C24—21no—
888C24—21no—
889C24—21no—
890C24—21no—
891C24—21no—
892C24—21no—
893C24—21no—
894C24—21no—
895C24—21no—
896C24—21no—
897C24—21no—
898C24—21no—
899C24—21no—
900C24—21no—
901C24—21no—
902C24—21no—
903C24—612no—
904C24—1221no—
905C24—1221no—
906C24—1221no—
907C24—1221no—
908C24—1221no—
909C24—1221no—
910C24—1221no—
911C24—1221no—
912C24—1221no—
913C24—1221no—
914C24—1221no—
915C24—1221no—
916C24—1221no—
917C24—1221no—
918C24C2×C4×D6112yes—
919C24C2×C4×D6112yes—
920C24C2×D24412yes—
921C24C2×D24412yes—
922C24#1175822212yes—
923C24#1175822212yes—
924C24C2×C22⋊D6112yes—
925C24C2×C22⋊D6112yes—
926C24C2×C22⋊D6112yes—
927C24C2×C22⋊D6112yes—
928C24C23×D6111yescharacteristic
929C2×D4—28no—
930C2×D4—28no—
931C2×D4—28no—
932C2×D4—28no—
933C2×D4—28no—
934C2×D4—28no—
935C2×D4—1228no—
936C2×D4—1228no—
937C2×D4—1228no—
938C2×D4—1228no—
939C2×D4—1228no—
940C2×D4—2444no—
941C2×D4—2444no—
942C2×D4—2444no—
943C2×D4—2444no—
944C2×D4—2444no—
945C2×D4—2444no—
946C2×D4—2444no—
947C2×D4—2444no—
948C2×D4—2444no—
949C2×D4#11758198116yescomplemented
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—28no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—28no—
978C22×C4—28no—
979C22×C4—44no—
980C22×C4—44no—
981C22×C4—44no—
982C22×C4—44no—
983C22×C4—44no—
984C22×C4—44no—
985C22×C4—44no—
986C22×C4—44no—
987C22×C4—44no—
988C22×C4—44no—
989C22×C4—44no—
990C22×C4—612no—
991C22×C4—612no—
992C22×C4—612no—
993C22×C4—612no—
994C22×C4—612no—
995C22×C4—612no—
996C22×C4—612no—
997C22×C4—1228no—
998C22×C4—1221no—
999C22×C4—1221no—
1000C22×C4—1221no—
1001C22×C4—1221no—
1002C22×C4—1228no—
1003C22×C4—1221no—
1004C22×C4—1221no—
1005C22×C4—1221no—
1006C22×C4—1221no—
1007C22×C4—1221no—
1008C22×C4—1221no—
1009C22×C4—1221no—
1010C22×C4—1221no—
1011C22×C4—1221no—
1012C22×C4—1221no—
1013C22×C4—1221no—
1014C22×C4—1221no—
1015C22×C4—1221no—
1016C22×C4—1221no—
1017C22×C4—1221no—
1018C22×C4—1221no—
1019C22×C4—1221no—
1020C22×C4—1221no—
1021C22×C4—1221no—
1022C22×C4—1221no—
1023C22×C4—1221no—
1024C22×C4—1221no—
1025C22×C4—1221no—
1026C22×C4—1221no—
1027C22×C4—1228no—
1028C22×C4—1221no—
1029C22×C4—1221no—
1030C22×C4—1221no—
1031C22×C4—1221no—
1032C22×C4—1221no—
1033C22×C4—1221no—
1034C22×C4—1221no—
1035C22×C4—1221no—
1036C22×C4—1221no—
1037C22×C4—1221no—
1038C22×C4—1221no—
1039C22×C4—1221no—
1040C22×C4—1221no—
1041C22×C4—1221no—
1042C22×C4—2444no—
1043C22×C4—2444no—
1044C22×C4—2444no—
1045C22×C4—2444no—
1046C22×C4—2444no—
1047C22×C4—2444no—
1048C22×C4—2444no—
1049C22×C4—2444no—
1050C22×C4—2444no—
1051C22×C4—2444no—
1052C22×C4—2444no—
1053C22×C4C2×C4×D6112yes—
1054C22×C4C2×D24412yes—
1055C22×C4D4×D6112yes—
1056C22×C4#1175822412yes—
1057C22×C4C2×C22⋊D6112yes—
1058C22×C4C2×C22⋊D6112yes—
1059C22×C4C2×C22⋊D6112yes—
1060C22×C4C2×C22⋊D6112yes—
1061C22×C4C2×C22⋊D6112yes—
1062C4⋊C4—28no—
1063C4⋊C4—1228no—
1064C22⋊C4—28no—
1065C22⋊C4—28no—
1066C22⋊C4—1228no—
1067C22⋊C4—1228no—
1068C22⋊C4—2444no—
1069C22⋊C4—2444no—
1070C22⋊C4—2444no—
1071C22⋊C4—2444no—
1072C22⋊C4—2444no—
1073C22⋊C4—2444no—
1074C22⋊C4—2444no—
1075C42—28no—
1076C23—22no—
1077C23—22no—
1078C23—22no—
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—22no—
1083C23—22no—
1084C23—22no—
1085C23—22no—
1086C23—22no—
1087C23—22no—
1088C23—22no—
1089C23—22no—
1090C23—22no—
1091C23—22no—
1092C23—22no—
1093C23—22no—
1094C23—22no—
1095C23—22no—
1096C23—22no—
1097C23—22no—
1098C23—22no—
1099C23—22no—
1100C23—22no—
1101C23—22no—
1102C23—22no—
1103C23—22no—
1104C23—22no—
1105C23—22no—
1106C23—22no—
1107C23—22no—
1108C23—22no—
1109C23—22no—
1110C23—22no—
1111C23—22no—
1112C23—22no—
1113C23—22no—
1114C23—22no—
1115C23—22no—
1116C23—22no—
1117C23—22no—
1118C23—22no—
1119C23—22no—
1120C23—22no—
1121C23—22no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—1222no—
1139C23—1222no—
1140C23—1222no—
1141C23—1222no—
1142C23—1222no—
1143C23—1222no—
1144C23—1222no—
1145C23—2441no—
1146C23—2441no—
1147C23—2441no—
1148C23—2441no—
1149C23—2441no—
1150C23—2441no—
1151C23—2441no—
1152C23—2441no—
1153C23—2441no—
1154C23—2441no—
1155C23—2441no—
1156C23—2441no—
1157C23—2441no—
1158C23—2441no—
1159C23—2441no—
1160C23—2441no—
1161C23—2441no—
1162C23—2441no—
1163C23—2441no—
1164C23—2441no—
1165C23—2441no—
1166C23—2441no—
1167C23—2441no—
1168C23—2441no—
1169C23—2441no—
1170C23—2441no—
1171C23—2441no—
1172C23—2441no—
1173C23C2×#1175819814yes—
1174C23C2×#1175819814yes—
1175C23C4×C22⋊D6114yes—
1176C23C4×C22⋊D6114yes—
1177C23#1451974614yes—
1178C23#1451975114yes—
1179C23#1451975114yes—
1180C23#1451976014yes—
1181C23C22×C4×D6111yescharacteristic
1182C23C2×D4×D6111yescharacteristic
1183C23C22×C22⋊D6111yescharacteristic
1184C23C22×C22⋊D6111yescharacteristic
1185C23C22×C22⋊D6111yescharacteristic
1186C23C22×D24411yescharacteristic
1187C23#41×D6111yescharacteristic
1188C23#41×D6111yescharacteristic
1189C23C2×#1175822411yescharacteristic
1190C23C2×#1175822211yescharacteristic
1191C23C2×#1175822211yescharacteristic
1192C23#1451982211yescharacteristic
1193C23#1451982211yescharacteristic
1194C23#1451982311yescharacteristic
1195C23#1451982411yescharacteristic
1196D4—232no—
1197D4—24416no—
1198D4—24416no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—416no—
1221C2×C4—416no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—614no—
1235C2×C4—1222no—
1236C2×C4—1222no—
1237C2×C4—1222no—
1238C2×C4—1222no—
1239C2×C4—1222no—
1240C2×C4—1222no—
1241C2×C4—1222no—
1242C2×C4—1222no—
1243C2×C4—1222no—
1244C2×C4—1222no—
1245C2×C4—1222no—
1246C2×C4—1222no—
1247C2×C4—1222no—
1248C2×C4—1222no—
1249C2×C4—1222no—
1250C2×C4—1222no—
1251C2×C4—1222no—
1252C2×C4—1222no—
1253C2×C4—24416no—
1254C2×C4—2441no—
1255C2×C4—2441no—
1256C2×C4—2441no—
1257C2×C4—2441no—
1258C2×C4—2441no—
1259C2×C4—2441no—
1260C2×C4—2441no—
1261C2×C4—2441no—
1262C2×C4—2441no—
1263C2×C4—2441no—
1264C2×C4—2441no—
1265C2×C4—2441no—
1266C2×C4—2441no—
1267C2×C4—2441no—
1268C2×C4—24416no—
1269C2×C4—2441no—
1270C2×C4—2441no—
1271C2×C4—2441no—
1272C2×C4—2441no—
1273C2×C4—2441no—
1274C2×C4—2441no—
1275C2×C4—2441no—
1276C2×C4—2441no—
1277C2×C4—2441no—
1278C2×C4—2441no—
1279C2×C4—2441no—
1280C2×C4—2441no—
1281C2×C4—2441no—
1282C2×C4—2441no—
1283C2×C4—2441no—
1284C2×C4—2441no—
1285C2×C4C2×#1175819814yes—
1286C2×C4#1451974914yescomplemented
1287C22—24no—
1288C22—24no—
1289C22—24no—
1290C22—24no—
1291C22—24no—
1292C22—24no—
1293C22—24no—
1294C22—24no—
1295C22—24no—
1296C22—24no—
1297C22—24no—
1298C22—24no—
1299C22—24no—
1300C22—24no—
1301C22—24no—
1302C22—24no—
1303C22—24no—
1304C22—42no—
1305C22—42no—
1306C22—42no—
1307C22—42no—
1308C22—42no—
1309C22—42no—
1310C22—42no—
1311C22—42no—
1312C22—42no—
1313C22—42no—
1314C22—42no—
1315C22—42no—
1316C22—4881no—
1317C22—4881no—
1318C22—4881no—
1319C22—4881no—
1320C22—4881no—
1321C22—4881no—
1322C22—4881no—
1323C22—4881no—
1324C22—2442no—
1325C22—2442no—
1326C22—2442no—
1327C22—2442no—
1328C22—2442no—
1329C22—2442no—
1330C22—2442no—
1331C22#1683964118yescomplemented
1332C22C22×#1175819811yescharacteristic
1333C22C4×D4×D6111yescharacteristic
1334C22C2×C4×C22⋊D6111yescharacteristic
1335C22C2×C4×C22⋊D6111yescharacteristic
1336C22C4×#1175822411yescharacteristic
1337C22#1684023411yescharacteristic
1338C22#1684024111yescharacteristic
1339C22C2×#1451974611yescharacteristic
1340C22C2×#1451974911yescharacteristic
1341C22C2×#1451975111yescharacteristic
1342C22C2×#1451975111yescharacteristic
1343C22C2×#1451976011yescharacteristic
1344C22#1684027111yescharacteristic
1345C22#1684029211yescharacteristic
1346C22#1684030811yescharacteristic
1347C22#1684032111yescharacteristic
1348C22#1684034011yescharacteristic
1349C22#1684034511yescharacteristic
1350C22#1684035411yescharacteristic
1351C22D4×C22⋊D6111yescharacteristic
1352C22D4×C22⋊D6111yescharacteristic
1353C22D4×D24411yescharacteristic
1354C22#1684040011yescharacteristic
1355C22#1684040011yescharacteristic
1356C22#1684040611yescharacteristic
1357C22#1684040611yescharacteristic
1358C22#1684040711yescharacteristic
1359C22#1684040711yescharacteristic
1360C22#1684041111yescharacteristic
1361C22#1684041111yescharacteristic
1362C22#1684041611yescharacteristic
1363C22#1684042111yescharacteristic
1364C22#1684045811yescharacteristic
1365C22#1684046111yescharacteristic
1366C22#1684046111yescharacteristic
1367C4—24no—
1368C4—24no—
1369C4—42no—
1370C4—42no—
1371C4—42no—
1372C4—1224no—
1373C4—4881no—
1374C4—4881no—
1375C4—2442no—
1376C4—2442no—
1377C4—2442no—
1378C4—2442no—
1379C2—28no—
1380C2—44no—
1381C2—4882no—
1382C2C2×#1683964111yescharacteristic
1383C2C4×#1451974911yescharacteristic
1384C2#2144851711yescharacteristic
1385C2D4×#1175819811yescharacteristic
1386C2#2144864411yescharacteristic
1387C2#2144883611yescharacteristic
1388C2#2144886411yescharacteristic
1389C2#2144919311yescharacteristic
1390C2#2144925911yescharacteristic
1391C2#2144934911yescharacteristic
1392C2#2144936411yescharacteristic
1393C2#2144942311yescharacteristic
1394C2#2144954811yescharacteristic
1395C2#2144956311yescharacteristic
1396C2#2145077511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC22×C4×D4×C61C2
socle, cosocleC24×C61C24
prime radicalC22×#14519749C2
hypercenterC22×C4×D4D61
hypocenterC61#14023
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×#16839642C2semidirect
3. C2×#16839641C2semidirect
4. C2×#16839641C2semidirect
5. C2×#16839639C2semidirect
6. C22×#14519684C2semidirect
7. #21444069C2semidirect
8. #21444066C2semidirect
9. #21444061C2semidirect
10. #21444058C2semidirect
11. #21444057C2semidirect
12. #21444052C2semidirect
13. #21444042C2semidirect
14. #21444041C2semidirect
15. C22×C4×D4×C61C2semidirect
22. C2×#14519749C4semidirect
75. C22×C22⋊D61C2×C4semidirect
76. C22×C22⋊D61C2×C4semidirect
90. C23×Dic61C2×C4semidirect
101. C2×#11758196C2×C4semidirect
113. C2×C22⋊Dic61C2×C4semidirect
128. C2×#11758198C2×C4semidirect
142. #14519684D4semidirect
165. C23×C4×C61D4semidirect
180. C2×C22⋊C4×C61D4semidirect
236. C2×D4×C61C22⋊C4semidirect
534. C2×C4×C61#121semidirect
587. C2×Dic61C4×D4semidirect
618. C22×C61#386semidirect
682. C22×C4×D4D61semidirect
760. C61#14023semidirect
819. C23×C4C22⋊D61semidirect
865. C2×C22⋊C4C22⋊D61semidirect
949. C2×D4#11758198semidirect
1286. C2×C4#14519749semidirect
1331. C22#16839641semidirect

Maximal subgroups

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

subgroupindex
C22×#145197492
C2×#168396422
C2×#168396412
C2×#168396392
C22×#145196842
#214440692
#214440662
#214440612
#214440582
#214440572
#214440522
#214440422
#214440412
C22×C4×D4×C612
#1402361