Finite Group Databasebeta

← #29601709

Subgroups — #29601709

Order 15616.

1814 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×Dic61C211yesmaximal, characteristic, complemented
2C2×#16839609C211yesmaximal, characteristic
3C2×#16839609C211yesmaximal, characteristic
4C2×#16839609C211yesmaximal, characteristic
5C2×#16839607C211yesmaximal, characteristic, complemented
6#21444080C211yesmaximal, characteristic, complemented
7#21444079C211yesmaximal, characteristic, complemented
8#21444076C211yesmaximal, characteristic, complemented
9#21444067C211yesmaximal, characteristic
10#21444067C211yesmaximal, characteristic
11#21444065C211yesmaximal, characteristic
12#21444061C211yesmaximal, characteristic
13#95×Dic61C211yesmaximal, characteristic, complemented
14#95×Dic61C211yesmaximal, characteristic, complemented
15C61×#1442C211yesmaximal, characteristic, complemented
16C23×C4×D61C2211yescharacteristic
17C22×C4⋊Dic61C2211yescharacteristic
18C22×#11758198C2211yescharacteristic
19C22×#11758198C2211yescharacteristic
20C22×#11758198C2211yescharacteristic
21C22×#11758198C2211yescharacteristic
22C22×#11758198C2211yescharacteristic
23C22×#11758198C2211yescharacteristic
24C22×C4×Dic61C2211yescharacteristic
25C22×C4×Dic61C2211yescharacteristic
26C22×C4×Dic61C2211yescharacteristic
27C22×C4×Dic61C2211yescharacteristic
28C22×C4×Dic61C2211yescharacteristic
29C22×C4×Dic61C2211yescharacteristic
30C4⋊C4×Dic61—24no—
31#16839609—24no—
32#16839609—24no—
33#16839609C418yescomplemented
34#16839607—24no—
35C2×#14519684C2211yescharacteristic
36C2×#14519684C2211yescharacteristic
37C2×#14519684C2211yescharacteristic
38C2×#14519684C2211yescharacteristic
39C2×#14519684C2211yescharacteristic
40C2×#14519684C2211yescharacteristic
41C2×#14519684C2211yescharacteristic
42C2×#14519684C2211yescharacteristic
43C2×#14519684C2211yescharacteristic
44C2×#14519684C2211yescharacteristic
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C22×C4⋊C4×C61C2211yescharacteristic
50C2×#95×C61C2211yescharacteristic
51C2×#95×C61C2211yescharacteristic
52C2×#95×C61C2211yescharacteristic
53C2×#95×C61C2211yescharacteristic
54C2×#95×C61C2211yescharacteristic
55C2×#95×C61C2211yescharacteristic
56C24×D61C2311yescharacteristic
57C23×Dic61C2311yescharacteristic
58C23×Dic61C2311yescharacteristic
59C23×Dic61C2311yescharacteristic
60C23×Dic61C2311yescharacteristic
61C23×Dic61C2311yescharacteristic
62C23×Dic61C2311yescharacteristic
63C23×Dic61C2311yescharacteristic
64C22×C4×D61—22no—
65C22×C4×D61—22no—
66C22×C4×D61—22no—
67C22×C4×D61—22no—
68C22×C4×D61—22no—
69C22×C4×D61—22no—
70C22×C4×D61C2×C414yes—
71C2×C4⋊Dic61—22no—
72C2×C4⋊Dic61—22no—
73C2×C4⋊Dic61—22no—
74C2×#11758198—22no—
75C2×#11758198—22no—
76C2×#11758198—22no—
77C2×#11758198—22no—
78C2×#11758198—22no—
79C2×#11758198—22no—
80C2×#11758198—22no—
81C2×#11758198—22no—
82C2×#11758198—22no—
83C2×#11758198—22no—
84C2×#11758198—22no—
85C2×#11758198—22no—
86C2×#11758198—22no—
87C2×#11758198—22no—
88C2×#11758198—22no—
89C2×#11758198—22no—
90C2×#11758198C2×C414yes—
91C2×#11758198C2×C414yes—
92C2×C4×Dic61—22no—
93C2×C4×Dic61—22no—
94C2×C4×Dic61—22no—
95C2×C4×Dic61—22no—
96C2×C4×Dic61—22no—
97C2×C4×Dic61—22no—
98C2×C4×Dic61—22no—
99C2×C4×Dic61—22no—
100C2×C4×Dic61—22no—
101C2×C4×Dic61—22no—
102C2×C4×Dic61—22no—
103C2×C4×Dic61—22no—
104C2×C4×Dic61—22no—
105C2×C4×Dic61—22no—
106C2×C4×Dic61C2×C414yes—
107C2×C4×Dic61C2×C414yes—
108C2×C4×Dic61D414yes—
109C2×C4×Dic61D414yes—
110#14519684—22no—
111#14519684—22no—
112#14519684—22no—
113#14519684—22no—
114#14519684—22no—
115#14519684—22no—
116#14519684—22no—
117#14519684—22no—
118#14519684—22no—
119#14519684—22no—
120#14519684—22no—
121#14519684—22no—
122#14519684—22no—
123#14519684C2×C414yes—
124C23×C4×C61C2311yescharacteristic
125C23×C4×C61C2311yescharacteristic
126C23×C4×C61C2311yescharacteristic
127C23×C4×C61C2311yescharacteristic
128C23×C4×C61C2311yescharacteristic
129C23×C4×C61C2311yescharacteristic
130C23×C4×C61C2311yescharacteristic
131C2×C4⋊C4×C61—22no—
132C2×C4⋊C4×C61—22no—
133C2×C4⋊C4×C61—22no—
134#95×C61—22no—
135#95×C61—22no—
136#95×C61—22no—
137#95×C61—22no—
138#95×C61—22no—
139#95×C61C2×C414yes—
140C24×C61C2411yescharacteristic
141C23×D61—21no—
142C23×D61—21no—
143C23×D61—21no—
144C23×D61—21no—
145C23×D61—21no—
146C23×D61—21no—
147C23×D61—21no—
148C23×D61—21no—
149C23×D61—21no—
150C23×D61—21no—
151C23×D61—21no—
152C23×D61—21no—
153C23×D61C22×C412yes—
154C23×D61#4112yes—
155C23×D61#4112yes—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61C22×C412yes—
197C22×C4×C61C22×C412yes—
198C22×C4×C61C22×C412yes—
199C22×C4×C61C2×D412yes—
200C22×C4×C61C2×D412yes—
201C22×C4×C61#4112yes—
202C22×C4×C61#4112yes—
203C22×C4×C61#4112yes—
204C22×C4×C61#4112yes—
205C22×Dic61—21no—
206C22×Dic61—21no—
207C22×Dic61—21no—
208C22×Dic61—21no—
209C22×Dic61—21no—
210C22×Dic61—21no—
211C22×Dic61—21no—
212C22×Dic61—21no—
213C22×Dic61—21no—
214C22×Dic61—21no—
215C22×Dic61—21no—
216C22×Dic61—21no—
217C22×Dic61—21no—
218C22×Dic61—21no—
219C22×Dic61—21no—
220C22×Dic61—21no—
221C22×Dic61—21no—
222C22×Dic61—21no—
223C22×Dic61—21no—
224C22×Dic61—21no—
225C22×Dic61—21no—
226C22×Dic61—21no—
227C22×Dic61—21no—
228C22×Dic61—21no—
229C22×Dic61—21no—
230C22×Dic61—21no—
231C22×Dic61—21no—
232C22×Dic61—21no—
233C22×Dic61—21no—
234C22×Dic61—21no—
235C22×Dic61—21no—
236C22×Dic61—21no—
237C22×Dic61—21no—
238C22×Dic61—21no—
239C22×Dic61—21no—
240C22×Dic61—21no—
241C22×Dic61C22×C412yes—
242C22×Dic61C22×C412yes—
243C22×Dic61C22×C412yes—
244C22×Dic61C2×D412yes—
245C22×Dic61C2×D412yes—
246C22×Dic61C2×D412yes—
247C22×Dic61C2×D412yes—
248C22×Dic61#4112yes—
249C22×Dic61#4112yes—
250C22×Dic61#4112yes—
251C22×Dic61#4112yes—
252C22×Dic61#4112yes—
253C22×Dic61#4112yes—
254C2×C4×D61—28no—
255C2×C4×D61—28no—
256C2×C4×D61—28no—
257C2×C4×D61—44no—
258C2×C4×D61—44no—
259C2×C4×D61—44no—
260C2×C4×D61—44no—
261C4⋊C4×C61—28no—
262#11758198—28no—
263#11758198—28no—
264#11758198—28no—
265#11758198—28no—
266#11758198—28no—
267#11758198—28no—
268C4⋊Dic61—28no—
269C4×Dic61—28no—
270C4×Dic61—28no—
271C4×Dic61—28no—
272C4×Dic61—28no—
273C4×Dic61—44no—
274C4×Dic61—44no—
275C23×C61C23×C411yescharacteristic
276C23×C61C22×D411yescharacteristic
277C23×C61C22×D411yescharacteristic
278C23×C61C2×#4111yescharacteristic
279C23×C61C2×#4111yescharacteristic
280C23×C61C2×#4111yescharacteristic
281C23×C61C2×#4111yescharacteristic
282C23×C61C2×#4111yescharacteristic
283C23×C61C2×#4111yescharacteristic
284C23×C61C2×#4111yescharacteristic
285C23×C61C2×#4111yescharacteristic
286C23×C61C2×#4111yescharacteristic
287C23×C61C2×#4111yescharacteristic
288C23×C61C2×#4111yescharacteristic
289C23×C61C2×#4111yescharacteristic
290C22×D61—22no—
291C22×D61—22no—
292C22×D61—22no—
293C22×D61—22no—
294C22×D61—22no—
295C22×D61—22no—
296C22×D61—22no—
297C22×D61—22no—
298C22×D61—22no—
299C22×D61—22no—
300C22×D61—22no—
301C22×D61—22no—
302C22×D61—22no—
303C22×D61—22no—
304C22×D61—22no—
305C22×D61—22no—
306C22×D61—22no—
307C22×D61—22no—
308C22×D61—41no—
309C22×D61—41no—
310C22×D61—41no—
311C22×D61—41no—
312C22×D61—41no—
313C22×D61—41no—
314C22×D61—41no—
315C22×D61—41no—
316C22×D61—41no—
317C22×D61—41no—
318C22×D61—41no—
319C22×D61—41no—
320C22×D61—41no—
321C22×D61—41no—
322C22×D61—41no—
323C22×D61—41no—
324C22×D61#11714yes—
325C2×C4×C61—22no—
326C2×C4×C61—22no—
327C2×C4×C61—22no—
328C2×C4×C61—22no—
329C2×C4×C61—22no—
330C2×C4×C61—22no—
331C2×C4×C61—22no—
332C2×C4×C61—22no—
333C2×C4×C61—22no—
334C2×C4×C61—22no—
335C2×C4×C61—22no—
336C2×C4×C61—22no—
337C2×C4×C61—22no—
338C2×C4×C61—22no—
339C2×C4×C61—22no—
340C2×C4×C61—22no—
341C2×C4×C61—22no—
342C2×C4×C61—22no—
343C2×C4×C61—22no—
344C2×C4×C61—22no—
345C2×C4×C61—22no—
346C2×C4×C61—22no—
347C2×C4×C61—22no—
348C2×C4×C61—22no—
349C2×C4×C61—41no—
350C2×C4×C61—41no—
351C2×C4×C61—41no—
352C2×C4×C61—41no—
353C2×C4×C61—41no—
354C2×C4×C61—41no—
355C2×C4×C61—41no—
356C2×C4×C61—41no—
357C2×C4×C61—41no—
358C2×C4×C61—41no—
359C2×C4×C61—41no—
360C2×C4×C61—41no—
361C2×C4×C61—41no—
362C2×C4×C61—41no—
363C2×C4×C61—41no—
364C2×C4×C61—41no—
365C2×C4×C61—41no—
366C2×C4×C61—41no—
367C2×C4×C61—41no—
368C2×C4×C61—41no—
369C2×C4×C61—41no—
370C2×C4×C61—41no—
371C2×C4×C61—41no—
372C2×C4×C61—41no—
373C2×C4×C61#11714yes—
374C2×Dic61—22no—
375C2×Dic61—22no—
376C2×Dic61—22no—
377C2×Dic61—22no—
378C2×Dic61—22no—
379C2×Dic61—22no—
380C2×Dic61—22no—
381C2×Dic61—22no—
382C2×Dic61—22no—
383C2×Dic61—22no—
384C2×Dic61—22no—
385C2×Dic61—22no—
386C2×Dic61—22no—
387C2×Dic61—22no—
388C2×Dic61—22no—
389C2×Dic61—22no—
390C2×Dic61—22no—
391C2×Dic61—22no—
392C2×Dic61—41no—
393C2×Dic61—41no—
394C2×Dic61—41no—
395C2×Dic61—41no—
396C2×Dic61—41no—
397C2×Dic61—41no—
398C2×Dic61—41no—
399C2×Dic61—41no—
400C2×Dic61—41no—
401C2×Dic61—41no—
402C2×Dic61—41no—
403C2×Dic61—41no—
404C2×Dic61—41no—
405C2×Dic61—41no—
406C2×Dic61—41no—
407C2×Dic61—41no—
408C2×Dic61—41no—
409C2×Dic61—41no—
410C2×Dic61—41no—
411C2×Dic61—41no—
412C2×Dic61—41no—
413C2×Dic61—41no—
414C2×Dic61—41no—
415C2×Dic61—41no—
416C2×Dic61#11714yes—
417C2×Dic61C4×D414yes—
418C2×Dic61C4×D414yes—
419C2×Dic61#12114yes—
420C2×Dic61#12314yes—
421C2×Dic61#12414yes—
422C2×Dic61#12614yes—
423C4×D61—416no—
424#13842—611nomaximal, Sylow
425C22×C61C2×#11711yescharacteristic
426C22×C61C2×#11711yescharacteristic
427C22×C61C2×#11711yescharacteristic
428C22×C61C2×C4×D411yescharacteristic
429C22×C61C2×C4×D411yescharacteristic
430C22×C61C4×#4111yescharacteristic
431C22×C61C4×#4111yescharacteristic
432C22×C61C2×#12111yescharacteristic
433C22×C61C2×#12311yescharacteristic
434C22×C61#52511yescharacteristic
435C22×C61#52511yescharacteristic
436C22×C61#52511yescharacteristic
437C22×C61#52511yescharacteristic
438C22×C61#52511yescharacteristic
439C22×C61#52511yescharacteristic
440C22×C61C2×#12411yescharacteristic
441C22×C61C2×#12611yescharacteristic
442C22×C61#52911yescharacteristic
443C22×C61#52911yescharacteristic
444C22×C61#52911yescharacteristic
445C22×C61#52911yescharacteristic
446C22×C61#52911yescharacteristic
447C22×C61#52911yescharacteristic
448C22×C61#52911yescharacteristic
449C22×C61#52911yescharacteristic
450C22×C61#52911yescharacteristic
451C22×C61#52911yescharacteristic
452C22×C61#52911yescharacteristic
453C22×C61#52911yescharacteristic
454C22×C61#52911yescharacteristic
455C22×C61#52911yescharacteristic
456C22×C61#52911yescharacteristic
457C22×C61#52911yescharacteristic
458C22×C61#53211yescharacteristic
459C22×C61#53211yescharacteristic
460C2×D61—24no—
461C2×D61—24no—
462C2×D61—24no—
463C2×D61—42no—
464C2×D61—42no—
465C2×D61—42no—
466C2×D61—42no—
467C2×D61—42no—
468C2×D61—42no—
469C2×D61—42no—
470C2×D61—42no—
471C2×D61—42no—
472C2×D61—42no—
473C2×D61—42no—
474C2×D61—42no—
475C4×C61—24no—
476C4×C61—42no—
477C4×C61—42no—
478C4×C61—42no—
479C4×C61—42no—
480C4×C61—42no—
481C4×C61—42no—
482Dic61—42no—
483Dic61—42no—
484Dic61—42no—
485Dic61—42no—
486Dic61—42no—
487Dic61—42no—
488Dic61#38818yes—
489C2×C4×C4⋊C4—611no—
490C2×C4×C22⋊C4—611no—
491C2×C4×C22⋊C4—611no—
492C2×C4×C22⋊C4—611no—
493C2×#376—611no—
494#1443—611no—
495#1443—611no—
496#1442—611no—
497#1442D6111yescharacteristic, complemented
498#1440—611no—
499#1440—611no—
500#1439—611no—
501#1439—611no—
502C4×#95—611no—
503C4×#95—611no—
504C2×C61#228311yescharacteristic
505C2×C61C2×#38811yescharacteristic
506C2×C61#229011yescharacteristic
507C2×C61#229011yescharacteristic
508C2×C61#229011yescharacteristic
509C2×C61#229311yescharacteristic
510C2×C61#229811yescharacteristic
511C2×C61#239211yescharacteristic
512C2×C61#239211yescharacteristic
513C2×C61#239511yescharacteristic
514C2×C61#239511yescharacteristic
515C2×C61#239811yescharacteristic
516C2×C61#239811yescharacteristic
517C2×C61#240111yescharacteristic
518C2×C61#240111yescharacteristic
519D61—44no—
520C24×C4—611no—
521C22×C4⋊C4—611no—
522C22×C4⋊C4C2×D6111yescharacteristic
523C22×C22⋊C4—611no—
524C22×C22⋊C4—611no—
525C22×C22⋊C4—611no—
526C22×C22⋊C4—611no—
527C22×C22⋊C4—611no—
528C22×C22⋊C4—611no—
529C22×C42—611no—
530C22×C42—611no—
531C22×C42—611no—
532C22×C42—611no—
533C22×C42—611no—
534C22×C42—611no—
535C4×C4⋊C4—1224no—
536C4×C22⋊C4—618no—
537C4×C22⋊C4—1224no—
538C4×C22⋊C4—1224no—
539#376—1224no—
540C2×#95—611no—
541C2×#95—611no—
542C2×#95—611no—
543C2×#95—611no—
544C2×#95—611no—
545C2×#95—611no—
546C2×#95—611no—
547C2×#95—611no—
548C2×#95—611no—
549C2×#95—611no—
550C2×#95—611no—
551C2×#95—611no—
552C2×#95—611no—
553C2×#95—611no—
554C2×#95C2×D6111yescharacteristic
555C2×#95C2×D6111yescharacteristic
556C2×#95C2×D6111yescharacteristic
557C2×#95C2×D6111yescharacteristic
558C2×#95C2×D6111yescharacteristic
559C2×#95C2×D6111yescharacteristic
560C61#1384211yescharacteristic, complemented, Sylow
561C25—611no—
562C23×C4—611no—
563C23×C4—611no—
564C23×C4—611no—
565C23×C4—611no—
566C23×C4—611no—
567C23×C4—611no—
568C23×C4—611no—
569C23×C4—614no—
570C23×C4—1222no—
571C23×C4—1222no—
572C23×C4—1222no—
573C23×C4—1222no—
574C23×C4—1222no—
575C23×C4—1222no—
576C23×C4C22×D6111yescharacteristic
577C23×C4C22×D6111yescharacteristic
578C23×C4C22×D6111yescharacteristic
579C23×C4C22×D6111yescharacteristic
580C23×C4C22×D6111yescharacteristic
581C23×C4C22×D6111yescharacteristic
582C23×C4C22×D6111yescharacteristic
583C2×C4⋊C4—22no—
584C2×C4⋊C4—22no—
585C2×C4⋊C4—22no—
586C2×C4⋊C4—1222no—
587C2×C4⋊C4—1222no—
588C2×C4⋊C4—1222no—
589C2×C22⋊C4—614no—
590C2×C22⋊C4—614no—
591C2×C22⋊C4—1222no—
592C2×C22⋊C4—1222no—
593C2×C22⋊C4—1222no—
594C2×C22⋊C4—1222no—
595C2×C22⋊C4—1222no—
596C2×C22⋊C4—1222no—
597C2×C22⋊C4—1222no—
598C2×C22⋊C4—1222no—
599C2×C22⋊C4—1222no—
600C2×C22⋊C4—1222no—
601C2×C22⋊C4—1222no—
602C2×C22⋊C4—1222no—
603C2×C22⋊C4—1222no—
604C2×C22⋊C4—1222no—
605C2×C22⋊C4—1222no—
606C2×C22⋊C4—1222no—
607C2×C42—614no—
608C2×C42—614no—
609C2×C42—614no—
610C2×C42—614no—
611C2×C42—1222no—
612C2×C42—1222no—
613C2×C42—1222no—
614C2×C42—1222no—
615C2×C42—1222no—
616C2×C42—1222no—
617C2×C42—1222no—
618C2×C42—1222no—
619C2×C42—1222no—
620C2×C42—1222no—
621C2×C42—1222no—
622C2×C42—1222no—
623C2×C42—1222no—
624C2×C42—1222no—
625#95—22no—
626#95—22no—
627#95—22no—
628#95—22no—
629#95—22no—
630#95—614no—
631#95—1222no—
632#95—1222no—
633#95—1222no—
634#95—1222no—
635#95—1222no—
636#95—1222no—
637#95—1222no—
638#95—1222no—
639#95—1222no—
640#95—1222no—
641#95—1222no—
642#95—1222no—
643#95—1222no—
644#95C4×D6114yes—
645C24—612no—
646C24—612no—
647C24—612no—
648C24—1221no—
649C24—1221no—
650C24—1221no—
651C24—1221no—
652C24—1221no—
653C24—1221no—
654C24—1221no—
655C24—1221no—
656C24—1221no—
657C24—1221no—
658C24—1221no—
659C24—1221no—
660C24C23×D6111yescharacteristic
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—612no—
702C22×C4—612no—
703C22×C4—612no—
704C22×C4—612no—
705C22×C4—612no—
706C22×C4—612no—
707C22×C4—612no—
708C22×C4—612no—
709C22×C4—612no—
710C22×C4—612no—
711C22×C4—612no—
712C22×C4—612no—
713C22×C4—612no—
714C22×C4—1228no—
715C22×C4—1228no—
716C22×C4—1228no—
717C22×C4—1221no—
718C22×C4—1221no—
719C22×C4—1221no—
720C22×C4—1221no—
721C22×C4—1221no—
722C22×C4—1221no—
723C22×C4—1221no—
724C22×C4—1221no—
725C22×C4—1221no—
726C22×C4—1221no—
727C22×C4—1221no—
728C22×C4—1221no—
729C22×C4—1221no—
730C22×C4—1221no—
731C22×C4—1221no—
732C22×C4—1221no—
733C22×C4—1221no—
734C22×C4—1221no—
735C22×C4—1221no—
736C22×C4—1221no—
737C22×C4—1221no—
738C22×C4—1221no—
739C22×C4—1221no—
740C22×C4—1221no—
741C22×C4—1221no—
742C22×C4—1221no—
743C22×C4—1221no—
744C22×C4—1221no—
745C22×C4—1221no—
746C22×C4—1221no—
747C22×C4—1221no—
748C22×C4—1221no—
749C22×C4—1221no—
750C22×C4—1221no—
751C22×C4—1221no—
752C22×C4—1221no—
753C22×C4—2444no—
754C22×C4—2444no—
755C22×C4—2444no—
756C22×C4—2444no—
757C22×C4C2×C4×D6112yes—
758C22×C4C2×C4×D6112yes—
759C22×C4C2×C4×D6112yes—
760C22×C4D4×D6112yes—
761C22×C4D4×D6112yes—
762C22×C4#1175822412yes—
763C22×C4#1175822412yes—
764C22×C4#1175822612yes—
765C22×C4#1175822612yes—
766C4⋊C4—28no—
767C4⋊C4—1228no—
768C22⋊C4—1228no—
769C22⋊C4—1228no—
770C22⋊C4—1228no—
771C22⋊C4—1228no—
772C22⋊C4—1228no—
773C22⋊C4—1228no—
774C42—1228no—
775C42—1228no—
776C42—1228no—
777C42—1228no—
778C42—2444no—
779C42—2444no—
780C23—614no—
781C23—1222no—
782C23—1222no—
783C23—1222no—
784C23—1222no—
785C23—1222no—
786C23—1222no—
787C23—1222no—
788C23—1222no—
789C23—1222no—
790C23—1222no—
791C23—1222no—
792C23—1222no—
793C23—1222no—
794C23—1222no—
795C23—1222no—
796C23—1222no—
797C23—1222no—
798C23—1222no—
799C23—2441no—
800C23—2441no—
801C23—2441no—
802C23—2441no—
803C23—2441no—
804C23—2441no—
805C23—2441no—
806C23—2441no—
807C23—2441no—
808C23—2441no—
809C23—2441no—
810C23—2441no—
811C23—2441no—
812C23—2441no—
813C23—2441no—
814C23—2441no—
815C23C22×C4×D6111yescharacteristic
816C23C2×D4×D6111yescharacteristic
817C23C2×D4×D6111yescharacteristic
818C23#41×D6111yescharacteristic
819C23#41×D6111yescharacteristic
820C23#41×D6111yescharacteristic
821C23#41×D6111yescharacteristic
822C23#41×D6111yescharacteristic
823C23#41×D6111yescharacteristic
824C23#41×D6111yescharacteristic
825C23#41×D6111yescharacteristic
826C23C2×#1175822411yescharacteristic
827C23C2×#1175822411yescharacteristic
828C23C2×#1175822611yescharacteristic
829C23C2×#1175822611yescharacteristic
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—614no—
879C2×C4—614no—
880C2×C4—614no—
881C2×C4—614no—
882C2×C4—614no—
883C2×C4—614no—
884C2×C4—614no—
885C2×C4—1222no—
886C2×C4—1222no—
887C2×C4—1222no—
888C2×C4—1222no—
889C2×C4—1222no—
890C2×C4—1222no—
891C2×C4—1222no—
892C2×C4—1222no—
893C2×C4—1222no—
894C2×C4—1222no—
895C2×C4—1222no—
896C2×C4—1222no—
897C2×C4—1222no—
898C2×C4—1222no—
899C2×C4—1222no—
900C2×C4—1222no—
901C2×C4—1222no—
902C2×C4—1222no—
903C2×C4—24416no—
904C2×C4—2441no—
905C2×C4—2441no—
906C2×C4—2441no—
907C2×C4—2441no—
908C2×C4—2441no—
909C2×C4—2441no—
910C2×C4—2441no—
911C2×C4—2441no—
912C2×C4—2441no—
913C2×C4—2441no—
914C2×C4—2441no—
915C2×C4—2441no—
916C2×C4—2441no—
917C2×C4—2441no—
918C2×C4—2441no—
919C2×C4—2441no—
920C2×C4—2441no—
921C2×C4—2441no—
922C2×C4—2441no—
923C2×C4—2441no—
924C2×C4—2441no—
925C2×C4—2441no—
926C2×C4—2441no—
927C2×C4—2441no—
928C2×C4#1451973514yes—
929C22—1224no—
930C22—1224no—
931C22—1224no—
932C22—2442no—
933C22—2442no—
934C22—2442no—
935C22—2442no—
936C22—2442no—
937C22—2442no—
938C22—2442no—
939C22—2442no—
940C22—2442no—
941C22—2442no—
942C22—2442no—
943C22—2442no—
944C22#117×D6111yescharacteristic
945C22#117×D6111yescharacteristic
946C22C2×#1451973511yescharacteristic
947C22C4×D4×D6111yescharacteristic
948C22C4×D4×D6111yescharacteristic
949C22C4×#1175822411yescharacteristic
950C22C4×#1175822611yescharacteristic
951C22#121×D6111yescharacteristic
952C22#123×D6111yescharacteristic
953C22#1684026811yescharacteristic
954C22#1684027011yescharacteristic
955C22#1684027011yescharacteristic
956C22#1684027211yescharacteristic
957C22#1684027511yescharacteristic
958C22#1684027511yescharacteristic
959C22#124×D6111yescharacteristic
960C22#126×D6111yescharacteristic
961C22#1684028911yescharacteristic
962C22#1684028911yescharacteristic
963C22#1684029111yescharacteristic
964C22#1684029111yescharacteristic
965C22#1684029111yescharacteristic
966C22#1684029511yescharacteristic
967C22#1684029511yescharacteristic
968C22#1684029511yescharacteristic
969C22#1684029711yescharacteristic
970C22#1684029711yescharacteristic
971C22#1684029711yescharacteristic
972C22#1684029711yescharacteristic
973C22#1684029711yescharacteristic
974C22#1684029811yescharacteristic
975C22#1684029811yescharacteristic
976C22#1684029811yescharacteristic
977C22#1684030711yescharacteristic
978C22#1684031311yescharacteristic
979C4—24no—
980C4—42no—
981C4—42no—
982C4—42no—
983C4—42no—
984C4—42no—
985C4—42no—
986C4—618no—
987C4—2442no—
988C4—2442no—
989C4—2442no—
990C4—2442no—
991C4—2442no—
992C4—2442no—
993C2—2444no—
994C2#2144821211yescharacteristic
995C2#388×D6111yescharacteristic
996C2#2144825511yescharacteristic
997C2#2144825711yescharacteristic
998C2#2144826111yescharacteristic
999C2#2144827711yescharacteristic
1000C2#2144831111yescharacteristic
1001C2#2144906011yescharacteristic
1002C2#2144906211yescharacteristic
1003C2#2144907711yescharacteristic
1004C2#2144908311yescharacteristic
1005C2#2144910111yescharacteristic
1006C2#2144910811yescharacteristic
1007C2#2144911811yescharacteristic
1008C2#2144911811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1442C2
socle, cosocleC24×C61C24
prime radicalC24×D61C23
hypercenter#1442D61
hypocenterC61#13842
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊C4×Dic61C2semidirect
5. C2×#16839607C2semidirect
6. #21444080C2semidirect
7. #21444079C2semidirect
8. #21444076C2semidirect
13. #95×Dic61C2semidirect
14. #95×Dic61C2semidirect
15. C61×#1442C2semidirect
33. #16839609C4semidirect
497. #1442D61semidirect
560. C61#13842semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×Dic612
C2×#168396092
C2×#168396072
#214440802
#214440792
#214440762
#214440672
#214440652
#214440612
#95×Dic612
C61×#14422
#1384261