Finite Group Databasebeta

← #29602890

Subgroups — #29602890

Order 15616.

2558 conjugacy classes of subgroups.

The subgroup lattice has 1230 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519737C211yesmaximal, characteristic
2C2×#16839662C211yesmaximal, characteristic
3C2×#16839662C211yesmaximal, characteristic
4C2×#16839659C211yesmaximal, characteristic, complemented
5C2×#16839637C211yesmaximal, characteristic, complemented
6C2×#16839636C211yesmaximal, characteristic, complemented
7C2×#16839634C211yesmaximal, characteristic, complemented
8C2×#16839633C211yesmaximal, characteristic, complemented
9C2×#16839631C211yesmaximal, characteristic, complemented
10#21444065C211yesmaximal, characteristic, complemented
11#21444063C211yesmaximal, characteristic, complemented
12#21444062C211yesmaximal, characteristic, complemented
13#21444047C211yesmaximal, characteristic, complemented
14#95×Dic61C211yesmaximal, characteristic, complemented
15C61×#1439C211yesmaximal, characteristic, complemented
16C23×C22⋊D61C2211yescharacteristic
17C24×Dic61C2211yescharacteristic
18C23×C4×D61C2211yescharacteristic
19C2×#14519737—24no—
20C2×#14519737—24no—
21C2×#14519737—24no—
22C22×C4⋊Dic61C2211yescharacteristic
23C22×C4⋊Dic61C2211yescharacteristic
24C22×#11758196C2211yescharacteristic
25C22×#11758196C2211yescharacteristic
26C22×#11758196C2211yescharacteristic
27C22×#11758196C2211yescharacteristic
28C22×#11758196C2211yescharacteristic
29C22×#11758196C2211yescharacteristic
30C22×C22⋊Dic61C2211yescharacteristic
31C22×C22⋊Dic61C2211yescharacteristic
32C22×#11758198C2211yescharacteristic
33C22×#11758198C2211yescharacteristic
34C22×#11758198C2211yescharacteristic
35C22×#11758198C2211yescharacteristic
36C22×#11758198C2211yescharacteristic
37C22×C4×Dic61C2211yescharacteristic
38C22×C4×Dic61C2211yescharacteristic
39C22×C4×Dic61C2211yescharacteristic
40#16839662—24no—
41#16839662C418yescomplemented
42#16839659—24no—
43#16839637—24no—
44#16839636—24no—
45#16839634—24no—
46#16839633—24no—
47#16839631—24no—
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50C2×#14519684C2211yescharacteristic
51C2×#14519684C2211yescharacteristic
52C2×#14519684C2211yescharacteristic
53C2×#14519684C2211yescharacteristic
54C2×#14519684C2211yescharacteristic
55C22×C4⋊C4×C61C2211yescharacteristic
56C22×C22⋊C4×C61C2211yescharacteristic
57C22×C22⋊C4×C61C2211yescharacteristic
58C22×C22⋊C4×C61C2211yescharacteristic
59C2×#95×C61C2211yescharacteristic
60C2×#95×C61C2211yescharacteristic
61C2×#95×C61C2211yescharacteristic
62C24×D61C2311yescharacteristic
63C22×C22⋊D61—22no—
64C22×C22⋊D61—22no—
65C22×C22⋊D61—22no—
66C22×C22⋊D61—22no—
67C22×C22⋊D61C2×C414yes—
68C22×C22⋊D61D414yes—
69C22×C22⋊D61Q814yes—
70C23×Dic61—22no—
71C23×Dic61—22no—
72C23×Dic61—22no—
73C23×Dic61—22no—
74C23×Dic61—22no—
75C23×Dic61—41no—
76C23×Dic61—41no—
77C23×Dic61C2311yescharacteristic
78C23×Dic61C2311yescharacteristic
79C23×Dic61C2311yescharacteristic
80C23×Dic61C2311yescharacteristic
81C23×Dic61C2311yescharacteristic
82C23×Dic61C2311yescharacteristic
83C23×Dic61C2311yescharacteristic
84C22×C4×D61—22no—
85C22×C4×D61—22no—
86C22×C4×D61—22no—
87C22×C4×D61—22no—
88C22×C4×D61—22no—
89C22×C4×D61—41no—
90C22×C4×D61—41no—
91#14519737—232no—
92C2×C4⋊Dic61—22no—
93C2×C4⋊Dic61—22no—
94C2×C4⋊Dic61—22no—
95C2×C4⋊Dic61—22no—
96C2×C4⋊Dic61—22no—
97C2×C4⋊Dic61—41no—
98C2×#11758196—22no—
99C2×#11758196—22no—
100C2×#11758196—22no—
101C2×#11758196—22no—
102C2×#11758196—22no—
103C2×#11758196—22no—
104C2×#11758196—22no—
105C2×#11758196—22no—
106C2×#11758196—22no—
107C2×#11758196—22no—
108C2×#11758196—22no—
109C2×#11758196—22no—
110C2×#11758196—22no—
111C2×#11758196—22no—
112C2×#11758196—41no—
113C2×#11758196—41no—
114C2×#11758196C2×C414yescomplemented
115C2×#11758196D414yes—
116C2×C22⋊Dic61—22no—
117C2×C22⋊Dic61—22no—
118C2×C22⋊Dic61—22no—
119C2×C22⋊Dic61—22no—
120C2×C22⋊Dic61—41no—
121C2×C22⋊Dic61C2×C414yescomplemented
122C2×#11758198—22no—
123C2×#11758198—22no—
124C2×#11758198—22no—
125C2×#11758198—22no—
126C2×#11758198—22no—
127C2×#11758198—22no—
128C2×#11758198—22no—
129C2×#11758198—22no—
130C2×#11758198—22no—
131C2×#11758198—22no—
132C2×#11758198—22no—
133C2×#11758198—41no—
134C2×#11758198—41no—
135C2×#11758198C2×C414yescomplemented
136C2×#11758198C2×C414yescomplemented
137C2×C4×Dic61—22no—
138C2×C4×Dic61—22no—
139C2×C4×Dic61—22no—
140C2×C4×Dic61—22no—
141C2×C4×Dic61—22no—
142C2×C4×Dic61—22no—
143C2×C4×Dic61—22no—
144C2×C4×Dic61C2×C414yescomplemented
145C2×C4×Dic61D414yes—
146#14519684—22no—
147#14519684—22no—
148#14519684—22no—
149#14519684—22no—
150#14519684—22no—
151#14519684D414yescomplemented
152#14519684D414yescomplemented
153C25×C61C2311yescharacteristic
154C23×C4×C61C2311yescharacteristic
155C23×C4×C61C2311yescharacteristic
156C23×C4×C61C2311yescharacteristic
157C23×C4×C61C2311yescharacteristic
158C23×C4×C61C2311yescharacteristic
159C23×C4×C61C2311yescharacteristic
160C2×C4⋊C4×C61—22no—
161C2×C4⋊C4×C61—22no—
162C2×C4⋊C4×C61—41no—
163C2×C22⋊C4×C61—22no—
164C2×C22⋊C4×C61—22no—
165C2×C22⋊C4×C61—22no—
166C2×C22⋊C4×C61—22no—
167C2×C22⋊C4×C61—22no—
168C2×C22⋊C4×C61—22no—
169C2×C22⋊C4×C61—22no—
170C2×C22⋊C4×C61—41no—
171C2×C22⋊C4×C61C2×C414yescomplemented
172#95×C61—22no—
173#95×C61—22no—
174#95×C61—22no—
175C24×C61—21no—
176C24×C61—21no—
177C24×C61—21no—
178C24×C61—21no—
179C24×C61—21no—
180C24×C61—21no—
181C24×C61—21no—
182C24×C61—21no—
183C24×C61—21no—
184C24×C61—21no—
185C24×C61—21no—
186C24×C61—21no—
187C24×C61C22×C412yes—
188C24×C61C2×D412yes—
189C24×C61C2×Q812yes—
190C24×C61C2411yescharacteristic
191C23×D61—21no—
192C23×D61—21no—
193C23×D61—21no—
194C23×D61—21no—
195C23×D61—21no—
196C23×D61—21no—
197C23×D61—21no—
198C23×D61—21no—
199C23×D61—21no—
200C23×D61—21no—
201C23×D61—21no—
202C23×D61—21no—
203C23×D61C22×C412yes—
204C23×D61C2×D412yes—
205C23×D61C2×Q812yes—
206C22×C4×C61—21no—
207C22×C4×C61—21no—
208C22×C4×C61—21no—
209C22×C4×C61—21no—
210C22×C4×C61—21no—
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61—21no—
215C22×C4×C61—21no—
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61—21no—
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61—21no—
222C22×C4×C61—21no—
223C22×C4×C61—21no—
224C22×C4×C61—21no—
225C22×C4×C61—21no—
226C22×C4×C61—21no—
227C22×C4×C61—21no—
228C22×C4×C61—21no—
229C22×C4×C61—21no—
230C22×C4×C61—21no—
231C22×C4×C61—21no—
232C22×C4×C61—21no—
233C22×C4×C61—21no—
234C22×C4×C61—21no—
235C22×C4×C61—21no—
236C22×C4×C61—21no—
237C22×C4×C61—21no—
238C22×C4×C61—21no—
239C22×C4×C61—21no—
240C22×C4×C61—21no—
241C22×C4×C61C22×C412yes—
242C22×C4×C61C22×C412yes—
243C22×C4×C61C2×D412yes—
244C22×C4×C61C2×D412yes—
245C22×C4×C61C2×D412yes—
246C22×C4×C61C2×D412yes—
247C22×C4×C61#4112yes—
248C2×C22⋊D61—28no—
249C2×C22⋊D61—28no—
250C2×C22⋊D61—28no—
251C2×C22⋊D61—28no—
252C2×C22⋊D61—28no—
253C2×C22⋊D61—28no—
254C2×C22⋊D61C4⋊C4116yescomplemented
255C22×Dic61—21no—
256C22×Dic61—21no—
257C22×Dic61—21no—
258C22×Dic61—21no—
259C22×Dic61—21no—
260C22×Dic61—21no—
261C22×Dic61—21no—
262C22×Dic61—21no—
263C22×Dic61—28no—
264C22×Dic61—21no—
265C22×Dic61—21no—
266C22×Dic61—21no—
267C22×Dic61—21no—
268C22×Dic61—21no—
269C22×Dic61—21no—
270C22×Dic61—21no—
271C22×Dic61—21no—
272C22×Dic61—21no—
273C22×Dic61—21no—
274C22×Dic61—21no—
275C22×Dic61—21no—
276C22×Dic61—21no—
277C22×Dic61—21no—
278C22×Dic61—21no—
279C22×Dic61—21no—
280C22×Dic61—21no—
281C22×Dic61—21no—
282C22×Dic61—21no—
283C22×Dic61—21no—
284C22×Dic61—21no—
285C22×Dic61—21no—
286C22×Dic61—21no—
287C22×Dic61—21no—
288C22×Dic61—21no—
289C22×Dic61—44no—
290C22×Dic61—44no—
291C22×Dic61—44no—
292C22×Dic61—44no—
293C22×Dic61—44no—
294C22×Dic61—44no—
295C22×Dic61C22×C412yes—
296C22×Dic61C22×C412yes—
297C22×Dic61C22×C412yes—
298C22×Dic61C2×D412yes—
299C22×Dic61C2×D412yes—
300C22×Dic61C2×D412yes—
301C22×Dic61C2×D412yes—
302C22×Dic61C2×D412yes—
303C22×Dic61C2×D412yes—
304C22×Dic61C2×D412yes—
305C22×Dic61C2×D412yes—
306C22×Dic61C2×D412yes—
307C22×Dic61C2×Q812yes—
308C22×Dic61#4112yes—
309C22×Dic61#4112yes—
310C22×Dic61#4112yes—
311C2×C4×D61—28no—
312C2×C4×D61—44no—
313C2×C4×D61—44no—
314C2×C4×D61—44no—
315C2×C4×D61—44no—
316C2×C4×D61—44no—
317C2×C4×D61—44no—
318C4⋊C4×C61—44no—
319C22⋊C4×C61—28no—
320C22⋊C4×C61—28no—
321C22⋊C4×C61—44no—
322C22⋊Dic61—28no—
323C22⋊Dic61—44no—
324#11758198—28no—
325#11758198—28no—
326#11758198—28no—
327#11758198—44no—
328#11758198—44no—
329C4⋊Dic61—44no—
330C4⋊Dic61—44no—
331#11758196—28no—
332#11758196—28no—
333#11758196—44no—
334#11758196—44no—
335#11758196—44no—
336#11758196—44no—
337C4×Dic61—28no—
338C4×Dic61—28no—
339C4×Dic61—44no—
340C23×C61—22no—
341C23×C61—22no—
342C23×C61—22no—
343C23×C61—22no—
344C23×C61—22no—
345C23×C61—22no—
346C23×C61—22no—
347C23×C61—22no—
348C23×C61—22no—
349C23×C61—22no—
350C23×C61—22no—
351C23×C61—22no—
352C23×C61—22no—
353C23×C61—22no—
354C23×C61—22no—
355C23×C61—22no—
356C23×C61—22no—
357C23×C61—22no—
358C23×C61—41no—
359C23×C61—41no—
360C23×C61—41no—
361C23×C61—41no—
362C23×C61—41no—
363C23×C61—41no—
364C23×C61—41no—
365C23×C61—41no—
366C23×C61—41no—
367C23×C61—41no—
368C23×C61—41no—
369C23×C61—41no—
370C23×C61—41no—
371C23×C61—41no—
372C23×C61—41no—
373C23×C61—41no—
374C23×C61C2×C4⋊C414yes—
375C23×C61C23×C411yescharacteristic
376C23×C61C22×D411yescharacteristic
377C23×C61C22×D411yescharacteristic
378C23×C61C22×D411yescharacteristic
379C23×C61C22×D411yescharacteristic
380C23×C61C22×D411yescharacteristic
381C23×C61C22×Q811yescharacteristic
382C23×C61C2×#4111yescharacteristic
383C23×C61C2×#4111yescharacteristic
384C23×C61C2×#4111yescharacteristic
385C23×C61C2×#4111yescharacteristic
386C23×C61H(5,𝔽2)11yescharacteristic
387C23×C61H(5,𝔽2)11yescharacteristic
388C23×C612−1+411yescharacteristic
389C23×C612−1+411yescharacteristic
390C22×D61—22no—
391C22×D61—22no—
392C22×D61—22no—
393C22×D61—22no—
394C22×D61—22no—
395C22×D61—22no—
396C22×D61—22no—
397C22×D61—22no—
398C22×D61—22no—
399C22×D61—22no—
400C22×D61—22no—
401C22×D61—22no—
402C22×D61—22no—
403C22×D61—22no—
404C22×D61—22no—
405C22×D61—22no—
406C22×D61—22no—
407C22×D61—22no—
408C22×D61—41no—
409C22×D61—41no—
410C22×D61—41no—
411C22×D61—41no—
412C22×D61—41no—
413C22×D61—41no—
414C22×D61—41no—
415C22×D61—41no—
416C22×D61—41no—
417C22×D61—41no—
418C22×D61—41no—
419C22×D61—41no—
420C22×D61—41no—
421C22×D61—41no—
422C22×D61—41no—
423C22×D61—41no—
424C22×D61C2×C4⋊C414yes—
425C2×C4×C61—22no—
426C2×C4×C61—22no—
427C2×C4×C61—22no—
428C2×C4×C61—22no—
429C2×C4×C61—22no—
430C2×C4×C61—22no—
431C2×C4×C61—22no—
432C2×C4×C61—22no—
433C2×C4×C61—22no—
434C2×C4×C61—22no—
435C2×C4×C61—22no—
436C2×C4×C61—22no—
437C2×C4×C61—22no—
438C2×C4×C61—22no—
439C2×C4×C61—22no—
440C2×C4×C61—22no—
441C2×C4×C61—22no—
442C2×C4×C61—22no—
443C2×C4×C61—41no—
444C2×C4×C61—41no—
445C2×C4×C61—41no—
446C2×C4×C61—41no—
447C2×C4×C61—41no—
448C2×C4×C61—41no—
449C2×C4×C61—41no—
450C2×C4×C61—41no—
451C2×C4×C61—41no—
452C2×C4×C61—41no—
453C2×C4×C61—41no—
454C2×C4×C61—41no—
455C2×C4×C61—41no—
456C2×C4×C61—41no—
457C2×C4×C61—41no—
458C2×C4×C61—41no—
459C2×C4×C61—41no—
460C2×C4×C61—41no—
461C2×C4×C61—41no—
462C2×C4×C61—41no—
463C2×C4×C61—41no—
464C2×C4×C61—41no—
465C2×C4×C61—41no—
466C2×C4×C61C4×D414yescomplemented
467C22⋊D61—232no—
468C2×Dic61—22no—
469C2×Dic61—22no—
470C2×Dic61—22no—
471C2×Dic61—22no—
472C2×Dic61—22no—
473C2×Dic61—22no—
474C2×Dic61—22no—
475C2×Dic61—22no—
476C2×Dic61—22no—
477C2×Dic61—22no—
478C2×Dic61—22no—
479C2×Dic61—22no—
480C2×Dic61—22no—
481C2×Dic61—22no—
482C2×Dic61—22no—
483C2×Dic61—22no—
484C2×Dic61—22no—
485C2×Dic61—22no—
486C2×Dic61—22no—
487C2×Dic61—22no—
488C2×Dic61—22no—
489C2×Dic61—416no—
490C2×Dic61—41no—
491C2×Dic61—41no—
492C2×Dic61—41no—
493C2×Dic61—41no—
494C2×Dic61—41no—
495C2×Dic61—41no—
496C2×Dic61—41no—
497C2×Dic61—41no—
498C2×Dic61—41no—
499C2×Dic61—41no—
500C2×Dic61—41no—
501C2×Dic61—41no—
502C2×Dic61—41no—
503C2×Dic61—41no—
504C2×Dic61—41no—
505C2×Dic61—41no—
506C2×Dic61—41no—
507C2×Dic61—41no—
508C2×Dic61—41no—
509C2×Dic61C2×C4⋊C414yes—
510C2×Dic61C4×D414yes—
511C2×Dic61C4×D414yes—
512C2×Dic61C4×D414yescomplemented
513C2×Dic61#12014yes—
514C2×Dic61C22⋊Q814yes—
515C2×Dic61C22⋊Q814yes—
516C2×Dic61#12314yes—
517C2×Dic61#12714yes—
518C4×D61—416no—
519#13977—611nomaximal, Sylow
520C22×C61—24no—
521C22×C61—24no—
522C22×C61—24no—
523C22×C61—42no—
524C22×C61—42no—
525C22×C61—42no—
526C22×C61—42no—
527C22×C61—42no—
528C22×C61—42no—
529C22×C61—42no—
530C22×C61—42no—
531C22×C61—42no—
532C22×C61—42no—
533C22×C61—42no—
534C22×C61—42no—
535C22×C61C22×C4⋊C411yescharacteristic
536C22×C61C2×C4×D411yescharacteristic
537C22×C61C2×C4×D411yescharacteristic
538C22×C61C2×C4×D411yescharacteristic
539C22×C61C2×C4×D411yescharacteristic
540C22×C61#52011yescharacteristic
541C22×C61#52011yescharacteristic
542C22×C61C2×#12011yescharacteristic
543C22×C61C2×C22⋊Q811yescharacteristic
544C22×C61C2×C22⋊Q811yescharacteristic
545C22×C61C2×#12311yescharacteristic
546C22×C61C2×#12711yescharacteristic
547C22×C61#53211yescharacteristic
548C22×C61#53211yescharacteristic
549C22×C61#53211yescharacteristic
550C22×C61#53511yescharacteristic
551C22×C61#53611yescharacteristic
552C22×C61#54211yescharacteristic
553C22×C61#54211yescharacteristic
554C22×C61D4211yescharacteristic
555C22×C61D4211yescharacteristic
556C22×C61D4211yescharacteristic
557C22×C61D4211yescharacteristic
558C22×C61#54711yescharacteristic
559C22×C61#54711yescharacteristic
560C22×C61#54711yescharacteristic
561C22×C61#54711yescharacteristic
562C22×C61#54811yescharacteristic
563C22×C61#54811yescharacteristic
564C22×C61D4×Q811yescharacteristic
565C22×C61D4×Q811yescharacteristic
566C22×C61#55311yescharacteristic
567C22×C61#55311yescharacteristic
568C22×C61#55411yescharacteristic
569C22×C61#55411yescharacteristic
570C2×D61—24no—
571C2×D61—24no—
572C2×D61—24no—
573C2×D61—42no—
574C2×D61—42no—
575C2×D61—42no—
576C2×D61—42no—
577C2×D61—42no—
578C2×D61—42no—
579C2×D61—42no—
580C2×D61—42no—
581C2×D61—42no—
582C2×D61—42no—
583C2×D61—42no—
584C2×D61—42no—
585C4×C61—24no—
586C4×C61—42no—
587C4×C61—42no—
588C4×C61—42no—
589C4×C61—42no—
590C4×C61—81no—
591Dic61—24no—
592Dic61—24no—
593Dic61—42no—
594Dic61—42no—
595Dic61—42no—
596Dic61—81no—
597Dic61#38518yescomplemented
598C22×C4×D4—611no—
599C2×#390—611no—
600C2×#390—611no—
601C2×#389—611no—
602C2×#385—611no—
603C2×#385—611no—
604C2×#385—611no—
605C2×#385—611no—
606C2×#384—611no—
607#1439—611no—
608#1439—611no—
609#1439—611no—
610#1439D6111yescharacteristic, complemented
611C4⋊#95—611no—
612C4×#95—611no—
613C2×C61—44no—
614C2×C61C2×#38511yescharacteristic
615C2×C61C4×#12711yescharacteristic
616C2×C61#232611yescharacteristic
617C2×C61D4×C4⋊C411yescharacteristic
618C2×C61D4×C4⋊C411yescharacteristic
619C2×C61#236111yescharacteristic
620C2×C61#236111yescharacteristic
621C2×C61#242211yescharacteristic
622C2×C61#242211yescharacteristic
623C2×C61#243211yescharacteristic
624C2×C61#243311yescharacteristic
625C2×C61#245211yescharacteristic
626C2×C61#245211yescharacteristic
627C2×C61#254211yescharacteristic
628C2×C61#256611yescharacteristic
629D61—44no—
630C23×D4—611no—
631C24×C4—611no—
632C24×C4—611no—
633C2×C4×D4—1224no—
634C2×C4×D4—1224no—
635C2×C4×D4—1224no—
636C22×C4⋊C4—611no—
637C22×C4⋊C4—611no—
638C22×C4⋊C4—611no—
639C22×C4⋊C4—611no—
640C22×C4⋊C4—611no—
641C22×C4⋊C4—611no—
642C22×C4⋊C4—611no—
643C22×C4⋊C4—611no—
644C22×C4⋊C4C2×D6111yescharacteristic
645C22×C22⋊C4—611no—
646C22×C22⋊C4—611no—
647C22×C22⋊C4—611no—
648C22×C22⋊C4—611no—
649C22×C22⋊C4—611no—
650C22×C22⋊C4—611no—
651C22×C22⋊C4—611no—
652C22×C22⋊C4C2×D6111yescharacteristic
653C22×C22⋊C4C2×D6111yescharacteristic
654C22×C22⋊C4C2×D6111yescharacteristic
655C22×C42—611no—
656C22×C42—611no—
657C22×C42—611no—
658#390—618no—
659#390—1224no—
660#389—1224no—
661#385—1224no—
662#385—1224no—
663#385—1224no—
664#385—1224no—
665#384—1224no—
666C2×#95—611no—
667C2×#95—611no—
668C2×#95—611no—
669C2×#95—611no—
670C2×#95—611no—
671C2×#95—611no—
672C2×#95—611no—
673C2×#95C2×D6111yescharacteristic
674C2×#95C2×D6111yescharacteristic
675C2×#95C2×D6111yescharacteristic
676C61#1397711yescharacteristic, complemented, Sylow
677C25—611no—
678C25C22×D6111yescharacteristic
679C22×D4—614no—
680C22×D4—614no—
681C22×D4—614no—
682C22×D4—1222no—
683C22×D4—1222no—
684C22×D4—1222no—
685C22×D4—1222no—
686C23×C4—611no—
687C23×C4—611no—
688C23×C4—611no—
689C23×C4—611no—
690C23×C4—611no—
691C23×C4—611no—
692C23×C4—611no—
693C23×C4—1222no—
694C23×C4—1222no—
695C23×C4—1222no—
696C23×C4—1222no—
697C23×C4—1222no—
698C23×C4—1222no—
699C23×C4—1222no—
700C23×C4—1222no—
701C23×C4—1222no—
702C23×C4—1222no—
703C23×C4—2441no—
704C23×C4—2441no—
705C23×C4—2441no—
706C23×C4—2441no—
707C23×C4C22×D6111yescharacteristic
708C23×C4C22×D6111yescharacteristic
709C23×C4C22×D6111yescharacteristic
710C23×C4C22×D6111yescharacteristic
711C23×C4C22×D6111yescharacteristic
712C23×C4C22×D6111yescharacteristic
713C4×D4—12232no—
714C2×C4⋊C4—22no—
715C2×C4⋊C4—22no—
716C2×C4⋊C4—41no—
717C2×C4⋊C4—614no—
718C2×C4⋊C4—614no—
719C2×C4⋊C4—1222no—
720C2×C4⋊C4—1222no—
721C2×C4⋊C4—1222no—
722C2×C4⋊C4—1222no—
723C2×C4⋊C4—1222no—
724C2×C4⋊C4—1222no—
725C2×C4⋊C4—1222no—
726C2×C4⋊C4—1222no—
727C2×C4⋊C4—1222no—
728C2×C4⋊C4—1222no—
729C2×C4⋊C4—1222no—
730C2×C4⋊C4—1222no—
731C2×C4⋊C4—1222no—
732C2×C4⋊C4—1222no—
733C2×C4⋊C4—1222no—
734C2×C4⋊C4—1222no—
735C2×C4⋊C4—1222no—
736C2×C4⋊C4—1222no—
737C2×C4⋊C4—1222no—
738C2×C4⋊C4—2441no—
739C2×C4⋊C4—2441no—
740C2×C4⋊C4—2441no—
741C2×C22⋊C4—22no—
742C2×C22⋊C4—22no—
743C2×C22⋊C4—22no—
744C2×C22⋊C4—22no—
745C2×C22⋊C4—22no—
746C2×C22⋊C4—22no—
747C2×C22⋊C4—22no—
748C2×C22⋊C4—41no—
749C2×C22⋊C4—614no—
750C2×C22⋊C4—614no—
751C2×C22⋊C4—614no—
752C2×C22⋊C4—1222no—
753C2×C22⋊C4—1222no—
754C2×C22⋊C4—1222no—
755C2×C22⋊C4—1222no—
756C2×C22⋊C4—1222no—
757C2×C22⋊C4—1222no—
758C2×C22⋊C4—1222no—
759C2×C22⋊C4—1222no—
760C2×C22⋊C4—1222no—
761C2×C22⋊C4—1222no—
762C2×C22⋊C4—1222no—
763C2×C22⋊C4—1222no—
764C2×C22⋊C4—1222no—
765C2×C22⋊C4—1222no—
766C2×C22⋊C4—1222no—
767C2×C22⋊C4—2441no—
768C2×C22⋊C4—2441no—
769C2×C22⋊C4—2441no—
770C2×C22⋊C4C4×D6114yescomplemented
771C2×C42—614no—
772C2×C42—614no—
773C2×C42—1222no—
774C2×C42—1222no—
775C2×C42—1222no—
776C2×C42—1222no—
777C2×C42—1222no—
778C2×C42—1222no—
779C2×C42—1222no—
780#95—22no—
781#95—22no—
782#95—22no—
783#95—614no—
784#95—614no—
785#95—1222no—
786#95—1222no—
787#95—1222no—
788#95—1222no—
789#95—1222no—
790C24—21no—
791C24—21no—
792C24—21no—
793C24—21no—
794C24—21no—
795C24—21no—
796C24—21no—
797C24—21no—
798C24—21no—
799C24—21no—
800C24—21no—
801C24—21no—
802C24—612no—
803C24—612no—
804C24—612no—
805C24—1221no—
806C24—1221no—
807C24—1221no—
808C24—1221no—
809C24—1221no—
810C24—1221no—
811C24—1221no—
812C24—1221no—
813C24—1221no—
814C24—1221no—
815C24—1221no—
816C24—1221no—
817C24C2×C4×D6112yes—
818C24D4×D6112yes—
819C24Q8×D6112yes—
820C24C23×D6111yescharacteristic
821C2×D4—6116no—
822C2×D4—1228no—
823C2×D4—1228no—
824C2×D4—1228no—
825C2×D4—1228no—
826C2×D4—1228no—
827C2×D4—1228no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—612no—
864C22×C4—612no—
865C22×C4—612no—
866C22×C4—612no—
867C22×C4—612no—
868C22×C4—612no—
869C22×C4—612no—
870C22×C4—612no—
871C22×C4—612no—
872C22×C4—612no—
873C22×C4—612no—
874C22×C4—612no—
875C22×C4—612no—
876C22×C4—612no—
877C22×C4—612no—
878C22×C4—612no—
879C22×C4—1228no—
880C22×C4—1221no—
881C22×C4—1221no—
882C22×C4—1221no—
883C22×C4—1221no—
884C22×C4—1221no—
885C22×C4—1221no—
886C22×C4—1221no—
887C22×C4—1221no—
888C22×C4—1228no—
889C22×C4—1221no—
890C22×C4—1221no—
891C22×C4—1221no—
892C22×C4—1221no—
893C22×C4—1221no—
894C22×C4—1221no—
895C22×C4—1221no—
896C22×C4—1221no—
897C22×C4—1221no—
898C22×C4—1221no—
899C22×C4—1221no—
900C22×C4—1221no—
901C22×C4—1221no—
902C22×C4—1221no—
903C22×C4—1221no—
904C22×C4—1221no—
905C22×C4—1221no—
906C22×C4—1221no—
907C22×C4—1221no—
908C22×C4—1221no—
909C22×C4—1221no—
910C22×C4—1221no—
911C22×C4—1221no—
912C22×C4—1221no—
913C22×C4—1221no—
914C22×C4—2444no—
915C22×C4—2444no—
916C22×C4—2444no—
917C22×C4—2444no—
918C22×C4—2444no—
919C22×C4—2444no—
920C22×C4—2444no—
921C22×C4—2444no—
922C22×C4—2444no—
923C22×C4—2444no—
924C22×C4—2444no—
925C22×C4—2444no—
926C22×C4C2×C4×D6112yes—
927C22×C4C2×C4×D6112yes—
928C22×C4D4×D6112yes—
929C22×C4D4×D6112yes—
930C22×C4D4×D6112yes—
931C22×C4D4×D6112yes—
932C22×C4#1175822412yes—
933C4⋊C4—44no—
934C4⋊C4—1228no—
935C4⋊C4—1228no—
936C4⋊C4—2444no—
937C4⋊C4—2444no—
938C4⋊C4—2444no—
939C4⋊C4—2444no—
940C4⋊C4—2444no—
941C4⋊C4—2444no—
942C22⋊C4—28no—
943C22⋊C4—28no—
944C22⋊C4—44no—
945C22⋊C4—1228no—
946C22⋊C4—1228no—
947C22⋊C4—1228no—
948C22⋊C4—1228no—
949C22⋊C4—2444no—
950C22⋊C4—2444no—
951C22⋊C4—2444no—
952C42—1228no—
953C42—1228no—
954C42—2444no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23—41no—
982C23—41no—
983C23—41no—
984C23—41no—
985C23—41no—
986C23—41no—
987C23—41no—
988C23—41no—
989C23—614no—
990C23—1222no—
991C23—1222no—
992C23—1222no—
993C23—1222no—
994C23—1222no—
995C23—1222no—
996C23—1222no—
997C23—1222no—
998C23—1222no—
999C23—1222no—
1000C23—1222no—
1001C23—1222no—
1002C23—1222no—
1003C23—1222no—
1004C23—1222no—
1005C23—1222no—
1006C23—1222no—
1007C23—1222no—
1008C23—2441no—
1009C23—2441no—
1010C23—2441no—
1011C23—2441no—
1012C23—2441no—
1013C23—2441no—
1014C23—2441no—
1015C23—2441no—
1016C23—2441no—
1017C23—2441no—
1018C23—2441no—
1019C23—2441no—
1020C23—2441no—
1021C23—2441no—
1022C23—2441no—
1023C23—2441no—
1024C23C4⋊C4×D6114yes—
1025C23C22×C4×D6111yescharacteristic
1026C23C2×D4×D6111yescharacteristic
1027C23C2×D4×D6111yescharacteristic
1028C23C2×D4×D6111yescharacteristic
1029C23C2×D4×D6111yescharacteristic
1030C23C2×D4×D6111yescharacteristic
1031C23C2×Q8×D6111yescharacteristic
1032C23#41×D6111yescharacteristic
1033C23#41×D6111yescharacteristic
1034C23#41×D6111yescharacteristic
1035C23C2×#1175822411yescharacteristic
1036C23#1451982211yescharacteristic
1037C23#1451982311yescharacteristic
1038C23#1451982411yescharacteristic
1039C23#1451982411yescharacteristic
1040D4—12232no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—614no—
1083C2×C4—614no—
1084C2×C4—614no—
1085C2×C4—614no—
1086C2×C4—614no—
1087C2×C4—614no—
1088C2×C4—614no—
1089C2×C4—614no—
1090C2×C4—614no—
1091C2×C4—1222no—
1092C2×C4—1222no—
1093C2×C4—1222no—
1094C2×C4—1222no—
1095C2×C4—1222no—
1096C2×C4—1222no—
1097C2×C4—1222no—
1098C2×C4—1222no—
1099C2×C4—1222no—
1100C2×C4—1222no—
1101C2×C4—1222no—
1102C2×C4—1222no—
1103C2×C4—1222no—
1104C2×C4—1222no—
1105C2×C4—1222no—
1106C2×C4—1222no—
1107C2×C4—1222no—
1108C2×C4—1222no—
1109C2×C4—1222no—
1110C2×C4—1222no—
1111C2×C4—1222no—
1112C2×C4—24416no—
1113C2×C4—24416no—
1114C2×C4—2441no—
1115C2×C4—2441no—
1116C2×C4—2441no—
1117C2×C4—2441no—
1118C2×C4—2441no—
1119C2×C4—2441no—
1120C2×C4—2441no—
1121C2×C4—2441no—
1122C2×C4—2441no—
1123C2×C4—2441no—
1124C2×C4—2441no—
1125C2×C4—2441no—
1126C2×C4—2441no—
1127C2×C4—2441no—
1128C2×C4—2441no—
1129C2×C4—2441no—
1130C2×C4—2441no—
1131C2×C4—2441no—
1132C2×C4—2441no—
1133C2×C4#1451973714yescomplemented
1134C22—24no—
1135C22—24no—
1136C22—24no—
1137C22—42no—
1138C22—42no—
1139C22—42no—
1140C22—42no—
1141C22—42no—
1142C22—42no—
1143C22—42no—
1144C22—42no—
1145C22—42no—
1146C22—42no—
1147C22—42no—
1148C22—42no—
1149C22—1224no—
1150C22—1224no—
1151C22—1224no—
1152C22—2442no—
1153C22—2442no—
1154C22—2442no—
1155C22—2442no—
1156C22—2442no—
1157C22—2442no—
1158C22—2442no—
1159C22—2442no—
1160C22—2442no—
1161C22—2442no—
1162C22—2442no—
1163C22—2442no—
1164C22C2×C4⋊C4×D6111yescharacteristic
1165C22C4×D4×D6111yescharacteristic
1166C22C4×D4×D6111yescharacteristic
1167C22C4×D4×D6111yescharacteristic
1168C22C2×#1451973711yescharacteristic
1169C22#1684024111yescharacteristic
1170C22#1684024211yescharacteristic
1171C22#120×D6111yescharacteristic
1172C22C22⋊Q8×D6111yescharacteristic
1173C22C22⋊Q8×D6111yescharacteristic
1174C22#123×D6111yescharacteristic
1175C22#127×D6111yescharacteristic
1176C22#1684030711yescharacteristic
1177C22#1684030711yescharacteristic
1178C22#1684031111yescharacteristic
1179C22#1684032811yescharacteristic
1180C22#1684033411yescharacteristic
1181C22#1684037611yescharacteristic
1182C22#1684037811yescharacteristic
1183C22#1684039411yescharacteristic
1184C22#1684039411yescharacteristic
1185C22#1684039611yescharacteristic
1186C22#1684039611yescharacteristic
1187C22#1684041011yescharacteristic
1188C22#1684041011yescharacteristic
1189C22#1684041011yescharacteristic
1190C22#1684041211yescharacteristic
1191C22#1684041811yescharacteristic
1192C22#1684042011yescharacteristic
1193C22#1684042511yescharacteristic
1194C22#1684042511yescharacteristic
1195C22#1684045511yescharacteristic
1196C22#1684046311yescharacteristic
1197C22#1684046611yescharacteristic
1198C22#1684047011yescharacteristic
1199C4—24no—
1200C4—42no—
1201C4—42no—
1202C4—42no—
1203C4—42no—
1204C4—81no—
1205C4—618no—
1206C4—1224no—
1207C4—1224no—
1208C4—4881no—
1209C4—2442no—
1210C4—2442no—
1211C4—2442no—
1212C2—44no—
1213C2—2444no—
1214C2#385×D6111yescharacteristic
1215C2#2144838311yescharacteristic
1216C2#2144852811yescharacteristic
1217C2#2144871511yescharacteristic
1218C2#2144871711yescharacteristic
1219C2#2144883011yescharacteristic
1220C2#2144883211yescharacteristic
1221C2#2144932611yescharacteristic
1222C2#2144932811yescharacteristic
1223C2#2144944211yescharacteristic
1224C2#2144945111yescharacteristic
1225C2#2144966211yescharacteristic
1226C2#2144966411yescharacteristic
1227C2#2145076711yescharacteristic
1228C2#2145101411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1439C2
socle, cosocleC24×C61C24
prime radicalC23×C22⋊D61C22
hypercenter#1439D61
hypocenterC61#13977
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
4. C2×#16839659C2semidirect
5. C2×#16839637C2semidirect
6. C2×#16839636C2semidirect
7. C2×#16839634C2semidirect
8. C2×#16839633C2semidirect
9. C2×#16839631C2semidirect
10. #21444065C2semidirect
11. #21444063C2semidirect
12. #21444062C2semidirect
13. #21444047C2semidirect
14. #95×Dic61C2semidirect
15. C61×#1439C2semidirect
41. #16839662C4semidirect
114. C2×#11758196C2×C4semidirect
121. C2×C22⋊Dic61C2×C4semidirect
135. C2×#11758198C2×C4semidirect
136. C2×#11758198C2×C4semidirect
144. C2×C4×Dic61C2×C4semidirect
151. #14519684D4semidirect
152. #14519684D4semidirect
171. C2×C22⋊C4×C61C2×C4semidirect
254. C2×C22⋊D61C4⋊C4semidirect
466. C2×C4×C61C4×D4semidirect
512. C2×Dic61C4×D4semidirect
597. Dic61#385semidirect
610. #1439D61semidirect
676. C61#13977semidirect
770. C2×C22⋊C4C4×D61semidirect
1133. C2×C4#14519737semidirect

Maximal subgroups

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

subgroupindex
C22×#145197372
C2×#168396622
C2×#168396592
C2×#168396372
C2×#168396362
C2×#168396342
C2×#168396332
C2×#168396312
#214440652
#214440632
#214440622
#214440472
#95×Dic612
C61×#14392
#1397761