Finite Group Databasebeta

← #29603594

Subgroups — #29603594

Order 15616.

1946 conjugacy classes of subgroups.

The subgroup lattice has 1158 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839664C211yesmaximal, characteristic
2C2×#16839651C211yesmaximal, characteristic, complemented
3C2×#16839647C211yesmaximal, characteristic, complemented
4C2×#16839640C211yesmaximal, characteristic
5C2×#16839609C211yesmaximal, characteristic, complemented
6#21444086C211yesmaximal, characteristic, complemented
7#21444067C211yesmaximal, characteristic, complemented
8#21444063C211yesmaximal, characteristic, complemented
9#21444059C211yesmaximal, characteristic
10#21444055C211yesmaximal, characteristic, complemented
11#21444055C211yesmaximal, characteristic, complemented
12#21444055C211yesmaximal, characteristic, complemented
13#21444040C211yesmaximal, characteristic, complemented
14C4×#14519684C211yesmaximal, characteristic, complemented
15C61×#1434C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C23×C4×D61C2211yescharacteristic
18C22×C4⋊Dic61C2211yescharacteristic
19C22×#11758196C2211yescharacteristic
20C22×#11758198C2211yescharacteristic
21C22×#11758198C2211yescharacteristic
22C22×#11758198C2211yescharacteristic
23C22×#11758198C2211yescharacteristic
24C22×#11758198C2211yescharacteristic
25C22×#11758198C2211yescharacteristic
26C22×#11758198C2211yescharacteristic
27C22×#11758198C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×C4×Dic61C2211yescharacteristic
32C22×C4×Dic61C2211yescharacteristic
33C22×C4×Dic61C2211yescharacteristic
34#16839664C418yescomplemented
35#16839651—24no—
36#16839647—24no—
37#16839640—24no—
38#16839609—24no—
39C2×#14519684C2211yescharacteristic
40C2×#14519684C2211yescharacteristic
41C2×#14519684C2211yescharacteristic
42C2×#14519684C2211yescharacteristic
43C2×#14519684C2211yescharacteristic
44C2×#14519684C2211yescharacteristic
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C22×C42×C61C2211yescharacteristic
50C2×#95×C61C2211yescharacteristic
51C2×#95×C61C2211yescharacteristic
52C2×#95×C61C2211yescharacteristic
53C2×#95×C61C2211yescharacteristic
54C2×#95×C61C2211yescharacteristic
55C2×#95×C61C2211yescharacteristic
56C24×D61C2311yescharacteristic
57C24×D61C2311yescharacteristic
58C22×D244—22no—
59C22×D244—22no—
60C22×D244—22no—
61C22×D244—22no—
62C22×D244—41no—
63C22×D244—41no—
64C22×D244C2×C414yes—
65C23×Dic61C2311yescharacteristic
66C23×Dic61C2311yescharacteristic
67C23×Dic61C2311yescharacteristic
68C23×Dic61C2311yescharacteristic
69C23×Dic61C2311yescharacteristic
70C23×Dic61C2311yescharacteristic
71C22×C4×D61—22no—
72C22×C4×D61—22no—
73C22×C4×D61—22no—
74C22×C4×D61—22no—
75C22×C4×D61—22no—
76C22×C4×D61—41no—
77C22×C4×D61—41no—
78C2×C4⋊Dic61—22no—
79C2×C4⋊Dic61—22no—
80C2×C4⋊Dic61C2×C414yescomplemented
81C2×#11758196—22no—
82C2×#11758196—22no—
83C2×#11758196—41no—
84C2×#11758198—22no—
85C2×#11758198—22no—
86C2×#11758198—22no—
87C2×#11758198—22no—
88C2×#11758198—22no—
89C2×#11758198—22no—
90C2×#11758198—22no—
91C2×#11758198—22no—
92C2×#11758198—22no—
93C2×#11758198—22no—
94C2×#11758198—22no—
95C2×#11758198—22no—
96C2×#11758198—22no—
97C2×#11758198—22no—
98C2×#11758198—22no—
99C2×#11758198—22no—
100C2×#11758198—22no—
101C2×#11758198—22no—
102C2×#11758198—22no—
103C2×#11758198—41no—
104C2×#11758198—41no—
105C2×#11758198—41no—
106C2×#11758198—41no—
107C2×#11758198—41no—
108C2×#11758198—41no—
109C2×#11758198—41no—
110C2×#11758198—41no—
111C2×#11758198—41no—
112C2×#11758198—41no—
113C2×#11758198C2×C414yes—
114C2×#11758198C2×C414yes—
115C2×#11758198C2×C414yescomplemented
116C2×#11758198C2×C414yescomplemented
117C2×C4×Dic61—22no—
118C2×C4×Dic61—22no—
119C2×C4×Dic61—22no—
120C2×C4×Dic61—22no—
121C2×C4×Dic61—22no—
122C2×C4×Dic61—22no—
123C2×C4×Dic61—41no—
124C2×C4×Dic61—41no—
125C2×C4×Dic61—41no—
126#14519684—22no—
127#14519684—22no—
128#14519684—22no—
129#14519684—22no—
130#14519684—22no—
131#14519684—22no—
132#14519684—22no—
133#14519684—41no—
134#14519684—41no—
135#14519684D414yes—
136C23×C4×C61C2311yescharacteristic
137C23×C4×C61C2311yescharacteristic
138C23×C4×C61C2311yescharacteristic
139C23×C4×C61C2311yescharacteristic
140C23×C4×C61C2311yescharacteristic
141C23×C4×C61C2311yescharacteristic
142C23×C4×C61C2311yescharacteristic
143C2×C42×C61—41no—
144C2×C42×C61—41no—
145C2×C42×C61C2×C414yescomplemented
146#95×C61—22no—
147#95×C61—22no—
148#95×C61—22no—
149#95×C61—41no—
150#95×C61—41no—
151#95×C61D414yescomplemented
152C24×C61C2411yescharacteristic
153C23×D61—21no—
154C23×D61—21no—
155C23×D61—21no—
156C23×D61—21no—
157C23×D61—21no—
158C23×D61—21no—
159C23×D61—21no—
160C23×D61—21no—
161C23×D61—21no—
162C23×D61—21no—
163C23×D61—21no—
164C23×D61—21no—
165C23×D61—21no—
166C23×D61—21no—
167C23×D61—21no—
168C23×D61—21no—
169C23×D61—21no—
170C23×D61—21no—
171C23×D61—21no—
172C23×D61—21no—
173C23×D61—21no—
174C23×D61—21no—
175C23×D61—21no—
176C23×D61—21no—
177C23×D61—21no—
178C23×D61—21no—
179C23×D61C22×C412yes—
180C23×D61C22×C412yes—
181C23×D61#4112yes—
182C23×D61#4112yes—
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×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61—21no—
204C22×C4×C61—21no—
205C22×C4×C61—21no—
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×C61C22×C412yes—
224C22×C4×C61C22×C412yes—
225C22×C4×C61C22×C412yes—
226C22×C4×C61C2×D412yes—
227C22×C4×C61C2×D412yes—
228C22×C4×C61C2×D412yes—
229C22×C4×C61C2×D412yes—
230C22×C4×C61#4112yes—
231C22×C4×C61#4112yes—
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×Dic61—21no—
242C22×Dic61—21no—
243C22×Dic61—21no—
244C22×Dic61—21no—
245C22×Dic61—21no—
246C22×Dic61—21no—
247C22×Dic61—21no—
248C22×Dic61—21no—
249C22×Dic61—21no—
250C22×Dic61—21no—
251C22×Dic61—21no—
252C22×Dic61—21no—
253C22×Dic61—21no—
254C22×Dic61—21no—
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—21no—
264C22×Dic61—21no—
265C22×Dic61—21no—
266C22×Dic61C22×C412yes—
267C22×Dic61C22×C412yes—
268C22×Dic61C2×D412yes—
269C22×Dic61C2×D412yes—
270C22×Dic61#4112yes—
271C22×Dic61#4112yes—
272C22×Dic61#4112yes—
273C22×Dic61#4112yes—
274C2×D244—28no—
275C2×D244—28no—
276C2×D244—44no—
277C2×D244—44no—
278C2×D244—44no—
279C2×D244—44no—
280C2×D244—44no—
281C2×C4×D61—28no—
282C2×C4×D61—44no—
283C2×C4×D61—44no—
284C2×C4×D61—44no—
285C2×C4×D61—44no—
286C2×C4×D61—44no—
287C2×C4×D61—44no—
288C42×C61—44no—
289#11758198—28no—
290#11758198—28no—
291#11758198—28no—
292#11758198—44no—
293#11758198—44no—
294#11758198—44no—
295#11758198—44no—
296#11758198—44no—
297#11758198—44no—
298#11758198—44no—
299#11758198—44no—
300C4⋊Dic61—28no—
301#11758196—44no—
302C4×Dic61—44no—
303C4×Dic61—44no—
304C4×Dic61—44no—
305C23×C61C23×C411yescharacteristic
306C23×C61C22×D411yescharacteristic
307C23×C61C22×D411yescharacteristic
308C23×C61C2×#4111yescharacteristic
309C23×C61C2×#4111yescharacteristic
310C23×C61C2×#4111yescharacteristic
311C23×C61C2×#4111yescharacteristic
312C23×C61C2×#4111yescharacteristic
313C23×C61C2×#4111yescharacteristic
314C23×C61C2×#4111yescharacteristic
315C23×C61C2×#4111yescharacteristic
316C23×C61H(5,𝔽2)11yescharacteristic
317C23×C61H(5,𝔽2)11yescharacteristic
318C23×C61H(5,𝔽2)11yescharacteristic
319C23×C61H(5,𝔽2)11yescharacteristic
320C22×D61—22no—
321C22×D61—22no—
322C22×D61—22no—
323C22×D61—22no—
324C22×D61—22no—
325C22×D61—22no—
326C22×D61—22no—
327C22×D61—22no—
328C22×D61—22no—
329C22×D61—22no—
330C22×D61—22no—
331C22×D61—22no—
332C22×D61—22no—
333C22×D61—22no—
334C22×D61—22no—
335C22×D61—22no—
336C22×D61—22no—
337C22×D61—22no—
338C22×D61—22no—
339C22×D61—22no—
340C22×D61—22no—
341C22×D61—22no—
342C22×D61—22no—
343C22×D61—22no—
344C22×D61—22no—
345C22×D61—41no—
346C22×D61—41no—
347C22×D61—41no—
348C22×D61—41no—
349C22×D61—41no—
350C22×D61—41no—
351C22×D61—41no—
352C22×D61—41no—
353C22×D61—41no—
354C22×D61—41no—
355C22×D61—41no—
356C22×D61—41no—
357C22×D61—41no—
358C22×D61—41no—
359C22×D61—41no—
360C22×D61—41no—
361C22×D61—41no—
362C22×D61—41no—
363C22×D61—41no—
364C22×D61—41no—
365C22×D61—41no—
366C22×D61—41no—
367C22×D61—41no—
368C22×D61—41no—
369C22×D61—41no—
370C22×D61—41no—
371C22×D61—41no—
372C22×D61—41no—
373C22×D61—41no—
374C22×D61—41no—
375C22×D61—41no—
376C22×D61—41no—
377C22×D61—41no—
378C22×D61—41no—
379C22×D61—41no—
380C22×D61—41no—
381C22×D61—41no—
382C22×D61—41no—
383C22×D61—41no—
384C22×D61—41no—
385C22×D61—41no—
386C22×D61—41no—
387C22×D61—41no—
388C22×D61—41no—
389C22×D61#11714yes—
390C2×C4×C61—22no—
391C2×C4×C61—22no—
392C2×C4×C61—22no—
393C2×C4×C61—22no—
394C2×C4×C61—22no—
395C2×C4×C61—22no—
396C2×C4×C61—22no—
397C2×C4×C61—22no—
398C2×C4×C61—22no—
399C2×C4×C61—22no—
400C2×C4×C61—22no—
401C2×C4×C61—22no—
402C2×C4×C61—22no—
403C2×C4×C61—22no—
404C2×C4×C61—22no—
405C2×C4×C61—22no—
406C2×C4×C61—22no—
407C2×C4×C61—22no—
408C2×C4×C61—22no—
409C2×C4×C61—22no—
410C2×C4×C61—22no—
411C2×C4×C61—41no—
412C2×C4×C61—41no—
413C2×C4×C61—41no—
414C2×C4×C61—41no—
415C2×C4×C61—41no—
416C2×C4×C61—41no—
417C2×C4×C61—41no—
418C2×C4×C61—41no—
419C2×C4×C61—41no—
420C2×C4×C61—41no—
421C2×C4×C61—41no—
422C2×C4×C61—41no—
423C2×C4×C61—41no—
424C2×C4×C61—41no—
425C2×C4×C61—41no—
426C2×C4×C61—41no—
427C2×C4×C61—41no—
428C2×C4×C61—41no—
429C2×C4×C61—41no—
430C2×C4×C61—41no—
431C2×C4×C61—41no—
432C2×C4×C61—41no—
433C2×C4×C61—41no—
434C2×C4×C61—41no—
435C2×C4×C61—41no—
436C2×C4×C61—41no—
437C2×C4×C61C4×D414yes—
438C2×C4×C61C4×D414yes—
439C2×Dic61—22no—
440C2×Dic61—22no—
441C2×Dic61—22no—
442C2×Dic61—22no—
443C2×Dic61—22no—
444C2×Dic61—22no—
445C2×Dic61—22no—
446C2×Dic61—22no—
447C2×Dic61—22no—
448C2×Dic61—22no—
449C2×Dic61—22no—
450C2×Dic61—22no—
451C2×Dic61—22no—
452C2×Dic61—22no—
453C2×Dic61—22no—
454C2×Dic61—22no—
455C2×Dic61—22no—
456C2×Dic61—22no—
457C2×Dic61—22no—
458C2×Dic61—22no—
459C2×Dic61—22no—
460C2×Dic61—41no—
461C2×Dic61—41no—
462C2×Dic61—41no—
463C2×Dic61—41no—
464C2×Dic61—41no—
465C2×Dic61—41no—
466C2×Dic61—41no—
467C2×Dic61—41no—
468C2×Dic61—41no—
469C2×Dic61—41no—
470C2×Dic61—41no—
471C2×Dic61—41no—
472C2×Dic61—41no—
473C2×Dic61—41no—
474C2×Dic61—41no—
475C2×Dic61—41no—
476C2×Dic61—41no—
477C2×Dic61—41no—
478C2×Dic61—41no—
479C2×Dic61—41no—
480C2×Dic61#12414yes—
481D244—416no—
482C4×D61—416no—
483#14034—611nomaximal, Sylow
484C22×C61C2×#11711yescharacteristic
485C22×C61C2×C4×D411yescharacteristic
486C22×C61C2×C4×D411yescharacteristic
487C22×C61C4×#4111yescharacteristic
488C22×C61C4×#4111yescharacteristic
489C22×C61#51811yescharacteristic
490C22×C61#51811yescharacteristic
491C22×C61#52511yescharacteristic
492C22×C61#52511yescharacteristic
493C22×C61C2×#12411yescharacteristic
494C22×C61#52911yescharacteristic
495C22×C61#52911yescharacteristic
496C22×C61#52911yescharacteristic
497C22×C61#52911yescharacteristic
498C22×C61#53211yescharacteristic
499C22×C61#53811yescharacteristic
500C22×C61#53811yescharacteristic
501C22×C61#54011yescharacteristic
502C22×C61#54011yescharacteristic
503C22×C61D4211yescharacteristic
504C22×C61#54611yescharacteristic
505C22×C61#54611yescharacteristic
506C22×C61#54611yescharacteristic
507C22×C61#54611yescharacteristic
508C22×C61#55011yescharacteristic
509C22×C61#55011yescharacteristic
510C22×C61#55111yescharacteristic
511C22×C61#55111yescharacteristic
512C22×C61#55111yescharacteristic
513C22×C61#55111yescharacteristic
514C22×C61#55311yescharacteristic
515C22×C61#55311yescharacteristic
516C22×C61#55311yescharacteristic
517C22×C61#55311yescharacteristic
518C22×C61#55911yescharacteristic
519C2×D61—24no—
520C2×D61—24no—
521C2×D61—24no—
522C2×D61—42no—
523C2×D61—42no—
524C2×D61—42no—
525C2×D61—42no—
526C2×D61—42no—
527C2×D61—42no—
528C2×D61—42no—
529C2×D61—42no—
530C2×D61—42no—
531C2×D61—42no—
532C2×D61—42no—
533C2×D61—42no—
534C2×D61—42no—
535C2×D61—42no—
536C2×D61—42no—
537C2×D61—42no—
538C2×D61—42no—
539C2×D61—42no—
540C2×D61—42no—
541C2×D61—81no—
542C2×D61—81no—
543C2×D61—81no—
544C2×D61—81no—
545C2×D61—81no—
546C2×D61—81no—
547C2×D61—81no—
548C2×D61—81no—
549C4×C61—24no—
550C4×C61—24no—
551C4×C61—42no—
552C4×C61—42no—
553C4×C61—42no—
554C4×C61—81no—
555C4×C61—81no—
556Dic61—24no—
557Dic61—42no—
558Dic61—42no—
559Dic61—42no—
560Dic61—42no—
561Dic61—42no—
562C2×#390—611no—
563C2×#388—611no—
564C2×#387—611no—
565C2×#386—611no—
566C2×C4×C22⋊C4—611no—
567#1445—611no—
568#1440—611no—
569#1439—611no—
570#1438—611no—
571#1437—611no—
572#1437—611no—
573#1437—611no—
574#1434D6111yescharacteristic, complemented
575C22⋊#95—611no—
576C4×#95—611no—
577C2×C61#229011yescharacteristic
578C2×C61C4×#12411yescharacteristic
579C2×C61#233311yescharacteristic
580C2×C61#234211yescharacteristic
581C2×C61#235311yescharacteristic
582C2×C61#236411yescharacteristic
583C2×C61#236611yescharacteristic
584C2×C61#246411yescharacteristic
585C2×C61#246711yescharacteristic
586C2×C61#247111yescharacteristic
587C2×C61#247211yescharacteristic
588C2×C61#249011yescharacteristic
589C2×C61#251611yescharacteristic
590C2×C61#255411yescharacteristic
591C2×C61#259511yescharacteristic
592D61—44no—
593D61—82no—
594C23×D4—611no—
595C24×C4—611no—
596C22×C4⋊C4—611no—
597C22×C4⋊C4—611no—
598C22×C22⋊C4—611no—
599C22×C22⋊C4—611no—
600C22×C22⋊C4—611no—
601C22×C22⋊C4—611no—
602C22×C22⋊C4—611no—
603C22×C22⋊C4—611no—
604C22×C22⋊C4—611no—
605C22×C22⋊C4—611no—
606C22×C22⋊C4—611no—
607C22×C22⋊C4—611no—
608C22×C22⋊C4—611no—
609C22×C42—611no—
610C22×C42—611no—
611C22×C42—611no—
612C22×C42C2×D6111yescharacteristic
613#390—618no—
614#388—1224no—
615#387—1224no—
616#386—1224no—
617C4×C22⋊C4—1224no—
618C2×#95—611no—
619C2×#95—611no—
620C2×#95—611no—
621C2×#95—611no—
622C2×#95—611no—
623C2×#95—611no—
624C2×#95—611no—
625C2×#95—611no—
626C2×#95—611no—
627C2×#95—611no—
628C2×#95C2×D6111yescharacteristic
629C2×#95C2×D6111yescharacteristic
630C2×#95C2×D6111yescharacteristic
631C2×#95C2×D6111yescharacteristic
632C2×#95C2×D6111yescharacteristic
633C2×#95C2×D6111yescharacteristic
634C61#1403411yescharacteristic, complemented, Sylow
635C25—611no—
636C25—611no—
637C22×D4—614no—
638C22×D4—1222no—
639C22×D4—1222no—
640C22×D4—1222no—
641C22×D4—1222no—
642C22×D4—2441no—
643C22×D4—2441no—
644C23×C4—611no—
645C23×C4—611no—
646C23×C4—611no—
647C23×C4—611no—
648C23×C4—611no—
649C23×C4—611no—
650C23×C4—1222no—
651C23×C4—1222no—
652C23×C4—1222no—
653C23×C4—1222no—
654C23×C4—1222no—
655C23×C4—2441no—
656C23×C4—2441no—
657C23×C4C22×D6111yescharacteristic
658C23×C4C22×D6111yescharacteristic
659C23×C4C22×D6111yescharacteristic
660C23×C4C22×D6111yescharacteristic
661C23×C4C22×D6111yescharacteristic
662C23×C4C22×D6111yescharacteristic
663C23×C4C22×D6111yescharacteristic
664C2×C4⋊C4—614no—
665C2×C4⋊C4—1222no—
666C2×C4⋊C4—1222no—
667C2×C4⋊C4—1222no—
668C2×C4⋊C4—1222no—
669C2×C4⋊C4—2441no—
670C2×C22⋊C4—614no—
671C2×C22⋊C4—614no—
672C2×C22⋊C4—614no—
673C2×C22⋊C4—614no—
674C2×C22⋊C4—1222no—
675C2×C22⋊C4—1222no—
676C2×C22⋊C4—1222no—
677C2×C22⋊C4—1222no—
678C2×C22⋊C4—1222no—
679C2×C22⋊C4—1222no—
680C2×C22⋊C4—1222no—
681C2×C22⋊C4—1222no—
682C2×C22⋊C4—1222no—
683C2×C22⋊C4—1222no—
684C2×C22⋊C4—1222no—
685C2×C22⋊C4—1222no—
686C2×C22⋊C4—1222no—
687C2×C22⋊C4—1222no—
688C2×C22⋊C4—1222no—
689C2×C22⋊C4—1222no—
690C2×C22⋊C4—1222no—
691C2×C22⋊C4—1222no—
692C2×C22⋊C4—1222no—
693C2×C22⋊C4—2441no—
694C2×C22⋊C4—2441no—
695C2×C22⋊C4—2441no—
696C2×C22⋊C4—2441no—
697C2×C22⋊C4—2441no—
698C2×C22⋊C4—2441no—
699C2×C22⋊C4—2441no—
700C2×C22⋊C4—2441no—
701C2×C22⋊C4—2441no—
702C2×C22⋊C4—2441no—
703C2×C42—41no—
704C2×C42—41no—
705C2×C42—1222no—
706C2×C42—1222no—
707C2×C42—1222no—
708C2×C42—1222no—
709C2×C42—1222no—
710C2×C42—1222no—
711C2×C42—2441no—
712C2×C42—2441no—
713C2×C42—2441no—
714C2×C42C4×D6114yescomplemented
715#95—22no—
716#95—22no—
717#95—22no—
718#95—41no—
719#95—41no—
720#95—614no—
721#95—1222no—
722#95—1222no—
723#95—1222no—
724#95—1222no—
725#95—1222no—
726#95—1222no—
727#95—1222no—
728#95—2441no—
729#95—2441no—
730#95D24414yescomplemented
731C24—612no—
732C24—612no—
733C24—612no—
734C24—612no—
735C24—1221no—
736C24—1221no—
737C24—1221no—
738C24—1221no—
739C24—1221no—
740C24—1221no—
741C24—1221no—
742C24—1221no—
743C24—1221no—
744C24—1221no—
745C24—1221no—
746C24—1221no—
747C24—1221no—
748C24—1221no—
749C24—1221no—
750C24—1221no—
751C24—1221no—
752C24—1221no—
753C24—1221no—
754C24—1221no—
755C24—1221no—
756C24—1221no—
757C24—1221no—
758C24—1221no—
759C24—1221no—
760C24—1221no—
761C24C23×D6111yescharacteristic
762C2×D4—1228no—
763C2×D4—1228no—
764C2×D4—2444no—
765C2×D4—2444no—
766C2×D4—2444no—
767C2×D4—2444no—
768C2×D4—2444no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—612no—
810C22×C4—612no—
811C22×C4—612no—
812C22×C4—612no—
813C22×C4—612no—
814C22×C4—612no—
815C22×C4—612no—
816C22×C4—612no—
817C22×C4—1228no—
818C22×C4—1221no—
819C22×C4—1221no—
820C22×C4—1221no—
821C22×C4—1221no—
822C22×C4—1221no—
823C22×C4—1221no—
824C22×C4—1221no—
825C22×C4—1221no—
826C22×C4—1221no—
827C22×C4—1221no—
828C22×C4—1221no—
829C22×C4—1221no—
830C22×C4—1221no—
831C22×C4—1221no—
832C22×C4—1221no—
833C22×C4—1221no—
834C22×C4—1221no—
835C22×C4—1221no—
836C22×C4—1221no—
837C22×C4—1221no—
838C22×C4—1221no—
839C22×C4—1221no—
840C22×C4—1221no—
841C22×C4—1221no—
842C22×C4—1221no—
843C22×C4—1221no—
844C22×C4—1221no—
845C22×C4—1221no—
846C22×C4—1221no—
847C22×C4—1221no—
848C22×C4—1221no—
849C22×C4—1221no—
850C22×C4—1221no—
851C22×C4—1221no—
852C22×C4—2444no—
853C22×C4—2444no—
854C22×C4—2444no—
855C22×C4—2444no—
856C22×C4—2444no—
857C22×C4—2444no—
858C22×C4C2×C4×D6112yes—
859C22×C4C2×C4×D6112yes—
860C22×C4C2×C4×D6112yes—
861C22×C4C2×D24412yes—
862C22×C4C2×D24412yes—
863C22×C4C2×D24412yes—
864C22×C4#1175822212yes—
865C22×C4D4×D6112yes—
866C22×C4#1175822612yes—
867C4⋊C4—1228no—
868C4⋊C4—2444no—
869C22⋊C4—1228no—
870C22⋊C4—1228no—
871C22⋊C4—1228no—
872C22⋊C4—2444no—
873C22⋊C4—2444no—
874C22⋊C4—2444no—
875C22⋊C4—2444no—
876C22⋊C4—2444no—
877C22⋊C4—2444no—
878C22⋊C4—2444no—
879C22⋊C4—2444no—
880C42—44no—
881C42—2444no—
882C42—2444no—
883C42—2444no—
884C23—614no—
885C23—1222no—
886C23—1222no—
887C23—1222no—
888C23—1222no—
889C23—1222no—
890C23—1222no—
891C23—1222no—
892C23—1222no—
893C23—1222no—
894C23—1222no—
895C23—1222no—
896C23—1222no—
897C23—1222no—
898C23—1222no—
899C23—1222no—
900C23—1222no—
901C23—1222no—
902C23—1222no—
903C23—1222no—
904C23—1222no—
905C23—1222no—
906C23—1222no—
907C23—1222no—
908C23—1222no—
909C23—1222no—
910C23—2441no—
911C23—2441no—
912C23—2441no—
913C23—2441no—
914C23—2441no—
915C23—2441no—
916C23—2441no—
917C23—2441no—
918C23—2441no—
919C23—2441no—
920C23—2441no—
921C23—2441no—
922C23—2441no—
923C23—2441no—
924C23—2441no—
925C23—2441no—
926C23—2441no—
927C23—2441no—
928C23—2441no—
929C23—2441no—
930C23—2441no—
931C23—2441no—
932C23—2441no—
933C23—2441no—
934C23—2441no—
935C23—2441no—
936C23—2441no—
937C23—2441no—
938C23—2441no—
939C23—2441no—
940C23—2441no—
941C23—2441no—
942C23—2441no—
943C23—2441no—
944C23—2441no—
945C23—2441no—
946C23—2441no—
947C23—2441no—
948C23—2441no—
949C23—2441no—
950C23—2441no—
951C23—2441no—
952C23—2441no—
953C23—2441no—
954C23C22×C4×D6111yescharacteristic
955C23C2×D4×D6111yescharacteristic
956C23C22×D24411yescharacteristic
957C23#41×D6111yescharacteristic
958C23#41×D6111yescharacteristic
959C23#41×D6111yescharacteristic
960C23#41×D6111yescharacteristic
961C23#41×D6111yescharacteristic
962C23#41×D6111yescharacteristic
963C23C2×#1175822211yescharacteristic
964C23C2×#1175822611yescharacteristic
965C23#1451982211yescharacteristic
966C23#1451982211yescharacteristic
967C23#1451982311yescharacteristic
968C23#1451982311yescharacteristic
969D4—24416no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—614no—
1018C2×C4—1222no—
1019C2×C4—1222no—
1020C2×C4—1222no—
1021C2×C4—1222no—
1022C2×C4—1222no—
1023C2×C4—1222no—
1024C2×C4—1222no—
1025C2×C4—1222no—
1026C2×C4—1222no—
1027C2×C4—1222no—
1028C2×C4—1222no—
1029C2×C4—1222no—
1030C2×C4—1222no—
1031C2×C4—1222no—
1032C2×C4—1222no—
1033C2×C4—1222no—
1034C2×C4—1222no—
1035C2×C4—1222no—
1036C2×C4—1222no—
1037C2×C4—1222no—
1038C2×C4—1222no—
1039C2×C4—24416no—
1040C2×C4—2441no—
1041C2×C4—2441no—
1042C2×C4—2441no—
1043C2×C4—2441no—
1044C2×C4—2441no—
1045C2×C4—2441no—
1046C2×C4—2441no—
1047C2×C4—2441no—
1048C2×C4—2441no—
1049C2×C4—2441no—
1050C2×C4—2441no—
1051C2×C4—2441no—
1052C2×C4—2441no—
1053C2×C4—2441no—
1054C2×C4—2441no—
1055C2×C4—2441no—
1056C2×C4—2441no—
1057C2×C4—2441no—
1058C2×C4—2441no—
1059C2×C4—2441no—
1060C2×C4#1451973914yes—
1061C2×C4C4×D24414yes—
1062C22—1224no—
1063C22—1224no—
1064C22—1224no—
1065C22—4881no—
1066C22—4881no—
1067C22—4881no—
1068C22—4881no—
1069C22—4881no—
1070C22—4881no—
1071C22—4881no—
1072C22—4881no—
1073C22—2442no—
1074C22—2442no—
1075C22—2442no—
1076C22—2442no—
1077C22—2442no—
1078C22—2442no—
1079C22—2442no—
1080C22—2442no—
1081C22—2442no—
1082C22—2442no—
1083C22—2442no—
1084C22—2442no—
1085C22—2442no—
1086C22—2442no—
1087C22—2442no—
1088C22—2442no—
1089C22—2442no—
1090C22—2442no—
1091C22—2442no—
1092C22#117×D6111yescharacteristic
1093C22C2×#1451973911yescharacteristic
1094C22C2×C4×D24411yescharacteristic
1095C22#1684023011yescharacteristic
1096C22#1684023011yescharacteristic
1097C22#1684023511yescharacteristic
1098C22#1684023611yescharacteristic
1099C22#1684027411yescharacteristic
1100C22#1684027411yescharacteristic
1101C22#124×D6111yescharacteristic
1102C22#1684029011yescharacteristic
1103C22#1684029011yescharacteristic
1104C22#1684029711yescharacteristic
1105C22#1684029711yescharacteristic
1106C22#1684031111yescharacteristic
1107C22#1684034811yescharacteristic
1108C22#1684034811yescharacteristic
1109C22#1684036411yescharacteristic
1110C22#1684036411yescharacteristic
1111C22D4×D24411yescharacteristic
1112C22#1684040111yescharacteristic
1113C22#1684040111yescharacteristic
1114C22#1684040711yescharacteristic
1115C22#1684040711yescharacteristic
1116C22#1684043311yescharacteristic
1117C22#1684043411yescharacteristic
1118C22#1684043711yescharacteristic
1119C22#1684043711yescharacteristic
1120C22#1684043911yescharacteristic
1121C22#1684043911yescharacteristic
1122C22#1684046111yescharacteristic
1123C22#1684046111yescharacteristic
1124C22#1684046311yescharacteristic
1125C22#1684046311yescharacteristic
1126C22#1684049711yescharacteristic
1127C4—24no—
1128C4—24no—
1129C4—42no—
1130C4—42no—
1131C4—42no—
1132C4—81no—
1133C4—81no—
1134C4—1224no—
1135C4—2442no—
1136C4—2442no—
1137C4—2442no—
1138C4—2442no—
1139C4—2442no—
1140C2—4882no—
1141C2—2444no—
1142C2#2144826311yescharacteristic
1143C2#2144835811yescharacteristic
1144C2#2144858111yescharacteristic
1145C2#2144866511yescharacteristic
1146C2#2144875211yescharacteristic
1147C2#2144886911yescharacteristic
1148C2#2144888311yescharacteristic
1149C2#2144982311yescharacteristic
1150C2#2144986811yescharacteristic
1151C2#2144992811yescharacteristic
1152C2#2144994311yescharacteristic
1153C2#2145017011yescharacteristic
1154C2#2145045211yescharacteristic
1155C2#2145088611yescharacteristic
1156C2#2145133811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1434C2
socle, cosocleC24×C61C24
prime radicalC23×D244C22
hypercenter#1434D61
hypocenterC61#14034
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
2. C2×#16839651C2semidirect
3. C2×#16839647C2semidirect
5. C2×#16839609C2semidirect
6. #21444086C2semidirect
7. #21444067C2semidirect
8. #21444063C2semidirect
10. #21444055C2semidirect
11. #21444055C2semidirect
12. #21444055C2semidirect
13. #21444040C2semidirect
14. C4×#14519684C2semidirect
15. C61×#1434C2semidirect
34. #16839664C4semidirect
80. C2×C4⋊Dic61C2×C4semidirect
115. C2×#11758198C2×C4semidirect
116. C2×#11758198C2×C4semidirect
145. C2×C42×C61C2×C4semidirect
151. #95×C61D4semidirect
574. #1434D61semidirect
634. C61#14034semidirect
714. C2×C42C4×D61semidirect
730. #95D244semidirect

Maximal subgroups

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

subgroupindex
C2×#168396642
C2×#168396512
C2×#168396472
C2×#168396402
C2×#168396092
#214440862
#214440672
#214440632
#214440592
#214440552
#214440402
C4×#145196842
C61×#14342
#1403461