Finite Group Databasebeta

← #29608274

Subgroups — #29608274

Order 15616.

1866 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×#16839662C211yesmaximal, characteristic
2C2×#16839653C211yesmaximal, characteristic, complemented
3C2×#16839646C211yesmaximal, characteristic, complemented
4C2×#16839639C211yesmaximal, characteristic
5C2×#16839634C211yesmaximal, characteristic, complemented
6#21444085C211yesmaximal, characteristic, complemented
7#21444067C211yesmaximal, characteristic, complemented
8#21444063C211yesmaximal, characteristic, complemented
9#21444063C211yesmaximal, characteristic, complemented
10#21444062C211yesmaximal, characteristic, complemented
11#21444058C211yesmaximal, characteristic
12#21444047C211yesmaximal, characteristic, complemented
13#21444043C211yesmaximal, characteristic, complemented
14#21444041C211yesmaximal, characteristic, complemented
15C61×#1437C211yesmaximal, characteristic, complemented
16C23×C22⋊D61C2211yescharacteristic
17C24×Dic61C2211yescharacteristic
18C22×#11758196C2211yescharacteristic
19C22×#11758196C2211yescharacteristic
20C22×#11758196C2211yescharacteristic
21C22×#11758196C2211yescharacteristic
22C22×C22⋊Dic61C2211yescharacteristic
23C22×C22⋊Dic61C2211yescharacteristic
24C22×#11758198C2211yescharacteristic
25C22×#11758198C2211yescharacteristic
26C22×#11758198C2211yescharacteristic
27C22×#11758198C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×C4×Dic61C2211yescharacteristic
31#16839662C418yescomplemented
32#16839653—24no—
33#16839646—24no—
34#16839639—24no—
35#16839634—24no—
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×C22⋊C4×C61C2211yescharacteristic
50C22×C22⋊C4×C61C2211yescharacteristic
51C22×C22⋊C4×C61C2211yescharacteristic
52C22×C42×C61C2211yescharacteristic
53C2×#95×C61C2211yescharacteristic
54C2×#95×C61C2211yescharacteristic
55C2×#95×C61C2211yescharacteristic
56C24×D61C2311yescharacteristic
57C22×C22⋊D61—22no—
58C22×C22⋊D61—22no—
59C22×C22⋊D61—22no—
60C22×C22⋊D61—22no—
61C22×C22⋊D61—41no—
62C22×C22⋊D61—41no—
63C22×C22⋊D61C2×C414yes—
64C23×Dic61—22no—
65C23×Dic61—22no—
66C23×Dic61—22no—
67C23×Dic61—41no—
68C23×Dic61—41no—
69C23×Dic61—41no—
70C23×Dic61—41no—
71C23×Dic61C2311yescharacteristic
72C23×Dic61C2311yescharacteristic
73C23×Dic61C2311yescharacteristic
74C23×Dic61C2311yescharacteristic
75C23×Dic61C2311yescharacteristic
76C23×Dic61C2311yescharacteristic
77C23×Dic61C2311yescharacteristic
78C2×#11758196—22no—
79C2×#11758196—22no—
80C2×#11758196—22no—
81C2×#11758196—22no—
82C2×#11758196—22no—
83C2×#11758196—41no—
84C2×#11758196—41no—
85C2×#11758196—41no—
86C2×#11758196—41no—
87C2×#11758196—41no—
88C2×#11758196C2×C414yescomplemented
89C2×#11758196D414yescomplemented
90C2×C22⋊Dic61—22no—
91C2×C22⋊Dic61—22no—
92C2×C22⋊Dic61—22no—
93C2×C22⋊Dic61—41no—
94C2×C22⋊Dic61—41no—
95C2×C22⋊Dic61C2×C414yes—
96C2×#11758198—22no—
97C2×#11758198—22no—
98C2×#11758198—22no—
99C2×#11758198—22no—
100C2×#11758198—22no—
101C2×#11758198—22no—
102C2×#11758198—41no—
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×#11758198C2×C414yescomplemented
113C2×#11758198C2×C414yescomplemented
114C2×C4×Dic61—41no—
115C2×C4×Dic61—41no—
116C2×C4×Dic61C2×C414yescomplemented
117#14519684—22no—
118#14519684—22no—
119#14519684—22no—
120#14519684—22no—
121#14519684—22no—
122#14519684—22no—
123#14519684—22no—
124#14519684—22no—
125#14519684—22no—
126#14519684—41no—
127#14519684—41no—
128#14519684—41no—
129#14519684D414yes—
130C25×C61C2311yescharacteristic
131C23×C4×C61C2311yescharacteristic
132C23×C4×C61C2311yescharacteristic
133C23×C4×C61C2311yescharacteristic
134C23×C4×C61C2311yescharacteristic
135C23×C4×C61C2311yescharacteristic
136C23×C4×C61C2311yescharacteristic
137C2×C22⋊C4×C61—22no—
138C2×C22⋊C4×C61—22no—
139C2×C22⋊C4×C61—22no—
140C2×C22⋊C4×C61—22no—
141C2×C22⋊C4×C61—41no—
142C2×C22⋊C4×C61—41no—
143C2×C22⋊C4×C61—41no—
144C2×C22⋊C4×C61—41no—
145C2×C22⋊C4×C61C2×C414yes—
146C2×C42×C61—22no—
147C2×C42×C61—22no—
148C2×C42×C61—41no—
149#95×C61—41no—
150#95×C61—41no—
151#95×C61—41no—
152C24×C61—21no—
153C24×C61—21no—
154C24×C61—21no—
155C24×C61—21no—
156C24×C61—21no—
157C24×C61—21no—
158C24×C61—21no—
159C24×C61—21no—
160C24×C61—21no—
161C24×C61—21no—
162C24×C61—21no—
163C24×C61—21no—
164C24×C61C22×C412yes—
165C24×C61#4112yes—
166C24×C61#4112yes—
167C24×C61C2411yescharacteristic
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×D61—21no—
180C23×D61—21no—
181C23×D61—21no—
182C23×D61C22×C412yes—
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×C61C22×C412yes—
222C22×C4×C61C22×C412yes—
223C22×C4×C61C2×D412yes—
224C22×C4×C61C2×D412yes—
225C2×C22⋊D61—28no—
226C2×C22⋊D61—28no—
227C2×C22⋊D61—44no—
228C2×C22⋊D61—44no—
229C2×C22⋊D61—44no—
230C2×C22⋊D61—44no—
231C2×C22⋊D61—44no—
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×Dic61—21no—
267C22×Dic61—21no—
268C22×Dic61—21no—
269C22×Dic61—21no—
270C22×Dic61—21no—
271C22×Dic61—21no—
272C22×Dic61—44no—
273C22×Dic61—44no—
274C22×Dic61—44no—
275C22×Dic61—44no—
276C22×Dic61—44no—
277C22×Dic61—44no—
278C22×Dic61—44no—
279C22×Dic61C22×C412yes—
280C22×Dic61C22×C412yes—
281C22×Dic61C22×C412yes—
282C22×Dic61C2×D412yes—
283C22×Dic61C2×D412yes—
284C22×Dic61C2×D412yes—
285C22×Dic61C2×D412yes—
286C22×Dic61#4112yes—
287C22×Dic61#4112yes—
288C22⋊C4×C61—44no—
289C22⋊C4×C61—44no—
290C22⋊C4×C61—44no—
291C42×C61—44no—
292C22⋊Dic61—28no—
293C22⋊Dic61—44no—
294#11758198—28no—
295#11758198—44no—
296#11758198—44no—
297#11758198—44no—
298#11758198—44no—
299#11758198—44no—
300#11758196—28no—
301#11758196—44no—
302#11758196—44no—
303#11758196—44no—
304C4×Dic61—44no—
305C23×C61—22no—
306C23×C61—22no—
307C23×C61—22no—
308C23×C61—22no—
309C23×C61—22no—
310C23×C61—22no—
311C23×C61—22no—
312C23×C61—22no—
313C23×C61—22no—
314C23×C61—22no—
315C23×C61—22no—
316C23×C61—22no—
317C23×C61—22no—
318C23×C61—22no—
319C23×C61—22no—
320C23×C61—22no—
321C23×C61—22no—
322C23×C61—22no—
323C23×C61—41no—
324C23×C61—41no—
325C23×C61—41no—
326C23×C61—41no—
327C23×C61—41no—
328C23×C61—41no—
329C23×C61—41no—
330C23×C61—41no—
331C23×C61—41no—
332C23×C61—41no—
333C23×C61—41no—
334C23×C61—41no—
335C23×C61—41no—
336C23×C61—41no—
337C23×C61—41no—
338C23×C61—41no—
339C23×C61#11714yes—
340C23×C61C23×C411yescharacteristic
341C23×C61C22×D411yescharacteristic
342C23×C61C22×D411yescharacteristic
343C23×C61C2×#4111yescharacteristic
344C23×C61C2×#4111yescharacteristic
345C23×C61C2×#4111yescharacteristic
346C23×C61C2×#4111yescharacteristic
347C23×C61H(5,𝔽2)11yescharacteristic
348C23×C61H(5,𝔽2)11yescharacteristic
349C23×C61H(5,𝔽2)11yescharacteristic
350C23×C61H(5,𝔽2)11yescharacteristic
351C23×C61H(5,𝔽2)11yescharacteristic
352C23×C61H(5,𝔽2)11yescharacteristic
353C23×C612−1+411yescharacteristic
354C23×C612−1+411yescharacteristic
355C22×D61—22no—
356C22×D61—22no—
357C22×D61—22no—
358C22×D61—22no—
359C22×D61—22no—
360C22×D61—22no—
361C22×D61—22no—
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—41no—
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—41no—
403C2×C4×C61—41no—
404C2×C4×C61—41no—
405C2×C4×C61—41no—
406C2×C4×C61—41no—
407C2×C4×C61—41no—
408C2×C4×C61—41no—
409C2×C4×C61—41no—
410C2×C4×C61—41no—
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—
432C22⋊D61—416no—
433C2×Dic61—22no—
434C2×Dic61—22no—
435C2×Dic61—22no—
436C2×Dic61—22no—
437C2×Dic61—22no—
438C2×Dic61—22no—
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—416no—
455C2×Dic61—41no—
456C2×Dic61—41no—
457C2×Dic61—41no—
458C2×Dic61—41no—
459C2×Dic61—41no—
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—41no—
481C2×Dic61C4×D414yes—
482C2×Dic61C4×D414yes—
483#14429—611nomaximal, Sylow
484C22×C61—24no—
485C22×C61—24no—
486C22×C61—24no—
487C22×C61—42no—
488C22×C61—42no—
489C22×C61—42no—
490C22×C61—42no—
491C22×C61—42no—
492C22×C61—42no—
493C22×C61—42no—
494C22×C61—42no—
495C22×C61—42no—
496C22×C61—42no—
497C22×C61—42no—
498C22×C61—42no—
499C22×C61C2×#11711yescharacteristic
500C22×C61C2×C4×D411yescharacteristic
501C22×C61C2×C4×D411yescharacteristic
502C22×C61#51811yescharacteristic
503C22×C61#51811yescharacteristic
504C22×C61#52011yescharacteristic
505C22×C61#52011yescharacteristic
506C22×C61#53411yescharacteristic
507C22×C61#53511yescharacteristic
508C22×C61#53611yescharacteristic
509C22×C61#53711yescharacteristic
510C22×C61#53811yescharacteristic
511C22×C61#53811yescharacteristic
512C22×C61#53811yescharacteristic
513C22×C61#53911yescharacteristic
514C22×C61#53911yescharacteristic
515C22×C61#53911yescharacteristic
516C22×C61#54211yescharacteristic
517C22×C61#54211yescharacteristic
518C22×C61D4211yescharacteristic
519C22×C61#54611yescharacteristic
520C22×C61#54611yescharacteristic
521C22×C61#54611yescharacteristic
522C22×C61#54811yescharacteristic
523C22×C61#55011yescharacteristic
524C22×C61#55011yescharacteristic
525C22×C61#55111yescharacteristic
526C22×C61#55111yescharacteristic
527C22×C61#55211yescharacteristic
528C22×C61#55311yescharacteristic
529C22×C61#55911yescharacteristic
530C22×C61#56011yescharacteristic
531C22×C61#56011yescharacteristic
532C22×C61#56211yescharacteristic
533C22×C61#56211yescharacteristic
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—42no—
550C4×C61—42no—
551C4×C61—42no—
552C4×C61—42no—
553C4×C61—81no—
554C4×C61—81no—
555Dic61—24no—
556Dic61—24no—
557Dic61—42no—
558Dic61—42no—
559Dic61—42no—
560Dic61—81no—
561Dic61—81no—
562C2×#390—611no—
563C2×#388—611no—
564C2×#387—611no—
565C2×#386—611no—
566C2×#385—611no—
567#1445—611no—
568#1440—611no—
569#1439—611no—
570#1439—611no—
571#1439—611no—
572#1438—611no—
573#1437D6111yescharacteristic, complemented
574C4⋊#95—611no—
575#1434—611no—
576C22⋊#95—611no—
577C2×C61—44no—
578C2×C61#231811yescharacteristic
579C2×C61#232511yescharacteristic
580C2×C61#232611yescharacteristic
581C2×C61#234211yescharacteristic
582C2×C61#235211yescharacteristic
583C2×C61#236611yescharacteristic
584C2×C61#237711yescharacteristic
585C2×C61#267811yescharacteristic
586C2×C61#268111yescharacteristic
587C2×C61#269411yescharacteristic
588C2×C61#270511yescharacteristic
589C2×C61#271411yescharacteristic
590C2×C61#273011yescharacteristic
591C2×C61#275111yescharacteristic
592C2×C61#279611yescharacteristic
593D61—82no—
594C23×D4—611no—
595C24×C4—611no—
596C22×C4⋊C4—611no—
597C22×C4⋊C4—611no—
598C22×C4⋊C4—611no—
599C22×C4⋊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⋊C4C2×D6111yescharacteristic
609C22×C22⋊C4C2×D6111yescharacteristic
610C22×C22⋊C4C2×D6111yescharacteristic
611C22×C42—611no—
612C22×C42C2×D6111yescharacteristic
613#390—618no—
614#388—1224no—
615#387—1224no—
616#386—1224no—
617#385—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×#95—611no—
629C2×#95—611no—
630C2×#95—611no—
631C2×#95C2×D6111yescharacteristic
632C2×#95C2×D6111yescharacteristic
633C2×#95C2×D6111yescharacteristic
634C61#1442911yescharacteristic, complemented, Sylow
635C25—611no—
636C25C22×D6111yescharacteristic
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—611no—
651C23×C4—1222no—
652C23×C4—1222no—
653C23×C4—1222no—
654C23×C4—2441no—
655C23×C4—2441no—
656C23×C4—2441no—
657C23×C4—2441no—
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—614no—
666C2×C4⋊C4—1222no—
667C2×C4⋊C4—1222no—
668C2×C4⋊C4—1222no—
669C2×C4⋊C4—1222no—
670C2×C4⋊C4—1222no—
671C2×C4⋊C4—2441no—
672C2×C4⋊C4—2441no—
673C2×C4⋊C4—2441no—
674C2×C4⋊C4—2441no—
675C2×C4⋊C4—2441no—
676C2×C22⋊C4—22no—
677C2×C22⋊C4—22no—
678C2×C22⋊C4—22no—
679C2×C22⋊C4—22no—
680C2×C22⋊C4—41no—
681C2×C22⋊C4—41no—
682C2×C22⋊C4—41no—
683C2×C22⋊C4—41no—
684C2×C22⋊C4—614no—
685C2×C22⋊C4—614no—
686C2×C22⋊C4—614no—
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—1222no—
694C2×C22⋊C4—1222no—
695C2×C22⋊C4—1222no—
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×C22⋊C4—2441no—
704C2×C22⋊C4—2441no—
705C2×C22⋊C4—2441no—
706C2×C22⋊C4—2441no—
707C2×C22⋊C4—2441no—
708C2×C22⋊C4C4×D6114yes—
709C2×C42—22no—
710C2×C42—22no—
711C2×C42—41no—
712C2×C42—614no—
713C2×C42—2441no—
714C2×C42—2441no—
715#95—41no—
716#95—41no—
717#95—41no—
718#95—614no—
719#95—1222no—
720#95—1222no—
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#95—2441no—
731C24—21no—
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
743C24—612no—
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—
758C24C2×C4×D6112yes—
759C24#1175822212yes—
760C24#1175822212yes—
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—612no—
808C22×C4—612no—
809C22×C4—612no—
810C22×C4—612no—
811C22×C4—612no—
812C22×C4—612no—
813C22×C4—612no—
814C22×C4—612no—
815C22×C4—612no—
816C22×C4—1221no—
817C22×C4—1221no—
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—1221no—
853C22×C4—1221no—
854C22×C4—1221no—
855C22×C4—1221no—
856C22×C4—2444no—
857C22×C4—2444no—
858C22×C4—2444no—
859C22×C4—2444no—
860C22×C4—2444no—
861C22×C4—2444no—
862C22×C4—2444no—
863C22×C4C2×C4×D6112yes—
864C22×C4C2×C4×D6112yes—
865C22×C4D4×D6112yes—
866C22×C4D4×D6112yes—
867C4⋊C4—1228no—
868C4⋊C4—2444no—
869C4⋊C4—2444no—
870C4⋊C4—2444no—
871C22⋊C4—44no—
872C22⋊C4—44no—
873C22⋊C4—44no—
874C22⋊C4—1228no—
875C22⋊C4—1228no—
876C22⋊C4—2444no—
877C22⋊C4—2444no—
878C22⋊C4—2444no—
879C22⋊C4—2444no—
880C22⋊C4—2444no—
881C22⋊C4—2444no—
882C42—44no—
883C42—2444no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—1222no—
919C23—1222no—
920C23—1222no—
921C23—1222no—
922C23—1222no—
923C23—1222no—
924C23—1222no—
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#1451973414yes—
954C23C22×C4×D6111yescharacteristic
955C23C2×D4×D6111yescharacteristic
956C23C2×D4×D6111yescharacteristic
957C23#41×D6111yescharacteristic
958C23#41×D6111yescharacteristic
959C23C2×#1175822211yescharacteristic
960C23C2×#1175822211yescharacteristic
961C23#1451982211yescharacteristic
962C23#1451982211yescharacteristic
963C23#1451982211yescharacteristic
964C23#1451982211yescharacteristic
965C23#1451982311yescharacteristic
966C23#1451982311yescharacteristic
967C23#1451982411yescharacteristic
968C23#1451982411yescharacteristic
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—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
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—614no—
1013C2×C4—614no—
1014C2×C4—1222no—
1015C2×C4—1222no—
1016C2×C4—1222no—
1017C2×C4—1222no—
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—2441no—
1036C2×C4—2441no—
1037C2×C4—2441no—
1038C2×C4—2441no—
1039C2×C4—2441no—
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—24416no—
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—2441no—
1061C2×C4—2441no—
1062C22—24no—
1063C22—24no—
1064C22—24no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—42no—
1070C22—42no—
1071C22—42no—
1072C22—42no—
1073C22—42no—
1074C22—42no—
1075C22—42no—
1076C22—42no—
1077C22—4881no—
1078C22—4881no—
1079C22—4881no—
1080C22—4881no—
1081C22—4881no—
1082C22—4881no—
1083C22—4881no—
1084C22—4881no—
1085C22—2442no—
1086C22—2442no—
1087C22—2442no—
1088C22—2442no—
1089C22—2442no—
1090C22—2442no—
1091C22—2442no—
1092C22C2×#1451973411yescharacteristic
1093C22C4×D4×D6111yescharacteristic
1094C22C4×D4×D6111yescharacteristic
1095C22#1684023411yescharacteristic
1096C22#1684023511yescharacteristic
1097C22#1684024111yescharacteristic
1098C22#1684024211yescharacteristic
1099C22#1684032311yescharacteristic
1100C22#1684032811yescharacteristic
1101C22#1684033411yescharacteristic
1102C22#1684034111yescharacteristic
1103C22#1684034511yescharacteristic
1104C22#1684034511yescharacteristic
1105C22#1684034611yescharacteristic
1106C22#1684035311yescharacteristic
1107C22#1684035411yescharacteristic
1108C22#1684035411yescharacteristic
1109C22#1684037611yescharacteristic
1110C22#1684037811yescharacteristic
1111C22#1684039411yescharacteristic
1112C22#1684040211yescharacteristic
1113C22#1684040211yescharacteristic
1114C22#1684040811yescharacteristic
1115C22#1684042111yescharacteristic
1116C22#1684043011yescharacteristic
1117C22#1684043011yescharacteristic
1118C22#1684043611yescharacteristic
1119C22#1684044111yescharacteristic
1120C22#1684044511yescharacteristic
1121C22#1684046111yescharacteristic
1122C22#1684049611yescharacteristic
1123C22#1684049911yescharacteristic
1124C22#1684050011yescharacteristic
1125C22#1684050611yescharacteristic
1126C22#1684050711yescharacteristic
1127C4—42no—
1128C4—42no—
1129C4—42no—
1130C4—42no—
1131C4—81no—
1132C4—81no—
1133C4—1224no—
1134C4—1224no—
1135C4—4881no—
1136C4—4881no—
1137C4—2442no—
1138C4—2442no—
1139C4—2442no—
1140C2—44no—
1141C2—4882no—
1142C2#2144844611yescharacteristic
1143C2#2144852311yescharacteristic
1144C2#2144852811yescharacteristic
1145C2#2144866211yescharacteristic
1146C2#2144874211yescharacteristic
1147C2#2144888211yescharacteristic
1148C2#2144897011yescharacteristic
1149C2#2145214511yescharacteristic
1150C2#2145217511yescharacteristic
1151C2#2145234211yescharacteristic
1152C2#2145249511yescharacteristic
1153C2#2145261511yescharacteristic
1154C2#2145281611yescharacteristic
1155C2#2145307011yescharacteristic
1156C2#2145365911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1437C2
socle, cosocleC24×C61C24
prime radicalC23×C22⋊D61C22
hypercenter#1437D61
hypocenterC61#14429
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
2. C2×#16839653C2semidirect
3. C2×#16839646C2semidirect
5. C2×#16839634C2semidirect
6. #21444085C2semidirect
7. #21444067C2semidirect
8. #21444063C2semidirect
9. #21444063C2semidirect
10. #21444062C2semidirect
12. #21444047C2semidirect
13. #21444043C2semidirect
14. #21444041C2semidirect
15. C61×#1437C2semidirect
31. #16839662C4semidirect
88. C2×#11758196C2×C4semidirect
89. C2×#11758196D4semidirect
112. C2×#11758198C2×C4semidirect
113. C2×#11758198C2×C4semidirect
116. C2×C4×Dic61C2×C4semidirect
573. #1437D61semidirect
634. C61#14429semidirect

Maximal subgroups

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

subgroupindex
C2×#168396622
C2×#168396532
C2×#168396462
C2×#168396392
C2×#168396342
#214440852
#214440672
#214440632
#214440622
#214440582
#214440472
#214440432
#214440412
C61×#14372
#1442961