Finite Group Databasebeta

← #29602145

Subgroups — #29602145

Order 15616.

2546 conjugacy classes of subgroups.

The subgroup lattice has 1206 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519737C211yesmaximal, characteristic
2C2×#16839641C211yesmaximal, characteristic
3C2×#16839639C211yesmaximal, characteristic
4C2×#16839624C211yesmaximal, characteristic, complemented
5C22×#14519684C211yesmaximal, characteristic, complemented
6#21444085C211yesmaximal, characteristic, complemented
7#21444085C211yesmaximal, characteristic, complemented
8#21444067C211yesmaximal, characteristic, complemented
9#21444067C211yesmaximal, characteristic, complemented
10#21444045C211yesmaximal, characteristic, complemented
11#21444044C211yesmaximal, characteristic, complemented
12#21444041C211yesmaximal, characteristic, complemented
13#21444041C211yesmaximal, characteristic, complemented
14#21444040C211yesmaximal, characteristic, complemented
15C61×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×C22⋊D61C2211yescharacteristic
17C24×Dic61C2211yescharacteristic
18C24×Dic61C2211yescharacteristic
19C23×C4×D61C2211yescharacteristic
20C2×#14519737—24no—
21C2×#14519737—24no—
22C2×#14519737C418yescomplemented
23C22×#11758196C2211yescharacteristic
24C22×C22⋊Dic61C2211yescharacteristic
25C22×#11758198C2211yescharacteristic
26C22×#11758198C2211yescharacteristic
27C22×#11758198C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×C4×Dic61C2211yescharacteristic
31#16839641—24no—
32#16839639—24no—
33#16839624—24no—
34C2×#14519684—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
49C2×#14519684C2211yescharacteristic
50C2×#14519684C2211yescharacteristic
51C24×C4×C61C2211yescharacteristic
52C22×C22⋊C4×C61C2211yescharacteristic
53C22×C22⋊C4×C61C2211yescharacteristic
54C2×#95×C61C2211yescharacteristic
55C2×#95×C61C2211yescharacteristic
56C2×#95×C61C2211yescharacteristic
57C2×#95×C61C2211yescharacteristic
58C24×D61C2311yescharacteristic
59C22×C22⋊D61—22no—
60C22×C22⋊D61—22no—
61C22×C22⋊D61—22no—
62C22×C22⋊D61—22no—
63C22×C22⋊D61C2×C414yes—
64C22×C22⋊D61D414yes—
65C22×C22⋊D61D414yes—
66C23×Dic61—22no—
67C23×Dic61—22no—
68C23×Dic61—22no—
69C23×Dic61—22no—
70C23×Dic61—22no—
71C23×Dic61—22no—
72C23×Dic61—22no—
73C23×Dic61—22no—
74C23×Dic61—22no—
75C23×Dic61—41no—
76C23×Dic61—41no—
77C23×Dic61—41no—
78C23×Dic61—41no—
79C23×Dic61C2×C414yes—
80C23×Dic61C2311yescharacteristic
81C23×Dic61C2311yescharacteristic
82C23×Dic61C2311yescharacteristic
83C23×Dic61C2311yescharacteristic
84C23×Dic61C2311yescharacteristic
85C23×Dic61C2311yescharacteristic
86C23×Dic61C2311yescharacteristic
87C22×C4×D61—22no—
88C22×C4×D61—22no—
89C22×C4×D61—22no—
90C22×C4×D61—22no—
91C22×C4×D61—41no—
92C22×C4×D61—41no—
93C22×C4×D61C2×C414yescomplemented
94#14519737—232no—
95C2×#11758196—22no—
96C2×#11758196—22no—
97C2×#11758196C2×C414yescomplemented
98C2×C22⋊Dic61—22no—
99C2×C22⋊Dic61—22no—
100C2×C22⋊Dic61—22no—
101C2×#11758198—22no—
102C2×#11758198—22no—
103C2×#11758198—22no—
104C2×#11758198—22no—
105C2×#11758198—22no—
106C2×#11758198—22no—
107C2×#11758198—22no—
108C2×#11758198—22no—
109C2×#11758198—22no—
110C2×#11758198—22no—
111C2×#11758198—41no—
112C2×#11758198—41no—
113C2×#11758198—41no—
114C2×#11758198—41no—
115C2×#11758198C2×C414yescomplemented
116C2×C4×Dic61—22no—
117C2×C4×Dic61—22no—
118C2×C4×Dic61C2×C414yescomplemented
119#14519684—22no—
120#14519684—22no—
121#14519684—22no—
122#14519684—22no—
123#14519684—22no—
124#14519684—22no—
125#14519684—22no—
126#14519684—22no—
127#14519684—22no—
128#14519684—22no—
129#14519684—22no—
130#14519684—41no—
131#14519684—41no—
132#14519684—41no—
133#14519684—41no—
134#14519684D414yescomplemented
135C25×C61C2311yescharacteristic
136C23×C4×C61—22no—
137C23×C4×C61—22no—
138C23×C4×C61—22no—
139C23×C4×C61—22no—
140C23×C4×C61—22no—
141C23×C4×C61—41no—
142C23×C4×C61—41no—
143C23×C4×C61C2311yescharacteristic
144C23×C4×C61C2311yescharacteristic
145C23×C4×C61C2311yescharacteristic
146C23×C4×C61C2311yescharacteristic
147C23×C4×C61C2311yescharacteristic
148C23×C4×C61C2311yescharacteristic
149C2×C22⋊C4×C61—22no—
150C2×C22⋊C4×C61—22no—
151C2×C22⋊C4×C61—22no—
152C2×C22⋊C4×C61—22no—
153C2×C22⋊C4×C61—22no—
154C2×C22⋊C4×C61C2×C414yes—
155#95×C61—22no—
156#95×C61—22no—
157#95×C61—41no—
158#95×C61—41no—
159C24×C61—21no—
160C24×C61—21no—
161C24×C61—21no—
162C24×C61—21no—
163C24×C61—21no—
164C24×C61—21no—
165C24×C61—21no—
166C24×C61—21no—
167C24×C61C22×C412yes—
168C24×C61C2×D412yes—
169C24×C61C2×D412yes—
170C24×C61#4112yes—
171C24×C61#4112yes—
172C24×C61#4112yes—
173C24×C61#4112yes—
174C24×C61C2411yescharacteristic
175C23×D61—21no—
176C23×D61—21no—
177C23×D61—21no—
178C23×D61—21no—
179C23×D61—21no—
180C23×D61—21no—
181C23×D61—21no—
182C23×D61—21no—
183C23×D61—21no—
184C23×D61—21no—
185C23×D61—21no—
186C23×D61—21no—
187C23×D61C22×C412yes—
188C23×D61C2×D412yes—
189C23×D61C2×D412yes—
190C22×C4×C61—28no—
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×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—44no—
230C22×C4×C61—44no—
231C22×C4×C61—44no—
232C22×C4×C61—44no—
233C22×C4×C61—44no—
234C22×C4×C61—44no—
235C22×C4×C61C22×C412yes—
236C22×C4×C61C22×C412yes—
237C22×C4×C61C2×D412yes—
238C22×C4×C61#4112yes—
239C2×C22⋊D61—28no—
240C2×C22⋊D61—28no—
241C2×C22⋊D61—28no—
242C2×C22⋊D61—28no—
243C2×C22⋊D61—28no—
244C2×C22⋊D61—28no—
245C2×C22⋊D61C22⋊C4116yes—
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—28no—
255C22×Dic61—28no—
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—21no—
273C22×Dic61—21no—
274C22×Dic61—28no—
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×Dic61—44no—
296C22×Dic61—44no—
297C22×Dic61—44no—
298C22×Dic61—44no—
299C22×Dic61—44no—
300C22×Dic61C22×C412yes—
301C22×Dic61C22×C412yes—
302C22×Dic61C22×C412yes—
303C22×Dic61C2×D412yes—
304C22×Dic61C2×D412yes—
305C22×Dic61C2×D412yes—
306C22×Dic61C2×D412yes—
307C22×Dic61#4112yes—
308C22×Dic61#4112yes—
309C2×C4×D61—28no—
310C2×C4×D61—28no—
311C2×C4×D61—44no—
312C2×C4×D61—44no—
313C2×C4×D61—44no—
314C2×C4×D61—44no—
315C2×C4×D61—44no—
316C22⋊C4×C61—28no—
317C22⋊C4×C61—44no—
318C22⋊Dic61—44no—
319#11758198—28no—
320#11758198—44no—
321#11758198—44no—
322#11758198—44no—
323#11758198—44no—
324#11758196—28no—
325C4×Dic61—28no—
326C23×C61—22no—
327C23×C61—22no—
328C23×C61—22no—
329C23×C61—22no—
330C23×C61—22no—
331C23×C61—22no—
332C23×C61—22no—
333C23×C61—22no—
334C23×C61—22no—
335C23×C61—22no—
336C23×C61—22no—
337C23×C61—22no—
338C23×C61—22no—
339C23×C61—22no—
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×C61C2×C22⋊C414yes—
355C23×C61#11714yes—
356C23×C61#11714yes—
357C23×C61#12314yes—
358C23×C61#12314yes—
359C23×C61#12314yes—
360C23×C61#12314yes—
361C23×C61C23×C411yescharacteristic
362C23×C61C22×D411yescharacteristic
363C23×C61C22×D411yescharacteristic
364C23×C61C22×D411yescharacteristic
365C23×C61C2×#4111yescharacteristic
366C23×C61C2×#4111yescharacteristic
367C23×C61C2×#4111yescharacteristic
368C23×C61C2×#4111yescharacteristic
369C23×C61C2×#4111yescharacteristic
370C23×C61C2×#4111yescharacteristic
371C23×C61C2×#4111yescharacteristic
372C23×C61H(5,𝔽2)11yescharacteristic
373C23×C61H(5,𝔽2)11yescharacteristic
374C23×C61H(5,𝔽2)11yescharacteristic
375C23×C612−1+411yescharacteristic
376C22×D61—22no—
377C22×D61—22no—
378C22×D61—22no—
379C22×D61—22no—
380C22×D61—22no—
381C22×D61—22no—
382C22×D61—22no—
383C22×D61—22no—
384C22×D61—22no—
385C22×D61—22no—
386C22×D61—22no—
387C22×D61—22no—
388C22×D61—22no—
389C22×D61—22no—
390C22×D61—22no—
391C22×D61—22no—
392C22×D61—22no—
393C22×D61—22no—
394C22×D61—41no—
395C22×D61—41no—
396C22×D61—41no—
397C22×D61—41no—
398C22×D61—41no—
399C22×D61—41no—
400C22×D61—41no—
401C22×D61—41no—
402C22×D61—41no—
403C22×D61—41no—
404C22×D61—41no—
405C22×D61—41no—
406C22×D61—41no—
407C22×D61—41no—
408C22×D61—41no—
409C22×D61—41no—
410C22×D61C2×C22⋊C414yes—
411C2×C4×C61—22no—
412C2×C4×C61—22no—
413C2×C4×C61—22no—
414C2×C4×C61—22no—
415C2×C4×C61—22no—
416C2×C4×C61—22no—
417C2×C4×C61—22no—
418C2×C4×C61—22no—
419C2×C4×C61—22no—
420C2×C4×C61—22no—
421C2×C4×C61—22no—
422C2×C4×C61—22no—
423C2×C4×C61—416no—
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×C61—41no—
438C2×C4×C61—41no—
439C2×C4×C61—41no—
440C2×C4×C61—41no—
441C2×C4×C61—41no—
442C2×C4×C61—41no—
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—
454C22⋊D61—232no—
455C2×Dic61—22no—
456C2×Dic61—22no—
457C2×Dic61—22no—
458C2×Dic61—22no—
459C2×Dic61—22no—
460C2×Dic61—22no—
461C2×Dic61—22no—
462C2×Dic61—22no—
463C2×Dic61—22no—
464C2×Dic61—22no—
465C2×Dic61—22no—
466C2×Dic61—22no—
467C2×Dic61—22no—
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—416no—
477C2×Dic61—416no—
478C2×Dic61—41no—
479C2×Dic61—41no—
480C2×Dic61—41no—
481C2×Dic61—41no—
482C2×Dic61—41no—
483C2×Dic61—41no—
484C2×Dic61—41no—
485C2×Dic61—41no—
486C2×Dic61—41no—
487C2×Dic61—41no—
488C2×Dic61—41no—
489C2×Dic61—41no—
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×Dic61C2×C22⋊C414yes—
505C2×Dic61C4×D414yes—
506C4×D61—416no—
507#13894—611nomaximal, Sylow
508C22×C61—24no—
509C22×C61—24no—
510C22×C61—24no—
511C22×C61—24no—
512C22×C61—24no—
513C22×C61—24no—
514C22×C61—24no—
515C22×C61—24no—
516C22×C61—24no—
517C22×C61—24no—
518C22×C61—24no—
519C22×C61—24no—
520C22×C61—24no—
521C22×C61—24no—
522C22×C61#38118yescomplemented
523C22×C61C22×C22⋊C411yescharacteristic
524C22×C61C2×#11711yescharacteristic
525C22×C61C2×#11711yescharacteristic
526C22×C61C2×C4×D411yescharacteristic
527C22×C61C4×#4111yescharacteristic
528C22×C61#51811yescharacteristic
529C22×C61#52011yescharacteristic
530C22×C61C2×#12311yescharacteristic
531C22×C61C2×#12311yescharacteristic
532C22×C61C2×#12311yescharacteristic
533C22×C61C2×#12311yescharacteristic
534C22×C61#52511yescharacteristic
535C22×C61#52511yescharacteristic
536C22×C61#52911yescharacteristic
537C22×C61#52911yescharacteristic
538C22×C61#53811yescharacteristic
539C22×C61#53811yescharacteristic
540C22×C61#53911yescharacteristic
541C22×C61#53911yescharacteristic
542C22×C61D4211yescharacteristic
543C22×C61D4211yescharacteristic
544C22×C61#54611yescharacteristic
545C22×C61#54611yescharacteristic
546C22×C61#54611yescharacteristic
547C22×C61#54611yescharacteristic
548C22×C61#54611yescharacteristic
549C22×C61#54711yescharacteristic
550C22×C61#54711yescharacteristic
551C22×C61#54811yescharacteristic
552C22×C61#55111yescharacteristic
553C22×C61#55111yescharacteristic
554C22×C61#55211yescharacteristic
555C22×C61#55311yescharacteristic
556C22×C61#55311yescharacteristic
557C22×C61#55311yescharacteristic
558C2×D61—24no—
559C2×D61—24no—
560C2×D61—24no—
561C2×D61—42no—
562C2×D61—42no—
563C2×D61—42no—
564C2×D61—42no—
565C2×D61—42no—
566C2×D61—42no—
567C2×D61—42no—
568C2×D61—42no—
569C2×D61—42no—
570C2×D61—42no—
571C2×D61—42no—
572C2×D61—42no—
573C4×C61—42no—
574C4×C61—42no—
575C4×C61—42no—
576C4×C61—42no—
577C4×C61—81no—
578C4×C61—81no—
579Dic61—24no—
580Dic61—24no—
581Dic61—42no—
582Dic61—42no—
583Dic61—42no—
584Dic61—81no—
585Dic61—81no—
586C22×C4×D4—611no—
587C2×#386—611no—
588C2×#386—611no—
589C2×#381—611no—
590C22×#95—611no—
591#1445—611no—
592#1445—611no—
593#1440—611no—
594#1440—611no—
595#1434—611no—
596#1434—611no—
597C22⋊#95—611no—
598C22⋊#95—611no—
599C22⋊#95—611no—
600C22⋊#95D6111yescharacteristic, complemented
601C2×C61—28no—
602C2×C61C2×#38111yescharacteristic
603C2×C61#229011yescharacteristic
604C2×C61#231811yescharacteristic
605C2×C61D4×C22⋊C411yescharacteristic
606C2×C61#233911yescharacteristic
607C2×C61#235211yescharacteristic
608C2×C61#235311yescharacteristic
609C2×C61#241811yescharacteristic
610C2×C61#241811yescharacteristic
611C2×C61#241911yescharacteristic
612C2×C61#241911yescharacteristic
613C2×C61#244311yescharacteristic
614C2×C61#244311yescharacteristic
615C2×C61#244411yescharacteristic
616C2×C61#244411yescharacteristic
617D61—44no—
618C23×D4—611no—
619C24×C4—611no—
620C24×C4—611no—
621C24×C4—611no—
622C24×C4C2×D6111yescharacteristic
623C2×C4×D4—618no—
624C2×C4×D4—1224no—
625C2×C4×D4—1224no—
626C22×C4⋊C4—611no—
627C22×C22⋊C4—611no—
628C22×C22⋊C4—611no—
629C22×C22⋊C4—611no—
630C22×C22⋊C4—611no—
631C22×C22⋊C4—611no—
632C22×C22⋊C4—611no—
633C22×C22⋊C4C2×D6111yescharacteristic
634C22×C22⋊C4C2×D6111yescharacteristic
635C22×C42—611no—
636#386—1224no—
637#386—1224no—
638#381—1224no—
639C2×#95—611no—
640C2×#95—611no—
641C2×#95—611no—
642C2×#95—611no—
643C2×#95—611no—
644C2×#95—611no—
645C2×#95—611no—
646C2×#95—611no—
647C2×#95—611no—
648C2×#95—611no—
649C2×#95—611no—
650C2×#95—611no—
651C2×#95—611no—
652C2×#95—611no—
653C2×#95—611no—
654C2×#95—611no—
655C2×#95—1224no—
656C2×#95C2×D6111yescharacteristic
657C2×#95C2×D6111yescharacteristic
658C2×#95C2×D6111yescharacteristic
659C2×#95C2×D6111yescharacteristic
660C61#1389411yescharacteristic, complemented, Sylow
661C25—611no—
662C25C22×D6111yescharacteristic
663C22×D4—614no—
664C22×D4—614no—
665C22×D4—614no—
666C22×D4—1222no—
667C22×D4—1222no—
668C22×D4—1222no—
669C22×D4—1222no—
670C23×C4—22no—
671C23×C4—22no—
672C23×C4—22no—
673C23×C4—22no—
674C23×C4—22no—
675C23×C4—41no—
676C23×C4—41no—
677C23×C4—611no—
678C23×C4—611no—
679C23×C4—611no—
680C23×C4—611no—
681C23×C4—611no—
682C23×C4—614no—
683C23×C4—614no—
684C23×C4—611no—
685C23×C4—611no—
686C23×C4—1222no—
687C23×C4—1222no—
688C23×C4—1222no—
689C23×C4—1222no—
690C23×C4—1222no—
691C23×C4—1222no—
692C23×C4—1222no—
693C23×C4—1222no—
694C23×C4—1222no—
695C23×C4—1222no—
696C23×C4—1222no—
697C23×C4—1222no—
698C23×C4—1222no—
699C23×C4—2441no—
700C23×C4—2441no—
701C23×C4—2441no—
702C23×C4—2441no—
703C23×C4—2441no—
704C23×C4—2441no—
705C23×C4C22×D6111yescharacteristic
706C23×C4C22×D6111yescharacteristic
707C23×C4C22×D6111yescharacteristic
708C23×C4C22×D6111yescharacteristic
709C23×C4C22×D6111yescharacteristic
710C23×C4C22×D6111yescharacteristic
711C4×D4—12232no—
712C2×C4⋊C4—614no—
713C2×C4⋊C4—1222no—
714C2×C4⋊C4—1222no—
715C2×C22⋊C4—22no—
716C2×C22⋊C4—22no—
717C2×C22⋊C4—22no—
718C2×C22⋊C4—22no—
719C2×C22⋊C4—22no—
720C2×C22⋊C4—614no—
721C2×C22⋊C4—1222no—
722C2×C22⋊C4—1222no—
723C2×C22⋊C4—1222no—
724C2×C22⋊C4—1222no—
725C2×C22⋊C4—1222no—
726C2×C22⋊C4—1222no—
727C2×C22⋊C4—1222no—
728C2×C22⋊C4—1222no—
729C2×C22⋊C4—1222no—
730C2×C22⋊C4—1222no—
731C2×C22⋊C4—1222no—
732C2×C22⋊C4—1222no—
733C2×C22⋊C4—1222no—
734C2×C22⋊C4—2441no—
735C2×C22⋊C4—2441no—
736C2×C22⋊C4—2441no—
737C2×C22⋊C4—2441no—
738C2×C22⋊C4C4×D6114yes—
739C2×C42—614no—
740C2×C42—1222no—
741C2×C42—1222no—
742#95—22no—
743#95—22no—
744#95—41no—
745#95—41no—
746#95—614no—
747#95—1222no—
748#95—1222no—
749#95—1222no—
750#95—1222no—
751#95—1222no—
752#95—1222no—
753#95—1222no—
754#95—1222no—
755#95—1222no—
756#95—1222no—
757#95—1222no—
758#95—2441no—
759#95—2441no—
760#95—2441no—
761#95—2441no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—612no—
771C24—612no—
772C24—612no—
773C24—1221no—
774C24—1221no—
775C24—1221no—
776C24—1221no—
777C24—1221no—
778C24—1221no—
779C24—1221no—
780C24—1221no—
781C24—1221no—
782C24—1221no—
783C24—1221no—
784C24—1221no—
785C24C2×C4×D6112yes—
786C24#1175822212yes—
787C24#1175822212yes—
788C24D4×D6112yes—
789C24D4×D6112yes—
790C24#1175822412yes—
791C24#1175822612yes—
792C24C23×D6111yescharacteristic
793C2×D4—6116no—
794C2×D4—1228no—
795C2×D4—1228no—
796C2×D4—1228no—
797C2×D4—1228no—
798C2×D4—1228no—
799C2×D4—1228no—
800C22×C4—28no—
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—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
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—44no—
840C22×C4—44no—
841C22×C4—44no—
842C22×C4—44no—
843C22×C4—44no—
844C22×C4—44no—
845C22×C4—612no—
846C22×C4—612no—
847C22×C4—612no—
848C22×C4—612no—
849C22×C4—612no—
850C22×C4—612no—
851C22×C4—612no—
852C22×C4—612no—
853C22×C4—612no—
854C22×C4—1228no—
855C22×C4—1228no—
856C22×C4—1228no—
857C22×C4—1221no—
858C22×C4—1221no—
859C22×C4—1221no—
860C22×C4—1221no—
861C22×C4—1221no—
862C22×C4—1221no—
863C22×C4—1221no—
864C22×C4—1221no—
865C22×C4—1228no—
866C22×C4—1221no—
867C22×C4—1221no—
868C22×C4—1221no—
869C22×C4—1221no—
870C22×C4—1221no—
871C22×C4—1221no—
872C22×C4—1221no—
873C22×C4—1221no—
874C22×C4—1221no—
875C22×C4—1221no—
876C22×C4—1221no—
877C22×C4—1221no—
878C22×C4—1221no—
879C22×C4—1221no—
880C22×C4—1221no—
881C22×C4—1221no—
882C22×C4—1221no—
883C22×C4—1221no—
884C22×C4—1228no—
885C22×C4—1221no—
886C22×C4—1221no—
887C22×C4—1221no—
888C22×C4—1221no—
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—2444no—
900C22×C4—2444no—
901C22×C4—2444no—
902C22×C4—2444no—
903C22×C4—2444no—
904C22×C4—2444no—
905C22×C4—2444no—
906C22×C4—2444no—
907C22×C4—2444no—
908C22×C4—2444no—
909C22×C4—2444no—
910C22×C4—2444no—
911C22×C4—2444no—
912C22×C4—2444no—
913C22×C4—2444no—
914C22×C4—2444no—
915C22×C4C2×C4×D6112yes—
916C22×C4C2×C4×D6112yes—
917C22×C4D4×D6112yes—
918C22×C4#1175822412yes—
919C4⋊C4—1228no—
920C22⋊C4—28no—
921C22⋊C4—44no—
922C22⋊C4—1228no—
923C22⋊C4—2444no—
924C22⋊C4—2444no—
925C22⋊C4—2444no—
926C22⋊C4—2444no—
927C22⋊C4—2444no—
928C42—1228no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—614no—
958C23—1222no—
959C23—1222no—
960C23—1222no—
961C23—1222no—
962C23—1222no—
963C23—1222no—
964C23—1222no—
965C23—1222no—
966C23—1222no—
967C23—1222no—
968C23—1222no—
969C23—1222no—
970C23—1222no—
971C23—1222no—
972C23—1222no—
973C23—1222no—
974C23—1222no—
975C23—1222no—
976C23—2441no—
977C23—2441no—
978C23—2441no—
979C23—2441no—
980C23—2441no—
981C23—2441no—
982C23—2441no—
983C23—2441no—
984C23—2441no—
985C23—2441no—
986C23—2441no—
987C23—2441no—
988C23—2441no—
989C23—2441no—
990C23—2441no—
991C23—2441no—
992C23C22⋊C4×D6114yes—
993C23#1451973414yes—
994C23#1451973514yes—
995C23#1451975914yes—
996C23#1451975914yes—
997C23#1451976214yes—
998C23#1451976214yes—
999C23C22×C4×D6111yescharacteristic
1000C23C2×D4×D6111yescharacteristic
1001C23C2×D4×D6111yescharacteristic
1002C23C2×D4×D6111yescharacteristic
1003C23#41×D6111yescharacteristic
1004C23#41×D6111yescharacteristic
1005C23C2×#1175822411yescharacteristic
1006C23C2×#1175822411yescharacteristic
1007C23C2×#1175822211yescharacteristic
1008C23C2×#1175822211yescharacteristic
1009C23C2×#1175822611yescharacteristic
1010C23#1451982211yescharacteristic
1011C23#1451982211yescharacteristic
1012C23#1451982311yescharacteristic
1013C23#1451982411yescharacteristic
1014D4—12232no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—416no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—614no—
1059C2×C4—614no—
1060C2×C4—1222no—
1061C2×C4—1222no—
1062C2×C4—1222no—
1063C2×C4—1222no—
1064C2×C4—1222no—
1065C2×C4—1222no—
1066C2×C4—1222no—
1067C2×C4—1222no—
1068C2×C4—1222no—
1069C2×C4—1222no—
1070C2×C4—1222no—
1071C2×C4—1222no—
1072C2×C4—1222no—
1073C2×C4—1222no—
1074C2×C4—1222no—
1075C2×C4—1222no—
1076C2×C4—1222no—
1077C2×C4—1222no—
1078C2×C4—1222no—
1079C2×C4—1222no—
1080C2×C4—1222no—
1081C2×C4—24416no—
1082C2×C4—24416no—
1083C2×C4—2441no—
1084C2×C4—2441no—
1085C2×C4—2441no—
1086C2×C4—2441no—
1087C2×C4—2441no—
1088C2×C4—2441no—
1089C2×C4—2441no—
1090C2×C4—2441no—
1091C2×C4—2441no—
1092C2×C4—2441no—
1093C2×C4—2441no—
1094C2×C4—2441no—
1095C2×C4—2441no—
1096C2×C4—2441no—
1097C2×C4—24416no—
1098C2×C4—2441no—
1099C2×C4—2441no—
1100C2×C4—2441no—
1101C2×C4—2441no—
1102C2×C4—2441no—
1103C2×C4—2441no—
1104C2×C4—2441no—
1105C2×C4—2441no—
1106C2×C4—2441no—
1107C2×C4—2441no—
1108C2×C4—2441no—
1109C2×C4—2441no—
1110C22—24no—
1111C22—24no—
1112C22—24no—
1113C22—24no—
1114C22—24no—
1115C22—24no—
1116C22—24no—
1117C22—24no—
1118C22—24no—
1119C22—24no—
1120C22—24no—
1121C22—24no—
1122C22—24no—
1123C22—24no—
1124C22—1224no—
1125C22—1224no—
1126C22—1224no—
1127C22—2442no—
1128C22—2442no—
1129C22—2442no—
1130C22—2442no—
1131C22—2442no—
1132C22—2442no—
1133C22—2442no—
1134C22—2442no—
1135C22—2442no—
1136C22—2442no—
1137C22—2442no—
1138C22—2442no—
1139C22#1683962418yescomplemented
1140C22C2×C22⋊C4×D6111yescharacteristic
1141C22C2×#1451973411yescharacteristic
1142C22C2×#1451973511yescharacteristic
1143C22C4×D4×D6111yescharacteristic
1144C22C4×#1175822411yescharacteristic
1145C22#1684023411yescharacteristic
1146C22#1684024111yescharacteristic
1147C22C2×#1451975911yescharacteristic
1148C22C2×#1451975911yescharacteristic
1149C22C2×#1451976211yescharacteristic
1150C22C2×#1451976211yescharacteristic
1151C22#1684026811yescharacteristic
1152C22#1684027511yescharacteristic
1153C22#1684028911yescharacteristic
1154C22#1684029811yescharacteristic
1155C22#1684034711yescharacteristic
1156C22#1684035211yescharacteristic
1157C22#1684035611yescharacteristic
1158C22#1684036111yescharacteristic
1159C22#1684039411yescharacteristic
1160C22#1684039611yescharacteristic
1161C22#1684039911yescharacteristic
1162C22#1684040111yescharacteristic
1163C22#1684040111yescharacteristic
1164C22#1684040211yescharacteristic
1165C22#1684040411yescharacteristic
1166C22#1684041011yescharacteristic
1167C22#1684041211yescharacteristic
1168C22#1684042111yescharacteristic
1169C22#1684043611yescharacteristic
1170C22#1684043811yescharacteristic
1171C22#1684044511yescharacteristic
1172C22#1684045811yescharacteristic
1173C22#1684046111yescharacteristic
1174C22#1684046111yescharacteristic
1175C4—42no—
1176C4—42no—
1177C4—42no—
1178C4—42no—
1179C4—81no—
1180C4—81no—
1181C4—1224no—
1182C4—1224no—
1183C4—4881no—
1184C4—4881no—
1185C4—2442no—
1186C4—2442no—
1187C4—2442no—
1188C2—28no—
1189C2—2444no—
1190C2C2×#1683962411yescharacteristic
1191C2#2144825511yescharacteristic
1192C2#2144844711yescharacteristic
1193C2#2144863711yescharacteristic
1194C2#2144864511yescharacteristic
1195C2#2144874211yescharacteristic
1196C2#2144875311yescharacteristic
1197C2#2144928511yescharacteristic
1198C2#2144928711yescharacteristic
1199C2#2144930011yescharacteristic
1200C2#2144930211yescharacteristic
1201C2#2144955811yescharacteristic
1202C2#2144956011yescharacteristic
1203C2#2144957311yescharacteristic
1204C2#2144957511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×C22⋊#95C2
socle, cosocleC24×C61C24
prime radicalC23×C22⋊D61C22
hypercenterC22⋊#95D61
hypocenterC61#13894
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
4. C2×#16839624C2semidirect
5. C22×#14519684C2semidirect
6. #21444085C2semidirect
7. #21444085C2semidirect
8. #21444067C2semidirect
9. #21444067C2semidirect
10. #21444045C2semidirect
11. #21444044C2semidirect
12. #21444041C2semidirect
13. #21444041C2semidirect
14. #21444040C2semidirect
15. C61×C22⋊#95C2semidirect
22. C2×#14519737C4semidirect
93. C22×C4×D61C2×C4semidirect
97. C2×#11758196C2×C4semidirect
115. C2×#11758198C2×C4semidirect
118. C2×C4×Dic61C2×C4semidirect
134. #14519684D4semidirect
522. C22×C61#381semidirect
600. C22⋊#95D61semidirect
660. C61#13894semidirect
1139. C22#16839624semidirect

Maximal subgroups

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

subgroupindex
C22×#145197372
C2×#168396412
C2×#168396392
C2×#168396242
C22×#145196842
#214440852
#214440672
#214440452
#214440442
#214440412
#214440402
C61×C22⋊#952
#1389461