Finite Group Databasebeta

← #29604494

Subgroups — #29604494

Order 15616.

2206 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519765C211yesmaximal, characteristic
2C2×#16839666C211yesmaximal, characteristic, complemented
3C2×#16839653C211yesmaximal, characteristic, complemented
4C2×#16839640C211yesmaximal, characteristic
5C2×C4×#11758198C211yesmaximal, characteristic, complemented
6#21444089C211yesmaximal, characteristic, complemented
7#21444067C211yesmaximal, characteristic, complemented
8#21444063C211yesmaximal, characteristic, complemented
9#21444059C211yesmaximal, characteristic
10#21444057C211yesmaximal, characteristic, complemented
11#21444057C211yesmaximal, characteristic, complemented
12#21444055C211yesmaximal, characteristic, complemented
13#21444046C211yesmaximal, characteristic, complemented
14#21444040C211yesmaximal, characteristic, complemented
15C4×#95×C61C211yesmaximal, characteristic, complemented
16C23×Dic122C2211yescharacteristic
17C23×D244C2211yescharacteristic
18C23×C4×D61C2211yescharacteristic
19C2×#14519765—24no—
20C2×#14519765—24no—
21C2×#14519765C418yescomplemented
22C22×#11758196C2211yescharacteristic
23C22×#11758198C2211yescharacteristic
24C22×#11758198C2211yescharacteristic
25C22×#11758198C2211yescharacteristic
26C22×#11758198C2211yescharacteristic
27C22×#11758198C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×#11758198C2211yescharacteristic
32C22×#11758198C2211yescharacteristic
33C22×#11758198C2211yescharacteristic
34C22×C4×Dic61C2211yescharacteristic
35#16839666—24no—
36#16839653—24no—
37#16839640—24no—
38C4×#11758198—24no—
39C2×#14519684C2211yescharacteristic
40C2×#14519684C2211yescharacteristic
41C2×#14519684C2211yescharacteristic
42C2×#14519684C2211yescharacteristic
43C2×#14519684C2211yescharacteristic
44C2×#14519684C2211yescharacteristic
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50C2×#14519684C2211yescharacteristic
51C22×C42×C61C2211yescharacteristic
52C22×C42×C61C2211yescharacteristic
53C22×C42×C61C2211yescharacteristic
54C2×#95×C61C2211yescharacteristic
55C2×#95×C61C2211yescharacteristic
56C2×#95×C61C2211yescharacteristic
57C2×#95×C61C2211yescharacteristic
58C24×D61C2311yescharacteristic
59C24×D61C2311yescharacteristic
60C22×Dic122—22no—
61C22×Dic122—22no—
62C22×Dic122—22no—
63C22×Dic122—22no—
64C22×Dic122—41no—
65C22×Dic122—41no—
66C22×Dic122C2×C414yescomplemented
67C22×D244—22no—
68C22×D244—22no—
69C22×D244—22no—
70C22×D244—22no—
71C22×D244—41no—
72C22×D244—41no—
73C22×D244C2×C414yes—
74C23×Dic61C2311yescharacteristic
75C23×Dic61C2311yescharacteristic
76C23×Dic61C2311yescharacteristic
77C23×Dic61C2311yescharacteristic
78C23×Dic61C2311yescharacteristic
79C23×Dic61C2311yescharacteristic
80C22×C4×D61—22no—
81C22×C4×D61—22no—
82C22×C4×D61—22no—
83C22×C4×D61—22no—
84C22×C4×D61—22no—
85C22×C4×D61—41no—
86C22×C4×D61—41no—
87#14519765—232no—
88C2×#11758196—22no—
89C2×#11758196—22no—
90C2×#11758196—41no—
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—22no—
104C2×#11758198—22no—
105C2×#11758198—22no—
106C2×#11758198—22no—
107C2×#11758198—22no—
108C2×#11758198—22no—
109C2×#11758198—22no—
110C2×#11758198—22no—
111C2×#11758198—22no—
112C2×#11758198—41no—
113C2×#11758198—41no—
114C2×#11758198—41no—
115C2×#11758198—41no—
116C2×#11758198—41no—
117C2×#11758198—41no—
118C2×#11758198C2×C414yes—
119C2×#11758198C2×C414yes—
120C2×#11758198C2×C414yescomplemented
121C2×#11758198C2×C414yescomplemented
122C2×#11758198D414yes—
123C2×#11758198D414yes—
124C2×C4×Dic61—22no—
125C2×C4×Dic61—22no—
126C2×C4×Dic61—41no—
127#14519684—22no—
128#14519684—22no—
129#14519684—22no—
130#14519684—22no—
131#14519684—22no—
132#14519684—22no—
133#14519684—22no—
134#14519684—22no—
135#14519684—22no—
136#14519684—22no—
137#14519684—41no—
138#14519684—41no—
139C23×C4×C61C2311yescharacteristic
140C23×C4×C61C2311yescharacteristic
141C23×C4×C61C2311yescharacteristic
142C23×C4×C61C2311yescharacteristic
143C23×C4×C61C2311yescharacteristic
144C23×C4×C61C2311yescharacteristic
145C23×C4×C61C2311yescharacteristic
146C2×C42×C61—22no—
147C2×C42×C61—22no—
148C2×C42×C61—22no—
149C2×C42×C61—22no—
150C2×C42×C61—22no—
151C2×C42×C61—22no—
152C2×C42×C61—41no—
153C2×C42×C61—41no—
154C2×C42×C61C2×C414yescomplemented
155#95×C61—22no—
156#95×C61—22no—
157#95×C61—22no—
158#95×C61D414yes—
159C24×C61C2411yescharacteristic
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×D61—21no—
180C23×D61—21no—
181C23×D61—21no—
182C23×D61—21no—
183C23×D61—21no—
184C23×D61—21no—
185C23×D61—21no—
186C23×D61C22×C412yes—
187C23×D61C22×C412yes—
188C23×D61C2×D412yes—
189C23×D61C2×D412yes—
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×C61—21no—
224C22×C4×C61—21no—
225C22×C4×C61—21no—
226C22×C4×C61C22×C412yes—
227C22×C4×C61C22×C412yes—
228C22×C4×C61C22×C412yes—
229C22×C4×C61C2×D412yes—
230C22×C4×C61C2×D412yes—
231C22×C4×C61C2×D412yes—
232C22×C4×C61C2×D412yes—
233C22×C4×C61C2×D412yes—
234C22×C4×C61#4112yes—
235C22×C4×C61#4112yes—
236C22×C4×C61#4112yes—
237C22×C4×C61#4112yes—
238C22×C4×C61#4112yes—
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—21no—
273C22×Dic61—21no—
274C22×Dic61—21no—
275C22×Dic61C22×C412yes—
276C22×Dic61C22×C412yes—
277C22×Dic61C2×D412yes—
278C22×Dic61C2×D412yes—
279C22×Dic61#4112yes—
280C22×Dic61#4112yes—
281C2×D244—28no—
282C2×D244—28no—
283C2×D244—44no—
284C2×D244—44no—
285C2×D244—44no—
286C2×D244—44no—
287C2×D244—44no—
288C2×C4×D61—28no—
289C2×C4×D61—44no—
290C2×C4×D61—44no—
291C2×C4×D61—44no—
292C2×C4×D61—44no—
293C2×C4×D61—44no—
294C2×C4×D61—44no—
295C2×Dic122—28no—
296C2×Dic122—28no—
297C2×Dic122—44no—
298C2×Dic122—44no—
299C2×Dic122—44no—
300C2×Dic122—44no—
301C2×Dic122—44no—
302C42×C61—28no—
303C42×C61—44no—
304C42×C61—44no—
305#11758198—28no—
306#11758198—28no—
307#11758198—28no—
308#11758198—28no—
309#11758198—44no—
310#11758198—44no—
311#11758198—44no—
312#11758198—44no—
313#11758198—44no—
314#11758198—44no—
315#11758198C22⋊C4116yescomplemented
316#11758196—44no—
317C4×Dic61—44no—
318C23×C61C23×C411yescharacteristic
319C23×C61C22×D411yescharacteristic
320C23×C61C22×D411yescharacteristic
321C23×C61C22×D411yescharacteristic
322C23×C61C2×#4111yescharacteristic
323C23×C61C2×#4111yescharacteristic
324C23×C61C2×#4111yescharacteristic
325C23×C61C2×#4111yescharacteristic
326C23×C61C2×#4111yescharacteristic
327C23×C61C2×#4111yescharacteristic
328C23×C61C2×#4111yescharacteristic
329C23×C61H(5,𝔽2)11yescharacteristic
330C23×C61H(5,𝔽2)11yescharacteristic
331C23×C61H(5,𝔽2)11yescharacteristic
332C23×C612−1+411yescharacteristic
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—22no—
346C22×D61—22no—
347C22×D61—22no—
348C22×D61—22no—
349C22×D61—22no—
350C22×D61—22no—
351C22×D61—22no—
352C22×D61—22no—
353C22×D61—22no—
354C22×D61—22no—
355C22×D61—22no—
356C22×D61—22no—
357C22×D61—22no—
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—41no—
390C22×D61—41no—
391C22×D61—41no—
392C22×D61—41no—
393C22×D61—41no—
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×D61C2×C22⋊C414yes—
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—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—22no—
424C2×C4×C61—22no—
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—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×C61C2×C22⋊C414yes—
450C2×C4×C61C4×D414yes—
451C2×C4×C61#12414yescomplemented
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—22no—
461C2×Dic61—22no—
462C2×Dic61—22no—
463C2×Dic61—22no—
464C2×Dic61—22no—
465C2×Dic61—22no—
466C2×Dic61—22no—
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×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×Dic61C2×C22⋊C414yes—
494D244—416no—
495C4×D61—416no—
496Dic122—416no—
497#14098—611nomaximal, Sylow
498C22×C61C22×C22⋊C411yescharacteristic
499C22×C61C2×C4×D411yescharacteristic
500C22×C61C4×#4111yescharacteristic
501C22×C61C4×#4111yescharacteristic
502C22×C61C4×#4111yescharacteristic
503C22×C61#51811yescharacteristic
504C22×C61#52011yescharacteristic
505C22×C61#52511yescharacteristic
506C22×C61#52511yescharacteristic
507C22×C61C2×#12411yescharacteristic
508C22×C61#52911yescharacteristic
509C22×C61#52911yescharacteristic
510C22×C61#53211yescharacteristic
511C22×C61#53211yescharacteristic
512C22×C61#53211yescharacteristic
513C22×C61#53811yescharacteristic
514C22×C61#53811yescharacteristic
515C22×C61#54211yescharacteristic
516C22×C61#54211yescharacteristic
517C22×C61D4211yescharacteristic
518C22×C61D4211yescharacteristic
519C22×C61#54611yescharacteristic
520C22×C61#54611yescharacteristic
521C22×C61#54611yescharacteristic
522C22×C61#54611yescharacteristic
523C22×C61#54611yescharacteristic
524C22×C61#54711yescharacteristic
525C22×C61#54711yescharacteristic
526C22×C61#54811yescharacteristic
527C22×C61#55111yescharacteristic
528C22×C61#55111yescharacteristic
529C22×C61#55511yescharacteristic
530C22×C61#55511yescharacteristic
531C22×C61#55611yescharacteristic
532C22×C61#55911yescharacteristic
533C2×D61—24no—
534C2×D61—24no—
535C2×D61—24no—
536C2×D61—42no—
537C2×D61—42no—
538C2×D61—42no—
539C2×D61—42no—
540C2×D61—42no—
541C2×D61—42no—
542C2×D61—42no—
543C2×D61—42no—
544C2×D61—42no—
545C2×D61—42no—
546C2×D61—42no—
547C2×D61—42no—
548C2×D61—42no—
549C2×D61—42no—
550C2×D61—42no—
551C2×D61—42no—
552C2×D61—42no—
553C2×D61—42no—
554C2×D61—42no—
555C2×D61—81no—
556C2×D61—81no—
557C2×D61—81no—
558C2×D61—81no—
559C2×D61—81no—
560C2×D61—81no—
561C2×D61—81no—
562C2×D61—81no—
563C4×C61—24no—
564C4×C61—24no—
565C4×C61—24no—
566C4×C61—42no—
567C4×C61—42no—
568C4×C61—42no—
569C4×C61—42no—
570Dic61—24no—
571Dic61—42no—
572Dic61—42no—
573Dic61—42no—
574Dic61—81no—
575Dic61—81no—
576C22×#124—611no—
577C2×#391—611no—
578C2×#388—611no—
579C2×#386—611no—
580C2×C4×C22⋊C4—611no—
581#1446—611no—
582#1440—611no—
583#1439—611no—
584#1438—611no—
585#1437—611no—
586#1437—611no—
587#1437—611no—
588#1434—611no—
589C22⋊#95—611no—
590C4×#95D6111yescharacteristic, complemented
591C2×C61#229711yescharacteristic
592C2×C61C4×#12411yescharacteristic
593C2×C61#233711yescharacteristic
594C2×C61D4×C22⋊C411yescharacteristic
595C2×C61#233911yescharacteristic
596C2×C61#236711yescharacteristic
597C2×C61#237211yescharacteristic
598C2×C61#245911yescharacteristic
599C2×C61#246111yescharacteristic
600C2×C61#247211yescharacteristic
601C2×C61#247411yescharacteristic
602C2×C61#249111yescharacteristic
603C2×C61#252111yescharacteristic
604C2×C61#255511yescharacteristic
605C2×C61#255711yescharacteristic
606D61—44no—
607D61—82no—
608C23×Q8—611no—
609C23×D4—611no—
610C24×C4—611no—
611C2×#124—618no—
612C2×#124—1224no—
613C2×#124—1224no—
614C22×C4⋊C4—611no—
615C22×C22⋊C4—611no—
616C22×C22⋊C4—611no—
617C22×C22⋊C4—611no—
618C22×C22⋊C4—611no—
619C22×C22⋊C4—611no—
620C22×C22⋊C4—611no—
621C22×C22⋊C4—611no—
622C22×C22⋊C4—611no—
623C22×C22⋊C4—611no—
624C22×C22⋊C4—611no—
625C22×C22⋊C4—611no—
626C22×C42—611no—
627C22×C42C2×D6111yescharacteristic
628C22×C42C2×D6111yescharacteristic
629C22×C42C2×D6111yescharacteristic
630#391—1224no—
631#388—1224no—
632#386—1224no—
633C4×C22⋊C4—1224no—
634C2×#95—611no—
635C2×#95—611no—
636C2×#95—611no—
637C2×#95—611no—
638C2×#95—611no—
639C2×#95—611no—
640C2×#95—611no—
641C2×#95—611no—
642C2×#95—611no—
643C2×#95—611no—
644C2×#95—611no—
645C2×#95—611no—
646C2×#95C2×D6111yescharacteristic
647C2×#95C2×D6111yescharacteristic
648C2×#95C2×D6111yescharacteristic
649C2×#95C2×D6111yescharacteristic
650C61#1409811yescharacteristic, complemented, Sylow
651C25—611no—
652C25—611no—
653C22×Q8—614no—
654C22×Q8—1222no—
655C22×Q8—1222no—
656C22×Q8—1222no—
657C22×Q8—1222no—
658C22×Q8—2441no—
659C22×Q8—2441no—
660C22×D4—614no—
661C22×D4—1222no—
662C22×D4—1222no—
663C22×D4—1222no—
664C22×D4—1222no—
665C22×D4—2441no—
666C22×D4—2441no—
667C23×C4—611no—
668C23×C4—611no—
669C23×C4—611no—
670C23×C4—611no—
671C23×C4—611no—
672C23×C4—611no—
673C23×C4—1222no—
674C23×C4—1222no—
675C23×C4—1222no—
676C23×C4—1222no—
677C23×C4—1222no—
678C23×C4—2441no—
679C23×C4—2441no—
680C23×C4C22×D6111yescharacteristic
681C23×C4C22×D6111yescharacteristic
682C23×C4C22×D6111yescharacteristic
683C23×C4C22×D6111yescharacteristic
684C23×C4C22×D6111yescharacteristic
685C23×C4C22×D6111yescharacteristic
686C23×C4C22×D6111yescharacteristic
687#124—12232no—
688C2×C4⋊C4—1222no—
689C2×C4⋊C4—1222no—
690C2×C4⋊C4—2441no—
691C2×C22⋊C4—614no—
692C2×C22⋊C4—614no—
693C2×C22⋊C4—614no—
694C2×C22⋊C4—614no—
695C2×C22⋊C4—614no—
696C2×C22⋊C4—614no—
697C2×C22⋊C4—1222no—
698C2×C22⋊C4—1222no—
699C2×C22⋊C4—1222no—
700C2×C22⋊C4—1222no—
701C2×C22⋊C4—1222no—
702C2×C22⋊C4—1222no—
703C2×C22⋊C4—1222no—
704C2×C22⋊C4—1222no—
705C2×C22⋊C4—1222no—
706C2×C22⋊C4—1222no—
707C2×C22⋊C4—1222no—
708C2×C22⋊C4—1222no—
709C2×C22⋊C4—1222no—
710C2×C22⋊C4—1222no—
711C2×C22⋊C4—1222no—
712C2×C22⋊C4—1222no—
713C2×C22⋊C4—1222no—
714C2×C22⋊C4—1222no—
715C2×C22⋊C4—1222no—
716C2×C22⋊C4—1222no—
717C2×C22⋊C4—1222no—
718C2×C22⋊C4—2441no—
719C2×C22⋊C4—2441no—
720C2×C22⋊C4—2441no—
721C2×C22⋊C4—2441no—
722C2×C22⋊C4—2441no—
723C2×C22⋊C4—2441no—
724C2×C42—22no—
725C2×C42—22no—
726C2×C42—22no—
727C2×C42—22no—
728C2×C42—22no—
729C2×C42—22no—
730C2×C42—41no—
731C2×C42—41no—
732C2×C42—1222no—
733C2×C42—1222no—
734C2×C42—2441no—
735C2×C42C4×D6114yescomplemented
736#95—22no—
737#95—22no—
738#95—22no—
739#95—1222no—
740#95—1222no—
741#95—1222no—
742#95—1222no—
743#95—1222no—
744#95—1222no—
745#95—1222no—
746#95—1222no—
747#95—1222no—
748#95—1222no—
749#95—2441no—
750#95—2441no—
751#95D24414yes—
752C24—612no—
753C24—612no—
754C24—612no—
755C24—612no—
756C24—1221no—
757C24—1221no—
758C24—1221no—
759C24—1221no—
760C24—1221no—
761C24—1221no—
762C24—1221no—
763C24—1221no—
764C24—1221no—
765C24—1221no—
766C24—1221no—
767C24—1221no—
768C24—1221no—
769C24—1221no—
770C24—1221no—
771C24—1221no—
772C24—1221no—
773C24—1221no—
774C24—1221no—
775C24—1221no—
776C24—1221no—
777C24—1221no—
778C24—1221no—
779C24—1221no—
780C24—1221no—
781C24—1221no—
782C24C23×D6111yescharacteristic
783C2×Q8—1228no—
784C2×Q8—1228no—
785C2×Q8—2444no—
786C2×Q8—2444no—
787C2×Q8—2444no—
788C2×Q8—2444no—
789C2×Q8—2444no—
790C2×D4—1228no—
791C2×D4—1228no—
792C2×D4—2444no—
793C2×D4—2444no—
794C2×D4—2444no—
795C2×D4—2444no—
796C2×D4—2444no—
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—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—612no—
834C22×C4—612no—
835C22×C4—612no—
836C22×C4—612no—
837C22×C4—612no—
838C22×C4—612no—
839C22×C4—1228no—
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—1221no—
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—1221no—
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—2444no—
877C22×C4—2444no—
878C22×C4—2444no—
879C22×C4—2444no—
880C22×C4—2444no—
881C22×C4—2444no—
882C22×C4C2×C4×D6112yes—
883C22×C4C2×C4×D6112yes—
884C22×C4C2×C4×D6112yes—
885C22×C4C2×D24412yes—
886C22×C4C2×D24412yes—
887C22×C4C2×D24412yes—
888C22×C4#1175822212yes—
889C22×C4#1175822212yes—
890C22×C4#1175822212yes—
891C22×C4#1175822212yes—
892C22×C4#1175822212yes—
893C22×C4D4×D6112yes—
894C22×C4D4×D6112yes—
895C4⋊C4—2444no—
896C22⋊C4—6116no—
897C22⋊C4—1228no—
898C22⋊C4—1228no—
899C22⋊C4—1228no—
900C22⋊C4—1228no—
901C22⋊C4—2444no—
902C22⋊C4—2444no—
903C22⋊C4—2444no—
904C22⋊C4—2444no—
905C22⋊C4—2444no—
906C22⋊C4—2444no—
907C42—28no—
908C42—44no—
909C42—44no—
910C42—2444no—
911C23—614no—
912C23—1222no—
913C23—1222no—
914C23—1222no—
915C23—1222no—
916C23—1222no—
917C23—1222no—
918C23—1222no—
919C23—1222no—
920C23—1222no—
921C23—1222no—
922C23—1222no—
923C23—1222no—
924C23—1222no—
925C23—1222no—
926C23—1222no—
927C23—1222no—
928C23—1222no—
929C23—1222no—
930C23—1222no—
931C23—1222no—
932C23—1222no—
933C23—1222no—
934C23—1222no—
935C23—1222no—
936C23—1222no—
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—
954C23—2441no—
955C23—2441no—
956C23—2441no—
957C23—2441no—
958C23—2441no—
959C23—2441no—
960C23—2441no—
961C23—2441no—
962C23—2441no—
963C23—2441no—
964C23—2441no—
965C23—2441no—
966C23—2441no—
967C23—2441no—
968C23—2441no—
969C23—2441no—
970C23—2441no—
971C23—2441no—
972C23—2441no—
973C23—2441no—
974C23—2441no—
975C23—2441no—
976C23—2441no—
977C23—2441no—
978C23—2441no—
979C23—2441no—
980C23—2441no—
981C23C22×C4×D6111yescharacteristic
982C23C2×D4×D6111yescharacteristic
983C23C2×D4×D6111yescharacteristic
984C23C22×D24411yescharacteristic
985C23#41×D6111yescharacteristic
986C23#41×D6111yescharacteristic
987C23C2×#1175822211yescharacteristic
988C23C2×#1175822211yescharacteristic
989C23C2×#1175822211yescharacteristic
990C23C2×#1175822211yescharacteristic
991C23C2×#1175822211yescharacteristic
992C23#1451982211yescharacteristic
993C23#1451982311yescharacteristic
994C23#1451982311yescharacteristic
995C23#1451982511yescharacteristic
996Q8—24416no—
997D4—24416no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
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—22no—
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—614no—
1045C2×C4—1222no—
1046C2×C4—1222no—
1047C2×C4—1222no—
1048C2×C4—1222no—
1049C2×C4—1222no—
1050C2×C4—1222no—
1051C2×C4—1222no—
1052C2×C4—1222no—
1053C2×C4—1222no—
1054C2×C4—1222no—
1055C2×C4—1222no—
1056C2×C4—1222no—
1057C2×C4—1222no—
1058C2×C4—1222no—
1059C2×C4—1222no—
1060C2×C4—24416no—
1061C2×C4—2441no—
1062C2×C4—2441no—
1063C2×C4—2441no—
1064C2×C4—2441no—
1065C2×C4—2441no—
1066C2×C4—2441no—
1067C2×C4—2441no—
1068C2×C4—2441no—
1069C2×C4—2441no—
1070C2×C4—2441no—
1071C2×C4—2441no—
1072C2×C4—2441no—
1073C2×C4—2441no—
1074C2×C4—2441no—
1075C2×C4—2441no—
1076C2×C4—2441no—
1077C2×C4—2441no—
1078C2×C4—2441no—
1079C2×C4—2441no—
1080C2×C4—2441no—
1081C2×C4—2441no—
1082C2×C4—2441no—
1083C2×C4—2441no—
1084C2×C4—2441no—
1085C2×C4—2441no—
1086C2×C4—2441no—
1087C2×C4C22⋊C4×D6114yes—
1088C2×C4C4×D24414yes—
1089C2×C4#1451976514yescomplemented
1090C22—1224no—
1091C22—1224no—
1092C22—1224no—
1093C22—4881no—
1094C22—4881no—
1095C22—4881no—
1096C22—4881no—
1097C22—4881no—
1098C22—4881no—
1099C22—4881no—
1100C22—4881no—
1101C22—2442no—
1102C22—2442no—
1103C22—2442no—
1104C22—2442no—
1105C22—2442no—
1106C22—2442no—
1107C22—2442no—
1108C22—2442no—
1109C22—2442no—
1110C22—2442no—
1111C22—2442no—
1112C22—2442no—
1113C22—2442no—
1114C22—2442no—
1115C22—2442no—
1116C22—2442no—
1117C22—2442no—
1118C22—2442no—
1119C22—2442no—
1120C22C2×C22⋊C4×D6111yescharacteristic
1121C22C2×C4×D24411yescharacteristic
1122C22#1684023011yescharacteristic
1123C22C4×#1175822211yescharacteristic
1124C22C4×#1175822211yescharacteristic
1125C22#1684023611yescharacteristic
1126C22#1684024311yescharacteristic
1127C22#1684027111yescharacteristic
1128C22#1684027111yescharacteristic
1129C22C2×#1451976511yescharacteristic
1130C22#1684029611yescharacteristic
1131C22#1684029611yescharacteristic
1132C22#1684030911yescharacteristic
1133C22#1684030911yescharacteristic
1134C22#1684031211yescharacteristic
1135C22#1684034511yescharacteristic
1136C22#1684034511yescharacteristic
1137C22#1684038411yescharacteristic
1138C22#1684038411yescharacteristic
1139C22D4×D24411yescharacteristic
1140C22D4×D24411yescharacteristic
1141C22#1684040211yescharacteristic
1142C22#1684040211yescharacteristic
1143C22#1684040711yescharacteristic
1144C22#1684040811yescharacteristic
1145C22#1684040811yescharacteristic
1146C22#1684041311yescharacteristic
1147C22#1684041311yescharacteristic
1148C22#1684042411yescharacteristic
1149C22#1684043611yescharacteristic
1150C22#1684043611yescharacteristic
1151C22#1684047511yescharacteristic
1152C22#1684047511yescharacteristic
1153C22#1684048411yescharacteristic
1154C22#1684049511yescharacteristic
1155C4—24no—
1156C4—24no—
1157C4—24no—
1158C4—42no—
1159C4—42no—
1160C4—42no—
1161C4—42no—
1162C4—1224no—
1163C4—4881no—
1164C4—4881no—
1165C4—2442no—
1166C4—2442no—
1167C4—2442no—
1168C2—4882no—
1169C2—2444no—
1170C2#2144830511yescharacteristic
1171C2C4×#1451976511yescharacteristic
1172C2#2144863211yescharacteristic
1173C2C22⋊C4×D24411yescharacteristic
1174C2#2144864611yescharacteristic
1175C2#2144889011yescharacteristic
1176C2#2144892911yescharacteristic
1177C2#2144975611yescharacteristic
1178C2#2144978611yescharacteristic
1179C2#2144994511yescharacteristic
1180C2#2144997511yescharacteristic
1181C2#2145017611yescharacteristic
1182C2#2145051611yescharacteristic
1183C2#2145088811yescharacteristic
1184C2#2145091811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC4×#95×C61C2
socle, cosocleC24×C61C24
prime radicalC23×D244C22
hypercenterC4×#95D61
hypocenterC61#14098
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
2. C2×#16839666C2semidirect
3. C2×#16839653C2semidirect
5. C2×C4×#11758198C2semidirect
6. #21444089C2semidirect
7. #21444067C2semidirect
8. #21444063C2semidirect
10. #21444057C2semidirect
11. #21444057C2semidirect
12. #21444055C2semidirect
13. #21444046C2semidirect
14. #21444040C2semidirect
15. C4×#95×C61C2semidirect
21. C2×#14519765C4semidirect
66. C22×Dic122C2×C4semidirect
120. C2×#11758198C2×C4semidirect
121. C2×#11758198C2×C4semidirect
154. C2×C42×C61C2×C4semidirect
315. #11758198C22⋊C4semidirect
451. C2×C4×C61#124semidirect
590. C4×#95D61semidirect
650. C61#14098semidirect
735. C2×C42C4×D61semidirect
1089. C2×C4#14519765semidirect

Maximal subgroups

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

subgroupindex
C22×#145197652
C2×#168396662
C2×#168396532
C2×#168396402
C2×C4×#117581982
#214440892
#214440672
#214440632
#214440592
#214440572
#214440552
#214440462
#214440402
C4×#95×C612
#1409861