Finite Group Databasebeta

← #29601964

Subgroups — #29601964

Order 15616.

1846 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839655C212yesmaximal
2C2×#16839632C211yesmaximal, characteristic, complemented
3C2×#16839622C211yesmaximal, characteristic
4C2×#16839622C211yesmaximal, characteristic
5C2×C4×C4⋊Dic61C211yesmaximal, characteristic, complemented
6#21444076C212yesmaximal, complemented
7#21444064C212yesmaximal
8#21444053C212yesmaximal, complemented
9#21444049C211yesmaximal, characteristic, complemented
10#21444049C211yesmaximal, characteristic, complemented
11C2×C4×C22⋊C4×C61C211yesmaximal, characteristic
12C22×C4⋊Dic61C2211yescharacteristic
13C22×C4⋊Dic61C2211yescharacteristic
14C22×C4⋊Dic61C2212yes—
15C22×C4⋊Dic61C2212yes—
16C22×C4⋊Dic61C2211yescharacteristic
17C22×C4⋊Dic61C2211yescharacteristic
18C22×C22⋊Dic61C2212yes—
19C22×C22⋊Dic61C2212yes—
20C22×C4×Dic61C2212yes—
21#16839655—28no—
22#16839632—24no—
23#16839622—24no—
24#16839622—24no—
25C4×C4⋊Dic61—24no—
26C2×#14519684C2212yes—
27C2×#14519684C2212yes—
28C2×#14519684C2212yes—
29C2×#14519684C2212yes—
30C2×#14519684C2212yes—
31C2×#14519684C2212yes—
32C2×#14519684C2212yes—
33C24×C4×C61C2211yescharacteristic
34C22×C22⋊C4×C61C2211yescharacteristic
35C22×C22⋊C4×C61C2211yescharacteristic
36C22×C42×C61C2211yescharacteristic
37C22×C42×C61C2211yescharacteristic
38C4×C22⋊C4×C61C418yescomplemented
39C2×#95×C61C2211yescharacteristic
40C2×#95×C61C2211yescharacteristic
41C23×Dic61C2312yes—
42C23×Dic61C2312yes—
43C23×Dic61C2312yes—
44C23×Dic61C2312yes—
45C2×C4⋊Dic61—22no—
46C2×C4⋊Dic61—22no—
47C2×C4⋊Dic61—22no—
48C2×C4⋊Dic61—22no—
49C2×C4⋊Dic61—22no—
50C2×C4⋊Dic61—22no—
51C2×C4⋊Dic61—22no—
52C2×C4⋊Dic61—24no—
53C2×C4⋊Dic61—24no—
54C2×C4⋊Dic61—22no—
55C2×C4⋊Dic61—22no—
56C2×C4⋊Dic61—22no—
57C2×C4⋊Dic61—24no—
58C2×C4⋊Dic61—24no—
59C2×C4⋊Dic61—42no—
60C2×C4⋊Dic61—42no—
61C2×C4⋊Dic61D414yes—
62C2×C4⋊Dic61D414yes—
63C2×C22⋊Dic61—24no—
64C2×C22⋊Dic61—24no—
65C2×C22⋊Dic61—24no—
66C2×C22⋊Dic61—24no—
67C2×C22⋊Dic61—42no—
68C2×C22⋊Dic61—42no—
69C2×C4×Dic61—24no—
70C2×C4×Dic61—24no—
71C2×C4×Dic61—42no—
72#14519684—24no—
73#14519684—24no—
74#14519684—24no—
75#14519684—24no—
76#14519684—24no—
77#14519684—24no—
78#14519684—42no—
79C25×C61C2311yescharacteristic
80C23×C4×C61—22no—
81C23×C4×C61—22no—
82C23×C4×C61—22no—
83C23×C4×C61—22no—
84C23×C4×C61—22no—
85C23×C4×C61—22no—
86C23×C4×C61C2×C414yes—
87C23×C4×C61C2311yescharacteristic
88C23×C4×C61C2311yescharacteristic
89C23×C4×C61C2311yescharacteristic
90C23×C4×C61C2311yescharacteristic
91C23×C4×C61C2311yescharacteristic
92C23×C4×C61C2311yescharacteristic
93C2×C22⋊C4×C61—22no—
94C2×C22⋊C4×C61—22no—
95C2×C22⋊C4×C61C2×C414yes—
96C2×C22⋊C4×C61C2×C414yes—
97C2×C22⋊C4×C61D414yes—
98C2×C22⋊C4×C61Q814yes—
99C2×C42×C61—22no—
100C2×C42×C61—22no—
101C2×C42×C61—22no—
102C2×C42×C61—22no—
103C2×C42×C61C2×C414yes—
104C2×C42×C61C2×C414yes—
105#95×C61C2×C414yes—
106#95×C61C2×C414yes—
107C24×C61—21no—
108C24×C61—21no—
109C24×C61—21no—
110C24×C61—21no—
111C24×C61—21no—
112C24×C61—21no—
113C24×C61—21no—
114C24×C61—21no—
115C24×C61—21no—
116C24×C61—21no—
117C24×C61—21no—
118C24×C61—21no—
119C24×C61C22×C412yes—
120C24×C61C2×D412yes—
121C24×C61C2×Q812yes—
122C24×C61C2411yescharacteristic
123C22×C4×C61—21no—
124C22×C4×C61—21no—
125C22×C4×C61—21no—
126C22×C4×C61—21no—
127C22×C4×C61—21no—
128C22×C4×C61—21no—
129C22×C4×C61—21no—
130C22×C4×C61—21no—
131C22×C4×C61—21no—
132C22×C4×C61—21no—
133C22×C4×C61—21no—
134C22×C4×C61—21no—
135C22×C4×C61—21no—
136C22×C4×C61—21no—
137C22×C4×C61—21no—
138C22×C4×C61—21no—
139C22×C4×C61—21no—
140C22×C4×C61—21no—
141C22×C4×C61—21no—
142C22×C4×C61—21no—
143C22×C4×C61—21no—
144C22×C4×C61—21no—
145C22×C4×C61—21no—
146C22×C4×C61—21no—
147C22×C4×C61—28no—
148C22×C4×C61—28no—
149C22×C4×C61—28no—
150C22×C4×C61—44no—
151C22×C4×C61—44no—
152C22×C4×C61—44no—
153C22×C4×C61—44no—
154C22×C4×C61C22×C412yes—
155C22×C4×C61C22×C412yes—
156C22×C4×C61C22×C412yes—
157C22×C4×C61C22×C412yes—
158C22×C4×C61C22×C412yes—
159C22×C4×C61C22×C412yes—
160C22×C4×C61C2×D412yes—
161C22×C4×C61C2×D412yes—
162C22×C4×C61C2×D412yes—
163C22×C4×C61C2×D412yes—
164C22×C4×C61C2×Q812yes—
165C22×C4×C61C2×Q812yes—
166C22×C4×C61#4112yes—
167C22×C4×C61#4112yes—
168C22×C4×C61#4112yes—
169C22×C4×C61#4112yes—
170C22×C4×C61#4112yes—
171C22×C4×C61#4112yes—
172C22×Dic61—22no—
173C22×Dic61—22no—
174C22×Dic61—22no—
175C22×Dic61—22no—
176C22×Dic61—22no—
177C22×Dic61—22no—
178C22×Dic61—22no—
179C22×Dic61—22no—
180C22×Dic61—22no—
181C22×Dic61—22no—
182C22×Dic61—22no—
183C22×Dic61—22no—
184C22×Dic61—22no—
185C22×Dic61—22no—
186C22×Dic61—22no—
187C22×Dic61—22no—
188C22×Dic61—22no—
189C22×Dic61—22no—
190C22×Dic61—22no—
191C22×Dic61—22no—
192C22×Dic61—22no—
193C22×Dic61—22no—
194C22×Dic61—22no—
195C22×Dic61—22no—
196C22×Dic61—22no—
197C22×Dic61—22no—
198C22×Dic61C2×D414yes—
199C22×Dic61C2×D414yes—
200C22⋊C4×C61—28no—
201C22⋊C4×C61C4⋊C4116yescomplemented
202C42×C61—28no—
203C42×C61—28no—
204C22⋊Dic61—48no—
205C22⋊Dic61—48no—
206C4⋊Dic61—28no—
207C4⋊Dic61—28no—
208C4⋊Dic61—48no—
209C4⋊Dic61—48no—
210C4⋊Dic61—44no—
211C4⋊Dic61—44no—
212C4×Dic61—48no—
213C23×C61—22no—
214C23×C61—22no—
215C23×C61—22no—
216C23×C61—22no—
217C23×C61—22no—
218C23×C61—22no—
219C23×C61—22no—
220C23×C61—22no—
221C23×C61—22no—
222C23×C61—22no—
223C23×C61—22no—
224C23×C61—22no—
225C23×C61—22no—
226C23×C61—22no—
227C23×C61—22no—
228C23×C61—22no—
229C23×C61—22no—
230C23×C61—22no—
231C23×C61—41no—
232C23×C61—41no—
233C23×C61—41no—
234C23×C61—41no—
235C23×C61—41no—
236C23×C61—41no—
237C23×C61—41no—
238C23×C61—41no—
239C23×C61—41no—
240C23×C61—41no—
241C23×C61—41no—
242C23×C61—41no—
243C23×C61—41no—
244C23×C61—41no—
245C23×C61—41no—
246C23×C61—41no—
247C23×C61C2×C4⋊C414yes—
248C23×C61C23×C411yescharacteristic
249C23×C61C22×D411yescharacteristic
250C23×C61C22×D411yescharacteristic
251C23×C61C22×D411yescharacteristic
252C23×C61C22×Q811yescharacteristic
253C23×C61C2×#4111yescharacteristic
254C23×C61C2×#4111yescharacteristic
255C23×C61C2×#4111yescharacteristic
256C23×C61C2×#4111yescharacteristic
257C23×C61C2×#4111yescharacteristic
258C23×C61C2×#4111yescharacteristic
259C23×C61H(5,𝔽2)11yescharacteristic
260C23×C61H(5,𝔽2)11yescharacteristic
261C23×C612−1+411yescharacteristic
262C23×C612−1+411yescharacteristic
263C2×C4×C61—22no—
264C2×C4×C61—22no—
265C2×C4×C61—22no—
266C2×C4×C61—22no—
267C2×C4×C61—22no—
268C2×C4×C61—22no—
269C2×C4×C61—22no—
270C2×C4×C61—22no—
271C2×C4×C61—22no—
272C2×C4×C61—22no—
273C2×C4×C61—22no—
274C2×C4×C61—22no—
275C2×C4×C61—22no—
276C2×C4×C61—22no—
277C2×C4×C61—22no—
278C2×C4×C61—22no—
279C2×C4×C61—22no—
280C2×C4×C61—22no—
281C2×C4×C61—22no—
282C2×C4×C61—22no—
283C2×C4×C61—22no—
284C2×C4×C61—22no—
285C2×C4×C61—22no—
286C2×C4×C61—22no—
287C2×C4×C61—41no—
288C2×C4×C61—41no—
289C2×C4×C61—41no—
290C2×C4×C61—41no—
291C2×C4×C61—41no—
292C2×C4×C61—41no—
293C2×C4×C61—41no—
294C2×C4×C61—41no—
295C2×C4×C61—416no—
296C2×C4×C61C2×C4⋊C414yes—
297C2×C4×C61C2×C4⋊C414yes—
298C2×C4×C61#11714yes—
299C2×C4×C61#11714yes—
300C2×C4×C61C4×D414yes—
301C2×C4×C61C4×D414yes—
302C2×C4×C61#12114yes—
303C2×C4×C61#12314yes—
304C2×C4×C61#12414yes—
305C2×C4×C61#12614yes—
306C2×Dic61—24no—
307C2×Dic61—24no—
308C2×Dic61—24no—
309C2×Dic61—24no—
310C2×Dic61—24no—
311C2×Dic61—24no—
312C2×Dic61—42no—
313C2×Dic61—42no—
314C2×Dic61—42no—
315C2×Dic61—42no—
316C2×Dic61—42no—
317C2×Dic61—42no—
318C2×Dic61—42no—
319C2×Dic61—42no—
320C2×Dic61—42no—
321C2×Dic61—42no—
322C2×Dic61—42no—
323C2×Dic61—42no—
324C2×Dic61—42no—
325C2×Dic61—42no—
326C2×Dic61—42no—
327C2×Dic61—42no—
328C2×Dic61—42no—
329C2×Dic61—42no—
330C2×Dic61—42no—
331C2×Dic61—42no—
332C2×Dic61—42no—
333C2×Dic61—42no—
334#13876—611nomaximal, Sylow
335C22×C61—24no—
336C22×C61—24no—
337C22×C61—24no—
338C22×C61—42no—
339C22×C61—42no—
340C22×C61—42no—
341C22×C61—42no—
342C22×C61—42no—
343C22×C61—42no—
344C22×C61—42no—
345C22×C61—42no—
346C22×C61—42no—
347C22×C61—42no—
348C22×C61—42no—
349C22×C61—42no—
350C22×C61C22×C4⋊C411yescharacteristic
351C22×C61C2×#11711yescharacteristic
352C22×C61C2×#11711yescharacteristic
353C22×C61C2×C4×D411yescharacteristic
354C22×C61C2×C4×D411yescharacteristic
355C22×C61#52011yescharacteristic
356C22×C61#52011yescharacteristic
357C22×C61C2×#12111yescharacteristic
358C22×C61C2×#12311yescharacteristic
359C22×C61C2×#12411yescharacteristic
360C22×C61C2×#12611yescharacteristic
361C22×C61#53211yescharacteristic
362C22×C61#53211yescharacteristic
363C22×C61#53311yescharacteristic
364C22×C61#53311yescharacteristic
365C22×C61#54011yescharacteristic
366C22×C61#54111yescharacteristic
367C22×C61#54211yescharacteristic
368C22×C61#54211yescharacteristic
369C22×C61D4211yescharacteristic
370C22×C61D4211yescharacteristic
371C22×C61#54611yescharacteristic
372C22×C61#54711yescharacteristic
373C22×C61#54711yescharacteristic
374C22×C61#54711yescharacteristic
375C22×C61#54811yescharacteristic
376C22×C61D4×Q811yescharacteristic
377C22×C61D4×Q811yescharacteristic
378C22×C61#55011yescharacteristic
379C22×C61#55211yescharacteristic
380C22×C61#55311yescharacteristic
381C22×C61#55411yescharacteristic
382C22×C61#55411yescharacteristic
383C22×C61#55511yescharacteristic
384C22×C61#55611yescharacteristic
385C4×C61—24no—
386C4×C61—24no—
387C4×C61—24no—
388C4×C61—42no—
389C4×C61—42no—
390C4×C61#38818yescomplemented
391Dic61—44no—
392Dic61—44no—
393Dic61—82no—
394Dic61—82no—
395C2×#388—612no—
396C2×#384—611no—
397C2×#380—611no—
398C2×#380—611no—
399C2×C4×C4⋊C4—611no—
400C2×C4×C22⋊C4D6111yescharacteristic
401#1442—612no—
402#1439—612no—
403#1436—612no—
404C4⋊#95—611no—
405C4⋊#95—611no—
406C2×C61—44no—
407C2×C61#228511yescharacteristic
408C2×C61C2×#38811yescharacteristic
409C2×C61#231411yescharacteristic
410C2×C61D4×C4⋊C411yescharacteristic
411C2×C61D4×C4⋊C411yescharacteristic
412C2×C61#235211yescharacteristic
413C2×C61#235411yescharacteristic
414C2×C61#242211yescharacteristic
415C2×C61#242311yescharacteristic
416C2×C61#242811yescharacteristic
417C2×C61#242911yescharacteristic
418C2×C61#249111yescharacteristic
419C2×C61#249211yescharacteristic
420C2×C61#249611yescharacteristic
421C2×C61#249711yescharacteristic
422C24×C4C2×D6111yescharacteristic
423C22×C4⋊C4—611no—
424C22×C4⋊C4—611no—
425C22×C4⋊C4—611no—
426C22×C4⋊C4—611no—
427C22×C4⋊C4—612no—
428C22×C4⋊C4—612no—
429C22×C22⋊C4—612no—
430C22×C22⋊C4—612no—
431C22×C22⋊C4C2×D6111yescharacteristic
432C22×C22⋊C4C2×D6111yescharacteristic
433C22×C42—612no—
434C22×C42C2×D6111yescharacteristic
435C22×C42C2×D6111yescharacteristic
436#388—1228no—
437#384—1224no—
438#380—1224no—
439#380—1224no—
440C4×C4⋊C4—1224no—
441C4×C22⋊C4Dic6118yescomplemented
442C2×#95—612no—
443C2×#95—612no—
444C2×#95—612no—
445C2×#95—612no—
446C2×#95—612no—
447C2×#95—612no—
448C2×#95—612no—
449C2×#95C2×D6111yescharacteristic
450C2×#95C2×D6111yescharacteristic
451C61#1387611yescharacteristic, complemented, Sylow
452C25C22×D6111yescharacteristic
453C23×C4—22no—
454C23×C4—22no—
455C23×C4—22no—
456C23×C4—22no—
457C23×C4—22no—
458C23×C4—22no—
459C23×C4—612no—
460C23×C4—612no—
461C23×C4—612no—
462C23×C4—612no—
463C23×C4C2×Dic6114yes—
464C23×C4C22×D6111yescharacteristic
465C23×C4C22×D6111yescharacteristic
466C23×C4C22×D6111yescharacteristic
467C23×C4C22×D6111yescharacteristic
468C23×C4C22×D6111yescharacteristic
469C23×C4C22×D6111yescharacteristic
470C2×C4⋊C4—614no—
471C2×C4⋊C4—614no—
472C2×C4⋊C4—1222no—
473C2×C4⋊C4—1222no—
474C2×C4⋊C4—1222no—
475C2×C4⋊C4—1222no—
476C2×C4⋊C4—1224no—
477C2×C4⋊C4—1224no—
478C2×C4⋊C4—1224no—
479C2×C4⋊C4—1224no—
480C2×C4⋊C4—1222no—
481C2×C4⋊C4—1222no—
482C2×C4⋊C4—1222no—
483C2×C4⋊C4—1222no—
484C2×C4⋊C4—1222no—
485C2×C4⋊C4—1222no—
486C2×C4⋊C4—2442no—
487C2×C4⋊C4—2442no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—1224no—
491C2×C22⋊C4—1224no—
492C2×C22⋊C4—1224no—
493C2×C22⋊C4—1224no—
494C2×C22⋊C4—2442no—
495C2×C22⋊C4—2442no—
496C2×C22⋊C4Dic12214yes—
497C2×C22⋊C4D24414yes—
498C2×C22⋊C4C2×Dic6114yes—
499C2×C22⋊C4C2×Dic6114yes—
500C2×C42—22no—
501C2×C42—22no—
502C2×C42—22no—
503C2×C42—22no—
504C2×C42—1224no—
505C2×C42—1224no—
506C2×C42—2442no—
507C2×C42C2×Dic6114yes—
508C2×C42C2×Dic6114yes—
509#95—1224no—
510#95—1224no—
511#95—1224no—
512#95—1224no—
513#95—1224no—
514#95—1224no—
515#95—2442no—
516#95C2×Dic6114yes—
517#95C2×Dic6114yes—
518C24—21no—
519C24—21no—
520C24—21no—
521C24—21no—
522C24—21no—
523C24—21no—
524C24—21no—
525C24—21no—
526C24—21no—
527C24—21no—
528C24—21no—
529C24—21no—
530C24C2×Dic12212yes—
531C24C2×D24412yes—
532C24C22×Dic6112yes—
533C24C23×D6111yescharacteristic
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—28no—
559C22×C4—28no—
560C22×C4—28no—
561C22×C4—44no—
562C22×C4—44no—
563C22×C4—44no—
564C22×C4—44no—
565C22×C4—614no—
566C22×C4—614no—
567C22×C4—1222no—
568C22×C4—1222no—
569C22×C4—1222no—
570C22×C4—1222no—
571C22×C4—1222no—
572C22×C4—1222no—
573C22×C4—1222no—
574C22×C4—1222no—
575C22×C4—1222no—
576C22×C4—1222no—
577C22×C4—1222no—
578C22×C4—1222no—
579C22×C4—1222no—
580C22×C4—1222no—
581C22×C4—1222no—
582C22×C4—1222no—
583C22×C4—1222no—
584C22×C4—1222no—
585C22×C4—1222no—
586C22×C4—1222no—
587C22×C4—1222no—
588C22×C4—1222no—
589C22×C4—1222no—
590C22×C4—1222no—
591C22×C4—1222no—
592C22×C4—1222no—
593C22×C4C2×Dic12212yes—
594C22×C4C2×Dic12212yes—
595C22×C4C2×D24412yes—
596C22×C4C2×D24412yes—
597C22×C4#1175822212yes—
598C22×C4#1175822212yes—
599C22×C4#1175822212yes—
600C22×C4#1175822212yes—
601C22×C4D4×D6112yes—
602C22×C4D4×D6112yes—
603C22×C4#1175822412yes—
604C22×C4#1175822412yes—
605C22×C4C22×Dic6112yes—
606C22×C4C22×Dic6112yes—
607C22×C4C22×Dic6112yes—
608C22×C4C22×Dic6112yes—
609C22×C4C22×Dic6112yes—
610C22×C4C22×Dic6112yes—
611C4⋊C4—1228no—
612C4⋊C4—1228no—
613C4⋊C4—2448no—
614C4⋊C4—2448no—
615C4⋊C4—2444no—
616C4⋊C4—2444no—
617C22⋊C4—28no—
618C22⋊C4—2448no—
619C22⋊C4—2448no—
620C22⋊C4C4⋊Dic61116yescomplemented
621C42—28no—
622C42—28no—
623C42—2448no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23C2×C4⋊Dic6114yes—
659C23C23×Dic6111yescharacteristic
660C23C2×D4×D6111yescharacteristic
661C23C2×D4×D6111yescharacteristic
662C23C22×D24411yescharacteristic
663C23C22×Dic12211yescharacteristic
664C23C2×#1175822411yescharacteristic
665C23C2×#1175822411yescharacteristic
666C23C2×#1175822211yescharacteristic
667C23C2×#1175822211yescharacteristic
668C23C2×#1175822211yescharacteristic
669C23C2×#1175822211yescharacteristic
670C23#1451982311yescharacteristic
671C23#1451982311yescharacteristic
672C23#1451982411yescharacteristic
673C23#1451982411yescharacteristic
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—416no—
707C2×C4—1224no—
708C2×C4—1224no—
709C2×C4—1224no—
710C2×C4—1224no—
711C2×C4—1224no—
712C2×C4—1224no—
713C2×C4—2442no—
714C2×C4—2442no—
715C2×C4—2442no—
716C2×C4—2442no—
717C2×C4—2442no—
718C2×C4—2442no—
719C2×C4—2442no—
720C2×C4—2442no—
721C2×C4—2442no—
722C2×C4—2442no—
723C2×C4—2442no—
724C2×C4—2442no—
725C2×C4—2442no—
726C2×C4—2442no—
727C2×C4—2442no—
728C2×C4—2442no—
729C2×C4—2442no—
730C2×C4—2442no—
731C2×C4—2442no—
732C2×C4—2442no—
733C2×C4—2442no—
734C2×C4—2442no—
735C2×C4C2×C4⋊Dic6114yes—
736C2×C4C2×C4⋊Dic6114yes—
737C2×C4#1451973614yes—
738C2×C4#1451973614yes—
739C2×C4D4×Dic6114yes—
740C2×C4D4×Dic6114yes—
741C2×C4#1451975014yes—
742C2×C4#1451975914yes—
743C2×C4#1451976314yes—
744C2×C4#1451977014yes—
745C22—24no—
746C22—24no—
747C22—24no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22C22×C4⋊Dic6111yescharacteristic
761C22C2×#1451973611yescharacteristic
762C22C2×#1451973611yescharacteristic
763C22C2×D4×Dic6111yescharacteristic
764C22C2×D4×Dic6111yescharacteristic
765C22#1684024511yescharacteristic
766C22#1684024511yescharacteristic
767C22C2×#1451975011yescharacteristic
768C22C2×#1451975911yescharacteristic
769C22C2×#1451976311yescharacteristic
770C22C2×#1451977011yescharacteristic
771C22#1684031211yescharacteristic
772C22#1684031211yescharacteristic
773C22#1684031911yescharacteristic
774C22#1684031911yescharacteristic
775C22#1684036711yescharacteristic
776C22#1684037411yescharacteristic
777C22#1684038311yescharacteristic
778C22#1684038311yescharacteristic
779C22D4×D24411yescharacteristic
780C22D4×D24411yescharacteristic
781C22#1684040811yescharacteristic
782C22#1684041611yescharacteristic
783C22#1684041611yescharacteristic
784C22#1684041711yescharacteristic
785C22#1684042111yescharacteristic
786C22D4×Dic12211yescharacteristic
787C22D4×Dic12211yescharacteristic
788C22#1684043311yescharacteristic
789C22#1684045211yescharacteristic
790C22#1684045811yescharacteristic
791C22#1684046911yescharacteristic
792C22#1684046911yescharacteristic
793C22#1684047711yescharacteristic
794C22#1684048211yescharacteristic
795C4—24no—
796C4—24no—
797C4—24no—
798C4—42no—
799C4—42no—
800C4—4882no—
801C4—4882no—
802C4—2444no—
803C4—2444no—
804C4#1683965518yescomplemented
805C2—44no—
806C2#2144822611yescharacteristic
807C2C2×#1683965511yescharacteristic
808C2#2144842811yescharacteristic
809C2D4×C4⋊Dic6111yescharacteristic
810C2D4×C4⋊Dic6111yescharacteristic
811C2#2144874811yescharacteristic
812C2#2144876811yescharacteristic
813C2#2144933311yescharacteristic
814C2#2144934411yescharacteristic
815C2#2144940711yescharacteristic
816C2#2144941811yescharacteristic
817C2#2145018211yescharacteristic
818C2#2145019311yescharacteristic
819C2#2145024111yescharacteristic
820C2#2145025211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C4×C22⋊C4×C61C2
socle, cosocleC24×C61C24
prime radicalC25×C61C23
hypercenterC2×C4×C22⋊C4D61
hypocenterC61#13876
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#16839632C2semidirect
5. C2×C4×C4⋊Dic61C2semidirect
6. #21444076C2semidirect
8. #21444053C2semidirect
9. #21444049C2semidirect
10. #21444049C2semidirect
38. C4×C22⋊C4×C61C4semidirect
201. C22⋊C4×C61C4⋊C4semidirect
390. C4×C61#388semidirect
441. C4×C22⋊C4Dic61semidirect
451. C61#13876semidirect
620. C22⋊C4C4⋊Dic61semidirect
804. C4#16839655semidirect

Maximal subgroups

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

subgroupindex
C2×#168396552
C2×#168396322
C2×#168396222
C2×C4×C4⋊Dic612
#214440762
#214440642
#214440532
#214440492
C2×C4×C22⋊C4×C612
#1387661