Finite Group Databasebeta

← C2×#21449971 #29848383

Subgroups — C2×#21449971 #29848383

Order 15616.

2962 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519733C211yesmaximal, characteristic, complemented
2#21449971C2116yesmaximal, direct product factor
3C2×#16839690C211yesmaximal, characteristic, complemented
4C2×#16839685C211yesmaximal, characteristic, complemented
5C2×#16839681C211yesmaximal, characteristic, complemented
6C2×#16839676C211yesmaximal, characteristic
7C2×#16839669C211yesmaximal, characteristic, complemented
8C2×#16839656C211yesmaximal, characteristic, complemented
9C2×#16839655C211yesmaximal, characteristic, complemented
10C2×#16839650C211yesmaximal, characteristic, complemented
11C2×#16839650C211yesmaximal, characteristic, complemented
12C2×#16839646C211yesmaximal, characteristic, complemented
13C2×#16839642C211yesmaximal, characteristic
14C2×#16839634C211yesmaximal, characteristic, complemented
15C2×C4×#11758196C211yesmaximal, characteristic, complemented
16C22×#124×C61C211yesmaximal, characteristic
17C24×Dic61C2211yescharacteristic
18C2×#14519733—28no—
19C2×#14519733C2218yescomplemented
20C22×C4⋊Dic61C2211yescharacteristic
21C22×#11758196C2211yescharacteristic
22C22×#11758196C2211yescharacteristic
23C22×#11758196C2211yescharacteristic
24C22×#11758196C2211yescharacteristic
25C22×#11758196C2211yescharacteristic
26C22×#11758196C2211yescharacteristic
27C22×C22⋊Dic61C2211yescharacteristic
28C22×C22⋊Dic61C2211yescharacteristic
29C22×C22⋊Dic61C2211yescharacteristic
30C22×C22⋊Dic61C2211yescharacteristic
31C22×C22⋊Dic61C2211yescharacteristic
32C22×C22⋊Dic61C2211yescharacteristic
33C22×C22⋊Dic61C2211yescharacteristic
34C22×C4×Dic61C2211yescharacteristic
35C22×C4×Dic61C2211yescharacteristic
36C22×C4×Dic61C2211yescharacteristic
37#16839690C2218yescomplemented
38#16839685C2218yescomplemented
39#16839681C2218yescomplemented
40#16839676C2218yes—
41#16839669C2218yescomplemented
42#16839656C2218yescomplemented
43#16839655C2218yescomplemented
44#16839650C2218yescomplemented
45#16839650C2218yescomplemented
46#16839646C2218yescomplemented
47#16839642C2218yes—
48#16839634C2218yescomplemented
49C4×#11758196C2218yescomplemented
50C2×#14519684C2211yescharacteristic
51C2×#14519684C2211yescharacteristic
52C2×#14519684C2211yescharacteristic
53C2×#14519684C2211yescharacteristic
54C2×#14519684C2211yescharacteristic
55C2×#14519684C2211yescharacteristic
56C2×#14519684C2211yescharacteristic
57C2×#14519684C2211yescharacteristic
58C2×#14519684C2211yescharacteristic
59C2×#14519684C2211yescharacteristic
60C23×Q8×C61C2211yescharacteristic
61C23×D4×C61C2211yescharacteristic
62C2×#124×C61—28no—
63C2×#124×C61C2218yes—
64C22×C22⋊C4×C61C2211yescharacteristic
65C22×C22⋊C4×C61C2211yescharacteristic
66C22×C22⋊C4×C61C2211yescharacteristic
67C22×C22⋊C4×C61C2211yescharacteristic
68C22×C42×C61C2211yescharacteristic
69C23×Dic61—24no—
70C23×Dic61—24no—
71C23×Dic61—24no—
72C23×Dic61C2311yescharacteristic
73C23×Dic61C2311yescharacteristic
74C23×Dic61C2311yescharacteristic
75C23×Dic61C2311yescharacteristic
76C23×Dic61C2311yescharacteristic
77C23×Dic61C2314yes—
78C23×Dic61C2311yescharacteristic
79C23×Dic61C2311yescharacteristic
80C23×Dic61C2311yescharacteristic
81#14519733—232no—
82C2×C4⋊Dic61—42no—
83C2×C4⋊Dic61C2314yes—
84C2×#11758196—24no—
85C2×#11758196—24no—
86C2×#11758196—24no—
87C2×#11758196—24no—
88C2×#11758196—24no—
89C2×#11758196—42no—
90C2×#11758196C2314yes—
91C2×#11758196C2314yes—
92C2×#11758196C2314yes—
93C2×#11758196C2314yes—
94C2×#11758196C2314yes—
95C2×#11758196C2314yes—
96C2×C22⋊Dic61—24no—
97C2×C22⋊Dic61—24no—
98C2×C22⋊Dic61—24no—
99C2×C22⋊Dic61—24no—
100C2×C22⋊Dic61—24no—
101C2×C22⋊Dic61—42no—
102C2×C22⋊Dic61—42no—
103C2×C22⋊Dic61C2314yes—
104C2×C22⋊Dic61C2314yes—
105C2×C22⋊Dic61C2314yes—
106C2×C22⋊Dic61C2314yes—
107C2×C22⋊Dic61C2314yes—
108C2×C22⋊Dic61C2314yes—
109C2×C22⋊Dic61C2314yes—
110C2×C4×Dic61—24no—
111C2×C4×Dic61—24no—
112C2×C4×Dic61—24no—
113C2×C4×Dic61C2314yes—
114C2×C4×Dic61C2314yes—
115C2×C4×Dic61C2314yes—
116#14519684C2314yes—
117#14519684C2314yes—
118#14519684C2314yes—
119#14519684C2314yes—
120#14519684C2314yes—
121#14519684C2314yes—
122#14519684C2314yes—
123#14519684C2314yes—
124#14519684C2314yes—
125#14519684C2314yes—
126C25×C61C2311yescharacteristic
127C25×C61C2311yescharacteristic
128C22×Q8×C61—24no—
129C22×Q8×C61—24no—
130C22×Q8×C61—42no—
131C22×Q8×C61C2314yes—
132C22×D4×C61—24no—
133C22×D4×C61—24no—
134C22×D4×C61—42no—
135C22×D4×C61C2314yes—
136C23×C4×C61C2311yescharacteristic
137C23×C4×C61C2311yescharacteristic
138C23×C4×C61C2311yescharacteristic
139C23×C4×C61C2311yescharacteristic
140C23×C4×C61C2311yescharacteristic
141#124×C61—232no—
142C2×C22⋊C4×C61—24no—
143C2×C22⋊C4×C61—24no—
144C2×C22⋊C4×C61—24no—
145C2×C22⋊C4×C61D418yes—
146C2×C22⋊C4×C61C2314yes—
147C2×C22⋊C4×C61C2314yes—
148C2×C22⋊C4×C61C2314yes—
149C2×C22⋊C4×C61C2314yes—
150C2×C42×C61—24no—
151C2×C42×C61C2314yes—
152C24×C61—22no—
153C24×C61—22no—
154C24×C61—22no—
155C24×C61—22no—
156C24×C61—22no—
157C24×C61—22no—
158C24×C61—22no—
159C24×C61—22no—
160C24×C61—22no—
161C24×C61—22no—
162C24×C61—22no—
163C24×C61—22no—
164C24×C61—22no—
165C24×C61C2×D414yes—
166C24×C61C2412yes—
167C24×C61C2412yes—
168C24×C61C2411yescharacteristic
169C2×Q8×C61—28no—
170C2×Q8×C61—28no—
171C2×Q8×C61—44no—
172C2×Q8×C61—416no—
173C2×D4×C61—28no—
174C2×D4×C61—28no—
175C2×D4×C61—44no—
176C2×D4×C61—416no—
177C22×C4×C61—22no—
178C22×C4×C61—22no—
179C22×C4×C61—22no—
180C22×C4×C61—22no—
181C22×C4×C61—22no—
182C22×C4×C61—22no—
183C22×C4×C61—22no—
184C22×C4×C61—22no—
185C22×C4×C61—22no—
186C22×C4×C61—22no—
187C22×C4×C61—22no—
188C22×C4×C61—22no—
189C22×C4×C61C2×D414yes—
190C22×C4×C61C2×D414yes—
191C22×C4×C61#4114yes—
192C22×C4×C61C2412yes—
193C22×C4×C61C2412yes—
194C22×C4×C61C2412yes—
195C22×C4×C61C2412yes—
196C22×C4×C61C2412yes—
197C22×Dic61—232no—
198C22×Dic61—22no—
199C22×Dic61—22no—
200C22×Dic61—28no—
201C22×Dic61—22no—
202C22×Dic61—22no—
203C22×Dic61—22no—
204C22×Dic61—22no—
205C22×Dic61—28no—
206C22×Dic61—28no—
207C22×Dic61—22no—
208C22×Dic61—22no—
209C22×Dic61—22no—
210C22×Dic61—22no—
211C22×Dic61—22no—
212C22×Dic61—22no—
213C22×Dic61—22no—
214C22×Dic61—22no—
215C22×Dic61—22no—
216C22×Dic61—22no—
217C22×Dic61—22no—
218C22×Dic61—22no—
219C22×Dic61—22no—
220C22×Dic61—22no—
221C22×Dic61—22no—
222C22×Dic61#4114yes—
223C22×Dic61#4114yes—
224C22×Dic61#4114yes—
225C22×Dic61C2412yes—
226C22×Dic61C2412yes—
227C22×Dic61C2412yes—
228C22×Dic61C2412yes—
229C22×Dic61C2412yes—
230C22×Dic61C2412yes—
231C22×Dic61C2412yes—
232C22×Dic61C2412yes—
233C22⋊C4×C61—28no—
234C22⋊C4×C61—28no—
235C22⋊C4×C61—28no—
236C22⋊C4×C61C2×D4116yes—
237C42×C61—28no—
238C22⋊Dic61—28no—
239C22⋊Dic61—28no—
240C22⋊Dic61—28no—
241C22⋊Dic61—28no—
242C22⋊Dic61—28no—
243C22⋊Dic61—44no—
244C22⋊Dic61—44no—
245C4⋊Dic61—44no—
246#11758196—28no—
247#11758196—28no—
248#11758196—28no—
249#11758196—28no—
250#11758196—28no—
251#11758196—44no—
252C4×Dic61—28no—
253C4×Dic61—28no—
254C4×Dic61—28no—
255C23×C61—28no—
256C23×C61—28no—
257C23×C61—28no—
258C23×C61—22no—
259C23×C61—22no—
260C23×C61—22no—
261C23×C61—22no—
262C23×C61—22no—
263C23×C61—22no—
264C23×C61—22no—
265C23×C61—22no—
266C23×C61—22no—
267C23×C61—22no—
268C23×C61—22no—
269C23×C61—22no—
270C23×C61—22no—
271C23×C61—44no—
272C23×C61—44no—
273C23×C61—44no—
274C23×C61—44no—
275C23×C61—44no—
276C23×C61—44no—
277C23×C61—44no—
278C23×C61—44no—
279C23×C61—44no—
280C23×C61—44no—
281C23×C61—44no—
282C23×C61C22×D414yes—
283C23×C61C22×D412yes—
284C23×C61C2×#4112yes—
285C23×C61C2×#4112yes—
286C23×C61C2×#4112yes—
287C23×C61C2×#4112yes—
288C23×C61H(5,𝔽2)12yes—
289C23×C612−1+412yes—
290C23×C61C2511yescharacteristic
291Q8×C61—416no—
292D4×C61—416no—
293C2×C4×C61—28no—
294C2×C4×C61—28no—
295C2×C4×C61—28no—
296C2×C4×C61—22no—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61—22no—
301C2×C4×C61—22no—
302C2×C4×C61—22no—
303C2×C4×C61—22no—
304C2×C4×C61—22no—
305C2×C4×C61—22no—
306C2×C4×C61—22no—
307C2×C4×C61—22no—
308C2×C4×C61—44no—
309C2×C4×C61—44no—
310C2×C4×C61C22×D414yes—
311C2×C4×C61C22×D414yes—
312C2×C4×C61C2×#4114yes—
313C2×Dic61—232no—
314C2×Dic61—28no—
315C2×Dic61—28no—
316C2×Dic61—28no—
317C2×Dic61—22no—
318C2×Dic61—22no—
319C2×Dic61—22no—
320C2×Dic61—22no—
321C2×Dic61—22no—
322C2×Dic61—22no—
323C2×Dic61—22no—
324C2×Dic61—22no—
325C2×Dic61—22no—
326C2×Dic61—22no—
327C2×Dic61—22no—
328C2×Dic61—22no—
329C2×Dic61—22no—
330C2×Dic61—22no—
331C2×Dic61—22no—
332C2×Dic61—22no—
333C2×Dic61—22no—
334C2×Dic61—22no—
335C2×Dic61—22no—
336C2×Dic61—22no—
337C2×Dic61—22no—
338C2×Dic61—44no—
339C2×Dic61—44no—
340C2×Dic61—44no—
341C2×Dic61—44no—
342C2×Dic61—44no—
343C2×Dic61C2×#4114yes—
344C2×Dic61C2×#4114yes—
345C2×Dic61C2×#4114yes—
346C2×#2474—611nomaximal, Sylow
347C22×C61—24no—
348C22×C61—24no—
349C22×C61—24no—
350C22×C61—42no—
351C22×C61—42no—
352C22×C61—42no—
353C22×C61—42no—
354C22×C61—416no—
355C22×C61—42no—
356C22×C61—42no—
357C22×C61—42no—
358C22×C61—42no—
359C22×C61—42no—
360C22×C61—42no—
361C22×C61—42no—
362C22×C61—88no—
363C22×C61#52514yes—
364C22×C61#52914yes—
365C22×C61#54214yes—
366C22×C61#54614yes—
367C22×C61#54714yes—
368C22×C61#55514yes—
369C22×C61#55614yes—
370C22×C61C23×D411yescharacteristic
371C22×C61C22×#4111yescharacteristic
372C22×C61C22×#4111yescharacteristic
373C22×C61C22×#4111yescharacteristic
374C22×C61C22×#4111yescharacteristic
375C22×C61C2×H(5,𝔽2)11yescharacteristic
376C22×C61C2×2−1+411yescharacteristic
377C4×C61—24no—
378C4×C61—24no—
379C4×C61—24no—
380C4×C61—42no—
381C4×C61—42no—
382Dic61—24no—
383Dic61—24no—
384Dic61—24no—
385Dic61—42no—
386Dic61—42no—
387Dic61—42no—
388Dic61—42no—
389Dic61—42no—
390C22×#124D6111yescharacteristic
391C22×#117—611no—
392#2474—6116no—
393C2×#397—611no—
394C2×#396—611no—
395C2×#395—611no—
396C2×#394—611no—
397C2×#391—611no—
398C2×#388—611no—
399C2×#388—611no—
400C2×#388—611no—
401C2×#388—611no—
402C2×#387—611no—
403C2×#386—611no—
404C2×#385—611no—
405C2×C4×C4⋊C4—611no—
406C2×C61—44no—
407C2×C61—82no—
408C2×C61#247418yescomplemented
409C2×C61C2×#52511yescharacteristic
410C2×C61C2×#52911yescharacteristic
411C2×C61C2×#54211yescharacteristic
412C2×C61C2×#54611yescharacteristic
413C2×C61C2×#54711yescharacteristic
414C2×C61C2×#55511yescharacteristic
415C2×C61C2×#55611yescharacteristic
416C23×Q8C2×D6111yescharacteristic
417C23×D4C2×D6111yescharacteristic
418C24×C4—611no—
419C2×#124—28no—
420C2×#124C2×D6118yes—
421C2×#117—618no—
422C2×#117—1228no—
423C22×C4⋊C4—611no—
424C22×C4⋊C4—611no—
425C22×C4⋊C4—611no—
426C22×C4⋊C4—611no—
427C22×C4⋊C4—611no—
428C22×C4⋊C4—611no—
429C22×C4⋊C4—611no—
430C22×C22⋊C4—611no—
431C22×C22⋊C4—611no—
432C22×C22⋊C4—611no—
433C22×C22⋊C4—611no—
434C22×C22⋊C4—611no—
435C22×C22⋊C4—611no—
436C22×C22⋊C4—611no—
437C22×C22⋊C4C2×D6111yescharacteristic
438C22×C22⋊C4C2×D6111yescharacteristic
439C22×C22⋊C4C2×D6111yescharacteristic
440C22×C22⋊C4C2×D6111yescharacteristic
441C22×C42—611no—
442C22×C42—611no—
443C22×C42—611no—
444C22×C42C2×D6111yescharacteristic
445#397—618no—
446#396—618no—
447#395—618no—
448#394—618no—
449#391—618no—
450#388—618no—
451#388—618no—
452#388—618no—
453#388—618no—
454#387—618no—
455#386—618no—
456#385—618no—
457C4×C4⋊C4—618no—
458C2×#95—611no—
459C2×#95—611no—
460C2×#95—611no—
461C2×#95—611no—
462C2×#95—611no—
463C2×#95—611no—
464C2×#95—611no—
465C2×#95—611no—
466C2×#95—611no—
467C2×#95—611no—
468C61C2×#247411yescharacteristic, complemented, Sylow
469C25C22×D6111yescharacteristic
470C25C22×D6111yescharacteristic
471C22×Q8—24no—
472C22×Q8—24no—
473C22×Q8—42no—
474C22×Q8C22×D6114yes—
475C22×D4—24no—
476C22×D4—24no—
477C22×D4—42no—
478C22×D4C22×D6114yes—
479C23×C4—611no—
480C23×C4—611no—
481C23×C4—611no—
482C23×C4—614no—
483C23×C4—611no—
484C23×C4—611no—
485C23×C4—611no—
486C23×C4—611no—
487C23×C4—611no—
488C23×C4—1224no—
489C23×C4—1224no—
490C23×C4—1224no—
491C23×C4C22×D6111yescharacteristic
492C23×C4C22×D6111yescharacteristic
493C23×C4C22×D6111yescharacteristic
494C23×C4C22×D6111yescharacteristic
495C23×C4C22×D6111yescharacteristic
496#124—232no—
497#117—12232no—
498C2×C4⋊C4—614no—
499C2×C4⋊C4—614no—
500C2×C4⋊C4—614no—
501C2×C4⋊C4—614no—
502C2×C4⋊C4—614no—
503C2×C4⋊C4—614no—
504C2×C4⋊C4—614no—
505C2×C4⋊C4—1224no—
506C2×C4⋊C4—1224no—
507C2×C4⋊C4—1224no—
508C2×C4⋊C4—1224no—
509C2×C4⋊C4—1224no—
510C2×C4⋊C4—2442no—
511C2×C4⋊C4—2442no—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—614no—
516C2×C22⋊C4—614no—
517C2×C22⋊C4—614no—
518C2×C22⋊C4—614no—
519C2×C22⋊C4—614no—
520C2×C22⋊C4—614no—
521C2×C22⋊C4—614no—
522C2×C22⋊C4—1224no—
523C2×C22⋊C4—1224no—
524C2×C22⋊C4—1224no—
525C2×C22⋊C4—1224no—
526C2×C22⋊C4—1224no—
527C2×C22⋊C4—2442no—
528C2×C22⋊C4—2442no—
529C2×C22⋊C4C22⋊D6118yes—
530C2×C22⋊C4C22×D6114yes—
531C2×C22⋊C4C22×D6114yes—
532C2×C22⋊C4C22×D6114yes—
533C2×C22⋊C4C22×D6114yes—
534C2×C42—24no—
535C2×C42—614no—
536C2×C42—614no—
537C2×C42—614no—
538C2×C42—1224no—
539C2×C42—1224no—
540C2×C42—1224no—
541C2×C42C22×D6114yes—
542#95—614no—
543#95—614no—
544#95—614no—
545#95—614no—
546#95—614no—
547#95—614no—
548#95—614no—
549#95—614no—
550#95—614no—
551#95—614no—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—22no—
556C24—22no—
557C24—22no—
558C24—22no—
559C24—22no—
560C24—22no—
561C24—22no—
562C24—22no—
563C24—22no—
564C24—22no—
565C24C2×C22⋊D6114yes—
566C24C23×D6112yes—
567C24C23×D6112yes—
568C24C23×D6111yescharacteristic
569C2×Q8—28no—
570C2×Q8—28no—
571C2×Q8—44no—
572C2×Q8—416no—
573C2×D4—28no—
574C2×D4—28no—
575C2×D4—44no—
576C2×D4—416no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—614no—
590C22×C4—614no—
591C22×C4—614no—
592C22×C4—612no—
593C22×C4—612no—
594C22×C4—612no—
595C22×C4—612no—
596C22×C4—612no—
597C22×C4—612no—
598C22×C4—612no—
599C22×C4—612no—
600C22×C4—1228no—
601C22×C4—1228no—
602C22×C4—12232no—
603C22×C4—1222no—
604C22×C4—1222no—
605C22×C4—1228no—
606C22×C4—1222no—
607C22×C4—1222no—
608C22×C4—1222no—
609C22×C4—1222no—
610C22×C4—1222no—
611C22×C4—1222no—
612C22×C4—1222no—
613C22×C4—1222no—
614C22×C4—1222no—
615C22×C4—1222no—
616C22×C4—1222no—
617C22×C4—1222no—
618C22×C4—1222no—
619C22×C4—1222no—
620C22×C4—1222no—
621C22×C4—1222no—
622C22×C4—1222no—
623C22×C4—1222no—
624C22×C4—1222no—
625C22×C4#1175822414yes—
626C22×C4C2×C22⋊D6114yes—
627C22×C4C2×C22⋊D6114yes—
628C22×C4C23×D6112yes—
629C22×C4C23×D6112yes—
630C22×C4C23×D6112yes—
631C22×C4C23×D6112yes—
632C22×C4C23×D6112yes—
633C4⋊C4—1228no—
634C4⋊C4—1228no—
635C4⋊C4—1228no—
636C4⋊C4—1228no—
637C4⋊C4—1228no—
638C4⋊C4—2444no—
639C4⋊C4—2444no—
640C22⋊C4—28no—
641C22⋊C4—28no—
642C22⋊C4—28no—
643C22⋊C4—1228no—
644C22⋊C4—1228no—
645C22⋊C4—1228no—
646C22⋊C4—1228no—
647C22⋊C4—1228no—
648C22⋊C4—2444no—
649C22⋊C4—2444no—
650C22⋊C4C2×C22⋊D61116yes—
651C42—28no—
652C42—1228no—
653C42—1228no—
654C42—1228no—
655C23—28no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—28no—
663C23—28no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—44no—
672C23—44no—
673C23—44no—
674C23—44no—
675C23—44no—
676C23—44no—
677C23—44no—
678C23—44no—
679C23—44no—
680C23—44no—
681C23—44no—
682C23C22×C22⋊D6114yes—
683C23C22×C22⋊D6112yes—
684C23#41×D6112yes—
685C23#41×D6112yes—
686C23#41×D6112yes—
687C23C2×#1175822412yes—
688C23#1451982212yes—
689C23#1451982412yes—
690C23C24×D6111yescharacteristic
691Q8—416no—
692D4—416no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—28no—
700C2×C4—28no—
701C2×C4—28no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—44no—
709C2×C4—44no—
710C2×C4—614no—
711C2×C4—614no—
712C2×C4—614no—
713C2×C4—12232no—
714C2×C4—1228no—
715C2×C4—1228no—
716C2×C4—1228no—
717C2×C4—1222no—
718C2×C4—1222no—
719C2×C4—1222no—
720C2×C4—1222no—
721C2×C4—1222no—
722C2×C4—1222no—
723C2×C4—1222no—
724C2×C4—1222no—
725C2×C4—1222no—
726C2×C4—1222no—
727C2×C4—1222no—
728C2×C4—1222no—
729C2×C4—1222no—
730C2×C4—1222no—
731C2×C4—1222no—
732C2×C4—1222no—
733C2×C4—1222no—
734C2×C4—1222no—
735C2×C4—1222no—
736C2×C4—1222no—
737C2×C4—1222no—
738C2×C4—2444no—
739C2×C4—2444no—
740C2×C4—2444no—
741C2×C4—2444no—
742C2×C4—2444no—
743C2×C4C22×C22⋊D6114yes—
744C2×C4C22×C22⋊D6114yes—
745C2×C4C2×#1175822414yes—
746C22—24no—
747C22—24no—
748C22—24no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—416no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—88no—
762C22#1684026914yes—
763C22#1684029114yes—
764C22#1684037614yes—
765C22#1684040614yes—
766C22#1684041114yes—
767C22#1684047414yes—
768C22#1684048114yes—
769C22C23×C22⋊D6111yescharacteristic
770C22C2×#41×D6111yescharacteristic
771C22C2×#41×D6111yescharacteristic
772C22C2×#41×D6111yescharacteristic
773C22C22×#1175822411yescharacteristic
774C22C2×#1451982211yescharacteristic
775C22C2×#1451982411yescharacteristic
776C4—24no—
777C4—24no—
778C4—24no—
779C4—42no—
780C4—42no—
781C4—1224no—
782C4—1224no—
783C4—1224no—
784C4—2442no—
785C4—2442no—
786C4—2442no—
787C4—2442no—
788C4—2442no—
789C2—44no—
790C2—82no—
791C2#2144997118yesdirect product factor
792C2C2×#1684026911yescharacteristic
793C2C2×#1684029111yescharacteristic
794C2C2×#1684037611yescharacteristic
795C2C2×#1684040611yescharacteristic
796C2C2×#1684041111yescharacteristic
797C2C2×#1684047411yescharacteristic
798C2C2×#1684048111yescharacteristic
subgroupG/H
centerC24C23×D61
commutator, cosocleC23×C61C25
FrattiniC23C24×D61
FittingC22×#124×C61C2
socleC24×C61C24
prime radicalC23×D4×C61C22
hypercenterC22×#124D61
hypocenterC61C2×#2474
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C22×#124

Complements

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

NH ≅ G/Ntype
1. C22×#14519733C2semidirect
2. #21449971C2direct (N × H)
3. C2×#16839690C2semidirect
4. C2×#16839685C2semidirect
5. C2×#16839681C2semidirect
7. C2×#16839669C2semidirect
8. C2×#16839656C2semidirect
9. C2×#16839655C2semidirect
10. C2×#16839650C2semidirect
11. C2×#16839650C2semidirect
12. C2×#16839646C2semidirect
14. C2×#16839634C2semidirect
15. C2×C4×#11758196C2semidirect
19. C2×#14519733C22semidirect
37. #16839690C22semidirect
38. #16839685C22semidirect
39. #16839681C22semidirect
41. #16839669C22semidirect
42. #16839656C22semidirect
43. #16839655C22semidirect
44. #16839650C22semidirect
45. #16839650C22semidirect
46. #16839646C22semidirect
48. #16839634C22semidirect
49. C4×#11758196C22semidirect
408. C2×C61#2474semidirect
468. C61C2×#2474semidirect
791. C2#21449971direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197332
#214499712
C2×#168396902
C2×#168396852
C2×#168396812
C2×#168396762
C2×#168396692
C2×#168396562
C2×#168396552
C2×#168396502
C2×#168396462
C2×#168396422
C2×#168396342
C2×C4×#117581962
C22×#124×C612
C2×#247461