Finite Group Databasebeta

← C2×#21456004 #30548245

Subgroups — C2×#21456004 #30548245

Order 15616.

2274 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840385C211yesmaximal, characteristic, complemented
2C2×#16840237C211yesmaximal, characteristic, complemented
3#21456004C2116yesmaximal, direct product factor
4C2×#16840100C211yesmaximal, characteristic, complemented
5C2×#16840087C211yesmaximal, characteristic, complemented
6C2×#16840050C211yesmaximal, characteristic, complemented
7C2×#16840040C211yesmaximal, characteristic, complemented
8C2×#16839979C211yesmaximal, characteristic, complemented
9C2×#16839979C211yesmaximal, characteristic, complemented
10C2×#16839896C211yesmaximal, characteristic
11C2×#16839871C211yesmaximal, characteristic, complemented
12C2×#16839863C211yesmaximal, characteristic, complemented
13C2×SD16×Dic61C211yesmaximal, characteristic, complemented
14C2×#16839842C211yesmaximal, characteristic, complemented
15C2×#16839820C211yesmaximal, characteristic, complemented
16C2×C61×#450C211yesmaximal, characteristic, complemented
17C22×#11758199C2211yescharacteristic
18C22×#11758199C2211yescharacteristic
19#16840385—24no—
20#16840385C2218yescomplemented
21C2×#14519776C2211yescharacteristic, complemented
22C2×#14519772—21no—
23C2×#14519766C2211yescharacteristic, complemented
24C2×#14519763—21no—
25C2×#14519759—21no—
26C2×#14519757—21no—
27C2×#14519751C2211yescharacteristic
28#16840237—24no—
29#16840237C2218yescomplemented
30C2×Q8×Dic61C2211yescharacteristic, complemented
31C2×D4×Dic61—21no—
32C2×D4×Dic61—21no—
33C2×D4×Dic61C2211yescharacteristic
34C2×D4×Dic61C2211yescharacteristic
35C2×D4×Dic61C2211yescharacteristic
36C2×D4×Dic61C2211yescharacteristic
37C2×#14519739C2211yescharacteristic, complemented
38C2×#14519736C2211yescharacteristic
39C2×#14519736C2211yescharacteristic
40C22×C22⋊Dic61—21no—
41C22×C22⋊Dic61—21no—
42#16840100C2218yescomplemented
43#16840087C2218yescomplemented
44#16840050C2218yescomplemented
45#16840040C2218yescomplemented
46#16839979C2218yescomplemented
47#16839979C2218yescomplemented
48#16839896C2218yes—
49#16839871C2218yescomplemented
50#16839863C2218yescomplemented
51SD16×Dic61C2218yescomplemented
52#16839842C2218yescomplemented
53#16839820C2218yescomplemented
54C2×#14519711C2211yescharacteristic, complemented
55C2×#14519710C2211yescharacteristic, complemented
56C2×#14519709C2211yescharacteristic, complemented
57C2×#14519708C2211yescharacteristic, complemented
58C2×#14519706C2211yescharacteristic, complemented
59C2×#14519706C2211yescharacteristic, complemented
60C2×#14519701C2211yescharacteristic, complemented
61C2×#14519701C2211yescharacteristic, complemented
62C2×#14519699C2211yescharacteristic, complemented
63C2×#14519699C2211yescharacteristic, complemented
64C2×#14519698C2211yescharacteristic
65C2×#14519698C2211yescharacteristic
66C2×C22⋊#92418C2211yescharacteristic
67C2×#14519687C2211yescharacteristic, complemented
68C2×C8×Dic61C2211yescharacteristic, complemented
69C23×D4×C61C2211yescharacteristic
70C22×SD16×C61C2211yescharacteristic
71C22×SD16×C61C2211yescharacteristic
72C2×C22⋊Q8×C61C2211yescharacteristic
73C61×#450C2218yescomplemented
74C2×#102×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×C22⋊C8×C61C2211yescharacteristic
77C22×Dic122—21no—
78C22×D244C2311yescharacteristic
79C22×C22⋊D61—21no—
80C23×Dic61—21no—
81C23×Dic61—21no—
82C23×Dic61—21no—
83C23×Dic61—21no—
84C22×C4×D61—21no—
85C2×#11758199—24no—
86C2×#11758199—24no—
87C2×#11758199C2314yes—
88C2×#11758199C2314yes—
89C22×#92418C2311yescharacteristic
90C22×#92418C2311yescharacteristic
91#14519776—22no—
92#14519776C2314yescomplemented
93#14519772—28no—
94#14519766—22no—
95#14519766C2314yescomplemented
96#14519763—28no—
97#14519759—28no—
98#14519757—28no—
99#14519751—22no—
100#14519751C2314yes—
101Q8×Dic61—22no—
102Q8×Dic61C2314yescomplemented
103D4×Dic61—28no—
104D4×Dic61—28no—
105D4×Dic61—22no—
106D4×Dic61—22no—
107D4×Dic61—22no—
108D4×Dic61—22no—
109D4×Dic61C2314yes—
110D4×Dic61C2314yes—
111D4×Dic61C2314yes—
112D4×Dic61C2314yes—
113#14519739—22no—
114#14519739C2314yescomplemented
115#14519736—22no—
116#14519736D414yes—
117#14519736C2314yes—
118#14519736C2314yes—
119C2×C4⋊Dic61—21no—
120C2×C4⋊Dic61D411yescharacteristic
121C2×C4⋊Dic61D411yescharacteristic
122C2×C4⋊Dic61C2311yescharacteristic
123C2×C4⋊Dic61C2311yescharacteristic
124C2×C4⋊Dic61C2311yescharacteristic
125C2×#11758196—21no—
126C2×C22⋊Dic61—21no—
127C2×C22⋊Dic61—21no—
128C2×C22⋊Dic61—21no—
129C2×C22⋊Dic61—21no—
130C2×C22⋊Dic61—21no—
131C2×C22⋊Dic61—28no—
132C2×C22⋊Dic61—28no—
133C2×C22⋊Dic61D411yescharacteristic
134C2×C22⋊Dic61D411yescharacteristic
135C2×#11758198—21no—
136C2×#11758198—21no—
137C2×#11758198—21no—
138C2×#11758198—21no—
139C2×C4×Dic61—21no—
140C2×C4×Dic61—21no—
141C2×C4×Dic61C2311yescharacteristic
142C2×C4×Dic61C2311yescharacteristic
143#14519711C2314yescomplemented
144#14519710C2314yescomplemented
145#14519709C2314yescomplemented
146#14519708C2314yescomplemented
147#14519706C2314yescomplemented
148#14519706C2314yescomplemented
149#14519701C2314yescomplemented
150#14519701C2314yescomplemented
151#14519699C2314yescomplemented
152#14519699C2314yescomplemented
153#14519698C2314yes—
154#14519698C2314yes—
155C22⋊#92418C2314yes—
156#14519687C2314yescomplemented
157C8×Dic61C2314yescomplemented
158C25×C61—21no—
159C22×Q8×C61C2311yescharacteristic
160C22×D4×C61—24no—
161C22×D4×C61—24no—
162C22×D4×C61—21no—
163C22×D4×C61—22no—
164C22×D4×C61C2314yes—
165C22×D4×C61C2311yescharacteristic
166C22×D4×C61C2311yescharacteristic
167C23×C4×C61C2311yescharacteristic
168C2×SD16×C61—24no—
169C2×SD16×C61—24no—
170C2×SD16×C61C2314yes—
171C2×SD16×C61C2314yes—
172C22×C8×C61C2311yescharacteristic
173C22×C8×C61C2311yescharacteristic
174C22⋊Q8×C61—22no—
175C22⋊Q8×C61C2314yes—
176C2×C4⋊C4×C61—21no—
177C2×C4⋊C4×C61C2311yescharacteristic
178C2×C22⋊C4×C61—21no—
179#102×C61C2314yes—
180#102×C61C2314yes—
181C22⋊C8×C61C2314yes—
182C24×C61—28no—
183C24×C61—21no—
184C24×C61—21no—
185C24×C61—24no—
186C24×C61—82no—
187C24×C61—82no—
188C24×C61C2×D411yescharacteristic
189C23×D61—21no—
190C2×Q8×C61—21no—
191C2×Q8×C61—22no—
192C2×Q8×C61—22no—
193C2×Q8×C61C2412yes—
194C2×D4×C61—28no—
195C2×D4×C61—216no—
196C2×D4×C61—28no—
197C2×D4×C61—28no—
198C2×D4×C61—24no—
199C2×D4×C61—21no—
200C2×D4×C61—21no—
201C2×D4×C61—22no—
202C2×D4×C61—22no—
203C2×D4×C61#4114yes—
204C2×D4×C61#4114yes—
205C2×D4×C61C2412yes—
206C2×D4×C61C2412yes—
207C22×C4×C61—22no—
208C22×C4×C61—22no—
209C22×C4×C61—21no—
210C22×C4×C61—21no—
211C22×C4×C61C2×D411yescharacteristic
212C22×C4×C61C2×D412yes—
213C22×C4×C61C2412yes—
214C22×C4×C61C2411yescharacteristic
215C2×C22⋊D61—24no—
216C2×C22⋊D61—82no—
217C22×Dic61—21no—
218C22×Dic61—21no—
219C22×Dic61—21no—
220C22×Dic61—24no—
221C22×Dic61—24no—
222C22×Dic61—24no—
223C22×Dic61—24no—
224C22×Dic61—82no—
225C22×Dic61—82no—
226C22×Dic61—82no—
227C22×Dic61—82no—
228C22×Dic61C2×D411yescharacteristic
229C22×Dic61C2×D411yescharacteristic
230C22×Dic61C2×D411yescharacteristic
231C22×Dic61C2×D411yescharacteristic
232C2×D244—22no—
233C2×D244—22no—
234C2×D244—21no—
235C2×D244C2412yes—
236C2×C4×D61—24no—
237C2×C4×D61—82no—
238C2×Dic122—24no—
239C2×Dic122—82no—
240SD16×C61—28no—
241SD16×C61—28no—
242C2×C8×C61—22no—
243C2×C8×C61—22no—
244C2×C8×C61C2412yes—
245C2×C8×C61C2412yes—
246C4⋊C4×C61—24no—
247C4⋊C4×C61—21no—
248C4⋊C4×C61C2412yes—
249C22⋊C4×C61—24no—
250C22⋊Dic61—24no—
251C22⋊Dic61—24no—
252C22⋊Dic61—24no—
253C22⋊Dic61—24no—
254C22⋊Dic61—24no—
255C22⋊Dic61C2×D414yes—
256C22⋊Dic61C2×D414yes—
257#11758199—28no—
258#11758199—28no—
259#11758198—24no—
260#11758198—24no—
261#11758198—24no—
262#11758198—24no—
263C4⋊Dic61—21no—
264C4⋊Dic61—21no—
265C4⋊Dic61—21no—
266C4⋊Dic61—24no—
267C4⋊Dic61C2×D414yes—
268C4⋊Dic61C2×D414yes—
269C4⋊Dic61C2412yes—
270C4⋊Dic61C2412yes—
271C4⋊Dic61C2412yes—
272#11758196—24no—
273C4×Dic61—24no—
274C4×Dic61—24no—
275C4×Dic61C2×D412yes—
276C4×Dic61C2×D412yes—
277C4×Dic61C2412yes—
278C4×Dic61C2412yes—
279C2×#92418—22no—
280C2×#92418—22no—
281C2×#92418C2412yes—
282C2×#92418C2412yes—
283C23×C61—216no—
284C23×C61—22no—
285C23×C61—24no—
286C23×C61—24no—
287C23×C61—22no—
288C23×C61—22no—
289C23×C61—22no—
290C23×C61—22no—
291C23×C61—42no—
292C23×C61—42no—
293C23×C61—42no—
294C23×C61—42no—
295C23×C61—84no—
296C23×C61—84no—
297C23×C61—816no—
298C23×C61C22×D412yes—
299C23×C61C22×D411yescharacteristic
300C22×D61—22no—
301C22×D61—42no—
302C22×D61—42no—
303C22×D61—42no—
304Q8×C61—22no—
305Q8×C61—22no—
306Q8×C61—42no—
307D4×C61—216no—
308D4×C61—24no—
309D4×C61—24no—
310D4×C61—22no—
311D4×C61—22no—
312D4×C61C2×#4114yes—
313D4×C61C2×#4114yes—
314C2×C4×C61—22no—
315C2×C4×C61—24no—
316C2×C4×C61—22no—
317C2×C4×C61—22no—
318C2×C4×C61—22no—
319C2×C4×C61—22no—
320C2×C4×C61—42no—
321C2×C4×C61—42no—
322C2×C4×C61C22×D412yes—
323C2×C4×C61C22×D411yescharacteristic
324C2×C4×C61C2×#4112yes—
325C2×C4×C61C2×#4112yes—
326C2×C4×C61C2511yescharacteristic
327C22⋊D61—84no—
328C2×Dic61—22no—
329C2×Dic61—22no—
330C2×Dic61—22no—
331C2×Dic61—22no—
332C2×Dic61—22no—
333C2×Dic61—22no—
334C2×Dic61—22no—
335C2×Dic61—42no—
336C2×Dic61—42no—
337C2×Dic61—42no—
338C2×Dic61—84no—
339C2×Dic61—84no—
340C2×Dic61—84no—
341C2×Dic61—84no—
342C2×Dic61C22×D412yes—
343C2×Dic61C22×D412yes—
344C2×Dic61C22×D412yes—
345C2×Dic61C22×D412yes—
346D244—22no—
347D244—22no—
348D244—42no—
349C4×D61—84no—
350Dic122—84no—
351C8×C61—22no—
352C8×C61—22no—
353#92418—22no—
354#92418—22no—
355C2×#3118—611nomaximal, Sylow
356C22×C61—22no—
357C22×C61—24no—
358C22×C61—24no—
359C22×C61—22no—
360C22×C61—22no—
361C22×C61—44no—
362C22×C61—48no—
363C22×C61—48no—
364C22×C61—42no—
365C22×C61—42no—
366C22×C61—42no—
367C22×C61—42no—
368C22×C61—816no—
369C22×C61#52512yes—
370C22×C61#57612yes—
371C22×C61#57712yes—
372C22×C61C23×D411yescharacteristic
373C2×D61—42no—
374C2×D61—42no—
375C2×D61—42no—
376C2×D61—84no—
377C4×C61—22no—
378C4×C61—42no—
379C4×C61—42no—
380C4×C61#52512yes—
381C4×C61C22×#4111yescharacteristic
382C4×C61C22×#4111yescharacteristic
383Dic61—22no—
384Dic61—22no—
385Dic61—22no—
386Dic61—22no—
387Dic61—42no—
388Dic61—42no—
389Dic61—42no—
390C2×#542—611no—
391C2×#518—611no—
392#3118—6116no—
393C2×#485—611no—
394C2×#482—611no—
395C2×#476—611no—
396C2×#474—611no—
397C2×#463—611no—
398C2×#463—611no—
399C2×#450D6111yescharacteristic, complemented
400C2×#447—611no—
401C2×#442—611no—
402C2×#440—611no—
403C2×C4×SD16—611no—
404C2×C4×D8—611no—
405C2×#433—611no—
406C2×C61—42no—
407C2×C61—44no—
408C2×C61—44no—
409C2×C61#311814yescomplemented
410C2×C61C2×#52511yescharacteristic
411C2×C61C2×#57611yescharacteristic
412C2×C61C2×#57711yescharacteristic
413D61—82no—
414C23×D4C2×D6111yescharacteristic
415C22×SD16C2×D6111yescharacteristic
416C22×SD16C2×D6111yescharacteristic
417C22×D8—611no—
418C22×D8—611no—
419#542—618no—
420#542—1224no—
421C2×C4⋊Q8—611no—
422C2×#126—1221no—
423C2×#124—611no—
424C2×#124—1221no—
425C2×#123—1221no—
426C2×C22⋊Q8—1221no—
427C2×C22⋊Q8C2×D6111yescharacteristic
428C2×#121—611no—
429#518—618no—
430#518—1224no—
431C2×C4×Q8—611no—
432C2×C4×D4—611no—
433C2×C4×D4—611no—
434C2×C4×D4—611no—
435C2×C4×D4—611no—
436C2×C4×D4—611no—
437C2×C4×D4—1221no—
438C2×C4×D4—1221no—
439C2×#117—611no—
440C2×#117—611no—
441C22×C22⋊C4—1221no—
442C22×C22⋊C4—1221no—
443#485—618no—
444#482—618no—
445#476—618no—
446#474—618no—
447#463—618no—
448#463—618no—
449#450C2×D6118yescomplemented
450#447—618no—
451#442—618no—
452#440—618no—
453C4×SD16—618no—
454C4×D8—618no—
455#433—618no—
456C2×#107—611no—
457C2×#107—611no—
458C2×#106—611no—
459C2×#106—611no—
460C2×C4⋊C8—611no—
461C2×C4⋊C8—611no—
462C2×#103—611no—
463C2×#103—611no—
464C2×#102—611no—
465C2×#102—611no—
466C2×#102—611no—
467C2×#102—611no—
468C2×#102C2×D6111yescharacteristic
469C2×#102C2×D6111yescharacteristic
470C2×C22⋊C8—611no—
471C2×C22⋊C8C2×D6111yescharacteristic
472C2×#97—611no—
473C2×C4×C8—611no—
474C61C2×#311811yescharacteristic, complemented, Sylow
475C25—21no—
476C22×Q8—1221no—
477C22×Q8C22×D6111yescharacteristic
478C22×D4—24no—
479C22×D4—24no—
480C22×D4—21no—
481C22×D4—22no—
482C22×D4—611no—
483C22×D4—1221no—
484C22×D4C22×D6114yes—
485C22×D4C22×D6111yescharacteristic
486C22×D4C22×D6111yescharacteristic
487C23×C4—1221no—
488C23×C4—1221no—
489C23×C4—1221no—
490C23×C4—1221no—
491C23×C4—1221no—
492C23×C4C22×D6111yescharacteristic
493C2×SD16—24no—
494C2×SD16—24no—
495C2×SD16C22×D6114yes—
496C2×SD16C22×D6114yes—
497C2×D8—614no—
498C2×D8—614no—
499C2×D8—1224no—
500C2×D8—1224no—
501C22×C8—611no—
502C22×C8—611no—
503C22×C8C22×D6111yescharacteristic
504C22×C8C22×D6111yescharacteristic
505C4⋊Q8—614no—
506C4⋊Q8—1222no—
507#126—1228no—
508#124—614no—
509#124—1222no—
510#124—1228no—
511#123—1228no—
512C22⋊Q8—22no—
513C22⋊Q8—1228no—
514C22⋊Q8C22×D6114yes—
515#121—614no—
516#121—1222no—
517C4×Q8—614no—
518C4×Q8—1222no—
519C4×D4—614no—
520C4×D4—614no—
521C4×D4—614no—
522C4×D4—614no—
523C4×D4—614no—
524C4×D4—1222no—
525C4×D4—1222no—
526C4×D4—1222no—
527C4×D4—1222no—
528C4×D4—1222no—
529C4×D4—1228no—
530C4×D4—1228no—
531#117—614no—
532#117—614no—
533#117—614no—
534#117—1222no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—611no—
537C2×C4⋊C4—611no—
538C2×C4⋊C4—611no—
539C2×C4⋊C4—611no—
540C2×C4⋊C4—611no—
541C2×C4⋊C4—1221no—
542C2×C4⋊C4—1221no—
543C2×C4⋊C4C22×D6111yescharacteristic
544C2×C22⋊C4—21no—
545C2×C22⋊C4—611no—
546C2×C22⋊C4—611no—
547C2×C22⋊C4—1228no—
548C2×C22⋊C4—1228no—
549C2×C22⋊C4—1221no—
550C2×C22⋊C4—1221no—
551C2×C22⋊C4—1221no—
552C2×C22⋊C4—1221no—
553C2×C22⋊C4—1221no—
554C2×C22⋊C4—1221no—
555C2×C22⋊C4—1221no—
556C2×C22⋊C4—1221no—
557C2×C22⋊C4—1221no—
558C2×C42—611no—
559C2×C42—611no—
560C2×C42—1221no—
561C2×C42—1221no—
562#107—614no—
563#107—614no—
564#106—614no—
565#106—614no—
566C4⋊C8—614no—
567C4⋊C8—614no—
568#103—614no—
569#103—614no—
570#102—614no—
571#102—614no—
572#102—614no—
573#102—614no—
574#102C22×D6114yes—
575#102C22×D6114yes—
576C22⋊C8—614no—
577C22⋊C8C22×D6114yes—
578#97—614no—
579C4×C8—614no—
580C24—28no—
581C24—21no—
582C24—21no—
583C24—24no—
584C24—82no—
585C24—82no—
586C24—1221no—
587C24D4×D6111yescharacteristic
588C2×Q8—21no—
589C2×Q8—22no—
590C2×Q8—22no—
591C2×Q8—1224no—
592C2×Q8—4882no—
593C2×Q8C23×D6112yes—
594C2×D4—28no—
595C2×D4—216no—
596C2×D4—28no—
597C2×D4—28no—
598C2×D4—24no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—22no—
602C2×D4—22no—
603C2×D4—612no—
604C2×D4—1224no—
605C2×D4—1221no—
606C2×D4—1222no—
607C2×D4—1222no—
608C2×D4—4882no—
609C2×D4#1175822414yes—
610C2×D4#1175822414yes—
611C2×D4C23×D6112yes—
612C2×D4C23×D6112yes—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—611no—
618C22×C4—611no—
619C22×C4—611no—
620C22×C4—611no—
621C22×C4—1224no—
622C22×C4—1224no—
623C22×C4—1224no—
624C22×C4—1224no—
625C22×C4—1224no—
626C22×C4—1221no—
627C22×C4—1221no—
628C22×C4—1221no—
629C22×C4—4882no—
630C22×C4—4882no—
631C22×C4—4882no—
632C22×C4—4882no—
633C22×C4—4882no—
634C22×C4D4×D6112yes—
635C22×C4D4×D6111yescharacteristic
636C22×C4C23×D6112yes—
637C22×C4C23×D6111yescharacteristic
638SD16—28no—
639SD16—28no—
640D8—1228no—
641D8—1228no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—612no—
645C2×C8—612no—
646C2×C8—1222no—
647C2×C8—1222no—
648C2×C8C23×D6112yes—
649C2×C8C23×D6112yes—
650C4⋊C4—24no—
651C4⋊C4—21no—
652C4⋊C4—614no—
653C4⋊C4—614no—
654C4⋊C4—612no—
655C4⋊C4—612no—
656C4⋊C4—612no—
657C4⋊C4—1224no—
658C4⋊C4—1224no—
659C4⋊C4—1221no—
660C4⋊C4—1221no—
661C4⋊C4—1221no—
662C4⋊C4C23×D6112yes—
663C22⋊C4—24no—
664C22⋊C4—614no—
665C22⋊C4—614no—
666C22⋊C4—1224no—
667C22⋊C4—1224no—
668C22⋊C4—1224no—
669C22⋊C4—1224no—
670C22⋊C4—1224no—
671C22⋊C4—1224no—
672C22⋊C4—1224no—
673C22⋊C4—1224no—
674C22⋊C4—1224no—
675C42—612no—
676C42—612no—
677C42—612no—
678C42—612no—
679C42—1224no—
680C42—1224no—
681C23—216no—
682C23—22no—
683C23—24no—
684C23—24no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—84no—
694C23—84no—
695C23—816no—
696C23—1222no—
697C23—2442no—
698C23—2442no—
699C23—2442no—
700C23C2×D4×D6112yes—
701C23C2×D4×D6111yescharacteristic
702Q8—22no—
703Q8—22no—
704Q8—42no—
705Q8—4884no—
706D4—216no—
707D4—24no—
708D4—24no—
709D4—22no—
710D4—22no—
711D4—1222no—
712D4—1222no—
713D4—4884no—
714D4—2442no—
715D4C2×#1175822414yes—
716D4C2×#1175822414yes—
717C2×C4—22no—
718C2×C4—24no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—612no—
726C2×C4—612no—
727C2×C4—612no—
728C2×C4—612no—
729C2×C4—1222no—
730C2×C4—1222no—
731C2×C4—1222no—
732C2×C4—1222no—
733C2×C4—1222no—
734C2×C4—1222no—
735C2×C4—1222no—
736C2×C4—4884no—
737C2×C4—4884no—
738C2×C4—4884no—
739C2×C4—4884no—
740C2×C4—4884no—
741C2×C4—2442no—
742C2×C4—2442no—
743C2×C4—2442no—
744C2×C4C2×D4×D6112yes—
745C2×C4C2×D4×D6111yescharacteristic
746C2×C4C2×#1175822412yes—
747C2×C4C2×#1175822412yes—
748C2×C4C24×D6111yescharacteristic
749C8—22no—
750C8—22no—
751C8—1222no—
752C8—1222no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—24no—
757C22—24no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—44no—
763C22—48no—
764C22—48no—
765C22—816no—
766C22—4884no—
767C22—2442no—
768C22—2442no—
769C22—2442no—
770C22#1684026812yes—
771C22#1684056612yes—
772C22#1684056812yes—
773C22C22×D4×D6111yescharacteristic
774C4—22no—
775C4—42no—
776C4—42no—
777C4—1222no—
778C4—1222no—
779C4—1222no—
780C4—1222no—
781C4—2442no—
782C4—2442no—
783C4—2442no—
784C4#1684026812yes—
785C4C22×#1175822411yescharacteristic
786C4C22×#1175822411yescharacteristic
787C2—42no—
788C2—44no—
789C2—44no—
790C2—4882no—
791C2#2145600414yesdirect product factor
792C2C2×#1684026811yescharacteristic
793C2C2×#1684056611yescharacteristic
794C2C2×#1684056811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#450C2
socleC23×C61C22×D4
prime radicalC2×#16839896C2
hypercenterC2×#450D61
hypocenterC61C2×#3118
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#450

Complements

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

NH ≅ G/Ntype
1. C2×#16840385C2semidirect
2. C2×#16840237C2semidirect
3. #21456004C2direct (N × H)
4. C2×#16840100C2semidirect
5. C2×#16840087C2semidirect
6. C2×#16840050C2semidirect
7. C2×#16840040C2semidirect
8. C2×#16839979C2semidirect
9. C2×#16839979C2semidirect
11. C2×#16839871C2semidirect
12. C2×#16839863C2semidirect
13. C2×SD16×Dic61C2semidirect
14. C2×#16839842C2semidirect
15. C2×#16839820C2semidirect
16. C2×C61×#450C2semidirect
20. #16840385C22semidirect
21. C2×#14519776C22semidirect
23. C2×#14519766C22semidirect
29. #16840237C22semidirect
30. C2×Q8×Dic61C22semidirect
37. C2×#14519739C22semidirect
42. #16840100C22semidirect
43. #16840087C22semidirect
44. #16840050C22semidirect
45. #16840040C22semidirect
46. #16839979C22semidirect
47. #16839979C22semidirect
49. #16839871C22semidirect
50. #16839863C22semidirect
51. SD16×Dic61C22semidirect
52. #16839842C22semidirect
53. #16839820C22semidirect
54. C2×#14519711C22semidirect
55. C2×#14519710C22semidirect
56. C2×#14519709C22semidirect
57. C2×#14519708C22semidirect
58. C2×#14519706C22semidirect
59. C2×#14519706C22semidirect
60. C2×#14519701C22semidirect
61. C2×#14519701C22semidirect
62. C2×#14519699C22semidirect
63. C2×#14519699C22semidirect
67. C2×#14519687C22semidirect
68. C2×C8×Dic61C22semidirect
73. C61×#450C22semidirect
92. #14519776C23semidirect
95. #14519766C23semidirect
102. Q8×Dic61C23semidirect
114. #14519739C23semidirect
143. #14519711C23semidirect
144. #14519710C23semidirect
145. #14519709C23semidirect
146. #14519708C23semidirect
147. #14519706C23semidirect
148. #14519706C23semidirect
149. #14519701C23semidirect
150. #14519701C23semidirect
151. #14519699C23semidirect
152. #14519699C23semidirect
156. #14519687C23semidirect
157. C8×Dic61C23semidirect
399. C2×#450D61semidirect
409. C2×C61#3118semidirect
449. #450C2×D61semidirect
474. C61C2×#3118semidirect
791. C2#21456004direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403852
C2×#168402372
#214560042
C2×#168401002
C2×#168400872
C2×#168400502
C2×#168400402
C2×#168399792
C2×#168398962
C2×#168398712
C2×#168398632
C2×SD16×Dic612
C2×#168398422
C2×#168398202
C2×C61×#4502
C2×#311861