Finite Group Databasebeta

← C2×#21456019 #30548261

Subgroups — C2×#21456019 #30548261

Order 15616.

2198 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840365C211yesmaximal, characteristic, complemented
2C2×#16840245C211yesmaximal, characteristic, complemented
3#21456019C2116yesmaximal, direct product factor
4C2×#16840081C211yesmaximal, characteristic, complemented
5C2×#16840073C211yesmaximal, characteristic, complemented
6C2×#16840067C211yesmaximal, characteristic, complemented
7C2×#16840064C211yesmaximal, characteristic, complemented
8C2×#16839960C211yesmaximal, characteristic, complemented
9C2×#16839955C211yesmaximal, characteristic, complemented
10C2×#16839907C211yesmaximal, characteristic, complemented
11C2×#16839874C211yesmaximal, characteristic, complemented
12C2×#16839865C211yesmaximal, characteristic, complemented
13C2×SD16×Dic61C211yesmaximal, characteristic, complemented
14C2×#16839842C211yesmaximal, characteristic, complemented
15C2×#16839820C211yesmaximal, characteristic, complemented
16C2×C61×#449C211yesmaximal, characteristic, complemented
17C22×#11758201C2211yescharacteristic
18C22×#11758199C2211yescharacteristic
19#16840365—24no—
20#16840365C2218yescomplemented
21C2×#14519773C2211yescharacteristic
22C2×#14519768C2211yescharacteristic
23C2×#14519761—21no—
24C2×#14519759—21no—
25C2×#14519751C2211yescharacteristic
26C2×#14519749—21no—
27C2×#14519748—21no—
28#16840245—24no—
29#16840245C2218yescomplemented
30C2×Q8×Dic61C2211yescharacteristic
31C2×Q8×Dic61C2211yescharacteristic
32C2×D4×Dic61—21no—
33C2×D4×Dic61—21no—
34C2×D4×Dic61C2211yescharacteristic
35C2×D4×Dic61C2211yescharacteristic
36C2×D4×Dic61C2211yescharacteristic
37C2×#14519739C2211yescharacteristic
38C2×#14519736—21no—
39C2×#14519736C2211yescharacteristic
40C22×C4⋊Dic61—21no—
41C22×C4⋊Dic61C2211yescharacteristic
42#16840081C2218yescomplemented
43#16840073C2218yescomplemented
44#16840067C2218yescomplemented
45#16840064C2218yescomplemented
46#16839960C2218yescomplemented
47#16839955C2218yescomplemented
48#16839907C2218yescomplemented
49#16839874C2218yescomplemented
50#16839865C2218yescomplemented
51SD16×Dic61C2218yescomplemented
52#16839842C2218yescomplemented
53#16839820C2218yescomplemented
54C2×#14519710C2211yescharacteristic
55C2×#14519710C2211yescharacteristic
56C2×#14519709C2211yescharacteristic
57C2×#14519709C2211yescharacteristic
58C2×#14519706C2211yescharacteristic
59C2×#14519706C2211yescharacteristic
60C2×#14519701C2211yescharacteristic
61C2×#14519699C2211yescharacteristic
62C2×#14519699C2211yescharacteristic
63C2×#14519698C2211yescharacteristic
64C2×#14519698C2211yescharacteristic
65C2×#14519698C2211yescharacteristic
66C2×C22⋊#92418C2211yescharacteristic
67C2×#14519687C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C22×#41×C61C2211yescharacteristic
70C22×SD16×C61C2211yescharacteristic
71C22×D8×C61C2211yescharacteristic
72C2×#121×C61C2211yescharacteristic
73C61×#449C2218yescomplemented
74C2×#103×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×C22⋊C8×C61C2211yescharacteristic
77C22×D244C2311yescharacteristic
78C22×C22⋊D61—21no—
79C22×C22⋊D61—21no—
80C22×C22⋊D61—21no—
81C23×Dic61—21no—
82C23×Dic61—21no—
83C23×Dic61—21no—
84C23×Dic61—21no—
85C22×C4×D61—21no—
86C2×#11758201—24no—
87C2×#11758201C2314yes—
88C2×#11758199—24no—
89C2×#11758199C2314yes—
90C22×#92418C2311yescharacteristic
91C22×#92418C2311yescharacteristic
92#14519773—22no—
93#14519773C2314yes—
94#14519768—22no—
95#14519768C2314yes—
96#14519761—28no—
97#14519759—28no—
98#14519751—22no—
99#14519751C2314yes—
100#14519749—28no—
101#14519748—28no—
102Q8×Dic61—22no—
103Q8×Dic61—22no—
104Q8×Dic61C2314yes—
105Q8×Dic61C2314yes—
106D4×Dic61—28no—
107D4×Dic61—28no—
108D4×Dic61—22no—
109D4×Dic61—22no—
110D4×Dic61—22no—
111D4×Dic61C2314yes—
112D4×Dic61C2314yes—
113D4×Dic61C2314yes—
114#14519739—22no—
115#14519739C2314yes—
116#14519736—28no—
117#14519736D414yes—
118#14519736C2314yes—
119C2×C4⋊Dic61—21no—
120C2×C4⋊Dic61—22no—
121C2×C4⋊Dic61—21no—
122C2×C4⋊Dic61—21no—
123C2×C4⋊Dic61—21no—
124C2×C4⋊Dic61—28no—
125C2×C4⋊Dic61D411yescharacteristic
126C2×C4⋊Dic61D411yescharacteristic
127C2×C4⋊Dic61C2311yescharacteristic
128C2×C4⋊Dic61C2311yescharacteristic
129C2×C4⋊Dic61C2314yes—
130C2×C4⋊Dic61C2311yescharacteristic
131C2×#11758196—21no—
132C2×C22⋊Dic61—21no—
133C2×C22⋊Dic61—21no—
134C2×C22⋊Dic61—21no—
135C2×C22⋊Dic61D411yescharacteristic
136C2×C22⋊Dic61D411yescharacteristic
137C2×#11758198—21no—
138C2×#11758198—21no—
139C2×C4×Dic61—21no—
140C2×C4×Dic61—21no—
141C2×C4×Dic61C2311yescharacteristic
142C2×C4×Dic61C2311yescharacteristic
143#14519710C2314yes—
144#14519710C2314yes—
145#14519709C2314yes—
146#14519709C2314yes—
147#14519706C2314yes—
148#14519706C2314yes—
149#14519701C2314yes—
150#14519699C2314yes—
151#14519699C2314yes—
152#14519698C2314yes—
153#14519698C2314yes—
154#14519698C2314yes—
155C22⋊#92418C2314yes—
156#14519687C2314yes—
157C8×Dic61C2314yes—
158C2×#41×C61—24no—
159C2×#41×C61—24no—
160C2×#41×C61—22no—
161C2×#41×C61C2314yes—
162C22×Q8×C61C2311yescharacteristic
163C22×D4×C61—21no—
164C22×D4×C61—21no—
165C22×D4×C61C2311yescharacteristic
166C22×D4×C61C2311yescharacteristic
167C23×C4×C61—21no—
168C23×C4×C61C2311yescharacteristic
169C2×SD16×C61—24no—
170C2×SD16×C61C2314yes—
171C2×D8×C61—24no—
172C2×D8×C61C2314yes—
173C22×C8×C61C2311yescharacteristic
174C22×C8×C61C2311yescharacteristic
175#121×C61—22no—
176#121×C61C2314yes—
177C2×C4⋊C4×C61C2311yescharacteristic
178C2×C22⋊C4×C61—21no—
179#103×C61C2314yes—
180#102×C61C2314yes—
181C22⋊C8×C61C2314yes—
182C24×C61—21no—
183C24×C61—21no—
184C24×C61C2×D411yescharacteristic
185C23×D61—21no—
186#41×C61—216no—
187#41×C61—28no—
188#41×C61—28no—
189C2×Q8×C61—21no—
190C2×Q8×C61—22no—
191C2×Q8×C61#4114yes—
192C2×Q8×C61C2412yes—
193C2×D4×C61—28no—
194C2×D4×C61—24no—
195C2×D4×C61—24no—
196C2×D4×C61—21no—
197C2×D4×C61—21no—
198C2×D4×C61—22no—
199C2×D4×C61—22no—
200C2×D4×C61—22no—
201C2×D4×C61—82no—
202C2×D4×C61#4114yes—
203C2×D4×C61C2412yes—
204C2×D4×C61C2412yes—
205C22×C4×C61—28no—
206C22×C4×C61—21no—
207C22×C4×C61—24no—
208C22×C4×C61—22no—
209C22×C4×C61—22no—
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—24no—
217C2×C22⋊D61—24no—
218C2×C22⋊D61—82no—
219C2×C22⋊D61—82no—
220C2×C22⋊D61—82no—
221C22×Dic61—21no—
222C22×Dic61—21no—
223C22×Dic61—21no—
224C22×Dic61—24no—
225C22×Dic61—24no—
226C22×Dic61—24no—
227C22×Dic61—24no—
228C22×Dic61—82no—
229C22×Dic61—82no—
230C22×Dic61—82no—
231C22×Dic61—82no—
232C22×Dic61C2×D411yescharacteristic
233C22×Dic61C2×D411yescharacteristic
234C22×Dic61C2×D411yescharacteristic
235C22×Dic61C2×D411yescharacteristic
236C2×D244—22no—
237C2×D244—22no—
238C2×D244—21no—
239C2×D244C2412yes—
240C2×C4×D61—24no—
241C2×C4×D61—82no—
242SD16×C61—28no—
243D8×C61—28no—
244C2×C8×C61—22no—
245C2×C8×C61—22no—
246C2×C8×C61C2412yes—
247C2×C8×C61C2412yes—
248C4⋊C4×C61—21no—
249C4⋊C4×C61C2412yes—
250C22⋊C4×C61—24no—
251C22⋊Dic61—24no—
252C22⋊Dic61—24no—
253C22⋊Dic61—24no—
254C22⋊Dic61C2×D414yes—
255C22⋊Dic61C2×D414yes—
256#11758201—28no—
257#11758199—28no—
258#11758198—24no—
259#11758198—24no—
260C4⋊Dic61—24no—
261C4⋊Dic61—21no—
262C4⋊Dic61—21no—
263C4⋊Dic61—21no—
264C4⋊Dic61—24no—
265C4⋊Dic61—24no—
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—22no—
284C23×C61—24no—
285C23×C61—22no—
286C23×C61—22no—
287C23×C61—22no—
288C23×C61—22no—
289C23×C61—42no—
290C23×C61—42no—
291C23×C61—42no—
292C23×C61—42no—
293C23×C61—42no—
294C23×C61C22×D412yes—
295C23×C61C22×D411yescharacteristic
296C22×D61—22no—
297C22×D61—42no—
298C22×D61—42no—
299C22×D61—42no—
300Q8×C61—24no—
301Q8×C61—22no—
302Q8×C61C2×#4114yes—
303D4×C61—216no—
304D4×C61—24no—
305D4×C61—22no—
306D4×C61—22no—
307D4×C61—22no—
308D4×C61—42no—
309D4×C61—84no—
310D4×C61C2×#4114yes—
311C2×C4×C61—216no—
312C2×C4×C61—22no—
313C2×C4×C61—24no—
314C2×C4×C61—22no—
315C2×C4×C61—24no—
316C2×C4×C61—22no—
317C2×C4×C61—22no—
318C2×C4×C61—22no—
319C2×C4×C61—42no—
320C2×C4×C61C22×D412yes—
321C2×C4×C61C22×D411yescharacteristic
322C2×C4×C61C2×#4112yes—
323C2×C4×C61C2×#4112yes—
324C2×C4×C61C2511yescharacteristic
325C22⋊D61—84no—
326C22⋊D61—84no—
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—
350C8×C61—22no—
351C8×C61—22no—
352#92418—22no—
353#92418—22no—
354C2×#3119—611nomaximal, Sylow
355C22×C61—22no—
356C22×C61—24no—
357C22×C61—22no—
358C22×C61—22no—
359C22×C61—44no—
360C22×C61—48no—
361C22×C61—42no—
362C22×C61—42no—
363C22×C61—42no—
364C22×C61—42no—
365C22×C61—42no—
366C22×C61—84no—
367C22×C61#52512yes—
368C22×C61#57612yes—
369C22×C61#57712yes—
370C22×C61C23×D411yescharacteristic
371C2×D61—42no—
372C2×D61—42no—
373C2×D61—42no—
374C2×D61—84no—
375C4×C61—22no—
376C4×C61—24no—
377C4×C61—42no—
378C4×C61#52512yes—
379C4×C61C22×#4111yescharacteristic
380C4×C61C22×#4111yescharacteristic
381Dic61—22no—
382Dic61—22no—
383Dic61—22no—
384Dic61—22no—
385Dic61—42no—
386Dic61—42no—
387Dic61—42no—
388C2×#540—611no—
389C2×#520—611no—
390#3119—6116no—
391C2×#481—611no—
392C2×#480—611no—
393C2×#479—611no—
394C2×#478—611no—
395C2×#460—611no—
396C2×#459—611no—
397C2×#449—611no—
398C2×#449D6111yescharacteristic, complemented
399C2×#442—611no—
400C2×#440—611no—
401C2×C4×SD16—611no—
402C2×C4×D8—611no—
403C2×#433—611no—
404C2×C61—42no—
405C2×C61—44no—
406C2×C61—82no—
407C2×C61#311914yescomplemented
408C2×C61C2×#52511yescharacteristic
409C2×C61C2×#57611yescharacteristic
410C2×C61C2×#57711yescharacteristic
411D61—82no—
412C22×#41C2×D6111yescharacteristic
413C22×SD16—611no—
414C22×SD16C2×D6111yescharacteristic
415C22×D8—611no—
416C22×D8C2×D6111yescharacteristic
417#540—618no—
418#540—1224no—
419C2×#127—611no—
420C2×#125—611no—
421C2×#123—1221no—
422C2×#123—1221no—
423C2×#121—611no—
424C2×#121—1221no—
425C2×#121—1221no—
426C2×#121C2×D6111yescharacteristic
427#520—618no—
428#520—1224no—
429C2×C4×Q8—611no—
430C2×C4×Q8—611no—
431C2×C4×D4—611no—
432C2×C4×D4—611no—
433C2×C4×D4—611no—
434C2×C4×D4—611no—
435C2×C4×D4—1221no—
436C2×C4×D4—1221no—
437C2×#117—611no—
438C2×#117—1221no—
439C22×C4⋊C4—611no—
440C22×C4⋊C4—1221no—
441#481—618no—
442#480—618no—
443#479—618no—
444#478—618no—
445#460—618no—
446#459—618no—
447#449—618no—
448#449C2×D6118yescomplemented
449#442—618no—
450#440—618no—
451C4×SD16—618no—
452C4×D8—618no—
453#433—618no—
454C2×#107—611no—
455C2×#107—611no—
456C2×#106—611no—
457C2×#106—611no—
458C2×C4⋊C8—611no—
459C2×C4⋊C8—611no—
460C2×#103—611no—
461C2×#103C2×D6111yescharacteristic
462C2×#102—611no—
463C2×#102—611no—
464C2×#102—611no—
465C2×#102—611no—
466C2×#102—611no—
467C2×#102C2×D6111yescharacteristic
468C2×C22⋊C8—611no—
469C2×C22⋊C8C2×D6111yescharacteristic
470C2×#97—611no—
471C2×C4×C8—611no—
472C61C2×#311911yescharacteristic, complemented, Sylow
473C2×#41—24no—
474C2×#41—24no—
475C2×#41—22no—
476C2×#41C22×D6114yes—
477C22×Q8C22×D6111yescharacteristic
478C22×D4—21no—
479C22×D4—21no—
480C22×D4—611no—
481C22×D4—1221no—
482C22×D4—1221no—
483C22×D4—1221no—
484C22×D4C22×D6111yescharacteristic
485C22×D4C22×D6111yescharacteristic
486C23×C4—21no—
487C23×C4—1221no—
488C23×C4—1221no—
489C23×C4—1221no—
490C23×C4—1221no—
491C23×C4—1221no—
492C23×C4C22×D6111yescharacteristic
493C2×SD16—24no—
494C2×SD16—614no—
495C2×SD16—1224no—
496C2×SD16C22×D6114yes—
497C2×D8—24no—
498C2×D8—614no—
499C2×D8—1224no—
500C2×D8C22×D6114yes—
501C22×C8—611no—
502C22×C8—611no—
503C22×C8C22×D6111yescharacteristic
504C22×C8C22×D6111yescharacteristic
505#127—614no—
506#127—1222no—
507#125—614no—
508#125—1222no—
509#123—1228no—
510#123—1228no—
511#121—22no—
512#121—614no—
513#121—1228no—
514#121—1228no—
515#121—1222no—
516#121C22×D6114yes—
517C4×Q8—614no—
518C4×Q8—614no—
519C4×Q8—1222no—
520C4×Q8—1222no—
521C4×D4—614no—
522C4×D4—614no—
523C4×D4—614no—
524C4×D4—614no—
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—1228no—
534C2×C4⋊C4—611no—
535C2×C4⋊C4—611no—
536C2×C4⋊C4—611no—
537C2×C4⋊C4—611no—
538C2×C4⋊C4—614no—
539C2×C4⋊C4—611no—
540C2×C4⋊C4—1228no—
541C2×C4⋊C4—1221no—
542C2×C4⋊C4—1221no—
543C2×C4⋊C4—1221no—
544C2×C4⋊C4—1221no—
545C2×C4⋊C4—1221no—
546C2×C4⋊C4—1222no—
547C2×C4⋊C4C22×D6111yescharacteristic
548C2×C22⋊C4—21no—
549C2×C22⋊C4—611no—
550C2×C22⋊C4—611no—
551C2×C22⋊C4—1221no—
552C2×C22⋊C4—1221no—
553C2×C22⋊C4—1221no—
554C2×C22⋊C4—1221no—
555C2×C22⋊C4—1221no—
556C2×C42—611no—
557C2×C42—611no—
558C2×C42—1221no—
559C2×C42—1221no—
560#107—614no—
561#107—614no—
562#106—614no—
563#106—614no—
564C4⋊C8—614no—
565C4⋊C8—614no—
566#103—614no—
567#103C22×D6114yes—
568#102—614no—
569#102—614no—
570#102—614no—
571#102—614no—
572#102—614no—
573#102C22×D6114yes—
574C22⋊C8—614no—
575C22⋊C8C22×D6114yes—
576#97—614no—
577C4×C8—614no—
578C24—21no—
579C24—21no—
580C24—1221no—
581C24D4×D6111yescharacteristic
582#41—216no—
583#41—28no—
584#41—28no—
585C2×Q8—21no—
586C2×Q8—22no—
587C2×Q8#1175822414yes—
588C2×Q8C23×D6112yes—
589C2×D4—28no—
590C2×D4—24no—
591C2×D4—24no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—22no—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—82no—
598C2×D4—612no—
599C2×D4—1224no—
600C2×D4—1224no—
601C2×D4—1224no—
602C2×D4—1221no—
603C2×D4—1222no—
604C2×D4—1222no—
605C2×D4—4882no—
606C2×D4—4882no—
607C2×D4—4882no—
608C2×D4#1175822414yes—
609C2×D4C23×D6112yes—
610C2×D4C23×D6112yes—
611C22×C4—28no—
612C22×C4—21no—
613C22×C4—24no—
614C22×C4—22no—
615C22×C4—22no—
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—1228no—
640D8—28no—
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—21no—
651C4⋊C4—614no—
652C4⋊C4—614no—
653C4⋊C4—612no—
654C4⋊C4—612no—
655C4⋊C4—612no—
656C4⋊C4—1224no—
657C4⋊C4—1224no—
658C4⋊C4—1224no—
659C4⋊C4—1224no—
660C4⋊C4—1224no—
661C4⋊C4—1221no—
662C4⋊C4—1221no—
663C4⋊C4—1221no—
664C4⋊C4C23×D6112yes—
665C22⋊C4—24no—
666C22⋊C4—614no—
667C22⋊C4—614no—
668C22⋊C4—1224no—
669C22⋊C4—1224no—
670C22⋊C4—1224no—
671C22⋊C4—1224no—
672C22⋊C4—1224no—
673C42—612no—
674C42—612no—
675C42—612no—
676C42—612no—
677C42—1224no—
678C42—1224no—
679C23—22no—
680C23—24no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—1222no—
691C23—2442no—
692C23—2442no—
693C23—2442no—
694C23C2×D4×D6112yes—
695C23C2×D4×D6111yescharacteristic
696Q8—24no—
697Q8—22no—
698Q8C2×#1175822414yes—
699D4—216no—
700D4—24no—
701D4—22no—
702D4—22no—
703D4—22no—
704D4—42no—
705D4—84no—
706D4—1222no—
707D4—1222no—
708D4—4884no—
709D4—4884no—
710D4—4884no—
711D4—2442no—
712D4C2×#1175822414yes—
713C2×C4—216no—
714C2×C4—22no—
715C2×C4—24no—
716C2×C4—22no—
717C2×C4—24no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—42no—
722C2×C4—612no—
723C2×C4—612no—
724C2×C4—612no—
725C2×C4—612no—
726C2×C4—1222no—
727C2×C4—1222no—
728C2×C4—1222no—
729C2×C4—1222no—
730C2×C4—1222no—
731C2×C4—1222no—
732C2×C4—1222no—
733C2×C4—4884no—
734C2×C4—4884no—
735C2×C4—4884no—
736C2×C4—4884no—
737C2×C4—4884no—
738C2×C4—2442no—
739C2×C4—2442no—
740C2×C4—2442no—
741C2×C4C2×D4×D6112yes—
742C2×C4C2×D4×D6111yescharacteristic
743C2×C4C2×#1175822412yes—
744C2×C4C2×#1175822412yes—
745C2×C4C24×D6111yescharacteristic
746C8—22no—
747C8—22no—
748C8—1222no—
749C8—1222no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—24no—
754C22—42no—
755C22—42no—
756C22—44no—
757C22—48no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—84no—
762C22—4884no—
763C22—2442no—
764C22—2442no—
765C22—2442no—
766C22#1684026812yes—
767C22#1684056612yes—
768C22#1684056912yes—
769C22C22×D4×D6111yescharacteristic
770C4—22no—
771C4—24no—
772C4—42no—
773C4—1222no—
774C4—1222no—
775C4—1222no—
776C4—1222no—
777C4—2442no—
778C4—2442no—
779C4—2442no—
780C4#1684026812yes—
781C4C22×#1175822411yescharacteristic
782C4C22×#1175822411yescharacteristic
783C2—42no—
784C2—44no—
785C2—82no—
786C2—4882no—
787C2#2145601914yesdirect product factor
788C2C2×#1684026811yescharacteristic
789C2C2×#1684056611yescharacteristic
790C2C2×#1684056911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#449C2
socleC23×C61C22×D4
hypercenterC2×#449D61
hypocenterC61C2×#3119
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. C2×#16840365C2semidirect
2. C2×#16840245C2semidirect
3. #21456019C2direct (N × H)
4. C2×#16840081C2semidirect
5. C2×#16840073C2semidirect
6. C2×#16840067C2semidirect
7. C2×#16840064C2semidirect
8. C2×#16839960C2semidirect
9. C2×#16839955C2semidirect
10. C2×#16839907C2semidirect
11. C2×#16839874C2semidirect
12. C2×#16839865C2semidirect
13. C2×SD16×Dic61C2semidirect
14. C2×#16839842C2semidirect
15. C2×#16839820C2semidirect
16. C2×C61×#449C2semidirect
20. #16840365C22semidirect
29. #16840245C22semidirect
42. #16840081C22semidirect
43. #16840073C22semidirect
44. #16840067C22semidirect
45. #16840064C22semidirect
46. #16839960C22semidirect
47. #16839955C22semidirect
48. #16839907C22semidirect
49. #16839874C22semidirect
50. #16839865C22semidirect
51. SD16×Dic61C22semidirect
52. #16839842C22semidirect
53. #16839820C22semidirect
73. C61×#449C22semidirect
398. C2×#449D61semidirect
407. C2×C61#3119semidirect
448. #449C2×D61semidirect
472. C61C2×#3119semidirect
787. C2#21456019direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403652
C2×#168402452
#214560192
C2×#168400812
C2×#168400732
C2×#168400672
C2×#168400642
C2×#168399602
C2×#168399552
C2×#168399072
C2×#168398742
C2×#168398652
C2×SD16×Dic612
C2×#168398422
C2×#168398202
C2×C61×#4492
C2×#311961