Finite Group Databasebeta

← C2×#21457138 #30552799

Subgroups — C2×#21457138 #30552799

Order 15616.

2210 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840307C211yesmaximal, characteristic, complemented
2C2×#16840293C211yesmaximal, characteristic, complemented
3#21457138C2116yesmaximal, direct product factor
4C2×#16840056C211yesmaximal, characteristic, complemented
5C2×#16840065C211yesmaximal, characteristic, complemented
6C2×#16840064C211yesmaximal, characteristic, complemented
7C2×#16840050C211yesmaximal, characteristic, complemented
8C2×#16839996C211yesmaximal, characteristic, complemented
9C2×#16839991C211yesmaximal, characteristic, complemented
10C2×#16839989C211yesmaximal, characteristic, complemented
11C2×#16839961C211yesmaximal, characteristic, complemented
12C2×#16839976C211yesmaximal, characteristic, complemented
13C2×#16839975C211yesmaximal, characteristic, complemented
14C2×#16839955C211yesmaximal, characteristic, complemented
15C22×#14519706C211yesmaximal, characteristic, complemented
16C2×C61×#466C211yesmaximal, characteristic, complemented
17C22×#11758224—21no—
18C22×#11758190C2211yescharacteristic
19C22×#11758200C2211yescharacteristic
20C22×#11758199C2211yescharacteristic
21C23×#92418C2211yescharacteristic
22#16840307—24no—
23#16840307C2218yescomplemented
24C2×#14519776C2211yescharacteristic
25C2×#14519773C2211yescharacteristic
26#16840293—24no—
27#16840293C2218yescomplemented
28C2×#14519770—21no—
29C2×#14519768C2211yescharacteristic
30C2×#14519764C2211yescharacteristic
31C2×#14519763—21no—
32C2×#14519758—21no—
33C2×#14519756C2211yescharacteristic
34C2×#14519751C2211yescharacteristic
35C2×#14519749—21no—
36C2×#14519742C2211yescharacteristic
37C2×D4×Dic61—21no—
38C2×D4×Dic61C2211yescharacteristic
39C2×D4×Dic61C2211yescharacteristic
40C2×#14519739C2211yescharacteristic
41C2×#14519737—21no—
42C2×#14519733—21no—
43C22×C4×Dic61C2211yescharacteristic
44#16840065C2218yescomplemented
45#16840064C2218yescomplemented
46#16840056C2218yescomplemented
47#16840050C2218yescomplemented
48#16839996C2218yescomplemented
49#16839991C2218yescomplemented
50#16839989C2218yescomplemented
51#16839976C2218yescomplemented
52#16839975C2218yescomplemented
53#16839961C2218yescomplemented
54#16839955C2218yescomplemented
55C2×#14519710C2211yescharacteristic
56C2×#14519709C2211yescharacteristic
57C2×#14519708C2211yescharacteristic
58C2×#14519706C2211yescharacteristic
59C2×#14519706C2211yescharacteristic
60C2×#14519706C2211yescharacteristic
61C2×#14519706C2211yescharacteristic
62C2×#14519706C2218yescomplemented
63C2×#14519702C2211yescharacteristic
64C2×#14519700C2211yescharacteristic
65C2×#14519699C2211yescharacteristic
66C2×#14519698C2211yescharacteristic
67C2×#14519698C2211yescharacteristic
68C2×#14519697C2211yescharacteristic
69C22×D8×C61C2211yescharacteristic
70C23×C8×C61C2211yescharacteristic
71C2×#121×C61C2211yescharacteristic
72C2×#121×C61C2211yescharacteristic
73C61×#466C2218yescomplemented
74C2×#107×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×#102×C61C2211yescharacteristic
77C2×#11758224—28no—
78C2×#11758224—48no—
79C22×Dic122—21no—
80C22×Dic122C2311yescharacteristic
81C22×D244C2311yescharacteristic
82C22×C22⋊D61—21no—
83C22×C22⋊D61—21no—
84C22×C22⋊D61—21no—
85C23×Dic61—21no—
86C23×Dic61—21no—
87C23×Dic61D411yescharacteristic
88C23×Dic61D411yescharacteristic
89C22×C4×D61—21no—
90C2×#11758190—42no—
91C2×#11758190C2314yes—
92C2×#11758200—42no—
93C2×#11758200C2314yes—
94C2×#11758199—42no—
95C2×#11758199C2314yes—
96C22×#92418—42no—
97C22×#92418C2311yescharacteristic
98C22×#92418C2311yescharacteristic
99C22×#92418C2314yes—
100#14519776—22no—
101#14519776C2314yes—
102#14519773—22no—
103#14519773C2314yes—
104#14519770—28no—
105#14519768—22no—
106#14519768C2314yes—
107#14519764—22no—
108#14519764C2314yes—
109#14519763—28no—
110#14519758—28no—
111#14519756—22no—
112#14519756C2314yes—
113#14519751—22no—
114#14519751C2314yes—
115#14519749—28no—
116#14519742—22no—
117#14519742C2314yes—
118D4×Dic61—28no—
119D4×Dic61—22no—
120D4×Dic61—22no—
121D4×Dic61C2314yes—
122D4×Dic61C2314yes—
123#14519739—22no—
124#14519739C2314yes—
125#14519737—28no—
126#14519733—28no—
127C2×C4⋊Dic61—21no—
128C2×C4⋊Dic61C2311yescharacteristic
129C2×C4⋊Dic61C2311yescharacteristic
130C2×#11758196—21no—
131C2×#11758196—21no—
132C2×#11758196—21no—
133C2×#11758196—21no—
134C2×C22⋊Dic61—21no—
135C2×C22⋊Dic61—21no—
136C2×C22⋊Dic61—21no—
137C2×C22⋊Dic61—21no—
138C2×C22⋊Dic61—21no—
139C2×#11758198—21no—
140C2×#11758198—21no—
141C2×C4×Dic61—21no—
142C2×C4×Dic61D411yescharacteristic
143C2×C4×Dic61D411yescharacteristic
144C2×C4×Dic61D414yes—
145C2×C4×Dic61C2311yescharacteristic
146C2×C4×Dic61C2311yescharacteristic
147C2×C4×Dic61C2314yes—
148#14519710C2314yes—
149#14519709C2314yes—
150#14519708C2314yes—
151#14519706C2314yes—
152#14519706C2314yes—
153#14519706C2314yes—
154#14519706C2314yes—
155#14519702C2314yes—
156#14519700C2314yes—
157#14519699C2314yes—
158#14519698C2314yes—
159#14519698C2314yes—
160#14519697C2314yes—
161C22×D4×C61—21no—
162C22×D4×C61—21no—
163C22×D4×C61C2311yescharacteristic
164C22×D4×C61C2311yescharacteristic
165C23×C4×C61C2311yescharacteristic
166C2×D8×C61—42no—
167C2×D8×C61C2314yes—
168C22×C8×C61—42no—
169C22×C8×C61C2311yescharacteristic
170C22×C8×C61C2311yescharacteristic
171C22×C8×C61C2314yes—
172#121×C61—22no—
173#121×C61—22no—
174#121×C61C2314yes—
175#121×C61C2314yes—
176C2×C4⋊C4×C61C2311yescharacteristic
177C2×C4⋊C4×C61C2311yescharacteristic
178C2×C22⋊C4×C61—21no—
179C2×C22⋊C4×C61—21no—
180#107×C61C2314yes—
181#102×C61C2314yes—
182#102×C61C2314yes—
183C24×C61—21no—
184C24×C61—21no—
185C24×C61C2×D411yescharacteristic
186C23×D61—21no—
187C2×D4×C61—24no—
188C2×D4×C61—24no—
189C2×D4×C61—21no—
190C2×D4×C61—21no—
191C2×D4×C61—22no—
192C2×D4×C61—22no—
193C2×D4×C61—22no—
194C2×D4×C61—22no—
195C2×D4×C61—44no—
196C2×D4×C61—44no—
197C2×D4×C61C2412yes—
198C2×D4×C61C2412yes—
199C22×C4×C61—22no—
200C22×C4×C61—22no—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61C2×D411yescharacteristic
204C22×C4×C61C2×D412yes—
205C22×C4×C61C2412yes—
206C22×C4×C61C2411yescharacteristic
207C2×C22⋊D61—24no—
208C2×C22⋊D61—24no—
209C2×C22⋊D61—24no—
210C2×C22⋊D61—44no—
211C2×C22⋊D61—44no—
212C2×C22⋊D61—44no—
213C22×Dic61—24no—
214C22×Dic61—24no—
215C22×Dic61—21no—
216C22×Dic61—21no—
217C22×Dic61—21no—
218C22×Dic61—24no—
219C22×Dic61—24no—
220C22×Dic61—44no—
221C22×Dic61—44no—
222C22×Dic61C2×D411yescharacteristic
223C22×Dic61C2×D411yescharacteristic
224C22×Dic61C2×D414yes—
225C22×Dic61C2×D411yescharacteristic
226C22×Dic61C2×D414yes—
227C22×Dic61C2×D411yescharacteristic
228#11758224—432no—
229C2×D244—22no—
230C2×D244—22no—
231C2×D244—21no—
232C2×D244C2412yes—
233C2×C4×D61—24no—
234C2×C4×D61—44no—
235C2×Dic122—22no—
236C2×Dic122—22no—
237C2×Dic122—21no—
238C2×Dic122—24no—
239C2×Dic122—44no—
240C2×Dic122C2412yes—
241D8×C61—44no—
242C2×C8×C61—22no—
243C2×C8×C61—22no—
244C2×C8×C61—44no—
245C2×C8×C61C2412yes—
246C2×C8×C61C2412yes—
247C4⋊C4×C61—21no—
248C4⋊C4×C61—21no—
249C4⋊C4×C61C2412yes—
250C4⋊C4×C61C2412yes—
251C22⋊C4×C61—24no—
252C22⋊C4×C61—24no—
253C22⋊Dic61—24no—
254C22⋊Dic61—24no—
255C22⋊Dic61—24no—
256C22⋊Dic61—24no—
257C22⋊Dic61—24no—
258#11758200—44no—
259#11758199—44no—
260#11758198—24no—
261#11758198—24no—
262C4⋊Dic61—21no—
263C4⋊Dic61—21no—
264C4⋊Dic61—24no—
265C4⋊Dic61C2412yes—
266C4⋊Dic61C2412yes—
267#11758196—24no—
268#11758196—24no—
269#11758196—24no—
270#11758196—24no—
271C4×Dic61—24no—
272C4×Dic61C2×D414yes—
273C4×Dic61C2×D412yes—
274C4×Dic61C2×D412yes—
275C4×Dic61C2×D414yes—
276C4×Dic61C2412yes—
277C4×Dic61C2412yes—
278C2×#92418—22no—
279C2×#92418—22no—
280C2×#92418—44no—
281C2×#92418C2412yes—
282C2×#92418C2412yes—
283#11758190—44no—
284C23×C61—22no—
285C23×C61—22no—
286C23×C61—22no—
287C23×C61—22no—
288C23×C61—42no—
289C23×C61—42no—
290C23×C61—42no—
291C23×C61—42no—
292C23×C61—42no—
293C23×C61—42no—
294C23×C61AGL(1,ℤ/8)14yes—
295C23×C61C22×D412yes—
296C23×C61C22×D411yescharacteristic
297C22×D61—22no—
298C22×D61—42no—
299C22×D61—42no—
300C22×D61—42no—
301D4×C61—22no—
302D4×C61—22no—
303D4×C61—22no—
304D4×C61—22no—
305D4×C61—48no—
306D4×C61—48no—
307D4×C61—42no—
308D4×C61—42no—
309C2×C4×C61—22no—
310C2×C4×C61—24no—
311C2×C4×C61—22no—
312C2×C4×C61—22no—
313C2×C4×C61—22no—
314C2×C4×C61—22no—
315C2×C4×C61—42no—
316C2×C4×C61—42no—
317C2×C4×C61C22×D412yes—
318C2×C4×C61C22×D411yescharacteristic
319C2×C4×C61H(5,𝔽2)12yes—
320C2×C4×C612−1+412yes—
321C2×C4×C61C2511yescharacteristic
322C22⋊D61—48no—
323C22⋊D61—48no—
324C22⋊D61—48no—
325C2×Dic61—22no—
326C2×Dic61—22no—
327C2×Dic61—22no—
328C2×Dic61—28no—
329C2×Dic61—28no—
330C2×Dic61—22no—
331C2×Dic61—22no—
332C2×Dic61—22no—
333C2×Dic61—48no—
334C2×Dic61—42no—
335C2×Dic61—42no—
336C2×Dic61—42no—
337C2×Dic61—48no—
338C2×Dic61#13514yes—
339C2×Dic61C22×D412yes—
340C2×Dic61C22×D412yes—
341C2×Dic61C22×D412yes—
342C2×Dic61C22×D412yes—
343D244—22no—
344D244—22no—
345D244—42no—
346C4×D61—48no—
347Dic122—22no—
348Dic122—22no—
349Dic122—48no—
350Dic122—42no—
351C8×C61—22no—
352C8×C61—22no—
353#92418—22no—
354#92418—22no—
355C2×#3247—611nomaximal, Sylow
356C22×C61—22no—
357C22×C61—28no—
358C22×C61—22no—
359C22×C61—42no—
360C22×C61—42no—
361C22×C61—42no—
362C22×C61—42no—
363C22×C61—42no—
364C22×C61—42no—
365C22×C61—84no—
366C22×C61—84no—
367C22×C61#53712yes—
368C22×C61C2×#13512yes—
369C22×C61C2×AGL(1,ℤ/8)14yes—
370C22×C61C2×AGL(1,ℤ/8)12yes—
371C22×C61C23×D411yescharacteristic
372C2×D61—42no—
373C2×D61—42no—
374C2×D61—42no—
375C2×D61—84no—
376C4×C61—22no—
377C4×C61—42no—
378C4×C61—42no—
379C4×C61#53712yes—
380C4×C61C2×H(5,𝔽2)11yescharacteristic
381C4×C61C2×2−1+411yescharacteristic
382Dic61—22no—
383Dic61—22no—
384Dic61—22no—
385Dic61—42no—
386Dic61—42no—
387Dic61—42no—
388Dic61C2×#13514yes—
389C2×#532—611no—
390C2×#529—611no—
391#3247—6116no—
392C2×#477—611no—
393C2×#478—611no—
394C2×#478—611no—
395C2×#476—611no—
396C2×#466—611no—
397C2×#466D6111yescharacteristic, complemented
398C2×#465—611no—
399C2×#465—611no—
400C2×#460—611no—
401C2×#463—611no—
402C2×#463—611no—
403C2×#459—611no—
404C22×C4⋊C8—611no—
405C2×C61—24no—
406C2×C61—82no—
407C2×C61—82no—
408C2×C61#324714yescomplemented
409C2×C61C2×#53711yescharacteristic
410C2×C61C22×#13511yescharacteristic
411C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
412D61—82no—
413C22×#41—1221no—
414C22×SD16—611no—
415C22×SD16—611no—
416C22×D8—611no—
417C22×D8C2×D6111yescharacteristic
418C23×C8—611no—
419C23×C8C2×D6111yescharacteristic
420#532—618no—
421#532—1224no—
422C2×C4⋊Q8—611no—
423C2×#127—611no—
424#529—618no—
425#529—1224no—
426C2×#126—1221no—
427C2×#125—611no—
428C2×#124—611no—
429C2×#124—1221no—
430C2×#123—1221no—
431C2×C22⋊Q8—611no—
432C2×#121—611no—
433C2×#121—1221no—
434C2×#121C2×D6111yescharacteristic
435C2×#121C2×D6111yescharacteristic
436C2×C4×Q8—611no—
437C2×C4×D4—611no—
438C2×C4×D4—611no—
439C2×C4×D4—611no—
440C2×C4×D4—1221no—
441C2×C4×D4—1221no—
442C2×#117—1221no—
443C22×C42—611no—
444#478—618no—
445#478—618no—
446#477—618no—
447#476—618no—
448#466—618no—
449#466C2×D6118yescomplemented
450#465—618no—
451#465—618no—
452#463—618no—
453#463—618no—
454#460—618no—
455#459—618no—
456C2×#107—611no—
457C2×#107C2×D6111yescharacteristic
458C2×#106—611no—
459C2×#106—611no—
460C2×C4⋊C8—611no—
461C2×C4⋊C8—611no—
462C2×C4⋊C8—611no—
463C2×C4⋊C8—611no—
464C2×C4⋊C8—618no—
465C2×#103—611no—
466C2×#103—611no—
467C2×#102—611no—
468C2×#102—611no—
469C2×#102—611no—
470C2×#102—611no—
471C2×#102C2×D6111yescharacteristic
472C2×#102C2×D6111yescharacteristic
473C61C2×#324711yescharacteristic, complemented, Sylow
474C2×#41—1228no—
475C2×#41—2448no—
476C22×Q8—611no—
477C22×Q8—1221no—
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—611no—
487C23×C4—611no—
488C23×C4—1221no—
489C23×C4—1221no—
490C23×C4—1221no—
491C23×C4C22×D6111yescharacteristic
492C2×SD16—614no—
493C2×SD16—614no—
494C2×SD16—2442no—
495C2×SD16—2442no—
496C2×D8—42no—
497C2×D8—614no—
498C2×D8—2442no—
499C2×D8C22×D6114yes—
500C22×C8—42no—
501C22×C8—611no—
502C22×C8—611no—
503C22×C8—614no—
504C22×C8—2442no—
505C22×C8C22×D6111yescharacteristic
506C22×C8C22×D6111yescharacteristic
507C22×C8C22×D6114yes—
508C4⋊Q8—614no—
509C4⋊Q8—1222no—
510#127—614no—
511#127—1222no—
512#126—1228no—
513#125—614no—
514#125—1222no—
515#124—614no—
516#124—1228no—
517#124—1222no—
518#123—1228no—
519C22⋊Q8—614no—
520C22⋊Q8—1222no—
521#121—22no—
522#121—22no—
523#121—614no—
524#121—1228no—
525#121—1222no—
526#121C22×D6114yes—
527#121C22×D6114yes—
528C4×Q8—614no—
529C4×Q8—1222no—
530C4×D4—614no—
531C4×D4—614no—
532C4×D4—614no—
533C4×D4—1228no—
534C4×D4—1222no—
535C4×D4—1222no—
536C4×D4—1222no—
537C4×D4—1228no—
538#117—1228no—
539C2×C4⋊C4—611no—
540C2×C4⋊C4—611no—
541C2×C4⋊C4—1221no—
542C2×C4⋊C4—1221no—
543C2×C4⋊C4—1221no—
544C2×C4⋊C4—1221no—
545C2×C4⋊C4—1221no—
546C2×C4⋊C4C22×D6111yescharacteristic
547C2×C4⋊C4C22×D6111yescharacteristic
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
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×C42—611no—
558C2×C42—611no—
559C2×C42—614no—
560C2×C42—611no—
561C2×C42—611no—
562C2×C42—614no—
563C2×C42—1221no—
564#107—614no—
565#107C22×D6114yes—
566#106—614no—
567#106—614no—
568C4⋊C8—614no—
569C4⋊C8—614no—
570C4⋊C8—614no—
571C4⋊C8—614no—
572#103—614no—
573#103—614no—
574#102—614no—
575#102—614no—
576#102—614no—
577#102—614no—
578#102C22×D6114yes—
579#102C22×D6114yes—
580C24—21no—
581C24—21no—
582C24—1221no—
583C24D4×D6111yescharacteristic
584#41—24432no—
585C2×Q8—612no—
586C2×Q8—1224no—
587C2×Q8—1221no—
588C2×Q8—1222no—
589C2×Q8—1222no—
590C2×Q8—2444no—
591C2×D4—24no—
592C2×D4—24no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—44no—
600C2×D4—44no—
601C2×D4—612no—
602C2×D4—1224no—
603C2×D4—1224no—
604C2×D4—1224no—
605C2×D4—1221no—
606C2×D4—1222no—
607C2×D4—1222no—
608C2×D4—2444no—
609C2×D4—2444no—
610C2×D4—2444no—
611C2×D4C23×D6112yes—
612C2×D4C23×D6112yes—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—611no—
618C22×C4—614no—
619C22×C4—614no—
620C22×C4—611no—
621C22×C4—611no—
622C22×C4—611no—
623C22×C4—1224no—
624C22×C4—1224no—
625C22×C4—1224no—
626C22×C4—1224no—
627C22×C4—1224no—
628C22×C4—1221no—
629C22×C4—1221no—
630C22×C4—1221no—
631C22×C4—2444no—
632C22×C4—2444no—
633C22×C4—2444no—
634C22×C4D4×D6112yes—
635C22×C4D4×D6111yescharacteristic
636C22×C4C23×D6112yes—
637C22×C4C23×D6111yescharacteristic
638SD16—2444no—
639SD16—2444no—
640D8—44no—
641D8—2444no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—44no—
645C2×C8—612no—
646C2×C8—612no—
647C2×C8—1222no—
648C2×C8—1222no—
649C2×C8—2444no—
650C2×C8C23×D6112yes—
651C2×C8C23×D6112yes—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—612no—
655C4⋊C4—612no—
656C4⋊C4—1224no—
657C4⋊C4—1224no—
658C4⋊C4—1224no—
659C4⋊C4—1224no—
660C4⋊C4—1221no—
661C4⋊C4—1221no—
662C4⋊C4—1224no—
663C4⋊C4C23×D6112yes—
664C4⋊C4C23×D6112yes—
665C22⋊C4—24no—
666C22⋊C4—24no—
667C22⋊C4—1224no—
668C22⋊C4—1224no—
669C22⋊C4—1224no—
670C22⋊C4—1224no—
671C22⋊C4—1224no—
672C22⋊C4—1224no—
673C22⋊C4—1224no—
674C42—614no—
675C42—612no—
676C42—612no—
677C42—614no—
678C42—612no—
679C42—612no—
680C42—1224no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—1222no—
692C23—2442no—
693C23—2442no—
694C23—2442no—
695C23#1451980114yes—
696C23C2×D4×D6112yes—
697C23C2×D4×D6111yescharacteristic
698Q8—1222no—
699Q8—1222no—
700Q8—2448no—
701Q8—2442no—
702D4—22no—
703D4—22no—
704D4—22no—
705D4—22no—
706D4—48no—
707D4—48no—
708D4—42no—
709D4—42no—
710D4—1222no—
711D4—1222no—
712D4—2448no—
713D4—2448no—
714D4—2448no—
715D4—2442no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—24no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—614no—
725C2×C4—612no—
726C2×C4—612no—
727C2×C4—612no—
728C2×C4—612no—
729C2×C4—1228no—
730C2×C4—1222no—
731C2×C4—1222no—
732C2×C4—1222no—
733C2×C4—1228no—
734C2×C4—1222no—
735C2×C4—1222no—
736C2×C4—1222no—
737C2×C4—2448no—
738C2×C4—2448no—
739C2×C4—2448no—
740C2×C4—2442no—
741C2×C4—2442no—
742C2×C4—2442no—
743C2×C4C2×D4×D6112yes—
744C2×C4C2×D4×D6111yescharacteristic
745C2×C4#1451982212yes—
746C2×C4#1451982412yes—
747C2×C4C24×D6111yescharacteristic
748C8—22no—
749C8—22no—
750C8—1222no—
751C8—1222no—
752C22—22no—
753C22—22no—
754C22—28no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—84no—
762C22—84no—
763C22—4884no—
764C22—2442no—
765C22—2442no—
766C22—2442no—
767C22#1684033912yes—
768C22#135×D6112yes—
769C22C2×#1451980114yes—
770C22C2×#1451980112yes—
771C22C22×D4×D6111yescharacteristic
772C4—22no—
773C4—42no—
774C4—42no—
775C4—614no—
776C4—1222no—
777C4—1222no—
778C4—1222no—
779C4—2442no—
780C4—2442no—
781C4—2442no—
782C4#1684033912yes—
783C4C2×#1451982211yescharacteristic
784C4C2×#1451982411yescharacteristic
785C2—24no—
786C2—82no—
787C2—82no—
788C2—4882no—
789C2#2145713814yesdirect product factor
790C2C2×#1684033911yescharacteristic
791C2C2×#135×D6111yescharacteristic
792C2C22×#1451980111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#466C2
socleC23×C61C22×D4
hypercenterC2×#466D61
hypocenterC61C2×#3247
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#466

Complements

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

NH ≅ G/Ntype
1. C2×#16840307C2semidirect
2. C2×#16840293C2semidirect
3. #21457138C2direct (N × H)
4. C2×#16840056C2semidirect
5. C2×#16840065C2semidirect
6. C2×#16840064C2semidirect
7. C2×#16840050C2semidirect
8. C2×#16839996C2semidirect
9. C2×#16839991C2semidirect
10. C2×#16839989C2semidirect
11. C2×#16839961C2semidirect
12. C2×#16839976C2semidirect
13. C2×#16839975C2semidirect
14. C2×#16839955C2semidirect
15. C22×#14519706C2semidirect
16. C2×C61×#466C2semidirect
23. #16840307C22semidirect
27. #16840293C22semidirect
44. #16840065C22semidirect
45. #16840064C22semidirect
46. #16840056C22semidirect
47. #16840050C22semidirect
48. #16839996C22semidirect
49. #16839991C22semidirect
50. #16839989C22semidirect
51. #16839976C22semidirect
52. #16839975C22semidirect
53. #16839961C22semidirect
54. #16839955C22semidirect
62. C2×#14519706C22semidirect
73. C61×#466C22semidirect
397. C2×#466D61semidirect
408. C2×C61#3247semidirect
449. #466C2×D61semidirect
473. C61C2×#3247semidirect
789. C2#21457138direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403072
C2×#168402932
#214571382
C2×#168400562
C2×#168400652
C2×#168400642
C2×#168400502
C2×#168399962
C2×#168399912
C2×#168399892
C2×#168399612
C2×#168399762
C2×#168399752
C2×#168399552
C22×#145197062
C2×C61×#4662
C2×#324761