Finite Group Databasebeta

← C2×#21457142 #30552803

Subgroups — C2×#21457142 #30552803

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×#16840309C211yesmaximal, characteristic, complemented
2C2×#16840291C211yesmaximal, characteristic, complemented
3#21457142C2116yesmaximal, direct product factor
4C2×#16840055C211yesmaximal, characteristic, complemented
5C2×#16840063C211yesmaximal, characteristic, complemented
6C2×#16840062C211yesmaximal, characteristic, complemented
7C2×#16840050C211yesmaximal, characteristic, complemented
8C2×#16839997C211yesmaximal, characteristic, complemented
9C2×#16839995C211yesmaximal, characteristic, complemented
10C2×#16839994C211yesmaximal, characteristic, complemented
11C2×#16839988C211yesmaximal, characteristic, complemented
12C2×#16839960C211yesmaximal, characteristic, complemented
13C2×#16839974C211yesmaximal, characteristic, complemented
14C2×#16839955C211yesmaximal, characteristic, complemented
15C2×C4⋊C8×D61C211yesmaximal, characteristic, complemented
16C2×C61×#463C211yesmaximal, characteristic, complemented
17C22×#11758222—21no—
18C22×#11758201C2211yescharacteristic
19C22×#11758199C2211yescharacteristic
20C22×C8×D61C2211yescharacteristic
21C22×C8×D61C2211yescharacteristic
22#16840309—24no—
23#16840309C2218yescomplemented
24C2×#14519776C2211yescharacteristic
25C2×#14519773C2211yescharacteristic
26#16840291—24no—
27#16840291C2218yescomplemented
28C2×#14519770—21no—
29C2×#14519769C2211yescharacteristic
30C2×#14519763—21no—
31C2×#14519759—21no—
32C2×#14519753C2211yescharacteristic
33C2×#14519752C2211yescharacteristic
34C2×#14519750—21no—
35C2×#14519748C2211yescharacteristic
36C2×#14519748C2211yescharacteristic
37C2×Q8×Dic61C2211yescharacteristic
38C2×C4×D244C2211yescharacteristic
39C2×D4×Dic61C2211yescharacteristic
40C2×C4×C22⋊D61—21no—
41C2×#14519737—21no—
42C2×#14519733—21no—
43C2×C42×D61C2211yescharacteristic
44#16840063C2218yescomplemented
45#16840062C2218yescomplemented
46#16840055C2218yescomplemented
47#16840050C2218yescomplemented
48#16839997C2218yescomplemented
49#16839995C2218yescomplemented
50#16839994C2218yescomplemented
51#16839988C2218yescomplemented
52#16839974C2218yescomplemented
53#16839960C2218yescomplemented
54#16839955C2218yescomplemented
55C2×#14519711C2211yescharacteristic
56C2×#14519710C2211yescharacteristic
57C2×#14519709C2211yescharacteristic
58C2×#14519708C2211yescharacteristic
59C2×C4⋊#92418C2211yescharacteristic
60C2×#14519706C2211yescharacteristic
61C2×#14519706C2211yescharacteristic
62C4⋊C8×D61C2218yescomplemented
63C2×#14519701C2211yescharacteristic
64C2×#14519699C2211yescharacteristic
65C2×#14519699C2211yescharacteristic
66C2×#14519698C2211yescharacteristic
67C2×#14519698C2211yescharacteristic
68C2×#14519698C2211yescharacteristic
69C22×SD16×C61C2211yescharacteristic
70C22×D8×C61C2211yescharacteristic
71C2×#124×C61C2211yescharacteristic
72C2×C4×D4×C61C2211yescharacteristic
73C61×#463C2218yescomplemented
74C2×C4⋊C8×C61C2211yescharacteristic
75C2×#103×C61C2211yescharacteristic
76C2×#102×C61C2211yescharacteristic
77C2×#11758222—28no—
78C2×#11758222—48no—
79C22×Dic122—21no—
80C22×D244—21no—
81C22×D244C2311yescharacteristic
82C22×C22⋊D61—21no—
83C22×C22⋊D61—21no—
84C22×C22⋊D61—21no—
85C22×C22⋊D61—21no—
86C23×Dic61—21no—
87C22×C4×D61—21no—
88C22×C4×D61D411yescharacteristic
89C22×C4×D61D411yescharacteristic
90C22×C4×D61C2311yescharacteristic
91C2×#11758201—42no—
92C2×#11758201C2314yes—
93C2×#11758199—42no—
94C2×#11758199C2314yes—
95C22×#92418C2311yescharacteristic
96C22×#92418C2311yescharacteristic
97C2×C8×D61—42no—
98C2×C8×D61—42no—
99C2×C8×D61C2314yes—
100C2×C8×D61C2314yes—
101#14519776—22no—
102#14519776C2314yes—
103#14519773—22no—
104#14519773C2314yes—
105#14519770—28no—
106#14519769—22no—
107#14519769C2314yes—
108#14519763—28no—
109#14519759—28no—
110#14519753—22no—
111#14519753C2314yes—
112#14519752—22no—
113#14519752C2314yes—
114#14519750—28no—
115#14519748—22no—
116#14519748—22no—
117#14519748C2314yes—
118#14519748C2314yes—
119Q8×Dic61—22no—
120Q8×Dic61C2314yes—
121C4×D244—22no—
122C4×D244C2314yes—
123D4×Dic61—22no—
124D4×Dic61C2314yes—
125C4×C22⋊D61—28no—
126#14519737—28no—
127#14519733—28no—
128C2×C4⋊Dic61—21no—
129C2×C4⋊Dic61C2311yescharacteristic
130C2×C4⋊Dic61C2311yescharacteristic
131C2×C4⋊Dic61C2311yescharacteristic
132C2×#11758196—21no—
133C2×#11758196—21no—
134C2×#11758196—21no—
135C2×#11758196—21no—
136C2×C22⋊Dic61—21no—
137C2×C22⋊Dic61—21no—
138C2×C22⋊Dic61—21no—
139C2×#11758198—21no—
140C2×#11758198—21no—
141C2×#11758198—21no—
142C2×C4×Dic61—21no—
143C2×C4×Dic61D411yescharacteristic
144C2×C4×Dic61D411yescharacteristic
145C2×C4×Dic61C2311yescharacteristic
146C42×D61D414yes—
147C42×D61C2314yes—
148#14519711C2314yes—
149#14519710C2314yes—
150#14519709C2314yes—
151#14519708C2314yes—
152C4⋊#92418C2314yes—
153#14519706C2314yes—
154#14519706C2314yes—
155#14519701C2314yes—
156#14519699C2314yes—
157#14519699C2314yes—
158#14519698C2314yes—
159#14519698C2314yes—
160#14519698C2314yes—
161C22×Q8×C61C2311yescharacteristic
162C22×D4×C61C2311yescharacteristic
163C22×D4×C61C2311yescharacteristic
164C23×C4×C61—21no—
165C2×SD16×C61—42no—
166C2×SD16×C61C2314yes—
167C2×D8×C61—42no—
168C2×D8×C61C2314yes—
169C22×C8×C61C2311yescharacteristic
170C22×C8×C61C2311yescharacteristic
171#124×C61—22no—
172#124×C61C2314yes—
173C4×D4×C61—22no—
174C4×D4×C61C2314yes—
175C2×C4⋊C4×C61C2311yescharacteristic
176C2×C22⋊C4×C61—21no—
177C2×C22⋊C4×C61—21no—
178C2×C22⋊C4×C61—21no—
179C2×C42×C61C2311yescharacteristic
180C4⋊C8×C61C2314yes—
181#103×C61C2314yes—
182#102×C61C2314yes—
183C24×C61—21no—
184C24×C61—21no—
185C23×D61—21no—
186C23×D61C2×D411yescharacteristic
187C2×Q8×C61—21no—
188C2×Q8×C61—22no—
189C2×Q8×C61—22no—
190C2×Q8×C61C2412yes—
191C2×D4×C61—21no—
192C2×D4×C61—21no—
193C2×D4×C61—22no—
194C2×D4×C61—22no—
195C2×D4×C61—22no—
196C2×D4×C61—22no—
197C2×D4×C61C2412yes—
198C2×D4×C61C2412yes—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—24no—
202C22×C4×C61—44no—
203C22×C4×C61C2×D411yescharacteristic
204C22×C4×C61C2×D411yescharacteristic
205C22×C4×C61C2411yescharacteristic
206C2×C22⋊D61—24no—
207C2×C22⋊D61—24no—
208C2×C22⋊D61—24no—
209C2×C22⋊D61—24no—
210C2×C22⋊D61—44no—
211C2×C22⋊D61—44no—
212C2×C22⋊D61—44no—
213C2×C22⋊D61—44no—
214C22×Dic61—21no—
215C22×Dic61—21no—
216C22×Dic61—21no—
217C22×Dic61—24no—
218C22×Dic61—44no—
219C22×Dic61C2×D411yescharacteristic
220C22×Dic61C2×D411yescharacteristic
221C22×Dic61C2×D411yescharacteristic
222#11758222—432no—
223C2×D244—22no—
224C2×D244—22no—
225C2×D244—24no—
226C2×D244—21no—
227C2×D244—44no—
228C2×D244C2412yes—
229C2×C4×D61—24no—
230C2×C4×D61—22no—
231C2×C4×D61—22no—
232C2×C4×D61—24no—
233C2×C4×D61—24no—
234C2×C4×D61—44no—
235C2×C4×D61C2×D414yes—
236C2×C4×D61C2×D414yes—
237C2×C4×D61C2×D412yes—
238C2×C4×D61C2412yes—
239C2×Dic122—24no—
240C2×Dic122—44no—
241SD16×C61—44no—
242D8×C61—44no—
243C2×C8×C61—22no—
244C2×C8×C61—22no—
245C2×C8×C61C2412yes—
246C2×C8×C61C2412yes—
247C4⋊C4×C61—21no—
248C4⋊C4×C61C2412yes—
249C22⋊C4×C61—24no—
250C22⋊C4×C61—24no—
251C22⋊C4×C61—24no—
252C42×C61C2×D412yes—
253C42×C61C2412yes—
254C22⋊Dic61—24no—
255C22⋊Dic61—24no—
256C22⋊Dic61—24no—
257#11758201—44no—
258#11758199—44no—
259#11758198—24no—
260#11758198—24no—
261#11758198—24no—
262C4⋊Dic61—21no—
263C4⋊Dic61—21no—
264C4⋊Dic61—21no—
265C4⋊Dic61—24no—
266C4⋊Dic61C2412yes—
267C4⋊Dic61C2412yes—
268C4⋊Dic61C2412yes—
269#11758196—24no—
270#11758196—24no—
271#11758196—24no—
272#11758196—24no—
273C4×Dic61—24no—
274C4×Dic61C2×D412yes—
275C4×Dic61C2×D414yes—
276C4×Dic61C2×D414yes—
277C4×Dic61C2412yes—
278C2×#92418—22no—
279C2×#92418—22no—
280C2×#92418C2412yes—
281C2×#92418C2412yes—
282C8×D61—44no—
283C8×D61—44no—
284C23×C61—22no—
285C23×C61—22no—
286C23×C61—42no—
287C23×C61—42no—
288C23×C61—42no—
289C23×C61—42no—
290C23×C61—42no—
291C23×C61—42no—
292C23×C61C22×D411yescharacteristic
293C22×D61—22no—
294C22×D61—22no—
295C22×D61—22no—
296C22×D61—42no—
297C22×D61—42no—
298C22×D61—42no—
299C22×D61AGL(1,ℤ/8)14yes—
300C22×D61C22×D412yes—
301Q8×C61—22no—
302Q8×C61—22no—
303Q8×C61—42no—
304D4×C61—22no—
305D4×C61—22no—
306D4×C61—22no—
307D4×C61—22no—
308D4×C61—42no—
309D4×C61—42no—
310C2×C4×C61—22no—
311C2×C4×C61—22no—
312C2×C4×C61—22no—
313C2×C4×C61—22no—
314C2×C4×C61—48no—
315C2×C4×C61—42no—
316C2×C4×C61—42no—
317C2×C4×C61C22×D412yes—
318C2×C4×C61C22×D412yes—
319C2×C4×C61C22×D411yescharacteristic
320C2×C4×C61H(5,𝔽2)12yes—
321C2×C4×C612−1+412yes—
322C2×C4×C61C2511yescharacteristic
323C22⋊D61—48no—
324C22⋊D61—48no—
325C22⋊D61—48no—
326C22⋊D61—48no—
327C2×Dic61—22no—
328C2×Dic61—22no—
329C2×Dic61—22no—
330C2×Dic61—22no—
331C2×Dic61—22no—
332C2×Dic61—42no—
333C2×Dic61—42no—
334C2×Dic61—42no—
335C2×Dic61—48no—
336C2×Dic61#13514yes—
337C2×Dic61C22×D412yes—
338C2×Dic61C22×D412yes—
339C2×Dic61C22×D412yes—
340D244—22no—
341D244—22no—
342D244—48no—
343D244—42no—
344C4×D61—28no—
345C4×D61—24no—
346C4×D61—22no—
347C4×D61—22no—
348C4×D61—28no—
349C4×D61—48no—
350Dic122—48no—
351C8×C61—22no—
352C8×C61—22no—
353#92418—22no—
354#92418—22no—
355C2×#3247—611nomaximal, Sylow
356C22×C61—42no—
357C22×C61—42no—
358C22×C61—42no—
359C22×C61—42no—
360C22×C61—42no—
361C22×C61—42no—
362C22×C61—84no—
363C22×C61—84no—
364C22×C61#53712yes—
365C22×C61C2×#13512yes—
366C22×C61C2×AGL(1,ℤ/8)12yes—
367C22×C61C23×D411yescharacteristic
368C2×D61—22no—
369C2×D61—28no—
370C2×D61—22no—
371C2×D61—42no—
372C2×D61—42no—
373C2×D61—42no—
374C2×D61—84no—
375C2×D61C2×AGL(1,ℤ/8)14yes—
376C4×C61—22no—
377C4×C61—22no—
378C4×C61—42no—
379C4×C61—42no—
380C4×C61#53712yes—
381C4×C61C2×H(5,𝔽2)11yescharacteristic
382C4×C61C2×2−1+411yescharacteristic
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×#466—611no—
398C2×#465—611no—
399C2×#465—611no—
400C2×#460—611no—
401C2×#463—611no—
402C2×#463D6111yescharacteristic, complemented
403C2×#459—611no—
404C22×C4⋊C8—611no—
405C2×C61—82no—
406C2×C61—82no—
407C2×C61#324714yescomplemented
408C2×C61C2×#53711yescharacteristic
409C2×C61C22×#13511yescharacteristic
410C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
411D61—24no—
412D61—82no—
413C22×#41—1221no—
414C22×SD16—611no—
415C22×SD16C2×D6111yescharacteristic
416C22×D8—611no—
417C22×D8C2×D6111yescharacteristic
418C23×C8—611no—
419C23×C8—611no—
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—1221no—
429C2×#124C2×D6111yescharacteristic
430C2×#123—1221no—
431C2×C22⋊Q8—611no—
432C2×#121—611no—
433C2×#121—611no—
434C2×#121—611no—
435C2×#121—1221no—
436C2×C4×Q8—611no—
437C2×C4×D4—611no—
438C2×C4×D4—611no—
439C2×C4×D4—1221no—
440C2×C4×D4—1221no—
441C2×C4×D4C2×D6111yescharacteristic
442C2×#117—1221no—
443C22×C42—611no—
444#478—618no—
445#478—618no—
446#477—618no—
447#476—618no—
448#466—618no—
449#466—618no—
450#465—618no—
451#465—618no—
452#463—618no—
453#463C2×D6118yescomplemented
454#460—618no—
455#459—618no—
456C2×#107—611no—
457C2×#107—611no—
458C2×#106—611no—
459C2×#106—611no—
460C2×C4⋊C8—611no—
461C2×C4⋊C8—611no—
462C2×C4⋊C8—611no—
463C2×C4⋊C8—618no—
464C2×C4⋊C8C2×D6111yescharacteristic
465C2×#103—611no—
466C2×#103C2×D6111yescharacteristic
467C2×#102—611no—
468C2×#102—611no—
469C2×#102—611no—
470C2×#102—611no—
471C2×#102—611no—
472C2×#102C2×D6111yescharacteristic
473C61C2×#324711yescharacteristic, complemented, Sylow
474C2×#41—1228no—
475C2×#41—2448no—
476C22×Q8—1221no—
477C22×Q8C22×D6111yescharacteristic
478C22×D4—611no—
479C22×D4—1221no—
480C22×D4—1221no—
481C22×D4—1221no—
482C22×D4—1221no—
483C22×D4—1221no—
484C22×D4C22×D6111yescharacteristic
485C22×D4C22×D6111yescharacteristic
486C23×C4—21no—
487C23×C4—611no—
488C23×C4—611no—
489C23×C4—611no—
490C23×C4—1221no—
491C23×C4—1221no—
492C2×SD16—42no—
493C2×SD16—614no—
494C2×SD16—2442no—
495C2×SD16C22×D6114yes—
496C2×D8—42no—
497C2×D8—614no—
498C2×D8—2442no—
499C2×D8C22×D6114yes—
500C22×C8—611no—
501C22×C8—611no—
502C22×C8—614no—
503C22×C8—614no—
504C22×C8—2442no—
505C22×C8—2442no—
506C22×C8C22×D6111yescharacteristic
507C22×C8C22×D6111yescharacteristic
508C4⋊Q8—614no—
509C4⋊Q8—1222no—
510#127—614no—
511#127—1222no—
512#126—1228no—
513#125—614no—
514#125—1222no—
515#124—22no—
516#124—1228no—
517#124C22×D6114yes—
518#123—1228no—
519C22⋊Q8—614no—
520C22⋊Q8—1222no—
521#121—614no—
522#121—614no—
523#121—614no—
524#121—1228no—
525#121—1222no—
526#121—1222no—
527#121—1222no—
528C4×Q8—614no—
529C4×Q8—1222no—
530C4×D4—22no—
531C4×D4—614no—
532C4×D4—614no—
533C4×D4—1228no—
534C4×D4—1222no—
535C4×D4—1228no—
536C4×D4—1222no—
537C4×D4C22×D6114yes—
538#117—1228no—
539C2×C4⋊C4—611no—
540C2×C4⋊C4—611no—
541C2×C4⋊C4—611no—
542C2×C4⋊C4—1221no—
543C2×C4⋊C4—1221no—
544C2×C4⋊C4—1221no—
545C2×C4⋊C4—1221no—
546C2×C4⋊C4—1221no—
547C2×C4⋊C4C22×D6111yescharacteristic
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
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—611no—
560C2×C42—614no—
561C2×C42—614no—
562C2×C42—1221no—
563C2×C42C22×D6111yescharacteristic
564#107—614no—
565#107—614no—
566#106—614no—
567#106—614no—
568C4⋊C8—614no—
569C4⋊C8—614no—
570C4⋊C8—614no—
571C4⋊C8C22×D6114yes—
572#103—614no—
573#103C22×D6114yes—
574#102—614no—
575#102—614no—
576#102—614no—
577#102—614no—
578#102—614no—
579#102C22×D6114yes—
580C24—21no—
581C24—21no—
582C24—611no—
583C24—1221no—
584#41—24432no—
585C2×Q8—21no—
586C2×Q8—22no—
587C2×Q8—22no—
588C2×Q8—1224no—
589C2×Q8—2444no—
590C2×Q8C23×D6112yes—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—22no—
594C2×D4—22no—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—612no—
598C2×D4—1224no—
599C2×D4—1224no—
600C2×D4—1224no—
601C2×D4—1224no—
602C2×D4—1224no—
603C2×D4—1221no—
604C2×D4—1222no—
605C2×D4—1222no—
606C2×D4—2444no—
607C2×D4—2444no—
608C2×D4—2444no—
609C2×D4—2444no—
610C2×D4—2444no—
611C2×D4C23×D6112yes—
612C2×D4C23×D6112yes—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—24no—
616C22×C4—44no—
617C22×C4—611no—
618C22×C4—611no—
619C22×C4—611no—
620C22×C4—614no—
621C22×C4—612no—
622C22×C4—614no—
623C22×C4—612no—
624C22×C4—1224no—
625C22×C4—1224no—
626C22×C4—1224no—
627C22×C4—1222no—
628C22×C4—1222no—
629C22×C4—1221no—
630C22×C4—1221no—
631C22×C4—1221no—
632C22×C4—1224no—
633C22×C4—2444no—
634C22×C4—2444no—
635C22×C4D4×D6111yescharacteristic
636C22×C4D4×D6111yescharacteristic
637C22×C4C23×D6111yescharacteristic
638SD16—44no—
639SD16—2444no—
640D8—44no—
641D8—2444no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—612no—
645C2×C8—612no—
646C2×C8—1222no—
647C2×C8—1222no—
648C2×C8—2444no—
649C2×C8—2444no—
650C2×C8C23×D6112yes—
651C2×C8C23×D6112yes—
652C4⋊C4—21no—
653C4⋊C4—612no—
654C4⋊C4—612no—
655C4⋊C4—612no—
656C4⋊C4—1224no—
657C4⋊C4—1224no—
658C4⋊C4—1224no—
659C4⋊C4—1221no—
660C4⋊C4—1221no—
661C4⋊C4—1221no—
662C4⋊C4—1224no—
663C4⋊C4—1224no—
664C4⋊C4C23×D6112yes—
665C22⋊C4—24no—
666C22⋊C4—24no—
667C22⋊C4—24no—
668C22⋊C4—1224no—
669C22⋊C4—1224no—
670C22⋊C4—1224no—
671C22⋊C4—1224no—
672C22⋊C4—1224no—
673C22⋊C4—1224no—
674C42—614no—
675C42—612no—
676C42—614no—
677C42—612no—
678C42—1224no—
679C42D4×D6112yes—
680C42C23×D6112yes—
681C23—22no—
682C23—22no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—614no—
690C23—612no—
691C23—1222no—
692C23—1222no—
693C23—1222no—
694C23—2442no—
695C23—2442no—
696C23—2442no—
697C23C2×D4×D6111yescharacteristic
698Q8—22no—
699Q8—22no—
700Q8—42no—
701Q8—2448no—
702D4—22no—
703D4—22no—
704D4—22no—
705D4—22no—
706D4—42no—
707D4—42no—
708D4—1222no—
709D4—1222no—
710D4—2448no—
711D4—2448no—
712D4—2448no—
713D4—2448no—
714D4—2448no—
715D4—2442no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—48no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—614no—
724C2×C4—612no—
725C2×C4—612no—
726C2×C4—612no—
727C2×C4—1228no—
728C2×C4—1228no—
729C2×C4—1222no—
730C2×C4—1222no—
731C2×C4—1222no—
732C2×C4—1222no—
733C2×C4—1224no—
734C2×C4—1222no—
735C2×C4—1222no—
736C2×C4—1222no—
737C2×C4—2448no—
738C2×C4—2448no—
739C2×C4—2442no—
740C2×C4—2442no—
741C2×C4—2442no—
742C2×C4C2×D4×D6112yes—
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—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—84no—
759C22—84no—
760C22—614no—
761C22—1222no—
762C22—1222no—
763C22—1228no—
764C22—4884no—
765C22—2442no—
766C22—2442no—
767C22—2442no—
768C22#1684034112yes—
769C22#135×D6112yes—
770C22AGL(1,ℤ/8)×D6112yes—
771C22C22×D4×D6111yescharacteristic
772C4—22no—
773C4—22no—
774C4—42no—
775C4—42no—
776C4—614no—
777C4—1222no—
778C4—1222no—
779C4—2442no—
780C4—2442no—
781C4—2442no—
782C4#1684034112yes—
783C4C2×#1451982211yescharacteristic
784C4C2×#1451982411yescharacteristic
785C2—82no—
786C2—82no—
787C2—1224no—
788C2—4882no—
789C2#2145714214yesdirect product factor
790C2C2×#1684034111yescharacteristic
791C2C2×#135×D6111yescharacteristic
792C2C2×AGL(1,ℤ/8)×D6111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#463C2
socleC23×C61C22×D4
hypercenterC2×#463D61
hypocenterC61C2×#3247
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#463

Complements

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

NH ≅ G/Ntype
1. C2×#16840309C2semidirect
2. C2×#16840291C2semidirect
3. #21457142C2direct (N × H)
4. C2×#16840055C2semidirect
5. C2×#16840063C2semidirect
6. C2×#16840062C2semidirect
7. C2×#16840050C2semidirect
8. C2×#16839997C2semidirect
9. C2×#16839995C2semidirect
10. C2×#16839994C2semidirect
11. C2×#16839988C2semidirect
12. C2×#16839960C2semidirect
13. C2×#16839974C2semidirect
14. C2×#16839955C2semidirect
15. C2×C4⋊C8×D61C2semidirect
16. C2×C61×#463C2semidirect
23. #16840309C22semidirect
27. #16840291C22semidirect
44. #16840063C22semidirect
45. #16840062C22semidirect
46. #16840055C22semidirect
47. #16840050C22semidirect
48. #16839997C22semidirect
49. #16839995C22semidirect
50. #16839994C22semidirect
51. #16839988C22semidirect
52. #16839974C22semidirect
53. #16839960C22semidirect
54. #16839955C22semidirect
62. C4⋊C8×D61C22semidirect
73. C61×#463C22semidirect
402. C2×#463D61semidirect
407. C2×C61#3247semidirect
453. #463C2×D61semidirect
473. C61C2×#3247semidirect
789. C2#21457142direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403092
C2×#168402912
#214571422
C2×#168400552
C2×#168400632
C2×#168400622
C2×#168400502
C2×#168399972
C2×#168399952
C2×#168399942
C2×#168399882
C2×#168399602
C2×#168399742
C2×#168399552
C2×C4⋊C8×D612
C2×C61×#4632
C2×#324761