Finite Group Databasebeta

← C2×#21456013 #30548255

Subgroups — C2×#21456013 #30548255

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×#16840243C211yesmaximal, characteristic, complemented
3#21456013C2116yesmaximal, direct product factor
4C2×#16840075C211yesmaximal, characteristic, complemented
5C2×#16840072C211yesmaximal, characteristic, complemented
6C2×#16840061C211yesmaximal, characteristic, complemented
7C2×#16839961C211yesmaximal, characteristic, complemented
8C2×#16839956C211yesmaximal, characteristic, complemented
9C2×#16839909C211yesmaximal, characteristic, complemented
10C2×#16839905C211yesmaximal, characteristic, complemented
11C2×#16839873C211yesmaximal, characteristic, complemented
12C2×#16839859C211yesmaximal, characteristic, complemented
13C2×#16839849C211yesmaximal, characteristic, complemented
14C2×#16839842C211yesmaximal, characteristic, complemented
15C2×#16839820C211yesmaximal, characteristic, complemented
16C2×C61×#481C211yesmaximal, characteristic, complemented
17C22×#11758222C2211yescharacteristic
18C22×#11758190C2211yescharacteristic
19C22×#11758200C2211yescharacteristic
20C22×D488C2211yescharacteristic
21C22×#11758199C2211yescharacteristic
22#16840365—24no—
23#16840365C2218yescomplemented
24C2×#14519773C2211yescharacteristic
25C2×#14519768C2211yescharacteristic
26C2×#14519761—21no—
27C2×#14519759—21no—
28C2×#14519751C2211yescharacteristic
29C2×#14519749—21no—
30C2×#14519748—21no—
31#16840243—24no—
32#16840243C2218yescomplemented
33C2×#14519742C2211yescharacteristic
34C2×#14519742C2211yescharacteristic
35C2×D4×Dic61C2211yescharacteristic
36C2×#14519739C2211yescharacteristic
37C2×#14519739C2211yescharacteristic
38C2×#14519739C2211yescharacteristic
39C2×C4×C22⋊D61—21no—
40C2×C4×C22⋊D61—21no—
41C2×#14519736C2211yescharacteristic
42C2×#14519735—21no—
43C2×C4⋊C4×D61—21no—
44#16840075C2218yescomplemented
45#16840072C2218yescomplemented
46#16840061C2218yescomplemented
47#16839961C2218yescomplemented
48#16839956C2218yescomplemented
49#16839909C2218yescomplemented
50#16839905C2218yescomplemented
51#16839873C2218yescomplemented
52#16839859C2218yescomplemented
53#16839849C2218yescomplemented
54#16839842C2218yescomplemented
55#16839820C2218yescomplemented
56C2×#14519710C2211yescharacteristic
57C2×#14519710C2211yescharacteristic
58C2×#14519706C2211yescharacteristic
59C2×#14519706C2211yescharacteristic
60C2×#14519702C2211yescharacteristic
61C2×#14519700C2211yescharacteristic
62C2×#14519699C2211yescharacteristic
63C2×#14519697C2211yescharacteristic
64C2×#14519697C2211yescharacteristic
65C2×#14519697C2211yescharacteristic
66C2×C22⋊#92418C2211yescharacteristic
67C2×#14519687C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C2×#121×C61C2211yescharacteristic
70C22×C4⋊C4×C61C2211yescharacteristic
71C61×#481C2218yescomplemented
72C2×#106×C61C2211yescharacteristic
73C2×#106×C61C2211yescharacteristic
74C2×#102×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×C22⋊C8×C61C2211yescharacteristic
77C2×#11758222—22no—
78C2×#11758222—24no—
79C2×#11758222—24no—
80C2×#11758222C2314yes—
81C22×Dic122C2311yescharacteristic
82C22×D244C2311yescharacteristic
83C22×D244C2311yescharacteristic
84C22×C22⋊D61—21no—
85C22×C22⋊D61—21no—
86C22×C22⋊D61—21no—
87C22×C22⋊D61—21no—
88C23×Dic61—21no—
89C22×C4×D61—21no—
90C22×C4×D61—21no—
91C22×C4×D61—21no—
92C22×C4×D61—21no—
93C2×#11758190—24no—
94C2×#11758190C2314yes—
95C2×#11758200—24no—
96C2×#11758200C2314yes—
97C2×D488—24no—
98C2×D488C2314yes—
99C2×#11758199—24no—
100C2×#11758199C2314yes—
101C22×#92418C2311yescharacteristic
102C22×#92418C2311yescharacteristic
103#14519773—22no—
104#14519773C2314yes—
105#14519768—22no—
106#14519768C2314yes—
107#14519761—28no—
108#14519759—28no—
109#14519751—22no—
110#14519751C2314yes—
111#14519749—28no—
112#14519748—28no—
113#14519742—22no—
114#14519742—22no—
115#14519742C2314yes—
116#14519742C2314yes—
117D4×Dic61—22no—
118D4×Dic61C2314yes—
119#14519739—22no—
120#14519739—22no—
121#14519739—22no—
122#14519739C2314yes—
123#14519739C2314yes—
124#14519739C2314yes—
125C4×C22⋊D61—28no—
126C4×C22⋊D61—28no—
127#14519736D414yes—
128#14519736C2314yes—
129#14519735—28no—
130C2×C4⋊Dic61—21no—
131C2×C4⋊Dic61D411yescharacteristic
132C2×C4⋊Dic61D411yescharacteristic
133C2×C4⋊Dic61C2311yescharacteristic
134C2×#11758196—21no—
135C2×#11758196—21no—
136C2×#11758196—21no—
137C4⋊C4×D61—28no—
138C2×C22⋊Dic61—21no—
139C2×C22⋊Dic61D411yescharacteristic
140C2×C22⋊Dic61D411yescharacteristic
141C2×#11758198—21no—
142C2×#11758198—21no—
143C2×#11758198—21no—
144C2×#11758198—21no—
145C2×C4×Dic61—21no—
146C2×C4×Dic61—21no—
147C2×C4×Dic61C2311yescharacteristic
148C2×C4×Dic61C2311yescharacteristic
149#14519710C2314yes—
150#14519710C2314yes—
151#14519706C2314yes—
152#14519706C2314yes—
153#14519702C2314yes—
154#14519700C2314yes—
155#14519699C2314yes—
156#14519697C2314yes—
157#14519697C2314yes—
158#14519697C2314yes—
159C22⋊#92418C2314yes—
160#14519687C2314yes—
161C8×Dic61C2314yes—
162C22×D4×C61—21no—
163C22×D4×C61C2311yescharacteristic
164C23×C4×C61—21no—
165C23×C4×C61C2311yescharacteristic
166C22×C8×C61C2311yescharacteristic
167C22×C8×C61C2311yescharacteristic
168#121×C61—22no—
169#121×C61C2314yes—
170C2×C4⋊C4×C61—21no—
171C2×C4⋊C4×C61—22no—
172C2×C4⋊C4×C61C2311yescharacteristic
173C2×C4⋊C4×C61C2311yescharacteristic
174C2×C4⋊C4×C61C2311yescharacteristic
175C2×C4⋊C4×C61C2314yes—
176C2×C22⋊C4×C61—21no—
177#106×C61C2314yes—
178#106×C61C2314yes—
179#102×C61C2314yes—
180#102×C61C2314yes—
181C22⋊C8×C61C2314yes—
182C24×C61—21no—
183C24×C61C2×D411yescharacteristic
184C23×D61—21no—
185C23×D61—21no—
186C2×D4×C61—24no—
187C2×D4×C61—21no—
188C2×D4×C61—22no—
189C2×D4×C61—22no—
190C2×D4×C61—82no—
191C2×D4×C61C2412yes—
192C22×C4×C61—22no—
193C22×C4×C61—22no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61—24no—
198C22×C4×C61—82no—
199C22×C4×C61C2×D411yescharacteristic
200C22×C4×C61C2×D412yes—
201C22×C4×C61C2412yes—
202C22×C4×C61C2411yescharacteristic
203C2×C22⋊D61—28no—
204C2×C22⋊D61—24no—
205C2×C22⋊D61—24no—
206C2×C22⋊D61—24no—
207C2×C22⋊D61—24no—
208C2×C22⋊D61—82no—
209C2×C22⋊D61—82no—
210C2×C22⋊D61—82no—
211C22×Dic61—21no—
212C22×Dic61—21no—
213C22×Dic61—24no—
214C22×Dic61—82no—
215C22×Dic61C2×D411yescharacteristic
216C22×Dic61C2×D411yescharacteristic
217C22×Dic61C2×D411yescharacteristic
218C22×Dic61C2×D411yescharacteristic
219#11758222—216no—
220#11758222—28no—
221#11758222—28no—
222C2×D244—21no—
223C2×D244—22no—
224C2×D244—22no—
225C2×D244—22no—
226C2×D244—21no—
227C2×D244#4114yes—
228C2×D244C2412yes—
229C2×D244C2412yes—
230C2×C4×D61—28no—
231C2×C4×D61—24no—
232C2×C4×D61—24no—
233C2×C4×D61—24no—
234C2×C4×D61—24no—
235C2×C4×D61—82no—
236C2×C4×D61—82no—
237C2×C4×D61—82no—
238C2×Dic122—21no—
239C2×Dic122—22no—
240C2×Dic122#4114yes—
241C2×Dic122C2412yes—
242C2×C8×C61—22no—
243C2×C8×C61—22no—
244C2×C8×C61C2412yes—
245C2×C8×C61C2412yes—
246C4⋊C4×C61—24no—
247C4⋊C4×C61—21no—
248C4⋊C4×C61—21no—
249C4⋊C4×C61—21no—
250C4⋊C4×C61C2412yes—
251C4⋊C4×C61C2412yes—
252C4⋊C4×C61C2412yes—
253C22⋊C4×C61—24no—
254C22⋊Dic61—24no—
255C22⋊Dic61C2×D414yes—
256C22⋊Dic61C2×D414yes—
257#11758200—28no—
258#11758199—28no—
259#11758198—24no—
260#11758198—24no—
261#11758198—24no—
262#11758198—24no—
263C4⋊Dic61—21no—
264C4⋊Dic61—24no—
265C4⋊Dic61C2×D414yes—
266C4⋊Dic61C2×D414yes—
267C4⋊Dic61C2412yes—
268#11758196—24no—
269#11758196—24no—
270#11758196—24no—
271C4×Dic61—24no—
272C4×Dic61—24no—
273C4×Dic61C2×D412yes—
274C4×Dic61C2×D412yes—
275C4×Dic61C2412yes—
276C4×Dic61C2412yes—
277C2×#92418—22no—
278C2×#92418—22no—
279C2×#92418C2412yes—
280C2×#92418C2412yes—
281D488—28no—
282#11758190—28no—
283C23×C61—22no—
284C23×C61—22no—
285C23×C61—22no—
286C23×C61—22no—
287C23×C61—42no—
288C23×C61—42no—
289C23×C61—42no—
290C23×C61C22×D412yes—
291C23×C61C22×D411yescharacteristic
292C22×D61—24no—
293C22×D61—22no—
294C22×D61—22no—
295C22×D61—42no—
296C22×D61—42no—
297C22×D61—42no—
298C22×D61—42no—
299C22×D61—42no—
300D4×C61—22no—
301D4×C61—22no—
302D4×C61—42no—
303D4×C61—84no—
304C2×C4×C61—22no—
305C2×C4×C61—24no—
306C2×C4×C61—22no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—22no—
310C2×C4×C61—22no—
311C2×C4×C61—42no—
312C2×C4×C61—42no—
313C2×C4×C61—42no—
314C2×C4×C61—84no—
315C2×C4×C61C22×D412yes—
316C2×C4×C61C22×D411yescharacteristic
317C2×C4×C61C2×#4112yes—
318C2×C4×C61C2×#4112yes—
319C2×C4×C61C2511yescharacteristic
320C22⋊D61—216no—
321C22⋊D61—84no—
322C22⋊D61—84no—
323C22⋊D61—84no—
324C2×Dic61—24no—
325C2×Dic61—22no—
326C2×Dic61—22no—
327C2×Dic61—22no—
328C2×Dic61—22no—
329C2×Dic61—22no—
330C2×Dic61—22no—
331C2×Dic61—42no—
332C2×Dic61—84no—
333C2×Dic61C22×D412yes—
334C2×Dic61C22×D412yes—
335C2×Dic61C22×D412yes—
336C2×Dic61C22×D412yes—
337D244—24no—
338D244—22no—
339D244—22no—
340D244—22no—
341D244—42no—
342D244C2×#4114yes—
343C4×D61—216no—
344C4×D61—84no—
345C4×D61—84no—
346C4×D61—84no—
347Dic122—24no—
348Dic122—22no—
349Dic122C2×#4114yes—
350C8×C61—22no—
351C8×C61—22no—
352#92418—22no—
353#92418—22no—
354C2×#3119—611nomaximal, Sylow
355C22×C61—22no—
356C22×C61—22no—
357C22×C61—22no—
358C22×C61—44no—
359C22×C61—42no—
360C22×C61—42no—
361C22×C61—42no—
362C22×C61—84no—
363C22×C61#52512yes—
364C22×C61#57612yes—
365C22×C61#57712yes—
366C22×C61C23×D411yescharacteristic
367C2×D61—24no—
368C2×D61—48no—
369C2×D61—42no—
370C2×D61—42no—
371C2×D61—42no—
372C2×D61—42no—
373C2×D61—42no—
374C2×D61—84no—
375C4×C61—22no—
376C4×C61—42no—
377C4×C61—42no—
378C4×C61—42no—
379C4×C61#52512yes—
380C4×C61C22×#4111yescharacteristic
381C4×C61C22×#4111yescharacteristic
382Dic61—24no—
383Dic61—22no—
384Dic61—22no—
385Dic61—22no—
386Dic61—22no—
387Dic61—42no—
388C2×#540—611no—
389C2×#520—611no—
390#3119—6116no—
391C2×#481D6111yescharacteristic, complemented
392C2×#480—611no—
393C2×#479—611no—
394C2×#478—611no—
395C2×#460—611no—
396C2×#459—611no—
397C2×#449—611no—
398C2×#449—611no—
399C2×#442—611no—
400C2×#440—611no—
401C2×C4×SD16—611no—
402C2×C4×D8—611no—
403C2×#433—611no—
404C2×C61—42no—
405C2×C61—82no—
406C2×C61#311914yescomplemented
407C2×C61C2×#52511yescharacteristic
408C2×C61C2×#57611yescharacteristic
409C2×C61C2×#57711yescharacteristic
410D61—44no—
411D61—82no—
412C22×#41—611no—
413C22×SD16—611no—
414C22×SD16—611no—
415C22×D8—611no—
416C22×D8—611no—
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—1221no—
440C22×C4⋊C4C2×D6111yescharacteristic
441#481C2×D6118yescomplemented
442#480—618no—
443#479—618no—
444#478—618no—
445#460—618no—
446#459—618no—
447#449—618no—
448#449—618no—
449#442—618no—
450#440—618no—
451C4×SD16—618no—
452C4×D8—618no—
453#433—618no—
454C2×#107—611no—
455C2×#107—611no—
456C2×#106C2×D6111yescharacteristic
457C2×#106C2×D6111yescharacteristic
458C2×C4⋊C8—611no—
459C2×C4⋊C8—611no—
460C2×#103—611no—
461C2×#103—611no—
462C2×#102—611no—
463C2×#102—611no—
464C2×#102—611no—
465C2×#102—611no—
466C2×#102C2×D6111yescharacteristic
467C2×#102C2×D6111yescharacteristic
468C2×C22⋊C8—611no—
469C2×C22⋊C8C2×D6111yescharacteristic
470C2×#97—611no—
471C2×C4×C8—611no—
472C61C2×#311911yescharacteristic, complemented, Sylow
473C2×#41—614no—
474C2×#41—1224no—
475C2×#41—1224no—
476C2×#41—1222no—
477C22×Q8—611no—
478C22×D4—21no—
479C22×D4—611no—
480C22×D4—611no—
481C22×D4—1221no—
482C22×D4—1221no—
483C22×D4—1221no—
484C22×D4—1221no—
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—614no—
494C2×SD16—614no—
495C2×SD16—1224no—
496C2×SD16—1224no—
497C2×D8—614no—
498C2×D8—614no—
499C2×D8—1224no—
500C2×D8—1224no—
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—21no—
535C2×C4⋊C4—22no—
536C2×C4⋊C4—611no—
537C2×C4⋊C4—611no—
538C2×C4⋊C4—611no—
539C2×C4⋊C4—1228no—
540C2×C4⋊C4—1221no—
541C2×C4⋊C4—1221no—
542C2×C4⋊C4—1221no—
543C2×C4⋊C4—1221no—
544C2×C4⋊C4C22×D6111yescharacteristic
545C2×C4⋊C4C22×D6111yescharacteristic
546C2×C4⋊C4C22×D6114yes—
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#106C22×D6114yes—
563#106C22×D6114yes—
564C4⋊C8—614no—
565C4⋊C8—614no—
566#103—614no—
567#103—614no—
568#102—614no—
569#102—614no—
570#102—614no—
571#102—614no—
572#102C22×D6114yes—
573#102C22×D6114yes—
574C22⋊C8—614no—
575C22⋊C8C22×D6114yes—
576#97—614no—
577C4×C8—614no—
578C24—21no—
579C24—1221no—
580C24—1221no—
581C24D4×D6111yescharacteristic
582#41—1228no—
583#41—1228no—
584#41—12216no—
585C2×Q8—614no—
586C2×Q8—612no—
587C2×Q8—1221no—
588C2×Q8—1222no—
589C2×D4—24no—
590C2×D4—21no—
591C2×D4—22no—
592C2×D4—22no—
593C2×D4—82no—
594C2×D4—614no—
595C2×D4—612no—
596C2×D4—612no—
597C2×D4—1224no—
598C2×D4—1224no—
599C2×D4—1228no—
600C2×D4—1224no—
601C2×D4—1224no—
602C2×D4—1221no—
603C2×D4—1221no—
604C2×D4—1222no—
605C2×D4—1222no—
606C2×D4—1222no—
607C2×D4—4882no—
608C2×D4—4882no—
609C2×D4—4882no—
610C2×D4C23×D6112yes—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—24no—
617C22×C4—82no—
618C22×C4—611no—
619C22×C4—611no—
620C22×C4—611no—
621C22×C4—611no—
622C22×C4—1224no—
623C22×C4—1224no—
624C22×C4—1224no—
625C22×C4—1228no—
626C22×C4—1224no—
627C22×C4—1221no—
628C22×C4—1224no—
629C22×C4—1221no—
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—1228no—
639SD16—1228no—
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—21no—
653C4⋊C4—21no—
654C4⋊C4—614no—
655C4⋊C4—614no—
656C4⋊C4—612no—
657C4⋊C4—1224no—
658C4⋊C4—1224no—
659C4⋊C4—1224no—
660C4⋊C4—1224no—
661C4⋊C4—1221no—
662C4⋊C4C23×D6112yes—
663C4⋊C4C23×D6112yes—
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—22no—
681C23—22no—
682C23—22no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—1224no—
687C23—1222no—
688C23—1222no—
689C23—2442no—
690C23—2442no—
691C23—2442no—
692C23—2442no—
693C23—2442no—
694C23C2×D4×D6112yes—
695C23C2×D4×D6111yescharacteristic
696Q8—614no—
697Q8—1224no—
698Q8—1222no—
699D4—22no—
700D4—22no—
701D4—42no—
702D4—84no—
703D4—614no—
704D4—12216no—
705D4—1224no—
706D4—1222no—
707D4—1222no—
708D4—1222no—
709D4—4884no—
710D4—4884no—
711D4—4884no—
712D4—2442no—
713C2×C4—22no—
714C2×C4—24no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—84no—
724C2×C4—612no—
725C2×C4—612no—
726C2×C4—612no—
727C2×C4—612no—
728C2×C4—12216no—
729C2×C4—1224no—
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—2442no—
741C2×C4C2×D4×D6112yes—
742C2×C4C2×D4×D6111yescharacteristic
743C2×C4#41×D6112yes—
744C2×C4#41×D6112yes—
745C2×C4C24×D6111yescharacteristic
746C8—22no—
747C8—22no—
748C8—1222no—
749C8—1222no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—44no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—84no—
758C22—1224no—
759C22—4884no—
760C22—2442no—
761C22—2442no—
762C22—2442no—
763C22—2442no—
764C22—2442no—
765C22—2448no—
766C22#1684027012yes—
767C22#1684056612yes—
768C22#1684056812yes—
769C22C22×D4×D6111yescharacteristic
770C4—22no—
771C4—42no—
772C4—42no—
773C4—42no—
774C4—1222no—
775C4—1222no—
776C4—1222no—
777C4—1222no—
778C4—1224no—
779C4—2442no—
780C4#1684027012yes—
781C4C2×#41×D6111yescharacteristic
782C4C2×#41×D6111yescharacteristic
783C2—42no—
784C2—82no—
785C2—4882no—
786C2—2444no—
787C2#2145601314yesdirect product factor
788C2C2×#1684027011yescharacteristic
789C2C2×#1684056611yescharacteristic
790C2C2×#1684056811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#481C2
socleC23×C61C22×D4
hypercenterC2×#481D61
hypocenterC61C2×#3119
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#481

Complements

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

NH ≅ G/Ntype
1. C2×#16840365C2semidirect
2. C2×#16840243C2semidirect
3. #21456013C2direct (N × H)
4. C2×#16840075C2semidirect
5. C2×#16840072C2semidirect
6. C2×#16840061C2semidirect
7. C2×#16839961C2semidirect
8. C2×#16839956C2semidirect
9. C2×#16839909C2semidirect
10. C2×#16839905C2semidirect
11. C2×#16839873C2semidirect
12. C2×#16839859C2semidirect
13. C2×#16839849C2semidirect
14. C2×#16839842C2semidirect
15. C2×#16839820C2semidirect
16. C2×C61×#481C2semidirect
23. #16840365C22semidirect
32. #16840243C22semidirect
44. #16840075C22semidirect
45. #16840072C22semidirect
46. #16840061C22semidirect
47. #16839961C22semidirect
48. #16839956C22semidirect
49. #16839909C22semidirect
50. #16839905C22semidirect
51. #16839873C22semidirect
52. #16839859C22semidirect
53. #16839849C22semidirect
54. #16839842C22semidirect
55. #16839820C22semidirect
71. C61×#481C22semidirect
391. C2×#481D61semidirect
406. C2×C61#3119semidirect
441. #481C2×D61semidirect
472. C61C2×#3119semidirect
787. C2#21456013direct (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×#168402432
#214560132
C2×#168400752
C2×#168400722
C2×#168400612
C2×#168399612
C2×#168399562
C2×#168399092
C2×#168399052
C2×#168398732
C2×#168398592
C2×#168398492
C2×#168398422
C2×#168398202
C2×C61×#4812
C2×#311961