Finite Group Databasebeta

← C2×#21458314 #30558603

Subgroups — C2×#21458314 #30558603

Order 15616.

1962 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840476C211yesmaximal, characteristic, complemented
2C2×#16840464C211yesmaximal, characteristic, complemented
3#21458314C2116yesmaximal, direct product factor
4C2×#16840169C211yesmaximal, characteristic, complemented
5C2×#16840085C211yesmaximal, characteristic, complemented
6C2×#16840084C211yesmaximal, characteristic, complemented
7C2×#16840083C211yesmaximal, characteristic, complemented
8C2×#16840073C211yesmaximal, characteristic, complemented
9C2×#16840064C211yesmaximal, characteristic, complemented
10C2×#16840040C211yesmaximal, characteristic, complemented
11C2×#16839995C211yesmaximal, characteristic, complemented
12C2×#16839874C211yesmaximal, characteristic, complemented
13C2×#16839831C211yesmaximal, characteristic, complemented
14C2×#16839804C211yesmaximal, characteristic, complemented
15C2×#16839797C211yesmaximal, characteristic, complemented
16C2×C61×#469C211yesmaximal, characteristic, complemented
17C22×C8×D61C2211yescharacteristic
18#16840476—24no—
19#16840476C2218yescomplemented
20#16840464—24no—
21#16840464C2218yescomplemented
22C2×#14519776C2211yescharacteristic
23C2×#14519770—21no—
24C2×#14519768C2211yescharacteristic
25C2×#14519764—21no—
26C2×#14519763—21no—
27C2×#14519761—21no—
28C2×#14519749—21no—
29C2×#14519749—21no—
30C2×#14519748C2211yescharacteristic
31C2×#14519748C2211yescharacteristic
32C2×D4×Dic61—21no—
33C2×D4×Dic61C2211yescharacteristic
34C2×D4×Dic61C2211yescharacteristic
35C2×C4×C22⋊D61C2211yescharacteristic
36C2×#14519736C2211yescharacteristic
37C2×#14519735C2211yescharacteristic
38C2×#14519735C2211yescharacteristic
39C2×#14519733—21no—
40C22×C4⋊Dic61C2211yescharacteristic
41#16840169C2218yescomplemented
42#16840085C2218yescomplemented
43#16840084C2218yescomplemented
44#16840083C2218yescomplemented
45#16840073C2218yescomplemented
46#16840064C2218yescomplemented
47#16840040C2218yescomplemented
48#16839995C2218yescomplemented
49#16839874C2218yescomplemented
50#16839831C2218yescomplemented
51#16839804C2218yescomplemented
52#16839797C2218yescomplemented
53C2×#14519711C2211yescharacteristic
54C2×#14519711C2211yescharacteristic
55C2×#14519710C2211yescharacteristic
56C2×#14519710C2211yescharacteristic
57C2×#14519710C2211yescharacteristic
58C2×#14519709C2211yescharacteristic
59C2×#14519709C2211yescharacteristic
60C2×#14519708C2211yescharacteristic
61C2×#14519706C2211yescharacteristic
62C2×#14519698C2211yescharacteristic
63C2×#14519698C2211yescharacteristic
64C2×#14519698C2211yescharacteristic
65C2×#14519698C2211yescharacteristic
66C2×C22⋊#92418C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×#14519687C2211yescharacteristic
69C22×D8×C61C2211yescharacteristic
70C22×M16×C61C2211yescharacteristic
71C2×#121×C61C2211yescharacteristic
72C2×#121×C61C2211yescharacteristic
73C61×#469C2218yescomplemented
74C2×#106×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×#102×C61C2211yescharacteristic
77C22×Dic122—21no—
78C22×C22⋊D61—21no—
79C22×C22⋊D61—21no—
80C22×C22⋊D61D411yescharacteristic
81C23×Dic61—21no—
82C23×Dic61—21no—
83C23×Dic61—21no—
84C22×C4×D61C2311yescharacteristic
85C22×#92418C2311yescharacteristic
86C22×#92418C2311yescharacteristic
87C2×C8×D61—24no—
88C2×C8×D61C2314yes—
89#14519776—22no—
90#14519776C2314yes—
91#14519770—28no—
92#14519768—22no—
93#14519768C2314yes—
94#14519764—28no—
95#14519763—28no—
96#14519761—28no—
97#14519749—28no—
98#14519749—28no—
99#14519748—22no—
100#14519748—22no—
101#14519748C2314yes—
102#14519748C2314yes—
103D4×Dic61—28no—
104D4×Dic61—22no—
105D4×Dic61—22no—
106D4×Dic61C2314yes—
107D4×Dic61C2314yes—
108C4×C22⋊D61D414yes—
109C4×C22⋊D61C2314yes—
110#14519736—22no—
111#14519736C2314yes—
112#14519735—22no—
113#14519735—22no—
114#14519735C2314yes—
115#14519735C2314yes—
116#14519733—28no—
117C2×C4⋊Dic61—22no—
118C2×C4⋊Dic61—21no—
119C2×C4⋊Dic61—21no—
120C2×C4⋊Dic61C2314yes—
121C2×C4⋊Dic61C2311yescharacteristic
122C2×C4⋊Dic61C2311yescharacteristic
123C2×C4⋊Dic61C2311yescharacteristic
124C2×C4⋊Dic61C2311yescharacteristic
125C2×#11758196—21no—
126C2×#11758196—21no—
127C2×#11758196D411yescharacteristic
128C2×C22⋊Dic61—21no—
129C2×C22⋊Dic61—21no—
130C2×C22⋊Dic61—21no—
131C2×C22⋊Dic61—21no—
132C2×C22⋊Dic61—21no—
133C2×C22⋊Dic61D411yescharacteristic
134C2×#11758198—21no—
135C2×#11758198—21no—
136C2×#11758198D411yescharacteristic
137C2×C4×Dic61—21no—
138C2×C4×Dic61—21no—
139C2×C4×Dic61—21no—
140C2×C4×Dic61C2311yescharacteristic
141#14519711C2314yes—
142#14519711C2314yes—
143#14519710C2314yes—
144#14519710C2314yes—
145#14519710C2314yes—
146#14519709C2314yes—
147#14519709C2314yes—
148#14519708C2314yes—
149#14519706C2314yes—
150#14519698C2314yes—
151#14519698C2314yes—
152#14519698C2314yes—
153#14519698C2314yes—
154C22⋊#92418C2314yes—
155#14519689C2314yes—
156#14519687C2314yes—
157C22×D4×C61—21no—
158C22×D4×C61—21no—
159C22×D4×C61C2311yescharacteristic
160C22×D4×C61C2311yescharacteristic
161C23×C4×C61C2311yescharacteristic
162C2×D8×C61—24no—
163C2×D8×C61C2314yes—
164C2×M16×C61—24no—
165C2×M16×C61C2314yes—
166C22×C8×C61C2311yescharacteristic
167C22×C8×C61C2311yescharacteristic
168#121×C61—22no—
169#121×C61—22no—
170#121×C61C2314yes—
171#121×C61C2314yes—
172C2×C4⋊C4×C61C2311yescharacteristic
173C2×C4⋊C4×C61C2311yescharacteristic
174C2×C22⋊C4×C61—21no—
175C2×C22⋊C4×C61—21no—
176#106×C61C2314yes—
177#102×C61C2314yes—
178#102×C61C2314yes—
179C24×C61—21no—
180C24×C61—21no—
181C24×C61C2×D411yescharacteristic
182C23×D61C2×D411yescharacteristic
183C2×D4×C61—24no—
184C2×D4×C61—24no—
185C2×D4×C61—21no—
186C2×D4×C61—21no—
187C2×D4×C61—22no—
188C2×D4×C61—22no—
189C2×D4×C61—22no—
190C2×D4×C61—22no—
191C2×D4×C61—44no—
192C2×D4×C61—82no—
193C2×D4×C61C2412yes—
194C2×D4×C61C2412yes—
195C22×C4×C61—22no—
196C22×C4×C61—22no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61C2×D411yescharacteristic
200C22×C4×C61C2×D412yes—
201C22×C4×C61C2412yes—
202C22×C4×C61C2411yescharacteristic
203C2×C22⋊D61—24no—
204C2×C22⋊D61—24no—
205C2×C22⋊D61—42no—
206C2×C22⋊D61—82no—
207C2×C22⋊D61—82no—
208C2×C22⋊D61C2×D414yes—
209C22×Dic61—21no—
210C22×Dic61—21no—
211C22×Dic61—21no—
212C22×Dic61—21no—
213C22×Dic61—24no—
214C22×Dic61—24no—
215C22×Dic61—24no—
216C22×Dic61—44no—
217C22×Dic61—82no—
218C22×Dic61—82no—
219C22×Dic61C2×D411yescharacteristic
220C22×Dic61C2×D411yescharacteristic
221C22×Dic61C2×D411yescharacteristic
222C2×C4×D61—22no—
223C2×C4×D61—22no—
224C2×C4×D61C2×D412yes—
225C2×C4×D61C2412yes—
226C2×Dic122—24no—
227C2×Dic122—82no—
228D8×C61—28no—
229M16×C61—28no—
230C2×C8×C61—22no—
231C2×C8×C61#4114yes—
232C2×C8×C61C2412yes—
233C2×C8×C61C2412yes—
234C4⋊C4×C61—21no—
235C4⋊C4×C61—21no—
236C4⋊C4×C61C2412yes—
237C4⋊C4×C61C2412yes—
238C22⋊C4×C61—24no—
239C22⋊C4×C61—24no—
240C22⋊Dic61—24no—
241C22⋊Dic61—24no—
242C22⋊Dic61—24no—
243C22⋊Dic61—24no—
244C22⋊Dic61—24no—
245C22⋊Dic61C2×D414yes—
246#11758198—24no—
247#11758198—24no—
248#11758198C2×D414yes—
249C4⋊Dic61—21no—
250C4⋊Dic61—21no—
251C4⋊Dic61—24no—
252C4⋊Dic61—21no—
253C4⋊Dic61—21no—
254C4⋊Dic61—24no—
255C4⋊Dic61C2412yes—
256C4⋊Dic61C2412yes—
257C4⋊Dic61C2412yes—
258C4⋊Dic61C2412yes—
259#11758196—24no—
260#11758196—24no—
261#11758196C2×D414yes—
262C4×Dic61—24no—
263C4×Dic61—24no—
264C4×Dic61—24no—
265C4×Dic61C2×D412yes—
266C4×Dic61C2412yes—
267C2×#92418—22no—
268C2×#92418—22no—
269C2×#92418C2412yes—
270C2×#92418C2412yes—
271C8×D61—28no—
272C23×C61—22no—
273C23×C61—22no—
274C23×C61—22no—
275C23×C61—22no—
276C23×C61—22no—
277C23×C61—42no—
278C23×C61—42no—
279C23×C61—42no—
280C23×C61—42no—
281C23×C61—42no—
282C23×C61—42no—
283C23×C61C22×D412yes—
284C23×C61C22×D411yescharacteristic
285C22×D61—22no—
286C22×D61—22no—
287C22×D61—22no—
288C22×D61C22×D412yes—
289D4×C61—22no—
290D4×C61—22no—
291D4×C61—22no—
292D4×C61—22no—
293D4×C61—48no—
294D4×C61—42no—
295D4×C61—42no—
296D4×C61—84no—
297C2×C4×C61—22no—
298C2×C4×C61—24no—
299C2×C4×C61—22no—
300C2×C4×C61—22no—
301C2×C4×C61—22no—
302C2×C4×C61—22no—
303C2×C4×C61—42no—
304C2×C4×C61—42no—
305C2×C4×C61C22×D412yes—
306C2×C4×C61C22×D411yescharacteristic
307C2×C4×C61C2×#4112yes—
308C2×C4×C612−1+412yes—
309C2×C4×C61C2511yescharacteristic
310C22⋊D61—44no—
311C22⋊D61—84no—
312C22⋊D61—84no—
313C2×Dic61—22no—
314C2×Dic61—22no—
315C2×Dic61—22no—
316C2×Dic61—22no—
317C2×Dic61—22no—
318C2×Dic61—22no—
319C2×Dic61—22no—
320C2×Dic61—48no—
321C2×Dic61—42no—
322C2×Dic61—42no—
323C2×Dic61—42no—
324C2×Dic61—42no—
325C2×Dic61—84no—
326C2×Dic61—84no—
327C2×Dic61C22×D412yes—
328C2×Dic61C22×D412yes—
329C2×Dic61C22×D412yes—
330C4×D61—24no—
331C4×D61—22no—
332C4×D61—22no—
333Dic122—84no—
334C8×C61—22no—
335C8×C61C2×#4114yes—
336#92418—22no—
337#92418—22no—
338C2×#3347—611nomaximal, Sylow
339C22×C61—22no—
340C22×C61—22no—
341C22×C61—22no—
342C22×C61—44no—
343C22×C61—42no—
344C22×C61—42no—
345C22×C61—42no—
346C22×C61—42no—
347C22×C61—42no—
348C22×C61—42no—
349C22×C61—84no—
350C22×C61—84no—
351C22×C61#54712yes—
352C22×C61#57512yes—
353C22×C61#57612yes—
354C22×C61C23×D411yescharacteristic
355C2×D61—22no—
356C2×D61—22no—
357C2×D61—22no—
358C2×D61—44no—
359C4×C61—22no—
360C4×C61—42no—
361C4×C61—42no—
362C4×C61#54712yes—
363C4×C61C22×#4111yescharacteristic
364C4×C61C2×2−1+411yescharacteristic
365Dic61—22no—
366Dic61—22no—
367Dic61—22no—
368Dic61—42no—
369Dic61—42no—
370Dic61—42no—
371Dic61—42no—
372C2×#555—611no—
373C2×#553—611no—
374#3347—6116no—
375C2×#501—611no—
376C2×#482—611no—
377C2×#482—611no—
378C2×#482—611no—
379C2×#480—611no—
380C2×#478—611no—
381C2×#474—611no—
382C2×#469D6111yescharacteristic, complemented
383C2×#466—611no—
384C2×#442—611no—
385C2×#435—611no—
386C2×#428—611no—
387C2×#427—611no—
388C2×C61—42no—
389C2×C61—82no—
390C2×C61—82no—
391C2×C61#334714yescomplemented
392C2×C61C2×#54711yescharacteristic
393C2×C61C2×#57511yescharacteristic
394C2×C61C2×#57611yescharacteristic
395D61—42no—
396C22×D8C2×D6111yescharacteristic
397C22×M16C2×D6111yescharacteristic
398C23×C8—611no—
399#555—618no—
400#555—1224no—
401#553—618no—
402#553—1224no—
403C2×C4⋊Q8—611no—
404C2×#126—1221no—
405C2×#125—611no—
406C2×#124—1221no—
407C2×#124—1221no—
408C2×#123—1221no—
409C2×#121—611no—
410C2×#121—611no—
411C2×#121—1221no—
412C2×#121—1221no—
413C2×#121C2×D6111yescharacteristic
414C2×#121C2×D6111yescharacteristic
415C2×C4×D4—611no—
416C2×C4×D4—611no—
417C2×C4×D4—611no—
418C2×C4×D4—1221no—
419C2×#117—611no—
420C2×#117—611no—
421C2×#117—611no—
422C2×#117—1221no—
423C22×C4⋊C4—611no—
424#501—618no—
425#482—618no—
426#482—618no—
427#482—618no—
428#480—618no—
429#478—618no—
430#474—618no—
431#469C2×D6118yescomplemented
432#466—618no—
433#442—618no—
434#435—618no—
435#428—618no—
436#427—618no—
437C2×#107—611no—
438C2×#107—611no—
439C2×#107—611no—
440C2×#107—611no—
441C2×#107—611no—
442C2×#106—611no—
443C2×#106—611no—
444C2×#106—611no—
445C2×#106C2×D6111yescharacteristic
446C2×C4⋊C8—611no—
447C2×#102—611no—
448C2×#102—611no—
449C2×#102—611no—
450C2×#102—611no—
451C2×#102C2×D6111yescharacteristic
452C2×#102C2×D6111yescharacteristic
453C2×C22⋊C8—611no—
454C2×C22⋊C8—611no—
455C2×#97—611no—
456C61C2×#334711yescharacteristic, complemented, Sylow
457C22×Q8—1221no—
458C22×D4—21no—
459C22×D4—21no—
460C22×D4—611no—
461C22×D4—1221no—
462C22×D4—1221no—
463C22×D4C22×D6111yescharacteristic
464C22×D4C22×D6111yescharacteristic
465C23×C4—611no—
466C23×C4—1221no—
467C23×C4—1221no—
468C23×C4—1221no—
469C23×C4C22×D6111yescharacteristic
470C2×D8—24no—
471C2×D8C22×D6114yes—
472C2×M16—24no—
473C2×M16C22×D6114yes—
474C22×C8—611no—
475C22×C8—611no—
476C22×C8—614no—
477C22×C8—1224no—
478C22×C8C22×D6111yescharacteristic
479C22×C8C22×D6111yescharacteristic
480C4⋊Q8—614no—
481C4⋊Q8—1222no—
482#126—1228no—
483#125—614no—
484#125—1222no—
485#124—1228no—
486#124—1228no—
487#123—1228no—
488#121—22no—
489#121—22no—
490#121—614no—
491#121—614no—
492#121—1222no—
493#121—1222no—
494#121—1228no—
495#121—1228no—
496#121C22×D6114yes—
497#121C22×D6114yes—
498C4×D4—614no—
499C4×D4—614no—
500C4×D4—614no—
501C4×D4—614no—
502C4×D4—1222no—
503C4×D4—1222no—
504C4×D4—1228no—
505#117—614no—
506#117—614no—
507#117—614no—
508#117—1228no—
509#117—1222no—
510#117—1222no—
511#117—1222no—
512C2×C4⋊C4—611no—
513C2×C4⋊C4—611no—
514C2×C4⋊C4—611no—
515C2×C4⋊C4—614no—
516C2×C4⋊C4—611no—
517C2×C4⋊C4—611no—
518C2×C4⋊C4—1221no—
519C2×C4⋊C4—1221no—
520C2×C4⋊C4—1221no—
521C2×C4⋊C4—1221no—
522C2×C4⋊C4—1222no—
523C2×C4⋊C4C22×D6111yescharacteristic
524C2×C4⋊C4C22×D6111yescharacteristic
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—611no—
528C2×C22⋊C4—611no—
529C2×C22⋊C4—1221no—
530C2×C22⋊C4—1221no—
531C2×C22⋊C4—1221no—
532C2×C22⋊C4—1221no—
533C2×C22⋊C4—1221no—
534C2×C22⋊C4—1221no—
535C2×C22⋊C4—1221no—
536C2×C42—611no—
537C2×C42—1221no—
538C2×C42—1221no—
539C2×C42—1221no—
540#107—614no—
541#107—614no—
542#107—614no—
543#107—614no—
544#107—614no—
545#106—614no—
546#106—614no—
547#106—614no—
548#106C22×D6114yes—
549C4⋊C8—614no—
550#102—614no—
551#102—614no—
552#102—614no—
553#102—614no—
554#102C22×D6114yes—
555#102C22×D6114yes—
556C22⋊C8—614no—
557C22⋊C8—614no—
558#97—614no—
559C24—21no—
560C24—21no—
561C24—611no—
562C24D4×D6111yescharacteristic
563C2×Q8—1224no—
564C2×Q8—4882no—
565C2×D4—24no—
566C2×D4—24no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—44no—
574C2×D4—82no—
575C2×D4—614no—
576C2×D4—1224no—
577C2×D4—1224no—
578C2×D4—4882no—
579C2×D4—4882no—
580C2×D4—2442no—
581C2×D4C23×D6112yes—
582C2×D4C23×D6112yes—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—611no—
588C22×C4—611no—
589C22×C4—611no—
590C22×C4—612no—
591C22×C4—612no—
592C22×C4—1224no—
593C22×C4—1224no—
594C22×C4—1222no—
595C22×C4—1222no—
596C22×C4—1224no—
597C22×C4—1221no—
598C22×C4—1221no—
599C22×C4—1221no—
600C22×C4—1221no—
601C22×C4—4882no—
602C22×C4—4882no—
603C22×C4—2444no—
604C22×C4D4×D6112yes—
605C22×C4D4×D6111yescharacteristic
606C22×C4C23×D6112yes—
607C22×C4C23×D6111yescharacteristic
608D8—28no—
609M16—28no—
610C2×C8—22no—
611C2×C8—612no—
612C2×C8—612no—
613C2×C8—1222no—
614C2×C8—1222no—
615C2×C8—1228no—
616C2×C8#1175822414yes—
617C2×C8C23×D6112yes—
618C2×C8C23×D6112yes—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—614no—
622C4⋊C4—612no—
623C4⋊C4—612no—
624C4⋊C4—612no—
625C4⋊C4—612no—
626C4⋊C4—1224no—
627C4⋊C4—1224no—
628C4⋊C4—1224no—
629C4⋊C4—1221no—
630C4⋊C4—1221no—
631C4⋊C4—1224no—
632C4⋊C4—1221no—
633C4⋊C4—1221no—
634C4⋊C4C23×D6112yes—
635C4⋊C4C23×D6112yes—
636C22⋊C4—24no—
637C22⋊C4—24no—
638C22⋊C4—614no—
639C22⋊C4—614no—
640C22⋊C4—1224no—
641C22⋊C4—1224no—
642C22⋊C4—1224no—
643C22⋊C4—1224no—
644C22⋊C4—1224no—
645C22⋊C4—1224no—
646C22⋊C4—1224no—
647C42—612no—
648C42—612no—
649C42—1224no—
650C42—1224no—
651C42—1224no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—612no—
664C23—1222no—
665C23—1222no—
666C23—1222no—
667C23C2×D4×D6112yes—
668C23C2×D4×D6111yescharacteristic
669Q8—4884no—
670D4—22no—
671D4—22no—
672D4—22no—
673D4—22no—
674D4—48no—
675D4—42no—
676D4—42no—
677D4—84no—
678D4—4884no—
679D4—4884no—
680D4—2444no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—24no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—612no—
690C2×C4—612no—
691C2×C4—612no—
692C2×C4—1222no—
693C2×C4—1222no—
694C2×C4—1222no—
695C2×C4—1222no—
696C2×C4—1222no—
697C2×C4—1224no—
698C2×C4—1222no—
699C2×C4—1222no—
700C2×C4—1222no—
701C2×C4—1222no—
702C2×C4—4884no—
703C2×C4—4884no—
704C2×C4—2448no—
705C2×C4—2442no—
706C2×C4—2442no—
707C2×C4—2442no—
708C2×C4—2442no—
709C2×C4C2×D4×D6112yes—
710C2×C4C2×D4×D6111yescharacteristic
711C2×C4C2×#1175822412yes—
712C2×C4#1451982412yes—
713C2×C4C24×D6111yescharacteristic
714C8—22no—
715C8—1222no—
716C8—1222no—
717C8C2×#1175822414yes—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—44no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—84no—
729C22—84no—
730C22—1222no—
731C22—1222no—
732C22—1222no—
733C22—2444no—
734C22#1684041212yes—
735C22#1684055812yes—
736C22#1684056612yes—
737C22C22×D4×D6111yescharacteristic
738C4—22no—
739C4—42no—
740C4—42no—
741C4—1222no—
742C4—1222no—
743C4—1222no—
744C4—2442no—
745C4—2442no—
746C4—2442no—
747C4—2442no—
748C4#1684041212yes—
749C4C22×#1175822411yescharacteristic
750C4C2×#1451982411yescharacteristic
751C2—42no—
752C2—82no—
753C2—82no—
754C2—2442no—
755C2#2145831414yesdirect product factor
756C2C2×#1684041211yescharacteristic
757C2C2×#1684055811yescharacteristic
758C2C2×#1684056611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#469C2
socleC23×C61C22×D4
hypercenterC2×#469D61
hypocenterC61C2×#3347
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#469

Complements

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

NH ≅ G/Ntype
1. C2×#16840476C2semidirect
2. C2×#16840464C2semidirect
3. #21458314C2direct (N × H)
4. C2×#16840169C2semidirect
5. C2×#16840085C2semidirect
6. C2×#16840084C2semidirect
7. C2×#16840083C2semidirect
8. C2×#16840073C2semidirect
9. C2×#16840064C2semidirect
10. C2×#16840040C2semidirect
11. C2×#16839995C2semidirect
12. C2×#16839874C2semidirect
13. C2×#16839831C2semidirect
14. C2×#16839804C2semidirect
15. C2×#16839797C2semidirect
16. C2×C61×#469C2semidirect
19. #16840476C22semidirect
21. #16840464C22semidirect
41. #16840169C22semidirect
42. #16840085C22semidirect
43. #16840084C22semidirect
44. #16840083C22semidirect
45. #16840073C22semidirect
46. #16840064C22semidirect
47. #16840040C22semidirect
48. #16839995C22semidirect
49. #16839874C22semidirect
50. #16839831C22semidirect
51. #16839804C22semidirect
52. #16839797C22semidirect
73. C61×#469C22semidirect
382. C2×#469D61semidirect
391. C2×C61#3347semidirect
431. #469C2×D61semidirect
456. C61C2×#3347semidirect
755. C2#21458314direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404762
C2×#168404642
#214583142
C2×#168401692
C2×#168400852
C2×#168400842
C2×#168400832
C2×#168400732
C2×#168400642
C2×#168400402
C2×#168399952
C2×#168398742
C2×#168398312
C2×#168398042
C2×#168397972
C2×C61×#4692
C2×#334761