Finite Group Databasebeta

← C2×#21458009 #30556767

Subgroups — C2×#21458009 #30556767

Order 15616.

2178 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840476C211yesmaximal, characteristic, complemented
2C2×#16840419C211yesmaximal, characteristic, complemented
3#21458009C2116yesmaximal, direct product factor
4C2×#16840120C211yesmaximal, characteristic, complemented
5C2×#16840104C211yesmaximal, characteristic, complemented
6C2×#16840084C211yesmaximal, characteristic, complemented
7C2×#16840045C211yesmaximal, characteristic, complemented
8C2×#16840012C211yesmaximal, characteristic, complemented
9C2×#16839989C211yesmaximal, characteristic, complemented
10C2×#16839975C211yesmaximal, characteristic, complemented
11C2×#16839899C211yesmaximal, characteristic, complemented
12C2×#16839863C211yesmaximal, characteristic, complemented
13C2×#16839830C211yesmaximal, characteristic, complemented
14C2×#16839769C211yesmaximal, characteristic, complemented
15C2×#16839758C211yesmaximal, characteristic, complemented
16C2×C61×#449C211yesmaximal, characteristic, complemented
17C22×Q8×D61C2211yescharacteristic
18C22×#11758200C2211yescharacteristic
19C22×#11758189C2211yescharacteristic
20C23×#92418C2211yescharacteristic
21#16840476—24no—
22#16840476C2218yescomplemented
23#16840419—24no—
24#16840419C2218yescomplemented
25C2×#14519776C2211yescharacteristic
26C2×#14519764—21no—
27C2×#14519764—21no—
28C2×#14519764C2211yescharacteristic
29C2×#14519763—21no—
30C2×#14519756—21no—
31C2×#14519756C2211yescharacteristic
32C2×#14519749—21no—
33C2×#14519748—21no—
34C2×#14519748C2211yescharacteristic
35C2×#14519748C2211yescharacteristic
36C2×Q8×Dic61C2211yescharacteristic
37C2×D4×Dic61C2211yescharacteristic
38C2×C4×C22⋊D61—21no—
39C2×C4×C22⋊D61C2211yescharacteristic
40C2×#14519736C2211yescharacteristic
41C2×#14519735C2211yescharacteristic
42C2×#14519733—21no—
43#16840120C2218yescomplemented
44#16840104C2218yescomplemented
45#16840084C2218yescomplemented
46#16840045C2218yescomplemented
47#16840012C2218yescomplemented
48#16839989C2218yescomplemented
49#16839975C2218yescomplemented
50#16839899C2218yescomplemented
51#16839863C2218yescomplemented
52#16839830C2218yescomplemented
53C2×#14519711C2211yescharacteristic
54C2×#14519709C2211yescharacteristic
55C2×#14519708C2211yescharacteristic
56C2×#14519706C2211yescharacteristic
57#16839769C2218yescomplemented
58#16839758C2218yescomplemented
59C2×#14519702C2211yescharacteristic
60C2×#14519702C2211yescharacteristic
61C2×#14519701C2211yescharacteristic
62C2×#14519701C2211yescharacteristic
63C2×#14519700C2211yescharacteristic
64C2×#14519698C2211yescharacteristic
65C2×#14519698C2211yescharacteristic
66C2×#14519698C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×#14519687C2211yescharacteristic
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×Dic122—21no—
78C22×Dic122—21no—
79C22×Dic122C2311yescharacteristic
80C2×Q8×D61—22no—
81C2×Q8×D61—24no—
82C2×Q8×D61—42no—
83C2×Q8×D61C2314yes—
84C22×C22⋊D61—21no—
85C22×C22⋊D61—21no—
86C22×C22⋊D61D411yescharacteristic
87C23×Dic61—21no—
88C22×C4×D61—21no—
89C22×C4×D61C2311yescharacteristic
90C2×#11758200—42no—
91C2×#11758200C2314yes—
92C2×#11758189—42no—
93C2×#11758189C2314yes—
94C22×#92418—42no—
95C22×#92418C2311yescharacteristic
96C22×#92418C2311yescharacteristic
97C22×#92418C2314yes—
98#14519776—22no—
99#14519776C2314yes—
100#14519764—28no—
101#14519764—28no—
102#14519764—22no—
103#14519764C2314yes—
104#14519763—28no—
105#14519756—22no—
106#14519756—28no—
107#14519756C2314yes—
108#14519749—28no—
109#14519748—28no—
110#14519748—22no—
111#14519748—22no—
112#14519748C2314yes—
113#14519748C2314yes—
114Q8×Dic61—22no—
115Q8×Dic61C2314yes—
116D4×Dic61—22no—
117D4×Dic61C2314yes—
118C4×C22⋊D61—28no—
119C4×C22⋊D61D414yes—
120C4×C22⋊D61C2314yes—
121#14519736—22no—
122#14519736C2314yes—
123#14519735—22no—
124#14519735C2314yes—
125#14519733—28no—
126C2×C4⋊Dic61—21no—
127C2×C4⋊Dic61C2311yescharacteristic
128C2×C4⋊Dic61C2311yescharacteristic
129C2×C4⋊Dic61C2311yescharacteristic
130C2×#11758196—21no—
131C2×#11758196—21no—
132C2×#11758196D411yescharacteristic
133C2×C22⋊Dic61—21no—
134C2×C22⋊Dic61—21no—
135C2×C22⋊Dic61—21no—
136C2×C22⋊Dic61—21no—
137C2×C22⋊Dic61—21no—
138C2×C22⋊Dic61—21no—
139C2×C22⋊Dic61—21no—
140C2×C22⋊Dic61D411yescharacteristic
141C2×#11758198—21no—
142C2×#11758198D411yescharacteristic
143C2×C4×Dic61—21no—
144C2×C4×Dic61—21no—
145C2×C4×Dic61—21no—
146C2×C4×Dic61C2311yescharacteristic
147#14519711C2314yes—
148#14519709C2314yes—
149#14519708C2314yes—
150#14519706C2314yes—
151#14519702C2314yes—
152#14519702C2314yes—
153#14519701C2314yes—
154#14519701C2314yes—
155#14519700C2314yes—
156#14519698C2314yes—
157#14519698C2314yes—
158#14519698C2314yes—
159#14519689C2314yes—
160#14519687C2314yes—
161C2×#41×C61—22no—
162C2×#41×C61—24no—
163C2×#41×C61—42no—
164C2×#41×C61C2314yes—
165C22×Q8×C61C2311yescharacteristic
166C22×D4×C61—21no—
167C22×D4×C61—21no—
168C22×D4×C61C2311yescharacteristic
169C22×D4×C61C2311yescharacteristic
170C23×C4×C61—21no—
171C23×C4×C61C2311yescharacteristic
172C2×SD16×C61—24no—
173C2×SD16×C61C2314yes—
174C2×D8×C61—42no—
175C2×D8×C61C2314yes—
176C22×C8×C61C2311yescharacteristic
177C22×C8×C61C2311yescharacteristic
178#121×C61—22no—
179#121×C61C2314yes—
180C2×C4⋊C4×C61C2311yescharacteristic
181C2×C22⋊C4×C61—21no—
182#103×C61C2314yes—
183#102×C61C2314yes—
184C22⋊C8×C61C2314yes—
185C24×C61—21no—
186C24×C61—21no—
187C24×C61C2×D411yescharacteristic
188C23×D61C2×D411yescharacteristic
189#41×C61—28no—
190#41×C61—44no—
191#41×C61—48no—
192C2×Q8×C61—21no—
193C2×Q8×C61—22no—
194C2×Q8×C61#4114yes—
195C2×Q8×C61C2412yes—
196C2×D4×C61—24no—
197C2×D4×C61—24no—
198C2×D4×C61—21no—
199C2×D4×C61—21no—
200C2×D4×C61—22no—
201C2×D4×C61—22no—
202C2×D4×C61—22no—
203C2×D4×C61—22no—
204C2×D4×C61—44no—
205C2×D4×C61—82no—
206C2×D4×C61C2412yes—
207C2×D4×C61C2412yes—
208C22×C4×C61—21no—
209C22×C4×C61—22no—
210C22×C4×C61—22no—
211C22×C4×C61—21no—
212C22×C4×C61—24no—
213C22×C4×C61—44no—
214C22×C4×C61C2×D411yescharacteristic
215C22×C4×C61C2×D412yes—
216C22×C4×C61C2412yes—
217C22×C4×C61C2411yescharacteristic
218C2×C22⋊D61—24no—
219C2×C22⋊D61—24no—
220C2×C22⋊D61—42no—
221C2×C22⋊D61—44no—
222C2×C22⋊D61—82no—
223C2×C22⋊D61C2×D414yes—
224C22×Dic61—21no—
225C22×Dic61—21no—
226C22×Dic61—21no—
227C22×Dic61—21no—
228C22×Dic61—24no—
229C22×Dic61—44no—
230C22×Dic61C2×D411yescharacteristic
231C22×Dic61C2×D411yescharacteristic
232C22×Dic61C2×D411yescharacteristic
233Q8×D61—28no—
234Q8×D61—44no—
235Q8×D61—48no—
236C2×C4×D61—22no—
237C2×C4×D61—22no—
238C2×C4×D61—24no—
239C2×C4×D61—44no—
240C2×C4×D61C2×D412yes—
241C2×C4×D61C2412yes—
242C2×Dic122—22no—
243C2×Dic122—22no—
244C2×Dic122—21no—
245C2×Dic122—24no—
246C2×Dic122—24no—
247C2×Dic122—44no—
248C2×Dic122—82no—
249C2×Dic122C2412yes—
250SD16×C61—28no—
251D8×C61—44no—
252C2×C8×C61—22no—
253C2×C8×C61—22no—
254C2×C8×C61C2412yes—
255C2×C8×C61C2412yes—
256C4⋊C4×C61—21no—
257C4⋊C4×C61C2412yes—
258C22⋊C4×C61—24no—
259C22⋊Dic61—24no—
260C22⋊Dic61—24no—
261C22⋊Dic61—24no—
262C22⋊Dic61—24no—
263C22⋊Dic61—24no—
264C22⋊Dic61—24no—
265C22⋊Dic61—24no—
266C22⋊Dic61C2×D414yes—
267#11758200—44no—
268#11758198—24no—
269#11758198C2×D414yes—
270C4⋊Dic61—21no—
271C4⋊Dic61—21no—
272C4⋊Dic61—21no—
273C4⋊Dic61—24no—
274C4⋊Dic61C2412yes—
275C4⋊Dic61C2412yes—
276C4⋊Dic61C2412yes—
277#11758196—24no—
278#11758196—24no—
279#11758196C2×D414yes—
280C4×Dic61—24no—
281C4×Dic61—24no—
282C4×Dic61—24no—
283C4×Dic61C2×D412yes—
284C4×Dic61C2412yes—
285C2×#92418—22no—
286C2×#92418—22no—
287C2×#92418—44no—
288C2×#92418C2412yes—
289C2×#92418C2412yes—
290#11758189—44no—
291C23×C61—22no—
292C23×C61—22no—
293C23×C61—22no—
294C23×C61—22no—
295C23×C61—22no—
296C23×C61—42no—
297C23×C61—42no—
298C23×C61—42no—
299C23×C61—42no—
300C23×C61—42no—
301C23×C61—42no—
302C23×C61C22×D412yes—
303C23×C61C22×D411yescharacteristic
304C22×D61—22no—
305C22×D61—22no—
306C22×D61—22no—
307C22×D61C22×D412yes—
308Q8×C61—24no—
309Q8×C61—22no—
310Q8×C61C2×#4114yes—
311D4×C61—22no—
312D4×C61—22no—
313D4×C61—22no—
314D4×C61—22no—
315D4×C61—48no—
316D4×C61—42no—
317D4×C61—42no—
318D4×C61—84no—
319C2×C4×C61—24no—
320C2×C4×C61—22no—
321C2×C4×C61—22no—
322C2×C4×C61—24no—
323C2×C4×C61—22no—
324C2×C4×C61—22no—
325C2×C4×C61—22no—
326C2×C4×C61—48no—
327C2×C4×C61—42no—
328C2×C4×C61C22×D412yes—
329C2×C4×C61C22×D411yescharacteristic
330C2×C4×C61C2×#4112yes—
331C2×C4×C61H(5,𝔽2)12yes—
332C2×C4×C61C2511yescharacteristic
333C22⋊D61—44no—
334C22⋊D61—48no—
335C22⋊D61—84no—
336C2×Dic61—22no—
337C2×Dic61—22no—
338C2×Dic61—22no—
339C2×Dic61—22no—
340C2×Dic61—22no—
341C2×Dic61—22no—
342C2×Dic61—22no—
343C2×Dic61—48no—
344C2×Dic61—42no—
345C2×Dic61—42no—
346C2×Dic61—42no—
347C2×Dic61—42no—
348C2×Dic61C22×D412yes—
349C2×Dic61C22×D412yes—
350C2×Dic61C22×D412yes—
351C4×D61—24no—
352C4×D61—22no—
353C4×D61—22no—
354C4×D61—48no—
355Dic122—22no—
356Dic122—22no—
357Dic122—48no—
358Dic122—42no—
359Dic122—84no—
360C8×C61—22no—
361C8×C61—22no—
362#92418—22no—
363#92418—22no—
364C2×#3321—611nomaximal, Sylow
365C22×C61—22no—
366C22×C61—22no—
367C22×C61—22no—
368C22×C61—44no—
369C22×C61—42no—
370C22×C61—42no—
371C22×C61—42no—
372C22×C61—42no—
373C22×C61—42no—
374C22×C61—42no—
375C22×C61—84no—
376C22×C61—84no—
377C22×C61#54612yes—
378C22×C61#57512yes—
379C22×C61#57712yes—
380C22×C61C23×D411yescharacteristic
381C2×D61—22no—
382C2×D61—22no—
383C2×D61—22no—
384C2×D61—44no—
385C4×C61—24no—
386C4×C61—22no—
387C4×C61—42no—
388C4×C61#54612yes—
389C4×C61C22×#4111yescharacteristic
390C4×C61C2×H(5,𝔽2)11yescharacteristic
391Dic61—22no—
392Dic61—22no—
393Dic61—22no—
394Dic61—42no—
395Dic61—42no—
396Dic61—42no—
397Dic61—42no—
398C2×#555—611no—
399C2×#548—611no—
400#3321—6116no—
401C2×#489—611no—
402C2×#485—611no—
403C2×#482—611no—
404C2×#475—611no—
405C2×#469—611no—
406C2×#465—611no—
407C2×#463—611no—
408C2×#449D6111yescharacteristic, complemented
409C2×#448—611no—
410C2×#440—611no—
411C2×#435—611no—
412C2×#419—611no—
413C2×#416—611no—
414C2×C61—42no—
415C2×C61—82no—
416C2×C61—82no—
417C2×C61#332114yescomplemented
418C2×C61C2×#54611yescharacteristic
419C2×C61C2×#57511yescharacteristic
420C2×C61C2×#57711yescharacteristic
421D61—42no—
422C22×#41C2×D6111yescharacteristic
423C23×Q8—611no—
424C22×SD16—611no—
425C22×SD16C2×D6111yescharacteristic
426C22×D8C2×D6111yescharacteristic
427C22×M16—611no—
428C23×C8—611no—
429#555—618no—
430#555—1224no—
431#548—618no—
432#548—1224no—
433C2×C4⋊Q8—611no—
434C2×#124—611no—
435C2×#124—1221no—
436C2×#124—1221no—
437C2×#124—1221no—
438C2×C22⋊Q8—611no—
439C2×C22⋊Q8—1221no—
440C2×#121—611no—
441C2×#121—611no—
442C2×#121—1221no—
443C2×#121—1221no—
444C2×#121C2×D6111yescharacteristic
445C2×C4×Q8—611no—
446C2×C4×D4—611no—
447C2×C4×D4—611no—
448C2×C4×D4—1221no—
449C2×#117—611no—
450C2×#117—611no—
451C2×#117—1221no—
452#489—618no—
453#485—618no—
454#482—618no—
455#475—618no—
456#469—618no—
457#465—618no—
458#463—618no—
459#449C2×D6118yescomplemented
460#448—618no—
461#440—618no—
462#435—618no—
463C2×#107—611no—
464C2×#106—611no—
465C2×#106—611no—
466C2×C4⋊C8—611no—
467#419—618no—
468#416—618no—
469C2×#103—611no—
470C2×#103—611no—
471C2×#103—611no—
472C2×#103—611no—
473C2×#103—611no—
474C2×#103C2×D6111yescharacteristic
475C2×#102—611no—
476C2×#102—611no—
477C2×#102—611no—
478C2×#102C2×D6111yescharacteristic
479C2×C22⋊C8—611no—
480C2×C22⋊C8C2×D6111yescharacteristic
481C2×#97—611no—
482C61C2×#332111yescharacteristic, complemented, Sylow
483C2×#41—22no—
484C2×#41—24no—
485C2×#41—42no—
486C2×#41C22×D6114yes—
487C22×Q8—614no—
488C22×Q8—611no—
489C22×Q8—1221no—
490C22×Q8—1221no—
491C22×Q8—1222no—
492C22×Q8—1224no—
493C22×Q8—2442no—
494C22×Q8C22×D6111yescharacteristic
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—611no—
498C22×D4—1221no—
499C22×D4—1221no—
500C22×D4C22×D6111yescharacteristic
501C22×D4C22×D6111yescharacteristic
502C23×C4—21no—
503C23×C4—611no—
504C23×C4—1221no—
505C23×C4—1221no—
506C23×C4C22×D6111yescharacteristic
507C2×SD16—24no—
508C2×SD16—614no—
509C2×SD16—2442no—
510C2×SD16C22×D6114yes—
511C2×D8—42no—
512C2×D8C22×D6114yes—
513C2×M16—614no—
514C2×M16—2442no—
515C22×C8—611no—
516C22×C8—611no—
517C22×C8—614no—
518C22×C8—2442no—
519C22×C8C22×D6111yescharacteristic
520C22×C8C22×D6111yescharacteristic
521C4⋊Q8—614no—
522C4⋊Q8—1222no—
523#124—614no—
524#124—1222no—
525#124—1228no—
526#124—1228no—
527#124—1228no—
528C22⋊Q8—614no—
529C22⋊Q8—1228no—
530C22⋊Q8—1222no—
531#121—22no—
532#121—614no—
533#121—614no—
534#121—1222no—
535#121—1222no—
536#121—1228no—
537#121—1228no—
538#121C22×D6114yes—
539C4×Q8—614no—
540C4×Q8—1222no—
541C4×D4—614no—
542C4×D4—614no—
543C4×D4—614no—
544C4×D4—1222no—
545C4×D4—1228no—
546#117—614no—
547#117—614no—
548#117—1228no—
549#117—1222no—
550#117—1222no—
551C2×C4⋊C4—611no—
552C2×C4⋊C4—611no—
553C2×C4⋊C4—611no—
554C2×C4⋊C4—611no—
555C2×C4⋊C4—1221no—
556C2×C4⋊C4—1221no—
557C2×C4⋊C4—1221no—
558C2×C4⋊C4C22×D6111yescharacteristic
559C2×C22⋊C4—21no—
560C2×C22⋊C4—611no—
561C2×C22⋊C4—611no—
562C2×C22⋊C4—1221no—
563C2×C22⋊C4—1221no—
564C2×C22⋊C4—1221no—
565C2×C22⋊C4—1221no—
566C2×C22⋊C4—1221no—
567C2×C22⋊C4—1221no—
568C2×C22⋊C4—1221no—
569C2×C22⋊C4—1221no—
570C2×C42—611no—
571C2×C42—1221no—
572C2×C42—1221no—
573C2×C42—1221no—
574#107—614no—
575#106—614no—
576#106—614no—
577C4⋊C8—614no—
578#103—614no—
579#103—614no—
580#103—614no—
581#103—614no—
582#103—614no—
583#103C22×D6114yes—
584#102—614no—
585#102—614no—
586#102—614no—
587#102C22×D6114yes—
588C22⋊C8—614no—
589C22⋊C8C22×D6114yes—
590#97—614no—
591C24—21no—
592C24—21no—
593C24—611no—
594C24D4×D6111yescharacteristic
595#41—28no—
596#41—44no—
597#41—48no—
598C2×Q8—21no—
599C2×Q8—22no—
600C2×Q8—612no—
601C2×Q8—1224no—
602C2×Q8—1224no—
603C2×Q8—1221no—
604C2×Q8—1228no—
605C2×Q8—1222no—
606C2×Q8—1222no—
607C2×Q8—4882no—
608C2×Q8—2444no—
609C2×Q8—2444no—
610C2×Q8—2448no—
611C2×Q8#1175822414yes—
612C2×Q8C23×D6112yes—
613C2×D4—24no—
614C2×D4—24no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—22no—
618C2×D4—22no—
619C2×D4—22no—
620C2×D4—22no—
621C2×D4—44no—
622C2×D4—82no—
623C2×D4—614no—
624C2×D4—1224no—
625C2×D4—1224no—
626C2×D4—4882no—
627C2×D4—2442no—
628C2×D4—2444no—
629C2×D4C23×D6112yes—
630C2×D4C23×D6112yes—
631C22×C4—21no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—21no—
635C22×C4—24no—
636C22×C4—44no—
637C22×C4—611no—
638C22×C4—611no—
639C22×C4—611no—
640C22×C4—612no—
641C22×C4—612no—
642C22×C4—1224no—
643C22×C4—1224no—
644C22×C4—1222no—
645C22×C4—1222no—
646C22×C4—1221no—
647C22×C4—1221no—
648C22×C4—1221no—
649C22×C4—1221no—
650C22×C4—2444no—
651C22×C4—2444no—
652C22×C4D4×D6112yes—
653C22×C4D4×D6111yescharacteristic
654C22×C4C23×D6112yes—
655C22×C4C23×D6111yescharacteristic
656SD16—28no—
657SD16—2444no—
658D8—44no—
659M16—2444no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—612no—
663C2×C8—612no—
664C2×C8—1222no—
665C2×C8—1222no—
666C2×C8—2444no—
667C2×C8C23×D6112yes—
668C2×C8C23×D6112yes—
669C4⋊C4—21no—
670C4⋊C4—614no—
671C4⋊C4—612no—
672C4⋊C4—612no—
673C4⋊C4—612no—
674C4⋊C4—1224no—
675C4⋊C4—1224no—
676C4⋊C4—1221no—
677C4⋊C4—1221no—
678C4⋊C4—1221no—
679C4⋊C4—1224no—
680C4⋊C4C23×D6112yes—
681C22⋊C4—24no—
682C22⋊C4—614no—
683C22⋊C4—614no—
684C22⋊C4—1224no—
685C22⋊C4—1224no—
686C22⋊C4—1224no—
687C22⋊C4—1224no—
688C22⋊C4—1224no—
689C22⋊C4—1224no—
690C22⋊C4—1224no—
691C22⋊C4—1224no—
692C42—612no—
693C42—612no—
694C42—1224no—
695C42—1224no—
696C42—1224no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—612no—
709C23—1222no—
710C23—1222no—
711C23—1222no—
712C23C2×D4×D6112yes—
713C23C2×D4×D6111yescharacteristic
714Q8—22no—
715Q8—24no—
716Q8—1222no—
717Q8—1222no—
718Q8—4884no—
719Q8—2448no—
720Q8—2442no—
721Q8C2×#1175822414yes—
722D4—22no—
723D4—22no—
724D4—22no—
725D4—22no—
726D4—48no—
727D4—42no—
728D4—42no—
729D4—84no—
730D4—4884no—
731D4—2444no—
732D4—2448no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—24no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—24no—
739C2×C4—22no—
740C2×C4—48no—
741C2×C4—42no—
742C2×C4—612no—
743C2×C4—612no—
744C2×C4—612no—
745C2×C4—1222no—
746C2×C4—1222no—
747C2×C4—1222no—
748C2×C4—1222no—
749C2×C4—1222no—
750C2×C4—1224no—
751C2×C4—1222no—
752C2×C4—1222no—
753C2×C4—1222no—
754C2×C4—1222no—
755C2×C4—2448no—
756C2×C4—2448no—
757C2×C4—2442no—
758C2×C4—2442no—
759C2×C4—2442no—
760C2×C4—2442no—
761C2×C4C2×D4×D6112yes—
762C2×C4C2×D4×D6111yescharacteristic
763C2×C4C2×#1175822412yes—
764C2×C4#1451982212yes—
765C2×C4C24×D6111yescharacteristic
766C8—22no—
767C8—22no—
768C8—1222no—
769C8—1222no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—44no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—84no—
781C22—84no—
782C22—1222no—
783C22—1222no—
784C22—1222no—
785C22—2444no—
786C22#1684039912yes—
787C22#1684055912yes—
788C22#1684057212yes—
789C22C22×D4×D6111yescharacteristic
790C4—22no—
791C4—24no—
792C4—42no—
793C4—1222no—
794C4—1222no—
795C4—1222no—
796C4—2442no—
797C4—2442no—
798C4—2442no—
799C4—2442no—
800C4#1684039912yes—
801C4C22×#1175822411yescharacteristic
802C4C2×#1451982211yescharacteristic
803C2—42no—
804C2—82no—
805C2—82no—
806C2—2442no—
807C2#2145800914yesdirect product factor
808C2C2×#1684039911yescharacteristic
809C2C2×#1684055911yescharacteristic
810C2C2×#1684057211yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#449C2
socleC23×C61C22×D4
hypercenterC2×#449D61
hypocenterC61C2×#3321
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×#16840476C2semidirect
2. C2×#16840419C2semidirect
3. #21458009C2direct (N × H)
4. C2×#16840120C2semidirect
5. C2×#16840104C2semidirect
6. C2×#16840084C2semidirect
7. C2×#16840045C2semidirect
8. C2×#16840012C2semidirect
9. C2×#16839989C2semidirect
10. C2×#16839975C2semidirect
11. C2×#16839899C2semidirect
12. C2×#16839863C2semidirect
13. C2×#16839830C2semidirect
14. C2×#16839769C2semidirect
15. C2×#16839758C2semidirect
16. C2×C61×#449C2semidirect
22. #16840476C22semidirect
24. #16840419C22semidirect
43. #16840120C22semidirect
44. #16840104C22semidirect
45. #16840084C22semidirect
46. #16840045C22semidirect
47. #16840012C22semidirect
48. #16839989C22semidirect
49. #16839975C22semidirect
50. #16839899C22semidirect
51. #16839863C22semidirect
52. #16839830C22semidirect
57. #16839769C22semidirect
58. #16839758C22semidirect
73. C61×#449C22semidirect
408. C2×#449D61semidirect
417. C2×C61#3321semidirect
459. #449C2×D61semidirect
482. C61C2×#3321semidirect
807. C2#21458009direct (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×#168404192
#214580092
C2×#168401202
C2×#168401042
C2×#168400842
C2×#168400452
C2×#168400122
C2×#168399892
C2×#168399752
C2×#168398992
C2×#168398632
C2×#168398302
C2×#168397692
C2×#168397582
C2×C61×#4492
C2×#332161