Finite Group Databasebeta

← C2×#21457818 #30556708

Subgroups — C2×#21457818 #30556708

Order 15616.

2242 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840464C211yesmaximal, characteristic, complemented
2C2×#16840431C211yesmaximal, characteristic, complemented
3#21457818C2116yesmaximal, direct product factor
4C2×#16840125C211yesmaximal, characteristic, complemented
5C2×#16840084C211yesmaximal, characteristic, complemented
6C2×#16840076C211yesmaximal, characteristic, complemented
7C2×#16840071C211yesmaximal, characteristic, complemented
8C2×#16840013C211yesmaximal, characteristic, complemented
9C2×#16839995C211yesmaximal, characteristic, complemented
10C2×#16839955C211yesmaximal, characteristic, complemented
11C2×#16839906C211yesmaximal, characteristic, complemented
12C2×#16839863C211yesmaximal, characteristic, complemented
13C2×#16839836C211yesmaximal, characteristic, complemented
14C2×#16839763C211yesmaximal, characteristic, complemented
15C2×#16839757C211yesmaximal, characteristic, complemented
16C2×C61×#449C211yesmaximal, characteristic, complemented
17C22×#11758226C2211yescharacteristic
18C22×#11758199C2211yescharacteristic
19C22×#11758194C2211yescharacteristic
20C22×C8×D61C2211yescharacteristic
21#16840464—24no—
22#16840464C2218yescomplemented
23#16840431—24no—
24#16840431C2218yescomplemented
25C2×#14519773—21no—
26C2×#14519773C2211yescharacteristic
27C2×#14519770—21no—
28C2×#14519768C2211yescharacteristic
29C2×#14519761—21no—
30C2×#14519751—21no—
31C2×#14519751C2211yescharacteristic
32C2×#14519749—21no—
33C2×#14519748—21no—
34C2×#14519748C2211yescharacteristic
35C2×#14519748C2211yescharacteristic
36C2×Q8×Dic61C2211yescharacteristic
37C2×D4×Dic61—21no—
38C2×D4×Dic61C2211yescharacteristic
39C2×C4×C22⋊D61—21no—
40C2×C4×C22⋊D61C2211yescharacteristic
41C2×#14519735C2211yescharacteristic
42C22×C4⋊Dic61C2211yescharacteristic
43#16840125C2218yescomplemented
44#16840084C2218yescomplemented
45#16840076C2218yescomplemented
46#16840071C2218yescomplemented
47#16840013C2218yescomplemented
48#16839995C2218yescomplemented
49#16839955C2218yescomplemented
50#16839906C2218yescomplemented
51#16839863C2218yescomplemented
52#16839836C2218yescomplemented
53C2×#14519711C2211yescharacteristic
54C2×#14519711C2211yescharacteristic
55C2×#14519708C2211yescharacteristic
56C2×#14519706C2211yescharacteristic
57#16839763C2218yescomplemented
58#16839757C2218yescomplemented
59C2×#14519701C2211yescharacteristic
60C2×#14519701C2211yescharacteristic
61C2×#14519699C2211yescharacteristic
62C2×#14519699C2211yescharacteristic
63C2×#14519698C2211yescharacteristic
64C2×#14519698C2211yescharacteristic
65C2×#14519698C2211yescharacteristic
66C2×#14519697C2211yescharacteristic
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
77C2×#11758226—22no—
78C2×#11758226—24no—
79C2×#11758226—42no—
80C2×#11758226C2314yes—
81C22×D244—21no—
82C22×D244C2311yescharacteristic
83C22×C22⋊D61—21no—
84C22×C22⋊D61—21no—
85C22×C22⋊D61—21no—
86C22×C22⋊D61—21no—
87C22×C22⋊D61—21no—
88C22×C22⋊D61D411yescharacteristic
89C23×Dic61—21no—
90C23×Dic61—21no—
91C22×C4×D61—21no—
92C22×C4×D61C2311yescharacteristic
93C2×#11758199—42no—
94C2×#11758199C2314yes—
95C2×#11758194—42no—
96C2×#11758194C2314yes—
97C22×#92418C2311yescharacteristic
98C22×#92418C2311yescharacteristic
99C2×C8×D61—42no—
100C2×C8×D61C2314yes—
101#14519773—28no—
102#14519773—22no—
103#14519773C2314yes—
104#14519770—28no—
105#14519768—22no—
106#14519768C2314yes—
107#14519761—28no—
108#14519751—22no—
109#14519751—28no—
110#14519751C2314yes—
111#14519749—28no—
112#14519748—22no—
113#14519748—22no—
114#14519748—28no—
115#14519748C2314yes—
116#14519748C2314yes—
117Q8×Dic61—22no—
118Q8×Dic61C2314yes—
119D4×Dic61—28no—
120D4×Dic61—22no—
121D4×Dic61C2314yes—
122C4×C22⋊D61—28no—
123C4×C22⋊D61D414yes—
124C4×C22⋊D61C2314yes—
125#14519735—22no—
126#14519735C2314yes—
127C2×C4⋊Dic61—22no—
128C2×C4⋊Dic61—21no—
129C2×C4⋊Dic61—21no—
130C2×C4⋊Dic61—21no—
131C2×C4⋊Dic61C2314yes—
132C2×C4⋊Dic61C2311yescharacteristic
133C2×C4⋊Dic61C2311yescharacteristic
134C2×C4⋊Dic61C2311yescharacteristic
135C2×#11758196—21no—
136C2×#11758196D411yescharacteristic
137C2×C22⋊Dic61—21no—
138C2×C22⋊Dic61—21no—
139C2×C22⋊Dic61—21no—
140C2×C22⋊Dic61D411yescharacteristic
141C2×#11758198—21no—
142C2×#11758198—21no—
143C2×#11758198D411yescharacteristic
144C2×C4×Dic61—21no—
145C2×C4×Dic61—21no—
146C2×C4×Dic61C2311yescharacteristic
147#14519711C2314yes—
148#14519711C2314yes—
149#14519708C2314yes—
150#14519706C2314yes—
151#14519701C2314yes—
152#14519701C2314yes—
153#14519699C2314yes—
154#14519699C2314yes—
155#14519698C2314yes—
156#14519698C2314yes—
157#14519698C2314yes—
158#14519697C2314yes—
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×D61—21no—
189C23×D61C2×D411yescharacteristic
190#41×C61—28no—
191#41×C61—44no—
192#41×C61—48no—
193C2×Q8×C61—21no—
194C2×Q8×C61—22no—
195C2×Q8×C61#4114yes—
196C2×Q8×C61C2412yes—
197C2×D4×C61—24no—
198C2×D4×C61—24no—
199C2×D4×C61—21no—
200C2×D4×C61—21no—
201C2×D4×C61—22no—
202C2×D4×C61—22no—
203C2×D4×C61—22no—
204C2×D4×C61—22no—
205C2×D4×C61—44no—
206C2×D4×C61—44no—
207C2×D4×C61C2412yes—
208C2×D4×C61C2412yes—
209C22×C4×C61—21no—
210C22×C4×C61—22no—
211C22×C4×C61—22no—
212C22×C4×C61—21no—
213C22×C4×C61—24no—
214C22×C4×C61—44no—
215C22×C4×C61C2×D411yescharacteristic
216C22×C4×C61C2×D412yes—
217C22×C4×C61C2412yes—
218C22×C4×C61C2411yescharacteristic
219C2×C22⋊D61—24no—
220C2×C22⋊D61—24no—
221C2×C22⋊D61—24no—
222C2×C22⋊D61—24no—
223C2×C22⋊D61—24no—
224C2×C22⋊D61—42no—
225C2×C22⋊D61—44no—
226C2×C22⋊D61—82no—
227C2×C22⋊D61—82no—
228C2×C22⋊D61—82no—
229C2×C22⋊D61—82no—
230C2×C22⋊D61C2×D414yes—
231C22×Dic61—21no—
232C22×Dic61—21no—
233C22×Dic61—21no—
234C22×Dic61—24no—
235C22×Dic61—24no—
236C22×Dic61—82no—
237C22×Dic61—82no—
238C22×Dic61C2×D411yescharacteristic
239C22×Dic61C2×D411yescharacteristic
240C22×Dic61C2×D411yescharacteristic
241#11758226—28no—
242#11758226—44no—
243#11758226—48no—
244C2×D244—22no—
245C2×D244—22no—
246C2×D244—24no—
247C2×D244—21no—
248C2×D244—44no—
249C2×D244C2412yes—
250C2×C4×D61—22no—
251C2×C4×D61—22no—
252C2×C4×D61—24no—
253C2×C4×D61—44no—
254C2×C4×D61C2×D412yes—
255C2×C4×D61C2412yes—
256SD16×C61—28no—
257D8×C61—44no—
258C2×C8×C61—22no—
259C2×C8×C61—22no—
260C2×C8×C61C2412yes—
261C2×C8×C61C2412yes—
262C4⋊C4×C61—21no—
263C4⋊C4×C61C2412yes—
264C22⋊C4×C61—24no—
265C22⋊Dic61—24no—
266C22⋊Dic61—24no—
267C22⋊Dic61—24no—
268C22⋊Dic61C2×D414yes—
269#11758199—44no—
270#11758198—24no—
271#11758198—24no—
272#11758198C2×D414yes—
273C4⋊Dic61—21no—
274C4⋊Dic61—21no—
275C4⋊Dic61—24no—
276C4⋊Dic61—21no—
277C4⋊Dic61—24no—
278C4⋊Dic61—24no—
279C4⋊Dic61C2412yes—
280C4⋊Dic61C2412yes—
281C4⋊Dic61C2412yes—
282#11758196—24no—
283#11758196C2×D414yes—
284C4×Dic61—24no—
285C4×Dic61—24no—
286C4×Dic61C2×D412yes—
287C4×Dic61C2412yes—
288#11758194—44no—
289C2×#92418—22no—
290C2×#92418—22no—
291C2×#92418C2412yes—
292C2×#92418C2412yes—
293C8×D61—44no—
294C23×C61—22no—
295C23×C61—22no—
296C23×C61—22no—
297C23×C61—22no—
298C23×C61—22no—
299C23×C61—42no—
300C23×C61—42no—
301C23×C61—42no—
302C23×C61—42no—
303C23×C61—42no—
304C23×C61—42no—
305C23×C61C22×D412yes—
306C23×C61C22×D411yescharacteristic
307C22×D61—22no—
308C22×D61—22no—
309C22×D61—22no—
310C22×D61—22no—
311C22×D61—42no—
312C22×D61—42no—
313C22×D61—42no—
314C22×D61C22×D412yes—
315Q8×C61—24no—
316Q8×C61—22no—
317Q8×C61C2×#4114yes—
318D4×C61—22no—
319D4×C61—22no—
320D4×C61—22no—
321D4×C61—22no—
322D4×C61—48no—
323D4×C61—48no—
324D4×C61—42no—
325D4×C61—42no—
326C2×C4×C61—24no—
327C2×C4×C61—22no—
328C2×C4×C61—22no—
329C2×C4×C61—24no—
330C2×C4×C61—22no—
331C2×C4×C61—22no—
332C2×C4×C61—22no—
333C2×C4×C61—48no—
334C2×C4×C61—42no—
335C2×C4×C61C22×D412yes—
336C2×C4×C61C22×D411yescharacteristic
337C2×C4×C61C2×#4112yes—
338C2×C4×C61H(5,𝔽2)12yes—
339C2×C4×C61C2511yescharacteristic
340C22⋊D61—44no—
341C22⋊D61—48no—
342C22⋊D61—84no—
343C22⋊D61—84no—
344C22⋊D61—84no—
345C22⋊D61—84no—
346C2×Dic61—22no—
347C2×Dic61—22no—
348C2×Dic61—22no—
349C2×Dic61—22no—
350C2×Dic61—22no—
351C2×Dic61—22no—
352C2×Dic61—42no—
353C2×Dic61—42no—
354C2×Dic61—42no—
355C2×Dic61—84no—
356C2×Dic61—84no—
357C2×Dic61C22×D412yes—
358C2×Dic61C22×D412yes—
359C2×Dic61C22×D412yes—
360D244—22no—
361D244—22no—
362D244—48no—
363D244—42no—
364C4×D61—24no—
365C4×D61—22no—
366C4×D61—22no—
367C4×D61—48no—
368C8×C61—22no—
369C8×C61—22no—
370#92418—22no—
371#92418—22no—
372C2×#3309—611nomaximal, Sylow
373C22×C61—22no—
374C22×C61—22no—
375C22×C61—22no—
376C22×C61—44no—
377C22×C61—42no—
378C22×C61—42no—
379C22×C61—42no—
380C22×C61—42no—
381C22×C61—42no—
382C22×C61—42no—
383C22×C61—84no—
384C22×C61—84no—
385C22×C61#54612yes—
386C22×C61#57512yes—
387C22×C61#57612yes—
388C22×C61C23×D411yescharacteristic
389C2×D61—22no—
390C2×D61—22no—
391C2×D61—22no—
392C2×D61—44no—
393C2×D61—42no—
394C2×D61—42no—
395C2×D61—42no—
396C2×D61—84no—
397C4×C61—24no—
398C4×C61—22no—
399C4×C61—42no—
400C4×C61#54612yes—
401C4×C61C22×#4111yescharacteristic
402C4×C61C2×H(5,𝔽2)11yescharacteristic
403Dic61—22no—
404Dic61—22no—
405Dic61—22no—
406Dic61—42no—
407Dic61—42no—
408Dic61—42no—
409C2×#553—611no—
410C2×#550—611no—
411#3309—6116no—
412C2×#490—611no—
413C2×#482—611no—
414C2×#480—611no—
415C2×#479—611no—
416C2×#469—611no—
417C2×#466—611no—
418C2×#459—611no—
419C2×#449—611no—
420C2×#449D6111yescharacteristic, complemented
421C2×#440—611no—
422C2×#435—611no—
423C2×#417—611no—
424C2×#416—611no—
425C2×C61—42no—
426C2×C61—82no—
427C2×C61—82no—
428C2×C61#330914yescomplemented
429C2×C61C2×#54611yescharacteristic
430C2×C61C2×#57511yescharacteristic
431C2×C61C2×#57611yescharacteristic
432D61—42no—
433D61—82no—
434C22×#41—611no—
435C22×#41C2×D6111yescharacteristic
436C22×SD16C2×D6111yescharacteristic
437C22×D8—611no—
438C22×D8C2×D6111yescharacteristic
439C22×M16—611no—
440C23×C8—611no—
441#553—618no—
442#553—1224no—
443#550—618no—
444#550—1224no—
445C2×#127—611no—
446C2×#127—1221no—
447C2×#126—1221no—
448C2×#125—611no—
449C2×#123—1221no—
450C2×#121—611no—
451C2×#121—611no—
452C2×#121—611no—
453C2×#121—1221no—
454C2×#121—1221no—
455C2×#121—1221no—
456C2×#121C2×D6111yescharacteristic
457C2×C4×Q8—611no—
458C2×C4×D4—611no—
459C2×C4×D4—611no—
460C2×C4×D4—1221no—
461C2×C4×D4—1221no—
462C2×#117—611no—
463C22×C4⋊C4—611no—
464#490—618no—
465#482—618no—
466#480—618no—
467#479—618no—
468#469—618no—
469#466—618no—
470#459—618no—
471#449—618no—
472#449C2×D6118yescomplemented
473#440—618no—
474#435—618no—
475C2×#107—611no—
476C2×#107—611no—
477C2×#106—611no—
478C2×C4⋊C8—611no—
479#417—618no—
480#416—618no—
481C2×#103—611no—
482C2×#103—611no—
483C2×#103C2×D6111yescharacteristic
484C2×#102—611no—
485C2×#102—611no—
486C2×#102—611no—
487C2×#102—611no—
488C2×#102—611no—
489C2×#102—611no—
490C2×#102C2×D6111yescharacteristic
491C2×C22⋊C8—611no—
492C2×C22⋊C8C2×D6111yescharacteristic
493C2×#97—611no—
494C61C2×#330911yescharacteristic, complemented, Sylow
495C2×#41—22no—
496C2×#41—24no—
497C2×#41—42no—
498C2×#41—614no—
499C2×#41—1222no—
500C2×#41—1224no—
501C2×#41—2442no—
502C2×#41C22×D6114yes—
503C22×Q8C22×D6111yescharacteristic
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—611no—
507C22×D4—611no—
508C22×D4—1221no—
509C22×D4—1221no—
510C22×D4—1221no—
511C22×D4—1221no—
512C22×D4—1221no—
513C22×D4—1221no—
514C22×D4C22×D6111yescharacteristic
515C22×D4C22×D6111yescharacteristic
516C23×C4—21no—
517C23×C4—611no—
518C23×C4—1221no—
519C23×C4—1221no—
520C23×C4—1221no—
521C23×C4C22×D6111yescharacteristic
522C2×SD16—24no—
523C2×SD16C22×D6114yes—
524C2×D8—42no—
525C2×D8—614no—
526C2×D8—2442no—
527C2×D8C22×D6114yes—
528C2×M16—614no—
529C2×M16—2442no—
530C22×C8—611no—
531C22×C8—611no—
532C22×C8—614no—
533C22×C8—2442no—
534C22×C8C22×D6111yescharacteristic
535C22×C8C22×D6111yescharacteristic
536#127—614no—
537#127—1222no—
538#127—1228no—
539#126—1228no—
540#125—614no—
541#125—1222no—
542#123—1228no—
543#121—22no—
544#121—614no—
545#121—614no—
546#121—614no—
547#121—1228no—
548#121—1228no—
549#121—1222no—
550#121—1222no—
551#121—1228no—
552#121—1222no—
553#121C22×D6114yes—
554C4×Q8—614no—
555C4×Q8—1222no—
556C4×D4—614no—
557C4×D4—614no—
558C4×D4—614no—
559C4×D4—1222no—
560C4×D4—1228no—
561C4×D4—1228no—
562#117—614no—
563#117—1222no—
564C2×C4⋊C4—611no—
565C2×C4⋊C4—611no—
566C2×C4⋊C4—611no—
567C2×C4⋊C4—614no—
568C2×C4⋊C4—611no—
569C2×C4⋊C4—1221no—
570C2×C4⋊C4—1221no—
571C2×C4⋊C4—1221no—
572C2×C4⋊C4—1221no—
573C2×C4⋊C4—1222no—
574C2×C4⋊C4C22×D6111yescharacteristic
575C2×C22⋊C4—21no—
576C2×C22⋊C4—611no—
577C2×C22⋊C4—611no—
578C2×C22⋊C4—1221no—
579C2×C22⋊C4—1221no—
580C2×C22⋊C4—1221no—
581C2×C22⋊C4—1221no—
582C2×C22⋊C4—1221no—
583C2×C42—611no—
584C2×C42—1221no—
585C2×C42—1221no—
586#107—614no—
587#107—614no—
588#106—614no—
589C4⋊C8—614no—
590#103—614no—
591#103—614no—
592#103C22×D6114yes—
593#102—614no—
594#102—614no—
595#102—614no—
596#102—614no—
597#102—614no—
598#102—614no—
599#102C22×D6114yes—
600C22⋊C8—614no—
601C22⋊C8C22×D6114yes—
602#97—614no—
603C24—21no—
604C24—21no—
605C24—611no—
606C24—1221no—
607C24D4×D6111yescharacteristic
608#41—28no—
609#41—44no—
610#41—48no—
611#41—1228no—
612#41—2444no—
613#41—2448no—
614C2×Q8—21no—
615C2×Q8—22no—
616C2×Q8#1175822414yes—
617C2×Q8C23×D6112yes—
618C2×D4—24no—
619C2×D4—24no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—22no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—22no—
626C2×D4—44no—
627C2×D4—44no—
628C2×D4—614no—
629C2×D4—612no—
630C2×D4—1224no—
631C2×D4—1224no—
632C2×D4—1224no—
633C2×D4—1224no—
634C2×D4—1224no—
635C2×D4—1224no—
636C2×D4—1221no—
637C2×D4—1222no—
638C2×D4—1222no—
639C2×D4—4882no—
640C2×D4—4882no—
641C2×D4—4882no—
642C2×D4—4882no—
643C2×D4—2444no—
644C2×D4—2442no—
645C2×D4—2444no—
646C2×D4C23×D6112yes—
647C2×D4C23×D6112yes—
648C22×C4—21no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—21no—
652C22×C4—24no—
653C22×C4—44no—
654C22×C4—611no—
655C22×C4—611no—
656C22×C4—611no—
657C22×C4—612no—
658C22×C4—612no—
659C22×C4—1224no—
660C22×C4—1224no—
661C22×C4—1222no—
662C22×C4—1222no—
663C22×C4—1224no—
664C22×C4—1221no—
665C22×C4—1221no—
666C22×C4—1221no—
667C22×C4—4882no—
668C22×C4—4882no—
669C22×C4—2444no—
670C22×C4D4×D6112yes—
671C22×C4D4×D6111yescharacteristic
672C22×C4C23×D6112yes—
673C22×C4C23×D6111yescharacteristic
674SD16—28no—
675D8—44no—
676D8—2444no—
677M16—2444no—
678C2×C8—22no—
679C2×C8—22no—
680C2×C8—612no—
681C2×C8—612no—
682C2×C8—1222no—
683C2×C8—1222no—
684C2×C8—2444no—
685C2×C8C23×D6112yes—
686C2×C8C23×D6112yes—
687C4⋊C4—21no—
688C4⋊C4—614no—
689C4⋊C4—612no—
690C4⋊C4—612no—
691C4⋊C4—612no—
692C4⋊C4—1224no—
693C4⋊C4—1224no—
694C4⋊C4—1224no—
695C4⋊C4—1221no—
696C4⋊C4—1221no—
697C4⋊C4—1224no—
698C4⋊C4—1221no—
699C4⋊C4C23×D6112yes—
700C22⋊C4—24no—
701C22⋊C4—614no—
702C22⋊C4—614no—
703C22⋊C4—1224no—
704C22⋊C4—1224no—
705C22⋊C4—1224no—
706C22⋊C4—1224no—
707C22⋊C4—1224no—
708C42—612no—
709C42—612no—
710C42—1224no—
711C42—1224no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—612no—
724C23—1222no—
725C23—1222no—
726C23—1222no—
727C23—1222no—
728C23—2442no—
729C23—2442no—
730C23—2442no—
731C23C2×D4×D6112yes—
732C23C2×D4×D6111yescharacteristic
733Q8—22no—
734Q8—24no—
735Q8C2×#1175822414yes—
736D4—22no—
737D4—22no—
738D4—22no—
739D4—22no—
740D4—48no—
741D4—48no—
742D4—42no—
743D4—42no—
744D4—1222no—
745D4—1222no—
746D4—4884no—
747D4—4884no—
748D4—4884no—
749D4—4884no—
750D4—2448no—
751D4—2444no—
752D4—2448no—
753D4—2442no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—24no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—24no—
760C2×C4—22no—
761C2×C4—48no—
762C2×C4—42no—
763C2×C4—612no—
764C2×C4—612no—
765C2×C4—612no—
766C2×C4—1222no—
767C2×C4—1222no—
768C2×C4—1222no—
769C2×C4—1222no—
770C2×C4—1222no—
771C2×C4—1224no—
772C2×C4—1222no—
773C2×C4—1222no—
774C2×C4—1222no—
775C2×C4—4884no—
776C2×C4—4884no—
777C2×C4—2448no—
778C2×C4—2442no—
779C2×C4—2442no—
780C2×C4—2442no—
781C2×C4C2×D4×D6112yes—
782C2×C4C2×D4×D6111yescharacteristic
783C2×C4C2×#1175822412yes—
784C2×C4#1451982212yes—
785C2×C4C24×D6111yescharacteristic
786C8—22no—
787C8—22no—
788C8—1222no—
789C8—1222no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—44no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—84no—
801C22—84no—
802C22—1222no—
803C22—1222no—
804C22—1222no—
805C22—4884no—
806C22—2442no—
807C22—2442no—
808C22—2442no—
809C22—2444no—
810C22#1684039912yes—
811C22#1684055812yes—
812C22#1684056412yes—
813C22C22×D4×D6111yescharacteristic
814C4—22no—
815C4—24no—
816C4—42no—
817C4—1222no—
818C4—1222no—
819C4—1222no—
820C4—2442no—
821C4—2442no—
822C4—2442no—
823C4#1684039912yes—
824C4C22×#1175822411yescharacteristic
825C4C2×#1451982211yescharacteristic
826C2—42no—
827C2—82no—
828C2—82no—
829C2—4882no—
830C2—2442no—
831C2#2145781814yesdirect product factor
832C2C2×#1684039911yescharacteristic
833C2C2×#1684055811yescharacteristic
834C2C2×#1684056411yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#449C2
socleC23×C61C22×D4
hypercenterC2×#449D61
hypocenterC61C2×#3309
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×#16840464C2semidirect
2. C2×#16840431C2semidirect
3. #21457818C2direct (N × H)
4. C2×#16840125C2semidirect
5. C2×#16840084C2semidirect
6. C2×#16840076C2semidirect
7. C2×#16840071C2semidirect
8. C2×#16840013C2semidirect
9. C2×#16839995C2semidirect
10. C2×#16839955C2semidirect
11. C2×#16839906C2semidirect
12. C2×#16839863C2semidirect
13. C2×#16839836C2semidirect
14. C2×#16839763C2semidirect
15. C2×#16839757C2semidirect
16. C2×C61×#449C2semidirect
22. #16840464C22semidirect
24. #16840431C22semidirect
43. #16840125C22semidirect
44. #16840084C22semidirect
45. #16840076C22semidirect
46. #16840071C22semidirect
47. #16840013C22semidirect
48. #16839995C22semidirect
49. #16839955C22semidirect
50. #16839906C22semidirect
51. #16839863C22semidirect
52. #16839836C22semidirect
57. #16839763C22semidirect
58. #16839757C22semidirect
73. C61×#449C22semidirect
420. C2×#449D61semidirect
428. C2×C61#3309semidirect
472. #449C2×D61semidirect
494. C61C2×#3309semidirect
831. C2#21457818direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404642
C2×#168404312
#214578182
C2×#168401252
C2×#168400842
C2×#168400762
C2×#168400712
C2×#168400132
C2×#168399952
C2×#168399552
C2×#168399062
C2×#168398632
C2×#168398362
C2×#168397632
C2×#168397572
C2×C61×#4492
C2×#330961