Finite Group Databasebeta

← C2×#21457981 #30556705

Subgroups — C2×#21457981 #30556705

Order 15616.

2318 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840476C211yesmaximal, characteristic, complemented
2C2×#16840409C211yesmaximal, characteristic, complemented
3#21457981C2116yesmaximal, direct product factor
4C2×#16840120C211yesmaximal, characteristic, complemented
5C2×#16840105C211yesmaximal, characteristic, complemented
6C2×#16840083C211yesmaximal, characteristic, complemented
7C2×#16840041C211yesmaximal, characteristic, complemented
8C2×#16840007C211yesmaximal, characteristic, complemented
9C2×#16839975C211yesmaximal, characteristic, complemented
10C2×#16839905C211yesmaximal, characteristic, complemented
11C2×#16839894C211yesmaximal, characteristic, complemented
12C2×#16839871C211yesmaximal, characteristic, complemented
13C2×#16839833C211yesmaximal, characteristic, complemented
14C2×#16839765C211yesmaximal, characteristic, complemented
15C2×#16839759C211yesmaximal, characteristic, complemented
16C2×C61×#466C211yesmaximal, characteristic, complemented
17C22×#11758222C2211yescharacteristic
18C22×D4×D61C2211yescharacteristic
19C22×#11758200C2211yescharacteristic, complemented
20C22×#11758199C2211yescharacteristic
21C22×#11758189C2211yescharacteristic
22#16840476—24no—
23#16840476C2218yescomplemented
24#16840409—24no—
25#16840409C2218yescomplemented
26C2×#14519776C2211yescharacteristic, complemented
27C2×#14519764—21no—
28C2×#14519764C2211yescharacteristic
29C2×#14519763—21no—
30C2×#14519759—21no—
31C2×#14519757C2211yescharacteristic
32C2×#14519749—21no—
33C2×#14519748—21no—
34C2×#14519748C2211yescharacteristic
35C2×#14519745—21no—
36C2×D4×Dic61C2211yescharacteristic, complemented
37C2×#14519739C2211yescharacteristic
38C2×C4×C22⋊D61C2211yescharacteristic
39C2×#14519736C2211yescharacteristic, complemented
40C2×#14519735C2211yescharacteristic
41C2×#14519733—21no—
42C2×C22⋊C4×D61—21no—
43#16840120C2218yescomplemented
44#16840105C2218yescomplemented
45#16840083C2218yescomplemented
46#16840041C2218yescomplemented
47#16840007C2218yescomplemented
48#16839975C2218yescomplemented
49#16839905C2218yescomplemented
50#16839894C2218yescomplemented
51#16839871C2218yescomplemented
52#16839833C2218yescomplemented
53C2×#14519710C2211yescharacteristic, complemented
54C2×#14519708C2211yescharacteristic, complemented
55C2×#14519706C2211yescharacteristic, complemented
56#16839765C2218yescomplemented
57#16839759C2218yescomplemented
58C2×#14519702C2211yescharacteristic, complemented
59C2×#14519702C2211yescharacteristic, complemented
60C2×#14519700C2211yescharacteristic, complemented
61C2×#14519699C2211yescharacteristic
62C2×#14519699C2211yescharacteristic
63C2×#14519698C2211yescharacteristic
64C2×#14519698C2211yescharacteristic
65C2×#14519697C2211yescharacteristic
66C2×C22⋊#92418C2211yescharacteristic, complemented
67C2×#14519689C2211yescharacteristic
68C2×#14519687C2211yescharacteristic, complemented
69C22×D8×C61C2211yescharacteristic
70C23×C8×C61C2211yescharacteristic, complemented
71C2×#121×C61C2211yescharacteristic
72C2×#121×C61C2211yescharacteristic, complemented
73C61×#466C2218yescomplemented
74C2×#107×C61C2211yescharacteristic, complemented
75C2×#102×C61C2211yescharacteristic
76C2×#102×C61C2211yescharacteristic, complemented
77C24×D61—21no—
78C2×#11758222—22no—
79C2×#11758222—24no—
80C2×#11758222—42no—
81C2×#11758222C2314yes—
82C22×Dic122—21no—
83C22×Dic122C2311yescharacteristic
84C22×D244C2311yescharacteristic
85C22×C22⋊D61—21no—
86C22×C22⋊D61—21no—
87C22×C22⋊D61—21no—
88C22×C22⋊D61D411yescharacteristic
89C2×D4×D61—24no—
90C2×D4×D61—22no—
91C2×D4×D61—42no—
92C2×D4×D61C2314yes—
93C23×Dic61—21no—
94C22×C4×D61—21no—
95C22×C4×D61—21no—
96C22×C4×D61C2311yescharacteristic
97C2×#11758200—42no—
98C2×#11758200C2314yescomplemented
99C2×#11758199—24no—
100C2×#11758199C2314yes—
101C2×#11758189—42no—
102C2×#11758189C2314yes—
103C22×#92418C2311yescharacteristic
104C22×#92418C2311yescharacteristic
105#14519776—22no—
106#14519776C2314yescomplemented
107#14519764—28no—
108#14519764—22no—
109#14519764C2314yes—
110#14519763—28no—
111#14519759—28no—
112#14519757—22no—
113#14519757C2314yes—
114#14519749—28no—
115#14519748—22no—
116#14519748—28no—
117#14519748C2314yes—
118#14519745—28no—
119D4×Dic61—22no—
120D4×Dic61C2314yescomplemented
121#14519739—22no—
122#14519739C2314yes—
123C4×C22⋊D61D414yes—
124C4×C22⋊D61C2314yes—
125#14519736—22no—
126#14519736C2314yescomplemented
127#14519735—22no—
128#14519735C2314yes—
129#14519733—28no—
130C2×C4⋊Dic61—21no—
131C2×C4⋊Dic61C2311yescharacteristic
132C2×C4⋊Dic61C2311yescharacteristic
133C2×#11758196—21no—
134C2×#11758196D411yescharacteristic
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×#11758198—21no—
143C2×#11758198—21no—
144C2×#11758198D411yescharacteristic
145C22⋊C4×D61—28no—
146C2×C4×Dic61—21no—
147C2×C4×Dic61—21no—
148C2×C4×Dic61C2311yescharacteristic
149#14519710C2314yescomplemented
150#14519708C2314yescomplemented
151#14519706C2314yescomplemented
152#14519702C2314yescomplemented
153#14519702C2314yescomplemented
154#14519700C2314yescomplemented
155#14519699C2314yes—
156#14519699C2314yes—
157#14519698C2314yes—
158#14519698C2314yes—
159#14519697C2314yes—
160C22⋊#92418C2314yescomplemented
161#14519689C2314yes—
162#14519687C2314yescomplemented
163C22×D4×C61—21no—
164C22×D4×C61—21no—
165C22×D4×C61C2311yescharacteristic
166C22×D4×C61C2311yescharacteristic
167C23×C4×C61C2311yescharacteristic
168C2×D8×C61—42no—
169C2×D8×C61C2314yes—
170C22×C8×C61—42no—
171C22×C8×C61C2311yescharacteristic
172C22×C8×C61C2311yescharacteristic
173C22×C8×C61C2314yescomplemented
174#121×C61—22no—
175#121×C61—22no—
176#121×C61C2314yes—
177#121×C61C2314yescomplemented
178C2×C4⋊C4×C61C2311yescharacteristic
179C2×C4⋊C4×C61C2311yescharacteristic
180C2×C22⋊C4×C61—21no—
181C2×C22⋊C4×C61—21no—
182#107×C61C2314yescomplemented
183#102×C61C2314yes—
184#102×C61C2314yescomplemented
185C24×C61—21no—
186C24×C61—21no—
187C24×C61C2×D411yescharacteristic
188C23×D61—21no—
189C23×D61—24no—
190C23×D61—44no—
191C23×D61—44no—
192C23×D61—82no—
193C23×D61C2×D411yescharacteristic
194C2×D4×C61—24no—
195C2×D4×C61—24no—
196C2×D4×C61—21no—
197C2×D4×C61—21no—
198C2×D4×C61—22no—
199C2×D4×C61—22no—
200C2×D4×C61—22no—
201C2×D4×C61—22no—
202C2×D4×C61—82no—
203C2×D4×C61—82no—
204C2×D4×C61C2412yes—
205C2×D4×C61C2412yes—
206C22×C4×C61—22no—
207C22×C4×C61—22no—
208C22×C4×C61—21no—
209C22×C4×C61—21no—
210C22×C4×C61C2×D411yescharacteristic
211C22×C4×C61C2×D412yes—
212C22×C4×C61C2412yes—
213C22×C4×C61C2411yescharacteristic
214C2×C22⋊D61—24no—
215C2×C22⋊D61—24no—
216C2×C22⋊D61—24no—
217C2×C22⋊D61—42no—
218C2×C22⋊D61—44no—
219C2×C22⋊D61—44no—
220C2×C22⋊D61—82no—
221C2×C22⋊D61C2×D414yes—
222C22×Dic61—21no—
223C22×Dic61—21no—
224C22×Dic61—21no—
225C22×Dic61—24no—
226C22×Dic61—44no—
227C22×Dic61C2×D411yescharacteristic
228C22×Dic61C2×D411yescharacteristic
229C22×Dic61C2×D411yescharacteristic
230D4×D61—28no—
231D4×D61—44no—
232D4×D61—48no—
233#11758222—28no—
234#11758222—44no—
235#11758222—48no—
236C2×D244—21no—
237C2×D244—22no—
238C2×D244#4114yes—
239C2×D244C2412yes—
240C2×C4×D61—22no—
241C2×C4×D61—22no—
242C2×C4×D61—24no—
243C2×C4×D61—24no—
244C2×C4×D61—44no—
245C2×C4×D61—82no—
246C2×C4×D61C2×D412yes—
247C2×C4×D61C2412yes—
248C2×Dic122—22no—
249C2×Dic122—22no—
250C2×Dic122—21no—
251C2×Dic122—24no—
252C2×Dic122—82no—
253C2×Dic122C2412yes—
254D8×C61—44no—
255C2×C8×C61—22no—
256C2×C8×C61—22no—
257C2×C8×C61—44no—
258C2×C8×C61C2412yes—
259C2×C8×C61C2412yes—
260C4⋊C4×C61—21no—
261C4⋊C4×C61—21no—
262C4⋊C4×C61C2412yes—
263C4⋊C4×C61C2412yes—
264C22⋊C4×C61—24no—
265C22⋊C4×C61—24no—
266C22⋊Dic61—24no—
267C22⋊Dic61—24no—
268C22⋊Dic61—24no—
269C22⋊Dic61—24no—
270C22⋊Dic61—24no—
271C22⋊Dic61C2×D414yes—
272#11758200—44no—
273#11758199—28no—
274#11758198—24no—
275#11758198—24no—
276#11758198—24no—
277#11758198C2×D414yes—
278C4⋊Dic61—21no—
279C4⋊Dic61—21no—
280C4⋊Dic61—24no—
281C4⋊Dic61C2412yes—
282C4⋊Dic61C2412yes—
283#11758196—24no—
284#11758196C2×D414yes—
285C4×Dic61—24no—
286C4×Dic61—24no—
287C4×Dic61C2×D412yes—
288C4×Dic61C2412yes—
289C2×#92418—22no—
290C2×#92418—22no—
291C2×#92418C2412yes—
292C2×#92418C2412yes—
293#11758189—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—24no—
309C22×D61—22no—
310C22×D61—22no—
311C22×D61—22no—
312C22×D61—48no—
313C22×D61—48no—
314C22×D61—42no—
315C22×D61—42no—
316C22×D61—84no—
317C22×D61—816no—
318C22×D61C22×D412yes—
319D4×C61—22no—
320D4×C61—22no—
321D4×C61—22no—
322D4×C61—22no—
323D4×C61—42no—
324D4×C61—42no—
325D4×C61—84no—
326D4×C61—84no—
327C2×C4×C61—22no—
328C2×C4×C61—24no—
329C2×C4×C61—22no—
330C2×C4×C61—22no—
331C2×C4×C61—22no—
332C2×C4×C61—22no—
333C2×C4×C61—42no—
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—48no—
343C22⋊D61—84no—
344C2×Dic61—22no—
345C2×Dic61—22no—
346C2×Dic61—22no—
347C2×Dic61—22no—
348C2×Dic61—22no—
349C2×Dic61—22no—
350C2×Dic61—48no—
351C2×Dic61—42no—
352C2×Dic61—42no—
353C2×Dic61—42no—
354C2×Dic61C22×D412yes—
355C2×Dic61C22×D412yes—
356C2×Dic61C22×D412yes—
357D244—24no—
358D244—22no—
359D244C2×#4114yes—
360C4×D61—24no—
361C4×D61—22no—
362C4×D61—22no—
363C4×D61—48no—
364C4×D61—84no—
365Dic122—22no—
366Dic122—22no—
367Dic122—42no—
368Dic122—84no—
369C8×C61—22no—
370C8×C61—22no—
371#92418—22no—
372#92418—22no—
373C2×#3319—611nomaximal, Sylow
374C22×C61—22no—
375C22×C61—22no—
376C22×C61—22no—
377C22×C61—44no—
378C22×C61—42no—
379C22×C61—42no—
380C22×C61—42no—
381C22×C61—42no—
382C22×C61—42no—
383C22×C61—42no—
384C22×C61—84no—
385C22×C61—84no—
386C22×C61#54612yes—
387C22×C61#57512yes—
388C22×C61#57612yes—
389C22×C61C23×D411yescharacteristic
390C2×D61—22no—
391C2×D61—24no—
392C2×D61—22no—
393C2×D61—22no—
394C2×D61—44no—
395C2×D61—48no—
396C2×D61—42no—
397C2×D61—42no—
398C2×D61—816no—
399C4×C61—22no—
400C4×C61—42no—
401C4×C61—42no—
402C4×C61#54612yes—
403C4×C61C22×#4111yescharacteristic
404C4×C61C2×H(5,𝔽2)11yescharacteristic
405Dic61—22no—
406Dic61—22no—
407Dic61—22no—
408Dic61—42no—
409Dic61—42no—
410Dic61—42no—
411C2×#555—611no—
412C2×#546—611no—
413#3319—6116no—
414C2×#489—611no—
415C2×#485—611no—
416C2×#482—611no—
417C2×#474—611no—
418C2×#468—611no—
419C2×#466D6111yescharacteristic, complemented
420C2×#463—611no—
421C2×#449—611no—
422C2×#447—611no—
423C2×#442—611no—
424C2×#435—611no—
425C2×#418—611no—
426C2×#416—611no—
427C2×C61—42no—
428C2×C61—82no—
429C2×C61—82no—
430C2×C61#331914yescomplemented
431C2×C61C2×#54611yescharacteristic
432C2×C61C2×#57511yescharacteristic
433C2×C61C2×#57611yescharacteristic
434D61—42no—
435D61—44no—
436C22×#41—611no—
437C23×D4—611no—
438C22×SD16—611no—
439C22×D8—611no—
440C22×D8C2×D6111yescharacteristic
441C22×M16—611no—
442C23×C8C2×D6111yescharacteristic, complemented
443#555—618no—
444#555—1224no—
445#546—618no—
446#546—1224no—
447C2×C4⋊Q8—611no—
448C2×#124—611no—
449C2×#124—1221no—
450C2×#124—1221no—
451C2×#123—1221no—
452C2×C22⋊Q8—611no—
453C2×#121—611no—
454C2×#121—1221no—
455C2×#121—1221no—
456C2×#121C2×D6111yescharacteristic
457C2×#121C2×D6111yescharacteristic, complemented
458C2×#120—1221no—
459C2×C4×D4—611no—
460C2×C4×D4—611no—
461C2×C4×D4—611no—
462C2×#117—611no—
463C2×#117—611no—
464C2×#117—1221no—
465C22×C22⋊C4—1221no—
466#489—618no—
467#485—618no—
468#482—618no—
469#474—618no—
470#468—618no—
471#466C2×D6118yescomplemented
472#463—618no—
473#449—618no—
474#447—618no—
475#442—618no—
476#435—618no—
477C2×#107—611no—
478C2×#107C2×D6111yescharacteristic, complemented
479C2×#106—611no—
480C2×C4⋊C8—611no—
481#418—618no—
482#416—618no—
483C2×#103—611no—
484C2×#103—611no—
485C2×#103—611no—
486C2×#102—611no—
487C2×#102—611no—
488C2×#102—611no—
489C2×#102—611no—
490C2×#102—611no—
491C2×#102C2×D6111yescharacteristic
492C2×#102C2×D6111yescharacteristic, complemented
493C2×C22⋊C8—611no—
494C2×C22⋊C8—611no—
495C2×#97—611no—
496C61C2×#331911yescharacteristic, complemented, Sylow
497C25—1221no—
498C2×#41—614no—
499C2×#41—1224no—
500C2×#41—1222no—
501C2×#41—2442no—
502C22×Q8—611no—
503C22×Q8—1221no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—611no—
507C22×D4—614no—
508C22×D4—611no—
509C22×D4—1222no—
510C22×D4—1221no—
511C22×D4—1224no—
512C22×D4—1221no—
513C22×D4—1221no—
514C22×D4—2442no—
515C22×D4C22×D6111yescharacteristic
516C22×D4C22×D6111yescharacteristic
517C23×C4—611no—
518C23×C4—1221no—
519C23×C4—1221no—
520C23×C4—1221no—
521C23×C4C22×D6111yescharacteristic
522C2×SD16—614no—
523C2×SD16—2442no—
524C2×D8—42no—
525C2×D8—614no—
526C2×D8—1224no—
527C2×D8C22×D6114yes—
528C2×M16—614no—
529C2×M16—2442no—
530C22×C8—42no—
531C22×C8—611no—
532C22×C8—611no—
533C22×C8C22×D6111yescharacteristic
534C22×C8C22×D6111yescharacteristic
535C22×C8C22×D6114yescomplemented
536C4⋊Q8—614no—
537C4⋊Q8—1222no—
538#124—614no—
539#124—1222no—
540#124—1228no—
541#124—1228no—
542#123—1228no—
543C22⋊Q8—614no—
544C22⋊Q8—1222no—
545#121—22no—
546#121—22no—
547#121—614no—
548#121—1228no—
549#121—1222no—
550#121—1228no—
551#121C22×D6114yes—
552#121C22×D6114yescomplemented
553#120—1228no—
554C4×D4—614no—
555C4×D4—614no—
556C4×D4—614no—
557C4×D4—614no—
558C4×D4—1222no—
559C4×D4—1222no—
560#117—614no—
561#117—614no—
562#117—1228no—
563#117—1222no—
564#117—1222no—
565C2×C4⋊C4—611no—
566C2×C4⋊C4—611no—
567C2×C4⋊C4—611no—
568C2×C4⋊C4—1221no—
569C2×C4⋊C4—1221no—
570C2×C4⋊C4C22×D6111yescharacteristic
571C2×C4⋊C4C22×D6111yescharacteristic
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—611no—
575C2×C22⋊C4—611no—
576C2×C22⋊C4—1228no—
577C2×C22⋊C4—1221no—
578C2×C22⋊C4—1221no—
579C2×C22⋊C4—1221no—
580C2×C22⋊C4—1221no—
581C2×C22⋊C4—1221no—
582C2×C22⋊C4—1221no—
583C2×C22⋊C4—1221no—
584C2×C22⋊C4—1221no—
585C2×C42—611no—
586C2×C42—1221no—
587C2×C42—1221no—
588#107—614no—
589#107C22×D6114yescomplemented
590#106—614no—
591C4⋊C8—614no—
592#103—614no—
593#103—614no—
594#103—614no—
595#102—614no—
596#102—614no—
597#102—614no—
598#102—614no—
599#102—614no—
600#102C22×D6114yes—
601#102C22×D6114yescomplemented
602C22⋊C8—614no—
603C22⋊C8—614no—
604#97—614no—
605C24—21no—
606C24—21no—
607C24—611no—
608C24—1224no—
609C24—1221no—
610C24—4882no—
611C24—2444no—
612C24—2444no—
613C24D4×D6111yescharacteristic
614#41—1228no—
615#41—2444no—
616#41—2448no—
617C2×Q8—612no—
618C2×Q8—1224no—
619C2×Q8—1221no—
620C2×Q8—1222no—
621C2×Q8—1222no—
622C2×Q8—4882no—
623C2×D4—24no—
624C2×D4—24no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—22no—
628C2×D4—22no—
629C2×D4—22no—
630C2×D4—22no—
631C2×D4—82no—
632C2×D4—82no—
633C2×D4—614no—
634C2×D4—614no—
635C2×D4—612no—
636C2×D4—1224no—
637C2×D4—1228no—
638C2×D4—1224no—
639C2×D4—1224no—
640C2×D4—1221no—
641C2×D4—1222no—
642C2×D4—4882no—
643C2×D4—2444no—
644C2×D4—2448no—
645C2×D4—2442no—
646C2×D4—2444no—
647C2×D4—2444no—
648C2×D4C23×D6112yes—
649C2×D4C23×D6112yes—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—21no—
653C22×C4—21no—
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—1221no—
664C22×C4—1221no—
665C22×C4—1221no—
666C22×C4—1224no—
667C22×C4—4882no—
668C22×C4—2444no—
669C22×C4—2444no—
670C22×C4D4×D6112yes—
671C22×C4D4×D6111yescharacteristic
672C22×C4C23×D6112yes—
673C22×C4C23×D6111yescharacteristic
674SD16—2444no—
675D8—44no—
676D8—1228no—
677M16—2444no—
678C2×C8—22no—
679C2×C8—22no—
680C2×C8—44no—
681C2×C8—612no—
682C2×C8—612no—
683C2×C8—1222no—
684C2×C8—1222no—
685C2×C8C23×D6112yes—
686C2×C8C23×D6112yes—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—614no—
690C4⋊C4—612no—
691C4⋊C4—612no—
692C4⋊C4—1224no—
693C4⋊C4—1224no—
694C4⋊C4—1221no—
695C4⋊C4—1221no—
696C4⋊C4C23×D6112yes—
697C4⋊C4C23×D6112yes—
698C22⋊C4—24no—
699C22⋊C4—24no—
700C22⋊C4—614no—
701C22⋊C4—614no—
702C22⋊C4—1224no—
703C22⋊C4—1224no—
704C22⋊C4—1224no—
705C22⋊C4—1224no—
706C22⋊C4—1224no—
707C22⋊C4—1224no—
708C22⋊C4—1224no—
709C22⋊C4—1224no—
710C42—612no—
711C42—612no—
712C42—1224no—
713C42—1224no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—612no—
726C23—1222no—
727C23—1222no—
728C23—1222no—
729C23—1222no—
730C23—1224no—
731C23—4884no—
732C23—48816no—
733C23—2448no—
734C23—2448no—
735C23—2442no—
736C23—2442no—
737C23C2×D4×D6112yes—
738C23C2×D4×D6111yescharacteristic
739Q8—1222no—
740Q8—1222no—
741Q8—4884no—
742Q8—2442no—
743D4—22no—
744D4—22no—
745D4—22no—
746D4—22no—
747D4—42no—
748D4—42no—
749D4—84no—
750D4—84no—
751D4—614no—
752D4—1222no—
753D4—1224no—
754D4—4884no—
755D4—2444no—
756D4—2448no—
757D4—2448no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—24no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—612no—
767C2×C4—612no—
768C2×C4—612no—
769C2×C4—1222no—
770C2×C4—1222no—
771C2×C4—1222no—
772C2×C4—1222no—
773C2×C4—1222no—
774C2×C4—1224no—
775C2×C4—1222no—
776C2×C4—1222no—
777C2×C4—1222no—
778C2×C4—4884no—
779C2×C4—2448no—
780C2×C4—2448no—
781C2×C4—2442no—
782C2×C4—2442no—
783C2×C4—2442no—
784C2×C4C2×D4×D6112yes—
785C2×C4C2×D4×D6111yescharacteristic
786C2×C4#41×D6112yes—
787C2×C4#1451982212yes—
788C2×C4C24×D6111yescharacteristic
789C8—22no—
790C8—22no—
791C8—1222no—
792C8—1222no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—44no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—42no—
802C22—42no—
803C22—84no—
804C22—84no—
805C22—1222no—
806C22—1224no—
807C22—1222no—
808C22—1222no—
809C22—48816no—
810C22—2444no—
811C22—2448no—
812C22—2442no—
813C22—2442no—
814C22#1684040112yes—
815C22#1684055912yes—
816C22#1684056312yes—
817C22C22×D4×D6111yescharacteristic
818C4—22no—
819C4—42no—
820C4—42no—
821C4—1222no—
822C4—1222no—
823C4—1222no—
824C4—2442no—
825C4—2442no—
826C4—2442no—
827C4#1684040112yes—
828C4C2×#41×D6111yescharacteristic
829C4C2×#1451982211yescharacteristic
830C2—42no—
831C2—82no—
832C2—82no—
833C2—2442no—
834C2—2444no—
835C2#2145798114yesdirect product factor
836C2C2×#1684040111yescharacteristic
837C2C2×#1684055911yescharacteristic
838C2C2×#1684056311yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#466C2
socleC23×C61C22×D4
hypercenterC2×#466D61
hypocenterC61C2×#3319
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#466

Complements

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

NH ≅ G/Ntype
1. C2×#16840476C2semidirect
2. C2×#16840409C2semidirect
3. #21457981C2direct (N × H)
4. C2×#16840120C2semidirect
5. C2×#16840105C2semidirect
6. C2×#16840083C2semidirect
7. C2×#16840041C2semidirect
8. C2×#16840007C2semidirect
9. C2×#16839975C2semidirect
10. C2×#16839905C2semidirect
11. C2×#16839894C2semidirect
12. C2×#16839871C2semidirect
13. C2×#16839833C2semidirect
14. C2×#16839765C2semidirect
15. C2×#16839759C2semidirect
16. C2×C61×#466C2semidirect
19. C22×#11758200C22semidirect
23. #16840476C22semidirect
25. #16840409C22semidirect
26. C2×#14519776C22semidirect
36. C2×D4×Dic61C22semidirect
39. C2×#14519736C22semidirect
43. #16840120C22semidirect
44. #16840105C22semidirect
45. #16840083C22semidirect
46. #16840041C22semidirect
47. #16840007C22semidirect
48. #16839975C22semidirect
49. #16839905C22semidirect
50. #16839894C22semidirect
51. #16839871C22semidirect
52. #16839833C22semidirect
53. C2×#14519710C22semidirect
54. C2×#14519708C22semidirect
55. C2×#14519706C22semidirect
56. #16839765C22semidirect
57. #16839759C22semidirect
58. C2×#14519702C22semidirect
59. C2×#14519702C22semidirect
60. C2×#14519700C22semidirect
66. C2×C22⋊#92418C22semidirect
68. C2×#14519687C22semidirect
70. C23×C8×C61C22semidirect
72. C2×#121×C61C22semidirect
73. C61×#466C22semidirect
74. C2×#107×C61C22semidirect
76. C2×#102×C61C22semidirect
98. C2×#11758200C23semidirect
106. #14519776C23semidirect
120. D4×Dic61C23semidirect
126. #14519736C23semidirect
149. #14519710C23semidirect
150. #14519708C23semidirect
151. #14519706C23semidirect
152. #14519702C23semidirect
153. #14519702C23semidirect
154. #14519700C23semidirect
160. C22⋊#92418C23semidirect
162. #14519687C23semidirect
173. C22×C8×C61C23semidirect
177. #121×C61C23semidirect
182. #107×C61C23semidirect
184. #102×C61C23semidirect
419. C2×#466D61semidirect
430. C2×C61#3319semidirect
442. C23×C8C2×D61semidirect
457. C2×#121C2×D61semidirect
471. #466C2×D61semidirect
478. C2×#107C2×D61semidirect
492. C2×#102C2×D61semidirect
496. C61C2×#3319semidirect
535. C22×C8C22×D61semidirect
552. #121C22×D61semidirect
589. #107C22×D61semidirect
601. #102C22×D61semidirect
835. C2#21457981direct (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×#168404092
#214579812
C2×#168401202
C2×#168401052
C2×#168400832
C2×#168400412
C2×#168400072
C2×#168399752
C2×#168399052
C2×#168398942
C2×#168398712
C2×#168398332
C2×#168397652
C2×#168397592
C2×C61×#4662
C2×#331961