Finite Group Databasebeta

← C2×#21455776 #30547839

Subgroups — C2×#21455776 #30547839

Order 15616.

2362 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840328C211yesmaximal, characteristic
2C2×#16840243C211yesmaximal, characteristic, complemented
3#21455776C2116yesmaximal, direct product factor
4C2×#16840082C211yesmaximal, characteristic, complemented
5C2×#16840088C211yesmaximal, characteristic, complemented
6C2×#16840087C211yesmaximal, characteristic, complemented
7C2×#16840085C211yesmaximal, characteristic, complemented
8C2×#16840083C211yesmaximal, characteristic, complemented
9C2×#16840075C211yesmaximal, characteristic, complemented
10C2×#16840074C211yesmaximal, characteristic, complemented
11C2×#16839801C211yesmaximal, characteristic, complemented
12C2×#16839797C211yesmaximal, characteristic, complemented
13C2×#16839765C211yesmaximal, characteristic, complemented
14C2×#102×D61C211yesmaximal, characteristic, complemented
15C2×#16839727C211yesmaximal, characteristic, complemented
16C2×C61×#481C211yesmaximal, characteristic, complemented
17C22×#11758222C2211yescharacteristic
18C22×D4×D61C2211yescharacteristic
19C22×#11758189C2211yescharacteristic
20C22×C8×D61C2211yescharacteristic
21#16840328—24no—
22#16840328C2218yes—
23C2×#14519773—21no—
24C2×#14519763—21no—
25C2×#14519752C2211yescharacteristic
26C2×#14519751C2211yescharacteristic
27C2×#14519748C2211yescharacteristic
28C2×#14519747—21no—
29C2×#14519745—21no—
30#16840243—24no—
31#16840243C2218yescomplemented
32C2×#14519742—21no—
33C2×#14519739—21no—
34C2×C4×C22⋊D61—21no—
35C2×C4×C22⋊D61—21no—
36C2×#14519736C2211yescharacteristic, complemented
37C2×#14519735C2211yescharacteristic
38C2×#14519735C2211yescharacteristic
39C2×#14519735C2211yescharacteristic, complemented
40C2×C4⋊C4×D61C2211yescharacteristic
41C2×C4⋊C4×D61C2211yescharacteristic, complemented
42#16840088C2218yescomplemented
43#16840087C2218yescomplemented
44#16840085C2218yescomplemented
45#16840083C2218yescomplemented
46#16840082C2218yescomplemented
47#16840075C2218yescomplemented
48#16840074C2218yescomplemented
49#16839801C2218yescomplemented
50#16839797C2218yescomplemented
51C2×#14519711C2211yescharacteristic, complemented
52C2×#14519710C2211yescharacteristic, complemented
53C2×#14519710C2211yescharacteristic, complemented
54C2×#14519710C2211yescharacteristic, complemented
55C2×#14519709C2211yescharacteristic, complemented
56C2×#14519708C2211yescharacteristic, complemented
57#16839765C2218yescomplemented
58C2×#14519699C2211yescharacteristic
59C2×#14519699C2211yescharacteristic
60C2×#14519698C2211yescharacteristic
61C2×#14519698C2211yescharacteristic
62C2×#14519697C2211yescharacteristic
63C2×#14519697C2211yescharacteristic
64#102×D61C2218yescomplemented
65#16839727C2218yescomplemented
66C2×C22⋊#92418C2211yescharacteristic, complemented
67C2×#14519689C2211yescharacteristic, complemented
68C2×#14519689C2211yescharacteristic, complemented
69C2×#121×C61C2211yescharacteristic
70C22×C4⋊C4×C61C2211yescharacteristic, complemented
71C61×#481C2218yescomplemented
72C2×#106×C61C2211yescharacteristic, complemented
73C2×#106×C61C2211yescharacteristic, complemented
74C2×#102×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×C22⋊C8×C61C2211yescharacteristic, complemented
77C24×D61—21no—
78C2×#11758222—24no—
79C2×#11758222—24no—
80C2×#11758222D414yes—
81C2×#11758222C2314yes—
82C22×Dic122D411yescharacteristic
83C22×D244—21no—
84C22×D244D411yescharacteristic
85C22×D244C2311yescharacteristic
86C22×C22⋊D61—21no—
87C22×C22⋊D61—21no—
88C22×C22⋊D61—21no—
89C22×C22⋊D61D411yescharacteristic
90C22×C22⋊D61D411yescharacteristic
91C2×D4×D61—22no—
92C2×D4×D61—24no—
93C2×D4×D61—24no—
94C2×D4×D61C2314yes—
95C22×C4×D61—21no—
96C22×C4×D61—21no—
97C22×C4×D61C2311yescharacteristic
98C22×C4×D61C2311yescharacteristic
99C2×#11758189—24no—
100C2×#11758189C2314yes—
101C22×#92418C2311yescharacteristic
102C22×#92418C2311yescharacteristic
103C2×C8×D61—24no—
104C2×C8×D61C2314yes—
105#14519773—28no—
106#14519763—28no—
107#14519752—22no—
108#14519752C2314yes—
109#14519751—22no—
110#14519751C2314yes—
111#14519748—22no—
112#14519748C2314yes—
113#14519747—28no—
114#14519745—28no—
115#14519742—28no—
116#14519739—28no—
117C4×C22⋊D61—28no—
118C4×C22⋊D61—28no—
119#14519736—22no—
120#14519736C2314yescomplemented
121#14519735—22no—
122#14519735—22no—
123#14519735—22no—
124#14519735C2314yes—
125#14519735C2314yes—
126#14519735C2314yescomplemented
127C2×C4⋊Dic61C2311yescharacteristic
128C2×C4⋊Dic61C2311yescharacteristic
129C2×C4⋊Dic61C2311yescharacteristic
130C2×#11758196—21no—
131C2×#11758196—21no—
132C4⋊C4×D61—22no—
133C4⋊C4×D61—22no—
134C4⋊C4×D61C2314yes—
135C4⋊C4×D61C2314yescomplemented
136C2×C22⋊Dic61—21no—
137C2×C22⋊Dic61—21no—
138C2×#11758198—21no—
139C2×#11758198—21no—
140C2×#11758198—21no—
141C2×#11758198—21no—
142C2×#11758198—21no—
143C2×C4×Dic61—21no—
144C2×C4×Dic61—21no—
145C2×C4×Dic61—21no—
146C2×C4×Dic61—21no—
147#14519711C2314yescomplemented
148#14519710C2314yescomplemented
149#14519710C2314yescomplemented
150#14519710C2314yescomplemented
151#14519709C2314yescomplemented
152#14519708C2314yescomplemented
153#14519699C2314yes—
154#14519699C2314yes—
155#14519698C2314yes—
156#14519698C2314yes—
157#14519697C2314yes—
158#14519697C2314yes—
159C22⋊#92418C2314yescomplemented
160#14519689C2314yescomplemented
161#14519689C2314yescomplemented
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×C61C2314yescomplemented
176C2×C22⋊C4×C61—21no—
177#106×C61C2314yescomplemented
178#106×C61C2314yescomplemented
179#102×C61C2314yes—
180#102×C61C2314yes—
181C22⋊C8×C61C2314yescomplemented
182C24×C61—21no—
183C24×C61C2×D411yescharacteristic
184C23×D61—21no—
185C23×D61—24no—
186C23×D61—44no—
187C23×D61—82no—
188C23×D61—82no—
189C23×D61C2×D411yescharacteristic
190C23×D61C2×D411yescharacteristic
191C2×D4×C61—24no—
192C2×D4×C61—21no—
193C2×D4×C61—22no—
194C2×D4×C61—22no—
195C2×D4×C61—82no—
196C2×D4×C61C2412yes—
197C22×C4×C61—22no—
198C22×C4×C61—22no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—24no—
203C22×C4×C61—82no—
204C22×C4×C61C2×D411yescharacteristic
205C22×C4×C61C2×D412yes—
206C22×C4×C61C2412yes—
207C22×C4×C61C2411yescharacteristic
208C2×C22⋊D61—24no—
209C2×C22⋊D61—24no—
210C2×C22⋊D61—24no—
211C2×C22⋊D61—24no—
212C2×C22⋊D61—24no—
213C2×C22⋊D61—44no—
214C2×C22⋊D61—82no—
215C2×C22⋊D61—82no—
216C2×C22⋊D61C2×D414yes—
217C2×C22⋊D61C2×D414yes—
218C22×Dic61—21no—
219C22×Dic61—21no—
220C22×Dic61—21no—
221C22×Dic61C2×D411yescharacteristic
222C22×Dic61C2×D411yescharacteristic
223D4×D61—28no—
224D4×D61—28no—
225D4×D61—48no—
226#11758222—216no—
227#11758222—28no—
228#11758222—28no—
229C2×D244—24no—
230C2×D244—22no—
231C2×D244—22no—
232C2×D244—21no—
233C2×D244—24no—
234C2×D244—82no—
235C2×D244C2×D414yes—
236C2×D244C2412yes—
237C2×C4×D61—22no—
238C2×C4×D61—22no—
239C2×C4×D61—24no—
240C2×C4×D61—24no—
241C2×C4×D61—82no—
242C2×C4×D61—82no—
243C2×C4×D61C2×D412yes—
244C2×C4×D61C2×D412yes—
245C2×C4×D61#4114yes—
246C2×C4×D61#4114yes—
247C2×C4×D61C2412yes—
248C2×C4×D61C2412yes—
249C2×Dic122—24no—
250C2×Dic122C2×D414yes—
251C2×C8×C61—22no—
252C2×C8×C61—22no—
253C2×C8×C61C2412yes—
254C2×C8×C61C2412yes—
255C4⋊C4×C61—21no—
256C4⋊C4×C61—21no—
257C4⋊C4×C61—24no—
258C4⋊C4×C61—21no—
259C4⋊C4×C61C2412yes—
260C4⋊C4×C61C2412yes—
261C4⋊C4×C61C2412yes—
262C22⋊C4×C61—24no—
263C22⋊Dic61—24no—
264C22⋊Dic61—24no—
265#11758198—24no—
266#11758198—24no—
267#11758198—24no—
268#11758198—24no—
269#11758198—24no—
270C4⋊Dic61—21no—
271C4⋊Dic61—21no—
272C4⋊Dic61—21no—
273C4⋊Dic61C2412yes—
274C4⋊Dic61C2412yes—
275C4⋊Dic61C2412yes—
276#11758196—24no—
277#11758196—24no—
278C4×Dic61—24no—
279C4×Dic61—24no—
280C4×Dic61—24no—
281C4×Dic61—24no—
282C2×#92418—22no—
283C2×#92418—22no—
284C2×#92418C2412yes—
285C2×#92418C2412yes—
286#11758189—28no—
287C8×D61—28no—
288C23×C61—22no—
289C23×C61—22no—
290C23×C61—22no—
291C23×C61—22no—
292C23×C61—42no—
293C23×C61—42no—
294C23×C61—42no—
295C23×C61C22×D412yes—
296C23×C61C22×D411yescharacteristic
297C22×D61—22no—
298C22×D61—22no—
299C22×D61—22no—
300C22×D61—22no—
301C22×D61—22no—
302C22×D61—22no—
303C22×D61—42no—
304C22×D61—42no—
305C22×D61—42no—
306C22×D61—48no—
307C22×D61—84no—
308C22×D61—84no—
309C22×D61—816no—
310C22×D61#12314yes—
311C22×D61C22×D412yes—
312C22×D61C22×D412yes—
313D4×C61—22no—
314D4×C61—22no—
315D4×C61—42no—
316D4×C61—84no—
317C2×C4×C61—22no—
318C2×C4×C61—24no—
319C2×C4×C61—22no—
320C2×C4×C61—22no—
321C2×C4×C61—22no—
322C2×C4×C61—22no—
323C2×C4×C61—22no—
324C2×C4×C61—42no—
325C2×C4×C61—42no—
326C2×C4×C61—42no—
327C2×C4×C61—84no—
328C2×C4×C61C22×D412yes—
329C2×C4×C61C22×D411yescharacteristic
330C2×C4×C61C2×#4112yes—
331C2×C4×C61C2×#4112yes—
332C2×C4×C61C2511yescharacteristic
333C22⋊D61—28no—
334C22⋊D61—28no—
335C22⋊D61—48no—
336C22⋊D61—84no—
337C22⋊D61—84no—
338C2×Dic61—22no—
339C2×Dic61—22no—
340C2×Dic61—22no—
341C2×Dic61—22no—
342C2×Dic61—42no—
343C2×Dic61—42no—
344C2×Dic61—42no—
345C2×Dic61#12314yes—
346C2×Dic61C22×D412yes—
347C2×Dic61C22×D412yes—
348D244—28no—
349D244—22no—
350D244—22no—
351D244—42no—
352D244—84no—
353C4×D61—24no—
354C4×D61—22no—
355C4×D61—22no—
356C4×D61—84no—
357C4×D61—84no—
358C4×D61#12318yes—
359C4×D61C2×#4114yes—
360C4×D61C2×#4114yes—
361Dic122—28no—
362C8×C61—22no—
363C8×C61—22no—
364#92418—22no—
365#92418—22no—
366C2×#3096—611nomaximal, Sylow
367C22×C61—22no—
368C22×C61—22no—
369C22×C61—22no—
370C22×C61—44no—
371C22×C61—42no—
372C22×C61—42no—
373C22×C61—42no—
374C22×C61—84no—
375C22×C61C2×#12312yes—
376C22×C61#57612yes—
377C22×C61#57712yes—
378C22×C61C23×D411yescharacteristic
379C2×D61—28no—
380C2×D61—22no—
381C2×D61—22no—
382C2×D61—22no—
383C2×D61—22no—
384C2×D61—22no—
385C2×D61—44no—
386C2×D61—42no—
387C2×D61—42no—
388C2×D61—42no—
389C2×D61—816no—
390C2×D61—84no—
391C2×D61C2×#12314yes—
392C4×C61—22no—
393C4×C61—42no—
394C4×C61—42no—
395C4×C61—42no—
396C4×C61C2×#12312yes—
397C4×C61C22×#4111yescharacteristic
398C4×C61C22×#4111yescharacteristic
399Dic61—22no—
400Dic61—42no—
401Dic61—42no—
402Dic61—42no—
403Dic61C2×#12314yes—
404C2×#535—611no—
405C2×#520—611no—
406#3096—6116no—
407C2×#481—611no—
408C2×#481D6111yescharacteristic, complemented
409C2×#482—611no—
410C2×#482—611no—
411C2×#482—611no—
412C2×#482—611no—
413C2×#480—611no—
414C2×#480—611no—
415C2×#428—611no—
416C2×#427—611no—
417C2×#418—611no—
418C22×#102—611no—
419C2×#408—611no—
420C2×C61—42no—
421C2×C61—82no—
422C2×C61#309614yescomplemented
423C2×C61C22×#12311yescharacteristic
424C2×C61C2×#57611yescharacteristic
425C2×C61C2×#57711yescharacteristic
426D61—24no—
427D61—42no—
428D61—82no—
429C22×#41—611no—
430C23×D4—611no—
431C22×M16—611no—
432C23×C8—611no—
433#535—618no—
434#535—1224no—
435C2×#127—1221no—
436C2×#124—1221no—
437C2×#121—611no—
438C2×#121—611no—
439C2×#121—611no—
440C2×#121C2×D6111yescharacteristic
441C2×#120—1221no—
442C2×#120—1221no—
443#520—618no—
444#520—1224no—
445C2×C4×Q8—1221no—
446C2×C4×D4—1221no—
447C2×C4×D4—1221no—
448C2×C4×D4—1221no—
449C2×#117—611no—
450C2×#117—611no—
451C2×#117—611no—
452C2×#117—611no—
453C22×C4⋊C4—611no—
454C22×C4⋊C4—611no—
455C22×C4⋊C4C2×D6111yescharacteristic, complemented
456#482—618no—
457#482—618no—
458#482—618no—
459#482—618no—
460#481—618no—
461#481C2×D6118yescomplemented
462#480—618no—
463#480—618no—
464#428—618no—
465#427—618no—
466C2×#107—611no—
467C2×#107—611no—
468C2×#107—611no—
469C2×#107—611no—
470C2×#106—611no—
471C2×#106—611no—
472C2×#106C2×D6111yescharacteristic, complemented
473C2×#106C2×D6111yescharacteristic, complemented
474#418—618no—
475C2×#102—611no—
476C2×#102—611no—
477C2×#102—611no—
478C2×#102—611no—
479C2×#102—611no—
480C2×#102—611no—
481C2×#102—618no—
482C2×#102C2×D6111yescharacteristic
483C2×#102C2×D6111yescharacteristic
484#408—618no—
485C2×C22⋊C8—611no—
486C2×C22⋊C8—611no—
487C2×C22⋊C8—611no—
488C2×C22⋊C8C2×D6111yescharacteristic, complemented
489C61C2×#309611yescharacteristic, complemented, Sylow
490C25—1221no—
491C2×#41—614no—
492C2×#41—614no—
493C2×#41—1224no—
494C2×#41—1224no—
495C22×Q8—611no—
496C22×D4—21no—
497C22×D4—611no—
498C22×D4—611no—
499C22×D4—614no—
500C22×D4—611no—
501C22×D4—611no—
502C22×D4—1221no—
503C22×D4—1224no—
504C22×D4—1224no—
505C22×D4—1222no—
506C22×D4—1221no—
507C22×D4—1221no—
508C22×D4—1221no—
509C22×D4C22×D6111yescharacteristic
510C23×C4—21no—
511C23×C4—611no—
512C23×C4—611no—
513C23×C4—1221no—
514C23×C4—1221no—
515C23×C4C22×D6111yescharacteristic
516C2×M16—614no—
517C2×M16—1224no—
518C22×C8—611no—
519C22×C8—611no—
520C22×C8—614no—
521C22×C8—1224no—
522C22×C8C22×D6111yescharacteristic
523C22×C8C22×D6111yescharacteristic
524#127—1228no—
525#124—1228no—
526#121—22no—
527#121—614no—
528#121—614no—
529#121—614no—
530#121—1222no—
531#121—1222no—
532#121—1222no—
533#121C22×D6114yes—
534#120—1228no—
535#120—1228no—
536C4×Q8—1228no—
537C4×D4—1228no—
538C4×D4—1228no—
539C4×D4—1228no—
540#117—614no—
541#117—614no—
542#117—614no—
543#117—614no—
544#117—1222no—
545#117—1222no—
546#117—1222no—
547#117—1222no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—22no—
550C2×C4⋊C4—611no—
551C2×C4⋊C4—611no—
552C2×C4⋊C4—611no—
553C2×C4⋊C4—614no—
554C2×C4⋊C4—614no—
555C2×C4⋊C4—1222no—
556C2×C4⋊C4—1222no—
557C2×C4⋊C4—1221no—
558C2×C4⋊C4—1221no—
559C2×C4⋊C4C22×D6111yescharacteristic
560C2×C4⋊C4C22×D6111yescharacteristic
561C2×C4⋊C4C22×D6111yescharacteristic
562C2×C4⋊C4C22×D6114yescomplemented
563C2×C22⋊C4—21no—
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×C22⋊C4—1221no—
571C2×C42—1221no—
572C2×C42—1221no—
573C2×C42—1221no—
574C2×C42—1221no—
575#107—614no—
576#107—614no—
577#107—614no—
578#107—614no—
579#106—614no—
580#106—614no—
581#106C22×D6114yescomplemented
582#106C22×D6114yescomplemented
583#102—614no—
584#102—614no—
585#102—614no—
586#102—614no—
587#102—614no—
588#102—614no—
589#102C22×D6114yes—
590#102C22×D6114yes—
591C22⋊C8—614no—
592C22⋊C8—614no—
593C22⋊C8—614no—
594C22⋊C8C22×D6114yescomplemented
595C24—21no—
596C24—611no—
597C24—611no—
598C24—1224no—
599C24—1221no—
600C24—4882no—
601C24—4882no—
602C24—2444no—
603C24D4×D6111yescharacteristic
604#41—12216no—
605#41—1228no—
606#41—1228no—
607C2×Q8—614no—
608C2×Q8—1224no—
609C2×D4—24no—
610C2×D4—21no—
611C2×D4—22no—
612C2×D4—22no—
613C2×D4—82no—
614C2×D4—614no—
615C2×D4—614no—
616C2×D4—614no—
617C2×D4—612no—
618C2×D4—1224no—
619C2×D4—1224no—
620C2×D4—1228no—
621C2×D4—1228no—
622C2×D4—1224no—
623C2×D4—1224no—
624C2×D4—1224no—
625C2×D4—1224no—
626C2×D4—1224no—
627C2×D4—1221no—
628C2×D4—1222no—
629C2×D4—1222no—
630C2×D4—4882no—
631C2×D4—4882no—
632C2×D4—4882no—
633C2×D4—2448no—
634C2×D4—2444no—
635C2×D4C23×D6112yes—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—24no—
642C22×C4—82no—
643C22×C4—611no—
644C22×C4—612no—
645C22×C4—614no—
646C22×C4—614no—
647C22×C4—612no—
648C22×C4—611no—
649C22×C4—612no—
650C22×C4—612no—
651C22×C4—1224no—
652C22×C4—1224no—
653C22×C4—1222no—
654C22×C4—1222no—
655C22×C4—1221no—
656C22×C4—1221no—
657C22×C4—1221no—
658C22×C4—4882no—
659C22×C4—4882no—
660C22×C4D4×D6112yes—
661C22×C4D4×D6111yescharacteristic
662C22×C4C23×D6112yes—
663C22×C4C23×D6111yescharacteristic
664M16—1228no—
665C2×C8—22no—
666C2×C8—22no—
667C2×C8—612no—
668C2×C8—612no—
669C2×C8—1228no—
670C2×C8—1222no—
671C2×C8—1222no—
672C2×C8C23×D6112yes—
673C2×C8C23×D6112yes—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—24no—
677C4⋊C4—21no—
678C4⋊C4—612no—
679C4⋊C4—612no—
680C4⋊C4—612no—
681C4⋊C4—1224no—
682C4⋊C4—1224no—
683C4⋊C4—1221no—
684C4⋊C4—1221no—
685C4⋊C4—1221no—
686C4⋊C4C23×D6112yes—
687C4⋊C4C23×D6112yes—
688C4⋊C4C23×D6112yes—
689C22⋊C4—24no—
690C22⋊C4—1224no—
691C22⋊C4—1224no—
692C22⋊C4—1224no—
693C22⋊C4—1224no—
694C22⋊C4—1224no—
695C22⋊C4—1224no—
696C22⋊C4—1224no—
697C42—1224no—
698C42—1224no—
699C42—1224no—
700C42—1224no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—614no—
709C23—612no—
710C23—612no—
711C23—1222no—
712C23—1222no—
713C23—1222no—
714C23—1222no—
715C23—1222no—
716C23—1222no—
717C23—4884no—
718C23—4884no—
719C23—48816no—
720C23—2448no—
721C23—2442no—
722C23—2442no—
723C23—2442no—
724C23C2×D4×D6112yes—
725C23C2×D4×D6111yescharacteristic
726Q8—1228no—
727D4—22no—
728D4—22no—
729D4—42no—
730D4—84no—
731D4—1228no—
732D4—1228no—
733D4—1228no—
734D4—1222no—
735D4—1222no—
736D4—4884no—
737D4—4884no—
738D4—4884no—
739D4—2448no—
740D4—2442no—
741C2×C4—22no—
742C2×C4—24no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—84no—
752C2×C4—614no—
753C2×C4—612no—
754C2×C4—618no—
755C2×C4—614no—
756C2×C4—614no—
757C2×C4—612no—
758C2×C4—1222no—
759C2×C4—1224no—
760C2×C4—1222no—
761C2×C4—1222no—
762C2×C4—1222no—
763C2×C4—1222no—
764C2×C4—1222no—
765C2×C4—4884no—
766C2×C4—4884no—
767C2×C4—2442no—
768C2×C4—2442no—
769C2×C4—2442no—
770C2×C4C2×D4×D6112yes—
771C2×C4C2×D4×D6111yescharacteristic
772C2×C4#41×D6112yes—
773C2×C4#41×D6112yes—
774C2×C4C24×D6111yescharacteristic
775C8—22no—
776C8—22no—
777C8—1222no—
778C8—1222no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—44no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—84no—
787C22—614no—
788C22—1222no—
789C22—1222no—
790C22—1228no—
791C22—1222no—
792C22—1222no—
793C22—1222no—
794C22—48816no—
795C22—4884no—
796C22—2442no—
797C22—2442no—
798C22—2442no—
799C22—2444no—
800C22#123×D6112yes—
801C22#1684056612yes—
802C22#1684056812yes—
803C22C22×D4×D6111yescharacteristic
804C4—22no—
805C4—42no—
806C4—42no—
807C4—42no—
808C4—614no—
809C4—1222no—
810C4—2442no—
811C4—2442no—
812C4—2442no—
813C4#123×D6112yes—
814C4C2×#41×D6111yescharacteristic
815C4C2×#41×D6111yescharacteristic
816C2—42no—
817C2—82no—
818C2—1224no—
819C2—4882no—
820C2—2442no—
821C2#2145577614yesdirect product factor
822C2C2×#123×D6111yescharacteristic
823C2C2×#1684056611yescharacteristic
824C2C2×#1684056811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#481C2
socleC23×C61C22×D4
prime radicalC2×#16840328C2
hypercenterC2×#481D61
hypocenterC61C2×#3096
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
2. C2×#16840243C2semidirect
3. #21455776C2direct (N × H)
4. C2×#16840082C2semidirect
5. C2×#16840088C2semidirect
6. C2×#16840087C2semidirect
7. C2×#16840085C2semidirect
8. C2×#16840083C2semidirect
9. C2×#16840075C2semidirect
10. C2×#16840074C2semidirect
11. C2×#16839801C2semidirect
12. C2×#16839797C2semidirect
13. C2×#16839765C2semidirect
14. C2×#102×D61C2semidirect
15. C2×#16839727C2semidirect
16. C2×C61×#481C2semidirect
31. #16840243C22semidirect
36. C2×#14519736C22semidirect
39. C2×#14519735C22semidirect
41. C2×C4⋊C4×D61C22semidirect
42. #16840088C22semidirect
43. #16840087C22semidirect
44. #16840085C22semidirect
45. #16840083C22semidirect
46. #16840082C22semidirect
47. #16840075C22semidirect
48. #16840074C22semidirect
49. #16839801C22semidirect
50. #16839797C22semidirect
51. C2×#14519711C22semidirect
52. C2×#14519710C22semidirect
53. C2×#14519710C22semidirect
54. C2×#14519710C22semidirect
55. C2×#14519709C22semidirect
56. C2×#14519708C22semidirect
57. #16839765C22semidirect
64. #102×D61C22semidirect
65. #16839727C22semidirect
66. C2×C22⋊#92418C22semidirect
67. C2×#14519689C22semidirect
68. C2×#14519689C22semidirect
70. C22×C4⋊C4×C61C22semidirect
71. C61×#481C22semidirect
72. C2×#106×C61C22semidirect
73. C2×#106×C61C22semidirect
76. C2×C22⋊C8×C61C22semidirect
120. #14519736C23semidirect
126. #14519735C23semidirect
135. C4⋊C4×D61C23semidirect
147. #14519711C23semidirect
148. #14519710C23semidirect
149. #14519710C23semidirect
150. #14519710C23semidirect
151. #14519709C23semidirect
152. #14519708C23semidirect
159. C22⋊#92418C23semidirect
160. #14519689C23semidirect
161. #14519689C23semidirect
175. C2×C4⋊C4×C61C23semidirect
177. #106×C61C23semidirect
178. #106×C61C23semidirect
181. C22⋊C8×C61C23semidirect
408. C2×#481D61semidirect
422. C2×C61#3096semidirect
455. C22×C4⋊C4C2×D61semidirect
461. #481C2×D61semidirect
472. C2×#106C2×D61semidirect
473. C2×#106C2×D61semidirect
488. C2×C22⋊C8C2×D61semidirect
489. C61C2×#3096semidirect
562. C2×C4⋊C4C22×D61semidirect
581. #106C22×D61semidirect
582. #106C22×D61semidirect
594. C22⋊C8C22×D61semidirect
821. C2#21455776direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403282
C2×#168402432
#214557762
C2×#168400822
C2×#168400882
C2×#168400872
C2×#168400852
C2×#168400832
C2×#168400752
C2×#168400742
C2×#168398012
C2×#168397972
C2×#168397652
C2×#102×D612
C2×#168397272
C2×C61×#4812
C2×#309661