Finite Group Databasebeta

← C2×#21457671 #30556382

Subgroups — C2×#21457671 #30556382

Order 15616.

2350 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×#16840458C211yesmaximal, characteristic, complemented
2C2×#16840408C211yesmaximal, characteristic, complemented
3#21457671C2116yesmaximal, direct product factor
4C2×#16840117C211yesmaximal, characteristic, complemented
5C2×#16840098C211yesmaximal, characteristic, complemented
6C2×#16840087C211yesmaximal, characteristic, complemented
7C2×#16840063C211yesmaximal, characteristic, complemented
8C2×#16839998C211yesmaximal, characteristic, complemented
9C2×#16839991C211yesmaximal, characteristic, complemented
10C2×#16839978C211yesmaximal, characteristic, complemented
11C2×#16839909C211yesmaximal, characteristic, complemented
12C2×#16839898C211yesmaximal, characteristic, complemented
13C2×C4×D488C211yesmaximal, characteristic, complemented
14C2×#16839759C211yesmaximal, characteristic, complemented
15C22×#14519699C211yesmaximal, characteristic, complemented
16C2×C8×D4×C61C211yesmaximal, characteristic, complemented
17C22×#11758222C2211yescharacteristic
18C23×D244C2211yescharacteristic
19C22×#11758190C2211yescharacteristic, complemented
20C22×D488C2211yescharacteristic
21C22×D488C2211yescharacteristic
22#16840458—24no—
23#16840458C2218yescomplemented
24#16840408—24no—
25#16840408C2218yescomplemented
26C2×#14519772—21no—
27C2×#14519769C2211yescharacteristic, complemented
28C2×#14519765C2211yescharacteristic
29C2×#14519762—21no—
30C2×#14519759—21no—
31C2×#14519756C2211yescharacteristic
32C2×#14519751C2211yescharacteristic
33C2×#14519751C2211yescharacteristic
34C2×#14519751C2211yescharacteristic, complemented
35C2×#14519750—21no—
36C2×#14519749—21no—
37C2×#14519745—21no—
38C2×C4×D244C2211yescharacteristic
39C2×C4×D244C2211yescharacteristic, complemented
40C2×#14519737—21no—
41C2×#14519736C2211yescharacteristic, complemented
42C22×C4⋊Dic61C2211yescharacteristic
43C2×C22⋊C4×D61—21no—
44#16840117C2218yescomplemented
45#16840098C2218yescomplemented
46#16840087C2218yescomplemented
47#16840063C2218yescomplemented
48#16839998C2218yescomplemented
49#16839991C2218yescomplemented
50#16839978C2218yescomplemented
51#16839909C2218yescomplemented
52#16839898C2218yescomplemented
53C4×D488C2218yescomplemented
54C2×#14519711C2211yescharacteristic, complemented
55C2×#14519711C2211yescharacteristic, complemented
56C2×#14519709C2211yescharacteristic, complemented
57#16839759C2218yescomplemented
58C2×#14519702C2211yescharacteristic, complemented
59C2×#14519702C2211yescharacteristic, complemented
60C2×#14519702C2211yescharacteristic, complemented
61C2×#14519699C2211yescharacteristic
62C2×#14519699C2211yescharacteristic
63C2×#14519699C2211yescharacteristic
64C2×#14519699C2211yescharacteristic
65C2×#14519699C2211yescharacteristic
66C2×#14519699C2211yescharacteristic
67C2×#14519699C2218yescomplemented
68C2×#14519699C2211yescharacteristic, complemented
69C23×C8×C61C2211yescharacteristic
70C23×C8×C61C2211yescharacteristic, complemented
71C2×C4×D4×C61C2211yescharacteristic
72C8×D4×C61C2218yescomplemented
73C2×C4⋊C8×C61C2211yescharacteristic, complemented
74C2×C22⋊C8×C61C2211yescharacteristic
75C2×C22⋊C8×C61C2211yescharacteristic, complemented
76C2×C4×C8×C61C2211yescharacteristic, complemented
77C24×D61—21no—
78C2×#11758222—22no—
79C2×#11758222—24no—
80C2×#11758222—42no—
81C2×#11758222C2314yes—
82C22×Dic122C2311yescharacteristic
83C22×D244—24no—
84C22×D244—21no—
85C22×D244—22no—
86C22×D244—42no—
87C22×D244C2311yescharacteristic
88C22×D244C2311yescharacteristic
89C22×D244C2314yes—
90C22×D244C2311yescharacteristic
91C22×C22⋊D61—21no—
92C22×C22⋊D61—21no—
93C22×C22⋊D61—21no—
94C22×C22⋊D61—21no—
95C23×Dic61—21no—
96C22×C4×D61—21no—
97C22×C4×D61—21no—
98C22×C4×D61—21no—
99C2×#11758190—42no—
100C2×#11758190C2314yescomplemented
101C2×D488—24no—
102C2×D488—42no—
103C2×D488C2314yes—
104C2×D488C2314yes—
105#14519772—28no—
106#14519769—22no—
107#14519769C2314yescomplemented
108#14519765—22no—
109#14519765C2314yes—
110#14519762—28no—
111#14519759—28no—
112#14519756—22no—
113#14519756C2314yes—
114#14519751—22no—
115#14519751—22no—
116#14519751—22no—
117#14519751C2314yes—
118#14519751C2314yes—
119#14519751C2314yescomplemented
120#14519750—28no—
121#14519749—28no—
122#14519745—28no—
123C4×D244—22no—
124C4×D244—22no—
125C4×D244C2314yes—
126C4×D244C2314yescomplemented
127#14519737—28no—
128#14519736—22no—
129#14519736C2314yescomplemented
130C2×C4⋊Dic61—22no—
131C2×C4⋊Dic61—21no—
132C2×C4⋊Dic61C2314yes—
133C2×C4⋊Dic61C2311yescharacteristic
134C2×C4⋊Dic61C2311yescharacteristic
135C2×C4⋊Dic61C2311yescharacteristic
136C2×C4⋊Dic61C2311yescharacteristic
137C2×#11758196—21no—
138C2×#11758196—21no—
139C2×#11758196—21no—
140C2×C22⋊Dic61—21no—
141C2×C22⋊Dic61—21no—
142C2×#11758198—21no—
143C2×#11758198—21no—
144C2×#11758198—21no—
145C2×#11758198—21no—
146C2×#11758198—21no—
147C2×#11758198—21no—
148C2×#11758198—21no—
149C22⋊C4×D61—28no—
150C2×C4×Dic61—21no—
151#14519711C2314yescomplemented
152#14519711C2314yescomplemented
153#14519709C2314yescomplemented
154#14519702C2314yescomplemented
155#14519702C2314yescomplemented
156#14519702C2314yescomplemented
157#14519699C2314yes—
158#14519699C2314yes—
159#14519699C2314yes—
160#14519699C2314yes—
161#14519699C2314yes—
162#14519699C2314yes—
163#14519699C2314yescomplemented
164C22×D4×C61D411yescharacteristic
165C23×C4×C61C2311yescharacteristic
166C23×C4×C61C2311yescharacteristic
167C22×C8×C61—42no—
168C22×C8×C61—42no—
169C22×C8×C61C2311yescharacteristic
170C22×C8×C61C2311yescharacteristic
171C22×C8×C61C2311yescharacteristic
172C22×C8×C61C2311yescharacteristic
173C22×C8×C61C2314yes—
174C22×C8×C61C2314yescomplemented
175C4×D4×C61D414yes—
176C4×D4×C61C2314yes—
177C2×C4⋊C4×C61D411yescharacteristic
178C2×C22⋊C4×C61D411yescharacteristic
179C2×C22⋊C4×C61D411yescharacteristic
180C2×C42×C61C2311yescharacteristic
181C4⋊C8×C61C2314yescomplemented
182C22⋊C8×C61C2314yes—
183C22⋊C8×C61C2314yescomplemented
184C4×C8×C61C2314yescomplemented
185C24×C61C2×D411yescharacteristic
186C24×C61C2×D411yescharacteristic
187C23×D61—21no—
188C23×D61—21no—
189C23×D61—21no—
190C23×D61—24no—
191C23×D61—44no—
192C23×D61—44no—
193C23×D61—82no—
194C2×D4×C61—24no—
195C2×D4×C61C2×D414yes—
196C22×C4×C61—22no—
197C22×C4×C61—22no—
198C22×C4×C61—22no—
199C22×C4×C61—22no—
200C22×C4×C61C2×D411yescharacteristic
201C22×C4×C61C2×D411yescharacteristic
202C22×C4×C61C2×D411yescharacteristic
203C22×C4×C61C2×D412yes—
204C22×C4×C61C2×D412yes—
205C22×C4×C61C2×D411yescharacteristic
206C22×C4×C61C2412yes—
207C22×C4×C61C2412yes—
208C22×C4×C61C2411yescharacteristic
209C2×C22⋊D61—24no—
210C2×C22⋊D61—24no—
211C2×C22⋊D61—24no—
212C2×C22⋊D61—24no—
213C2×C22⋊D61—44no—
214C2×C22⋊D61—44no—
215C2×C22⋊D61—82no—
216C2×C22⋊D61—82no—
217C22×Dic61—21no—
218C22×Dic61—21no—
219C22×Dic61—21no—
220C22×Dic61—21no—
221C22×Dic61—21no—
222C22×Dic61—24no—
223C22×Dic61—82no—
224#11758222—28no—
225#11758222—44no—
226#11758222—48no—
227C2×D244—21no—
228C2×D244—22no—
229C2×D244—22no—
230C2×D244—22no—
231C2×D244—22no—
232C2×D244—22no—
233C2×D244—28no—
234C2×D244—24no—
235C2×D244—21no—
236C2×D244—21no—
237C2×D244—44no—
238C2×D244—48no—
239C2×D244—44no—
240C2×D244#4114yes—
241C2×D244C2412yes—
242C2×D244C2412yes—
243C2×D244C2412yes—
244C2×C4×D61—24no—
245C2×C4×D61—24no—
246C2×C4×D61—24no—
247C2×C4×D61—44no—
248C2×C4×D61—82no—
249C2×C4×D61—82no—
250C2×Dic122—22no—
251C2×Dic122—22no—
252C2×Dic122—21no—
253C2×Dic122C2412yes—
254C2×C8×C61—22no—
255C2×C8×C61—22no—
256C2×C8×C61—22no—
257C2×C8×C61—22no—
258C2×C8×C61—44no—
259C2×C8×C61—44no—
260C2×C8×C61C2412yes—
261C2×C8×C61C2412yes—
262C2×C8×C61C2412yes—
263C2×C8×C61C2412yes—
264C4⋊C4×C61C2×D414yes—
265C22⋊C4×C61C2×D414yes—
266C22⋊C4×C61C2×D414yes—
267C42×C61C2×D412yes—
268C42×C61C2412yes—
269C22⋊Dic61—24no—
270C22⋊Dic61—24no—
271#11758198—24no—
272#11758198—24no—
273#11758198—24no—
274#11758198—24no—
275#11758198—24no—
276#11758198—24no—
277#11758198—24no—
278C4⋊Dic61—21no—
279C4⋊Dic61—21no—
280C4⋊Dic61—24no—
281C4⋊Dic61—21no—
282C4⋊Dic61—21no—
283C4⋊Dic61C2412yes—
284C4⋊Dic61C2412yes—
285C4⋊Dic61C2412yes—
286C4⋊Dic61C2412yes—
287#11758196—24no—
288#11758196—24no—
289#11758196—24no—
290C4×Dic61—24no—
291D488—28no—
292D488—44no—
293#11758190—44no—
294C23×C61—22no—
295C23×C61—22no—
296C23×C61—22no—
297C23×C61—22no—
298C23×C61—22no—
299C23×C61#13514yes—
300C23×C61C22×D412yes—
301C23×C61C22×D412yes—
302C23×C61C22×D411yescharacteristic
303C22×D61—24no—
304C22×D61—22no—
305C22×D61—22no—
306C22×D61—22no—
307C22×D61—48no—
308C22×D61—42no—
309C22×D61—42no—
310C22×D61—42no—
311C22×D61—42no—
312C22×D61—42no—
313C22×D61—48no—
314C22×D61—42no—
315C22×D61—42no—
316C22×D61—42no—
317C22×D61—84no—
318C22×D61—816no—
319D4×C61—28no—
320C2×C4×C61—22no—
321C2×C4×C61—22no—
322C2×C4×C61—22no—
323C2×C4×C61—22no—
324C2×C4×C61—24no—
325C2×C4×C61—24no—
326C2×C4×C61—22no—
327C2×C4×C61—22no—
328C2×C4×C61—22no—
329C2×C4×C61—22no—
330C2×C4×C61C22×D412yes—
331C2×C4×C61C22×D412yes—
332C2×C4×C61C22×D412yes—
333C2×C4×C61C22×D412yes—
334C2×C4×C61C22×D411yescharacteristic
335C2×C4×C61C2×#4112yes—
336C2×C4×C61H(5,𝔽2)12yes—
337C2×C4×C61C2511yescharacteristic
338C22⋊D61—48no—
339C22⋊D61—48no—
340C22⋊D61—84no—
341C22⋊D61—84no—
342C2×Dic61—22no—
343C2×Dic61—22no—
344C2×Dic61—22no—
345C2×Dic61—22no—
346C2×Dic61—22no—
347C2×Dic61—42no—
348C2×Dic61—42no—
349C2×Dic61—42no—
350C2×Dic61—42no—
351C2×Dic61—42no—
352C2×Dic61—84no—
353D244—24no—
354D244—22no—
355D244—22no—
356D244—22no—
357D244—22no—
358D244—22no—
359D244—48no—
360D244—42no—
361D244—42no—
362D244C2×#4114yes—
363C4×D61—48no—
364C4×D61—84no—
365C4×D61—84no—
366Dic122—22no—
367Dic122—22no—
368Dic122—42no—
369C8×C61—22no—
370C8×C61—22no—
371C8×C61—22no—
372C8×C61—22no—
373C2×#3297—611nomaximal, Sylow
374C22×C61—22no—
375C22×C61—28no—
376C22×C61—22no—
377C22×C61—22no—
378C22×C61—22no—
379C22×C61—22no—
380C22×C61—44no—
381C22×C61#54612yes—
382C22×C61C2×#13514yes—
383C22×C61C2×#13512yes—
384C22×C61#57612yes—
385C22×C61C23×D411yescharacteristic
386C2×D61—24no—
387C2×D61—48no—
388C2×D61—42no—
389C2×D61—42no—
390C2×D61—42no—
391C2×D61—42no—
392C2×D61—42no—
393C2×D61—42no—
394C2×D61—42no—
395C2×D61—42no—
396C2×D61—816no—
397C2×D61—84no—
398C2×D61—84no—
399C4×C61—22no—
400C4×C61—22no—
401C4×C61—22no—
402C4×C61—22no—
403C4×C61#54612yes—
404C4×C61C22×#4111yescharacteristic
405C4×C61C2×H(5,𝔽2)11yescharacteristic
406Dic61—42no—
407Dic61—42no—
408Dic61—42no—
409Dic61—42no—
410Dic61—42no—
411C2×#553—611no—
412C2×#546—611no—
413#3297—6116no—
414C2×#488—611no—
415C2×#484—611no—
416C2×#482—611no—
417C2×#478—611no—
418C2×#466—611no—
419C2×#465—611no—
420C2×#463—611no—
421C2×#449—611no—
422C2×#447—611no—
423C2×C4×D8—611no—
424C2×C8×D4D6111yescharacteristic, complemented
425C2×#416—611no—
426C22×#102—611no—
427C2×C61—24no—
428C2×C61—42no—
429C2×C61#329714yescomplemented
430C2×C61C2×#54611yescharacteristic
431C2×C61C22×#13511yescharacteristic
432C2×C61C2×#57611yescharacteristic
433D61—44no—
434D61—82no—
435D61—82no—
436C22×#41—611no—
437C23×D4—611no—
438C22×SD16—611no—
439C22×D8—611no—
440C22×D8—611no—
441C23×C8C2×D6111yescharacteristic
442C23×C8C2×D6111yescharacteristic, complemented
443#553—618no—
444#553—1224no—
445#546—618no—
446#546—1224no—
447C2×#126—1221no—
448C2×#125—611no—
449C2×#124—611no—
450C2×#123—1221no—
451C2×#123—1221no—
452C2×C22⋊Q8—611no—
453C2×#121—611no—
454C2×#121—611no—
455C2×#121—611no—
456C2×#121—1221no—
457C2×#121—1221no—
458C2×#120—1221no—
459C2×C4×D4—611no—
460C2×C4×D4—611no—
461C2×C4×D4—1221no—
462C2×C4×D4C2×D6111yescharacteristic
463C2×#117—611no—
464C22×C4⋊C4—611no—
465C22×C22⋊C4—1221no—
466#488—618no—
467#484—618no—
468#482—618no—
469#478—618no—
470#466—618no—
471#465—618no—
472#463—618no—
473#449—618no—
474#447—618no—
475C4×D8—618no—
476C8×D4C2×D6118yescomplemented
477C2×#107—611no—
478C2×#107—611no—
479C2×#106—611no—
480C2×C4⋊C8C2×D6111yescharacteristic, complemented
481#416—618no—
482C2×#103—611no—
483C2×#103—611no—
484C2×#103—611no—
485C2×#102—611no—
486C2×#102—611no—
487C2×#102—611no—
488C2×#102—611no—
489C2×#102—611no—
490C2×#102—611no—
491C2×#102—618no—
492C2×#102—611no—
493C2×C22⋊C8C2×D6111yescharacteristic
494C2×C22⋊C8C2×D6111yescharacteristic, complemented
495C2×C4×C8C2×D6111yescharacteristic, complemented
496C61C2×#329711yescharacteristic, complemented, Sylow
497C25—1221no—
498C2×#41—614no—
499C2×#41—1224no—
500C2×#41—1222no—
501C2×#41—2442no—
502C22×Q8—611no—
503C22×D4—611no—
504C22×D4—611no—
505C22×D4—611no—
506C22×D4—614no—
507C22×D4—1224no—
508C22×D4—1221no—
509C22×D4—1221no—
510C22×D4—1221no—
511C22×D4—1221no—
512C22×D4—1221no—
513C22×D4—1222no—
514C22×D4—2442no—
515C22×D4D24411yescharacteristic
516C23×C4—1221no—
517C23×C4—1221no—
518C23×C4—1221no—
519C23×C4—1221no—
520C23×C4C22×D6111yescharacteristic
521C23×C4C22×D6111yescharacteristic
522C2×SD16—614no—
523C2×SD16—2442no—
524C2×D8—614no—
525C2×D8—614no—
526C2×D8—1224no—
527C2×D8—2442no—
528C22×C8—42no—
529C22×C8—42no—
530C22×C8C22×D6111yescharacteristic
531C22×C8C22×D6111yescharacteristic
532C22×C8C22×D6111yescharacteristic
533C22×C8C22×D6111yescharacteristic
534C22×C8C22×D6114yes—
535C22×C8C22×D6114yescomplemented
536#126—1228no—
537#125—614no—
538#125—1222no—
539#124—614no—
540#124—1222no—
541#123—1228no—
542#123—1228no—
543C22⋊Q8—614no—
544C22⋊Q8—1222no—
545#121—614no—
546#121—614no—
547#121—614no—
548#121—1228no—
549#121—1222no—
550#121—1222no—
551#121—1222no—
552#121—1228no—
553#120—1228no—
554C4×D4—614no—
555C4×D4—614no—
556C4×D4—1228no—
557C4×D4—1222no—
558C4×D4—1222no—
559C4×D4D24414yes—
560C4×D4C22×D6114yes—
561#117—614no—
562#117—1222no—
563C2×C4⋊C4—611no—
564C2×C4⋊C4—611no—
565C2×C4⋊C4—614no—
566C2×C4⋊C4—611no—
567C2×C4⋊C4—611no—
568C2×C4⋊C4—1221no—
569C2×C4⋊C4—1222no—
570C2×C4⋊C4—1221no—
571C2×C4⋊C4—1221no—
572C2×C4⋊C4—1221no—
573C2×C4⋊C4D24411yescharacteristic
574C2×C22⋊C4—1221no—
575C2×C22⋊C4—1221no—
576C2×C22⋊C4—1221no—
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—1228no—
584C2×C22⋊C4D24411yescharacteristic
585C2×C22⋊C4D24411yescharacteristic
586C2×C42—1221no—
587C2×C42C22×D6111yescharacteristic
588#107—614no—
589#107—614no—
590#106—614no—
591C4⋊C8C22×D6114yescomplemented
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#102—614no—
601#102—614no—
602C22⋊C8C22×D6114yes—
603C22⋊C8C22×D6114yescomplemented
604C4×C8C22×D6114yescomplemented
605C24—1221no—
606C24—1224no—
607C24—1221no—
608C24—1221no—
609C24—4882no—
610C24—2444no—
611C24—2444no—
612C24C2×D24411yescharacteristic
613C24C2×D24411yescharacteristic
614#41—1228no—
615#41—2444no—
616#41—2448no—
617C2×Q8—612no—
618C2×Q8—1221no—
619C2×Q8—1222no—
620C2×Q8—1222no—
621C2×D4—24no—
622C2×D4—614no—
623C2×D4—612no—
624C2×D4—612no—
625C2×D4—612no—
626C2×D4—1228no—
627C2×D4—1224no—
628C2×D4—1224no—
629C2×D4—1224no—
630C2×D4—1224no—
631C2×D4—1221no—
632C2×D4—1221no—
633C2×D4—1224no—
634C2×D4—1221no—
635C2×D4—1222no—
636C2×D4—1222no—
637C2×D4—1222no—
638C2×D4—1222no—
639C2×D4—1222no—
640C2×D4—4882no—
641C2×D4—4882no—
642C2×D4—2444no—
643C2×D4—2448no—
644C2×D4—2444no—
645C2×D4—2444no—
646C2×D4—2444no—
647C2×D4C2×D24414yes—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—1224no—
653C22×C4—1221no—
654C22×C4—1221no—
655C22×C4—1221no—
656C22×C4—1221no—
657C22×C4—1221no—
658C22×C4—1224no—
659C22×C4—1224no—
660C22×C4—1224no—
661C22×C4—4882no—
662C22×C4—4882no—
663C22×C4—4882no—
664C22×C4—2444no—
665C22×C4C2×D24412yes—
666C22×C4C2×D24412yes—
667C22×C4C2×D24411yescharacteristic
668C22×C4C2×D24411yescharacteristic
669C22×C4C2×D24411yescharacteristic
670C22×C4C2×D24411yescharacteristic
671C22×C4C23×D6112yes—
672C22×C4C23×D6112yes—
673C22×C4C23×D6111yescharacteristic
674SD16—2444no—
675D8—1228no—
676D8—2444no—
677C2×C8—22no—
678C2×C8—22no—
679C2×C8—22no—
680C2×C8—22no—
681C2×C8—44no—
682C2×C8—44no—
683C2×C8C23×D6112yes—
684C2×C8C23×D6112yes—
685C2×C8C23×D6112yes—
686C2×C8C23×D6112yes—
687C4⋊C4—612no—
688C4⋊C4—612no—
689C4⋊C4—612no—
690C4⋊C4—612no—
691C4⋊C4—1221no—
692C4⋊C4—1221no—
693C4⋊C4—1224no—
694C4⋊C4—1221no—
695C4⋊C4—1221no—
696C4⋊C4—1224no—
697C4⋊C4—1224no—
698C4⋊C4—1224no—
699C4⋊C4C2×D24414yes—
700C22⋊C4—1224no—
701C22⋊C4—1224no—
702C22⋊C4—1224no—
703C22⋊C4—1224no—
704C22⋊C4—1224no—
705C22⋊C4—1224no—
706C22⋊C4—1224no—
707C22⋊C4—1224no—
708C22⋊C4—1224no—
709C22⋊C4C2×D24414yes—
710C22⋊C4C2×D24414yes—
711C42—1224no—
712C42C2×D24412yes—
713C42C23×D6112yes—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—1222no—
720C23—1224no—
721C23—1222no—
722C23—1222no—
723C23—48816no—
724C23—4884no—
725C23—2448no—
726C23—2442no—
727C23—2448no—
728C23—2442no—
729C23—2442no—
730C23—2442no—
731C23—2442no—
732C23—2442no—
733C23—2442no—
734C23—2442no—
735C23#1451979914yes—
736C23C22×D24412yes—
737C23C22×D24412yes—
738C23C22×D24411yescharacteristic
739Q8—1222no—
740Q8—1222no—
741Q8—2442no—
742D4—28no—
743D4—614no—
744D4—1222no—
745D4—1222no—
746D4—1222no—
747D4—1222no—
748D4—1222no—
749D4—1224no—
750D4—4884no—
751D4—4884no—
752D4—2448no—
753D4—2448no—
754D4—2448no—
755D4—2442no—
756D4—2442no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—1222no—
768C2×C4—1222no—
769C2×C4—1222no—
770C2×C4—1222no—
771C2×C4—1222no—
772C2×C4—4884no—
773C2×C4—4884no—
774C2×C4—4884no—
775C2×C4—2448no—
776C2×C4—2442no—
777C2×C4—2442no—
778C2×C4—2442no—
779C2×C4—2442no—
780C2×C4—2442no—
781C2×C4C22×D24412yes—
782C2×C4C22×D24412yes—
783C2×C4C22×D24412yes—
784C2×C4C22×D24412yes—
785C2×C4C22×D24411yescharacteristic
786C2×C4#41×D6112yes—
787C2×C4#1451982212yes—
788C2×C4C24×D6111yescharacteristic
789C8—22no—
790C8—22no—
791C8—22no—
792C8—22no—
793C22—28no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—44no—
800C22—1224no—
801C22—48816no—
802C22—4884no—
803C22—4884no—
804C22—2442no—
805C22—2442no—
806C22—2442no—
807C22—2442no—
808C22—2442no—
809C22—2442no—
810C22—2448no—
811C22—2442no—
812C22—2442no—
813C22#1684040712yes—
814C22C2×#1451979914yes—
815C22C2×#1451979912yes—
816C22#1684056712yes—
817C22C23×D24411yescharacteristic
818C4—22no—
819C4—22no—
820C4—22no—
821C4—22no—
822C4—2442no—
823C4—2442no—
824C4—2442no—
825C4—2442no—
826C4—2442no—
827C4#1684040712yes—
828C4C2×#41×D6111yescharacteristic
829C4C2×#1451982211yescharacteristic
830C2—24no—
831C2—42no—
832C2—4882no—
833C2—4882no—
834C2—2444no—
835C2#2145767114yesdirect product factor
836C2C2×#1684040711yescharacteristic
837C2C22×#1451979911yescharacteristic
838C2C2×#1684056711yescharacteristic
subgroupG/H
centerC23C22×D244
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C8×D4×C61C2
socleC23×C61C22×D4
hypercenterC2×C8×D4D61
hypocenterC61C2×#3297
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×C8×D4

Complements

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

NH ≅ G/Ntype
1. C2×#16840458C2semidirect
2. C2×#16840408C2semidirect
3. #21457671C2direct (N × H)
4. C2×#16840117C2semidirect
5. C2×#16840098C2semidirect
6. C2×#16840087C2semidirect
7. C2×#16840063C2semidirect
8. C2×#16839998C2semidirect
9. C2×#16839991C2semidirect
10. C2×#16839978C2semidirect
11. C2×#16839909C2semidirect
12. C2×#16839898C2semidirect
13. C2×C4×D488C2semidirect
14. C2×#16839759C2semidirect
15. C22×#14519699C2semidirect
16. C2×C8×D4×C61C2semidirect
19. C22×#11758190C22semidirect
23. #16840458C22semidirect
25. #16840408C22semidirect
27. C2×#14519769C22semidirect
34. C2×#14519751C22semidirect
39. C2×C4×D244C22semidirect
41. C2×#14519736C22semidirect
44. #16840117C22semidirect
45. #16840098C22semidirect
46. #16840087C22semidirect
47. #16840063C22semidirect
48. #16839998C22semidirect
49. #16839991C22semidirect
50. #16839978C22semidirect
51. #16839909C22semidirect
52. #16839898C22semidirect
53. C4×D488C22semidirect
54. C2×#14519711C22semidirect
55. C2×#14519711C22semidirect
56. C2×#14519709C22semidirect
57. #16839759C22semidirect
58. C2×#14519702C22semidirect
59. C2×#14519702C22semidirect
60. C2×#14519702C22semidirect
67. C2×#14519699C22semidirect
68. C2×#14519699C22semidirect
70. C23×C8×C61C22semidirect
72. C8×D4×C61C22semidirect
73. C2×C4⋊C8×C61C22semidirect
75. C2×C22⋊C8×C61C22semidirect
76. C2×C4×C8×C61C22semidirect
100. C2×#11758190C23semidirect
107. #14519769C23semidirect
119. #14519751C23semidirect
126. C4×D244C23semidirect
129. #14519736C23semidirect
151. #14519711C23semidirect
152. #14519711C23semidirect
153. #14519709C23semidirect
154. #14519702C23semidirect
155. #14519702C23semidirect
156. #14519702C23semidirect
163. #14519699C23semidirect
174. C22×C8×C61C23semidirect
181. C4⋊C8×C61C23semidirect
183. C22⋊C8×C61C23semidirect
184. C4×C8×C61C23semidirect
424. C2×C8×D4D61semidirect
429. C2×C61#3297semidirect
442. C23×C8C2×D61semidirect
476. C8×D4C2×D61semidirect
480. C2×C4⋊C8C2×D61semidirect
494. C2×C22⋊C8C2×D61semidirect
495. C2×C4×C8C2×D61semidirect
496. C61C2×#3297semidirect
535. C22×C8C22×D61semidirect
591. C4⋊C8C22×D61semidirect
603. C22⋊C8C22×D61semidirect
604. C4×C8C22×D61semidirect
835. C2#21457671direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404582
C2×#168404082
#214576712
C2×#168401172
C2×#168400982
C2×#168400872
C2×#168400632
C2×#168399982
C2×#168399912
C2×#168399782
C2×#168399092
C2×#168398982
C2×C4×D4882
C2×#168397592
C22×#145196992
C2×C8×D4×C612
C2×#329761