Finite Group Databasebeta

← C2×#21456061 #30548306

Subgroups — C2×#21456061 #30548306

Order 15616.

2338 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840363C211yesmaximal, characteristic, complemented
2C2×#16840234C211yesmaximal, characteristic, complemented
3#21456061C2116yesmaximal, direct product factor
4C2×#16840088C211yesmaximal, characteristic, complemented
5C2×#16840085C211yesmaximal, characteristic, complemented
6C2×#16840064C211yesmaximal, characteristic, complemented
7C2×#16840061C211yesmaximal, characteristic, complemented
8C2×#16839956C211yesmaximal, characteristic, complemented
9C2×#16839955C211yesmaximal, characteristic, complemented
10C2×#16839897C211yesmaximal, characteristic, complemented
11C2×#16839894C211yesmaximal, characteristic, complemented
12C2×#16839875C211yesmaximal, characteristic, complemented
13C2×C4×#11758199C211yesmaximal, characteristic, complemented
14C2×C4×#11758199C211yesmaximal, characteristic, complemented
15C2×#16839824C211yesmaximal, characteristic, complemented
16C2×C61×#442C211yesmaximal, characteristic, complemented
17C22×D4×D61C2211yescharacteristic
18C22×D488C2211yescharacteristic
19C22×#11758199C2211yescharacteristic
20C22×#11758199C2211yescharacteristic
21#16840363—24no—
22#16840363C2218yescomplemented
23C2×#14519773C2211yescharacteristic, complemented
24C2×#14519768C2211yescharacteristic, complemented
25C2×#14519760—21no—
26C2×#14519759—21no—
27C2×#14519752C2211yescharacteristic
28C2×#14519751—21no—
29C2×#14519750—21no—
30C2×#14519748C2211yescharacteristic
31#16840234—24no—
32#16840234C2218yescomplemented
33C2×C4×D244C2211yescharacteristic
34C2×C4×D244C2211yescharacteristic, complemented
35C2×D4×Dic61C2211yescharacteristic
36C2×#14519739C2211yescharacteristic
37C2×C4×C22⋊D61—21no—
38C2×#14519737—21no—
39C2×#14519735C2211yescharacteristic
40C2×#14519734C2211yescharacteristic
41C22×#11758198—21no—
42C2×C22⋊C4×D61—21no—
43#16840088C2218yescomplemented
44#16840085C2218yescomplemented
45#16840064C2218yescomplemented
46#16840061C2218yescomplemented
47#16839956C2218yescomplemented
48#16839955C2218yescomplemented
49#16839897C2218yescomplemented
50#16839894C2218yescomplemented
51#16839875C2218yescomplemented
52C4×#11758199C2218yescomplemented
53C4×#11758199C2218yescomplemented
54#16839824C2218yescomplemented
55C2×#14519710C2211yescharacteristic, complemented
56C2×#14519710C2211yescharacteristic, complemented
57C2×#14519709C2211yescharacteristic, complemented
58C2×#14519706C2211yescharacteristic, complemented
59C2×#14519706C2211yescharacteristic, complemented
60C2×#14519699C2211yescharacteristic
61C2×#14519699C2211yescharacteristic, complemented
62C2×#14519698C2211yescharacteristic
63C2×#14519698C2211yescharacteristic, complemented
64C2×#14519697C2211yescharacteristic
65C2×#14519697C2211yescharacteristic, complemented
66C2×#14519689C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×C4×#92418C2211yescharacteristic, complemented
69C22×D8×C61C2211yescharacteristic
70C2×C4×D4×C61C2211yescharacteristic
71C2×C4×D4×C61C2211yescharacteristic, complemented
72C61×#442C2218yescomplemented
73C2×#106×C61C2211yescharacteristic, complemented
74C2×#102×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic, complemented
76C2×#97×C61C2211yescharacteristic, complemented
77C24×D61—21no—
78C22×D244—21no—
79C22×D244C2311yescharacteristic
80C22×D244C2311yescharacteristic
81C22×C22⋊D61—21no—
82C22×C22⋊D61—21no—
83C22×C22⋊D61—21no—
84C22×C22⋊D61—21no—
85C2×D4×D61—24no—
86C2×D4×D61—24no—
87C2×D4×D61—22no—
88C2×D4×D61C2314yes—
89C23×Dic61—21no—
90C22×C4×D61—21no—
91C22×C4×D61—21no—
92C22×C4×D61—21no—
93C22×C4×D61C2311yescharacteristic
94C2×D488—24no—
95C2×D488C2314yes—
96C2×#11758199—24no—
97C2×#11758199—24no—
98C2×#11758199C2314yes—
99C2×#11758199C2314yes—
100C22×#92418C2311yescharacteristic
101C22×#92418C2311yescharacteristic
102#14519773—22no—
103#14519773C2314yescomplemented
104#14519768—22no—
105#14519768C2314yescomplemented
106#14519760—28no—
107#14519759—28no—
108#14519752—22no—
109#14519752C2314yes—
110#14519751—28no—
111#14519750—28no—
112#14519748—22no—
113#14519748C2314yes—
114C4×D244—22no—
115C4×D244—22no—
116C4×D244C2314yes—
117C4×D244C2314yescomplemented
118D4×Dic61—22no—
119D4×Dic61C2314yes—
120#14519739—22no—
121#14519739C2314yes—
122C4×C22⋊D61—28no—
123#14519737—28no—
124#14519735—22no—
125#14519735C2314yes—
126#14519734D414yes—
127#14519734C2314yes—
128C2×C4⋊Dic61—21no—
129C2×C4⋊Dic61C2311yescharacteristic
130C2×C4⋊Dic61C2311yescharacteristic
131C2×#11758196—21no—
132C2×#11758196D411yescharacteristic
133C2×#11758196D411yescharacteristic
134C2×C22⋊Dic61—21no—
135C2×C22⋊Dic61—21no—
136C2×#11758198—21no—
137C2×#11758198—21no—
138C2×#11758198—21no—
139C2×#11758198—21no—
140C2×#11758198—21no—
141C2×#11758198—28no—
142C2×#11758198D411yescharacteristic
143C2×#11758198D411yescharacteristic
144C22⋊C4×D61—28no—
145C2×C4×Dic61—21no—
146C2×C4×Dic61C2311yescharacteristic
147#14519710C2314yescomplemented
148#14519710C2314yescomplemented
149#14519709C2314yescomplemented
150#14519706C2314yescomplemented
151#14519706C2314yescomplemented
152#14519699C2314yes—
153#14519699C2314yescomplemented
154#14519698C2314yes—
155#14519698C2314yescomplemented
156#14519697C2314yes—
157#14519697C2314yescomplemented
158#14519689C2314yes—
159#14519689C2314yes—
160C4×#92418C2314yescomplemented
161C22×D4×C61C2311yescharacteristic
162C22×D4×C61C2311yescharacteristic
163C23×C4×C61—21no—
164C23×C4×C61—21no—
165C2×D8×C61—24no—
166C2×D8×C61C2314yes—
167C22×C8×C61C2311yescharacteristic
168C22×C8×C61C2311yescharacteristic
169C4×D4×C61—22no—
170C4×D4×C61—22no—
171C4×D4×C61C2314yes—
172C4×D4×C61C2314yescomplemented
173C2×C4⋊C4×C61C2311yescharacteristic
174C2×C4⋊C4×C61C2311yescharacteristic
175C2×C22⋊C4×C61—21no—
176C2×C22⋊C4×C61—21no—
177C2×C42×C61C2311yescharacteristic
178#106×C61C2314yescomplemented
179#102×C61C2314yes—
180#102×C61C2314yescomplemented
181#97×C61C2314yescomplemented
182C24×C61—21no—
183C24×C61—21no—
184C23×D61—21no—
185C23×D61—28no—
186C23×D61—24no—
187C23×D61—21no—
188C23×D61—82no—
189C23×D61—82no—
190C23×D61C2×D411yescharacteristic
191C2×D4×C61—21no—
192C2×D4×C61—21no—
193C2×D4×C61—22no—
194C2×D4×C61—22no—
195C2×D4×C61—22no—
196C2×D4×C61#4114yes—
197C2×D4×C61C2412yes—
198C2×D4×C61C2412yes—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—24no—
202C22×C4×C61—24no—
203C22×C4×C61—82no—
204C22×C4×C61—82no—
205C22×C4×C61C2×D411yescharacteristic
206C22×C4×C61C2×D411yescharacteristic
207C22×C4×C61C2411yescharacteristic
208C2×C22⋊D61—28no—
209C2×C22⋊D61—24no—
210C2×C22⋊D61—24no—
211C2×C22⋊D61—24no—
212C2×C22⋊D61—24no—
213C2×C22⋊D61—82no—
214C2×C22⋊D61—82no—
215C2×C22⋊D61—82no—
216C22×Dic61—21no—
217C22×Dic61—21no—
218C22×Dic61—24no—
219C22×Dic61—82no—
220C22×Dic61C2×D411yescharacteristic
221C22×Dic61C2×D411yescharacteristic
222C22×Dic61C2×D411yescharacteristic
223D4×D61—216no—
224D4×D61—28no—
225D4×D61—28no—
226C2×D244—21no—
227C2×D244—22no—
228C2×D244—22no—
229C2×D244—22no—
230C2×D244—21no—
231C2×D244—24no—
232C2×D244—82no—
233C2×D244#4114yes—
234C2×D244C2412yes—
235C2×D244C2412yes—
236C2×C4×D61—22no—
237C2×C4×D61—22no—
238C2×C4×D61—24no—
239C2×C4×D61—24no—
240C2×C4×D61—24no—
241C2×C4×D61—82no—
242C2×C4×D61—82no—
243C2×C4×D61—82no—
244C2×C4×D61C2×D412yes—
245C2×C4×D61C2412yes—
246D8×C61—28no—
247C2×C8×C61—22no—
248C2×C8×C61—22no—
249C2×C8×C61C2412yes—
250C2×C8×C61C2412yes—
251C4⋊C4×C61—21no—
252C4⋊C4×C61—21no—
253C4⋊C4×C61C2412yes—
254C4⋊C4×C61C2412yes—
255C22⋊C4×C61—24no—
256C22⋊C4×C61—24no—
257C42×C61C2×D412yes—
258C42×C61C2412yes—
259C22⋊Dic61—24no—
260C22⋊Dic61—24no—
261#11758199—28no—
262#11758199—28no—
263#11758198—24no—
264#11758198—24no—
265#11758198—24no—
266#11758198—24no—
267#11758198—24no—
268#11758198C2×D414yes—
269#11758198C2×D414yes—
270C4⋊Dic61—21no—
271C4⋊Dic61—21no—
272C4⋊Dic61—24no—
273C4⋊Dic61C2412yes—
274C4⋊Dic61C2412yes—
275#11758196—24no—
276#11758196C2×D414yes—
277#11758196C2×D414yes—
278C4×Dic61—24no—
279C4×Dic61C2×D412yes—
280C4×Dic61C2412yes—
281C2×#92418—22no—
282C2×#92418—22no—
283C2×#92418C2412yes—
284C2×#92418C2412yes—
285D488—28no—
286C23×C61—24no—
287C23×C61—22no—
288C23×C61—22no—
289C23×C61—42no—
290C23×C61—42no—
291C23×C61—42no—
292C23×C61—42no—
293C23×C61—42no—
294C23×C61C22×D411yescharacteristic
295C22×D61—22no—
296C22×D61—24no—
297C22×D61—22no—
298C22×D61—22no—
299C22×D61—22no—
300C22×D61—216no—
301C22×D61—22no—
302C22×D61—42no—
303C22×D61—42no—
304C22×D61—42no—
305C22×D61—42no—
306C22×D61—42no—
307C22×D61—84no—
308C22×D61—84no—
309C22×D61—816no—
310C22×D61C22×D412yes—
311D4×C61—24no—
312D4×C61—22no—
313D4×C61—22no—
314D4×C61—22no—
315D4×C61—42no—
316D4×C61C2×#4114yes—
317C2×C4×C61—22no—
318C2×C4×C61—22no—
319C2×C4×C61—22no—
320C2×C4×C61—22no—
321C2×C4×C61—42no—
322C2×C4×C61—42no—
323C2×C4×C61—84no—
324C2×C4×C61—84no—
325C2×C4×C61C22×D412yes—
326C2×C4×C61C22×D412yes—
327C2×C4×C61C22×D411yescharacteristic
328C2×C4×C61C2×#4112yes—
329C2×C4×C61C2×#4112yes—
330C2×C4×C61C2511yescharacteristic
331C22⋊D61—216no—
332C22⋊D61—84no—
333C22⋊D61—84no—
334C22⋊D61—84no—
335C2×Dic61—22no—
336C2×Dic61—22no—
337C2×Dic61—22no—
338C2×Dic61—22no—
339C2×Dic61—22no—
340C2×Dic61—42no—
341C2×Dic61—42no—
342C2×Dic61—84no—
343C2×Dic61C22×D412yes—
344C2×Dic61C22×D412yes—
345C2×Dic61C22×D412yes—
346D244—24no—
347D244—22no—
348D244—22no—
349D244—22no—
350D244—42no—
351D244—84no—
352D244C2×#4114yes—
353C4×D61—24no—
354C4×D61—22no—
355C4×D61—22no—
356C4×D61—84no—
357C4×D61—84no—
358C4×D61—84no—
359C8×C61—22no—
360C8×C61—22no—
361#92418—22no—
362#92418—22no—
363C2×#3122—611nomaximal, Sylow
364C22×C61—24no—
365C22×C61—48no—
366C22×C61—42no—
367C22×C61—42no—
368C22×C61—42no—
369C22×C61—42no—
370C22×C61—42no—
371C22×C61—84no—
372C22×C61#52512yes—
373C22×C61#57612yes—
374C22×C61#57612yes—
375C22×C61C23×D411yescharacteristic
376C2×D61—22no—
377C2×D61—24no—
378C2×D61—22no—
379C2×D61—22no—
380C2×D61—44no—
381C2×D61—48no—
382C2×D61—42no—
383C2×D61—42no—
384C2×D61—42no—
385C2×D61—42no—
386C2×D61—42no—
387C2×D61—816no—
388C2×D61—84no—
389C4×C61—22no—
390C4×C61—22no—
391C4×C61—42no—
392C4×C61—42no—
393C4×C61#52512yes—
394C4×C61C22×#4111yescharacteristic
395C4×C61C22×#4111yescharacteristic
396Dic61—22no—
397Dic61—22no—
398Dic61—22no—
399Dic61—42no—
400Dic61—42no—
401C2×#540—611no—
402C2×#518—611no—
403#3122—6116no—
404C2×#482—611no—
405C2×#482—611no—
406C2×#478—611no—
407C2×#478—611no—
408C2×#459—611no—
409C2×#459—611no—
410C2×#447—611no—
411C2×#447—611no—
412C2×#442—611no—
413C2×#442D6111yescharacteristic, complemented
414C2×C4×D8—611no—
415C2×C4×D8—611no—
416C2×#433—611no—
417C2×C61—44no—
418C2×C61—82no—
419C2×C61#312214yescomplemented
420C2×C61C2×#52511yescharacteristic
421C2×C61C2×#57611yescharacteristic
422C2×C61C2×#57611yescharacteristic
423D61—42no—
424D61—44no—
425D61—82no—
426C23×D4—611no—
427C22×D8—611no—
428C22×D8—611no—
429C22×D8—611no—
430C22×D8C2×D6111yescharacteristic
431#540—618no—
432#540—1224no—
433C2×#127—611no—
434C2×#125—611no—
435C2×#123—1221no—
436C2×#123—1221no—
437C2×#121—611no—
438C2×#121—611no—
439C2×#121—1221no—
440C2×#121—1221no—
441#518—618no—
442#518—1224no—
443C2×C4×D4—611no—
444C2×C4×D4—611no—
445C2×C4×D4—611no—
446C2×C4×D4—611no—
447C2×C4×D4—1221no—
448C2×C4×D4—1221no—
449C2×C4×D4C2×D6111yescharacteristic
450C2×C4×D4C2×D6111yescharacteristic, complemented
451C2×#117—611no—
452C2×#117—611no—
453C22×C22⋊C4—1221no—
454C22×C22⋊C4—1221no—
455#482—618no—
456#482—618no—
457#478—618no—
458#478—618no—
459#459—618no—
460#459—618no—
461#447—618no—
462#447—618no—
463#442—618no—
464#442C2×D6118yescomplemented
465C4×D8—618no—
466C4×D8—618no—
467#433—618no—
468C2×#107—611no—
469C2×#107—611no—
470C2×#106—611no—
471C2×#106C2×D6111yescharacteristic, complemented
472C2×C4⋊C8—611no—
473C2×C4⋊C8—611no—
474C2×#102—611no—
475C2×#102—611no—
476C2×#102—611no—
477C2×#102—611no—
478C2×#102—611no—
479C2×#102—611no—
480C2×#102C2×D6111yescharacteristic
481C2×#102C2×D6111yescharacteristic, complemented
482C2×C22⋊C8—611no—
483C2×C22⋊C8—611no—
484C2×#97C2×D6111yescharacteristic, complemented
485C2×C4×C8—611no—
486C61C2×#312211yescharacteristic, complemented, Sylow
487C25—1221no—
488C22×D4—614no—
489C22×D4—611no—
490C22×D4—611no—
491C22×D4—1221no—
492C22×D4—1222no—
493C22×D4—1221no—
494C22×D4—1221no—
495C22×D4—1221no—
496C22×D4—1224no—
497C22×D4—1224no—
498C22×D4—1221no—
499C22×D4C22×D6111yescharacteristic
500C22×D4C22×D6111yescharacteristic
501C23×C4—21no—
502C23×C4—21no—
503C23×C4—611no—
504C23×C4—1221no—
505C23×C4—1221no—
506C23×C4—1221no—
507C23×C4—1221no—
508C2×D8—24no—
509C2×D8—614no—
510C2×D8—614no—
511C2×D8—614no—
512C2×D8—1224no—
513C2×D8—1224no—
514C2×D8—1224no—
515C2×D8C22×D6114yes—
516C22×C8—611no—
517C22×C8—611no—
518C22×C8C22×D6111yescharacteristic
519C22×C8C22×D6111yescharacteristic
520#127—614no—
521#127—1222no—
522#125—614no—
523#125—1222no—
524#123—1228no—
525#123—1228no—
526#121—614no—
527#121—614no—
528#121—1228no—
529#121—1228no—
530#121—1222no—
531#121—1222no—
532C4×D4—22no—
533C4×D4—22no—
534C4×D4—614no—
535C4×D4—614no—
536C4×D4—614no—
537C4×D4—614no—
538C4×D4—1222no—
539C4×D4—1222no—
540C4×D4—1228no—
541C4×D4—1228no—
542C4×D4—1222no—
543C4×D4—1222no—
544C4×D4C22×D6114yes—
545C4×D4C22×D6114yescomplemented
546#117—614no—
547#117—614no—
548#117—614no—
549#117—1222no—
550C2×C4⋊C4—611no—
551C2×C4⋊C4—611no—
552C2×C4⋊C4—611no—
553C2×C4⋊C4—611no—
554C2×C4⋊C4—1221no—
555C2×C4⋊C4—1221no—
556C2×C4⋊C4C22×D6111yescharacteristic
557C2×C4⋊C4C22×D6111yescharacteristic
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—611no—
561C2×C22⋊C4—611no—
562C2×C22⋊C4—1228no—
563C2×C22⋊C4—1228no—
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—611no—
572C2×C42—1221no—
573C2×C42C22×D6111yescharacteristic
574#107—614no—
575#107—614no—
576#106—614no—
577#106C22×D6114yescomplemented
578C4⋊C8—614no—
579C4⋊C8—614no—
580#102—614no—
581#102—614no—
582#102—614no—
583#102—614no—
584#102—614no—
585#102—614no—
586#102C22×D6114yes—
587#102C22×D6114yescomplemented
588C22⋊C8—614no—
589C22⋊C8—614no—
590#97C22×D6114yescomplemented
591C4×C8—614no—
592C24—21no—
593C24—21no—
594C24—611no—
595C24—1224no—
596C24—1228no—
597C24—1221no—
598C24—1221no—
599C24—4882no—
600C24—4882no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—22no—
604C2×D4—22no—
605C2×D4—22no—
606C2×D4—614no—
607C2×D4—612no—
608C2×D4—612no—
609C2×D4—1224no—
610C2×D4—1224no—
611C2×D4—1224no—
612C2×D4—1224no—
613C2×D4—1228no—
614C2×D4—12216no—
615C2×D4—1228no—
616C2×D4—1228no—
617C2×D4—1224no—
618C2×D4—1221no—
619C2×D4—1221no—
620C2×D4—1222no—
621C2×D4—1222no—
622C2×D4—1222no—
623C2×D4—4882no—
624C2×D4—4882no—
625C2×D4—4882no—
626C2×D4—4882no—
627C2×D4#1175822214yes—
628C2×D4C23×D6112yes—
629C2×D4C23×D6112yes—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—24no—
633C22×C4—24no—
634C22×C4—82no—
635C22×C4—82no—
636C22×C4—611no—
637C22×C4—611no—
638C22×C4—611no—
639C22×C4—612no—
640C22×C4—612no—
641C22×C4—1224no—
642C22×C4—1224no—
643C22×C4—1222no—
644C22×C4—1222no—
645C22×C4—1221no—
646C22×C4—1221no—
647C22×C4—1224no—
648C22×C4—1224no—
649C22×C4—4882no—
650C22×C4—4882no—
651C22×C4—4882no—
652C22×C4—4882no—
653C22×C4D4×D6111yescharacteristic
654C22×C4D4×D6111yescharacteristic
655C22×C4C23×D6111yescharacteristic
656D8—28no—
657D8—1228no—
658D8—1228no—
659D8—1228no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—612no—
663C2×C8—612no—
664C2×C8—1222no—
665C2×C8—1222no—
666C2×C8C23×D6112yes—
667C2×C8C23×D6112yes—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—614no—
671C4⋊C4—614no—
672C4⋊C4—612no—
673C4⋊C4—612no—
674C4⋊C4—1224no—
675C4⋊C4—1224no—
676C4⋊C4—1221no—
677C4⋊C4—1221no—
678C4⋊C4C23×D6112yes—
679C4⋊C4C23×D6112yes—
680C22⋊C4—24no—
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—
691C42—612no—
692C42—612no—
693C42—1224no—
694C42D4×D6112yes—
695C42C23×D6112yes—
696C23—24no—
697C23—22no—
698C23—22no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—612no—
705C23—12216no—
706C23—1222no—
707C23—1224no—
708C23—1222no—
709C23—1222no—
710C23—1222no—
711C23—1222no—
712C23—4884no—
713C23—4884no—
714C23—48816no—
715C23—2442no—
716C23—2442no—
717C23—2442no—
718C23—2442no—
719C23—2442no—
720C23C2×D4×D6111yescharacteristic
721D4—24no—
722D4—22no—
723D4—22no—
724D4—22no—
725D4—42no—
726D4—614no—
727D4—12216no—
728D4—1224no—
729D4—1222no—
730D4—1222no—
731D4—1222no—
732D4—4884no—
733D4—4884no—
734D4—4884no—
735D4—4884no—
736D4—2442no—
737D4C2×#1175822214yes—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—84no—
745C2×C4—84no—
746C2×C4—612no—
747C2×C4—612no—
748C2×C4—612no—
749C2×C4—1222no—
750C2×C4—1222no—
751C2×C4—1222no—
752C2×C4—1224no—
753C2×C4—1222no—
754C2×C4—1222no—
755C2×C4—1222no—
756C2×C4—1222no—
757C2×C4—4884no—
758C2×C4—4884no—
759C2×C4—4884no—
760C2×C4—4884no—
761C2×C4—2442no—
762C2×C4—2442no—
763C2×C4C2×D4×D6112yes—
764C2×C4C2×D4×D6112yes—
765C2×C4C2×D4×D6111yescharacteristic
766C2×C4#41×D6112yes—
767C2×C4C2×#1175822212yes—
768C2×C4C24×D6111yescharacteristic
769C8—22no—
770C8—22no—
771C8—1222no—
772C8—1222no—
773C22—24no—
774C22—42no—
775C22—42no—
776C22—48no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—84no—
781C22—1222no—
782C22—1222no—
783C22—1222no—
784C22—1224no—
785C22—48816no—
786C22—4884no—
787C22—2442no—
788C22—2442no—
789C22—2442no—
790C22—2442no—
791C22—2442no—
792C22—2444no—
793C22—2448no—
794C22#1684027112yes—
795C22#1684056612yes—
796C22#1684056612yes—
797C22C22×D4×D6111yescharacteristic
798C4—22no—
799C4—22no—
800C4—42no—
801C4—42no—
802C4—1222no—
803C4—1222no—
804C4—1222no—
805C4—2442no—
806C4—2442no—
807C4#1684027112yes—
808C4C2×#41×D6111yescharacteristic
809C4C22×#1175822211yescharacteristic
810C2—44no—
811C2—82no—
812C2—4882no—
813C2—2442no—
814C2—2444no—
815C2#2145606114yesdirect product factor
816C2C2×#1684027111yescharacteristic
817C2C2×#1684056611yescharacteristic
818C2C2×#1684056611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#442C2
socleC23×C61C22×D4
hypercenterC2×#442D61
hypocenterC61C2×#3122
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
1. C2×#16840363C2semidirect
2. C2×#16840234C2semidirect
3. #21456061C2direct (N × H)
4. C2×#16840088C2semidirect
5. C2×#16840085C2semidirect
6. C2×#16840064C2semidirect
7. C2×#16840061C2semidirect
8. C2×#16839956C2semidirect
9. C2×#16839955C2semidirect
10. C2×#16839897C2semidirect
11. C2×#16839894C2semidirect
12. C2×#16839875C2semidirect
13. C2×C4×#11758199C2semidirect
14. C2×C4×#11758199C2semidirect
15. C2×#16839824C2semidirect
16. C2×C61×#442C2semidirect
22. #16840363C22semidirect
23. C2×#14519773C22semidirect
24. C2×#14519768C22semidirect
32. #16840234C22semidirect
34. C2×C4×D244C22semidirect
43. #16840088C22semidirect
44. #16840085C22semidirect
45. #16840064C22semidirect
46. #16840061C22semidirect
47. #16839956C22semidirect
48. #16839955C22semidirect
49. #16839897C22semidirect
50. #16839894C22semidirect
51. #16839875C22semidirect
52. C4×#11758199C22semidirect
53. C4×#11758199C22semidirect
54. #16839824C22semidirect
55. C2×#14519710C22semidirect
56. C2×#14519710C22semidirect
57. C2×#14519709C22semidirect
58. C2×#14519706C22semidirect
59. C2×#14519706C22semidirect
61. C2×#14519699C22semidirect
63. C2×#14519698C22semidirect
65. C2×#14519697C22semidirect
68. C2×C4×#92418C22semidirect
71. C2×C4×D4×C61C22semidirect
72. C61×#442C22semidirect
73. C2×#106×C61C22semidirect
75. C2×#102×C61C22semidirect
76. C2×#97×C61C22semidirect
103. #14519773C23semidirect
105. #14519768C23semidirect
117. C4×D244C23semidirect
147. #14519710C23semidirect
148. #14519710C23semidirect
149. #14519709C23semidirect
150. #14519706C23semidirect
151. #14519706C23semidirect
153. #14519699C23semidirect
155. #14519698C23semidirect
157. #14519697C23semidirect
160. C4×#92418C23semidirect
172. C4×D4×C61C23semidirect
178. #106×C61C23semidirect
180. #102×C61C23semidirect
181. #97×C61C23semidirect
413. C2×#442D61semidirect
419. C2×C61#3122semidirect
450. C2×C4×D4C2×D61semidirect
464. #442C2×D61semidirect
471. C2×#106C2×D61semidirect
481. C2×#102C2×D61semidirect
484. C2×#97C2×D61semidirect
486. C61C2×#3122semidirect
545. C4×D4C22×D61semidirect
577. #106C22×D61semidirect
587. #102C22×D61semidirect
590. #97C22×D61semidirect
815. C2#21456061direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403632
C2×#168402342
#214560612
C2×#168400882
C2×#168400852
C2×#168400642
C2×#168400612
C2×#168399562
C2×#168399552
C2×#168398972
C2×#168398942
C2×#168398752
C2×C4×#117581992
C2×#168398242
C2×C61×#4422
C2×#312261