Finite Group Databasebeta

← C2×#21458903 #30561039

Subgroups — C2×#21458903 #30561039

Order 15616.

2066 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840497C211yesmaximal, characteristic, complemented
2#21458903C2116yesmaximal, direct product factor
3C2×#16840152C211yesmaximal, characteristic, complemented
4C2×#16840149C211yesmaximal, characteristic, complemented
5C2×#16840144C211yesmaximal, characteristic, complemented
6C2×#16839984C211yesmaximal, characteristic, complemented
7C2×#16839981C211yesmaximal, characteristic, complemented
8C2×#16839977C211yesmaximal, characteristic, complemented
9C2×#16839974C211yesmaximal, characteristic, complemented
10C2×#16839957C211yesmaximal, characteristic, complemented
11C2×#16839954C211yesmaximal, characteristic, complemented
12C2×#16839893C211yesmaximal, characteristic, complemented
13C2×#16839862C211yesmaximal, characteristic, complemented
14C2×#16839860C211yesmaximal, characteristic, complemented
15C2×C4×#11758199C211yesmaximal, characteristic, complemented
16C2×C61×#559C211yesmaximal, characteristic, complemented
17C22×#11758202C2211yescharacteristic
18C22×#11758200C2211yescharacteristic
19C22×#11758200C2211yescharacteristic
20C22×#11758201C2211yescharacteristic
21C22×#11758201C2211yescharacteristic
22C22×#11758199C2211yescharacteristic
23C22×#11758199C2211yescharacteristic
24C22×#11758199C2211yescharacteristic
25C22×#11758199C2211yescharacteristic
26#16840497—24no—
27#16840497C2218yescomplemented
28C2×#14519774C2211yescharacteristic
29C2×#14519766—21no—
30C2×#14519765C2211yescharacteristic
31C2×#14519765C2211yescharacteristic
32C2×#14519762—21no—
33C2×#14519762—21no—
34C2×C4×Dic122C2211yescharacteristic
35C2×C4×D244C2211yescharacteristic
36C2×C4×D244C2211yescharacteristic
37C2×#14519739—21no—
38#16840152C2218yescomplemented
39#16840149C2218yescomplemented
40#16840144C2218yescomplemented
41#16839984C2218yescomplemented
42#16839981C2218yescomplemented
43#16839977C2218yescomplemented
44#16839974C2218yescomplemented
45#16839957C2218yescomplemented
46#16839954C2218yescomplemented
47#16839893C2218yescomplemented
48#16839862C2218yescomplemented
49#16839860C2218yescomplemented
50C4×#11758199C2218yescomplemented
51C2×#14519710C2211yescharacteristic
52C2×C4⋊#92418C2211yescharacteristic
53C2×C4⋊#92418C2211yescharacteristic
54C2×C4⋊#92418C2211yescharacteristic
55C2×#14519701C2211yescharacteristic
56C2×#14519700C2211yescharacteristic
57C2×#14519698C2211yescharacteristic
58C2×#14519698C2211yescharacteristic
59C2×#14519697C2211yescharacteristic
60C2×#14519697C2211yescharacteristic
61C2×#14519688C2211yescharacteristic
62C2×#14519688C2211yescharacteristic
63C2×C4×#92418C2211yescharacteristic
64C61×#559—24no—
65C61×#559C2218yescomplemented
66C2×#127×C61C2211yescharacteristic
67C2×#124×C61—21no—
68C2×#124×C61C2211yescharacteristic
69C2×#124×C61C2211yescharacteristic
70C2×#123×C61—21no—
71C2×#123×C61—21no—
72C2×C4×Q8×C61C2211yescharacteristic
73C2×C4×Q8×C61C2211yescharacteristic
74C2×C4×D4×C61—21no—
75C2×C4×D4×C61C2211yescharacteristic
76C2×C4×D4×C61C2211yescharacteristic
77C22×Dic122C2311yescharacteristic
78C22×D244—21no—
79C22×D244—21no—
80C22×D244C2311yescharacteristic
81C22×D244C2311yescharacteristic
82C22×C4×D61—21no—
83C22×C4×D61—21no—
84C2×#11758202—42no—
85C2×#11758202C2314yes—
86C2×#11758200—24no—
87C2×#11758200—42no—
88C2×#11758200C2314yes—
89C2×#11758200C2314yes—
90C2×#11758201—24no—
91C2×#11758201—42no—
92C2×#11758201C2314yes—
93C2×#11758201C2314yes—
94C2×#11758199—24no—
95C2×#11758199—42no—
96C2×#11758199—42no—
97C2×#11758199—42no—
98C2×#11758199C2314yes—
99C2×#11758199C2314yes—
100C2×#11758199C2314yes—
101C2×#11758199C2314yes—
102C22×#92418C2311yescharacteristic
103C22×#92418C2311yescharacteristic
104C22×#92418C2311yescharacteristic
105C22×#92418C2311yescharacteristic
106#14519774—22no—
107#14519774C2314yes—
108#14519766—28no—
109#14519765—22no—
110#14519765—22no—
111#14519765C2314yes—
112#14519765C2314yes—
113#14519762—28no—
114#14519762—28no—
115C4×Dic122—22no—
116C4×Dic122C2314yes—
117C4×D244—22no—
118C4×D244—22no—
119C4×D244C2314yes—
120C4×D244C2314yes—
121#14519739—28no—
122C2×C4⋊Dic61C2311yescharacteristic
123C2×#11758196—21no—
124C2×#11758198—21no—
125C2×#11758198—21no—
126C2×#11758198—21no—
127C2×#11758198—21no—
128C2×#11758198—21no—
129C2×#11758198—21no—
130C2×C4×Dic61—21no—
131#14519710C2314yes—
132C4⋊#92418C2314yes—
133C4⋊#92418C2314yes—
134C4⋊#92418C2314yes—
135#14519701C2314yes—
136#14519700C2314yes—
137#14519698C2314yes—
138#14519698C2314yes—
139#14519697C2314yes—
140#14519697C2314yes—
141#14519688C2314yes—
142#14519688C2314yes—
143C4×#92418C2314yes—
144C22×Q8×C61D411yescharacteristic
145C22×Q8×C61C2311yescharacteristic
146C22×D4×C61—21no—
147C22×D4×C61—21no—
148C22×D4×C61C2311yescharacteristic
149C22×D4×C61C2311yescharacteristic
150C23×C4×C61—21no—
151C23×C4×C61—21no—
152#127×C61—22no—
153#127×C61C2314yes—
154#124×C61—28no—
155#124×C61—22no—
156#124×C61—22no—
157#124×C61C2314yes—
158#124×C61C2314yes—
159#123×C61—28no—
160#123×C61—28no—
161C4×Q8×C61—22no—
162C4×Q8×C61D414yes—
163C4×Q8×C61C2314yes—
164C4×Q8×C61C2314yes—
165C4×D4×C61—28no—
166C4×D4×C61—22no—
167C4×D4×C61—22no—
168C4×D4×C61C2314yes—
169C4×D4×C61C2314yes—
170C2×C4⋊C4×C61—21no—
171C2×C4⋊C4×C61D411yescharacteristic
172C2×C4⋊C4×C61D411yescharacteristic
173C2×C4⋊C4×C61D411yescharacteristic
174C2×C4⋊C4×C61C2311yescharacteristic
175C2×C22⋊C4×C61—21no—
176C2×C22⋊C4×C61—21no—
177C2×C22⋊C4×C61—21no—
178C2×C22⋊C4×C61—21no—
179C2×C22⋊C4×C61—21no—
180C2×C22⋊C4×C61—21no—
181C2×C42×C61—21no—
182C2×C42×C61C2311yescharacteristic
183C2×C42×C61C2311yescharacteristic
184C2×C42×C61C2311yescharacteristic
185C24×C61—21no—
186C24×C61—21no—
187C23×D61—21no—
188C23×D61—21no—
189C2×Q8×C61—21no—
190C2×Q8×C61—22no—
191C2×Q8×C61—22no—
192C2×Q8×C61—42no—
193C2×Q8×C61C2×D414yes—
194C2×Q8×C61C2412yes—
195C2×D4×C61—21no—
196C2×D4×C61—21no—
197C2×D4×C61—24no—
198C2×D4×C61—24no—
199C2×D4×C61—22no—
200C2×D4×C61—22no—
201C2×D4×C61—22no—
202C2×D4×C61—22no—
203C2×D4×C61—44no—
204C2×D4×C61—82no—
205C2×D4×C61C2412yes—
206C2×D4×C61C2412yes—
207C22×C4×C61—21no—
208C22×C4×C61—21no—
209C22×C4×C61—24no—
210C22×C4×C61—24no—
211C22×C4×C61—82no—
212C22×C4×C61—82no—
213C22×C4×C61C2×D411yescharacteristic
214C22×C4×C61C2×D411yescharacteristic
215C22×C4×C61C2×D411yescharacteristic
216C22×C4×C61C2×D411yescharacteristic
217C22×C4×C61C2×D411yescharacteristic
218C22×C4×C61C2×D411yescharacteristic
219C22×C4×C61C2411yescharacteristic
220C22×Dic61—21no—
221C22×Dic61—21no—
222C2×D244—22no—
223C2×D244—22no—
224C2×D244—22no—
225C2×D244—22no—
226C2×D244—24no—
227C2×D244—21no—
228C2×D244—21no—
229C2×D244—24no—
230C2×D244—44no—
231C2×D244—82no—
232C2×D244C2412yes—
233C2×D244C2412yes—
234C2×C4×D61—24no—
235C2×C4×D61—24no—
236C2×C4×D61—82no—
237C2×C4×D61—82no—
238C2×Dic122—22no—
239C2×Dic122—22no—
240C2×Dic122—21no—
241C2×Dic122C2412yes—
242C4⋊C4×C61—24no—
243C4⋊C4×C61—21no—
244C4⋊C4×C61C2×D414yes—
245C4⋊C4×C61C2×D414yes—
246C4⋊C4×C61C2×D414yes—
247C4⋊C4×C61C2412yes—
248C22⋊C4×C61—24no—
249C22⋊C4×C61—24no—
250C22⋊C4×C61—24no—
251C22⋊C4×C61—24no—
252C22⋊C4×C61—24no—
253C22⋊C4×C61—24no—
254C42×C61—24no—
255C42×C61C2×D412yes—
256C42×C61C2×D412yes—
257C42×C61C2×D412yes—
258C42×C61C2412yes—
259C42×C61C2412yes—
260C42×C61C2412yes—
261#11758202—44no—
262#11758201—28no—
263#11758201—44no—
264#11758200—28no—
265#11758200—44no—
266#11758199—28no—
267#11758199—44no—
268#11758199—44no—
269#11758199—44no—
270#11758198—24no—
271#11758198—24no—
272#11758198—24no—
273#11758198—24no—
274#11758198—24no—
275#11758198—24no—
276C4⋊Dic61—21no—
277C4⋊Dic61C2412yes—
278#11758196—24no—
279C4×Dic61—24no—
280C2×#92418—22no—
281C2×#92418—22no—
282C2×#92418—22no—
283C2×#92418#4114yes—
284C2×#92418C2412yes—
285C2×#92418C2412yes—
286C2×#92418C2412yes—
287C2×#92418C2412yes—
288C23×C61—22no—
289C23×C61—22no—
290C23×C61—42no—
291C23×C61—42no—
292C23×C61—42no—
293C23×C61—42no—
294C23×C61—42no—
295C23×C61—42no—
296C23×C61C22×D411yescharacteristic
297C22×D61—22no—
298C22×D61—22no—
299C22×D61—42no—
300C22×D61—42no—
301C22×D61—42no—
302C22×D61—42no—
303C22×D61—42no—
304C22×D61—42no—
305Q8×C61—22no—
306Q8×C61—22no—
307Q8×C61—44no—
308Q8×C61—42no—
309D4×C61—22no—
310D4×C61—22no—
311D4×C61—22no—
312D4×C61—22no—
313D4×C61—48no—
314D4×C61—42no—
315D4×C61—42no—
316D4×C61—84no—
317C2×C4×C61—22no—
318C2×C4×C61—22no—
319C2×C4×C61—22no—
320C2×C4×C61—22no—
321C2×C4×C61—22no—
322C2×C4×C61—22no—
323C2×C4×C61—22no—
324C2×C4×C61—22no—
325C2×C4×C61—42no—
326C2×C4×C61—42no—
327C2×C4×C61—84no—
328C2×C4×C61—84no—
329C2×C4×C61C22×D412yes—
330C2×C4×C61C22×D412yes—
331C2×C4×C61C22×D412yes—
332C2×C4×C61C22×D412yes—
333C2×C4×C61C22×D412yes—
334C2×C4×C61C22×D412yes—
335C2×C4×C61C22×D411yescharacteristic
336C2×C4×C61C2×#4112yes—
337C2×C4×C61H(5,𝔽2)12yes—
338C2×C4×C61C2511yescharacteristic
339C2×Dic61—22no—
340C2×Dic61—22no—
341C2×Dic61—42no—
342C2×Dic61—42no—
343D244—22no—
344D244—22no—
345D244—22no—
346D244—22no—
347D244—48no—
348D244—42no—
349D244—42no—
350D244—84no—
351C4×D61—84no—
352C4×D61—84no—
353Dic122—22no—
354Dic122—22no—
355Dic122—42no—
356#92418—22no—
357#92418—22no—
358#92418—22no—
359#92418C2×#4114yes—
360C2×#3403—611nomaximal, Sylow
361C22×C61—42no—
362C22×C61—42no—
363C22×C61—42no—
364C22×C61—42no—
365C22×C61—42no—
366C22×C61—42no—
367C22×C61—84no—
368C22×C61—84no—
369C22×C61#55012yes—
370C22×C61#57512yes—
371C22×C61#57612yes—
372C22×C61C23×D411yescharacteristic
373C2×D61—42no—
374C2×D61—42no—
375C2×D61—42no—
376C2×D61—42no—
377C2×D61—42no—
378C2×D61—42no—
379C2×D61—84no—
380C2×D61—84no—
381C4×C61—22no—
382C4×C61—22no—
383C4×C61—22no—
384C4×C61—22no—
385C4×C61—22no—
386C4×C61—22no—
387C4×C61—42no—
388C4×C61—42no—
389C4×C61#55012yes—
390C4×C61C22×#4111yescharacteristic
391C4×C61C2×H(5,𝔽2)11yescharacteristic
392Dic61—42no—
393Dic61—42no—
394C2×#559—611no—
395C2×#559D6111yescharacteristic, complemented
396#3403—6116no—
397C2×#496—611no—
398C2×#496—611no—
399C2×#495—611no—
400C2×#464—611no—
401C2×#464—611no—
402C2×#463—611no—
403C2×#463—611no—
404C2×#459—611no—
405C2×#459—611no—
406C2×#446—611no—
407C2×#440—611no—
408C2×#440—611no—
409C2×C4×D8—611no—
410C2×C61—82no—
411C2×C61—82no—
412C2×C61#340314yescomplemented
413C2×C61C2×#55011yescharacteristic
414C2×C61C2×#57511yescharacteristic
415C2×C61C2×#57611yescharacteristic
416D61—82no—
417D61—82no—
418C22×Q16—611no—
419C22×SD16—611no—
420C22×SD16—611no—
421C22×SD16—611no—
422C22×SD16—611no—
423C22×D8—611no—
424C22×D8—611no—
425C22×D8—611no—
426C22×D8—611no—
427#559—24no—
428#559—618no—
429#559—1224no—
430#559C2×D6118yescomplemented
431C2×#127—611no—
432C2×#127C2×D6111yescharacteristic
433C2×#124—21no—
434C2×#124—611no—
435C2×#124—611no—
436C2×#124—1221no—
437C2×#124C2×D6111yescharacteristic
438C2×#124C2×D6111yescharacteristic
439C2×#123—21no—
440C2×#123—21no—
441C2×#123—1221no—
442C2×#123—1221no—
443C2×C4×Q8—611no—
444C2×C4×Q8C2×D6111yescharacteristic
445C2×C4×Q8C2×D6111yescharacteristic
446C2×C4×D4—21no—
447C2×C4×D4—611no—
448C2×C4×D4—611no—
449C2×C4×D4—1221no—
450C2×C4×D4C2×D6111yescharacteristic
451C2×C4×D4C2×D6111yescharacteristic
452#496—618no—
453#496—618no—
454#495—618no—
455#464—618no—
456#464—618no—
457#463—618no—
458#463—618no—
459#459—618no—
460#459—618no—
461#446—618no—
462#440—618no—
463#440—618no—
464C4×D8—618no—
465C2×#107—611no—
466C2×C4⋊C8—611no—
467C2×C4⋊C8—611no—
468C2×C4⋊C8—611no—
469C2×#103—611no—
470C2×#103—611no—
471C2×#102—611no—
472C2×#102—611no—
473C2×#102—611no—
474C2×#102—611no—
475C2×#97—611no—
476C2×#97—611no—
477C2×C4×C8—611no—
478C61C2×#340311yescharacteristic, complemented, Sylow
479C22×Q8—611no—
480C22×Q8C22⋊D6111yescharacteristic
481C22×Q8C22×D6111yescharacteristic
482C22×D4—21no—
483C22×D4—21no—
484C22×D4—611no—
485C22×D4—611no—
486C22×D4—1221no—
487C22×D4—1221no—
488C22×D4C22×D6111yescharacteristic
489C22×D4C22×D6111yescharacteristic
490C23×C4—21no—
491C23×C4—21no—
492C23×C4—1221no—
493C23×C4—1221no—
494C2×Q16—614no—
495C2×Q16—2442no—
496C2×SD16—614no—
497C2×SD16—614no—
498C2×SD16—614no—
499C2×SD16—614no—
500C2×SD16—1224no—
501C2×SD16—1224no—
502C2×SD16—2442no—
503C2×SD16—2442no—
504C2×D8—614no—
505C2×D8—614no—
506C2×D8—614no—
507C2×D8—614no—
508C2×D8—1224no—
509C2×D8—2442no—
510C2×D8—2442no—
511C2×D8—2442no—
512C22×C8—611no—
513C22×C8—611no—
514C22×C8—611no—
515C22×C8—611no—
516#127—22no—
517#127—614no—
518#127—1222no—
519#127C22×D6114yes—
520#124—28no—
521#124—22no—
522#124—22no—
523#124—614no—
524#124—614no—
525#124—1228no—
526#124—1222no—
527#124—1222no—
528#124C22×D6114yes—
529#124C22×D6114yes—
530#123—28no—
531#123—28no—
532#123—1228no—
533#123—1228no—
534C4×Q8—22no—
535C4×Q8—614no—
536C4×Q8—1222no—
537C4×Q8C22⋊D6114yes—
538C4×Q8C22×D6114yes—
539C4×Q8C22×D6114yes—
540C4×D4—28no—
541C4×D4—22no—
542C4×D4—22no—
543C4×D4—614no—
544C4×D4—614no—
545C4×D4—1228no—
546C4×D4—1222no—
547C4×D4—1222no—
548C4×D4C22×D6114yes—
549C4×D4C22×D6114yes—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—611no—
552C2×C4⋊C4—1221no—
553C2×C4⋊C4C22⋊D6111yescharacteristic
554C2×C4⋊C4C22⋊D6111yescharacteristic
555C2×C4⋊C4C22⋊D6111yescharacteristic
556C2×C4⋊C4C22×D6111yescharacteristic
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—1221no—
564C2×C22⋊C4—1221no—
565C2×C22⋊C4—1221no—
566C2×C22⋊C4—1221no—
567C2×C22⋊C4—1221no—
568C2×C22⋊C4—1221no—
569C2×C42—21no—
570C2×C42—1221no—
571C2×C42C22×D6111yescharacteristic
572C2×C42C22×D6111yescharacteristic
573C2×C42C22×D6111yescharacteristic
574#107—614no—
575C4⋊C8—614no—
576C4⋊C8—614no—
577C4⋊C8—614no—
578#103—614no—
579#103—614no—
580#102—614no—
581#102—614no—
582#102—614no—
583#102—614no—
584#97—614no—
585#97—614no—
586C4×C8—614no—
587C24—21no—
588C24—21no—
589C24—1221no—
590C24—1221no—
591C2×Q8—21no—
592C2×Q8—22no—
593C2×Q8—22no—
594C2×Q8—42no—
595C2×Q8—612no—
596C2×Q8—1221no—
597C2×Q8—1222no—
598C2×Q8—1222no—
599C2×Q8C2×C22⋊D6114yes—
600C2×Q8C23×D6112yes—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—24no—
604C2×D4—24no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—22no—
609C2×D4—44no—
610C2×D4—82no—
611C2×D4—612no—
612C2×D4—612no—
613C2×D4—1224no—
614C2×D4—1224no—
615C2×D4—1221no—
616C2×D4—1221no—
617C2×D4—1222no—
618C2×D4—1222no—
619C2×D4—1222no—
620C2×D4—1222no—
621C2×D4—4882no—
622C2×D4—2444no—
623C2×D4C23×D6112yes—
624C2×D4C23×D6112yes—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—24no—
628C22×C4—24no—
629C22×C4—82no—
630C22×C4—82no—
631C22×C4—1221no—
632C22×C4—1221no—
633C22×C4—1224no—
634C22×C4—1224no—
635C22×C4—4882no—
636C22×C4—4882no—
637C22×C4C2×C22⋊D6111yescharacteristic
638C22×C4C2×C22⋊D6111yescharacteristic
639C22×C4C2×C22⋊D6111yescharacteristic
640C22×C4C2×C22⋊D6111yescharacteristic
641C22×C4C2×C22⋊D6111yescharacteristic
642C22×C4C2×C22⋊D6111yescharacteristic
643C22×C4C23×D6111yescharacteristic
644Q16—2444no—
645SD16—1228no—
646SD16—1228no—
647SD16—2444no—
648SD16—2444no—
649D8—1228no—
650D8—2444no—
651D8—2444no—
652D8—2444no—
653C2×C8—614no—
654C2×C8—612no—
655C2×C8—612no—
656C2×C8—612no—
657C2×C8—612no—
658C2×C8—1222no—
659C2×C8—1222no—
660C2×C8—1222no—
661C4⋊C4—24no—
662C4⋊C4—21no—
663C4⋊C4—612no—
664C4⋊C4—1221no—
665C4⋊C4—1224no—
666C4⋊C4C2×C22⋊D6114yes—
667C4⋊C4C2×C22⋊D6114yes—
668C4⋊C4C2×C22⋊D6114yes—
669C4⋊C4C23×D6112yes—
670C22⋊C4—24no—
671C22⋊C4—24no—
672C22⋊C4—24no—
673C22⋊C4—24no—
674C22⋊C4—24no—
675C22⋊C4—24no—
676C22⋊C4—1224no—
677C22⋊C4—1224no—
678C22⋊C4—1224no—
679C22⋊C4—1224no—
680C22⋊C4—1224no—
681C22⋊C4—1224no—
682C42—24no—
683C42—1224no—
684C42C2×C22⋊D6112yes—
685C42C2×C22⋊D6112yes—
686C42C2×C22⋊D6112yes—
687C42C23×D6112yes—
688C42C23×D6112yes—
689C42C23×D6112yes—
690C23—22no—
691C23—22no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—1222no—
699C23—1222no—
700C23—2442no—
701C23—2442no—
702C23—2442no—
703C23—2442no—
704C23—2442no—
705C23—2442no—
706C23C22×C22⋊D6111yescharacteristic
707Q8—22no—
708Q8—22no—
709Q8—44no—
710Q8—42no—
711Q8—1222no—
712Q8—1222no—
713Q8—2442no—
714D4—22no—
715D4—22no—
716D4—22no—
717D4—22no—
718D4—48no—
719D4—42no—
720D4—42no—
721D4—84no—
722D4—1222no—
723D4—1222no—
724D4—1222no—
725D4—1222no—
726D4—4884no—
727D4—2448no—
728D4—2442no—
729D4—2442no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—84no—
741C2×C4—84no—
742C2×C4—1222no—
743C2×C4—1222no—
744C2×C4—4884no—
745C2×C4—4884no—
746C2×C4—2442no—
747C2×C4—2442no—
748C2×C4C22×C22⋊D6112yes—
749C2×C4C22×C22⋊D6112yes—
750C2×C4C22×C22⋊D6112yes—
751C2×C4C22×C22⋊D6112yes—
752C2×C4C22×C22⋊D6112yes—
753C2×C4C22×C22⋊D6112yes—
754C2×C4C22×C22⋊D6111yescharacteristic
755C2×C4#41×D6112yes—
756C2×C4#1451982312yes—
757C2×C4C24×D6111yescharacteristic
758C8—614no—
759C8—1222no—
760C8—1222no—
761C8—1222no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—84no—
769C22—84no—
770C22—4884no—
771C22—4884no—
772C22—2442no—
773C22—2442no—
774C22—2442no—
775C22—2442no—
776C22—2442no—
777C22—2442no—
778C22#1684043112yes—
779C22#1684056012yes—
780C22#1684056512yes—
781C22C23×C22⋊D6111yescharacteristic
782C4—22no—
783C4—22no—
784C4—22no—
785C4—22no—
786C4—22no—
787C4—22no—
788C4—42no—
789C4—42no—
790C4—2442no—
791C4—2442no—
792C4#1684043112yes—
793C4C2×#41×D6111yescharacteristic
794C4C2×#1451982311yescharacteristic
795C2—82no—
796C2—82no—
797C2—4882no—
798C2—4882no—
799C2#2145890314yesdirect product factor
800C2C2×#1684043111yescharacteristic
801C2C2×#1684056011yescharacteristic
802C2C2×#1684056511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#559C2
socleC23×C61C22×D4
hypercenterC2×#559D61
hypocenterC61C2×#3403
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#559

Complements

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

NH ≅ G/Ntype
1. C2×#16840497C2semidirect
2. #21458903C2direct (N × H)
3. C2×#16840152C2semidirect
4. C2×#16840149C2semidirect
5. C2×#16840144C2semidirect
6. C2×#16839984C2semidirect
7. C2×#16839981C2semidirect
8. C2×#16839977C2semidirect
9. C2×#16839974C2semidirect
10. C2×#16839957C2semidirect
11. C2×#16839954C2semidirect
12. C2×#16839893C2semidirect
13. C2×#16839862C2semidirect
14. C2×#16839860C2semidirect
15. C2×C4×#11758199C2semidirect
16. C2×C61×#559C2semidirect
27. #16840497C22semidirect
38. #16840152C22semidirect
39. #16840149C22semidirect
40. #16840144C22semidirect
41. #16839984C22semidirect
42. #16839981C22semidirect
43. #16839977C22semidirect
44. #16839974C22semidirect
45. #16839957C22semidirect
46. #16839954C22semidirect
47. #16839893C22semidirect
48. #16839862C22semidirect
49. #16839860C22semidirect
50. C4×#11758199C22semidirect
65. C61×#559C22semidirect
395. C2×#559D61semidirect
412. C2×C61#3403semidirect
430. #559C2×D61semidirect
478. C61C2×#3403semidirect
799. C2#21458903direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404972
#214589032
C2×#168401522
C2×#168401492
C2×#168401442
C2×#168399842
C2×#168399812
C2×#168399772
C2×#168399742
C2×#168399572
C2×#168399542
C2×#168398932
C2×#168398622
C2×#168398602
C2×C4×#117581992
C2×C61×#5592
C2×#340361