Finite Group Databasebeta

← C2×#14541868 #17915350

Subgroups — C2×#14541868 #17915350

Order 4352.

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×#11763544C211yesmaximal, characteristic, complemented
2#14541868C2116yesmaximal, direct product factor
3C2×#11763199C211yesmaximal, characteristic, complemented
4C2×#11763196C211yesmaximal, characteristic, complemented
5C2×#11763191C211yesmaximal, characteristic, complemented
6C2×#11763031C211yesmaximal, characteristic, complemented
7C2×#11763028C211yesmaximal, characteristic, complemented
8C2×#11763024C211yesmaximal, characteristic, complemented
9C2×#11763021C211yesmaximal, characteristic, complemented
10C2×#11763004C211yesmaximal, characteristic, complemented
11C2×#11763001C211yesmaximal, characteristic, complemented
12C2×#11762940C211yesmaximal, characteristic, complemented
13C2×#11762909C211yesmaximal, characteristic, complemented
14C2×#11762907C211yesmaximal, characteristic, complemented
15C2×C4×#63228C211yesmaximal, characteristic, complemented
16C2×C17×#559C211yesmaximal, characteristic, complemented
17C22×#63231C2211yescharacteristic
18C22×#63229C2211yescharacteristic
19C22×#63229C2211yescharacteristic
20C22×#63230C2211yescharacteristic
21C22×#63230C2211yescharacteristic
22C22×#63228C2211yescharacteristic
23C22×#63228C2211yescharacteristic
24C22×#63228C2211yescharacteristic
25C22×#63228C2211yescharacteristic
26#11763544—24no—
27#11763544C2218yescomplemented
28C2×#10587560C2211yescharacteristic
29C2×#10587633—21no—
30C2×#10587561C2211yescharacteristic
31C2×#10587561C2211yescharacteristic
32C2×#10587580—21no—
33C2×#10587580—21no—
34C2×C4×Dic34C2211yescharacteristic
35C2×C4×D68C2211yescharacteristic
36C2×C4×D68C2211yescharacteristic
37C2×#10587579—21no—
38#11763199C2218yescomplemented
39#11763196C2218yescomplemented
40#11763191C2218yescomplemented
41#11763031C2218yescomplemented
42#11763028C2218yescomplemented
43#11763024C2218yescomplemented
44#11763021C2218yescomplemented
45#11763004C2218yescomplemented
46#11763001C2218yescomplemented
47#11762940C2218yescomplemented
48#11762909C2218yescomplemented
49#11762907C2218yescomplemented
50C4×#63228C2218yescomplemented
51C2×#10587478C2211yescharacteristic
52C2×C4⋊#3622C2211yescharacteristic
53C2×C4⋊#3622C2211yescharacteristic
54C2×C4⋊#3622C2211yescharacteristic
55C2×#10587506C2211yescharacteristic
56C2×#10587481C2211yescharacteristic
57C2×#10587503C2211yescharacteristic
58C2×#10587503C2211yescharacteristic
59C2×#10587480C2211yescharacteristic
60C2×#10587480C2211yescharacteristic
61C2×#10587474C2211yescharacteristic
62C2×#10587474C2211yescharacteristic
63C2×C4×#3622C2211yescharacteristic
64C17×#559—24no—
65C17×#559C2218yescomplemented
66C2×C17×#127C2211yescharacteristic
67C2×C17×#124—21no—
68C2×C17×#124C2211yescharacteristic
69C2×C17×#124C2211yescharacteristic
70C2×C17×#123—21no—
71C2×C17×#123—21no—
72C2×C4×Q8×C17C2211yescharacteristic
73C2×C4×Q8×C17C2211yescharacteristic
74C2×C4×D4×C17—21no—
75C2×C4×D4×C17C2211yescharacteristic
76C2×C4×D4×C17C2211yescharacteristic
77C22×Q8×C17D411yescharacteristic
78C22×Q8×C17C2311yescharacteristic
79C22×D4×C17—21no—
80C22×D4×C17—21no—
81C22×D4×C17C2311yescharacteristic
82C22×D4×C17C2311yescharacteristic
83C23×C4×C17—21no—
84C23×C4×C17—21no—
85C22×D68—21no—
86C22×D68—21no—
87C22×D68C2311yescharacteristic
88C22×D68C2311yescharacteristic
89C22×C4×D17—21no—
90C22×C4×D17—21no—
91C22×Dic34C2311yescharacteristic
92C17×#127—22no—
93C17×#127C2314yes—
94C17×#124—28no—
95C17×#124—22no—
96C17×#124—22no—
97C17×#124C2314yes—
98C17×#124C2314yes—
99C17×#123—28no—
100C17×#123—28no—
101C4×Q8×C17—22no—
102C4×Q8×C17D414yes—
103C4×Q8×C17C2314yes—
104C4×Q8×C17C2314yes—
105C4×D4×C17—28no—
106C4×D4×C17—22no—
107C4×D4×C17—22no—
108C4×D4×C17C2314yes—
109C4×D4×C17C2314yes—
110C2×C4⋊C4×C17—21no—
111C2×C4⋊C4×C17D411yescharacteristic
112C2×C4⋊C4×C17D411yescharacteristic
113C2×C4⋊C4×C17D411yescharacteristic
114C2×C4⋊C4×C17C2311yescharacteristic
115C2×C22⋊C4×C17—21no—
116C2×C22⋊C4×C17—21no—
117C2×C22⋊C4×C17—21no—
118C2×C22⋊C4×C17—21no—
119C2×C22⋊C4×C17—21no—
120C2×C22⋊C4×C17—21no—
121C2×C42×C17—21no—
122C2×C42×C17C2311yescharacteristic
123C2×C42×C17C2311yescharacteristic
124C2×C42×C17C2311yescharacteristic
125#10587633—28no—
126C2×#63231—42no—
127C2×#63231C2314yes—
128C2×#63230—24no—
129C2×#63230—42no—
130C2×#63230C2314yes—
131C2×#63230C2314yes—
132C2×#63229—24no—
133C2×#63229—42no—
134C2×#63229C2314yes—
135C2×#63229C2314yes—
136C2×#63228—24no—
137C2×#63228—42no—
138C2×#63228—42no—
139C2×#63228—42no—
140C2×#63228C2314yes—
141C2×#63228C2314yes—
142C2×#63228C2314yes—
143C2×#63228C2314yes—
144C2×#63227—21no—
145C2×#63227—21no—
146C2×#63227—21no—
147C2×#63227—21no—
148C2×#63227—21no—
149C2×#63227—21no—
150C2×C4⋊Dic17C2311yescharacteristic
151C2×#63225—21no—
152C2×C4×Dic17—21no—
153C22×#3622C2311yescharacteristic
154C22×#3622C2311yescharacteristic
155C22×#3622C2311yescharacteristic
156C22×#3622C2311yescharacteristic
157#10587580—28no—
158#10587580—28no—
159#10587579—28no—
160#10587561—22no—
161#10587561—22no—
162#10587561C2314yes—
163#10587561C2314yes—
164#10587560—22no—
165#10587560C2314yes—
166C4×D68—22no—
167C4×D68—22no—
168C4×D68C2314yes—
169C4×D68C2314yes—
170C4×Dic34—22no—
171C4×Dic34C2314yes—
172#10587506C2314yes—
173#10587503C2314yes—
174#10587503C2314yes—
175#10587481C2314yes—
176#10587480C2314yes—
177#10587480C2314yes—
178#10587478C2314yes—
179C4⋊#3622C2314yes—
180C4⋊#3622C2314yes—
181C4⋊#3622C2314yes—
182#10587474C2314yes—
183#10587474C2314yes—
184C4×#3622C2314yes—
185C24×C17—21no—
186C24×C17—21no—
187C23×D17—21no—
188C23×D17—21no—
189C2×Q8×C17—21no—
190C2×Q8×C17—22no—
191C2×Q8×C17—22no—
192C2×Q8×C17—42no—
193C2×Q8×C17C2×D414yes—
194C2×Q8×C17C2412yes—
195C2×D4×C17—21no—
196C2×D4×C17—21no—
197C2×D4×C17—24no—
198C2×D4×C17—24no—
199C2×D4×C17—22no—
200C2×D4×C17—22no—
201C2×D4×C17—22no—
202C2×D4×C17—22no—
203C2×D4×C17—44no—
204C2×D4×C17—82no—
205C2×D4×C17C2412yes—
206C2×D4×C17C2412yes—
207C22×C4×C17—21no—
208C22×C4×C17—21no—
209C22×C4×C17—24no—
210C22×C4×C17—24no—
211C22×C4×C17—82no—
212C22×C4×C17—82no—
213C22×C4×C17C2×D411yescharacteristic
214C22×C4×C17C2×D411yescharacteristic
215C22×C4×C17C2×D411yescharacteristic
216C22×C4×C17C2×D411yescharacteristic
217C22×C4×C17C2×D411yescharacteristic
218C22×C4×C17C2×D411yescharacteristic
219C22×C4×C17C2411yescharacteristic
220C22×Dic17—21no—
221C22×Dic17—21no—
222C2×D68—22no—
223C2×D68—22no—
224C2×D68—22no—
225C2×D68—22no—
226C2×D68—24no—
227C2×D68—21no—
228C2×D68—21no—
229C2×D68—24no—
230C2×D68—44no—
231C2×D68—82no—
232C2×D68C2412yes—
233C2×D68C2412yes—
234C2×C4×D17—24no—
235C2×C4×D17—24no—
236C2×C4×D17—82no—
237C2×C4×D17—82no—
238C2×Dic34—22no—
239C2×Dic34—22no—
240C2×Dic34—21no—
241C2×Dic34C2412yes—
242C4⋊C4×C17—24no—
243C4⋊C4×C17—21no—
244C4⋊C4×C17C2×D414yes—
245C4⋊C4×C17C2×D414yes—
246C4⋊C4×C17C2×D414yes—
247C4⋊C4×C17C2412yes—
248C22⋊C4×C17—24no—
249C22⋊C4×C17—24no—
250C22⋊C4×C17—24no—
251C22⋊C4×C17—24no—
252C22⋊C4×C17—24no—
253C22⋊C4×C17—24no—
254C42×C17—24no—
255C42×C17C2×D412yes—
256C42×C17C2×D412yes—
257C42×C17C2×D412yes—
258C42×C17C2412yes—
259C42×C17C2412yes—
260C42×C17C2412yes—
261#63231—44no—
262#63230—28no—
263#63230—44no—
264#63229—28no—
265#63229—44no—
266#63228—28no—
267#63228—44no—
268#63228—44no—
269#63228—44no—
270#63227—24no—
271#63227—24no—
272#63227—24no—
273#63227—24no—
274#63227—24no—
275#63227—24no—
276C4⋊Dic17—21no—
277C4⋊Dic17C2412yes—
278#63225—24no—
279C4×Dic17—24no—
280C2×#3622—22no—
281C2×#3622—22no—
282C2×#3622—22no—
283C2×#3622#4114yes—
284C2×#3622C2412yes—
285C2×#3622C2412yes—
286C2×#3622C2412yes—
287C2×#3622C2412yes—
288C2×#3403—171nomaximal, Sylow
289C23×C17—22no—
290C23×C17—22no—
291C23×C17—42no—
292C23×C17—42no—
293C23×C17—42no—
294C23×C17—42no—
295C23×C17—42no—
296C23×C17—42no—
297C23×C17C22×D411yescharacteristic
298C22×D17—22no—
299C22×D17—22no—
300C22×D17—42no—
301C22×D17—42no—
302C22×D17—42no—
303C22×D17—42no—
304C22×D17—42no—
305C22×D17—42no—
306Q8×C17—22no—
307Q8×C17—22no—
308Q8×C17—44no—
309Q8×C17—42no—
310D4×C17—22no—
311D4×C17—22no—
312D4×C17—22no—
313D4×C17—22no—
314D4×C17—48no—
315D4×C17—42no—
316D4×C17—42no—
317D4×C17—84no—
318C2×C4×C17—22no—
319C2×C4×C17—22no—
320C2×C4×C17—22no—
321C2×C4×C17—22no—
322C2×C4×C17—22no—
323C2×C4×C17—22no—
324C2×C4×C17—22no—
325C2×C4×C17—22no—
326C2×C4×C17—42no—
327C2×C4×C17—42no—
328C2×C4×C17—84no—
329C2×C4×C17—84no—
330C2×C4×C17C22×D412yes—
331C2×C4×C17C22×D412yes—
332C2×C4×C17C22×D412yes—
333C2×C4×C17C22×D412yes—
334C2×C4×C17C22×D412yes—
335C2×C4×C17C22×D412yes—
336C2×C4×C17C22×D411yescharacteristic
337C2×C4×C17C2×#4112yes—
338C2×C4×C17H(5,𝔽2)12yes—
339C2×C4×C17C2511yescharacteristic
340C2×Dic17—22no—
341C2×Dic17—22no—
342C2×Dic17—42no—
343C2×Dic17—42no—
344D68—22no—
345D68—22no—
346D68—22no—
347D68—22no—
348D68—48no—
349D68—42no—
350D68—42no—
351D68—84no—
352C4×D17—84no—
353C4×D17—84no—
354Dic34—22no—
355Dic34—22no—
356Dic34—42no—
357#3622—22no—
358#3622—22no—
359#3622—22no—
360#3622C2×#4114yes—
361C2×#559—171no—
362C2×#559D1711yescharacteristic, complemented
363#3403—1716no—
364C2×#496—171no—
365C2×#496—171no—
366C2×#495—171no—
367C2×#464—171no—
368C2×#464—171no—
369C2×#463—171no—
370C2×#463—171no—
371C2×#459—171no—
372C2×#459—171no—
373C2×#446—171no—
374C2×#440—171no—
375C2×#440—171no—
376C2×C4×D8—171no—
377C22×C17—42no—
378C22×C17—42no—
379C22×C17—42no—
380C22×C17—42no—
381C22×C17—42no—
382C22×C17—42no—
383C22×C17—84no—
384C22×C17—84no—
385C22×C17#55012yes—
386C22×C17#57512yes—
387C22×C17#57612yes—
388C22×C17C23×D411yescharacteristic
389C2×D17—42no—
390C2×D17—42no—
391C2×D17—42no—
392C2×D17—42no—
393C2×D17—42no—
394C2×D17—42no—
395C2×D17—84no—
396C2×D17—84no—
397C4×C17—22no—
398C4×C17—22no—
399C4×C17—22no—
400C4×C17—22no—
401C4×C17—22no—
402C4×C17—22no—
403C4×C17—42no—
404C4×C17—42no—
405C4×C17#55012yes—
406C4×C17C22×#4111yescharacteristic
407C4×C17C2×H(5,𝔽2)11yescharacteristic
408Dic17—42no—
409Dic17—42no—
410C22×Q16—171no—
411C22×SD16—171no—
412C22×SD16—171no—
413C22×SD16—171no—
414C22×SD16—171no—
415C22×D8—171no—
416C22×D8—171no—
417C22×D8—171no—
418C22×D8—171no—
419#559—24no—
420#559—178no—
421#559—344no—
422#559C2×D1718yescomplemented
423C2×#127—171no—
424C2×#127C2×D1711yescharacteristic
425C2×#124—21no—
426C2×#124—171no—
427C2×#124—171no—
428C2×#124—341no—
429C2×#124C2×D1711yescharacteristic
430C2×#124C2×D1711yescharacteristic
431C2×#123—21no—
432C2×#123—21no—
433C2×#123—341no—
434C2×#123—341no—
435C2×C4×Q8—171no—
436C2×C4×Q8C2×D1711yescharacteristic
437C2×C4×Q8C2×D1711yescharacteristic
438C2×C4×D4—21no—
439C2×C4×D4—171no—
440C2×C4×D4—171no—
441C2×C4×D4—341no—
442C2×C4×D4C2×D1711yescharacteristic
443C2×C4×D4C2×D1711yescharacteristic
444#496—178no—
445#496—178no—
446#495—178no—
447#464—178no—
448#464—178no—
449#463—178no—
450#463—178no—
451#459—178no—
452#459—178no—
453#446—178no—
454#440—178no—
455#440—178no—
456C4×D8—178no—
457C2×#107—171no—
458C2×C4⋊C8—171no—
459C2×C4⋊C8—171no—
460C2×C4⋊C8—171no—
461C2×#103—171no—
462C2×#103—171no—
463C2×#102—171no—
464C2×#102—171no—
465C2×#102—171no—
466C2×#102—171no—
467C2×#97—171no—
468C2×#97—171no—
469C2×C4×C8—171no—
470C2×C17—82no—
471C2×C17—82no—
472C2×C17#340314yescomplemented
473C2×C17C2×#55011yescharacteristic
474C2×C17C2×#57511yescharacteristic
475C2×C17C2×#57611yescharacteristic
476D17—82no—
477D17—82no—
478C22×Q8—171no—
479C22×Q8C22⋊D1711yescharacteristic
480C22×Q8C22×D1711yescharacteristic
481C22×D4—21no—
482C22×D4—21no—
483C22×D4—171no—
484C22×D4—171no—
485C22×D4—341no—
486C22×D4—341no—
487C22×D4C22×D1711yescharacteristic
488C22×D4C22×D1711yescharacteristic
489C23×C4—21no—
490C23×C4—21no—
491C23×C4—341no—
492C23×C4—341no—
493C2×Q16—174no—
494C2×Q16—682no—
495C2×SD16—174no—
496C2×SD16—174no—
497C2×SD16—174no—
498C2×SD16—174no—
499C2×SD16—344no—
500C2×SD16—344no—
501C2×SD16—682no—
502C2×SD16—682no—
503C2×D8—174no—
504C2×D8—174no—
505C2×D8—174no—
506C2×D8—174no—
507C2×D8—344no—
508C2×D8—682no—
509C2×D8—682no—
510C2×D8—682no—
511C22×C8—171no—
512C22×C8—171no—
513C22×C8—171no—
514C22×C8—171no—
515#127—22no—
516#127—174no—
517#127—342no—
518#127C22×D1714yes—
519#124—28no—
520#124—22no—
521#124—22no—
522#124—174no—
523#124—174no—
524#124—348no—
525#124—342no—
526#124—342no—
527#124C22×D1714yes—
528#124C22×D1714yes—
529#123—28no—
530#123—28no—
531#123—348no—
532#123—348no—
533C4×Q8—22no—
534C4×Q8—174no—
535C4×Q8—342no—
536C4×Q8C22⋊D1714yes—
537C4×Q8C22×D1714yes—
538C4×Q8C22×D1714yes—
539C4×D4—28no—
540C4×D4—22no—
541C4×D4—22no—
542C4×D4—174no—
543C4×D4—174no—
544C4×D4—348no—
545C4×D4—342no—
546C4×D4—342no—
547C4×D4C22×D1714yes—
548C4×D4C22×D1714yes—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—171no—
551C2×C4⋊C4—341no—
552C2×C4⋊C4C22⋊D1711yescharacteristic
553C2×C4⋊C4C22⋊D1711yescharacteristic
554C2×C4⋊C4C22⋊D1711yescharacteristic
555C2×C4⋊C4C22×D1711yescharacteristic
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—341no—
563C2×C22⋊C4—341no—
564C2×C22⋊C4—341no—
565C2×C22⋊C4—341no—
566C2×C22⋊C4—341no—
567C2×C22⋊C4—341no—
568C2×C42—21no—
569C2×C42—341no—
570C2×C42C22×D1711yescharacteristic
571C2×C42C22×D1711yescharacteristic
572C2×C42C22×D1711yescharacteristic
573#107—174no—
574C4⋊C8—174no—
575C4⋊C8—174no—
576C4⋊C8—174no—
577#103—174no—
578#103—174no—
579#102—174no—
580#102—174no—
581#102—174no—
582#102—174no—
583#97—174no—
584#97—174no—
585C4×C8—174no—
586C17C2×#340311yescharacteristic, complemented, Sylow
587C24—21no—
588C24—21no—
589C24—341no—
590C24—341no—
591C2×Q8—21no—
592C2×Q8—22no—
593C2×Q8—22no—
594C2×Q8—42no—
595C2×Q8—172no—
596C2×Q8—341no—
597C2×Q8—342no—
598C2×Q8—342no—
599C2×Q8C2×C22⋊D1714yes—
600C2×Q8C23×D1712yes—
601C2×D4—22no—
602C2×D4—22no—
603C2×D4—22no—
604C2×D4—22no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—24no—
608C2×D4—24no—
609C2×D4—44no—
610C2×D4—82no—
611C2×D4—172no—
612C2×D4—172no—
613C2×D4—342no—
614C2×D4—342no—
615C2×D4—342no—
616C2×D4—342no—
617C2×D4—344no—
618C2×D4—341no—
619C2×D4—341no—
620C2×D4—344no—
621C2×D4—684no—
622C2×D4—1362no—
623C2×D4C23×D1712yes—
624C2×D4C23×D1712yes—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—24no—
628C22×C4—24no—
629C22×C4—82no—
630C22×C4—82no—
631C22×C4—341no—
632C22×C4—341no—
633C22×C4—344no—
634C22×C4—344no—
635C22×C4—1362no—
636C22×C4—1362no—
637C22×C4C2×C22⋊D1711yescharacteristic
638C22×C4C2×C22⋊D1711yescharacteristic
639C22×C4C2×C22⋊D1711yescharacteristic
640C22×C4C2×C22⋊D1711yescharacteristic
641C22×C4C2×C22⋊D1711yescharacteristic
642C22×C4C2×C22⋊D1711yescharacteristic
643C22×C4C23×D1711yescharacteristic
644Q16—684no—
645SD16—348no—
646SD16—348no—
647SD16—684no—
648SD16—684no—
649D8—348no—
650D8—684no—
651D8—684no—
652D8—684no—
653C2×C8—174no—
654C2×C8—172no—
655C2×C8—172no—
656C2×C8—172no—
657C2×C8—172no—
658C2×C8—342no—
659C2×C8—342no—
660C2×C8—342no—
661C4⋊C4—24no—
662C4⋊C4—21no—
663C4⋊C4—172no—
664C4⋊C4—341no—
665C4⋊C4—344no—
666C4⋊C4C2×C22⋊D1714yes—
667C4⋊C4C2×C22⋊D1714yes—
668C4⋊C4C2×C22⋊D1714yes—
669C4⋊C4C23×D1712yes—
670C22⋊C4—24no—
671C22⋊C4—24no—
672C22⋊C4—24no—
673C22⋊C4—24no—
674C22⋊C4—24no—
675C22⋊C4—24no—
676C22⋊C4—344no—
677C22⋊C4—344no—
678C22⋊C4—344no—
679C22⋊C4—344no—
680C22⋊C4—344no—
681C22⋊C4—344no—
682C42—24no—
683C42—344no—
684C42C2×C22⋊D1712yes—
685C42C2×C22⋊D1712yes—
686C42C2×C22⋊D1712yes—
687C42C23×D1712yes—
688C42C23×D1712yes—
689C42C23×D1712yes—
690C23—22no—
691C23—22no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—342no—
699C23—342no—
700C23—682no—
701C23—682no—
702C23—682no—
703C23—682no—
704C23—682no—
705C23—682no—
706C23C22×C22⋊D1711yescharacteristic
707Q8—22no—
708Q8—22no—
709Q8—44no—
710Q8—42no—
711Q8—342no—
712Q8—342no—
713Q8—682no—
714D4—22no—
715D4—22no—
716D4—22no—
717D4—22no—
718D4—48no—
719D4—42no—
720D4—42no—
721D4—84no—
722D4—342no—
723D4—342no—
724D4—342no—
725D4—342no—
726D4—688no—
727D4—682no—
728D4—682no—
729D4—1364no—
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—342no—
743C2×C4—342no—
744C2×C4—682no—
745C2×C4—682no—
746C2×C4—1364no—
747C2×C4—1364no—
748C2×C4#41×D1712yes—
749C2×C4#1058769612yes—
750C2×C4C22×C22⋊D1712yes—
751C2×C4C22×C22⋊D1712yes—
752C2×C4C22×C22⋊D1712yes—
753C2×C4C22×C22⋊D1712yes—
754C2×C4C22×C22⋊D1712yes—
755C2×C4C22×C22⋊D1712yes—
756C2×C4C22×C22⋊D1711yescharacteristic
757C2×C4C24×D1711yescharacteristic
758C8—174no—
759C8—342no—
760C8—342no—
761C8—342no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—84no—
769C22—84no—
770C22—682no—
771C22—682no—
772C22—682no—
773C22—682no—
774C22—682no—
775C22—682no—
776C22—1364no—
777C22—1364no—
778C22#1176347812yes—
779C22#1176360712yes—
780C22#1176361212yes—
781C22C23×C22⋊D1711yescharacteristic
782C4—22no—
783C4—22no—
784C4—22no—
785C4—22no—
786C4—22no—
787C4—22no—
788C4—42no—
789C4—42no—
790C4—682no—
791C4—682no—
792C4#1176347812yes—
793C4C2×#41×D1711yescharacteristic
794C4C2×#1058769611yescharacteristic
795C2—82no—
796C2—82no—
797C2—1362no—
798C2—1362no—
799C2#1454186814yesdirect product factor
800C2C2×#1176347811yescharacteristic
801C2C2×#1176360711yescharacteristic
802C2C2×#1176361211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#559C2
socleC23×C17C22×D4
hypercenterC2×#559D17
hypocenterC17C2×#3403
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#559

Complements

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

NH ≅ G/Ntype
1. C2×#11763544C2semidirect
2. #14541868C2direct (N × H)
3. C2×#11763199C2semidirect
4. C2×#11763196C2semidirect
5. C2×#11763191C2semidirect
6. C2×#11763031C2semidirect
7. C2×#11763028C2semidirect
8. C2×#11763024C2semidirect
9. C2×#11763021C2semidirect
10. C2×#11763004C2semidirect
11. C2×#11763001C2semidirect
12. C2×#11762940C2semidirect
13. C2×#11762909C2semidirect
14. C2×#11762907C2semidirect
15. C2×C4×#63228C2semidirect
16. C2×C17×#559C2semidirect
27. #11763544C22semidirect
38. #11763199C22semidirect
39. #11763196C22semidirect
40. #11763191C22semidirect
41. #11763031C22semidirect
42. #11763028C22semidirect
43. #11763024C22semidirect
44. #11763021C22semidirect
45. #11763004C22semidirect
46. #11763001C22semidirect
47. #11762940C22semidirect
48. #11762909C22semidirect
49. #11762907C22semidirect
50. C4×#63228C22semidirect
65. C17×#559C22semidirect
362. C2×#559D17semidirect
422. #559C2×D17semidirect
472. C2×C17#3403semidirect
586. C17C2×#3403semidirect
799. C2#14541868direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117635442
#145418682
C2×#117631992
C2×#117631962
C2×#117631912
C2×#117630312
C2×#117630282
C2×#117630242
C2×#117630212
C2×#117630042
C2×#117630012
C2×#117629402
C2×#117629092
C2×#117629072
C2×C4×#632282
C2×C17×#5592
C2×#340317