Finite Group Databasebeta

← C2×#14540249 #17907294

Subgroups — C2×#14540249 #17907294

Order 4352.

1882 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763430C211yesmaximal, characteristic, complemented
2#14540249C2116yesmaximal, direct product factor
3C2×#11763094C211yesmaximal, characteristic, complemented
4C2×#11763091C211yesmaximal, characteristic, complemented
5C2×#11763099C211yesmaximal, characteristic, complemented
6C2×#11763096C211yesmaximal, characteristic, complemented
7C2×#11763065C211yesmaximal, characteristic, complemented
8C2×#11763060C211yesmaximal, characteristic
9C2×#11763040C211yesmaximal, characteristic, complemented
10C2×#11763036C211yesmaximal, characteristic, complemented
11C2×#11763031C211yesmaximal, characteristic, complemented
12C2×#11763028C211yesmaximal, characteristic, complemented
13C2×#11763024C211yesmaximal, characteristic, complemented
14C2×#11763021C211yesmaximal, characteristic, complemented
15C2×#11762836C211yesmaximal, characteristic, complemented
16C2×C17×#542C211yesmaximal, characteristic, complemented
17C22×#63231C2211yescharacteristic
18C22×#63229C2211yescharacteristic
19C22×#63230C2211yescharacteristic
20C22×#63228C2211yescharacteristic
21C22×#63223C2211yescharacteristic
22C23×#3622C2211yescharacteristic
23#11763430—24no—
24#11763430C2218yescomplemented
25C2×#10587555C2211yescharacteristic
26C2×#10587584—21no—
27C2×#10587561C2211yescharacteristic
28C2×#10587571—21no—
29C2×#10587569—21no—
30C2×#10587610C2211yescharacteristic
31C2×#10587582—21no—
32C2×#10587616C2211yescharacteristic
33C2×C4×Dic34C2211yescharacteristic
34C2×C4×D68C2211yescharacteristic
35#11763099C2218yescomplemented
36#11763096C2218yescomplemented
37#11763094C2218yescomplemented
38#11763091C2218yescomplemented
39#11763065C2218yescomplemented
40#11763060C2218yes—
41#11763040C2218yescomplemented
42#11763036C2218yescomplemented
43#11763031C2218yescomplemented
44#11763028C2218yescomplemented
45#11763024C2218yescomplemented
46#11763021C2218yescomplemented
47C2×#10587479C2211yescharacteristic
48C2×#10587479C2211yescharacteristic
49C2×#10587479C2211yescharacteristic
50C2×#10587479C2211yescharacteristic
51#11762836C2218yescomplemented
52C2×C4⋊#3622C2211yescharacteristic
53C2×C4⋊#3622C2211yescharacteristic
54C2×C4⋊#3622C2211yescharacteristic
55C2×C4⋊#3622C2211yescharacteristic
56C2×#10587506C2211yescharacteristic
57C2×#10587506C2211yescharacteristic
58C2×#10587481C2211yescharacteristic
59C2×#10587481C2211yescharacteristic
60C2×#10587503C2211yescharacteristic
61C2×#10587503C2211yescharacteristic
62C2×#10587480C2211yescharacteristic
63C2×#10587480C2211yescharacteristic
64C17×#542—24no—
65C17×#542C2218yescomplemented
66C2×C17×C4⋊Q8C2211yescharacteristic
67C2×C17×#126—21no—
68C2×C17×#124—21no—
69C2×C17×#124C2211yescharacteristic
70C2×C17×#123—21no—
71C2×C17×C22⋊Q8—21no—
72C2×C17×C22⋊Q8C2211yescharacteristic
73C2×C17×#121C2211yescharacteristic
74C2×C4×Q8×C17C2211yescharacteristic
75C2×C4×D4×C17C2211yescharacteristic
76C2×C17×#117C2211yescharacteristic
77C22×Q8×C17—21no—
78C22×Q8×C17C2311yescharacteristic
79C22×D4×C17—21no—
80C22×D4×C17C2311yescharacteristic
81C23×C4×C17—21no—
82C23×C4×C17C2311yescharacteristic
83C22×C22⋊D17—21no—
84C22×D68C2311yescharacteristic
85C22×C4×D17—21no—
86C22×Dic34—21no—
87C22×Dic34C2311yescharacteristic
88C17×C4⋊Q8—22no—
89C17×C4⋊Q8C2314yes—
90C17×#126—28no—
91C17×#124—28no—
92C17×#124—22no—
93C17×#124C2314yes—
94C17×#123—28no—
95C17×C22⋊Q8—22no—
96C17×C22⋊Q8—28no—
97C17×C22⋊Q8C2314yes—
98C17×#121—22no—
99C17×#121C2314yes—
100C4×Q8×C17—22no—
101C4×Q8×C17C2314yes—
102C4×D4×C17—22no—
103C4×D4×C17C2314yes—
104C17×#117D414yes—
105C17×#117C2314yes—
106C2×C4⋊C4×C17—21no—
107C2×C4⋊C4×C17—21no—
108C2×C4⋊C4×C17—21no—
109C2×C4⋊C4×C17D411yescharacteristic
110C2×C4⋊C4×C17D411yescharacteristic
111C2×C4⋊C4×C17C2311yescharacteristic
112C2×C4⋊C4×C17C2311yescharacteristic
113C2×C22⋊C4×C17—21no—
114C2×C22⋊C4×C17—21no—
115C2×C22⋊C4×C17—21no—
116C2×C22⋊C4×C17—21no—
117C2×C22⋊C4×C17—21no—
118C2×C22⋊C4×C17D411yescharacteristic
119C2×C22⋊C4×C17D411yescharacteristic
120C2×C42×C17—21no—
121C2×C42×C17C2311yescharacteristic
122C2×C42×C17C2311yescharacteristic
123C2×C22⋊Dic17—21no—
124C2×#63231—42no—
125C2×#63231C2314yes—
126C2×#63230—42no—
127C2×#63230C2314yes—
128C2×#63229—42no—
129C2×#63229C2314yes—
130C2×#63228—42no—
131C2×#63228C2314yes—
132#10587616—22no—
133#10587616C2314yes—
134C2×#63227—21no—
135C2×#63227—21no—
136C2×#63227—21no—
137C2×#63227—21no—
138C2×C4⋊Dic17—21no—
139C2×C4⋊Dic17C2311yescharacteristic
140C2×C4⋊Dic17C2311yescharacteristic
141#10587610—22no—
142#10587610C2314yes—
143C2×#63225—21no—
144C2×#63225—21no—
145C2×C4×Dic17—21no—
146C2×#63223—42no—
147C2×#63223C2314yes—
148C22×#3622—42no—
149C22×#3622C2311yescharacteristic
150C22×#3622C2311yescharacteristic
151C22×#3622C2311yescharacteristic
152C22×#3622C2311yescharacteristic
153C22×#3622C2314yes—
154#10587584—28no—
155#10587582—28no—
156#10587571—28no—
157#10587569—28no—
158#10587561—22no—
159#10587561C2314yes—
160C4×D68—22no—
161C4×D68C2314yes—
162#10587555—22no—
163#10587555C2314yes—
164C4×Dic34—22no—
165C4×Dic34C2314yes—
166#10587506C2314yes—
167#10587506C2314yes—
168#10587503C2314yes—
169#10587503C2314yes—
170#10587481C2314yes—
171#10587481C2314yes—
172#10587480C2314yes—
173#10587480C2314yes—
174#10587479C2314yes—
175#10587479C2314yes—
176#10587479C2314yes—
177#10587479C2314yes—
178C4⋊#3622C2314yes—
179C4⋊#3622C2314yes—
180C4⋊#3622C2314yes—
181C4⋊#3622C2314yes—
182C24×C17—21no—
183C24×C17C2×D411yescharacteristic
184C23×D17—21no—
185C2×Q8×C17—21no—
186C2×Q8×C17—24no—
187C2×Q8×C17—22no—
188C2×Q8×C17—22no—
189C2×Q8×C17—82no—
190C2×Q8×C17C2412yes—
191C2×D4×C17—24no—
192C2×D4×C17—21no—
193C2×D4×C17—22no—
194C2×D4×C17—22no—
195C2×D4×C17—82no—
196C2×D4×C17C2412yes—
197C22×C4×C17—22no—
198C22×C4×C17—22no—
199C22×C4×C17—21no—
200C22×C4×C17—21no—
201C22×C4×C17—21no—
202C22×C4×C17—24no—
203C22×C4×C17—82no—
204C22×C4×C17C2×D412yes—
205C22×C4×C17C2×D411yescharacteristic
206C22×C4×C17C2×D411yescharacteristic
207C22×C4×C17C2×D411yescharacteristic
208C22×C4×C17C2×D411yescharacteristic
209C22×C4×C17C2×D411yescharacteristic
210C22×C4×C17C2412yes—
211C22×C4×C17C2411yescharacteristic
212C2×C22⋊D17—24no—
213C2×C22⋊D17—82no—
214C22×Dic17—21no—
215C22×Dic17—21no—
216C22×Dic17—21no—
217C2×D68—22no—
218C2×D68—22no—
219C2×D68—21no—
220C2×D68C2412yes—
221C2×C4×D17—24no—
222C2×C4×D17—82no—
223C2×Dic34—22no—
224C2×Dic34—22no—
225C2×Dic34—21no—
226C2×Dic34—24no—
227C2×Dic34—82no—
228C2×Dic34C2412yes—
229C4⋊C4×C17—24no—
230C4⋊C4×C17—24no—
231C4⋊C4×C17—21no—
232C4⋊C4×C17—24no—
233C4⋊C4×C17—21no—
234C4⋊C4×C17C2×D414yes—
235C4⋊C4×C17C2×D414yes—
236C4⋊C4×C17C2412yes—
237C4⋊C4×C17C2412yes—
238C22⋊C4×C17—24no—
239C22⋊C4×C17—24no—
240C22⋊C4×C17—24no—
241C22⋊C4×C17—24no—
242C22⋊C4×C17—24no—
243C22⋊C4×C17C2×D414yes—
244C22⋊C4×C17C2×D414yes—
245C42×C17—24no—
246C42×C17C2×D412yes—
247C42×C17C2×D412yes—
248C42×C17C2412yes—
249C42×C17C2412yes—
250C22⋊Dic17—24no—
251#63231—44no—
252#63230—44no—
253#63229—44no—
254#63228—44no—
255#63227—24no—
256#63227—24no—
257#63227—24no—
258#63227—24no—
259C4⋊Dic17—21no—
260C4⋊Dic17—21no—
261C4⋊Dic17—24no—
262C4⋊Dic17C2412yes—
263C4⋊Dic17C2412yes—
264#63225—24no—
265#63225—24no—
266C4×Dic17—24no—
267#63223—44no—
268C2×#3622—22no—
269C2×#3622—22no—
270C2×#3622—22no—
271C2×#3622—22no—
272C2×#3622—44no—
273C2×#3622C2412yes—
274C2×#3622C2412yes—
275C2×#3622C2412yes—
276C2×#3622C2412yes—
277C2×#3263—171nomaximal, Sylow
278C23×C17—22no—
279C23×C17—22no—
280C23×C17—22no—
281C23×C17—22no—
282C23×C17—42no—
283C23×C17—42no—
284C23×C17—42no—
285C23×C17C22×D412yes—
286C23×C17C22×D411yescharacteristic
287C22×D17—22no—
288C22×D17—42no—
289C22×D17—42no—
290C22×D17—42no—
291Q8×C17—22no—
292Q8×C17—22no—
293Q8×C17—42no—
294Q8×C17—84no—
295D4×C17—22no—
296D4×C17—22no—
297D4×C17—42no—
298D4×C17—84no—
299C2×C4×C17—22no—
300C2×C4×C17—22no—
301C2×C4×C17—22no—
302C2×C4×C17—22no—
303C2×C4×C17—22no—
304C2×C4×C17—24no—
305C2×C4×C17—22no—
306C2×C4×C17—22no—
307C2×C4×C17—22no—
308C2×C4×C17—22no—
309C2×C4×C17—22no—
310C2×C4×C17—42no—
311C2×C4×C17—42no—
312C2×C4×C17—42no—
313C2×C4×C17—84no—
314C2×C4×C17C22×D412yes—
315C2×C4×C17C22×D412yes—
316C2×C4×C17C22×D412yes—
317C2×C4×C17C22×D412yes—
318C2×C4×C17C22×D412yes—
319C2×C4×C17C22×D411yescharacteristic
320C2×C4×C17H(5,𝔽2)12yes—
321C2×C4×C172−1+412yes—
322C2×C4×C17C2511yescharacteristic
323C22⋊D17—84no—
324C2×Dic17—22no—
325C2×Dic17—22no—
326C2×Dic17—22no—
327C2×Dic17—42no—
328C2×Dic17—42no—
329C2×Dic17—42no—
330D68—22no—
331D68—22no—
332D68—42no—
333C4×D17—84no—
334Dic34—22no—
335Dic34—22no—
336Dic34—42no—
337Dic34—84no—
338#3622—22no—
339#3622—22no—
340#3622—22no—
341#3622—22no—
342C2×#542—171no—
343C2×#542D1711yescharacteristic, complemented
344#3263—1716no—
345C2×#475—171no—
346C2×#475—171no—
347C2×#476—171no—
348C2×#476—171no—
349C2×#470—171no—
350C2×#469—171no—
351C2×#465—171no—
352C2×#465—171no—
353C2×#464—171no—
354C2×#464—171no—
355C2×#463—171no—
356C2×#463—171no—
357C2×#424—171no—
358C22×C17—22no—
359C22×C17—22no—
360C22×C17—22no—
361C22×C17—44no—
362C22×C17—42no—
363C22×C17—42no—
364C22×C17—42no—
365C22×C17—84no—
366C22×C17#53712yes—
367C22×C17#57712yes—
368C22×C17#57712yes—
369C22×C17C23×D411yescharacteristic
370C2×D17—42no—
371C2×D17—42no—
372C2×D17—42no—
373C2×D17—84no—
374C4×C17—22no—
375C4×C17—22no—
376C4×C17—22no—
377C4×C17—22no—
378C4×C17—22no—
379C4×C17—42no—
380C4×C17—42no—
381C4×C17—42no—
382C4×C17#53712yes—
383C4×C17C2×H(5,𝔽2)11yescharacteristic
384C4×C17C2×2−1+411yescharacteristic
385Dic17—42no—
386Dic17—42no—
387Dic17—42no—
388C22×Q16—171no—
389C22×SD16—171no—
390C22×SD16—171no—
391C22×D8—171no—
392C22×M16—171no—
393C23×C8—171no—
394#542—24no—
395#542—178no—
396#542—344no—
397#542C2×D1718yescomplemented
398C2×C4⋊Q8—171no—
399C2×C4⋊Q8C2×D1711yescharacteristic
400C2×#126—21no—
401C2×#126—341no—
402C2×#124—21no—
403C2×#124—171no—
404C2×#124—341no—
405C2×#124C2×D1711yescharacteristic
406C2×#123—21no—
407C2×#123—341no—
408C2×C22⋊Q8—21no—
409C2×C22⋊Q8—171no—
410C2×C22⋊Q8—341no—
411C2×C22⋊Q8C2×D1711yescharacteristic
412C2×#121—171no—
413C2×#121C2×D1711yescharacteristic
414C2×C4×Q8—171no—
415C2×C4×Q8C2×D1711yescharacteristic
416C2×C4×D4—171no—
417C2×C4×D4C2×D1711yescharacteristic
418C2×#117C2×D1711yescharacteristic
419#476—178no—
420#476—178no—
421#475—178no—
422#475—178no—
423#470—178no—
424#469—178no—
425#465—178no—
426#465—178no—
427#464—178no—
428#464—178no—
429#463—178no—
430#463—178no—
431C2×#106—171no—
432C2×#106—171no—
433C2×#106—171no—
434C2×#106—171no—
435#424—178no—
436C2×C4⋊C8—171no—
437C2×C4⋊C8—171no—
438C2×C4⋊C8—171no—
439C2×C4⋊C8—171no—
440C2×#103—171no—
441C2×#103—171no—
442C2×#103—171no—
443C2×#103—171no—
444C2×#102—171no—
445C2×#102—171no—
446C2×#102—171no—
447C2×#102—171no—
448C2×C17—42no—
449C2×C17—82no—
450C2×C17#326314yescomplemented
451C2×C17C2×#53711yescharacteristic
452C2×C17C2×#57711yescharacteristic
453C2×C17C2×#57711yescharacteristic
454D17—82no—
455C22×Q8—21no—
456C22×Q8—171no—
457C22×Q8—341no—
458C22×Q8C22×D1711yescharacteristic
459C22×D4—21no—
460C22×D4—171no—
461C22×D4—341no—
462C22×D4C22×D1711yescharacteristic
463C23×C4—21no—
464C23×C4—341no—
465C23×C4C22×D1711yescharacteristic
466C2×Q16—174no—
467C2×Q16—682no—
468C2×SD16—174no—
469C2×SD16—174no—
470C2×SD16—682no—
471C2×SD16—682no—
472C2×D8—174no—
473C2×D8—682no—
474C2×M16—174no—
475C2×M16—682no—
476C22×C8—171no—
477C22×C8—171no—
478C22×C8—171no—
479C22×C8—171no—
480C22×C8—174no—
481C22×C8—682no—
482C4⋊Q8—22no—
483C4⋊Q8—174no—
484C4⋊Q8—342no—
485C4⋊Q8C22×D1714yes—
486#126—28no—
487#126—348no—
488#124—28no—
489#124—22no—
490#124—174no—
491#124—348no—
492#124—342no—
493#124C22×D1714yes—
494#123—28no—
495#123—348no—
496C22⋊Q8—22no—
497C22⋊Q8—28no—
498C22⋊Q8—174no—
499C22⋊Q8—342no—
500C22⋊Q8—348no—
501C22⋊Q8C22×D1714yes—
502#121—22no—
503#121—174no—
504#121—342no—
505#121C22×D1714yes—
506C4×Q8—22no—
507C4×Q8—174no—
508C4×Q8—342no—
509C4×Q8C22×D1714yes—
510C4×D4—22no—
511C4×D4—174no—
512C4×D4—342no—
513C4×D4C22×D1714yes—
514#117C22⋊D1714yes—
515#117C22×D1714yes—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—171no—
520C2×C4⋊C4—171no—
521C2×C4⋊C4—341no—
522C2×C4⋊C4—341no—
523C2×C4⋊C4—341no—
524C2×C4⋊C4C22⋊D1711yescharacteristic
525C2×C4⋊C4C22⋊D1711yescharacteristic
526C2×C4⋊C4C22×D1711yescharacteristic
527C2×C4⋊C4C22×D1711yescharacteristic
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—341no—
534C2×C22⋊C4—341no—
535C2×C22⋊C4—341no—
536C2×C22⋊C4—341no—
537C2×C22⋊C4—341no—
538C2×C22⋊C4C22⋊D1711yescharacteristic
539C2×C22⋊C4C22⋊D1711yescharacteristic
540C2×C42—21no—
541C2×C42—341no—
542C2×C42C22×D1711yescharacteristic
543C2×C42C22×D1711yescharacteristic
544#106—174no—
545#106—174no—
546#106—174no—
547#106—174no—
548C4⋊C8—174no—
549C4⋊C8—174no—
550C4⋊C8—174no—
551C4⋊C8—174no—
552#103—174no—
553#103—174no—
554#103—174no—
555#103—174no—
556#102—174no—
557#102—174no—
558#102—174no—
559#102—174no—
560C17C2×#326311yescharacteristic, complemented, Sylow
561C24—21no—
562C24—341no—
563C24C2×C22⋊D1711yescharacteristic
564C2×Q8—21no—
565C2×Q8—24no—
566C2×Q8—22no—
567C2×Q8—22no—
568C2×Q8—82no—
569C2×Q8—172no—
570C2×Q8—341no—
571C2×Q8—344no—
572C2×Q8—342no—
573C2×Q8—342no—
574C2×Q8—1362no—
575C2×Q8C23×D1712yes—
576C2×D4—24no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—21no—
580C2×D4—82no—
581C2×D4—172no—
582C2×D4—344no—
583C2×D4—342no—
584C2×D4—342no—
585C2×D4—341no—
586C2×D4—1362no—
587C2×D4C23×D1712yes—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—24no—
594C22×C4—82no—
595C22×C4—341no—
596C22×C4—341no—
597C22×C4—341no—
598C22×C4—344no—
599C22×C4—1362no—
600C22×C4C2×C22⋊D1712yes—
601C22×C4C2×C22⋊D1711yescharacteristic
602C22×C4C2×C22⋊D1711yescharacteristic
603C22×C4C2×C22⋊D1711yescharacteristic
604C22×C4C2×C22⋊D1711yescharacteristic
605C22×C4C2×C22⋊D1711yescharacteristic
606C22×C4C23×D1712yes—
607C22×C4C23×D1711yescharacteristic
608Q16—684no—
609SD16—684no—
610SD16—684no—
611D8—684no—
612M16—684no—
613C2×C8—172no—
614C2×C8—172no—
615C2×C8—172no—
616C2×C8—172no—
617C2×C8—342no—
618C2×C8—342no—
619C2×C8—342no—
620C2×C8—342no—
621C2×C8—684no—
622C4⋊C4—24no—
623C4⋊C4—24no—
624C4⋊C4—24no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—172no—
628C4⋊C4—172no—
629C4⋊C4—341no—
630C4⋊C4—341no—
631C4⋊C4—344no—
632C4⋊C4—344no—
633C4⋊C4—344no—
634C4⋊C4C2×C22⋊D1714yes—
635C4⋊C4C2×C22⋊D1714yes—
636C4⋊C4C23×D1712yes—
637C4⋊C4C23×D1712yes—
638C22⋊C4—24no—
639C22⋊C4—24no—
640C22⋊C4—24no—
641C22⋊C4—24no—
642C22⋊C4—24no—
643C22⋊C4—344no—
644C22⋊C4—344no—
645C22⋊C4—344no—
646C22⋊C4—344no—
647C22⋊C4—344no—
648C22⋊C4C2×C22⋊D1714yes—
649C22⋊C4C2×C22⋊D1714yes—
650C42—24no—
651C42—344no—
652C42C2×C22⋊D1712yes—
653C42C2×C22⋊D1712yes—
654C42C23×D1712yes—
655C42C23×D1712yes—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—342no—
664C23—682no—
665C23—682no—
666C23—682no—
667C23C22×C22⋊D1712yes—
668C23C22×C22⋊D1711yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—42no—
672Q8—84no—
673Q8—342no—
674Q8—342no—
675Q8—682no—
676Q8—1364no—
677D4—22no—
678D4—22no—
679D4—42no—
680D4—84no—
681D4—342no—
682D4—342no—
683D4—682no—
684D4—1364no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—24no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—84no—
700C2×C4—342no—
701C2×C4—342no—
702C2×C4—342no—
703C2×C4—682no—
704C2×C4—682no—
705C2×C4—682no—
706C2×C4—1364no—
707C2×C4#1058769612yes—
708C2×C4#1058769712yes—
709C2×C4C22×C22⋊D1712yes—
710C2×C4C22×C22⋊D1712yes—
711C2×C4C22×C22⋊D1712yes—
712C2×C4C22×C22⋊D1712yes—
713C2×C4C22×C22⋊D1712yes—
714C2×C4C22×C22⋊D1711yescharacteristic
715C2×C4C24×D1711yescharacteristic
716C8—342no—
717C8—342no—
718C8—342no—
719C8—342no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—44no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—84no—
728C22—682no—
729C22—682no—
730C22—682no—
731C22—1364no—
732C22#1176338712yes—
733C22#1176361712yes—
734C22#1176362012yes—
735C22C23×C22⋊D1711yescharacteristic
736C4—22no—
737C4—22no—
738C4—22no—
739C4—22no—
740C4—22no—
741C4—42no—
742C4—42no—
743C4—42no—
744C4—682no—
745C4—682no—
746C4—682no—
747C4#1176338712yes—
748C4C2×#1058769611yescharacteristic
749C4C2×#1058769711yescharacteristic
750C2—42no—
751C2—82no—
752C2—1362no—
753C2#1454024914yesdirect product factor
754C2C2×#1176338711yescharacteristic
755C2C2×#1176361711yescharacteristic
756C2C2×#1176362011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#542C2
socleC23×C17C22×D4
prime radicalC2×#11763060C2
hypercenterC2×#542D17
hypocenterC17C2×#3263
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#11763430C2semidirect
2. #14540249C2direct (N × H)
3. C2×#11763094C2semidirect
4. C2×#11763091C2semidirect
5. C2×#11763099C2semidirect
6. C2×#11763096C2semidirect
7. C2×#11763065C2semidirect
9. C2×#11763040C2semidirect
10. C2×#11763036C2semidirect
11. C2×#11763031C2semidirect
12. C2×#11763028C2semidirect
13. C2×#11763024C2semidirect
14. C2×#11763021C2semidirect
15. C2×#11762836C2semidirect
16. C2×C17×#542C2semidirect
24. #11763430C22semidirect
35. #11763099C22semidirect
36. #11763096C22semidirect
37. #11763094C22semidirect
38. #11763091C22semidirect
39. #11763065C22semidirect
41. #11763040C22semidirect
42. #11763036C22semidirect
43. #11763031C22semidirect
44. #11763028C22semidirect
45. #11763024C22semidirect
46. #11763021C22semidirect
51. #11762836C22semidirect
65. C17×#542C22semidirect
343. C2×#542D17semidirect
397. #542C2×D17semidirect
450. C2×C17#3263semidirect
560. C17C2×#3263semidirect
753. C2#14540249direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117634302
#145402492
C2×#117630942
C2×#117630912
C2×#117630992
C2×#117630962
C2×#117630652
C2×#117630602
C2×#117630402
C2×#117630362
C2×#117630312
C2×#117630282
C2×#117630242
C2×#117630212
C2×#117628362
C2×C17×#5422
C2×#326317