Finite Group Databasebeta

← C2×#14541338 #17912996

Subgroups — C2×#14541338 #17912996

Order 4352.

1898 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763499C211yesmaximal, characteristic, complemented
2#14541338C2116yesmaximal, direct product factor
3C2×#11763208C211yesmaximal, characteristic, complemented
4C2×#11763125C211yesmaximal, characteristic, complemented
5C2×#11763150C211yesmaximal, characteristic, complemented
6C2×#11763130C211yesmaximal, characteristic, complemented
7C2×#11763139C211yesmaximal, characteristic, complemented
8C2×#11763113C211yesmaximal, characteristic, complemented
9C2×#11763109C211yesmaximal, characteristic, complemented
10C2×#11763053C211yesmaximal, characteristic, complemented
11C2×#11763053C211yesmaximal, characteristic, complemented
12C2×C4×#63229C211yesmaximal, characteristic, complemented
13C2×#11762887C211yesmaximal, characteristic, complemented
14C2×#11762852C211yesmaximal, characteristic, complemented
15C2×#11762849C211yesmaximal, characteristic, complemented
16C2×C17×#553C211yesmaximal, characteristic
17C22×#63229C2211yescharacteristic
18C22×#63223C2211yescharacteristic
19C22×#63223C2211yescharacteristic
20#11763499—24no—
21#11763499C2218yescomplemented
22C2×#10587565—21no—
23C2×#10587556C2211yescharacteristic
24C2×#10587575—21no—
25C2×#10587621—21no—
26C2×#10587610C2211yescharacteristic
27C2×#10587610C2211yescharacteristic
28C2×C4×Dic34C2211yescharacteristic
29C2×#10587612C2211yescharacteristic
30C2×#10587563—21no—
31C22×C4⋊Dic17C2211yescharacteristic
32#11763208C2218yescomplemented
33#11763150C2218yescomplemented
34#11763139C2218yescomplemented
35#11763130C2218yescomplemented
36#11763125C2218yescomplemented
37#11763113C2218yescomplemented
38#11763109C2218yescomplemented
39#11763053C2218yescomplemented
40#11763053C2218yescomplemented
41C4×#63229C2218yescomplemented
42#11762887C2218yescomplemented
43#11762852C2218yescomplemented
44#11762849C2218yescomplemented
45C2×#10587478C2211yescharacteristic
46C2×#10587478C2211yescharacteristic
47C2×#10587478C2211yescharacteristic
48C2×#10587478C2211yescharacteristic
49C2×#10587479C2211yescharacteristic
50C2×#10587479C2211yescharacteristic
51C2×#10587479C2211yescharacteristic
52C2×#10587479C2211yescharacteristic
53C2×#10587479C2211yescharacteristic
54C2×C4⋊#3622C2211yescharacteristic
55C2×#10587481C2211yescharacteristic
56C2×#10587481C2211yescharacteristic
57C2×#10587481C2211yescharacteristic
58C2×#10587503C2211yescharacteristic
59C2×#10587503C2211yescharacteristic
60C2×#10587503C2211yescharacteristic
61C2×C22⋊#3622C2211yescharacteristic
62C2×C22⋊#3622C2211yescharacteristic
63C2×C4×#3622C2211yescharacteristic
64C17×#553—24no—
65C17×#553C2218yes—
66C2×C17×#126—21no—
67C2×C17×#125C2211yescharacteristic
68C2×C17×#123—21no—
69C2×C17×#121—21no—
70C2×C17×#121C2211yescharacteristic
71C2×C17×#121C2211yescharacteristic
72C2×C4×D4×C17—21no—
73C2×C4×D4×C17C2211yescharacteristic
74C2×C4×D4×C17C2211yescharacteristic
75C2×C17×#117C2211yescharacteristic
76C22×C4⋊C4×C17C2211yescharacteristic
77C22×D4×C17—21no—
78C22×D4×C17—21no—
79C22×D4×C17D411yescharacteristic
80C22×D4×C17C2311yescharacteristic
81C23×C4×C17—21no—
82C23×C4×C17—21no—
83C23×C4×C17C2311yescharacteristic
84C23×C4×C17C2311yescharacteristic
85C23×Dic17—21no—
86C22×Dic34C2311yescharacteristic
87C17×#126—28no—
88C17×#125—22no—
89C17×#125C2314yes—
90C17×#123—28no—
91C17×#121—28no—
92C17×#121—22no—
93C17×#121—22no—
94C17×#121C2314yes—
95C17×#121C2314yes—
96C4×D4×C17—28no—
97C4×D4×C17—22no—
98C4×D4×C17D414yes—
99C4×D4×C17C2314yes—
100C4×D4×C17C2314yes—
101C17×#117—22no—
102C17×#117C2314yes—
103C2×C4⋊C4×C17—21no—
104C2×C4⋊C4×C17—22no—
105C2×C4⋊C4×C17—21no—
106C2×C4⋊C4×C17—21no—
107C2×C4⋊C4×C17D411yescharacteristic
108C2×C4⋊C4×C17C2311yescharacteristic
109C2×C4⋊C4×C17C2311yescharacteristic
110C2×C4⋊C4×C17C2314yes—
111C2×C4⋊C4×C17C2311yescharacteristic
112C2×C22⋊C4×C17—21no—
113C2×C22⋊C4×C17—21no—
114C2×C22⋊C4×C17—21no—
115C2×C22⋊C4×C17—21no—
116C2×C22⋊C4×C17D411yescharacteristic
117C2×C22⋊C4×C17D411yescharacteristic
118C2×C42×C17—21no—
119C2×C42×C17C2311yescharacteristic
120C2×C22⋊Dic17—21no—
121C2×C22⋊Dic17—21no—
122C2×C22⋊Dic17—21no—
123#10587621—28no—
124C2×#63229—24no—
125C2×#63229C2314yes—
126#10587612—22no—
127#10587612C2314yes—
128C2×C4⋊Dic17—22no—
129C2×C4⋊Dic17—21no—
130C2×C4⋊Dic17C2314yes—
131C2×C4⋊Dic17C2311yescharacteristic
132C2×C4⋊Dic17C2311yescharacteristic
133C2×C4⋊Dic17C2311yescharacteristic
134#10587610—22no—
135#10587610—22no—
136#10587610C2314yes—
137#10587610C2314yes—
138C2×#63225—21no—
139C2×#63225—21no—
140C2×#63225—21no—
141C2×#63225—21no—
142C2×#63225—21no—
143C2×C4×Dic17—21no—
144C2×C4×Dic17—21no—
145C2×#63223—24no—
146C2×#63223—24no—
147C2×#63223C2314yes—
148C2×#63223C2314yes—
149C22×#3622C2311yescharacteristic
150C22×#3622C2311yescharacteristic
151C22×#3622C2311yescharacteristic
152C22×#3622C2311yescharacteristic
153#10587575—28no—
154#10587565—28no—
155#10587563—28no—
156#10587556—22no—
157#10587556C2314yes—
158C4×Dic34—22no—
159C4×Dic34C2314yes—
160#10587503C2314yes—
161#10587503C2314yes—
162#10587503C2314yes—
163C22⋊#3622C2314yes—
164C22⋊#3622C2314yes—
165#10587481C2314yes—
166#10587481C2314yes—
167#10587481C2314yes—
168#10587479C2314yes—
169#10587479C2314yes—
170#10587479C2314yes—
171#10587479C2314yes—
172#10587479C2314yes—
173#10587478C2314yes—
174#10587478C2314yes—
175#10587478C2314yes—
176#10587478C2314yes—
177C4⋊#3622C2314yes—
178C4×#3622C2314yes—
179C24×C17—21no—
180C24×C17C2×D411yescharacteristic
181C24×C17C2×D411yescharacteristic
182C2×D4×C17—24no—
183C2×D4×C17—24no—
184C2×D4×C17—21no—
185C2×D4×C17—22no—
186C2×D4×C17—22no—
187C2×D4×C17—42no—
188C2×D4×C17—44no—
189C2×D4×C17—82no—
190C2×D4×C17C2×D414yes—
191C2×D4×C17C2412yes—
192C22×C4×C17—22no—
193C22×C4×C17—22no—
194C22×C4×C17—22no—
195C22×C4×C17—22no—
196C22×C4×C17—21no—
197C22×C4×C17—21no—
198C22×C4×C17—21no—
199C22×C4×C17—24no—
200C22×C4×C17—24no—
201C22×C4×C17—82no—
202C22×C4×C17—82no—
203C22×C4×C17C2×D411yescharacteristic
204C22×C4×C17C2×D411yescharacteristic
205C22×C4×C17C2×D411yescharacteristic
206C22×C4×C17C2×D412yes—
207C22×C4×C17C2×D412yes—
208C22×C4×C17C2×D411yescharacteristic
209C22×C4×C17C2412yes—
210C22×C4×C17C2412yes—
211C22×C4×C17C2411yescharacteristic
212C22×Dic17—21no—
213C22×Dic17—24no—
214C22×Dic17—21no—
215C22×Dic17—21no—
216C22×Dic17—21no—
217C22×Dic17—44no—
218C2×Dic34—22no—
219C2×Dic34—22no—
220C2×Dic34—21no—
221C2×Dic34C2412yes—
222C4⋊C4×C17—24no—
223C4⋊C4×C17—24no—
224C4⋊C4×C17—21no—
225C4⋊C4×C17—21no—
226C4⋊C4×C17—24no—
227C4⋊C4×C17—21no—
228C4⋊C4×C17C2×D414yes—
229C4⋊C4×C17C2412yes—
230C4⋊C4×C17C2412yes—
231C4⋊C4×C17C2412yes—
232C22⋊C4×C17—24no—
233C22⋊C4×C17—24no—
234C22⋊C4×C17—24no—
235C22⋊C4×C17—24no—
236C22⋊C4×C17C2×D414yes—
237C22⋊C4×C17C2×D414yes—
238C42×C17—24no—
239C42×C17C2×D412yes—
240C42×C17C2412yes—
241C22⋊Dic17—24no—
242C22⋊Dic17—24no—
243C22⋊Dic17—24no—
244#63229—28no—
245C4⋊Dic17—21no—
246C4⋊Dic17—21no—
247C4⋊Dic17—21no—
248C4⋊Dic17—24no—
249C4⋊Dic17C2412yes—
250C4⋊Dic17C2412yes—
251C4⋊Dic17C2412yes—
252#63225—24no—
253#63225—24no—
254#63225—24no—
255#63225—24no—
256#63225—24no—
257C4×Dic17—24no—
258C4×Dic17—24no—
259#63223—28no—
260#63223—28no—
261C2×#3622—22no—
262C2×#3622—22no—
263C2×#3622—22no—
264C2×#3622#4114yes—
265C2×#3622C2412yes—
266C2×#3622C2412yes—
267C2×#3622C2412yes—
268C2×#3622C2412yes—
269C2×#3351—171nomaximal, Sylow
270C23×C17—22no—
271C23×C17—22no—
272C23×C17—22no—
273C23×C17—22no—
274C23×C17—22no—
275C23×C17—22no—
276C23×C17—22no—
277C23×C17—42no—
278C23×C17—42no—
279C23×C17—42no—
280C23×C17C22×D412yes—
281C23×C17C22×D412yes—
282C23×C17C22×D411yescharacteristic
283D4×C17—22no—
284D4×C17—22no—
285D4×C17—44no—
286D4×C17—48no—
287D4×C17—42no—
288D4×C17—84no—
289C2×C4×C17—22no—
290C2×C4×C17—22no—
291C2×C4×C17—22no—
292C2×C4×C17—22no—
293C2×C4×C17—24no—
294C2×C4×C17—24no—
295C2×C4×C17—22no—
296C2×C4×C17—22no—
297C2×C4×C17—22no—
298C2×C4×C17—22no—
299C2×C4×C17—22no—
300C2×C4×C17—22no—
301C2×C4×C17—22no—
302C2×C4×C17—42no—
303C2×C4×C17—42no—
304C2×C4×C17—42no—
305C2×C4×C17—84no—
306C2×C4×C17—84no—
307C2×C4×C17C22×D412yes—
308C2×C4×C17C22×D412yes—
309C2×C4×C17C22×D412yes—
310C2×C4×C17C22×D412yes—
311C2×C4×C17C22×D411yescharacteristic
312C2×C4×C17C2×#4112yes—
313C2×C4×C172−1+412yes—
314C2×C4×C17C2511yescharacteristic
315C2×Dic17—22no—
316C2×Dic17—22no—
317C2×Dic17—22no—
318C2×Dic17—22no—
319C2×Dic17—48no—
320C2×Dic17—42no—
321C2×Dic17—42no—
322C2×Dic17—42no—
323C2×Dic17—42no—
324Dic34—22no—
325Dic34—22no—
326Dic34—42no—
327#3622—22no—
328#3622—22no—
329#3622—22no—
330#3622C2×#4114yes—
331C2×#553D1711yescharacteristic
332C2×#552—171no—
333#3351—1716no—
334C2×#499—171no—
335C2×#481—171no—
336C2×#485—171no—
337C2×#482—171no—
338C2×#483—171no—
339C2×#479—171no—
340C2×#478—171no—
341C2×#468—171no—
342C2×#468—171no—
343C2×C4×SD16—171no—
344C2×#436—171no—
345C2×#428—171no—
346C2×#428—171no—
347C22×C17—22no—
348C22×C17—22no—
349C22×C17—22no—
350C22×C17—22no—
351C22×C17—22no—
352C22×C17—22no—
353C22×C17—44no—
354C22×C17—44no—
355C22×C17—42no—
356C22×C17—42no—
357C22×C17—42no—
358C22×C17—84no—
359C22×C17#54712yes—
360C22×C17#57512yes—
361C22×C17#57712yes—
362C22×C17C23×D411yescharacteristic
363C4×C17—22no—
364C4×C17—22no—
365C4×C17—22no—
366C4×C17—22no—
367C4×C17—42no—
368C4×C17—42no—
369C4×C17—42no—
370C4×C17#54712yes—
371C4×C17C22×#4111yescharacteristic
372C4×C17C2×2−1+411yescharacteristic
373Dic17—42no—
374Dic17—42no—
375Dic17—42no—
376Dic17—42no—
377C22×SD16—171no—
378C22×M16—171no—
379C22×M16—171no—
380#553—24no—
381#553C2×D1718yes—
382#552—178no—
383#552—344no—
384C2×#126—21no—
385C2×#126—341no—
386C2×#125—171no—
387C2×#125—341no—
388C2×#125C2×D1711yescharacteristic
389C2×#123—21no—
390C2×#123—341no—
391C2×C22⋊Q8—171no—
392C2×C22⋊Q8—171no—
393C2×#121—21no—
394C2×#121C2×D1711yescharacteristic
395C2×#121C2×D1711yescharacteristic
396C2×C4×Q8—171no—
397C2×C4×D4—21no—
398C2×C4×D4C2×D1711yescharacteristic
399C2×C4×D4C2×D1711yescharacteristic
400C2×#117—171no—
401C2×#117—341no—
402C2×#117C2×D1711yescharacteristic
403C22×C4⋊C4—171no—
404C22×C4⋊C4C2×D1711yescharacteristic
405#499—178no—
406#485—178no—
407#483—178no—
408#482—178no—
409#481—178no—
410#479—178no—
411#478—178no—
412#468—178no—
413#468—178no—
414C4×SD16—178no—
415#436—178no—
416#428—178no—
417#428—178no—
418C2×#107—171no—
419C2×#107—171no—
420C2×#107—171no—
421C2×#107—171no—
422C2×#106—171no—
423C2×#106—171no—
424C2×#106—171no—
425C2×#106—171no—
426C2×#106—171no—
427C2×C4⋊C8—171no—
428C2×#103—171no—
429C2×#103—171no—
430C2×#103—171no—
431C2×#102—171no—
432C2×#102—171no—
433C2×#102—171no—
434C2×C22⋊C8—171no—
435C2×C22⋊C8—171no—
436C2×C4×C8—171no—
437C2×C17—42no—
438C2×C17—42no—
439C2×C17—82no—
440C2×C17#335114yescomplemented
441C2×C17C2×#54711yescharacteristic
442C2×C17C2×#57511yescharacteristic
443C2×C17C2×#57711yescharacteristic
444C22×Q8—171no—
445C22×D4—21no—
446C22×D4—21no—
447C22×D4C22⋊D1711yescharacteristic
448C22×D4C22×D1711yescharacteristic
449C23×C4—21no—
450C23×C4—21no—
451C23×C4—341no—
452C23×C4C22×D1711yescharacteristic
453C23×C4C22×D1711yescharacteristic
454C2×SD16—174no—
455C2×SD16—344no—
456C2×M16—174no—
457C2×M16—174no—
458C2×M16—344no—
459C2×M16—344no—
460C22×C8—171no—
461C22×C8—171no—
462C22×C8—171no—
463C22×C8—171no—
464#126—28no—
465#126—348no—
466#125—22no—
467#125—174no—
468#125—348no—
469#125—342no—
470#125C22×D1714yes—
471#123—28no—
472#123—348no—
473C22⋊Q8—174no—
474C22⋊Q8—174no—
475C22⋊Q8—342no—
476C22⋊Q8—342no—
477#121—28no—
478#121—22no—
479#121—22no—
480#121C22×D1714yes—
481#121C22×D1714yes—
482C4×Q8—174no—
483C4×Q8—342no—
484C4×D4—28no—
485C4×D4—22no—
486C4×D4C22⋊D1714yes—
487C4×D4C22×D1714yes—
488C4×D4C22×D1714yes—
489#117—22no—
490#117—174no—
491#117—342no—
492#117—348no—
493#117C22×D1714yes—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—22no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—171no—
499C2×C4⋊C4—171no—
500C2×C4⋊C4—174no—
501C2×C4⋊C4—171no—
502C2×C4⋊C4—341no—
503C2×C4⋊C4—342no—
504C2×C4⋊C4—341no—
505C2×C4⋊C4—341no—
506C2×C4⋊C4—341no—
507C2×C4⋊C4—341no—
508C2×C4⋊C4—341no—
509C2×C4⋊C4C22⋊D1711yescharacteristic
510C2×C4⋊C4C22×D1711yescharacteristic
511C2×C4⋊C4C22×D1711yescharacteristic
512C2×C4⋊C4C22×D1714yes—
513C2×C4⋊C4C22×D1711yescharacteristic
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—341no—
519C2×C22⋊C4—341no—
520C2×C22⋊C4—341no—
521C2×C22⋊C4C22⋊D1711yescharacteristic
522C2×C22⋊C4C22⋊D1711yescharacteristic
523C2×C42—21no—
524C2×C42—341no—
525C2×C42—341no—
526C2×C42C22×D1711yescharacteristic
527#107—174no—
528#107—174no—
529#107—174no—
530#107—174no—
531#106—174no—
532#106—174no—
533#106—174no—
534#106—174no—
535#106—174no—
536C4⋊C8—174no—
537#103—174no—
538#103—174no—
539#103—174no—
540#102—174no—
541#102—174no—
542#102—174no—
543C22⋊C8—174no—
544C22⋊C8—174no—
545C4×C8—174no—
546C17C2×#335111yescharacteristic, complemented, Sylow
547C24—21no—
548C24C2×C22⋊D1711yescharacteristic
549C24C2×C22⋊D1711yescharacteristic
550C2×Q8—172no—
551C2×Q8—341no—
552C2×Q8—342no—
553C2×Q8—342no—
554C2×D4—24no—
555C2×D4—24no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—21no—
559C2×D4—42no—
560C2×D4—44no—
561C2×D4—82no—
562C2×D4C2×C22⋊D1714yes—
563C2×D4C23×D1712yes—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—24no—
572C22×C4—24no—
573C22×C4—82no—
574C22×C4—82no—
575C22×C4—344no—
576C22×C4—341no—
577C22×C4—341no—
578C22×C4—341no—
579C22×C4—341no—
580C22×C4—684no—
581C22×C4C2×C22⋊D1712yes—
582C22×C4C2×C22⋊D1712yes—
583C22×C4C2×C22⋊D1711yescharacteristic
584C22×C4C2×C22⋊D1711yescharacteristic
585C22×C4C2×C22⋊D1711yescharacteristic
586C22×C4C2×C22⋊D1711yescharacteristic
587C22×C4C23×D1712yes—
588C22×C4C23×D1712yes—
589C22×C4C23×D1711yescharacteristic
590SD16—348no—
591M16—348no—
592M16—348no—
593C2×C8—174no—
594C2×C8—172no—
595C2×C8—172no—
596C2×C8—172no—
597C2×C8—172no—
598C2×C8—342no—
599C2×C8—342no—
600C2×C8—342no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—24no—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—21no—
607C4⋊C4—172no—
608C4⋊C4—172no—
609C4⋊C4—172no—
610C4⋊C4—341no—
611C4⋊C4—341no—
612C4⋊C4—344no—
613C4⋊C4—341no—
614C4⋊C4—344no—
615C4⋊C4—344no—
616C4⋊C4—344no—
617C4⋊C4—344no—
618C4⋊C4—344no—
619C4⋊C4C2×C22⋊D1714yes—
620C4⋊C4C23×D1712yes—
621C4⋊C4C23×D1712yes—
622C4⋊C4C23×D1712yes—
623C22⋊C4—24no—
624C22⋊C4—24no—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—344no—
628C22⋊C4—344no—
629C22⋊C4—344no—
630C22⋊C4C2×C22⋊D1714yes—
631C22⋊C4C2×C22⋊D1714yes—
632C42—24no—
633C42—344no—
634C42—344no—
635C42C2×C22⋊D1712yes—
636C42C23×D1712yes—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23C22×C22⋊D1712yes—
648C23C22×C22⋊D1712yes—
649C23C22×C22⋊D1711yescharacteristic
650Q8—342no—
651Q8—342no—
652Q8—682no—
653D4—22no—
654D4—22no—
655D4—44no—
656D4—48no—
657D4—42no—
658D4—84no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—84no—
676C2×C4—84no—
677C2×C4—342no—
678C2×C4—342no—
679C2×C4—342no—
680C2×C4—342no—
681C2×C4—688no—
682C2×C4—682no—
683C2×C4—682no—
684C2×C4—682no—
685C2×C4—682no—
686C2×C4#41×D1712yes—
687C2×C4#1058769712yes—
688C2×C4C22×C22⋊D1712yes—
689C2×C4C22×C22⋊D1712yes—
690C2×C4C22×C22⋊D1712yes—
691C2×C4C22×C22⋊D1712yes—
692C2×C4C22×C22⋊D1711yescharacteristic
693C2×C4C24×D1711yescharacteristic
694C8—174no—
695C8—342no—
696C8—342no—
697C8—342no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—44no—
705C22—44no—
706C22—42no—
707C22—42no—
708C22—42no—
709C22—84no—
710C22#1176345812yes—
711C22#1176360712yes—
712C22#1176362012yes—
713C22C23×C22⋊D1711yescharacteristic
714C4—22no—
715C4—22no—
716C4—22no—
717C4—22no—
718C4—42no—
719C4—42no—
720C4—42no—
721C4—682no—
722C4—682no—
723C4—682no—
724C4—682no—
725C4#1176345812yes—
726C4C2×#41×D1711yescharacteristic
727C4C2×#1058769711yescharacteristic
728C2—42no—
729C2—42no—
730C2—82no—
731C2#1454133814yesdirect product factor
732C2C2×#1176345811yescharacteristic
733C2C2×#1176360711yescharacteristic
734C2C2×#1176362011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
Fitting, prime radicalC2×C17×#553C2
socleC23×C17C22×D4
hypercenterC2×#553D17
hypocenterC17C2×#3351
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×#11763499C2semidirect
2. #14541338C2direct (N × H)
3. C2×#11763208C2semidirect
4. C2×#11763125C2semidirect
5. C2×#11763150C2semidirect
6. C2×#11763130C2semidirect
7. C2×#11763139C2semidirect
8. C2×#11763113C2semidirect
9. C2×#11763109C2semidirect
10. C2×#11763053C2semidirect
11. C2×#11763053C2semidirect
12. C2×C4×#63229C2semidirect
13. C2×#11762887C2semidirect
14. C2×#11762852C2semidirect
15. C2×#11762849C2semidirect
21. #11763499C22semidirect
32. #11763208C22semidirect
33. #11763150C22semidirect
34. #11763139C22semidirect
35. #11763130C22semidirect
36. #11763125C22semidirect
37. #11763113C22semidirect
38. #11763109C22semidirect
39. #11763053C22semidirect
40. #11763053C22semidirect
41. C4×#63229C22semidirect
42. #11762887C22semidirect
43. #11762852C22semidirect
44. #11762849C22semidirect
440. C2×C17#3351semidirect
546. C17C2×#3351semidirect
731. C2#14541338direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117634992
#145413382
C2×#117632082
C2×#117631252
C2×#117631502
C2×#117631302
C2×#117631392
C2×#117631132
C2×#117631092
C2×#117630532
C2×C4×#632292
C2×#117628872
C2×#117628522
C2×#117628492
C2×C17×#5532
C2×#335117