Finite Group Databasebeta

← C2×#14541167 #17912775

Subgroups — C2×#14541167 #17912775

Order 4352.

1930 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×#11763511C211yesmaximal, characteristic
2C2×#11763494C211yesmaximal, characteristic, complemented
3#14541167C2116yesmaximal, direct product factor
4C2×#11763210C211yesmaximal, characteristic, complemented
5C2×#11763145C211yesmaximal, characteristic, complemented
6C2×#11763152C211yesmaximal, characteristic, complemented
7C2×#11763131C211yesmaximal, characteristic, complemented
8C2×#11763115C211yesmaximal, characteristic, complemented
9C2×#11763107C211yesmaximal, characteristic, complemented
10C2×#11763037C211yesmaximal, characteristic, complemented
11C2×#11763036C211yesmaximal, characteristic, complemented
12C2×#11762900C211yesmaximal, characteristic, complemented
13C2×#11762872C211yesmaximal, characteristic, complemented
14C2×#11762846C211yesmaximal, characteristic, complemented
15C22×#10587479C211yesmaximal, characteristic, complemented
16C2×C17×#480C211yesmaximal, characteristic, complemented
17C22×#63229C2211yescharacteristic
18C23×#3622C2211yescharacteristic
19C22×C8×D17C2211yescharacteristic
20#11763511—24no—
21#11763511C2218yes—
22#11763494—24no—
23#11763494C2218yescomplemented
24C2×#10587584—21no—
25C2×#10587565—21no—
26C2×#10587576C2211yescharacteristic
27C2×#10587576C2211yescharacteristic
28C2×#10587575—21no—
29C2×#10587572—21no—
30C2×#10587615—21no—
31C2×#10587583C2211yescharacteristic
32C2×#10587610C2211yescharacteristic
33C2×#10587625—21no—
34C2×#10587624C2211yescharacteristic
35C2×#10587573C2211yescharacteristic
36C2×D4×Dic17—21no—
37C2×D4×Dic17C2211yescharacteristic
38C2×C4×C22⋊D17C2211yescharacteristic
39C2×#10587612—21no—
40C2×#10587578C2211yescharacteristic
41C2×#10587578C2211yescharacteristic
42C22×C4⋊Dic17C2211yescharacteristic
43#11763210C2218yescomplemented
44#11763152C2218yescomplemented
45#11763145C2218yescomplemented
46#11763131C2218yescomplemented
47#11763115C2218yescomplemented
48#11763107C2218yescomplemented
49#11763037C2218yescomplemented
50#11763036C2218yescomplemented
51#11762900C2218yescomplemented
52#11762872C2218yescomplemented
53#11762846C2218yescomplemented
54C2×#10587489C2211yescharacteristic
55C2×#10587489C2211yescharacteristic
56C2×#10587479C2211yescharacteristic
57C2×#10587479C2211yescharacteristic
58C2×#10587479C2211yescharacteristic
59C2×#10587479C2211yescharacteristic
60C2×#10587479C2211yescharacteristic
61C2×#10587479C2218yescomplemented
62C2×#10587485C2211yescharacteristic
63C2×#10587487C2211yescharacteristic
64C2×#10587487C2211yescharacteristic
65C2×#10587481C2211yescharacteristic
66C2×#10587503C2211yescharacteristic
67C2×#10587491C2211yescharacteristic
68C2×C8×Dic17C2211yescharacteristic
69C2×C17×#121C2211yescharacteristic
70C22×C4⋊C4×C17C2211yescharacteristic
71C17×#480C2218yescomplemented
72C2×C17×#107C2211yescharacteristic
73C2×C17×#107C2211yescharacteristic
74C2×C17×#102C2211yescharacteristic
75C2×C17×#102C2211yescharacteristic
76C2×C17×C22⋊C8C2211yescharacteristic
77C22×D4×C17—21no—
78C22×D4×C17C2311yescharacteristic
79C23×C4×C17—21no—
80C23×C4×C17C2311yescharacteristic
81C22×C22⋊D17—21no—
82C22×C22⋊D17D411yescharacteristic
83C23×Dic17—21no—
84C23×Dic17—21no—
85C22×C4×D17C2311yescharacteristic
86C22×Dic34C2311yescharacteristic
87C22×C8×C17C2311yescharacteristic
88C22×C8×C17C2311yescharacteristic
89C17×#121—22no—
90C17×#121C2314yes—
91C2×C4⋊C4×C17—22no—
92C2×C4⋊C4×C17—21no—
93C2×C4⋊C4×C17C2314yes—
94C2×C4⋊C4×C17C2311yescharacteristic
95C2×C4⋊C4×C17C2311yescharacteristic
96C2×C4⋊C4×C17C2311yescharacteristic
97C2×C22⋊C4×C17—21no—
98C2×C22⋊Dic17—21no—
99C2×C22⋊Dic17—21no—
100C2×C22⋊Dic17—21no—
101C2×C22⋊Dic17D411yescharacteristic
102#10587625—28no—
103#10587624—22no—
104#10587624C2314yes—
105D4×Dic17—22no—
106D4×Dic17—28no—
107D4×Dic17C2314yes—
108C2×#63229—24no—
109C2×#63229C2314yes—
110#10587615—28no—
111C4×C22⋊D17D414yes—
112C4×C22⋊D17C2314yes—
113C2×#63227—21no—
114C2×#63227—21no—
115C2×#63227—21no—
116C2×#63227D411yescharacteristic
117#10587612—28no—
118C2×C4⋊Dic17—22no—
119C2×C4⋊Dic17—21no—
120C2×C4⋊Dic17—21no—
121C2×C4⋊Dic17—21no—
122C2×C4⋊Dic17—21no—
123C2×C4⋊Dic17C2314yes—
124C2×C4⋊Dic17C2311yescharacteristic
125C2×C4⋊Dic17C2311yescharacteristic
126C2×C4⋊Dic17C2311yescharacteristic
127#10587610—22no—
128#10587610C2314yes—
129C2×#63225—21no—
130C2×#63225—21no—
131C2×#63225—21no—
132C2×#63225—21no—
133C2×#63225D411yescharacteristic
134C2×C4×Dic17—21no—
135C2×C4×Dic17—21no—
136C2×C4×Dic17—21no—
137C2×C4×Dic17C2311yescharacteristic
138C22×#3622—24no—
139C22×#3622C2311yescharacteristic
140C22×#3622C2314yes—
141C22×#3622C2311yescharacteristic
142C2×C8×D17—24no—
143C2×C8×D17C2314yes—
144#10587584—28no—
145#10587583—22no—
146#10587583C2314yes—
147#10587578—22no—
148#10587578—22no—
149#10587578C2314yes—
150#10587578C2314yes—
151#10587576—22no—
152#10587576—22no—
153#10587576C2314yes—
154#10587576C2314yes—
155#10587575—28no—
156#10587573—22no—
157#10587573C2314yes—
158#10587572—28no—
159#10587565—28no—
160C17×#107C2314yes—
161C17×#107C2314yes—
162C17×#102C2314yes—
163C17×#102C2314yes—
164C17×C22⋊C8C2314yes—
165#10587503C2314yes—
166#10587491C2314yes—
167#10587489C2314yes—
168#10587489C2314yes—
169#10587487C2314yes—
170#10587487C2314yes—
171#10587485C2314yes—
172C8×Dic17C2314yes—
173#10587481C2314yes—
174#10587479C2314yes—
175#10587479C2314yes—
176#10587479C2314yes—
177#10587479C2314yes—
178#10587479C2314yes—
179C24×C17—21no—
180C24×C17C2×D411yescharacteristic
181C23×D17C2×D411yescharacteristic
182C2×D4×C17—24no—
183C2×D4×C17—21no—
184C2×D4×C17—22no—
185C2×D4×C17—22no—
186C2×D4×C17—44no—
187C2×D4×C17C2412yes—
188C22×C4×C17—22no—
189C22×C4×C17—22no—
190C22×C4×C17—21no—
191C22×C4×C17—21no—
192C22×C4×C17—24no—
193C22×C4×C17—21no—
194C22×C4×C17—44no—
195C22×C4×C17C2×D411yescharacteristic
196C22×C4×C17C2×D412yes—
197C22×C4×C17C2412yes—
198C22×C4×C17C2411yescharacteristic
199C2×C22⋊D17—24no—
200C2×C22⋊D17—24no—
201C2×C22⋊D17—82no—
202C2×C22⋊D17C2×D414yes—
203C22×Dic17—21no—
204C22×Dic17—21no—
205C22×Dic17—21no—
206C22×Dic17—21no—
207C22×Dic17—24no—
208C22×Dic17—24no—
209C22×Dic17—82no—
210C22×Dic17—82no—
211C22×Dic17C2×D411yescharacteristic
212C22×Dic17C2×D411yescharacteristic
213C22×Dic17C2×D411yescharacteristic
214C2×C4×D17—22no—
215C2×C4×D17—22no—
216C2×C4×D17C2×D412yes—
217C2×C4×D17C2412yes—
218C2×Dic34—22no—
219C2×Dic34—22no—
220C2×Dic34—21no—
221C2×Dic34C2412yes—
222C2×C8×C17—22no—
223C2×C8×C17—22no—
224C2×C8×C17C2412yes—
225C2×C8×C17C2412yes—
226C4⋊C4×C17—21no—
227C4⋊C4×C17—24no—
228C4⋊C4×C17—21no—
229C4⋊C4×C17—21no—
230C4⋊C4×C17C2412yes—
231C4⋊C4×C17C2412yes—
232C4⋊C4×C17C2412yes—
233C22⋊C4×C17—24no—
234C22⋊Dic17—24no—
235C22⋊Dic17—24no—
236C22⋊Dic17—24no—
237C22⋊Dic17C2×D414yes—
238#63229—28no—
239#63227—24no—
240#63227—24no—
241#63227—24no—
242#63227C2×D414yes—
243C4⋊Dic17—24no—
244C4⋊Dic17—21no—
245C4⋊Dic17—21no—
246C4⋊Dic17—21no—
247C4⋊Dic17—24no—
248C4⋊Dic17—24no—
249C4⋊Dic17—24no—
250C4⋊Dic17C2412yes—
251C4⋊Dic17C2412yes—
252C4⋊Dic17C2412yes—
253#63225—24no—
254#63225—24no—
255#63225—24no—
256#63225—24no—
257#63225C2×D414yes—
258C4×Dic17—24no—
259C4×Dic17—24no—
260C4×Dic17—24no—
261C4×Dic17C2×D412yes—
262C4×Dic17C2412yes—
263C2×#3622—22no—
264C2×#3622—28no—
265C2×#3622#4114yes—
266C2×#3622C2412yes—
267C2×#3622C2412yes—
268C8×D17—28no—
269C2×#3337—171nomaximal, Sylow
270C23×C17—22no—
271C23×C17—22no—
272C23×C17—22no—
273C23×C17—42no—
274C23×C17—42no—
275C23×C17—42no—
276C23×C17#13514yes—
277C23×C17C22×D412yes—
278C23×C17C22×D411yescharacteristic
279C22×D17—22no—
280C22×D17—22no—
281C22×D17—22no—
282C22×D17C22×D412yes—
283D4×C17—22no—
284D4×C17—22no—
285D4×C17—48no—
286D4×C17—42no—
287C2×C4×C17—22no—
288C2×C4×C17—24no—
289C2×C4×C17—22no—
290C2×C4×C17—22no—
291C2×C4×C17—22no—
292C2×C4×C17—22no—
293C2×C4×C17—22no—
294C2×C4×C17—48no—
295C2×C4×C17—42no—
296C2×C4×C17—42no—
297C2×C4×C17—42no—
298C2×C4×C17C22×D412yes—
299C2×C4×C17C22×D411yescharacteristic
300C2×C4×C17C2×#4112yes—
301C2×C4×C172−1+412yes—
302C2×C4×C17C2511yescharacteristic
303C22⋊D17—28no—
304C22⋊D17—84no—
305C2×Dic17—22no—
306C2×Dic17—22no—
307C2×Dic17—22no—
308C2×Dic17—22no—
309C2×Dic17—22no—
310C2×Dic17—22no—
311C2×Dic17—22no—
312C2×Dic17—42no—
313C2×Dic17—42no—
314C2×Dic17—42no—
315C2×Dic17—42no—
316C2×Dic17—84no—
317C2×Dic17—84no—
318C2×Dic17C22×D412yes—
319C2×Dic17C22×D412yes—
320C2×Dic17C22×D412yes—
321C4×D17—24no—
322C4×D17—22no—
323C4×D17—22no—
324Dic34—22no—
325Dic34—22no—
326Dic34—42no—
327C8×C17—22no—
328C8×C17—22no—
329#3622—22no—
330#3622C2×#4114yes—
331C2×#553—171no—
332C2×#552—171no—
333#3337—1716no—
334C2×#499—171no—
335C2×#484—171no—
336C2×#485—171no—
337C2×#482—171no—
338C2×#480D1711yescharacteristic, complemented
339C2×#479—171no—
340C2×#478—171no—
341C2×#465—171no—
342C2×#465—171no—
343C2×C4×SD16—171no—
344C2×C8×D4—171no—
345C2×#427—171no—
346C22×#106—171no—
347C22×C17—28no—
348C22×C17—22no—
349C22×C17—22no—
350C22×C17—42no—
351C22×C17—42no—
352C22×C17—42no—
353C22×C17—84no—
354C22×C17#54712yes—
355C22×C17C2×#13514yes—
356C22×C17C2×#13512yes—
357C22×C17#57712yes—
358C22×C17C23×D411yescharacteristic
359C2×D17—22no—
360C2×D17—22no—
361C2×D17—22no—
362C2×D17—44no—
363C4×C17—22no—
364C4×C17—42no—
365C4×C17—42no—
366C4×C17—42no—
367C4×C17#54712yes—
368C4×C17C22×#4111yescharacteristic
369C4×C17C2×2−1+411yescharacteristic
370Dic17—22no—
371Dic17—22no—
372Dic17—22no—
373Dic17—42no—
374Dic17—42no—
375Dic17—42no—
376Dic17—42no—
377C22×SD16—171no—
378C23×C8—171no—
379C23×C8—171no—
380#553—178no—
381#553—344no—
382#552—178no—
383#552—344no—
384C2×#126—341no—
385C2×#126—341no—
386C2×#125—171no—
387C2×#125—171no—
388C2×#125—341no—
389C2×#123—341no—
390C2×#123—341no—
391C2×C22⋊Q8—171no—
392C2×C22⋊Q8—171no—
393C2×#121—171no—
394C2×#121—341no—
395C2×#121C2×D1711yescharacteristic
396C2×C4×Q8—171no—
397C2×C4×D4—171no—
398C2×C4×D4—171no—
399C2×C4×D4—341no—
400C2×#117—171no—
401C2×#117—171no—
402C2×#117—341no—
403C22×C4⋊C4—171no—
404C22×C4⋊C4C2×D1711yescharacteristic
405#499—178no—
406#485—178no—
407#484—178no—
408#482—178no—
409#480C2×D1718yescomplemented
410#479—178no—
411#478—178no—
412#465—178no—
413#465—178no—
414C4×SD16—178no—
415C8×D4—178no—
416#427—178no—
417C2×#107—171no—
418C2×#107—171no—
419C2×#107C2×D1711yescharacteristic
420C2×#107C2×D1711yescharacteristic
421C2×#106—171no—
422C2×#106—171no—
423C2×#106—178no—
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×#102C2×D1711yescharacteristic
433C2×#102C2×D1711yescharacteristic
434C2×C22⋊C8—171no—
435C2×C22⋊C8C2×D1711yescharacteristic
436C2×C4×C8—171no—
437C2×C17—24no—
438C2×C17—82no—
439C2×C17#333714yescomplemented
440C2×C17C2×#54711yescharacteristic
441C2×C17C22×#13511yescharacteristic
442C2×C17C2×#57711yescharacteristic
443D17—42no—
444C22×Q8—171no—
445C22×D4—21no—
446C22×D4—171no—
447C22×D4—341no—
448C22×D4C22×D1711yescharacteristic
449C23×C4—21no—
450C23×C4—171no—
451C23×C4—341no—
452C23×C4—341no—
453C23×C4C22×D1711yescharacteristic
454C2×SD16—174no—
455C2×SD16—344no—
456C22×C8—171no—
457C22×C8—171no—
458C22×C8—174no—
459C22×C8—174no—
460C22×C8—344no—
461C22×C8—344no—
462C22×C8C22×D1711yescharacteristic
463C22×C8C22×D1711yescharacteristic
464#126—348no—
465#126—348no—
466#125—174no—
467#125—174no—
468#125—342no—
469#125—342no—
470#125—348no—
471#123—348no—
472#123—348no—
473C22⋊Q8—174no—
474C22⋊Q8—174no—
475C22⋊Q8—342no—
476C22⋊Q8—342no—
477#121—22no—
478#121—174no—
479#121—342no—
480#121—348no—
481#121C22×D1714yes—
482C4×Q8—174no—
483C4×Q8—342no—
484C4×D4—174no—
485C4×D4—174no—
486C4×D4—174no—
487C4×D4—342no—
488C4×D4—348no—
489#117—174no—
490#117—174no—
491#117—348no—
492#117—342no—
493#117—342no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—22no—
496C2×C4⋊C4—171no—
497C2×C4⋊C4—171no—
498C2×C4⋊C4—171no—
499C2×C4⋊C4—174no—
500C2×C4⋊C4—171no—
501C2×C4⋊C4—341no—
502C2×C4⋊C4—341no—
503C2×C4⋊C4—341no—
504C2×C4⋊C4—341no—
505C2×C4⋊C4—341no—
506C2×C4⋊C4—341no—
507C2×C4⋊C4—341no—
508C2×C4⋊C4—342no—
509C2×C4⋊C4—341no—
510C2×C4⋊C4C22×D1711yescharacteristic
511C2×C4⋊C4C22×D1711yescharacteristic
512C2×C4⋊C4C22×D1714yes—
513C2×C4⋊C4C22×D1711yescharacteristic
514C2×C22⋊C4—21no—
515C2×C22⋊C4—171no—
516C2×C22⋊C4—171no—
517C2×C22⋊C4—341no—
518C2×C22⋊C4—341no—
519C2×C22⋊C4—341no—
520C2×C22⋊C4—341no—
521C2×C22⋊C4—341no—
522C2×C22⋊C4—341no—
523C2×C42—171no—
524C2×C42—341no—
525C2×C42—341no—
526C2×C42—341no—
527#107—174no—
528#107—174no—
529#107C22×D1714yes—
530#107C22×D1714yes—
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#102C22×D1714yes—
542#102C22×D1714yes—
543C22⋊C8—174no—
544C22⋊C8C22×D1714yes—
545C4×C8—174no—
546C17C2×#333711yescharacteristic, complemented, Sylow
547C24—21no—
548C24—171no—
549C24D4×D1711yescharacteristic
550C2×Q8—172no—
551C2×Q8—341no—
552C2×Q8—342no—
553C2×Q8—342no—
554C2×D4—24no—
555C2×D4—21no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—44no—
559C2×D4—174no—
560C2×D4—344no—
561C2×D4—344no—
562C2×D4—1362no—
563C2×D4C23×D1712yes—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—24no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—44no—
571C22×C4—171no—
572C22×C4—171no—
573C22×C4—171no—
574C22×C4—172no—
575C22×C4—172no—
576C22×C4—344no—
577C22×C4—342no—
578C22×C4—342no—
579C22×C4—341no—
580C22×C4—341no—
581C22×C4—341no—
582C22×C4—341no—
583C22×C4—344no—
584C22×C4—1362no—
585C22×C4—1362no—
586C22×C4D4×D1712yes—
587C22×C4D4×D1711yescharacteristic
588C22×C4C23×D1712yes—
589C22×C4C23×D1711yescharacteristic
590SD16—348no—
591C2×C8—22no—
592C2×C8—22no—
593C2×C8—174no—
594C2×C8—172no—
595C2×C8—172no—
596C2×C8—348no—
597C2×C8—348no—
598C2×C8—342no—
599C2×C8C23×D1712yes—
600C2×C8C23×D1712yes—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—24no—
604C4⋊C4—21no—
605C4⋊C4—174no—
606C4⋊C4—172no—
607C4⋊C4—172no—
608C4⋊C4—172no—
609C4⋊C4—344no—
610C4⋊C4—344no—
611C4⋊C4—344no—
612C4⋊C4—344no—
613C4⋊C4—344no—
614C4⋊C4—344no—
615C4⋊C4—341no—
616C4⋊C4—341no—
617C4⋊C4—344no—
618C4⋊C4—341no—
619C4⋊C4—344no—
620C4⋊C4C23×D1712yes—
621C4⋊C4C23×D1712yes—
622C4⋊C4C23×D1712yes—
623C22⋊C4—24no—
624C22⋊C4—174no—
625C22⋊C4—174no—
626C22⋊C4—344no—
627C22⋊C4—344no—
628C22⋊C4—344no—
629C22⋊C4—344no—
630C22⋊C4—344no—
631C22⋊C4—344no—
632C42—172no—
633C42—172no—
634C42—344no—
635C42—344no—
636C42—344no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—172no—
644C23—342no—
645C23—342no—
646C23—342no—
647C23#1058759814yes—
648C23C2×D4×D1712yes—
649C23C2×D4×D1711yescharacteristic
650Q8—342no—
651Q8—342no—
652Q8—682no—
653D4—22no—
654D4—22no—
655D4—48no—
656D4—42no—
657D4—348no—
658D4—1364no—
659C2×C4—22no—
660C2×C4—24no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—48no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—172no—
671C2×C4—172no—
672C2×C4—172no—
673C2×C4—342no—
674C2×C4—342no—
675C2×C4—342no—
676C2×C4—344no—
677C2×C4—342no—
678C2×C4—342no—
679C2×C4—342no—
680C2×C4—342no—
681C2×C4—342no—
682C2×C4—342no—
683C2×C4—682no—
684C2×C4—682no—
685C2×C4—682no—
686C2×C4—682no—
687C2×C4—1364no—
688C2×C4—1364no—
689C2×C4C2×D4×D1712yes—
690C2×C4C2×D4×D1711yescharacteristic
691C2×C4#41×D1712yes—
692C2×C4#1058769712yes—
693C2×C4C24×D1711yescharacteristic
694C8—22no—
695C8—22no—
696C8—174no—
697C8—342no—
698C22—28no—
699C22—22no—
700C22—22no—
701C22—42no—
702C22—42no—
703C22—42no—
704C22—84no—
705C22—342no—
706C22—342no—
707C22—342no—
708C22—684no—
709C22#1176345712yes—
710C22C2×#1058759814yes—
711C22C2×#1058759812yes—
712C22#1176361812yes—
713C22C22×D4×D1711yescharacteristic
714C4—22no—
715C4—42no—
716C4—42no—
717C4—42no—
718C4—342no—
719C4—342no—
720C4—342no—
721C4—682no—
722C4—682no—
723C4—682no—
724C4—682no—
725C4#1176345712yes—
726C4C2×#41×D1711yescharacteristic
727C4C2×#1058769711yescharacteristic
728C2—24no—
729C2—82no—
730C2—682no—
731C2#1454116714yesdirect product factor
732C2C2×#1176345711yescharacteristic
733C2C22×#1058759811yescharacteristic
734C2C2×#1176361811yescharacteristic
subgroupG/H
centerC23C2×D4×D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#480C2
socleC23×C17C22×D4
prime radicalC2×#11763511C2
hypercenterC2×#480D17
hypocenterC17C2×#3337
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#480

Complements

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

NH ≅ G/Ntype
2. C2×#11763494C2semidirect
3. #14541167C2direct (N × H)
4. C2×#11763210C2semidirect
5. C2×#11763145C2semidirect
6. C2×#11763152C2semidirect
7. C2×#11763131C2semidirect
8. C2×#11763115C2semidirect
9. C2×#11763107C2semidirect
10. C2×#11763037C2semidirect
11. C2×#11763036C2semidirect
12. C2×#11762900C2semidirect
13. C2×#11762872C2semidirect
14. C2×#11762846C2semidirect
15. C22×#10587479C2semidirect
16. C2×C17×#480C2semidirect
23. #11763494C22semidirect
43. #11763210C22semidirect
44. #11763152C22semidirect
45. #11763145C22semidirect
46. #11763131C22semidirect
47. #11763115C22semidirect
48. #11763107C22semidirect
49. #11763037C22semidirect
50. #11763036C22semidirect
51. #11762900C22semidirect
52. #11762872C22semidirect
53. #11762846C22semidirect
61. C2×#10587479C22semidirect
71. C17×#480C22semidirect
338. C2×#480D17semidirect
409. #480C2×D17semidirect
439. C2×C17#3337semidirect
546. C17C2×#3337semidirect
731. C2#14541167direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117635112
C2×#117634942
#145411672
C2×#117632102
C2×#117631452
C2×#117631522
C2×#117631312
C2×#117631152
C2×#117631072
C2×#117630372
C2×#117630362
C2×#117629002
C2×#117628722
C2×#117628462
C22×#105874792
C2×C17×#4802
C2×#333717