Finite Group Databasebeta

← C2×#14541346 #17913004

Subgroups — C2×#14541346 #17913004

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×#11763505C211yesmaximal, characteristic
2C2×#11763499C211yesmaximal, characteristic, complemented
3#14541346C2116yesmaximal, direct product factor
4C2×#11763211C211yesmaximal, characteristic, complemented
5C2×#11763128C211yesmaximal, characteristic, complemented
6C2×#11763151C211yesmaximal, characteristic, complemented
7C2×#11763134C211yesmaximal, characteristic, complemented
8C2×#11763140C211yesmaximal, characteristic, complemented
9C2×#11763117C211yesmaximal, characteristic, complemented
10C2×#11763110C211yesmaximal, characteristic, complemented
11C2×#11763055C211yesmaximal, characteristic, complemented
12C2×#11763055C211yesmaximal, characteristic, complemented
13C2×C4×#63219C211yesmaximal, characteristic, complemented
14C2×#11762851C211yesmaximal, characteristic, complemented
15C2×#11762851C211yesmaximal, characteristic, complemented
16C2×C17×#436C211yesmaximal, characteristic, complemented
17C22×#63219C2211yescharacteristic
18#11763505—24no—
19#11763505C2218yes—
20#11763499—24no—
21#11763499C2218yescomplemented
22C2×#10587584—21no—
23C2×#10587565—21no—
24C2×#10587556C2211yescharacteristic
25C2×#10587556C2211yescharacteristic
26C2×#10587575—21no—
27C2×#10587569—21no—
28C2×#10587621—21no—
29C2×#10587610C2211yescharacteristic
30C2×#10587610C2211yescharacteristic
31C2×#10587616C2211yescharacteristic
32C2×#10587616C2211yescharacteristic
33C2×#10587625—21no—
34C2×C4×Dic34C2211yescharacteristic
35C2×C4×D68C2211yescharacteristic
36C2×#10587567—21no—
37C2×#10587612C2211yescharacteristic
38C2×#10587612C2211yescharacteristic
39C2×#10587563—21no—
40C22×C4⋊Dic17C2211yescharacteristic
41C22×C4⋊Dic17C2211yescharacteristic
42#11763211C2218yescomplemented
43#11763151C2218yescomplemented
44#11763140C2218yescomplemented
45#11763134C2218yescomplemented
46#11763128C2218yescomplemented
47#11763117C2218yescomplemented
48#11763110C2218yescomplemented
49#11763055C2218yescomplemented
50#11763055C2218yescomplemented
51C4×#63219C2218yescomplemented
52#11762851C2218yescomplemented
53#11762851C2218yescomplemented
54C2×#10587489C2211yescharacteristic
55C2×#10587489C2211yescharacteristic
56C2×#10587489C2211yescharacteristic
57C2×#10587489C2211yescharacteristic
58C2×#10587488C2211yescharacteristic
59C2×#10587488C2211yescharacteristic
60C2×#10587488C2211yescharacteristic
61C2×#10587488C2211yescharacteristic
62C2×#10587488C2211yescharacteristic
63C2×#10587487C2211yescharacteristic
64C2×#10587487C2211yescharacteristic
65C2×#10587487C2211yescharacteristic
66C2×#10587492C2211yescharacteristic
67C2×#10587492C2211yescharacteristic
68C2×#10587492C2211yescharacteristic
69C22×M16×C17C2211yescharacteristic
70C22×M16×C17C2211yescharacteristic
71C2×C4×D4×C17C2211yescharacteristic
72C17×#436C2218yescomplemented
73C2×C17×C4⋊C8C2211yescharacteristic
74C2×C17×C22⋊C8C2211yescharacteristic
75C2×C17×C22⋊C8C2211yescharacteristic
76C2×C4×C8×C17C2211yescharacteristic
77C22×D4×C17D411yescharacteristic
78C23×C4×C17C2311yescharacteristic
79C23×C4×C17C2311yescharacteristic
80C22×C22⋊D17—21no—
81C22×C22⋊D17—21no—
82C23×Dic17—21no—
83C23×Dic17—21no—
84C22×D68C2311yescharacteristic
85C22×C4×D17—21no—
86C22×Dic34C2311yescharacteristic
87C2×M16×C17—24no—
88C2×M16×C17—24no—
89C2×M16×C17C2314yes—
90C2×M16×C17C2314yes—
91C22×C8×C17C2311yescharacteristic
92C22×C8×C17C2311yescharacteristic
93C22×C8×C17C2311yescharacteristic
94C22×C8×C17C2311yescharacteristic
95C4×D4×C17D414yes—
96C4×D4×C17C2314yes—
97C2×C4⋊C4×C17D411yescharacteristic
98C2×C22⋊C4×C17D411yescharacteristic
99C2×C22⋊C4×C17D411yescharacteristic
100C2×C42×C17C2311yescharacteristic
101C2×C22⋊Dic17—21no—
102C2×C22⋊Dic17—21no—
103C2×C22⋊Dic17—21no—
104C2×C22⋊Dic17—21no—
105#10587625—28no—
106#10587621—28no—
107#10587616—22no—
108#10587616—22no—
109#10587616C2314yes—
110#10587616C2314yes—
111C2×#63227—21no—
112C2×#63227—21no—
113C2×#63227—21no—
114#10587612—22no—
115#10587612—22no—
116#10587612C2314yes—
117#10587612C2314yes—
118C2×C4⋊Dic17—22no—
119C2×C4⋊Dic17—22no—
120C2×C4⋊Dic17—21no—
121C2×C4⋊Dic17—21no—
122C2×C4⋊Dic17C2314yes—
123C2×C4⋊Dic17C2314yes—
124C2×C4⋊Dic17C2311yescharacteristic
125C2×C4⋊Dic17C2311yescharacteristic
126C2×C4⋊Dic17C2311yescharacteristic
127C2×C4⋊Dic17C2311yescharacteristic
128C2×C4⋊Dic17C2311yescharacteristic
129C2×C4⋊Dic17C2311yescharacteristic
130#10587610—22no—
131#10587610—22no—
132#10587610C2314yes—
133#10587610C2314yes—
134C2×#63225—21no—
135C2×#63225—21no—
136C2×#63225—21no—
137C2×#63225—21no—
138C2×#63225—21no—
139C2×#63225—21no—
140C2×#63225—21no—
141C2×C4×Dic17—21no—
142C2×C4×Dic17—21no—
143C2×C4×Dic17—21no—
144C2×#63219—24no—
145C2×#63219C2314yes—
146#10587584—28no—
147#10587575—28no—
148#10587569—28no—
149#10587567—28no—
150#10587565—28no—
151#10587563—28no—
152C4×D68—22no—
153C4×D68C2314yes—
154#10587556—22no—
155#10587556—22no—
156#10587556C2314yes—
157#10587556C2314yes—
158C4×Dic34—22no—
159C4×Dic34C2314yes—
160C17×C4⋊C8C2314yes—
161C17×C22⋊C8C2314yes—
162C17×C22⋊C8C2314yes—
163C4×C8×C17C2314yes—
164#10587492C2314yes—
165#10587492C2314yes—
166#10587492C2314yes—
167#10587489C2314yes—
168#10587489C2314yes—
169#10587489C2314yes—
170#10587489C2314yes—
171#10587488C2314yes—
172#10587488C2314yes—
173#10587488C2314yes—
174#10587488C2314yes—
175#10587488C2314yes—
176#10587487C2314yes—
177#10587487C2314yes—
178#10587487C2314yes—
179C24×C17C2×D411yescharacteristic
180C24×C17C2×D411yescharacteristic
181C23×D17—21no—
182C2×D4×C17—42no—
183C2×D4×C17C2×D414yes—
184C22×C4×C17—22no—
185C22×C4×C17—22no—
186C22×C4×C17—22no—
187C22×C4×C17—22no—
188C22×C4×C17C2×D411yescharacteristic
189C22×C4×C17C2×D411yescharacteristic
190C22×C4×C17C2×D411yescharacteristic
191C22×C4×C17C2×D412yes—
192C22×C4×C17C2×D412yes—
193C22×C4×C17C2×D411yescharacteristic
194C22×C4×C17C2412yes—
195C22×C4×C17C2412yes—
196C22×C4×C17C2411yescharacteristic
197C2×C22⋊D17—24no—
198C2×C22⋊D17—24no—
199C2×C22⋊D17—44no—
200C2×C22⋊D17—82no—
201C22×Dic17—21no—
202C22×Dic17—21no—
203C22×Dic17—21no—
204C22×Dic17—24no—
205C22×Dic17—21no—
206C22×Dic17—21no—
207C22×Dic17—21no—
208C22×Dic17—21no—
209C22×Dic17—24no—
210C22×Dic17—44no—
211C22×Dic17—82no—
212C2×D68—22no—
213C2×D68—22no—
214C2×D68—21no—
215C2×D68C2412yes—
216C2×C4×D17—24no—
217C2×C4×D17—82no—
218C2×Dic34—22no—
219C2×Dic34—22no—
220C2×Dic34—21no—
221C2×Dic34C2412yes—
222M16×C17—28no—
223M16×C17—28no—
224C2×C8×C17—22no—
225C2×C8×C17—22no—
226C2×C8×C17—22no—
227C2×C8×C17#4114yes—
228C2×C8×C17C2412yes—
229C2×C8×C17C2412yes—
230C2×C8×C17C2412yes—
231C2×C8×C17C2412yes—
232C4⋊C4×C17C2×D414yes—
233C22⋊C4×C17C2×D414yes—
234C22⋊C4×C17C2×D414yes—
235C42×C17C2×D412yes—
236C42×C17C2412yes—
237C22⋊Dic17—24no—
238C22⋊Dic17—24no—
239C22⋊Dic17—24no—
240C22⋊Dic17—24no—
241#63227—24no—
242#63227—24no—
243#63227—24no—
244C4⋊Dic17—21no—
245C4⋊Dic17—21no—
246C4⋊Dic17—21no—
247C4⋊Dic17—21no—
248C4⋊Dic17—21no—
249C4⋊Dic17—21no—
250C4⋊Dic17—24no—
251C4⋊Dic17—24no—
252C4⋊Dic17C2412yes—
253C4⋊Dic17C2412yes—
254C4⋊Dic17C2412yes—
255C4⋊Dic17C2412yes—
256C4⋊Dic17C2412yes—
257C4⋊Dic17C2412yes—
258#63225—24no—
259#63225—24no—
260#63225—24no—
261#63225—24no—
262#63225—24no—
263#63225—24no—
264#63225—24no—
265C4×Dic17—24no—
266C4×Dic17—24no—
267C4×Dic17—24no—
268#63219—28no—
269C2×#3351—171nomaximal, Sylow
270C23×C17—22no—
271C23×C17—22no—
272C23×C17—22no—
273C23×C17—22no—
274C23×C17—22no—
275C23×C17—22no—
276C23×C17C22×D412yes—
277C23×C17C22×D412yes—
278C23×C17C22×D411yescharacteristic
279C22×D17—22no—
280C22×D17—42no—
281C22×D17—42no—
282C22×D17—42no—
283D4×C17—44no—
284C2×C4×C17—22no—
285C2×C4×C17—22no—
286C2×C4×C17—22no—
287C2×C4×C17—22no—
288C2×C4×C17—24no—
289C2×C4×C17—24no—
290C2×C4×C17—22no—
291C2×C4×C17—22no—
292C2×C4×C17—22no—
293C2×C4×C17—22no—
294C2×C4×C17C22×D412yes—
295C2×C4×C17C22×D412yes—
296C2×C4×C17C22×D412yes—
297C2×C4×C17C22×D412yes—
298C2×C4×C17C22×D411yescharacteristic
299C2×C4×C17C2×#4112yes—
300C2×C4×C172−1+412yes—
301C2×C4×C17C2511yescharacteristic
302C22⋊D17—48no—
303C22⋊D17—84no—
304C2×Dic17—22no—
305C2×Dic17—22no—
306C2×Dic17—22no—
307C2×Dic17—22no—
308C2×Dic17—22no—
309C2×Dic17—22no—
310C2×Dic17—22no—
311C2×Dic17—48no—
312C2×Dic17—42no—
313C2×Dic17—42no—
314C2×Dic17—42no—
315C2×Dic17—42no—
316C2×Dic17—42no—
317C2×Dic17—42no—
318C2×Dic17—42no—
319C2×Dic17—84no—
320D68—22no—
321D68—22no—
322D68—42no—
323C4×D17—84no—
324Dic34—22no—
325Dic34—22no—
326Dic34—42no—
327C8×C17—22no—
328C8×C17—22no—
329C8×C17—22no—
330C8×C17C2×#4114yes—
331C2×#553—171no—
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×#436D1711yescharacteristic, complemented
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#54712yes—
356C22×C17#57512yes—
357C22×C17#57712yes—
358C22×C17C23×D411yescharacteristic
359C2×D17—42no—
360C2×D17—42no—
361C2×D17—42no—
362C2×D17—84no—
363C4×C17—22no—
364C4×C17—22no—
365C4×C17—22no—
366C4×C17—22no—
367C4×C17#54712yes—
368C4×C17C22×#4111yescharacteristic
369C4×C17C2×2−1+411yescharacteristic
370Dic17—42no—
371Dic17—42no—
372Dic17—42no—
373Dic17—42no—
374Dic17—42no—
375Dic17—42no—
376Dic17—42no—
377C22×SD16—171no—
378C22×M16C2×D1711yescharacteristic
379C22×M16C2×D1711yescharacteristic
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—171no—
395C2×#121—341no—
396C2×C4×Q8—171no—
397C2×C4×D4—171no—
398C2×C4×D4—341no—
399C2×C4×D4C2×D1711yescharacteristic
400C2×#117—171no—
401C2×#117—171no—
402C2×#117—341no—
403C22×C4⋊C4—171no—
404C22×C4⋊C4—171no—
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#436C2×D1718yescomplemented
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⋊C8C2×D1711yescharacteristic
428C2×#103—171no—
429C2×#103—171no—
430C2×#103—171no—
431C2×#102—171no—
432C2×#102—171no—
433C2×#102—171no—
434C2×C22⋊C8C2×D1711yescharacteristic
435C2×C22⋊C8C2×D1711yescharacteristic
436C2×C4×C8C2×D1711yescharacteristic
437C2×C17—42no—
438C2×C17—42no—
439C2×C17#335114yescomplemented
440C2×C17C2×#54711yescharacteristic
441C2×C17C2×#57511yescharacteristic
442C2×C17C2×#57711yescharacteristic
443D17—82no—
444C22×Q8—171no—
445C22×D4—171no—
446C22×D4—341no—
447C22×D4—341no—
448C22×D4D6811yescharacteristic
449C23×C4—341no—
450C23×C4—341no—
451C23×C4—341no—
452C23×C4C22×D1711yescharacteristic
453C23×C4C22×D1711yescharacteristic
454C2×SD16—174no—
455C2×SD16—344no—
456C2×M16—24no—
457C2×M16—24no—
458C2×M16C22×D1714yes—
459C2×M16C22×D1714yes—
460C22×C8C22×D1711yescharacteristic
461C22×C8C22×D1711yescharacteristic
462C22×C8C22×D1711yescharacteristic
463C22×C8C22×D1711yescharacteristic
464#126—348no—
465#126—348no—
466#125—174no—
467#125—174no—
468#125—348no—
469#125—342no—
470#125—342no—
471#123—348no—
472#123—348no—
473C22⋊Q8—174no—
474C22⋊Q8—174no—
475C22⋊Q8—342no—
476C22⋊Q8—342no—
477#121—174no—
478#121—174no—
479#121—348no—
480#121—342no—
481#121—342no—
482C4×Q8—174no—
483C4×Q8—342no—
484C4×D4—174no—
485C4×D4—348no—
486C4×D4—342no—
487C4×D4D6814yes—
488C4×D4C22×D1714yes—
489#117—174no—
490#117—174no—
491#117—342no—
492#117—342no—
493#117—348no—
494C2×C4⋊C4—171no—
495C2×C4⋊C4—171no—
496C2×C4⋊C4—171no—
497C2×C4⋊C4—171no—
498C2×C4⋊C4—174no—
499C2×C4⋊C4—174no—
500C2×C4⋊C4—171no—
501C2×C4⋊C4—171no—
502C2×C4⋊C4—341no—
503C2×C4⋊C4—341no—
504C2×C4⋊C4—342no—
505C2×C4⋊C4—342no—
506C2×C4⋊C4—341no—
507C2×C4⋊C4—341no—
508C2×C4⋊C4—341no—
509C2×C4⋊C4—341no—
510C2×C4⋊C4—341no—
511C2×C4⋊C4—341no—
512C2×C4⋊C4—341no—
513C2×C4⋊C4D6811yescharacteristic
514C2×C22⋊C4—341no—
515C2×C22⋊C4—341no—
516C2×C22⋊C4—341no—
517C2×C22⋊C4—341no—
518C2×C22⋊C4—341no—
519C2×C22⋊C4—341no—
520C2×C22⋊C4—341no—
521C2×C22⋊C4D6811yescharacteristic
522C2×C22⋊C4D6811yescharacteristic
523C2×C42—341no—
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⋊C8C22×D1714yes—
537#103—174no—
538#103—174no—
539#103—174no—
540#102—174no—
541#102—174no—
542#102—174no—
543C22⋊C8C22×D1714yes—
544C22⋊C8C22×D1714yes—
545C4×C8C22×D1714yes—
546C17C2×#335111yescharacteristic, complemented, Sylow
547C24—341no—
548C24C2×D6811yescharacteristic
549C24C2×D6811yescharacteristic
550C2×Q8—172no—
551C2×Q8—341no—
552C2×Q8—342no—
553C2×Q8—342no—
554C2×D4—42no—
555C2×D4—172no—
556C2×D4—344no—
557C2×D4—344no—
558C2×D4—341no—
559C2×D4—342no—
560C2×D4—342no—
561C2×D4—684no—
562C2×D4—1362no—
563C2×D4C2×D6814yes—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—344no—
569C22×C4—341no—
570C22×C4—341no—
571C22×C4—341no—
572C22×C4—341no—
573C22×C4—341no—
574C22×C4—341no—
575C22×C4—341no—
576C22×C4—344no—
577C22×C4—344no—
578C22×C4—684no—
579C22×C4—1362no—
580C22×C4—1362no—
581C22×C4C2×D6812yes—
582C22×C4C2×D6812yes—
583C22×C4C2×D6811yescharacteristic
584C22×C4C2×D6811yescharacteristic
585C22×C4C2×D6811yescharacteristic
586C22×C4C2×D6811yescharacteristic
587C22×C4C23×D1712yes—
588C22×C4C23×D1712yes—
589C22×C4C23×D1711yescharacteristic
590SD16—348no—
591M16—28no—
592M16—28no—
593C2×C8—22no—
594C2×C8—22no—
595C2×C8—22no—
596C2×C8#6325414yes—
597C2×C8C23×D1712yes—
598C2×C8C23×D1712yes—
599C2×C8C23×D1712yes—
600C2×C8C23×D1712yes—
601C4⋊C4—172no—
602C4⋊C4—172no—
603C4⋊C4—172no—
604C4⋊C4—172no—
605C4⋊C4—172no—
606C4⋊C4—172no—
607C4⋊C4—341no—
608C4⋊C4—341no—
609C4⋊C4—341no—
610C4⋊C4—341no—
611C4⋊C4—344no—
612C4⋊C4—344no—
613C4⋊C4—341no—
614C4⋊C4—341no—
615C4⋊C4—344no—
616C4⋊C4—344no—
617C4⋊C4—344no—
618C4⋊C4—344no—
619C4⋊C4—344no—
620C4⋊C4—344no—
621C4⋊C4—344no—
622C4⋊C4C2×D6814yes—
623C22⋊C4—344no—
624C22⋊C4—344no—
625C22⋊C4—344no—
626C22⋊C4—344no—
627C22⋊C4—344no—
628C22⋊C4—344no—
629C22⋊C4—344no—
630C22⋊C4C2×D6814yes—
631C22⋊C4C2×D6814yes—
632C42—344no—
633C42—344no—
634C42—344no—
635C42C2×D6812yes—
636C42C23×D1712yes—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—342no—
644C23—682no—
645C23—682no—
646C23—682no—
647C23C22×D6812yes—
648C23C22×D6812yes—
649C23C22×D6811yescharacteristic
650Q8—342no—
651Q8—342no—
652Q8—682no—
653D4—44no—
654D4—342no—
655D4—342no—
656D4—688no—
657D4—682no—
658D4—1364no—
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—342no—
670C2×C4—342no—
671C2×C4—342no—
672C2×C4—342no—
673C2×C4—342no—
674C2×C4—342no—
675C2×C4—342no—
676C2×C4—688no—
677C2×C4—682no—
678C2×C4—682no—
679C2×C4—682no—
680C2×C4—682no—
681C2×C4—682no—
682C2×C4—682no—
683C2×C4—682no—
684C2×C4—1364no—
685C2×C4—1364no—
686C2×C4C22×D6812yes—
687C2×C4C22×D6812yes—
688C2×C4C22×D6812yes—
689C2×C4C22×D6812yes—
690C2×C4C22×D6811yescharacteristic
691C2×C4C2×#6325412yes—
692C2×C4#1058769712yes—
693C2×C4C24×D1711yescharacteristic
694C8—22no—
695C8—22no—
696C8—22no—
697C8C2×#6325414yes—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—44no—
705C22—44no—
706C22—682no—
707C22—682no—
708C22—682no—
709C22—1364no—
710C22#1176346312yes—
711C22#1176360912yes—
712C22#1176362112yes—
713C22C23×D6811yescharacteristic
714C4—22no—
715C4—22no—
716C4—22no—
717C4—22no—
718C4—682no—
719C4—682no—
720C4—682no—
721C4—682no—
722C4—682no—
723C4—682no—
724C4—682no—
725C4#1176346312yes—
726C4C22×#6325411yescharacteristic
727C4C2×#1058769711yescharacteristic
728C2—42no—
729C2—42no—
730C2—1362no—
731C2#1454134614yesdirect product factor
732C2C2×#1176346311yescharacteristic
733C2C2×#1176360911yescharacteristic
734C2C2×#1176362111yescharacteristic
subgroupG/H
centerC23C22×D68
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#436C2
socleC23×C17C22×D4
prime radicalC2×#11763505C2
hypercenterC2×#436D17
hypocenterC17C2×#3351
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#436

Complements

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

NH ≅ G/Ntype
2. C2×#11763499C2semidirect
3. #14541346C2direct (N × H)
4. C2×#11763211C2semidirect
5. C2×#11763128C2semidirect
6. C2×#11763151C2semidirect
7. C2×#11763134C2semidirect
8. C2×#11763140C2semidirect
9. C2×#11763117C2semidirect
10. C2×#11763110C2semidirect
11. C2×#11763055C2semidirect
12. C2×#11763055C2semidirect
13. C2×C4×#63219C2semidirect
14. C2×#11762851C2semidirect
15. C2×#11762851C2semidirect
16. C2×C17×#436C2semidirect
21. #11763499C22semidirect
42. #11763211C22semidirect
43. #11763151C22semidirect
44. #11763140C22semidirect
45. #11763134C22semidirect
46. #11763128C22semidirect
47. #11763117C22semidirect
48. #11763110C22semidirect
49. #11763055C22semidirect
50. #11763055C22semidirect
51. C4×#63219C22semidirect
52. #11762851C22semidirect
53. #11762851C22semidirect
72. C17×#436C22semidirect
344. C2×#436D17semidirect
415. #436C2×D17semidirect
439. C2×C17#3351semidirect
546. C17C2×#3351semidirect
731. C2#14541346direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117635052
C2×#117634992
#145413462
C2×#117632112
C2×#117631282
C2×#117631512
C2×#117631342
C2×#117631402
C2×#117631172
C2×#117631102
C2×#117630552
C2×C4×#632192
C2×#117628512
C2×C17×#4362
C2×#335117