Finite Group Databasebeta

← C2×#14541552 #17914105

Subgroups — C2×#14541552 #17914105

Order 4352.

1874 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763544C211yesmaximal, characteristic
2#14541552C2116yesmaximal, direct product factor
3C2×#11763175C211yesmaximal, characteristic
4C2×#11763171C211yesmaximal, characteristic, complemented
5C2×#11763166C211yesmaximal, characteristic, complemented
6C2×#11763113C211yesmaximal, characteristic, complemented
7C2×#11763106C211yesmaximal, characteristic, complemented
8C2×#11763096C211yesmaximal, characteristic, complemented
9C2×#11763031C211yesmaximal, characteristic, complemented
10C2×#11763031C211yesmaximal, characteristic, complemented
11C2×#11763009C211yesmaximal, characteristic
12C2×#11762940C211yesmaximal, characteristic, complemented
13C2×#11762914C211yesmaximal, characteristic, complemented
14C2×#11762907C211yesmaximal, characteristic, complemented
15C2×C4×#63230C211yesmaximal, characteristic, complemented
16C2×C17×#557C211yesmaximal, characteristic, complemented
17C22×#63231C2211yescharacteristic
18C22×#63230C2211yescharacteristic
19C22×#63230C2211yescharacteristic
20#11763544—24no—
21#11763544C2218yes—
22C2×#10587560C2211yescharacteristic
23C2×#10587633—21no—
24C2×#10587561C2211yescharacteristic
25C2×#10587561C2211yescharacteristic
26C2×#10587580—21no—
27C2×#10587580—21no—
28C2×C4×Dic34C2211yescharacteristic
29C2×C4×D68C2211yescharacteristic
30C2×C4×D68C2211yescharacteristic
31C2×#10587579—21no—
32#11763175C2218yes—
33#11763171C2218yescomplemented
34#11763166C2218yescomplemented
35#11763113C2218yescomplemented
36#11763106C2218yescomplemented
37#11763096C2218yescomplemented
38#11763031C2218yescomplemented
39#11763031C2218yescomplemented
40#11763009C2218yes—
41#11762940C2218yescomplemented
42#11762914C2218yescomplemented
43#11762907C2218yescomplemented
44C4×#63230C2218yescomplemented
45C2×#10587478C2211yescharacteristic
46C2×#10587479C2211yescharacteristic
47C2×#10587479C2211yescharacteristic
48C2×C4⋊#3622C2211yescharacteristic
49C2×C4⋊#3622C2211yescharacteristic
50C2×C4⋊#3622C2211yescharacteristic
51C2×#10587506C2211yescharacteristic
52C2×#10587481C2211yescharacteristic
53C2×#10587481C2211yescharacteristic
54C2×#10587481C2211yescharacteristic
55C2×#10587480C2211yescharacteristic
56C2×#10587480C2211yescharacteristic
57C2×#10587480C2211yescharacteristic
58C2×#10587480C2211yescharacteristic
59C2×#10587480C2211yescharacteristic
60C2×#10587480C2211yescharacteristic
61C2×#10587474C2211yescharacteristic
62C2×#10587474C2211yescharacteristic
63C2×C4×#3622C2211yescharacteristic
64C17×#557—24no—
65C17×#557C2218yescomplemented
66C2×C17×C4⋊Q8—21no—
67C2×C17×C4⋊Q8C2211yescharacteristic
68C2×C17×#125—21no—
69C2×C17×#125—21no—
70C2×C17×#125C2211yescharacteristic
71C2×C17×#125C2211yescharacteristic
72C2×C4×Q8×C17—21no—
73C2×C4×Q8×C17C2211yescharacteristic
74C2×C4×Q8×C17C2211yescharacteristic
75C2×C4×Q8×C17C2211yescharacteristic
76C2×C4×Q8×C17C2211yescharacteristic
77C22×Q8×C17—21no—
78C22×Q8×C17D411yescharacteristic
79C22×Q8×C17C2311yescharacteristic
80C22×D68—21no—
81C22×D68—21no—
82C22×D68C2311yescharacteristic
83C22×D68C2311yescharacteristic
84C22×C4×D17—21no—
85C22×C4×D17—21no—
86C22×Dic34C2311yescharacteristic
87C17×C4⋊Q8—28no—
88C17×C4⋊Q8—22no—
89C17×C4⋊Q8C2314yes—
90C17×#125—28no—
91C17×#125—28no—
92C17×#125—22no—
93C17×#125—22no—
94C17×#125C2314yes—
95C17×#125C2314yes—
96C4×Q8×C17—28no—
97C4×Q8×C17—22no—
98C4×Q8×C17—22no—
99C4×Q8×C17—22no—
100C4×Q8×C17D414yes—
101C4×Q8×C17C2314yes—
102C4×Q8×C17C2314yes—
103C4×Q8×C17C2314yes—
104C4×Q8×C17C2314yes—
105C2×C4⋊C4×C17—21no—
106C2×C4⋊C4×C17—21no—
107C2×C4⋊C4×C17—21no—
108C2×C4⋊C4×C17—21no—
109C2×C4⋊C4×C17—21no—
110C2×C4⋊C4×C17—21no—
111C2×C4⋊C4×C17—21no—
112C2×C4⋊C4×C17—21no—
113C2×C4⋊C4×C17D411yescharacteristic
114C2×C4⋊C4×C17D411yescharacteristic
115C2×C4⋊C4×C17D411yescharacteristic
116C2×C4⋊C4×C17C2311yescharacteristic
117C2×C4⋊C4×C17C2311yescharacteristic
118C2×C4⋊C4×C17C2311yescharacteristic
119C2×C42×C17—21no—
120C2×C42×C17—21no—
121C2×C42×C17—21no—
122C2×C42×C17C2311yescharacteristic
123C2×C42×C17C2311yescharacteristic
124C2×C42×C17C2311yescharacteristic
125#10587633—28no—
126C2×#63231—24no—
127C2×#63231C2314yes—
128C2×#63230—24no—
129C2×#63230—24no—
130C2×#63230C2314yes—
131C2×#63230C2314yes—
132C2×#63227—21no—
133C2×#63227—21no—
134C2×#63227—21no—
135C2×#63227—21no—
136C2×#63227—21no—
137C2×#63227—21no—
138C2×C4⋊Dic17C2311yescharacteristic
139C2×#63225—21no—
140C2×C4×Dic17—21no—
141C22×#3622C2311yescharacteristic
142C22×#3622C2311yescharacteristic
143C22×#3622C2311yescharacteristic
144C22×#3622C2311yescharacteristic
145#10587580—28no—
146#10587580—28no—
147#10587579—28no—
148#10587561—22no—
149#10587561—22no—
150#10587561C2314yes—
151#10587561C2314yes—
152#10587560—22no—
153#10587560C2314yes—
154C4×D68—22no—
155C4×D68—22no—
156C4×D68C2314yes—
157C4×D68C2314yes—
158C4×Dic34—22no—
159C4×Dic34C2314yes—
160#10587506C2314yes—
161#10587481C2314yes—
162#10587481C2314yes—
163#10587481C2314yes—
164#10587480C2314yes—
165#10587480C2314yes—
166#10587480C2314yes—
167#10587480C2314yes—
168#10587480C2314yes—
169#10587480C2314yes—
170#10587479C2314yes—
171#10587479C2314yes—
172#10587478C2314yes—
173C4⋊#3622C2314yes—
174C4⋊#3622C2314yes—
175C4⋊#3622C2314yes—
176#10587474C2314yes—
177#10587474C2314yes—
178C4×#3622C2314yes—
179C23×D17—21no—
180C23×D17—21no—
181C2×Q8×C17—21no—
182C2×Q8×C17—24no—
183C2×Q8×C17—22no—
184C2×Q8×C17—42no—
185C2×Q8×C17—44no—
186C2×Q8×C17C2×D414yes—
187C2×Q8×C17#4114yes—
188C2×Q8×C17C2412yes—
189C22×C4×C17—21no—
190C22×C4×C17—21no—
191C22×C4×C17—21no—
192C22×C4×C17—21no—
193C22×C4×C17C2×D411yescharacteristic
194C22×C4×C17C2×D411yescharacteristic
195C22×C4×C17C2×D411yescharacteristic
196C22×C4×C17C2×D411yescharacteristic
197C22×C4×C17C2×D411yescharacteristic
198C22×C4×C17C2×D411yescharacteristic
199C22×C4×C17C2411yescharacteristic
200C22×Dic17—21no—
201C22×Dic17—21no—
202C2×D68—22no—
203C2×D68—22no—
204C2×D68—22no—
205C2×D68—22no—
206C2×D68—24no—
207C2×D68—21no—
208C2×D68—21no—
209C2×D68—24no—
210C2×D68—44no—
211C2×D68—82no—
212C2×D68C2412yes—
213C2×D68C2412yes—
214C2×C4×D17—24no—
215C2×C4×D17—24no—
216C2×C4×D17—82no—
217C2×C4×D17—82no—
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—24no—
226C4⋊C4×C17—24no—
227C4⋊C4×C17—24no—
228C4⋊C4×C17—24no—
229C4⋊C4×C17—24no—
230C4⋊C4×C17—24no—
231C4⋊C4×C17—21no—
232C4⋊C4×C17—21no—
233C4⋊C4×C17C2×D414yes—
234C4⋊C4×C17C2×D414yes—
235C4⋊C4×C17C2×D414yes—
236C4⋊C4×C17C2412yes—
237C4⋊C4×C17C2412yes—
238C4⋊C4×C17C2412yes—
239C42×C17—24no—
240C42×C17—24no—
241C42×C17—24no—
242C42×C17C2×D412yes—
243C42×C17C2×D412yes—
244C42×C17C2×D412yes—
245C42×C17C2412yes—
246C42×C17C2412yes—
247C42×C17C2412yes—
248#63231—28no—
249#63230—28no—
250#63230—28no—
251#63227—24no—
252#63227—24no—
253#63227—24no—
254#63227—24no—
255#63227—24no—
256#63227—24no—
257C4⋊Dic17—21no—
258C4⋊Dic17C2412yes—
259#63225—24no—
260C4×Dic17—24no—
261C2×#3622—22no—
262C2×#3622—22no—
263C2×#3622—22no—
264C2×#3622—22no—
265C2×#3622C2412yes—
266C2×#3622C2412yes—
267C2×#3622C2412yes—
268C2×#3622C2412yes—
269C2×#3371—171nomaximal, Sylow
270C23×C17C22×D411yescharacteristic
271C22×D17—22no—
272C22×D17—22no—
273C22×D17—42no—
274C22×D17—42no—
275C22×D17—42no—
276C22×D17—42no—
277C22×D17—42no—
278C22×D17—42no—
279Q8×C17—24no—
280Q8×C17—22no—
281Q8×C17—44no—
282Q8×C17—48no—
283Q8×C17C2×#4114yes—
284C2×C4×C17—24no—
285C2×C4×C17—22no—
286C2×C4×C17—22no—
287C2×C4×C17—22no—
288C2×C4×C17—22no—
289C2×C4×C17—22no—
290C2×C4×C17—22no—
291C2×C4×C17—22no—
292C2×C4×C17—22no—
293C2×C4×C17—22no—
294C2×C4×C17—22no—
295C2×C4×C17—42no—
296C2×C4×C17—42no—
297C2×C4×C17—42no—
298C2×C4×C17C22×D412yes—
299C2×C4×C17C22×D412yes—
300C2×C4×C17C22×D412yes—
301C2×C4×C17C22×D412yes—
302C2×C4×C17C22×D412yes—
303C2×C4×C17C22×D412yes—
304C2×C4×C17C22×D411yescharacteristic
305C2×C4×C17C2×#4112yes—
306C2×C4×C172−1+412yes—
307C2×C4×C17C2511yescharacteristic
308C2×Dic17—22no—
309C2×Dic17—22no—
310C2×Dic17—42no—
311C2×Dic17—42no—
312D68—22no—
313D68—22no—
314D68—22no—
315D68—22no—
316D68—48no—
317D68—42no—
318D68—42no—
319D68—84no—
320C4×D17—84no—
321C4×D17—84no—
322Dic34—22no—
323Dic34—22no—
324Dic34—42no—
325#3622—22no—
326#3622—22no—
327#3622—22no—
328#3622—22no—
329C2×#559—171no—
330C2×#557D1711yescharacteristic, complemented
331#3371—1716no—
332C2×#490—171no—
333C2×#489—171no—
334C2×#488—171no—
335C2×#479—171no—
336C2×#478—171no—
337C2×#476—171no—
338C2×#464—171no—
339C2×#464—171no—
340C2×#460—171no—
341C2×#446—171no—
342C2×#441—171no—
343C2×#440—171no—
344C2×C4×SD16—171no—
345C22×C17#54812yes—
346C22×C17#57512yes—
347C22×C17#57712yes—
348C22×C17C23×D411yescharacteristic
349C2×D17—42no—
350C2×D17—42no—
351C2×D17—42no—
352C2×D17—42no—
353C2×D17—42no—
354C2×D17—42no—
355C2×D17—84no—
356C2×D17—84no—
357C4×C17—24no—
358C4×C17—22no—
359C4×C17—22no—
360C4×C17—22no—
361C4×C17—22no—
362C4×C17—22no—
363C4×C17—22no—
364C4×C17—42no—
365C4×C17—42no—
366C4×C17—42no—
367C4×C17#54812yes—
368C4×C17C22×#4111yescharacteristic
369C4×C17C2×2−1+411yescharacteristic
370Dic17—42no—
371Dic17—42no—
372C22×Q16—171no—
373C22×SD16—171no—
374C22×SD16—171no—
375#559—178no—
376#559—344no—
377#557—24no—
378#557C2×D1718yescomplemented
379C2×C4⋊Q8—21no—
380C2×C4⋊Q8C2×D1711yescharacteristic
381C2×#127—171no—
382C2×#125—21no—
383C2×#125—21no—
384C2×#125C2×D1711yescharacteristic
385C2×#125C2×D1711yescharacteristic
386C2×#124—171no—
387C2×#124—171no—
388C2×#124—341no—
389C2×#123—341no—
390C2×#123—341no—
391C2×C4×Q8—21no—
392C2×C4×Q8—171no—
393C2×C4×Q8C2×D1711yescharacteristic
394C2×C4×Q8C2×D1711yescharacteristic
395C2×C4×Q8C2×D1711yescharacteristic
396C2×C4×Q8C2×D1711yescharacteristic
397C2×C4×D4—171no—
398C2×C4×D4—171no—
399C2×C4×D4—341no—
400#490—178no—
401#489—178no—
402#488—178no—
403#479—178no—
404#478—178no—
405#476—178no—
406#464—178no—
407#464—178no—
408#460—178no—
409#446—178no—
410#441—178no—
411#440—178no—
412C4×SD16—178no—
413C2×#107—171no—
414C2×#106—171no—
415C2×#106—171no—
416C2×C4⋊C8—171no—
417C2×C4⋊C8—171no—
418C2×C4⋊C8—171no—
419C2×#103—171no—
420C2×#103—171no—
421C2×#103—171no—
422C2×#103—171no—
423C2×#102—171no—
424C2×#102—171no—
425C2×#102—171no—
426C2×#102—171no—
427C2×#102—171no—
428C2×#102—171no—
429C2×#97—171no—
430C2×#97—171no—
431C2×C4×C8—171no—
432C2×C17#337114yescomplemented
433C2×C17C2×#54811yescharacteristic
434C2×C17C2×#57511yescharacteristic
435C2×C17C2×#57711yescharacteristic
436D17—82no—
437D17—82no—
438C22×Q8—21no—
439C22×Q8—171no—
440C22×Q8C22⋊D1711yescharacteristic
441C22×Q8C22×D1711yescharacteristic
442C22×D4—171no—
443C22×D4—171no—
444C22×D4—341no—
445C22×D4—341no—
446C23×C4—341no—
447C23×C4—341no—
448C2×Q16—174no—
449C2×Q16—344no—
450C2×SD16—174no—
451C2×SD16—174no—
452C2×SD16—344no—
453C2×SD16—344no—
454C22×C8—171no—
455C22×C8—171no—
456C22×C8—171no—
457C22×C8—171no—
458C4⋊Q8—28no—
459C4⋊Q8—22no—
460C4⋊Q8C22×D1714yes—
461#127—174no—
462#127—342no—
463#125—28no—
464#125—28no—
465#125—22no—
466#125—22no—
467#125C22×D1714yes—
468#125C22×D1714yes—
469#124—174no—
470#124—174no—
471#124—348no—
472#124—342no—
473#124—342no—
474#123—348no—
475#123—348no—
476C4×Q8—28no—
477C4×Q8—22no—
478C4×Q8—22no—
479C4×Q8—22no—
480C4×Q8—174no—
481C4×Q8—342no—
482C4×Q8C22⋊D1714yes—
483C4×Q8C22×D1714yes—
484C4×Q8C22×D1714yes—
485C4×Q8C22×D1714yes—
486C4×Q8C22×D1714yes—
487C4×D4—174no—
488C4×D4—174no—
489C4×D4—348no—
490C4×D4—342no—
491C4×D4—342no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—171no—
501C2×C4⋊C4—341no—
502C2×C4⋊C4C22⋊D1711yescharacteristic
503C2×C4⋊C4C22⋊D1711yescharacteristic
504C2×C4⋊C4C22⋊D1711yescharacteristic
505C2×C4⋊C4C22×D1711yescharacteristic
506C2×C4⋊C4C22×D1711yescharacteristic
507C2×C4⋊C4C22×D1711yescharacteristic
508C2×C22⋊C4—341no—
509C2×C22⋊C4—341no—
510C2×C22⋊C4—341no—
511C2×C22⋊C4—341no—
512C2×C22⋊C4—341no—
513C2×C22⋊C4—341no—
514C2×C42—21no—
515C2×C42—21no—
516C2×C42—21no—
517C2×C42—341no—
518C2×C42C22×D1711yescharacteristic
519C2×C42C22×D1711yescharacteristic
520C2×C42C22×D1711yescharacteristic
521#107—174no—
522#106—174no—
523#106—174no—
524C4⋊C8—174no—
525C4⋊C8—174no—
526C4⋊C8—174no—
527#103—174no—
528#103—174no—
529#103—174no—
530#103—174no—
531#102—174no—
532#102—174no—
533#102—174no—
534#102—174no—
535#102—174no—
536#102—174no—
537#97—174no—
538#97—174no—
539C4×C8—174no—
540C17C2×#337111yescharacteristic, complemented, Sylow
541C24—341no—
542C24—341no—
543C2×Q8—22no—
544C2×Q8—21no—
545C2×Q8—24no—
546C2×Q8—42no—
547C2×Q8—44no—
548C2×Q8—172no—
549C2×Q8—341no—
550C2×Q8—342no—
551C2×Q8—342no—
552C2×Q8#6325614yes—
553C2×Q8C2×C22⋊D1714yes—
554C2×Q8C23×D1712yes—
555C2×D4—172no—
556C2×D4—172no—
557C2×D4—342no—
558C2×D4—342no—
559C2×D4—342no—
560C2×D4—342no—
561C2×D4—344no—
562C2×D4—341no—
563C2×D4—341no—
564C2×D4—344no—
565C2×D4—684no—
566C2×D4—1362no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—341no—
572C22×C4—341no—
573C22×C4—344no—
574C22×C4—344no—
575C22×C4—1362no—
576C22×C4—1362no—
577C22×C4C2×C22⋊D1711yescharacteristic
578C22×C4C2×C22⋊D1711yescharacteristic
579C22×C4C2×C22⋊D1711yescharacteristic
580C22×C4C2×C22⋊D1711yescharacteristic
581C22×C4C2×C22⋊D1711yescharacteristic
582C22×C4C2×C22⋊D1711yescharacteristic
583C22×C4C23×D1711yescharacteristic
584Q16—348no—
585SD16—348no—
586SD16—348no—
587C2×C8—172no—
588C2×C8—172no—
589C2×C8—172no—
590C2×C8—172no—
591C2×C8—342no—
592C2×C8—342no—
593C2×C8—342no—
594C2×C8—342no—
595C4⋊C4—24no—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—24no—
599C4⋊C4—24no—
600C4⋊C4—24no—
601C4⋊C4—24no—
602C4⋊C4—24no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—172no—
607C4⋊C4—341no—
608C4⋊C4—344no—
609C4⋊C4C2×C22⋊D1714yes—
610C4⋊C4C2×C22⋊D1714yes—
611C4⋊C4C2×C22⋊D1714yes—
612C4⋊C4C23×D1712yes—
613C4⋊C4C23×D1712yes—
614C4⋊C4C23×D1712yes—
615C22⋊C4—344no—
616C22⋊C4—344no—
617C22⋊C4—344no—
618C22⋊C4—344no—
619C22⋊C4—344no—
620C22⋊C4—344no—
621C42—24no—
622C42—24no—
623C42—24no—
624C42—344no—
625C42C2×C22⋊D1712yes—
626C42C2×C22⋊D1712yes—
627C42C2×C22⋊D1712yes—
628C42C23×D1712yes—
629C42C23×D1712yes—
630C42C23×D1712yes—
631C23—342no—
632C23—342no—
633C23—682no—
634C23—682no—
635C23—682no—
636C23—682no—
637C23—682no—
638C23—682no—
639C23C22×C22⋊D1711yescharacteristic
640Q8—24no—
641Q8—22no—
642Q8—44no—
643Q8—48no—
644Q8—342no—
645Q8—342no—
646Q8—682no—
647Q8C2×#6325614yes—
648D4—342no—
649D4—342no—
650D4—342no—
651D4—342no—
652D4—688no—
653D4—682no—
654D4—682no—
655D4—1364no—
656C2×C4—24no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—342no—
671C2×C4—342no—
672C2×C4—682no—
673C2×C4—682no—
674C2×C4—1364no—
675C2×C4—1364no—
676C2×C4C2×#6325612yes—
677C2×C4#1058769412yes—
678C2×C4C22×C22⋊D1712yes—
679C2×C4C22×C22⋊D1712yes—
680C2×C4C22×C22⋊D1712yes—
681C2×C4C22×C22⋊D1712yes—
682C2×C4C22×C22⋊D1712yes—
683C2×C4C22×C22⋊D1712yes—
684C2×C4C22×C22⋊D1711yescharacteristic
685C2×C4C24×D1711yescharacteristic
686C8—342no—
687C8—342no—
688C8—342no—
689C8—342no—
690C22—682no—
691C22—682no—
692C22—682no—
693C22—682no—
694C22—682no—
695C22—682no—
696C22—1364no—
697C22—1364no—
698C22#1176347012yes—
699C22#1176360712yes—
700C22#1176361712yes—
701C22C23×C22⋊D1711yescharacteristic
702C4—22no—
703C4—22no—
704C4—22no—
705C4—24no—
706C4—22no—
707C4—22no—
708C4—22no—
709C4—42no—
710C4—42no—
711C4—42no—
712C4—682no—
713C4—682no—
714C4#1176347012yes—
715C4C22×#6325611yescharacteristic
716C4C2×#1058769411yescharacteristic
717C2—1362no—
718C2—1362no—
719C2#1454155214yesdirect product factor
720C2C2×#1176347011yescharacteristic
721C2C2×#1176360711yescharacteristic
722C2C2×#1176361711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#557C2
socleC23×C17C22×D4
prime radicalC2×#10587560C22
hypercenterC2×#557D17
hypocenterC17C2×#3371
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
2. #14541552C2direct (N × H)
4. C2×#11763171C2semidirect
5. C2×#11763166C2semidirect
6. C2×#11763113C2semidirect
7. C2×#11763106C2semidirect
8. C2×#11763096C2semidirect
9. C2×#11763031C2semidirect
10. C2×#11763031C2semidirect
12. C2×#11762940C2semidirect
13. C2×#11762914C2semidirect
14. C2×#11762907C2semidirect
15. C2×C4×#63230C2semidirect
16. C2×C17×#557C2semidirect
33. #11763171C22semidirect
34. #11763166C22semidirect
35. #11763113C22semidirect
36. #11763106C22semidirect
37. #11763096C22semidirect
38. #11763031C22semidirect
39. #11763031C22semidirect
41. #11762940C22semidirect
42. #11762914C22semidirect
43. #11762907C22semidirect
44. C4×#63230C22semidirect
65. C17×#557C22semidirect
330. C2×#557D17semidirect
378. #557C2×D17semidirect
432. C2×C17#3371semidirect
540. C17C2×#3371semidirect
719. C2#14541552direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117635442
#145415522
C2×#117631752
C2×#117631712
C2×#117631662
C2×#117631132
C2×#117631062
C2×#117630962
C2×#117630312
C2×#117630092
C2×#117629402
C2×#117629142
C2×#117629072
C2×C4×#632302
C2×C17×#5572
C2×#337117