Finite Group Databasebeta

← C2×#14541546 #17914099

Subgroups — C2×#14541546 #17914099

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×#11763537C211yesmaximal, characteristic, complemented
2#14541546C2116yesmaximal, direct product factor
3C2×#11763173C211yesmaximal, characteristic
4C2×#11763168C211yesmaximal, characteristic, complemented
5C2×#11763163C211yesmaximal, characteristic, complemented
6C2×#11763116C211yesmaximal, characteristic, complemented
7C2×#11763109C211yesmaximal, characteristic, complemented
8C2×#11763099C211yesmaximal, characteristic, complemented
9C2×#11763028C211yesmaximal, characteristic, complemented
10C2×#11763028C211yesmaximal, characteristic, complemented
11C2×#11763006C211yesmaximal, characteristic
12C2×#11762940C211yesmaximal, characteristic, complemented
13C2×#11762914C211yesmaximal, characteristic, complemented
14C2×#11762909C211yesmaximal, characteristic, complemented
15C2×C4×#63229C211yesmaximal, characteristic, complemented
16C2×C17×#559C211yesmaximal, characteristic
17C22×#63231C2211yescharacteristic
18C22×#63229C2211yescharacteristic
19C22×#63229C2211yescharacteristic
20#11763537—24no—
21#11763537C2218yescomplemented
22C2×#10587555C2211yescharacteristic
23C2×#10587630—21no—
24C2×#10587556C2211yescharacteristic
25C2×#10587556C2211yescharacteristic
26C2×#10587575—21no—
27C2×#10587575—21no—
28C2×C4×Dic34C2211yescharacteristic
29C2×C4×Dic34C2211yescharacteristic
30C2×C4×Dic34C2211yescharacteristic
31C2×#10587573—21no—
32#11763173C2218yes—
33#11763168C2218yescomplemented
34#11763163C2218yescomplemented
35#11763116C2218yescomplemented
36#11763109C2218yescomplemented
37#11763099C2218yescomplemented
38#11763028C2218yescomplemented
39#11763028C2218yescomplemented
40#11763006C2218yes—
41#11762940C2218yescomplemented
42#11762914C2218yescomplemented
43#11762909C2218yescomplemented
44C4×#63229C2218yescomplemented
45C2×#10587478C2211yescharacteristic
46C2×#10587479C2211yescharacteristic
47C2×#10587479C2211yescharacteristic
48C2×C4⋊#3622C2211yescharacteristic
49C2×C4⋊#3622C2211yescharacteristic
50C2×C4⋊#3622C2211yescharacteristic
51C2×#10587506C2211yescharacteristic
52C2×#10587506C2211yescharacteristic
53C2×#10587506C2211yescharacteristic
54C2×#10587481C2211yescharacteristic
55C2×#10587503C2211yescharacteristic
56C2×#10587503C2211yescharacteristic
57C2×#10587503C2211yescharacteristic
58C2×#10587503C2211yescharacteristic
59C2×#10587503C2211yescharacteristic
60C2×#10587503C2211yescharacteristic
61C2×#10587474C2211yescharacteristic
62C2×#10587474C2211yescharacteristic
63C2×C4×#3622C2211yescharacteristic
64C17×#559—24no—
65C17×#559C2218yes—
66C2×C17×#127C2211yescharacteristic
67C2×C17×#124—21no—
68C2×C17×#124C2211yescharacteristic
69C2×C17×#124C2211yescharacteristic
70C2×C17×#123—21no—
71C2×C17×#123—21no—
72C2×C4×Q8×C17C2211yescharacteristic
73C2×C4×Q8×C17C2211yescharacteristic
74C2×C4×D4×C17—21no—
75C2×C4×D4×C17C2211yescharacteristic
76C2×C4×D4×C17C2211yescharacteristic
77C22×Q8×C17D411yescharacteristic
78C22×Q8×C17C2311yescharacteristic
79C22×D4×C17—21no—
80C22×D4×C17—21no—
81C22×D4×C17C2311yescharacteristic
82C22×D4×C17C2311yescharacteristic
83C23×C4×C17—21no—
84C23×C4×C17—21no—
85C22×Dic34—21no—
86C22×Dic34C2311yescharacteristic
87C17×#127—22no—
88C17×#127C2314yes—
89C17×#124—28no—
90C17×#124—22no—
91C17×#124—22no—
92C17×#124C2314yes—
93C17×#124C2314yes—
94C17×#123—28no—
95C17×#123—28no—
96C4×Q8×C17—22no—
97C4×Q8×C17D414yes—
98C4×Q8×C17C2314yes—
99C4×Q8×C17C2314yes—
100C4×D4×C17—28no—
101C4×D4×C17—22no—
102C4×D4×C17—22no—
103C4×D4×C17C2314yes—
104C4×D4×C17C2314yes—
105C2×C4⋊C4×C17—21no—
106C2×C4⋊C4×C17D411yescharacteristic
107C2×C4⋊C4×C17D411yescharacteristic
108C2×C4⋊C4×C17D411yescharacteristic
109C2×C4⋊C4×C17C2311yescharacteristic
110C2×C22⋊C4×C17—21no—
111C2×C22⋊C4×C17—21no—
112C2×C22⋊C4×C17—21no—
113C2×C22⋊C4×C17—21no—
114C2×C22⋊C4×C17—21no—
115C2×C22⋊C4×C17—21no—
116C2×C42×C17—21no—
117C2×C42×C17C2311yescharacteristic
118C2×C42×C17C2311yescharacteristic
119C2×C42×C17C2311yescharacteristic
120#10587630—28no—
121C2×#63231—24no—
122C2×#63231C2314yes—
123C2×#63229—24no—
124C2×#63229—24no—
125C2×#63229C2314yes—
126C2×#63229C2314yes—
127C2×C4⋊Dic17—21no—
128C2×C4⋊Dic17C2311yescharacteristic
129C2×C4⋊Dic17C2311yescharacteristic
130C2×C4⋊Dic17C2311yescharacteristic
131C2×#63225—21no—
132C2×#63225—21no—
133C2×#63225—21no—
134C2×#63225—21no—
135C2×#63225—21no—
136C2×#63225—21no—
137C2×#63225—21no—
138C2×C4×Dic17—21no—
139C2×C4×Dic17—21no—
140C2×C4×Dic17—21no—
141C22×#3622C2311yescharacteristic
142C22×#3622C2311yescharacteristic
143C22×#3622C2311yescharacteristic
144C22×#3622C2311yescharacteristic
145#10587575—28no—
146#10587575—28no—
147#10587573—28no—
148#10587556—22no—
149#10587556—22no—
150#10587556C2314yes—
151#10587556C2314yes—
152#10587555—22no—
153#10587555C2314yes—
154C4×Dic34—22no—
155C4×Dic34—22no—
156C4×Dic34—22no—
157C4×Dic34C2314yes—
158C4×Dic34C2314yes—
159C4×Dic34C2314yes—
160#10587506C2314yes—
161#10587506C2314yes—
162#10587506C2314yes—
163#10587503C2314yes—
164#10587503C2314yes—
165#10587503C2314yes—
166#10587503C2314yes—
167#10587503C2314yes—
168#10587503C2314yes—
169#10587481C2314yes—
170#10587479C2314yes—
171#10587479C2314yes—
172#10587478C2314yes—
173C4⋊#3622C2314yes—
174C4⋊#3622C2314yes—
175C4⋊#3622C2314yes—
176#10587474C2314yes—
177#10587474C2314yes—
178C4×#3622C2314yes—
179C24×C17—21no—
180C24×C17—21no—
181C2×Q8×C17—21no—
182C2×Q8×C17—22no—
183C2×Q8×C17—22no—
184C2×Q8×C17—42no—
185C2×Q8×C17C2×D414yes—
186C2×Q8×C17C2412yes—
187C2×D4×C17—21no—
188C2×D4×C17—21no—
189C2×D4×C17—24no—
190C2×D4×C17—24no—
191C2×D4×C17—22no—
192C2×D4×C17—22no—
193C2×D4×C17—22no—
194C2×D4×C17—22no—
195C2×D4×C17—44no—
196C2×D4×C17—82no—
197C2×D4×C17C2412yes—
198C2×D4×C17C2412yes—
199C22×C4×C17—21no—
200C22×C4×C17—21no—
201C22×C4×C17—24no—
202C22×C4×C17—24no—
203C22×C4×C17—82no—
204C22×C4×C17—82no—
205C22×C4×C17C2×D411yescharacteristic
206C22×C4×C17C2×D411yescharacteristic
207C22×C4×C17C2×D411yescharacteristic
208C22×C4×C17C2×D411yescharacteristic
209C22×C4×C17C2×D411yescharacteristic
210C22×C4×C17C2×D411yescharacteristic
211C22×C4×C17C2411yescharacteristic
212C22×Dic17—21no—
213C22×Dic17—21no—
214C22×Dic17—21no—
215C22×Dic17—21no—
216C2×Dic34—21no—
217C2×Dic34—22no—
218C2×Dic34—24no—
219C2×Dic34—44no—
220C2×Dic34#4114yes—
221C2×Dic34C2412yes—
222C4⋊C4×C17—24no—
223C4⋊C4×C17—21no—
224C4⋊C4×C17C2×D414yes—
225C4⋊C4×C17C2×D414yes—
226C4⋊C4×C17C2×D414yes—
227C4⋊C4×C17C2412yes—
228C22⋊C4×C17—24no—
229C22⋊C4×C17—24no—
230C22⋊C4×C17—24no—
231C22⋊C4×C17—24no—
232C22⋊C4×C17—24no—
233C22⋊C4×C17—24no—
234C42×C17—24no—
235C42×C17C2×D412yes—
236C42×C17C2×D412yes—
237C42×C17C2×D412yes—
238C42×C17C2412yes—
239C42×C17C2412yes—
240C42×C17C2412yes—
241#63231—28no—
242#63229—28no—
243#63229—28no—
244C4⋊Dic17—21no—
245C4⋊Dic17—21no—
246C4⋊Dic17—21no—
247C4⋊Dic17—24no—
248C4⋊Dic17C2412yes—
249C4⋊Dic17C2412yes—
250C4⋊Dic17C2412yes—
251#63225—24no—
252#63225—24no—
253#63225—24no—
254#63225—24no—
255#63225—24no—
256#63225—24no—
257#63225—24no—
258C4×Dic17—24no—
259C4×Dic17—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×C17—22no—
271C23×C17—22no—
272C23×C17—42no—
273C23×C17—42no—
274C23×C17—42no—
275C23×C17—42no—
276C23×C17—42no—
277C23×C17—42no—
278C23×C17C22×D411yescharacteristic
279Q8×C17—22no—
280Q8×C17—22no—
281Q8×C17—44no—
282Q8×C17—42no—
283D4×C17—22no—
284D4×C17—22no—
285D4×C17—22no—
286D4×C17—22no—
287D4×C17—48no—
288D4×C17—42no—
289D4×C17—42no—
290D4×C17—84no—
291C2×C4×C17—22no—
292C2×C4×C17—22no—
293C2×C4×C17—22no—
294C2×C4×C17—22no—
295C2×C4×C17—22no—
296C2×C4×C17—22no—
297C2×C4×C17—22no—
298C2×C4×C17—22no—
299C2×C4×C17—42no—
300C2×C4×C17—42no—
301C2×C4×C17—84no—
302C2×C4×C17—84no—
303C2×C4×C17C22×D412yes—
304C2×C4×C17C22×D412yes—
305C2×C4×C17C22×D412yes—
306C2×C4×C17C22×D412yes—
307C2×C4×C17C22×D412yes—
308C2×C4×C17C22×D412yes—
309C2×C4×C17C22×D411yescharacteristic
310C2×C4×C17C2×#4112yes—
311C2×C4×C172−1+412yes—
312C2×C4×C17C2511yescharacteristic
313C2×Dic17—24no—
314C2×Dic17—22no—
315C2×Dic17—22no—
316C2×Dic17—22no—
317C2×Dic17—22no—
318C2×Dic17—42no—
319C2×Dic17—42no—
320C2×Dic17—42no—
321Dic34—24no—
322Dic34—22no—
323Dic34—48no—
324Dic34C2×#4114yes—
325#3622—22no—
326#3622—22no—
327#3622—22no—
328#3622—22no—
329C2×#559D1711yescharacteristic
330C2×#557—171no—
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—42no—
346C22×C17—42no—
347C22×C17—42no—
348C22×C17—42no—
349C22×C17—42no—
350C22×C17—42no—
351C22×C17—84no—
352C22×C17—84no—
353C22×C17#54812yes—
354C22×C17#57512yes—
355C22×C17#57712yes—
356C22×C17C23×D411yescharacteristic
357C4×C17—22no—
358C4×C17—22no—
359C4×C17—22no—
360C4×C17—22no—
361C4×C17—22no—
362C4×C17—22no—
363C4×C17—42no—
364C4×C17—42no—
365C4×C17#54812yes—
366C4×C17C22×#4111yescharacteristic
367C4×C17C2×2−1+411yescharacteristic
368Dic17—24no—
369Dic17—42no—
370Dic17—42no—
371Dic17—42no—
372C22×Q16—171no—
373C22×SD16—171no—
374C22×SD16—171no—
375#559—24no—
376#559C2×D1718yes—
377#557—178no—
378#557—344no—
379C2×C4⋊Q8—171no—
380C2×C4⋊Q8—341no—
381C2×#127C2×D1711yescharacteristic
382C2×#125—171no—
383C2×#125—171no—
384C2×#125—341no—
385C2×#125—341no—
386C2×#124—21no—
387C2×#124C2×D1711yescharacteristic
388C2×#124C2×D1711yescharacteristic
389C2×#123—21no—
390C2×#123—21no—
391C2×C4×Q8—171no—
392C2×C4×Q8—171no—
393C2×C4×Q8—171no—
394C2×C4×Q8—341no—
395C2×C4×Q8C2×D1711yescharacteristic
396C2×C4×Q8C2×D1711yescharacteristic
397C2×C4×D4—21no—
398C2×C4×D4C2×D1711yescharacteristic
399C2×C4×D4C2×D1711yescharacteristic
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—82no—
433C2×C17—82no—
434C2×C17#337114yescomplemented
435C2×C17C2×#54811yescharacteristic
436C2×C17C2×#57511yescharacteristic
437C2×C17C2×#57711yescharacteristic
438C22×Q8—171no—
439C22×Q8—341no—
440C22×Q8C22⋊D1711yescharacteristic
441C22×Q8C22×D1711yescharacteristic
442C22×D4—21no—
443C22×D4—21no—
444C22×D4C22×D1711yescharacteristic
445C22×D4C22×D1711yescharacteristic
446C23×C4—21no—
447C23×C4—21no—
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—174no—
459C4⋊Q8—348no—
460C4⋊Q8—342no—
461#127—22no—
462#127C22×D1714yes—
463#125—174no—
464#125—174no—
465#125—348no—
466#125—348no—
467#125—342no—
468#125—342no—
469#124—28no—
470#124—22no—
471#124—22no—
472#124C22×D1714yes—
473#124C22×D1714yes—
474#123—28no—
475#123—28no—
476C4×Q8—22no—
477C4×Q8—174no—
478C4×Q8—174no—
479C4×Q8—174no—
480C4×Q8—348no—
481C4×Q8—342no—
482C4×Q8—342no—
483C4×Q8—342no—
484C4×Q8C22⋊D1714yes—
485C4×Q8C22×D1714yes—
486C4×Q8C22×D1714yes—
487C4×D4—28no—
488C4×D4—22no—
489C4×D4—22no—
490C4×D4C22×D1714yes—
491C4×D4C22×D1714yes—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—171no—
494C2×C4⋊C4—171no—
495C2×C4⋊C4—171no—
496C2×C4⋊C4—341no—
497C2×C4⋊C4—341no—
498C2×C4⋊C4—341no—
499C2×C4⋊C4—341no—
500C2×C4⋊C4—341no—
501C2×C4⋊C4—341no—
502C2×C4⋊C4—341no—
503C2×C4⋊C4—341no—
504C2×C4⋊C4C22⋊D1711yescharacteristic
505C2×C4⋊C4C22⋊D1711yescharacteristic
506C2×C4⋊C4C22⋊D1711yescharacteristic
507C2×C4⋊C4C22×D1711yescharacteristic
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C42—21no—
515C2×C42—341no—
516C2×C42—341no—
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—21no—
542C24—21no—
543C2×Q8—21no—
544C2×Q8—22no—
545C2×Q8—22no—
546C2×Q8—42no—
547C2×Q8—174no—
548C2×Q8—172no—
549C2×Q8—342no—
550C2×Q8—341no—
551C2×Q8—344no—
552C2×Q8—684no—
553C2×Q8C2×C22⋊D1714yes—
554C2×Q8C23×D1712yes—
555C2×D4—22no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—24no—
562C2×D4—24no—
563C2×D4—44no—
564C2×D4—82no—
565C2×D4C23×D1712yes—
566C2×D4C23×D1712yes—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—82no—
572C22×C4—82no—
573C22×C4—341no—
574C22×C4—341no—
575C22×C4—341no—
576C22×C4—341no—
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—21no—
597C4⋊C4—172no—
598C4⋊C4—172no—
599C4⋊C4—172no—
600C4⋊C4—341no—
601C4⋊C4—341no—
602C4⋊C4—341no—
603C4⋊C4—344no—
604C4⋊C4—344no—
605C4⋊C4—344no—
606C4⋊C4—344no—
607C4⋊C4—344no—
608C4⋊C4—344no—
609C4⋊C4—344no—
610C4⋊C4—344no—
611C4⋊C4C2×C22⋊D1714yes—
612C4⋊C4C2×C22⋊D1714yes—
613C4⋊C4C2×C22⋊D1714yes—
614C4⋊C4C23×D1712yes—
615C22⋊C4—24no—
616C22⋊C4—24no—
617C22⋊C4—24no—
618C22⋊C4—24no—
619C22⋊C4—24no—
620C22⋊C4—24no—
621C42—24no—
622C42—344no—
623C42—344no—
624C42—344no—
625C42C2×C22⋊D1712yes—
626C42C2×C22⋊D1712yes—
627C42C2×C22⋊D1712yes—
628C42C23×D1712yes—
629C42C23×D1712yes—
630C42C23×D1712yes—
631C23—22no—
632C23—22no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23C22×C22⋊D1711yescharacteristic
640Q8—22no—
641Q8—22no—
642Q8—44no—
643Q8—42no—
644Q8—174no—
645Q8—344no—
646Q8—342no—
647Q8—688no—
648D4—22no—
649D4—22no—
650D4—22no—
651D4—22no—
652D4—48no—
653D4—42no—
654D4—42no—
655D4—84no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—84no—
667C2×C4—84no—
668C2×C4—344no—
669C2×C4—342no—
670C2×C4—342no—
671C2×C4—342no—
672C2×C4—342no—
673C2×C4—682no—
674C2×C4—682no—
675C2×C4—682no—
676C2×C4#41×D1712yes—
677C2×C4#1058769712yes—
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—42no—
691C22—42no—
692C22—42no—
693C22—42no—
694C22—42no—
695C22—42no—
696C22—84no—
697C22—84no—
698C22#1176346612yes—
699C22#1176360712yes—
700C22#1176362012yes—
701C22C23×C22⋊D1711yescharacteristic
702C4—22no—
703C4—22no—
704C4—22no—
705C4—22no—
706C4—22no—
707C4—22no—
708C4—42no—
709C4—42no—
710C4—344no—
711C4—682no—
712C4—682no—
713C4—682no—
714C4#1176346612yes—
715C4C2×#41×D1711yescharacteristic
716C4C2×#1058769711yescharacteristic
717C2—82no—
718C2—82no—
719C2#1454154614yesdirect product factor
720C2C2×#1176346611yescharacteristic
721C2C2×#1176360711yescharacteristic
722C2C2×#1176362011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#559C2
socleC23×C17C22×D4
prime radicalC2×C17×#127C22
hypercenterC2×#559D17
hypocenterC17C2×#3371
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#559

Complements

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

NH ≅ G/Ntype
1. C2×#11763537C2semidirect
2. #14541546C2direct (N × H)
4. C2×#11763168C2semidirect
5. C2×#11763163C2semidirect
6. C2×#11763116C2semidirect
7. C2×#11763109C2semidirect
8. C2×#11763099C2semidirect
9. C2×#11763028C2semidirect
10. C2×#11763028C2semidirect
12. C2×#11762940C2semidirect
13. C2×#11762914C2semidirect
14. C2×#11762909C2semidirect
15. C2×C4×#63229C2semidirect
21. #11763537C22semidirect
33. #11763168C22semidirect
34. #11763163C22semidirect
35. #11763116C22semidirect
36. #11763109C22semidirect
37. #11763099C22semidirect
38. #11763028C22semidirect
39. #11763028C22semidirect
41. #11762940C22semidirect
42. #11762914C22semidirect
43. #11762909C22semidirect
44. C4×#63229C22semidirect
434. C2×C17#3371semidirect
540. C17C2×#3371semidirect
719. C2#14541546direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117635372
#145415462
C2×#117631732
C2×#117631682
C2×#117631632
C2×#117631162
C2×#117631092
C2×#117630992
C2×#117630282
C2×#117630062
C2×#117629402
C2×#117629142
C2×#117629092
C2×C4×#632292
C2×C17×#5592
C2×#337117