Finite Group Databasebeta

← C2×#14540037 #17906513

Subgroups — C2×#14540037 #17906513

Order 4352.

1806 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763414C211yesmaximal, characteristic
2#14540037C2116yesmaximal, direct product factor
3C2×#11763215C211yesmaximal, characteristic, complemented
4C2×#11763208C211yesmaximal, characteristic, complemented
5C2×#11763175C211yesmaximal, characteristic, complemented
6C2×#11763157C211yesmaximal, characteristic, complemented
7C2×#11763127C211yesmaximal, characteristic, complemented
8C2×#11763133C211yesmaximal, characteristic, complemented
9C2×#11763133C211yesmaximal, characteristic, complemented
10C2×#11763122C211yesmaximal, characteristic, complemented
11C2×#11763106C211yesmaximal, characteristic, complemented
12C2×#11763106C211yesmaximal, characteristic, complemented
13C2×#11763096C211yesmaximal, characteristic, complemented
14C2×#11763086C211yesmaximal, characteristic, complemented
15C2×#11762870C211yesmaximal, characteristic, complemented
16C2×C17×#544C211yesmaximal, characteristic, complemented
17#11763414—24no—
18#11763414C2218yes—
19C2×#10587560C2211yescharacteristic
20C2×#10587556C2211yescharacteristic
21C2×#10587580—21no—
22C2×#10587580—21no—
23C2×#10587616C2211yescharacteristic
24C2×#10587616C2211yescharacteristic
25C2×#10587570—21no—
26C2×#10587570—21no—
27C2×C4×D68C2211yescharacteristic
28C2×C4×D68C2211yescharacteristic
29#11763215C2218yescomplemented
30#11763208C2218yescomplemented
31#11763175C2218yescomplemented
32#11763157C2218yescomplemented
33#11763133C2218yescomplemented
34#11763133C2218yescomplemented
35#11763127C2218yescomplemented
36#11763122C2218yescomplemented
37#11763106C2218yescomplemented
38#11763106C2218yescomplemented
39#11763096C2218yescomplemented
40#11763086C2218yescomplemented
41#11762870C2218yescomplemented
42C2×#10587478C2211yescharacteristic
43C2×#10587478C2211yescharacteristic
44C2×#10587478C2211yescharacteristic
45C2×#10587478C2211yescharacteristic
46C2×#10587479C2211yescharacteristic
47C2×#10587479C2211yescharacteristic
48C2×#10587479C2211yescharacteristic
49C2×#10587479C2211yescharacteristic
50C2×C4⋊#3622C2211yescharacteristic
51C2×C4⋊#3622C2211yescharacteristic
52C2×#10587480C2211yescharacteristic
53C2×#10587480C2211yescharacteristic
54C2×#10587480C2211yescharacteristic
55C2×#10587480C2211yescharacteristic
56C2×#10587480C2211yescharacteristic
57C2×#10587480C2211yescharacteristic
58C2×#10587480C2211yescharacteristic
59C2×#10587480C2211yescharacteristic
60C2×C22⋊#3622C2211yescharacteristic
61C2×C22⋊#3622C2211yescharacteristic
62C2×#10587474C2211yescharacteristic
63C2×C4×#3622C2211yescharacteristic
64C17×#544—24no—
65C17×#544C2218yescomplemented
66C2×C17×C4⋊Q8—21no—
67C2×C17×C4⋊Q8C2211yescharacteristic
68C2×C17×C4⋊Q8C2211yescharacteristic
69C2×C17×#125—21no—
70C2×C17×#125C2211yescharacteristic
71C2×C17×#125C2211yescharacteristic
72C2×C17×C22⋊Q8—21no—
73C2×C17×C22⋊Q8—21no—
74C2×C17×#117C2211yescharacteristic
75C2×C17×#117C2211yescharacteristic
76C22×C4⋊C4×C17C2211yescharacteristic
77C22×Q8×C17—21no—
78C22×Q8×C17—21no—
79C23×C4×C17—21no—
80C23×C4×C17C2311yescharacteristic
81C22×C22⋊D17—21no—
82C22×C22⋊D17—21no—
83C22×D68—21no—
84C22×D68—21no—
85C22×D68C2311yescharacteristic
86C22×D68C2311yescharacteristic
87C22×C4×D17—21no—
88C22×C4×D17—21no—
89C17×C4⋊Q8—28no—
90C17×C4⋊Q8—22no—
91C17×C4⋊Q8—22no—
92C17×C4⋊Q8C2314yes—
93C17×C4⋊Q8C2314yes—
94C17×#125—28no—
95C17×#125—22no—
96C17×#125—22no—
97C17×#125C2314yes—
98C17×#125C2314yes—
99C17×C22⋊Q8—28no—
100C17×C22⋊Q8—28no—
101C17×#117—22no—
102C17×#117D414yes—
103C17×#117C2314yes—
104C17×#117C2314yes—
105C2×C4⋊C4×C17—21no—
106C2×C4⋊C4×C17—22no—
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×C17C2311yescharacteristic
116C2×C4⋊C4×C17C2311yescharacteristic
117C2×C4⋊C4×C17C2314yes—
118C2×C4⋊C4×C17C2311yescharacteristic
119C2×C4⋊C4×C17C2311yescharacteristic
120C2×C22⋊C4×C17—21no—
121C2×C22⋊C4×C17D411yescharacteristic
122C2×C22⋊C4×C17D411yescharacteristic
123C2×C42×C17—21no—
124C2×C42×C17C2311yescharacteristic
125C2×C42×C17C2311yescharacteristic
126#10587616—22no—
127#10587616—22no—
128#10587616C2314yes—
129#10587616C2314yes—
130C2×#63227—21no—
131C2×#63227—21no—
132C2×#63227—21no—
133C2×#63227—21no—
134C2×C4⋊Dic17C2311yescharacteristic
135C2×C4⋊Dic17C2311yescharacteristic
136C2×#63225—21no—
137C2×#63225—21no—
138C22×#3622C2311yescharacteristic
139C22×#3622C2311yescharacteristic
140C22×#3622C2311yescharacteristic
141C22×#3622C2311yescharacteristic
142#10587580—28no—
143#10587580—28no—
144#10587570—28no—
145#10587570—28no—
146#10587560—22no—
147#10587560C2314yes—
148C4×D68—22no—
149C4×D68—22no—
150C4×D68C2314yes—
151C4×D68C2314yes—
152#10587556—22no—
153#10587556C2314yes—
154C22⋊#3622C2314yes—
155C22⋊#3622C2314yes—
156#10587480C2314yes—
157#10587480C2314yes—
158#10587480C2314yes—
159#10587480C2314yes—
160#10587480C2314yes—
161#10587480C2314yes—
162#10587480C2314yes—
163#10587480C2314yes—
164#10587479C2314yes—
165#10587479C2314yes—
166#10587479C2314yes—
167#10587479C2314yes—
168#10587478C2314yes—
169#10587478C2314yes—
170#10587478C2314yes—
171#10587478C2314yes—
172C4⋊#3622C2314yes—
173C4⋊#3622C2314yes—
174#10587474C2314yes—
175C4×#3622C2314yes—
176C24×C17C2×D411yescharacteristic
177C23×D17—21no—
178C23×D17—21no—
179C2×Q8×C17—24no—
180C2×Q8×C17—24no—
181C2×Q8×C17—82no—
182C2×Q8×C17—82no—
183C22×C4×C17—22no—
184C22×C4×C17—22no—
185C22×C4×C17—21no—
186C22×C4×C17—21no—
187C22×C4×C17—21no—
188C22×C4×C17—21no—
189C22×C4×C17—24no—
190C22×C4×C17—82no—
191C22×C4×C17C2×D411yescharacteristic
192C22×C4×C17C2×D411yescharacteristic
193C22×C4×C17C2×D411yescharacteristic
194C22×C4×C17C2×D411yescharacteristic
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⋊D17—82no—
203C22×Dic17—21no—
204C22×Dic17—21no—
205C2×D68—22no—
206C2×D68—22no—
207C2×D68—22no—
208C2×D68—22no—
209C2×D68—21no—
210C2×D68—21no—
211C2×D68—24no—
212C2×D68—24no—
213C2×D68—82no—
214C2×D68—82no—
215C2×D68C2412yes—
216C2×D68C2412yes—
217C2×C4×D17—24no—
218C2×C4×D17—24no—
219C2×C4×D17—82no—
220C2×C4×D17—82no—
221C4⋊C4×C17—24no—
222C4⋊C4×C17—24no—
223C4⋊C4×C17—24no—
224C4⋊C4×C17—24no—
225C4⋊C4×C17—24no—
226C4⋊C4×C17—24no—
227C4⋊C4×C17—21no—
228C4⋊C4×C17—24no—
229C4⋊C4×C17—21no—
230C4⋊C4×C17—21no—
231C4⋊C4×C17—21no—
232C4⋊C4×C17C2×D414yes—
233C4⋊C4×C17C2×D414yes—
234C4⋊C4×C17C2412yes—
235C4⋊C4×C17C2412yes—
236C4⋊C4×C17C2412yes—
237C4⋊C4×C17C2412yes—
238C22⋊C4×C17—24no—
239C22⋊C4×C17C2×D414yes—
240C22⋊C4×C17C2×D414yes—
241C42×C17—24no—
242C42×C17C2×D412yes—
243C42×C17C2×D412yes—
244C42×C17C2412yes—
245C42×C17C2412yes—
246#63227—24no—
247#63227—24no—
248#63227—24no—
249#63227—24no—
250C4⋊Dic17—21no—
251C4⋊Dic17—21no—
252C4⋊Dic17C2412yes—
253C4⋊Dic17C2412yes—
254#63225—24no—
255#63225—24no—
256C2×#3622—22no—
257C2×#3622—22no—
258C2×#3622—22no—
259C2×#3622—22no—
260C2×#3622C2412yes—
261C2×#3622C2412yes—
262C2×#3622C2412yes—
263C2×#3622C2412yes—
264C2×#3241—171nomaximal, Sylow
265C23×C17—22no—
266C23×C17—22no—
267C23×C17—22no—
268C23×C17C22×D412yes—
269C23×C17C22×D411yescharacteristic
270C22×D17—22no—
271C22×D17—22no—
272C22×D17—42no—
273C22×D17—42no—
274C22×D17—42no—
275C22×D17—42no—
276C22×D17—42no—
277C22×D17—42no—
278Q8×C17—84no—
279Q8×C17—84no—
280C2×C4×C17—22no—
281C2×C4×C17—22no—
282C2×C4×C17—22no—
283C2×C4×C17—22no—
284C2×C4×C17—22no—
285C2×C4×C17—24no—
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—42no—
293C2×C4×C17—42no—
294C2×C4×C17—42no—
295C2×C4×C17—42no—
296C2×C4×C17—84no—
297C2×C4×C17C22×D412yes—
298C2×C4×C17C22×D412yes—
299C2×C4×C17C22×D412yes—
300C2×C4×C17C22×D412yes—
301C2×C4×C17C22×D412yes—
302C2×C4×C17C22×D411yescharacteristic
303C2×C4×C172−1+412yes—
304C2×C4×C172−1+412yes—
305C2×C4×C17C2511yescharacteristic
306C22⋊D17—84no—
307C22⋊D17—84no—
308C2×Dic17—22no—
309C2×Dic17—22no—
310C2×Dic17—42no—
311C2×Dic17—42no—
312D68—22no—
313D68—22no—
314D68—22no—
315D68—22no—
316D68—42no—
317D68—42no—
318D68—84no—
319D68—84no—
320C4×D17—84no—
321C4×D17—84no—
322#3622—22no—
323#3622—22no—
324#3622—22no—
325#3622—22no—
326C2×#544D1711yescharacteristic, complemented
327C2×#540—171no—
328#3241—1716no—
329C2×#501—171no—
330C2×#499—171no—
331C2×#490—171no—
332C2×#486—171no—
333C2×#481—171no—
334C2×#482—171no—
335C2×#482—171no—
336C2×#480—171no—
337C2×#478—171no—
338C2×#478—171no—
339C2×#476—171no—
340C2×#474—171no—
341C2×#433—171no—
342C22×C17—22no—
343C22×C17—22no—
344C22×C17—22no—
345C22×C17—44no—
346C22×C17#53612yes—
347C22×C17#57612yes—
348C22×C17#57712yes—
349C22×C17C23×D411yescharacteristic
350C2×D17—42no—
351C2×D17—42no—
352C2×D17—42no—
353C2×D17—42no—
354C2×D17—42no—
355C2×D17—42no—
356C2×D17—84no—
357C2×D17—84no—
358C4×C17—22no—
359C4×C17—22no—
360C4×C17—22no—
361C4×C17—22no—
362C4×C17—22no—
363C4×C17—42no—
364C4×C17—42no—
365C4×C17—42no—
366C4×C17—42no—
367C4×C17#53612yes—
368C4×C17C2×2−1+411yescharacteristic
369C4×C17C2×2−1+411yescharacteristic
370Dic17—42no—
371Dic17—42no—
372#544—24no—
373#544C2×D1718yescomplemented
374#540—178no—
375#540—344no—
376C2×C4⋊Q8—21no—
377C2×C4⋊Q8C2×D1711yescharacteristic
378C2×C4⋊Q8C2×D1711yescharacteristic
379C2×#127—171no—
380C2×#125—21no—
381C2×#125—171no—
382C2×#125C2×D1711yescharacteristic
383C2×#125C2×D1711yescharacteristic
384C2×#123—341no—
385C2×#123—341no—
386C2×C22⋊Q8—21no—
387C2×C22⋊Q8—21no—
388C2×#121—171no—
389C2×#121—171no—
390C2×#121—341no—
391C2×#121—341no—
392C2×C4×D4—171no—
393C2×C4×D4—171no—
394C2×#117C2×D1711yescharacteristic
395C2×#117C2×D1711yescharacteristic
396C22×C4⋊C4C2×D1711yescharacteristic
397#501—178no—
398#499—178no—
399#490—178no—
400#486—178no—
401#482—178no—
402#482—178no—
403#481—178no—
404#480—178no—
405#478—178no—
406#478—178no—
407#476—178no—
408#474—178no—
409#433—178no—
410C2×#107—171no—
411C2×#107—171no—
412C2×#107—171no—
413C2×#107—171no—
414C2×#106—171no—
415C2×#106—171no—
416C2×#106—171no—
417C2×#106—171no—
418C2×C4⋊C8—171no—
419C2×C4⋊C8—171no—
420C2×#102—171no—
421C2×#102—171no—
422C2×#102—171no—
423C2×#102—171no—
424C2×#102—171no—
425C2×#102—171no—
426C2×#102—171no—
427C2×#102—171no—
428C2×C22⋊C8—171no—
429C2×C22⋊C8—171no—
430C2×#97—171no—
431C2×C4×C8—171no—
432C2×C17—42no—
433C2×C17#324114yescomplemented
434C2×C17C2×#53611yescharacteristic
435C2×C17C2×#57611yescharacteristic
436C2×C17C2×#57711yescharacteristic
437D17—82no—
438D17—82no—
439C22×Q8—21no—
440C22×Q8—21no—
441C22×D4—171no—
442C22×D4—171no—
443C22×D4—341no—
444C22×D4—341no—
445C22×D4—341no—
446C22×D4—341no—
447C23×C4—21no—
448C23×C4—341no—
449C23×C4—341no—
450C23×C4C22×D1711yescharacteristic
451C22×C8—171no—
452C22×C8—171no—
453C22×C8—171no—
454C22×C8—171no—
455C4⋊Q8—28no—
456C4⋊Q8—22no—
457C4⋊Q8—22no—
458C4⋊Q8C22×D1714yes—
459C4⋊Q8C22×D1714yes—
460#127—174no—
461#127—342no—
462#125—28no—
463#125—22no—
464#125—22no—
465#125—174no—
466#125—342no—
467#125C22×D1714yes—
468#125C22×D1714yes—
469#123—348no—
470#123—348no—
471C22⋊Q8—28no—
472C22⋊Q8—28no—
473#121—174no—
474#121—174no—
475#121—342no—
476#121—342no—
477#121—348no—
478#121—348no—
479C4×D4—174no—
480C4×D4—174no—
481C4×D4—342no—
482C4×D4—342no—
483#117—22no—
484#117C22⋊D1714yes—
485#117C22×D1714yes—
486#117C22×D1714yes—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—22no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—171no—
496C2×C4⋊C4—171no—
497C2×C4⋊C4—341no—
498C2×C4⋊C4—341no—
499C2×C4⋊C4C22⋊D1711yescharacteristic
500C2×C4⋊C4C22⋊D1711yescharacteristic
501C2×C4⋊C4C22×D1711yescharacteristic
502C2×C4⋊C4C22×D1711yescharacteristic
503C2×C4⋊C4C22×D1714yes—
504C2×C4⋊C4C22×D1711yescharacteristic
505C2×C4⋊C4C22×D1711yescharacteristic
506C2×C22⋊C4—21no—
507C2×C22⋊C4—341no—
508C2×C22⋊C4—341no—
509C2×C22⋊C4—341no—
510C2×C22⋊C4—341no—
511C2×C22⋊C4C22⋊D1711yescharacteristic
512C2×C22⋊C4C22⋊D1711yescharacteristic
513C2×C42—21no—
514C2×C42C22×D1711yescharacteristic
515C2×C42C22×D1711yescharacteristic
516#107—174no—
517#107—174no—
518#107—174no—
519#107—174no—
520#106—174no—
521#106—174no—
522#106—174no—
523#106—174no—
524C4⋊C8—174no—
525C4⋊C8—174no—
526#102—174no—
527#102—174no—
528#102—174no—
529#102—174no—
530#102—174no—
531#102—174no—
532#102—174no—
533#102—174no—
534C22⋊C8—174no—
535C22⋊C8—174no—
536#97—174no—
537C4×C8—174no—
538C17C2×#324111yescharacteristic, complemented, Sylow
539C24—341no—
540C24—341no—
541C24C2×C22⋊D1711yescharacteristic
542C2×Q8—24no—
543C2×Q8—24no—
544C2×Q8—82no—
545C2×Q8—82no—
546C2×D4—172no—
547C2×D4—172no—
548C2×D4—344no—
549C2×D4—344no—
550C2×D4—342no—
551C2×D4—342no—
552C2×D4—342no—
553C2×D4—342no—
554C2×D4—341no—
555C2×D4—341no—
556C2×D4—344no—
557C2×D4—344no—
558C2×D4—1362no—
559C2×D4—1362no—
560C2×D4—1362no—
561C2×D4—1362no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—24no—
569C22×C4—82no—
570C22×C4—341no—
571C22×C4—341no—
572C22×C4—344no—
573C22×C4—344no—
574C22×C4—1362no—
575C22×C4—1362no—
576C22×C4C2×C22⋊D1712yes—
577C22×C4C2×C22⋊D1711yescharacteristic
578C22×C4C2×C22⋊D1711yescharacteristic
579C22×C4C2×C22⋊D1711yescharacteristic
580C22×C4C2×C22⋊D1711yescharacteristic
581C22×C4C2×C22⋊D1711yescharacteristic
582C22×C4C23×D1712yes—
583C22×C4C23×D1711yescharacteristic
584C2×C8—172no—
585C2×C8—172no—
586C2×C8—172no—
587C2×C8—172no—
588C2×C8—342no—
589C2×C8—342no—
590C2×C8—342no—
591C2×C8—342no—
592C4⋊C4—24no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—24no—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—24no—
599C4⋊C4—24no—
600C4⋊C4—24no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—172no—
604C4⋊C4—172no—
605C4⋊C4—341no—
606C4⋊C4—341no—
607C4⋊C4—344no—
608C4⋊C4—344no—
609C4⋊C4C2×C22⋊D1714yes—
610C4⋊C4C2×C22⋊D1714yes—
611C4⋊C4C23×D1712yes—
612C4⋊C4C23×D1712yes—
613C4⋊C4C23×D1712yes—
614C4⋊C4C23×D1712yes—
615C22⋊C4—24no—
616C22⋊C4—344no—
617C22⋊C4—344no—
618C22⋊C4—344no—
619C22⋊C4—344no—
620C22⋊C4C2×C22⋊D1714yes—
621C22⋊C4C2×C22⋊D1714yes—
622C42—24no—
623C42C2×C22⋊D1712yes—
624C42C2×C22⋊D1712yes—
625C42C23×D1712yes—
626C42C23×D1712yes—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—342no—
631C23—342no—
632C23—682no—
633C23—682no—
634C23—682no—
635C23—682no—
636C23—682no—
637C23—682no—
638C23C22×C22⋊D1712yes—
639C23C22×C22⋊D1711yescharacteristic
640Q8—84no—
641Q8—84no—
642D4—342no—
643D4—342no—
644D4—342no—
645D4—342no—
646D4—682no—
647D4—682no—
648D4—1364no—
649D4—1364no—
650D4—1364no—
651D4—1364no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—24no—
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—42no—
667C2×C4—42no—
668C2×C4—84no—
669C2×C4—342no—
670C2×C4—342no—
671C2×C4—682no—
672C2×C4—682no—
673C2×C4—1364no—
674C2×C4—1364no—
675C2×C4#1058769412yes—
676C2×C4#1058769412yes—
677C2×C4C22×C22⋊D1712yes—
678C2×C4C22×C22⋊D1712yes—
679C2×C4C22×C22⋊D1712yes—
680C2×C4C22×C22⋊D1712yes—
681C2×C4C22×C22⋊D1712yes—
682C2×C4C22×C22⋊D1711yescharacteristic
683C2×C4C24×D1711yescharacteristic
684C8—342no—
685C8—342no—
686C8—342no—
687C8—342no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—44no—
692C22—682no—
693C22—682no—
694C22—682no—
695C22—682no—
696C22—682no—
697C22—682no—
698C22—1364no—
699C22—1364no—
700C22#1176338312yes—
701C22#1176361212yes—
702C22#1176361712yes—
703C22C23×C22⋊D1711yescharacteristic
704C4—22no—
705C4—22no—
706C4—22no—
707C4—22no—
708C4—22no—
709C4—42no—
710C4—42no—
711C4—42no—
712C4—42no—
713C4—682no—
714C4—682no—
715C4#1176338312yes—
716C4C2×#1058769411yescharacteristic
717C4C2×#1058769411yescharacteristic
718C2—42no—
719C2—1362no—
720C2—1362no—
721C2#1454003714yesdirect product factor
722C2C2×#1176338311yescharacteristic
723C2C2×#1176361211yescharacteristic
724C2C2×#1176361711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#544C2
socleC23×C17C22×D4
prime radicalC2×#11763414C2
hypercenterC2×#544D17
hypocenterC17C2×#3241
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
2. #14540037C2direct (N × H)
3. C2×#11763215C2semidirect
4. C2×#11763208C2semidirect
5. C2×#11763175C2semidirect
6. C2×#11763157C2semidirect
7. C2×#11763127C2semidirect
8. C2×#11763133C2semidirect
9. C2×#11763133C2semidirect
10. C2×#11763122C2semidirect
11. C2×#11763106C2semidirect
12. C2×#11763106C2semidirect
13. C2×#11763096C2semidirect
14. C2×#11763086C2semidirect
15. C2×#11762870C2semidirect
16. C2×C17×#544C2semidirect
29. #11763215C22semidirect
30. #11763208C22semidirect
31. #11763175C22semidirect
32. #11763157C22semidirect
33. #11763133C22semidirect
34. #11763133C22semidirect
35. #11763127C22semidirect
36. #11763122C22semidirect
37. #11763106C22semidirect
38. #11763106C22semidirect
39. #11763096C22semidirect
40. #11763086C22semidirect
41. #11762870C22semidirect
65. C17×#544C22semidirect
326. C2×#544D17semidirect
373. #544C2×D17semidirect
433. C2×C17#3241semidirect
538. C17C2×#3241semidirect
721. C2#14540037direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117634142
#145400372
C2×#117632152
C2×#117632082
C2×#117631752
C2×#117631572
C2×#117631272
C2×#117631332
C2×#117631222
C2×#117631062
C2×#117630962
C2×#117630862
C2×#117628702
C2×C17×#5442
C2×#324117