Finite Group Databasebeta

← C2×#14540031 #17906507

Subgroups — C2×#14540031 #17906507

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×#11763437C211yesmaximal, characteristic, complemented
2#14540031C2116yesmaximal, direct product factor
3C2×#11763219C211yesmaximal, characteristic, complemented
4C2×#11763208C211yesmaximal, characteristic, complemented
5C2×#11763173C211yesmaximal, characteristic, complemented
6C2×#11763155C211yesmaximal, characteristic, complemented
7C2×#11763125C211yesmaximal, characteristic, complemented
8C2×#11763130C211yesmaximal, characteristic, complemented
9C2×#11763130C211yesmaximal, characteristic, complemented
10C2×#11763120C211yesmaximal, characteristic, complemented
11C2×#11763109C211yesmaximal, characteristic, complemented
12C2×#11763109C211yesmaximal, characteristic, complemented
13C2×#11763099C211yesmaximal, characteristic, complemented
14C2×#11763089C211yesmaximal, characteristic, complemented
15C2×#11762870C211yesmaximal, characteristic, complemented
16C2×C17×#540C211yesmaximal, characteristic
17#11763437—24no—
18#11763437C2218yescomplemented
19C2×#10587555C2211yescharacteristic
20C2×#10587555C2211yescharacteristic
21C2×#10587574—21no—
22C2×#10587556C2211yescharacteristic
23C2×#10587556C2211yescharacteristic
24C2×#10587576—21no—
25C2×#10587564—21no—
26C2×#10587564—21no—
27C2×#10587612C2211yescharacteristic
28C22×C4⋊Dic17C2211yescharacteristic
29#11763219C2218yescomplemented
30#11763208C2218yescomplemented
31#11763173C2218yescomplemented
32#11763155C2218yescomplemented
33#11763130C2218yescomplemented
34#11763130C2218yescomplemented
35#11763125C2218yescomplemented
36#11763120C2218yescomplemented
37#11763109C2218yescomplemented
38#11763109C2218yescomplemented
39#11763099C2218yescomplemented
40#11763089C2218yescomplemented
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×#10587503C2211yescharacteristic
53C2×#10587503C2211yescharacteristic
54C2×#10587503C2211yescharacteristic
55C2×#10587503C2211yescharacteristic
56C2×#10587503C2211yescharacteristic
57C2×#10587503C2211yescharacteristic
58C2×#10587503C2211yescharacteristic
59C2×#10587503C2211yescharacteristic
60C2×C22⋊#3622C2211yescharacteristic
61C2×C22⋊#3622C2211yescharacteristic
62C2×#10587474C2211yescharacteristic
63C2×C4×#3622C2211yescharacteristic
64C17×#540—24no—
65C17×#540C2218yes—
66C2×C17×#127C2211yescharacteristic
67C2×C17×#125C2211yescharacteristic
68C2×C17×#123—21no—
69C2×C17×#123—21no—
70C2×C17×#121—21no—
71C2×C17×#121—21no—
72C2×C17×#121C2211yescharacteristic
73C2×C17×#121C2211yescharacteristic
74C2×C4×D4×C17C2211yescharacteristic
75C2×C4×D4×C17C2211yescharacteristic
76C2×C17×#117C2211yescharacteristic
77C22×D4×C17—21no—
78C22×D4×C17—21no—
79C22×D4×C17—21no—
80C22×D4×C17—21no—
81C22×D4×C17C2311yescharacteristic
82C22×D4×C17C2311yescharacteristic
83C23×C4×C17—21no—
84C23×C4×C17—21no—
85C23×C4×C17C2311yescharacteristic
86C23×Dic17—21no—
87C22×Dic34—21no—
88C22×Dic34—21no—
89C17×#127—22no—
90C17×#127C2314yes—
91C17×#125—22no—
92C17×#125C2314yes—
93C17×#123—28no—
94C17×#123—28no—
95C17×#121—22no—
96C17×#121—22no—
97C17×#121—28no—
98C17×#121—28no—
99C17×#121C2314yes—
100C17×#121C2314yes—
101C4×D4×C17—22no—
102C4×D4×C17—22no—
103C4×D4×C17C2314yes—
104C4×D4×C17C2314yes—
105C17×#117D414yes—
106C17×#117C2314yes—
107C2×C4⋊C4×C17—21no—
108C2×C4⋊C4×C17—21no—
109C2×C4⋊C4×C17D411yescharacteristic
110C2×C4⋊C4×C17D411yescharacteristic
111C2×C4⋊C4×C17C2311yescharacteristic
112C2×C4⋊C4×C17C2311yescharacteristic
113C2×C22⋊C4×C17—21no—
114C2×C22⋊C4×C17—21no—
115C2×C22⋊C4×C17—21no—
116C2×C22⋊C4×C17—21no—
117C2×C22⋊C4×C17D411yescharacteristic
118C2×C22⋊C4×C17D411yescharacteristic
119C2×C42×C17C2311yescharacteristic
120C2×C42×C17C2311yescharacteristic
121C2×C22⋊Dic17—21no—
122#10587612—22no—
123#10587612C2314yes—
124C2×C4⋊Dic17—21no—
125C2×C4⋊Dic17—22no—
126C2×C4⋊Dic17—21no—
127C2×C4⋊Dic17—21no—
128C2×C4⋊Dic17C2311yescharacteristic
129C2×C4⋊Dic17C2311yescharacteristic
130C2×C4⋊Dic17C2314yes—
131C2×C4⋊Dic17C2311yescharacteristic
132C2×C4⋊Dic17C2311yescharacteristic
133C2×#63225—21no—
134C2×#63225—21no—
135C2×#63225—21no—
136C2×#63225—21no—
137C2×C4×Dic17—21no—
138C22×#3622C2311yescharacteristic
139C22×#3622C2311yescharacteristic
140C22×#3622C2311yescharacteristic
141C22×#3622C2311yescharacteristic
142#10587576—28no—
143#10587574—28no—
144#10587564—28no—
145#10587564—28no—
146#10587556—22no—
147#10587556—22no—
148#10587556C2314yes—
149#10587556C2314yes—
150#10587555—22no—
151#10587555—22no—
152#10587555C2314yes—
153#10587555C2314yes—
154#10587503C2314yes—
155#10587503C2314yes—
156#10587503C2314yes—
157#10587503C2314yes—
158#10587503C2314yes—
159#10587503C2314yes—
160#10587503C2314yes—
161#10587503C2314yes—
162C22⋊#3622C2314yes—
163C22⋊#3622C2314yes—
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×C17—21no—
177C24×C17—21no—
178C24×C17C2×D411yescharacteristic
179C2×D4×C17—24no—
180C2×D4×C17—24no—
181C2×D4×C17—21no—
182C2×D4×C17—21no—
183C2×D4×C17—24no—
184C2×D4×C17—24no—
185C2×D4×C17—22no—
186C2×D4×C17—22no—
187C2×D4×C17—22no—
188C2×D4×C17—22no—
189C2×D4×C17—82no—
190C2×D4×C17—82no—
191C2×D4×C17—82no—
192C2×D4×C17—82no—
193C2×D4×C17C2412yes—
194C2×D4×C17C2412yes—
195C22×C4×C17—22no—
196C22×C4×C17—22no—
197C22×C4×C17—21no—
198C22×C4×C17—21no—
199C22×C4×C17—24no—
200C22×C4×C17—24no—
201C22×C4×C17—82no—
202C22×C4×C17—82no—
203C22×C4×C17C2×D411yescharacteristic
204C22×C4×C17C2×D411yescharacteristic
205C22×C4×C17C2×D411yescharacteristic
206C22×C4×C17C2×D411yescharacteristic
207C22×C4×C17C2×D412yes—
208C22×C4×C17C2×D411yescharacteristic
209C22×C4×C17C2412yes—
210C22×C4×C17C2411yescharacteristic
211C22×Dic17—21no—
212C22×Dic17—21no—
213C22×Dic17—21no—
214C22×Dic17—21no—
215C22×Dic17—24no—
216C22×Dic17—82no—
217C2×Dic34—24no—
218C2×Dic34—24no—
219C2×Dic34—82no—
220C2×Dic34—82no—
221C4⋊C4×C17—24no—
222C4⋊C4×C17—24no—
223C4⋊C4×C17—21no—
224C4⋊C4×C17—21no—
225C4⋊C4×C17C2×D414yes—
226C4⋊C4×C17C2×D414yes—
227C4⋊C4×C17C2412yes—
228C4⋊C4×C17C2412yes—
229C22⋊C4×C17—24no—
230C22⋊C4×C17—24no—
231C22⋊C4×C17—24no—
232C22⋊C4×C17—24no—
233C22⋊C4×C17C2×D414yes—
234C22⋊C4×C17C2×D414yes—
235C42×C17C2×D412yes—
236C42×C17C2×D412yes—
237C42×C17C2412yes—
238C42×C17C2412yes—
239C22⋊Dic17—24no—
240C4⋊Dic17—21no—
241C4⋊Dic17—21no—
242C4⋊Dic17—21no—
243C4⋊Dic17—24no—
244C4⋊Dic17—24no—
245C4⋊Dic17—21no—
246C4⋊Dic17—24no—
247C4⋊Dic17C2412yes—
248C4⋊Dic17C2412yes—
249C4⋊Dic17C2412yes—
250C4⋊Dic17C2412yes—
251#63225—24no—
252#63225—24no—
253#63225—24no—
254#63225—24no—
255C4×Dic17—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×C17—22no—
269C23×C17—22no—
270C23×C17—42no—
271C23×C17—42no—
272C23×C17—42no—
273C23×C17—42no—
274C23×C17—42no—
275C23×C17—42no—
276C23×C17C22×D412yes—
277C23×C17C22×D411yescharacteristic
278D4×C17—22no—
279D4×C17—22no—
280D4×C17—22no—
281D4×C17—22no—
282D4×C17—42no—
283D4×C17—42no—
284D4×C17—84no—
285D4×C17—84no—
286D4×C17—84no—
287D4×C17—84no—
288C2×C4×C17—22no—
289C2×C4×C17—22no—
290C2×C4×C17—22no—
291C2×C4×C17—22no—
292C2×C4×C17—22no—
293C2×C4×C17—24no—
294C2×C4×C17—22no—
295C2×C4×C17—22no—
296C2×C4×C17—22no—
297C2×C4×C17—22no—
298C2×C4×C17—42no—
299C2×C4×C17—42no—
300C2×C4×C17—84no—
301C2×C4×C17—84no—
302C2×C4×C17C22×D412yes—
303C2×C4×C17C22×D412yes—
304C2×C4×C17C22×D412yes—
305C2×C4×C17C22×D412yes—
306C2×C4×C17C22×D412yes—
307C2×C4×C17C22×D411yescharacteristic
308C2×C4×C172−1+412yes—
309C2×C4×C172−1+412yes—
310C2×C4×C17C2511yescharacteristic
311C2×Dic17—22no—
312C2×Dic17—22no—
313C2×Dic17—22no—
314C2×Dic17—22no—
315C2×Dic17—42no—
316C2×Dic17—42no—
317C2×Dic17—42no—
318C2×Dic17—42no—
319C2×Dic17—84no—
320Dic34—84no—
321Dic34—84no—
322#3622—22no—
323#3622—22no—
324#3622—22no—
325#3622—22no—
326C2×#544—171no—
327C2×#540D1711yescharacteristic
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—42no—
347C22×C17—42no—
348C22×C17—42no—
349C22×C17—42no—
350C22×C17—42no—
351C22×C17—42no—
352C22×C17—84no—
353C22×C17—84no—
354C22×C17#53612yes—
355C22×C17#57612yes—
356C22×C17#57712yes—
357C22×C17C23×D411yescharacteristic
358C4×C17—22no—
359C4×C17—22no—
360C4×C17—22no—
361C4×C17—22no—
362C4×C17—22no—
363C4×C17—42no—
364C4×C17—42no—
365C4×C17#53612yes—
366C4×C17C2×2−1+411yescharacteristic
367C4×C17C2×2−1+411yescharacteristic
368Dic17—42no—
369Dic17—42no—
370Dic17—42no—
371Dic17—42no—
372#544—178no—
373#544—344no—
374#540—24no—
375#540C2×D1718yes—
376C2×C4⋊Q8—171no—
377C2×C4⋊Q8—171no—
378C2×C4⋊Q8—341no—
379C2×#127C2×D1711yescharacteristic
380C2×#125—171no—
381C2×#125—171no—
382C2×#125—341no—
383C2×#125C2×D1711yescharacteristic
384C2×#123—21no—
385C2×#123—21no—
386C2×C22⋊Q8—341no—
387C2×C22⋊Q8—341no—
388C2×#121—21no—
389C2×#121—21no—
390C2×#121C2×D1711yescharacteristic
391C2×#121C2×D1711yescharacteristic
392C2×C4×D4C2×D1711yescharacteristic
393C2×C4×D4C2×D1711yescharacteristic
394C2×#117—171no—
395C2×#117C2×D1711yescharacteristic
396C22×C4⋊C4—171no—
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—82no—
434C2×C17—82no—
435C2×C17#324114yescomplemented
436C2×C17C2×#53611yescharacteristic
437C2×C17C2×#57611yescharacteristic
438C2×C17C2×#57711yescharacteristic
439C22×Q8—341no—
440C22×Q8—341no—
441C22×D4—21no—
442C22×D4—21no—
443C22×D4—21no—
444C22×D4—21no—
445C22×D4C22×D1711yescharacteristic
446C22×D4C22×D1711yescharacteristic
447C23×C4—21no—
448C23×C4—21no—
449C23×C4—341no—
450C23×C4C22×D1711yescharacteristic
451C22×C8—171no—
452C22×C8—171no—
453C22×C8—171no—
454C22×C8—171no—
455C4⋊Q8—174no—
456C4⋊Q8—174no—
457C4⋊Q8—348no—
458C4⋊Q8—342no—
459C4⋊Q8—342no—
460#127—22no—
461#127C22×D1714yes—
462#125—22no—
463#125—174no—
464#125—174no—
465#125—348no—
466#125—342no—
467#125—342no—
468#125C22×D1714yes—
469#123—28no—
470#123—28no—
471C22⋊Q8—348no—
472C22⋊Q8—348no—
473#121—22no—
474#121—22no—
475#121—28no—
476#121—28no—
477#121C22×D1714yes—
478#121C22×D1714yes—
479C4×D4—22no—
480C4×D4—22no—
481C4×D4C22×D1714yes—
482C4×D4C22×D1714yes—
483#117—174no—
484#117—342no—
485#117C22⋊D1714yes—
486#117C22×D1714yes—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—171no—
490C2×C4⋊C4—171no—
491C2×C4⋊C4—174no—
492C2×C4⋊C4—171no—
493C2×C4⋊C4—171no—
494C2×C4⋊C4—341no—
495C2×C4⋊C4—342no—
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⋊C4C22⋊D1711yescharacteristic
503C2×C4⋊C4C22⋊D1711yescharacteristic
504C2×C4⋊C4C22×D1711yescharacteristic
505C2×C4⋊C4C22×D1711yescharacteristic
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—341no—
511C2×C22⋊C4C22⋊D1711yescharacteristic
512C2×C22⋊C4C22⋊D1711yescharacteristic
513C2×C42—341no—
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—21no—
540C24—21no—
541C24C2×C22⋊D1711yescharacteristic
542C2×Q8—344no—
543C2×Q8—344no—
544C2×Q8—1362no—
545C2×Q8—1362no—
546C2×D4—24no—
547C2×D4—24no—
548C2×D4—22no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—24no—
555C2×D4—24no—
556C2×D4—82no—
557C2×D4—82no—
558C2×D4—82no—
559C2×D4—82no—
560C2×D4C23×D1712yes—
561C2×D4C23×D1712yes—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—24no—
567C22×C4—24no—
568C22×C4—82no—
569C22×C4—82no—
570C22×C4—341no—
571C22×C4—341no—
572C22×C4—341no—
573C22×C4—341no—
574C22×C4—344no—
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—24no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—172no—
597C4⋊C4—172no—
598C4⋊C4—172no—
599C4⋊C4—172no—
600C4⋊C4—344no—
601C4⋊C4—341no—
602C4⋊C4—341no—
603C4⋊C4—341no—
604C4⋊C4—341no—
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⋊C4C23×D1712yes—
614C4⋊C4C23×D1712yes—
615C22⋊C4—24no—
616C22⋊C4—24no—
617C22⋊C4—24no—
618C22⋊C4—24no—
619C22⋊C4—344no—
620C22⋊C4C2×C22⋊D1714yes—
621C22⋊C4C2×C22⋊D1714yes—
622C42—344no—
623C42C2×C22⋊D1712yes—
624C42C2×C22⋊D1712yes—
625C42C23×D1712yes—
626C42C23×D1712yes—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23C22×C22⋊D1712yes—
639C23C22×C22⋊D1711yescharacteristic
640Q8—1364no—
641Q8—1364no—
642D4—22no—
643D4—22no—
644D4—22no—
645D4—22no—
646D4—42no—
647D4—42no—
648D4—84no—
649D4—84no—
650D4—84no—
651D4—84no—
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—42no—
663C2×C4—42no—
664C2×C4—84no—
665C2×C4—84no—
666C2×C4—342no—
667C2×C4—342no—
668C2×C4—342no—
669C2×C4—342no—
670C2×C4—682no—
671C2×C4—682no—
672C2×C4—682no—
673C2×C4—682no—
674C2×C4—1364no—
675C2×C4#1058769712yes—
676C2×C4#1058769712yes—
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—42no—
693C22—42no—
694C22—42no—
695C22—42no—
696C22—42no—
697C22—42no—
698C22—84no—
699C22—84no—
700C22#1176338012yes—
701C22#1176361212yes—
702C22#1176362012yes—
703C22C23×C22⋊D1711yescharacteristic
704C4—22no—
705C4—22no—
706C4—22no—
707C4—22no—
708C4—22no—
709C4—42no—
710C4—42no—
711C4—682no—
712C4—682no—
713C4—682no—
714C4—682no—
715C4#1176338012yes—
716C4C2×#1058769711yescharacteristic
717C4C2×#1058769711yescharacteristic
718C2—42no—
719C2—82no—
720C2—82no—
721C2#1454003114yesdirect product factor
722C2C2×#1176338011yescharacteristic
723C2C2×#1176361211yescharacteristic
724C2C2×#1176362011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
Fitting, prime radicalC2×C17×#540C2
socleC23×C17C22×D4
hypercenterC2×#540D17
hypocenterC17C2×#3241
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#540

Complements

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

NH ≅ G/Ntype
1. C2×#11763437C2semidirect
2. #14540031C2direct (N × H)
3. C2×#11763219C2semidirect
4. C2×#11763208C2semidirect
5. C2×#11763173C2semidirect
6. C2×#11763155C2semidirect
7. C2×#11763125C2semidirect
8. C2×#11763130C2semidirect
9. C2×#11763130C2semidirect
10. C2×#11763120C2semidirect
11. C2×#11763109C2semidirect
12. C2×#11763109C2semidirect
13. C2×#11763099C2semidirect
14. C2×#11763089C2semidirect
15. C2×#11762870C2semidirect
18. #11763437C22semidirect
29. #11763219C22semidirect
30. #11763208C22semidirect
31. #11763173C22semidirect
32. #11763155C22semidirect
33. #11763130C22semidirect
34. #11763130C22semidirect
35. #11763125C22semidirect
36. #11763120C22semidirect
37. #11763109C22semidirect
38. #11763109C22semidirect
39. #11763099C22semidirect
40. #11763089C22semidirect
41. #11762870C22semidirect
435. C2×C17#3241semidirect
538. C17C2×#3241semidirect
721. C2#14540031direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117634372
#145400312
C2×#117632192
C2×#117632082
C2×#117631732
C2×#117631552
C2×#117631252
C2×#117631302
C2×#117631202
C2×#117631092
C2×#117630992
C2×#117630892
C2×#117628702
C2×C17×#5402
C2×#324117