Finite Group Databasebeta

← C2×#14541267 #17912901

Subgroups — C2×#14541267 #17912901

Order 4352.

1942 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763514C211yesmaximal, characteristic, complemented
2C2×#11763511C211yesmaximal, characteristic
3#14541267C2116yesmaximal, direct product factor
4C2×#11763216C211yesmaximal, characteristic, complemented
5C2×#11763145C211yesmaximal, characteristic, complemented
6C2×#11763153C211yesmaximal, characteristic, complemented
7C2×#11763121C211yesmaximal, characteristic, complemented
8C2×#11763119C211yesmaximal, characteristic, complemented
9C2×#11763087C211yesmaximal, characteristic, complemented
10C2×#11763054C211yesmaximal, characteristic, complemented
11C2×#11763036C211yesmaximal, characteristic, complemented
12C2×#11762906C211yesmaximal, characteristic, complemented
13C2×#11762877C211yesmaximal, characteristic, complemented
14C2×#11762848C211yesmaximal, characteristic, complemented
15C22×#10587478C211yesmaximal, characteristic, complemented
16C2×C17×#481C211yesmaximal, characteristic, complemented
17C22×#63229C2211yescharacteristic
18C22×#63218C2211yescharacteristic
19C23×#3622C2211yescharacteristic
20#11763514—24no—
21#11763514C2218yescomplemented
22#11763511—24no—
23#11763511C2218yes—
24C2×#10587574C2211yescharacteristic
25C2×#10587565—21no—
26C2×#10587576C2211yescharacteristic
27C2×#10587575—21no—
28C2×#10587572—21no—
29C2×#10587583C2211yescharacteristic
30C2×#10587610—21no—
31C2×#10587610C2211yescharacteristic
32C2×#10587582—21no—
33C2×#10587625—21no—
34C2×#10587624C2211yescharacteristic
35C2×#10587573C2211yescharacteristic
36C2×D4×Dic17—21no—
37C2×D4×Dic17C2211yescharacteristic
38C2×C4×C22⋊D17—21no—
39C2×C4×C22⋊D17C2211yescharacteristic
40C2×#10587578C2211yescharacteristic
41C22×C4⋊Dic17C2211yescharacteristic
42C2×C4⋊C4×D17C2211yescharacteristic
43#11763216C2218yescomplemented
44#11763153C2218yescomplemented
45#11763145C2218yescomplemented
46#11763121C2218yescomplemented
47#11763119C2218yescomplemented
48#11763087C2218yescomplemented
49#11763054C2218yescomplemented
50#11763036C2218yescomplemented
51#11762906C2218yescomplemented
52#11762877C2218yescomplemented
53#11762848C2218yescomplemented
54C2×#10587489C2211yescharacteristic
55C2×#10587489C2211yescharacteristic
56C2×#10587478C2211yescharacteristic
57C2×#10587478C2211yescharacteristic
58C2×#10587478C2211yescharacteristic
59C2×#10587478C2211yescharacteristic
60C2×#10587478C2218yescomplemented
61C2×#10587479C2211yescharacteristic
62C2×#10587485C2211yescharacteristic
63C2×#10587487C2211yescharacteristic
64C2×#10587487C2211yescharacteristic
65C2×#10587481C2211yescharacteristic
66C2×#10587503C2211yescharacteristic
67C2×#10587491C2211yescharacteristic
68C2×#10587486C2211yescharacteristic
69C2×C17×#121C2211yescharacteristic
70C22×C4⋊C4×C17C2211yescharacteristic
71C17×#481C2218yescomplemented
72C2×C17×#106C2211yescharacteristic
73C2×C17×#106C2211yescharacteristic
74C2×C17×#102C2211yescharacteristic
75C2×C17×#102C2211yescharacteristic
76C2×C17×C22⋊C8C2211yescharacteristic
77C22×D4×C17—21no—
78C22×D4×C17C2311yescharacteristic
79C23×C4×C17—21no—
80C23×C4×C17C2311yescharacteristic
81C22×C22⋊D17—21no—
82C22×C22⋊D17D411yescharacteristic
83C23×Dic17—21no—
84C23×Dic17—21no—
85C22×C4×D17—21no—
86C22×C4×D17C2311yescharacteristic
87C22×Dic34—21no—
88C22×Dic34C2311yescharacteristic
89C22×C8×C17C2311yescharacteristic
90C22×C8×C17C2311yescharacteristic
91C17×#121—22no—
92C17×#121C2314yes—
93C2×C4⋊C4×C17—22no—
94C2×C4⋊C4×C17—21no—
95C2×C4⋊C4×C17C2311yescharacteristic
96C2×C4⋊C4×C17C2314yes—
97C2×C4⋊C4×C17C2311yescharacteristic
98C2×C4⋊C4×C17C2311yescharacteristic
99C2×C22⋊C4×C17—21no—
100C2×C22⋊Dic17—21no—
101C2×C22⋊Dic17—21no—
102C2×C22⋊Dic17—21no—
103C2×C22⋊Dic17D411yescharacteristic
104#10587625—28no—
105#10587624—22no—
106#10587624C2314yes—
107D4×Dic17—22no—
108D4×Dic17—28no—
109D4×Dic17C2314yes—
110C2×#63229—24no—
111C2×#63229C2314yes—
112C4×C22⋊D17—28no—
113C4×C22⋊D17D414yes—
114C4×C22⋊D17C2314yes—
115C2×#63227—21no—
116C2×#63227—21no—
117C2×#63227D411yescharacteristic
118C2×C4⋊Dic17—22no—
119C2×C4⋊Dic17—21no—
120C2×C4⋊Dic17—21no—
121C2×C4⋊Dic17—21no—
122C2×C4⋊Dic17C2314yes—
123C2×C4⋊Dic17C2311yescharacteristic
124C2×C4⋊Dic17C2311yescharacteristic
125C2×C4⋊Dic17C2311yescharacteristic
126#10587610—22no—
127#10587610—28no—
128#10587610C2314yes—
129C2×#63225—21no—
130C2×#63225—21no—
131C2×#63225—21no—
132C2×#63225—21no—
133C2×#63225—21no—
134C2×#63225D411yescharacteristic
135C2×C4×Dic17—21no—
136C2×C4×Dic17—21no—
137C2×C4×Dic17C2311yescharacteristic
138C22×#3622—24no—
139C22×#3622C2311yescharacteristic
140C22×#3622C2314yes—
141C22×#3622C2311yescharacteristic
142C2×#63218—24no—
143C2×#63218C2314yes—
144#10587583—22no—
145#10587583C2314yes—
146#10587582—28no—
147#10587578—22no—
148#10587578C2314yes—
149C4⋊C4×D17—22no—
150C4⋊C4×D17C2314yes—
151#10587576—22no—
152#10587576C2314yes—
153#10587575—28no—
154#10587574—22no—
155#10587574C2314yes—
156#10587573—22no—
157#10587573C2314yes—
158#10587572—28no—
159#10587565—28no—
160C17×#106C2314yes—
161C17×#106C2314yes—
162C17×#102C2314yes—
163C17×#102C2314yes—
164C17×C22⋊C8C2314yes—
165#10587503C2314yes—
166#10587491C2314yes—
167#10587489C2314yes—
168#10587489C2314yes—
169#10587487C2314yes—
170#10587487C2314yes—
171#10587486C2314yes—
172#10587485C2314yes—
173#10587481C2314yes—
174#10587479C2314yes—
175#10587478C2314yes—
176#10587478C2314yes—
177#10587478C2314yes—
178#10587478C2314yes—
179C24×C17—21no—
180C24×C17C2×D411yescharacteristic
181C23×D17C2×D411yescharacteristic
182C2×D4×C17—24no—
183C2×D4×C17—21no—
184C2×D4×C17—22no—
185C2×D4×C17—22no—
186C2×D4×C17—44no—
187C2×D4×C17C2412yes—
188C22×C4×C17—22no—
189C22×C4×C17—22no—
190C22×C4×C17—21no—
191C22×C4×C17—21no—
192C22×C4×C17—21no—
193C22×C4×C17—24no—
194C22×C4×C17—82no—
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⋊D17C2×D414yes—
203C22×Dic17—21no—
204C22×Dic17—21no—
205C22×Dic17—21no—
206C22×Dic17—21no—
207C22×Dic17—24no—
208C22×Dic17—24no—
209C22×Dic17—82no—
210C22×Dic17—82no—
211C22×Dic17C2×D411yescharacteristic
212C22×Dic17C2×D411yescharacteristic
213C22×Dic17C2×D411yescharacteristic
214C2×C4×D17—22no—
215C2×C4×D17—22no—
216C2×C4×D17—24no—
217C2×C4×D17—82no—
218C2×C4×D17C2×D412yes—
219C2×C4×D17C2412yes—
220C2×Dic34—22no—
221C2×Dic34—22no—
222C2×Dic34—21no—
223C2×Dic34—24no—
224C2×Dic34—82no—
225C2×Dic34C2412yes—
226C2×C8×C17—22no—
227C2×C8×C17—22no—
228C2×C8×C17C2412yes—
229C2×C8×C17C2412yes—
230C4⋊C4×C17—21no—
231C4⋊C4×C17—21no—
232C4⋊C4×C17—24no—
233C4⋊C4×C17—21no—
234C4⋊C4×C17C2412yes—
235C4⋊C4×C17C2412yes—
236C4⋊C4×C17C2412yes—
237C22⋊C4×C17—24no—
238C22⋊Dic17—24no—
239C22⋊Dic17—24no—
240C22⋊Dic17—24no—
241C22⋊Dic17C2×D414yes—
242#63229—28no—
243#63227—24no—
244#63227—24no—
245#63227C2×D414yes—
246C4⋊Dic17—24no—
247C4⋊Dic17—21no—
248C4⋊Dic17—21no—
249C4⋊Dic17—21no—
250C4⋊Dic17—24no—
251C4⋊Dic17—24no—
252C4⋊Dic17C2412yes—
253C4⋊Dic17C2412yes—
254C4⋊Dic17C2412yes—
255#63225—24no—
256#63225—24no—
257#63225—24no—
258#63225—24no—
259#63225—24no—
260#63225C2×D414yes—
261C4×Dic17—24no—
262C4×Dic17—24no—
263C4×Dic17C2×D412yes—
264C4×Dic17C2412yes—
265C2×#3622—22no—
266C2×#3622—28no—
267C2×#3622#4114yes—
268C2×#3622C2412yes—
269C2×#3622C2412yes—
270#63218—28no—
271C2×#3346—171nomaximal, Sylow
272C23×C17—22no—
273C23×C17—22no—
274C23×C17—22no—
275C23×C17—42no—
276C23×C17—42no—
277C23×C17—42no—
278C23×C17#13714yes—
279C23×C17C22×D412yes—
280C23×C17C22×D411yescharacteristic
281C22×D17—22no—
282C22×D17—22no—
283C22×D17—22no—
284C22×D17C22×D412yes—
285D4×C17—22no—
286D4×C17—22no—
287D4×C17—48no—
288D4×C17—42no—
289C2×C4×C17—22no—
290C2×C4×C17—24no—
291C2×C4×C17—22no—
292C2×C4×C17—22no—
293C2×C4×C17—22no—
294C2×C4×C17—22no—
295C2×C4×C17—22no—
296C2×C4×C17—42no—
297C2×C4×C17—42no—
298C2×C4×C17—42no—
299C2×C4×C17—84no—
300C2×C4×C17C22×D412yes—
301C2×C4×C17C22×D411yescharacteristic
302C2×C4×C17C2×#4112yes—
303C2×C4×C172−1+412yes—
304C2×C4×C17C2511yescharacteristic
305C22⋊D17—28no—
306C22⋊D17—84no—
307C2×Dic17—22no—
308C2×Dic17—22no—
309C2×Dic17—22no—
310C2×Dic17—22no—
311C2×Dic17—22no—
312C2×Dic17—22no—
313C2×Dic17—22no—
314C2×Dic17—42no—
315C2×Dic17—42no—
316C2×Dic17—42no—
317C2×Dic17—42no—
318C2×Dic17—84no—
319C2×Dic17—84no—
320C2×Dic17C22×D412yes—
321C2×Dic17C22×D412yes—
322C2×Dic17C22×D412yes—
323C4×D17—24no—
324C4×D17—22no—
325C4×D17—22no—
326C4×D17—84no—
327Dic34—22no—
328Dic34—22no—
329Dic34—42no—
330Dic34—84no—
331C8×C17—22no—
332C8×C17—22no—
333#3622—22no—
334#3622C2×#4114yes—
335C2×#554—171no—
336C2×#553—171no—
337#3346—1716no—
338C2×#501—171no—
339C2×#484—171no—
340C2×#481D1711yescharacteristic, complemented
341C2×#485—171no—
342C2×#480—171no—
343C2×#479—171no—
344C2×#474—171no—
345C2×#468—171no—
346C2×#465—171no—
347C2×#440—171no—
348C2×#435—171no—
349C2×#428—171no—
350C22×#107—171no—
351C22×C17—28no—
352C22×C17—22no—
353C22×C17—22no—
354C22×C17—42no—
355C22×C17—42no—
356C22×C17—42no—
357C22×C17—84no—
358C22×C17#54712yes—
359C22×C17C2×#13714yes—
360C22×C17C2×#13712yes—
361C22×C17#57612yes—
362C22×C17C23×D411yescharacteristic
363C2×D17—22no—
364C2×D17—22no—
365C2×D17—22no—
366C2×D17—44no—
367C4×C17—22no—
368C4×C17—42no—
369C4×C17—42no—
370C4×C17—42no—
371C4×C17#54712yes—
372C4×C17C22×#4111yescharacteristic
373C4×C17C2×2−1+411yescharacteristic
374Dic17—22no—
375Dic17—22no—
376Dic17—22no—
377Dic17—42no—
378Dic17—42no—
379Dic17—42no—
380Dic17—42no—
381C22×SD16—171no—
382C22×M16—171no—
383C23×C8—171no—
384#554—178no—
385#554—344no—
386#553—178no—
387#553—344no—
388C2×C4⋊Q8—171no—
389C2×#126—341no—
390C2×#125—171no—
391C2×#125—341no—
392C2×#123—341no—
393C2×C22⋊Q8—171no—
394C2×C22⋊Q8—171no—
395C2×C22⋊Q8—341no—
396C2×C22⋊Q8—341no—
397C2×#121—171no—
398C2×#121—341no—
399C2×#121C2×D1711yescharacteristic
400C2×C4×Q8—171no—
401C2×C4×D4—171no—
402C2×C4×D4—171no—
403C2×C4×D4—341no—
404C2×C4×D4—341no—
405C2×#117—171no—
406C22×C4⋊C4—171no—
407C22×C4⋊C4—171no—
408C22×C4⋊C4C2×D1711yescharacteristic
409#501—178no—
410#485—178no—
411#484—178no—
412#481C2×D1718yescomplemented
413#480—178no—
414#479—178no—
415#474—178no—
416#468—178no—
417#465—178no—
418#440—178no—
419#435—178no—
420#428—178no—
421C2×#107—171no—
422C2×#107—171no—
423C2×#107—171no—
424C2×#107—171no—
425C2×#107—178no—
426C2×#107—171no—
427C2×#107—171no—
428C2×#106—171no—
429C2×#106C2×D1711yescharacteristic
430C2×#106C2×D1711yescharacteristic
431C2×C4⋊C8—171no—
432C2×#103—171no—
433C2×#103—171no—
434C2×#103—171no—
435C2×#102—171no—
436C2×#102C2×D1711yescharacteristic
437C2×#102C2×D1711yescharacteristic
438C2×C22⋊C8—171no—
439C2×C22⋊C8C2×D1711yescharacteristic
440C2×#97—171no—
441C2×C17—24no—
442C2×C17—82no—
443C2×C17#334614yescomplemented
444C2×C17C2×#54711yescharacteristic
445C2×C17C22×#13711yescharacteristic
446C2×C17C2×#57611yescharacteristic
447D17—42no—
448C22×Q8—171no—
449C22×Q8—341no—
450C22×D4—21no—
451C22×D4—171no—
452C22×D4—341no—
453C22×D4C22×D1711yescharacteristic
454C23×C4—21no—
455C23×C4—171no—
456C23×C4—341no—
457C23×C4—341no—
458C23×C4—341no—
459C23×C4C22×D1711yescharacteristic
460C2×SD16—174no—
461C2×SD16—344no—
462C2×M16—174no—
463C2×M16—344no—
464C22×C8—171no—
465C22×C8—171no—
466C22×C8—174no—
467C22×C8—344no—
468C22×C8C22×D1711yescharacteristic
469C22×C8C22×D1711yescharacteristic
470C4⋊Q8—174no—
471C4⋊Q8—342no—
472#126—348no—
473#125—174no—
474#125—342no—
475#125—348no—
476#123—348no—
477C22⋊Q8—174no—
478C22⋊Q8—174no—
479C22⋊Q8—348no—
480C22⋊Q8—348no—
481C22⋊Q8—342no—
482C22⋊Q8—342no—
483#121—22no—
484#121—174no—
485#121—342no—
486#121—348no—
487#121C22×D1714yes—
488C4×Q8—174no—
489C4×Q8—342no—
490C4×D4—174no—
491C4×D4—174no—
492C4×D4—174no—
493C4×D4—342no—
494C4×D4—348no—
495C4×D4—348no—
496#117—174no—
497#117—342no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—171no—
501C2×C4⋊C4—171no—
502C2×C4⋊C4—171no—
503C2×C4⋊C4—171no—
504C2×C4⋊C4—174no—
505C2×C4⋊C4—174no—
506C2×C4⋊C4—342no—
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⋊C4—341no—
514C2×C4⋊C4—342no—
515C2×C4⋊C4—341no—
516C2×C4⋊C4C22×D1711yescharacteristic
517C2×C4⋊C4C22×D1711yescharacteristic
518C2×C4⋊C4C22×D1714yes—
519C2×C4⋊C4C22×D1711yescharacteristic
520C2×C22⋊C4—21no—
521C2×C22⋊C4—171no—
522C2×C22⋊C4—171no—
523C2×C22⋊C4—341no—
524C2×C22⋊C4—341no—
525C2×C22⋊C4—341no—
526C2×C22⋊C4—341no—
527C2×C22⋊C4—341no—
528C2×C42—171no—
529C2×C42—341no—
530C2×C42—341no—
531#107—174no—
532#107—174no—
533#107—174no—
534#107—174no—
535#107—174no—
536#107—174no—
537#106—174no—
538#106C22×D1714yes—
539#106C22×D1714yes—
540C4⋊C8—174no—
541#103—174no—
542#103—174no—
543#103—174no—
544#102—174no—
545#102C22×D1714yes—
546#102C22×D1714yes—
547C22⋊C8—174no—
548C22⋊C8C22×D1714yes—
549#97—174no—
550C17C2×#334611yescharacteristic, complemented, Sylow
551C24—21no—
552C24—171no—
553C24D4×D1711yescharacteristic
554C2×Q8—172no—
555C2×Q8—344no—
556C2×Q8—341no—
557C2×Q8—342no—
558C2×Q8—342no—
559C2×Q8—1362no—
560C2×D4—24no—
561C2×D4—21no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—44no—
565C2×D4—174no—
566C2×D4—344no—
567C2×D4—344no—
568C2×D4—1362no—
569C2×D4C23×D1712yes—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—24no—
576C22×C4—82no—
577C22×C4—171no—
578C22×C4—171no—
579C22×C4—171no—
580C22×C4—172no—
581C22×C4—172no—
582C22×C4—344no—
583C22×C4—344no—
584C22×C4—342no—
585C22×C4—342no—
586C22×C4—341no—
587C22×C4—341no—
588C22×C4—341no—
589C22×C4—341no—
590C22×C4—344no—
591C22×C4—1362no—
592C22×C4—1362no—
593C22×C4—1362no—
594C22×C4D4×D1712yes—
595C22×C4D4×D1711yescharacteristic
596C22×C4C23×D1712yes—
597C22×C4C23×D1711yescharacteristic
598SD16—348no—
599M16—348no—
600C2×C8—22no—
601C2×C8—22no—
602C2×C8—174no—
603C2×C8—172no—
604C2×C8—172no—
605C2×C8—348no—
606C2×C8—342no—
607C2×C8C23×D1712yes—
608C2×C8C23×D1712yes—
609C4⋊C4—21no—
610C4⋊C4—24no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—174no—
614C4⋊C4—172no—
615C4⋊C4—172no—
616C4⋊C4—172no—
617C4⋊C4—344no—
618C4⋊C4—344no—
619C4⋊C4—344no—
620C4⋊C4—344no—
621C4⋊C4—344no—
622C4⋊C4—344no—
623C4⋊C4—341no—
624C4⋊C4—341no—
625C4⋊C4—341no—
626C4⋊C4—344no—
627C4⋊C4—344no—
628C4⋊C4C23×D1712yes—
629C4⋊C4C23×D1712yes—
630C4⋊C4C23×D1712yes—
631C22⋊C4—24no—
632C22⋊C4—174no—
633C22⋊C4—174no—
634C22⋊C4—344no—
635C22⋊C4—344no—
636C22⋊C4—344no—
637C22⋊C4—344no—
638C22⋊C4—344no—
639C42—172no—
640C42—172no—
641C42—344no—
642C42—344no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—172no—
650C23—342no—
651C23—342no—
652C23—342no—
653C23#1058760114yes—
654C23C2×D4×D1712yes—
655C23C2×D4×D1711yescharacteristic
656Q8—342no—
657Q8—342no—
658Q8—682no—
659Q8—1364no—
660D4—22no—
661D4—22no—
662D4—48no—
663D4—42no—
664D4—348no—
665D4—1364no—
666C2×C4—22no—
667C2×C4—24no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—84no—
677C2×C4—172no—
678C2×C4—172no—
679C2×C4—172no—
680C2×C4—342no—
681C2×C4—342no—
682C2×C4—342no—
683C2×C4—344no—
684C2×C4—342no—
685C2×C4—342no—
686C2×C4—342no—
687C2×C4—342no—
688C2×C4—342no—
689C2×C4—342no—
690C2×C4—682no—
691C2×C4—682no—
692C2×C4—682no—
693C2×C4—682no—
694C2×C4—1364no—
695C2×C4—1364no—
696C2×C4—1364no—
697C2×C4C2×D4×D1712yes—
698C2×C4C2×D4×D1711yescharacteristic
699C2×C4#41×D1712yes—
700C2×C4#1058769712yes—
701C2×C4C24×D1711yescharacteristic
702C8—22no—
703C8—22no—
704C8—174no—
705C8—342no—
706C22—22no—
707C22—22no—
708C22—28no—
709C22—42no—
710C22—42no—
711C22—42no—
712C22—84no—
713C22—342no—
714C22—342no—
715C22—342no—
716C22—684no—
717C22#1176345712yes—
718C22C2×#1058760114yes—
719C22C2×#1058760112yes—
720C22#1176361312yes—
721C22C22×D4×D1711yescharacteristic
722C4—22no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—342no—
727C4—342no—
728C4—342no—
729C4—682no—
730C4—682no—
731C4—682no—
732C4—682no—
733C4#1176345712yes—
734C4C2×#41×D1711yescharacteristic
735C4C2×#1058769711yescharacteristic
736C2—24no—
737C2—82no—
738C2—682no—
739C2#1454126714yesdirect product factor
740C2C2×#1176345711yescharacteristic
741C2C22×#1058760111yescharacteristic
742C2C2×#1176361311yescharacteristic
subgroupG/H
centerC23C2×D4×D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#481C2
socleC23×C17C22×D4
prime radicalC2×#11763511C2
hypercenterC2×#481D17
hypocenterC17C2×#3346
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#481

Complements

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

NH ≅ G/Ntype
1. C2×#11763514C2semidirect
3. #14541267C2direct (N × H)
4. C2×#11763216C2semidirect
5. C2×#11763145C2semidirect
6. C2×#11763153C2semidirect
7. C2×#11763121C2semidirect
8. C2×#11763119C2semidirect
9. C2×#11763087C2semidirect
10. C2×#11763054C2semidirect
11. C2×#11763036C2semidirect
12. C2×#11762906C2semidirect
13. C2×#11762877C2semidirect
14. C2×#11762848C2semidirect
15. C22×#10587478C2semidirect
16. C2×C17×#481C2semidirect
21. #11763514C22semidirect
43. #11763216C22semidirect
44. #11763153C22semidirect
45. #11763145C22semidirect
46. #11763121C22semidirect
47. #11763119C22semidirect
48. #11763087C22semidirect
49. #11763054C22semidirect
50. #11763036C22semidirect
51. #11762906C22semidirect
52. #11762877C22semidirect
53. #11762848C22semidirect
60. C2×#10587478C22semidirect
71. C17×#481C22semidirect
340. C2×#481D17semidirect
412. #481C2×D17semidirect
443. C2×C17#3346semidirect
550. C17C2×#3346semidirect
739. C2#14541267direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117635142
C2×#117635112
#145412672
C2×#117632162
C2×#117631452
C2×#117631532
C2×#117631212
C2×#117631192
C2×#117630872
C2×#117630542
C2×#117630362
C2×#117629062
C2×#117628772
C2×#117628482
C22×#105874782
C2×C17×#4812
C2×#334617