Finite Group Databasebeta

← C2×#14541171 #17912780

Subgroups — C2×#14541171 #17912780

Order 4352.

1942 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763517C211yesmaximal, characteristic
2C2×#11763514C211yesmaximal, characteristic
3#14541171C2116yesmaximal, direct product factor
4C2×#11763213C211yesmaximal, characteristic, complemented
5C2×#11763146C211yesmaximal, characteristic, complemented
6C2×#11763145C211yesmaximal, characteristic, complemented
7C2×#11763143C211yesmaximal, characteristic, complemented
8C2×#11763103C211yesmaximal, characteristic, complemented
9C2×#11763102C211yesmaximal, characteristic, complemented
10C2×#11763049C211yesmaximal, characteristic, complemented
11C2×#11763048C211yesmaximal, characteristic, complemented
12C2×#11762901C211yesmaximal, characteristic, complemented
13C2×#11762872C211yesmaximal, characteristic
14C22×#10587478C211yesmaximal, characteristic, complemented
15C2×#107×D17C211yesmaximal, characteristic, complemented
16C2×C17×#484C211yesmaximal, characteristic, complemented
17C22×#63231C2211yescharacteristic
18C23×#3622C2211yescharacteristic
19C22×C8×D17C2211yescharacteristic
20#11763517—24no—
21#11763517C2218yes—
22#11763514—24no—
23#11763514C2218yes—
24C2×#10587574C2211yescharacteristic
25C2×#10587574C2211yescharacteristic
26C2×#10587575—21no—
27C2×#10587575—21no—
28C2×#10587583—21no—
29C2×#10587583C2211yescharacteristic
30C2×#10587610—21no—
31C2×#10587610C2211yescharacteristic
32C2×#10587582—21no—
33C2×#10587564—21no—
34C2×#10587632C2211yescharacteristic
35C2×Q8×Dic17C2211yescharacteristic
36C2×#10587573C2211yescharacteristic
37C2×C4×C22⋊D17—21no—
38C2×C4×C22⋊D17C2211yescharacteristic
39C2×#10587567—21no—
40C22×C4⋊Dic17C2211yescharacteristic
41C2×C4⋊C4×D17C2211yescharacteristic
42C2×C4⋊C4×D17C2211yescharacteristic
43#11763213C2218yescomplemented
44#11763146C2218yescomplemented
45#11763145C2218yescomplemented
46#11763143C2218yescomplemented
47#11763103C2218yescomplemented
48#11763102C2218yescomplemented
49#11763049C2218yescomplemented
50#11763048C2218yescomplemented
51#11762901C2218yescomplemented
52#11762872C2218yes—
53C2×#10587489C2211yescharacteristic
54C2×#10587489C2211yescharacteristic
55C2×#10587478C2211yescharacteristic
56C2×#10587478C2211yescharacteristic
57C2×#10587478C2211yescharacteristic
58C2×#10587478C2211yescharacteristic
59C2×#10587478C2211yescharacteristic
60C2×#10587478C2218yescomplemented
61#107×D17C2218yescomplemented
62C2×#10587485C2211yescharacteristic
63C2×#10587487C2211yescharacteristic
64C2×#10587487C2211yescharacteristic
65C2×#10587506C2211yescharacteristic
66C2×#10587481C2211yescharacteristic
67C2×#10587491C2211yescharacteristic
68C2×C8×Dic17C2211yescharacteristic
69C2×C17×C22⋊Q8C2211yescharacteristic
70C22×C4⋊C4×C17C2211yescharacteristic
71C17×#484C2218yescomplemented
72C2×C17×#107C2211yescharacteristic
73C2×C17×#107C2211yescharacteristic
74C2×C17×#103C2211yescharacteristic
75C2×C17×#103C2211yescharacteristic
76C2×C17×C22⋊C8C2211yescharacteristic
77C22×Q8×C17C2311yescharacteristic
78C23×C4×C17—21no—
79C23×C4×C17C2311yescharacteristic
80C22×C22⋊D17D411yescharacteristic
81C23×Dic17—21no—
82C22×C4×D17—21no—
83C22×C4×D17—21no—
84C22×C4×D17C2311yescharacteristic
85C22×Dic34—21no—
86C22×Dic34—21no—
87C22×Dic34C2311yescharacteristic
88C22×C8×C17C2311yescharacteristic
89C22×C8×C17C2311yescharacteristic
90C17×C22⋊Q8—22no—
91C17×C22⋊Q8C2314yes—
92C2×C4⋊C4×C17—22no—
93C2×C4⋊C4×C17—21no—
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⋊Dic17D411yescharacteristic
102#10587632—22no—
103#10587632C2314yes—
104Q8×Dic17—22no—
105Q8×Dic17C2314yes—
106C2×#63231—24no—
107C2×#63231C2314yes—
108C4×C22⋊D17—28no—
109C4×C22⋊D17D414yes—
110C4×C22⋊D17C2314yes—
111C2×#63227—21no—
112C2×#63227—21no—
113C2×#63227D411yescharacteristic
114C2×C4⋊Dic17—22no—
115C2×C4⋊Dic17—21no—
116C2×C4⋊Dic17—21no—
117C2×C4⋊Dic17—21no—
118C2×C4⋊Dic17C2311yescharacteristic
119C2×C4⋊Dic17C2311yescharacteristic
120C2×C4⋊Dic17C2314yes—
121C2×C4⋊Dic17C2311yescharacteristic
122#10587610—22no—
123#10587610—28no—
124#10587610C2314yes—
125C2×#63225—21no—
126C2×#63225—21no—
127C2×#63225—21no—
128C2×#63225—21no—
129C2×#63225—21no—
130C2×#63225—21no—
131C2×#63225—21no—
132C2×#63225D411yescharacteristic
133C2×C4×Dic17—21no—
134C2×C4×Dic17—21no—
135C2×C4×Dic17C2311yescharacteristic
136C22×#3622—24no—
137C22×#3622C2311yescharacteristic
138C22×#3622C2314yes—
139C22×#3622C2311yescharacteristic
140C2×C8×D17—24no—
141C2×C8×D17C2314yes—
142#10587583—28no—
143#10587583—22no—
144#10587583C2314yes—
145#10587582—28no—
146C4⋊C4×D17—22no—
147C4⋊C4×D17—22no—
148C4⋊C4×D17C2314yes—
149C4⋊C4×D17C2314yes—
150#10587575—28no—
151#10587575—28no—
152#10587574—22no—
153#10587574—22no—
154#10587574C2314yes—
155#10587574C2314yes—
156#10587573—22no—
157#10587573C2314yes—
158#10587567—28no—
159#10587564—28no—
160C17×#107C2314yes—
161C17×#107C2314yes—
162C17×#103C2314yes—
163C17×#103C2314yes—
164C17×C22⋊C8C2314yes—
165#10587506C2314yes—
166#10587491C2314yes—
167#10587489C2314yes—
168#10587489C2314yes—
169#10587487C2314yes—
170#10587487C2314yes—
171#10587485C2314yes—
172C8×Dic17C2314yes—
173#10587481C2314yes—
174#10587478C2314yes—
175#10587478C2314yes—
176#10587478C2314yes—
177#10587478C2314yes—
178#10587478C2314yes—
179C24×C17C2×D411yescharacteristic
180C23×D17C2×D411yescharacteristic
181C2×Q8×C17—21no—
182C2×Q8×C17—22no—
183C2×Q8×C17—22no—
184C2×Q8×C17C2412yes—
185C22×C4×C17—22no—
186C22×C4×C17—22no—
187C22×C4×C17—21no—
188C22×C4×C17—21no—
189C22×C4×C17—21no—
190C22×C4×C17—21no—
191C22×C4×C17—24no—
192C22×C4×C17—82no—
193C22×C4×C17C2×D412yes—
194C22×C4×C17C2×D411yescharacteristic
195C22×C4×C17C2412yes—
196C22×C4×C17C2411yescharacteristic
197C2×C22⋊D17Q1618yescomplemented
198C2×C22⋊D17C2×D414yes—
199C22×Dic17—21no—
200C22×Dic17—21no—
201C22×Dic17—21no—
202C22×Dic17—21no—
203C22×Dic17—24no—
204C22×Dic17—82no—
205C22×Dic17C2×D411yescharacteristic
206C22×Dic17C2×D411yescharacteristic
207C22×Dic17C2×D411yescharacteristic
208C2×C4×D17—22no—
209C2×C4×D17—22no—
210C2×C4×D17—24no—
211C2×C4×D17—24no—
212C2×C4×D17—82no—
213C2×C4×D17—82no—
214C2×C4×D17C2×D412yes—
215C2×C4×D17C2412yes—
216C2×Dic34—22no—
217C2×Dic34—22no—
218C2×Dic34—21no—
219C2×Dic34—24no—
220C2×Dic34—24no—
221C2×Dic34—82no—
222C2×Dic34—82no—
223C2×Dic34C2412yes—
224C2×C8×C17—22no—
225C2×C8×C17—22no—
226C2×C8×C17C2412yes—
227C2×C8×C17C2412yes—
228C4⋊C4×C17—21no—
229C4⋊C4×C17—24no—
230C4⋊C4×C17—21no—
231C4⋊C4×C17—21no—
232C4⋊C4×C17—24no—
233C4⋊C4×C17C2412yes—
234C4⋊C4×C17C2412yes—
235C4⋊C4×C17C2412yes—
236C22⋊C4×C17—24no—
237C22⋊Dic17—24no—
238C22⋊Dic17C2×D414yes—
239#63231—28no—
240#63227—24no—
241#63227—24no—
242#63227C2×D414yes—
243C4⋊Dic17—21no—
244C4⋊Dic17—21no—
245C4⋊Dic17—24no—
246C4⋊Dic17—21no—
247C4⋊Dic17—24no—
248C4⋊Dic17—24no—
249C4⋊Dic17C2412yes—
250C4⋊Dic17C2412yes—
251C4⋊Dic17C2412yes—
252#63225—24no—
253#63225—24no—
254#63225—24no—
255#63225—24no—
256#63225—24no—
257#63225—24no—
258#63225—24no—
259#63225C2×D414yes—
260C4×Dic17—24no—
261C4×Dic17—24no—
262C4×Dic17C2×D412yes—
263C4×Dic17C2412yes—
264C2×#3622—22no—
265C2×#3622—28no—
266C2×#3622#4114yes—
267C2×#3622C2412yes—
268C2×#3622C2412yes—
269C8×D17—28no—
270C2×#3338—171nomaximal, Sylow
271C23×C17—22no—
272C23×C17—22no—
273C23×C17C2×Q1614yes—
274C23×C17C22×D412yes—
275C23×C17C22×D411yescharacteristic
276C22×D17—22no—
277C22×D17—22no—
278C22×D17C2×Q1614yes—
279C22×D17C22×D412yes—
280Q8×C17—22no—
281Q8×C17—22no—
282Q8×C17—42no—
283C2×C4×C17—22no—
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—42no—
292C2×C4×C17—42no—
293C2×C4×C17—42no—
294C2×C4×C17—42no—
295C2×C4×C17—84no—
296C2×C4×C17C22×D412yes—
297C2×C4×C17C22×D411yescharacteristic
298C2×C4×C17C2×#4112yes—
299C2×C4×C172−1+412yes—
300C2×C4×C17C2511yescharacteristic
301C22⋊D17C2×Q16116yescomplemented
302C2×Dic17—22no—
303C2×Dic17—22no—
304C2×Dic17—22no—
305C2×Dic17—22no—
306C2×Dic17—22no—
307C2×Dic17—22no—
308C2×Dic17—42no—
309C2×Dic17—42no—
310C2×Dic17—42no—
311C2×Dic17—42no—
312C2×Dic17—84no—
313C2×Dic17C2×Q1614yes—
314C2×Dic17C22×D412yes—
315C2×Dic17C22×D412yes—
316C2×Dic17C22×D412yes—
317C4×D17—24no—
318C4×D17—22no—
319C4×D17—22no—
320C4×D17—84no—
321C4×D17—84no—
322Dic34—22no—
323Dic34—22no—
324Dic34—42no—
325Dic34—84no—
326Dic34—84no—
327C8×C17—22no—
328C8×C17—22no—
329#3622—22no—
330#3622C2×#4114yes—
331C2×#554—171no—
332C2×#554—171no—
333#3338—1716no—
334C2×#500—171no—
335C2×#484—171no—
336C2×#484—171no—
337C2×#484—171no—
338C2×#484D1711yescharacteristic, complemented
339C2×#477—171no—
340C2×#477—171no—
341C2×#467—171no—
342C2×#467—171no—
343C2×C4×Q16—171no—
344C2×C8×D4—171no—
345C22×#107—171no—
346C22×#107—171no—
347C22×C17—28no—
348C22×C17—22no—
349C22×C17—22no—
350C22×C17#54712yes—
351C22×C17C22×Q1614yes—
352C22×C17C22×Q1612yes—
353C22×C17#57612yes—
354C22×C17C23×D411yescharacteristic
355C2×D17—28no—
356C2×D17—22no—
357C2×D17—22no—
358C2×D17C22×Q1614yes—
359C4×C17—22no—
360C4×C17—42no—
361C4×C17—42no—
362C4×C17—42no—
363C4×C17—42no—
364C4×C17#54712yes—
365C4×C17C22×#4111yescharacteristic
366C4×C17C2×2−1+411yescharacteristic
367Dic17—22no—
368Dic17—22no—
369Dic17—42no—
370Dic17—42no—
371Dic17—42no—
372Dic17—42no—
373Dic17C22×Q1614yes—
374C22×Q16—171no—
375C23×C8—171no—
376C23×C8—171no—
377#554—178no—
378#554—178no—
379#554—344no—
380#554—344no—
381C2×C4⋊Q8—171no—
382C2×C4⋊Q8—171no—
383C2×#125—341no—
384C2×#125—341no—
385C2×C22⋊Q8—171no—
386C2×C22⋊Q8—171no—
387C2×C22⋊Q8—171no—
388C2×C22⋊Q8—341no—
389C2×C22⋊Q8—341no—
390C2×C22⋊Q8—341no—
391C2×C22⋊Q8—341no—
392C2×C22⋊Q8C2×D1711yescharacteristic
393C2×C4×Q8—171no—
394C2×C4×Q8—171no—
395C2×C4×D4—171no—
396C2×C4×D4—341no—
397C2×C4×D4—341no—
398C22×C4⋊C4—171no—
399C22×C4⋊C4—171no—
400C22×C4⋊C4—171no—
401C22×C4⋊C4C2×D1711yescharacteristic
402#500—178no—
403#484—178no—
404#484—178no—
405#484—178no—
406#484C2×D1718yescomplemented
407#477—178no—
408#477—178no—
409#467—178no—
410#467—178no—
411C4×Q16—178no—
412C8×D4—178no—
413C2×#107—171no—
414C2×#107—171no—
415C2×#107—171no—
416C2×#107—171no—
417C2×#107—178no—
418C2×#107—171no—
419C2×#107—171no—
420C2×#107—171no—
421C2×#107—178no—
422C2×#107C2×D1711yescharacteristic
423C2×#107C2×D1711yescharacteristic
424C2×C4⋊C8—171no—
425C2×#103—171no—
426C2×#103—171no—
427C2×#103—171no—
428C2×#103—171no—
429C2×#103C2×D1711yescharacteristic
430C2×#103C2×D1711yescharacteristic
431C2×C22⋊C8—171no—
432C2×C22⋊C8C2×D1711yescharacteristic
433C2×C4×C8—171no—
434C2×C17—24no—
435C2×C17#333814yescomplemented
436C2×C17C2×#54711yescharacteristic
437C2×C17C23×Q1611yescharacteristic
438C2×C17C2×#57611yescharacteristic
439D17—24no—
440C22×Q8—171no—
441C22×Q8—341no—
442C22×Q8—341no—
443C22×Q8C22×D1711yescharacteristic
444C22×D4—171no—
445C23×C4—21no—
446C23×C4—171no—
447C23×C4—341no—
448C23×C4—341no—
449C23×C4—341no—
450C23×C4C22×D1711yescharacteristic
451C2×Q16—174no—
452C2×Q16—344no—
453C22×C8—171no—
454C22×C8—171no—
455C22×C8—174no—
456C22×C8—174no—
457C22×C8—344no—
458C22×C8—344no—
459C22×C8C22×D1711yescharacteristic
460C22×C8C22×D1711yescharacteristic
461C4⋊Q8—174no—
462C4⋊Q8—174no—
463C4⋊Q8—342no—
464C4⋊Q8—342no—
465#125—348no—
466#125—348no—
467C22⋊Q8—22no—
468C22⋊Q8—174no—
469C22⋊Q8—174no—
470C22⋊Q8—174no—
471C22⋊Q8—348no—
472C22⋊Q8—348no—
473C22⋊Q8—348no—
474C22⋊Q8—348no—
475C22⋊Q8—342no—
476C22⋊Q8—342no—
477C22⋊Q8—342no—
478C22⋊Q8C22×D1714yes—
479C4×Q8—174no—
480C4×Q8—174no—
481C4×Q8—342no—
482C4×Q8—342no—
483C4×D4—174no—
484C4×D4—174no—
485C4×D4—348no—
486C4×D4—348no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—22no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—171no—
491C2×C4⋊C4—171no—
492C2×C4⋊C4—171no—
493C2×C4⋊C4—171no—
494C2×C4⋊C4—174no—
495C2×C4⋊C4—174no—
496C2×C4⋊C4—174no—
497C2×C4⋊C4—342no—
498C2×C4⋊C4—342no—
499C2×C4⋊C4—341no—
500C2×C4⋊C4—341no—
501C2×C4⋊C4—341no—
502C2×C4⋊C4—341no—
503C2×C4⋊C4—341no—
504C2×C4⋊C4—341no—
505C2×C4⋊C4—341no—
506C2×C4⋊C4—341no—
507C2×C4⋊C4—341no—
508C2×C4⋊C4—342no—
509C2×C4⋊C4—341no—
510C2×C4⋊C4C22×D1711yescharacteristic
511C2×C4⋊C4C22×D1711yescharacteristic
512C2×C4⋊C4C22×D1711yescharacteristic
513C2×C4⋊C4C22×D1714yes—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—171no—
516C2×C22⋊C4—171no—
517C2×C22⋊C4—341no—
518C2×C22⋊C4—341no—
519C2×C22⋊C4—341no—
520C2×C42—171no—
521C2×C42—341no—
522C2×C42—341no—
523#107—174no—
524#107—174no—
525#107—174no—
526#107—174no—
527#107—174no—
528#107—174no—
529#107—174no—
530#107C22×D1714yes—
531#107C22×D1714yes—
532C4⋊C8—174no—
533#103—174no—
534#103—174no—
535#103—174no—
536#103—174no—
537#103C22×D1714yes—
538#103C22×D1714yes—
539C22⋊C8—174no—
540C22⋊C8C22×D1714yes—
541C4×C8—174no—
542C17C2×#333811yescharacteristic, complemented, Sylow
543C24—171no—
544C24D4×D1711yescharacteristic
545C2×Q8—21no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8—172no—
549C2×Q8—344no—
550C2×Q8—344no—
551C2×Q8—341no—
552C2×Q8—342no—
553C2×Q8—342no—
554C2×Q8—1362no—
555C2×Q8—1362no—
556C2×Q8C23×D1712yes—
557C2×D4—174no—
558C2×D4—178no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—24no—
566C22×C4—82no—
567C22×C4—171no—
568C22×C4—171no—
569C22×C4—171no—
570C22×C4—172no—
571C22×C4—172no—
572C22×C4—344no—
573C22×C4—344no—
574C22×C4—342no—
575C22×C4—342no—
576C22×C4—341no—
577C22×C4—341no—
578C22×C4—341no—
579C22×C4—341no—
580C22×C4—344no—
581C22×C4—1362no—
582C22×C4—1362no—
583C22×C4—1362no—
584C22×C4D4×D1712yes—
585C22×C4D4×D1711yescharacteristic
586C22×C4C23×D1712yes—
587C22×C4C23×D1711yescharacteristic
588Q16—348no—
589C2×C8—22no—
590C2×C8—22no—
591C2×C8—174no—
592C2×C8—172no—
593C2×C8—172no—
594C2×C8—348no—
595C2×C8—348no—
596C2×C8—342no—
597C2×C8C23×D1712yes—
598C2×C8C23×D1712yes—
599C4⋊C4—21no—
600C4⋊C4—24no—
601C4⋊C4—21no—
602C4⋊C4—24no—
603C4⋊C4—21no—
604C4⋊C4—174no—
605C4⋊C4—172no—
606C4⋊C4—172no—
607C4⋊C4—172no—
608C4⋊C4—344no—
609C4⋊C4—344no—
610C4⋊C4—344no—
611C4⋊C4—344no—
612C4⋊C4—344no—
613C4⋊C4—344no—
614C4⋊C4—344no—
615C4⋊C4—344no—
616C4⋊C4—341no—
617C4⋊C4—344no—
618C4⋊C4—341no—
619C4⋊C4—341no—
620C4⋊C4—344no—
621C4⋊C4C23×D1712yes—
622C4⋊C4C23×D1712yes—
623C4⋊C4C23×D1712yes—
624C22⋊C4—24no—
625C22⋊C4—174no—
626C22⋊C4—174no—
627C22⋊C4—344no—
628C22⋊C4—344no—
629C22⋊C4—344no—
630C42—172no—
631C42—172no—
632C42—344no—
633C42—344no—
634C23—22no—
635C23—22no—
636C23—174no—
637C23—172no—
638C23—342no—
639C23—342no—
640C23Q16×D1714yes—
641C23C2×D4×D1712yes—
642C23C2×D4×D1711yescharacteristic
643Q8—22no—
644Q8—22no—
645Q8—42no—
646Q8—342no—
647Q8—342no—
648Q8—682no—
649Q8—1364no—
650Q8—1364no—
651D4—1716no—
652C2×C4—22no—
653C2×C4—24no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—84no—
665C2×C4—174no—
666C2×C4—172no—
667C2×C4—172no—
668C2×C4—172no—
669C2×C4—342no—
670C2×C4—342no—
671C2×C4—344no—
672C2×C4—342no—
673C2×C4—342no—
674C2×C4—342no—
675C2×C4—342no—
676C2×C4—342no—
677C2×C4—342no—
678C2×C4—682no—
679C2×C4—682no—
680C2×C4—682no—
681C2×C4—682no—
682C2×C4—1364no—
683C2×C4—1364no—
684C2×C4—1364no—
685C2×C4C2×D4×D1712yes—
686C2×C4C2×D4×D1711yescharacteristic
687C2×C4#41×D1712yes—
688C2×C4#1058769712yes—
689C2×C4C24×D1711yescharacteristic
690C8—22no—
691C8—22no—
692C8—174no—
693C8—342no—
694C22—28no—
695C22—22no—
696C22—22no—
697C22—174no—
698C22—348no—
699C22—342no—
700C22—342no—
701C22#1176345712yes—
702C22C2×Q16×D1714yes—
703C22C2×Q16×D1712yes—
704C22#1176361312yes—
705C22C22×D4×D1711yescharacteristic
706C4—22no—
707C4—42no—
708C4—42no—
709C4—42no—
710C4—42no—
711C4—174no—
712C4—342no—
713C4—342no—
714C4—682no—
715C4—682no—
716C4—682no—
717C4—682no—
718C4#1176345712yes—
719C4C2×#41×D1711yescharacteristic
720C4C2×#1058769711yescharacteristic
721C2—24no—
722C2—344no—
723C2#1454117114yesdirect product factor
724C2C2×#1176345711yescharacteristic
725C2C22×Q16×D1711yescharacteristic
726C2C2×#1176361311yescharacteristic
subgroupG/H
centerC23C2×D4×D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#484C2
socleC23×C17C22×D4
prime radicalC22×C22⋊D17D4
hypercenterC2×#484D17
hypocenterC17C2×#3338
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#484

Complements

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

NH ≅ G/Ntype
3. #14541171C2direct (N × H)
4. C2×#11763213C2semidirect
5. C2×#11763146C2semidirect
6. C2×#11763145C2semidirect
7. C2×#11763143C2semidirect
8. C2×#11763103C2semidirect
9. C2×#11763102C2semidirect
10. C2×#11763049C2semidirect
11. C2×#11763048C2semidirect
12. C2×#11762901C2semidirect
14. C22×#10587478C2semidirect
15. C2×#107×D17C2semidirect
16. C2×C17×#484C2semidirect
43. #11763213C22semidirect
44. #11763146C22semidirect
45. #11763145C22semidirect
46. #11763143C22semidirect
47. #11763103C22semidirect
48. #11763102C22semidirect
49. #11763049C22semidirect
50. #11763048C22semidirect
51. #11762901C22semidirect
60. C2×#10587478C22semidirect
61. #107×D17C22semidirect
71. C17×#484C22semidirect
197. C2×C22⋊D17Q16semidirect
301. C22⋊D17C2×Q16semidirect
338. C2×#484D17semidirect
406. #484C2×D17semidirect
435. C2×C17#3338semidirect
542. C17C2×#3338semidirect
723. C2#14541171direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117635172
C2×#117635142
#145411712
C2×#117632132
C2×#117631462
C2×#117631452
C2×#117631432
C2×#117631032
C2×#117631022
C2×#117630492
C2×#117630482
C2×#117629012
C2×#117628722
C22×#105874782
C2×#107×D172
C2×C17×#4842
C2×#333817