Finite Group Databasebeta

← C2×#14541272 #17912906

Subgroups — C2×#14541272 #17912906

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×#11763506C211yesmaximal, characteristic
3#14541272C2116yesmaximal, direct product factor
4C2×#11763217C211yesmaximal, characteristic, complemented
5C2×#11763146C211yesmaximal, characteristic, complemented
6C2×#11763126C211yesmaximal, characteristic, complemented
7C2×#11763151C211yesmaximal, characteristic, complemented
8C2×#11763115C211yesmaximal, characteristic, complemented
9C2×#11763087C211yesmaximal, characteristic, complemented
10C2×#11763053C211yesmaximal, characteristic, complemented
11C2×#11763037C211yesmaximal, characteristic, complemented
12C2×#11762906C211yesmaximal, characteristic, complemented
13C2×#11762883C211yesmaximal, characteristic, complemented
14C2×#11762849C211yesmaximal, characteristic, complemented
15C2×#107×D17C211yesmaximal, characteristic, complemented
16C2×C17×#480C211yesmaximal, characteristic, complemented
17C22×#63229C2211yescharacteristic
18C22×#63223C2211yescharacteristic
19C22×C8×D17C2211yescharacteristic
20#11763514—24no—
21#11763514C2218yescomplemented
22#11763506—24no—
23#11763506C2218yes—
24C2×#10587574C2211yescharacteristic
25C2×#10587565—21no—
26C2×#10587576C2211yescharacteristic
27C2×#10587575—21no—
28C2×#10587621—21no—
29C2×#10587583C2211yescharacteristic
30C2×#10587610—21no—
31C2×#10587610C2211yescharacteristic
32C2×#10587582—21no—
33C2×#10587624—21no—
34C2×#10587624C2211yescharacteristic
35C2×#10587573C2211yescharacteristic
36C2×D4×Dic17C2211yescharacteristic
37C2×C4×C22⋊D17—21no—
38C2×C4×C22⋊D17C2211yescharacteristic
39C2×#10587567—21no—
40C2×#10587612C2211yescharacteristic
41C2×C4⋊C4×D17C2211yescharacteristic
42C2×C4⋊C4×D17C2211yescharacteristic
43#11763217C2218yescomplemented
44#11763151C2218yescomplemented
45#11763146C2218yescomplemented
46#11763126C2218yescomplemented
47#11763115C2218yescomplemented
48#11763087C2218yescomplemented
49#11763053C2218yescomplemented
50#11763037C2218yescomplemented
51#11762906C2218yescomplemented
52#11762883C2218yescomplemented
53#11762849C2218yescomplemented
54C2×#10587489C2211yescharacteristic
55C2×#10587478C2211yescharacteristic
56C2×#10587478C2211yescharacteristic
57C2×#10587478C2211yescharacteristic
58#107×D17C2218yescomplemented
59C2×#10587488C2211yescharacteristic
60C2×#10587479C2211yescharacteristic
61C2×#10587479C2211yescharacteristic
62C2×#10587485C2211yescharacteristic
63C2×#10587487C2211yescharacteristic
64C2×#10587487C2211yescharacteristic
65C2×#10587481C2211yescharacteristic
66C2×#10587503C2211yescharacteristic
67C2×#10587491C2211yescharacteristic
68C2×#10587486C2211yescharacteristic
69C2×C17×#121C2211yescharacteristic
70C22×C4⋊C4×C17C2211yescharacteristic
71C17×#480C2218yescomplemented
72C2×C17×#107C2211yescharacteristic
73C2×C17×#107C2211yescharacteristic
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—
84C22×C4×D17—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⋊Dic17—21no—
104C2×C22⋊Dic17D411yescharacteristic
105#10587624—28no—
106#10587624—22no—
107#10587624C2314yes—
108#10587621—28no—
109D4×Dic17—22no—
110D4×Dic17C2314yes—
111C2×#63229—24no—
112C2×#63229C2314yes—
113C4×C22⋊D17—28no—
114C4×C22⋊D17D414yes—
115C4×C22⋊D17C2314yes—
116C2×#63227—21no—
117C2×#63227D411yescharacteristic
118#10587612—22no—
119#10587612C2314yes—
120C2×C4⋊Dic17—21no—
121C2×C4⋊Dic17—21no—
122C2×C4⋊Dic17C2311yescharacteristic
123C2×C4⋊Dic17C2311yescharacteristic
124C2×C4⋊Dic17C2311yescharacteristic
125#10587610—22no—
126#10587610—28no—
127#10587610C2314yes—
128C2×#63225—21no—
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
138C2×#63223—24no—
139C2×#63223C2314yes—
140C22×#3622C2311yescharacteristic
141C22×#3622C2311yescharacteristic
142C2×C8×D17—24no—
143C2×C8×D17C2314yes—
144#10587583—22no—
145#10587583C2314yes—
146#10587582—28no—
147C4⋊C4×D17—22no—
148C4⋊C4×D17—22no—
149C4⋊C4×D17C2314yes—
150C4⋊C4×D17C2314yes—
151#10587576—22no—
152#10587576C2314yes—
153#10587575—28no—
154#10587574—22no—
155#10587574C2314yes—
156#10587573—22no—
157#10587573C2314yes—
158#10587567—28no—
159#10587565—28no—
160C17×#107C2314yes—
161C17×#107C2314yes—
162C17×#102C2314yes—
163C17×#102C2314yes—
164C17×C22⋊C8C2314yes—
165#10587503C2314yes—
166#10587491C2314yes—
167#10587489C2314yes—
168#10587488C2314yes—
169#10587487C2314yes—
170#10587487C2314yes—
171#10587486C2314yes—
172#10587485C2314yes—
173#10587481C2314yes—
174#10587479C2314yes—
175#10587479C2314yes—
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—82no—
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—44no—
202C2×C22⋊D17C2×D414yes—
203C22×Dic17—21no—
204C22×Dic17—21no—
205C22×Dic17—21no—
206C22×Dic17—21no—
207C22×Dic17—24no—
208C22×Dic17—82no—
209C22×Dic17C2×D411yescharacteristic
210C22×Dic17C2×D411yescharacteristic
211C22×Dic17C2×D411yescharacteristic
212C2×C4×D17—22no—
213C2×C4×D17—22no—
214C2×C4×D17—24no—
215C2×C4×D17—24no—
216C2×C4×D17—82no—
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⋊Dic17—24no—
242C22⋊Dic17C2×D414yes—
243#63229—28no—
244#63227—24no—
245#63227C2×D414yes—
246C4⋊Dic17—21no—
247C4⋊Dic17—21no—
248C4⋊Dic17—21no—
249C4⋊Dic17—24no—
250C4⋊Dic17—24no—
251C4⋊Dic17C2412yes—
252C4⋊Dic17C2412yes—
253C4⋊Dic17C2412yes—
254#63225—24no—
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—
265#63223—28no—
266C2×#3622—22no—
267C2×#3622#4114yes—
268C2×#3622C2412yes—
269C2×#3622C2412yes—
270C8×D17—28no—
271C2×#3346—171nomaximal, Sylow
272C23×C17—22no—
273C23×C17—22no—
274C23×C17—22no—
275C23×C17—22no—
276C23×C17—42no—
277C23×C17—42no—
278C23×C17—42no—
279C23×C17C22×D412yes—
280C23×C17C22×D411yescharacteristic
281C22×D17—22no—
282C22×D17—22no—
283C22×D17#13714yes—
284C22×D17C22×D412yes—
285D4×C17—22no—
286D4×C17—22no—
287D4×C17—42no—
288D4×C17—84no—
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—48no—
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×Dic17C22×D412yes—
320C2×Dic17C22×D412yes—
321C2×Dic17C22×D412yes—
322C4×D17—24no—
323C4×D17—22no—
324C4×D17—22no—
325C4×D17—84no—
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×#481—171no—
341C2×#485—171no—
342C2×#480D1711yescharacteristic, complemented
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—22no—
352C22×C17—22no—
353C22×C17—22no—
354C22×C17—44no—
355C22×C17—42no—
356C22×C17—42no—
357C22×C17—42no—
358C22×C17—84no—
359C22×C17#54712yes—
360C22×C17C2×#13712yes—
361C22×C17#57612yes—
362C22×C17C23×D411yescharacteristic
363C2×D17—28no—
364C2×D17—22no—
365C2×D17—22no—
366C2×D17C2×#13714yes—
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#481—178no—
413#480C2×D1718yescomplemented
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×#107C2×D1711yescharacteristic
427C2×#107C2×D1711yescharacteristic
428C2×#106—171no—
429C2×#106—171no—
430C2×#106—171no—
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—42no—
442C2×C17—82no—
443C2×C17#334614yescomplemented
444C2×C17C2×#54711yescharacteristic
445C2×C17C22×#13711yescharacteristic
446C2×C17C2×#57611yescharacteristic
447D17—24no—
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—342no—
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—341no—
515C2×C4⋊C4—341no—
516C2×C4⋊C4C22×D1711yescharacteristic
517C2×C4⋊C4C22×D1711yescharacteristic
518C2×C4⋊C4C22×D1711yescharacteristic
519C2×C4⋊C4C22×D1714yes—
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#107C22×D1714yes—
536#107C22×D1714yes—
537#106—174no—
538#106—174no—
539#106—174no—
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—82no—
565C2×D4—174no—
566C2×D4—344no—
567C2×D4—344no—
568C2×D4—684no—
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—344no—
585C22×C4—342no—
586C22×C4—342no—
587C22×C4—341no—
588C22×C4—341no—
589C22×C4—341no—
590C22×C4—341no—
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—344no—
624C4⋊C4—341no—
625C4⋊C4—341no—
626C4⋊C4—341no—
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—22no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—174no—
651C23—172no—
652C23—342no—
653C23—342no—
654C23C2×D4×D1712yes—
655C23C2×D4×D1711yescharacteristic
656Q8—342no—
657Q8—342no—
658Q8—682no—
659Q8—1364no—
660D4—22no—
661D4—22no—
662D4—42no—
663D4—84no—
664D4—348no—
665D4—688no—
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—22no—
709C22—44no—
710C22—42no—
711C22—42no—
712C22—42no—
713C22—84no—
714C22—174no—
715C22—342no—
716C22—342no—
717C22—348no—
718C22#1176345712yes—
719C22#137×D1712yes—
720C22#1176361012yes—
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—42no—
737C2—82no—
738C2—344no—
739C2#1454127214yesdirect product factor
740C2C2×#1176345711yescharacteristic
741C2C2×#137×D1711yescharacteristic
742C2C2×#1176361011yescharacteristic
subgroupG/H
centerC23C2×D4×D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#480C2
socleC23×C17C22×D4
prime radicalC2×#11763506C2
hypercenterC2×#480D17
hypocenterC17C2×#3346
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#480

Complements

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

NH ≅ G/Ntype
1. C2×#11763514C2semidirect
3. #14541272C2direct (N × H)
4. C2×#11763217C2semidirect
5. C2×#11763146C2semidirect
6. C2×#11763126C2semidirect
7. C2×#11763151C2semidirect
8. C2×#11763115C2semidirect
9. C2×#11763087C2semidirect
10. C2×#11763053C2semidirect
11. C2×#11763037C2semidirect
12. C2×#11762906C2semidirect
13. C2×#11762883C2semidirect
14. C2×#11762849C2semidirect
15. C2×#107×D17C2semidirect
16. C2×C17×#480C2semidirect
21. #11763514C22semidirect
43. #11763217C22semidirect
44. #11763151C22semidirect
45. #11763146C22semidirect
46. #11763126C22semidirect
47. #11763115C22semidirect
48. #11763087C22semidirect
49. #11763053C22semidirect
50. #11763037C22semidirect
51. #11762906C22semidirect
52. #11762883C22semidirect
53. #11762849C22semidirect
58. #107×D17C22semidirect
71. C17×#480C22semidirect
342. C2×#480D17semidirect
413. #480C2×D17semidirect
443. C2×C17#3346semidirect
550. C17C2×#3346semidirect
739. C2#14541272direct (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×#117635062
#145412722
C2×#117632172
C2×#117631462
C2×#117631262
C2×#117631512
C2×#117631152
C2×#117630872
C2×#117630532
C2×#117630372
C2×#117629062
C2×#117628832
C2×#117628492
C2×#107×D172
C2×C17×#4802
C2×#334617