Finite Group Databasebeta

← #16939608

Subgroups — #16939608

Order 4352.

1510 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×M16×D17C211yesmaximal, characteristic
2#14531163C211yesmaximal, characteristic
3C2×C4×#63227C211yesmaximal, characteristic
4C2×#11762570C211yesmaximal, characteristic, complemented
5C2×#11762569C211yesmaximal, characteristic, complemented
6C2×#11762568C211yesmaximal, characteristic, complemented
7C2×C17×#339C211yesmaximal, characteristic, complemented
8C23×C4×D17C2211yescharacteristic
9C22×#63223C2211yescharacteristic
10C22×#63218—21no—
11C2×M16×D17—22no—
12C2×M16×D17—22no—
13C2×M16×D17—22no—
14C2×M16×D17—22no—
15C2×M16×D17—22no—
16C2×M16×D17C414yescomplemented
17C22×C8×D17—21no—
18C2×#10587612C2211yescharacteristic
19C22×#63227—21no—
20C22×C4×Dic17C2211yescharacteristic
21#11762670—21no—
22#11762666C412yescomplemented
23#11762666C412yescomplemented
24#11762664—21no—
25C4×#63227—22no—
26C4×#63227—21no—
27C4×#63227—21no—
28C4×#63227C414yescomplemented
29C2×#10587502—21no—
30#11762570—22no—
31#11762569—22no—
32#11762568—22no—
33C22×M16×C17C2211yescharacteristic
34C2×C17×#117C2211yescharacteristic
35C22×C42×C17C2211yescharacteristic
36C17×#339—22no—
37C24×D17D411yescharacteristic
38C23×C4×C17—21no—
39C23×C4×C17C2311yescharacteristic
40C23×Dic17—21no—
41C23×Dic17D411yescharacteristic
42C22×C4×D17—21no—
43C22×C4×D17—21no—
44C22×C4×D17—21no—
45C22×C4×D17—21no—
46C22×C4×D17—21no—
47C22×C4×D17—21no—
48C22×C4×D17—21no—
49C22×C4×D17—21no—
50C22×C4×D17C2×C412yes—
51C22×C4×D17C2×C412yes—
52C22×C4×D17C2×C411yescharacteristic
53C22×C4×D17C2×C411yescharacteristic
54C22×C4×D17D411yescharacteristic
55C22×C4×D17D412yes—
56C22×C4×D17D411yescharacteristic
57C22×C4×D17Q812yes—
58C2×M16×C17—21no—
59C2×M16×C17—21no—
60C2×M16×C17—21no—
61C2×M16×C17C2×C412yes—
62C2×M16×C17D412yes—
63C2×M16×C17D412yes—
64C22×C8×C17—21no—
65C17×#117—21no—
66C17×#117—21no—
67C17×#117—21no—
68C17×#117—21no—
69C2×C4⋊C4×C17C2×C412yes—
70C2×C22⋊C4×C17—21no—
71C2×C42×C17—21no—
72C2×C42×C17—21no—
73C2×C42×C17—21no—
74C2×C42×C17—21no—
75C2×C42×C17—21no—
76C2×C42×C17—21no—
77C2×C42×C17C2×C412yes—
78C2×C22⋊Dic17—21no—
79C2×#63227—28no—
80C2×#63227—24no—
81C2×#63227—22no—
82C2×#63227—22no—
83#10587612—21no—
84#10587612—21no—
85#10587612—21no—
86#10587612—21no—
87C2×C4⋊Dic17C2×C412yes—
88C2×C4×Dic17—21no—
89C2×C4×Dic17—21no—
90C2×C4×Dic17—21no—
91C2×C4×Dic17—21no—
92C2×C4×Dic17—21no—
93C2×C4×Dic17—21no—
94C2×C4×Dic17C2×C412yes—
95C2×#63223—21no—
96C2×#63223—21no—
97C2×#63223—21no—
98C2×#63223C2×C412yes—
99C2×#63223D412yes—
100C2×#63223D412yes—
101C22×#3622—21no—
102M16×D17—28no—
103M16×D17—28no—
104M16×D17—28no—
105M16×D17—28no—
106C2×#63218—24no—
107C2×#63218—24no—
108C2×#63218—24no—
109C2×C8×D17—24no—
110C2×C8×D17—24no—
111C2×C8×D17—24no—
112#10587502—24no—
113#10587502—22no—
114#10587502—22no—
115C24×C17C2×D411yescharacteristic
116C23×D17—21no—
117C23×D17—21no—
118C23×D17—21no—
119C23×D17—21no—
120C23×D17—24no—
121C23×D17—42no—
122C23×D17C22⋊C411yescharacteristic
123C23×D17C22⋊C412yes—
124C23×D17C22⋊C411yescharacteristic
125C23×D17C4⋊C412yes—
126C22×C4×C17—24no—
127C22×C4×C17—22no—
128C22×C4×C17—22no—
129C22×C4×C17—42no—
130C22×C4×C17—41no—
131C22×C4×C17—41no—
132C22×C4×C17C22×C411yescharacteristic
133C22×C4×C17C22×C411yescharacteristic
134C22×C4×C17C22×C411yescharacteristic
135C22×C4×C17C2×D411yescharacteristic
136C22×C4×C17C2×D411yescharacteristic
137C22×C4×C17C2×D411yescharacteristic
138C22×C4×C17C2×D411yescharacteristic
139C22×C4×C17C2×D411yescharacteristic
140C22×C4×C17C2×D411yescharacteristic
141C22×C4×C17C2×Q811yescharacteristic
142C22×C4×C17#4111yescharacteristic
143C22×C4×C17#4111yescharacteristic
144C22×C4×C17#4111yescharacteristic
145C22×C4×C17#4111yescharacteristic
146C22×Dic17—21no—
147C22×Dic17—21no—
148C22×Dic17—21no—
149C22×Dic17—21no—
150C22×Dic17—24no—
151C22×Dic17—22no—
152C22×Dic17—22no—
153C22×Dic17—42no—
154C22×Dic17—41no—
155C22×Dic17—41no—
156C22×Dic17C22⋊C412yes—
157C22×Dic17C22⋊C411yescharacteristic
158C22×Dic17C22⋊C411yescharacteristic
159C22×Dic17C4⋊C412yes—
160C2×C4×D17—22no—
161C2×C4×D17—22no—
162C2×C4×D17—22no—
163C2×C4×D17—22no—
164C2×C4×D17—22no—
165C2×C4×D17—21no—
166C2×C4×D17—21no—
167C2×C4×D17—22no—
168C2×C4×D17—21no—
169C2×C4×D17—21no—
170C2×C4×D17—22no—
171C2×C4×D17—21no—
172C2×C4×D17—21no—
173C2×C4×D17—22no—
174C2×C4×D17—21no—
175C2×C4×D17—21no—
176C2×C4×D17—21no—
177C2×C4×D17—21no—
178C2×C4×D17—21no—
179C2×C4×D17—21no—
180C2×C4×D17—22no—
181C2×C4×D17—22no—
182C2×C4×D17—22no—
183C2×C4×D17—22no—
184C2×C4×D17—22no—
185C2×C4×D17—22no—
186C2×C4×D17—21no—
187C2×C4×D17—22no—
188C2×C4×D17—21no—
189C2×C4×D17—21no—
190C2×C4×D17—22no—
191C2×C4×D17—21no—
192C2×C4×D17C4212yes—
193C2×C4×D17C4212yes—
194C2×C4×D17C22⋊C412yes—
195C2×C4×D17C22⋊C412yes—
196C2×C4×D17C4⋊C412yes—
197C2×C4×D17C4⋊C412yes—
198C2×C4×D17C4⋊C412yes—
199C2×C4×D17C4⋊C412yes—
200M16×C17—22no—
201M16×C17—22no—
202M16×C17—22no—
203M16×C17C22⋊C414yescomplemented
204C2×C8×C17—22no—
205C2×C8×C17—22no—
206C2×C8×C17—22no—
207C4⋊C4×C17—22no—
208C4⋊C4×C17—22no—
209C22⋊C4×C17—41no—
210C22⋊C4×C17—41no—
211C42×C17—22no—
212C42×C17—22no—
213C42×C17—41no—
214C42×C17—41no—
215C42×C17—41no—
216C42×C17—41no—
217C22⋊Dic17—41no—
218C22⋊Dic17—41no—
219#63227—216no—
220#63227—44no—
221#63227—44no—
222C4⋊Dic17—22no—
223C4⋊Dic17—22no—
224C4×Dic17—22no—
225C4×Dic17—22no—
226C4×Dic17—41no—
227C4×Dic17—41no—
228C4×Dic17—41no—
229C4×Dic17—41no—
230#63223—22no—
231#63223—22no—
232#63223—22no—
233#63223C22⋊C414yescomplemented
234C2×#3622—22no—
235C2×#3622—22no—
236C2×#3622—22no—
237#63218—216no—
238C8×D17—216no—
239#10732—171nomaximal, Sylow
240C23×C17—22no—
241C23×C17—22no—
242C23×C17C2×C22⋊C411yescharacteristic
243C23×C17C2×C22⋊C411yescharacteristic
244C23×C17C2×C4⋊C411yescharacteristic
245C23×C17#12111yescharacteristic
246C23×C17#12111yescharacteristic
247C23×C17#12111yescharacteristic
248C23×C17#12111yescharacteristic
249C22×D17—21no—
250C22×D17—21no—
251C22×D17—22no—
252C22×D17—22no—
253C22×D17—22no—
254C22×D17—22no—
255C22×D17—21no—
256C22×D17—22no—
257C22×D17—21no—
258C22×D17—22no—
259C22×D17—22no—
260C22×D17—24no—
261C22×D17—24no—
262C22×D17—42no—
263C22×D17—42no—
264C22×D17—44no—
265C22×D17—44no—
266C22×D17—44no—
267C22×D17—44no—
268C22×D17#9512yes—
269C22×D17#9512yes—
270C22×D17#10414yes—
271C2×C4×C17—24no—
272C2×C4×C17—44no—
273C2×C4×C17—44no—
274C2×C4×C17—42no—
275C2×C4×C17—42no—
276C2×C4×C17—42no—
277C2×C4×C17—42no—
278C2×C4×C17—42no—
279C2×C4×C17C2×C4211yescharacteristic
280C2×C4×C17C2×C22⋊C411yescharacteristic
281C2×C4×C17C2×C22⋊C411yescharacteristic
282C2×C4×C17C2×C22⋊C411yescharacteristic
283C2×C4×C17C2×C4⋊C411yescharacteristic
284C2×C4×C17C2×C4⋊C411yescharacteristic
285C2×C4×C17#11711yescharacteristic
286C2×C4×C17#11711yescharacteristic
287C2×C4×C17C4×D411yescharacteristic
288C2×C4×C17C4×D411yescharacteristic
289C2×C4×C17C4×D411yescharacteristic
290C2×C4×C17C4×D411yescharacteristic
291C2×C4×C17C4×D411yescharacteristic
292C2×C4×C17C4×D411yescharacteristic
293C2×C4×C17C4×D411yescharacteristic
294C2×C4×C17C4×D411yescharacteristic
295C2×C4×C17#12011yescharacteristic
296C2×C4×C17#12011yescharacteristic
297C2×C4×C17#12011yescharacteristic
298C2×C4×C17#12011yescharacteristic
299C2×C4×C17C22⋊Q811yescharacteristic
300C2×C4×C17C22⋊Q811yescharacteristic
301C2×C4×C17C22⋊Q811yescharacteristic
302C2×C4×C17C22⋊Q811yescharacteristic
303C2×C4×C17#12311yescharacteristic
304C2×C4×C17#12311yescharacteristic
305C2×C4×C17#12311yescharacteristic
306C2×C4×C17#12311yescharacteristic
307C2×Dic17—22no—
308C2×Dic17—22no—
309C2×Dic17—22no—
310C2×Dic17—21no—
311C2×Dic17—21no—
312C2×Dic17—22no—
313C2×Dic17—21no—
314C2×Dic17—21no—
315C2×Dic17—24no—
316C2×Dic17—44no—
317C2×Dic17—44no—
318C2×Dic17—42no—
319C2×Dic17—42no—
320C2×Dic17—42no—
321C2×Dic17—42no—
322C2×Dic17—42no—
323C2×Dic17#9512yes—
324C2×Dic17#9512yes—
325C4×D17—22no—
326C4×D17—22no—
327C4×D17—22no—
328C4×D17—22no—
329C4×D17—22no—
330C4×D17—22no—
331C4×D17—22no—
332C4×D17—22no—
333C4×D17—22no—
334C4×D17—22no—
335C4×D17—22no—
336C4×D17—22no—
337C4×D17—22no—
338C4×D17—22no—
339C4×D17—22no—
340C4×D17—22no—
341C8×C17—24no—
342#3622—24no—
343C23×M16—171no—
344#2280—171no—
345C2×C4×C22⋊C4—171no—
346C2×#339—171no—
347C2×#339—171no—
348C2×#339—171no—
349C2×#339D1711yescharacteristic, complemented
350C22×C17—22no—
351C22×C17—22no—
352C22×C17—22no—
353C22×C17—22no—
354C22×C17—21no—
355C22×C17—21no—
356C22×C17—21no—
357C22×C17—21no—
358C22×C17C2×#9511yescharacteristic
359C22×C17#38011yescharacteristic
360C22×C17#38011yescharacteristic
361C22×C17#38611yescharacteristic
362C22×C17#38611yescharacteristic
363C22×C17#38611yescharacteristic
364C22×C17#38611yescharacteristic
365C22×C17C2×#10412yes—
366C22×C17#42112yes—
367C2×D17—24no—
368C2×D17—24no—
369C2×D17—22no—
370C2×D17—22no—
371C2×D17—22no—
372C2×D17—22no—
373C2×D17—22no—
374C2×D17—44no—
375C2×D17—44no—
376C2×D17—44no—
377C2×D17—44no—
378C2×D17—42no—
379C2×D17—42no—
380C2×D17#33914yescomplemented
381C4×C17—44no—
382C4×C17—82no—
383C4×C17C4×C22⋊C411yescharacteristic
384C4×C17C4×C22⋊C411yescharacteristic
385C4×C17#37911yescharacteristic
386C4×C17#38111yescharacteristic
387C4×C17#38511yescharacteristic
388C4×C17#38511yescharacteristic
389C4×C17#38511yescharacteristic
390C4×C17#38511yescharacteristic
391Dic17—22no—
392Dic17—22no—
393Dic17—44no—
394Dic17—82no—
395C24×C4—171no—
396C22×M16—171no—
397C22×M16—174no—
398C22×M16—341no—
399C22×M16—342no—
400C22×M16—342no—
401C22×M16—342no—
402C22×M16—342no—
403C22×M16—342no—
404C22×M16C2×D1711yescharacteristic
405C23×C8—341no—
406C2×#117—171no—
407C2×#117C2×D1711yescharacteristic
408C22×C22⋊C4—341no—
409C22×C42—171no—
410C22×C42C2×D1711yescharacteristic
411#381—341no—
412#380—172no—
413#380—172no—
414#379—341no—
415C4×C22⋊C4—174no—
416C4×C22⋊C4—342no—
417C4×C22⋊C4—341no—
418C4×C22⋊C4—341no—
419C2×#95—341no—
420#339—22no—
421#339—342no—
422#339—342no—
423#339—342no—
424C2×C17—21no—
425C2×C17—21no—
426C2×C17—21no—
427C2×C17—21no—
428C2×C17C22⋊#9511yescharacteristic
429C2×C17C2×#33911yescharacteristic
430C2×C17#173311yescharacteristic
431C2×C17#187112yes—
432C2×C17#187112yes—
433D17—24no—
434D17—42no—
435C25—171no—
436C23×C4—21no—
437C23×C4—171no—
438C23×C4—172no—
439C23×C4—172no—
440C23×C4—171no—
441C23×C4—171no—
442C23×C4—172no—
443C23×C4—171no—
444C23×C4—171no—
445C23×C4—172no—
446C23×C4—341no—
447C23×C4—341no—
448C23×C4—341no—
449C23×C4—341no—
450C23×C4—341no—
451C23×C4—341no—
452C23×C4—341no—
453C23×C4—341no—
454C23×C4—341no—
455C23×C4C22×D1711yescharacteristic
456C2×M16—21no—
457C2×M16—21no—
458C2×M16—21no—
459C2×M16—172no—
460C2×M16—172no—
461C2×M16—172no—
462C2×M16—344no—
463C2×M16—344no—
464C2×M16—344no—
465C2×M16—348no—
466C2×M16—348no—
467C2×M16—348no—
468C2×M16—341no—
469C2×M16—341no—
470C2×M16—341no—
471C2×M16—348no—
472C2×M16C4×D1712yes—
473C2×M16D6812yes—
474C2×M16C22⋊D1712yes—
475C22×C8—21no—
476C22×C8—344no—
477C22×C8—344no—
478C22×C8—344no—
479C22×C8—341no—
480#117—21no—
481#117—21no—
482#117—21no—
483#117—21no—
484#117—341no—
485#117—341no—
486#117—341no—
487#117—341no—
488C2×C4⋊C4—172no—
489C2×C4⋊C4C4×D1712yes—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—344no—
492C2×C22⋊C4—348no—
493C2×C22⋊C4—342no—
494C2×C22⋊C4—342no—
495C2×C22⋊C4—341no—
496C2×C42—21no—
497C2×C42—21no—
498C2×C42—21no—
499C2×C42—21no—
500C2×C42—21no—
501C2×C42—21no—
502C2×C42—172no—
503C2×C42—341no—
504C2×C42—341no—
505C2×C42—341no—
506C2×C42—341no—
507C2×C42—341no—
508C2×C42—341no—
509C2×C42C4×D1712yes—
510#95—344no—
511#95—342no—
512#95—342no—
513C17#1073211yescharacteristic, complemented, Sylow
514C24—171no—
515C24—171no—
516C24—172no—
517C24—172no—
518C24—344no—
519C24—341no—
520C24—341no—
521C24—341no—
522C24—341no—
523C24—682no—
524C24D4×D1711yescharacteristic
525C22×C4—24no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—42no—
529C22×C4—41no—
530C22×C4—41no—
531C22×C4—172no—
532C22×C4—171no—
533C22×C4—171no—
534C22×C4—172no—
535C22×C4—172no—
536C22×C4—172no—
537C22×C4—172no—
538C22×C4—172no—
539C22×C4—172no—
540C22×C4—172no—
541C22×C4—172no—
542C22×C4—172no—
543C22×C4—341no—
544C22×C4—341no—
545C22×C4—341no—
546C22×C4—341no—
547C22×C4—342no—
548C22×C4—342no—
549C22×C4—341no—
550C22×C4—341no—
551C22×C4—342no—
552C22×C4—342no—
553C22×C4—341no—
554C22×C4—341no—
555C22×C4—341no—
556C22×C4—342no—
557C22×C4—341no—
558C22×C4—342no—
559C22×C4—341no—
560C22×C4—341no—
561C22×C4—342no—
562C22×C4—342no—
563C22×C4—341no—
564C22×C4—341no—
565C22×C4—342no—
566C22×C4—341no—
567C22×C4—341no—
568C22×C4—342no—
569C22×C4—342no—
570C22×C4—342no—
571C22×C4—342no—
572C22×C4—342no—
573C22×C4—341no—
574C22×C4—341no—
575C22×C4—341no—
576C22×C4—342no—
577C22×C4—341no—
578C22×C4—342no—
579C22×C4—344no—
580C22×C4—342no—
581C22×C4—342no—
582C22×C4—682no—
583C22×C4—681no—
584C22×C4—681no—
585C22×C4C2×C4×D1711yescharacteristic
586C22×C4C2×C4×D1711yescharacteristic
587C22×C4C2×C4×D1711yescharacteristic
588C22×C4C2×D6811yescharacteristic
589C22×C4#6325211yescharacteristic
590C22×C4#6325211yescharacteristic
591C22×C4D4×D1711yescharacteristic
592C22×C4D4×D1711yescharacteristic
593C22×C4D4×D1711yescharacteristic
594C22×C4D4×D1711yescharacteristic
595C22×C4#6325411yescharacteristic
596C22×C4Q8×D1711yescharacteristic
597C22×C4#6325611yescharacteristic
598C22×C4C2×C22⋊D1711yescharacteristic
599M16—22no—
600M16—22no—
601M16—22no—
602M16—174no—
603M16—3416no—
604M16—342no—
605M16—342no—
606M16—342no—
607M16#6322714yescomplemented
608C2×C8—22no—
609C2×C8—22no—
610C2×C8—22no—
611C2×C8—3416no—
612C2×C8—342no—
613C2×C8—342no—
614C2×C8—342no—
615C4⋊C4—22no—
616C4⋊C4—22no—
617C4⋊C4—342no—
618C4⋊C4—342no—
619C22⋊C4—41no—
620C22⋊C4—41no—
621C22⋊C4—3416no—
622C22⋊C4—684no—
623C22⋊C4—684no—
624C22⋊C4—681no—
625C22⋊C4—681no—
626C42—22no—
627C42—22no—
628C42—41no—
629C42—41no—
630C42—41no—
631C42—41no—
632C42—342no—
633C42—342no—
634C42—681no—
635C42—681no—
636C42—681no—
637C42—681no—
638C23—22no—
639C23—22no—
640C23—174no—
641C23—172no—
642C23—172no—
643C23—344no—
644C23—344no—
645C23—342no—
646C23—341no—
647C23—341no—
648C23—342no—
649C23—342no—
650C23—342no—
651C23—342no—
652C23—342no—
653C23—341no—
654C23—342no—
655C23—341no—
656C23—682no—
657C23—682no—
658C23—684no—
659C23—684no—
660C23—684no—
661C23—684no—
662C23C22⋊C4×D1711yescharacteristic
663C23C22⋊C4×D1711yescharacteristic
664C23#1058757011yescharacteristic
665C23#1058757011yescharacteristic
666C23C4⋊C4×D1711yescharacteristic
667C23#1058758111yescharacteristic
668C23#1058762411yescharacteristic
669C2×C4—24no—
670C2×C4—44no—
671C2×C4—44no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—172no—
678C2×C4—172no—
679C2×C4—342no—
680C2×C4—342no—
681C2×C4—342no—
682C2×C4—341no—
683C2×C4—341no—
684C2×C4—342no—
685C2×C4—341no—
686C2×C4—341no—
687C2×C4—342no—
688C2×C4—342no—
689C2×C4—342no—
690C2×C4—342no—
691C2×C4—342no—
692C2×C4—342no—
693C2×C4—342no—
694C2×C4—342no—
695C2×C4—342no—
696C2×C4—342no—
697C2×C4—342no—
698C2×C4—342no—
699C2×C4—342no—
700C2×C4—342no—
701C2×C4—342no—
702C2×C4—342no—
703C2×C4—344no—
704C2×C4—684no—
705C2×C4—684no—
706C2×C4—682no—
707C2×C4—682no—
708C2×C4—682no—
709C2×C4—682no—
710C2×C4—682no—
711C2×C4C42×D1711yescharacteristic
712C2×C4#1058755811yescharacteristic
713C2×C4C4×D6811yescharacteristic
714C2×C4C4×D6811yescharacteristic
715C2×C4C22⋊C4×D1711yescharacteristic
716C2×C4C22⋊C4×D1711yescharacteristic
717C2×C4#1058756711yescharacteristic
718C2×C4#1058756711yescharacteristic
719C2×C4#1058756811yescharacteristic
720C2×C4#1058756811yescharacteristic
721C2×C4#1058756911yescharacteristic
722C2×C4#1058756911yescharacteristic
723C2×C4C4⋊C4×D1711yescharacteristic
724C2×C4C4⋊C4×D1711yescharacteristic
725C2×C4#1058757811yescharacteristic
726C2×C4#1058757911yescharacteristic
727C2×C4#1058757911yescharacteristic
728C2×C4#1058758011yescharacteristic
729C2×C4#1058758011yescharacteristic
730C2×C4#1058758211yescharacteristic
731C2×C4#1058758211yescharacteristic
732C2×C4#1058758311yescharacteristic
733C2×C4C2×#6322711yescharacteristic
734C2×C4C4×C22⋊D1711yescharacteristic
735C2×C4C4×C22⋊D1711yescharacteristic
736C2×C4#1058762311yescharacteristic
737C2×C4#1058762311yescharacteristic
738C2×C4#1058763211yescharacteristic
739C8—24no—
740C8—344no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—21no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—174no—
750C22—342no—
751C22—344no—
752C22—344no—
753C22—342no—
754C22—342no—
755C22—342no—
756C22—342no—
757C22—684no—
758C22—684no—
759C22—684no—
760C22—684no—
761C22—682no—
762C22—682no—
763C22#95×D1711yescharacteristic
764C22#1176266611yescharacteristic
765C22#1176266811yescharacteristic
766C22#1176268511yescharacteristic
767C22#1176268511yescharacteristic
768C22#1176268711yescharacteristic
769C22#1176268711yescharacteristic
770C22#104×D1712yes—
771C22#1176282412yes—
772C4—44no—
773C4—82no—
774C4—342no—
775C4—342no—
776C4—684no—
777C4—1362no—
778C4#1176265611yescharacteristic
779C4C4×#6322711yescharacteristic
780C4#1176266411yescharacteristic
781C4#1176267111yescharacteristic
782C4#1176268011yescharacteristic
783C4#1176268011yescharacteristic
784C4#1176268311yescharacteristic
785C4#1176268311yescharacteristic
786C2—21no—
787C2—21no—
788C2—21no—
789C2—21no—
790C2—344no—
791C2—682no—
792C2#1452700511yescharacteristic
793C2D17×#33911yescharacteristic
794C2#1452849211yescharacteristic
795C2#1452908312yes—
796C2#1452908512yes—
subgroupG/H
centerC22×C4D4×D17
commutatorC2×C4×C17C2×C42
FrattiniC23×C4C22×D17
FittingC2×C17×#339C2
socleC23×C17C2×C22⋊C4
prime radicalC24×D17D4
cosocleC23×C4×C17C23
hypercenterC2×#339D17
hypocenterC17#10732
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#339

Complements

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

NH ≅ G/Ntype
4. C2×#11762570C2semidirect
5. C2×#11762569C2semidirect
6. C2×#11762568C2semidirect
7. C2×C17×#339C2semidirect
16. C2×M16×D17C4semidirect
22. #11762666C4semidirect
23. #11762666C4semidirect
28. C4×#63227C4semidirect
203. M16×C17C22⋊C4semidirect
233. #63223C22⋊C4semidirect
349. C2×#339D17semidirect
380. C2×D17#339semidirect
513. C17#10732semidirect
607. M16#63227semidirect

Maximal subgroups

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

subgroupindex
C22×M16×D172
#145311632
C2×C4×#632272
C2×#117625702
C2×#117625692
C2×#117625682
C2×C17×#3392
#1073217