Finite Group Databasebeta

← #16960686

Subgroups — #16960686

Order 4352.

2554 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587580C211yesmaximal, characteristic
2C22×C4⋊C4×D17C211yesmaximal, characteristic, complemented
3C2×#11762687C212yesmaximal
4C2×#11762671C211yesmaximal, characteristic, complemented
5#14527037C211yesmaximal, characteristic, complemented
6#14527035C212yesmaximal, complemented
7#14527030C211yesmaximal, characteristic, complemented
8#14527028C212yesmaximal, complemented
9#14527026C211yesmaximal, characteristic, complemented
10#14527005C212yesmaximal, complemented
11C17×#1441C211yesmaximal, characteristic, complemented
12C23×D68C2211yescharacteristic
13C23×C4×D17C2211yescharacteristic
14C23×C4×D17C2212yes—
15C2×#10587580—24no—
16C2×#10587580—24no—
17C2×#10587580C418yescomplemented
18C22×C4⋊Dic17C2211yescharacteristic
19C22×#63225C2212yes—
20C22×#63225C2211yescharacteristic
21C2×C4⋊C4×D17—28no—
22C2×C4⋊C4×D17—24no—
23C22×#63227C2212yes—
24C22×#63227C2211yescharacteristic
25C22×#63227C2211yescharacteristic
26C22×#63227C2211yescharacteristic
27C22×#63227C2212yes—
28C22×#63227C2212yes—
29#11762687—28no—
30#11762671—24no—
31C2×#10587502C2211yescharacteristic
32C2×#10587502C2212yes—
33C2×#10587502C2212yes—
34C2×#10587502C2212yes—
35C2×#10587502C2212yes—
36C2×#10587502C2212yes—
37C22×C4⋊C4×C17C2211yescharacteristic
38C22×C4⋊C4×C17C2211yescharacteristic
39C2×C17×#95C2211yescharacteristic
40C2×C17×#95C2212yes—
41C2×C17×#95C2212yes—
42C24×D17C2311yescharacteristic
43C24×D17C2311yescharacteristic
44C23×C4×C17C2312yes—
45C23×C4×C17C2311yescharacteristic
46C23×C4×C17C2311yescharacteristic
47C23×C4×C17C2312yes—
48C23×C4×C17C2311yescharacteristic
49C23×Dic17C2312yes—
50C23×Dic17C2311yescharacteristic
51C23×Dic17C2312yes—
52C23×Dic17C2311yescharacteristic
53C22×D68—22no—
54C22×D68—22no—
55C22×D68—24no—
56C22×D68—24no—
57C22×D68C2×C414yes—
58C22×C4×D17—24no—
59C22×C4×D17—24no—
60C22×C4×D17—24no—
61C22×C4×D17—24no—
62C22×C4×D17—42no—
63C22×C4×D17—42no—
64C22×C4×D17—42no—
65C22×C4×D17—42no—
66C22×C4×D17C2×C414yes—
67C22×C4×D17D414yes—
68C22×C4×D17D414yes—
69C22×C4×D17D418yes—
70C2×C4⋊C4×C17—24no—
71C2×C4⋊C4×C17—22no—
72C2×C4⋊C4×C17—22no—
73C2×C4⋊C4×C17—22no—
74C2×C4⋊C4×C17C2×C414yescomplemented
75C2×#63227—22no—
76C2×#63227—22no—
77C2×#63227—24no—
78C2×#63227—24no—
79C2×#63227—24no—
80C2×#63227—22no—
81C2×#63227—22no—
82C2×#63227—24no—
83C2×#63227—22no—
84C2×#63227—22no—
85C2×#63227—24no—
86C2×#63227—42no—
87C2×#63227—42no—
88C2×#63227—42no—
89C2×#63227—42no—
90C2×#63227C2×C414yes—
91C2×#63227C2×C414yescomplemented
92C2×#63227C2×C414yescomplemented
93C2×C4⋊Dic17—22no—
94C2×C4⋊Dic17—24no—
95C2×#63225—24no—
96C2×#63225—24no—
97C2×#63225—24no—
98C2×#63225—22no—
99C2×#63225—22no—
100C2×#63225C2×C414yescomplemented
101#10587580—232no—
102C4⋊C4×D17—232no—
103C17×#95—22no—
104C17×#95—24no—
105C17×#95—42no—
106#10587502—22no—
107#10587502—24no—
108#10587502—24no—
109#10587502—42no—
110#10587502—42no—
111#10587502—42no—
112C24×C17C2411yescharacteristic
113C23×D17—21no—
114C23×D17—21no—
115C23×D17—22no—
116C23×D17—21no—
117C23×D17—22no—
118C23×D17—21no—
119C23×D17—21no—
120C23×D17—21no—
121C23×D17—22no—
122C23×D17—22no—
123C23×D17—21no—
124C23×D17—21no—
125C23×D17—22no—
126C23×D17—21no—
127C23×D17—22no—
128C23×D17—21no—
129C23×D17C22×C412yes—
130C23×D17C22×C412yes—
131C23×D17C2×D412yes—
132C23×D17C2×D412yes—
133C23×D17C2×D414yes—
134C23×D17#4114yes—
135C22×C4×C17—22no—
136C22×C4×C17—22no—
137C22×C4×C17—22no—
138C22×C4×C17—22no—
139C22×C4×C17—22no—
140C22×C4×C17—21no—
141C22×C4×C17—21no—
142C22×C4×C17—21no—
143C22×C4×C17—21no—
144C22×C4×C17—22no—
145C22×C4×C17—22no—
146C22×C4×C17—22no—
147C22×C4×C17—22no—
148C22×C4×C17—22no—
149C22×C4×C17—21no—
150C22×C4×C17—21no—
151C22×C4×C17—21no—
152C22×C4×C17—21no—
153C22×C4×C17—22no—
154C22×C4×C17—22no—
155C22×C4×C17—22no—
156C22×C4×C17—22no—
157C22×C4×C17—22no—
158C22×C4×C17—22no—
159C22×C4×C17—22no—
160C22×C4×C17C22×C412yes—
161C22×C4×C17C22×C412yes—
162C22×C4×C17C22×C412yes—
163C22×C4×C17C2×D414yes—
164C22×C4×C17C2×D412yes—
165C22×C4×C17C2×D412yes—
166C22×Dic17—22no—
167C22×Dic17—22no—
168C22×Dic17—22no—
169C22×Dic17—22no—
170C22×Dic17—21no—
171C22×Dic17—21no—
172C22×Dic17—22no—
173C22×Dic17—22no—
174C22×Dic17—22no—
175C22×Dic17—22no—
176C22×Dic17—22no—
177C22×Dic17—22no—
178C22×Dic17—22no—
179C22×Dic17—22no—
180C22×Dic17—22no—
181C22×Dic17—22no—
182C22×Dic17—22no—
183C22×Dic17—22no—
184C22×Dic17—22no—
185C22×Dic17C22×C412yes—
186C22×Dic17C22×C412yes—
187C22×Dic17C2×D414yes—
188C22×Dic17C2×D412yes—
189C22×Dic17C2×D412yes—
190C2×D68—28no—
191C2×D68—216no—
192C2×D68—44no—
193C2×D68—48no—
194C2×D68—44no—
195C2×C4×D17—216no—
196C2×C4×D17—28no—
197C2×C4×D17—216no—
198C2×C4×D17—28no—
199C2×C4×D17—216no—
200C2×C4×D17—48no—
201C2×C4×D17—48no—
202C2×C4×D17—48no—
203C2×C4×D17—48no—
204C2×C4×D17—48no—
205C2×C4×D17—48no—
206C2×C4×D17C22⋊C4116yescomplemented
207C4⋊C4×C17—28no—
208C4⋊C4×C17—28no—
209#63227—28no—
210#63227—28no—
211#63227—28no—
212#63227—48no—
213#63227—48no—
214#63227—48no—
215C4⋊Dic17—28no—
216#63225—216no—
217#63225—28no—
218#14256—171nomaximal, Sylow
219C23×C17C23×C411yescharacteristic
220C23×C17C22×D411yescharacteristic
221C23×C17C22×D411yescharacteristic
222C23×C17C22×D412yes—
223C23×C17C2×#4112yes—
224C23×C17H(5,𝔽2)11yescharacteristic
225C23×C17H(5,𝔽2)11yescharacteristic
226C23×C17H(5,𝔽2)12yes—
227C23×C172−1+411yescharacteristic
228C23×C172−1+412yes—
229C23×C172−1+411yescharacteristic
230C22×D17—22no—
231C22×D17—22no—
232C22×D17—24no—
233C22×D17—24no—
234C22×D17—24no—
235C22×D17—22no—
236C22×D17—22no—
237C22×D17—22no—
238C22×D17—24no—
239C22×D17—22no—
240C22×D17—24no—
241C22×D17—22no—
242C22×D17—22no—
243C22×D17—24no—
244C22×D17—24no—
245C22×D17—24no—
246C22×D17—24no—
247C22×D17—24no—
248C22×D17—22no—
249C22×D17—24no—
250C22×D17—22no—
251C22×D17—22no—
252C22×D17—24no—
253C22×D17—41no—
254C22×D17—42no—
255C22×D17—41no—
256C22×D17—42no—
257C22×D17—42no—
258C22×D17—41no—
259C22×D17—41no—
260C22×D17—41no—
261C22×D17—42no—
262C22×D17—41no—
263C22×D17—42no—
264C22×D17—41no—
265C22×D17—41no—
266C22×D17—42no—
267C22×D17—42no—
268C22×D17—42no—
269C22×D17—42no—
270C22×D17—42no—
271C22×D17C2×C22⋊C414yes—
272C22×D17C4×D418yes—
273C22×D17#12014yes—
274C22×D17#12118yes—
275C22×D17#12314yes—
276C2×C4×C17—24no—
277C2×C4×C17—22no—
278C2×C4×C17—24no—
279C2×C4×C17—22no—
280C2×C4×C17—22no—
281C2×C4×C17—22no—
282C2×C4×C17—24no—
283C2×C4×C17—22no—
284C2×C4×C17—22no—
285C2×C4×C17—24no—
286C2×C4×C17—24no—
287C2×C4×C17—24no—
288C2×C4×C17—41no—
289C2×C4×C17—42no—
290C2×C4×C17—41no—
291C2×C4×C17—42no—
292C2×C4×C17—42no—
293C2×C4×C17—42no—
294C2×C4×C17—42no—
295C2×C4×C17—41no—
296C2×C4×C17—41no—
297C2×C4×C17—41no—
298C2×C4×C17—41no—
299C2×C4×C17—42no—
300C2×C4×C17—42no—
301C2×C4×C17—42no—
302C2×C4×C17—42no—
303C2×C4×C17—42no—
304C2×C4×C17—42no—
305C2×C4×C17—42no—
306C2×C4×C17C2×C22⋊C414yes—
307C2×Dic17—24no—
308C2×Dic17—22no—
309C2×Dic17—24no—
310C2×Dic17—22no—
311C2×Dic17—22no—
312C2×Dic17—24no—
313C2×Dic17—24no—
314C2×Dic17—24no—
315C2×Dic17—24no—
316C2×Dic17—42no—
317C2×Dic17—42no—
318C2×Dic17—42no—
319C2×Dic17—42no—
320C2×Dic17—41no—
321C2×Dic17—41no—
322C2×Dic17—42no—
323C2×Dic17—42no—
324C2×Dic17—42no—
325C2×Dic17—42no—
326C2×Dic17—42no—
327C2×Dic17—42no—
328C2×Dic17—42no—
329C2×Dic17—42no—
330C2×Dic17C2×C22⋊C414yes—
331D68—416no—
332C4×D17—232no—
333C4×D17—432no—
334C22×#123—171no—
335C23×C4⋊C4—171no—
336C2×#386—172no—
337C2×#381—171no—
338#1441—172no—
339#1441—171no—
340#1441D1711yescharacteristic, complemented
341#1439—172no—
342#1439—171no—
343#1439—171no—
344C22⋊#95—172no—
345C22×C17C22×C22⋊C411yescharacteristic
346C22×C17C2×C4×D412yes—
347C22×C17#52011yescharacteristic
348C22×C17#52011yescharacteristic
349C22×C17#52012yes—
350C22×C17C2×#12011yescharacteristic
351C22×C17C2×#12112yes—
352C22×C17C2×#12311yescharacteristic
353C22×C17#53412yes—
354C22×C17#53412yes—
355C22×C17#53511yescharacteristic
356C22×C17#53511yescharacteristic
357C22×C17#53611yescharacteristic
358C22×C17#53612yes—
359C22×C17#53611yescharacteristic
360C22×C17#53612yes—
361C22×C17#53711yescharacteristic
362C22×C17#53711yescharacteristic
363C22×C17#53712yes—
364C22×C17#53912yes—
365C22×C17#53912yes—
366C22×C17#53912yes—
367C22×C17#53912yes—
368C2×D17—24no—
369C2×D17—24no—
370C2×D17—28no—
371C2×D17—28no—
372C2×D17—24no—
373C2×D17—24no—
374C2×D17—28no—
375C2×D17—28no—
376C2×D17—24no—
377C2×D17—24no—
378C2×D17—42no—
379C2×D17—42no—
380C2×D17—44no—
381C2×D17—44no—
382C2×D17—42no—
383C2×D17—81no—
384C2×D17—81no—
385C2×D17—82no—
386C2×D17—82no—
387C2×D17—81no—
388C2×D17—81no—
389C2×D17#38618yes—
390C4×C17—24no—
391C4×C17—42no—
392C4×C17—44no—
393C4×C17—42no—
394C4×C17—82no—
395Dic17—24no—
396Dic17—42no—
397Dic17—44no—
398Dic17—82no—
399C23×D4—171no—
400C24×C4—171no—
401C24×C4—172no—
402C2×#123—178no—
403C2×#123—344no—
404C2×#123—344no—
405C22×C4⋊C4—171no—
406C22×C4⋊C4—172no—
407C22×C4⋊C4—171no—
408C22×C4⋊C4—344no—
409C22×C4⋊C4—348no—
410C22×C4⋊C4C2×D1711yescharacteristic
411C22×C4⋊C4C2×D1711yescharacteristic
412C22×C22⋊C4—171no—
413C22×C22⋊C4—171no—
414C22×C22⋊C4—171no—
415C22×C22⋊C4—172no—
416C22×C22⋊C4—172no—
417C22×C22⋊C4—172no—
418#386—348no—
419#381—344no—
420C2×#95—172no—
421C2×#95—171no—
422C2×#95—172no—
423C2×#95—172no—
424C2×#95—172no—
425C2×#95—172no—
426C2×#95C2×D1711yescharacteristic
427C2×#95C2×D1712yes—
428C2×#95C2×D1712yes—
429C2×C17C2×#38611yescharacteristic
430C2×C17#231111yescharacteristic
431C2×C17#231111yescharacteristic
432C2×C17#232212yes—
433C2×C17#232212yes—
434C2×C17#261311yescharacteristic
435C2×C17#261411yescharacteristic
436C2×C17#261812yes—
437C2×C17#261812yes—
438C2×C17#262311yescharacteristic
439C2×C17#262311yescharacteristic
440D17—28no—
441D17—82no—
442C25—171no—
443C25—171no—
444C22×D4—174no—
445C22×D4—342no—
446C22×D4—342no—
447C22×D4—344no—
448C22×D4—344no—
449C23×C4—171no—
450C23×C4—174no—
451C23×C4—174no—
452C23×C4—174no—
453C23×C4—171no—
454C23×C4—172no—
455C23×C4—178no—
456C23×C4—172no—
457C23×C4—344no—
458C23×C4—344no—
459C23×C4—344no—
460C23×C4—344no—
461C23×C4—682no—
462C23×C4—682no—
463C23×C4—682no—
464C23×C4—682no—
465C23×C4C22×D1712yes—
466C23×C4C22×D1711yescharacteristic
467C23×C4C22×D1711yescharacteristic
468C23×C4C22×D1712yes—
469C23×C4C22×D1711yescharacteristic
470#123—3432no—
471C2×C4⋊C4—24no—
472C2×C4⋊C4—22no—
473C2×C4⋊C4—22no—
474C2×C4⋊C4—22no—
475C2×C4⋊C4—174no—
476C2×C4⋊C4—3432no—
477C2×C4⋊C4—344no—
478C2×C4⋊C4—344no—
479C2×C4⋊C4—344no—
480C2×C4⋊C4—342no—
481C2×C4⋊C4—342no—
482C2×C4⋊C4—344no—
483C2×C4⋊C4—342no—
484C2×C4⋊C4C4×D1714yescomplemented
485C2×C22⋊C4—174no—
486C2×C22⋊C4—174no—
487C2×C22⋊C4—174no—
488C2×C22⋊C4—342no—
489C2×C22⋊C4—342no—
490C2×C22⋊C4—342no—
491C2×C22⋊C4—342no—
492C2×C22⋊C4—342no—
493C2×C22⋊C4—342no—
494C2×C22⋊C4—344no—
495C2×C22⋊C4—344no—
496C2×C22⋊C4—344no—
497C2×C22⋊C4—344no—
498C2×C22⋊C4—344no—
499C2×C22⋊C4—682no—
500C2×C22⋊C4—682no—
501C2×C22⋊C4—682no—
502C2×C22⋊C4—682no—
503#95—22no—
504#95—24no—
505#95—42no—
506#95—344no—
507#95—344no—
508#95—342no—
509#95—682no—
510#95—682no—
511#95—682no—
512C17#1425611yescharacteristic, complemented, Sylow
513C24—172no—
514C24—172no—
515C24—172no—
516C24—174no—
517C24—174no—
518C24—172no—
519C24—341no—
520C24—341no—
521C24—342no—
522C24—341no—
523C24—342no—
524C24—341no—
525C24—341no—
526C24—341no—
527C24—342no—
528C24—341no—
529C24—341no—
530C24—342no—
531C24—342no—
532C24—341no—
533C24—342no—
534C24—341no—
535C24C23×D1711yescharacteristic
536C2×D4—348no—
537C2×D4—3416no—
538C2×D4—684no—
539C2×D4—688no—
540C2×D4—684no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—22no—
552C22×C4—21no—
553C22×C4—22no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—21no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—172no—
567C22×C4—172no—
568C22×C4—172no—
569C22×C4—1716no—
570C22×C4—172no—
571C22×C4—174no—
572C22×C4—348no—
573C22×C4—3416no—
574C22×C4—3416no—
575C22×C4—348no—
576C22×C4—3416no—
577C22×C4—342no—
578C22×C4—342no—
579C22×C4—341no—
580C22×C4—341no—
581C22×C4—342no—
582C22×C4—342no—
583C22×C4—342no—
584C22×C4—342no—
585C22×C4—342no—
586C22×C4—342no—
587C22×C4—342no—
588C22×C4—342no—
589C22×C4—342no—
590C22×C4—342no—
591C22×C4—342no—
592C22×C4—342no—
593C22×C4—342no—
594C22×C4—342no—
595C22×C4—342no—
596C22×C4—688no—
597C22×C4—688no—
598C22×C4—688no—
599C22×C4—688no—
600C22×C4—688no—
601C22×C4—688no—
602C22×C4C2×C4×D1712yes—
603C22×C4C2×C4×D1712yes—
604C22×C4C2×C4×D1712yes—
605C22×C4D4×D1714yes—
606C22×C4D4×D1712yes—
607C22×C4D4×D1712yes—
608C4⋊C4—28no—
609C4⋊C4—28no—
610C4⋊C4—348no—
611C4⋊C4—3416no—
612C4⋊C4—348no—
613C22⋊C4—348no—
614C22⋊C4—348no—
615C22⋊C4—348no—
616C22⋊C4—688no—
617C22⋊C4—688no—
618C22⋊C4—688no—
619C23—174no—
620C23—178no—
621C23—174no—
622C23—178no—
623C23—174no—
624C23—342no—
625C23—342no—
626C23—344no—
627C23—344no—
628C23—344no—
629C23—342no—
630C23—342no—
631C23—342no—
632C23—344no—
633C23—342no—
634C23—344no—
635C23—342no—
636C23—342no—
637C23—344no—
638C23—344no—
639C23—344no—
640C23—344no—
641C23—344no—
642C23—342no—
643C23—344no—
644C23—342no—
645C23—342no—
646C23—344no—
647C23—681no—
648C23—682no—
649C23—681no—
650C23—682no—
651C23—682no—
652C23—681no—
653C23—681no—
654C23—681no—
655C23—682no—
656C23—681no—
657C23—682no—
658C23—681no—
659C23—681no—
660C23—682no—
661C23—682no—
662C23—682no—
663C23—682no—
664C23—682no—
665C23C22×C4×D1711yescharacteristic
666C23C2×D4×D1711yescharacteristic
667C23C2×D4×D1711yescharacteristic
668C23C2×D4×D1712yes—
669C23#1058769111yescharacteristic
670C23#1058769411yescharacteristic
671C23#1058769412yes—
672C23#41×D1712yes—
673C23#1058769611yescharacteristic
674C23#1058769612yes—
675C23#1058769711yescharacteristic
676D4—6816no—
677C2×C4—24no—
678C2×C4—22no—
679C2×C4—24no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—24no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—41no—
690C2×C4—42no—
691C2×C4—41no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—41no—
696C2×C4—42no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—174no—
708C2×C4—3432no—
709C2×C4—344no—
710C2×C4—342no—
711C2×C4—344no—
712C2×C4—342no—
713C2×C4—342no—
714C2×C4—344no—
715C2×C4—344no—
716C2×C4—344no—
717C2×C4—344no—
718C2×C4—6832no—
719C2×C4—682no—
720C2×C4—682no—
721C2×C4—682no—
722C2×C4—682no—
723C2×C4—681no—
724C2×C4—681no—
725C2×C4—682no—
726C2×C4—682no—
727C2×C4—682no—
728C2×C4—682no—
729C2×C4—682no—
730C2×C4—682no—
731C2×C4—682no—
732C2×C4—682no—
733C2×C4C22⋊C4×D1714yes—
734C22—178no—
735C22—344no—
736C22—344no—
737C22—344no—
738C22—344no—
739C22—348no—
740C22—348no—
741C22—348no—
742C22—348no—
743C22—344no—
744C22—344no—
745C22—682no—
746C22—682no—
747C22—684no—
748C22—682no—
749C22—684no—
750C22—1361no—
751C22—1361no—
752C22—1362no—
753C22—1362no—
754C22—1361no—
755C22—1361no—
756C22C2×C22⋊C4×D1711yescharacteristic
757C22C4×D4×D1712yes—
758C22#1176328911yescharacteristic
759C22#1176329011yescharacteristic
760C22#1176329112yes—
761C22#120×D1711yescharacteristic
762C22#121×D1712yes—
763C22#123×D1711yescharacteristic
764C22#1176336712yes—
765C22#1176337012yes—
766C22#1176337511yescharacteristic
767C22#1176337711yescharacteristic
768C22#1176338211yescharacteristic
769C22#1176338212yes—
770C22#1176338411yescharacteristic
771C22#1176338412yes—
772C22#1176338811yescharacteristic
773C22#1176338911yescharacteristic
774C22#1176338912yes—
775C22#1176340012yes—
776C22#1176340512yes—
777C22#1176340712yes—
778C22#1176340712yes—
779C4—24no—
780C4—42no—
781C4—44no—
782C4—42no—
783C4—82no—
784C4—344no—
785C4—682no—
786C4—684no—
787C4—1362no—
788C2—348no—
789C2—1362no—
790C2D17×#38611yescharacteristic
791C2#1453137311yescharacteristic
792C2#1453137511yescharacteristic
793C2#1453144812yes—
794C2#1453145712yes—
795C2#1453449711yescharacteristic
796C2#1453450411yescharacteristic
797C2#1453452712yes—
798C2#1453453112yes—
799C2#1453456511yescharacteristic
800C2#1453457111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1441C2
socle, cosocleC24×C17C24
prime radicalC23×D68C22
hypercenter#1441D17
hypocenterC17#14256
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊C4×D17C2semidirect
4. C2×#11762671C2semidirect
5. #14527037C2semidirect
6. #14527035C2semidirect
7. #14527030C2semidirect
8. #14527028C2semidirect
9. #14527026C2semidirect
10. #14527005C2semidirect
11. C17×#1441C2semidirect
17. C2×#10587580C4semidirect
74. C2×C4⋊C4×C17C2×C4semidirect
91. C2×#63227C2×C4semidirect
92. C2×#63227C2×C4semidirect
100. C2×#63225C2×C4semidirect
206. C2×C4×D17C22⋊C4semidirect
340. #1441D17semidirect
484. C2×C4⋊C4C4×D17semidirect
512. C17#14256semidirect

Maximal subgroups

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

subgroupindex
C22×#105875802
C22×C4⋊C4×D172
C2×#117626872
C2×#117626712
#145270372
#145270352
#145270302
#145270282
#145270262
#145270052
C17×#14412
#1425617