Finite Group Databasebeta

← #16961076

Subgroups — #16961076

Order 4352.

2566 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×Dic17C211yesmaximal, characteristic, complemented
2C2×#11762702C211yesmaximal, characteristic, complemented
3C2×#11762689C212yesmaximal, complemented
4#14527041C211yesmaximal, characteristic, complemented
5#14527029C211yesmaximal, characteristic, complemented
6#14527029C212yesmaximal, complemented
7#14527025C212yesmaximal, complemented
8#14527025C211yesmaximal, characteristic, complemented
9#14527009C211yesmaximal, characteristic, complemented
10#14527006C212yesmaximal, complemented
11C2×C17×#392C211yesmaximal, characteristic
12C24×Dic17C2212yes—
13C2×D4×Dic17—24no—
14C2×D4×Dic17—28no—
15C22×C4⋊Dic17C2211yescharacteristic
16C22×C4⋊Dic17C2211yescharacteristic
17C22×C22⋊Dic17C2212yes—
18C22×C22⋊Dic17C2211yescharacteristic
19C22×C22⋊Dic17C2212yes—
20C22×C22⋊Dic17C2211yescharacteristic
21C22×C22⋊Dic17C2212yes—
22C22×C22⋊Dic17C2212yes—
23C22×C4×Dic17C2211yescharacteristic
24#11762702—24no—
25#11762689—28no—
26C2×#10587502C2211yescharacteristic
27C2×#10587502C2212yes—
28C2×#10587502C2211yescharacteristic
29C2×#10587502C2211yescharacteristic
30C2×#10587502C2212yes—
31C2×#10587502C2212yes—
32C2×#10587502C2212yes—
33C2×#10587502C2212yes—
34C23×D4×C17C2211yescharacteristic
35C23×D4×C17C2212yes—
36C22×C22⋊C4×C17C2211yescharacteristic
37C22×C22⋊C4×C17C2212yes—
38C17×#392C418yescomplemented
39C2×C17×#95C2211yescharacteristic
40C25×C17C2311yescharacteristic
41C25×C17C2312yes—
42C22×D4×C17—24no—
43C22×D4×C17—24no—
44C22×D4×C17—24no—
45C22×D4×C17—24no—
46C22×D4×C17—22no—
47C22×D4×C17—22no—
48C22×D4×C17—42no—
49C22×D4×C17—42no—
50C22×D4×C17—42no—
51C22×D4×C17—42no—
52C22×D4×C17C2×C414yes—
53C22×D4×C17C2×C418yescomplemented
54C23×C4×C17C2311yescharacteristic
55C23×C4×C17C2312yes—
56C23×C4×C17C2311yescharacteristic
57C23×Dic17—24no—
58C23×Dic17—24no—
59C23×Dic17—42no—
60C23×Dic17—42no—
61C23×Dic17—42no—
62C23×Dic17—42no—
63C23×Dic17D418yescomplemented
64C23×Dic17C2311yescharacteristic
65C23×Dic17C2311yescharacteristic
66C23×Dic17C2312yes—
67C23×Dic17C2311yescharacteristic
68C23×Dic17C2312yes—
69C23×Dic17C2311yescharacteristic
70C2×C22⋊C4×C17—22no—
71C2×C22⋊C4×C17—22no—
72C2×C22⋊C4×C17—42no—
73C2×C22⋊C4×C17—42no—
74C2×C22⋊C4×C17C2×C414yescomplemented
75C2×C22⋊C4×C17C2×C418yescomplemented
76C2×C22⋊Dic17—24no—
77C2×C22⋊Dic17—24no—
78C2×C22⋊Dic17—24no—
79C2×C22⋊Dic17—24no—
80C2×C22⋊Dic17—24no—
81C2×C22⋊Dic17—24no—
82C2×C22⋊Dic17—24no—
83C2×C22⋊Dic17—22no—
84C2×C22⋊Dic17—22no—
85C2×C22⋊Dic17—42no—
86C2×C22⋊Dic17—42no—
87C2×C22⋊Dic17—42no—
88C2×C22⋊Dic17—42no—
89C2×C22⋊Dic17—42no—
90C2×C22⋊Dic17—42no—
91C2×C22⋊Dic17—42no—
92D4×Dic17—232no—
93C2×C4⋊Dic17—22no—
94C2×C4⋊Dic17—24no—
95C2×C4⋊Dic17—22no—
96C2×C4⋊Dic17—42no—
97C2×C4×Dic17—24no—
98C2×C4×Dic17D414yescomplemented
99C17×#95C2×C414yescomplemented
100#10587502—22no—
101#10587502—22no—
102#10587502—24no—
103#10587502—24no—
104#10587502—22no—
105#10587502—42no—
106#10587502—42no—
107#10587502—42no—
108C24×C17—22no—
109C24×C17—22no—
110C24×C17—22no—
111C24×C17—22no—
112C24×C17—22no—
113C24×C17—22no—
114C24×C17—22no—
115C24×C17—22no—
116C24×C17—22no—
117C24×C17—22no—
118C24×C17—22no—
119C24×C17—22no—
120C24×C17—22no—
121C24×C17—21no—
122C24×C17—22no—
123C24×C17—21no—
124C24×C17—21no—
125C24×C17—21no—
126C24×C17—22no—
127C24×C17—22no—
128C24×C17—21no—
129C24×C17—21no—
130C24×C17C22×C412yes—
131C24×C17C22×C414yes—
132C24×C17C2×D414yes—
133C24×C17#4114yes—
134C24×C17C2411yescharacteristic
135C2×D4×C17—28no—
136C2×D4×C17—216no—
137C2×D4×C17—28no—
138C2×D4×C17—216no—
139C2×D4×C17—216no—
140C2×D4×C17—28no—
141C2×D4×C17—48no—
142C2×D4×C17—48no—
143C2×D4×C17—48no—
144C2×D4×C17—48no—
145C2×D4×C17—48no—
146C2×D4×C17—48no—
147C22×C4×C17—22no—
148C22×C4×C17—22no—
149C22×C4×C17—22no—
150C22×C4×C17—21no—
151C22×C4×C17—22no—
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×C17C22×C414yes—
160C22×C4×C17C22×C412yes—
161C22×C4×C17C22×C412yes—
162C22×C4×C17C2×D412yes—
163C22×C4×C17#4112yes—
164C22×Dic17—21no—
165C22×Dic17—22no—
166C22×Dic17—21no—
167C22×Dic17—22no—
168C22×Dic17—22no—
169C22×Dic17—22no—
170C22×Dic17—22no—
171C22×Dic17—22no—
172C22×Dic17—22no—
173C22×Dic17—22no—
174C22×Dic17—21no—
175C22×Dic17—22no—
176C22×Dic17—21no—
177C22×Dic17—216no—
178C22×Dic17—21no—
179C22×Dic17—21no—
180C22×Dic17—22no—
181C22×Dic17—22no—
182C22×Dic17—22no—
183C22×Dic17—22no—
184C22×Dic17—22no—
185C22×Dic17—21no—
186C22×Dic17—22no—
187C22×Dic17—22no—
188C22×Dic17—22no—
189C22×Dic17—21no—
190C22×Dic17—22no—
191C22×Dic17—22no—
192C22×Dic17—22no—
193C22×Dic17—21no—
194C22×Dic17—21no—
195C22×Dic17—48no—
196C22×Dic17—48no—
197C22×Dic17—48no—
198C22×Dic17—48no—
199C22×Dic17—48no—
200C22×Dic17—48no—
201C22×Dic17C2×D414yes—
202C22×Dic17C2×D412yes—
203C22×Dic17C2×D412yes—
204C22×Dic17C2×D414yes—
205C22⋊C4×C17—28no—
206C22⋊C4×C17—48no—
207C22⋊Dic17—216no—
208C22⋊Dic17—48no—
209C22⋊Dic17—44no—
210C22⋊Dic17—48no—
211C22⋊Dic17—48no—
212C22⋊Dic17—44no—
213C4⋊Dic17—28no—
214C4⋊Dic17—44no—
215C4×Dic17—28no—
216#14299—171nomaximal, Sylow
217C23×C17—24no—
218C23×C17—24no—
219C23×C17—24no—
220C23×C17—24no—
221C23×C17—24no—
222C23×C17—24no—
223C23×C17—24no—
224C23×C17—24no—
225C23×C17—24no—
226C23×C17—24no—
227C23×C17—24no—
228C23×C17—24no—
229C23×C17—24no—
230C23×C17—24no—
231C23×C17—24no—
232C23×C17—24no—
233C23×C17—24no—
234C23×C17—24no—
235C23×C17—22no—
236C23×C17—24no—
237C23×C17—22no—
238C23×C17—24no—
239C23×C17—22no—
240C23×C17—42no—
241C23×C17—42no—
242C23×C17—42no—
243C23×C17—42no—
244C23×C17—42no—
245C23×C17—42no—
246C23×C17—42no—
247C23×C17—42no—
248C23×C17—42no—
249C23×C17—42no—
250C23×C17—42no—
251C23×C17—42no—
252C23×C17—42no—
253C23×C17—42no—
254C23×C17—42no—
255C23×C17—42no—
256C23×C17—41no—
257C23×C17—42no—
258C23×C17—41no—
259C23×C17—42no—
260C23×C17—42no—
261C23×C17—41no—
262C23×C17—42no—
263C23×C17—41no—
264C23×C17—41no—
265C23×C17—42no—
266C23×C17—41no—
267C23×C17—42no—
268C23×C17—42no—
269C23×C17—42no—
270C23×C17—42no—
271C23×C17—41no—
272C23×C17—42no—
273C23×C17—41no—
274C23×C17C4×D418yes—
275C23×C17C23×C411yescharacteristic
276C23×C17C22×D412yes—
277C23×C17C22×D411yescharacteristic
278C23×C17C2×#4112yes—
279C23×C17C2×#4111yescharacteristic
280C23×C17H(5,𝔽2)11yescharacteristic
281C23×C17H(5,𝔽2)12yes—
282C23×C17H(5,𝔽2)12yes—
283C23×C17H(5,𝔽2)11yescharacteristic
284C23×C17H(5,𝔽2)11yescharacteristic
285C23×C172−1+411yescharacteristic
286D4×C17—232no—
287D4×C17—432no—
288C2×C4×C17—24no—
289C2×C4×C17—22no—
290C2×C4×C17—22no—
291C2×C4×C17—24no—
292C2×C4×C17—22no—
293C2×C4×C17—24no—
294C2×C4×C17—24no—
295C2×C4×C17—24no—
296C2×C4×C17—24no—
297C2×C4×C17—42no—
298C2×C4×C17—41no—
299C2×C4×C17—42no—
300C2×C4×C17—41no—
301C2×C4×C17—42no—
302C2×C4×C17—42no—
303C2×C4×C17—42no—
304C2×C4×C17C4×D414yes—
305C2×Dic17—24no—
306C2×Dic17—24no—
307C2×Dic17—22no—
308C2×Dic17—22no—
309C2×Dic17—22no—
310C2×Dic17—24no—
311C2×Dic17—24no—
312C2×Dic17—24no—
313C2×Dic17—22no—
314C2×Dic17—22no—
315C2×Dic17—432no—
316C2×Dic17—42no—
317C2×Dic17—42no—
318C2×Dic17—42no—
319C2×Dic17—42no—
320C2×Dic17—42no—
321C2×Dic17—42no—
322C2×Dic17—41no—
323C2×Dic17—41no—
324C2×Dic17—42no—
325C2×Dic17—42no—
326C2×Dic17—41no—
327C2×Dic17—42no—
328C2×Dic17—42no—
329C2×Dic17—41no—
330C2×Dic17—41no—
331C2×Dic17—42no—
332C2×Dic17—41no—
333C2×Dic17—42no—
334C2×Dic17—42no—
335C2×Dic17—42no—
336C2×Dic17—42no—
337C2×Dic17—42no—
338C2×Dic17—42no—
339C2×Dic17#12014yes—
340C22×C4×D4—171no—
341C2×#392D1711yescharacteristic
342C2×#388—171no—
343C2×#386—172no—
344#1442—171no—
345#1439—172no—
346#1439—171no—
347#1438—172no—
348#1438—171no—
349#1434—171no—
350C22⋊#95—172no—
351C22×C17—28no—
352C22×C17—28no—
353C22×C17—28no—
354C22×C17—44no—
355C22×C17—44no—
356C22×C17—44no—
357C22×C17—44no—
358C22×C17—44no—
359C22×C17—44no—
360C22×C17—44no—
361C22×C17—44no—
362C22×C17—44no—
363C22×C17—44no—
364C22×C17—44no—
365C22×C17—44no—
366C22×C17—44no—
367C22×C17—42no—
368C22×C17—44no—
369C22×C17—42no—
370C22×C17—42no—
371C22×C17—81no—
372C22×C17—81no—
373C22×C17—82no—
374C22×C17—81no—
375C22×C17—82no—
376C22×C17—81no—
377C22×C17C2×C4×D412yes—
378C22×C17C2×C4×D411yescharacteristic
379C22×C17#51811yescharacteristic
380C22×C17#51812yes—
381C22×C17#52011yescharacteristic
382C22×C17C2×#12011yescharacteristic
383C22×C17#52512yes—
384C22×C17#52511yescharacteristic
385C22×C17#53412yes—
386C22×C17#53412yes—
387C22×C17#53511yescharacteristic
388C22×C17#53511yescharacteristic
389C22×C17#53512yes—
390C22×C17#53511yescharacteristic
391C22×C17#53712yes—
392C22×C17#53711yescharacteristic
393C22×C17#53812yes—
394C22×C17#53812yes—
395C22×C17#53812yes—
396C22×C17#53912yes—
397C22×C17#54011yescharacteristic
398C22×C17#54012yes—
399C22×C17#54211yescharacteristic
400C4×C17—24no—
401C4×C17—44no—
402C4×C17—42no—
403Dic17—24no—
404Dic17—44no—
405Dic17—42no—
406Dic17—81no—
407Dic17—81no—
408Dic17—82no—
409C23×D4C2×D1711yescharacteristic
410C23×D4C2×D1712yes—
411C24×C4—172no—
412C2×C4×D4—344no—
413C2×C4×D4—348no—
414C22×C4⋊C4—171no—
415C22×C4⋊C4—171no—
416C22×C22⋊C4—172no—
417C22×C22⋊C4—171no—
418C22×C22⋊C4—172no—
419C22×C22⋊C4—171no—
420C22×C22⋊C4—172no—
421C22×C22⋊C4—172no—
422C22×C22⋊C4C2×D1711yescharacteristic
423C22×C22⋊C4C2×D1712yes—
424C22×C42—171no—
425#392Dic1718yescomplemented
426#388—344no—
427#386—348no—
428C2×#95—171no—
429C2×#95—172no—
430C2×#95—171no—
431C2×#95—171no—
432C2×#95—172no—
433C2×#95—172no—
434C2×#95—172no—
435C2×#95—172no—
436C2×#95C2×D1711yescharacteristic
437C2×C17—48no—
438C2×C17—82no—
439C2×C17C4×#12011yescharacteristic
440C2×C17#232112yes—
441C2×C17#232411yescharacteristic
442C2×C17#232512yes—
443C2×C17#232811yescharacteristic
444C2×C17#261311yescharacteristic
445C2×C17#261511yescharacteristic
446C2×C17#263012yes—
447C2×C17#263111yescharacteristic
448C2×C17#263512yes—
449C2×C17#263611yescharacteristic
450C25C22×D1711yescharacteristic
451C25C22×D1712yes—
452C22×D4—24no—
453C22×D4—24no—
454C22×D4—24no—
455C22×D4—24no—
456C22×D4—22no—
457C22×D4—22no—
458C22×D4—42no—
459C22×D4—42no—
460C22×D4—42no—
461C22×D4—42no—
462C22×D4C2×Dic1714yes—
463C22×D4C2×Dic1718yescomplemented
464C23×C4—171no—
465C23×C4—171no—
466C23×C4—172no—
467C23×C4—178no—
468C23×C4—171no—
469C23×C4—171no—
470C23×C4—172no—
471C23×C4—344no—
472C23×C4—344no—
473C23×C4—682no—
474C23×C4—682no—
475C23×C4—682no—
476C23×C4—682no—
477C23×C4C22×D1711yescharacteristic
478C23×C4C22×D1712yes—
479C23×C4C22×D1711yescharacteristic
480C4×D4—3432no—
481C2×C4⋊C4—344no—
482C2×C4⋊C4—342no—
483C2×C4⋊C4—342no—
484C2×C4⋊C4—682no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4—42no—
488C2×C22⋊C4—42no—
489C2×C22⋊C4—344no—
490C2×C22⋊C4—344no—
491C2×C22⋊C4—344no—
492C2×C22⋊C4—344no—
493C2×C22⋊C4—344no—
494C2×C22⋊C4—342no—
495C2×C22⋊C4—342no—
496C2×C22⋊C4—344no—
497C2×C22⋊C4—344no—
498C2×C22⋊C4—682no—
499C2×C22⋊C4—682no—
500C2×C22⋊C4—682no—
501C2×C22⋊C4—682no—
502C2×C22⋊C4—682no—
503C2×C22⋊C4—682no—
504C2×C22⋊C4—682no—
505C2×C22⋊C4C2×Dic1714yescomplemented
506C2×C22⋊C4C2×Dic1718yescomplemented
507C2×C42—174no—
508C2×C42—344no—
509#95—344no—
510#95—344no—
511#95—342no—
512#95—342no—
513#95—342no—
514#95—682no—
515#95—682no—
516#95—682no—
517#95C2×Dic1714yescomplemented
518C17#1429911yescharacteristic, complemented, Sylow
519C24—22no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—21no—
532C24—22no—
533C24—21no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—21no—
538C24—21no—
539C24—21no—
540C24—21no—
541C24D4×D1714yes—
542C24#6325414yes—
543C24C22×Dic1712yes—
544C24C22×Dic1714yes—
545C24C23×D1711yescharacteristic
546C2×D4—28no—
547C2×D4—28no—
548C2×D4—216no—
549C2×D4—216no—
550C2×D4—216no—
551C2×D4—28no—
552C2×D4—48no—
553C2×D4—48no—
554C2×D4—48no—
555C2×D4—48no—
556C2×D4—48no—
557C2×D4—48no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—172no—
571C22×C4—174no—
572C22×C4—174no—
573C22×C4—172no—
574C22×C4—3416no—
575C22×C4—342no—
576C22×C4—341no—
577C22×C4—341no—
578C22×C4—342no—
579C22×C4—342no—
580C22×C4—342no—
581C22×C4—341no—
582C22×C4—342no—
583C22×C4—342no—
584C22×C4—342no—
585C22×C4—342no—
586C22×C4—342no—
587C22×C4—341no—
588C22×C4—341no—
589C22×C4—342no—
590C22×C4—342no—
591C22×C4—341no—
592C22×C4—342no—
593C22×C4—342no—
594C22×C4—342no—
595C22×C4—341no—
596C22×C4—342no—
597C22×C4—342no—
598C22×C4—342no—
599C22×C4—341no—
600C22×C4—342no—
601C22×C4—342no—
602C22×C4—342no—
603C22×C4—341no—
604C22×C4—341no—
605C22×C4—688no—
606C22×C4—688no—
607C22×C4—688no—
608C22×C4—688no—
609C22×C4—688no—
610C22×C4—688no—
611C22×C4D4×D1712yes—
612C22×C4#6325412yes—
613C22×C4C22×Dic1714yes—
614C22×C4C22×Dic1712yes—
615C22×C4C22×Dic1712yes—
616C4⋊C4—348no—
617C4⋊C4—684no—
618C22⋊C4—28no—
619C22⋊C4—48no—
620C22⋊C4—3416no—
621C22⋊C4—684no—
622C22⋊C4—688no—
623C22⋊C4—684no—
624C22⋊C4—688no—
625C22⋊C4—688no—
626C42—348no—
627C23—24no—
628C23—24no—
629C23—24no—
630C23—24no—
631C23—24no—
632C23—24no—
633C23—24no—
634C23—24no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—22no—
646C23—24no—
647C23—22no—
648C23—24no—
649C23—22no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—41no—
667C23—42no—
668C23—41no—
669C23—42no—
670C23—42no—
671C23—41no—
672C23—41no—
673C23—42no—
674C23—41no—
675C23—42no—
676C23—41no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—41no—
682C23—42no—
683C23—41no—
684C23D4×Dic1718yes—
685C23C2×D4×D1712yes—
686C23C2×D4×D1711yescharacteristic
687C23C2×#6325412yes—
688C23C2×#6325411yescharacteristic
689C23#1058769112yes—
690C23#1058769111yescharacteristic
691C23#1058769112yes—
692C23#1058769111yescharacteristic
693C23#1058769611yescharacteristic
694C23#1058769711yescharacteristic
695C23C23×Dic1711yescharacteristic
696D4—232no—
697D4—432no—
698C2×C4—24no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—24no—
702C2×C4—22no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—42no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—174no—
715C2×C4—344no—
716C2×C4—344no—
717C2×C4—342no—
718C2×C4—342no—
719C2×C4—342no—
720C2×C4—344no—
721C2×C4—344no—
722C2×C4—344no—
723C2×C4—342no—
724C2×C4—342no—
725C2×C4—6832no—
726C2×C4—682no—
727C2×C4—682no—
728C2×C4—682no—
729C2×C4—682no—
730C2×C4—682no—
731C2×C4—682no—
732C2×C4—681no—
733C2×C4—682no—
734C2×C4—681no—
735C2×C4—682no—
736C2×C4—681no—
737C2×C4—681no—
738C2×C4—682no—
739C2×C4—682no—
740C2×C4—681no—
741C2×C4—682no—
742C2×C4—681no—
743C2×C4—682no—
744C2×C4—682no—
745C2×C4—682no—
746C2×C4—682no—
747C2×C4—682no—
748C2×C4—682no—
749C2×C4D4×Dic1714yes—
750C22—28no—
751C22—28no—
752C22—28no—
753C22—44no—
754C22—44no—
755C22—44no—
756C22—44no—
757C22—44no—
758C22—44no—
759C22—44no—
760C22—44no—
761C22—44no—
762C22—44no—
763C22—44no—
764C22—44no—
765C22—44no—
766C22—42no—
767C22—44no—
768C22—42no—
769C22—42no—
770C22—82no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—82no—
775C22—81no—
776C22C2×D4×Dic1712yes—
777C22C2×D4×Dic1711yescharacteristic
778C22#1176328411yescharacteristic
779C22#1176328412yes—
780C22#1176329211yescharacteristic
781C22#120×D1711yescharacteristic
782C22#1176331512yes—
783C22#1176331511yescharacteristic
784C22#1176336712yes—
785C22#1176336912yes—
786C22#1176337211yescharacteristic
787C22#1176337211yescharacteristic
788C22#1176337412yes—
789C22#1176337511yescharacteristic
790C22#1176338612yes—
791C22#1176338811yescharacteristic
792C22#1176339412yes—
793C22#1176339412yes—
794C22#1176339612yes—
795C22#1176340412yes—
796C22#1176341211yescharacteristic
797C22#1176341312yes—
798C22#1176342611yescharacteristic
799C4—24no—
800C4—44no—
801C4—42no—
802C4—344no—
803C4—684no—
804C4—682no—
805C4—1362no—
806C4—1361no—
807C4—1361no—
808C2—48no—
809C2—82no—
810C2#120×Dic1711yescharacteristic
811C2#1453144512yes—
812C2#1453147911yescharacteristic
813C2#1453148912yes—
814C2#1453151011yescharacteristic
815C2#1453449511yescharacteristic
816C2#1453450711yescharacteristic
817C2#1453462012yes—
818C2#1453463511yescharacteristic
819C2#1453466712yes—
820C2#1453467811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
Fitting, prime radicalC2×C17×#392C2
socle, cosocleC24×C17C24
hypercenterC2×#392D17
hypocenterC17#14299
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. C22×D4×Dic17C2semidirect
2. C2×#11762702C2semidirect
3. C2×#11762689C2semidirect
4. #14527041C2semidirect
5. #14527029C2semidirect
6. #14527029C2semidirect
7. #14527025C2semidirect
8. #14527025C2semidirect
9. #14527009C2semidirect
10. #14527006C2semidirect
38. C17×#392C4semidirect
53. C22×D4×C17C2×C4semidirect
63. C23×Dic17D4semidirect
74. C2×C22⋊C4×C17C2×C4semidirect
75. C2×C22⋊C4×C17C2×C4semidirect
98. C2×C4×Dic17D4semidirect
99. C17×#95C2×C4semidirect
425. #392Dic17semidirect
463. C22×D4C2×Dic17semidirect
505. C2×C22⋊C4C2×Dic17semidirect
506. C2×C22⋊C4C2×Dic17semidirect
517. #95C2×Dic17semidirect
518. C17#14299semidirect

Maximal subgroups

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

subgroupindex
C22×D4×Dic172
C2×#117627022
C2×#117626892
#145270412
#145270292
#145270252
#145270092
#145270062
C2×C17×#3922
#1429917