Finite Group Databasebeta

← #16957450

Subgroups — #16957450

Order 4352.

2474 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587572C211yesmaximal, characteristic
2C2×#11762688C211yesmaximal, characteristic
3C2×#11762686C211yesmaximal, characteristic
4C2×#11762670C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×Dic17C211yesmaximal, characteristic, complemented
6C22×#10587502C211yesmaximal, characteristic, complemented
7#14527053C212yesmaximal, complemented
8#14527026C212yesmaximal, complemented
9#14527020C212yesmaximal, complemented
10#14527013C212yesmaximal, complemented
11C2×C17×#385C211yesmaximal, characteristic, complemented
12C23×C22⋊D17C2211yescharacteristic
13C24×Dic17C2211yescharacteristic
14C24×Dic17C2211yescharacteristic
15C2×#10587572—24no—
16C2×#10587572—24no—
17C2×#10587572C418yescomplemented
18C22×C4⋊Dic17C2212yes—
19C22×C22⋊Dic17C2211yescharacteristic
20C22×#63227C2211yescharacteristic
21C22×#63227C2212yes—
22C22×#63227C2212yes—
23C22×#63227C2211yescharacteristic
24C22×C4×Dic17C2212yes—
25#11762688—24no—
26#11762686—24no—
27#11762670—24no—
28C22⋊C4×Dic17—24no—
29C2×#10587502—24no—
30C2×#10587502C2212yes—
31C2×#10587502C2212yes—
32C2×#10587502C2211yescharacteristic
33C2×#10587502C2212yes—
34C2×#10587502C2212yes—
35C2×#10587502C2212yes—
36C2×#10587502C2212yes—
37C2×#10587502C2211yescharacteristic
38C24×C4×C17C2211yescharacteristic
39C22×C4⋊C4×C17C2212yes—
40C22×C22⋊C4×C17C2211yescharacteristic
41C22×C22⋊C4×C17C2211yescharacteristic
42C17×#385—24no—
43C2×C17×#95C2212yes—
44C25×C17C2311yescharacteristic
45C24×D17C2311yescharacteristic
46C23×C4×C17—22no—
47C23×C4×C17—24no—
48C23×C4×C17—22no—
49C23×C4×C17—22no—
50C23×C4×C17—42no—
51C23×C4×C17C2311yescharacteristic
52C23×C4×C17C2311yescharacteristic
53C23×C4×C17C2312yes—
54C23×C4×C17C2312yes—
55C22×C22⋊D17—22no—
56C22×C22⋊D17—22no—
57C22×C22⋊D17—22no—
58C22×C22⋊D17—22no—
59C22×C22⋊D17—22no—
60C22×C22⋊D17—22no—
61C22×C22⋊D17C2×C414yes—
62C23×Dic17—22no—
63C23×Dic17—22no—
64C23×Dic17—22no—
65C23×Dic17—22no—
66C23×Dic17—22no—
67C23×Dic17—22no—
68C23×Dic17—22no—
69C23×Dic17—22no—
70C23×Dic17—24no—
71C23×Dic17—42no—
72C23×Dic17C2×C414yes—
73C23×Dic17D414yes—
74C23×Dic17C2312yes—
75C23×Dic17C2311yescharacteristic
76C23×Dic17C2312yes—
77C23×Dic17C2311yescharacteristic
78C23×Dic17C2311yescharacteristic
79C2×C4⋊C4×C17—24no—
80C2×C4⋊C4×C17—24no—
81C2×C4⋊C4×C17—42no—
82C2×C22⋊C4×C17—22no—
83C2×C22⋊C4×C17—22no—
84C2×C22⋊C4×C17—22no—
85C2×C22⋊C4×C17C2×C414yes—
86C2×C22⋊C4×C17D414yes—
87C2×C22⋊C4×C17D414yes—
88C2×C22⋊Dic17—22no—
89C2×C22⋊Dic17—22no—
90C2×C22⋊Dic17D414yes—
91C2×#63227—24no—
92C2×#63227—24no—
93C2×#63227—24no—
94C2×#63227—24no—
95C2×#63227—22no—
96C2×#63227—22no—
97C2×#63227—24no—
98C2×#63227—42no—
99C2×#63227—42no—
100C2×#63227C2×C418yescomplemented
101C2×C4⋊Dic17—24no—
102C2×C4⋊Dic17—24no—
103C2×C4⋊Dic17C2×C418yescomplemented
104C2×C4×Dic17—24no—
105C2×C4×Dic17—24no—
106C2×C4×Dic17—42no—
107#10587572—232no—
108C17×#95—24no—
109#10587502—24no—
110#10587502—24no—
111#10587502—24no—
112#10587502—24no—
113#10587502—24no—
114#10587502—24no—
115#10587502—22no—
116#10587502—22no—
117C24×C17—22no—
118C24×C17—22no—
119C24×C17—22no—
120C24×C17—22no—
121C24×C17C22×C412yes—
122C24×C17C2×D412yes—
123C24×C17C2×D412yes—
124C24×C17C2×D412yes—
125C24×C17C2×D412yes—
126C24×C17#4112yes—
127C24×C17#4112yes—
128C24×C17C2411yescharacteristic
129C23×D17—21no—
130C23×D17—21no—
131C23×D17—21no—
132C23×D17—21no—
133C23×D17—21no—
134C23×D17—21no—
135C23×D17—22no—
136C23×D17—22no—
137C23×D17—22no—
138C23×D17—22no—
139C23×D17C22×C412yes—
140C22×C4×C17—22no—
141C22×C4×C17—22no—
142C22×C4×C17—22no—
143C22×C4×C17—22no—
144C22×C4×C17—28no—
145C22×C4×C17—22no—
146C22×C4×C17—22no—
147C22×C4×C17—22no—
148C22×C4×C17—22no—
149C22×C4×C17—22no—
150C22×C4×C17—22no—
151C22×C4×C17—21no—
152C22×C4×C17—21no—
153C22×C4×C17—21no—
154C22×C4×C17—21no—
155C22×C4×C17—21no—
156C22×C4×C17—21no—
157C22×C4×C17—22no—
158C22×C4×C17—22no—
159C22×C4×C17—22no—
160C22×C4×C17—22no—
161C22×C4×C17—48no—
162C22×C4×C17—48no—
163C22×C4×C17—44no—
164C22×C4×C17—44no—
165C22×C4×C17C22×C414yes—
166C22×C4×C17C2×D414yes—
167C22×C4×C17C2×D414yes—
168C22×C4×C17#4114yes—
169C2×C22⋊D17—28no—
170C2×C22⋊D17—28no—
171C2×C22⋊D17—28no—
172C2×C22⋊D17—44no—
173C2×C22⋊D17—44no—
174C2×C22⋊D17—44no—
175C2×C22⋊D17—44no—
176C22×Dic17—21no—
177C22×Dic17—21no—
178C22×Dic17—22no—
179C22×Dic17—28no—
180C22×Dic17—28no—
181C22×Dic17—28no—
182C22×Dic17—28no—
183C22×Dic17—21no—
184C22×Dic17—22no—
185C22×Dic17—22no—
186C22×Dic17—22no—
187C22×Dic17—22no—
188C22×Dic17—21no—
189C22×Dic17—21no—
190C22×Dic17—21no—
191C22×Dic17—21no—
192C22×Dic17—22no—
193C22×Dic17—22no—
194C22×Dic17—22no—
195C22×Dic17—21no—
196C22×Dic17—22no—
197C22×Dic17—21no—
198C22×Dic17—21no—
199C22×Dic17—22no—
200C22×Dic17—22no—
201C22×Dic17—22no—
202C22×Dic17—22no—
203C22×Dic17—22no—
204C22×Dic17—22no—
205C22×Dic17—28no—
206C22×Dic17—44no—
207C22×Dic17—48no—
208C22×Dic17—48no—
209C22×Dic17—44no—
210C22×Dic17—44no—
211C22×Dic17—44no—
212C22×Dic17—44no—
213C22×Dic17C22×C414yes—
214C22×Dic17C22×C412yes—
215C22×Dic17C2×D412yes—
216C22×Dic17C2×D414yes—
217C22×Dic17C2×D412yes—
218C22×Dic17#4114yes—
219C4⋊C4×C17—48no—
220C22⋊C4×C17—44no—
221C22⋊C4×C17C22⋊C4116yescomplemented
222C22⋊Dic17—28no—
223#63227—216no—
224#63227—48no—
225#63227—44no—
226#63227—44no—
227C4⋊Dic17—216no—
228C4×Dic17—48no—
229#13996—171nomaximal, Sylow
230C23×C17—24no—
231C23×C17—24no—
232C23×C17—22no—
233C23×C17—22no—
234C23×C17—24no—
235C23×C17—22no—
236C23×C17—22no—
237C23×C17—24no—
238C23×C17—24no—
239C23×C17—24no—
240C23×C17—24no—
241C23×C17—24no—
242C23×C17—24no—
243C23×C17—24no—
244C23×C17—24no—
245C23×C17—24no—
246C23×C17C2×C22⋊C414yes—
247C23×C17C4×D414yes—
248C23×C17C4×D414yes—
249C23×C17#12114yes—
250C23×C17#12114yes—
251C23×C17#12414yes—
252C23×C17#12714yes—
253C23×C17C23×C411yescharacteristic
254C23×C17C22×D411yescharacteristic
255C23×C17C22×D411yescharacteristic
256C23×C17C22×D411yescharacteristic
257C23×C17C22×D411yescharacteristic
258C23×C17C2×#4112yes—
259C23×C17C2×#4111yescharacteristic
260C23×C17C2×#4111yescharacteristic
261C23×C17C2×#4112yes—
262C23×C17H(5,𝔽2)12yes—
263C23×C172−1+412yes—
264C22×D17—22no—
265C22×D17—22no—
266C22×D17—22no—
267C22×D17—24no—
268C22×D17—24no—
269C22×D17—41no—
270C22×D17—41no—
271C22×D17—41no—
272C22×D17—41no—
273C22×D17—41no—
274C22×D17—42no—
275C22×D17—41no—
276C22×D17—41no—
277C22×D17—41no—
278C22×D17—42no—
279C22×D17—42no—
280C22×D17—42no—
281C22×D17—42no—
282C22×D17—42no—
283C22×D17—42no—
284C22×D17—42no—
285C22×D17—42no—
286C22×D17—42no—
287C2×C4×C17—24no—
288C2×C4×C17—24no—
289C2×C4×C17—24no—
290C2×C4×C17—24no—
291C2×C4×C17—24no—
292C2×C4×C17—24no—
293C2×C4×C17—24no—
294C2×C4×C17—24no—
295C2×C4×C17—24no—
296C2×C4×C17—416no—
297C2×C4×C17—42no—
298C2×C4×C17—42no—
299C2×C4×C17—42no—
300C2×C4×C17—42no—
301C2×C4×C17—41no—
302C2×C4×C17—41no—
303C2×C4×C17—41no—
304C2×C4×C17—41no—
305C2×C4×C17—41no—
306C2×C4×C17—41no—
307C2×C4×C17—42no—
308C2×C4×C17—42no—
309C2×C4×C17—42no—
310C2×C4×C17—42no—
311C2×C4×C17C2×C22⋊C418yes—
312C22⋊D17—416no—
313C2×Dic17—22no—
314C2×Dic17—22no—
315C2×Dic17—24no—
316C2×Dic17—24no—
317C2×Dic17—24no—
318C2×Dic17—22no—
319C2×Dic17—24no—
320C2×Dic17—24no—
321C2×Dic17—22no—
322C2×Dic17—22no—
323C2×Dic17—24no—
324C2×Dic17—22no—
325C2×Dic17—22no—
326C2×Dic17—22no—
327C2×Dic17—24no—
328C2×Dic17—24no—
329C2×Dic17—416no—
330C2×Dic17—42no—
331C2×Dic17—42no—
332C2×Dic17—41no—
333C2×Dic17—41no—
334C2×Dic17—42no—
335C2×Dic17—41no—
336C2×Dic17—42no—
337C2×Dic17—42no—
338C2×Dic17—41no—
339C2×Dic17—42no—
340C2×Dic17—42no—
341C2×Dic17—42no—
342C2×Dic17—42no—
343C2×Dic17—42no—
344C2×Dic17—416no—
345C2×Dic17#12314yescomplemented
346C22×#123—171no—
347C2×#386—171no—
348C2×#386—171no—
349C2×#385D1711yescharacteristic, complemented
350C2×#381—171no—
351C2×C4×C22⋊C4—171no—
352C22×#95—171no—
353#1445—172no—
354#1439—172no—
355#1437—172no—
356C4⋊#95—172no—
357C22×C17—24no—
358C22×C17—28no—
359C22×C17—28no—
360C22×C17—24no—
361C22×C17—24no—
362C22×C17—28no—
363C22×C17—28no—
364C22×C17—24no—
365C22×C17—24no—
366C22×C17—24no—
367C22×C17#39018yes—
368C22×C17C22×C22⋊C411yescharacteristic
369C22×C17C2×C4×D411yescharacteristic
370C22×C17C2×C4×D411yescharacteristic
371C22×C17C4×#4112yes—
372C22×C17#52012yes—
373C22×C17C2×#12111yescharacteristic
374C22×C17C2×#12111yescharacteristic
375C22×C17C2×#12311yescharacteristic
376C22×C17#52511yescharacteristic
377C22×C17C2×#12411yescharacteristic
378C22×C17#52912yes—
379C22×C17C2×#12711yescharacteristic
380C22×C17#53411yescharacteristic
381C22×C17#53611yescharacteristic
382C22×C17#53912yes—
383C22×C17#54612yes—
384C22×C17#54612yes—
385C22×C17#54612yes—
386C22×C17#54712yes—
387C22×C17#54712yes—
388C22×C17#54712yes—
389C22×C17#55112yes—
390C22×C17#55212yes—
391C2×D17—42no—
392C2×D17—44no—
393C2×D17—44no—
394C2×D17—42no—
395C2×D17—42no—
396C2×D17—81no—
397C2×D17—81no—
398C2×D17—82no—
399C2×D17—82no—
400C2×D17—81no—
401C2×D17—81no—
402C4×C17—28no—
403C4×C17—44no—
404C4×C17—81no—
405C4×C17—81no—
406Dic17—24no—
407Dic17—42no—
408Dic17—44no—
409Dic17—44no—
410Dic17—42no—
411C23×D4—171no—
412C24×C4—171no—
413C24×C4—171no—
414C24×C4C2×D1711yescharacteristic
415C2×#123—178no—
416C2×#123—344no—
417C2×#123—344no—
418C22×C4⋊C4—172no—
419C22×C4⋊C4C2×D1712yes—
420C22×C22⋊C4—171no—
421C22×C22⋊C4—172no—
422C22×C22⋊C4—171no—
423C22×C22⋊C4—172no—
424C22×C22⋊C4—171no—
425C22×C22⋊C4C2×D1711yescharacteristic
426C22×C22⋊C4C2×D1711yescharacteristic
427C22×C42—172no—
428#386—344no—
429#386—344no—
430#385—24no—
431#381—344no—
432C4×C22⋊C4—344no—
433C2×#95—171no—
434C2×#95—172no—
435C2×#95—172no—
436C2×#95—172no—
437C2×#95—172no—
438C2×#95—172no—
439C2×#95—172no—
440C2×#95—171no—
441C2×#95—344no—
442C2×#95C2×D1712yes—
443C2×C17—28no—
444C2×C17C2×#39011yescharacteristic
445C2×C17C4×#12311yescharacteristic
446C2×C17#232211yescharacteristic
447C2×C17#233912yes—
448C2×C17#235912yes—
449C2×C17#241211yescharacteristic
450C2×C17#241311yescharacteristic
451C2×C17#242512yes—
452C2×C17#248812yes—
453C2×C17#250111yescharacteristic
454C2×C17#253911yescharacteristic
455D17—82no—
456C25—171no—
457C25C22×D1711yescharacteristic
458C22×D4—174no—
459C22×D4—342no—
460C22×D4—342no—
461C22×D4—342no—
462C22×D4—342no—
463C22×D4—342no—
464C22×D4—342no—
465C23×C4—22no—
466C23×C4—24no—
467C23×C4—22no—
468C23×C4—22no—
469C23×C4—42no—
470C23×C4—171no—
471C23×C4—174no—
472C23×C4—172no—
473C23×C4—172no—
474C23×C4—171no—
475C23×C4—171no—
476C23×C4—174no—
477C23×C4—344no—
478C23×C4—342no—
479C23×C4—342no—
480C23×C4—342no—
481C23×C4—342no—
482C23×C4—342no—
483C23×C4—342no—
484C23×C4—342no—
485C23×C4—342no—
486C23×C4—682no—
487C23×C4C22×D1711yescharacteristic
488C23×C4C22×D1711yescharacteristic
489C23×C4C22×D1712yes—
490C23×C4C22×D1712yes—
491#123—3432no—
492C2×C4⋊C4—24no—
493C2×C4⋊C4—24no—
494C2×C4⋊C4—42no—
495C2×C4⋊C4—178no—
496C2×C4⋊C4—344no—
497C2×C4⋊C4—344no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—174no—
502C2×C22⋊C4—178no—
503C2×C22⋊C4—342no—
504C2×C22⋊C4—342no—
505C2×C22⋊C4—344no—
506C2×C22⋊C4—344no—
507C2×C22⋊C4—344no—
508C2×C22⋊C4—342no—
509C2×C22⋊C4—342no—
510C2×C22⋊C4—344no—
511C2×C22⋊C4—344no—
512C2×C22⋊C4—682no—
513C2×C22⋊C4—682no—
514C2×C22⋊C4C4×D1714yes—
515C2×C22⋊C4D6814yes—
516C2×C22⋊C4C22⋊D1714yes—
517C2×C42—344no—
518C2×C42—344no—
519C2×C42—682no—
520#95—24no—
521#95—344no—
522#95—344no—
523#95—344no—
524#95—344no—
525#95—344no—
526#95—342no—
527#95—342no—
528#95—344no—
529C17#1399611yescharacteristic, complemented, Sylow
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—172no—
535C24—341no—
536C24—341no—
537C24—341no—
538C24—342no—
539C24—342no—
540C24—341no—
541C24—341no—
542C24—342no—
543C24—342no—
544C24—341no—
545C24C2×C4×D1712yes—
546C24C2×D6812yes—
547C24D4×D1712yes—
548C24D4×D1712yes—
549C24#6325612yes—
550C24#6325612yes—
551C24C2×C22⋊D1712yes—
552C24C23×D1711yescharacteristic
553C2×D4—348no—
554C2×D4—348no—
555C2×D4—348no—
556C2×D4—684no—
557C2×D4—684no—
558C2×D4—684no—
559C2×D4—684no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—28no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—48no—
582C22×C4—48no—
583C22×C4—44no—
584C22×C4—44no—
585C22×C4—172no—
586C22×C4—174no—
587C22×C4—174no—
588C22×C4—172no—
589C22×C4—174no—
590C22×C4—172no—
591C22×C4—348no—
592C22×C4—341no—
593C22×C4—342no—
594C22×C4—341no—
595C22×C4—341no—
596C22×C4—342no—
597C22×C4—342no—
598C22×C4—341no—
599C22×C4—342no—
600C22×C4—342no—
601C22×C4—341no—
602C22×C4—341no—
603C22×C4—342no—
604C22×C4—342no—
605C22×C4—342no—
606C22×C4—342no—
607C22×C4—342no—
608C22×C4—342no—
609C22×C4—341no—
610C22×C4—341no—
611C22×C4—341no—
612C22×C4—342no—
613C22×C4—342no—
614C22×C4—342no—
615C22×C4—342no—
616C22×C4—341no—
617C22×C4—348no—
618C22×C4—348no—
619C22×C4—348no—
620C22×C4—348no—
621C22×C4—684no—
622C22×C4—688no—
623C22×C4—688no—
624C22×C4—684no—
625C22×C4—684no—
626C22×C4—684no—
627C22×C4—684no—
628C22×C4C2×C4×D1714yes—
629C22×C4C2×D6814yes—
630C22×C4#6325414yes—
631C22×C4C2×C22⋊D1714yes—
632C4⋊C4—48no—
633C4⋊C4—3416no—
634C22⋊C4—44no—
635C22⋊C4—348no—
636C22⋊C4—3416no—
637C22⋊C4—688no—
638C22⋊C4—684no—
639C22⋊C4—684no—
640C22⋊C4#63227116yescomplemented
641C42—688no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—22no—
650C23—22no—
651C23—24no—
652C23—22no—
653C23—22no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—342no—
659C23—342no—
660C23—342no—
661C23—344no—
662C23—344no—
663C23—682no—
664C23—682no—
665C23—682no—
666C23—682no—
667C23—682no—
668C23—681no—
669C23—681no—
670C23—681no—
671C23—681no—
672C23—681no—
673C23—682no—
674C23—681no—
675C23—681no—
676C23—681no—
677C23—682no—
678C23—682no—
679C23—682no—
680C23—682no—
681C23#1058757914yes—
682C23#1058757914yes—
683C23#1058758114yes—
684C23#1058758114yes—
685C23C2×#6322714yes—
686C23#1058762614yes—
687C23#1058763314yes—
688C23C22×C4×D1711yescharacteristic
689C23C22×D6811yescharacteristic
690C23C2×D4×D1711yescharacteristic
691C23C2×D4×D1711yescharacteristic
692C23C2×#6325412yes—
693C23#1058769112yes—
694C23C2×#6325611yescharacteristic
695C23C2×#6325611yescharacteristic
696C23#41×D1712yes—
697C23#1058769712yes—
698C23C22×C22⋊D1711yescharacteristic
699D4—6816no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—416no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—174no—
725C2×C4—344no—
726C2×C4—342no—
727C2×C4—342no—
728C2×C4—344no—
729C2×C4—344no—
730C2×C4—344no—
731C2×C4—342no—
732C2×C4—344no—
733C2×C4—344no—
734C2×C4—342no—
735C2×C4—342no—
736C2×C4—344no—
737C2×C4—342no—
738C2×C4—342no—
739C2×C4—342no—
740C2×C4—344no—
741C2×C4—6816no—
742C2×C4—682no—
743C2×C4—6816no—
744C2×C4—682no—
745C2×C4—682no—
746C2×C4—682no—
747C2×C4—681no—
748C2×C4—681no—
749C2×C4—682no—
750C2×C4—681no—
751C2×C4—682no—
752C2×C4—682no—
753C2×C4—681no—
754C2×C4—682no—
755C2×C4—682no—
756C2×C4—682no—
757C2×C4C2×#6322718yes—
758C22—28no—
759C22—24no—
760C22—24no—
761C22—24no—
762C22—24no—
763C22—24no—
764C22—28no—
765C22—24no—
766C22—28no—
767C22—28no—
768C22—684no—
769C22—682no—
770C22—682no—
771C22—684no—
772C22—682no—
773C22—1361no—
774C22—1361no—
775C22—1361no—
776C22—1361no—
777C22—1362no—
778C22—1362no—
779C22#1176271018yes—
780C22C22×#6322711yescharacteristic
781C22C2×#1058757911yescharacteristic
782C22C2×#1058757911yescharacteristic
783C22C4×#6325412yes—
784C22#1176328812yes—
785C22C2×#1058758111yescharacteristic
786C22C2×#1058758111yescharacteristic
787C22#123×D1711yescharacteristic
788C22#1176331511yescharacteristic
789C22C2×#1058763311yescharacteristic
790C22#1176334512yes—
791C22C2×#1058762611yescharacteristic
792C22#1176336911yescharacteristic
793C22#1176338111yescharacteristic
794C22#1176340812yes—
795C22#1176344612yes—
796C22#1176345312yes—
797C22#1176345412yes—
798C22#1176345712yes—
799C22#1176345812yes—
800C22#1176346312yes—
801C22#1176348612yes—
802C22#1176350112yes—
803C4—28no—
804C4—44no—
805C4—81no—
806C4—81no—
807C4—344no—
808C4—682no—
809C4—684no—
810C4—682no—
811C4—684no—
812C2—28no—
813C2—1362no—
814C2C2×#1176271011yescharacteristic
815C2#1453130311yescharacteristic
816C2#1453145211yescharacteristic
817C2#1453160912yes—
818C2#1453177412yes—
819C2#1453217811yescharacteristic
820C2#1453218911yescharacteristic
821C2#1453233312yes—
822C2#1453311612yes—
823C2#1453325311yescharacteristic
824C2#1453371211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC2×C17×#385C2
socle, cosocleC24×C17C24
prime radicalC23×C22⋊D17C22
hypercenterC2×#385D17
hypocenterC17#13996
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
4. C2×#11762670C2semidirect
5. C2×C22⋊C4×Dic17C2semidirect
6. C22×#10587502C2semidirect
7. #14527053C2semidirect
8. #14527026C2semidirect
9. #14527020C2semidirect
10. #14527013C2semidirect
11. C2×C17×#385C2semidirect
17. C2×#10587572C4semidirect
100. C2×#63227C2×C4semidirect
103. C2×C4⋊Dic17C2×C4semidirect
221. C22⋊C4×C17C22⋊C4semidirect
345. C2×Dic17#123semidirect
349. C2×#385D17semidirect
529. C17#13996semidirect
640. C22⋊C4#63227semidirect

Maximal subgroups

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

subgroupindex
C22×#105875722
C2×#117626882
C2×#117626862
C2×#117626702
C2×C22⋊C4×Dic172
C22×#105875022
#145270532
#145270262
#145270202
#145270132
C2×C17×#3852
#1399617