Finite Group Databasebeta

← #16957447

Subgroups — #16957447

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×#10587615C211yesmaximal, characteristic
2C2×#11762688C211yesmaximal, characteristic
3C2×#11762688C211yesmaximal, characteristic
4C2×#11762682C211yesmaximal, characteristic, complemented
5C2×#11762672C211yesmaximal, characteristic, complemented
6C2×C4×C22⋊Dic17C211yesmaximal, characteristic, complemented
7#14527050C212yesmaximal, complemented
8#14527028C212yesmaximal, complemented
9#14527020C212yesmaximal, complemented
10#14527012C212yesmaximal, complemented
11C22×C17×#95C211yesmaximal, characteristic, complemented
12C23×C22⋊D17C2211yescharacteristic
13C2×#10587615—24no—
14C2×#10587615—24no—
15C2×#10587615C418yescomplemented
16C22×#63225C2212yes—
17C22×#63225C2212yes—
18C22×C22⋊Dic17C2211yescharacteristic
19C22×C22⋊Dic17C2211yescharacteristic
20C22×C22⋊Dic17C2211yescharacteristic
21C22×#63227C2211yescharacteristic
22C22×#63227C2212yes—
23C22×#63227C2212yes—
24C22×#63227C2211yescharacteristic
25C22×C4×Dic17C2212yes—
26#11762688—24no—
27#11762688—24no—
28#11762682—24no—
29#11762672—24no—
30C4×C22⋊Dic17—24no—
31C2×#10587502C2211yescharacteristic
32C2×#10587502C2212yes—
33C2×#10587502C2212yes—
34C2×#10587502C2212yes—
35C2×#10587502C2212yes—
36C2×#10587502C2212yes—
37C2×#10587502C2211yescharacteristic
38C24×C4×C17C2211yescharacteristic
39C24×C4×C17C2211yescharacteristic
40C24×C4×C17C2211yescharacteristic
41C2×C17×#95—24no—
42C2×C17×#95C2212yes—
43C2×C17×#95C2212yes—
44C25×C17C2311yescharacteristic
45C24×D17C2311yescharacteristic
46C23×C4×C17—22no—
47C23×C4×C17—22no—
48C23×C4×C17—22no—
49C23×C4×C17—22no—
50C23×C4×C17—22no—
51C23×C4×C17—22no—
52C23×C4×C17—22no—
53C23×C4×C17—22no—
54C23×C4×C17—22no—
55C23×C4×C17—24no—
56C23×C4×C17—24no—
57C23×C4×C17—22no—
58C23×C4×C17—22no—
59C23×C4×C17—42no—
60C23×C4×C17—42no—
61C23×C4×C17C2×C414yes—
62C23×C4×C17D414yes—
63C23×C4×C17C2312yes—
64C23×C4×C17C2311yescharacteristic
65C23×C4×C17C2312yes—
66C23×C4×C17C2311yescharacteristic
67C22×C22⋊D17—22no—
68C22×C22⋊D17—22no—
69C22×C22⋊D17—22no—
70C22×C22⋊D17—22no—
71C22×C22⋊D17—22no—
72C22×C22⋊D17—22no—
73C22×C22⋊D17C2×C414yes—
74C23×Dic17C2311yescharacteristic
75C23×Dic17C2311yescharacteristic
76C23×Dic17C2311yescharacteristic
77C23×Dic17C2312yes—
78C23×Dic17C2312yes—
79C2×C22⋊Dic17—22no—
80C2×C22⋊Dic17—22no—
81C2×C22⋊Dic17—22no—
82C2×C22⋊Dic17—22no—
83C2×C22⋊Dic17—22no—
84C2×C22⋊Dic17C2×C414yes—
85C2×C22⋊Dic17D414yes—
86C2×C22⋊Dic17D414yes—
87C2×C22⋊Dic17D414yes—
88#10587615—232no—
89C2×#63227—22no—
90C2×#63227—22no—
91C2×#63227—24no—
92C2×#63227—24no—
93C2×#63227—24no—
94C2×#63227—24no—
95C2×#63227—24no—
96C2×#63227—42no—
97C2×#63227—42no—
98C2×#63227C2×C418yescomplemented
99C2×#63225—24no—
100C2×#63225—24no—
101C2×#63225—24no—
102C2×#63225—24no—
103C2×#63225—42no—
104C2×#63225C2×C418yescomplemented
105C2×C4×Dic17—24no—
106C2×C4×Dic17—24no—
107C2×C4×Dic17—42no—
108C17×#95—24no—
109C17×#95—24no—
110#10587502—22no—
111#10587502—22no—
112#10587502—24no—
113#10587502—24no—
114#10587502—24no—
115#10587502—24no—
116#10587502—24no—
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—21no—
141C22×C4×C17—21no—
142C22×C4×C17—22no—
143C22×C4×C17—28no—
144C22×C4×C17—28no—
145C22×C4×C17—28no—
146C22×C4×C17—28no—
147C22×C4×C17—28no—
148C22×C4×C17—22no—
149C22×C4×C17—21no—
150C22×C4×C17—22no—
151C22×C4×C17—22no—
152C22×C4×C17—22no—
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×C17—21no—
161C22×C4×C17—22no—
162C22×C4×C17—22no—
163C22×C4×C17—22no—
164C22×C4×C17—28no—
165C22×C4×C17—44no—
166C22×C4×C17—48no—
167C22×C4×C17—48no—
168C22×C4×C17—48no—
169C22×C4×C17—48no—
170C22×C4×C17—44no—
171C22×C4×C17—44no—
172C22×C4×C17—44no—
173C22×C4×C17—44no—
174C22×C4×C17—44no—
175C22×C4×C17—44no—
176C22×C4×C17C22×C414yes—
177C22×C4×C17C2×D412yes—
178C22×C4×C17C2×D412yes—
179C22×C4×C17#4114yes—
180C22×C4×C17#4114yes—
181C2×C22⋊D17—28no—
182C2×C22⋊D17—28no—
183C2×C22⋊D17—28no—
184C2×C22⋊D17—44no—
185C2×C22⋊D17—44no—
186C2×C22⋊D17—44no—
187C2×C22⋊D17—44no—
188C22×Dic17—22no—
189C22×Dic17—22no—
190C22×Dic17—22no—
191C22×Dic17—22no—
192C22×Dic17—21no—
193C22×Dic17—21no—
194C22×Dic17—21no—
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—21no—
205C22×Dic17—21no—
206C22×Dic17—21no—
207C22×Dic17—21no—
208C22×Dic17—21no—
209C22×Dic17—21no—
210C22×Dic17—22no—
211C22×Dic17—22no—
212C22×Dic17—22no—
213C22×Dic17—22no—
214C22×Dic17C22×C412yes—
215C22×Dic17C22×C414yes—
216C22×Dic17C2×D414yes—
217C22×Dic17C2×D414yes—
218C22×Dic17C2×D414yes—
219C22⋊Dic17—28no—
220C22⋊Dic17—44no—
221C22⋊Dic17C22⋊C4116yescomplemented
222#63227—216no—
223#63227—48no—
224#63227—44no—
225#63227—44no—
226#63225—216no—
227#63225—48no—
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×#4111yescharacteristic
259C23×C17C2×#4112yes—
260C23×C17C2×#4112yes—
261C23×C17C2×#4111yescharacteristic
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—22no—
288C2×C4×C17—22no—
289C2×C4×C17—24no—
290C2×C4×C17—24no—
291C2×C4×C17—24no—
292C2×C4×C17—24no—
293C2×C4×C17—24no—
294C2×C4×C17—22no—
295C2×C4×C17—22no—
296C2×C4×C17—24no—
297C2×C4×C17—22no—
298C2×C4×C17—24no—
299C2×C4×C17—24no—
300C2×C4×C17—416no—
301C2×C4×C17—416no—
302C2×C4×C17—42no—
303C2×C4×C17—42no—
304C2×C4×C17—42no—
305C2×C4×C17—42no—
306C2×C4×C17—42no—
307C2×C4×C17—42no—
308C2×C4×C17—42no—
309C2×C4×C17—42no—
310C2×C4×C17—42no—
311C2×C4×C17—42no—
312C2×C4×C17—416no—
313C2×C4×C17#12314yescomplemented
314C22⋊D17—416no—
315C2×Dic17—24no—
316C2×Dic17—24no—
317C2×Dic17—24no—
318C2×Dic17—24no—
319C2×Dic17—24no—
320C2×Dic17—24no—
321C2×Dic17—22no—
322C2×Dic17—22no—
323C2×Dic17—22no—
324C2×Dic17—24no—
325C2×Dic17—24no—
326C2×Dic17—24no—
327C2×Dic17—41no—
328C2×Dic17—41no—
329C2×Dic17—41no—
330C2×Dic17—42no—
331C2×Dic17—41no—
332C2×Dic17—42no—
333C2×Dic17—42no—
334C2×Dic17—42no—
335C2×Dic17—41no—
336C2×Dic17—41no—
337C2×Dic17—41no—
338C2×Dic17—41no—
339C2×Dic17—41no—
340C2×Dic17—41no—
341C2×Dic17—42no—
342C2×Dic17—42no—
343C2×Dic17—42no—
344C2×Dic17—42no—
345C2×Dic17C2×C22⋊C418yes—
346C22×#123—171no—
347C2×#386—171no—
348C2×#386—171no—
349C2×#385—171no—
350C2×#381—171no—
351C2×C4×C22⋊C4—171no—
352C22×#95D1711yescharacteristic, complemented
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—24no—
403C4×C17—42no—
404C4×C17—44no—
405C4×C17—44no—
406Dic17—28no—
407Dic17—44no—
408Dic17—42no—
409Dic17—81no—
410Dic17—81no—
411C23×D4—171no—
412C24×C4C2×D1711yescharacteristic
413C24×C4C2×D1711yescharacteristic
414C24×C4C2×D1711yescharacteristic
415C2×#123—178no—
416C2×#123—344no—
417C2×#123—344no—
418C22×C4⋊C4—172no—
419C22×C4⋊C4—172no—
420C22×C22⋊C4—171no—
421C22×C22⋊C4—171no—
422C22×C22⋊C4—172no—
423C22×C22⋊C4—171no—
424C22×C22⋊C4—171no—
425C22×C22⋊C4—172no—
426C22×C22⋊C4—171no—
427C22×C42—172no—
428#386—344no—
429#386—344no—
430#385—344no—
431#381—344no—
432C4×C22⋊C4—344no—
433C2×#95—24no—
434C2×#95—171no—
435C2×#95—172no—
436C2×#95—172no—
437C2×#95—172no—
438C2×#95—172no—
439C2×#95—172no—
440C2×#95—171no—
441C2×#95C2×D1712yes—
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—22no—
467C23×C4—22no—
468C23×C4—22no—
469C23×C4—22no—
470C23×C4—22no—
471C23×C4—22no—
472C23×C4—22no—
473C23×C4—22no—
474C23×C4—24no—
475C23×C4—24no—
476C23×C4—22no—
477C23×C4—22no—
478C23×C4—42no—
479C23×C4—42no—
480C23×C4—172no—
481C23×C4—172no—
482C23×C4—171no—
483C23×C4—171no—
484C23×C4—171no—
485C23×C4C4×D1714yes—
486C23×C4C22⋊D1714yes—
487C23×C4C22×D1712yes—
488C23×C4C22×D1712yes—
489C23×C4C22×D1711yescharacteristic
490C23×C4C22×D1711yescharacteristic
491#123—3432no—
492C2×C4⋊C4—178no—
493C2×C4⋊C4—344no—
494C2×C4⋊C4—344no—
495C2×C4⋊C4—344no—
496C2×C4⋊C4—344no—
497C2×C4⋊C4—682no—
498C2×C22⋊C4—174no—
499C2×C22⋊C4—174no—
500C2×C22⋊C4—174no—
501C2×C22⋊C4—174no—
502C2×C22⋊C4—178no—
503C2×C22⋊C4—344no—
504C2×C22⋊C4—344no—
505C2×C22⋊C4—342no—
506C2×C22⋊C4—342no—
507C2×C22⋊C4—344no—
508C2×C22⋊C4—342no—
509C2×C22⋊C4—342no—
510C2×C22⋊C4—342no—
511C2×C22⋊C4—344no—
512C2×C22⋊C4—344no—
513C2×C22⋊C4—342no—
514C2×C22⋊C4—342no—
515C2×C22⋊C4—682no—
516C2×C22⋊C4—682no—
517C2×C42—344no—
518C2×C42—344no—
519C2×C42—682no—
520#95—24no—
521#95—24no—
522#95—344no—
523#95—344no—
524#95—344no—
525#95—344no—
526#95—344no—
527#95—342no—
528#95—342no—
529C17#1399611yescharacteristic, complemented, Sylow
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—172no—
535C24—342no—
536C24—342no—
537C24—341no—
538C24—341no—
539C24—341no—
540C24—341no—
541C24—341no—
542C24—342no—
543C24—342no—
544C24—341no—
545C24C2×C4×D1712yes—
546C24#6325212yes—
547C24D4×D1712yes—
548C24D4×D1712yes—
549C24D4×D1712yes—
550C24#6325412yes—
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—21no—
561C22×C4—21no—
562C22×C4—22no—
563C22×C4—28no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—28no—
581C22×C4—28no—
582C22×C4—28no—
583C22×C4—28no—
584C22×C4—28no—
585C22×C4—44no—
586C22×C4—48no—
587C22×C4—48no—
588C22×C4—48no—
589C22×C4—48no—
590C22×C4—44no—
591C22×C4—44no—
592C22×C4—44no—
593C22×C4—44no—
594C22×C4—44no—
595C22×C4—44no—
596C22×C4—174no—
597C22×C4—174no—
598C22×C4—174no—
599C22×C4—172no—
600C22×C4—174no—
601C22×C4—342no—
602C22×C4—342no—
603C22×C4—342no—
604C22×C4—342no—
605C22×C4—342no—
606C22×C4—342no—
607C22×C4—342no—
608C22×C4—341no—
609C22×C4—341no—
610C22×C4—342no—
611C22×C4—341no—
612C22×C4—341no—
613C22×C4—341no—
614C22×C4—342no—
615C22×C4—342no—
616C22×C4—341no—
617C22×C4—342no—
618C22×C4—342no—
619C22×C4—341no—
620C22×C4—341no—
621C22×C4—341no—
622C22×C4—341no—
623C22×C4—342no—
624C22×C4—342no—
625C22×C4—341no—
626C22×C4—341no—
627C22×C4C2×C4×D1714yes—
628C22×C4#6325214yes—
629C22×C4#6325214yes—
630C22×C4C2×C22⋊D1712yes—
631C22×C4C2×C22⋊D1712yes—
632C4⋊C4—3416no—
633C4⋊C4—688no—
634C22⋊C4—1716no—
635C22⋊C4—3416no—
636C22⋊C4—348no—
637C22⋊C4—688no—
638C22⋊C4—684no—
639C22⋊C4—684no—
640C22⋊C4—684no—
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—
681C23C22⋊C4×D1714yes—
682C23#1058756714yes—
683C23#1058757014yes—
684C23#1058757114yes—
685C23C4×C22⋊D1714yes—
686C23#1058762514yes—
687C23#1058762614yes—
688C23C22×C4×D1711yescharacteristic
689C23C2×#6325212yes—
690C23C2×#6325212yes—
691C23C2×#6325211yescharacteristic
692C23C2×D4×D1711yescharacteristic
693C23C2×D4×D1711yescharacteristic
694C23C2×D4×D1711yescharacteristic
695C23C2×#6325411yescharacteristic
696C23#1058769112yes—
697C23#1058769412yes—
698C23C22×C22⋊D1711yescharacteristic
699D4—6816no—
700C2×C4—24no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—24no—
710C2×C4—22no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—416no—
714C2×C4—416no—
715C2×C4—416no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—178no—
727C2×C4—344no—
728C2×C4—344no—
729C2×C4—344no—
730C2×C4—344no—
731C2×C4—344no—
732C2×C4—344no—
733C2×C4—344no—
734C2×C4—342no—
735C2×C4—342no—
736C2×C4—342no—
737C2×C4—344no—
738C2×C4—344no—
739C2×C4—682no—
740C2×C4—681no—
741C2×C4—681no—
742C2×C4—681no—
743C2×C4—682no—
744C2×C4—681no—
745C2×C4—682no—
746C2×C4—682no—
747C2×C4—682no—
748C2×C4—682no—
749C2×C4—681no—
750C2×C4—681no—
751C2×C4—681no—
752C2×C4—681no—
753C2×C4—681no—
754C2×C4—681no—
755C2×C4—682no—
756C2×C4—682no—
757C2×C4#1058761514yescomplemented
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#1176270918yes—
780C22C2×C22⋊C4×D1711yescharacteristic
781C22C2×#1058756711yescharacteristic
782C22C2×C4×C22⋊D1711yescharacteristic
783C22C4×#6325212yes—
784C22#1176329012yes—
785C22C2×#1058762511yescharacteristic
786C22C2×#1058757011yescharacteristic
787C22C2×#1058761511yescharacteristic
788C22#1176332011yescharacteristic
789C22C2×#1058757111yescharacteristic
790C22#1176334312yes—
791C22C2×#1058762611yescharacteristic
792C22#1176336811yescharacteristic
793C22#1176338311yescharacteristic
794C22#1176340612yes—
795C22#1176344912yes—
796C22#1176344912yes—
797C22#1176344912yes—
798C22#1176346012yes—
799C22#1176346012yes—
800C22#1176346012yes—
801C22#1176348512yes—
802C22#1176349412yes—
803C4—24no—
804C4—44no—
805C4—42no—
806C4—44no—
807C4—348no—
808C4—682no—
809C4—684no—
810C4—1361no—
811C4—1361no—
812C2—28no—
813C2—1362no—
814C2C2×#1176270911yescharacteristic
815C2C4×#1058761511yescharacteristic
816C2#1453145311yescharacteristic
817C2#1453161112yes—
818C2#1453177212yes—
819C2#1453218011yescharacteristic
820C2#1453219111yescharacteristic
821C2#1453233512yes—
822C2#1453311012yes—
823C2#1453325111yescharacteristic
824C2#1453371511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC22×C17×#95C2
socle, cosocleC24×C17C24
prime radicalC23×C22⋊D17C22
hypercenterC22×#95D17
hypocenterC17#13996
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C22×#95

Complements

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

NH ≅ G/Ntype
4. C2×#11762682C2semidirect
5. C2×#11762672C2semidirect
6. C2×C4×C22⋊Dic17C2semidirect
7. #14527050C2semidirect
8. #14527028C2semidirect
9. #14527020C2semidirect
10. #14527012C2semidirect
11. C22×C17×#95C2semidirect
15. C2×#10587615C4semidirect
98. C2×#63227C2×C4semidirect
104. C2×#63225C2×C4semidirect
221. C22⋊Dic17C22⋊C4semidirect
313. C2×C4×C17#123semidirect
352. C22×#95D17semidirect
529. C17#13996semidirect
757. C2×C4#10587615semidirect

Maximal subgroups

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

subgroupindex
C22×#105876152
C2×#117626882
C2×#117626822
C2×#117626722
C2×C4×C22⋊Dic172
#145270502
#145270282
#145270202
#145270122
C22×C17×#952
#1399617