Finite Group Databasebeta

← #16957697

Subgroups — #16957697

Order 4352.

2590 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D17C211yesmaximal, characteristic
2C2×#11762688C211yesmaximal, characteristic
3C2×#11762688C211yesmaximal, characteristic
4C2×#11762682C211yesmaximal, characteristic, complemented
5#14527042C212yesmaximal, complemented
6#14527028C212yesmaximal, complemented
7#14527015C212yesmaximal, complemented
8#14527007C211yesmaximal, characteristic, complemented
9#14527007C211yesmaximal, characteristic, complemented
10#14527005C212yesmaximal, complemented
11C22×C17×#95C211yesmaximal, characteristic, complemented
12C23×C22⋊D17C2211yescharacteristic
13C23×C4×D17C2211yescharacteristic
14C2×C4×C22⋊D17—24no—
15C2×C4×C22⋊D17—24no—
16C2×C4×C22⋊D17—24no—
17C22×#63225C2211yescharacteristic
18C22×#63225C2212yes—
19C22×C22⋊Dic17C2211yescharacteristic
20C22×C22⋊Dic17C2211yescharacteristic
21C22×C22⋊Dic17C2211yescharacteristic
22C22×#63227C2211yescharacteristic
23C22×#63227C2212yes—
24C22×#63227C2212yes—
25C22×C4×Dic17C2211yescharacteristic
26#11762688—24no—
27#11762688C418yescomplemented
28#11762682—24no—
29C2×#10587502C2212yes—
30C2×#10587502C2212yes—
31C2×#10587502C2212yes—
32C2×#10587502C2212yes—
33C2×#10587502C2212yes—
34C2×#10587502C2212yes—
35C2×#10587502C2212yes—
36C24×C4×C17C2211yescharacteristic
37C24×C4×C17C2211yescharacteristic
38C24×C4×C17C2211yescharacteristic
39C2×C17×#95—24no—
40C2×C17×#95C2212yes—
41C2×C17×#95C2212yes—
42C25×C17C2311yescharacteristic
43C24×D17C2311yescharacteristic
44C23×C4×C17—22no—
45C23×C4×C17—22no—
46C23×C4×C17—22no—
47C23×C4×C17—22no—
48C23×C4×C17—22no—
49C23×C4×C17—24no—
50C23×C4×C17—24no—
51C23×C4×C17—22no—
52C23×C4×C17—22no—
53C23×C4×C17—42no—
54C23×C4×C17—42no—
55C23×C4×C17—42no—
56C23×C4×C17—42no—
57C23×C4×C17C2×C414yescomplemented
58C23×C4×C17D414yes—
59C23×C4×C17C2312yes—
60C23×C4×C17C2311yescharacteristic
61C23×C4×C17C2312yes—
62C23×C4×C17C2311yescharacteristic
63C22×C22⋊D17—22no—
64C22×C22⋊D17—22no—
65C22×C22⋊D17—22no—
66C22×C22⋊D17—22no—
67C22×C22⋊D17C2×C414yes—
68C22×C22⋊D17D414yes—
69C22×C22⋊D17Q814yes—
70C23×Dic17C2312yes—
71C23×Dic17C2312yes—
72C23×Dic17C2311yescharacteristic
73C23×Dic17C2311yescharacteristic
74C23×Dic17C2311yescharacteristic
75C22×C4×D17—22no—
76C22×C4×D17—22no—
77C22×C4×D17—22no—
78C22×C4×D17—24no—
79C22×C4×D17—42no—
80C2×C22⋊Dic17—22no—
81C2×C22⋊Dic17—22no—
82C2×C22⋊Dic17—22no—
83C2×C22⋊Dic17—22no—
84C2×C22⋊Dic17—22no—
85C2×C22⋊Dic17—22no—
86C2×C22⋊Dic17—22no—
87C2×C22⋊Dic17C2×C414yescomplemented
88C2×C22⋊Dic17D414yes—
89C4×C22⋊D17—232no—
90C2×#63227—22no—
91C2×#63227—24no—
92C2×#63227—22no—
93C2×#63227—24no—
94C2×#63227—22no—
95C2×#63227—42no—
96C2×#63227—42no—
97C2×#63227—42no—
98C2×#63227C2×C418yescomplemented
99C2×#63225—22no—
100C2×#63225—24no—
101C2×#63225—22no—
102C2×#63225—22no—
103C2×#63225—24no—
104C2×#63225—42no—
105C2×C4×Dic17—22no—
106C2×C4×Dic17—22no—
107C2×C4×Dic17—22no—
108C17×#95—24no—
109C17×#95—24no—
110#10587502—24no—
111#10587502—24no—
112#10587502—24no—
113#10587502—42no—
114#10587502—42no—
115#10587502—42no—
116#10587502C2×C418yescomplemented
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×Q812yes—
126C24×C17#4112yes—
127C24×C17#4112yes—
128C24×C17C2411yescharacteristic
129C23×D17—21no—
130C23×D17—21no—
131C23×D17—22no—
132C23×D17—21no—
133C23×D17—21no—
134C23×D17—22no—
135C23×D17—22no—
136C23×D17—22no—
137C23×D17C22×C412yes—
138C23×D17C2×D412yes—
139C23×D17C2×Q812yes—
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—22no—
147C22×C4×C17—22no—
148C22×C4×C17—22no—
149C22×C4×C17—22no—
150C22×C4×C17—21no—
151C22×C4×C17—21no—
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—22no—
161C22×C4×C17—22no—
162C22×C4×C17—28no—
163C22×C4×C17—48no—
164C22×C4×C17—44no—
165C22×C4×C17—48no—
166C22×C4×C17—48no—
167C22×C4×C17—48no—
168C22×C4×C17—48no—
169C22×C4×C17—44no—
170C22×C4×C17—44no—
171C22×C4×C17—44no—
172C22×C4×C17—48no—
173C22×C4×C17—44no—
174C22×C4×C17C22×C414yes—
175C22×C4×C17C2×D412yes—
176C22×C4×C17C2×D412yes—
177C22×C4×C17#4114yes—
178C22×C4×C17#4114yes—
179C2×C22⋊D17—28no—
180C2×C22⋊D17—28no—
181C2×C22⋊D17—28no—
182C2×C22⋊D17—28no—
183C2×C22⋊D17—28no—
184C2×C22⋊D17—28no—
185C2×C22⋊D17C4⋊C4116yescomplemented
186C22×Dic17—21no—
187C22×Dic17—21no—
188C22×Dic17—21no—
189C22×Dic17—21no—
190C22×Dic17—21no—
191C22×Dic17—21no—
192C22×Dic17—22no—
193C22×Dic17—21no—
194C22×Dic17—21no—
195C22×Dic17—22no—
196C22×Dic17—22no—
197C22×Dic17—22no—
198C22×Dic17—22no—
199C22×Dic17—22no—
200C22×Dic17—22no—
201C22×Dic17—22no—
202C22×Dic17—22no—
203C22×Dic17—22no—
204C22×Dic17—22no—
205C22×Dic17—22no—
206C22×Dic17—22no—
207C22×Dic17—22no—
208C22×Dic17—22no—
209C22×Dic17—22no—
210C22×Dic17—22no—
211C22×Dic17C22×C414yes—
212C22×Dic17C22×C412yes—
213C22×Dic17C2×D412yes—
214C22×Dic17C2×D412yes—
215C22×Dic17C2×D412yes—
216C22×Dic17C2×Q812yes—
217C2×C4×D17—28no—
218C2×C4×D17—48no—
219C2×C4×D17—48no—
220C2×C4×D17—44no—
221C2×C4×D17—44no—
222C22⋊Dic17—28no—
223C22⋊Dic17—28no—
224C22⋊Dic17—44no—
225#63227—28no—
226#63227—48no—
227#63227—48no—
228#63225—28no—
229#63225—48no—
230C4×Dic17—28no—
231#14016—171nomaximal, Sylow
232C23×C17—24no—
233C23×C17—24no—
234C23×C17—22no—
235C23×C17—22no—
236C23×C17—24no—
237C23×C17—22no—
238C23×C17—22no—
239C23×C17—24no—
240C23×C17—24no—
241C23×C17—24no—
242C23×C17—24no—
243C23×C17—24no—
244C23×C17—24no—
245C23×C17—24no—
246C23×C17—24no—
247C23×C17—24no—
248C23×C17C2×C4⋊C414yes—
249C23×C17C4×D414yes—
250C23×C17C4×D414yes—
251C23×C17#12014yes—
252C23×C17C22⋊Q814yes—
253C23×C17C22⋊Q814yes—
254C23×C17#12314yes—
255C23×C17C23×C411yescharacteristic
256C23×C17C22×D411yescharacteristic
257C23×C17C22×D411yescharacteristic
258C23×C17C22×D411yescharacteristic
259C23×C17C22×Q811yescharacteristic
260C23×C17C2×#4111yescharacteristic
261C23×C17C2×#4112yes—
262C23×C17C2×#4112yes—
263C23×C17C2×#4111yescharacteristic
264C23×C17H(5,𝔽2)12yes—
265C23×C17H(5,𝔽2)12yes—
266C22×D17—22no—
267C22×D17—22no—
268C22×D17—24no—
269C22×D17—24no—
270C22×D17—22no—
271C22×D17—22no—
272C22×D17—22no—
273C22×D17—22no—
274C22×D17—24no—
275C22×D17—24no—
276C22×D17—24no—
277C22×D17—24no—
278C22×D17—41no—
279C22×D17—41no—
280C22×D17—42no—
281C22×D17—41no—
282C22×D17—41no—
283C22×D17—42no—
284C22×D17—42no—
285C22×D17—42no—
286C22×D17—42no—
287C22×D17—42no—
288C22×D17C2×C4⋊C414yes—
289C2×C4×C17—22no—
290C2×C4×C17—22no—
291C2×C4×C17—24no—
292C2×C4×C17—24no—
293C2×C4×C17—24no—
294C2×C4×C17—24no—
295C2×C4×C17—24no—
296C2×C4×C17—22no—
297C2×C4×C17—22no—
298C2×C4×C17—24no—
299C2×C4×C17—22no—
300C2×C4×C17—24no—
301C2×C4×C17—24no—
302C2×C4×C17—416no—
303C2×C4×C17—416no—
304C2×C4×C17—416no—
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—42no—
313C2×C4×C17—42no—
314C2×C4×C17—42no—
315C2×C4×C17#12314yes—
316C22⋊D17—232no—
317C2×Dic17—22no—
318C2×Dic17—22no—
319C2×Dic17—22no—
320C2×Dic17—22no—
321C2×Dic17—22no—
322C2×Dic17—22no—
323C2×Dic17—24no—
324C2×Dic17—24no—
325C2×Dic17—24no—
326C2×Dic17—22no—
327C2×Dic17—22no—
328C2×Dic17—24no—
329C2×Dic17—24no—
330C2×Dic17—41no—
331C2×Dic17—41no—
332C2×Dic17—41no—
333C2×Dic17—41no—
334C2×Dic17—42no—
335C2×Dic17—42no—
336C2×Dic17—42no—
337C2×Dic17—42no—
338C2×Dic17—42no—
339C2×Dic17—42no—
340C2×Dic17—42no—
341C2×Dic17—42no—
342C2×Dic17—42no—
343C2×Dic17—42no—
344C2×Dic17—42no—
345C2×Dic17—42no—
346C2×Dic17—42no—
347C2×Dic17C2×C4⋊C414yes—
348C4×D17—416no—
349C22×C4×D4—171no—
350C2×#386—171no—
351C2×#386—171no—
352C2×#385—171no—
353C22×#95D1711yescharacteristic, complemented
354#1442—172no—
355#1439—172no—
356#1436—172no—
357C22⋊#95—172no—
358C22⋊#95—171no—
359C22⋊#95—171no—
360C22×C17—24no—
361C22×C17—24no—
362C22×C17—28no—
363C22×C17—28no—
364C22×C17—24no—
365C22×C17—24no—
366C22×C17—28no—
367C22×C17—28no—
368C22×C17—24no—
369C22×C17—24no—
370C22×C17#38518yes—
371C22×C17C22×C4⋊C411yescharacteristic
372C22×C17C2×C4×D411yescharacteristic
373C22×C17C2×C4×D411yescharacteristic
374C22×C17C4×#4112yes—
375C22×C17#51812yes—
376C22×C17C2×#12011yescharacteristic
377C22×C17C2×C22⋊Q811yescharacteristic
378C22×C17C2×C22⋊Q811yescharacteristic
379C22×C17C2×#12311yescharacteristic
380C22×C17C2×#12311yescharacteristic
381C22×C17#52511yescharacteristic
382C22×C17#52912yes—
383C22×C17#53411yescharacteristic
384C22×C17#53511yescharacteristic
385C22×C17#53812yes—
386C22×C17#54612yes—
387C22×C17#54612yes—
388C22×C17#54612yes—
389C22×C17#54612yes—
390C22×C17#55312yes—
391C22×C17#55312yes—
392C22×C17#55412yes—
393C22×C17#55412yes—
394C2×D17—28no—
395C2×D17—24no—
396C2×D17—42no—
397C2×D17—42no—
398C2×D17—44no—
399C2×D17—42no—
400C2×D17—42no—
401C2×D17—44no—
402C2×D17—44no—
403C2×D17—42no—
404C2×D17—42no—
405C4×C17—24no—
406C4×C17—44no—
407C4×C17—44no—
408C4×C17—42no—
409Dic17—24no—
410Dic17—44no—
411Dic17—42no—
412Dic17—42no—
413Dic17—82no—
414C23×D4—171no—
415C24×C4—171no—
416C24×C4C2×D1711yescharacteristic
417C24×C4C2×D1711yescharacteristic
418C24×C4C2×D1711yescharacteristic
419C2×C4×D4—344no—
420C2×C4×D4—344no—
421C2×C4×D4—344no—
422C22×C4⋊C4—171no—
423C22×C4⋊C4—172no—
424C22×C22⋊C4—171no—
425C22×C22⋊C4—171no—
426C22×C22⋊C4—172no—
427C22×C22⋊C4—171no—
428C22×C22⋊C4—171no—
429C22×C22⋊C4—172no—
430C22×C42—171no—
431#386—178no—
432#386—344no—
433#385—344no—
434C2×#95—24no—
435C2×#95—172no—
436C2×#95—172no—
437C2×#95—172no—
438C2×#95—172no—
439C2×#95—172no—
440C2×#95—172no—
441C2×#95—172no—
442C2×#95C2×D1712yes—
443C2×#95C2×D1712yes—
444C2×C17—28no—
445C2×C17C2×#38511yescharacteristic
446C2×C17C4×#12311yescharacteristic
447C2×C17#232111yescharacteristic
448C2×C17#234912yes—
449C2×C17#236412yes—
450C2×C17#240411yescharacteristic
451C2×C17#240511yescharacteristic
452C2×C17#244412yes—
453C2×C17#245012yes—
454C2×C17#248711yescharacteristic
455C2×C17#257911yescharacteristic
456D17—44no—
457C25—171no—
458C25C22×D1711yescharacteristic
459C22×D4—174no—
460C22×D4—174no—
461C22×D4—174no—
462C22×D4—342no—
463C22×D4—342no—
464C22×D4—342no—
465C22×D4—342no—
466C23×C4—22no—
467C23×C4—22no—
468C23×C4—22no—
469C23×C4—22no—
470C23×C4—22no—
471C23×C4—24no—
472C23×C4—24no—
473C23×C4—22no—
474C23×C4—22no—
475C23×C4—42no—
476C23×C4—42no—
477C23×C4—42no—
478C23×C4—42no—
479C23×C4—171no—
480C23×C4—171no—
481C23×C4—172no—
482C23×C4—171no—
483C23×C4—172no—
484C23×C4—342no—
485C23×C4—342no—
486C23×C4—342no—
487C23×C4—344no—
488C23×C4—682no—
489C23×C4C4×D1714yescomplemented
490C23×C4C22⋊D1714yes—
491C23×C4C22×D1712yes—
492C23×C4C22×D1712yes—
493C23×C4C22×D1711yescharacteristic
494C23×C4C22×D1711yescharacteristic
495C4×D4—3432no—
496C2×C4⋊C4—342no—
497C2×C4⋊C4—342no—
498C2×C4⋊C4—342no—
499C2×C4⋊C4—344no—
500C2×C4⋊C4—344no—
501C2×C4⋊C4—682no—
502C2×C22⋊C4—174no—
503C2×C22⋊C4—174no—
504C2×C22⋊C4—178no—
505C2×C22⋊C4—342no—
506C2×C22⋊C4—342no—
507C2×C22⋊C4—342no—
508C2×C22⋊C4—342no—
509C2×C22⋊C4—342no—
510C2×C22⋊C4—342no—
511C2×C22⋊C4—342no—
512C2×C22⋊C4—344no—
513C2×C22⋊C4—342no—
514C2×C22⋊C4—342no—
515C2×C22⋊C4—342no—
516C2×C22⋊C4—344no—
517C2×C22⋊C4—682no—
518C2×C22⋊C4—682no—
519C2×C22⋊C4—682no—
520C2×C42—342no—
521C2×C42—342no—
522C2×C42—342no—
523#95—24no—
524#95—24no—
525#95—178no—
526#95—344no—
527#95—344no—
528#95—344no—
529#95—682no—
530#95—682no—
531#95—682no—
532C17#1401611yescharacteristic, complemented, Sylow
533C24—22no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—172no—
538C24—172no—
539C24—172no—
540C24—342no—
541C24—342no—
542C24—341no—
543C24—341no—
544C24—342no—
545C24—342no—
546C24—341no—
547C24—341no—
548C24C2×C4×D1712yes—
549C24#6325212yes—
550C24D4×D1712yes—
551C24D4×D1712yes—
552C24Q8×D1712yes—
553C24#6325612yes—
554C24C2×C22⋊D1712yes—
555C24C23×D1711yescharacteristic
556C2×D4—1716no—
557C2×D4—348no—
558C2×D4—348no—
559C2×D4—348no—
560C2×D4—348no—
561C2×D4—348no—
562C2×D4—348no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—28no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—28no—
584C22×C4—28no—
585C22×C4—28no—
586C22×C4—48no—
587C22×C4—44no—
588C22×C4—48no—
589C22×C4—48no—
590C22×C4—48no—
591C22×C4—48no—
592C22×C4—44no—
593C22×C4—44no—
594C22×C4—44no—
595C22×C4—48no—
596C22×C4—44no—
597C22×C4—172no—
598C22×C4—172no—
599C22×C4—172no—
600C22×C4—174no—
601C22×C4—172no—
602C22×C4—172no—
603C22×C4—348no—
604C22×C4—341no—
605C22×C4—341no—
606C22×C4—341no—
607C22×C4—341no—
608C22×C4—342no—
609C22×C4—342no—
610C22×C4—342no—
611C22×C4—342no—
612C22×C4—342no—
613C22×C4—341no—
614C22×C4—341no—
615C22×C4—342no—
616C22×C4—342no—
617C22×C4—342no—
618C22×C4—342no—
619C22×C4—342no—
620C22×C4—341no—
621C22×C4—341no—
622C22×C4—342no—
623C22×C4—342no—
624C22×C4—342no—
625C22×C4—342no—
626C22×C4—342no—
627C22×C4—342no—
628C22×C4—342no—
629C22×C4—688no—
630C22×C4—688no—
631C22×C4—684no—
632C22×C4—684no—
633C22×C4C2×C4×D1714yes—
634C22×C4#6325214yes—
635C22×C4#6325214yes—
636C22×C4C2×C22⋊D1712yes—
637C22×C4C2×C22⋊D1712yes—
638C4⋊C4—348no—
639C4⋊C4—688no—
640C22⋊C4—348no—
641C22⋊C4—348no—
642C22⋊C4—348no—
643C22⋊C4—688no—
644C22⋊C4—688no—
645C22⋊C4—684no—
646C42—348no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—22no—
654C23—22no—
655C23—24no—
656C23—22no—
657C23—22no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—174no—
664C23—344no—
665C23—344no—
666C23—342no—
667C23—342no—
668C23—344no—
669C23—344no—
670C23—342no—
671C23—342no—
672C23—342no—
673C23—342no—
674C23—344no—
675C23—344no—
676C23—682no—
677C23—682no—
678C23—681no—
679C23—681no—
680C23—682no—
681C23—681no—
682C23—681no—
683C23—682no—
684C23—682no—
685C23—682no—
686C23C4⋊C4×D1714yes—
687C23#1058757914yes—
688C23#1058758014yes—
689C23#1058758214yes—
690C23C4×C22⋊D1714yes—
691C23#1058762314yes—
692C23#1058763214yes—
693C23C22×C4×D1711yescharacteristic
694C23C2×#6325212yes—
695C23C2×#6325212yes—
696C23C2×#6325211yescharacteristic
697C23C2×D4×D1711yescharacteristic
698C23C2×D4×D1711yescharacteristic
699C23#1058769112yes—
700C23#1058769112yes—
701C23C2×Q8×D1711yescharacteristic
702C23C2×#6325611yescharacteristic
703C23C22×C22⋊D1711yescharacteristic
704D4—3432no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—24no—
715C2×C4—22no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—416no—
719C2×C4—416no—
720C2×C4—416no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—174no—
732C2×C4—342no—
733C2×C4—342no—
734C2×C4—342no—
735C2×C4—342no—
736C2×C4—342no—
737C2×C4—342no—
738C2×C4—344no—
739C2×C4—344no—
740C2×C4—344no—
741C2×C4—342no—
742C2×C4—342no—
743C2×C4—344no—
744C2×C4—344no—
745C2×C4—6816no—
746C2×C4—682no—
747C2×C4—682no—
748C2×C4—681no—
749C2×C4—681no—
750C2×C4—681no—
751C2×C4—681no—
752C2×C4—682no—
753C2×C4—682no—
754C2×C4—682no—
755C2×C4—682no—
756C2×C4—682no—
757C2×C4—682no—
758C2×C4—682no—
759C2×C4—682no—
760C2×C4—682no—
761C2×C4—682no—
762C2×C4—682no—
763C2×C4#1058761514yes—
764C22—28no—
765C22—24no—
766C22—24no—
767C22—28no—
768C22—24no—
769C22—28no—
770C22—24no—
771C22—24no—
772C22—24no—
773C22—28no—
774C22—348no—
775C22—344no—
776C22—684no—
777C22—682no—
778C22—682no—
779C22—682no—
780C22—684no—
781C22—682no—
782C22—682no—
783C22—682no—
784C22—684no—
785C22#1176268018yes—
786C22C2×C4⋊C4×D1711yescharacteristic
787C22C2×C4×C22⋊D1711yescharacteristic
788C22C2×#1058757911yescharacteristic
789C22C4×#6325212yes—
790C22#1176328212yes—
791C22C2×#1058762311yescharacteristic
792C22C2×#1058763211yescharacteristic
793C22C2×#1058758211yescharacteristic
794C22C2×#1058761511yescharacteristic
795C22C2×#1058758011yescharacteristic
796C22#1176332011yescharacteristic
797C22#1176334312yes—
798C22#1176336811yescharacteristic
799C22#1176337611yescharacteristic
800C22#1176339712yes—
801C22#1176344912yes—
802C22#1176344912yes—
803C22#1176344912yes—
804C22#1176344912yes—
805C22#1176350712yes—
806C22#1176350712yes—
807C22#1176351412yes—
808C22#1176351412yes—
809C4—24no—
810C4—44no—
811C4—42no—
812C4—44no—
813C4—344no—
814C4—682no—
815C4—682no—
816C4—684no—
817C4—1362no—
818C2—28no—
819C2—684no—
820C2C2×#1176268011yescharacteristic
821C2C4×#1058761511yescharacteristic
822C2#1453144211yescharacteristic
823C2#1453169112yes—
824C2#1453183112yes—
825C2#1453210311yescharacteristic
826C2#1453211111yescharacteristic
827C2#1453253412yes—
828C2#1453260812yes—
829C2#1453309511yescharacteristic
830C2#1453413111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC22×C17×#95C2
socle, cosocleC24×C17C24
prime radicalC23×C22⋊D17C22
hypercenterC22×#95D17
hypocenterC17#14016
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. #14527042C2semidirect
6. #14527028C2semidirect
7. #14527015C2semidirect
8. #14527007C2semidirect
9. #14527007C2semidirect
10. #14527005C2semidirect
11. C22×C17×#95C2semidirect
27. #11762688C4semidirect
57. C23×C4×C17C2×C4semidirect
87. C2×C22⋊Dic17C2×C4semidirect
98. C2×#63227C2×C4semidirect
116. #10587502C2×C4semidirect
185. C2×C22⋊D17C4⋊C4semidirect
353. C22×#95D17semidirect
489. C23×C4C4×D17semidirect
532. C17#14016semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D172
C2×#117626882
C2×#117626822
#145270422
#145270282
#145270152
#145270072
#145270052
C22×C17×#952
#1401617