Finite Group Databasebeta

← #16965601

Subgroups — #16965601

Order 4352.

1674 conjugacy classes of subgroups.

The subgroup lattice has 1000 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762700C211yesmaximal, characteristic
2C2×#11762698C211yesmaximal, characteristic
3C2×#11762698C211yesmaximal, characteristic
4C2×#11762691C211yesmaximal, characteristic, complemented
5C2×C42×Dic17C211yesmaximal, characteristic, complemented
6#14527020C211yesmaximal, characteristic
7#14527020C211yesmaximal, characteristic
8#14527020C211yesmaximal, characteristic
9#14527020C211yesmaximal, characteristic
10#14527019C211yesmaximal, characteristic, complemented
11#14527015C211yesmaximal, characteristic, complemented
12#14527015C211yesmaximal, characteristic, complemented
13#14527015C211yesmaximal, characteristic, complemented
14#14527009C211yesmaximal, characteristic, complemented
15C17×#1434C211yesmaximal, characteristic, complemented
16C22×#63225C2211yescharacteristic
17C22×#63225C2211yescharacteristic
18C22×#63225C2211yescharacteristic
19C22×#63227C2211yescharacteristic
20C22×#63227C2211yescharacteristic
21C22×#63227C2211yescharacteristic
22C22×#63227C2211yescharacteristic
23C22×#63227C2211yescharacteristic
24C22×#63227C2211yescharacteristic
25C22×#63227C2211yescharacteristic
26C22×C4×Dic17C2211yescharacteristic
27C22×C4×Dic17C2211yescharacteristic
28C22×C4×Dic17C2211yescharacteristic
29C22×C4×Dic17C2211yescharacteristic
30C22×C4×Dic17C2211yescharacteristic
31C22×C4×Dic17C2211yescharacteristic
32#11762700C418yescomplemented
33#11762698—24no—
34#11762698—24no—
35#11762691—24no—
36C2×#10587502C2211yescharacteristic
37C2×#10587502C2211yescharacteristic
38C2×#10587502C2211yescharacteristic
39C2×#10587502C2211yescharacteristic
40C2×#10587502C2211yescharacteristic
41C2×#10587502C2211yescharacteristic
42C2×#10587502C2211yescharacteristic
43C2×#10587502C2211yescharacteristic
44C2×#10587502C2211yescharacteristic
45C2×#10587502C2211yescharacteristic
46C2×#10587502C2211yescharacteristic
47C2×#10587502C2211yescharacteristic
48C42×Dic17—24no—
49C22×C42×C17C2211yescharacteristic
50C2×C17×#95C2211yescharacteristic
51C2×C17×#95C2211yescharacteristic
52C2×C17×#95C2211yescharacteristic
53C2×C17×#95C2211yescharacteristic
54C2×C17×#95C2211yescharacteristic
55C2×C17×#95C2211yescharacteristic
56C24×D17C2311yescharacteristic
57C23×C4×C17C2311yescharacteristic
58C23×C4×C17C2311yescharacteristic
59C23×C4×C17C2311yescharacteristic
60C23×C4×C17C2311yescharacteristic
61C23×C4×C17C2311yescharacteristic
62C23×C4×C17C2311yescharacteristic
63C23×C4×C17C2311yescharacteristic
64C23×Dic17C2311yescharacteristic
65C23×Dic17C2311yescharacteristic
66C23×Dic17C2311yescharacteristic
67C23×Dic17C2311yescharacteristic
68C23×Dic17C2311yescharacteristic
69C23×Dic17C2311yescharacteristic
70C23×Dic17C2311yescharacteristic
71C2×C42×C17—22no—
72C2×C42×C17—22no—
73C2×C42×C17C2×C414yes—
74C2×#63227—22no—
75C2×#63227—22no—
76C2×#63227—22no—
77C2×#63227—22no—
78C2×#63227—22no—
79C2×#63227—22no—
80C2×#63227—22no—
81C2×#63227—22no—
82C2×#63227—22no—
83C2×#63227—22no—
84C2×#63227—22no—
85C2×#63227—22no—
86C2×#63227—22no—
87C2×#63227—22no—
88C2×#63227—22no—
89C2×#63227—22no—
90C2×#63227—22no—
91C2×#63227—22no—
92C2×#63227C2×C414yes—
93C2×#63227C2×C414yes—
94C2×#63227C2×C414yes—
95C2×#63225—22no—
96C2×#63225—22no—
97C2×#63225—22no—
98C2×#63225—22no—
99C2×#63225—22no—
100C2×#63225—22no—
101C2×#63225—22no—
102C2×#63225—22no—
103C2×#63225C2×C414yes—
104C2×C4×Dic17—22no—
105C2×C4×Dic17—22no—
106C2×C4×Dic17—22no—
107C2×C4×Dic17—22no—
108C2×C4×Dic17—22no—
109C2×C4×Dic17—22no—
110C2×C4×Dic17—22no—
111C2×C4×Dic17—22no—
112C2×C4×Dic17—22no—
113C2×C4×Dic17—22no—
114C2×C4×Dic17—22no—
115C2×C4×Dic17—22no—
116C2×C4×Dic17—22no—
117C2×C4×Dic17—22no—
118C2×C4×Dic17—22no—
119C2×C4×Dic17—22no—
120C2×C4×Dic17D414yes—
121C2×C4×Dic17D414yes—
122C17×#95—22no—
123C17×#95—22no—
124C17×#95—22no—
125C17×#95—22no—
126C17×#95—22no—
127C17×#95—22no—
128#10587502—22no—
129#10587502—22no—
130#10587502—22no—
131#10587502—22no—
132#10587502—22no—
133#10587502—22no—
134#10587502—22no—
135#10587502—22no—
136#10587502—22no—
137#10587502—22no—
138#10587502C2×C414yes—
139#10587502C2×C414yes—
140C24×C17C2411yescharacteristic
141C23×D17—21no—
142C23×D17—21no—
143C23×D17—21no—
144C23×D17—21no—
145C23×D17—21no—
146C23×D17—21no—
147C23×D17—21no—
148C23×D17—21no—
149C23×D17—21no—
150C23×D17—21no—
151C23×D17—21no—
152C23×D17—21no—
153C23×D17—21no—
154C23×D17—21no—
155C23×D17C22×C412yes—
156C22×C4×C17—21no—
157C22×C4×C17—21no—
158C22×C4×C17—21no—
159C22×C4×C17—21no—
160C22×C4×C17—21no—
161C22×C4×C17—21no—
162C22×C4×C17—21no—
163C22×C4×C17—21no—
164C22×C4×C17—21no—
165C22×C4×C17—21no—
166C22×C4×C17—21no—
167C22×C4×C17—21no—
168C22×C4×C17—21no—
169C22×C4×C17—21no—
170C22×C4×C17—21no—
171C22×C4×C17—21no—
172C22×C4×C17—21no—
173C22×C4×C17—21no—
174C22×C4×C17—21no—
175C22×C4×C17—21no—
176C22×C4×C17—21no—
177C22×C4×C17—21no—
178C22×C4×C17—21no—
179C22×C4×C17—21no—
180C22×C4×C17—21no—
181C22×C4×C17—21no—
182C22×C4×C17—21no—
183C22×C4×C17—21no—
184C22×C4×C17—21no—
185C22×C4×C17—21no—
186C22×C4×C17—21no—
187C22×C4×C17—21no—
188C22×C4×C17—21no—
189C22×C4×C17—21no—
190C22×C4×C17—21no—
191C22×C4×C17—21no—
192C22×C4×C17—21no—
193C22×C4×C17—21no—
194C22×C4×C17—21no—
195C22×C4×C17—21no—
196C22×C4×C17C22×C412yes—
197C22×C4×C17C22×C412yes—
198C22×C4×C17C22×C412yes—
199C22×C4×C17C2×D412yes—
200C22×C4×C17C2×D412yes—
201C22×C4×C17#4112yes—
202C22×C4×C17#4112yes—
203C22×C4×C17#4112yes—
204C22×C4×C17#4112yes—
205C22×Dic17—21no—
206C22×Dic17—21no—
207C22×Dic17—21no—
208C22×Dic17—21no—
209C22×Dic17—21no—
210C22×Dic17—21no—
211C22×Dic17—21no—
212C22×Dic17—21no—
213C22×Dic17—21no—
214C22×Dic17—21no—
215C22×Dic17—21no—
216C22×Dic17—21no—
217C22×Dic17—21no—
218C22×Dic17—21no—
219C22×Dic17—21no—
220C22×Dic17—21no—
221C22×Dic17—21no—
222C22×Dic17—21no—
223C22×Dic17—21no—
224C22×Dic17—21no—
225C22×Dic17—21no—
226C22×Dic17—21no—
227C22×Dic17—21no—
228C22×Dic17—21no—
229C22×Dic17—21no—
230C22×Dic17—21no—
231C22×Dic17—21no—
232C22×Dic17—21no—
233C22×Dic17—21no—
234C22×Dic17—21no—
235C22×Dic17—21no—
236C22×Dic17—21no—
237C22×Dic17—21no—
238C22×Dic17—21no—
239C22×Dic17C22×C412yes—
240C22×Dic17C22×C412yes—
241C22×Dic17C22×C412yes—
242C22×Dic17C2×D412yes—
243C22×Dic17C2×D412yes—
244C22×Dic17C2×D412yes—
245C22×Dic17C2×D412yes—
246C22×Dic17#4112yes—
247C22×Dic17#4112yes—
248C22×Dic17#4112yes—
249C22×Dic17#4112yes—
250C22×Dic17#4112yes—
251C22×Dic17#4112yes—
252C22×Dic17#4112yes—
253C22×Dic17#4112yes—
254C42×C17—28no—
255#63227—28no—
256#63227—28no—
257#63227—28no—
258#63227—44no—
259#63227—44no—
260#63227—44no—
261#63227—44no—
262#63225—28no—
263#63225—44no—
264#63225—44no—
265C4×Dic17—28no—
266C4×Dic17—28no—
267C4×Dic17—28no—
268C4×Dic17—28no—
269C4×Dic17—28no—
270C4×Dic17—28no—
271#14701—171nomaximal, Sylow
272C23×C17C23×C411yescharacteristic
273C23×C17C22×D411yescharacteristic
274C23×C17C22×D411yescharacteristic
275C23×C17C2×#4111yescharacteristic
276C23×C17C2×#4111yescharacteristic
277C23×C17C2×#4111yescharacteristic
278C23×C17C2×#4111yescharacteristic
279C23×C17C2×#4111yescharacteristic
280C23×C17C2×#4111yescharacteristic
281C23×C17C2×#4111yescharacteristic
282C23×C17C2×#4111yescharacteristic
283C23×C17C2×#4111yescharacteristic
284C23×C17C2×#4111yescharacteristic
285C23×C17C2×#4111yescharacteristic
286C23×C17C2×#4111yescharacteristic
287C22×D17—22no—
288C22×D17—22no—
289C22×D17—22no—
290C22×D17—22no—
291C22×D17—22no—
292C22×D17—22no—
293C22×D17—22no—
294C22×D17—41no—
295C22×D17—41no—
296C22×D17—41no—
297C22×D17—41no—
298C22×D17—41no—
299C22×D17—41no—
300C22×D17—41no—
301C22×D17—41no—
302C22×D17—41no—
303C22×D17—41no—
304C22×D17—41no—
305C22×D17—41no—
306C22×D17—41no—
307C22×D17—41no—
308C22×D17—41no—
309C22×D17—41no—
310C22×D17—41no—
311C22×D17—41no—
312C22×D17—41no—
313C22×D17—41no—
314C22×D17—41no—
315C22×D17—41no—
316C22×D17—41no—
317C22×D17—41no—
318C22×D17—41no—
319C22×D17—41no—
320C22×D17—41no—
321C22×D17—41no—
322C2×C4×C17—22no—
323C2×C4×C17—22no—
324C2×C4×C17—22no—
325C2×C4×C17—22no—
326C2×C4×C17—22no—
327C2×C4×C17—22no—
328C2×C4×C17—22no—
329C2×C4×C17—22no—
330C2×C4×C17—22no—
331C2×C4×C17—22no—
332C2×C4×C17—22no—
333C2×C4×C17—22no—
334C2×C4×C17—22no—
335C2×C4×C17—22no—
336C2×C4×C17—22no—
337C2×C4×C17—22no—
338C2×C4×C17—22no—
339C2×C4×C17—22no—
340C2×C4×C17—41no—
341C2×C4×C17—41no—
342C2×C4×C17—41no—
343C2×C4×C17—41no—
344C2×C4×C17—41no—
345C2×C4×C17—41no—
346C2×C4×C17—41no—
347C2×C4×C17—41no—
348C2×C4×C17—41no—
349C2×C4×C17—41no—
350C2×C4×C17—41no—
351C2×C4×C17—41no—
352C2×C4×C17—41no—
353C2×C4×C17—41no—
354C2×C4×C17—41no—
355C2×C4×C17—41no—
356C2×C4×C17—41no—
357C2×C4×C17—41no—
358C2×C4×C17—41no—
359C2×C4×C17—41no—
360C2×C4×C17—41no—
361C2×C4×C17—41no—
362C2×C4×C17—41no—
363C2×C4×C17—41no—
364C2×C4×C17—41no—
365C2×C4×C17—41no—
366C2×C4×C17—41no—
367C2×C4×C17—41no—
368C2×C4×C17#11714yes—
369C2×C4×C17C4×D414yes—
370C2×C4×C17C4×D414yes—
371C2×Dic17—22no—
372C2×Dic17—22no—
373C2×Dic17—22no—
374C2×Dic17—22no—
375C2×Dic17—22no—
376C2×Dic17—22no—
377C2×Dic17—22no—
378C2×Dic17—22no—
379C2×Dic17—22no—
380C2×Dic17—22no—
381C2×Dic17—22no—
382C2×Dic17—22no—
383C2×Dic17—22no—
384C2×Dic17—22no—
385C2×Dic17—22no—
386C2×Dic17—22no—
387C2×Dic17—22no—
388C2×Dic17—22no—
389C2×Dic17—22no—
390C2×Dic17—22no—
391C2×Dic17—22no—
392C2×Dic17—22no—
393C2×Dic17—22no—
394C2×Dic17—22no—
395C2×Dic17—22no—
396C2×Dic17—22no—
397C2×Dic17—22no—
398C2×Dic17—22no—
399C2×Dic17—22no—
400C2×Dic17—22no—
401C2×Dic17—22no—
402C2×Dic17—22no—
403C2×Dic17—22no—
404C2×Dic17—41no—
405C2×Dic17—41no—
406C2×Dic17—41no—
407C2×Dic17—41no—
408C2×Dic17—41no—
409C2×Dic17—41no—
410C2×Dic17—41no—
411C2×Dic17—41no—
412C2×Dic17—41no—
413C2×Dic17—41no—
414C2×Dic17—41no—
415C2×Dic17—41no—
416C2×Dic17#12114yes—
417C2×Dic17#12314yes—
418C2×Dic17#12414yes—
419C2×Dic17#12614yes—
420C2×#388—171no—
421C2×#388—171no—
422C2×#388—171no—
423C2×#387—171no—
424C2×C43—171no—
425#1437—171no—
426#1437—171no—
427#1437—171no—
428#1437—171no—
429#1436—171no—
430#1436—171no—
431#1436—171no—
432#1436—171no—
433#1434—171no—
434#1434D1711yescharacteristic, complemented
435C22×C17C2×#11711yescharacteristic
436C22×C17C2×C4×D411yescharacteristic
437C22×C17C2×C4×D411yescharacteristic
438C22×C17C4×#4111yescharacteristic
439C22×C17C4×#4111yescharacteristic
440C22×C17C4×#4111yescharacteristic
441C22×C17C4×#4111yescharacteristic
442C22×C17C2×#12111yescharacteristic
443C22×C17C2×#12311yescharacteristic
444C22×C17#52511yescharacteristic
445C22×C17#52511yescharacteristic
446C22×C17#52511yescharacteristic
447C22×C17#52511yescharacteristic
448C22×C17C2×#12411yescharacteristic
449C22×C17C2×#12611yescharacteristic
450C22×C17#52911yescharacteristic
451C22×C17#52911yescharacteristic
452C22×C17#52911yescharacteristic
453C22×C17#52911yescharacteristic
454C22×C17#52911yescharacteristic
455C22×C17#52911yescharacteristic
456C22×C17#52911yescharacteristic
457C22×C17#52911yescharacteristic
458C22×C17#52911yescharacteristic
459C22×C17#52911yescharacteristic
460C22×C17#52911yescharacteristic
461C22×C17#52911yescharacteristic
462C22×C17#52911yescharacteristic
463C22×C17#52911yescharacteristic
464C22×C17#52911yescharacteristic
465C22×C17#52911yescharacteristic
466C22×C17#53211yescharacteristic
467C22×C17#53211yescharacteristic
468C22×C17#53211yescharacteristic
469C22×C17#53211yescharacteristic
470C2×D17—42no—
471C2×D17—42no—
472C2×D17—42no—
473C2×D17—42no—
474C2×D17—42no—
475C2×D17—42no—
476C2×D17—42no—
477C2×D17—81no—
478C2×D17—81no—
479C2×D17—81no—
480C2×D17—81no—
481C2×D17—81no—
482C2×D17—81no—
483C2×D17—81no—
484C2×D17—81no—
485C4×C17—24no—
486C4×C17—24no—
487C4×C17—24no—
488C4×C17—81no—
489C4×C17—81no—
490C4×C17—81no—
491C4×C17—81no—
492Dic17—24no—
493Dic17—24no—
494Dic17—24no—
495Dic17—24no—
496Dic17—42no—
497Dic17—42no—
498Dic17—42no—
499C22×C4⋊C4—171no—
500C22×C4⋊C4—171no—
501C22×C4⋊C4—171no—
502C22×C22⋊C4—171no—
503C22×C22⋊C4—171no—
504C22×C22⋊C4—171no—
505C22×C22⋊C4—171no—
506C22×C22⋊C4—171no—
507C22×C22⋊C4—171no—
508C22×C22⋊C4—171no—
509C22×C42—171no—
510C22×C42—171no—
511C22×C42—171no—
512C22×C42—171no—
513C22×C42—171no—
514C22×C42—171no—
515C22×C42C2×D1711yescharacteristic
516#388—178no—
517#388—344no—
518#388—344no—
519#387—344no—
520C2×#95—171no—
521C2×#95—171no—
522C2×#95—171no—
523C2×#95—171no—
524C2×#95—171no—
525C2×#95—171no—
526C2×#95—171no—
527C2×#95—171no—
528C2×#95—171no—
529C2×#95—171no—
530C2×#95—171no—
531C2×#95—171no—
532C2×#95C2×D1711yescharacteristic
533C2×#95C2×D1711yescharacteristic
534C2×#95C2×D1711yescharacteristic
535C2×#95C2×D1711yescharacteristic
536C2×#95C2×D1711yescharacteristic
537C2×#95C2×D1711yescharacteristic
538C43—344no—
539C2×C17#229011yescharacteristic
540C2×C17#229311yescharacteristic
541C2×C17#229811yescharacteristic
542C2×C17C4×#12111yescharacteristic
543C2×C17C4×#12311yescharacteristic
544C2×C17C4×#12411yescharacteristic
545C2×C17C4×#12611yescharacteristic
546C2×C17#285011yescharacteristic
547C2×C17#285211yescharacteristic
548C2×C17#285311yescharacteristic
549C2×C17#285411yescharacteristic
550C2×C17#286011yescharacteristic
551C2×C17#286111yescharacteristic
552C2×C17#286511yescharacteristic
553C2×C17#286611yescharacteristic
554D17—82no—
555C25—171no—
556C23×C4—171no—
557C23×C4—171no—
558C23×C4—171no—
559C23×C4—171no—
560C23×C4—171no—
561C23×C4—171no—
562C23×C4—171no—
563C23×C4C22×D1711yescharacteristic
564C23×C4C22×D1711yescharacteristic
565C23×C4C22×D1711yescharacteristic
566C23×C4C22×D1711yescharacteristic
567C23×C4C22×D1711yescharacteristic
568C23×C4C22×D1711yescharacteristic
569C23×C4C22×D1711yescharacteristic
570C2×C4⋊C4—174no—
571C2×C4⋊C4—342no—
572C2×C4⋊C4—342no—
573C2×C4⋊C4—342no—
574C2×C4⋊C4—342no—
575C2×C4⋊C4—342no—
576C2×C4⋊C4—342no—
577C2×C4⋊C4—342no—
578C2×C4⋊C4—342no—
579C2×C22⋊C4—174no—
580C2×C22⋊C4—174no—
581C2×C22⋊C4—174no—
582C2×C22⋊C4—342no—
583C2×C22⋊C4—342no—
584C2×C22⋊C4—342no—
585C2×C22⋊C4—342no—
586C2×C22⋊C4—342no—
587C2×C22⋊C4—342no—
588C2×C22⋊C4—342no—
589C2×C22⋊C4—342no—
590C2×C22⋊C4—342no—
591C2×C22⋊C4—342no—
592C2×C22⋊C4—342no—
593C2×C22⋊C4—342no—
594C2×C22⋊C4—342no—
595C2×C22⋊C4—342no—
596C2×C22⋊C4—342no—
597C2×C22⋊C4—342no—
598C2×C22⋊C4—342no—
599C2×C22⋊C4—342no—
600C2×C42—22no—
601C2×C42—22no—
602C2×C42—174no—
603C2×C42—174no—
604C2×C42—342no—
605C2×C42—342no—
606C2×C42—342no—
607C2×C42—342no—
608C2×C42—342no—
609C2×C42—342no—
610C2×C42—342no—
611C2×C42—342no—
612C2×C42—342no—
613C2×C42—342no—
614C2×C42—342no—
615C2×C42—342no—
616C2×C42—342no—
617C2×C42—342no—
618C2×C42—342no—
619C2×C42—342no—
620C2×C42C4×D1714yes—
621#95—22no—
622#95—22no—
623#95—22no—
624#95—22no—
625#95—22no—
626#95—22no—
627#95—174no—
628#95—174no—
629#95—342no—
630#95—342no—
631#95—342no—
632#95—342no—
633#95—342no—
634#95—342no—
635#95—342no—
636#95—342no—
637#95—342no—
638#95—342no—
639C17#1470111yescharacteristic, complemented, Sylow
640C24—172no—
641C24—341no—
642C24—341no—
643C24—341no—
644C24—341no—
645C24—341no—
646C24—341no—
647C24—341no—
648C24—341no—
649C24—341no—
650C24—341no—
651C24—341no—
652C24—341no—
653C24—341no—
654C24—341no—
655C24C23×D1711yescharacteristic
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—172no—
697C22×C4—172no—
698C22×C4—172no—
699C22×C4—172no—
700C22×C4—172no—
701C22×C4—172no—
702C22×C4—172no—
703C22×C4—172no—
704C22×C4—172no—
705C22×C4—172no—
706C22×C4—172no—
707C22×C4—172no—
708C22×C4—172no—
709C22×C4—172no—
710C22×C4—172no—
711C22×C4—341no—
712C22×C4—341no—
713C22×C4—341no—
714C22×C4—341no—
715C22×C4—341no—
716C22×C4—341no—
717C22×C4—341no—
718C22×C4—341no—
719C22×C4—341no—
720C22×C4—341no—
721C22×C4—341no—
722C22×C4—341no—
723C22×C4—341no—
724C22×C4—341no—
725C22×C4—341no—
726C22×C4—341no—
727C22×C4—341no—
728C22×C4—341no—
729C22×C4—341no—
730C22×C4—341no—
731C22×C4—341no—
732C22×C4—341no—
733C22×C4—341no—
734C22×C4—341no—
735C22×C4—341no—
736C22×C4—341no—
737C22×C4—341no—
738C22×C4—341no—
739C22×C4—341no—
740C22×C4—341no—
741C22×C4—341no—
742C22×C4—341no—
743C22×C4—341no—
744C22×C4—341no—
745C22×C4C2×C4×D1712yes—
746C22×C4C2×C4×D1712yes—
747C22×C4C2×C4×D1712yes—
748C22×C4#6325212yes—
749C22×C4#6325212yes—
750C22×C4D4×D1712yes—
751C22×C4D4×D1712yes—
752C22×C4#6325412yes—
753C22×C4#6325612yes—
754C4⋊C4—348no—
755C4⋊C4—684no—
756C4⋊C4—684no—
757C22⋊C4—348no—
758C22⋊C4—348no—
759C22⋊C4—348no—
760C22⋊C4—684no—
761C22⋊C4—684no—
762C22⋊C4—684no—
763C22⋊C4—684no—
764C42—28no—
765C42—348no—
766C42—348no—
767C42—348no—
768C42—348no—
769C42—348no—
770C42—348no—
771C23—342no—
772C23—342no—
773C23—342no—
774C23—342no—
775C23—342no—
776C23—342no—
777C23—342no—
778C23—681no—
779C23—681no—
780C23—681no—
781C23—681no—
782C23—681no—
783C23—681no—
784C23—681no—
785C23—681no—
786C23—681no—
787C23—681no—
788C23—681no—
789C23—681no—
790C23—681no—
791C23—681no—
792C23—681no—
793C23—681no—
794C23—681no—
795C23—681no—
796C23—681no—
797C23—681no—
798C23—681no—
799C23—681no—
800C23—681no—
801C23—681no—
802C23—681no—
803C23—681no—
804C23—681no—
805C23—681no—
806C23C22×C4×D1711yescharacteristic
807C23C2×#6325211yescharacteristic
808C23C2×#6325211yescharacteristic
809C23C2×D4×D1711yescharacteristic
810C23C2×D4×D1711yescharacteristic
811C23C2×#6325411yescharacteristic
812C23C2×#6325611yescharacteristic
813C23#41×D1711yescharacteristic
814C23#41×D1711yescharacteristic
815C23#41×D1711yescharacteristic
816C23#41×D1711yescharacteristic
817C23#41×D1711yescharacteristic
818C23#41×D1711yescharacteristic
819C23#41×D1711yescharacteristic
820C23#41×D1711yescharacteristic
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—174no—
868C2×C4—174no—
869C2×C4—174no—
870C2×C4—174no—
871C2×C4—342no—
872C2×C4—342no—
873C2×C4—342no—
874C2×C4—342no—
875C2×C4—342no—
876C2×C4—342no—
877C2×C4—342no—
878C2×C4—342no—
879C2×C4—342no—
880C2×C4—342no—
881C2×C4—342no—
882C2×C4—342no—
883C2×C4—342no—
884C2×C4—342no—
885C2×C4—342no—
886C2×C4—342no—
887C2×C4—342no—
888C2×C4—342no—
889C2×C4—342no—
890C2×C4—342no—
891C2×C4—342no—
892C2×C4—342no—
893C2×C4—342no—
894C2×C4—342no—
895C2×C4—342no—
896C2×C4—342no—
897C2×C4—342no—
898C2×C4—342no—
899C2×C4—342no—
900C2×C4—342no—
901C2×C4—342no—
902C2×C4—342no—
903C2×C4—342no—
904C2×C4—681no—
905C2×C4—681no—
906C2×C4—681no—
907C2×C4—681no—
908C2×C4—681no—
909C2×C4—681no—
910C2×C4—681no—
911C2×C4—681no—
912C2×C4—681no—
913C2×C4—681no—
914C2×C4—681no—
915C2×C4—681no—
916C2×C4#1058755814yes—
917C2×C4#1058756714yes—
918C2×C4#1058757914yes—
919C22—682no—
920C22—682no—
921C22—682no—
922C22—682no—
923C22—682no—
924C22—682no—
925C22—682no—
926C22—1361no—
927C22—1361no—
928C22—1361no—
929C22—1361no—
930C22—1361no—
931C22—1361no—
932C22—1361no—
933C22—1361no—
934C22C2×#1058755811yescharacteristic
935C22C2×#1058756711yescharacteristic
936C22C2×#1058757911yescharacteristic
937C22#1176327711yescharacteristic
938C22#1176327711yescharacteristic
939C22#1176327711yescharacteristic
940C22#1176327711yescharacteristic
941C22#121×D1711yescharacteristic
942C22#123×D1711yescharacteristic
943C22#1176331711yescharacteristic
944C22#1176331811yescharacteristic
945C22#1176331811yescharacteristic
946C22#1176332211yescharacteristic
947C22#124×D1711yescharacteristic
948C22#126×D1711yescharacteristic
949C22#1176333611yescharacteristic
950C22#1176333611yescharacteristic
951C22#1176333711yescharacteristic
952C22#1176333711yescharacteristic
953C22#1176333711yescharacteristic
954C22#1176333711yescharacteristic
955C22#1176333911yescharacteristic
956C22#1176333911yescharacteristic
957C22#1176334211yescharacteristic
958C22#1176334211yescharacteristic
959C22#1176334211yescharacteristic
960C22#1176334411yescharacteristic
961C22#1176334411yescharacteristic
962C22#1176334511yescharacteristic
963C22#1176334611yescharacteristic
964C22#1176334611yescharacteristic
965C22#1176335411yescharacteristic
966C22#1176335611yescharacteristic
967C22#1176335611yescharacteristic
968C22#1176335811yescharacteristic
969C4—24no—
970C4—24no—
971C4—24no—
972C4—81no—
973C4—81no—
974C4—81no—
975C4—81no—
976C4—344no—
977C4—344no—
978C4—344no—
979C4—344no—
980C4—682no—
981C4—682no—
982C4—682no—
983C2—1362no—
984C2#1453122311yescharacteristic
985C2#1453124511yescharacteristic
986C2#1453127911yescharacteristic
987C2#1453129011yescharacteristic
988C2#1453130111yescharacteristic
989C2#1453132311yescharacteristic
990C2#1453133211yescharacteristic
991C2#1453708211yescharacteristic
992C2#1453710211yescharacteristic
993C2#1453710811yescharacteristic
994C2#1453711111yescharacteristic
995C2#1453715011yescharacteristic
996C2#1453715311yescharacteristic
997C2#1453717411yescharacteristic
998C2#1453717711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1434C2
socle, cosocleC24×C17C24
prime radicalC24×D17C23
hypercenter#1434D17
hypocenterC17#14701
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
4. C2×#11762691C2semidirect
5. C2×C42×Dic17C2semidirect
10. #14527019C2semidirect
11. #14527015C2semidirect
12. #14527015C2semidirect
13. #14527015C2semidirect
14. #14527009C2semidirect
15. C17×#1434C2semidirect
32. #11762700C4semidirect
434. #1434D17semidirect
639. C17#14701semidirect

Maximal subgroups

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

subgroupindex
C2×#117627002
C2×#117626982
C2×#117626912
C2×C42×Dic172
#145270202
#145270192
#145270152
#145270092
C17×#14342
#1470117