Finite Group Databasebeta

← #16959623

Subgroups — #16959623

Order 4352.

2062 conjugacy classes of subgroups.

The subgroup lattice has 1050 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587573C211yesmaximal, characteristic, complemented
2C2×#11762722C211yesmaximal, characteristic
3C2×#11762683C211yesmaximal, characteristic
4C2×#11762680C211yesmaximal, characteristic
5C2×C4×#63227C211yesmaximal, characteristic
6#14527054C211yesmaximal, characteristic, complemented
7#14527048C211yesmaximal, characteristic, complemented
8#14527028C211yesmaximal, characteristic
9#14527020C211yesmaximal, characteristic
10#14527020C211yesmaximal, characteristic
11#14527019C211yesmaximal, characteristic, complemented
12#14527018C211yesmaximal, characteristic, complemented
13#14527017C211yesmaximal, characteristic, complemented
14#14527008C211yesmaximal, characteristic, complemented
15C17×#1436C211yesmaximal, characteristic, complemented
16C23×Dic34C2211yescharacteristic
17C23×C4×D17C2211yescharacteristic
18C2×#10587573—24no—
19C2×#10587573—24no—
20C2×#10587573—24no—
21C22×C4⋊Dic17C2211yescharacteristic
22C22×#63225C2211yescharacteristic
23C22×#63225C2211yescharacteristic
24C22×#63225C2211yescharacteristic
25C22×#63227C2211yescharacteristic
26C22×#63227C2211yescharacteristic
27C22×#63227C2211yescharacteristic
28C22×#63227C2211yescharacteristic
29C22×#63227C2211yescharacteristic
30C22×#63227C2211yescharacteristic
31C22×C4×Dic17C2211yescharacteristic
32C22×C4×Dic17C2211yescharacteristic
33C22×C4×Dic17C2211yescharacteristic
34#11762722C418yescomplemented
35#11762683—24no—
36#11762680—24no—
37C4×#63227—24no—
38C2×#10587502C2211yescharacteristic
39C2×#10587502C2211yescharacteristic
40C2×#10587502C2211yescharacteristic
41C2×#10587502C2211yescharacteristic
42C2×#10587502C2211yescharacteristic
43C2×#10587502C2211yescharacteristic
44C2×#10587502C2211yescharacteristic
45C2×#10587502C2211yescharacteristic
46C2×#10587502C2211yescharacteristic
47C2×#10587502C2211yescharacteristic
48C2×#10587502C2211yescharacteristic
49C2×#10587502C2211yescharacteristic
50C2×#10587502C2211yescharacteristic
51C22×C4⋊C4×C17C2211yescharacteristic
52C22×C42×C17C2211yescharacteristic
53C2×C17×#95C2211yescharacteristic
54C2×C17×#95C2211yescharacteristic
55C2×C17×#95C2211yescharacteristic
56C2×C17×#95C2211yescharacteristic
57C2×C17×#95C2211yescharacteristic
58C24×D17C2311yescharacteristic
59C23×C4×C17C2311yescharacteristic
60C23×C4×C17C2311yescharacteristic
61C23×C4×C17C2311yescharacteristic
62C23×C4×C17C2311yescharacteristic
63C23×C4×C17C2311yescharacteristic
64C23×C4×C17C2311yescharacteristic
65C23×C4×C17C2311yescharacteristic
66C23×Dic17C2311yescharacteristic
67C23×Dic17C2311yescharacteristic
68C23×Dic17C2311yescharacteristic
69C23×Dic17C2311yescharacteristic
70C23×Dic17C2311yescharacteristic
71C23×Dic17C2311yescharacteristic
72C23×Dic17C2311yescharacteristic
73C22×C4×D17—22no—
74C22×C4×D17—22no—
75C22×C4×D17—22no—
76C22×C4×D17—22no—
77C22×C4×D17—22no—
78C22×C4×D17—41no—
79C22×C4×D17—41no—
80C22×Dic34—22no—
81C22×Dic34—22no—
82C22×Dic34—22no—
83C22×Dic34—22no—
84C22×Dic34—22no—
85C22×Dic34—22no—
86C22×Dic34C2×C414yescomplemented
87C2×C4⋊C4×C17—22no—
88C2×C4⋊C4×C17—22no—
89C2×C4⋊C4×C17D414yes—
90C2×C42×C17—22no—
91C2×C42×C17—41no—
92C2×C42×C17—41no—
93C2×#63227—22no—
94C2×#63227—22no—
95C2×#63227—22no—
96C2×#63227—22no—
97C2×#63227—22no—
98C2×#63227—22no—
99C2×#63227—22no—
100C2×#63227—22no—
101C2×#63227—22no—
102C2×#63227—22no—
103C2×#63227—22no—
104C2×#63227—22no—
105C2×#63227—41no—
106C2×#63227—41no—
107C2×#63227C2×C414yes—
108C2×#63227C2×C414yes—
109C2×#63227C2×C414yes—
110C2×#63227Q814yescomplemented
111C2×C4⋊Dic17—22no—
112C2×C4⋊Dic17—22no—
113C2×C4⋊Dic17—41no—
114C2×#63225—22no—
115C2×#63225—22no—
116C2×#63225—22no—
117C2×#63225—22no—
118C2×#63225—22no—
119C2×#63225—22no—
120C2×#63225—22no—
121C2×#63225—41no—
122C2×#63225D414yes—
123C2×C4×Dic17—22no—
124C2×C4×Dic17—22no—
125C2×C4×Dic17—22no—
126C2×C4×Dic17—22no—
127C2×C4×Dic17—22no—
128C2×C4×Dic17—22no—
129C2×C4×Dic17—22no—
130C2×C4×Dic17—22no—
131C2×C4×Dic17D414yes—
132#10587573—232no—
133C17×#95—22no—
134C17×#95—22no—
135C17×#95—41no—
136C17×#95—41no—
137C17×#95C2×C414yescomplemented
138#10587502—22no—
139#10587502—22no—
140#10587502—22no—
141#10587502—22no—
142#10587502—22no—
143#10587502—22no—
144#10587502—22no—
145#10587502—22no—
146#10587502—22no—
147#10587502—41no—
148#10587502—41no—
149#10587502C2×C414yescomplemented
150#10587502C2×C414yescomplemented
151C24×C17C2411yescharacteristic
152C23×D17—21no—
153C23×D17—21no—
154C23×D17—21no—
155C23×D17—21no—
156C23×D17—21no—
157C23×D17—21no—
158C23×D17—21no—
159C23×D17—21no—
160C23×D17—21no—
161C23×D17—21no—
162C23×D17—21no—
163C23×D17—21no—
164C23×D17C22×C412yes—
165C23×D17C2×Q812yes—
166C23×D17#4112yes—
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×C17—21no—
197C22×C4×C17—21no—
198C22×C4×C17—21no—
199C22×C4×C17—21no—
200C22×C4×C17—21no—
201C22×C4×C17—21no—
202C22×C4×C17—21no—
203C22×C4×C17—21no—
204C22×C4×C17—21no—
205C22×C4×C17—21no—
206C22×C4×C17C22×C412yes—
207C22×C4×C17C22×C412yes—
208C22×C4×C17C22×C412yes—
209C22×C4×C17C2×D412yes—
210C22×C4×C17C2×D412yes—
211C22×C4×C17C2×D412yes—
212C22×C4×C17C2×D412yes—
213C22×C4×C17C2×D412yes—
214C22×C4×C17C2×Q812yes—
215C22×C4×C17#4112yes—
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×Dic17—21no—
240C22×Dic17—21no—
241C22×Dic17—21no—
242C22×Dic17—21no—
243C22×Dic17—21no—
244C22×Dic17—21no—
245C22×Dic17—21no—
246C22×Dic17—21no—
247C22×Dic17—21no—
248C22×Dic17—21no—
249C22×Dic17—21no—
250C22×Dic17—21no—
251C22×Dic17—21no—
252C22×Dic17—21no—
253C22×Dic17C22×C412yes—
254C22×Dic17C22×C412yes—
255C22×Dic17C22×C412yes—
256C22×Dic17C2×D412yes—
257C22×Dic17C2×D412yes—
258C22×Dic17C2×D412yes—
259C22×Dic17C2×D412yes—
260C22×Dic17C2×Q812yes—
261C22×Dic17#4112yes—
262C22×Dic17#4112yes—
263C22×Dic17#4112yes—
264C22×Dic17#4112yes—
265C2×C4×D17—28no—
266C2×C4×D17—44no—
267C2×C4×D17—44no—
268C2×C4×D17—44no—
269C2×C4×D17—44no—
270C2×C4×D17—44no—
271C2×C4×D17—44no—
272C2×Dic34—28no—
273C2×Dic34—28no—
274C2×Dic34—28no—
275C2×Dic34—28no—
276C2×Dic34—28no—
277C2×Dic34—28no—
278C2×Dic34—28no—
279C4⋊C4×C17—28no—
280C42×C17—44no—
281#63227—28no—
282#63227—28no—
283#63227—28no—
284#63227—28no—
285#63227—44no—
286#63227—44no—
287C4⋊Dic17—44no—
288#63225—28no—
289#63225—28no—
290#63225—44no—
291C4×Dic17—28no—
292C4×Dic17—28no—
293C4×Dic17—28no—
294#14172—171nomaximal, Sylow
295C23×C17C23×C411yescharacteristic
296C23×C17C22×D411yescharacteristic
297C23×C17C22×D411yescharacteristic
298C23×C17C22×D411yescharacteristic
299C23×C17C22×Q811yescharacteristic
300C23×C17C2×#4111yescharacteristic
301C23×C17C2×#4111yescharacteristic
302C23×C17C2×#4111yescharacteristic
303C23×C17C2×#4111yescharacteristic
304C23×C17C2×#4111yescharacteristic
305C23×C17C2×#4111yescharacteristic
306C23×C17H(5,𝔽2)11yescharacteristic
307C23×C17H(5,𝔽2)11yescharacteristic
308C23×C172−1+411yescharacteristic
309C23×C172−1+411yescharacteristic
310C22×D17—22no—
311C22×D17—22no—
312C22×D17—22no—
313C22×D17—22no—
314C22×D17—22no—
315C22×D17—22no—
316C22×D17—22no—
317C22×D17—22no—
318C22×D17—22no—
319C22×D17—22no—
320C22×D17—22no—
321C22×D17—22no—
322C22×D17—22no—
323C22×D17—22no—
324C22×D17—22no—
325C22×D17—22no—
326C22×D17—22no—
327C22×D17—22no—
328C22×D17—41no—
329C22×D17—41no—
330C22×D17—41no—
331C22×D17—41no—
332C22×D17—41no—
333C22×D17—41no—
334C22×D17—41no—
335C22×D17—41no—
336C22×D17—41no—
337C22×D17—41no—
338C22×D17—41no—
339C22×D17—41no—
340C22×D17—41no—
341C22×D17—41no—
342C22×D17—41no—
343C22×D17—41no—
344C22×D17C4×Q814yescomplemented
345C2×C4×C17—22no—
346C2×C4×C17—22no—
347C2×C4×C17—22no—
348C2×C4×C17—22no—
349C2×C4×C17—22no—
350C2×C4×C17—22no—
351C2×C4×C17—22no—
352C2×C4×C17—22no—
353C2×C4×C17—22no—
354C2×C4×C17—22no—
355C2×C4×C17—22no—
356C2×C4×C17—22no—
357C2×C4×C17—22no—
358C2×C4×C17—22no—
359C2×C4×C17—22no—
360C2×C4×C17—22no—
361C2×C4×C17—22no—
362C2×C4×C17—22no—
363C2×C4×C17—22no—
364C2×C4×C17—22no—
365C2×C4×C17—22no—
366C2×C4×C17—22no—
367C2×C4×C17—22no—
368C2×C4×C17—22no—
369C2×C4×C17—41no—
370C2×C4×C17—41no—
371C2×C4×C17—41no—
372C2×C4×C17—41no—
373C2×C4×C17—41no—
374C2×C4×C17—41no—
375C2×C4×C17—41no—
376C2×C4×C17—41no—
377C2×C4×C17—41no—
378C2×C4×C17—41no—
379C2×C4×C17—41no—
380C2×C4×C17—41no—
381C2×C4×C17—41no—
382C2×C4×C17—41no—
383C2×C4×C17—41no—
384C2×C4×C17—41no—
385C2×C4×C17—41no—
386C2×C4×C17—41no—
387C2×C4×C17—41no—
388C2×C4×C17—41no—
389C2×C4×C17—41no—
390C2×C4×C17—41no—
391C2×C4×C17—41no—
392C2×C4×C17C4×D414yes—
393C2×C4×C17#12014yes—
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—22no—
405C2×Dic17—22no—
406C2×Dic17—22no—
407C2×Dic17—22no—
408C2×Dic17—22no—
409C2×Dic17—22no—
410C2×Dic17—22no—
411C2×Dic17—22no—
412C2×Dic17—22no—
413C2×Dic17—22no—
414C2×Dic17—22no—
415C2×Dic17—22no—
416C2×Dic17—22no—
417C2×Dic17—22no—
418C2×Dic17—22no—
419C2×Dic17—22no—
420C2×Dic17—22no—
421C2×Dic17—41no—
422C2×Dic17—41no—
423C2×Dic17—41no—
424C2×Dic17—41no—
425C2×Dic17—41no—
426C2×Dic17—41no—
427C2×Dic17—41no—
428C2×Dic17—41no—
429C2×Dic17—41no—
430C2×Dic17—41no—
431C2×Dic17—41no—
432C2×Dic17—41no—
433C2×Dic17—41no—
434C2×Dic17—41no—
435C2×Dic17—41no—
436C2×Dic17—41no—
437C2×Dic17—41no—
438C2×Dic17—41no—
439C2×Dic17—41no—
440C2×Dic17C4×D414yes—
441C2×Dic17C4×D414yes—
442C2×Dic17C22⋊Q814yes—
443C4×D17—416no—
444Dic34—232no—
445C22×C4×Q8—171no—
446C2×#393—171no—
447C2×#385—171no—
448C2×#385—171no—
449C2×C4×C22⋊C4—171no—
450#1446—171no—
451#1444—171no—
452#1439—171no—
453#1437—171no—
454#1437—171no—
455#1436—171no—
456#1436—171no—
457#1436—171no—
458#1436D1711yescharacteristic, complemented
459#1434—171no—
460C22×C17C2×C4×D411yescharacteristic
461C22×C17C2×C4×D411yescharacteristic
462C22×C17C2×C4×D411yescharacteristic
463C22×C17C2×C4×Q811yescharacteristic
464C22×C17C4×#4111yescharacteristic
465C22×C17#52011yescharacteristic
466C22×C17#52011yescharacteristic
467C22×C17C2×#12011yescharacteristic
468C22×C17C2×C22⋊Q811yescharacteristic
469C22×C17#52511yescharacteristic
470C22×C17#52511yescharacteristic
471C22×C17#52511yescharacteristic
472C22×C17#52511yescharacteristic
473C22×C17#52911yescharacteristic
474C22×C17#53311yescharacteristic
475C22×C17#53511yescharacteristic
476C22×C17#53611yescharacteristic
477C22×C17#54211yescharacteristic
478C22×C17#54211yescharacteristic
479C22×C17#54611yescharacteristic
480C22×C17#54611yescharacteristic
481C22×C17#54611yescharacteristic
482C22×C17#54611yescharacteristic
483C22×C17#54811yescharacteristic
484C22×C17#54811yescharacteristic
485C22×C17D4×Q811yescharacteristic
486C22×C17D4×Q811yescharacteristic
487C22×C17#55211yescharacteristic
488C22×C17#55211yescharacteristic
489C22×C17#55411yescharacteristic
490C22×C17#55411yescharacteristic
491C22×C17#55611yescharacteristic
492C22×C17#55611yescharacteristic
493C22×C17#55911yescharacteristic
494C22×C17#55911yescharacteristic
495C2×D17—24no—
496C2×D17—24no—
497C2×D17—24no—
498C2×D17—42no—
499C2×D17—42no—
500C2×D17—42no—
501C2×D17—42no—
502C2×D17—42no—
503C2×D17—42no—
504C2×D17—42no—
505C2×D17—42no—
506C2×D17—42no—
507C2×D17—42no—
508C2×D17—42no—
509C2×D17—42no—
510C4×C17—24no—
511C4×C17—24no—
512C4×C17—42no—
513C4×C17—42no—
514C4×C17—42no—
515C4×C17—42no—
516C4×C17—81no—
517Dic17—24no—
518Dic17—24no—
519Dic17—24no—
520Dic17—42no—
521Dic17—42no—
522Dic17—42no—
523Dic17—81no—
524C23×Q8—171no—
525C24×C4—171no—
526C2×C4×Q8—344no—
527C2×C4×Q8—344no—
528C2×C4×Q8—344no—
529C22×C4⋊C4—171no—
530C22×C4⋊C4—171no—
531C22×C4⋊C4—171no—
532C22×C4⋊C4—171no—
533C22×C4⋊C4C2×D1711yescharacteristic
534C22×C22⋊C4—171no—
535C22×C22⋊C4—171no—
536C22×C22⋊C4—171no—
537C22×C22⋊C4—171no—
538C22×C22⋊C4—171no—
539C22×C22⋊C4—171no—
540C22×C42—171no—
541C22×C42—171no—
542C22×C42—171no—
543C22×C42C2×D1711yescharacteristic
544#393—178no—
545#385—344no—
546#385—344no—
547C4×C22⋊C4—344no—
548C2×#95—171no—
549C2×#95—171no—
550C2×#95—171no—
551C2×#95—171no—
552C2×#95—171no—
553C2×#95—171no—
554C2×#95—171no—
555C2×#95—171no—
556C2×#95—171no—
557C2×#95—171no—
558C2×#95—171no—
559C2×#95—171no—
560C2×#95—171no—
561C2×#95C2×D1711yescharacteristic
562C2×#95C2×D1711yescharacteristic
563C2×#95C2×D1711yescharacteristic
564C2×#95C2×D1711yescharacteristic
565C2×#95C2×D1711yescharacteristic
566C2×C17C4×#12011yescharacteristic
567C2×C17C4×C22⋊Q811yescharacteristic
568C2×C17#232611yescharacteristic
569C2×C17#236011yescharacteristic
570C2×C17#236011yescharacteristic
571C2×C17#236711yescharacteristic
572C2×C17#236711yescharacteristic
573C2×C17#240411yescharacteristic
574C2×C17#240911yescharacteristic
575C2×C17#245811yescharacteristic
576C2×C17#245811yescharacteristic
577C2×C17#246511yescharacteristic
578C2×C17#246511yescharacteristic
579C2×C17#258011yescharacteristic
580C2×C17#259911yescharacteristic
581D17—44no—
582C25—171no—
583C22×Q8—174no—
584C22×Q8—342no—
585C22×Q8—342no—
586C22×Q8—342no—
587C22×Q8—342no—
588C22×Q8—342no—
589C22×Q8—342no—
590C23×C4—171no—
591C23×C4—171no—
592C23×C4—171no—
593C23×C4—171no—
594C23×C4—171no—
595C23×C4—171no—
596C23×C4—171no—
597C23×C4—342no—
598C23×C4—342no—
599C23×C4—342no—
600C23×C4—342no—
601C23×C4—342no—
602C23×C4—681no—
603C23×C4—681no—
604C23×C4C22×D1711yescharacteristic
605C23×C4C22×D1711yescharacteristic
606C23×C4C22×D1711yescharacteristic
607C23×C4C22×D1711yescharacteristic
608C23×C4C22×D1711yescharacteristic
609C23×C4C22×D1711yescharacteristic
610C23×C4C22×D1711yescharacteristic
611C4×Q8—3432no—
612C2×C4⋊C4—22no—
613C2×C4⋊C4—22no—
614C2×C4⋊C4—174no—
615C2×C4⋊C4—342no—
616C2×C4⋊C4—342no—
617C2×C4⋊C4—342no—
618C2×C4⋊C4—342no—
619C2×C4⋊C4—342no—
620C2×C4⋊C4—342no—
621C2×C4⋊C4—342no—
622C2×C4⋊C4—342no—
623C2×C4⋊C4—342no—
624C2×C4⋊C4—681no—
625C2×C4⋊C4—681no—
626C2×C4⋊C4D6814yes—
627C2×C22⋊C4—174no—
628C2×C22⋊C4—174no—
629C2×C22⋊C4—174no—
630C2×C22⋊C4—174no—
631C2×C22⋊C4—342no—
632C2×C22⋊C4—342no—
633C2×C22⋊C4—342no—
634C2×C22⋊C4—342no—
635C2×C22⋊C4—342no—
636C2×C22⋊C4—342no—
637C2×C22⋊C4—342no—
638C2×C22⋊C4—342no—
639C2×C22⋊C4—342no—
640C2×C22⋊C4—342no—
641C2×C22⋊C4—342no—
642C2×C22⋊C4—342no—
643C2×C22⋊C4—681no—
644C2×C22⋊C4—681no—
645C2×C42—22no—
646C2×C42—41no—
647C2×C42—41no—
648C2×C42—174no—
649C2×C42—342no—
650C2×C42—342no—
651C2×C42—342no—
652C2×C42—342no—
653C2×C42—342no—
654C2×C42—342no—
655C2×C42—342no—
656C2×C42—342no—
657#95—22no—
658#95—22no—
659#95—41no—
660#95—41no—
661#95—174no—
662#95—174no—
663#95—342no—
664#95—342no—
665#95—342no—
666#95—342no—
667#95—342no—
668#95—342no—
669#95—342no—
670#95—342no—
671#95—342no—
672#95—681no—
673#95—681no—
674#95C4×D1714yescomplemented
675C17#1417211yescharacteristic, complemented, Sylow
676C24—172no—
677C24—172no—
678C24—172no—
679C24—341no—
680C24—341no—
681C24—341no—
682C24—341no—
683C24—341no—
684C24—341no—
685C24—341no—
686C24—341no—
687C24—341no—
688C24—341no—
689C24—341no—
690C24—341no—
691C24C23×D1711yescharacteristic
692C2×Q8—348no—
693C2×Q8—348no—
694C2×Q8—348no—
695C2×Q8—348no—
696C2×Q8—348no—
697C2×Q8—348no—
698C2×Q8—348no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—172no—
739C22×C4—172no—
740C22×C4—172no—
741C22×C4—172no—
742C22×C4—172no—
743C22×C4—172no—
744C22×C4—172no—
745C22×C4—172no—
746C22×C4—172no—
747C22×C4—172no—
748C22×C4—172no—
749C22×C4—172no—
750C22×C4—348no—
751C22×C4—341no—
752C22×C4—341no—
753C22×C4—341no—
754C22×C4—341no—
755C22×C4—341no—
756C22×C4—341no—
757C22×C4—341no—
758C22×C4—341no—
759C22×C4—341no—
760C22×C4—341no—
761C22×C4—341no—
762C22×C4—341no—
763C22×C4—341no—
764C22×C4—341no—
765C22×C4—341no—
766C22×C4—341no—
767C22×C4—341no—
768C22×C4—341no—
769C22×C4—341no—
770C22×C4—341no—
771C22×C4—341no—
772C22×C4—341no—
773C22×C4—341no—
774C22×C4—341no—
775C22×C4—341no—
776C22×C4—341no—
777C22×C4—341no—
778C22×C4—341no—
779C22×C4—341no—
780C22×C4—341no—
781C22×C4—341no—
782C22×C4—341no—
783C22×C4—341no—
784C22×C4—341no—
785C22×C4—341no—
786C22×C4—341no—
787C22×C4—341no—
788C22×C4—684no—
789C22×C4—684no—
790C22×C4—684no—
791C22×C4—684no—
792C22×C4—684no—
793C22×C4—684no—
794C22×C4C2×C4×D1712yes—
795C22×C4C2×C4×D1712yes—
796C22×C4C2×C4×D1712yes—
797C22×C4C2×D6812yes—
798C22×C4C2×D6812yes—
799C22×C4C2×D6812yes—
800C22×C4#6325212yes—
801C22×C4D4×D1712yes—
802C22×C4D4×D1712yes—
803C22×C4Q8×D1712yes—
804C4⋊C4—28no—
805C4⋊C4—348no—
806C4⋊C4—348no—
807C4⋊C4—684no—
808C4⋊C4—684no—
809C22⋊C4—348no—
810C22⋊C4—348no—
811C22⋊C4—348no—
812C22⋊C4—348no—
813C22⋊C4—684no—
814C22⋊C4—684no—
815C42—44no—
816C42—348no—
817C42—348no—
818C42—348no—
819C23—174no—
820C23—342no—
821C23—342no—
822C23—342no—
823C23—342no—
824C23—342no—
825C23—342no—
826C23—342no—
827C23—342no—
828C23—342no—
829C23—342no—
830C23—342no—
831C23—342no—
832C23—342no—
833C23—342no—
834C23—342no—
835C23—342no—
836C23—342no—
837C23—342no—
838C23—681no—
839C23—681no—
840C23—681no—
841C23—681no—
842C23—681no—
843C23—681no—
844C23—681no—
845C23—681no—
846C23—681no—
847C23—681no—
848C23—681no—
849C23—681no—
850C23—681no—
851C23—681no—
852C23—681no—
853C23—681no—
854C23C22×C4×D1711yescharacteristic
855C23C22×D6811yescharacteristic
856C23C2×#6325211yescharacteristic
857C23C2×D4×D1711yescharacteristic
858C23C2×D4×D1711yescharacteristic
859C23#1058769111yescharacteristic
860C23#1058769111yescharacteristic
861C23C2×Q8×D1711yescharacteristic
862C23#1058769411yescharacteristic
863C23#41×D1711yescharacteristic
864C23#41×D1711yescharacteristic
865C23#41×D1711yescharacteristic
866C23#41×D1711yescharacteristic
867C23#41×D1711yescharacteristic
868C23#1058769711yescharacteristic
869Q8—3432no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—174no—
918C2×C4—174no—
919C2×C4—174no—
920C2×C4—342no—
921C2×C4—342no—
922C2×C4—342no—
923C2×C4—342no—
924C2×C4—342no—
925C2×C4—342no—
926C2×C4—342no—
927C2×C4—342no—
928C2×C4—342no—
929C2×C4—342no—
930C2×C4—342no—
931C2×C4—342no—
932C2×C4—342no—
933C2×C4—342no—
934C2×C4—342no—
935C2×C4—342no—
936C2×C4—342no—
937C2×C4—342no—
938C2×C4—342no—
939C2×C4—342no—
940C2×C4—342no—
941C2×C4—342no—
942C2×C4—342no—
943C2×C4—342no—
944C2×C4—342no—
945C2×C4—342no—
946C2×C4—342no—
947C2×C4—6816no—
948C2×C4—681no—
949C2×C4—681no—
950C2×C4—681no—
951C2×C4—681no—
952C2×C4—681no—
953C2×C4—681no—
954C2×C4—681no—
955C2×C4—681no—
956C2×C4—681no—
957C2×C4—681no—
958C2×C4—681no—
959C2×C4—681no—
960C2×C4—681no—
961C2×C4—681no—
962C2×C4—681no—
963C2×C4—681no—
964C2×C4—681no—
965C2×C4—681no—
966C2×C4—681no—
967C2×C4C4×D6814yes—
968C2×C4#1058756814yes—
969C22—344no—
970C22—344no—
971C22—344no—
972C22—682no—
973C22—682no—
974C22—682no—
975C22—682no—
976C22—682no—
977C22—682no—
978C22—682no—
979C22—682no—
980C22—682no—
981C22—682no—
982C22—682no—
983C22—682no—
984C22C4×D4×D1711yescharacteristic
985C22C4×D4×D1711yescharacteristic
986C22C2×C4×D6811yescharacteristic
987C22C4×Q8×D1711yescharacteristic
988C22#1176327711yescharacteristic
989C22#1176328811yescharacteristic
990C22#1176329011yescharacteristic
991C22C2×#1058756811yescharacteristic
992C22C22⋊Q8×D1711yescharacteristic
993C22#1176331711yescharacteristic
994C22#1176331811yescharacteristic
995C22#1176331811yescharacteristic
996C22#1176332111yescharacteristic
997C22#1176334211yescharacteristic
998C22#1176336511yescharacteristic
999C22#1176337411yescharacteristic
1000C22#1176338211yescharacteristic
1001C22#1176342711yescharacteristic
1002C22#1176342911yescharacteristic
1003C22#1176344811yescharacteristic
1004C22#1176344811yescharacteristic
1005C22#1176345411yescharacteristic
1006C22#1176345411yescharacteristic
1007C22#1176346711yescharacteristic
1008C22#1176347111yescharacteristic
1009C22#1176347411yescharacteristic
1010C22Q8×D6811yescharacteristic
1011C22#1176349111yescharacteristic
1012C22#1176349811yescharacteristic
1013C22#1176351311yescharacteristic
1014C22#1176351411yescharacteristic
1015C22#1176352611yescharacteristic
1016C22#1176353111yescharacteristic
1017C22#1176354211yescharacteristic
1018C22#1176354311yescharacteristic
1019C4—24no—
1020C4—24no—
1021C4—42no—
1022C4—42no—
1023C4—42no—
1024C4—42no—
1025C4—81no—
1026C4—344no—
1027C4—344no—
1028C4—344no—
1029C4—682no—
1030C4—682no—
1031C4—682no—
1032C4—1361no—
1033C2—684no—
1034C2C4×#1058756811yescharacteristic
1035C2#1453131811yescharacteristic
1036C2#1453149011yescharacteristic
1037C2#1453178611yescharacteristic
1038C2#1453179111yescharacteristic
1039C2#1453185011yescharacteristic
1040C2#1453185511yescharacteristic
1041C2#1453210211yescharacteristic
1042C2#1453214711yescharacteristic
1043C2#1453270411yescharacteristic
1044C2#1453271211yescharacteristic
1045C2#1453280311yescharacteristic
1046C2#1453281111yescharacteristic
1047C2#1453414111yescharacteristic
1048C2#1453435911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1436C2
socle, cosocleC24×C17C24
prime radicalC24×D17C23
hypercenter#1436D17
hypocenterC17#14172
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
1. C22×#10587573C2semidirect
6. #14527054C2semidirect
7. #14527048C2semidirect
11. #14527019C2semidirect
12. #14527018C2semidirect
13. #14527017C2semidirect
14. #14527008C2semidirect
15. C17×#1436C2semidirect
34. #11762722C4semidirect
86. C22×Dic34C2×C4semidirect
110. C2×#63227Q8semidirect
137. C17×#95C2×C4semidirect
149. #10587502C2×C4semidirect
150. #10587502C2×C4semidirect
344. C22×D17C4×Q8semidirect
458. #1436D17semidirect
674. #95C4×D17semidirect
675. C17#14172semidirect

Maximal subgroups

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

subgroupindex
C22×#105875732
C2×#117627222
C2×#117626832
C2×#117626802
C2×C4×#632272
#145270542
#145270482
#145270282
#145270202
#145270192
#145270182
#145270172
#145270082
C17×#14362
#1417217