Finite Group Databasebeta

← #16958561

Subgroups — #16958561

Order 4352.

1962 conjugacy classes of subgroups.

The subgroup lattice has 1158 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762711C211yesmaximal, characteristic
2C2×#11762698C211yesmaximal, characteristic, complemented
3C2×#11762687C211yesmaximal, characteristic
4C2×#11762656C211yesmaximal, characteristic, complemented
5C2×#11762655C211yesmaximal, characteristic, complemented
6#14527036C211yesmaximal, characteristic, complemented
7#14527032C211yesmaximal, characteristic, complemented
8#14527028C211yesmaximal, characteristic, complemented
9#14527024C211yesmaximal, characteristic
10#14527020C211yesmaximal, characteristic, complemented
11#14527020C211yesmaximal, characteristic, complemented
12#14527020C211yesmaximal, characteristic, complemented
13#14527018C211yesmaximal, characteristic, complemented
14#14527005C211yesmaximal, characteristic, complemented
15C17×#1434C211yesmaximal, characteristic, complemented
16C23×D68C2211yescharacteristic
17C23×C4×D17C2211yescharacteristic
18C22×C4⋊Dic17C2211yescharacteristic
19C22×#63225C2211yescharacteristic
20C22×#63227C2211yescharacteristic
21C22×#63227C2211yescharacteristic
22C22×#63227C2211yescharacteristic
23C22×#63227C2211yescharacteristic
24C22×#63227C2211yescharacteristic
25C22×#63227C2211yescharacteristic
26C22×#63227C2211yescharacteristic
27C22×#63227C2211yescharacteristic
28C22×#63227C2211yescharacteristic
29C22×#63227C2211yescharacteristic
30C22×#63227C2211yescharacteristic
31C22×C4×Dic17C2211yescharacteristic
32C22×C4×Dic17C2211yescharacteristic
33C22×C4×Dic17C2211yescharacteristic
34#11762711C418yescomplemented
35#11762698—24no—
36#11762687—24no—
37#11762656—24no—
38#11762655—24no—
39C2×#10587502C2211yescharacteristic
40C2×#10587502C2211yescharacteristic
41C2×#10587502C2211yescharacteristic
42C2×#10587502C2211yescharacteristic
43C2×#10587502C2211yescharacteristic
44C2×#10587502C2211yescharacteristic
45C2×#10587502C2211yescharacteristic
46C2×#10587502C2211yescharacteristic
47C2×#10587502C2211yescharacteristic
48C2×#10587502C2211yescharacteristic
49C22×C42×C17C2211yescharacteristic
50C2×C17×#95C2211yescharacteristic
51C2×C17×#95C2211yescharacteristic
52C2×C17×#95C2211yescharacteristic
53C2×C17×#95C2211yescharacteristic
54C2×C17×#95C2211yescharacteristic
55C2×C17×#95C2211yescharacteristic
56C24×D17C2311yescharacteristic
57C24×D17C2311yescharacteristic
58C23×C4×C17C2311yescharacteristic
59C23×C4×C17C2311yescharacteristic
60C23×C4×C17C2311yescharacteristic
61C23×C4×C17C2311yescharacteristic
62C23×C4×C17C2311yescharacteristic
63C23×C4×C17C2311yescharacteristic
64C23×C4×C17C2311yescharacteristic
65C23×Dic17C2311yescharacteristic
66C23×Dic17C2311yescharacteristic
67C23×Dic17C2311yescharacteristic
68C23×Dic17C2311yescharacteristic
69C23×Dic17C2311yescharacteristic
70C23×Dic17C2311yescharacteristic
71C22×D68—22no—
72C22×D68—22no—
73C22×D68—22no—
74C22×D68—22no—
75C22×D68—41no—
76C22×D68—41no—
77C22×D68C2×C414yes—
78C22×C4×D17—22no—
79C22×C4×D17—22no—
80C22×C4×D17—22no—
81C22×C4×D17—22no—
82C22×C4×D17—22no—
83C22×C4×D17—41no—
84C22×C4×D17—41no—
85C2×C42×C17—22no—
86C2×C42×C17—22no—
87C2×C42×C17C2×C414yescomplemented
88C2×#63227—22no—
89C2×#63227—22no—
90C2×#63227—22no—
91C2×#63227—22no—
92C2×#63227—22no—
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—22no—
106C2×#63227—22no—
107C2×#63227—41no—
108C2×#63227—41no—
109C2×#63227—41no—
110C2×#63227—41no—
111C2×#63227—41no—
112C2×#63227—41no—
113C2×#63227—41no—
114C2×#63227—41no—
115C2×#63227—41no—
116C2×#63227—41no—
117C2×#63227C2×C414yes—
118C2×#63227C2×C414yes—
119C2×#63227C2×C414yescomplemented
120C2×#63227C2×C414yescomplemented
121C2×C4⋊Dic17—41no—
122C2×C4⋊Dic17—41no—
123C2×C4⋊Dic17C2×C414yescomplemented
124C2×#63225—22no—
125C2×#63225—41no—
126C2×#63225—41no—
127C2×C4×Dic17—22no—
128C2×C4×Dic17—22no—
129C2×C4×Dic17—22no—
130C2×C4×Dic17—22no—
131C2×C4×Dic17—22no—
132C2×C4×Dic17—22no—
133C2×C4×Dic17—41no—
134C2×C4×Dic17—41no—
135C2×C4×Dic17D414yescomplemented
136C17×#95—22no—
137C17×#95—22no—
138C17×#95—22no—
139C17×#95—22no—
140C17×#95—22no—
141C17×#95—22no—
142#10587502—22no—
143#10587502—22no—
144#10587502—22no—
145#10587502—22no—
146#10587502—22no—
147#10587502—41no—
148#10587502—41no—
149#10587502—41no—
150#10587502—41no—
151#10587502D414yes—
152C24×C17C2411yescharacteristic
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×D17—21no—
165C23×D17—21no—
166C23×D17—21no—
167C23×D17—21no—
168C23×D17—21no—
169C23×D17—21no—
170C23×D17—21no—
171C23×D17—21no—
172C23×D17—21no—
173C23×D17—21no—
174C23×D17—21no—
175C23×D17—21no—
176C23×D17—21no—
177C23×D17—21no—
178C23×D17—21no—
179C23×D17C22×C412yes—
180C23×D17C22×C412yes—
181C23×D17#4112yes—
182C23×D17#4112yes—
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×C17—21no—
207C22×C4×C17—21no—
208C22×C4×C17—21no—
209C22×C4×C17—21no—
210C22×C4×C17—21no—
211C22×C4×C17—21no—
212C22×C4×C17—21no—
213C22×C4×C17—21no—
214C22×C4×C17—21no—
215C22×C4×C17—21no—
216C22×C4×C17—21no—
217C22×C4×C17—21no—
218C22×C4×C17—21no—
219C22×C4×C17—21no—
220C22×C4×C17—21no—
221C22×C4×C17—21no—
222C22×C4×C17—21no—
223C22×C4×C17C22×C412yes—
224C22×C4×C17C22×C412yes—
225C22×C4×C17C22×C412yes—
226C22×C4×C17C2×D412yes—
227C22×C4×C17C2×D412yes—
228C22×C4×C17#4112yes—
229C22×C4×C17#4112yes—
230C22×C4×C17#4112yes—
231C22×C4×C17#4112yes—
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×Dic17—21no—
254C22×Dic17—21no—
255C22×Dic17—21no—
256C22×Dic17—21no—
257C22×Dic17—21no—
258C22×Dic17—21no—
259C22×Dic17—21no—
260C22×Dic17—21no—
261C22×Dic17—21no—
262C22×Dic17—21no—
263C22×Dic17—21no—
264C22×Dic17—21no—
265C22×Dic17—21no—
266C22×Dic17C22×C412yes—
267C22×Dic17C22×C412yes—
268C22×Dic17C2×D412yes—
269C22×Dic17C2×D412yes—
270C22×Dic17C2×D412yes—
271C22×Dic17C2×D412yes—
272C22×Dic17#4112yes—
273C22×Dic17#4112yes—
274C2×D68—28no—
275C2×D68—28no—
276C2×D68—44no—
277C2×D68—44no—
278C2×D68—44no—
279C2×D68—44no—
280C2×D68—44no—
281C2×C4×D17—28no—
282C2×C4×D17—44no—
283C2×C4×D17—44no—
284C2×C4×D17—44no—
285C2×C4×D17—44no—
286C2×C4×D17—44no—
287C2×C4×D17—44no—
288C42×C17—28no—
289#63227—28no—
290#63227—28no—
291#63227—28no—
292#63227—44no—
293#63227—44no—
294#63227—44no—
295#63227—44no—
296#63227—44no—
297#63227—44no—
298#63227—44no—
299#63227—44no—
300C4⋊Dic17—44no—
301#63225—44no—
302C4×Dic17—28no—
303C4×Dic17—28no—
304C4×Dic17—44no—
305#14082—171nomaximal, Sylow
306C23×C17C23×C411yescharacteristic
307C23×C17C22×D411yescharacteristic
308C23×C17C22×D411yescharacteristic
309C23×C17C2×#4111yescharacteristic
310C23×C17C2×#4111yescharacteristic
311C23×C17C2×#4111yescharacteristic
312C23×C17C2×#4111yescharacteristic
313C23×C17C2×#4111yescharacteristic
314C23×C17C2×#4111yescharacteristic
315C23×C17C2×#4111yescharacteristic
316C23×C17C2×#4111yescharacteristic
317C23×C17H(5,𝔽2)11yescharacteristic
318C23×C17H(5,𝔽2)11yescharacteristic
319C23×C17H(5,𝔽2)11yescharacteristic
320C23×C17H(5,𝔽2)11yescharacteristic
321C22×D17—22no—
322C22×D17—22no—
323C22×D17—22no—
324C22×D17—22no—
325C22×D17—22no—
326C22×D17—22no—
327C22×D17—22no—
328C22×D17—22no—
329C22×D17—22no—
330C22×D17—22no—
331C22×D17—22no—
332C22×D17—22no—
333C22×D17—22no—
334C22×D17—22no—
335C22×D17—22no—
336C22×D17—22no—
337C22×D17—22no—
338C22×D17—22no—
339C22×D17—22no—
340C22×D17—22no—
341C22×D17—22no—
342C22×D17—22no—
343C22×D17—22no—
344C22×D17—22no—
345C22×D17—22no—
346C22×D17—41no—
347C22×D17—41no—
348C22×D17—41no—
349C22×D17—41no—
350C22×D17—41no—
351C22×D17—41no—
352C22×D17—41no—
353C22×D17—41no—
354C22×D17—41no—
355C22×D17—41no—
356C22×D17—41no—
357C22×D17—41no—
358C22×D17—41no—
359C22×D17—41no—
360C22×D17—41no—
361C22×D17—41no—
362C22×D17—41no—
363C22×D17—41no—
364C22×D17—41no—
365C22×D17—41no—
366C22×D17—41no—
367C22×D17—41no—
368C22×D17—41no—
369C22×D17—41no—
370C22×D17—41no—
371C22×D17—41no—
372C22×D17—41no—
373C22×D17—41no—
374C22×D17—41no—
375C22×D17—41no—
376C22×D17—41no—
377C22×D17—41no—
378C22×D17—41no—
379C22×D17—41no—
380C22×D17—41no—
381C22×D17—41no—
382C22×D17—41no—
383C22×D17—41no—
384C22×D17—41no—
385C22×D17—41no—
386C22×D17—41no—
387C22×D17—41no—
388C22×D17—41no—
389C22×D17—41no—
390C22×D17#11714yes—
391C2×C4×C17—22no—
392C2×C4×C17—22no—
393C2×C4×C17—22no—
394C2×C4×C17—22no—
395C2×C4×C17—22no—
396C2×C4×C17—22no—
397C2×C4×C17—22no—
398C2×C4×C17—22no—
399C2×C4×C17—22no—
400C2×C4×C17—22no—
401C2×C4×C17—22no—
402C2×C4×C17—22no—
403C2×C4×C17—22no—
404C2×C4×C17—22no—
405C2×C4×C17—22no—
406C2×C4×C17—22no—
407C2×C4×C17—22no—
408C2×C4×C17—22no—
409C2×C4×C17—22no—
410C2×C4×C17—22no—
411C2×C4×C17—22no—
412C2×C4×C17—41no—
413C2×C4×C17—41no—
414C2×C4×C17—41no—
415C2×C4×C17—41no—
416C2×C4×C17—41no—
417C2×C4×C17—41no—
418C2×C4×C17—41no—
419C2×C4×C17—41no—
420C2×C4×C17—41no—
421C2×C4×C17—41no—
422C2×C4×C17—41no—
423C2×C4×C17—41no—
424C2×C4×C17—41no—
425C2×C4×C17—41no—
426C2×C4×C17—41no—
427C2×C4×C17—41no—
428C2×C4×C17—41no—
429C2×C4×C17—41no—
430C2×C4×C17—41no—
431C2×C4×C17—41no—
432C2×C4×C17—41no—
433C2×C4×C17—41no—
434C2×C4×C17—41no—
435C2×C4×C17—41no—
436C2×C4×C17—41no—
437C2×C4×C17—41no—
438C2×C4×C17C4×D414yes—
439C2×C4×C17C4×D414yes—
440C2×Dic17—22no—
441C2×Dic17—22no—
442C2×Dic17—22no—
443C2×Dic17—22no—
444C2×Dic17—22no—
445C2×Dic17—22no—
446C2×Dic17—22no—
447C2×Dic17—22no—
448C2×Dic17—22no—
449C2×Dic17—22no—
450C2×Dic17—22no—
451C2×Dic17—22no—
452C2×Dic17—22no—
453C2×Dic17—22no—
454C2×Dic17—22no—
455C2×Dic17—22no—
456C2×Dic17—22no—
457C2×Dic17—22no—
458C2×Dic17—22no—
459C2×Dic17—22no—
460C2×Dic17—22no—
461C2×Dic17—41no—
462C2×Dic17—41no—
463C2×Dic17—41no—
464C2×Dic17—41no—
465C2×Dic17—41no—
466C2×Dic17—41no—
467C2×Dic17—41no—
468C2×Dic17—41no—
469C2×Dic17—41no—
470C2×Dic17—41no—
471C2×Dic17—41no—
472C2×Dic17—41no—
473C2×Dic17—41no—
474C2×Dic17—41no—
475C2×Dic17—41no—
476C2×Dic17—41no—
477C2×Dic17—41no—
478C2×Dic17—41no—
479C2×Dic17—41no—
480C2×Dic17—41no—
481C2×Dic17#12114yes—
482D68—416no—
483C4×D17—416no—
484C2×#390—171no—
485C2×#388—171no—
486C2×#386—171no—
487C2×C4×C22⋊C4—171no—
488C2×#376—171no—
489#1441—171no—
490#1440—171no—
491#1439—171no—
492#1438—171no—
493#1437—171no—
494#1437—171no—
495#1437—171no—
496#1436—171no—
497#1434D1711yescharacteristic, complemented
498C22⋊#95—171no—
499C22×C17C2×#11711yescharacteristic
500C22×C17C2×C4×D411yescharacteristic
501C22×C17C2×C4×D411yescharacteristic
502C22×C17C4×#4111yescharacteristic
503C22×C17C4×#4111yescharacteristic
504C22×C17#51811yescharacteristic
505C22×C17#51811yescharacteristic
506C22×C17C2×#12111yescharacteristic
507C22×C17#52511yescharacteristic
508C22×C17#52511yescharacteristic
509C22×C17#52511yescharacteristic
510C22×C17#52911yescharacteristic
511C22×C17#52911yescharacteristic
512C22×C17#52911yescharacteristic
513C22×C17#53211yescharacteristic
514C22×C17#53511yescharacteristic
515C22×C17#53511yescharacteristic
516C22×C17#54011yescharacteristic
517C22×C17#54011yescharacteristic
518C22×C17#54611yescharacteristic
519C22×C17#54611yescharacteristic
520C22×C17#54611yescharacteristic
521C22×C17#55011yescharacteristic
522C22×C17#55111yescharacteristic
523C22×C17#55111yescharacteristic
524C22×C17#55111yescharacteristic
525C22×C17#55111yescharacteristic
526C22×C17#55111yescharacteristic
527C22×C17#55111yescharacteristic
528C22×C17#55311yescharacteristic
529C22×C17#55311yescharacteristic
530C22×C17#55311yescharacteristic
531C22×C17#55511yescharacteristic
532C22×C17#55511yescharacteristic
533C22×C17#55511yescharacteristic
534C2×D17—24no—
535C2×D17—24no—
536C2×D17—24no—
537C2×D17—42no—
538C2×D17—42no—
539C2×D17—42no—
540C2×D17—42no—
541C2×D17—42no—
542C2×D17—42no—
543C2×D17—42no—
544C2×D17—42no—
545C2×D17—42no—
546C2×D17—42no—
547C2×D17—42no—
548C2×D17—42no—
549C2×D17—42no—
550C2×D17—42no—
551C2×D17—42no—
552C2×D17—42no—
553C2×D17—42no—
554C2×D17—42no—
555C2×D17—42no—
556C2×D17—81no—
557C2×D17—81no—
558C2×D17—81no—
559C2×D17—81no—
560C2×D17—81no—
561C2×D17—81no—
562C2×D17—81no—
563C2×D17—81no—
564C4×C17—24no—
565C4×C17—24no—
566C4×C17—42no—
567C4×C17—42no—
568C4×C17—42no—
569C4×C17—81no—
570C4×C17—81no—
571Dic17—24no—
572Dic17—42no—
573Dic17—42no—
574Dic17—42no—
575Dic17—42no—
576Dic17—42no—
577C23×D4—171no—
578C24×C4—171no—
579C22×C4⋊C4—171no—
580C22×C4⋊C4—171no—
581C22×C22⋊C4—171no—
582C22×C22⋊C4—171no—
583C22×C22⋊C4—171no—
584C22×C22⋊C4—171no—
585C22×C22⋊C4—171no—
586C22×C22⋊C4—171no—
587C22×C22⋊C4—171no—
588C22×C22⋊C4—171no—
589C22×C22⋊C4—171no—
590C22×C22⋊C4—171no—
591C22×C22⋊C4—171no—
592C22×C42—171no—
593C22×C42—171no—
594C22×C42—171no—
595C22×C42C2×D1711yescharacteristic
596#390—178no—
597#388—344no—
598#386—344no—
599C4×C22⋊C4—344no—
600#376—344no—
601C2×#95—171no—
602C2×#95—171no—
603C2×#95—171no—
604C2×#95—171no—
605C2×#95—171no—
606C2×#95—171no—
607C2×#95—171no—
608C2×#95—171no—
609C2×#95—171no—
610C2×#95—171no—
611C2×#95C2×D1711yescharacteristic
612C2×#95C2×D1711yescharacteristic
613C2×#95C2×D1711yescharacteristic
614C2×#95C2×D1711yescharacteristic
615C2×#95C2×D1711yescharacteristic
616C2×#95C2×D1711yescharacteristic
617C2×C17#229011yescharacteristic
618C2×C17C4×#12111yescharacteristic
619C2×C17#232811yescharacteristic
620C2×C17#234211yescharacteristic
621C2×C17#235311yescharacteristic
622C2×C17#236311yescharacteristic
623C2×C17#237211yescharacteristic
624C2×C17#241111yescharacteristic
625C2×C17#241411yescharacteristic
626C2×C17#247111yescharacteristic
627C2×C17#247611yescharacteristic
628C2×C17#252611yescharacteristic
629C2×C17#253111yescharacteristic
630C2×C17#260311yescharacteristic
631C2×C17#261011yescharacteristic
632D17—44no—
633D17—82no—
634C25—171no—
635C25—171no—
636C22×D4—174no—
637C22×D4—342no—
638C22×D4—342no—
639C22×D4—342no—
640C22×D4—342no—
641C22×D4—681no—
642C22×D4—681no—
643C23×C4—171no—
644C23×C4—171no—
645C23×C4—171no—
646C23×C4—171no—
647C23×C4—171no—
648C23×C4—171no—
649C23×C4—342no—
650C23×C4—342no—
651C23×C4—342no—
652C23×C4—342no—
653C23×C4—342no—
654C23×C4—681no—
655C23×C4—681no—
656C23×C4C22×D1711yescharacteristic
657C23×C4C22×D1711yescharacteristic
658C23×C4C22×D1711yescharacteristic
659C23×C4C22×D1711yescharacteristic
660C23×C4C22×D1711yescharacteristic
661C23×C4C22×D1711yescharacteristic
662C23×C4C22×D1711yescharacteristic
663C2×C4⋊C4—174no—
664C2×C4⋊C4—342no—
665C2×C4⋊C4—681no—
666C2×C4⋊C4—681no—
667C2×C4⋊C4—681no—
668C2×C4⋊C4—681no—
669C2×C22⋊C4—174no—
670C2×C22⋊C4—174no—
671C2×C22⋊C4—174no—
672C2×C22⋊C4—174no—
673C2×C22⋊C4—342no—
674C2×C22⋊C4—342no—
675C2×C22⋊C4—342no—
676C2×C22⋊C4—342no—
677C2×C22⋊C4—342no—
678C2×C22⋊C4—342no—
679C2×C22⋊C4—342no—
680C2×C22⋊C4—342no—
681C2×C22⋊C4—342no—
682C2×C22⋊C4—342no—
683C2×C22⋊C4—342no—
684C2×C22⋊C4—342no—
685C2×C22⋊C4—342no—
686C2×C22⋊C4—342no—
687C2×C22⋊C4—342no—
688C2×C22⋊C4—342no—
689C2×C22⋊C4—342no—
690C2×C22⋊C4—342no—
691C2×C22⋊C4—342no—
692C2×C22⋊C4—681no—
693C2×C22⋊C4—681no—
694C2×C22⋊C4—681no—
695C2×C22⋊C4—681no—
696C2×C22⋊C4—681no—
697C2×C22⋊C4—681no—
698C2×C22⋊C4—681no—
699C2×C22⋊C4—681no—
700C2×C22⋊C4—681no—
701C2×C22⋊C4—681no—
702C2×C42—22no—
703C2×C42—22no—
704C2×C42—174no—
705C2×C42—342no—
706C2×C42—342no—
707C2×C42—342no—
708C2×C42—342no—
709C2×C42—342no—
710C2×C42—342no—
711C2×C42—681no—
712C2×C42—681no—
713C2×C42C4×D1714yescomplemented
714#95—22no—
715#95—22no—
716#95—22no—
717#95—22no—
718#95—22no—
719#95—22no—
720#95—174no—
721#95—342no—
722#95—342no—
723#95—342no—
724#95—342no—
725#95—342no—
726#95—681no—
727#95—681no—
728#95—681no—
729#95—681no—
730C17#1408211yescharacteristic, complemented, Sylow
731C24—172no—
732C24—172no—
733C24—172no—
734C24—172no—
735C24—341no—
736C24—341no—
737C24—341no—
738C24—341no—
739C24—341no—
740C24—341no—
741C24—341no—
742C24—341no—
743C24—341no—
744C24—341no—
745C24—341no—
746C24—341no—
747C24—341no—
748C24—341no—
749C24—341no—
750C24—341no—
751C24—341no—
752C24—341no—
753C24—341no—
754C24—341no—
755C24—341no—
756C24—341no—
757C24—341no—
758C24—341no—
759C24—341no—
760C24—341no—
761C24C23×D1711yescharacteristic
762C2×D4—348no—
763C2×D4—348no—
764C2×D4—684no—
765C2×D4—684no—
766C2×D4—684no—
767C2×D4—684no—
768C2×D4—684no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—172no—
810C22×C4—172no—
811C22×C4—172no—
812C22×C4—172no—
813C22×C4—172no—
814C22×C4—172no—
815C22×C4—172no—
816C22×C4—172no—
817C22×C4—348no—
818C22×C4—341no—
819C22×C4—341no—
820C22×C4—341no—
821C22×C4—341no—
822C22×C4—341no—
823C22×C4—341no—
824C22×C4—341no—
825C22×C4—341no—
826C22×C4—341no—
827C22×C4—341no—
828C22×C4—341no—
829C22×C4—341no—
830C22×C4—341no—
831C22×C4—341no—
832C22×C4—341no—
833C22×C4—341no—
834C22×C4—341no—
835C22×C4—341no—
836C22×C4—341no—
837C22×C4—341no—
838C22×C4—341no—
839C22×C4—341no—
840C22×C4—341no—
841C22×C4—341no—
842C22×C4—341no—
843C22×C4—341no—
844C22×C4—341no—
845C22×C4—341no—
846C22×C4—341no—
847C22×C4—341no—
848C22×C4—341no—
849C22×C4—341no—
850C22×C4—341no—
851C22×C4—341no—
852C22×C4—684no—
853C22×C4—684no—
854C22×C4—684no—
855C22×C4—684no—
856C22×C4—684no—
857C22×C4—684no—
858C22×C4C2×C4×D1712yes—
859C22×C4C2×C4×D1712yes—
860C22×C4C2×C4×D1712yes—
861C22×C4#6325212yes—
862C22×C4#6325212yes—
863C22×C4D4×D1712yes—
864C22×C4D4×D1712yes—
865C22×C4#6325412yes—
866C22×C4#6325612yes—
867C4⋊C4—684no—
868C4⋊C4—684no—
869C22⋊C4—348no—
870C22⋊C4—348no—
871C22⋊C4—348no—
872C22⋊C4—684no—
873C22⋊C4—684no—
874C22⋊C4—684no—
875C22⋊C4—684no—
876C22⋊C4—684no—
877C22⋊C4—684no—
878C22⋊C4—684no—
879C22⋊C4—684no—
880C42—28no—
881C42—348no—
882C42—348no—
883C42—684no—
884C23—174no—
885C23—342no—
886C23—342no—
887C23—342no—
888C23—342no—
889C23—342no—
890C23—342no—
891C23—342no—
892C23—342no—
893C23—342no—
894C23—342no—
895C23—342no—
896C23—342no—
897C23—342no—
898C23—342no—
899C23—342no—
900C23—342no—
901C23—342no—
902C23—342no—
903C23—342no—
904C23—342no—
905C23—342no—
906C23—342no—
907C23—342no—
908C23—342no—
909C23—342no—
910C23—681no—
911C23—681no—
912C23—681no—
913C23—681no—
914C23—681no—
915C23—681no—
916C23—681no—
917C23—681no—
918C23—681no—
919C23—681no—
920C23—681no—
921C23—681no—
922C23—681no—
923C23—681no—
924C23—681no—
925C23—681no—
926C23—681no—
927C23—681no—
928C23—681no—
929C23—681no—
930C23—681no—
931C23—681no—
932C23—681no—
933C23—681no—
934C23—681no—
935C23—681no—
936C23—681no—
937C23—681no—
938C23—681no—
939C23—681no—
940C23—681no—
941C23—681no—
942C23—681no—
943C23—681no—
944C23—681no—
945C23—681no—
946C23—681no—
947C23—681no—
948C23—681no—
949C23—681no—
950C23—681no—
951C23—681no—
952C23—681no—
953C23—681no—
954C23C22×C4×D1711yescharacteristic
955C23C2×#6325211yescharacteristic
956C23C2×#6325211yescharacteristic
957C23C2×D4×D1711yescharacteristic
958C23C2×D4×D1711yescharacteristic
959C23C2×#6325411yescharacteristic
960C23C2×#6325611yescharacteristic
961C23#41×D1711yescharacteristic
962C23#41×D1711yescharacteristic
963C23#41×D1711yescharacteristic
964C23#41×D1711yescharacteristic
965C23#1058769611yescharacteristic
966C23#1058769611yescharacteristic
967C23#1058769611yescharacteristic
968C23#1058769611yescharacteristic
969D4—6816no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—174no—
1018C2×C4—342no—
1019C2×C4—342no—
1020C2×C4—342no—
1021C2×C4—342no—
1022C2×C4—342no—
1023C2×C4—342no—
1024C2×C4—342no—
1025C2×C4—342no—
1026C2×C4—342no—
1027C2×C4—342no—
1028C2×C4—342no—
1029C2×C4—342no—
1030C2×C4—342no—
1031C2×C4—342no—
1032C2×C4—342no—
1033C2×C4—342no—
1034C2×C4—342no—
1035C2×C4—342no—
1036C2×C4—342no—
1037C2×C4—342no—
1038C2×C4—342no—
1039C2×C4—6816no—
1040C2×C4—681no—
1041C2×C4—681no—
1042C2×C4—681no—
1043C2×C4—681no—
1044C2×C4—681no—
1045C2×C4—681no—
1046C2×C4—681no—
1047C2×C4—681no—
1048C2×C4—681no—
1049C2×C4—681no—
1050C2×C4—681no—
1051C2×C4—681no—
1052C2×C4—681no—
1053C2×C4—681no—
1054C2×C4—681no—
1055C2×C4—681no—
1056C2×C4—681no—
1057C2×C4—681no—
1058C2×C4—681no—
1059C2×C4—681no—
1060C2×C4#1058756714yes—
1061C2×C4#1058757914yes—
1062C22—344no—
1063C22—344no—
1064C22—344no—
1065C22—682no—
1066C22—682no—
1067C22—682no—
1068C22—682no—
1069C22—682no—
1070C22—682no—
1071C22—682no—
1072C22—682no—
1073C22—682no—
1074C22—682no—
1075C22—682no—
1076C22—682no—
1077C22—682no—
1078C22—682no—
1079C22—682no—
1080C22—682no—
1081C22—682no—
1082C22—682no—
1083C22—682no—
1084C22—1361no—
1085C22—1361no—
1086C22—1361no—
1087C22—1361no—
1088C22—1361no—
1089C22—1361no—
1090C22—1361no—
1091C22—1361no—
1092C22#117×D1711yescharacteristic
1093C22C2×#1058756711yescharacteristic
1094C22C2×#1058757911yescharacteristic
1095C22#1176327711yescharacteristic
1096C22C4×#6325211yescharacteristic
1097C22#1176328311yescharacteristic
1098C22#1176328311yescharacteristic
1099C22#121×D1711yescharacteristic
1100C22#1176331811yescharacteristic
1101C22#1176331811yescharacteristic
1102C22#1176332211yescharacteristic
1103C22#1176334511yescharacteristic
1104C22#1176334611yescharacteristic
1105C22#1176334611yescharacteristic
1106C22#1176335411yescharacteristic
1107C22#1176337711yescharacteristic
1108C22#1176337711yescharacteristic
1109C22#1176341511yescharacteristic
1110C22#1176341511yescharacteristic
1111C22#1176345111yescharacteristic
1112C22#1176345111yescharacteristic
1113C22#1176345511yescharacteristic
1114C22#1176348011yescharacteristic
1115C22#1176348211yescharacteristic
1116C22#1176348211yescharacteristic
1117C22#1176348311yescharacteristic
1118C22#1176348311yescharacteristic
1119C22#1176348411yescharacteristic
1120C22#1176348411yescharacteristic
1121C22#1176350511yescharacteristic
1122C22#1176351011yescharacteristic
1123C22#1176351011yescharacteristic
1124C22#1176352211yescharacteristic
1125C22#1176352211yescharacteristic
1126C22#1176352411yescharacteristic
1127C4—24no—
1128C4—24no—
1129C4—42no—
1130C4—42no—
1131C4—42no—
1132C4—81no—
1133C4—81no—
1134C4—344no—
1135C4—682no—
1136C4—682no—
1137C4—682no—
1138C4—682no—
1139C4—682no—
1140C2—684no—
1141C2—1362no—
1142C2#1453122511yescharacteristic
1143C2#1453129011yescharacteristic
1144C2#1453150711yescharacteristic
1145C2#1453162611yescharacteristic
1146C2#1453171711yescharacteristic
1147C2#1453182011yescharacteristic
1148C2#1453189411yescharacteristic
1149C2#1453216811yescharacteristic
1150C2#1453220111yescharacteristic
1151C2#1453290211yescharacteristic
1152C2#1453297711yescharacteristic
1153C2#1453356311yescharacteristic
1154C2#1453363811yescharacteristic
1155C2#1453440911yescharacteristic
1156C2#1453447011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1434C2
socle, cosocleC24×C17C24
prime radicalC23×D68C22
hypercenter#1434D17
hypocenterC17#14082
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
2. C2×#11762698C2semidirect
4. C2×#11762656C2semidirect
5. C2×#11762655C2semidirect
6. #14527036C2semidirect
7. #14527032C2semidirect
8. #14527028C2semidirect
10. #14527020C2semidirect
11. #14527020C2semidirect
12. #14527020C2semidirect
13. #14527018C2semidirect
14. #14527005C2semidirect
15. C17×#1434C2semidirect
34. #11762711C4semidirect
87. C2×C42×C17C2×C4semidirect
119. C2×#63227C2×C4semidirect
120. C2×#63227C2×C4semidirect
123. C2×C4⋊Dic17C2×C4semidirect
135. C2×C4×Dic17D4semidirect
497. #1434D17semidirect
713. C2×C42C4×D17semidirect
730. C17#14082semidirect

Maximal subgroups

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

subgroupindex
C2×#117627112
C2×#117626982
C2×#117626872
C2×#117626562
C2×#117626552
#145270362
#145270322
#145270282
#145270242
#145270202
#145270182
#145270052
C17×#14342
#1408217