Finite Group Databasebeta

← #16962440

Subgroups — #16962440

Order 4352.

1766 conjugacy classes of subgroups.

The subgroup lattice has 1142 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762701C211yesmaximal, characteristic, complemented
2C2×#11762687C211yesmaximal, characteristic
3C2×#11762666C211yesmaximal, characteristic, complemented
4#14527045C211yesmaximal, characteristic, complemented
5#14527032C211yesmaximal, characteristic, complemented
6#14527026C211yesmaximal, characteristic, complemented
7#14527024C211yesmaximal, characteristic
8#14527024C211yesmaximal, characteristic
9#14527020C211yesmaximal, characteristic, complemented
10#14527020C211yesmaximal, characteristic, complemented
11#14527020C211yesmaximal, characteristic, complemented
12#14527018C211yesmaximal, characteristic, complemented
13#14527010C211yesmaximal, characteristic, complemented
14#14527005C211yesmaximal, characteristic, complemented
15C17×#1442C211yesmaximal, characteristic, complemented
16C23×D68C2211yescharacteristic
17C23×C4×D17C2211yescharacteristic
18C22×C4⋊Dic17C2211yescharacteristic
19C22×#63227C2211yescharacteristic
20C22×#63227C2211yescharacteristic
21C22×#63227C2211yescharacteristic
22C22×#63227C2211yescharacteristic
23C22×#63227C2211yescharacteristic
24C22×#63227C2211yescharacteristic
25C22×#63227C2211yescharacteristic
26C22×#63227C2211yescharacteristic
27C22×#63227C2211yescharacteristic
28C22×#63227C2211yescharacteristic
29C22×#63227C2211yescharacteristic
30C22×C4×Dic17C2211yescharacteristic
31C22×C4×Dic17C2211yescharacteristic
32#11762701—24no—
33#11762687C418yescomplemented
34#11762666—24no—
35C2×#10587502C2211yescharacteristic
36C2×#10587502C2211yescharacteristic
37C2×#10587502C2211yescharacteristic
38C2×#10587502C2211yescharacteristic
39C2×#10587502C2211yescharacteristic
40C2×#10587502C2211yescharacteristic
41C2×#10587502C2211yescharacteristic
42C2×#10587502C2211yescharacteristic
43C2×#10587502C2211yescharacteristic
44C2×#10587502C2211yescharacteristic
45C2×#10587502C2211yescharacteristic
46C2×#10587502C2211yescharacteristic
47C22×C4⋊C4×C17C2211yescharacteristic
48C2×C17×#95C2211yescharacteristic
49C2×C17×#95C2211yescharacteristic
50C2×C17×#95C2211yescharacteristic
51C2×C17×#95C2211yescharacteristic
52C2×C17×#95C2211yescharacteristic
53C2×C17×#95C2211yescharacteristic
54C24×D17C2311yescharacteristic
55C24×D17C2311yescharacteristic
56C23×C4×C17C2311yescharacteristic
57C23×C4×C17C2311yescharacteristic
58C23×C4×C17C2311yescharacteristic
59C23×C4×C17C2311yescharacteristic
60C23×C4×C17C2311yescharacteristic
61C23×C4×C17C2311yescharacteristic
62C23×C4×C17C2311yescharacteristic
63C23×Dic17C2311yescharacteristic
64C23×Dic17C2311yescharacteristic
65C23×Dic17C2311yescharacteristic
66C23×Dic17C2311yescharacteristic
67C23×Dic17C2311yescharacteristic
68C23×Dic17C2311yescharacteristic
69C22×D68—22no—
70C22×D68—22no—
71C22×D68—41no—
72C22×D68—41no—
73C22×D68—41no—
74C22×D68—41no—
75C22×D68C2×C414yes—
76C22×C4×D17—22no—
77C22×C4×D17—22no—
78C22×C4×D17—41no—
79C22×C4×D17—41no—
80C22×C4×D17—41no—
81C22×C4×D17—41no—
82C22×C4×D17C2×C414yes—
83C2×C4⋊C4×C17—22no—
84C2×C4⋊C4×C17—41no—
85C2×C4⋊C4×C17—41no—
86C2×#63227—22no—
87C2×#63227—22no—
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—41no—
101C2×#63227—41no—
102C2×#63227—41no—
103C2×#63227—41no—
104C2×#63227—41no—
105C2×#63227—41no—
106C2×#63227—41no—
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×#63227C2×C414yes—
117C2×#63227C2×C414yes—
118C2×#63227C2×C414yes—
119C2×C4⋊Dic17—41no—
120C2×C4⋊Dic17—41no—
121C2×C4⋊Dic17D414yescomplemented
122C2×C4×Dic17—22no—
123C2×C4×Dic17—22no—
124C2×C4×Dic17—41no—
125C2×C4×Dic17—41no—
126C2×C4×Dic17—41no—
127C2×C4×Dic17—41no—
128C17×#95—22no—
129C17×#95—41no—
130C17×#95—41no—
131C17×#95—41no—
132C17×#95—41no—
133C17×#95C2×C414yes—
134#10587502—22no—
135#10587502—22no—
136#10587502—22no—
137#10587502—22no—
138#10587502—22no—
139#10587502—41no—
140#10587502—41no—
141#10587502—41no—
142#10587502—41no—
143#10587502—41no—
144#10587502—41no—
145#10587502C2×C414yes—
146C24×C17C2411yescharacteristic
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×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×D17C22×C412yes—
174C23×D17C22×C412yes—
175C23×D17#4112yes—
176C23×D17#4112yes—
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×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×C17C22×C412yes—
221C22×C4×C17C22×C412yes—
222C22×C4×C17C22×C412yes—
223C22×C4×C17C2×D412yes—
224C22×C4×C17#4112yes—
225C22×C4×C17#4112yes—
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×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×Dic17C22×C412yes—
264C22×Dic17C22×C412yes—
265C22×Dic17C2×D412yes—
266C22×Dic17C2×D412yes—
267C22×Dic17#4112yes—
268C2×D68—28no—
269C2×D68—44no—
270C2×D68—44no—
271C2×D68—44no—
272C2×D68—44no—
273C2×D68—44no—
274C2×D68—44no—
275C2×C4×D17—28no—
276C2×C4×D17—44no—
277C2×C4×D17—44no—
278C2×C4×D17—44no—
279C2×C4×D17—44no—
280C2×C4×D17—44no—
281C2×C4×D17—44no—
282C4⋊C4×C17—44no—
283#63227—28no—
284#63227—44no—
285#63227—44no—
286#63227—44no—
287#63227—44no—
288#63227—44no—
289#63227—44no—
290#63227—44no—
291#63227—44no—
292#63227—44no—
293#63227—44no—
294C4⋊Dic17—44no—
295C4×Dic17—44no—
296C4×Dic17—44no—
297#14415—171nomaximal, Sylow
298C23×C17C23×C411yescharacteristic
299C23×C17C22×D411yescharacteristic
300C23×C17C2×#4111yescharacteristic
301C23×C17C2×#4111yescharacteristic
302C23×C17C2×#4111yescharacteristic
303C23×C17C2×#4111yescharacteristic
304C23×C17C2×#4111yescharacteristic
305C23×C17H(5,𝔽2)11yescharacteristic
306C23×C17H(5,𝔽2)11yescharacteristic
307C23×C17H(5,𝔽2)11yescharacteristic
308C23×C17H(5,𝔽2)11yescharacteristic
309C23×C17H(5,𝔽2)11yescharacteristic
310C23×C17H(5,𝔽2)11yescharacteristic
311C23×C17H(5,𝔽2)11yescharacteristic
312C23×C172−1+411yescharacteristic
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—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—41no—
339C22×D17—41no—
340C22×D17—41no—
341C22×D17—41no—
342C22×D17—41no—
343C22×D17—41no—
344C22×D17—41no—
345C22×D17—41no—
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#11714yes—
383C2×C4×C17—22no—
384C2×C4×C17—22no—
385C2×C4×C17—22no—
386C2×C4×C17—22no—
387C2×C4×C17—22no—
388C2×C4×C17—22no—
389C2×C4×C17—22no—
390C2×C4×C17—22no—
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—41no—
399C2×C4×C17—41no—
400C2×C4×C17—41no—
401C2×C4×C17—41no—
402C2×C4×C17—41no—
403C2×C4×C17—41no—
404C2×C4×C17—41no—
405C2×C4×C17—41no—
406C2×C4×C17—41no—
407C2×C4×C17—41no—
408C2×C4×C17—41no—
409C2×C4×C17—41no—
410C2×C4×C17—41no—
411C2×C4×C17—41no—
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×C17C4×D414yes—
432C2×Dic17—22no—
433C2×Dic17—22no—
434C2×Dic17—22no—
435C2×Dic17—22no—
436C2×Dic17—22no—
437C2×Dic17—22no—
438C2×Dic17—22no—
439C2×Dic17—22no—
440C2×Dic17—22no—
441C2×Dic17—22no—
442C2×Dic17—22no—
443C2×Dic17—22no—
444C2×Dic17—22no—
445C2×Dic17—22no—
446C2×Dic17—22no—
447C2×Dic17—41no—
448C2×Dic17—41no—
449C2×Dic17—41no—
450C2×Dic17—41no—
451C2×Dic17—41no—
452C2×Dic17—41no—
453C2×Dic17—41no—
454C2×Dic17—41no—
455C2×Dic17—41no—
456C2×Dic17—41no—
457C2×Dic17—41no—
458C2×Dic17—41no—
459C2×Dic17—41no—
460C2×Dic17—41no—
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—
474D68—416no—
475C4×D17—416no—
476C2×#388—171no—
477C2×#386—171no—
478C2×#380—171no—
479#1443—171no—
480#1442D1711yescharacteristic, complemented
481#1440—171no—
482#1439—171no—
483#1438—171no—
484#1438—171no—
485#1437—171no—
486#1437—171no—
487#1437—171no—
488#1436—171no—
489#1434—171no—
490C22⋊#95—171no—
491C22×C17C2×#11711yescharacteristic
492C22×C17C2×C4×D411yescharacteristic
493C22×C17C4×#4111yescharacteristic
494C22×C17#51811yescharacteristic
495C22×C17#51811yescharacteristic
496C22×C17#51811yescharacteristic
497C22×C17#52011yescharacteristic
498C22×C17#53411yescharacteristic
499C22×C17#53511yescharacteristic
500C22×C17#53811yescharacteristic
501C22×C17#53811yescharacteristic
502C22×C17#53811yescharacteristic
503C22×C17#53811yescharacteristic
504C22×C17#53811yescharacteristic
505C22×C17#53811yescharacteristic
506C22×C17#53811yescharacteristic
507C22×C17#53911yescharacteristic
508C22×C17#54011yescharacteristic
509C22×C17#54211yescharacteristic
510C22×C17#54611yescharacteristic
511C22×C17#54611yescharacteristic
512C22×C17#54811yescharacteristic
513C22×C17#55011yescharacteristic
514C22×C17#55111yescharacteristic
515C22×C17#55111yescharacteristic
516C22×C17#55211yescharacteristic
517C22×C17#55311yescharacteristic
518C22×C17#55311yescharacteristic
519C22×C17#55311yescharacteristic
520C22×C17#55311yescharacteristic
521C22×C17#55511yescharacteristic
522C22×C17#56011yescharacteristic
523C22×C17#56011yescharacteristic
524C22×C17#56211yescharacteristic
525C22×C17#56211yescharacteristic
526C2×D17—24no—
527C2×D17—24no—
528C2×D17—24no—
529C2×D17—42no—
530C2×D17—42no—
531C2×D17—42no—
532C2×D17—42no—
533C2×D17—42no—
534C2×D17—42no—
535C2×D17—42no—
536C2×D17—42no—
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—81no—
549C2×D17—81no—
550C2×D17—81no—
551C2×D17—81no—
552C2×D17—81no—
553C2×D17—81no—
554C2×D17—81no—
555C2×D17—81no—
556C4×C17—24no—
557C4×C17—42no—
558C4×C17—42no—
559C4×C17—42no—
560C4×C17—81no—
561C4×C17—81no—
562C4×C17—81no—
563Dic17—42no—
564Dic17—42no—
565Dic17—42no—
566Dic17—42no—
567Dic17—42no—
568Dic17—81no—
569C23×D4—171no—
570C24×C4—171no—
571C22×C4⋊C4—171no—
572C22×C4⋊C4C2×D1711yescharacteristic
573C22×C22⋊C4—171no—
574C22×C22⋊C4—171no—
575C22×C22⋊C4—171no—
576C22×C22⋊C4—171no—
577C22×C22⋊C4—171no—
578C22×C22⋊C4—171no—
579C22×C22⋊C4—171no—
580C22×C22⋊C4—171no—
581C22×C22⋊C4—171no—
582C22×C22⋊C4—171no—
583C22×C22⋊C4—171no—
584C22×C42—171no—
585C22×C42—171no—
586#388—344no—
587#386—178no—
588#380—344no—
589C2×#95—171no—
590C2×#95—171no—
591C2×#95—171no—
592C2×#95—171no—
593C2×#95—171no—
594C2×#95—171no—
595C2×#95—171no—
596C2×#95—171no—
597C2×#95—171no—
598C2×#95—171no—
599C2×#95—171no—
600C2×#95—171no—
601C2×#95C2×D1711yescharacteristic
602C2×#95C2×D1711yescharacteristic
603C2×#95C2×D1711yescharacteristic
604C2×#95C2×D1711yescharacteristic
605C2×#95C2×D1711yescharacteristic
606C2×#95C2×D1711yescharacteristic
607C2×C17#231211yescharacteristic
608C2×C17#232111yescharacteristic
609C2×C17#233511yescharacteristic
610C2×C17#235211yescharacteristic
611C2×C17#235311yescharacteristic
612C2×C17#236311yescharacteristic
613C2×C17#237711yescharacteristic
614C2×C17#268811yescharacteristic
615C2×C17#269611yescharacteristic
616C2×C17#271411yescharacteristic
617C2×C17#273011yescharacteristic
618C2×C17#275611yescharacteristic
619C2×C17#277811yescharacteristic
620C2×C17#277911yescharacteristic
621C2×C17#278111yescharacteristic
622D17—44no—
623D17—82no—
624C25—171no—
625C25—171no—
626C22×D4—174no—
627C22×D4—342no—
628C22×D4—342no—
629C22×D4—681no—
630C22×D4—681no—
631C22×D4—681no—
632C22×D4—681no—
633C23×C4—171no—
634C23×C4—171no—
635C23×C4—171no—
636C23×C4—171no—
637C23×C4—171no—
638C23×C4—174no—
639C23×C4—171no—
640C23×C4—342no—
641C23×C4—342no—
642C23×C4—681no—
643C23×C4—681no—
644C23×C4—681no—
645C23×C4—681no—
646C23×C4C22×D1711yescharacteristic
647C23×C4C22×D1711yescharacteristic
648C23×C4C22×D1711yescharacteristic
649C23×C4C22×D1711yescharacteristic
650C23×C4C22×D1711yescharacteristic
651C23×C4C22×D1711yescharacteristic
652C23×C4C22×D1711yescharacteristic
653C2×C4⋊C4—22no—
654C2×C4⋊C4—41no—
655C2×C4⋊C4—41no—
656C2×C4⋊C4—174no—
657C2×C4⋊C4—681no—
658C2×C4⋊C4—681no—
659C2×C22⋊C4—174no—
660C2×C22⋊C4—174no—
661C2×C22⋊C4—174no—
662C2×C22⋊C4—342no—
663C2×C22⋊C4—342no—
664C2×C22⋊C4—342no—
665C2×C22⋊C4—342no—
666C2×C22⋊C4—342no—
667C2×C22⋊C4—342no—
668C2×C22⋊C4—342no—
669C2×C22⋊C4—342no—
670C2×C22⋊C4—342no—
671C2×C22⋊C4—342no—
672C2×C22⋊C4—342no—
673C2×C22⋊C4—342no—
674C2×C22⋊C4—342no—
675C2×C22⋊C4—342no—
676C2×C22⋊C4—681no—
677C2×C22⋊C4—681no—
678C2×C22⋊C4—681no—
679C2×C22⋊C4—681no—
680C2×C22⋊C4—681no—
681C2×C22⋊C4—681no—
682C2×C22⋊C4—681no—
683C2×C22⋊C4—681no—
684C2×C22⋊C4—681no—
685C2×C22⋊C4—681no—
686C2×C22⋊C4—681no—
687C2×C22⋊C4—681no—
688C2×C22⋊C4—681no—
689C2×C22⋊C4—681no—
690C2×C22⋊C4—681no—
691C2×C22⋊C4—681no—
692C2×C42—342no—
693C2×C42—342no—
694C2×C42—681no—
695C2×C42—681no—
696C2×C42—681no—
697C2×C42—681no—
698#95—22no—
699#95—41no—
700#95—41no—
701#95—41no—
702#95—41no—
703#95—174no—
704#95—342no—
705#95—342no—
706#95—342no—
707#95—342no—
708#95—342no—
709#95—681no—
710#95—681no—
711#95—681no—
712#95—681no—
713#95—681no—
714#95—681no—
715#95C4×D1714yes—
716C17#1441511yescharacteristic, complemented, Sylow
717C24—172no—
718C24—172no—
719C24—172no—
720C24—172no—
721C24—341no—
722C24—341no—
723C24—341no—
724C24—341no—
725C24—341no—
726C24—341no—
727C24—341no—
728C24—341no—
729C24—341no—
730C24—341no—
731C24—341no—
732C24—341no—
733C24—341no—
734C24—341no—
735C24—341no—
736C24—341no—
737C24—341no—
738C24—341no—
739C24—341no—
740C24—341no—
741C24—341no—
742C24—341no—
743C24—341no—
744C24—341no—
745C24—341no—
746C24—341no—
747C24C23×D1711yescharacteristic
748C2×D4—348no—
749C2×D4—684no—
750C2×D4—684no—
751C2×D4—684no—
752C2×D4—684no—
753C2×D4—684no—
754C2×D4—684no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
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—172no—
799C22×C4—172no—
800C22×C4—172no—
801C22×C4—172no—
802C22×C4—172no—
803C22×C4—341no—
804C22×C4—341no—
805C22×C4—341no—
806C22×C4—341no—
807C22×C4—341no—
808C22×C4—341no—
809C22×C4—341no—
810C22×C4—341no—
811C22×C4—341no—
812C22×C4—341no—
813C22×C4—341no—
814C22×C4—341no—
815C22×C4—341no—
816C22×C4—341no—
817C22×C4—341no—
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—348no—
834C22×C4—341no—
835C22×C4—341no—
836C22×C4—341no—
837C22×C4—341no—
838C22×C4—341no—
839C22×C4—341no—
840C22×C4—341no—
841C22×C4—684no—
842C22×C4—684no—
843C22×C4—684no—
844C22×C4—684no—
845C22×C4—684no—
846C22×C4—684no—
847C22×C4C2×C4×D1712yes—
848C22×C4C2×C4×D1712yes—
849C22×C4C2×C4×D1712yes—
850C22×C4D4×D1712yes—
851C22×C4#6325612yes—
852C22×C4#6325612yes—
853C4⋊C4—44no—
854C4⋊C4—684no—
855C22⋊C4—348no—
856C22⋊C4—684no—
857C22⋊C4—684no—
858C22⋊C4—684no—
859C22⋊C4—684no—
860C22⋊C4—684no—
861C22⋊C4—684no—
862C22⋊C4—684no—
863C22⋊C4—684no—
864C22⋊C4—684no—
865C22⋊C4—684no—
866C42—684no—
867C42—684no—
868C23—174no—
869C23—342no—
870C23—342no—
871C23—342no—
872C23—342no—
873C23—342no—
874C23—342no—
875C23—342no—
876C23—342no—
877C23—342no—
878C23—342no—
879C23—342no—
880C23—342no—
881C23—342no—
882C23—342no—
883C23—342no—
884C23—342no—
885C23—342no—
886C23—342no—
887C23—342no—
888C23—342no—
889C23—342no—
890C23—342no—
891C23—342no—
892C23—342no—
893C23—342no—
894C23—681no—
895C23—681no—
896C23—681no—
897C23—681no—
898C23—681no—
899C23—681no—
900C23—681no—
901C23—681no—
902C23—681no—
903C23—681no—
904C23—681no—
905C23—681no—
906C23—681no—
907C23—681no—
908C23—681no—
909C23—681no—
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—
938C23C22×C4×D1711yescharacteristic
939C23C2×D4×D1711yescharacteristic
940C23#1058769111yescharacteristic
941C23#1058769111yescharacteristic
942C23#1058769111yescharacteristic
943C23C2×#6325611yescharacteristic
944C23C2×#6325611yescharacteristic
945C23#41×D1711yescharacteristic
946C23#41×D1711yescharacteristic
947C23#41×D1711yescharacteristic
948C23#1058769611yescharacteristic
949C23#1058769611yescharacteristic
950C23#1058769611yescharacteristic
951C23#1058769611yescharacteristic
952C23#1058769711yescharacteristic
953D4—6816no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
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—342no—
1003C2×C4—342no—
1004C2×C4—342no—
1005C2×C4—342no—
1006C2×C4—342no—
1007C2×C4—342no—
1008C2×C4—342no—
1009C2×C4—342no—
1010C2×C4—342no—
1011C2×C4—342no—
1012C2×C4—342no—
1013C2×C4—342no—
1014C2×C4—342no—
1015C2×C4—342no—
1016C2×C4—342no—
1017C2×C4—6816no—
1018C2×C4—681no—
1019C2×C4—681no—
1020C2×C4—681no—
1021C2×C4—681no—
1022C2×C4—681no—
1023C2×C4—681no—
1024C2×C4—681no—
1025C2×C4—681no—
1026C2×C4—681no—
1027C2×C4—681no—
1028C2×C4—681no—
1029C2×C4—681no—
1030C2×C4—681no—
1031C2×C4—681no—
1032C2×C4—681no—
1033C2×C4—681no—
1034C2×C4—681no—
1035C2×C4—681no—
1036C2×C4—681no—
1037C2×C4—681no—
1038C2×C4—681no—
1039C2×C4—681no—
1040C2×C4—681no—
1041C2×C4—681no—
1042C2×C4—681no—
1043C2×C4—681no—
1044C2×C4—681no—
1045C2×C4#1058757914yes—
1046C22—344no—
1047C22—344no—
1048C22—344no—
1049C22—682no—
1050C22—682no—
1051C22—682no—
1052C22—682no—
1053C22—682no—
1054C22—682no—
1055C22—682no—
1056C22—682no—
1057C22—682no—
1058C22—682no—
1059C22—682no—
1060C22—682no—
1061C22—682no—
1062C22—682no—
1063C22—682no—
1064C22—682no—
1065C22—682no—
1066C22—682no—
1067C22—682no—
1068C22—1361no—
1069C22—1361no—
1070C22—1361no—
1071C22—1361no—
1072C22—1361no—
1073C22—1361no—
1074C22—1361no—
1075C22—1361no—
1076C22#117×D1711yescharacteristic
1077C22C2×#1058757911yescharacteristic
1078C22C4×#6325611yescharacteristic
1079C22#1176328111yescharacteristic
1080C22#1176328111yescharacteristic
1081C22#1176328111yescharacteristic
1082C22#1176328911yescharacteristic
1083C22#1176337011yescharacteristic
1084C22#1176337411yescharacteristic
1085C22#1176339111yescharacteristic
1086C22#1176339311yescharacteristic
1087C22#1176339511yescharacteristic
1088C22#1176339511yescharacteristic
1089C22#1176339811yescharacteristic
1090C22#1176339911yescharacteristic
1091C22#1176339911yescharacteristic
1092C22#1176340811yescharacteristic
1093C22#1176341511yescharacteristic
1094C22#1176342511yescharacteristic
1095C22#1176345011yescharacteristic
1096C22#1176345211yescharacteristic
1097C22#1176346711yescharacteristic
1098C22#1176347711yescharacteristic
1099C22#1176348411yescharacteristic
1100C22#1176348611yescharacteristic
1101C22#1176349711yescharacteristic
1102C22#1176350411yescharacteristic
1103C22#1176351211yescharacteristic
1104C22#1176351211yescharacteristic
1105C22#1176351211yescharacteristic
1106C22#1176352511yescharacteristic
1107C22#1176354711yescharacteristic
1108C22#1176355011yescharacteristic
1109C22#1176355311yescharacteristic
1110C22#1176355611yescharacteristic
1111C4—24no—
1112C4—42no—
1113C4—42no—
1114C4—42no—
1115C4—81no—
1116C4—81no—
1117C4—81no—
1118C4—682no—
1119C4—682no—
1120C4—682no—
1121C4—682no—
1122C4—682no—
1123C4—1361no—
1124C2—684no—
1125C2—1362no—
1126C2#1453137811yescharacteristic
1127C2#1453144111yescharacteristic
1128C2#1453157311yescharacteristic
1129C2#1453171011yescharacteristic
1130C2#1453172311yescharacteristic
1131C2#1453182111yescharacteristic
1132C2#1453193711yescharacteristic
1133C2#1453522711yescharacteristic
1134C2#1453534111yescharacteristic
1135C2#1453558511yescharacteristic
1136C2#1453578611yescharacteristic
1137C2#1453611211yescharacteristic
1138C2#1453640811yescharacteristic
1139C2#1453642311yescharacteristic
1140C2#1453645311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1442C2
socle, cosocleC24×C17C24
prime radicalC23×D68C22
hypercenter#1442D17
hypocenterC17#14415
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
1. C2×#11762701C2semidirect
3. C2×#11762666C2semidirect
4. #14527045C2semidirect
5. #14527032C2semidirect
6. #14527026C2semidirect
9. #14527020C2semidirect
10. #14527020C2semidirect
11. #14527020C2semidirect
12. #14527018C2semidirect
13. #14527010C2semidirect
14. #14527005C2semidirect
15. C17×#1442C2semidirect
33. #11762687C4semidirect
121. C2×C4⋊Dic17D4semidirect
480. #1442D17semidirect
716. C17#14415semidirect

Maximal subgroups

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

subgroupindex
C2×#117627012
C2×#117626872
C2×#117626662
#145270452
#145270322
#145270262
#145270242
#145270202
#145270182
#145270102
#145270052
C17×#14422
#1441517