Finite Group Databasebeta

← #16957935

Subgroups — #16957935

Order 4352.

2062 conjugacy classes of subgroups.

The subgroup lattice has 1174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762711C211yesmaximal, characteristic
2C2×#11762701C211yesmaximal, characteristic, complemented
3C2×#11762698C211yesmaximal, characteristic, complemented
4C2×#11762687C211yesmaximal, characteristic
5C2×#11762683C211yesmaximal, characteristic, complemented
6C2×C4×C4⋊Dic17C211yesmaximal, characteristic, complemented
7C2×#11762656C211yesmaximal, characteristic, complemented
8#14527036C211yesmaximal, characteristic, complemented
9#14527030C211yesmaximal, characteristic, complemented
10#14527030C211yesmaximal, characteristic, complemented
11#14527024C211yesmaximal, characteristic
12#14527020C211yesmaximal, characteristic, complemented
13#14527020C211yesmaximal, characteristic, complemented
14#14527018C211yesmaximal, characteristic, complemented
15C17×#1434C211yesmaximal, characteristic, complemented
16C23×D68C2211yescharacteristic
17C23×C4×D17C2211yescharacteristic
18C22×C4⋊Dic17C2211yescharacteristic
19C22×C4⋊Dic17C2211yescharacteristic
20C22×C4⋊Dic17C2211yescharacteristic
21C22×#63225C2211yescharacteristic
22C22×#63227C2211yescharacteristic
23C22×#63227C2211yescharacteristic
24C22×#63227C2211yescharacteristic
25C22×#63227C2211yescharacteristic
26C22×#63227C2211yescharacteristic
27C22×#63227C2211yescharacteristic
28C22×#63227C2211yescharacteristic
29C22×#63227C2211yescharacteristic
30C22×#63227C2211yescharacteristic
31C22×#63227C2211yescharacteristic
32C22×#63227C2211yescharacteristic
33C22×C4×Dic17C2211yescharacteristic
34C22×C4×Dic17C2211yescharacteristic
35C22×C4×Dic17C2211yescharacteristic
36#11762711C418yescomplemented
37#11762701—24no—
38#11762698—24no—
39#11762687—24no—
40#11762683—24no—
41C4×C4⋊Dic17—24no—
42#11762656—24no—
43C2×#10587502C2211yescharacteristic
44C2×#10587502C2211yescharacteristic
45C2×#10587502C2211yescharacteristic
46C2×#10587502C2211yescharacteristic
47C2×#10587502C2211yescharacteristic
48C2×#10587502C2211yescharacteristic
49C2×#10587502C2211yescharacteristic
50C2×#10587502C2211yescharacteristic
51C22×C42×C17C2211yescharacteristic
52C2×C17×#95C2211yescharacteristic
53C2×C17×#95C2211yescharacteristic
54C2×C17×#95C2211yescharacteristic
55C2×C17×#95C2211yescharacteristic
56C2×C17×#95C2211yescharacteristic
57C2×C17×#95C2211yescharacteristic
58C24×D17C2311yescharacteristic
59C24×D17C2311yescharacteristic
60C23×C4×C17C2311yescharacteristic
61C23×C4×C17C2311yescharacteristic
62C23×C4×C17C2311yescharacteristic
63C23×C4×C17C2311yescharacteristic
64C23×C4×C17C2311yescharacteristic
65C23×C4×C17C2311yescharacteristic
66C23×C4×C17C2311yescharacteristic
67C23×Dic17C2311yescharacteristic
68C23×Dic17C2311yescharacteristic
69C23×Dic17C2311yescharacteristic
70C23×Dic17C2311yescharacteristic
71C23×Dic17C2311yescharacteristic
72C23×Dic17C2311yescharacteristic
73C22×D68—22no—
74C22×D68—22no—
75C22×D68—22no—
76C22×D68—22no—
77C22×D68—41no—
78C22×D68—41no—
79C22×D68C2×C414yes—
80C22×C4×D17—22no—
81C22×C4×D17—22no—
82C22×C4×D17—22no—
83C22×C4×D17—22no—
84C22×C4×D17—22no—
85C22×C4×D17—41no—
86C22×C4×D17—41no—
87C2×C42×C17—22no—
88C2×C42×C17—22no—
89C2×C42×C17C2×C414yescomplemented
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—22no—
108C2×#63227—22no—
109C2×#63227—22no—
110C2×#63227—22no—
111C2×#63227—22no—
112C2×#63227—22no—
113C2×#63227—41no—
114C2×#63227—41no—
115C2×#63227—41no—
116C2×#63227—41no—
117C2×#63227—41no—
118C2×#63227—41no—
119C2×#63227C2×C414yes—
120C2×#63227C2×C414yes—
121C2×#63227C2×C414yescomplemented
122C2×#63227C2×C414yescomplemented
123C2×C4⋊Dic17—22no—
124C2×C4⋊Dic17—22no—
125C2×C4⋊Dic17—22no—
126C2×C4⋊Dic17—22no—
127C2×C4⋊Dic17—22no—
128C2×C4⋊Dic17—41no—
129C2×C4⋊Dic17—41no—
130C2×C4⋊Dic17C2×C414yescomplemented
131C2×C4⋊Dic17D414yescomplemented
132C2×#63225—22no—
133C2×#63225—22no—
134C2×#63225—41no—
135C2×C4×Dic17—22no—
136C2×C4×Dic17—22no—
137C2×C4×Dic17—22no—
138C2×C4×Dic17—22no—
139C2×C4×Dic17—22no—
140C2×C4×Dic17—22no—
141C2×C4×Dic17—41no—
142C2×C4×Dic17—41no—
143C2×C4×Dic17—41no—
144C17×#95—22no—
145C17×#95—22no—
146C17×#95—22no—
147C17×#95—22no—
148C17×#95—22no—
149C17×#95D414yescomplemented
150#10587502—22no—
151#10587502—22no—
152#10587502—22no—
153#10587502—22no—
154#10587502—22no—
155#10587502—41no—
156#10587502—41no—
157#10587502D414yes—
158C24×C17C2411yescharacteristic
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×D17—21no—
180C23×D17—21no—
181C23×D17—21no—
182C23×D17—21no—
183C23×D17—21no—
184C23×D17—21no—
185C23×D17C22×C412yes—
186C23×D17C22×C412yes—
187C23×D17#4112yes—
188C23×D17#4112yes—
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×C17—21no—
224C22×C4×C17—21no—
225C22×C4×C17—21no—
226C22×C4×C17—21no—
227C22×C4×C17C22×C412yes—
228C22×C4×C17C22×C412yes—
229C22×C4×C17C22×C412yes—
230C22×C4×C17C2×D412yes—
231C22×C4×C17C2×D412yes—
232C22×C4×C17C2×D412yes—
233C22×C4×C17C2×D412yes—
234C22×C4×C17C2×D412yes—
235C22×C4×C17#4112yes—
236C22×C4×C17#4112yes—
237C22×C4×C17#4112yes—
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×Dic17—21no—
267C22×Dic17—21no—
268C22×Dic17—21no—
269C22×Dic17—21no—
270C22×Dic17—21no—
271C22×Dic17—21no—
272C22×Dic17C22×C412yes—
273C22×Dic17C22×C412yes—
274C22×Dic17C2×D412yes—
275C22×Dic17C2×D412yes—
276C22×Dic17C2×D412yes—
277C22×Dic17C2×D412yes—
278C22×Dic17#4112yes—
279C22×Dic17#4112yes—
280C2×D68—28no—
281C2×D68—28no—
282C2×D68—44no—
283C2×D68—44no—
284C2×D68—44no—
285C2×D68—44no—
286C2×D68—44no—
287C2×C4×D17—28no—
288C2×C4×D17—44no—
289C2×C4×D17—44no—
290C2×C4×D17—44no—
291C2×C4×D17—44no—
292C2×C4×D17—44no—
293C2×C4×D17—44no—
294C42×C17—28no—
295#63227—28no—
296#63227—28no—
297#63227—28no—
298#63227—28no—
299#63227—28no—
300#63227—44no—
301#63227—44no—
302#63227—44no—
303#63227—44no—
304#63227—44no—
305#63227—44no—
306C4⋊Dic17—28no—
307C4⋊Dic17—28no—
308C4⋊Dic17—44no—
309#63225—44no—
310C4×Dic17—44no—
311C4×Dic17—44no—
312C4×Dic17—44no—
313#14036—171nomaximal, Sylow
314C23×C17C23×C411yescharacteristic
315C23×C17C22×D411yescharacteristic
316C23×C17C22×D411yescharacteristic
317C23×C17C22×D411yescharacteristic
318C23×C17C2×#4111yescharacteristic
319C23×C17C2×#4111yescharacteristic
320C23×C17C2×#4111yescharacteristic
321C23×C17C2×#4111yescharacteristic
322C23×C17C2×#4111yescharacteristic
323C23×C17C2×#4111yescharacteristic
324C23×C17C2×#4111yescharacteristic
325C23×C17H(5,𝔽2)11yescharacteristic
326C23×C17H(5,𝔽2)11yescharacteristic
327C23×C17H(5,𝔽2)11yescharacteristic
328C23×C172−1+411yescharacteristic
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—22no—
347C22×D17—22no—
348C22×D17—22no—
349C22×D17—22no—
350C22×D17—22no—
351C22×D17—22no—
352C22×D17—22no—
353C22×D17—22no—
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—41no—
391C22×D17—41no—
392C22×D17—41no—
393C22×D17—41no—
394C22×D17—41no—
395C22×D17—41no—
396C22×D17—41no—
397C22×D17—41no—
398C22×D17#11714yes—
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—22no—
413C2×C4×C17—22no—
414C2×C4×C17—22no—
415C2×C4×C17—22no—
416C2×C4×C17—22no—
417C2×C4×C17—22no—
418C2×C4×C17—22no—
419C2×C4×C17—22no—
420C2×C4×C17—22no—
421C2×C4×C17—22no—
422C2×C4×C17—22no—
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×C17—41no—
439C2×C4×C17—41no—
440C2×C4×C17—41no—
441C2×C4×C17—41no—
442C2×C4×C17—41no—
443C2×C4×C17—41no—
444C2×C4×C17—41no—
445C2×C4×C17C4×D414yes—
446C2×C4×C17C4×D414yes—
447C2×C4×C17C4×D414yes—
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—22no—
462C2×Dic17—22no—
463C2×Dic17—22no—
464C2×Dic17—22no—
465C2×Dic17—22no—
466C2×Dic17—22no—
467C2×Dic17—22no—
468C2×Dic17—22no—
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—41no—
482C2×Dic17—41no—
483C2×Dic17—41no—
484C2×Dic17—41no—
485C2×Dic17—41no—
486C2×Dic17—41no—
487C2×Dic17—41no—
488C2×Dic17—41no—
489C2×Dic17#12114yes—
490D68—416no—
491C4×D17—416no—
492C2×#390—171no—
493C2×#388—171no—
494C2×#388—171no—
495C2×#386—171no—
496C2×#385—171no—
497C2×C4×C4⋊C4—171no—
498C2×C4×C22⋊C4—171no—
499#1441—171no—
500#1439—171no—
501#1439—171no—
502#1438—171no—
503#1437—171no—
504#1437—171no—
505#1436—171no—
506#1434D1711yescharacteristic, complemented
507C22×C17C2×#11711yescharacteristic
508C22×C17C2×C4×D411yescharacteristic
509C22×C17C2×C4×D411yescharacteristic
510C22×C17C2×C4×D411yescharacteristic
511C22×C17C4×#4111yescharacteristic
512C22×C17#51811yescharacteristic
513C22×C17#52011yescharacteristic
514C22×C17C2×#12111yescharacteristic
515C22×C17#52511yescharacteristic
516C22×C17#52511yescharacteristic
517C22×C17#52511yescharacteristic
518C22×C17#52911yescharacteristic
519C22×C17#52911yescharacteristic
520C22×C17#52911yescharacteristic
521C22×C17#53211yescharacteristic
522C22×C17#53811yescharacteristic
523C22×C17#53811yescharacteristic
524C22×C17#54211yescharacteristic
525C22×C17#54211yescharacteristic
526C22×C17D4211yescharacteristic
527C22×C17D4211yescharacteristic
528C22×C17#54611yescharacteristic
529C22×C17#54611yescharacteristic
530C22×C17#54611yescharacteristic
531C22×C17#54711yescharacteristic
532C22×C17#54811yescharacteristic
533C22×C17#54811yescharacteristic
534C22×C17#55011yescharacteristic
535C22×C17#55011yescharacteristic
536C22×C17#55111yescharacteristic
537C22×C17#55111yescharacteristic
538C22×C17#55211yescharacteristic
539C22×C17#55311yescharacteristic
540C22×C17#55311yescharacteristic
541C22×C17#55911yescharacteristic
542C2×D17—24no—
543C2×D17—24no—
544C2×D17—24no—
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—42no—
557C2×D17—42no—
558C2×D17—42no—
559C2×D17—42no—
560C2×D17—42no—
561C2×D17—42no—
562C2×D17—42no—
563C2×D17—42no—
564C2×D17—81no—
565C2×D17—81no—
566C2×D17—81no—
567C2×D17—81no—
568C2×D17—81no—
569C2×D17—81no—
570C2×D17—81no—
571C2×D17—81no—
572C4×C17—24no—
573C4×C17—24no—
574C4×C17—24no—
575C4×C17—42no—
576C4×C17—42no—
577C4×C17—81no—
578C4×C17—81no—
579Dic17—24no—
580Dic17—42no—
581Dic17—42no—
582Dic17—42no—
583Dic17—42no—
584Dic17—42no—
585C23×D4—171no—
586C24×C4—171no—
587C22×C4⋊C4—171no—
588C22×C4⋊C4—171no—
589C22×C4⋊C4—171no—
590C22×C4⋊C4—171no—
591C22×C22⋊C4—171no—
592C22×C22⋊C4—171no—
593C22×C22⋊C4—171no—
594C22×C22⋊C4—171no—
595C22×C22⋊C4—171no—
596C22×C22⋊C4—171no—
597C22×C22⋊C4—171no—
598C22×C22⋊C4—171no—
599C22×C22⋊C4—171no—
600C22×C22⋊C4—171no—
601C22×C22⋊C4—171no—
602C22×C42—171no—
603C22×C42—171no—
604C22×C42—171no—
605C22×C42C2×D1711yescharacteristic
606#390—178no—
607#388—344no—
608#388—344no—
609#386—344no—
610#385—344no—
611C4×C4⋊C4—344no—
612C4×C22⋊C4—344no—
613C2×#95—171no—
614C2×#95—171no—
615C2×#95—171no—
616C2×#95—171no—
617C2×#95—171no—
618C2×#95—171no—
619C2×#95—171no—
620C2×#95—171no—
621C2×#95C2×D1711yescharacteristic
622C2×#95C2×D1711yescharacteristic
623C2×#95C2×D1711yescharacteristic
624C2×#95C2×D1711yescharacteristic
625C2×#95C2×D1711yescharacteristic
626C2×#95C2×D1711yescharacteristic
627C2×C17#229011yescharacteristic
628C2×C17C4×#12111yescharacteristic
629C2×C17#233711yescharacteristic
630C2×C17#234211yescharacteristic
631C2×C17#235211yescharacteristic
632C2×C17#236111yescharacteristic
633C2×C17#236611yescharacteristic
634C2×C17#242411yescharacteristic
635C2×C17#242611yescharacteristic
636C2×C17#245611yescharacteristic
637C2×C17#245811yescharacteristic
638C2×C17#246111yescharacteristic
639C2×C17#247911yescharacteristic
640C2×C17#255411yescharacteristic
641C2×C17#259711yescharacteristic
642D17—44no—
643D17—82no—
644C25—171no—
645C25—171no—
646C22×D4—174no—
647C22×D4—342no—
648C22×D4—342no—
649C22×D4—342no—
650C22×D4—342no—
651C22×D4—681no—
652C22×D4—681no—
653C23×C4—171no—
654C23×C4—171no—
655C23×C4—171no—
656C23×C4—171no—
657C23×C4—171no—
658C23×C4—171no—
659C23×C4—342no—
660C23×C4—342no—
661C23×C4—342no—
662C23×C4—342no—
663C23×C4—342no—
664C23×C4—681no—
665C23×C4—681no—
666C23×C4C22×D1711yescharacteristic
667C23×C4C22×D1711yescharacteristic
668C23×C4C22×D1711yescharacteristic
669C23×C4C22×D1711yescharacteristic
670C23×C4C22×D1711yescharacteristic
671C23×C4C22×D1711yescharacteristic
672C23×C4C22×D1711yescharacteristic
673C2×C4⋊C4—174no—
674C2×C4⋊C4—174no—
675C2×C4⋊C4—342no—
676C2×C4⋊C4—342no—
677C2×C4⋊C4—342no—
678C2×C4⋊C4—342no—
679C2×C4⋊C4—342no—
680C2×C4⋊C4—342no—
681C2×C4⋊C4—342no—
682C2×C4⋊C4—681no—
683C2×C4⋊C4—681no—
684C2×C4⋊C4—681no—
685C2×C22⋊C4—174no—
686C2×C22⋊C4—174no—
687C2×C22⋊C4—174no—
688C2×C22⋊C4—174no—
689C2×C22⋊C4—342no—
690C2×C22⋊C4—342no—
691C2×C22⋊C4—342no—
692C2×C22⋊C4—342no—
693C2×C22⋊C4—342no—
694C2×C22⋊C4—342no—
695C2×C22⋊C4—342no—
696C2×C22⋊C4—342no—
697C2×C22⋊C4—342no—
698C2×C22⋊C4—342no—
699C2×C22⋊C4—342no—
700C2×C22⋊C4—342no—
701C2×C22⋊C4—342no—
702C2×C22⋊C4—342no—
703C2×C22⋊C4—342no—
704C2×C22⋊C4—342no—
705C2×C22⋊C4—342no—
706C2×C22⋊C4—342no—
707C2×C22⋊C4—342no—
708C2×C22⋊C4—342no—
709C2×C22⋊C4—342no—
710C2×C22⋊C4—342no—
711C2×C22⋊C4—342no—
712C2×C22⋊C4—681no—
713C2×C22⋊C4—681no—
714C2×C22⋊C4—681no—
715C2×C22⋊C4—681no—
716C2×C22⋊C4—681no—
717C2×C22⋊C4—681no—
718C2×C42—22no—
719C2×C42—22no—
720C2×C42—342no—
721C2×C42—342no—
722C2×C42—342no—
723C2×C42—342no—
724C2×C42—342no—
725C2×C42—342no—
726C2×C42—681no—
727C2×C42—681no—
728C2×C42—681no—
729C2×C42C4×D1714yescomplemented
730#95—22no—
731#95—22no—
732#95—22no—
733#95—22no—
734#95—22no—
735#95—174no—
736#95—342no—
737#95—342no—
738#95—342no—
739#95—342no—
740#95—342no—
741#95—681no—
742#95—681no—
743#95D6814yescomplemented
744C17#1403611yescharacteristic, complemented, Sylow
745C24—172no—
746C24—172no—
747C24—172no—
748C24—172no—
749C24—341no—
750C24—341no—
751C24—341no—
752C24—341no—
753C24—341no—
754C24—341no—
755C24—341no—
756C24—341no—
757C24—341no—
758C24—341no—
759C24—341no—
760C24—341no—
761C24—341no—
762C24—341no—
763C24—341no—
764C24—341no—
765C24—341no—
766C24—341no—
767C24—341no—
768C24—341no—
769C24—341no—
770C24—341no—
771C24—341no—
772C24—341no—
773C24—341no—
774C24—341no—
775C24C23×D1711yescharacteristic
776C2×D4—348no—
777C2×D4—348no—
778C2×D4—684no—
779C2×D4—684no—
780C2×D4—684no—
781C2×D4—684no—
782C2×D4—684no—
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—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—172no—
822C22×C4—172no—
823C22×C4—172no—
824C22×C4—172no—
825C22×C4—172no—
826C22×C4—172no—
827C22×C4—172no—
828C22×C4—172no—
829C22×C4—348no—
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—341no—
853C22×C4—341no—
854C22×C4—341no—
855C22×C4—341no—
856C22×C4—341no—
857C22×C4—341no—
858C22×C4—341no—
859C22×C4—341no—
860C22×C4—341no—
861C22×C4—341no—
862C22×C4—341no—
863C22×C4—341no—
864C22×C4—684no—
865C22×C4—684no—
866C22×C4—684no—
867C22×C4—684no—
868C22×C4—684no—
869C22×C4—684no—
870C22×C4C2×C4×D1712yes—
871C22×C4C2×C4×D1712yes—
872C22×C4C2×C4×D1712yes—
873C22×C4C2×D6812yes—
874C22×C4C2×D6812yes—
875C22×C4C2×D6812yes—
876C22×C4#6325212yes—
877C22×C4D4×D1712yes—
878C22×C4D4×D1712yes—
879C22×C4#6325412yes—
880C22×C4#6325612yes—
881C4⋊C4—348no—
882C4⋊C4—348no—
883C4⋊C4—684no—
884C4⋊C4—684no—
885C22⋊C4—348no—
886C22⋊C4—348no—
887C22⋊C4—348no—
888C22⋊C4—348no—
889C22⋊C4—348no—
890C22⋊C4—684no—
891C22⋊C4—684no—
892C22⋊C4—684no—
893C22⋊C4—684no—
894C22⋊C4—684no—
895C22⋊C4—684no—
896C42—28no—
897C42—684no—
898C42—684no—
899C42—684no—
900C23—174no—
901C23—342no—
902C23—342no—
903C23—342no—
904C23—342no—
905C23—342no—
906C23—342no—
907C23—342no—
908C23—342no—
909C23—342no—
910C23—342no—
911C23—342no—
912C23—342no—
913C23—342no—
914C23—342no—
915C23—342no—
916C23—342no—
917C23—342no—
918C23—342no—
919C23—342no—
920C23—342no—
921C23—342no—
922C23—342no—
923C23—342no—
924C23—342no—
925C23—342no—
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—
954C23—681no—
955C23—681no—
956C23—681no—
957C23—681no—
958C23—681no—
959C23—681no—
960C23—681no—
961C23—681no—
962C23—681no—
963C23—681no—
964C23—681no—
965C23—681no—
966C23—681no—
967C23—681no—
968C23—681no—
969C23—681no—
970C23C22×C4×D1711yescharacteristic
971C23C22×D6811yescharacteristic
972C23C2×#6325211yescharacteristic
973C23C2×D4×D1711yescharacteristic
974C23C2×D4×D1711yescharacteristic
975C23C2×#6325411yescharacteristic
976C23C2×#6325611yescharacteristic
977C23#41×D1711yescharacteristic
978C23#41×D1711yescharacteristic
979C23#41×D1711yescharacteristic
980C23#41×D1711yescharacteristic
981C23#1058769611yescharacteristic
982C23#1058769611yescharacteristic
983C23#1058769611yescharacteristic
984C23#1058769711yescharacteristic
985D4—6816no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—174no—
1033C2×C4—342no—
1034C2×C4—342no—
1035C2×C4—342no—
1036C2×C4—342no—
1037C2×C4—342no—
1038C2×C4—342no—
1039C2×C4—342no—
1040C2×C4—342no—
1041C2×C4—342no—
1042C2×C4—342no—
1043C2×C4—342no—
1044C2×C4—342no—
1045C2×C4—342no—
1046C2×C4—342no—
1047C2×C4—342no—
1048C2×C4—342no—
1049C2×C4—342no—
1050C2×C4—342no—
1051C2×C4—342no—
1052C2×C4—342no—
1053C2×C4—342no—
1054C2×C4—6816no—
1055C2×C4—681no—
1056C2×C4—681no—
1057C2×C4—681no—
1058C2×C4—681no—
1059C2×C4—681no—
1060C2×C4—681no—
1061C2×C4—681no—
1062C2×C4—681no—
1063C2×C4—681no—
1064C2×C4—681no—
1065C2×C4—681no—
1066C2×C4—681no—
1067C2×C4—681no—
1068C2×C4—681no—
1069C2×C4—681no—
1070C2×C4—681no—
1071C2×C4—681no—
1072C2×C4—681no—
1073C2×C4—681no—
1074C2×C4—681no—
1075C2×C4C4×D6814yes—
1076C2×C4#1058756714yes—
1077C2×C4#1058757914yes—
1078C22—344no—
1079C22—344no—
1080C22—344no—
1081C22—682no—
1082C22—682no—
1083C22—682no—
1084C22—682no—
1085C22—682no—
1086C22—682no—
1087C22—682no—
1088C22—682no—
1089C22—682no—
1090C22—682no—
1091C22—682no—
1092C22—682no—
1093C22—682no—
1094C22—682no—
1095C22—682no—
1096C22—682no—
1097C22—682no—
1098C22—682no—
1099C22—682no—
1100C22—1361no—
1101C22—1361no—
1102C22—1361no—
1103C22—1361no—
1104C22—1361no—
1105C22—1361no—
1106C22—1361no—
1107C22—1361no—
1108C22#117×D1711yescharacteristic
1109C22C2×#1058756711yescharacteristic
1110C22C2×#1058757911yescharacteristic
1111C22C2×C4×D6811yescharacteristic
1112C22#1176327711yescharacteristic
1113C22#1176328311yescharacteristic
1114C22#1176328911yescharacteristic
1115C22#121×D1711yescharacteristic
1116C22#1176332111yescharacteristic
1117C22#1176332111yescharacteristic
1118C22#1176332211yescharacteristic
1119C22#1176333711yescharacteristic
1120C22#1176333711yescharacteristic
1121C22#1176334511yescharacteristic
1122C22#1176335411yescharacteristic
1123C22#1176339811yescharacteristic
1124C22#1176339811yescharacteristic
1125C22#1176342511yescharacteristic
1126C22#1176342511yescharacteristic
1127C22D4×D6811yescharacteristic
1128C22D4×D6811yescharacteristic
1129C22#1176345111yescharacteristic
1130C22#1176345111yescharacteristic
1131C22#1176345211yescharacteristic
1132C22#1176346311yescharacteristic
1133C22#1176346711yescharacteristic
1134C22#1176346811yescharacteristic
1135C22#1176348011yescharacteristic
1136C22#1176348111yescharacteristic
1137C22#1176348211yescharacteristic
1138C22#1176348211yescharacteristic
1139C22#1176349711yescharacteristic
1140C22#1176350511yescharacteristic
1141C22#1176351211yescharacteristic
1142C22#1176354411yescharacteristic
1143C4—24no—
1144C4—24no—
1145C4—24no—
1146C4—42no—
1147C4—42no—
1148C4—81no—
1149C4—81no—
1150C4—344no—
1151C4—682no—
1152C4—682no—
1153C4—682no—
1154C4—682no—
1155C4—682no—
1156C2—684no—
1157C2—1362no—
1158C2#1453122811yescharacteristic
1159C2#1453129011yescharacteristic
1160C2#1453159411yescharacteristic
1161C2#1453162611yescharacteristic
1162C2#1453171011yescharacteristic
1163C2#1453179811yescharacteristic
1164C2#1453184811yescharacteristic
1165C2#1453232511yescharacteristic
1166C2#1453234911yescharacteristic
1167C2#1453267411yescharacteristic
1168C2#1453271311yescharacteristic
1169C2#1453274911yescharacteristic
1170C2#1453301311yescharacteristic
1171C2#1453384311yescharacteristic
1172C2#1453433111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1434C2
socle, cosocleC24×C17C24
prime radicalC23×D68C22
hypercenter#1434D17
hypocenterC17#14036
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
2. C2×#11762701C2semidirect
3. C2×#11762698C2semidirect
5. C2×#11762683C2semidirect
6. C2×C4×C4⋊Dic17C2semidirect
7. C2×#11762656C2semidirect
8. #14527036C2semidirect
9. #14527030C2semidirect
10. #14527030C2semidirect
12. #14527020C2semidirect
13. #14527020C2semidirect
14. #14527018C2semidirect
15. C17×#1434C2semidirect
36. #11762711C4semidirect
89. C2×C42×C17C2×C4semidirect
121. C2×#63227C2×C4semidirect
122. C2×#63227C2×C4semidirect
130. C2×C4⋊Dic17C2×C4semidirect
131. C2×C4⋊Dic17D4semidirect
149. C17×#95D4semidirect
506. #1434D17semidirect
729. C2×C42C4×D17semidirect
743. #95D68semidirect
744. C17#14036semidirect

Maximal subgroups

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

subgroupindex
C2×#117627112
C2×#117627012
C2×#117626982
C2×#117626872
C2×#117626832
C2×C4×C4⋊Dic172
C2×#117626562
#145270362
#145270302
#145270242
#145270202
#145270182
C17×#14342
#1403617