Finite Group Databasebeta

← #16958398

Subgroups — #16958398

Order 4352.

2206 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587558C211yesmaximal, characteristic, complemented
2C2×#11762709C211yesmaximal, characteristic
3C2×#11762702C211yesmaximal, characteristic, complemented
4C2×#11762697C211yesmaximal, characteristic, complemented
5C2×#11762685C211yesmaximal, characteristic
6#14527048C211yesmaximal, characteristic, complemented
7#14527030C211yesmaximal, characteristic, complemented
8#14527027C211yesmaximal, characteristic, complemented
9#14527023C211yesmaximal, characteristic
10#14527020C211yesmaximal, characteristic, complemented
11#14527017C211yesmaximal, characteristic, complemented
12#14527015C211yesmaximal, characteristic, complemented
13#14527005C211yesmaximal, characteristic, complemented
14#95×Dic17C211yesmaximal, characteristic, complemented
15C17×#1437C211yesmaximal, characteristic, complemented
16C23×C22⋊D17C2211yescharacteristic
17C23×C4×D17C2211yescharacteristic
18C2×#10587558—24no—
19C2×#10587558—24no—
20C2×#10587558—24no—
21C22×C4⋊Dic17C2211yescharacteristic
22C22×#63225C2211yescharacteristic
23C22×#63225C2211yescharacteristic
24C22×#63225C2211yescharacteristic
25C22×C22⋊Dic17C2211yescharacteristic
26C22×C22⋊Dic17C2211yescharacteristic
27C22×C22⋊Dic17C2211yescharacteristic
28C22×#63227C2211yescharacteristic
29C22×#63227C2211yescharacteristic
30C22×#63227C2211yescharacteristic
31C22×#63227C2211yescharacteristic
32C22×#63227C2211yescharacteristic
33C22×C4×Dic17C2211yescharacteristic
34C22×C4×Dic17C2211yescharacteristic
35C22×C4×Dic17C2211yescharacteristic
36#11762709—24no—
37#11762702—24no—
38#11762697—24no—
39#11762685C418yescomplemented
40C2×#10587502C2211yescharacteristic
41C2×#10587502C2211yescharacteristic
42C2×#10587502C2211yescharacteristic
43C2×#10587502C2211yescharacteristic
44C2×#10587502C2211yescharacteristic
45C2×#10587502C2211yescharacteristic
46C2×#10587502C2211yescharacteristic
47C2×#10587502C2211yescharacteristic
48C2×#10587502C2211yescharacteristic
49C2×#10587502C2211yescharacteristic
50C2×#10587502C2211yescharacteristic
51C22×C22⋊C4×C17C2211yescharacteristic
52C22×C22⋊C4×C17C2211yescharacteristic
53C22×C22⋊C4×C17C2211yescharacteristic
54C22×C42×C17C2211yescharacteristic
55C2×C17×#95C2211yescharacteristic
56C2×C17×#95C2211yescharacteristic
57C2×C17×#95C2211yescharacteristic
58C25×C17C2311yescharacteristic
59C24×D17C2311yescharacteristic
60C23×C4×C17C2311yescharacteristic
61C23×C4×C17C2311yescharacteristic
62C23×C4×C17C2311yescharacteristic
63C23×C4×C17C2311yescharacteristic
64C23×C4×C17C2311yescharacteristic
65C23×C4×C17C2311yescharacteristic
66C22×C22⋊D17—22no—
67C22×C22⋊D17—22no—
68C22×C22⋊D17—22no—
69C22×C22⋊D17—22no—
70C22×C22⋊D17—41no—
71C22×C22⋊D17—41no—
72C22×C22⋊D17C2×C414yes—
73C23×Dic17C2311yescharacteristic
74C23×Dic17C2311yescharacteristic
75C23×Dic17C2311yescharacteristic
76C23×Dic17C2311yescharacteristic
77C23×Dic17C2311yescharacteristic
78C23×Dic17C2311yescharacteristic
79C23×Dic17C2311yescharacteristic
80C22×C4×D17—22no—
81C22×C4×D17—22no—
82C22×C4×D17—22no—
83C22×C4×D17—22no—
84C22×C4×D17—22no—
85C22×C4×D17—22no—
86C22×C4×D17C2×C414yes—
87C2×C22⋊C4×C17—22no—
88C2×C22⋊C4×C17—22no—
89C2×C22⋊C4×C17—22no—
90C2×C22⋊C4×C17—22no—
91C2×C22⋊C4×C17—22no—
92C2×C22⋊C4×C17—22no—
93C2×C22⋊C4×C17—41no—
94C2×C22⋊C4×C17—41no—
95C2×C22⋊C4×C17C2×C414yes—
96C2×C42×C17—22no—
97C2×C42×C17—22no—
98C2×C42×C17—22no—
99C2×C22⋊Dic17—22no—
100C2×C22⋊Dic17—22no—
101C2×C22⋊Dic17—22no—
102C2×C22⋊Dic17—22no—
103C2×C22⋊Dic17—22no—
104C2×C22⋊Dic17—22no—
105C2×C22⋊Dic17—41no—
106C2×C22⋊Dic17—41no—
107C2×C22⋊Dic17C2×C414yes—
108C2×#63227—22no—
109C2×#63227—22no—
110C2×#63227—22no—
111C2×#63227—22no—
112C2×#63227—22no—
113C2×#63227—22no—
114C2×#63227—22no—
115C2×#63227—22no—
116C2×#63227—22no—
117C2×#63227—41no—
118C2×#63227—41no—
119C2×#63227—41no—
120C2×#63227—41no—
121C2×#63227C2×C414yes—
122C2×#63227D414yes—
123C2×C4⋊Dic17—22no—
124C2×C4⋊Dic17—41no—
125C2×C4⋊Dic17—41no—
126C2×#63225—22no—
127C2×#63225—22no—
128C2×#63225—22no—
129C2×#63225—22no—
130C2×#63225—22no—
131C2×#63225—22no—
132C2×#63225—22no—
133C2×#63225—41no—
134C2×#63225D414yescomplemented
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×Dic17D414yescomplemented
144#10587558—232no—
145C17×#95—22no—
146C17×#95—41no—
147C17×#95—41no—
148#10587502—22no—
149#10587502—22no—
150#10587502—22no—
151#10587502—22no—
152#10587502—22no—
153#10587502—22no—
154#10587502—22no—
155#10587502—22no—
156#10587502—41no—
157#10587502C2×C414yes—
158#10587502C2×C414yes—
159C24×C17—21no—
160C24×C17—21no—
161C24×C17—21no—
162C24×C17—21no—
163C24×C17—21no—
164C24×C17—21no—
165C24×C17—21no—
166C24×C17—21no—
167C24×C17—21no—
168C24×C17—21no—
169C24×C17—21no—
170C24×C17—21no—
171C24×C17—21no—
172C24×C17—21no—
173C24×C17C22×C412yes—
174C24×C17C2411yescharacteristic
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×D17—21no—
186C23×D17—21no—
187C23×D17C22×C412yes—
188C23×D17C2×D412yes—
189C23×D17#4112yes—
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×C17C22×C412yes—
225C22×C4×C17C22×C412yes—
226C22×C4×C17C2×D412yes—
227C22×C4×C17C2×D412yes—
228C22×C4×C17C2×D412yes—
229C22×C4×C17#4112yes—
230C22×C4×C17#4112yes—
231C22×C4×C17#4112yes—
232C2×C22⋊D17—28no—
233C2×C22⋊D17—28no—
234C2×C22⋊D17—44no—
235C2×C22⋊D17—44no—
236C2×C22⋊D17—44no—
237C2×C22⋊D17—44no—
238C2×C22⋊D17—44no—
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×Dic17—21no—
273C22×Dic17—21no—
274C22×Dic17—21no—
275C22×Dic17—21no—
276C22×Dic17—21no—
277C22×Dic17C22×C412yes—
278C22×Dic17C22×C412yes—
279C22×Dic17C22×C412yes—
280C22×Dic17C2×D412yes—
281C22×Dic17C2×D412yes—
282C22×Dic17C2×D412yes—
283C22×Dic17C2×D412yes—
284C22×Dic17C2×D412yes—
285C22×Dic17#4112yes—
286C22×Dic17#4112yes—
287C22×Dic17#4112yes—
288C2×C4×D17—28no—
289C2×C4×D17—28no—
290C2×C4×D17—28no—
291C2×C4×D17—28no—
292C2×C4×D17—28no—
293C2×C4×D17—28no—
294C2×C4×D17—28no—
295C22⋊C4×C17—28no—
296C22⋊C4×C17—44no—
297C22⋊C4×C17—44no—
298C42×C17—28no—
299C22⋊Dic17—28no—
300C22⋊Dic17—44no—
301C22⋊Dic17—44no—
302#63227—28no—
303#63227—28no—
304#63227—44no—
305#63227—44no—
306#63227—44no—
307C4⋊Dic17—44no—
308#63225—28no—
309#63225—28no—
310#63225—44no—
311C4×Dic17—28no—
312C4×Dic17—44no—
313C4×Dic17—44no—
314#14071—171nomaximal, Sylow
315C23×C17—22no—
316C23×C17—22no—
317C23×C17—22no—
318C23×C17—22no—
319C23×C17—22no—
320C23×C17—22no—
321C23×C17—22no—
322C23×C17—41no—
323C23×C17—41no—
324C23×C17—41no—
325C23×C17—41no—
326C23×C17—41no—
327C23×C17—41no—
328C23×C17—41no—
329C23×C17—41no—
330C23×C17—41no—
331C23×C17—41no—
332C23×C17—41no—
333C23×C17—41no—
334C23×C17—41no—
335C23×C17—41no—
336C23×C17—41no—
337C23×C17—41no—
338C23×C17—41no—
339C23×C17—41no—
340C23×C17—41no—
341C23×C17—41no—
342C23×C17—41no—
343C23×C17—41no—
344C23×C17—41no—
345C23×C17—41no—
346C23×C17—41no—
347C23×C17—41no—
348C23×C17—41no—
349C23×C17—41no—
350C23×C17C23×C411yescharacteristic
351C23×C17C22×D411yescharacteristic
352C23×C17C22×D411yescharacteristic
353C23×C17C22×D411yescharacteristic
354C23×C17C2×#4111yescharacteristic
355C23×C17C2×#4111yescharacteristic
356C23×C17C2×#4111yescharacteristic
357C23×C17C2×#4111yescharacteristic
358C23×C17C2×#4111yescharacteristic
359C23×C17C2×#4111yescharacteristic
360C23×C17C2×#4111yescharacteristic
361C23×C17H(5,𝔽2)11yescharacteristic
362C23×C17H(5,𝔽2)11yescharacteristic
363C23×C17H(5,𝔽2)11yescharacteristic
364C23×C172−1+411yescharacteristic
365C22×D17—22no—
366C22×D17—22no—
367C22×D17—22no—
368C22×D17—22no—
369C22×D17—22no—
370C22×D17—22no—
371C22×D17—22no—
372C22×D17—22no—
373C22×D17—22no—
374C22×D17—22no—
375C22×D17—22no—
376C22×D17—22no—
377C22×D17—22no—
378C22×D17—22no—
379C22×D17—22no—
380C22×D17—22no—
381C22×D17—22no—
382C22×D17—22no—
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—41no—
399C22×D17C4×D414yes—
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—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×C17—41no—
439C2×C4×C17—41no—
440C2×C4×C17—41no—
441C2×C4×C17C4×D414yes—
442C22⋊D17—416no—
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—22no—
462C2×Dic17—22no—
463C2×Dic17—22no—
464C2×Dic17—22no—
465C2×Dic17—22no—
466C2×Dic17—22no—
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—41no—
482C2×Dic17—41no—
483C2×Dic17—41no—
484C2×Dic17—41no—
485C2×Dic17—41no—
486C2×Dic17—41no—
487C2×Dic17—41no—
488C2×Dic17—41no—
489C2×Dic17#11714yescomplemented
490C2×Dic17C4×D414yes—
491C2×Dic17#12014yes—
492C4×D17—232no—
493C22×#117—171no—
494C2×#390—171no—
495C2×#388—171no—
496C2×#388—171no—
497C2×#386—171no—
498#1444—171no—
499#1439—171no—
500#1439—171no—
501#1438—171no—
502#1437—171no—
503#1437D1711yescharacteristic, complemented
504#1436—171no—
505#1436—171no—
506C22⋊#95—171no—
507C4×#95—171no—
508C22×C17—42no—
509C22×C17—42no—
510C22×C17—42no—
511C22×C17—42no—
512C22×C17—42no—
513C22×C17—42no—
514C22×C17—42no—
515C22×C17—81no—
516C22×C17—81no—
517C22×C17—81no—
518C22×C17—81no—
519C22×C17—81no—
520C22×C17—81no—
521C22×C17—81no—
522C22×C17—81no—
523C22×C17C2×#11711yescharacteristic
524C22×C17C2×C4×D411yescharacteristic
525C22×C17C2×C4×D411yescharacteristic
526C22×C17C2×C4×D411yescharacteristic
527C22×C17C4×#4111yescharacteristic
528C22×C17#51811yescharacteristic
529C22×C17#52011yescharacteristic
530C22×C17C2×#12011yescharacteristic
531C22×C17#52511yescharacteristic
532C22×C17#52511yescharacteristic
533C22×C17#52511yescharacteristic
534C22×C17#52911yescharacteristic
535C22×C17#52911yescharacteristic
536C22×C17#53211yescharacteristic
537C22×C17#53211yescharacteristic
538C22×C17#53511yescharacteristic
539C22×C17#53711yescharacteristic
540C22×C17#54011yescharacteristic
541C22×C17#54211yescharacteristic
542C22×C17#54611yescharacteristic
543C22×C17#54611yescharacteristic
544C22×C17#54611yescharacteristic
545C22×C17#54611yescharacteristic
546C22×C17#54711yescharacteristic
547C22×C17#54711yescharacteristic
548C22×C17#55011yescharacteristic
549C22×C17#55011yescharacteristic
550C22×C17#55111yescharacteristic
551C22×C17#55111yescharacteristic
552C22×C17#55111yescharacteristic
553C22×C17#55211yescharacteristic
554C22×C17#55311yescharacteristic
555C22×C17#55511yescharacteristic
556C22×C17#55511yescharacteristic
557C22×C17#55611yescharacteristic
558C2×D17—24no—
559C2×D17—24no—
560C2×D17—24no—
561C2×D17—42no—
562C2×D17—42no—
563C2×D17—42no—
564C2×D17—42no—
565C2×D17—42no—
566C2×D17—42no—
567C2×D17—42no—
568C2×D17—42no—
569C2×D17—42no—
570C2×D17—42no—
571C2×D17—42no—
572C2×D17—42no—
573C4×C17—24no—
574C4×C17—42no—
575C4×C17—42no—
576C4×C17—42no—
577C4×C17—42no—
578C4×C17—42no—
579Dic17—24no—
580Dic17—24no—
581Dic17—24no—
582Dic17—42no—
583Dic17—42no—
584Dic17—81no—
585Dic17—81no—
586C23×D4—171no—
587C24×C4—171no—
588C2×#117—344no—
589C2×#117—344no—
590C2×#117—344no—
591C22×C4⋊C4—171no—
592C22×C4⋊C4—171no—
593C22×C4⋊C4—171no—
594C22×C4⋊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×C22⋊C4—171no—
603C22×C22⋊C4C2×D1711yescharacteristic
604C22×C22⋊C4C2×D1711yescharacteristic
605C22×C22⋊C4C2×D1711yescharacteristic
606C22×C42—171no—
607C22×C42—171no—
608C22×C42—171no—
609C22×C42C2×D1711yescharacteristic
610#390—344no—
611#388—344no—
612#388—344no—
613#386—178no—
614C2×#95—171no—
615C2×#95—171no—
616C2×#95—171no—
617C2×#95—171no—
618C2×#95—171no—
619C2×#95—171no—
620C2×#95—171no—
621C2×#95—171no—
622C2×#95—171no—
623C2×#95—171no—
624C2×#95—171no—
625C2×#95C2×D1711yescharacteristic
626C2×#95C2×D1711yescharacteristic
627C2×#95C2×D1711yescharacteristic
628C2×C17—82no—
629C2×C17#229311yescharacteristic
630C2×C17C4×#12011yescharacteristic
631C2×C17#232411yescharacteristic
632C2×C17#234211yescharacteristic
633C2×C17#235411yescharacteristic
634C2×C17#235911yescharacteristic
635C2×C17#236311yescharacteristic
636C2×C17#243011yescharacteristic
637C2×C17#243111yescharacteristic
638C2×C17#247111yescharacteristic
639C2×C17#247411yescharacteristic
640C2×C17#247611yescharacteristic
641C2×C17#247911yescharacteristic
642C2×C17#260111yescharacteristic
643C2×C17#261011yescharacteristic
644D17—44no—
645C25—171no—
646C25C22×D1711yescharacteristic
647C22×D4—174no—
648C22×D4—342no—
649C22×D4—342no—
650C22×D4—342no—
651C22×D4—342no—
652C22×D4—681no—
653C22×D4—681no—
654C23×C4—171no—
655C23×C4—171no—
656C23×C4—171no—
657C23×C4—171no—
658C23×C4—171no—
659C23×C4—174no—
660C23×C4—171no—
661C23×C4—171no—
662C23×C4—342no—
663C23×C4—342no—
664C23×C4—342no—
665C23×C4—342no—
666C23×C4—342no—
667C23×C4—342no—
668C23×C4C22×D1711yescharacteristic
669C23×C4C22×D1711yescharacteristic
670C23×C4C22×D1711yescharacteristic
671C23×C4C22×D1711yescharacteristic
672C23×C4C22×D1711yescharacteristic
673C23×C4C22×D1711yescharacteristic
674#117—3432no—
675C2×C4⋊C4—174no—
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—342no—
683C2×C4⋊C4—342no—
684C2×C4⋊C4—681no—
685C2×C4⋊C4—681no—
686C2×C4⋊C4—681no—
687C2×C22⋊C4—22no—
688C2×C22⋊C4—22no—
689C2×C22⋊C4—22no—
690C2×C22⋊C4—22no—
691C2×C22⋊C4—22no—
692C2×C22⋊C4—22no—
693C2×C22⋊C4—41no—
694C2×C22⋊C4—41no—
695C2×C22⋊C4—174no—
696C2×C22⋊C4—174no—
697C2×C22⋊C4—174no—
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—342no—
713C2×C22⋊C4—681no—
714C2×C22⋊C4—681no—
715C2×C22⋊C4—681no—
716C2×C22⋊C4—681no—
717C2×C22⋊C4—681no—
718C2×C22⋊C4—681no—
719C2×C22⋊C4C4×D1714yes—
720C2×C42—22no—
721C2×C42—22no—
722C2×C42—22no—
723C2×C42—174no—
724C2×C42—342no—
725C2×C42—342no—
726C2×C42—342no—
727C2×C42—342no—
728C2×C42—342no—
729C2×C42—342no—
730C2×C42—681no—
731C2×C42—681no—
732#95—22no—
733#95—41no—
734#95—41no—
735#95—174no—
736#95—174no—
737#95—342no—
738#95—342no—
739#95—342no—
740#95—342no—
741#95—342no—
742#95—342no—
743#95—342no—
744#95—342no—
745#95—681no—
746C17#1407111yescharacteristic, complemented, Sylow
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—172no—
762C24—172no—
763C24—172no—
764C24—341no—
765C24—341no—
766C24—341no—
767C24—341no—
768C24—341no—
769C24—341no—
770C24—341no—
771C24—341no—
772C24—341no—
773C24—341no—
774C24—341no—
775C24—341no—
776C24C2×C4×D1712yes—
777C24C23×D1711yescharacteristic
778C2×D4—348no—
779C2×D4—348no—
780C2×D4—684no—
781C2×D4—684no—
782C2×D4—684no—
783C2×D4—684no—
784C2×D4—684no—
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—172no—
820C22×C4—172no—
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—172no—
830C22×C4—348no—
831C22×C4—348no—
832C22×C4—348no—
833C22×C4—348no—
834C22×C4—348no—
835C22×C4—348no—
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—348no—
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—341no—
865C22×C4—341no—
866C22×C4—341no—
867C22×C4—341no—
868C22×C4—341no—
869C22×C4—341no—
870C22×C4—341no—
871C22×C4—341no—
872C22×C4—341no—
873C22×C4—341no—
874C22×C4—341no—
875C22×C4C2×C4×D1712yes—
876C22×C4C2×C4×D1712yes—
877C22×C4#6325212yes—
878C22×C4#6325212yes—
879C22×C4D4×D1712yes—
880C22×C4D4×D1712yes—
881C22×C4D4×D1712yes—
882C22×C4#6325412yes—
883C4⋊C4—348no—
884C4⋊C4—348no—
885C4⋊C4—684no—
886C4⋊C4—684no—
887C22⋊C4—28no—
888C22⋊C4—44no—
889C22⋊C4—44no—
890C22⋊C4—348no—
891C22⋊C4—348no—
892C22⋊C4—348no—
893C22⋊C4—684no—
894C22⋊C4—684no—
895C22⋊C4—684no—
896C22⋊C4—684no—
897C22⋊C4—684no—
898C42—28no—
899C42—348no—
900C42—684no—
901C42—684no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—174no—
938C23—342no—
939C23—342no—
940C23—342no—
941C23—342no—
942C23—342no—
943C23—342no—
944C23—342no—
945C23—342no—
946C23—342no—
947C23—342no—
948C23—342no—
949C23—342no—
950C23—342no—
951C23—342no—
952C23—342no—
953C23—342no—
954C23—342no—
955C23—342no—
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—
970C23—681no—
971C23—681no—
972C23C22×C4×D1711yescharacteristic
973C23C2×#6325211yescharacteristic
974C23C2×#6325211yescharacteristic
975C23C2×D4×D1711yescharacteristic
976C23C2×D4×D1711yescharacteristic
977C23C2×D4×D1711yescharacteristic
978C23C2×#6325411yescharacteristic
979C23#1058769111yescharacteristic
980C23#1058769111yescharacteristic
981C23#41×D1711yescharacteristic
982C23#41×D1711yescharacteristic
983C23#41×D1711yescharacteristic
984C23#41×D1711yescharacteristic
985C23#1058769611yescharacteristic
986C23#1058769711yescharacteristic
987D4—6816no—
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—41no—
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—174no—
1030C2×C4—174no—
1031C2×C4—174no—
1032C2×C4—3432no—
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—342no—
1055C2×C4—342no—
1056C2×C4—342no—
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×C4—681no—
1076C2×C4—681no—
1077C2×C4—681no—
1078C2×C4—681no—
1079C2×C4#1058756714yes—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—81no—
1088C22—81no—
1089C22—81no—
1090C22—81no—
1091C22—81no—
1092C22—81no—
1093C22—81no—
1094C22—81no—
1095C22—344no—
1096C22—344no—
1097C22—344no—
1098C22—682no—
1099C22—682no—
1100C22—682no—
1101C22—682no—
1102C22—682no—
1103C22—682no—
1104C22—682no—
1105C22—682no—
1106C22—682no—
1107C22—682no—
1108C22—682no—
1109C22—682no—
1110C22#117×D1711yescharacteristic
1111C22C4×D4×D1711yescharacteristic
1112C22C4×D4×D1711yescharacteristic
1113C22C2×#1058756711yescharacteristic
1114C22C4×#6325211yescharacteristic
1115C22#1176328111yescharacteristic
1116C22#1176328811yescharacteristic
1117C22#120×D1711yescharacteristic
1118C22#1176331711yescharacteristic
1119C22#1176331911yescharacteristic
1120C22#1176331911yescharacteristic
1121C22#1176333911yescharacteristic
1122C22#1176333911yescharacteristic
1123C22#1176335611yescharacteristic
1124C22#1176335611yescharacteristic
1125C22#1176337511yescharacteristic
1126C22#1176338811yescharacteristic
1127C22#1176341311yescharacteristic
1128C22#1176342811yescharacteristic
1129C22#1176344911yescharacteristic
1130C22#1176344911yescharacteristic
1131C22#1176345111yescharacteristic
1132C22#1176345611yescharacteristic
1133C22#1176345711yescharacteristic
1134C22#1176346411yescharacteristic
1135C22#1176347711yescharacteristic
1136C22#1176348011yescharacteristic
1137C22#1176348411yescharacteristic
1138C22#1176348811yescharacteristic
1139C22#1176348911yescharacteristic
1140C22#1176349811yescharacteristic
1141C22#1176350811yescharacteristic
1142C22#1176352111yescharacteristic
1143C22#1176352211yescharacteristic
1144C22#1176352611yescharacteristic
1145C4—24no—
1146C4—42no—
1147C4—42no—
1148C4—42no—
1149C4—42no—
1150C4—42no—
1151C4—344no—
1152C4—344no—
1153C4—344no—
1154C4—682no—
1155C4—682no—
1156C4—1361no—
1157C4—1361no—
1158C2—82no—
1159C2—684no—
1160C2#1453124711yescharacteristic
1161C2#1453128911yescharacteristic
1162C2#1453148011yescharacteristic
1163C2#1453162811yescharacteristic
1164C2#1453173011yescharacteristic
1165C2#1453177711yescharacteristic
1166C2#1453182311yescharacteristic
1167C2#1453239111yescharacteristic
1168C2#1453240111yescharacteristic
1169C2#1453290011yescharacteristic
1170C2#1453294511yescharacteristic
1171C2#1453297511yescharacteristic
1172C2#1453302011yescharacteristic
1173C2#1453438711yescharacteristic
1174C2#1453446911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1437C2
socle, cosocleC24×C17C24
prime radicalC23×C22⋊D17C22
hypercenter#1437D17
hypocenterC17#14071
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
1. C22×#10587558C2semidirect
3. C2×#11762702C2semidirect
4. C2×#11762697C2semidirect
6. #14527048C2semidirect
7. #14527030C2semidirect
8. #14527027C2semidirect
10. #14527020C2semidirect
11. #14527017C2semidirect
12. #14527015C2semidirect
13. #14527005C2semidirect
14. #95×Dic17C2semidirect
15. C17×#1437C2semidirect
39. #11762685C4semidirect
134. C2×#63225D4semidirect
143. C2×C4×Dic17D4semidirect
489. C2×Dic17#117semidirect
503. #1437D17semidirect
746. C17#14071semidirect

Maximal subgroups

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

subgroupindex
C22×#105875582
C2×#117627092
C2×#117627022
C2×#117626972
C2×#117626852
#145270482
#145270302
#145270272
#145270232
#145270202
#145270172
#145270152
#145270052
#95×Dic172
C17×#14372
#1407117