Finite Group Databasebeta

← #16957487

Subgroups — #16957487

Order 4352.

2278 conjugacy classes of subgroups.

The subgroup lattice has 1194 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762697C211yesmaximal, characteristic, complemented
2C2×#11762685C211yesmaximal, characteristic
3C2×#11762685C211yesmaximal, characteristic
4C2×#11762685C211yesmaximal, characteristic
5C2×#11762668C211yesmaximal, characteristic, complemented
6C2×C4×#63227C211yesmaximal, characteristic, complemented
7C2×#95×D17C211yesmaximal, characteristic, complemented
8#14527045C211yesmaximal, characteristic, complemented
9#14527042C211yesmaximal, characteristic, complemented
10#14527033C211yesmaximal, characteristic, complemented
11#14527027C211yesmaximal, characteristic, complemented
12#14527017C211yesmaximal, characteristic, complemented
13#14527008C211yesmaximal, characteristic, complemented
14#14527005C211yesmaximal, characteristic, complemented
15C17×#1437C211yesmaximal, characteristic, complemented
16C23×C22⋊D17C2211yescharacteristic
17C23×C4×D17C2211yescharacteristic
18C23×C4×D17C2211yescharacteristic
19C23×C4×D17C2211yescharacteristic
20C22×#63225C2211yescharacteristic
21C22×#63225C2211yescharacteristic
22C22×C22⋊Dic17C2211yescharacteristic
23C22×C22⋊Dic17C2211yescharacteristic
24C22×C22⋊Dic17C2211yescharacteristic
25C22×#63227C2211yescharacteristic
26C22×#63227C2211yescharacteristic
27C22×#63227C2211yescharacteristic
28C22×C4×Dic17C2211yescharacteristic
29#11762697—24no—
30#11762685—24no—
31#11762685—24no—
32#11762685C418yescomplemented
33#11762668—24no—
34C4×#63227—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
47C2×#10587502C2211yescharacteristic
48C2×#10587502C2211yescharacteristic
49C2×#10587502C2211yescharacteristic
50#95×D17—24no—
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—22no—
71C22×C22⋊D17—22no—
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×D17—22no—
87C22×C4×D17—22no—
88C22×C4×D17—22no—
89C22×C4×D17—22no—
90C22×C4×D17—22no—
91C22×C4×D17—22no—
92C22×C4×D17—22no—
93C22×C4×D17—41no—
94C22×C4×D17—41no—
95C22×C4×D17—41no—
96C22×C4×D17—41no—
97C22×C4×D17—41no—
98C22×C4×D17—41no—
99C22×C4×D17C2×C414yes—
100C22×C4×D17D414yes—
101C2×C22⋊C4×C17—22no—
102C2×C22⋊C4×C17—22no—
103C2×C22⋊C4×C17—22no—
104C2×C22⋊C4×C17—22no—
105C2×C22⋊C4×C17—22no—
106C2×C22⋊C4×C17—41no—
107C2×C22⋊C4×C17—41no—
108C2×C22⋊C4×C17—41no—
109C2×C22⋊C4×C17C2×C414yescomplemented
110C2×C42×C17—22no—
111C2×C42×C17—41no—
112C2×C42×C17—41no—
113C2×C22⋊Dic17—22no—
114C2×C22⋊Dic17—22no—
115C2×C22⋊Dic17—22no—
116C2×C22⋊Dic17—22no—
117C2×C22⋊Dic17—22no—
118C2×C22⋊Dic17—41no—
119C2×C22⋊Dic17—41no—
120C2×C22⋊Dic17—41no—
121C2×C22⋊Dic17C2×C414yescomplemented
122C2×#63227—22no—
123C2×#63227—22no—
124C2×#63227—22no—
125C2×#63227—22no—
126C2×#63227—22no—
127C2×#63227—22no—
128C2×#63227—22no—
129C2×#63227C2×C414yes—
130C2×#63227D414yes—
131C2×#63225—22no—
132C2×#63225—22no—
133C2×#63225—22no—
134C2×#63225—22no—
135C2×#63225—41no—
136C2×#63225—41no—
137C2×C4×Dic17—22no—
138C2×C4×Dic17—22no—
139C2×C4×Dic17—22no—
140C17×#95—22no—
141C17×#95—22no—
142C17×#95—41no—
143#10587502—22no—
144#10587502—22no—
145#10587502—22no—
146#10587502—22no—
147#10587502—22no—
148#10587502—22no—
149#10587502—22no—
150#10587502—22no—
151#10587502—22no—
152#10587502—22no—
153#10587502—22no—
154#10587502—41no—
155#10587502C2×C414yescomplemented
156#10587502C2×C414yescomplemented
157#10587502D414yescomplemented
158C24×C17—21no—
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×C17C22×C412yes—
173C24×C17C2411yescharacteristic
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×D17C22×C412yes—
183C23×D17C2×D412yes—
184C23×D17C2×D412yes—
185C23×D17#4112yes—
186C23×D17#4112yes—
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×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—
231C2×C22⋊D17—28no—
232C2×C22⋊D17—28no—
233C2×C22⋊D17—28no—
234C2×C22⋊D17—44no—
235C2×C22⋊D17—44no—
236C2×C22⋊D17—44no—
237C2×C22⋊D17—44no—
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×Dic17—21no—
273C22×Dic17—21no—
274C22×Dic17—21no—
275C22×Dic17—21no—
276C22×Dic17—21no—
277C22×Dic17—21no—
278C22×Dic17—21no—
279C22×Dic17C22×C412yes—
280C22×Dic17C22×C412yes—
281C22×Dic17C22×C412yes—
282C22×Dic17C2×D412yes—
283C22×Dic17C2×D412yes—
284C22×Dic17C2×D412yes—
285C22×Dic17C2×D412yes—
286C22×Dic17#4112yes—
287C2×C4×D17—28no—
288C2×C4×D17—28no—
289C2×C4×D17—28no—
290C2×C4×D17—28no—
291C2×C4×D17—28no—
292C2×C4×D17—44no—
293C2×C4×D17—44no—
294C2×C4×D17—44no—
295C2×C4×D17—44no—
296C2×C4×D17—44no—
297C2×C4×D17—44no—
298C2×C4×D17—44no—
299C2×C4×D17—44no—
300C2×C4×D17—44no—
301C2×C4×D17—44no—
302C2×C4×D17—44no—
303C2×C4×D17—44no—
304C2×C4×D17—44no—
305C2×C4×D17—44no—
306C2×C4×D17—44no—
307C2×C4×D17—44no—
308C22⋊C4×C17—44no—
309C22⋊C4×C17—44no—
310C22⋊C4×C17—44no—
311C42×C17—44no—
312C22⋊Dic17—28no—
313C22⋊Dic17—44no—
314C22⋊Dic17—44no—
315#63227—28no—
316#63227—28no—
317#63227—44no—
318#63225—44no—
319#63225—44no—
320C4×Dic17—44no—
321#13999—171nomaximal, Sylow
322C23×C17—22no—
323C23×C17—22no—
324C23×C17—22no—
325C23×C17—22no—
326C23×C17—22no—
327C23×C17—22no—
328C23×C17—22no—
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×C17—41no—
351C23×C17—41no—
352C23×C17—41no—
353C23×C17—41no—
354C23×C17—41no—
355C23×C17—41no—
356C23×C17—41no—
357C23×C17C23×C411yescharacteristic
358C23×C17C22×D411yescharacteristic
359C23×C17C22×D411yescharacteristic
360C23×C17C22×D411yescharacteristic
361C23×C17C2×#4111yescharacteristic
362C23×C17C2×#4111yescharacteristic
363C23×C17C2×#4111yescharacteristic
364C23×C17C2×#4111yescharacteristic
365C23×C17C2×#4111yescharacteristic
366C23×C17C2×#4111yescharacteristic
367C23×C17C2×#4111yescharacteristic
368C23×C17H(5,𝔽2)11yescharacteristic
369C23×C17H(5,𝔽2)11yescharacteristic
370C23×C17H(5,𝔽2)11yescharacteristic
371C23×C172−1+411yescharacteristic
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—22no—
384C22×D17—22no—
385C22×D17—22no—
386C22×D17—22no—
387C22×D17—22no—
388C22×D17—22no—
389C22×D17—22no—
390C22×D17—22no—
391C22×D17—22no—
392C22×D17—22no—
393C22×D17—22no—
394C22×D17—22no—
395C22×D17—22no—
396C22×D17—22no—
397C22×D17—22no—
398C22×D17—22no—
399C22×D17—22no—
400C22×D17#11714yes—
401C22×D17C4×D414yes—
402C22×D17C4×D414yes—
403C22×D17#12114yes—
404C22×D17#12314yes—
405C22×D17#12414yes—
406C22×D17#12614yes—
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—22no—
424C2×C4×C17—22no—
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×C17—41no—
446C2×C4×C17—41no—
447C2×C4×C17—41no—
448C2×C4×C17#12114yes—
449C22⋊D17—416no—
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—22no—
470C2×Dic17—22no—
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—41no—
490C2×Dic17—41no—
491C2×Dic17—41no—
492C2×Dic17—41no—
493C2×Dic17—41no—
494C2×Dic17—41no—
495C2×Dic17—41no—
496C2×Dic17—41no—
497C2×Dic17—41no—
498C2×Dic17C4×D414yes—
499C4×D17—416no—
500C4×D17—416no—
501C4×D17—416no—
502C2×#388—171no—
503C2×#386—171no—
504C2×#386—171no—
505C2×#386—171no—
506C2×#380—171no—
507C2×C4×C22⋊C4—171no—
508C22×#95—171no—
509#1443—171no—
510#1442—171no—
511#1440—171no—
512#1439—171no—
513#1437D1711yescharacteristic, complemented
514#1436—171no—
515#1434—171no—
516C22⋊#95—171no—
517C22×C17—42no—
518C22×C17—42no—
519C22×C17—42no—
520C22×C17—42no—
521C22×C17—42no—
522C22×C17—42no—
523C22×C17—42no—
524C22×C17—81no—
525C22×C17—81no—
526C22×C17—81no—
527C22×C17—81no—
528C22×C17—81no—
529C22×C17—81no—
530C22×C17—81no—
531C22×C17—81no—
532C22×C17C2×#11711yescharacteristic
533C22×C17C2×C4×D411yescharacteristic
534C22×C17C2×C4×D411yescharacteristic
535C22×C17C2×C4×D411yescharacteristic
536C22×C17C4×#4111yescharacteristic
537C22×C17#51811yescharacteristic
538C22×C17#52011yescharacteristic
539C22×C17C2×#12111yescharacteristic
540C22×C17C2×#12111yescharacteristic
541C22×C17C2×#12311yescharacteristic
542C22×C17#52511yescharacteristic
543C22×C17C2×#12411yescharacteristic
544C22×C17C2×#12611yescharacteristic
545C22×C17#52911yescharacteristic
546C22×C17#53211yescharacteristic
547C22×C17#53411yescharacteristic
548C22×C17#53711yescharacteristic
549C22×C17#53811yescharacteristic
550C22×C17#53911yescharacteristic
551C22×C17D4211yescharacteristic
552C22×C17#54611yescharacteristic
553C22×C17#54611yescharacteristic
554C22×C17#54611yescharacteristic
555C22×C17#54611yescharacteristic
556C22×C17#54711yescharacteristic
557C22×C17#54811yescharacteristic
558C22×C17#55111yescharacteristic
559C22×C17#55111yescharacteristic
560C22×C17#55111yescharacteristic
561C22×C17#55111yescharacteristic
562C22×C17#55211yescharacteristic
563C22×C17#55211yescharacteristic
564C22×C17#55311yescharacteristic
565C22×C17#55311yescharacteristic
566C22×C17#55311yescharacteristic
567C2×D17—24no—
568C2×D17—24no—
569C2×D17—24no—
570C2×D17—24no—
571C2×D17—24no—
572C2×D17—24no—
573C2×D17—24no—
574C2×D17—24no—
575C2×D17—24no—
576C2×D17—24no—
577C2×D17—24no—
578C2×D17—24no—
579C2×D17—24no—
580C2×D17—24no—
581C2×D17#38818yescomplemented
582C4×C17—24no—
583C4×C17—42no—
584C4×C17—42no—
585C4×C17—42no—
586C4×C17—42no—
587C4×C17—81no—
588Dic17—24no—
589Dic17—42no—
590Dic17—42no—
591Dic17—42no—
592Dic17—42no—
593Dic17—42no—
594Dic17—81no—
595C23×D4—171no—
596C24×C4—171no—
597C24×C4—171no—
598C24×C4—171no—
599C22×C4⋊C4—171no—
600C22×C4⋊C4—171no—
601C22×C22⋊C4—171no—
602C22×C22⋊C4—171no—
603C22×C22⋊C4—171no—
604C22×C22⋊C4—171no—
605C22×C22⋊C4—171no—
606C22×C22⋊C4—171no—
607C22×C22⋊C4C2×D1711yescharacteristic
608C22×C22⋊C4C2×D1711yescharacteristic
609C22×C22⋊C4C2×D1711yescharacteristic
610C22×C42—171no—
611C22×C42C2×D1711yescharacteristic
612#388—344no—
613#386—178no—
614#386—344no—
615#386—344no—
616#380—344no—
617C4×C22⋊C4—344no—
618C2×#95—171no—
619C2×#95—171no—
620C2×#95—171no—
621C2×#95—171no—
622C2×#95—171no—
623C2×#95—171no—
624C2×#95—171no—
625C2×#95—171no—
626C2×#95—171no—
627C2×#95—171no—
628C2×#95—171no—
629C2×#95—171no—
630C2×#95—171no—
631C2×#95—171no—
632C2×#95—171no—
633C2×#95—344no—
634C2×#95C2×D1711yescharacteristic
635C2×#95C2×D1711yescharacteristic
636C2×#95C2×D1711yescharacteristic
637C2×C17—82no—
638C2×C17C2×#38811yescharacteristic
639C2×C17C4×#12111yescharacteristic
640C2×C17#232511yescharacteristic
641C2×C17#235211yescharacteristic
642C2×C17#235311yescharacteristic
643C2×C17#235811yescharacteristic
644C2×C17#235911yescharacteristic
645C2×C17#241211yescharacteristic
646C2×C17#241611yescharacteristic
647C2×C17#247211yescharacteristic
648C2×C17#248111yescharacteristic
649C2×C17#248811yescharacteristic
650C2×C17#249811yescharacteristic
651C2×C17#251011yescharacteristic
652C2×C17#254311yescharacteristic
653D17—28no—
654C25—171no—
655C25C22×D1711yescharacteristic
656C22×D4—174no—
657C22×D4—342no—
658C22×D4—342no—
659C22×D4—342no—
660C22×D4—342no—
661C22×D4—342no—
662C22×D4—342no—
663C23×C4—171no—
664C23×C4—171no—
665C23×C4—171no—
666C23×C4—171no—
667C23×C4—171no—
668C23×C4—171no—
669C23×C4—174no—
670C23×C4—174no—
671C23×C4—171no—
672C23×C4—342no—
673C23×C4—342no—
674C23×C4—342no—
675C23×C4—342no—
676C23×C4—342no—
677C23×C4—342no—
678C23×C4—342no—
679C23×C4—342no—
680C23×C4—342no—
681C23×C4—342no—
682C23×C4—342no—
683C23×C4—342no—
684C23×C4—342no—
685C23×C4—681no—
686C23×C4—681no—
687C23×C4—681no—
688C23×C4—681no—
689C23×C4—681no—
690C23×C4—681no—
691C23×C4C22×D1711yescharacteristic
692C23×C4C22×D1711yescharacteristic
693C23×C4C22×D1711yescharacteristic
694C23×C4C22×D1711yescharacteristic
695C23×C4C22×D1711yescharacteristic
696C23×C4C22×D1711yescharacteristic
697C2×C4⋊C4—342no—
698C2×C4⋊C4—342no—
699C2×C4⋊C4—342no—
700C2×C4⋊C4—342no—
701C2×C4⋊C4—681no—
702C2×C4⋊C4—681no—
703C2×C22⋊C4—22no—
704C2×C22⋊C4—22no—
705C2×C22⋊C4—22no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—22no—
708C2×C22⋊C4—41no—
709C2×C22⋊C4—41no—
710C2×C22⋊C4—41no—
711C2×C22⋊C4—174no—
712C2×C22⋊C4—174no—
713C2×C22⋊C4—174no—
714C2×C22⋊C4—342no—
715C2×C22⋊C4—342no—
716C2×C22⋊C4—342no—
717C2×C22⋊C4—342no—
718C2×C22⋊C4—342no—
719C2×C22⋊C4—342no—
720C2×C22⋊C4—342no—
721C2×C22⋊C4—342no—
722C2×C22⋊C4—342no—
723C2×C22⋊C4—342no—
724C2×C22⋊C4—342no—
725C2×C22⋊C4—342no—
726C2×C22⋊C4—681no—
727C2×C22⋊C4—681no—
728C2×C22⋊C4—681no—
729C2×C22⋊C4C4×D1714yescomplemented
730C2×C42—22no—
731C2×C42—41no—
732C2×C42—41no—
733C2×C42—342no—
734C2×C42—342no—
735C2×C42—342no—
736#95—22no—
737#95—22no—
738#95—41no—
739#95—174no—
740#95—174no—
741#95—174no—
742#95—342no—
743#95—342no—
744#95—342no—
745#95—342no—
746#95—342no—
747#95—342no—
748#95—342no—
749#95—342no—
750#95—342no—
751#95—342no—
752#95—342no—
753#95—681no—
754C17#1399911yescharacteristic, complemented, Sylow
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—172no—
770C24—172no—
771C24—172no—
772C24—172no—
773C24—172no—
774C24—172no—
775C24—172no—
776C24—341no—
777C24—341no—
778C24—341no—
779C24—341no—
780C24—341no—
781C24—341no—
782C24—341no—
783C24—341no—
784C24C2×C4×D1712yes—
785C24C23×D1711yescharacteristic
786C2×D4—348no—
787C2×D4—348no—
788C2×D4—348no—
789C2×D4—684no—
790C2×D4—684no—
791C2×D4—684no—
792C2×D4—684no—
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—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—172no—
829C22×C4—172no—
830C22×C4—172no—
831C22×C4—172no—
832C22×C4—172no—
833C22×C4—172no—
834C22×C4—172no—
835C22×C4—172no—
836C22×C4—348no—
837C22×C4—348no—
838C22×C4—348no—
839C22×C4—348no—
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—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—348no—
875C22×C4—341no—
876C22×C4—341no—
877C22×C4—341no—
878C22×C4—341no—
879C22×C4—341no—
880C22×C4—341no—
881C22×C4—341no—
882C22×C4—684no—
883C22×C4—684no—
884C22×C4—684no—
885C22×C4—684no—
886C22×C4—684no—
887C22×C4—684no—
888C22×C4—684no—
889C22×C4—684no—
890C22×C4—684no—
891C22×C4—684no—
892C22×C4—684no—
893C22×C4—684no—
894C22×C4—684no—
895C22×C4—684no—
896C22×C4—684no—
897C22×C4—684no—
898C22×C4C2×C4×D1712yes—
899C22×C4C2×C4×D1712yes—
900C22×C4#6325212yes—
901C22×C4#6325212yes—
902C22×C4D4×D1712yes—
903C22×C4D4×D1712yes—
904C22×C4D4×D1712yes—
905C4⋊C4—684no—
906C4⋊C4—684no—
907C22⋊C4—44no—
908C22⋊C4—44no—
909C22⋊C4—44no—
910C22⋊C4—348no—
911C22⋊C4—348no—
912C22⋊C4—348no—
913C22⋊C4—684no—
914C22⋊C4—684no—
915C22⋊C4—684no—
916C42—44no—
917C42—684no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
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—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—174no—
954C23—174no—
955C23—174no—
956C23—174no—
957C23—174no—
958C23—174no—
959C23—174no—
960C23—342no—
961C23—342no—
962C23—342no—
963C23—342no—
964C23—342no—
965C23—342no—
966C23—342no—
967C23—342no—
968C23—342no—
969C23—342no—
970C23—342no—
971C23—342no—
972C23—342no—
973C23—342no—
974C23—342no—
975C23—342no—
976C23—342no—
977C23—342no—
978C23—342no—
979C23—342no—
980C23—342no—
981C23—342no—
982C23—342no—
983C23—342no—
984C23—342no—
985C23—342no—
986C23—342no—
987C23—342no—
988C23C22×C4×D1711yescharacteristic
989C23C2×#6325211yescharacteristic
990C23C2×#6325211yescharacteristic
991C23C2×D4×D1711yescharacteristic
992C23C2×D4×D1711yescharacteristic
993C23C2×D4×D1711yescharacteristic
994C23#1058769111yescharacteristic
995C23#1058769111yescharacteristic
996C23#1058769111yescharacteristic
997C23#41×D1711yescharacteristic
998C23#41×D1711yescharacteristic
999C23#41×D1711yescharacteristic
1000C23#41×D1711yescharacteristic
1001C23#41×D1711yescharacteristic
1002C23#1058769711yescharacteristic
1003D4—6816no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
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—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—174no—
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—342no—
1058C2×C4—342no—
1059C2×C4—342no—
1060C2×C4—342no—
1061C2×C4—342no—
1062C2×C4—342no—
1063C2×C4—342no—
1064C2×C4—342no—
1065C2×C4—342no—
1066C2×C4—342no—
1067C2×C4—6816no—
1068C2×C4—6816no—
1069C2×C4—6816no—
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—681no—
1080C2×C4—681no—
1081C2×C4—681no—
1082C2×C4—681no—
1083C2×C4—681no—
1084C2×C4—681no—
1085C2×C4—681no—
1086C2×C4—681no—
1087C2×C4—681no—
1088C2×C4—681no—
1089C2×C4—681no—
1090C2×C4—681no—
1091C2×C4—681no—
1092C2×C4—681no—
1093C2×C4—681no—
1094C2×C4—681no—
1095C2×C4—681no—
1096C2×C4—681no—
1097C2×C4#1058757014yes—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—81no—
1106C22—81no—
1107C22—81no—
1108C22—81no—
1109C22—81no—
1110C22—81no—
1111C22—81no—
1112C22—81no—
1113C22—178no—
1114C22—344no—
1115C22—344no—
1116C22—344no—
1117C22—344no—
1118C22—344no—
1119C22—344no—
1120C22—344no—
1121C22—344no—
1122C22—344no—
1123C22—344no—
1124C22—344no—
1125C22—344no—
1126C22—344no—
1127C22—344no—
1128C22#117×D1711yescharacteristic
1129C22C4×D4×D1711yescharacteristic
1130C22C4×D4×D1711yescharacteristic
1131C22C4×D4×D1711yescharacteristic
1132C22C4×#6325211yescharacteristic
1133C22#1176328211yescharacteristic
1134C22#1176328811yescharacteristic
1135C22#121×D1711yescharacteristic
1136C22C2×#1058757011yescharacteristic
1137C22#123×D1711yescharacteristic
1138C22#1176331811yescharacteristic
1139C22#124×D1711yescharacteristic
1140C22#126×D1711yescharacteristic
1141C22#1176333711yescharacteristic
1142C22#1176335611yescharacteristic
1143C22#1176336911yescharacteristic
1144C22#1176338811yescharacteristic
1145C22#1176339111yescharacteristic
1146C22#1176340211yescharacteristic
1147C22#1176344411yescharacteristic
1148C22#1176344811yescharacteristic
1149C22#1176344811yescharacteristic
1150C22#1176344811yescharacteristic
1151C22#1176344911yescharacteristic
1152C22#1176346411yescharacteristic
1153C22#1176346711yescharacteristic
1154C22#1176348811yescharacteristic
1155C22#1176348811yescharacteristic
1156C22#1176348811yescharacteristic
1157C22#1176348911yescharacteristic
1158C22#1176349511yescharacteristic
1159C22#1176349811yescharacteristic
1160C22#1176350411yescharacteristic
1161C22#1176350911yescharacteristic
1162C22#1176350911yescharacteristic
1163C4—24no—
1164C4—42no—
1165C4—42no—
1166C4—42no—
1167C4—42no—
1168C4—81no—
1169C4—344no—
1170C4—682no—
1171C4—682no—
1172C4—682no—
1173C4—682no—
1174C4—682no—
1175C4—1361no—
1176C2—82no—
1177C2—348no—
1178C2D17×#38811yescharacteristic
1179C2C4×#1058757011yescharacteristic
1180C2#1453148611yescharacteristic
1181C2#1453171211yescharacteristic
1182C2#1453172711yescharacteristic
1183C2#1453176511yescharacteristic
1184C2#1453177711yescharacteristic
1185C2#1453218311yescharacteristic
1186C2#1453222711yescharacteristic
1187C2#1453291611yescharacteristic
1188C2#1453305111yescharacteristic
1189C2#1453311511yescharacteristic
1190C2#1453322711yescharacteristic
1191C2#1453334311yescharacteristic
1192C2#1453374311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1437C2
socle, cosocleC24×C17C24
prime radicalC23×C22⋊D17C22
hypercenter#1437D17
hypocenterC17#13999
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
1. C2×#11762697C2semidirect
5. C2×#11762668C2semidirect
6. C2×C4×#63227C2semidirect
7. C2×#95×D17C2semidirect
8. #14527045C2semidirect
9. #14527042C2semidirect
10. #14527033C2semidirect
11. #14527027C2semidirect
12. #14527017C2semidirect
13. #14527008C2semidirect
14. #14527005C2semidirect
15. C17×#1437C2semidirect
32. #11762685C4semidirect
109. C2×C22⋊C4×C17C2×C4semidirect
121. C2×C22⋊Dic17C2×C4semidirect
155. #10587502C2×C4semidirect
156. #10587502C2×C4semidirect
157. #10587502D4semidirect
513. #1437D17semidirect
581. C2×D17#388semidirect
729. C2×C22⋊C4C4×D17semidirect
754. C17#13999semidirect

Maximal subgroups

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

subgroupindex
C2×#117626972
C2×#117626852
C2×#117626682
C2×C4×#632272
C2×#95×D172
#145270452
#145270422
#145270332
#145270272
#145270172
#145270082
#145270052
C17×#14372
#1399917