Finite Group Databasebeta

← #16958772

Subgroups — #16958772

Order 4352.

2266 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587572C211yesmaximal, characteristic
2C2×#11762701C211yesmaximal, characteristic, complemented
3C2×#11762685C211yesmaximal, characteristic
4C2×C22⋊C4×Dic17C211yesmaximal, characteristic, complemented
5C2×C4×#63227C211yesmaximal, characteristic, complemented
6#14527051C211yesmaximal, characteristic, complemented
7#14527032C211yesmaximal, characteristic, complemented
8#14527029C211yesmaximal, characteristic, complemented
9#14527023C211yesmaximal, characteristic
10#14527018C211yesmaximal, characteristic, complemented
11#14527018C211yesmaximal, characteristic, complemented
12#14527014C211yesmaximal, characteristic, complemented
13#14527006C211yesmaximal, characteristic, complemented
14#14527005C211yesmaximal, characteristic, complemented
15C17×#1437C211yesmaximal, characteristic, complemented
16C23×C22⋊D17C2211yescharacteristic
17C24×Dic17C2211yescharacteristic
18C23×C4×D17C2211yescharacteristic
19C2×#10587572—24no—
20C2×#10587572—24no—
21C2×#10587572C418yescomplemented
22C22×C4⋊Dic17C2211yescharacteristic
23C22×C4⋊Dic17C2211yescharacteristic
24C22×C4⋊Dic17C2211yescharacteristic
25C22×C22⋊Dic17C2211yescharacteristic
26C22×C22⋊Dic17C2211yescharacteristic
27C22×#63227C2211yescharacteristic
28C22×#63227C2211yescharacteristic
29C22×#63227C2211yescharacteristic
30C22×#63227C2211yescharacteristic
31C22×#63227C2211yescharacteristic
32C22×C4×Dic17C2211yescharacteristic
33C22×C4×Dic17C2211yescharacteristic
34#11762701—24no—
35#11762685—24no—
36C22⋊C4×Dic17—24no—
37C4×#63227—24no—
38C2×#10587502C2211yescharacteristic
39C2×#10587502C2211yescharacteristic
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×Dic17—22no—
74C23×Dic17—22no—
75C23×Dic17—22no—
76C23×Dic17—22no—
77C23×Dic17—41no—
78C23×Dic17—41no—
79C23×Dic17C2×C414yescomplemented
80C23×Dic17C2311yescharacteristic
81C23×Dic17C2311yescharacteristic
82C23×Dic17C2311yescharacteristic
83C23×Dic17C2311yescharacteristic
84C23×Dic17C2311yescharacteristic
85C23×Dic17C2311yescharacteristic
86C23×Dic17C2311yescharacteristic
87C22×C4×D17—22no—
88C22×C4×D17—22no—
89C22×C4×D17—22no—
90C22×C4×D17—22no—
91C22×C4×D17—22no—
92C22×C4×D17—41no—
93C22×C4×D17—41no—
94C2×C22⋊C4×C17—22no—
95C2×C22⋊C4×C17—22no—
96C2×C22⋊C4×C17—22no—
97C2×C22⋊C4×C17—22no—
98C2×C22⋊C4×C17—22no—
99C2×C22⋊C4×C17—22no—
100C2×C22⋊C4×C17—41no—
101C2×C22⋊C4×C17C2×C414yescomplemented
102C2×C22⋊C4×C17D414yes—
103C2×C42×C17—22no—
104C2×C42×C17—22no—
105C2×C42×C17—41no—
106C2×C22⋊Dic17—22no—
107C2×C22⋊Dic17—22no—
108C2×C22⋊Dic17—22no—
109C2×C22⋊Dic17—22no—
110C2×C22⋊Dic17—22no—
111C2×C22⋊Dic17—41no—
112C2×#63227—22no—
113C2×#63227—22no—
114C2×#63227—22no—
115C2×#63227—22no—
116C2×#63227—22no—
117C2×#63227—22no—
118C2×#63227—22no—
119C2×#63227—22no—
120C2×#63227—22no—
121C2×#63227—41no—
122C2×#63227—41no—
123C2×#63227C2×C414yes—
124C2×#63227C2×C414yes—
125C2×#63227D414yes—
126C2×#63227D414yes—
127C2×C4⋊Dic17—22no—
128C2×C4⋊Dic17—22no—
129C2×C4⋊Dic17—22no—
130C2×C4⋊Dic17—22no—
131C2×C4⋊Dic17—22no—
132C2×C4⋊Dic17—22no—
133C2×C4⋊Dic17—41no—
134C2×C4⋊Dic17C2×C414yescomplemented
135C2×C4⋊Dic17C2×C414yescomplemented
136C2×C4×Dic17—22no—
137C2×C4×Dic17—22no—
138C2×C4×Dic17—22no—
139C2×C4×Dic17—22no—
140C2×C4×Dic17—41no—
141C2×C4×Dic17—41no—
142#10587572—232no—
143C17×#95—22no—
144C17×#95—22no—
145C17×#95—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—22no—
155#10587502—41no—
156#10587502—41no—
157#10587502—41no—
158#10587502—41no—
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×C17C22×C412yes—
172C24×C17C2×D412yes—
173C24×C17#4112yes—
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×D17C2×D412yes—
190C22×C4×C17—21no—
191C22×C4×C17—21no—
192C22×C4×C17—21no—
193C22×C4×C17—21no—
194C22×C4×C17—21no—
195C22×C4×C17—21no—
196C22×C4×C17—21no—
197C22×C4×C17—21no—
198C22×C4×C17—21no—
199C22×C4×C17—21no—
200C22×C4×C17—21no—
201C22×C4×C17—21no—
202C22×C4×C17—21no—
203C22×C4×C17—21no—
204C22×C4×C17—21no—
205C22×C4×C17—21no—
206C22×C4×C17—21no—
207C22×C4×C17—21no—
208C22×C4×C17—21no—
209C22×C4×C17—21no—
210C22×C4×C17—21no—
211C22×C4×C17—21no—
212C22×C4×C17—21no—
213C22×C4×C17—21no—
214C22×C4×C17—21no—
215C22×C4×C17—21no—
216C22×C4×C17—21no—
217C22×C4×C17—21no—
218C22×C4×C17—21no—
219C22×C4×C17—21no—
220C22×C4×C17—21no—
221C22×C4×C17—21no—
222C22×C4×C17—21no—
223C22×C4×C17C22×C412yes—
224C22×C4×C17C22×C412yes—
225C22×C4×C17C2×D412yes—
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—28no—
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—28no—
275C22×Dic17—21no—
276C22×Dic17—21no—
277C22×Dic17—21no—
278C22×Dic17—21no—
279C22×Dic17—21no—
280C22×Dic17—21no—
281C22×Dic17—21no—
282C22×Dic17—44no—
283C22×Dic17—44no—
284C22×Dic17—44no—
285C22×Dic17—44no—
286C22×Dic17—44no—
287C22×Dic17C22×C412yes—
288C22×Dic17C22×C412yes—
289C22×Dic17C22×C412yes—
290C22×Dic17C2×D412yes—
291C22×Dic17C2×D412yes—
292C22×Dic17#4112yes—
293C22×Dic17#4112yes—
294C22×Dic17#4112yes—
295C2×C4×D17—28no—
296C2×C4×D17—44no—
297C2×C4×D17—44no—
298C2×C4×D17—44no—
299C2×C4×D17—44no—
300C2×C4×D17—44no—
301C2×C4×D17—44no—
302C22⋊C4×C17—28no—
303C22⋊C4×C17—28no—
304C22⋊C4×C17—44no—
305C42×C17—44no—
306C22⋊Dic17—28no—
307C22⋊Dic17—44no—
308#63227—28no—
309#63227—28no—
310#63227—44no—
311#63227—44no—
312#63227C22⋊C4116yescomplemented
313C4⋊Dic17—28no—
314C4⋊Dic17—28no—
315C4⋊Dic17—44no—
316C4×Dic17—44no—
317C4×Dic17—44no—
318#14096—171nomaximal, Sylow
319C23×C17—22no—
320C23×C17—22no—
321C23×C17—22no—
322C23×C17—22no—
323C23×C17—22no—
324C23×C17—22no—
325C23×C17—22no—
326C23×C17—22no—
327C23×C17—22no—
328C23×C17—22no—
329C23×C17—22no—
330C23×C17—22no—
331C23×C17—22no—
332C23×C17—22no—
333C23×C17—22no—
334C23×C17—22no—
335C23×C17—22no—
336C23×C17—22no—
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×C17C4×D414yes—
354C23×C17C23×C411yescharacteristic
355C23×C17C22×D411yescharacteristic
356C23×C17C22×D411yescharacteristic
357C23×C17C22×D411yescharacteristic
358C23×C17C2×#4111yescharacteristic
359C23×C17C2×#4111yescharacteristic
360C23×C17C2×#4111yescharacteristic
361C23×C17C2×#4111yescharacteristic
362C23×C17C2×#4111yescharacteristic
363C23×C17C2×#4111yescharacteristic
364C23×C17C2×#4111yescharacteristic
365C23×C17H(5,𝔽2)11yescharacteristic
366C23×C17H(5,𝔽2)11yescharacteristic
367C23×C17H(5,𝔽2)11yescharacteristic
368C23×C172−1+411yescharacteristic
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—22no—
384C22×D17—22no—
385C22×D17—22no—
386C22×D17—22no—
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×D17—41no—
400C22×D17—41no—
401C22×D17—41no—
402C22×D17—41no—
403C22×D17C2×C22⋊C414yes—
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—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×C17C2×C22⋊C414yes—
445C2×C4×C17#12314yescomplemented
446C22⋊D17—416no—
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—22no—
468C2×Dic17—416no—
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—41no—
490C2×Dic17—41no—
491C2×Dic17—41no—
492C2×Dic17—41no—
493C2×Dic17—41no—
494C2×Dic17—41no—
495C2×Dic17—41no—
496C2×Dic17C2×C22⋊C414yes—
497C4×D17—416no—
498C22×#123—171no—
499C2×#388—171no—
500C2×#386—171no—
501C2×C4×C22⋊C4—171no—
502C2×C4×C22⋊C4—171no—
503#1445—171no—
504#1440—171no—
505#1439—171no—
506#1438—171no—
507#1437D1711yescharacteristic, complemented
508#1436—171no—
509#1436—171no—
510C4⋊#95—171no—
511C22⋊#95—171no—
512C22⋊#95—171no—
513C22×C17—24no—
514C22×C17—24no—
515C22×C17—24no—
516C22×C17—42no—
517C22×C17—42no—
518C22×C17—42no—
519C22×C17—42no—
520C22×C17—42no—
521C22×C17—42no—
522C22×C17—42no—
523C22×C17—42no—
524C22×C17—42no—
525C22×C17—42no—
526C22×C17—42no—
527C22×C17—42no—
528C22×C17C22×C22⋊C411yescharacteristic
529C22×C17C2×C4×D411yescharacteristic
530C22×C17C4×#4111yescharacteristic
531C22×C17C4×#4111yescharacteristic
532C22×C17C4×#4111yescharacteristic
533C22×C17#51811yescharacteristic
534C22×C17#52011yescharacteristic
535C22×C17C2×#12311yescharacteristic
536C22×C17#52511yescharacteristic
537C22×C17#52511yescharacteristic
538C22×C17#52511yescharacteristic
539C22×C17#52911yescharacteristic
540C22×C17#52911yescharacteristic
541C22×C17#53211yescharacteristic
542C22×C17#53211yescharacteristic
543C22×C17#53811yescharacteristic
544C22×C17#53911yescharacteristic
545C22×C17#54011yescharacteristic
546C22×C17#54211yescharacteristic
547C22×C17D4211yescharacteristic
548C22×C17D4211yescharacteristic
549C22×C17#54611yescharacteristic
550C22×C17#54611yescharacteristic
551C22×C17#54611yescharacteristic
552C22×C17#54611yescharacteristic
553C22×C17#54611yescharacteristic
554C22×C17#54711yescharacteristic
555C22×C17#54711yescharacteristic
556C22×C17#54711yescharacteristic
557C22×C17#55111yescharacteristic
558C22×C17#55111yescharacteristic
559C22×C17#55211yescharacteristic
560C22×C17#55311yescharacteristic
561C22×C17#55311yescharacteristic
562C22×C17#55911yescharacteristic
563C2×D17—24no—
564C2×D17—24no—
565C2×D17—24no—
566C2×D17—42no—
567C2×D17—42no—
568C2×D17—42no—
569C2×D17—42no—
570C2×D17—42no—
571C2×D17—42no—
572C2×D17—42no—
573C2×D17—42no—
574C2×D17—42no—
575C2×D17—42no—
576C2×D17—42no—
577C2×D17—42no—
578C4×C17—24no—
579C4×C17—24no—
580C4×C17—42no—
581C4×C17—42no—
582C4×C17—42no—
583C4×C17—81no—
584Dic17—24no—
585Dic17—42no—
586Dic17—42no—
587Dic17—42no—
588Dic17—42no—
589Dic17—42no—
590Dic17—81no—
591C23×D4—171no—
592C24×C4—171no—
593C24×C4—171no—
594C2×#123—178no—
595C2×#123—344no—
596C2×#123—344no—
597C22×C4⋊C4—171no—
598C22×C4⋊C4—171no—
599C22×C4⋊C4—171no—
600C22×C22⋊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×C42—171no—
612C22×C42C2×D1711yescharacteristic
613#388—344no—
614#386—344no—
615C4×C22⋊C4—344no—
616C4×C22⋊C4—344no—
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×#95—171no—
626C2×#95—171no—
627C2×#95—171no—
628C2×#95—171no—
629C2×#95—171no—
630C2×#95C2×D1711yescharacteristic
631C2×#95C2×D1711yescharacteristic
632C2×#95C2×D1711yescharacteristic
633C2×C17—44no—
634C2×C17#229711yescharacteristic
635C2×C17C4×#12311yescharacteristic
636C2×C17#233511yescharacteristic
637C2×C17D4×C22⋊C411yescharacteristic
638C2×C17#233911yescharacteristic
639C2×C17#235911yescharacteristic
640C2×C17#237411yescharacteristic
641C2×C17#241811yescharacteristic
642C2×C17#242211yescharacteristic
643C2×C17#245511yescharacteristic
644C2×C17#245711yescharacteristic
645C2×C17#246411yescharacteristic
646C2×C17#247011yescharacteristic
647C2×C17#255311yescharacteristic
648C2×C17#255711yescharacteristic
649D17—44no—
650C25—171no—
651C25C22×D1711yescharacteristic
652C22×D4—174no—
653C22×D4—342no—
654C22×D4—342no—
655C22×D4—342no—
656C22×D4—342no—
657C22×D4—681no—
658C22×D4—681no—
659C23×C4—171no—
660C23×C4—171no—
661C23×C4—171no—
662C23×C4—171no—
663C23×C4—171no—
664C23×C4—171no—
665C23×C4—174no—
666C23×C4—171no—
667C23×C4—342no—
668C23×C4—342no—
669C23×C4—342no—
670C23×C4—342no—
671C23×C4—342no—
672C23×C4—342no—
673C23×C4—342no—
674C23×C4—342no—
675C23×C4—342no—
676C23×C4—681no—
677C23×C4—681no—
678C23×C4—681no—
679C23×C4—681no—
680C23×C4C22×D1711yescharacteristic
681C23×C4C22×D1711yescharacteristic
682C23×C4C22×D1711yescharacteristic
683C23×C4C22×D1711yescharacteristic
684C23×C4C22×D1711yescharacteristic
685C23×C4C22×D1711yescharacteristic
686#123—3432no—
687C2×C4⋊C4—174no—
688C2×C4⋊C4—174no—
689C2×C4⋊C4—342no—
690C2×C4⋊C4—342no—
691C2×C4⋊C4—342no—
692C2×C4⋊C4—342no—
693C2×C4⋊C4—342no—
694C2×C4⋊C4—342no—
695C2×C4⋊C4—681no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—22no—
701C2×C22⋊C4—22no—
702C2×C22⋊C4—41no—
703C2×C22⋊C4—174no—
704C2×C22⋊C4—174no—
705C2×C22⋊C4—174no—
706C2×C22⋊C4—174no—
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—342no—
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—681no—
722C2×C22⋊C4—681no—
723C2×C22⋊C4—681no—
724C2×C22⋊C4C4×D1714yescomplemented
725C2×C22⋊C4D6814yes—
726C2×C42—22no—
727C2×C42—22no—
728C2×C42—41no—
729C2×C42—342no—
730C2×C42—342no—
731C2×C42—342no—
732C2×C42—342no—
733C2×C42—681no—
734C2×C42—681no—
735#95—22no—
736#95—22no—
737#95—22no—
738#95—342no—
739#95—342no—
740#95—342no—
741#95—342no—
742#95—342no—
743#95—342no—
744#95—342no—
745#95—342no—
746#95—342no—
747#95—681no—
748#95—681no—
749#95—681no—
750#95—681no—
751C17#1409611yescharacteristic, complemented, Sylow
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—172no—
765C24—172no—
766C24—172no—
767C24—341no—
768C24—341no—
769C24—341no—
770C24—341no—
771C24—341no—
772C24—341no—
773C24—341no—
774C24—341no—
775C24—341no—
776C24—341no—
777C24—341no—
778C24—341no—
779C24C2×C4×D1712yes—
780C24C2×D6812yes—
781C24#6325212yes—
782C24C23×D1711yescharacteristic
783C2×D4—348no—
784C2×D4—348no—
785C2×D4—684no—
786C2×D4—684no—
787C2×D4—684no—
788C2×D4—684no—
789C2×D4—684no—
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—21no—
822C22×C4—21no—
823C22×C4—172no—
824C22×C4—172no—
825C22×C4—172no—
826C22×C4—172no—
827C22×C4—172no—
828C22×C4—172no—
829C22×C4—172no—
830C22×C4—172no—
831C22×C4—348no—
832C22×C4—348no—
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—341no—
865C22×C4—341no—
866C22×C4—341no—
867C22×C4—348no—
868C22×C4—341no—
869C22×C4—341no—
870C22×C4—341no—
871C22×C4—341no—
872C22×C4—341no—
873C22×C4—341no—
874C22×C4—341no—
875C22×C4—684no—
876C22×C4—684no—
877C22×C4—684no—
878C22×C4—684no—
879C22×C4—684no—
880C22×C4—684no—
881C22×C4—684no—
882C22×C4—684no—
883C22×C4—684no—
884C22×C4—684no—
885C22×C4—684no—
886C22×C4C2×C4×D1712yes—
887C22×C4C2×C4×D1712yes—
888C22×C4C2×D6812yes—
889C22×C4C2×D6812yes—
890C22×C4D4×D1712yes—
891C22×C4D4×D1712yes—
892C22×C4#6325412yes—
893C22×C4#6325412yes—
894C22×C4#6325412yes—
895C4⋊C4—348no—
896C4⋊C4—348no—
897C4⋊C4—684no—
898C22⋊C4—28no—
899C22⋊C4—28no—
900C22⋊C4—44no—
901C22⋊C4—1716no—
902C22⋊C4—348no—
903C22⋊C4—348no—
904C22⋊C4—348no—
905C22⋊C4—684no—
906C22⋊C4—684no—
907C22⋊C4—684no—
908C42—44no—
909C42—684no—
910C42—684no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
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—174no—
946C23—342no—
947C23—342no—
948C23—342no—
949C23—342no—
950C23—342no—
951C23—342no—
952C23—342no—
953C23—342no—
954C23—342no—
955C23—342no—
956C23—342no—
957C23—342no—
958C23—342no—
959C23—342no—
960C23—342no—
961C23—342no—
962C23—342no—
963C23—342no—
964C23—681no—
965C23—681no—
966C23—681no—
967C23—681no—
968C23—681no—
969C23—681no—
970C23—681no—
971C23—681no—
972C23—681no—
973C23—681no—
974C23—681no—
975C23—681no—
976C23—681no—
977C23—681no—
978C23—681no—
979C23—681no—
980C23C4×D6814yes—
981C23C22×C4×D1711yescharacteristic
982C23C22×D6811yescharacteristic
983C23C2×#6325211yescharacteristic
984C23C2×D4×D1711yescharacteristic
985C23C2×D4×D1711yescharacteristic
986C23C2×#6325411yescharacteristic
987C23C2×#6325411yescharacteristic
988C23C2×#6325411yescharacteristic
989C23#1058769111yescharacteristic
990C23#41×D1711yescharacteristic
991C23#41×D1711yescharacteristic
992C23#41×D1711yescharacteristic
993C23#1058769611yescharacteristic
994C23#1058769611yescharacteristic
995C23#1058769711yescharacteristic
996D4—6816no—
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—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
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—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—174no—
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—342no—
1058C2×C4—342no—
1059C2×C4—6816no—
1060C2×C4—6816no—
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—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×C4C22⋊C4×D1714yes—
1089C2×C4#1058757214yescomplemented
1090C22—24no—
1091C22—24no—
1092C22—24no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—344no—
1106C22—344no—
1107C22—344no—
1108C22—682no—
1109C22—682no—
1110C22—682no—
1111C22—682no—
1112C22—682no—
1113C22—682no—
1114C22—682no—
1115C22—682no—
1116C22—682no—
1117C22—682no—
1118C22—682no—
1119C22—682no—
1120C22C2×C22⋊C4×D1711yescharacteristic
1121C22C2×C4×D6811yescharacteristic
1122C22C4×#6325411yescharacteristic
1123C22C4×#6325411yescharacteristic
1124C22C4×#6325411yescharacteristic
1125C22#1176328311yescharacteristic
1126C22#1176328811yescharacteristic
1127C22C2×#1058757211yescharacteristic
1128C22#1176331911yescharacteristic
1129C22#1176331911yescharacteristic
1130C22#1176332111yescharacteristic
1131C22#1176333911yescharacteristic
1132C22#1176333911yescharacteristic
1133C22#1176335711yescharacteristic
1134C22#1176335811yescharacteristic
1135C22#1176339611yescharacteristic
1136C22#1176340011yescharacteristic
1137C22#1176341111yescharacteristic
1138C22#1176342811yescharacteristic
1139C22D4×D6811yescharacteristic
1140C22D4×D6811yescharacteristic
1141C22#1176344611yescharacteristic
1142C22#1176344811yescharacteristic
1143C22#1176345411yescharacteristic
1144C22#1176345511yescharacteristic
1145C22#1176345511yescharacteristic
1146C22#1176345711yescharacteristic
1147C22#1176345911yescharacteristic
1148C22#1176346311yescharacteristic
1149C22#1176348211yescharacteristic
1150C22#1176348511yescharacteristic
1151C22#1176349211yescharacteristic
1152C22#1176351011yescharacteristic
1153C22#1176351111yescharacteristic
1154C22#1176354111yescharacteristic
1155C4—24no—
1156C4—24no—
1157C4—42no—
1158C4—42no—
1159C4—42no—
1160C4—81no—
1161C4—344no—
1162C4—682no—
1163C4—682no—
1164C4—682no—
1165C4—682no—
1166C4—682no—
1167C4—1361no—
1168C2—44no—
1169C2—684no—
1170C2#1453127111yescharacteristic
1171C2C4×#1058757211yescharacteristic
1172C2#1453156711yescharacteristic
1173C2C22⋊C4×D6811yescharacteristic
1174C2#1453161011yescharacteristic
1175C2#1453177811yescharacteristic
1176C2#1453191411yescharacteristic
1177C2#1453224411yescharacteristic
1178C2#1453229611yescharacteristic
1179C2#1453266411yescharacteristic
1180C2#1453269611yescharacteristic
1181C2#1453278811yescharacteristic
1182C2#1453288511yescharacteristic
1183C2#1453383411yescharacteristic
1184C2#1453388811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1437C2
socle, cosocleC24×C17C24
prime radicalC23×C22⋊D17C22
hypercenter#1437D17
hypocenterC17#14096
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
2. C2×#11762701C2semidirect
4. C2×C22⋊C4×Dic17C2semidirect
5. C2×C4×#63227C2semidirect
6. #14527051C2semidirect
7. #14527032C2semidirect
8. #14527029C2semidirect
10. #14527018C2semidirect
11. #14527018C2semidirect
12. #14527014C2semidirect
13. #14527006C2semidirect
14. #14527005C2semidirect
15. C17×#1437C2semidirect
21. C2×#10587572C4semidirect
79. C23×Dic17C2×C4semidirect
101. C2×C22⋊C4×C17C2×C4semidirect
134. C2×C4⋊Dic17C2×C4semidirect
135. C2×C4⋊Dic17C2×C4semidirect
312. #63227C22⋊C4semidirect
445. C2×C4×C17#123semidirect
507. #1437D17semidirect
724. C2×C22⋊C4C4×D17semidirect
751. C17#14096semidirect
1089. C2×C4#10587572semidirect

Maximal subgroups

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

subgroupindex
C22×#105875722
C2×#117627012
C2×#117626852
C2×C22⋊C4×Dic172
C2×C4×#632272
#145270512
#145270322
#145270292
#145270232
#145270182
#145270142
#145270062
#145270052
C17×#14372
#1409617