Finite Group Databasebeta

← #16957103

Subgroups — #16957103

Order 4352.

2742 conjugacy classes of subgroups.

The subgroup lattice has 1224 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587569C211yesmaximal, characteristic
2C22×C4×C22⋊D17C211yesmaximal, characteristic
3C2×#11762685C211yesmaximal, characteristic
4C2×#11762671C211yesmaximal, characteristic, complemented
5C2×#95×D17C211yesmaximal, characteristic, complemented
6#14527036C211yesmaximal, characteristic, complemented
7#14527035C211yesmaximal, characteristic, complemented
8#14527033C211yesmaximal, characteristic, complemented
9#14527031C211yesmaximal, characteristic, complemented
10#14527018C211yesmaximal, characteristic, complemented
11#14527015C211yesmaximal, characteristic, complemented
12#14527007C211yesmaximal, characteristic, complemented
13#14527005C211yesmaximal, characteristic, complemented
14#14527005C211yesmaximal, characteristic, complemented
15C17×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×C22⋊D17C2211yescharacteristic
17C23×C4×D17C2211yescharacteristic
18C23×C4×D17C2211yescharacteristic
19C23×C4×D17C2211yescharacteristic
20C2×#10587569—24no—
21C2×#10587569—24no—
22C2×#10587569C418yescomplemented
23C2×C4×C22⋊D17—24no—
24C2×C4×C22⋊D17—24no—
25C2×C4×C22⋊D17—24no—
26C22×C4⋊Dic17C2211yescharacteristic
27C22×#63225C2211yescharacteristic
28C22×#63225C2211yescharacteristic
29C22×C22⋊Dic17C2211yescharacteristic
30C22×C22⋊Dic17C2211yescharacteristic
31C22×C22⋊Dic17C2211yescharacteristic
32C22×#63227C2211yescharacteristic
33C22×#63227C2211yescharacteristic
34C22×#63227C2211yescharacteristic
35C22×C4×Dic17C2211yescharacteristic
36#11762685—24no—
37#11762671—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
51C2×#10587502C2211yescharacteristic
52#95×D17—24no—
53C24×C4×C17C2211yescharacteristic
54C22×C22⋊C4×C17C2211yescharacteristic
55C22×C22⋊C4×C17C2211yescharacteristic
56C2×C17×#95C2211yescharacteristic
57C2×C17×#95C2211yescharacteristic
58C2×C17×#95C2211yescharacteristic
59C2×C17×#95C2211yescharacteristic
60C25×C17C2311yescharacteristic
61C24×D17C2311yescharacteristic
62C23×C4×C17—22no—
63C23×C4×C17—22no—
64C23×C4×C17—22no—
65C23×C4×C17—22no—
66C23×C4×C17—22no—
67C23×C4×C17—41no—
68C23×C4×C17—41no—
69C23×C4×C17C2311yescharacteristic
70C23×C4×C17C2311yescharacteristic
71C23×C4×C17C2311yescharacteristic
72C23×C4×C17C2311yescharacteristic
73C23×C4×C17C2311yescharacteristic
74C23×C4×C17C2311yescharacteristic
75C22×C22⋊D17—22no—
76C22×C22⋊D17—22no—
77C22×C22⋊D17—22no—
78C22×C22⋊D17—22no—
79C22×C22⋊D17C2×C414yes—
80C22×C22⋊D17D414yes—
81C22×C22⋊D17D414yes—
82C23×Dic17C2311yescharacteristic
83C23×Dic17C2311yescharacteristic
84C23×Dic17C2311yescharacteristic
85C23×Dic17C2311yescharacteristic
86C23×Dic17C2311yescharacteristic
87C23×Dic17C2311yescharacteristic
88C23×Dic17C2311yescharacteristic
89C22×C4×D17—22no—
90C22×C4×D17—22no—
91C22×C4×D17—22no—
92C22×C4×D17—22no—
93C22×C4×D17—22no—
94C22×C4×D17—22no—
95C22×C4×D17—22no—
96C22×C4×D17—22no—
97C22×C4×D17—22no—
98C22×C4×D17—22no—
99C22×C4×D17—22no—
100C22×C4×D17—22no—
101C22×C4×D17—22no—
102C22×C4×D17—22no—
103C22×C4×D17—22no—
104C22×C4×D17—41no—
105C22×C4×D17—41no—
106C22×C4×D17—41no—
107C22×C4×D17—41no—
108C22×C4×D17C2×C414yescomplemented
109C22×C4×D17D414yes—
110C2×C22⋊C4×C17—22no—
111C2×C22⋊C4×C17—22no—
112C2×C22⋊C4×C17—22no—
113C2×C22⋊C4×C17—22no—
114C2×C22⋊C4×C17—41no—
115C2×C22⋊C4×C17C2×C414yescomplemented
116C2×C22⋊Dic17—22no—
117C2×C22⋊Dic17—22no—
118C2×C22⋊Dic17—22no—
119C2×C22⋊Dic17—22no—
120C2×C22⋊Dic17—22no—
121C2×C22⋊Dic17—22no—
122C2×C22⋊Dic17—22no—
123C2×C22⋊Dic17—41no—
124C2×C22⋊Dic17C2×C414yescomplemented
125C4×C22⋊D17—232no—
126C2×#63227—22no—
127C2×#63227—22no—
128C2×#63227—22no—
129C2×#63227—22no—
130C2×#63227—22no—
131C2×#63227—22no—
132C2×#63227—22no—
133C2×#63227C2×C414yescomplemented
134C2×#63227D414yes—
135C2×C4⋊Dic17—22no—
136C2×C4⋊Dic17—22no—
137C2×C4⋊Dic17C2×C414yescomplemented
138C2×#63225—22no—
139C2×#63225—22no—
140C2×#63225—22no—
141C2×#63225—22no—
142C2×#63225—22no—
143C2×#63225C2×C414yescomplemented
144C2×C4×Dic17—22no—
145C2×C4×Dic17—22no—
146C2×C4×Dic17—22no—
147#10587569—232no—
148C17×#95—22no—
149C17×#95—22no—
150C17×#95—22no—
151C17×#95—41no—
152#10587502—22no—
153#10587502—22no—
154#10587502—22no—
155#10587502—22no—
156#10587502—22no—
157#10587502—22no—
158#10587502—22no—
159#10587502—22no—
160#10587502—22no—
161#10587502—22no—
162#10587502—22no—
163#10587502—41no—
164#10587502—41no—
165#10587502—41no—
166C24×C17—21no—
167C24×C17—21no—
168C24×C17—21no—
169C24×C17—21no—
170C24×C17—21no—
171C24×C17—21no—
172C24×C17—21no—
173C24×C17—21no—
174C24×C17—21no—
175C24×C17—21no—
176C24×C17—21no—
177C24×C17—21no—
178C24×C17C22×C412yes—
179C24×C17C2×D412yes—
180C24×C17C2×D412yes—
181C24×C17C2411yescharacteristic
182C23×D17—21no—
183C23×D17—21no—
184C23×D17—21no—
185C23×D17—21no—
186C23×D17—21no—
187C23×D17—21no—
188C23×D17—21no—
189C23×D17—21no—
190C23×D17C22×C412yes—
191C23×D17C2×D412yes—
192C23×D17C2×D412yes—
193C23×D17C2×D412yes—
194C23×D17C2×D412yes—
195C23×D17#4112yes—
196C23×D17#4112yes—
197C22×C4×C17—21no—
198C22×C4×C17—21no—
199C22×C4×C17—21no—
200C22×C4×C17—21no—
201C22×C4×C17—28no—
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×C17—21no—
228C22×C4×C17—21no—
229C22×C4×C17—21no—
230C22×C4×C17—21no—
231C22×C4×C17—21no—
232C22×C4×C17—21no—
233C22×C4×C17—44no—
234C22×C4×C17—44no—
235C22×C4×C17—44no—
236C22×C4×C17—44no—
237C22×C4×C17—44no—
238C22×C4×C17—44no—
239C22×C4×C17C22×C412yes—
240C22×C4×C17C22×C412yes—
241C22×C4×C17C2×D412yes—
242C22×C4×C17C2×D412yes—
243C22×C4×C17#4112yes—
244C22×C4×C17#4112yes—
245C22×C4×C17#4112yes—
246C2×C22⋊D17—28no—
247C2×C22⋊D17—28no—
248C2×C22⋊D17—28no—
249C2×C22⋊D17—28no—
250C2×C22⋊D17—28no—
251C2×C22⋊D17—28no—
252C2×C22⋊D17C22⋊C4116yes—
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×Dic17—21no—
280C22×Dic17—21no—
281C22×Dic17—21no—
282C22×Dic17—21no—
283C22×Dic17—21no—
284C22×Dic17—21no—
285C22×Dic17—21no—
286C22×Dic17—21no—
287C22×Dic17—21no—
288C22×Dic17—21no—
289C22×Dic17—21no—
290C22×Dic17—21no—
291C22×Dic17—21no—
292C22×Dic17—21no—
293C22×Dic17—21no—
294C22×Dic17C22×C412yes—
295C22×Dic17C22×C412yes—
296C22×Dic17C22×C412yes—
297C22×Dic17C2×D412yes—
298C22×Dic17C2×D412yes—
299C22×Dic17C2×D412yes—
300C22×Dic17C2×D412yes—
301C22×Dic17#4112yes—
302C2×C4×D17—28no—
303C2×C4×D17—28no—
304C2×C4×D17—28no—
305C2×C4×D17—28no—
306C2×C4×D17—28no—
307C2×C4×D17—28no—
308C2×C4×D17—44no—
309C2×C4×D17—44no—
310C2×C4×D17—44no—
311C2×C4×D17—44no—
312C2×C4×D17—44no—
313C2×C4×D17—44no—
314C2×C4×D17—44no—
315C2×C4×D17—44no—
316C2×C4×D17—44no—
317C2×C4×D17—44no—
318C2×C4×D17—44no—
319C2×C4×D17—44no—
320C2×C4×D17—44no—
321C2×C4×D17—44no—
322C2×C4×D17—44no—
323C22⋊C4×C17—28no—
324C22⋊C4×C17—44no—
325C22⋊Dic17—28no—
326C22⋊Dic17—28no—
327C22⋊Dic17—44no—
328#63227—28no—
329#63227—28no—
330#63227—44no—
331C4⋊Dic17—28no—
332#63225—28no—
333#63225—28no—
334C4×Dic17—28no—
335#13968—171nomaximal, Sylow
336C23×C17—22no—
337C23×C17—22no—
338C23×C17—22no—
339C23×C17—22no—
340C23×C17—22no—
341C23×C17—22no—
342C23×C17—22no—
343C23×C17—22no—
344C23×C17—22no—
345C23×C17—22no—
346C23×C17—22no—
347C23×C17—22no—
348C23×C17—22no—
349C23×C17—22no—
350C23×C17—22no—
351C23×C17—22no—
352C23×C17—22no—
353C23×C17—22no—
354C23×C17—41no—
355C23×C17—41no—
356C23×C17—41no—
357C23×C17—41no—
358C23×C17—41no—
359C23×C17—41no—
360C23×C17—41no—
361C23×C17—41no—
362C23×C17—41no—
363C23×C17—41no—
364C23×C17—41no—
365C23×C17—41no—
366C23×C17—41no—
367C23×C17—41no—
368C23×C17—41no—
369C23×C17—41no—
370C23×C17C2×C22⋊C414yes—
371C23×C17C23×C411yescharacteristic
372C23×C17C22×D411yescharacteristic
373C23×C17C22×D411yescharacteristic
374C23×C17C22×D411yescharacteristic
375C23×C17C22×D411yescharacteristic
376C23×C17C2×#4111yescharacteristic
377C23×C17C2×#4111yescharacteristic
378C23×C17C2×#4111yescharacteristic
379C23×C17C2×#4111yescharacteristic
380C23×C17C2×#4111yescharacteristic
381C23×C17C2×#4111yescharacteristic
382C23×C17H(5,𝔽2)11yescharacteristic
383C23×C17H(5,𝔽2)11yescharacteristic
384C23×C172−1+411yescharacteristic
385C23×C172−1+411yescharacteristic
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—22no—
401C22×D17—22no—
402C22×D17—22no—
403C22×D17—22no—
404C22×D17—22no—
405C22×D17—22no—
406C22×D17—22no—
407C22×D17—22no—
408C22×D17—22no—
409C22×D17—22no—
410C22×D17—22no—
411C22×D17—22no—
412C22×D17—22no—
413C22×D17—22no—
414C22×D17C2×C22⋊C414yes—
415C22×D17C4×D414yes—
416C22×D17C4×D414yes—
417C22×D17#12014yes—
418C22×D17#12114yes—
419C22×D17#12114yes—
420C22×D17#12314yes—
421C2×C4×C17—22no—
422C2×C4×C17—22no—
423C2×C4×C17—22no—
424C2×C4×C17—22no—
425C2×C4×C17—22no—
426C2×C4×C17—22no—
427C2×C4×C17—22no—
428C2×C4×C17—22no—
429C2×C4×C17—22no—
430C2×C4×C17—22no—
431C2×C4×C17—22no—
432C2×C4×C17—22no—
433C2×C4×C17—22no—
434C2×C4×C17—22no—
435C2×C4×C17—22no—
436C2×C4×C17—22no—
437C2×C4×C17—22no—
438C2×C4×C17—22no—
439C2×C4×C17—416no—
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—41no—
449C2×C4×C17—41no—
450C2×C4×C17—41no—
451C2×C4×C17—41no—
452C2×C4×C17—41no—
453C2×C4×C17—41no—
454C2×C4×C17—41no—
455C2×C4×C17—41no—
456C2×C4×C17—41no—
457C2×C4×C17—41no—
458C2×C4×C17—41no—
459C2×C4×C17—41no—
460C2×C4×C17—41no—
461C2×C4×C17—41no—
462C2×C4×C17—41no—
463C2×C4×C17#12314yescomplemented
464C22⋊D17—232no—
465C2×Dic17—22no—
466C2×Dic17—22no—
467C2×Dic17—22no—
468C2×Dic17—22no—
469C2×Dic17—22no—
470C2×Dic17—22no—
471C2×Dic17—22no—
472C2×Dic17—22no—
473C2×Dic17—22no—
474C2×Dic17—22no—
475C2×Dic17—22no—
476C2×Dic17—22no—
477C2×Dic17—22no—
478C2×Dic17—22no—
479C2×Dic17—22no—
480C2×Dic17—22no—
481C2×Dic17—22no—
482C2×Dic17—22no—
483C2×Dic17—22no—
484C2×Dic17—22no—
485C2×Dic17—22no—
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×Dic17—41no—
499C2×Dic17—41no—
500C2×Dic17—41no—
501C2×Dic17—41no—
502C2×Dic17—41no—
503C2×Dic17—41no—
504C2×Dic17—41no—
505C2×Dic17—41no—
506C2×Dic17—41no—
507C2×Dic17—41no—
508C2×Dic17—41no—
509C2×Dic17—41no—
510C2×Dic17—41no—
511C2×Dic17—41no—
512C2×Dic17—41no—
513C2×Dic17C2×C22⋊C414yes—
514C4×D17—416no—
515C4×D17—416no—
516C4×D17—416no—
517C22×#123—171no—
518C22×C4×D4—171no—
519C2×#386—171no—
520C2×#381—171no—
521C22×#95—171no—
522#1441—171no—
523#1441—171no—
524#1440—171no—
525#1440—171no—
526#1436—171no—
527#1436—171no—
528C22⋊#95—171no—
529C22⋊#95—171no—
530C22⋊#95—171no—
531C22⋊#95D1711yescharacteristic, complemented
532C22×C17—24no—
533C22×C17—24no—
534C22×C17—24no—
535C22×C17—42no—
536C22×C17—42no—
537C22×C17—42no—
538C22×C17—42no—
539C22×C17—42no—
540C22×C17—42no—
541C22×C17—42no—
542C22×C17—42no—
543C22×C17—42no—
544C22×C17—42no—
545C22×C17—42no—
546C22×C17—42no—
547C22×C17C22×C22⋊C411yescharacteristic
548C22×C17C2×C4×D411yescharacteristic
549C22×C17C2×C4×D411yescharacteristic
550C22×C17C4×#4111yescharacteristic
551C22×C17C4×#4111yescharacteristic
552C22×C17#52011yescharacteristic
553C22×C17#52011yescharacteristic
554C22×C17C2×#12011yescharacteristic
555C22×C17C2×#12111yescharacteristic
556C22×C17C2×#12111yescharacteristic
557C22×C17C2×#12311yescharacteristic
558C22×C17C2×#12311yescharacteristic
559C22×C17#52511yescharacteristic
560C22×C17#52911yescharacteristic
561C22×C17#52911yescharacteristic
562C22×C17#53411yescharacteristic
563C22×C17#53611yescharacteristic
564C22×C17#53911yescharacteristic
565C22×C17#53911yescharacteristic
566C22×C17#54611yescharacteristic
567C22×C17#54611yescharacteristic
568C22×C17#54611yescharacteristic
569C22×C17#54611yescharacteristic
570C22×C17#54611yescharacteristic
571C22×C17#54611yescharacteristic
572C22×C17#54711yescharacteristic
573C22×C17#54711yescharacteristic
574C22×C17#54711yescharacteristic
575C22×C17#54711yescharacteristic
576C22×C17#54711yescharacteristic
577C22×C17#54711yescharacteristic
578C22×C17#55111yescharacteristic
579C22×C17#55111yescharacteristic
580C22×C17#55211yescharacteristic
581C22×C17#55211yescharacteristic
582C2×D17—24no—
583C2×D17—24no—
584C2×D17—24no—
585C2×D17—24no—
586C2×D17—24no—
587C2×D17—24no—
588C2×D17—24no—
589C2×D17—24no—
590C2×D17—24no—
591C2×D17—24no—
592C2×D17—24no—
593C2×D17—24no—
594C2×D17—24no—
595C2×D17—24no—
596C2×D17#38618yes—
597C4×C17—24no—
598C4×C17—42no—
599C4×C17—42no—
600C4×C17—42no—
601C4×C17—42no—
602C4×C17—81no—
603Dic17—24no—
604Dic17—42no—
605Dic17—42no—
606Dic17—42no—
607Dic17—42no—
608Dic17—42no—
609Dic17—81no—
610C23×D4—171no—
611C24×C4—171no—
612C24×C4—171no—
613C24×C4—171no—
614C24×C4C2×D1711yescharacteristic
615C2×#123—178no—
616C2×#123—344no—
617C2×#123—344no—
618C2×C4×D4—344no—
619C2×C4×D4—344no—
620C2×C4×D4—344no—
621C22×C4⋊C4—171no—
622C22×C4⋊C4—171no—
623C22×C4⋊C4—171no—
624C22×C22⋊C4—171no—
625C22×C22⋊C4—171no—
626C22×C22⋊C4—171no—
627C22×C22⋊C4—171no—
628C22×C22⋊C4—171no—
629C22×C22⋊C4—171no—
630C22×C22⋊C4C2×D1711yescharacteristic
631C22×C22⋊C4C2×D1711yescharacteristic
632C22×C42—171no—
633#386—344no—
634#381—344no—
635C2×#95—171no—
636C2×#95—171no—
637C2×#95—171no—
638C2×#95—171no—
639C2×#95—171no—
640C2×#95—171no—
641C2×#95—171no—
642C2×#95—171no—
643C2×#95—171no—
644C2×#95—171no—
645C2×#95—171no—
646C2×#95—171no—
647C2×#95—171no—
648C2×#95—171no—
649C2×#95—344no—
650C2×#95C2×D1711yescharacteristic
651C2×#95C2×D1711yescharacteristic
652C2×#95C2×D1711yescharacteristic
653C2×#95C2×D1711yescharacteristic
654C2×C17—44no—
655C2×C17C2×#38611yescharacteristic
656C2×C17C4×#12311yescharacteristic
657C2×C17#232211yescharacteristic
658C2×C17#233911yescharacteristic
659C2×C17#233911yescharacteristic
660C2×C17#235911yescharacteristic
661C2×C17#235911yescharacteristic
662C2×C17#240511yescharacteristic
663C2×C17#240611yescharacteristic
664C2×C17#241911yescharacteristic
665C2×C17#241911yescharacteristic
666C2×C17#242511yescharacteristic
667C2×C17#242511yescharacteristic
668C2×C17#248611yescharacteristic
669C2×C17#253411yescharacteristic
670D17—28no—
671C25—171no—
672C25C22×D1711yescharacteristic
673C22×D4—174no—
674C22×D4—174no—
675C22×D4—174no—
676C22×D4—342no—
677C22×D4—342no—
678C22×D4—342no—
679C22×D4—342no—
680C23×C4—22no—
681C23×C4—22no—
682C23×C4—22no—
683C23×C4—22no—
684C23×C4—22no—
685C23×C4—41no—
686C23×C4—41no—
687C23×C4—171no—
688C23×C4—171no—
689C23×C4—171no—
690C23×C4—171no—
691C23×C4—171no—
692C23×C4—171no—
693C23×C4—174no—
694C23×C4—174no—
695C23×C4—171no—
696C23×C4—342no—
697C23×C4—342no—
698C23×C4—342no—
699C23×C4—342no—
700C23×C4—342no—
701C23×C4—342no—
702C23×C4—342no—
703C23×C4—342no—
704C23×C4—342no—
705C23×C4—342no—
706C23×C4—342no—
707C23×C4—342no—
708C23×C4—342no—
709C23×C4—342no—
710C23×C4—342no—
711C23×C4—681no—
712C23×C4—681no—
713C23×C4—681no—
714C23×C4—681no—
715C23×C4C22×D1711yescharacteristic
716C23×C4C22×D1711yescharacteristic
717C23×C4C22×D1711yescharacteristic
718C23×C4C22×D1711yescharacteristic
719C23×C4C22×D1711yescharacteristic
720C23×C4C22×D1711yescharacteristic
721#123—3432no—
722C4×D4—3432no—
723C2×C4⋊C4—174no—
724C2×C4⋊C4—174no—
725C2×C4⋊C4—342no—
726C2×C4⋊C4—342no—
727C2×C4⋊C4—342no—
728C2×C4⋊C4—342no—
729C2×C4⋊C4—342no—
730C2×C4⋊C4—342no—
731C2×C4⋊C4—342no—
732C2×C22⋊C4—22no—
733C2×C22⋊C4—22no—
734C2×C22⋊C4—22no—
735C2×C22⋊C4—22no—
736C2×C22⋊C4—41no—
737C2×C22⋊C4—174no—
738C2×C22⋊C4—174no—
739C2×C22⋊C4—174no—
740C2×C22⋊C4—342no—
741C2×C22⋊C4—342no—
742C2×C22⋊C4—342no—
743C2×C22⋊C4—342no—
744C2×C22⋊C4—342no—
745C2×C22⋊C4—342no—
746C2×C22⋊C4—342no—
747C2×C22⋊C4—342no—
748C2×C22⋊C4—342no—
749C2×C22⋊C4—342no—
750C2×C22⋊C4—342no—
751C2×C22⋊C4—342no—
752C2×C22⋊C4—342no—
753C2×C22⋊C4—342no—
754C2×C22⋊C4—681no—
755C2×C22⋊C4C4×D1714yescomplemented
756C2×C42—342no—
757C2×C42—342no—
758C2×C42—342no—
759#95—22no—
760#95—22no—
761#95—22no—
762#95—41no—
763#95—342no—
764#95—342no—
765#95—342no—
766#95—342no—
767#95—342no—
768#95—342no—
769#95—342no—
770#95—342no—
771#95—342no—
772#95—342no—
773#95—342no—
774#95—681no—
775#95—681no—
776#95—681no—
777C17#1396811yescharacteristic, complemented, Sylow
778C24—21no—
779C24—21no—
780C24—21no—
781C24—21no—
782C24—21no—
783C24—21no—
784C24—21no—
785C24—21no—
786C24—21no—
787C24—21no—
788C24—21no—
789C24—21no—
790C24—172no—
791C24—172no—
792C24—172no—
793C24—172no—
794C24—172no—
795C24—172no—
796C24—172no—
797C24—341no—
798C24—341no—
799C24—341no—
800C24—341no—
801C24—341no—
802C24—341no—
803C24—341no—
804C24—341no—
805C24C2×C4×D1712yes—
806C24D4×D1712yes—
807C24D4×D1712yes—
808C24C23×D1711yescharacteristic
809C2×D4—1716no—
810C2×D4—348no—
811C2×D4—348no—
812C2×D4—348no—
813C2×D4—348no—
814C2×D4—348no—
815C2×D4—348no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—28no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—44no—
853C22×C4—44no—
854C22×C4—44no—
855C22×C4—44no—
856C22×C4—44no—
857C22×C4—44no—
858C22×C4—172no—
859C22×C4—172no—
860C22×C4—172no—
861C22×C4—172no—
862C22×C4—172no—
863C22×C4—172no—
864C22×C4—172no—
865C22×C4—172no—
866C22×C4—348no—
867C22×C4—348no—
868C22×C4—348no—
869C22×C4—348no—
870C22×C4—348no—
871C22×C4—341no—
872C22×C4—341no—
873C22×C4—341no—
874C22×C4—341no—
875C22×C4—341no—
876C22×C4—341no—
877C22×C4—341no—
878C22×C4—341no—
879C22×C4—341no—
880C22×C4—341no—
881C22×C4—341no—
882C22×C4—341no—
883C22×C4—341no—
884C22×C4—341no—
885C22×C4—341no—
886C22×C4—341no—
887C22×C4—341no—
888C22×C4—341no—
889C22×C4—341no—
890C22×C4—341no—
891C22×C4—341no—
892C22×C4—341no—
893C22×C4—341no—
894C22×C4—341no—
895C22×C4—341no—
896C22×C4—341no—
897C22×C4—341no—
898C22×C4—341no—
899C22×C4—341no—
900C22×C4—341no—
901C22×C4—341no—
902C22×C4—341no—
903C22×C4—341no—
904C22×C4—341no—
905C22×C4—348no—
906C22×C4—341no—
907C22×C4—341no—
908C22×C4—341no—
909C22×C4—341no—
910C22×C4—341no—
911C22×C4—341no—
912C22×C4—341no—
913C22×C4—684no—
914C22×C4—684no—
915C22×C4—684no—
916C22×C4—684no—
917C22×C4—684no—
918C22×C4—684no—
919C22×C4—684no—
920C22×C4—684no—
921C22×C4—684no—
922C22×C4—684no—
923C22×C4—684no—
924C22×C4—684no—
925C22×C4—684no—
926C22×C4—684no—
927C22×C4—684no—
928C22×C4C2×C4×D1712yes—
929C22×C4C2×C4×D1712yes—
930C22×C4#6325212yes—
931C22×C4#6325212yes—
932C22×C4D4×D1712yes—
933C22×C4D4×D1712yes—
934C22×C4#6325412yes—
935C4⋊C4—348no—
936C4⋊C4—348no—
937C4⋊C4—348no—
938C22⋊C4—28no—
939C22⋊C4—44no—
940C22⋊C4—348no—
941C22⋊C4—348no—
942C22⋊C4—348no—
943C22⋊C4—348no—
944C22⋊C4—684no—
945C22⋊C4—684no—
946C42—348no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23—174no—
982C23—174no—
983C23—174no—
984C23—174no—
985C23—174no—
986C23—174no—
987C23—174no—
988C23—342no—
989C23—342no—
990C23—342no—
991C23—342no—
992C23—342no—
993C23—342no—
994C23—342no—
995C23—342no—
996C23—342no—
997C23—342no—
998C23—342no—
999C23—342no—
1000C23—342no—
1001C23—342no—
1002C23—342no—
1003C23—342no—
1004C23—342no—
1005C23—342no—
1006C23—342no—
1007C23—342no—
1008C23—342no—
1009C23—342no—
1010C23—342no—
1011C23—342no—
1012C23—342no—
1013C23—342no—
1014C23—342no—
1015C23—342no—
1016C23C22⋊C4×D1714yes—
1017C23C22×C4×D1711yescharacteristic
1018C23C2×#6325211yescharacteristic
1019C23C2×#6325211yescharacteristic
1020C23C2×D4×D1711yescharacteristic
1021C23C2×D4×D1711yescharacteristic
1022C23C2×D4×D1711yescharacteristic
1023C23C2×D4×D1711yescharacteristic
1024C23C2×#6325411yescharacteristic
1025C23#1058769111yescharacteristic
1026C23#1058769111yescharacteristic
1027C23#1058769411yescharacteristic
1028C23#41×D1711yescharacteristic
1029C23#41×D1711yescharacteristic
1030C23#41×D1711yescharacteristic
1031C23#1058769711yescharacteristic
1032D4—3432no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—416no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—174no—
1076C2×C4—342no—
1077C2×C4—342no—
1078C2×C4—342no—
1079C2×C4—342no—
1080C2×C4—342no—
1081C2×C4—342no—
1082C2×C4—342no—
1083C2×C4—342no—
1084C2×C4—342no—
1085C2×C4—342no—
1086C2×C4—342no—
1087C2×C4—342no—
1088C2×C4—342no—
1089C2×C4—342no—
1090C2×C4—342no—
1091C2×C4—342no—
1092C2×C4—342no—
1093C2×C4—342no—
1094C2×C4—342no—
1095C2×C4—342no—
1096C2×C4—342no—
1097C2×C4—6816no—
1098C2×C4—6816no—
1099C2×C4—6816no—
1100C2×C4—681no—
1101C2×C4—681no—
1102C2×C4—681no—
1103C2×C4—681no—
1104C2×C4—681no—
1105C2×C4—681no—
1106C2×C4—681no—
1107C2×C4—681no—
1108C2×C4—681no—
1109C2×C4—681no—
1110C2×C4—681no—
1111C2×C4—681no—
1112C2×C4—681no—
1113C2×C4—681no—
1114C2×C4—681no—
1115C2×C4—681no—
1116C2×C4—681no—
1117C2×C4—681no—
1118C2×C4—681no—
1119C2×C4—681no—
1120C2×C4—681no—
1121C2×C4—681no—
1122C2×C4—681no—
1123C2×C4—681no—
1124C2×C4—681no—
1125C2×C4—681no—
1126C2×C4—681no—
1127C2×C4#1058756914yescomplemented
1128C22—24no—
1129C22—24no—
1130C22—24no—
1131C22—42no—
1132C22—42no—
1133C22—42no—
1134C22—42no—
1135C22—42no—
1136C22—42no—
1137C22—42no—
1138C22—42no—
1139C22—42no—
1140C22—42no—
1141C22—42no—
1142C22—42no—
1143C22—178no—
1144C22—344no—
1145C22—344no—
1146C22—344no—
1147C22—344no—
1148C22—344no—
1149C22—344no—
1150C22—344no—
1151C22—344no—
1152C22—344no—
1153C22—344no—
1154C22—344no—
1155C22—344no—
1156C22—344no—
1157C22—344no—
1158C22C2×C22⋊C4×D1711yescharacteristic
1159C22C4×D4×D1711yescharacteristic
1160C22C4×D4×D1711yescharacteristic
1161C22C4×#6325411yescharacteristic
1162C22C4×#6325211yescharacteristic
1163C22#1176328811yescharacteristic
1164C22#1176329011yescharacteristic
1165C22#120×D1711yescharacteristic
1166C22#121×D1711yescharacteristic
1167C22#121×D1711yescharacteristic
1168C22#123×D1711yescharacteristic
1169C22C2×#1058756911yescharacteristic
1170C22#1176331811yescharacteristic
1171C22#1176333711yescharacteristic
1172C22#1176334111yescharacteristic
1173C22#1176336911yescharacteristic
1174C22#1176338211yescharacteristic
1175C22#1176340211yescharacteristic
1176C22#1176340511yescharacteristic
1177C22#1176344611yescharacteristic
1178C22#1176344611yescharacteristic
1179C22#1176344811yescharacteristic
1180C22#1176344911yescharacteristic
1181C22#1176344911yescharacteristic
1182C22#1176344911yescharacteristic
1183C22#1176345711yescharacteristic
1184C22#1176345911yescharacteristic
1185C22#1176346011yescharacteristic
1186C22#1176346011yescharacteristic
1187C22#1176346111yescharacteristic
1188C22#1176346411yescharacteristic
1189C22#1176348711yescharacteristic
1190C22#1176348811yescharacteristic
1191C22#1176349311yescharacteristic
1192C22#1176349811yescharacteristic
1193C4—24no—
1194C4—42no—
1195C4—42no—
1196C4—42no—
1197C4—42no—
1198C4—81no—
1199C4—344no—
1200C4—682no—
1201C4—682no—
1202C4—682no—
1203C4—682no—
1204C4—682no—
1205C4—1361no—
1206C2—44no—
1207C2—348no—
1208C2D17×#38611yescharacteristic
1209C2C4×#1058756911yescharacteristic
1210C2#1453145111yescharacteristic
1211C2#1453161011yescharacteristic
1212C2#1453161111yescharacteristic
1213C2#1453177711yescharacteristic
1214C2#1453177911yescharacteristic
1215C2#1453210911yescharacteristic
1216C2#1453211711yescharacteristic
1217C2#1453225811yescharacteristic
1218C2#1453226011yescharacteristic
1219C2#1453233211yescharacteristic
1220C2#1453233411yescharacteristic
1221C2#1453308811yescharacteristic
1222C2#1453367211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×C22⋊#95C2
socle, cosocleC24×C17C24
prime radicalC23×C22⋊D17C22
hypercenterC22⋊#95D17
hypocenterC17#13968
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
4. C2×#11762671C2semidirect
5. C2×#95×D17C2semidirect
6. #14527036C2semidirect
7. #14527035C2semidirect
8. #14527033C2semidirect
9. #14527031C2semidirect
10. #14527018C2semidirect
11. #14527015C2semidirect
12. #14527007C2semidirect
13. #14527005C2semidirect
14. #14527005C2semidirect
15. C17×C22⋊#95C2semidirect
22. C2×#10587569C4semidirect
108. C22×C4×D17C2×C4semidirect
115. C2×C22⋊C4×C17C2×C4semidirect
124. C2×C22⋊Dic17C2×C4semidirect
133. C2×#63227C2×C4semidirect
137. C2×C4⋊Dic17C2×C4semidirect
143. C2×#63225C2×C4semidirect
463. C2×C4×C17#123semidirect
531. C22⋊#95D17semidirect
755. C2×C22⋊C4C4×D17semidirect
777. C17#13968semidirect
1127. C2×C4#10587569semidirect

Maximal subgroups

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

subgroupindex
C22×#105875692
C22×C4×C22⋊D172
C2×#117626852
C2×#117626712
C2×#95×D172
#145270362
#145270352
#145270332
#145270312
#145270182
#145270152
#145270072
#145270052
C17×C22⋊#952
#1396817