Finite Group Databasebeta

← #16957720

Subgroups — #16957720

Order 4352.

2474 conjugacy classes of subgroups.

The subgroup lattice has 1214 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D17C211yesmaximal, characteristic
2C2×#11762709C211yesmaximal, characteristic
3C2×#11762709C211yesmaximal, characteristic
4C2×#11762706C211yesmaximal, characteristic, complemented
5C2×#11762683C211yesmaximal, characteristic, complemented
6C2×#11762682C211yesmaximal, characteristic, complemented
7C2×#11762660C211yesmaximal, characteristic, complemented
8#14527029C211yesmaximal, characteristic, complemented
9#14527028C211yesmaximal, characteristic, complemented
10#14527028C211yesmaximal, characteristic, complemented
11#14527027C211yesmaximal, characteristic, complemented
12#14527012C211yesmaximal, characteristic, complemented
13#14527012C211yesmaximal, characteristic, complemented
14#14527005C211yesmaximal, characteristic, complemented
15C17×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×C22⋊D17C2211yescharacteristic
17C23×C4×D17C2211yescharacteristic
18C2×C4×C22⋊D17—24no—
19C2×C4×C22⋊D17—24no—
20C2×C4×C22⋊D17—24no—
21C22×C4⋊Dic17C2211yescharacteristic
22C22×#63225C2211yescharacteristic
23C22×#63225C2211yescharacteristic
24C22×#63225C2211yescharacteristic
25C22×#63225C2211yescharacteristic
26C22×#63225C2211yescharacteristic
27C22×#63225C2211yescharacteristic
28C22×C22⋊Dic17C2211yescharacteristic
29C22×C22⋊Dic17C2211yescharacteristic
30C22×C22⋊Dic17C2211yescharacteristic
31C22×#63227C2211yescharacteristic
32C22×#63227C2211yescharacteristic
33C22×#63227C2211yescharacteristic
34C22×#63227C2211yescharacteristic
35C22×#63227C2211yescharacteristic
36C22×C4×Dic17C2211yescharacteristic
37C22×C4×Dic17C2211yescharacteristic
38C22×C4×Dic17C2211yescharacteristic
39#11762709—24no—
40#11762709C418yescomplemented
41#11762706—24no—
42#11762683—24no—
43#11762682—24no—
44#11762660—24no—
45C2×#10587502C2211yescharacteristic
46C2×#10587502C2211yescharacteristic
47C2×#10587502C2211yescharacteristic
48C2×#10587502C2211yescharacteristic
49C2×#10587502C2211yescharacteristic
50C2×#10587502C2211yescharacteristic
51C2×#10587502C2211yescharacteristic
52C2×#10587502C2211yescharacteristic
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⋊D17Q814yes—
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—41no—
95C22×C4×D17—41no—
96C2×C22⋊C4×C17—22no—
97C2×C22⋊C4×C17—22no—
98C2×C22⋊C4×C17—41no—
99C2×C22⋊C4×C17—41no—
100C2×C22⋊C4×C17—41no—
101C2×C22⋊C4×C17C2×C414yescomplemented
102C2×C22⋊Dic17—22no—
103C2×C22⋊Dic17—22no—
104C2×C22⋊Dic17—22no—
105C2×C22⋊Dic17—22no—
106C2×C22⋊Dic17—22no—
107C2×C22⋊Dic17—22no—
108C2×C22⋊Dic17—22no—
109C2×C22⋊Dic17—41no—
110C2×C22⋊Dic17C2×C414yescomplemented
111C4×C22⋊D17—232no—
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×#63227—41no—
124C2×#63227—41no—
125C2×#63227C2×C414yescomplemented
126C2×#63227C2×C414yescomplemented
127C2×C4⋊Dic17—22no—
128C2×C4⋊Dic17—22no—
129C2×C4⋊Dic17—41no—
130C2×#63225—22no—
131C2×#63225—22no—
132C2×#63225—22no—
133C2×#63225—22no—
134C2×#63225—22no—
135C2×#63225—22no—
136C2×#63225—22no—
137C2×#63225—22no—
138C2×#63225—22no—
139C2×#63225—22no—
140C2×#63225—22no—
141C2×#63225—22no—
142C2×#63225—22no—
143C2×#63225—22no—
144C2×#63225—41no—
145C2×#63225C2×C414yescomplemented
146C2×#63225D414yes—
147C2×#63225D414yescomplemented
148C2×C4×Dic17—22no—
149C2×C4×Dic17—22no—
150C2×C4×Dic17—22no—
151C2×C4×Dic17—22no—
152C2×C4×Dic17—22no—
153C2×C4×Dic17—22no—
154C2×C4×Dic17—22no—
155C2×C4×Dic17C2×C414yescomplemented
156C2×C4×Dic17D414yes—
157C17×#95—22no—
158C17×#95—22no—
159C17×#95—22no—
160C17×#95—41no—
161#10587502—22no—
162#10587502—22no—
163#10587502—22no—
164#10587502—22no—
165#10587502—22no—
166#10587502—41no—
167#10587502—41no—
168#10587502—41no—
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×C17—21no—
179C24×C17—21no—
180C24×C17—21no—
181C24×C17C22×C412yes—
182C24×C17C2×D412yes—
183C24×C17C2×Q812yes—
184C24×C17C2411yescharacteristic
185C23×D17—21no—
186C23×D17—21no—
187C23×D17—21no—
188C23×D17—21no—
189C23×D17—21no—
190C23×D17—21no—
191C23×D17—21no—
192C23×D17—21no—
193C23×D17—21no—
194C23×D17—21no—
195C23×D17—21no—
196C23×D17—21no—
197C23×D17C22×C412yes—
198C23×D17C2×D412yes—
199C23×D17C2×Q812yes—
200C22×C4×C17—21no—
201C22×C4×C17—21no—
202C22×C4×C17—21no—
203C22×C4×C17—21no—
204C22×C4×C17—28no—
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—21no—
234C22×C4×C17—21no—
235C22×C4×C17—21no—
236C22×C4×C17—44no—
237C22×C4×C17—44no—
238C22×C4×C17—44no—
239C22×C4×C17—44no—
240C22×C4×C17—44no—
241C22×C4×C17—44no—
242C22×C4×C17C22×C412yes—
243C22×C4×C17C22×C412yes—
244C22×C4×C17C2×D412yes—
245C22×C4×C17C2×D412yes—
246C22×C4×C17C2×D412yes—
247C22×C4×C17#4112yes—
248C22×C4×C17#4112yes—
249C2×C22⋊D17—28no—
250C2×C22⋊D17—28no—
251C2×C22⋊D17—28no—
252C2×C22⋊D17—28no—
253C2×C22⋊D17—28no—
254C2×C22⋊D17—28no—
255C2×C22⋊D17C4⋊C4116yescomplemented
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×Dic17C22×C412yes—
292C22×Dic17C22×C412yes—
293C22×Dic17C22×C412yes—
294C22×Dic17C2×D412yes—
295C22×Dic17C2×D412yes—
296C22×Dic17C2×D412yes—
297C22×Dic17C2×D412yes—
298C22×Dic17C2×D412yes—
299C22×Dic17C2×D412yes—
300C22×Dic17C2×D412yes—
301C22×Dic17C2×Q812yes—
302C22×Dic17#4112yes—
303C22×Dic17#4112yes—
304C22×Dic17#4112yes—
305C2×C4×D17—28no—
306C2×C4×D17—44no—
307C2×C4×D17—44no—
308C2×C4×D17—44no—
309C2×C4×D17—44no—
310C2×C4×D17—44no—
311C2×C4×D17—44no—
312C22⋊C4×C17—44no—
313C22⋊C4×C17—44no—
314C22⋊Dic17—28no—
315C22⋊Dic17—28no—
316C22⋊Dic17—44no—
317#63227—28no—
318#63227—28no—
319#63227—44no—
320#63227—44no—
321#63227—44no—
322C4⋊Dic17—44no—
323#63225—28no—
324#63225—28no—
325#63225—28no—
326#63225—28no—
327#63225—44no—
328#63225—44no—
329C4×Dic17—28no—
330C4×Dic17—28no—
331C4×Dic17—44no—
332#14018—171nomaximal, Sylow
333C23×C17—22no—
334C23×C17—22no—
335C23×C17—22no—
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—41no—
352C23×C17—41no—
353C23×C17—41no—
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×C17C2×C4⋊C414yes—
368C23×C17C23×C411yescharacteristic
369C23×C17C22×D411yescharacteristic
370C23×C17C22×D411yescharacteristic
371C23×C17C22×D411yescharacteristic
372C23×C17C22×D411yescharacteristic
373C23×C17C22×Q811yescharacteristic
374C23×C17C2×#4111yescharacteristic
375C23×C17C2×#4111yescharacteristic
376C23×C17C2×#4111yescharacteristic
377C23×C17C2×#4111yescharacteristic
378C23×C17C2×#4111yescharacteristic
379C23×C17H(5,𝔽2)11yescharacteristic
380C23×C17H(5,𝔽2)11yescharacteristic
381C23×C17H(5,𝔽2)11yescharacteristic
382C23×C172−1+411yescharacteristic
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—22no—
401C22×D17—41no—
402C22×D17—41no—
403C22×D17—41no—
404C22×D17—41no—
405C22×D17—41no—
406C22×D17—41no—
407C22×D17—41no—
408C22×D17—41no—
409C22×D17—41no—
410C22×D17—41no—
411C22×D17—41no—
412C22×D17—41no—
413C22×D17—41no—
414C22×D17—41no—
415C22×D17—41no—
416C22×D17—41no—
417C22×D17C2×C4⋊C414yes—
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—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—416no—
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—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#12114yes—
461C22⋊D17—232no—
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—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—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×Dic17—41no—
499C2×Dic17—41no—
500C2×Dic17—41no—
501C2×Dic17—41no—
502C2×Dic17—41no—
503C2×Dic17C2×C4⋊C414yes—
504C2×Dic17C4×D414yes—
505C2×Dic17C4×D414yes—
506C2×Dic17C4×D414yescomplemented
507C2×Dic17#12014yes—
508C2×Dic17C22⋊Q814yes—
509C2×Dic17C22⋊Q814yes—
510C2×Dic17#12314yes—
511C4×D17—416no—
512C22×C4×D4—171no—
513C2×#390—171no—
514C2×#390—171no—
515C2×#389—171no—
516C2×#385—171no—
517C2×#385—171no—
518C2×C4×C4⋊C4—171no—
519#1439—171no—
520#1439—171no—
521#1439—171no—
522#1439—171no—
523C4⋊#95—171no—
524C4⋊#95—171no—
525C22⋊#95—171no—
526C22⋊#95D1711yescharacteristic, complemented
527C22×C17—24no—
528C22×C17—24no—
529C22×C17—24no—
530C22×C17—42no—
531C22×C17—42no—
532C22×C17—42no—
533C22×C17—42no—
534C22×C17—42no—
535C22×C17—42no—
536C22×C17—42no—
537C22×C17—42no—
538C22×C17—42no—
539C22×C17—42no—
540C22×C17—42no—
541C22×C17—42no—
542C22×C17C22×C4⋊C411yescharacteristic
543C22×C17C2×C4×D411yescharacteristic
544C22×C17C2×C4×D411yescharacteristic
545C22×C17C2×C4×D411yescharacteristic
546C22×C17C4×#4111yescharacteristic
547C22×C17#51811yescharacteristic
548C22×C17#52011yescharacteristic
549C22×C17C2×#12011yescharacteristic
550C22×C17C2×#12111yescharacteristic
551C22×C17C2×C22⋊Q811yescharacteristic
552C22×C17C2×C22⋊Q811yescharacteristic
553C22×C17C2×#12311yescharacteristic
554C22×C17#52511yescharacteristic
555C22×C17#52911yescharacteristic
556C22×C17#53211yescharacteristic
557C22×C17#53511yescharacteristic
558C22×C17#53711yescharacteristic
559C22×C17#54011yescharacteristic
560C22×C17#54211yescharacteristic
561C22×C17D4211yescharacteristic
562C22×C17D4211yescharacteristic
563C22×C17#54611yescharacteristic
564C22×C17#54611yescharacteristic
565C22×C17#54611yescharacteristic
566C22×C17#54711yescharacteristic
567C22×C17#54811yescharacteristic
568C22×C17D4×Q811yescharacteristic
569C22×C17#55011yescharacteristic
570C22×C17#55011yescharacteristic
571C22×C17#55411yescharacteristic
572C22×C17#55411yescharacteristic
573C22×C17#55411yescharacteristic
574C22×C17#55611yescharacteristic
575C22×C17#55911yescharacteristic
576C22×C17#55911yescharacteristic
577C2×D17—24no—
578C2×D17—24no—
579C2×D17—24no—
580C2×D17—42no—
581C2×D17—42no—
582C2×D17—42no—
583C2×D17—42no—
584C2×D17—42no—
585C2×D17—42no—
586C2×D17—42no—
587C2×D17—42no—
588C2×D17—42no—
589C2×D17—42no—
590C2×D17—42no—
591C2×D17—42no—
592C4×C17—24no—
593C4×C17—42no—
594C4×C17—42no—
595C4×C17—42no—
596C4×C17—42no—
597C4×C17—81no—
598Dic17—24no—
599Dic17—42no—
600Dic17—42no—
601Dic17—42no—
602Dic17—42no—
603Dic17—81no—
604Dic17#38518yescomplemented
605C23×D4—171no—
606C24×C4—171no—
607C24×C4C2×D1711yescharacteristic
608C2×C4×D4—344no—
609C2×C4×D4—344no—
610C2×C4×D4—344no—
611C22×C4⋊C4—171no—
612C22×C4⋊C4—171no—
613C22×C4⋊C4—171no—
614C22×C4⋊C4—171no—
615C22×C4⋊C4—171no—
616C22×C4⋊C4—171no—
617C22×C4⋊C4—171no—
618C22×C22⋊C4—171no—
619C22×C22⋊C4—171no—
620C22×C22⋊C4—171no—
621C22×C22⋊C4—171no—
622C22×C22⋊C4—171no—
623C22×C22⋊C4—171no—
624C22×C22⋊C4—171no—
625C22×C22⋊C4—171no—
626C22×C22⋊C4C2×D1711yescharacteristic
627C22×C22⋊C4C2×D1711yescharacteristic
628C22×C42—171no—
629C22×C42—171no—
630C22×C42—171no—
631#390—178no—
632#390—344no—
633#389—344no—
634#385—344no—
635#385—344no—
636C4×C4⋊C4—344no—
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×#95C2×D1711yescharacteristic
646C2×#95C2×D1711yescharacteristic
647C2×#95C2×D1711yescharacteristic
648C2×#95C2×D1711yescharacteristic
649C2×C17—44no—
650C2×C17C2×#38511yescharacteristic
651C2×C17C4×#12111yescharacteristic
652C2×C17#232411yescharacteristic
653C2×C17D4×C4⋊C411yescharacteristic
654C2×C17#234911yescharacteristic
655C2×C17#236611yescharacteristic
656C2×C17#236711yescharacteristic
657C2×C17#240711yescharacteristic
658C2×C17#240811yescharacteristic
659C2×C17#244511yescharacteristic
660C2×C17#244711yescharacteristic
661C2×C17#245211yescharacteristic
662C2×C17#245411yescharacteristic
663C2×C17#253811yescharacteristic
664C2×C17#258011yescharacteristic
665D17—44no—
666C25—171no—
667C25C22×D1711yescharacteristic
668C22×D4—174no—
669C22×D4—174no—
670C22×D4—174no—
671C22×D4—342no—
672C22×D4—342no—
673C22×D4—342no—
674C22×D4—342no—
675C23×C4—22no—
676C23×C4—22no—
677C23×C4—22no—
678C23×C4—22no—
679C23×C4—22no—
680C23×C4—41no—
681C23×C4—41no—
682C23×C4—171no—
683C23×C4—171no—
684C23×C4—171no—
685C23×C4—171no—
686C23×C4—171no—
687C23×C4—171no—
688C23×C4—171no—
689C23×C4—342no—
690C23×C4—342no—
691C23×C4—342no—
692C23×C4—342no—
693C23×C4—342no—
694C23×C4—681no—
695C23×C4—681no—
696C23×C4C22×D1711yescharacteristic
697C23×C4C22×D1711yescharacteristic
698C23×C4C22×D1711yescharacteristic
699C23×C4C22×D1711yescharacteristic
700C23×C4C22×D1711yescharacteristic
701C23×C4C22×D1711yescharacteristic
702C4×D4—3432no—
703C2×C4⋊C4—174no—
704C2×C4⋊C4—174no—
705C2×C4⋊C4—174no—
706C2×C4⋊C4—342no—
707C2×C4⋊C4—342no—
708C2×C4⋊C4—342no—
709C2×C4⋊C4—342no—
710C2×C4⋊C4—342no—
711C2×C4⋊C4—342no—
712C2×C4⋊C4—342no—
713C2×C4⋊C4—342no—
714C2×C4⋊C4—342no—
715C2×C4⋊C4—342no—
716C2×C4⋊C4—342no—
717C2×C4⋊C4—342no—
718C2×C4⋊C4—342no—
719C2×C4⋊C4—342no—
720C2×C4⋊C4—342no—
721C2×C4⋊C4—342no—
722C2×C4⋊C4—681no—
723C2×C4⋊C4—681no—
724C2×C22⋊C4—22no—
725C2×C22⋊C4—22no—
726C2×C22⋊C4—41no—
727C2×C22⋊C4—41no—
728C2×C22⋊C4—41no—
729C2×C22⋊C4—174no—
730C2×C22⋊C4—174no—
731C2×C22⋊C4—174no—
732C2×C22⋊C4—342no—
733C2×C22⋊C4—342no—
734C2×C22⋊C4—342no—
735C2×C22⋊C4—342no—
736C2×C22⋊C4—342no—
737C2×C22⋊C4—342no—
738C2×C22⋊C4—342no—
739C2×C22⋊C4—342no—
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—681no—
749C2×C22⋊C4—681no—
750C2×C22⋊C4—681no—
751C2×C22⋊C4—681no—
752C2×C22⋊C4—681no—
753C2×C22⋊C4C4×D1714yescomplemented
754C2×C42—174no—
755C2×C42—174no—
756C2×C42—342no—
757C2×C42—342no—
758C2×C42—342no—
759C2×C42—342no—
760C2×C42—342no—
761C2×C42—342no—
762C2×C42—342no—
763#95—22no—
764#95—22no—
765#95—22no—
766#95—41no—
767#95—342no—
768#95—342no—
769#95—342no—
770#95—342no—
771#95—342no—
772#95—681no—
773#95—681no—
774#95—681no—
775C17#1401811yescharacteristic, complemented, Sylow
776C24—21no—
777C24—21no—
778C24—21no—
779C24—21no—
780C24—21no—
781C24—21no—
782C24—21no—
783C24—21no—
784C24—21no—
785C24—21no—
786C24—21no—
787C24—21no—
788C24—172no—
789C24—172no—
790C24—172no—
791C24—341no—
792C24—341no—
793C24—341no—
794C24—341no—
795C24—341no—
796C24—341no—
797C24—341no—
798C24—341no—
799C24—341no—
800C24—341no—
801C24—341no—
802C24—341no—
803C24C2×C4×D1712yes—
804C24D4×D1712yes—
805C24Q8×D1712yes—
806C24C23×D1711yescharacteristic
807C2×D4—1716no—
808C2×D4—348no—
809C2×D4—348no—
810C2×D4—348no—
811C2×D4—348no—
812C2×D4—348no—
813C2×D4—348no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—28no—
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—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—44no—
851C22×C4—44no—
852C22×C4—44no—
853C22×C4—44no—
854C22×C4—44no—
855C22×C4—44no—
856C22×C4—172no—
857C22×C4—172no—
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—172no—
867C22×C4—172no—
868C22×C4—172no—
869C22×C4—172no—
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—341no—
906C22×C4—684no—
907C22×C4—684no—
908C22×C4—684no—
909C22×C4—684no—
910C22×C4—684no—
911C22×C4—684no—
912C22×C4C2×C4×D1712yes—
913C22×C4C2×C4×D1712yes—
914C22×C4#6325212yes—
915C22×C4#6325212yes—
916C22×C4D4×D1712yes—
917C22×C4D4×D1712yes—
918C22×C4D4×D1712yes—
919C4⋊C4—348no—
920C4⋊C4—348no—
921C4⋊C4—348no—
922C4⋊C4—348no—
923C4⋊C4—684no—
924C4⋊C4—684no—
925C4⋊C4—684no—
926C22⋊C4—44no—
927C22⋊C4—44no—
928C22⋊C4—348no—
929C22⋊C4—348no—
930C22⋊C4—348no—
931C22⋊C4—348no—
932C22⋊C4—684no—
933C22⋊C4—684no—
934C22⋊C4—684no—
935C22⋊C4—684no—
936C42—348no—
937C42—348no—
938C42—684no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—174no—
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—
988C23—342no—
989C23—342no—
990C23—342no—
991C23—342no—
992C23—681no—
993C23—681no—
994C23—681no—
995C23—681no—
996C23—681no—
997C23—681no—
998C23—681no—
999C23—681no—
1000C23—681no—
1001C23—681no—
1002C23—681no—
1003C23—681no—
1004C23—681no—
1005C23—681no—
1006C23—681no—
1007C23—681no—
1008C23C4⋊C4×D1714yes—
1009C23C22×C4×D1711yescharacteristic
1010C23C2×#6325211yescharacteristic
1011C23C2×#6325211yescharacteristic
1012C23C2×D4×D1711yescharacteristic
1013C23C2×D4×D1711yescharacteristic
1014C23C2×D4×D1711yescharacteristic
1015C23C2×D4×D1711yescharacteristic
1016C23#1058769111yescharacteristic
1017C23#1058769111yescharacteristic
1018C23#1058769111yescharacteristic
1019C23C2×Q8×D1711yescharacteristic
1020C23#41×D1711yescharacteristic
1021C23#41×D1711yescharacteristic
1022C23#41×D1711yescharacteristic
1023C23#1058769711yescharacteristic
1024D4—3432no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
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—416no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
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—174no—
1068C2×C4—174no—
1069C2×C4—174no—
1070C2×C4—174no—
1071C2×C4—174no—
1072C2×C4—174no—
1073C2×C4—174no—
1074C2×C4—174no—
1075C2×C4—342no—
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—6816no—
1094C2×C4—681no—
1095C2×C4—681no—
1096C2×C4—681no—
1097C2×C4—681no—
1098C2×C4—681no—
1099C2×C4—681no—
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#1058757014yes—
1118C22—24no—
1119C22—24no—
1120C22—24no—
1121C22—42no—
1122C22—42no—
1123C22—42no—
1124C22—42no—
1125C22—42no—
1126C22—42no—
1127C22—42no—
1128C22—42no—
1129C22—42no—
1130C22—42no—
1131C22—42no—
1132C22—42no—
1133C22—344no—
1134C22—344no—
1135C22—344no—
1136C22—682no—
1137C22—682no—
1138C22—682no—
1139C22—682no—
1140C22—682no—
1141C22—682no—
1142C22—682no—
1143C22—682no—
1144C22—682no—
1145C22—682no—
1146C22—682no—
1147C22—682no—
1148C22C2×C4⋊C4×D1711yescharacteristic
1149C22C4×D4×D1711yescharacteristic
1150C22C4×D4×D1711yescharacteristic
1151C22C4×D4×D1711yescharacteristic
1152C22C4×#6325211yescharacteristic
1153C22#1176328211yescharacteristic
1154C22#1176328811yescharacteristic
1155C22#120×D1711yescharacteristic
1156C22C2×#1058757011yescharacteristic
1157C22C22⋊Q8×D1711yescharacteristic
1158C22C22⋊Q8×D1711yescharacteristic
1159C22#123×D1711yescharacteristic
1160C22#1176331811yescharacteristic
1161C22#1176333711yescharacteristic
1162C22#1176335611yescharacteristic
1163C22#1176337411yescharacteristic
1164C22#1176338811yescharacteristic
1165C22#1176340911yescharacteristic
1166C22#1176342711yescharacteristic
1167C22#1176344111yescharacteristic
1168C22#1176344111yescharacteristic
1169C22#1176344911yescharacteristic
1170C22#1176344911yescharacteristic
1171C22#1176344911yescharacteristic
1172C22#1176345711yescharacteristic
1173C22#1176346811yescharacteristic
1174C22#1176347211yescharacteristic
1175C22#1176347711yescharacteristic
1176C22#1176347711yescharacteristic
1177C22#1176351311yescharacteristic
1178C22#1176351411yescharacteristic
1179C22#1176351411yescharacteristic
1180C22#1176352711yescharacteristic
1181C22#1176354211yescharacteristic
1182C22#1176354311yescharacteristic
1183C4—24no—
1184C4—42no—
1185C4—42no—
1186C4—42no—
1187C4—42no—
1188C4—81no—
1189C4—178no—
1190C4—344no—
1191C4—682no—
1192C4—682no—
1193C4—682no—
1194C4—682no—
1195C4—1361no—
1196C2—44no—
1197C2—684no—
1198C2D17×#38511yescharacteristic
1199C2C4×#1058757011yescharacteristic
1200C2#1453147411yescharacteristic
1201C2#1453168211yescharacteristic
1202C2#1453169111yescharacteristic
1203C2#1453184711yescharacteristic
1204C2#1453185611yescharacteristic
1205C2#1453212611yescharacteristic
1206C2#1453213911yescharacteristic
1207C2#1453254611yescharacteristic
1208C2#1453257011yescharacteristic
1209C2#1453263111yescharacteristic
1210C2#1453265511yescharacteristic
1211C2#1453370811yescharacteristic
1212C2#1453414111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×C22⋊#95C2
socle, cosocleC24×C17C24
prime radicalC23×C22⋊D17C22
hypercenterC22⋊#95D17
hypocenterC17#14018
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
4. C2×#11762706C2semidirect
5. C2×#11762683C2semidirect
6. C2×#11762682C2semidirect
7. C2×#11762660C2semidirect
8. #14527029C2semidirect
9. #14527028C2semidirect
10. #14527028C2semidirect
11. #14527027C2semidirect
12. #14527012C2semidirect
13. #14527012C2semidirect
14. #14527005C2semidirect
15. C17×C22⋊#95C2semidirect
40. #11762709C4semidirect
101. C2×C22⋊C4×C17C2×C4semidirect
110. C2×C22⋊Dic17C2×C4semidirect
125. C2×#63227C2×C4semidirect
126. C2×#63227C2×C4semidirect
145. C2×#63225C2×C4semidirect
147. C2×#63225D4semidirect
155. C2×C4×Dic17C2×C4semidirect
255. C2×C22⋊D17C4⋊C4semidirect
506. C2×Dic17C4×D4semidirect
526. C22⋊#95D17semidirect
604. Dic17#385semidirect
753. C2×C22⋊C4C4×D17semidirect
775. C17#14018semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D172
C2×#117627092
C2×#117627062
C2×#117626832
C2×#117626822
C2×#117626602
#145270292
#145270282
#145270272
#145270122
#145270052
C17×C22⋊#952
#1401817