Finite Group Databasebeta

← #16957814

Subgroups — #16957814

Order 4352.

2574 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×#10587571C211yesmaximal, characteristic
2C22×C4×C22⋊D17C211yesmaximal, characteristic
3C2×#11762713C211yesmaximal, characteristic, complemented
4C2×#11762713C211yesmaximal, characteristic, complemented
5C2×#11762709C211yesmaximal, characteristic
6#14527033C211yesmaximal, characteristic, complemented
7#14527032C211yesmaximal, characteristic, complemented
8#14527032C211yesmaximal, characteristic, complemented
9#14527031C211yesmaximal, characteristic, complemented
10#14527012C211yesmaximal, characteristic, complemented
11#14527007C211yesmaximal, characteristic, complemented
12#14527005C211yesmaximal, characteristic, complemented
13#14527005C211yesmaximal, characteristic, complemented
14#95×Dic17C211yesmaximal, characteristic, complemented
15C17×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×Dic34C2211yescharacteristic
17C23×C22⋊D17C2211yescharacteristic
18C23×C4×D17C2211yescharacteristic
19C2×#10587571—24no—
20C2×#10587571—24no—
21C2×#10587571C418yescomplemented
22C2×C4×C22⋊D17—24no—
23C2×C4×C22⋊D17—24no—
24C2×C4×C22⋊D17—24no—
25C22×#63225C2211yescharacteristic
26C22×#63225C2211yescharacteristic
27C22×C22⋊Dic17C2211yescharacteristic
28C22×C22⋊Dic17C2211yescharacteristic
29C22×C22⋊Dic17C2211yescharacteristic
30C22×#63227C2211yescharacteristic
31C22×#63227C2211yescharacteristic
32C22×#63227C2211yescharacteristic
33C22×#63227C2211yescharacteristic
34C22×#63227C2211yescharacteristic
35C22×C4×Dic17C2211yescharacteristic
36C22×C4×Dic17C2211yescharacteristic
37C22×C4×Dic17C2211yescharacteristic
38#11762713—24no—
39#11762713—24no—
40#11762709—24no—
41C2×#10587502C2211yescharacteristic
42C2×#10587502C2211yescharacteristic
43C2×#10587502C2211yescharacteristic
44C2×#10587502C2211yescharacteristic
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⋊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—41no—
95C22×C4×D17—41no—
96C22×Dic34—22no—
97C22×Dic34—22no—
98C22×Dic34—22no—
99C22×Dic34—22no—
100C22×Dic34—22no—
101C22×Dic34—22no—
102C22×Dic34C2×C414yescomplemented
103C2×C22⋊C4×C17—22no—
104C2×C22⋊C4×C17—22no—
105C2×C22⋊C4×C17—22no—
106C2×C22⋊C4×C17—22no—
107C2×C22⋊C4×C17—41no—
108C2×C22⋊C4×C17C2×C414yescomplemented
109C2×C22⋊Dic17—22no—
110C2×C22⋊Dic17—22no—
111C2×C22⋊Dic17—22no—
112C2×C22⋊Dic17—22no—
113C2×C22⋊Dic17—22no—
114C2×C22⋊Dic17—22no—
115C2×C22⋊Dic17—22no—
116C2×C22⋊Dic17—41no—
117C2×C22⋊Dic17C2×C414yescomplemented
118C4×C22⋊D17—232no—
119C2×#63227—22no—
120C2×#63227—22no—
121C2×#63227—22no—
122C2×#63227—22no—
123C2×#63227—22no—
124C2×#63227—22no—
125C2×#63227—22no—
126C2×#63227—22no—
127C2×#63227—22no—
128C2×#63227—22no—
129C2×#63227—22no—
130C2×#63227—41no—
131C2×#63227—41no—
132C2×#63227C2×C414yescomplemented
133C2×#63227C2×C414yescomplemented
134C2×#63225—22no—
135C2×#63225—22no—
136C2×#63225—22no—
137C2×#63225—22no—
138C2×#63225—22no—
139C2×#63225D414yes—
140C2×C4×Dic17—22no—
141C2×C4×Dic17—22no—
142C2×C4×Dic17—22no—
143C2×C4×Dic17—22no—
144C2×C4×Dic17—22no—
145C2×C4×Dic17—22no—
146C2×C4×Dic17—22no—
147C2×C4×Dic17C2×C414yescomplemented
148C2×C4×Dic17D414yes—
149#10587571—232no—
150C17×#95—22no—
151C17×#95—22no—
152C17×#95—22no—
153C17×#95—41no—
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×D17—21no—
191C23×D17—21no—
192C23×D17—21no—
193C23×D17—21no—
194C23×D17C22×C412yes—
195C23×D17C2×D412yes—
196C23×D17C2×D412yes—
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×Dic17C22×C412yes—
291C22×Dic17C22×C412yes—
292C22×Dic17C22×C412yes—
293C22×Dic17C2×D412yes—
294C22×Dic17C2×D412yes—
295C22×Dic17C2×D412yes—
296C22×Dic17C2×D412yes—
297C22×Dic17C2×D412yes—
298C22×Dic17C2×D412yes—
299C22×Dic17#4112yes—
300C22×Dic17#4112yes—
301C22×Dic17#4112yes—
302C2×C4×D17—28no—
303C2×C4×D17—44no—
304C2×C4×D17—44no—
305C2×C4×D17—44no—
306C2×C4×D17—44no—
307C2×C4×D17—44no—
308C2×C4×D17—44no—
309C2×Dic34—28no—
310C2×Dic34—28no—
311C2×Dic34—28no—
312C2×Dic34—44no—
313C2×Dic34—44no—
314C2×Dic34—44no—
315C2×Dic34—44no—
316C22⋊C4×C17—28no—
317C22⋊C4×C17—44no—
318C22⋊Dic17—28no—
319C22⋊Dic17—28no—
320C22⋊Dic17—44no—
321#63227—28no—
322#63227—28no—
323#63227—28no—
324#63227—44no—
325#63227—44no—
326#63225—28no—
327#63225—44no—
328C4×Dic17—28no—
329C4×Dic17—28no—
330C4×Dic17—44no—
331#14027—171nomaximal, Sylow
332C23×C17—22no—
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—41no—
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×C17C2×C22⋊C414yes—
367C23×C17C23×C411yescharacteristic
368C23×C17C22×D411yescharacteristic
369C23×C17C22×D411yescharacteristic
370C23×C17C22×D411yescharacteristic
371C23×C17C22×D411yescharacteristic
372C23×C17C2×#4111yescharacteristic
373C23×C17C2×#4111yescharacteristic
374C23×C17C2×#4111yescharacteristic
375C23×C17C2×#4111yescharacteristic
376C23×C17C2×#4111yescharacteristic
377C23×C17C2×#4111yescharacteristic
378C23×C17H(5,𝔽2)11yescharacteristic
379C23×C17H(5,𝔽2)11yescharacteristic
380C23×C172−1+411yescharacteristic
381C23×C172−1+411yescharacteristic
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—41no—
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×D17C2×C22⋊C414yes—
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—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—416no—
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—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#12414yescomplemented
460C22⋊D17—232no—
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—22no—
472C2×Dic17—22no—
473C2×Dic17—22no—
474C2×Dic17—22no—
475C2×Dic17—22no—
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×Dic17—41no—
499C2×Dic17—41no—
500C2×Dic17—41no—
501C2×Dic17—41no—
502C2×Dic17—41no—
503C2×Dic17C2×C22⋊C414yes—
504C2×Dic17C4×D414yes—
505C2×Dic17C4×D414yes—
506C2×Dic17#12014yes—
507C2×Dic17#12114yes—
508C2×Dic17#12114yes—
509C2×Dic17#12314yes—
510C4×D17—416no—
511Dic34—416no—
512C22×#124—171no—
513C22×C4×D4—171no—
514C2×#391—171no—
515C2×#391—171no—
516C2×#390—171no—
517#1440—171no—
518#1440—171no—
519#1440—171no—
520#1440—171no—
521C4⋊#95—171no—
522C22⋊#95—171no—
523C22⋊#95—171no—
524C22⋊#95—171no—
525C22⋊#95D1711yescharacteristic, complemented
526C4×#95—171no—
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×C22⋊C411yescharacteristic
543C22×C17C2×C4×D411yescharacteristic
544C22×C17C2×C4×D411yescharacteristic
545C22×C17C4×#4111yescharacteristic
546C22×C17C4×#4111yescharacteristic
547C22×C17#52011yescharacteristic
548C22×C17#52011yescharacteristic
549C22×C17C2×#12011yescharacteristic
550C22×C17C2×#12111yescharacteristic
551C22×C17C2×#12111yescharacteristic
552C22×C17C2×#12311yescharacteristic
553C22×C17C2×#12411yescharacteristic
554C22×C17#52911yescharacteristic
555C22×C17#52911yescharacteristic
556C22×C17#53211yescharacteristic
557C22×C17#53511yescharacteristic
558C22×C17#53611yescharacteristic
559C22×C17#54211yescharacteristic
560C22×C17#54211yescharacteristic
561C22×C17#54611yescharacteristic
562C22×C17#54611yescharacteristic
563C22×C17#54611yescharacteristic
564C22×C17#54611yescharacteristic
565C22×C17#54611yescharacteristic
566C22×C17#54611yescharacteristic
567C22×C17#54711yescharacteristic
568C22×C17#54711yescharacteristic
569C22×C17#54711yescharacteristic
570C22×C17#54711yescharacteristic
571C22×C17#54811yescharacteristic
572C22×C17#54811yescharacteristic
573C22×C17#55611yescharacteristic
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—42no—
599Dic17—42no—
600Dic17—42no—
601Dic17—42no—
602Dic17—42no—
603Dic17—81no—
604Dic17#38618yes—
605C23×Q8—171no—
606C23×D4—171no—
607C24×C4—171no—
608C24×C4C2×D1711yescharacteristic
609C2×#124—178no—
610C2×#124—344no—
611C2×#124—344no—
612C2×C4×D4—344no—
613C2×C4×D4—344no—
614C2×C4×D4—344no—
615C22×C4⋊C4—171no—
616C22×C4⋊C4—171no—
617C22×C22⋊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⋊C4C2×D1711yescharacteristic
626C22×C22⋊C4C2×D1711yescharacteristic
627C22×C42—171no—
628C22×C42—171no—
629C22×C42—171no—
630#391—344no—
631#391—344no—
632#390—344no—
633C2×#95—171no—
634C2×#95—171no—
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×#95C2×D1711yescharacteristic
646C2×#95C2×D1711yescharacteristic
647C2×#95C2×D1711yescharacteristic
648C2×#95C2×D1711yescharacteristic
649C2×C17—44no—
650C2×C17C2×#38611yescharacteristic
651C2×C17C4×#12411yescharacteristic
652C2×C17#232611yescharacteristic
653C2×C17#233911yescharacteristic
654C2×C17#233911yescharacteristic
655C2×C17#236711yescharacteristic
656C2×C17#236711yescharacteristic
657C2×C17#242711yescharacteristic
658C2×C17#242711yescharacteristic
659C2×C17#243211yescharacteristic
660C2×C17#243511yescharacteristic
661C2×C17#244711yescharacteristic
662C2×C17#244711yescharacteristic
663C2×C17#254411yescharacteristic
664C2×C17#254711yescharacteristic
665D17—44no—
666C25—171no—
667C25C22×D1711yescharacteristic
668C22×Q8—174no—
669C22×Q8—342no—
670C22×Q8—342no—
671C22×Q8—342no—
672C22×Q8—342no—
673C22×Q8—342no—
674C22×Q8—342no—
675C22×D4—174no—
676C22×D4—174no—
677C22×D4—174no—
678C22×D4—342no—
679C22×D4—342no—
680C22×D4—342no—
681C22×D4—342no—
682C23×C4—22no—
683C23×C4—22no—
684C23×C4—22no—
685C23×C4—22no—
686C23×C4—22no—
687C23×C4—41no—
688C23×C4—41no—
689C23×C4—171no—
690C23×C4—171no—
691C23×C4—171no—
692C23×C4—171no—
693C23×C4—171no—
694C23×C4—171no—
695C23×C4—171no—
696C23×C4—342no—
697C23×C4—342no—
698C23×C4—342no—
699C23×C4—342no—
700C23×C4—342no—
701C23×C4—681no—
702C23×C4—681no—
703C23×C4C22×D1711yescharacteristic
704C23×C4C22×D1711yescharacteristic
705C23×C4C22×D1711yescharacteristic
706C23×C4C22×D1711yescharacteristic
707C23×C4C22×D1711yescharacteristic
708C23×C4C22×D1711yescharacteristic
709#124—3432no—
710C4×D4—3432no—
711C2×C4⋊C4—174no—
712C2×C4⋊C4—342no—
713C2×C4⋊C4—342no—
714C2×C4⋊C4—342no—
715C2×C4⋊C4—342no—
716C2×C4⋊C4—342no—
717C2×C22⋊C4—22no—
718C2×C22⋊C4—22no—
719C2×C22⋊C4—22no—
720C2×C22⋊C4—22no—
721C2×C22⋊C4—41no—
722C2×C22⋊C4—174no—
723C2×C22⋊C4—174no—
724C2×C22⋊C4—174no—
725C2×C22⋊C4—342no—
726C2×C22⋊C4—342no—
727C2×C22⋊C4—342no—
728C2×C22⋊C4—342no—
729C2×C22⋊C4—342no—
730C2×C22⋊C4—342no—
731C2×C22⋊C4—342no—
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—681no—
744C2×C22⋊C4—681no—
745C2×C22⋊C4—681no—
746C2×C22⋊C4C4×D1714yescomplemented
747C2×C42—174no—
748C2×C42—174no—
749C2×C42—342no—
750C2×C42—342no—
751C2×C42—342no—
752C2×C42—342no—
753C2×C42—342no—
754C2×C42—342no—
755C2×C42—342no—
756#95—22no—
757#95—22no—
758#95—22no—
759#95—41no—
760#95—342no—
761#95—342no—
762#95—342no—
763#95—342no—
764#95—342no—
765#95—342no—
766#95—342no—
767#95—342no—
768#95—342no—
769#95—681no—
770#95—681no—
771#95—681no—
772C17#1402711yescharacteristic, complemented, Sylow
773C24—21no—
774C24—21no—
775C24—21no—
776C24—21no—
777C24—21no—
778C24—21no—
779C24—21no—
780C24—21no—
781C24—21no—
782C24—21no—
783C24—21no—
784C24—21no—
785C24—172no—
786C24—172no—
787C24—172no—
788C24—341no—
789C24—341no—
790C24—341no—
791C24—341no—
792C24—341no—
793C24—341no—
794C24—341no—
795C24—341no—
796C24—341no—
797C24—341no—
798C24—341no—
799C24—341no—
800C24C2×C4×D1712yes—
801C24D4×D1712yes—
802C24D4×D1712yes—
803C24C23×D1711yescharacteristic
804C2×Q8—348no—
805C2×Q8—348no—
806C2×Q8—348no—
807C2×Q8—684no—
808C2×Q8—684no—
809C2×Q8—684no—
810C2×Q8—684no—
811C2×D4—1716no—
812C2×D4—348no—
813C2×D4—348no—
814C2×D4—348no—
815C2×D4—348no—
816C2×D4—348no—
817C2×D4—348no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—28no—
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—21no—
853C22×C4—21no—
854C22×C4—44no—
855C22×C4—44no—
856C22×C4—44no—
857C22×C4—44no—
858C22×C4—44no—
859C22×C4—44no—
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—172no—
871C22×C4—172no—
872C22×C4—348no—
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—341no—
907C22×C4—341no—
908C22×C4—341no—
909C22×C4—341no—
910C22×C4—684no—
911C22×C4—684no—
912C22×C4—684no—
913C22×C4—684no—
914C22×C4—684no—
915C22×C4—684no—
916C22×C4C2×C4×D1712yes—
917C22×C4C2×C4×D1712yes—
918C22×C4#6325212yes—
919C22×C4#6325212yes—
920C22×C4D4×D1712yes—
921C22×C4D4×D1712yes—
922C22×C4#6325412yes—
923C4⋊C4—348no—
924C4⋊C4—684no—
925C22⋊C4—28no—
926C22⋊C4—44no—
927C22⋊C4—348no—
928C22⋊C4—348no—
929C22⋊C4—348no—
930C22⋊C4—348no—
931C22⋊C4—348no—
932C22⋊C4—684no—
933C22⋊C4—684no—
934C22⋊C4—684no—
935C42—348no—
936C42—348no—
937C42—684no—
938C23—22no—
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—41no—
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—174no—
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—
988C23—342no—
989C23—342no—
990C23—342no—
991C23—681no—
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—
1007C23C22⋊C4×D1714yes—
1008C23C22×C4×D1711yescharacteristic
1009C23C2×#6325211yescharacteristic
1010C23C2×#6325211yescharacteristic
1011C23C2×D4×D1711yescharacteristic
1012C23C2×D4×D1711yescharacteristic
1013C23C2×D4×D1711yescharacteristic
1014C23C2×D4×D1711yescharacteristic
1015C23C2×#6325411yescharacteristic
1016C23#1058769111yescharacteristic
1017C23#1058769111yescharacteristic
1018C23#1058769411yescharacteristic
1019C23#41×D1711yescharacteristic
1020C23#41×D1711yescharacteristic
1021C23#41×D1711yescharacteristic
1022C23#1058769711yescharacteristic
1023Q8—6816no—
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—342no—
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—6816no—
1090C2×C4—681no—
1091C2×C4—681no—
1092C2×C4—681no—
1093C2×C4—681no—
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#1058757114yescomplemented
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×C22⋊C4×D1711yescharacteristic
1149C22C4×D4×D1711yescharacteristic
1150C22C4×D4×D1711yescharacteristic
1151C22C4×#6325411yescharacteristic
1152C22C4×#6325211yescharacteristic
1153C22#1176328811yescharacteristic
1154C22#1176329011yescharacteristic
1155C22#120×D1711yescharacteristic
1156C22#121×D1711yescharacteristic
1157C22#121×D1711yescharacteristic
1158C22#123×D1711yescharacteristic
1159C22C2×#1058757111yescharacteristic
1160C22#1176333711yescharacteristic
1161C22#1176333911yescharacteristic
1162C22#1176335611yescharacteristic
1163C22#1176337411yescharacteristic
1164C22#1176338211yescharacteristic
1165C22#1176342711yescharacteristic
1166C22#1176342911yescharacteristic
1167C22#1176344611yescharacteristic
1168C22#1176344611yescharacteristic
1169C22#1176344811yescharacteristic
1170C22#1176344911yescharacteristic
1171C22#1176344911yescharacteristic
1172C22#1176344911yescharacteristic
1173C22#1176345711yescharacteristic
1174C22#1176345911yescharacteristic
1175C22#1176346011yescharacteristic
1176C22#1176346011yescharacteristic
1177C22#1176346811yescharacteristic
1178C22#1176346911yescharacteristic
1179C22#1176352711yescharacteristic
1180C22#1176353011yescharacteristic
1181C22#1176354211yescharacteristic
1182C22#1176354311yescharacteristic
1183C4—24no—
1184C4—42no—
1185C4—42no—
1186C4—42no—
1187C4—42no—
1188C4—81no—
1189C4—178no—
1190C4—682no—
1191C4—682no—
1192C4—682no—
1193C4—682no—
1194C4—682no—
1195C4—1361no—
1196C2—44no—
1197C2—684no—
1198C2D17×#38611yescharacteristic
1199C2C4×#1058757111yescharacteristic
1200C2#1453149011yescharacteristic
1201C2#1453161011yescharacteristic
1202C2#1453161111yescharacteristic
1203C2#1453185211yescharacteristic
1204C2#1453185611yescharacteristic
1205C2#1453235811yescharacteristic
1206C2#1453236011yescharacteristic
1207C2#1453241011yescharacteristic
1208C2#1453243311yescharacteristic
1209C2#1453256811yescharacteristic
1210C2#1453257011yescharacteristic
1211C2#1453375311yescharacteristic
1212C2#1453377811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×C22⋊#95C2
socle, cosocleC24×C17C24
prime radicalC23×C22⋊D17C22
hypercenterC22⋊#95D17
hypocenterC17#14027
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×#11762713C2semidirect
4. C2×#11762713C2semidirect
6. #14527033C2semidirect
7. #14527032C2semidirect
8. #14527032C2semidirect
9. #14527031C2semidirect
10. #14527012C2semidirect
11. #14527007C2semidirect
12. #14527005C2semidirect
13. #14527005C2semidirect
14. #95×Dic17C2semidirect
15. C17×C22⋊#95C2semidirect
21. C2×#10587571C4semidirect
102. C22×Dic34C2×C4semidirect
108. C2×C22⋊C4×C17C2×C4semidirect
117. C2×C22⋊Dic17C2×C4semidirect
132. C2×#63227C2×C4semidirect
133. C2×#63227C2×C4semidirect
147. C2×C4×Dic17C2×C4semidirect
459. C2×C4×C17#124semidirect
525. C22⋊#95D17semidirect
746. C2×C22⋊C4C4×D17semidirect
772. C17#14027semidirect
1117. C2×C4#10587571semidirect

Maximal subgroups

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

subgroupindex
C22×#105875712
C22×C4×C22⋊D172
C2×#117627132
C2×#117627092
#145270332
#145270322
#145270312
#145270122
#145270072
#145270052
#95×Dic172
C17×C22⋊#952
#1402717