Finite Group Databasebeta

← #16957802

Subgroups — #16957802

Order 4352.

2358 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587571C211yesmaximal, characteristic
2C22×#10587573C211yesmaximal, characteristic, complemented
3C2×#11762713C211yesmaximal, characteristic, complemented
4C2×#11762709C211yesmaximal, characteristic
5C2×#11762709C211yesmaximal, characteristic
6#14527028C211yesmaximal, characteristic, complemented
7#14527027C211yesmaximal, characteristic, complemented
8#14527026C211yesmaximal, characteristic, complemented
9#14527021C211yesmaximal, characteristic, complemented
10#14527021C211yesmaximal, characteristic, complemented
11#14527020C211yesmaximal, characteristic, complemented
12#14527020C211yesmaximal, characteristic, complemented
13#14527012C211yesmaximal, characteristic, complemented
14#95×Dic17C211yesmaximal, characteristic, complemented
15C17×#1439C211yesmaximal, characteristic, complemented
16C23×Dic34C2211yescharacteristic
17C23×C22⋊D17C2211yescharacteristic
18C2×#10587571—24no—
19C2×#10587571—24no—
20C2×#10587571C418yescomplemented
21C2×#10587573—24no—
22C2×#10587573—24no—
23C2×#10587573—24no—
24C22×#63225C2211yescharacteristic
25C22×#63225C2211yescharacteristic
26C22×#63225C2211yescharacteristic
27C22×C22⋊Dic17C2211yescharacteristic
28C22×C22⋊Dic17C2211yescharacteristic
29C22×C22⋊Dic17C2211yescharacteristic
30C22×#63227C2211yescharacteristic
31C22×#63227C2211yescharacteristic
32C22×#63227C2211yescharacteristic
33C22×#63227C2211yescharacteristic
34C22×#63227C2211yescharacteristic
35C22×#63227C2211yescharacteristic
36C22×C4×Dic17C2211yescharacteristic
37C22×C4×Dic17C2211yescharacteristic
38C22×C4×Dic17C2211yescharacteristic
39C22×C4×Dic17C2211yescharacteristic
40C22×C4×Dic17C2211yescharacteristic
41#11762713—24no—
42#11762709—24no—
43#11762709—24no—
44C2×#10587502C2211yescharacteristic
45C2×#10587502C2211yescharacteristic
46C2×#10587502C2211yescharacteristic
47C2×#10587502C2211yescharacteristic
48C2×#10587502C2211yescharacteristic
49C2×#10587502C2211yescharacteristic
50C2×#10587502C2211yescharacteristic
51C2×#10587502C2211yescharacteristic
52C2×#10587502C2211yescharacteristic
53C22×C4⋊C4×C17C2211yescharacteristic
54C22×C22⋊C4×C17C2211yescharacteristic
55C22×C22⋊C4×C17C2211yescharacteristic
56C22×C22⋊C4×C17C2211yescharacteristic
57C2×C17×#95C2211yescharacteristic
58C2×C17×#95C2211yescharacteristic
59C2×C17×#95C2211yescharacteristic
60C25×C17C2311yescharacteristic
61C24×D17C2311yescharacteristic
62C23×C4×C17C2311yescharacteristic
63C23×C4×C17C2311yescharacteristic
64C23×C4×C17C2311yescharacteristic
65C23×C4×C17C2311yescharacteristic
66C23×C4×C17C2311yescharacteristic
67C23×C4×C17C2311yescharacteristic
68C22×C22⋊D17—22no—
69C22×C22⋊D17—22no—
70C22×C22⋊D17—22no—
71C22×C22⋊D17—22no—
72C22×C22⋊D17—22no—
73C22×C22⋊D17—22no—
74C22×C22⋊D17C2×C414yes—
75C23×Dic17C2311yescharacteristic
76C23×Dic17C2311yescharacteristic
77C23×Dic17C2311yescharacteristic
78C23×Dic17C2311yescharacteristic
79C23×Dic17C2311yescharacteristic
80C23×Dic17C2311yescharacteristic
81C23×Dic17C2311yescharacteristic
82C22×Dic34—22no—
83C22×Dic34—22no—
84C22×Dic34—22no—
85C22×Dic34—22no—
86C22×Dic34C2×C414yes—
87C22×Dic34D414yes—
88C22×Dic34D414yes—
89C2×C4⋊C4×C17—22no—
90C2×C4⋊C4×C17—22no—
91C2×C4⋊C4×C17—22no—
92C2×C22⋊C4×C17—22no—
93C2×C22⋊C4×C17—22no—
94C2×C22⋊C4×C17—22no—
95C2×C22⋊C4×C17—22no—
96C2×C22⋊C4×C17—22no—
97C2×C22⋊C4×C17—41no—
98C2×C22⋊C4×C17—41no—
99C2×C22⋊C4×C17—41no—
100C2×C22⋊C4×C17C2×C414yes—
101C2×C22⋊Dic17—22no—
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—41no—
109C2×C22⋊Dic17C2×C414yes—
110C2×#63227—22no—
111C2×#63227—22no—
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—22no—
122C2×#63227—41no—
123C2×#63227—41no—
124C2×#63227—41no—
125C2×#63227—41no—
126C2×#63227C2×C414yes—
127C2×#63227C2×C414yes—
128C2×#63225—22no—
129C2×#63225—22no—
130C2×#63225—22no—
131C2×#63225—22no—
132C2×#63225—22no—
133C2×#63225—22no—
134C2×#63225—22no—
135C2×#63225—22no—
136C2×#63225D414yes—
137C2×C4×Dic17—22no—
138C2×C4×Dic17—22no—
139C2×C4×Dic17—22no—
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×Dic17—22no—
148C2×C4×Dic17—22no—
149C2×C4×Dic17—22no—
150C2×C4×Dic17C2×C414yes—
151C2×C4×Dic17D414yes—
152#10587573—232no—
153#10587571—232no—
154C17×#95—22no—
155C17×#95—22no—
156C17×#95—41no—
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×C17—21no—
179C24×C17—21no—
180C24×C17C22×C412yes—
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×D17—21no—
195C23×D17—21no—
196C23×D17C22×C412yes—
197C22×C4×C17—21no—
198C22×C4×C17—21no—
199C22×C4×C17—21no—
200C22×C4×C17—21no—
201C22×C4×C17—21no—
202C22×C4×C17—21no—
203C22×C4×C17—21no—
204C22×C4×C17—21no—
205C22×C4×C17—21no—
206C22×C4×C17—21no—
207C22×C4×C17—21no—
208C22×C4×C17—21no—
209C22×C4×C17—21no—
210C22×C4×C17—21no—
211C22×C4×C17—21no—
212C22×C4×C17—21no—
213C22×C4×C17—21no—
214C22×C4×C17—21no—
215C22×C4×C17—21no—
216C22×C4×C17—21no—
217C22×C4×C17—21no—
218C22×C4×C17—21no—
219C22×C4×C17—21no—
220C22×C4×C17—21no—
221C22×C4×C17—21no—
222C22×C4×C17—21no—
223C22×C4×C17—21no—
224C22×C4×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×C17C22×C412yes—
233C22×C4×C17C22×C412yes—
234C22×C4×C17C2×D412yes—
235C22×C4×C17C2×D412yes—
236C22×C4×C17C2×D412yes—
237C22×C4×C17C2×D412yes—
238C22×C4×C17#4112yes—
239C2×C22⋊D17—28no—
240C2×C22⋊D17—28no—
241C2×C22⋊D17—28no—
242C2×C22⋊D17—44no—
243C2×C22⋊D17—44no—
244C2×C22⋊D17—44no—
245C2×C22⋊D17—44no—
246C22×Dic17—21no—
247C22×Dic17—21no—
248C22×Dic17—21no—
249C22×Dic17—21no—
250C22×Dic17—21no—
251C22×Dic17—21no—
252C22×Dic17—21no—
253C22×Dic17—21no—
254C22×Dic17—21no—
255C22×Dic17—21no—
256C22×Dic17—21no—
257C22×Dic17—21no—
258C22×Dic17—21no—
259C22×Dic17—21no—
260C22×Dic17—21no—
261C22×Dic17—21no—
262C22×Dic17—21no—
263C22×Dic17—21no—
264C22×Dic17—21no—
265C22×Dic17—21no—
266C22×Dic17—21no—
267C22×Dic17—21no—
268C22×Dic17—21no—
269C22×Dic17—21no—
270C22×Dic17—21no—
271C22×Dic17—21no—
272C22×Dic17—21no—
273C22×Dic17—21no—
274C22×Dic17—21no—
275C22×Dic17—21no—
276C22×Dic17—21no—
277C22×Dic17—21no—
278C22×Dic17—21no—
279C22×Dic17C22×C412yes—
280C22×Dic17C22×C412yes—
281C22×Dic17C22×C412yes—
282C22×Dic17C2×D412yes—
283C22×Dic17C2×D412yes—
284C22×Dic17C2×D412yes—
285C22×Dic17C2×D412yes—
286C22×Dic17C2×D412yes—
287C22×Dic17C2×D412yes—
288C22×Dic17C2×D412yes—
289C22×Dic17C2×D412yes—
290C22×Dic17#4112yes—
291C22×Dic17#4112yes—
292C22×Dic17#4112yes—
293C22×Dic17#4112yes—
294C22×Dic17#4112yes—
295C2×Dic34—28no—
296C2×Dic34—28no—
297C2×Dic34—28no—
298C2×Dic34—28no—
299C2×Dic34—28no—
300C2×Dic34—28no—
301C2×Dic34C22⋊C4116yescomplemented
302C4⋊C4×C17—28no—
303C22⋊C4×C17—28no—
304C22⋊C4×C17—44no—
305C22⋊C4×C17—44no—
306C22⋊Dic17—28no—
307C22⋊Dic17—44no—
308C22⋊Dic17—44no—
309#63227—28no—
310#63227—28no—
311#63227—44no—
312#63227—44no—
313#63227—44no—
314#63227—44no—
315#63225—28no—
316#63225—28no—
317#63225—44no—
318C4×Dic17—28no—
319C4×Dic17—28no—
320C4×Dic17—28no—
321C4×Dic17—28no—
322C4×Dic17—44no—
323#14026—171nomaximal, Sylow
324C23×C17—22no—
325C23×C17—22no—
326C23×C17—22no—
327C23×C17—22no—
328C23×C17—22no—
329C23×C17—22no—
330C23×C17—22no—
331C23×C17—41no—
332C23×C17—41no—
333C23×C17—41no—
334C23×C17—41no—
335C23×C17—41no—
336C23×C17—41no—
337C23×C17—41no—
338C23×C17—41no—
339C23×C17—41no—
340C23×C17—41no—
341C23×C17—41no—
342C23×C17—41no—
343C23×C17—41no—
344C23×C17—41no—
345C23×C17—41no—
346C23×C17—41no—
347C23×C17—41no—
348C23×C17—41no—
349C23×C17—41no—
350C23×C17—41no—
351C23×C17—41no—
352C23×C17—41no—
353C23×C17—41no—
354C23×C17—41no—
355C23×C17—41no—
356C23×C17—41no—
357C23×C17—41no—
358C23×C17—41no—
359C23×C17C23×C411yescharacteristic
360C23×C17C22×D411yescharacteristic
361C23×C17C22×D411yescharacteristic
362C23×C17C22×D411yescharacteristic
363C23×C17C22×D411yescharacteristic
364C23×C17C2×#4111yescharacteristic
365C23×C17C2×#4111yescharacteristic
366C23×C17C2×#4111yescharacteristic
367C23×C17C2×#4111yescharacteristic
368C23×C17C2×#4111yescharacteristic
369C23×C17C2×#4111yescharacteristic
370C23×C17H(5,𝔽2)11yescharacteristic
371C23×C17H(5,𝔽2)11yescharacteristic
372C23×C172−1+411yescharacteristic
373C23×C172−1+411yescharacteristic
374C22×D17—22no—
375C22×D17—22no—
376C22×D17—22no—
377C22×D17—22no—
378C22×D17—22no—
379C22×D17—22no—
380C22×D17—22no—
381C22×D17—41no—
382C22×D17—41no—
383C22×D17—41no—
384C22×D17—41no—
385C22×D17—41no—
386C22×D17—41no—
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×D17—41no—
404C22×D17—41no—
405C22×D17—41no—
406C22×D17—41no—
407C22×D17—41no—
408C22×D17—41no—
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—22no—
426C2×C4×C17—22no—
427C2×C4×C17—41no—
428C2×C4×C17—41no—
429C2×C4×C17—41no—
430C2×C4×C17—41no—
431C2×C4×C17—41no—
432C2×C4×C17—41no—
433C2×C4×C17—41no—
434C2×C4×C17—41no—
435C2×C4×C17—41no—
436C2×C4×C17—41no—
437C2×C4×C17—41no—
438C2×C4×C17—41no—
439C2×C4×C17—41no—
440C2×C4×C17—41no—
441C2×C4×C17—41no—
442C2×C4×C17—41no—
443C2×C4×C17—41no—
444C2×C4×C17—41no—
445C2×C4×C17—41no—
446C2×C4×C17—41no—
447C2×C4×C17—41no—
448C2×C4×C17—41no—
449C2×C4×C17—41no—
450C2×C4×C17C2×C22⋊C414yes—
451C22⋊D17—416no—
452C2×Dic17—22no—
453C2×Dic17—22no—
454C2×Dic17—22no—
455C2×Dic17—22no—
456C2×Dic17—22no—
457C2×Dic17—22no—
458C2×Dic17—22no—
459C2×Dic17—22no—
460C2×Dic17—22no—
461C2×Dic17—22no—
462C2×Dic17—22no—
463C2×Dic17—22no—
464C2×Dic17—22no—
465C2×Dic17—22no—
466C2×Dic17—22no—
467C2×Dic17—22no—
468C2×Dic17—22no—
469C2×Dic17—22no—
470C2×Dic17—22no—
471C2×Dic17—22no—
472C2×Dic17—22no—
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×Dic17C2×C22⋊C414yes—
493C2×Dic17C2×C22⋊C414yes—
494C2×Dic17C4×D414yes—
495C2×Dic17C4×D414yes—
496C2×Dic17#12014yes—
497C2×Dic17#12114yes—
498C2×Dic17#12114yes—
499C2×Dic17#12314yes—
500C2×Dic17#12414yescomplemented
501Dic34—232no—
502C22×#124—171no—
503C22×C4×Q8—171no—
504C2×#391—171no—
505C2×#390—171no—
506C2×#390—171no—
507#1439—171no—
508#1439—171no—
509#1439—171no—
510#1439D1711yescharacteristic, complemented
511#1437—171no—
512#1437—171no—
513#1437—171no—
514#1437—171no—
515C4⋊#95—171no—
516C4×#95—171no—
517C22×C17—42no—
518C22×C17—42no—
519C22×C17—42no—
520C22×C17—42no—
521C22×C17—42no—
522C22×C17—42no—
523C22×C17—42no—
524C22×C17—81no—
525C22×C17—81no—
526C22×C17—81no—
527C22×C17—81no—
528C22×C17—81no—
529C22×C17—81no—
530C22×C17—81no—
531C22×C17—81no—
532C22×C17C22×C22⋊C411yescharacteristic
533C22×C17C2×C4×D411yescharacteristic
534C22×C17C2×C4×D411yescharacteristic
535C22×C17C4×#4111yescharacteristic
536C22×C17C4×#4111yescharacteristic
537C22×C17#52011yescharacteristic
538C22×C17#52011yescharacteristic
539C22×C17C2×#12011yescharacteristic
540C22×C17C2×#12111yescharacteristic
541C22×C17C2×#12111yescharacteristic
542C22×C17C2×#12311yescharacteristic
543C22×C17C2×#12411yescharacteristic
544C22×C17#52911yescharacteristic
545C22×C17#52911yescharacteristic
546C22×C17#53211yescharacteristic
547C22×C17#53511yescharacteristic
548C22×C17#53611yescharacteristic
549C22×C17#54211yescharacteristic
550C22×C17#54211yescharacteristic
551C22×C17#54611yescharacteristic
552C22×C17#54611yescharacteristic
553C22×C17#54811yescharacteristic
554C22×C17#54811yescharacteristic
555C22×C17#54811yescharacteristic
556C22×C17#54811yescharacteristic
557C22×C17#54811yescharacteristic
558C22×C17#54811yescharacteristic
559C22×C17#55011yescharacteristic
560C22×C17#55011yescharacteristic
561C22×C17#55011yescharacteristic
562C22×C17#55011yescharacteristic
563C22×C17#55611yescharacteristic
564C22×C17#55611yescharacteristic
565C22×C17#55911yescharacteristic
566C22×C17#55911yescharacteristic
567C2×D17—42no—
568C2×D17—42no—
569C2×D17—42no—
570C2×D17—42no—
571C2×D17—42no—
572C2×D17—42no—
573C2×D17—42no—
574C2×D17—81no—
575C2×D17—81no—
576C2×D17—81no—
577C2×D17—81no—
578C2×D17—81no—
579C2×D17—81no—
580C2×D17—81no—
581C2×D17—81no—
582C4×C17—24no—
583C4×C17—42no—
584C4×C17—42no—
585C4×C17—42no—
586C4×C17—42no—
587C4×C17—81no—
588Dic17—24no—
589Dic17—24no—
590Dic17—42no—
591Dic17—42no—
592Dic17—42no—
593Dic17—81no—
594Dic17#38618yes—
595C23×Q8—171no—
596C23×D4—171no—
597C2×#124—178no—
598C2×#124—344no—
599C2×#124—344no—
600C2×C4×Q8—344no—
601C2×C4×Q8—344no—
602C2×C4×Q8—344no—
603C22×C4⋊C4—171no—
604C22×C4⋊C4—171no—
605C22×C4⋊C4—171no—
606C22×C4⋊C4C2×D1711yescharacteristic
607C22×C22⋊C4—171no—
608C22×C22⋊C4—171no—
609C22×C22⋊C4—171no—
610C22×C22⋊C4—171no—
611C22×C22⋊C4—171no—
612C22×C22⋊C4—171no—
613C22×C22⋊C4—171no—
614C22×C22⋊C4—171no—
615C22×C22⋊C4—171no—
616C22×C22⋊C4C2×D1711yescharacteristic
617C22×C22⋊C4C2×D1711yescharacteristic
618C22×C22⋊C4C2×D1711yescharacteristic
619C22×C42—171no—
620C22×C42—171no—
621C22×C42—171no—
622C22×C42—171no—
623C22×C42—171no—
624#391—344no—
625#390—344no—
626#390—344no—
627C2×#95—171no—
628C2×#95—171no—
629C2×#95—171no—
630C2×#95—171no—
631C2×#95—171no—
632C2×#95—171no—
633C2×#95—171no—
634C2×#95—171no—
635C2×#95—171no—
636C2×#95C2×D1711yescharacteristic
637C2×#95C2×D1711yescharacteristic
638C2×#95C2×D1711yescharacteristic
639C2×C17—82no—
640C2×C17C2×#38611yescharacteristic
641C2×C17C4×#12411yescharacteristic
642C2×C17#232611yescharacteristic
643C2×C17#234111yescharacteristic
644C2×C17#234111yescharacteristic
645C2×C17#236711yescharacteristic
646C2×C17#236711yescharacteristic
647C2×C17#242611yescharacteristic
648C2×C17#242611yescharacteristic
649C2×C17#243111yescharacteristic
650C2×C17#243611yescharacteristic
651C2×C17#244811yescharacteristic
652C2×C17#244811yescharacteristic
653C2×C17#254511yescharacteristic
654C2×C17#254811yescharacteristic
655D17—82no—
656C25—171no—
657C25C22×D1711yescharacteristic
658C22×Q8—174no—
659C22×Q8—174no—
660C22×Q8—174no—
661C22×Q8—342no—
662C22×Q8—342no—
663C22×Q8—342no—
664C22×Q8—342no—
665C22×D4—174no—
666C22×D4—342no—
667C22×D4—342no—
668C22×D4—342no—
669C22×D4—342no—
670C22×D4—342no—
671C22×D4—342no—
672C23×C4—171no—
673C23×C4—171no—
674C23×C4—171no—
675C23×C4—171no—
676C23×C4—171no—
677C23×C4—171no—
678C23×C4—171no—
679C23×C4C22×D1711yescharacteristic
680C23×C4C22×D1711yescharacteristic
681C23×C4C22×D1711yescharacteristic
682C23×C4C22×D1711yescharacteristic
683C23×C4C22×D1711yescharacteristic
684C23×C4C22×D1711yescharacteristic
685#124—3432no—
686C4×Q8—3432no—
687C2×C4⋊C4—22no—
688C2×C4⋊C4—22no—
689C2×C4⋊C4—22no—
690C2×C4⋊C4—174no—
691C2×C4⋊C4—342no—
692C2×C4⋊C4—342no—
693C2×C4⋊C4—342no—
694C2×C4⋊C4—342no—
695C2×C4⋊C4—342no—
696C2×C4⋊C4—342no—
697C2×C4⋊C4—342no—
698C2×C4⋊C4—342no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—22no—
701C2×C22⋊C4—22no—
702C2×C22⋊C4—22no—
703C2×C22⋊C4—22no—
704C2×C22⋊C4—41no—
705C2×C22⋊C4—41no—
706C2×C22⋊C4—41no—
707C2×C22⋊C4—174no—
708C2×C22⋊C4—174no—
709C2×C22⋊C4—174no—
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—342no—
722C2×C22⋊C4—342no—
723C2×C22⋊C4—342no—
724C2×C22⋊C4—342no—
725C2×C22⋊C4—342no—
726C2×C22⋊C4—342no—
727C2×C22⋊C4—342no—
728C2×C22⋊C4—342no—
729C2×C22⋊C4—681no—
730C2×C22⋊C4—681no—
731C2×C22⋊C4—681no—
732C2×C22⋊C4—681no—
733C2×C22⋊C4—681no—
734C2×C22⋊C4C4×D1714yes—
735C2×C42—174no—
736C2×C42—174no—
737C2×C42—342no—
738C2×C42—342no—
739C2×C42—342no—
740C2×C42—342no—
741C2×C42—342no—
742C2×C42—342no—
743C2×C42—342no—
744C2×C42—342no—
745C2×C42—342no—
746C2×C42—342no—
747C2×C42—342no—
748C2×C42—342no—
749C2×C42—342no—
750#95—22no—
751#95—22no—
752#95—41no—
753#95—342no—
754#95—342no—
755#95—342no—
756#95—342no—
757#95—342no—
758#95—342no—
759#95—681no—
760#95—681no—
761#95—681no—
762C17#1402611yescharacteristic, complemented, Sylow
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24—21no—
777C24—172no—
778C24—341no—
779C24—341no—
780C24—341no—
781C24—341no—
782C24—341no—
783C24—341no—
784C24—341no—
785C24—341no—
786C24—341no—
787C24—341no—
788C24—341no—
789C24—341no—
790C24—341no—
791C24—341no—
792C24C2×C4×D1712yes—
793C24C23×D1711yescharacteristic
794C2×Q8—1716no—
795C2×Q8—348no—
796C2×Q8—348no—
797C2×Q8—348no—
798C2×Q8—348no—
799C2×Q8—348no—
800C2×Q8—348no—
801C2×D4—348no—
802C2×D4—348no—
803C2×D4—348no—
804C2×D4—684no—
805C2×D4—684no—
806C2×D4—684no—
807C2×D4—684no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—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—172no—
844C22×C4—172no—
845C22×C4—172no—
846C22×C4—172no—
847C22×C4—172no—
848C22×C4—172no—
849C22×C4—172no—
850C22×C4—172no—
851C22×C4—172no—
852C22×C4—172no—
853C22×C4—172no—
854C22×C4—172no—
855C22×C4—172no—
856C22×C4—172no—
857C22×C4—172no—
858C22×C4—172no—
859C22×C4—341no—
860C22×C4—341no—
861C22×C4—341no—
862C22×C4—341no—
863C22×C4—341no—
864C22×C4—341no—
865C22×C4—341no—
866C22×C4—341no—
867C22×C4—341no—
868C22×C4—341no—
869C22×C4—341no—
870C22×C4—341no—
871C22×C4—341no—
872C22×C4—341no—
873C22×C4—341no—
874C22×C4—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×C4C2×C4×D1712yes—
893C22×C4C2×C4×D1712yes—
894C22×C4D4×D1712yes—
895C22×C4D4×D1712yes—
896C22×C4D4×D1712yes—
897C22×C4D4×D1712yes—
898C22×C4#6325412yes—
899C4⋊C4—28no—
900C4⋊C4—348no—
901C4⋊C4—348no—
902C4⋊C4—684no—
903C22⋊C4—28no—
904C22⋊C4—44no—
905C22⋊C4—44no—
906C22⋊C4—348no—
907C22⋊C4—348no—
908C22⋊C4—348no—
909C22⋊C4—684no—
910C22⋊C4—684no—
911C22⋊C4—684no—
912C22⋊C4—684no—
913C22⋊C4—684no—
914C22⋊C4—684no—
915C42—348no—
916C42—348no—
917C42—348no—
918C42—348no—
919C42—684no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—342no—
956C23—342no—
957C23—342no—
958C23—342no—
959C23—342no—
960C23—342no—
961C23—342no—
962C23—681no—
963C23—681no—
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—
980C23—681no—
981C23—681no—
982C23—681no—
983C23—681no—
984C23—681no—
985C23—681no—
986C23—681no—
987C23—681no—
988C23—681no—
989C23—681no—
990C23C22×C4×D1711yescharacteristic
991C23C2×D4×D1711yescharacteristic
992C23C2×D4×D1711yescharacteristic
993C23C2×D4×D1711yescharacteristic
994C23C2×D4×D1711yescharacteristic
995C23C2×#6325411yescharacteristic
996C23#1058769111yescharacteristic
997C23#1058769111yescharacteristic
998C23#1058769411yescharacteristic
999C23#41×D1711yescharacteristic
1000C23#41×D1711yescharacteristic
1001C23#41×D1711yescharacteristic
1002C23#41×D1711yescharacteristic
1003C23#41×D1711yescharacteristic
1004C23#1058769711yescharacteristic
1005Q8—3432no—
1006D4—6816no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—174no—
1049C2×C4—174no—
1050C2×C4—174no—
1051C2×C4—174no—
1052C2×C4—174no—
1053C2×C4—174no—
1054C2×C4—174no—
1055C2×C4—174no—
1056C2×C4—174no—
1057C2×C4—342no—
1058C2×C4—342no—
1059C2×C4—342no—
1060C2×C4—342no—
1061C2×C4—342no—
1062C2×C4—342no—
1063C2×C4—342no—
1064C2×C4—342no—
1065C2×C4—342no—
1066C2×C4—342no—
1067C2×C4—342no—
1068C2×C4—342no—
1069C2×C4—342no—
1070C2×C4—342no—
1071C2×C4—342no—
1072C2×C4—342no—
1073C2×C4—342no—
1074C2×C4—342no—
1075C2×C4—342no—
1076C2×C4—342no—
1077C2×C4—342no—
1078C2×C4—681no—
1079C2×C4—681no—
1080C2×C4—681no—
1081C2×C4—681no—
1082C2×C4—681no—
1083C2×C4—681no—
1084C2×C4—681no—
1085C2×C4—681no—
1086C2×C4—681no—
1087C2×C4—681no—
1088C2×C4—681no—
1089C2×C4—681no—
1090C2×C4—681no—
1091C2×C4—681no—
1092C2×C4—681no—
1093C2×C4—681no—
1094C2×C4—681no—
1095C2×C4—681no—
1096C2×C4—681no—
1097C2×C4C22⋊C4×D1714yes—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—81no—
1106C22—81no—
1107C22—81no—
1108C22—81no—
1109C22—81no—
1110C22—81no—
1111C22—81no—
1112C22—81no—
1113C22—682no—
1114C22—682no—
1115C22—682no—
1116C22—682no—
1117C22—682no—
1118C22—682no—
1119C22—682no—
1120C22—1361no—
1121C22—1361no—
1122C22—1361no—
1123C22—1361no—
1124C22—1361no—
1125C22—1361no—
1126C22—1361no—
1127C22—1361no—
1128C22C2×C22⋊C4×D1711yescharacteristic
1129C22C4×D4×D1711yescharacteristic
1130C22C4×D4×D1711yescharacteristic
1131C22C4×#6325411yescharacteristic
1132C22#1176327711yescharacteristic
1133C22#1176328811yescharacteristic
1134C22#1176329011yescharacteristic
1135C22#120×D1711yescharacteristic
1136C22#121×D1711yescharacteristic
1137C22#121×D1711yescharacteristic
1138C22#123×D1711yescharacteristic
1139C22#124×D1711yescharacteristic
1140C22#1176333611yescharacteristic
1141C22#1176334211yescharacteristic
1142C22#1176335411yescharacteristic
1143C22#1176337411yescharacteristic
1144C22#1176338211yescharacteristic
1145C22#1176342711yescharacteristic
1146C22#1176342911yescharacteristic
1147C22#1176344611yescharacteristic
1148C22#1176344811yescharacteristic
1149C22#1176346511yescharacteristic
1150C22#1176346711yescharacteristic
1151C22#1176346711yescharacteristic
1152C22#1176346911yescharacteristic
1153C22#1176346911yescharacteristic
1154C22#1176346911yescharacteristic
1155C22#1176347711yescharacteristic
1156C22#1176347711yescharacteristic
1157C22#1176347711yescharacteristic
1158C22#1176347911yescharacteristic
1159C22#1176352611yescharacteristic
1160C22#1176353011yescharacteristic
1161C22#1176354311yescharacteristic
1162C22#1176354311yescharacteristic
1163C4—24no—
1164C4—42no—
1165C4—42no—
1166C4—42no—
1167C4—42no—
1168C4—81no—
1169C4—178no—
1170C4—344no—
1171C4—344no—
1172C4—682no—
1173C4—682no—
1174C4—682no—
1175C4—1361no—
1176C2—82no—
1177C2—1362no—
1178C2D17×#38611yescharacteristic
1179C2#1453132511yescharacteristic
1180C2#1453149011yescharacteristic
1181C2#1453162111yescharacteristic
1182C2#1453162311yescharacteristic
1183C2#1453185011yescharacteristic
1184C2#1453185211yescharacteristic
1185C2#1453234311yescharacteristic
1186C2#1453234511yescharacteristic
1187C2#1453239811yescharacteristic
1188C2#1453243711yescharacteristic
1189C2#1453257511yescharacteristic
1190C2#1453257711yescharacteristic
1191C2#1453375911yescharacteristic
1192C2#1453378211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1439C2
socle, cosocleC24×C17C24
prime radicalC23×C22⋊D17C22
hypercenter#1439D17
hypocenterC17#14026
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. C22×#10587573C2semidirect
3. C2×#11762713C2semidirect
6. #14527028C2semidirect
7. #14527027C2semidirect
8. #14527026C2semidirect
9. #14527021C2semidirect
10. #14527021C2semidirect
11. #14527020C2semidirect
12. #14527020C2semidirect
13. #14527012C2semidirect
14. #95×Dic17C2semidirect
15. C17×#1439C2semidirect
20. C2×#10587571C4semidirect
301. C2×Dic34C22⋊C4semidirect
500. C2×Dic17#124semidirect
510. #1439D17semidirect
762. C17#14026semidirect

Maximal subgroups

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

subgroupindex
C22×#105875712
C22×#105875732
C2×#117627132
C2×#117627092
#145270282
#145270272
#145270262
#145270212
#145270202
#145270122
#95×Dic172
C17×#14392
#1402617