Finite Group Databasebeta

← #16957687

Subgroups — #16957687

Order 4352.

2950 conjugacy classes of subgroups.

The subgroup lattice has 1252 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587567C211yesmaximal, characteristic
2C22×C4⋊C4×D17C211yesmaximal, characteristic, complemented
3C2×#11762685C211yesmaximal, characteristic
4C2×#11762685C211yesmaximal, characteristic
5C2×#11762684C211yesmaximal, characteristic, complemented
6C2×#11762683C211yesmaximal, characteristic, complemented
7C2×#11762681C211yesmaximal, characteristic, complemented
8#14527048C211yesmaximal, characteristic, complemented
9#14527047C211yesmaximal, characteristic, complemented
10#14527027C211yesmaximal, characteristic, complemented
11#14527018C211yesmaximal, characteristic, complemented
12#14527015C211yesmaximal, characteristic, complemented
13#14527005C211yesmaximal, characteristic, complemented
14#14527005C211yesmaximal, characteristic, complemented
15C17×#1439C211yesmaximal, characteristic, complemented
16C23×C22⋊D17C2211yescharacteristic
17C24×Dic17C2211yescharacteristic
18C23×C4×D17C2211yescharacteristic
19C23×C4×D17C2211yescharacteristic
20C23×C4×D17C2211yescharacteristic
21C2×#10587567—24no—
22C2×#10587567—24no—
23C2×#10587567—24no—
24C22×C4⋊Dic17C2211yescharacteristic
25C22×C4⋊Dic17C2211yescharacteristic
26C22×#63225C2211yescharacteristic
27C22×#63225C2211yescharacteristic
28C22×#63225C2211yescharacteristic
29C22×#63225C2211yescharacteristic
30C2×C4⋊C4×D17—24no—
31C2×C4⋊C4×D17—24no—
32C2×C4⋊C4×D17—24no—
33C22×C22⋊Dic17C2211yescharacteristic
34C22×C22⋊Dic17C2211yescharacteristic
35C22×#63227C2211yescharacteristic
36C22×#63227C2211yescharacteristic
37C22×#63227C2211yescharacteristic
38C22×C4×Dic17C2211yescharacteristic
39#11762685—24no—
40#11762685C418yescomplemented
41#11762684—24no—
42#11762683—24no—
43#11762681—24no—
44C2×#10587502C2211yescharacteristic
45C2×#10587502C2211yescharacteristic
46C2×#10587502C2211yescharacteristic
47C2×#10587502C2211yescharacteristic
48C2×#10587502C2211yescharacteristic
49C2×#10587502C2211yescharacteristic
50C2×#10587502C2211yescharacteristic
51C2×#10587502C2211yescharacteristic
52C2×#10587502C2211yescharacteristic
53C2×#10587502C2211yescharacteristic
54C2×#10587502C2211yescharacteristic
55C22×C4⋊C4×C17C2211yescharacteristic
56C22×C22⋊C4×C17C2211yescharacteristic
57C22×C22⋊C4×C17C2211yescharacteristic
58C22×C22⋊C4×C17C2211yescharacteristic
59C2×C17×#95C2211yescharacteristic
60C2×C17×#95C2211yescharacteristic
61C2×C17×#95C2211yescharacteristic
62C25×C17C2311yescharacteristic
63C24×D17C2311yescharacteristic
64C23×C4×C17C2311yescharacteristic
65C23×C4×C17C2311yescharacteristic
66C23×C4×C17C2311yescharacteristic
67C23×C4×C17C2311yescharacteristic
68C23×C4×C17C2311yescharacteristic
69C23×C4×C17C2311yescharacteristic
70C22×C22⋊D17—22no—
71C22×C22⋊D17—22no—
72C22×C22⋊D17—22no—
73C22×C22⋊D17—22no—
74C22×C22⋊D17C2×C414yes—
75C22×C22⋊D17D414yes—
76C22×C22⋊D17Q814yes—
77C23×Dic17—22no—
78C23×Dic17—22no—
79C23×Dic17—22no—
80C23×Dic17—22no—
81C23×Dic17—22no—
82C23×Dic17—41no—
83C23×Dic17—41no—
84C23×Dic17C2311yescharacteristic
85C23×Dic17C2311yescharacteristic
86C23×Dic17C2311yescharacteristic
87C23×Dic17C2311yescharacteristic
88C23×Dic17C2311yescharacteristic
89C23×Dic17C2311yescharacteristic
90C23×Dic17C2311yescharacteristic
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—22no—
105C22×C4×D17—22no—
106C22×C4×D17—41no—
107C22×C4×D17—41no—
108C22×C4×D17—41no—
109C22×C4×D17—41no—
110C22×C4×D17C2×C414yescomplemented
111C22×C4×D17D414yes—
112C2×C4⋊C4×C17—22no—
113C2×C4⋊C4×C17—22no—
114C2×C4⋊C4×C17—22no—
115C2×C22⋊C4×C17—22no—
116C2×C22⋊C4×C17—22no—
117C2×C22⋊C4×C17—22no—
118C2×C22⋊C4×C17—22no—
119C2×C22⋊C4×C17—22no—
120C2×C22⋊C4×C17—22no—
121C2×C22⋊C4×C17—22no—
122C2×C22⋊C4×C17—41no—
123C2×C22⋊C4×C17C2×C414yescomplemented
124C2×C22⋊Dic17—22no—
125C2×C22⋊Dic17—22no—
126C2×C22⋊Dic17—22no—
127C2×C22⋊Dic17—22no—
128C2×C22⋊Dic17—41no—
129C2×C22⋊Dic17C2×C414yescomplemented
130C2×#63227—22no—
131C2×#63227—22no—
132C2×#63227—22no—
133C2×#63227—22no—
134C2×#63227—22no—
135C2×#63227—22no—
136C2×#63227—22no—
137C2×#63227C2×C414yescomplemented
138C2×#63227D414yes—
139C2×C4⋊Dic17—22no—
140C2×C4⋊Dic17—22no—
141C2×C4⋊Dic17—22no—
142C2×C4⋊Dic17—22no—
143C2×C4⋊Dic17—41no—
144C2×C4⋊Dic17D414yescomplemented
145C2×#63225—22no—
146C2×#63225—22no—
147C2×#63225—22no—
148C2×#63225—22no—
149C2×#63225—22no—
150C2×#63225—22no—
151C2×#63225—22no—
152C2×#63225—22no—
153C2×#63225—22no—
154C2×#63225—22no—
155C2×#63225—41no—
156C2×#63225D414yescomplemented
157C2×C4×Dic17—22no—
158C2×C4×Dic17—22no—
159C2×C4×Dic17—22no—
160C4⋊C4×D17—232no—
161#10587567—232no—
162C17×#95—22no—
163C17×#95—22no—
164C17×#95—41no—
165#10587502—22no—
166#10587502—22no—
167#10587502—22no—
168#10587502—22no—
169#10587502—22no—
170#10587502—22no—
171#10587502—22no—
172#10587502—22no—
173#10587502—41no—
174#10587502C2×C414yescomplemented
175#10587502C2×C414yescomplemented
176C24×C17—21no—
177C24×C17—21no—
178C24×C17—21no—
179C24×C17—21no—
180C24×C17—21no—
181C24×C17—21no—
182C24×C17—21no—
183C24×C17—21no—
184C24×C17—21no—
185C24×C17—21no—
186C24×C17—21no—
187C24×C17—21no—
188C24×C17C22×C412yes—
189C24×C17C2×D412yes—
190C24×C17C2×Q812yes—
191C24×C17C2411yescharacteristic
192C23×D17—21no—
193C23×D17—21no—
194C23×D17—21no—
195C23×D17—21no—
196C23×D17—21no—
197C23×D17—21no—
198C23×D17—21no—
199C23×D17—21no—
200C23×D17C22×C412yes—
201C23×D17C2×D412yes—
202C23×D17C2×D412yes—
203C23×D17C2×D412yes—
204C23×D17C2×Q812yes—
205C23×D17#4112yes—
206C23×D17#4112yes—
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—21no—
237C22×C4×C17—21no—
238C22×C4×C17—21no—
239C22×C4×C17—21no—
240C22×C4×C17—21no—
241C22×C4×C17—21no—
242C22×C4×C17C22×C412yes—
243C22×C4×C17C22×C412yes—
244C22×C4×C17C2×D412yes—
245C22×C4×C17C2×D412yes—
246C22×C4×C17C2×D412yes—
247C22×C4×C17C2×D412yes—
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—28no—
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×Dic17—44no—
295C22×Dic17—44no—
296C22×Dic17—44no—
297C22×Dic17—44no—
298C22×Dic17—44no—
299C22×Dic17—44no—
300C22×Dic17C22×C412yes—
301C22×Dic17C22×C412yes—
302C22×Dic17C22×C412yes—
303C22×Dic17C2×D412yes—
304C22×Dic17C2×D412yes—
305C22×Dic17C2×D412yes—
306C22×Dic17C2×D412yes—
307C22×Dic17C2×D412yes—
308C22×Dic17C2×D412yes—
309C22×Dic17C2×D412yes—
310C22×Dic17C2×Q812yes—
311C22×Dic17#4112yes—
312C2×C4×D17—28no—
313C2×C4×D17—28no—
314C2×C4×D17—28no—
315C2×C4×D17—28no—
316C2×C4×D17—28no—
317C2×C4×D17—28no—
318C2×C4×D17—28no—
319C2×C4×D17—28no—
320C2×C4×D17—28no—
321C2×C4×D17—28no—
322C2×C4×D17—44no—
323C2×C4×D17—44no—
324C2×C4×D17—44no—
325C2×C4×D17—44no—
326C2×C4×D17—44no—
327C2×C4×D17—44no—
328C2×C4×D17—44no—
329C2×C4×D17—44no—
330C2×C4×D17—44no—
331C2×C4×D17—44no—
332C2×C4×D17—44no—
333C4⋊C4×C17—28no—
334C22⋊C4×C17—28no—
335C22⋊C4×C17—28no—
336C22⋊C4×C17—44no—
337C22⋊Dic17—28no—
338C22⋊Dic17—44no—
339#63227—28no—
340#63227—28no—
341#63227—44no—
342C4⋊Dic17—28no—
343C4⋊Dic17—44no—
344#63225—28no—
345#63225—28no—
346#63225—28no—
347#63225—44no—
348C4×Dic17—28no—
349#14015—171nomaximal, Sylow
350C23×C17—22no—
351C23×C17—22no—
352C23×C17—22no—
353C23×C17—22no—
354C23×C17—22no—
355C23×C17—22no—
356C23×C17—22no—
357C23×C17—22no—
358C23×C17—22no—
359C23×C17—22no—
360C23×C17—22no—
361C23×C17—22no—
362C23×C17—22no—
363C23×C17—22no—
364C23×C17—22no—
365C23×C17—22no—
366C23×C17—22no—
367C23×C17—22no—
368C23×C17—41no—
369C23×C17—41no—
370C23×C17—41no—
371C23×C17—41no—
372C23×C17—41no—
373C23×C17—41no—
374C23×C17—41no—
375C23×C17—41no—
376C23×C17—41no—
377C23×C17—41no—
378C23×C17—41no—
379C23×C17—41no—
380C23×C17—41no—
381C23×C17—41no—
382C23×C17—41no—
383C23×C17—41no—
384C23×C17C2×C4⋊C414yescomplemented
385C23×C17C23×C411yescharacteristic
386C23×C17C22×D411yescharacteristic
387C23×C17C22×D411yescharacteristic
388C23×C17C22×D411yescharacteristic
389C23×C17C22×D411yescharacteristic
390C23×C17C22×D411yescharacteristic
391C23×C17C22×Q811yescharacteristic
392C23×C17C2×#4111yescharacteristic
393C23×C17C2×#4111yescharacteristic
394C23×C17C2×#4111yescharacteristic
395C23×C17C2×#4111yescharacteristic
396C23×C17H(5,𝔽2)11yescharacteristic
397C23×C17H(5,𝔽2)11yescharacteristic
398C23×C172−1+411yescharacteristic
399C23×C172−1+411yescharacteristic
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×D17—22no—
415C22×D17—22no—
416C22×D17—22no—
417C22×D17—22no—
418C22×D17—22no—
419C22×D17—22no—
420C22×D17—22no—
421C22×D17—22no—
422C22×D17—22no—
423C22×D17—22no—
424C22×D17—22no—
425C22×D17—22no—
426C22×D17—22no—
427C22×D17—22no—
428C22×D17C2×C4⋊C414yes—
429C22×D17C4×D414yes—
430C22×D17C4×D414yes—
431C22×D17#12014yes—
432C22×D17C22⋊Q814yes—
433C22×D17C22⋊Q814yes—
434C22×D17#12314yes—
435C2×C4×C17—22no—
436C2×C4×C17—22no—
437C2×C4×C17—22no—
438C2×C4×C17—22no—
439C2×C4×C17—22no—
440C2×C4×C17—22no—
441C2×C4×C17—22no—
442C2×C4×C17—22no—
443C2×C4×C17—22no—
444C2×C4×C17—22no—
445C2×C4×C17—22no—
446C2×C4×C17—22no—
447C2×C4×C17—22no—
448C2×C4×C17—22no—
449C2×C4×C17—22no—
450C2×C4×C17—22no—
451C2×C4×C17—22no—
452C2×C4×C17—22no—
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—41no—
464C2×C4×C17—41no—
465C2×C4×C17—41no—
466C2×C4×C17—41no—
467C2×C4×C17—41no—
468C2×C4×C17—41no—
469C2×C4×C17—41no—
470C2×C4×C17—41no—
471C2×C4×C17—41no—
472C2×C4×C17—41no—
473C2×C4×C17—41no—
474C2×C4×C17—41no—
475C2×C4×C17—41no—
476C2×C4×C17C4×D414yescomplemented
477C22⋊D17—232no—
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—22no—
487C2×Dic17—22no—
488C2×Dic17—22no—
489C2×Dic17—22no—
490C2×Dic17—22no—
491C2×Dic17—22no—
492C2×Dic17—22no—
493C2×Dic17—22no—
494C2×Dic17—22no—
495C2×Dic17—22no—
496C2×Dic17—22no—
497C2×Dic17—22no—
498C2×Dic17—22no—
499C2×Dic17—22no—
500C2×Dic17—22no—
501C2×Dic17—22no—
502C2×Dic17—22no—
503C2×Dic17—22no—
504C2×Dic17—22no—
505C2×Dic17—416no—
506C2×Dic17—41no—
507C2×Dic17—41no—
508C2×Dic17—41no—
509C2×Dic17—41no—
510C2×Dic17—41no—
511C2×Dic17—41no—
512C2×Dic17—41no—
513C2×Dic17—41no—
514C2×Dic17—41no—
515C2×Dic17—41no—
516C2×Dic17—41no—
517C2×Dic17—41no—
518C2×Dic17—41no—
519C2×Dic17—41no—
520C2×Dic17—41no—
521C2×Dic17—41no—
522C2×Dic17—41no—
523C2×Dic17—41no—
524C2×Dic17—41no—
525C2×Dic17C2×C4⋊C414yescomplemented
526C2×Dic17C4×D414yescomplemented
527C2×Dic17#12014yes—
528C4×D17—232no—
529C4×D17—416no—
530C4×D17—416no—
531C22×C4×D4—171no—
532C23×C4⋊C4—171no—
533C2×#386—171no—
534C2×#386—171no—
535C2×#385—171no—
536C2×#385—171no—
537C2×#385—171no—
538#1444—171no—
539#1444—171no—
540#1439—171no—
541#1439D1711yescharacteristic, complemented
542#1436—171no—
543#1436—171no—
544C22⋊#95—171no—
545C22⋊#95—171no—
546C22×C17—24no—
547C22×C17—24no—
548C22×C17—24no—
549C22×C17—42no—
550C22×C17—42no—
551C22×C17—42no—
552C22×C17—42no—
553C22×C17—42no—
554C22×C17—42no—
555C22×C17—42no—
556C22×C17—42no—
557C22×C17—42no—
558C22×C17—42no—
559C22×C17—42no—
560C22×C17—42no—
561C22×C17C22×C4⋊C411yescharacteristic
562C22×C17C2×C4×D411yescharacteristic
563C22×C17C2×C4×D411yescharacteristic
564C22×C17C2×C4×D411yescharacteristic
565C22×C17C2×C4×D411yescharacteristic
566C22×C17#52011yescharacteristic
567C22×C17#52011yescharacteristic
568C22×C17C2×#12011yescharacteristic
569C22×C17C2×#12011yescharacteristic
570C22×C17C2×C22⋊Q811yescharacteristic
571C22×C17C2×C22⋊Q811yescharacteristic
572C22×C17C2×#12311yescharacteristic
573C22×C17#52511yescharacteristic
574C22×C17#52511yescharacteristic
575C22×C17#52511yescharacteristic
576C22×C17#53411yescharacteristic
577C22×C17#53611yescharacteristic
578C22×C17#53911yescharacteristic
579C22×C17#53911yescharacteristic
580C22×C17D4211yescharacteristic
581C22×C17D4211yescharacteristic
582C22×C17D4211yescharacteristic
583C22×C17D4211yescharacteristic
584C22×C17#54711yescharacteristic
585C22×C17#54711yescharacteristic
586C22×C17#54711yescharacteristic
587C22×C17#54711yescharacteristic
588C22×C17#54811yescharacteristic
589C22×C17#54811yescharacteristic
590C22×C17D4×Q811yescharacteristic
591C22×C17D4×Q811yescharacteristic
592C22×C17#55311yescharacteristic
593C22×C17#55311yescharacteristic
594C22×C17#55411yescharacteristic
595C22×C17#55411yescharacteristic
596C2×D17—24no—
597C2×D17—24no—
598C2×D17—24no—
599C2×D17—24no—
600C2×D17—24no—
601C2×D17—24no—
602C2×D17—24no—
603C2×D17—24no—
604C2×D17—24no—
605C2×D17—24no—
606C2×D17—24no—
607C2×D17—24no—
608C2×D17—24no—
609C2×D17—24no—
610C2×D17#38518yescomplemented
611C4×C17—24no—
612C4×C17—42no—
613C4×C17—42no—
614C4×C17—42no—
615C4×C17—42no—
616C4×C17—81no—
617Dic17—24no—
618Dic17—24no—
619Dic17—24no—
620Dic17—42no—
621Dic17—42no—
622Dic17—42no—
623Dic17—81no—
624C23×D4—171no—
625C24×C4—171no—
626C24×C4—171no—
627C24×C4—171no—
628C24×C4—171no—
629C2×C4×D4—344no—
630C2×C4×D4—344no—
631C2×C4×D4—344no—
632C22×C4⋊C4—171no—
633C22×C4⋊C4—171no—
634C22×C4⋊C4—171no—
635C22×C4⋊C4—171no—
636C22×C4⋊C4—171no—
637C22×C4⋊C4—171no—
638C22×C4⋊C4—344no—
639C22×C4⋊C4—344no—
640C22×C4⋊C4—344no—
641C22×C4⋊C4C2×D1711yescharacteristic
642C22×C22⋊C4—171no—
643C22×C22⋊C4—171no—
644C22×C22⋊C4—171no—
645C22×C22⋊C4—171no—
646C22×C22⋊C4—171no—
647C22×C22⋊C4C2×D1711yescharacteristic
648C22×C22⋊C4C2×D1711yescharacteristic
649C22×C22⋊C4C2×D1711yescharacteristic
650C22×C42—171no—
651#386—178no—
652#386—344no—
653#385—344no—
654#385—344no—
655#385—344no—
656C2×#95—171no—
657C2×#95—171no—
658C2×#95—171no—
659C2×#95—171no—
660C2×#95—171no—
661C2×#95—171no—
662C2×#95—171no—
663C2×#95—171no—
664C2×#95—171no—
665C2×#95—171no—
666C2×#95—171no—
667C2×#95C2×D1711yescharacteristic
668C2×#95C2×D1711yescharacteristic
669C2×#95C2×D1711yescharacteristic
670C2×C17—44no—
671C2×C17C2×#38511yescharacteristic
672C2×C17C4×#12011yescharacteristic
673C2×C17#232211yescharacteristic
674C2×C17D4×C4⋊C411yescharacteristic
675C2×C17D4×C4⋊C411yescharacteristic
676C2×C17#236111yescharacteristic
677C2×C17#236111yescharacteristic
678C2×C17#240311yescharacteristic
679C2×C17#240611yescharacteristic
680C2×C17#240911yescharacteristic
681C2×C17#244311yescharacteristic
682C2×C17#244311yescharacteristic
683C2×C17#244911yescharacteristic
684C2×C17#244911yescharacteristic
685C2×C17#257911yescharacteristic
686D17—28no—
687C25—171no—
688C25C22×D1711yescharacteristic
689C22×D4—174no—
690C22×D4—174no—
691C22×D4—174no—
692C22×D4—342no—
693C22×D4—342no—
694C22×D4—342no—
695C22×D4—342no—
696C23×C4—171no—
697C23×C4—171no—
698C23×C4—171no—
699C23×C4—171no—
700C23×C4—171no—
701C23×C4—171no—
702C23×C4—174no—
703C23×C4—174no—
704C23×C4—171no—
705C23×C4—342no—
706C23×C4—342no—
707C23×C4—342no—
708C23×C4—342no—
709C23×C4—342no—
710C23×C4—342no—
711C23×C4—342no—
712C23×C4—342no—
713C23×C4—342no—
714C23×C4—342no—
715C23×C4—342no—
716C23×C4—342no—
717C23×C4—342no—
718C23×C4—342no—
719C23×C4—342no—
720C23×C4—342no—
721C23×C4—342no—
722C23×C4—342no—
723C23×C4—342no—
724C23×C4—342no—
725C23×C4—681no—
726C23×C4—681no—
727C23×C4—681no—
728C23×C4—681no—
729C23×C4—681no—
730C23×C4—681no—
731C23×C4C22×D1711yescharacteristic
732C23×C4C22×D1711yescharacteristic
733C23×C4C22×D1711yescharacteristic
734C23×C4C22×D1711yescharacteristic
735C23×C4C22×D1711yescharacteristic
736C23×C4C22×D1711yescharacteristic
737C4×D4—3432no—
738C2×C4⋊C4—22no—
739C2×C4⋊C4—22no—
740C2×C4⋊C4—22no—
741C2×C4⋊C4—174no—
742C2×C4⋊C4—174no—
743C2×C4⋊C4—3432no—
744C2×C4⋊C4—342no—
745C2×C4⋊C4—342no—
746C2×C4⋊C4—342no—
747C2×C4⋊C4—342no—
748C2×C4⋊C4—342no—
749C2×C4⋊C4—342no—
750C2×C4⋊C4—342no—
751C2×C4⋊C4—342no—
752C2×C4⋊C4—342no—
753C2×C4⋊C4—342no—
754C2×C4⋊C4—342no—
755C2×C4⋊C4—342no—
756C2×C4⋊C4—342no—
757C2×C4⋊C4—342no—
758C2×C4⋊C4—681no—
759C2×C4⋊C4—681no—
760C2×C22⋊C4—22no—
761C2×C22⋊C4—22no—
762C2×C22⋊C4—22no—
763C2×C22⋊C4—22no—
764C2×C22⋊C4—22no—
765C2×C22⋊C4—22no—
766C2×C22⋊C4—22no—
767C2×C22⋊C4—41no—
768C2×C22⋊C4—174no—
769C2×C22⋊C4—174no—
770C2×C22⋊C4—174no—
771C2×C22⋊C4—342no—
772C2×C22⋊C4—342no—
773C2×C22⋊C4—342no—
774C2×C22⋊C4—342no—
775C2×C22⋊C4—342no—
776C2×C22⋊C4—342no—
777C2×C22⋊C4—342no—
778C2×C22⋊C4—342no—
779C2×C22⋊C4—342no—
780C2×C22⋊C4—342no—
781C2×C22⋊C4—342no—
782C2×C22⋊C4—681no—
783C2×C22⋊C4C4×D1714yescomplemented
784C2×C42—342no—
785C2×C42—342no—
786C2×C42—342no—
787#95—22no—
788#95—22no—
789#95—41no—
790#95—174no—
791#95—174no—
792#95—342no—
793#95—342no—
794#95—342no—
795#95—342no—
796#95—342no—
797#95—342no—
798#95—342no—
799#95—342no—
800#95—681no—
801C17#1401511yescharacteristic, complemented, Sylow
802C24—21no—
803C24—21no—
804C24—21no—
805C24—21no—
806C24—21no—
807C24—21no—
808C24—21no—
809C24—21no—
810C24—21no—
811C24—21no—
812C24—21no—
813C24—21no—
814C24—172no—
815C24—172no—
816C24—172no—
817C24—172no—
818C24—172no—
819C24—172no—
820C24—172no—
821C24—341no—
822C24—341no—
823C24—341no—
824C24—341no—
825C24—341no—
826C24—341no—
827C24—341no—
828C24—341no—
829C24C2×C4×D1712yes—
830C24D4×D1712yes—
831C24Q8×D1712yes—
832C24C23×D1711yescharacteristic
833C2×D4—1716no—
834C2×D4—348no—
835C2×D4—348no—
836C2×D4—348no—
837C2×D4—348no—
838C2×D4—348no—
839C2×D4—348no—
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—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—172no—
876C22×C4—172no—
877C22×C4—172no—
878C22×C4—172no—
879C22×C4—172no—
880C22×C4—172no—
881C22×C4—172no—
882C22×C4—172no—
883C22×C4—172no—
884C22×C4—172no—
885C22×C4—172no—
886C22×C4—172no—
887C22×C4—348no—
888C22×C4—348no—
889C22×C4—348no—
890C22×C4—348no—
891C22×C4—348no—
892C22×C4—348no—
893C22×C4—348no—
894C22×C4—348no—
895C22×C4—348no—
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—348no—
909C22×C4—348no—
910C22×C4—341no—
911C22×C4—341no—
912C22×C4—341no—
913C22×C4—341no—
914C22×C4—341no—
915C22×C4—341no—
916C22×C4—341no—
917C22×C4—341no—
918C22×C4—341no—
919C22×C4—341no—
920C22×C4—341no—
921C22×C4—341no—
922C22×C4—341no—
923C22×C4—341no—
924C22×C4—341no—
925C22×C4—341no—
926C22×C4—341no—
927C22×C4—341no—
928C22×C4—341no—
929C22×C4—341no—
930C22×C4—341no—
931C22×C4—341no—
932C22×C4—341no—
933C22×C4—341no—
934C22×C4—341no—
935C22×C4—684no—
936C22×C4—684no—
937C22×C4—684no—
938C22×C4—684no—
939C22×C4—684no—
940C22×C4—684no—
941C22×C4—684no—
942C22×C4—684no—
943C22×C4—684no—
944C22×C4—684no—
945C22×C4—684no—
946C22×C4—684no—
947C22×C4—684no—
948C22×C4—684no—
949C22×C4—684no—
950C22×C4—684no—
951C22×C4—684no—
952C22×C4C2×C4×D1712yes—
953C22×C4C2×C4×D1712yes—
954C22×C4D4×D1712yes—
955C22×C4D4×D1712yes—
956C22×C4D4×D1712yes—
957C22×C4D4×D1712yes—
958C22×C4#6325412yes—
959C4⋊C4—28no—
960C4⋊C4—348no—
961C4⋊C4—348no—
962C4⋊C4—348no—
963C4⋊C4—348no—
964C4⋊C4—684no—
965C4⋊C4—684no—
966C22⋊C4—28no—
967C22⋊C4—28no—
968C22⋊C4—44no—
969C22⋊C4—348no—
970C22⋊C4—348no—
971C22⋊C4—348no—
972C22⋊C4—684no—
973C22⋊C4—684no—
974C42—348no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—41no—
994C23—41no—
995C23—41no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23—41no—
1001C23—41no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—174no—
1010C23—174no—
1011C23—174no—
1012C23—174no—
1013C23—174no—
1014C23—174no—
1015C23—174no—
1016C23—342no—
1017C23—342no—
1018C23—342no—
1019C23—342no—
1020C23—342no—
1021C23—342no—
1022C23—342no—
1023C23—342no—
1024C23—342no—
1025C23—342no—
1026C23—342no—
1027C23—342no—
1028C23—342no—
1029C23—342no—
1030C23—342no—
1031C23—342no—
1032C23—342no—
1033C23—342no—
1034C23—342no—
1035C23—342no—
1036C23—342no—
1037C23—342no—
1038C23—342no—
1039C23—342no—
1040C23—342no—
1041C23—342no—
1042C23—342no—
1043C23—342no—
1044C23C4⋊C4×D1714yescomplemented
1045C23C22×C4×D1711yescharacteristic
1046C23C2×D4×D1711yescharacteristic
1047C23C2×D4×D1711yescharacteristic
1048C23C2×D4×D1711yescharacteristic
1049C23C2×D4×D1711yescharacteristic
1050C23C2×D4×D1711yescharacteristic
1051C23C2×#6325411yescharacteristic
1052C23#1058769111yescharacteristic
1053C23C2×Q8×D1711yescharacteristic
1054C23#41×D1711yescharacteristic
1055C23#41×D1711yescharacteristic
1056C23#41×D1711yescharacteristic
1057C23#1058769611yescharacteristic
1058C23#1058769711yescharacteristic
1059C23#1058769711yescharacteristic
1060D4—3432no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—174no—
1103C2×C4—174no—
1104C2×C4—174no—
1105C2×C4—3432no—
1106C2×C4—342no—
1107C2×C4—342no—
1108C2×C4—342no—
1109C2×C4—342no—
1110C2×C4—342no—
1111C2×C4—342no—
1112C2×C4—342no—
1113C2×C4—342no—
1114C2×C4—342no—
1115C2×C4—342no—
1116C2×C4—342no—
1117C2×C4—342no—
1118C2×C4—342no—
1119C2×C4—342no—
1120C2×C4—342no—
1121C2×C4—342no—
1122C2×C4—342no—
1123C2×C4—342no—
1124C2×C4—342no—
1125C2×C4—342no—
1126C2×C4—342no—
1127C2×C4—342no—
1128C2×C4—342no—
1129C2×C4—342no—
1130C2×C4—342no—
1131C2×C4—342no—
1132C2×C4—342no—
1133C2×C4—6816no—
1134C2×C4—6816no—
1135C2×C4—6816no—
1136C2×C4—681no—
1137C2×C4—681no—
1138C2×C4—681no—
1139C2×C4—681no—
1140C2×C4—681no—
1141C2×C4—681no—
1142C2×C4—681no—
1143C2×C4—681no—
1144C2×C4—681no—
1145C2×C4—681no—
1146C2×C4—681no—
1147C2×C4—681no—
1148C2×C4—681no—
1149C2×C4—681no—
1150C2×C4—681no—
1151C2×C4—681no—
1152C2×C4—681no—
1153C2×C4—681no—
1154C2×C4—681no—
1155C2×C4#1058756714yescomplemented
1156C22—24no—
1157C22—24no—
1158C22—24no—
1159C22—42no—
1160C22—42no—
1161C22—42no—
1162C22—42no—
1163C22—42no—
1164C22—42no—
1165C22—42no—
1166C22—42no—
1167C22—42no—
1168C22—42no—
1169C22—42no—
1170C22—42no—
1171C22—178no—
1172C22—344no—
1173C22—344no—
1174C22—344no—
1175C22—344no—
1176C22—344no—
1177C22—344no—
1178C22—344no—
1179C22—344no—
1180C22—344no—
1181C22—344no—
1182C22—344no—
1183C22—344no—
1184C22—344no—
1185C22—344no—
1186C22C2×C4⋊C4×D1711yescharacteristic
1187C22C4×D4×D1711yescharacteristic
1188C22C4×D4×D1711yescharacteristic
1189C22C4×D4×D1711yescharacteristic
1190C22C2×#1058756711yescharacteristic
1191C22#1176328811yescharacteristic
1192C22#1176328911yescharacteristic
1193C22#120×D1711yescharacteristic
1194C22#120×D1711yescharacteristic
1195C22C22⋊Q8×D1711yescharacteristic
1196C22C22⋊Q8×D1711yescharacteristic
1197C22#123×D1711yescharacteristic
1198C22#1176331711yescharacteristic
1199C22#1176331911yescharacteristic
1200C22#1176331911yescharacteristic
1201C22#1176336711yescharacteristic
1202C22#1176337911yescharacteristic
1203C22#1176340011yescharacteristic
1204C22#1176340211yescharacteristic
1205C22#1176344111yescharacteristic
1206C22#1176344311yescharacteristic
1207C22#1176344311yescharacteristic
1208C22#1176344411yescharacteristic
1209C22#1176345711yescharacteristic
1210C22#1176345711yescharacteristic
1211C22#1176345911yescharacteristic
1212C22#1176345911yescharacteristic
1213C22#1176346711yescharacteristic
1214C22#1176346711yescharacteristic
1215C22#1176347211yescharacteristic
1216C22#1176347211yescharacteristic
1217C22#1176350611yescharacteristic
1218C22#1176351011yescharacteristic
1219C22#1176351311yescharacteristic
1220C22#1176351711yescharacteristic
1221C4—24no—
1222C4—42no—
1223C4—42no—
1224C4—42no—
1225C4—42no—
1226C4—81no—
1227C4—344no—
1228C4—344no—
1229C4—344no—
1230C4—682no—
1231C4—682no—
1232C4—682no—
1233C4—1361no—
1234C2—44no—
1235C2—348no—
1236C2D17×#38511yescharacteristic
1237C2#1453128911yescharacteristic
1238C2#1453145411yescharacteristic
1239C2#1453168011yescharacteristic
1240C2#1453168211yescharacteristic
1241C2#1453179711yescharacteristic
1242C2#1453180511yescharacteristic
1243C2#1453209311yescharacteristic
1244C2#1453211411yescharacteristic
1245C2#1453214211yescharacteristic
1246C2#1453251211yescharacteristic
1247C2#1453251411yescharacteristic
1248C2#1453259411yescharacteristic
1249C2#1453259611yescharacteristic
1250C2#1453412611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1439C2
socle, cosocleC24×C17C24
prime radicalC23×C22⋊D17C22
hypercenter#1439D17
hypocenterC17#14015
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊C4×D17C2semidirect
5. C2×#11762684C2semidirect
6. C2×#11762683C2semidirect
7. C2×#11762681C2semidirect
8. #14527048C2semidirect
9. #14527047C2semidirect
10. #14527027C2semidirect
11. #14527018C2semidirect
12. #14527015C2semidirect
13. #14527005C2semidirect
14. #14527005C2semidirect
15. C17×#1439C2semidirect
40. #11762685C4semidirect
110. C22×C4×D17C2×C4semidirect
123. C2×C22⋊C4×C17C2×C4semidirect
129. C2×C22⋊Dic17C2×C4semidirect
137. C2×#63227C2×C4semidirect
144. C2×C4⋊Dic17D4semidirect
156. C2×#63225D4semidirect
174. #10587502C2×C4semidirect
175. #10587502C2×C4semidirect
255. C2×C22⋊D17C4⋊C4semidirect
384. C23×C17C2×C4⋊C4semidirect
476. C2×C4×C17C4×D4semidirect
525. C2×Dic17C2×C4⋊C4semidirect
526. C2×Dic17C4×D4semidirect
541. #1439D17semidirect
610. C2×D17#385semidirect
783. C2×C22⋊C4C4×D17semidirect
801. C17#14015semidirect
1044. C23C4⋊C4×D17semidirect
1155. C2×C4#10587567semidirect

Maximal subgroups

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

subgroupindex
C22×#105875672
C22×C4⋊C4×D172
C2×#117626852
C2×#117626842
C2×#117626832
C2×#117626812
#145270482
#145270472
#145270272
#145270182
#145270152
#145270052
C17×#14392
#1401517