Finite Group Databasebeta

← #16957690

Subgroups — #16957690

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×C4×D68C211yesmaximal, characteristic
2C22×C4⋊C4×D17C211yesmaximal, characteristic, complemented
3C2×#11762687C211yesmaximal, characteristic
4C2×#11762687C211yesmaximal, characteristic
5C2×#11762683C211yesmaximal, characteristic, complemented
6C2×#11762683C211yesmaximal, characteristic, complemented
7C2×#11762680C211yesmaximal, characteristic, complemented
8#14527049C211yesmaximal, characteristic, complemented
9#14527048C211yesmaximal, characteristic, complemented
10#14527030C211yesmaximal, characteristic, complemented
11#14527028C211yesmaximal, characteristic, complemented
12#14527017C211yesmaximal, characteristic, complemented
13#14527005C211yesmaximal, characteristic, complemented
14#14527005C211yesmaximal, characteristic, complemented
15C17×#1436C211yesmaximal, characteristic, complemented
16C23×D68C2211yescharacteristic
17C23×C4×D17C2211yescharacteristic
18C23×C4×D17C2211yescharacteristic
19C23×C4×D17C2211yescharacteristic
20C23×C4×D17C2211yescharacteristic
21C2×C4×D68—24no—
22C2×C4×D68—24no—
23C2×C4×D68—24no—
24C22×C4⋊Dic17C2211yescharacteristic
25C22×C4⋊Dic17C2211yescharacteristic
26C22×C4⋊Dic17C2211yescharacteristic
27C22×#63225C2211yescharacteristic
28C22×#63225C2211yescharacteristic
29C22×#63225C2211yescharacteristic
30C2×C4⋊C4×D17—24no—
31C2×C4⋊C4×D17—24no—
32C2×C4⋊C4×D17—24no—
33C22×#63227C2211yescharacteristic
34C22×#63227C2211yescharacteristic
35C22×#63227C2211yescharacteristic
36C22×#63227C2211yescharacteristic
37C22×#63227C2211yescharacteristic
38C22×#63227C2211yescharacteristic
39C22×#63227C2211yescharacteristic
40C22×#63227C2211yescharacteristic
41#11762687—24no—
42#11762687C418yescomplemented
43#11762683—24no—
44#11762683—24no—
45#11762680—24no—
46C2×#10587502C2211yescharacteristic
47C2×#10587502C2211yescharacteristic
48C2×#10587502C2211yescharacteristic
49C2×#10587502C2211yescharacteristic
50C2×#10587502C2211yescharacteristic
51C2×#10587502C2211yescharacteristic
52C2×#10587502C2211yescharacteristic
53C2×#10587502C2211yescharacteristic
54C2×#10587502C2211yescharacteristic
55C22×C4⋊C4×C17C2211yescharacteristic
56C22×C42×C17C2211yescharacteristic
57C2×C17×#95C2211yescharacteristic
58C2×C17×#95C2211yescharacteristic
59C2×C17×#95C2211yescharacteristic
60C2×C17×#95C2211yescharacteristic
61C2×C17×#95C2211yescharacteristic
62C24×D17C2311yescharacteristic
63C24×D17C2311yescharacteristic
64C23×C4×C17C2311yescharacteristic
65C23×C4×C17C2311yescharacteristic
66C23×C4×C17C2311yescharacteristic
67C23×C4×C17C2311yescharacteristic
68C23×C4×C17C2311yescharacteristic
69C23×C4×C17C2311yescharacteristic
70C23×C4×C17C2311yescharacteristic
71C23×Dic17C2311yescharacteristic
72C23×Dic17C2311yescharacteristic
73C23×Dic17C2311yescharacteristic
74C23×Dic17C2311yescharacteristic
75C23×Dic17C2311yescharacteristic
76C23×Dic17C2311yescharacteristic
77C22×D68—22no—
78C22×D68—22no—
79C22×D68—22no—
80C22×D68—22no—
81C22×D68C2×C414yes—
82C22×D68D414yes—
83C22×D68Q814yes—
84C22×C4×D17—22no—
85C22×C4×D17—22no—
86C22×C4×D17—22no—
87C22×C4×D17—22no—
88C22×C4×D17—22no—
89C22×C4×D17—22no—
90C22×C4×D17—22no—
91C22×C4×D17—22no—
92C22×C4×D17—22no—
93C22×C4×D17—22no—
94C22×C4×D17—22no—
95C22×C4×D17—22no—
96C22×C4×D17—22no—
97C22×C4×D17—22no—
98C22×C4×D17—22no—
99C22×C4×D17—22no—
100C22×C4×D17—22no—
101C22×C4×D17—22no—
102C22×C4×D17—22no—
103C22×C4×D17—22no—
104C22×C4×D17—41no—
105C22×C4×D17—41no—
106C22×C4×D17—41no—
107C22×C4×D17—41no—
108C22×C4×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×C17D414yescomplemented
115C2×C42×C17—22no—
116C2×C42×C17—22no—
117C2×C42×C17—22no—
118C2×#63227—22no—
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—22no—
131C2×#63227—22no—
132C2×#63227—22no—
133C2×#63227—22no—
134C2×#63227—22no—
135C2×#63227—22no—
136C2×#63227—41no—
137C2×#63227—41no—
138C2×#63227C2×C414yescomplemented
139C2×#63227C2×C414yescomplemented
140C2×#63227C2×C414yescomplemented
141C2×#63227D414yes—
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⋊Dic17—41no—
151C2×#63225—22no—
152C2×#63225—22no—
153C2×#63225—22no—
154C2×#63225—22no—
155C2×#63225—22no—
156C2×#63225—22no—
157C2×#63225—22no—
158C2×#63225—41no—
159C2×#63225D414yescomplemented
160C4⋊C4×D17—232no—
161C4×D68—232no—
162C17×#95—22no—
163C17×#95—22no—
164C17×#95—22no—
165C17×#95—22no—
166C17×#95C2×C414yescomplemented
167#10587502—22no—
168#10587502—22no—
169#10587502—22no—
170#10587502—22no—
171#10587502—22no—
172#10587502—22no—
173#10587502—41no—
174#10587502—41no—
175#10587502C2×C414yescomplemented
176C24×C17C2411yescharacteristic
177C23×D17—21no—
178C23×D17—21no—
179C23×D17—21no—
180C23×D17—21no—
181C23×D17—21no—
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×D17—21no—
197C23×D17C22×C412yes—
198C23×D17C22×C412yes—
199C23×D17C2×D412yes—
200C23×D17C2×D412yes—
201C23×D17C2×D412yes—
202C23×D17C2×D412yes—
203C23×D17C2×Q812yes—
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×C17—21no—
243C22×C4×C17—21no—
244C22×C4×C17C22×C412yes—
245C22×C4×C17C22×C412yes—
246C22×C4×C17C22×C412yes—
247C22×C4×C17C2×D412yes—
248C22×C4×C17C2×D412yes—
249C22×C4×C17C2×D412yes—
250C22×C4×C17C2×D412yes—
251C22×C4×C17C2×D412yes—
252C22×C4×C17C2×D412yes—
253C22×C4×C17C2×D412yes—
254C22×C4×C17C2×Q812yes—
255C22×C4×C17#4112yes—
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×Dic17C2×D412yes—
294C22×Dic17C2×D412yes—
295C22×Dic17C2×D412yes—
296C22×Dic17C2×D412yes—
297C22×Dic17#4112yes—
298C2×D68—28no—
299C2×D68—28no—
300C2×D68—28no—
301C2×D68—28no—
302C2×D68—28no—
303C2×D68—28no—
304C2×D68C4⋊C4116yescomplemented
305C2×C4×D17—28no—
306C2×C4×D17—28no—
307C2×C4×D17—28no—
308C2×C4×D17—28no—
309C2×C4×D17—28no—
310C2×C4×D17—28no—
311C2×C4×D17—28no—
312C2×C4×D17—28no—
313C2×C4×D17—28no—
314C2×C4×D17—28no—
315C2×C4×D17—28no—
316C2×C4×D17—44no—
317C2×C4×D17—44no—
318C2×C4×D17—44no—
319C2×C4×D17—44no—
320C2×C4×D17—44no—
321C2×C4×D17—44no—
322C2×C4×D17—44no—
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—
334C42×C17—28no—
335#63227—28no—
336#63227—28no—
337#63227—28no—
338#63227—28no—
339#63227—28no—
340#63227—44no—
341#63227—44no—
342#63227—44no—
343C4⋊Dic17—28no—
344C4⋊Dic17—28no—
345C4⋊Dic17—44no—
346#63225—28no—
347#63225—28no—
348#63225—44no—
349#14015—171nomaximal, Sylow
350C23×C17C23×C411yescharacteristic
351C23×C17C22×D411yescharacteristic
352C23×C17C22×D411yescharacteristic
353C23×C17C22×D411yescharacteristic
354C23×C17C22×D411yescharacteristic
355C23×C17C22×D411yescharacteristic
356C23×C17C22×Q811yescharacteristic
357C23×C17C2×#4111yescharacteristic
358C23×C17C2×#4111yescharacteristic
359C23×C17C2×#4111yescharacteristic
360C23×C17C2×#4111yescharacteristic
361C23×C17H(5,𝔽2)11yescharacteristic
362C23×C17H(5,𝔽2)11yescharacteristic
363C23×C172−1+411yescharacteristic
364C23×C172−1+411yescharacteristic
365C22×D17—22no—
366C22×D17—22no—
367C22×D17—22no—
368C22×D17—22no—
369C22×D17—22no—
370C22×D17—22no—
371C22×D17—22no—
372C22×D17—22no—
373C22×D17—22no—
374C22×D17—22no—
375C22×D17—22no—
376C22×D17—22no—
377C22×D17—22no—
378C22×D17—22no—
379C22×D17—22no—
380C22×D17—22no—
381C22×D17—22no—
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—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—41no—
412C22×D17—41no—
413C22×D17—41no—
414C22×D17—41no—
415C22×D17—41no—
416C22×D17—41no—
417C22×D17—41no—
418C22×D17—41no—
419C22×D17—41no—
420C22×D17—41no—
421C22×D17—41no—
422C22×D17—41no—
423C22×D17—41no—
424C22×D17—41no—
425C22×D17—41no—
426C22×D17—41no—
427C22×D17C2×C4⋊C414yes—
428C22×D17C2×C4⋊C414yescomplemented
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—22no—
454C2×C4×C17—22no—
455C2×C4×C17—22no—
456C2×C4×C17—22no—
457C2×C4×C17—22no—
458C2×C4×C17—22no—
459C2×C4×C17—22no—
460C2×C4×C17—22no—
461C2×C4×C17—22no—
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×C17—41no—
477C2×C4×C17—41no—
478C2×C4×C17—41no—
479C2×C4×C17—41no—
480C2×C4×C17—41no—
481C2×C4×C17C2×C4⋊C414yescomplemented
482C2×C4×C17C4×D414yescomplemented
483C2×C4×C17#12014yes—
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—41no—
503C2×Dic17—41no—
504C2×Dic17—41no—
505C2×Dic17—41no—
506C2×Dic17—41no—
507C2×Dic17—41no—
508C2×Dic17—41no—
509C2×Dic17—41no—
510C2×Dic17—41no—
511C2×Dic17—41no—
512C2×Dic17—41no—
513C2×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×Dic17C4×D414yescomplemented
526D68—232no—
527C4×D17—232no—
528C4×D17—416no—
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#1439—171no—
542#1436—171no—
543#1436D1711yescharacteristic, complemented
544C22⋊#95—171no—
545C22⋊#95—171no—
546C22×C17C22×C4⋊C411yescharacteristic
547C22×C17C2×C4×D411yescharacteristic
548C22×C17C2×C4×D411yescharacteristic
549C22×C17C2×C4×D411yescharacteristic
550C22×C17C2×C4×D411yescharacteristic
551C22×C17#52011yescharacteristic
552C22×C17#52011yescharacteristic
553C22×C17C2×#12011yescharacteristic
554C22×C17C2×#12011yescharacteristic
555C22×C17C2×C22⋊Q811yescharacteristic
556C22×C17C2×C22⋊Q811yescharacteristic
557C22×C17C2×#12311yescharacteristic
558C22×C17#52511yescharacteristic
559C22×C17#52511yescharacteristic
560C22×C17#52511yescharacteristic
561C22×C17#53411yescharacteristic
562C22×C17#53611yescharacteristic
563C22×C17#53911yescharacteristic
564C22×C17#53911yescharacteristic
565C22×C17D4211yescharacteristic
566C22×C17D4211yescharacteristic
567C22×C17D4211yescharacteristic
568C22×C17D4211yescharacteristic
569C22×C17#54711yescharacteristic
570C22×C17#54711yescharacteristic
571C22×C17#54711yescharacteristic
572C22×C17#54711yescharacteristic
573C22×C17#54811yescharacteristic
574C22×C17#54811yescharacteristic
575C22×C17D4×Q811yescharacteristic
576C22×C17D4×Q811yescharacteristic
577C22×C17#55311yescharacteristic
578C22×C17#55311yescharacteristic
579C22×C17#55411yescharacteristic
580C22×C17#55411yescharacteristic
581C2×D17—24no—
582C2×D17—24no—
583C2×D17—24no—
584C2×D17—24no—
585C2×D17—24no—
586C2×D17—24no—
587C2×D17—24no—
588C2×D17—24no—
589C2×D17—24no—
590C2×D17—24no—
591C2×D17—24no—
592C2×D17—24no—
593C2×D17—24no—
594C2×D17—24no—
595C2×D17—24no—
596C2×D17—24no—
597C2×D17—24no—
598C2×D17—42no—
599C2×D17—42no—
600C2×D17—42no—
601C2×D17—42no—
602C2×D17—42no—
603C2×D17—42no—
604C2×D17—42no—
605C2×D17—42no—
606C2×D17—42no—
607C2×D17—42no—
608C2×D17—42no—
609C2×D17—42no—
610C2×D17#38518yescomplemented
611C4×C17—24no—
612C4×C17—24no—
613C4×C17—24no—
614C4×C17—42no—
615C4×C17—42no—
616C4×C17—42no—
617C4×C17—81no—
618Dic17—24no—
619Dic17—42no—
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⋊C4—171no—
648C22×C22⋊C4—171no—
649C22×C22⋊C4—171no—
650C22×C42C2×D1711yescharacteristic
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×#95C2×D1711yescharacteristic
666C2×#95C2×D1711yescharacteristic
667C2×#95C2×D1711yescharacteristic
668C2×#95C2×D1711yescharacteristic
669C2×#95C2×D1711yescharacteristic
670C2×C17C2×#38511yescharacteristic
671C2×C17C4×#12011yescharacteristic
672C2×C17#232211yescharacteristic
673C2×C17D4×C4⋊C411yescharacteristic
674C2×C17D4×C4⋊C411yescharacteristic
675C2×C17#236111yescharacteristic
676C2×C17#236111yescharacteristic
677C2×C17#240311yescharacteristic
678C2×C17#240611yescharacteristic
679C2×C17#240911yescharacteristic
680C2×C17#244311yescharacteristic
681C2×C17#244311yescharacteristic
682C2×C17#244911yescharacteristic
683C2×C17#244911yescharacteristic
684C2×C17#257911yescharacteristic
685D17—28no—
686D17—44no—
687C25—171no—
688C25—171no—
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—174no—
702C23×C4—174no—
703C23×C4—171no—
704C23×C4—342no—
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—681no—
725C23×C4—681no—
726C23×C4—681no—
727C23×C4—681no—
728C23×C4—681no—
729C23×C4—681no—
730C23×C4C22×D1711yescharacteristic
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—174no—
741C2×C4⋊C4—3432no—
742C2×C4⋊C4—342no—
743C2×C4⋊C4—342no—
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—681no—
758C2×C4⋊C4—681no—
759C2×C4⋊C4D6814yescomplemented
760C2×C22⋊C4—174no—
761C2×C22⋊C4—174no—
762C2×C22⋊C4—174no—
763C2×C22⋊C4—174no—
764C2×C22⋊C4—342no—
765C2×C22⋊C4—342no—
766C2×C22⋊C4—342no—
767C2×C22⋊C4—342no—
768C2×C22⋊C4—342no—
769C2×C22⋊C4—342no—
770C2×C22⋊C4—342no—
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⋊C4—681no—
784C2×C42—22no—
785C2×C42—22no—
786C2×C42—22no—
787#95—22no—
788#95—22no—
789#95—22no—
790#95—22no—
791#95—174no—
792#95—342no—
793#95—342no—
794#95—342no—
795#95—342no—
796#95—342no—
797#95—342no—
798#95—681no—
799#95—681no—
800#95C4×D1714yescomplemented
801C17#1401511yescharacteristic, complemented, Sylow
802C24—172no—
803C24—172no—
804C24—172no—
805C24—172no—
806C24—172no—
807C24—172no—
808C24—172no—
809C24—172no—
810C24—172no—
811C24—172no—
812C24—341no—
813C24—341no—
814C24—341no—
815C24—341no—
816C24—341no—
817C24—341no—
818C24—341no—
819C24—341no—
820C24—341no—
821C24—341no—
822C24—341no—
823C24—341no—
824C24—341no—
825C24—341no—
826C24—341no—
827C24—341no—
828C24—341no—
829C24—341no—
830C24—341no—
831C24—341no—
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—21no—
876C22×C4—21no—
877C22×C4—172no—
878C22×C4—172no—
879C22×C4—172no—
880C22×C4—172no—
881C22×C4—172no—
882C22×C4—172no—
883C22×C4—172no—
884C22×C4—348no—
885C22×C4—348no—
886C22×C4—348no—
887C22×C4—348no—
888C22×C4—348no—
889C22×C4—348no—
890C22×C4—348no—
891C22×C4—348no—
892C22×C4—348no—
893C22×C4—341no—
894C22×C4—341no—
895C22×C4—341no—
896C22×C4—341no—
897C22×C4—348no—
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—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—348no—
923C22×C4—341no—
924C22×C4—341no—
925C22×C4—341no—
926C22×C4—341no—
927C22×C4—341no—
928C22×C4—341no—
929C22×C4—341no—
930C22×C4—684no—
931C22×C4—684no—
932C22×C4—684no—
933C22×C4—684no—
934C22×C4—684no—
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×C4C2×C4×D1712yes—
948C22×C4C2×C4×D1712yes—
949C22×C4C2×C4×D1712yes—
950C22×C4C2×D6812yes—
951C22×C4C2×D6812yes—
952C22×C4C2×D6812yes—
953C22×C4#6325212yes—
954C22×C4D4×D1712yes—
955C22×C4D4×D1712yes—
956C22×C4D4×D1712yes—
957C22×C4D4×D1712yes—
958C22×C4Q8×D1712yes—
959C4⋊C4—28no—
960C4⋊C4—348no—
961C4⋊C4—348no—
962C4⋊C4—348no—
963C4⋊C4—348no—
964C4⋊C4—684no—
965C4⋊C4—684no—
966C22⋊C4—348no—
967C22⋊C4—348no—
968C22⋊C4—348no—
969C22⋊C4—348no—
970C22⋊C4—348no—
971C22⋊C4—684no—
972C22⋊C4—684no—
973C22⋊C4—684no—
974C42—28no—
975C23—174no—
976C23—174no—
977C23—174no—
978C23—174no—
979C23—174no—
980C23—174no—
981C23—174no—
982C23—174no—
983C23—342no—
984C23—342no—
985C23—342no—
986C23—342no—
987C23—342no—
988C23—342no—
989C23—342no—
990C23—342no—
991C23—342no—
992C23—342no—
993C23—342no—
994C23—342no—
995C23—342no—
996C23—342no—
997C23—342no—
998C23—342no—
999C23—342no—
1000C23—342no—
1001C23—342no—
1002C23—342no—
1003C23—342no—
1004C23—342no—
1005C23—342no—
1006C23—342no—
1007C23—342no—
1008C23—342no—
1009C23—342no—
1010C23—342no—
1011C23—342no—
1012C23—342no—
1013C23—342no—
1014C23—342no—
1015C23—342no—
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—681no—
1030C23—681no—
1031C23—681no—
1032C23—681no—
1033C23—681no—
1034C23—681no—
1035C23—681no—
1036C23—681no—
1037C23—681no—
1038C23—681no—
1039C23—681no—
1040C23—681no—
1041C23—681no—
1042C23—681no—
1043C23—681no—
1044C23—681no—
1045C23C22×C4×D1711yescharacteristic
1046C23C22×D6811yescharacteristic
1047C23C2×#6325211yescharacteristic
1048C23C2×D4×D1711yescharacteristic
1049C23C2×D4×D1711yescharacteristic
1050C23C2×D4×D1711yescharacteristic
1051C23C2×D4×D1711yescharacteristic
1052C23C2×Q8×D1711yescharacteristic
1053C23#1058769411yescharacteristic
1054C23#41×D1711yescharacteristic
1055C23#41×D1711yescharacteristic
1056C23#41×D1711yescharacteristic
1057C23#1058769611yescharacteristic
1058C23#1058769611yescharacteristic
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—22no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—22no—
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—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—174no—
1108C2×C4—3432no—
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—6816no—
1128C2×C4—6816no—
1129C2×C4—6816no—
1130C2×C4—681no—
1131C2×C4—681no—
1132C2×C4—681no—
1133C2×C4—681no—
1134C2×C4—681no—
1135C2×C4—681no—
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×C4C4×D6814yescomplemented
1154C2×C4#1058756814yes—
1155C2×C4C4⋊C4×D1714yescomplemented
1156C22—178no—
1157C22—344no—
1158C22—344no—
1159C22—344no—
1160C22—344no—
1161C22—344no—
1162C22—344no—
1163C22—344no—
1164C22—344no—
1165C22—344no—
1166C22—344no—
1167C22—344no—
1168C22—344no—
1169C22—344no—
1170C22—344no—
1171C22—344no—
1172C22—344no—
1173C22—344no—
1174C22—682no—
1175C22—682no—
1176C22—682no—
1177C22—682no—
1178C22—682no—
1179C22—682no—
1180C22—682no—
1181C22—682no—
1182C22—682no—
1183C22—682no—
1184C22—682no—
1185C22—682no—
1186C22C2×C4⋊C4×D1711yescharacteristic
1187C22C4×D4×D1711yescharacteristic
1188C22C4×D4×D1711yescharacteristic
1189C22C4×D4×D1711yescharacteristic
1190C22C2×C4×D6811yescharacteristic
1191C22#1176328911yescharacteristic
1192C22#1176329111yescharacteristic
1193C22#120×D1711yescharacteristic
1194C22C2×#1058756811yescharacteristic
1195C22C22⋊Q8×D1711yescharacteristic
1196C22C22⋊Q8×D1711yescharacteristic
1197C22#123×D1711yescharacteristic
1198C22#1176331811yescharacteristic
1199C22#1176331811yescharacteristic
1200C22#1176332111yescharacteristic
1201C22#1176337011yescharacteristic
1202C22#1176338211yescharacteristic
1203C22#1176340011yescharacteristic
1204C22#1176340711yescharacteristic
1205C22#1176344311yescharacteristic
1206C22#1176344311yescharacteristic
1207C22D4×D6811yescharacteristic
1208C22D4×D6811yescharacteristic
1209C22#1176345711yescharacteristic
1210C22#1176346011yescharacteristic
1211C22#1176346111yescharacteristic
1212C22#1176346411yescharacteristic
1213C22#1176346711yescharacteristic
1214C22#1176347111yescharacteristic
1215C22#1176347411yescharacteristic
1216C22Q8×D6811yescharacteristic
1217C22#1176350311yescharacteristic
1218C22#1176351011yescharacteristic
1219C22#1176351511yescharacteristic
1220C22#1176351911yescharacteristic
1221C4—24no—
1222C4—24no—
1223C4—24no—
1224C4—42no—
1225C4—42no—
1226C4—42no—
1227C4—81no—
1228C4—344no—
1229C4—682no—
1230C4—682no—
1231C4—682no—
1232C4—682no—
1233C4—1361no—
1234C2—348no—
1235C2—684no—
1236C2D17×#38511yescharacteristic
1237C2C4×#1058756811yescharacteristic
1238C2#1453145711yescharacteristic
1239C2#1453168511yescharacteristic
1240C2C4⋊C4×D6811yescharacteristic
1241C2#1453179711yescharacteristic
1242C2#1453180211yescharacteristic
1243C2#1453209611yescharacteristic
1244C2#1453211711yescharacteristic
1245C2#1453214711yescharacteristic
1246C2#1453252411yescharacteristic
1247C2#1453252611yescharacteristic
1248C2#1453259811yescharacteristic
1249C2#1453260011yescharacteristic
1250C2#1453413511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1436C2
socle, cosocleC24×C17C24
prime radicalC23×D68C22
hypercenter#1436D17
hypocenterC17#14015
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊C4×D17C2semidirect
5. C2×#11762683C2semidirect
6. C2×#11762683C2semidirect
7. C2×#11762680C2semidirect
8. #14527049C2semidirect
9. #14527048C2semidirect
10. #14527030C2semidirect
11. #14527028C2semidirect
12. #14527017C2semidirect
13. #14527005C2semidirect
14. #14527005C2semidirect
15. C17×#1436C2semidirect
42. #11762687C4semidirect
110. C22×C4×D17C2×C4semidirect
114. C2×C4⋊C4×C17D4semidirect
138. C2×#63227C2×C4semidirect
139. C2×#63227C2×C4semidirect
140. C2×#63227C2×C4semidirect
159. C2×#63225D4semidirect
166. C17×#95C2×C4semidirect
175. #10587502C2×C4semidirect
304. C2×D68C4⋊C4semidirect
428. C22×D17C2×C4⋊C4semidirect
481. C2×C4×C17C2×C4⋊C4semidirect
482. C2×C4×C17C4×D4semidirect
525. C2×Dic17C4×D4semidirect
543. #1436D17semidirect
610. C2×D17#385semidirect
759. C2×C4⋊C4D68semidirect
800. #95C4×D17semidirect
801. C17#14015semidirect
1153. C2×C4C4×D68semidirect
1155. C2×C4C4⋊C4×D17semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D682
C22×C4⋊C4×D172
C2×#117626872
C2×#117626832
C2×#117626802
#145270492
#145270482
#145270302
#145270282
#145270172
#145270052
C17×#14362
#1401517