Finite Group Databasebeta

← #16957731

Subgroups — #16957731

Order 4352.

2538 conjugacy classes of subgroups.

The subgroup lattice has 1212 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D17C211yesmaximal, characteristic, complemented
2C2×#11762700C211yesmaximal, characteristic, complemented
3C2×#11762699C211yesmaximal, characteristic, complemented
4C2×#11762687C211yesmaximal, characteristic
5C2×#11762687C211yesmaximal, characteristic
6C2×#11762687C211yesmaximal, characteristic
7C2×C4×#63227C211yesmaximal, characteristic, complemented
8#14527041C211yesmaximal, characteristic, complemented
9#14527039C211yesmaximal, characteristic, complemented
10#14527030C211yesmaximal, characteristic, complemented
11#14527028C211yesmaximal, characteristic, complemented
12#14527019C211yesmaximal, 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
20C22×C4⋊Dic17C2211yescharacteristic
21C22×#63225C2211yescharacteristic
22C22×#63225C2211yescharacteristic
23C2×C4⋊C4×D17—24no—
24C2×C4⋊C4×D17—24no—
25C2×C4⋊C4×D17—24no—
26C22×#63227C2211yescharacteristic
27C22×#63227C2211yescharacteristic
28C22×#63227C2211yescharacteristic
29C22×#63227C2211yescharacteristic
30C22×#63227C2211yescharacteristic
31C22×#63227C2211yescharacteristic
32C22×#63227C2211yescharacteristic
33C22×#63227C2211yescharacteristic
34C22×#63227C2211yescharacteristic
35C22×C4×Dic17C2211yescharacteristic
36#11762700—24no—
37#11762699—24no—
38#11762687—24no—
39#11762687—24no—
40#11762687C418yescomplemented
41C4×#63227—24no—
42C2×#10587502C2211yescharacteristic
43C2×#10587502C2211yescharacteristic
44C2×#10587502C2211yescharacteristic
45C2×#10587502C2211yescharacteristic
46C2×#10587502C2211yescharacteristic
47C2×#10587502C2211yescharacteristic
48C2×#10587502C2211yescharacteristic
49C2×#10587502C2211yescharacteristic
50C2×#10587502C2211yescharacteristic
51C2×#10587502C2211yescharacteristic
52C2×#10587502C2211yescharacteristic
53C22×C4⋊C4×C17C2211yescharacteristic
54C22×C42×C17C2211yescharacteristic
55C2×C17×#95C2211yescharacteristic
56C2×C17×#95C2211yescharacteristic
57C2×C17×#95C2211yescharacteristic
58C2×C17×#95C2211yescharacteristic
59C2×C17×#95C2211yescharacteristic
60C24×D17C2311yescharacteristic
61C24×D17C2311yescharacteristic
62C23×C4×C17C2311yescharacteristic
63C23×C4×C17C2311yescharacteristic
64C23×C4×C17C2311yescharacteristic
65C23×C4×C17C2311yescharacteristic
66C23×C4×C17C2311yescharacteristic
67C23×C4×C17C2311yescharacteristic
68C23×C4×C17C2311yescharacteristic
69C23×Dic17C2311yescharacteristic
70C23×Dic17C2311yescharacteristic
71C23×Dic17C2311yescharacteristic
72C23×Dic17C2311yescharacteristic
73C23×Dic17C2311yescharacteristic
74C23×Dic17C2311yescharacteristic
75C22×D68—22no—
76C22×D68—22no—
77C22×D68—22no—
78C22×D68—22no—
79C22×D68—22no—
80C22×D68—22no—
81C22×D68C2×C414yes—
82C22×C4×D17—22no—
83C22×C4×D17—22no—
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—41no—
98C22×C4×D17—41no—
99C22×C4×D17—41no—
100C22×C4×D17—41no—
101C22×C4×D17C2×C414yes—
102C22×C4×D17D414yes—
103C2×C4⋊C4×C17—22no—
104C2×C4⋊C4×C17—22no—
105C2×C4⋊C4×C17D414yescomplemented
106C2×C42×C17—22no—
107C2×C42×C17—22no—
108C2×C42×C17—41no—
109C2×#63227—22no—
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—22no—
123C2×#63227—22no—
124C2×#63227—22no—
125C2×#63227—22no—
126C2×#63227—22no—
127C2×#63227—22no—
128C2×#63227—41no—
129C2×#63227—41no—
130C2×#63227—41no—
131C2×#63227—41no—
132C2×#63227C2×C414yes—
133C2×#63227C2×C414yescomplemented
134C2×#63227C2×C414yescomplemented
135C2×#63227D414yes—
136C2×C4⋊Dic17—22no—
137C2×C4⋊Dic17—22no—
138C2×C4⋊Dic17—22no—
139C2×#63225—22no—
140C2×#63225—22no—
141C2×#63225—22no—
142C2×#63225—22no—
143C2×#63225—22no—
144C2×#63225D414yescomplemented
145C2×C4×Dic17—22no—
146C2×C4×Dic17—22no—
147C2×C4×Dic17—41no—
148C4⋊C4×D17—232no—
149C17×#95—22no—
150C17×#95—22no—
151C17×#95—22no—
152C17×#95—41no—
153C17×#95C2×C414yescomplemented
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#10587502C2×C414yescomplemented
165C24×C17C2411yescharacteristic
166C23×D17—21no—
167C23×D17—21no—
168C23×D17—21no—
169C23×D17—21no—
170C23×D17—21no—
171C23×D17—21no—
172C23×D17—21no—
173C23×D17—21no—
174C23×D17—21no—
175C23×D17—21no—
176C23×D17—21no—
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×D17C22×C412yes—
189C23×D17C22×C412yes—
190C23×D17C2×D412yes—
191C23×D17C2×D412yes—
192C23×D17#4112yes—
193C23×D17#4112yes—
194C23×D17#4112yes—
195C23×D17#4112yes—
196C22×C4×C17—21no—
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×C17—21no—
233C22×C4×C17—21no—
234C22×C4×C17—21no—
235C22×C4×C17C22×C412yes—
236C22×C4×C17C22×C412yes—
237C22×C4×C17C22×C412yes—
238C22×C4×C17C2×D412yes—
239C22×C4×C17C2×D412yes—
240C22×C4×C17C2×D412yes—
241C22×C4×C17C2×D412yes—
242C22×C4×C17C2×D412yes—
243C22×C4×C17C2×D412yes—
244C22×C4×C17#4112yes—
245C22×Dic17—21no—
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×Dic17—21no—
280C22×Dic17C22×C412yes—
281C22×Dic17C22×C412yes—
282C22×Dic17C2×D412yes—
283C22×Dic17C2×D412yes—
284C22×Dic17C2×D412yes—
285C22×Dic17C2×D412yes—
286C22×Dic17#4112yes—
287C2×D68—28no—
288C2×D68—28no—
289C2×D68—28no—
290C2×D68—44no—
291C2×D68—44no—
292C2×D68—44no—
293C2×D68—44no—
294C2×C4×D17—28no—
295C2×C4×D17—28no—
296C2×C4×D17—28no—
297C2×C4×D17—28no—
298C2×C4×D17—28no—
299C2×C4×D17—28no—
300C2×C4×D17—28no—
301C2×C4×D17—28no—
302C2×C4×D17—28no—
303C2×C4×D17—28no—
304C2×C4×D17—44no—
305C2×C4×D17—44no—
306C2×C4×D17—44no—
307C2×C4×D17—44no—
308C2×C4×D17—44no—
309C2×C4×D17—44no—
310C2×C4×D17—44no—
311C2×C4×D17—44no—
312C2×C4×D17—44no—
313C2×C4×D17—44no—
314C2×C4×D17—44no—
315C4⋊C4×C17—28no—
316C42×C17—44no—
317#63227—28no—
318#63227—28no—
319#63227—28no—
320#63227—28no—
321#63227—44no—
322#63227—44no—
323#63227—44no—
324#63227—44no—
325#63227—44no—
326C4⋊Dic17—28no—
327#63225—28no—
328#63225—28no—
329C4×Dic17—44no—
330#14019—171nomaximal, Sylow
331C23×C17C23×C411yescharacteristic
332C23×C17C22×D411yescharacteristic
333C23×C17C22×D411yescharacteristic
334C23×C17C22×D411yescharacteristic
335C23×C17C22×D411yescharacteristic
336C23×C17C2×#4111yescharacteristic
337C23×C17C2×#4111yescharacteristic
338C23×C17C2×#4111yescharacteristic
339C23×C17C2×#4111yescharacteristic
340C23×C17C2×#4111yescharacteristic
341C23×C17C2×#4111yescharacteristic
342C23×C17H(5,𝔽2)11yescharacteristic
343C23×C17H(5,𝔽2)11yescharacteristic
344C23×C172−1+411yescharacteristic
345C23×C172−1+411yescharacteristic
346C22×D17—22no—
347C22×D17—22no—
348C22×D17—22no—
349C22×D17—22no—
350C22×D17—22no—
351C22×D17—22no—
352C22×D17—22no—
353C22×D17—22no—
354C22×D17—22no—
355C22×D17—22no—
356C22×D17—22no—
357C22×D17—22no—
358C22×D17—22no—
359C22×D17—22no—
360C22×D17—22no—
361C22×D17—22no—
362C22×D17—22no—
363C22×D17—22no—
364C22×D17—22no—
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—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—
409C22×D17#11714yes—
410C22×D17C4×D414yes—
411C22×D17C4×D414yes—
412C22×D17#12114yes—
413C22×D17#12314yes—
414C22×D17#12414yes—
415C22×D17#12614yes—
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—22no—
428C2×C4×C17—22no—
429C2×C4×C17—22no—
430C2×C4×C17—22no—
431C2×C4×C17—22no—
432C2×C4×C17—22no—
433C2×C4×C17—22no—
434C2×C4×C17—22no—
435C2×C4×C17—22no—
436C2×C4×C17—22no—
437C2×C4×C17—22no—
438C2×C4×C17—22no—
439C2×C4×C17—22no—
440C2×C4×C17—41no—
441C2×C4×C17—41no—
442C2×C4×C17—41no—
443C2×C4×C17—41no—
444C2×C4×C17—41no—
445C2×C4×C17—41no—
446C2×C4×C17—41no—
447C2×C4×C17—41no—
448C2×C4×C17—41no—
449C2×C4×C17—41no—
450C2×C4×C17—41no—
451C2×C4×C17—41no—
452C2×C4×C17—41no—
453C2×C4×C17—41no—
454C2×C4×C17—41no—
455C2×C4×C17—41no—
456C2×C4×C17—41no—
457C2×C4×C17—41no—
458C2×C4×C17—41no—
459C2×C4×C17—41no—
460C2×C4×C17—41no—
461C2×C4×C17—41no—
462C2×C4×C17—41no—
463C2×C4×C17C4×D414yes—
464C2×C4×C17#12014yes—
465C2×Dic17—22no—
466C2×Dic17—22no—
467C2×Dic17—22no—
468C2×Dic17—22no—
469C2×Dic17—22no—
470C2×Dic17—22no—
471C2×Dic17—22no—
472C2×Dic17—22no—
473C2×Dic17—22no—
474C2×Dic17—22no—
475C2×Dic17—22no—
476C2×Dic17—22no—
477C2×Dic17—22no—
478C2×Dic17—22no—
479C2×Dic17—22no—
480C2×Dic17—22no—
481C2×Dic17—22no—
482C2×Dic17—22no—
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×Dic17—41no—
504C2×Dic17—41no—
505C2×Dic17—41no—
506C2×Dic17C4×D414yes—
507D68—416no—
508C4×D17—232no—
509C4×D17—416no—
510C4×D17—416no—
511C23×C4⋊C4—171no—
512C2×#388—171no—
513C2×#388—171no—
514C2×#386—171no—
515C2×#386—171no—
516C2×#386—171no—
517C2×C4×C22⋊C4—171no—
518#1442—171no—
519#1442—171no—
520#1439—171no—
521#1439—171no—
522#1436—171no—
523#1436D1711yescharacteristic, complemented
524C22⋊#95—171no—
525C22⋊#95—171no—
526C22×C17C2×#11711yescharacteristic
527C22×C17C2×C4×D411yescharacteristic
528C22×C17C2×C4×D411yescharacteristic
529C22×C17C2×C4×D411yescharacteristic
530C22×C17C2×C4×D411yescharacteristic
531C22×C17#52011yescharacteristic
532C22×C17#52011yescharacteristic
533C22×C17C2×#12011yescharacteristic
534C22×C17C2×#12111yescharacteristic
535C22×C17C2×#12311yescharacteristic
536C22×C17#52511yescharacteristic
537C22×C17#52511yescharacteristic
538C22×C17#52511yescharacteristic
539C22×C17C2×#12411yescharacteristic
540C22×C17C2×#12611yescharacteristic
541C22×C17#53411yescharacteristic
542C22×C17#53611yescharacteristic
543C22×C17#53911yescharacteristic
544C22×C17#53911yescharacteristic
545C22×C17D4211yescharacteristic
546C22×C17D4211yescharacteristic
547C22×C17#54611yescharacteristic
548C22×C17#54611yescharacteristic
549C22×C17#54711yescharacteristic
550C22×C17#54711yescharacteristic
551C22×C17#54811yescharacteristic
552C22×C17#54811yescharacteristic
553C22×C17#54811yescharacteristic
554C22×C17#54811yescharacteristic
555C22×C17#55211yescharacteristic
556C22×C17#55211yescharacteristic
557C22×C17#55311yescharacteristic
558C22×C17#55311yescharacteristic
559C22×C17#55311yescharacteristic
560C22×C17#55311yescharacteristic
561C2×D17—24no—
562C2×D17—24no—
563C2×D17—24no—
564C2×D17—24no—
565C2×D17—24no—
566C2×D17—24no—
567C2×D17—24no—
568C2×D17—24no—
569C2×D17—24no—
570C2×D17—24no—
571C2×D17—24no—
572C2×D17—24no—
573C2×D17—24no—
574C2×D17—24no—
575C2×D17—42no—
576C2×D17—42no—
577C2×D17—42no—
578C2×D17—42no—
579C2×D17—42no—
580C2×D17—42no—
581C2×D17—42no—
582C2×D17—81no—
583C2×D17—81no—
584C2×D17—81no—
585C2×D17—81no—
586C2×D17—81no—
587C2×D17—81no—
588C2×D17—81no—
589C2×D17—81no—
590C2×D17#38818yescomplemented
591C4×C17—24no—
592C4×C17—24no—
593C4×C17—42no—
594C4×C17—42no—
595C4×C17—42no—
596C4×C17—42no—
597C4×C17—81no—
598Dic17—24no—
599Dic17—42no—
600Dic17—42no—
601Dic17—42no—
602Dic17—42no—
603Dic17—81no—
604C23×D4—171no—
605C24×C4—171no—
606C24×C4—171no—
607C24×C4—171no—
608C22×C4⋊C4—171no—
609C22×C4⋊C4—171no—
610C22×C4⋊C4—171no—
611C22×C4⋊C4—344no—
612C22×C4⋊C4—344no—
613C22×C4⋊C4—344no—
614C22×C4⋊C4C2×D1711yescharacteristic
615C22×C22⋊C4—171no—
616C22×C22⋊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×C42—171no—
625C22×C42C2×D1711yescharacteristic
626#388—344no—
627#388—344no—
628#386—178no—
629#386—344no—
630#386—344no—
631C4×C22⋊C4—344no—
632C2×#95—171no—
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×#95C2×D1711yescharacteristic
644C2×#95C2×D1711yescharacteristic
645C2×#95C2×D1711yescharacteristic
646C2×#95C2×D1711yescharacteristic
647C2×#95C2×D1711yescharacteristic
648C2×C17C2×#38811yescharacteristic
649C2×C17C4×#12011yescharacteristic
650C2×C17#232211yescharacteristic
651C2×C17#235211yescharacteristic
652C2×C17#235211yescharacteristic
653C2×C17#236111yescharacteristic
654C2×C17#236111yescharacteristic
655C2×C17#241011yescharacteristic
656C2×C17#241311yescharacteristic
657C2×C17#243611yescharacteristic
658C2×C17#244311yescharacteristic
659C2×C17#244311yescharacteristic
660C2×C17#248111yescharacteristic
661C2×C17#248111yescharacteristic
662C2×C17#259111yescharacteristic
663D17—28no—
664D17—82no—
665C25—171no—
666C25—171no—
667C22×D4—174no—
668C22×D4—342no—
669C22×D4—342no—
670C22×D4—342no—
671C22×D4—342no—
672C22×D4—342no—
673C22×D4—342no—
674C23×C4—171no—
675C23×C4—171no—
676C23×C4—171no—
677C23×C4—171no—
678C23×C4—171no—
679C23×C4—174no—
680C23×C4—174no—
681C23×C4—171no—
682C23×C4—342no—
683C23×C4—342no—
684C23×C4—342no—
685C23×C4—342no—
686C23×C4—342no—
687C23×C4—342no—
688C23×C4—342no—
689C23×C4—342no—
690C23×C4—342no—
691C23×C4—342no—
692C23×C4—342no—
693C23×C4—342no—
694C23×C4—342no—
695C23×C4—342no—
696C23×C4—342no—
697C23×C4—681no—
698C23×C4—681no—
699C23×C4—681no—
700C23×C4—681no—
701C23×C4C22×D1711yescharacteristic
702C23×C4C22×D1711yescharacteristic
703C23×C4C22×D1711yescharacteristic
704C23×C4C22×D1711yescharacteristic
705C23×C4C22×D1711yescharacteristic
706C23×C4C22×D1711yescharacteristic
707C23×C4C22×D1711yescharacteristic
708C2×C4⋊C4—22no—
709C2×C4⋊C4—22no—
710C2×C4⋊C4—174no—
711C2×C4⋊C4—3432no—
712C2×C4⋊C4—342no—
713C2×C4⋊C4—342no—
714C2×C4⋊C4—342no—
715C2×C4⋊C4—342no—
716C2×C4⋊C4—342no—
717C2×C4⋊C4—342no—
718C2×C4⋊C4—342no—
719C2×C4⋊C4—342no—
720C2×C4⋊C4D6814yescomplemented
721C2×C22⋊C4—174no—
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—342no—
744C2×C22⋊C4—681no—
745C2×C22⋊C4—681no—
746C2×C22⋊C4—681no—
747C2×C22⋊C4—681no—
748C2×C42—22no—
749C2×C42—22no—
750C2×C42—41no—
751C2×C42—342no—
752C2×C42—342no—
753C2×C42—681no—
754#95—22no—
755#95—22no—
756#95—22no—
757#95—41no—
758#95—174no—
759#95—342no—
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—681no—
769#95C4×D1714yescomplemented
770C17#1401911yescharacteristic, complemented, Sylow
771C24—172no—
772C24—172no—
773C24—172no—
774C24—172no—
775C24—172no—
776C24—172no—
777C24—172no—
778C24—172no—
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—
792C24—341no—
793C24—341no—
794C24—341no—
795C24—341no—
796C24—341no—
797C24—341no—
798C24—341no—
799C24—341no—
800C24—341no—
801C24C23×D1711yescharacteristic
802C2×D4—348no—
803C2×D4—348no—
804C2×D4—348no—
805C2×D4—684no—
806C2×D4—684no—
807C2×D4—684no—
808C2×D4—684no—
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—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—172no—
849C22×C4—172no—
850C22×C4—172no—
851C22×C4—172no—
852C22×C4—172no—
853C22×C4—172no—
854C22×C4—172no—
855C22×C4—348no—
856C22×C4—348no—
857C22×C4—348no—
858C22×C4—348no—
859C22×C4—348no—
860C22×C4—348no—
861C22×C4—348no—
862C22×C4—348no—
863C22×C4—341no—
864C22×C4—341no—
865C22×C4—341no—
866C22×C4—341no—
867C22×C4—348no—
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×C4—348no—
893C22×C4—341no—
894C22×C4—341no—
895C22×C4—341no—
896C22×C4—341no—
897C22×C4—341no—
898C22×C4—341no—
899C22×C4—341no—
900C22×C4—684no—
901C22×C4—684no—
902C22×C4—684no—
903C22×C4—684no—
904C22×C4—684no—
905C22×C4—684no—
906C22×C4—684no—
907C22×C4—684no—
908C22×C4—684no—
909C22×C4—684no—
910C22×C4—684no—
911C22×C4C2×C4×D1712yes—
912C22×C4C2×C4×D1712yes—
913C22×C4C2×C4×D1712yes—
914C22×C4C2×D6812yes—
915C22×C4C2×D6812yes—
916C22×C4C2×D6812yes—
917C22×C4#6325212yes—
918C22×C4D4×D1712yes—
919C22×C4D4×D1712yes—
920C22×C4D4×D1712yes—
921C4⋊C4—28no—
922C4⋊C4—348no—
923C4⋊C4—348no—
924C4⋊C4—348no—
925C22⋊C4—348no—
926C22⋊C4—348no—
927C22⋊C4—348no—
928C22⋊C4—348no—
929C22⋊C4—684no—
930C22⋊C4—684no—
931C22⋊C4—684no—
932C22⋊C4—684no—
933C22⋊C4—684no—
934C42—44no—
935C42—684no—
936C23—174no—
937C23—174no—
938C23—174no—
939C23—174no—
940C23—174no—
941C23—174no—
942C23—174no—
943C23—342no—
944C23—342no—
945C23—342no—
946C23—342no—
947C23—342no—
948C23—342no—
949C23—342no—
950C23—342no—
951C23—342no—
952C23—342no—
953C23—342no—
954C23—342no—
955C23—342no—
956C23—342no—
957C23—342no—
958C23—342no—
959C23—342no—
960C23—342no—
961C23—342no—
962C23—342no—
963C23—342no—
964C23—342no—
965C23—342no—
966C23—342no—
967C23—342no—
968C23—342no—
969C23—342no—
970C23—342no—
971C23—342no—
972C23—342no—
973C23—342no—
974C23—342no—
975C23—342no—
976C23—342no—
977C23—342no—
978C23—681no—
979C23—681no—
980C23—681no—
981C23—681no—
982C23—681no—
983C23—681no—
984C23—681no—
985C23—681no—
986C23—681no—
987C23—681no—
988C23—681no—
989C23—681no—
990C23—681no—
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—
1006C23C22×C4×D1711yescharacteristic
1007C23C22×D6811yescharacteristic
1008C23C2×#6325211yescharacteristic
1009C23C2×D4×D1711yescharacteristic
1010C23C2×D4×D1711yescharacteristic
1011C23C2×D4×D1711yescharacteristic
1012C23#1058769111yescharacteristic
1013C23#1058769411yescharacteristic
1014C23#1058769411yescharacteristic
1015C23#41×D1711yescharacteristic
1016C23#41×D1711yescharacteristic
1017C23#41×D1711yescharacteristic
1018C23#41×D1711yescharacteristic
1019C23#41×D1711yescharacteristic
1020C23#1058769611yescharacteristic
1021D4—6816no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
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—22no—
1044C2×C4—22no—
1045C2×C4—22no—
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—41no—
1068C2×C4—41no—
1069C2×C4—174no—
1070C2×C4—3432no—
1071C2×C4—342no—
1072C2×C4—342no—
1073C2×C4—342no—
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—6816no—
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×C4C4×D6814yes—
1115C2×C4#1058756814yes—
1116C22—178no—
1117C22—344no—
1118C22—344no—
1119C22—344no—
1120C22—344no—
1121C22—344no—
1122C22—344no—
1123C22—344no—
1124C22—344no—
1125C22—344no—
1126C22—344no—
1127C22—344no—
1128C22—344no—
1129C22—344no—
1130C22—344no—
1131C22—682no—
1132C22—682no—
1133C22—682no—
1134C22—682no—
1135C22—682no—
1136C22—682no—
1137C22—682no—
1138C22—1361no—
1139C22—1361no—
1140C22—1361no—
1141C22—1361no—
1142C22—1361no—
1143C22—1361no—
1144C22—1361no—
1145C22—1361no—
1146C22#117×D1711yescharacteristic
1147C22C4×D4×D1711yescharacteristic
1148C22C4×D4×D1711yescharacteristic
1149C22C4×D4×D1711yescharacteristic
1150C22C2×C4×D6811yescharacteristic
1151C22#1176329011yescharacteristic
1152C22#1176329111yescharacteristic
1153C22C2×#1058756811yescharacteristic
1154C22#121×D1711yescharacteristic
1155C22#123×D1711yescharacteristic
1156C22#1176331811yescharacteristic
1157C22#1176331811yescharacteristic
1158C22#1176332111yescharacteristic
1159C22#124×D1711yescharacteristic
1160C22#126×D1711yescharacteristic
1161C22#1176336711yescharacteristic
1162C22#1176338411yescharacteristic
1163C22#1176340511yescharacteristic
1164C22#1176340711yescharacteristic
1165C22#1176344111yescharacteristic
1166C22D4×D6811yescharacteristic
1167C22#1176345111yescharacteristic
1168C22#1176345411yescharacteristic
1169C22#1176346011yescharacteristic
1170C22#1176346111yescharacteristic
1171C22#1176346911yescharacteristic
1172C22#1176346911yescharacteristic
1173C22#1176347111yescharacteristic
1174C22#1176347111yescharacteristic
1175C22#1176349111yescharacteristic
1176C22#1176350011yescharacteristic
1177C22#1176350311yescharacteristic
1178C22#1176350411yescharacteristic
1179C22#1176350911yescharacteristic
1180C22#1176351011yescharacteristic
1181C4—24no—
1182C4—24no—
1183C4—42no—
1184C4—42no—
1185C4—42no—
1186C4—42no—
1187C4—81no—
1188C4—344no—
1189C4—682no—
1190C4—682no—
1191C4—682no—
1192C4—682no—
1193C4—1361no—
1194C2—348no—
1195C2—1362no—
1196C2D17×#38811yescharacteristic
1197C2C4×#1058756811yescharacteristic
1198C2#1453144811yescharacteristic
1199C2#1453170811yescharacteristic
1200C2#1453171611yescharacteristic
1201C2#1453180211yescharacteristic
1202C2#1453180311yescharacteristic
1203C2#1453215711yescharacteristic
1204C2#1453218811yescharacteristic
1205C2#1453244111yescharacteristic
1206C2#1453251811yescharacteristic
1207C2#1453252411yescharacteristic
1208C2#1453304311yescharacteristic
1209C2#1453304911yescharacteristic
1210C2#1453426211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1436C2
socle, cosocleC24×C17C24
prime radicalC23×D68C22
hypercenter#1436D17
hypocenterC17#14019
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
1. C22×C4⋊C4×D17C2semidirect
2. C2×#11762700C2semidirect
3. C2×#11762699C2semidirect
7. C2×C4×#63227C2semidirect
8. #14527041C2semidirect
9. #14527039C2semidirect
10. #14527030C2semidirect
11. #14527028C2semidirect
12. #14527019C2semidirect
13. #14527005C2semidirect
14. #14527005C2semidirect
15. C17×#1436C2semidirect
40. #11762687C4semidirect
105. C2×C4⋊C4×C17D4semidirect
133. C2×#63227C2×C4semidirect
134. C2×#63227C2×C4semidirect
144. C2×#63225D4semidirect
153. C17×#95C2×C4semidirect
164. #10587502C2×C4semidirect
523. #1436D17semidirect
590. C2×D17#388semidirect
720. C2×C4⋊C4D68semidirect
769. #95C4×D17semidirect
770. C17#14019semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D172
C2×#117627002
C2×#117626992
C2×#117626872
C2×C4×#632272
#145270412
#145270392
#145270302
#145270282
#145270192
#145270052
C17×#14362
#1401917