Finite Group Databasebeta

← #16964268

Subgroups — #16964268

Order 4352.

1750 conjugacy classes of subgroups.

The subgroup lattice has 1148 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762726C211yesmaximal, characteristic
2C2×#11762711C211yesmaximal, characteristic
3C2×#11762708C211yesmaximal, characteristic, complemented
4C2×#11762701C211yesmaximal, characteristic, complemented
5C2×#11762698C211yesmaximal, characteristic, complemented
6#14527030C211yesmaximal, characteristic, complemented
7#14527030C211yesmaximal, characteristic, complemented
8#14527030C211yesmaximal, characteristic, complemented
9#14527028C211yesmaximal, characteristic, complemented
10#14527024C211yesmaximal, characteristic
11#14527020C211yesmaximal, characteristic, complemented
12#14527020C211yesmaximal, characteristic, complemented
13#14527018C211yesmaximal, characteristic, complemented
14#14527017C211yesmaximal, characteristic, complemented
15C17×#1436C211yesmaximal, characteristic, complemented
16C23×D68C2211yescharacteristic
17C22×C4⋊Dic17C2211yescharacteristic
18C22×C4⋊Dic17C2211yescharacteristic
19C22×C4⋊Dic17C2211yescharacteristic
20C22×#63225C2211yescharacteristic
21C22×#63227C2211yescharacteristic
22C22×#63227C2211yescharacteristic
23C22×#63227C2211yescharacteristic
24C22×#63227C2211yescharacteristic
25C22×#63227C2211yescharacteristic
26C22×#63227C2211yescharacteristic
27C22×#63227C2211yescharacteristic
28C22×#63227C2211yescharacteristic
29C22×#63227C2211yescharacteristic
30C22×#63227C2211yescharacteristic
31C22×#63227C2211yescharacteristic
32C22×#63227C2211yescharacteristic
33C22×C4×Dic17C2211yescharacteristic
34C22×C4×Dic17C2211yescharacteristic
35#11762726C418yescomplemented
36#11762711—24no—
37#11762708—24no—
38#11762701—24no—
39#11762698—24no—
40C2×#10587502C2211yescharacteristic
41C2×#10587502C2211yescharacteristic
42C2×#10587502C2211yescharacteristic
43C2×#10587502C2211yescharacteristic
44C2×#10587502C2211yescharacteristic
45C2×#10587502C2211yescharacteristic
46C2×#10587502C2211yescharacteristic
47C2×#10587502C2211yescharacteristic
48C2×#10587502C2211yescharacteristic
49C22×C4⋊C4×C17C2211yescharacteristic
50C22×C42×C17C2211yescharacteristic
51C2×C17×#95C2211yescharacteristic
52C2×C17×#95C2211yescharacteristic
53C2×C17×#95C2211yescharacteristic
54C2×C17×#95C2211yescharacteristic
55C2×C17×#95C2211yescharacteristic
56C24×D17C2311yescharacteristic
57C24×D17C2311yescharacteristic
58C23×C4×C17C2311yescharacteristic
59C23×C4×C17C2311yescharacteristic
60C23×C4×C17C2311yescharacteristic
61C23×C4×C17C2311yescharacteristic
62C23×C4×C17C2311yescharacteristic
63C23×C4×C17C2311yescharacteristic
64C23×C4×C17C2311yescharacteristic
65C23×Dic17C2311yescharacteristic
66C23×Dic17C2311yescharacteristic
67C23×Dic17C2311yescharacteristic
68C23×Dic17C2311yescharacteristic
69C23×Dic17C2311yescharacteristic
70C23×Dic17C2311yescharacteristic
71C22×D68—22no—
72C22×D68—22no—
73C22×D68—41no—
74C22×D68—41no—
75C22×D68—41no—
76C22×D68—41no—
77C22×D68C2×C414yes—
78C2×C4⋊C4×C17—22no—
79C2×C4⋊C4×C17—22no—
80C2×C4⋊C4×C17C2×C414yes—
81C2×C42×C17—22no—
82C2×C42×C17—41no—
83C2×C42×C17—41no—
84C2×#63227—22no—
85C2×#63227—22no—
86C2×#63227—22no—
87C2×#63227—22no—
88C2×#63227—22no—
89C2×#63227—22no—
90C2×#63227—22no—
91C2×#63227—22no—
92C2×#63227—22no—
93C2×#63227—22no—
94C2×#63227—22no—
95C2×#63227—22no—
96C2×#63227—22no—
97C2×#63227—22no—
98C2×#63227—22no—
99C2×#63227—22no—
100C2×#63227—41no—
101C2×#63227—41no—
102C2×#63227—41no—
103C2×#63227—41no—
104C2×#63227—41no—
105C2×#63227—41no—
106C2×#63227—41no—
107C2×#63227—41no—
108C2×#63227—41no—
109C2×#63227—41no—
110C2×#63227—41no—
111C2×#63227—41no—
112C2×#63227—41no—
113C2×#63227—41no—
114C2×#63227—41no—
115C2×#63227—41no—
116C2×#63227C2×C414yes—
117C2×#63227C2×C414yes—
118C2×#63227C2×C414yes—
119C2×#63227C2×C414yes—
120C2×C4⋊Dic17—22no—
121C2×C4⋊Dic17—22no—
122C2×C4⋊Dic17—22no—
123C2×C4⋊Dic17—41no—
124C2×C4⋊Dic17—41no—
125C2×C4⋊Dic17—41no—
126C2×C4⋊Dic17—41no—
127C2×C4⋊Dic17—41no—
128C2×C4⋊Dic17D414yes—
129C2×#63225—22no—
130C2×#63225—22no—
131C2×#63225—41no—
132C2×C4×Dic17—22no—
133C2×C4×Dic17—22no—
134C2×C4×Dic17—22no—
135C2×C4×Dic17—41no—
136C2×C4×Dic17—41no—
137C2×C4×Dic17—41no—
138C17×#95—22no—
139C17×#95—22no—
140C17×#95—41no—
141C17×#95—41no—
142C17×#95D414yescomplemented
143#10587502—22no—
144#10587502—22no—
145#10587502—22no—
146#10587502—22no—
147#10587502—22no—
148#10587502—41no—
149#10587502—41no—
150#10587502—41no—
151#10587502C2×C414yes—
152C24×C17C2411yescharacteristic
153C23×D17—21no—
154C23×D17—21no—
155C23×D17—21no—
156C23×D17—21no—
157C23×D17—21no—
158C23×D17—21no—
159C23×D17—21no—
160C23×D17—21no—
161C23×D17—21no—
162C23×D17—21no—
163C23×D17—21no—
164C23×D17—21no—
165C23×D17—21no—
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×D17C22×C412yes—
182C23×D17C22×C412yes—
183C22×C4×C17—21no—
184C22×C4×C17—21no—
185C22×C4×C17—21no—
186C22×C4×C17—21no—
187C22×C4×C17—21no—
188C22×C4×C17—21no—
189C22×C4×C17—21no—
190C22×C4×C17—21no—
191C22×C4×C17—21no—
192C22×C4×C17—21no—
193C22×C4×C17—21no—
194C22×C4×C17—21no—
195C22×C4×C17—21no—
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×C17C22×C412yes—
223C22×C4×C17C22×C412yes—
224C22×C4×C17C22×C412yes—
225C22×C4×C17C2×D412yes—
226C22×C4×C17C2×D412yes—
227C22×C4×C17C2×D412yes—
228C22×C4×C17C2×D412yes—
229C22×C4×C17#4112yes—
230C22×C4×C17#4112yes—
231C22×C4×C17#4112yes—
232C22×Dic17—21no—
233C22×Dic17—21no—
234C22×Dic17—21no—
235C22×Dic17—21no—
236C22×Dic17—21no—
237C22×Dic17—21no—
238C22×Dic17—21no—
239C22×Dic17—21no—
240C22×Dic17—21no—
241C22×Dic17—21no—
242C22×Dic17—21no—
243C22×Dic17—21no—
244C22×Dic17—21no—
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×Dic17C22×C412yes—
270C22×Dic17C22×C412yes—
271C22×Dic17C2×D412yes—
272C22×Dic17C2×D412yes—
273C22×Dic17#4112yes—
274C2×D68—28no—
275C2×D68—44no—
276C2×D68—44no—
277C2×D68—44no—
278C2×D68—44no—
279C2×D68—44no—
280C2×D68—44no—
281C4⋊C4×C17—28no—
282C42×C17—44no—
283#63227—28no—
284#63227—28no—
285#63227—44no—
286#63227—44no—
287#63227—44no—
288#63227—44no—
289#63227—44no—
290#63227—44no—
291#63227—44no—
292#63227—44no—
293#63227—44no—
294#63227—44no—
295C4⋊Dic17—44no—
296C4⋊Dic17—44no—
297C4⋊Dic17—44no—
298#63225—44no—
299C4×Dic17—44no—
300C4×Dic17—44no—
301#14563—171nomaximal, Sylow
302C23×C17C23×C411yescharacteristic
303C23×C17C22×D411yescharacteristic
304C23×C17C22×D411yescharacteristic
305C23×C17C2×#4111yescharacteristic
306C23×C17C2×#4111yescharacteristic
307C23×C17C2×#4111yescharacteristic
308C23×C17C2×#4111yescharacteristic
309C23×C17H(5,𝔽2)11yescharacteristic
310C23×C17H(5,𝔽2)11yescharacteristic
311C23×C17H(5,𝔽2)11yescharacteristic
312C23×C17H(5,𝔽2)11yescharacteristic
313C23×C17H(5,𝔽2)11yescharacteristic
314C23×C17H(5,𝔽2)11yescharacteristic
315C23×C172−1+411yescharacteristic
316C23×C172−1+411yescharacteristic
317C22×D17—22no—
318C22×D17—22no—
319C22×D17—22no—
320C22×D17—22no—
321C22×D17—22no—
322C22×D17—22no—
323C22×D17—22no—
324C22×D17—22no—
325C22×D17—22no—
326C22×D17—22no—
327C22×D17—22no—
328C22×D17—22no—
329C22×D17—22no—
330C22×D17—22no—
331C22×D17—41no—
332C22×D17—41no—
333C22×D17—41no—
334C22×D17—41no—
335C22×D17—41no—
336C22×D17—41no—
337C22×D17—41no—
338C22×D17—41no—
339C22×D17—41no—
340C22×D17—41no—
341C22×D17—41no—
342C22×D17—41no—
343C22×D17—41no—
344C22×D17—41no—
345C22×D17—41no—
346C22×D17—41no—
347C22×D17—41no—
348C22×D17—41no—
349C22×D17—41no—
350C22×D17—41no—
351C22×D17—41no—
352C22×D17—41no—
353C22×D17—41no—
354C22×D17—41no—
355C22×D17—41no—
356C22×D17—41no—
357C22×D17—41no—
358C22×D17—41no—
359C22×D17—41no—
360C22×D17—41no—
361C22×D17—41no—
362C22×D17—41no—
363C22×D17—41no—
364C22×D17—41no—
365C22×D17—41no—
366C22×D17—41no—
367C22×D17—41no—
368C22×D17—41no—
369C22×D17—41no—
370C22×D17—41no—
371C22×D17—41no—
372C22×D17—41no—
373C22×D17—41no—
374C22×D17—41no—
375C22×D17—41no—
376C22×D17—41no—
377C22×D17—41no—
378C22×D17—41no—
379C22×D17—41no—
380C22×D17—41no—
381C22×D17—41no—
382C22×D17—41no—
383C22×D17—41no—
384C22×D17—41no—
385C22×D17—41no—
386C22×D17—41no—
387C2×C4×C17—22no—
388C2×C4×C17—22no—
389C2×C4×C17—22no—
390C2×C4×C17—22no—
391C2×C4×C17—22no—
392C2×C4×C17—22no—
393C2×C4×C17—22no—
394C2×C4×C17—22no—
395C2×C4×C17—22no—
396C2×C4×C17—22no—
397C2×C4×C17—22no—
398C2×C4×C17—22no—
399C2×C4×C17—22no—
400C2×C4×C17—22no—
401C2×C4×C17—22no—
402C2×C4×C17—22no—
403C2×C4×C17—22no—
404C2×C4×C17—22no—
405C2×C4×C17—22no—
406C2×C4×C17—22no—
407C2×C4×C17—22no—
408C2×C4×C17—22no—
409C2×C4×C17—22no—
410C2×C4×C17—22no—
411C2×C4×C17—41no—
412C2×C4×C17—41no—
413C2×C4×C17—41no—
414C2×C4×C17—41no—
415C2×C4×C17—41no—
416C2×C4×C17—41no—
417C2×C4×C17—41no—
418C2×C4×C17—41no—
419C2×C4×C17—41no—
420C2×C4×C17—41no—
421C2×C4×C17—41no—
422C2×C4×C17—41no—
423C2×C4×C17—41no—
424C2×C4×C17—41no—
425C2×C4×C17—41no—
426C2×C4×C17—41no—
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×C17C4×D414yes—
435C2×C4×C17C4×D414yes—
436C2×Dic17—22no—
437C2×Dic17—22no—
438C2×Dic17—22no—
439C2×Dic17—22no—
440C2×Dic17—22no—
441C2×Dic17—22no—
442C2×Dic17—22no—
443C2×Dic17—22no—
444C2×Dic17—22no—
445C2×Dic17—22no—
446C2×Dic17—22no—
447C2×Dic17—22no—
448C2×Dic17—22no—
449C2×Dic17—22no—
450C2×Dic17—22no—
451C2×Dic17—41no—
452C2×Dic17—41no—
453C2×Dic17—41no—
454C2×Dic17—41no—
455C2×Dic17—41no—
456C2×Dic17—41no—
457C2×Dic17—41no—
458C2×Dic17—41no—
459C2×Dic17—41no—
460C2×Dic17—41no—
461C2×Dic17—41no—
462C2×Dic17—41no—
463C2×Dic17—41no—
464C2×Dic17—41no—
465C2×Dic17—41no—
466C2×Dic17—41no—
467C2×Dic17—41no—
468C2×Dic17—41no—
469C2×Dic17—41no—
470C2×Dic17—41no—
471C2×Dic17—41no—
472C2×Dic17—41no—
473C2×Dic17—41no—
474C2×Dic17—41no—
475C2×Dic17—41no—
476C2×Dic17—41no—
477C2×Dic17—41no—
478D68—416no—
479C2×#394—171no—
480C2×#390—171no—
481C2×#389—171no—
482C2×#388—171no—
483C2×#388—171no—
484#1439—171no—
485#1439—171no—
486#1439—171no—
487#1439—171no—
488#1438—171no—
489#1437—171no—
490#1437—171no—
491#1436—171no—
492#1436—171no—
493#1436D1711yescharacteristic, complemented
494C22×C17C2×C4×D411yescharacteristic
495C22×C17C2×C4×D411yescharacteristic
496C22×C17C4×#4111yescharacteristic
497C22×C17#51811yescharacteristic
498C22×C17#51811yescharacteristic
499C22×C17#52011yescharacteristic
500C22×C17#52011yescharacteristic
501C22×C17#53411yescharacteristic
502C22×C17#53511yescharacteristic
503C22×C17#53511yescharacteristic
504C22×C17#53711yescharacteristic
505C22×C17#53811yescharacteristic
506C22×C17#53811yescharacteristic
507C22×C17#53811yescharacteristic
508C22×C17#53911yescharacteristic
509C22×C17#54011yescharacteristic
510C22×C17#54011yescharacteristic
511C22×C17#54211yescharacteristic
512C22×C17#54211yescharacteristic
513C22×C17D4211yescharacteristic
514C22×C17#54611yescharacteristic
515C22×C17#54611yescharacteristic
516C22×C17#54711yescharacteristic
517C22×C17#54811yescharacteristic
518C22×C17#54811yescharacteristic
519C22×C17#55011yescharacteristic
520C22×C17#55311yescharacteristic
521C22×C17#55311yescharacteristic
522C22×C17#55511yescharacteristic
523C22×C17#55611yescharacteristic
524C22×C17#55911yescharacteristic
525C22×C17#56011yescharacteristic
526C22×C17#56211yescharacteristic
527C22×C17#56211yescharacteristic
528C22×C17#56311yescharacteristic
529C2×D17—42no—
530C2×D17—42no—
531C2×D17—42no—
532C2×D17—42no—
533C2×D17—42no—
534C2×D17—42no—
535C2×D17—42no—
536C2×D17—42no—
537C2×D17—42no—
538C2×D17—42no—
539C2×D17—42no—
540C2×D17—42no—
541C2×D17—42no—
542C2×D17—42no—
543C2×D17—81no—
544C2×D17—81no—
545C2×D17—81no—
546C2×D17—81no—
547C2×D17—81no—
548C2×D17—81no—
549C2×D17—81no—
550C2×D17—81no—
551C2×D17—81no—
552C2×D17—81no—
553C2×D17—81no—
554C2×D17—81no—
555C2×D17—81no—
556C2×D17—81no—
557C2×D17—81no—
558C2×D17—81no—
559C4×C17—24no—
560C4×C17—24no—
561C4×C17—42no—
562C4×C17—42no—
563C4×C17—42no—
564C4×C17—42no—
565C4×C17—81no—
566Dic17—42no—
567Dic17—42no—
568Dic17—42no—
569Dic17—42no—
570Dic17—42no—
571Dic17—81no—
572C23×D4—171no—
573C22×C4⋊C4—171no—
574C22×C4⋊C4—171no—
575C22×C4⋊C4—171no—
576C22×C4⋊C4—171no—
577C22×C4⋊C4C2×D1711yescharacteristic
578C22×C22⋊C4—171no—
579C22×C22⋊C4—171no—
580C22×C22⋊C4—171no—
581C22×C22⋊C4—171no—
582C22×C22⋊C4—171no—
583C22×C22⋊C4—171no—
584C22×C22⋊C4—171no—
585C22×C22⋊C4—171no—
586C22×C22⋊C4—171no—
587C22×C22⋊C4—171no—
588C22×C22⋊C4—171no—
589C22×C22⋊C4—171no—
590C22×C42—171no—
591C22×C42—171no—
592C22×C42C2×D1711yescharacteristic
593#394—178no—
594#390—344no—
595#389—344no—
596#388—344no—
597#388—344no—
598C2×#95—171no—
599C2×#95—171no—
600C2×#95—171no—
601C2×#95—171no—
602C2×#95—171no—
603C2×#95—171no—
604C2×#95—171no—
605C2×#95—171no—
606C2×#95—171no—
607C2×#95C2×D1711yescharacteristic
608C2×#95C2×D1711yescharacteristic
609C2×#95C2×D1711yescharacteristic
610C2×#95C2×D1711yescharacteristic
611C2×#95C2×D1711yescharacteristic
612C2×C17#232111yescharacteristic
613C2×C17#232411yescharacteristic
614C2×C17#233511yescharacteristic
615C2×C17#236111yescharacteristic
616C2×C17#236311yescharacteristic
617C2×C17#236711yescharacteristic
618C2×C17#237611yescharacteristic
619C2×C17#267311yescharacteristic
620C2×C17#267611yescharacteristic
621C2×C17#271011yescharacteristic
622C2×C17#271111yescharacteristic
623C2×C17#272711yescharacteristic
624C2×C17#273111yescharacteristic
625C2×C17#280011yescharacteristic
626C2×C17#280311yescharacteristic
627D17—82no—
628D17—82no—
629C25—171no—
630C25—171no—
631C22×D4—174no—
632C22×D4—342no—
633C22×D4—342no—
634C22×D4—681no—
635C22×D4—681no—
636C22×D4—681no—
637C22×D4—681no—
638C23×C4—171no—
639C23×C4—171no—
640C23×C4—171no—
641C23×C4—171no—
642C23×C4—171no—
643C23×C4—171no—
644C23×C4C22×D1711yescharacteristic
645C23×C4C22×D1711yescharacteristic
646C23×C4C22×D1711yescharacteristic
647C23×C4C22×D1711yescharacteristic
648C23×C4C22×D1711yescharacteristic
649C23×C4C22×D1711yescharacteristic
650C23×C4C22×D1711yescharacteristic
651C2×C4⋊C4—22no—
652C2×C4⋊C4—22no—
653C2×C4⋊C4—174no—
654C2×C4⋊C4—342no—
655C2×C4⋊C4—342no—
656C2×C4⋊C4—342no—
657C2×C4⋊C4—342no—
658C2×C4⋊C4—342no—
659C2×C4⋊C4—681no—
660C2×C4⋊C4—681no—
661C2×C4⋊C4—681no—
662C2×C4⋊C4—681no—
663C2×C4⋊C4—681no—
664C2×C4⋊C4—681no—
665C2×C4⋊C4C4×D1714yes—
666C2×C22⋊C4—174no—
667C2×C22⋊C4—174no—
668C2×C22⋊C4—174no—
669C2×C22⋊C4—174no—
670C2×C22⋊C4—342no—
671C2×C22⋊C4—342no—
672C2×C22⋊C4—342no—
673C2×C22⋊C4—342no—
674C2×C22⋊C4—342no—
675C2×C22⋊C4—342no—
676C2×C22⋊C4—342no—
677C2×C22⋊C4—342no—
678C2×C22⋊C4—342no—
679C2×C22⋊C4—342no—
680C2×C22⋊C4—342no—
681C2×C22⋊C4—342no—
682C2×C22⋊C4—342no—
683C2×C22⋊C4—342no—
684C2×C22⋊C4—342no—
685C2×C22⋊C4—342no—
686C2×C22⋊C4—681no—
687C2×C22⋊C4—681no—
688C2×C22⋊C4—681no—
689C2×C22⋊C4—681no—
690C2×C22⋊C4—681no—
691C2×C22⋊C4—681no—
692C2×C22⋊C4—681no—
693C2×C22⋊C4—681no—
694C2×C22⋊C4—681no—
695C2×C22⋊C4—681no—
696C2×C22⋊C4—681no—
697C2×C22⋊C4—681no—
698C2×C22⋊C4—681no—
699C2×C22⋊C4—681no—
700C2×C22⋊C4—681no—
701C2×C22⋊C4—681no—
702C2×C42—22no—
703C2×C42—41no—
704C2×C42—41no—
705C2×C42—342no—
706C2×C42—342no—
707C2×C42—342no—
708C2×C42—681no—
709C2×C42—681no—
710C2×C42—681no—
711#95—22no—
712#95—22no—
713#95—41no—
714#95—41no—
715#95—174no—
716#95—342no—
717#95—342no—
718#95—342no—
719#95—342no—
720#95—342no—
721#95—681no—
722#95—681no—
723#95—681no—
724#95D6814yescomplemented
725C17#1456311yescharacteristic, complemented, Sylow
726C24—172no—
727C24—172no—
728C24—341no—
729C24—341no—
730C24—341no—
731C24—341no—
732C24—341no—
733C24—341no—
734C24—341no—
735C24—341no—
736C24—341no—
737C24—341no—
738C24—341no—
739C24—341no—
740C24—341no—
741C24—341no—
742C24—341no—
743C24—341no—
744C24—341no—
745C24—341no—
746C24—341no—
747C24—341no—
748C24—341no—
749C24—341no—
750C24—341no—
751C24—341no—
752C24—341no—
753C24—341no—
754C24—341no—
755C24—341no—
756C24C23×D1711yescharacteristic
757C2×D4—348no—
758C2×D4—684no—
759C2×D4—684no—
760C2×D4—684no—
761C2×D4—684no—
762C2×D4—684no—
763C2×D4—684no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—172no—
804C22×C4—172no—
805C22×C4—172no—
806C22×C4—172no—
807C22×C4—172no—
808C22×C4—341no—
809C22×C4—341no—
810C22×C4—341no—
811C22×C4—341no—
812C22×C4—341no—
813C22×C4—341no—
814C22×C4—341no—
815C22×C4—341no—
816C22×C4—341no—
817C22×C4—341no—
818C22×C4—341no—
819C22×C4—341no—
820C22×C4—341no—
821C22×C4—341no—
822C22×C4—341no—
823C22×C4—341no—
824C22×C4—341no—
825C22×C4—341no—
826C22×C4—341no—
827C22×C4—341no—
828C22×C4—341no—
829C22×C4—341no—
830C22×C4—341no—
831C22×C4—341no—
832C22×C4—341no—
833C22×C4—341no—
834C22×C4—341no—
835C22×C4—341no—
836C22×C4—341no—
837C22×C4—341no—
838C22×C4—341no—
839C22×C4—341no—
840C22×C4—341no—
841C22×C4—341no—
842C22×C4—341no—
843C22×C4—341no—
844C22×C4—341no—
845C22×C4C2×C4×D1712yes—
846C22×C4C2×C4×D1712yes—
847C22×C4C2×C4×D1712yes—
848C22×C4C2×D6812yes—
849C22×C4C2×D6812yes—
850C22×C4C2×D6812yes—
851C22×C4#6325212yes—
852C22×C4D4×D1712yes—
853C22×C4#6325412yes—
854C22×C4#6325612yes—
855C4⋊C4—28no—
856C4⋊C4—684no—
857C4⋊C4—684no—
858C4⋊C4—684no—
859C4⋊C4—684no—
860C22⋊C4—348no—
861C22⋊C4—348no—
862C22⋊C4—684no—
863C22⋊C4—684no—
864C22⋊C4—684no—
865C22⋊C4—684no—
866C22⋊C4—684no—
867C22⋊C4—684no—
868C22⋊C4—684no—
869C22⋊C4—684no—
870C22⋊C4—684no—
871C22⋊C4—684no—
872C42—44no—
873C42—684no—
874C42—684no—
875C23—342no—
876C23—342no—
877C23—342no—
878C23—342no—
879C23—342no—
880C23—342no—
881C23—342no—
882C23—342no—
883C23—342no—
884C23—342no—
885C23—342no—
886C23—342no—
887C23—342no—
888C23—342no—
889C23—681no—
890C23—681no—
891C23—681no—
892C23—681no—
893C23—681no—
894C23—681no—
895C23—681no—
896C23—681no—
897C23—681no—
898C23—681no—
899C23—681no—
900C23—681no—
901C23—681no—
902C23—681no—
903C23—681no—
904C23—681no—
905C23—681no—
906C23—681no—
907C23—681no—
908C23—681no—
909C23—681no—
910C23—681no—
911C23—681no—
912C23—681no—
913C23—681no—
914C23—681no—
915C23—681no—
916C23—681no—
917C23—681no—
918C23—681no—
919C23—681no—
920C23—681no—
921C23—681no—
922C23—681no—
923C23—681no—
924C23—681no—
925C23—681no—
926C23—681no—
927C23—681no—
928C23—681no—
929C23—681no—
930C23—681no—
931C23—681no—
932C23—681no—
933C23—681no—
934C23—681no—
935C23—681no—
936C23—681no—
937C23—681no—
938C23—681no—
939C23—681no—
940C23—681no—
941C23—681no—
942C23—681no—
943C23—681no—
944C23—681no—
945C23C22×C4×D1711yescharacteristic
946C23C22×D6811yescharacteristic
947C23C2×#6325211yescharacteristic
948C23C2×D4×D1711yescharacteristic
949C23C2×#6325411yescharacteristic
950C23#1058769111yescharacteristic
951C23#1058769111yescharacteristic
952C23C2×#6325611yescharacteristic
953C23#1058769411yescharacteristic
954C23#41×D1711yescharacteristic
955C23#1058769611yescharacteristic
956C23#1058769611yescharacteristic
957C23#1058769611yescharacteristic
958C23#1058769611yescharacteristic
959C23#1058769711yescharacteristic
960D4—6816no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—342no—
1009C2×C4—342no—
1010C2×C4—342no—
1011C2×C4—342no—
1012C2×C4—342no—
1013C2×C4—342no—
1014C2×C4—342no—
1015C2×C4—342no—
1016C2×C4—342no—
1017C2×C4—342no—
1018C2×C4—342no—
1019C2×C4—342no—
1020C2×C4—342no—
1021C2×C4—342no—
1022C2×C4—342no—
1023C2×C4—681no—
1024C2×C4—681no—
1025C2×C4—681no—
1026C2×C4—681no—
1027C2×C4—681no—
1028C2×C4—681no—
1029C2×C4—681no—
1030C2×C4—681no—
1031C2×C4—681no—
1032C2×C4—681no—
1033C2×C4—681no—
1034C2×C4—681no—
1035C2×C4—681no—
1036C2×C4—681no—
1037C2×C4—681no—
1038C2×C4—681no—
1039C2×C4—681no—
1040C2×C4—681no—
1041C2×C4—681no—
1042C2×C4—681no—
1043C2×C4—681no—
1044C2×C4—681no—
1045C2×C4—681no—
1046C2×C4—681no—
1047C2×C4—681no—
1048C2×C4—681no—
1049C2×C4—681no—
1050C2×C4C4×D6814yes—
1051C2×C4#1058756714yes—
1052C22—682no—
1053C22—682no—
1054C22—682no—
1055C22—682no—
1056C22—682no—
1057C22—682no—
1058C22—682no—
1059C22—682no—
1060C22—682no—
1061C22—682no—
1062C22—682no—
1063C22—682no—
1064C22—682no—
1065C22—682no—
1066C22—1361no—
1067C22—1361no—
1068C22—1361no—
1069C22—1361no—
1070C22—1361no—
1071C22—1361no—
1072C22—1361no—
1073C22—1361no—
1074C22—1361no—
1075C22—1361no—
1076C22—1361no—
1077C22—1361no—
1078C22—1361no—
1079C22—1361no—
1080C22—1361no—
1081C22—1361no—
1082C22C2×#1058756711yescharacteristic
1083C22C2×C4×D6811yescharacteristic
1084C22C4×#6325611yescharacteristic
1085C22#1176328111yescharacteristic
1086C22#1176328111yescharacteristic
1087C22#1176328911yescharacteristic
1088C22#1176329111yescharacteristic
1089C22#1176337011yescharacteristic
1090C22#1176337411yescharacteristic
1091C22#1176337811yescharacteristic
1092C22#1176339011yescharacteristic
1093C22#1176339511yescharacteristic
1094C22#1176339611yescharacteristic
1095C22#1176339611yescharacteristic
1096C22#1176340811yescharacteristic
1097C22#1176341011yescharacteristic
1098C22#1176341511yescharacteristic
1099C22#1176342511yescharacteristic
1100C22#1176343111yescharacteristic
1101C22D4×D6811yescharacteristic
1102C22#1176345011yescharacteristic
1103C22#1176345411yescharacteristic
1104C22#1176346311yescharacteristic
1105C22#1176346811yescharacteristic
1106C22#1176346911yescharacteristic
1107C22#1176348111yescharacteristic
1108C22#1176350511yescharacteristic
1109C22#1176350711yescharacteristic
1110C22#1176352211yescharacteristic
1111C22#1176353311yescharacteristic
1112C22#1176354111yescharacteristic
1113C22#1176355011yescharacteristic
1114C22#1176355511yescharacteristic
1115C22#1176355611yescharacteristic
1116C22#1176356311yescharacteristic
1117C4—24no—
1118C4—24no—
1119C4—42no—
1120C4—42no—
1121C4—42no—
1122C4—42no—
1123C4—81no—
1124C4—682no—
1125C4—682no—
1126C4—682no—
1127C4—682no—
1128C4—682no—
1129C4—1361no—
1130C2—1362no—
1131C2—1362no—
1132C2#1453144711yescharacteristic
1133C2#1453147811yescharacteristic
1134C2#1453157311yescharacteristic
1135C2#1453179811yescharacteristic
1136C2#1453182411yescharacteristic
1137C2#1453186011yescharacteristic
1138C2#1453193111yescharacteristic
1139C2#1453505311yescharacteristic
1140C2#1453508811yescharacteristic
1141C2#1453552411yescharacteristic
1142C2#1453554211yescharacteristic
1143C2#1453574511yescharacteristic
1144C2#1453579411yescharacteristic
1145C2#1453667411yescharacteristic
1146C2#1453671711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1436C2
socle, cosocleC24×C17C24
prime radicalC23×D68C22
hypercenter#1436D17
hypocenterC17#14563
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
3. C2×#11762708C2semidirect
4. C2×#11762701C2semidirect
5. C2×#11762698C2semidirect
6. #14527030C2semidirect
7. #14527030C2semidirect
8. #14527030C2semidirect
9. #14527028C2semidirect
11. #14527020C2semidirect
12. #14527020C2semidirect
13. #14527018C2semidirect
14. #14527017C2semidirect
15. C17×#1436C2semidirect
35. #11762726C4semidirect
142. C17×#95D4semidirect
493. #1436D17semidirect
724. #95D68semidirect
725. C17#14563semidirect

Maximal subgroups

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

subgroupindex
C2×#117627262
C2×#117627112
C2×#117627082
C2×#117627012
C2×#117626982
#145270302
#145270282
#145270242
#145270202
#145270182
#145270172
C17×#14362
#1456317