Finite Group Databasebeta

← #16955816

Subgroups — #16955816

Order 4352.

2882 conjugacy classes of subgroups.

The subgroup lattice has 1234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587579C211yesmaximal, characteristic
2C2×#11762687C211yesmaximal, characteristic
3C2×#11762687C211yesmaximal, characteristic
4C2×C4×#63227C211yesmaximal, characteristic, complemented
5C2×C4×#63227C211yesmaximal, characteristic, complemented
6C2×#11762656C211yesmaximal, characteristic, complemented
7C2×#95×D17C211yesmaximal, characteristic, complemented
8#14527020C211yesmaximal, characteristic, complemented
9#14527020C211yesmaximal, characteristic, complemented
10#14527016C211yesmaximal, characteristic, complemented
11#14527009C211yesmaximal, characteristic, complemented
12#14527005C211yesmaximal, characteristic, complemented
13#14527005C211yesmaximal, characteristic, complemented
14#95×Dic17C211yesmaximal, characteristic, complemented
15C17×#1436C211yesmaximal, characteristic, complemented
16C23×D68C2211yescharacteristic
17C23×C4×D17C2211yescharacteristic
18C23×C4×D17C2211yescharacteristic
19C23×C4×D17C2211yescharacteristic
20C23×C4×D17C2211yescharacteristic
21C2×#10587579—24no—
22C2×#10587579—24no—
23C2×#10587579C418yescomplemented
24C22×#63227C2211yescharacteristic
25C22×#63227C2211yescharacteristic
26C22×#63227C2211yescharacteristic
27C22×#63227C2211yescharacteristic
28C22×#63227C2211yescharacteristic
29C22×#63227C2211yescharacteristic
30C22×#63227C2211yescharacteristic
31C22×#63227C2211yescharacteristic
32C22×C4×Dic17C2211yescharacteristic
33C22×C4×Dic17C2211yescharacteristic
34C22×C4×Dic17C2211yescharacteristic
35C22×C4×Dic17C2211yescharacteristic
36#11762687C418yescomplemented
37#11762687C418yescomplemented
38C4×#63227—24no—
39C4×#63227—24no—
40#11762656—24no—
41C2×#10587502C2211yescharacteristic
42C2×#10587502C2211yescharacteristic
43C2×#10587502C2211yescharacteristic
44C2×#10587502C2211yescharacteristic
45C2×#10587502C2211yescharacteristic
46C2×#10587502C2211yescharacteristic
47C2×#10587502C2211yescharacteristic
48C2×#10587502C2211yescharacteristic
49C2×#10587502C2211yescharacteristic
50C2×#10587502C2211yescharacteristic
51C2×#10587502C2211yescharacteristic
52#95×D17—24no—
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×D68C2×C414yes—
80C22×D68C2×C414yes—
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—22no—
98C22×C4×D17—41no—
99C22×C4×D17—41no—
100C22×C4×D17—41no—
101C22×C4×D17—41no—
102C22×C4×D17—41no—
103C22×C4×D17—41no—
104C22×C4×D17—41no—
105C22×C4×D17—41no—
106C22×C4×D17C2×C414yes—
107C22×C4×D17C2×C414yescomplemented
108C22×C4×D17C2×C414yescomplemented
109C22×C4×D17C2×C414yescomplemented
110C2×C4⋊C4×C17—22no—
111C2×C4⋊C4×C17—22no—
112C2×C4⋊C4×C17C2×C414yescomplemented
113C2×C42×C17—22no—
114C2×C42×C17—22no—
115C2×C42×C17—41no—
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—41no—
127C2×#63227—41no—
128C2×#63227—41no—
129C2×#63227—41no—
130C2×#63227C2×C414yes—
131C2×#63227C2×C414yescomplemented
132C2×#63227C2×C414yescomplemented
133C2×#63227C2×C414yescomplemented
134C2×#63227C2×C414yescomplemented
135C2×#63227C2×C414yescomplemented
136C2×#63227C2×C414yescomplemented
137C2×#63227C2×C414yescomplemented
138C2×#63227D414yes—
139C2×#63227D414yes—
140C2×C4×Dic17—22no—
141C2×C4×Dic17—22no—
142C2×C4×Dic17—22no—
143C2×C4×Dic17—22no—
144C2×C4×Dic17—22no—
145C2×C4×Dic17—22no—
146C2×C4×Dic17—22no—
147C2×C4×Dic17—22no—
148C2×C4×Dic17—41no—
149C2×C4×Dic17—41no—
150C2×C4×Dic17—41no—
151C2×C4×Dic17C2×C414yescomplemented
152#10587579—232no—
153C17×#95—22no—
154C17×#95—22no—
155C17×#95—41no—
156C17×#95C2×C414yescomplemented
157C17×#95C2×C414yescomplemented
158#10587502—22no—
159#10587502—22no—
160#10587502—22no—
161#10587502—22no—
162#10587502—22no—
163#10587502—22no—
164#10587502—22no—
165#10587502—41no—
166#10587502C2×C414yescomplemented
167#10587502C2×C414yescomplemented
168#10587502D414yescomplemented
169C24×C17C2411yescharacteristic
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×D17—21no—
189C23×D17—21no—
190C23×D17C22×C412yes—
191C23×D17C22×C412yes—
192C23×D17C22×C412yes—
193C23×D17C22×C412yes—
194C23×D17C22×C412yes—
195C23×D17C22×C412yes—
196C23×D17C2×D412yes—
197C23×D17C2×D412yes—
198C23×D17#4112yes—
199C23×D17#4112yes—
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×C17—21no—
236C22×C4×C17C22×C412yes—
237C22×C4×C17C22×C412yes—
238C22×C4×C17C22×C412yes—
239C22×C4×C17C22×C412yes—
240C22×C4×C17C22×C412yes—
241C22×C4×C17C22×C412yes—
242C22×C4×C17C22×C412yes—
243C22×C4×C17C22×C412yes—
244C22×C4×C17C22×C412yes—
245C22×C4×C17C2×D412yes—
246C22×C4×C17C2×D412yes—
247C22×C4×C17C2×D412yes—
248C22×C4×C17#4112yes—
249C22×Dic17—21no—
250C22×Dic17—21no—
251C22×Dic17—21no—
252C22×Dic17—21no—
253C22×Dic17—21no—
254C22×Dic17—21no—
255C22×Dic17—21no—
256C22×Dic17—21no—
257C22×Dic17—21no—
258C22×Dic17—21no—
259C22×Dic17—21no—
260C22×Dic17—21no—
261C22×Dic17—21no—
262C22×Dic17—21no—
263C22×Dic17—21no—
264C22×Dic17—21no—
265C22×Dic17—21no—
266C22×Dic17—21no—
267C22×Dic17—21no—
268C22×Dic17—21no—
269C22×Dic17—21no—
270C22×Dic17—21no—
271C22×Dic17—21no—
272C22×Dic17—21no—
273C22×Dic17—21no—
274C22×Dic17—21no—
275C22×Dic17—21no—
276C22×Dic17—21no—
277C22×Dic17—21no—
278C22×Dic17—21no—
279C22×Dic17C22×C412yes—
280C22×Dic17C22×C412yes—
281C22×Dic17C22×C412yes—
282C22×Dic17C22×C412yes—
283C22×Dic17C22×C412yes—
284C22×Dic17C22×C412yes—
285C22×Dic17C2×D412yes—
286C22×Dic17C2×D412yes—
287C22×Dic17C2×D412yes—
288C22×Dic17C2×D412yes—
289C22×Dic17#4112yes—
290C22×Dic17#4112yes—
291C2×D68—28no—
292C2×D68—28no—
293C2×D68—28no—
294C2×D68—28no—
295C2×D68—28no—
296C2×D68—28no—
297C2×D68C42116yescomplemented
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—28no—
305C2×C4×D17—28no—
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—
315C2×C4×D17—44no—
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—
326C4⋊C4×C17—28no—
327C42×C17—44no—
328#63227—28no—
329#63227—28no—
330#63227—28no—
331#63227—28no—
332#63227—28no—
333#63227—44no—
334#63227—44no—
335#63227C22⋊C4116yescomplemented
336C4×Dic17—28no—
337C4×Dic17—44no—
338C4×Dic17—44no—
339C4×Dic17—44no—
340#13813—171nomaximal, Sylow
341C23×C17C23×C411yescharacteristic
342C23×C17C23×C411yescharacteristic
343C23×C17C23×C411yescharacteristic
344C23×C17C22×D411yescharacteristic
345C23×C17C22×D411yescharacteristic
346C23×C17C22×D411yescharacteristic
347C23×C17C2×#4111yescharacteristic
348C23×C17C2×#4111yescharacteristic
349C23×C17C2×#4111yescharacteristic
350C23×C17C2×#4111yescharacteristic
351C23×C17C2×#4111yescharacteristic
352C23×C17H(5,𝔽2)11yescharacteristic
353C23×C17H(5,𝔽2)11yescharacteristic
354C23×C17H(5,𝔽2)11yescharacteristic
355C23×C172−1+411yescharacteristic
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—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—41no—
403C22×D17—41no—
404C22×D17—41no—
405C22×D17—41no—
406C22×D17—41no—
407C22×D17—41no—
408C22×D17—41no—
409C22×D17—41no—
410C22×D17—41no—
411C22×D17—41no—
412C22×D17—41no—
413C22×D17—41no—
414C22×D17—41no—
415C22×D17—41no—
416C22×D17—41no—
417C22×D17—41no—
418C22×D17C2×C4214yes—
419C22×D17C2×C4214yes—
420C22×D17C2×C22⋊C414yes—
421C22×D17#11714yes—
422C22×D17C4×D414yes—
423C22×D17C4×D414yes—
424C22×D17C4×D414yes—
425C22×D17C4×D414yes—
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—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—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×C17C2×C4214yes—
473C2×C4×C17C2×C22⋊C414yes—
474C2×C4×C17C4×D414yescomplemented
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—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—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×Dic17C2×C22⋊C414yes—
515C2×Dic17C4×D414yes—
516C2×Dic17C4×D414yescomplemented
517D68—232no—
518C4×D17—416no—
519C4×D17—416no—
520C4×D17—416no—
521C4×D17—416no—
522C22×C4×D4—171no—
523C2×#386—171no—
524C2×#386—171no—
525C2×C4×C22⋊C4—171no—
526C2×C4×C22⋊C4—171no—
527C2×C4×C22⋊C4—171no—
528C22×#95—171no—
529#1437—171no—
530#1437—171no—
531#1436—171no—
532#1436D1711yescharacteristic, complemented
533#1434—171no—
534C22⋊#95—171no—
535C22⋊#95—171no—
536C4×#95—171no—
537C22×C17C22×C4211yescharacteristic
538C22×C17C22×C22⋊C411yescharacteristic
539C22×C17C2×#11711yescharacteristic
540C22×C17C2×C4×D411yescharacteristic
541C22×C17C2×C4×D411yescharacteristic
542C22×C17C2×C4×D411yescharacteristic
543C22×C17C2×C4×D411yescharacteristic
544C22×C17C2×C4×D411yescharacteristic
545C22×C17C2×C4×D411yescharacteristic
546C22×C17C2×C4×D411yescharacteristic
547C22×C17C4×#4111yescharacteristic
548C22×C17C4×#4111yescharacteristic
549C22×C17C4×#4111yescharacteristic
550C22×C17#51811yescharacteristic
551C22×C17#51811yescharacteristic
552C22×C17#51811yescharacteristic
553C22×C17#52011yescharacteristic
554C22×C17#52011yescharacteristic
555C22×C17#52011yescharacteristic
556C22×C17D4211yescharacteristic
557C22×C17D4211yescharacteristic
558C22×C17#54611yescharacteristic
559C22×C17#54611yescharacteristic
560C22×C17#54611yescharacteristic
561C22×C17#54611yescharacteristic
562C22×C17#54611yescharacteristic
563C22×C17#54711yescharacteristic
564C22×C17#54711yescharacteristic
565C22×C17#54811yescharacteristic
566C22×C17#55111yescharacteristic
567C22×C17#55111yescharacteristic
568C22×C17#55211yescharacteristic
569C22×C17#55311yescharacteristic
570C22×C17#55311yescharacteristic
571C22×C17#55311yescharacteristic
572C2×D17—24no—
573C2×D17—24no—
574C2×D17—24no—
575C2×D17—24no—
576C2×D17—24no—
577C2×D17—24no—
578C2×D17—24no—
579C2×D17—24no—
580C2×D17—24no—
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—42no—
590C2×D17—42no—
591C2×D17—42no—
592C2×D17—42no—
593C2×D17—42no—
594C2×D17—42no—
595C2×D17—42no—
596C2×D17—42no—
597C2×D17—42no—
598C2×D17—42no—
599C2×D17—42no—
600C2×D17—42no—
601C2×D17C4×C22⋊C418yescomplemented
602C4×C17—24no—
603C4×C17—24no—
604C4×C17—24no—
605C4×C17—42no—
606C4×C17—42no—
607C4×C17—42no—
608C4×C17—42no—
609Dic17—24no—
610Dic17—24no—
611Dic17—24no—
612Dic17—42no—
613Dic17—42no—
614Dic17—42no—
615C23×D4—171no—
616C24×C4—171no—
617C24×C4—171no—
618C24×C4—171no—
619C24×C4—171no—
620C2×C4×D4—178no—
621C2×C4×D4—344no—
622C2×C4×D4—344no—
623C22×C4⋊C4C2×D1711yescharacteristic
624C22×C22⋊C4—171no—
625C22×C22⋊C4—171no—
626C22×C22⋊C4—171no—
627C22×C22⋊C4—171no—
628C22×C22⋊C4—171no—
629C22×C22⋊C4—171no—
630C22×C22⋊C4—171no—
631C22×C22⋊C4—171no—
632C22×C42—171no—
633C22×C42—171no—
634C22×C42—171no—
635C22×C42—171no—
636C22×C42C2×D1711yescharacteristic
637#386—178no—
638#386—178no—
639C4×C22⋊C4—344no—
640C4×C22⋊C4—344no—
641C4×C22⋊C4—344no—
642C2×#95—171no—
643C2×#95—171no—
644C2×#95—171no—
645C2×#95—171no—
646C2×#95—171no—
647C2×#95—171no—
648C2×#95—171no—
649C2×#95—171no—
650C2×#95—171no—
651C2×#95—171no—
652C2×#95—171no—
653C2×#95—344no—
654C2×#95C2×D1711yescharacteristic
655C2×#95C2×D1711yescharacteristic
656C2×#95C2×D1711yescharacteristic
657C2×#95C2×D1711yescharacteristic
658C2×#95C2×D1711yescharacteristic
659C2×C17C2×C4×C22⋊C411yescharacteristic
660C2×C17C42×D411yescharacteristic
661C2×C17#227511yescharacteristic
662C2×C17D4×C22⋊C411yescharacteristic
663C2×C17#233911yescharacteristic
664C2×C17#235211yescharacteristic
665C2×C17#235311yescharacteristic
666C2×C17#235811yescharacteristic
667C2×C17#235811yescharacteristic
668C2×C17#235911yescharacteristic
669C2×C17#235911yescharacteristic
670C2×C17#236111yescharacteristic
671C2×C17#236111yescharacteristic
672C2×C17#236411yescharacteristic
673C2×C17#236411yescharacteristic
674D17—28no—
675D17—44no—
676C25—171no—
677C25—171no—
678C22×D4—174no—
679C22×D4—174no—
680C22×D4—174no—
681C22×D4—342no—
682C22×D4—342no—
683C22×D4—342no—
684C22×D4—342no—
685C23×C4—171no—
686C23×C4—171no—
687C23×C4—171no—
688C23×C4—171no—
689C23×C4—171no—
690C23×C4—171no—
691C23×C4—174no—
692C23×C4—174no—
693C23×C4—174no—
694C23×C4—174no—
695C23×C4—342no—
696C23×C4—342no—
697C23×C4—342no—
698C23×C4—342no—
699C23×C4—342no—
700C23×C4—342no—
701C23×C4—342no—
702C23×C4—342no—
703C23×C4—342no—
704C23×C4—342no—
705C23×C4—342no—
706C23×C4—342no—
707C23×C4—342no—
708C23×C4—342no—
709C23×C4—342no—
710C23×C4—342no—
711C23×C4—681no—
712C23×C4—681no—
713C23×C4—681no—
714C23×C4—681no—
715C23×C4—681no—
716C23×C4—681no—
717C23×C4—681no—
718C23×C4—681no—
719C23×C4C22×D1711yescharacteristic
720C23×C4C22×D1711yescharacteristic
721C23×C4C22×D1711yescharacteristic
722C23×C4C22×D1711yescharacteristic
723C23×C4C22×D1711yescharacteristic
724C23×C4C22×D1711yescharacteristic
725C23×C4C22×D1711yescharacteristic
726C4×D4—3432no—
727C2×C4⋊C4—22no—
728C2×C4⋊C4—22no—
729C2×C4⋊C4C4×D1714yescomplemented
730C2×C22⋊C4—174no—
731C2×C22⋊C4—174no—
732C2×C22⋊C4—174no—
733C2×C22⋊C4—174no—
734C2×C22⋊C4—174no—
735C2×C22⋊C4—174no—
736C2×C22⋊C4—174no—
737C2×C22⋊C4—174no—
738C2×C22⋊C4—174no—
739C2×C22⋊C4—174no—
740C2×C22⋊C4—342no—
741C2×C22⋊C4—342no—
742C2×C22⋊C4—342no—
743C2×C22⋊C4—342no—
744C2×C22⋊C4—342no—
745C2×C22⋊C4—342no—
746C2×C22⋊C4—342no—
747C2×C22⋊C4—342no—
748C2×C22⋊C4—342no—
749C2×C22⋊C4—342no—
750C2×C22⋊C4—681no—
751C2×C22⋊C4—681no—
752C2×C22⋊C4—681no—
753C2×C22⋊C4—681no—
754C2×C42—22no—
755C2×C42—22no—
756C2×C42—41no—
757C2×C42—174no—
758C2×C42—342no—
759C2×C42—342no—
760C2×C42—342no—
761C2×C42—342no—
762C2×C42—342no—
763C2×C42—342no—
764C2×C42—342no—
765C2×C42—342no—
766C2×C42—681no—
767C2×C42—681no—
768C2×C42—681no—
769#95—22no—
770#95—22no—
771#95—41no—
772#95—174no—
773#95—174no—
774#95—174no—
775#95—342no—
776#95—342no—
777#95—342no—
778#95—342no—
779#95—342no—
780#95—342no—
781#95—342no—
782#95—681no—
783#95C4×D1714yescomplemented
784#95C4×D1714yescomplemented
785C17#1381311yescharacteristic, complemented, Sylow
786C24—172no—
787C24—172no—
788C24—172no—
789C24—172no—
790C24—172no—
791C24—172no—
792C24—172no—
793C24—172no—
794C24—172no—
795C24—172no—
796C24—341no—
797C24—341no—
798C24—341no—
799C24—341no—
800C24—341no—
801C24—341no—
802C24—341no—
803C24—341no—
804C24—341no—
805C24—341no—
806C24—341no—
807C24—341no—
808C24—341no—
809C24—341no—
810C24—341no—
811C24—341no—
812C24—341no—
813C24—341no—
814C24—341no—
815C24—341no—
816C24C23×D1711yescharacteristic
817C2×D4—1716no—
818C2×D4—348no—
819C2×D4—348no—
820C2×D4—348no—
821C2×D4—348no—
822C2×D4—348no—
823C2×D4—348no—
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—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—172no—
861C22×C4—172no—
862C22×C4—172no—
863C22×C4—172no—
864C22×C4—172no—
865C22×C4—172no—
866C22×C4—172no—
867C22×C4—172no—
868C22×C4—172no—
869C22×C4—172no—
870C22×C4—172no—
871C22×C4—172no—
872C22×C4—348no—
873C22×C4—348no—
874C22×C4—348no—
875C22×C4—348no—
876C22×C4—348no—
877C22×C4—348no—
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—341no—
893C22×C4—341no—
894C22×C4—341no—
895C22×C4—341no—
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—684no—
911C22×C4—684no—
912C22×C4—684no—
913C22×C4—684no—
914C22×C4—684no—
915C22×C4—684no—
916C22×C4—684no—
917C22×C4—684no—
918C22×C4—684no—
919C22×C4—684no—
920C22×C4—684no—
921C22×C4—684no—
922C22×C4—684no—
923C22×C4—684no—
924C22×C4—684no—
925C22×C4—684no—
926C22×C4—684no—
927C22×C4—684no—
928C22×C4—684no—
929C22×C4—684no—
930C22×C4C2×C4×D1712yes—
931C22×C4C2×C4×D1712yes—
932C22×C4C2×C4×D1712yes—
933C22×C4C2×C4×D1712yes—
934C22×C4C2×C4×D1712yes—
935C22×C4C2×C4×D1712yes—
936C22×C4C2×C4×D1712yes—
937C22×C4C2×C4×D1712yes—
938C22×C4C2×C4×D1712yes—
939C22×C4D4×D1712yes—
940C22×C4D4×D1712yes—
941C22×C4D4×D1712yes—
942C22×C4#6325612yes—
943C4⋊C4—28no—
944C22⋊C4—1716no—
945C22⋊C4—348no—
946C22⋊C4—348no—
947C22⋊C4—348no—
948C22⋊C4—348no—
949C22⋊C4—348no—
950C22⋊C4—684no—
951C22⋊C4—684no—
952C42—44no—
953C42—348no—
954C42—684no—
955C42—684no—
956C42—684no—
957C23—174no—
958C23—174no—
959C23—174no—
960C23—174no—
961C23—174no—
962C23—174no—
963C23—174no—
964C23—174no—
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—342no—
979C23—342no—
980C23—342no—
981C23—342no—
982C23—342no—
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—681no—
1012C23—681no—
1013C23—681no—
1014C23—681no—
1015C23—681no—
1016C23—681no—
1017C23—681no—
1018C23—681no—
1019C23—681no—
1020C23—681no—
1021C23—681no—
1022C23—681no—
1023C23—681no—
1024C23—681no—
1025C23—681no—
1026C23—681no—
1027C23C22×C4×D1711yescharacteristic
1028C23C22×C4×D1711yescharacteristic
1029C23C22×C4×D1711yescharacteristic
1030C23C2×D4×D1711yescharacteristic
1031C23C2×D4×D1711yescharacteristic
1032C23C2×D4×D1711yescharacteristic
1033C23#1058769111yescharacteristic
1034C23C2×#6325611yescharacteristic
1035C23#1058769411yescharacteristic
1036C23#41×D1711yescharacteristic
1037C23#41×D1711yescharacteristic
1038C23#41×D1711yescharacteristic
1039C23#41×D1711yescharacteristic
1040C23#1058769611yescharacteristic
1041C23#1058769611yescharacteristic
1042D4—3432no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
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—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
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—174no—
1090C2×C4—174no—
1091C2×C4—174no—
1092C2×C4—342no—
1093C2×C4—342no—
1094C2×C4—342no—
1095C2×C4—342no—
1096C2×C4—342no—
1097C2×C4—342no—
1098C2×C4—342no—
1099C2×C4—342no—
1100C2×C4—342no—
1101C2×C4—342no—
1102C2×C4—342no—
1103C2×C4—342no—
1104C2×C4—342no—
1105C2×C4—342no—
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—6816no—
1120C2×C4—6816no—
1121C2×C4—6816no—
1122C2×C4—6816no—
1123C2×C4—681no—
1124C2×C4—681no—
1125C2×C4—681no—
1126C2×C4—681no—
1127C2×C4—681no—
1128C2×C4—681no—
1129C2×C4—681no—
1130C2×C4—681no—
1131C2×C4—681no—
1132C2×C4—681no—
1133C2×C4—681no—
1134C2×C4—681no—
1135C2×C4C42×D1714yes—
1136C2×C4C22⋊C4×D1714yes—
1137C2×C4#1058757914yescomplemented
1138C22—178no—
1139C22—344no—
1140C22—344no—
1141C22—344no—
1142C22—344no—
1143C22—344no—
1144C22—344no—
1145C22—344no—
1146C22—344no—
1147C22—344no—
1148C22—344no—
1149C22—344no—
1150C22—344no—
1151C22—344no—
1152C22—344no—
1153C22—344no—
1154C22—344no—
1155C22—344no—
1156C22—682no—
1157C22—682no—
1158C22—682no—
1159C22—682no—
1160C22—682no—
1161C22—682no—
1162C22—682no—
1163C22—682no—
1164C22—682no—
1165C22—682no—
1166C22—682no—
1167C22—682no—
1168C22C2×C42×D1711yescharacteristic
1169C22C2×C22⋊C4×D1711yescharacteristic
1170C22#117×D1711yescharacteristic
1171C22C4×D4×D1711yescharacteristic
1172C22C4×D4×D1711yescharacteristic
1173C22C4×D4×D1711yescharacteristic
1174C22C4×D4×D1711yescharacteristic
1175C22C4×D4×D1711yescharacteristic
1176C22C4×D4×D1711yescharacteristic
1177C22C2×#1058757911yescharacteristic
1178C22#1176327711yescharacteristic
1179C22C4×#6325611yescharacteristic
1180C22C4×#6325611yescharacteristic
1181C22#1176328111yescharacteristic
1182C22#1176328111yescharacteristic
1183C22#1176328311yescharacteristic
1184C22#1176329011yescharacteristic
1185C22#1176329111yescharacteristic
1186C22#1176329111yescharacteristic
1187C22#1176344111yescharacteristic
1188C22#1176344311yescharacteristic
1189C22#1176344811yescharacteristic
1190C22#1176345011yescharacteristic
1191C22#1176345111yescharacteristic
1192C22#1176345111yescharacteristic
1193C22#1176345211yescharacteristic
1194C22#1176346111yescharacteristic
1195C22#1176346211yescharacteristic
1196C22#1176346911yescharacteristic
1197C22#1176348411yescharacteristic
1198C22#1176348611yescharacteristic
1199C22#1176349111yescharacteristic
1200C22#1176350411yescharacteristic
1201C22#1176351011yescharacteristic
1202C22#1176351211yescharacteristic
1203C4—24no—
1204C4—24no—
1205C4—24no—
1206C4—42no—
1207C4—42no—
1208C4—42no—
1209C4—42no—
1210C4—344no—
1211C4—344no—
1212C4—344no—
1213C4—682no—
1214C4—682no—
1215C4—682no—
1216C2—348no—
1217C2—684no—
1218C2C4×C22⋊C4×D1711yescharacteristic
1219C2C4×#1058757911yescharacteristic
1220C2#1453114411yescharacteristic
1221C2#1453160211yescharacteristic
1222C2#1453161311yescharacteristic
1223C2#1453170811yescharacteristic
1224C2#1453172311yescharacteristic
1225C2#1453176011yescharacteristic
1226C2#1453176211yescharacteristic
1227C2#1453176911yescharacteristic
1228C2#1453177111yescharacteristic
1229C2#1453179911yescharacteristic
1230C2#1453180311yescharacteristic
1231C2#1453182811yescharacteristic
1232C2#1453183011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC22×C17C22×C42
FittingC17×#1436C2
socle, cosocleC24×C17C24
prime radicalC23×D68C22
hypercenter#1436D17
hypocenterC17#13813
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
4. C2×C4×#63227C2semidirect
5. C2×C4×#63227C2semidirect
6. C2×#11762656C2semidirect
7. C2×#95×D17C2semidirect
8. #14527020C2semidirect
9. #14527020C2semidirect
10. #14527016C2semidirect
11. #14527009C2semidirect
12. #14527005C2semidirect
13. #14527005C2semidirect
14. #95×Dic17C2semidirect
15. C17×#1436C2semidirect
23. C2×#10587579C4semidirect
36. #11762687C4semidirect
37. #11762687C4semidirect
107. C22×C4×D17C2×C4semidirect
108. C22×C4×D17C2×C4semidirect
109. C22×C4×D17C2×C4semidirect
112. C2×C4⋊C4×C17C2×C4semidirect
131. C2×#63227C2×C4semidirect
132. C2×#63227C2×C4semidirect
133. C2×#63227C2×C4semidirect
134. C2×#63227C2×C4semidirect
135. C2×#63227C2×C4semidirect
136. C2×#63227C2×C4semidirect
137. C2×#63227C2×C4semidirect
151. C2×C4×Dic17C2×C4semidirect
156. C17×#95C2×C4semidirect
157. C17×#95C2×C4semidirect
166. #10587502C2×C4semidirect
167. #10587502C2×C4semidirect
168. #10587502D4semidirect
297. C2×D68C42semidirect
335. #63227C22⋊C4semidirect
474. C2×C4×C17C4×D4semidirect
516. C2×Dic17C4×D4semidirect
532. #1436D17semidirect
601. C2×D17C4×C22⋊C4semidirect
729. C2×C4⋊C4C4×D17semidirect
783. #95C4×D17semidirect
784. #95C4×D17semidirect
785. C17#13813semidirect
1137. C2×C4#10587579semidirect

Maximal subgroups

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

subgroupindex
C22×#105875792
C2×#117626872
C2×C4×#632272
C2×#117626562
C2×#95×D172
#145270202
#145270162
#145270092
#145270052
#95×Dic172
C17×#14362
#1381317