Finite Group Databasebeta

← #16957188

Subgroups — #16957188

Order 4352.

2690 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×D4×Dic17C211yesmaximal, characteristic
2C2×#11762689C211yesmaximal, characteristic
3C2×#11762684C211yesmaximal, characteristic, complemented
4C2×#11762684C211yesmaximal, characteristic, complemented
5C2×#11762669C211yesmaximal, characteristic, complemented
6C22×#10587502C211yesmaximal, characteristic, complemented
7#14527049C211yesmaximal, characteristic, complemented
8#14527041C211yesmaximal, characteristic, complemented
9#14527029C211yesmaximal, characteristic, complemented
10#14527029C211yesmaximal, characteristic, complemented
11#14527018C211yesmaximal, characteristic, complemented
12#14527018C211yesmaximal, characteristic, complemented
13#14527006C211yesmaximal, characteristic, complemented
14#14527006C211yesmaximal, characteristic, complemented
15C2×C17×#386C211yesmaximal, characteristic
16C24×Dic17C2211yescharacteristic
17C24×Dic17C2211yescharacteristic
18C24×Dic17C2211yescharacteristic
19C2×D4×Dic17—24no—
20C2×D4×Dic17—24no—
21C2×D4×Dic17—24no—
22C22×C4⋊Dic17C2211yescharacteristic
23C22×C4⋊Dic17C2211yescharacteristic
24C22×C4⋊Dic17C2211yescharacteristic
25C22×C4⋊Dic17C2211yescharacteristic
26C22×C4⋊Dic17C2211yescharacteristic
27C22×C22⋊Dic17C2211yescharacteristic
28C22×C22⋊Dic17C2211yescharacteristic
29C22×C22⋊Dic17C2211yescharacteristic
30C22×C22⋊Dic17C2211yescharacteristic
31C22×C22⋊Dic17C2211yescharacteristic
32C22×C4×Dic17C2211yescharacteristic
33#11762689—24no—
34#11762684—24no—
35#11762684—24no—
36#11762669—24no—
37C2×#10587502—24no—
38C2×#10587502C2211yescharacteristic
39C2×#10587502C2211yescharacteristic
40C2×#10587502C2211yescharacteristic
41C2×#10587502C2211yescharacteristic
42C2×#10587502C2211yescharacteristic
43C2×#10587502C2211yescharacteristic
44C2×#10587502C2211yescharacteristic
45C2×#10587502C2211yescharacteristic
46C2×#10587502C2211yescharacteristic
47C2×#10587502C2211yescharacteristic
48C2×#10587502C2211yescharacteristic
49C2×#10587502C2211yescharacteristic
50C2×#10587502C2211yescharacteristic
51C2×#10587502C2211yescharacteristic
52C23×D4×C17C2211yescharacteristic
53C24×C4×C17C2211yescharacteristic
54C22×C22⋊C4×C17C2211yescharacteristic
55C22×C22⋊C4×C17C2211yescharacteristic
56C22×C22⋊C4×C17C2211yescharacteristic
57C17×#386C418yescomplemented
58C2×C17×#95C2211yescharacteristic
59C2×C17×#95C2211yescharacteristic
60C25×C17C2311yescharacteristic
61C25×C17C2311yescharacteristic
62C22×D4×C17—22no—
63C22×D4×C17—22no—
64C22×D4×C17—22no—
65C22×D4×C17—22no—
66C22×D4×C17C2×C414yes—
67C22×D4×C17D414yes—
68C22×D4×C17Q814yes—
69C23×C4×C17—22no—
70C23×C4×C17—22no—
71C23×C4×C17—22no—
72C23×C4×C17—22no—
73C23×C4×C17—41no—
74C23×C4×C17—41no—
75C23×C4×C17C2×C414yescomplemented
76C23×C4×C17C2311yescharacteristic
77C23×C4×C17C2311yescharacteristic
78C23×C4×C17C2311yescharacteristic
79C23×C4×C17C2311yescharacteristic
80C23×C4×C17C2311yescharacteristic
81C23×Dic17—22no—
82C23×Dic17—22no—
83C23×Dic17—22no—
84C23×Dic17—22no—
85C23×Dic17—22no—
86C23×Dic17—22no—
87C23×Dic17—22no—
88C23×Dic17—22no—
89C23×Dic17—22no—
90C23×Dic17—22no—
91C23×Dic17—22no—
92C23×Dic17—22no—
93C23×Dic17—22no—
94C23×Dic17—22no—
95C23×Dic17—41no—
96C23×Dic17—41no—
97C23×Dic17—41no—
98C23×Dic17—41no—
99C23×Dic17—41no—
100C23×Dic17—41no—
101C23×Dic17D414yes—
102C23×Dic17C2311yescharacteristic
103C23×Dic17C2311yescharacteristic
104C23×Dic17C2311yescharacteristic
105C23×Dic17C2311yescharacteristic
106C23×Dic17C2311yescharacteristic
107C23×Dic17C2311yescharacteristic
108C23×Dic17C2311yescharacteristic
109C23×Dic17C2311yescharacteristic
110C2×C22⋊C4×C17—22no—
111C2×C22⋊C4×C17—22no—
112C2×C22⋊C4×C17—22no—
113C2×C22⋊C4×C17—22no—
114C2×C22⋊C4×C17—41no—
115C2×C22⋊C4×C17—41no—
116C2×C22⋊C4×C17C2×C414yescomplemented
117C2×C22⋊C4×C17C2×C414yescomplemented
118C2×C22⋊C4×C17C2×C414yescomplemented
119C2×C22⋊Dic17—22no—
120C2×C22⋊Dic17—22no—
121C2×C22⋊Dic17—22no—
122C2×C22⋊Dic17—22no—
123C2×C22⋊Dic17—22no—
124C2×C22⋊Dic17—22no—
125C2×C22⋊Dic17—22no—
126C2×C22⋊Dic17—22no—
127C2×C22⋊Dic17—22no—
128C2×C22⋊Dic17—22no—
129C2×C22⋊Dic17—22no—
130C2×C22⋊Dic17—22no—
131C2×C22⋊Dic17—41no—
132C2×C22⋊Dic17—41no—
133C2×C22⋊Dic17D414yes—
134D4×Dic17—232no—
135C2×C4⋊Dic17—22no—
136C2×C4⋊Dic17—22no—
137C2×C4⋊Dic17—22no—
138C2×C4⋊Dic17—22no—
139C2×C4⋊Dic17—22no—
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—41no—
147C2×C4⋊Dic17—41no—
148C2×C4⋊Dic17—41no—
149C2×C4⋊Dic17—41no—
150C2×C4×Dic17—22no—
151C2×C4×Dic17—22no—
152C2×C4×Dic17—22no—
153C17×#95C2×C414yescomplemented
154C17×#95C2×C414yescomplemented
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—22no—
164#10587502—22no—
165#10587502—22no—
166#10587502—41no—
167#10587502—41no—
168#10587502D414yescomplemented
169C24×C17—21no—
170C24×C17—21no—
171C24×C17—21no—
172C24×C17—21no—
173C24×C17—21no—
174C24×C17—21no—
175C24×C17—21no—
176C24×C17—21no—
177C24×C17—21no—
178C24×C17—21no—
179C24×C17—21no—
180C24×C17—21no—
181C24×C17—21no—
182C24×C17—21no—
183C24×C17—21no—
184C24×C17—21no—
185C24×C17—21no—
186C24×C17—21no—
187C24×C17—21no—
188C24×C17—21no—
189C24×C17C22×C412yes—
190C24×C17C22×C412yes—
191C24×C17C2×D412yes—
192C24×C17C2×D412yes—
193C24×C17C2×D412yes—
194C24×C17C2×D412yes—
195C24×C17C2×Q812yes—
196C24×C17C2×Q812yes—
197C24×C17#4112yes—
198C24×C17#4112yes—
199C24×C17C2411yescharacteristic
200C2×D4×C17—28no—
201C2×D4×C17—28no—
202C2×D4×C17—28no—
203C2×D4×C17—28no—
204C2×D4×C17—28no—
205C2×D4×C17—28no—
206C2×D4×C17C4⋊C4116yescomplemented
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—28no—
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—28no—
235C22×C4×C17—44no—
236C22×C4×C17—44no—
237C22×C4×C17—44no—
238C22×C4×C17—44no—
239C22×C4×C17—44no—
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×Q812yes—
248C22×C4×C17#4112yes—
249C22×Dic17—21no—
250C22×Dic17—21no—
251C22×Dic17—21no—
252C22×Dic17—21no—
253C22×Dic17—28no—
254C22×Dic17—28no—
255C22×Dic17—28no—
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—28no—
287C22×Dic17—21no—
288C22×Dic17—21no—
289C22×Dic17—21no—
290C22×Dic17—21no—
291C22×Dic17—21no—
292C22×Dic17—21no—
293C22×Dic17—21no—
294C22×Dic17—21no—
295C22×Dic17—21no—
296C22×Dic17—21no—
297C22×Dic17—21no—
298C22×Dic17—21no—
299C22×Dic17—21no—
300C22×Dic17—21no—
301C22×Dic17—44no—
302C22×Dic17—44no—
303C22×Dic17—44no—
304C22×Dic17—44no—
305C22×Dic17—44no—
306C22×Dic17—44no—
307C22×Dic17—44no—
308C22×Dic17—44no—
309C22×Dic17—44no—
310C22×Dic17—44no—
311C22×Dic17—44no—
312C22×Dic17—44no—
313C22×Dic17—44no—
314C22×Dic17—44no—
315C22×Dic17—44no—
316C22×Dic17—44no—
317C22×Dic17—44no—
318C22×Dic17C2×D412yes—
319C22×Dic17C2×D412yes—
320C22×Dic17C2×D412yes—
321C22×Dic17C2×D412yes—
322C22×Dic17C2×D412yes—
323C22×Dic17C2×D412yes—
324C22×Dic17#4112yes—
325C22×Dic17#4112yes—
326C22⋊C4×C17—28no—
327C22⋊C4×C17—28no—
328C22⋊C4×C17—44no—
329C22⋊Dic17—28no—
330C22⋊Dic17—28no—
331C22⋊Dic17—44no—
332C22⋊Dic17—44no—
333C22⋊Dic17—44no—
334C4⋊Dic17—28no—
335C4⋊Dic17—44no—
336C4⋊Dic17—44no—
337C4⋊Dic17—44no—
338C4⋊Dic17—44no—
339C4×Dic17—28no—
340#13975—171nomaximal, Sylow
341C23×C17—22no—
342C23×C17—22no—
343C23×C17—22no—
344C23×C17—22no—
345C23×C17—22no—
346C23×C17—22no—
347C23×C17—22no—
348C23×C17—22no—
349C23×C17—22no—
350C23×C17—22no—
351C23×C17—22no—
352C23×C17—22no—
353C23×C17—22no—
354C23×C17—22no—
355C23×C17—22no—
356C23×C17—22no—
357C23×C17—22no—
358C23×C17—22no—
359C23×C17—22no—
360C23×C17—22no—
361C23×C17—22no—
362C23×C17—22no—
363C23×C17—22no—
364C23×C17—22no—
365C23×C17—22no—
366C23×C17—22no—
367C23×C17—22no—
368C23×C17—22no—
369C23×C17—22no—
370C23×C17—22no—
371C23×C17—22no—
372C23×C17—22no—
373C23×C17—22no—
374C23×C17—22no—
375C23×C17—22no—
376C23×C17—22no—
377C23×C17—22no—
378C23×C17—22no—
379C23×C17—22no—
380C23×C17—22no—
381C23×C17—22no—
382C23×C17—22no—
383C23×C17—22no—
384C23×C17—22no—
385C23×C17—22no—
386C23×C17—22no—
387C23×C17—41no—
388C23×C17—41no—
389C23×C17—41no—
390C23×C17—41no—
391C23×C17—41no—
392C23×C17—41no—
393C23×C17—41no—
394C23×C17—41no—
395C23×C17—41no—
396C23×C17—41no—
397C23×C17—41no—
398C23×C17—41no—
399C23×C17—41no—
400C23×C17—41no—
401C23×C17—41no—
402C23×C17—41no—
403C23×C17C2×C4⋊C414yes—
404C23×C17C2×C4⋊C414yes—
405C23×C17C4×D414yes—
406C23×C17C4×D414yes—
407C23×C17#12014yes—
408C23×C17C22⋊Q814yes—
409C23×C17C22⋊Q814yes—
410C23×C17#12314yes—
411C23×C17C23×C411yescharacteristic
412C23×C17C22×D411yescharacteristic
413C23×C17C22×D411yescharacteristic
414C23×C17C22×D411yescharacteristic
415C23×C17C22×D411yescharacteristic
416C23×C17C22×Q811yescharacteristic
417C23×C17C2×#4111yescharacteristic
418C23×C17C2×#4111yescharacteristic
419C23×C17C2×#4111yescharacteristic
420C23×C17C2×#4111yescharacteristic
421C23×C17C2×#4111yescharacteristic
422C23×C17H(5,𝔽2)11yescharacteristic
423C23×C17H(5,𝔽2)11yescharacteristic
424C23×C17H(5,𝔽2)11yescharacteristic
425C23×C172−1+411yescharacteristic
426D4×C17—232no—
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—416no—
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×C17C2×C4⋊C414yes—
462C2×C4×C17C4×D414yescomplemented
463C2×Dic17—22no—
464C2×Dic17—22no—
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—22no—
484C2×Dic17—416no—
485C2×Dic17—416no—
486C2×Dic17—416no—
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×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#12114yes—
522C22×C4×D4—171no—
523C2×#386—171no—
524C2×#386D1711yescharacteristic
525C2×#385—171no—
526C2×#385—171no—
527C2×#380—171no—
528C22×#95—171no—
529#1444—171no—
530#1442—171no—
531#1439—171no—
532#1439—171no—
533#1436—171no—
534#1436—171no—
535C22⋊#95—171no—
536C22⋊#95—171no—
537C22×C17—24no—
538C22×C17—24no—
539C22×C17—24no—
540C22×C17—24no—
541C22×C17—24no—
542C22×C17—24no—
543C22×C17—24no—
544C22×C17—24no—
545C22×C17—24no—
546C22×C17—24no—
547C22×C17—24no—
548C22×C17—24no—
549C22×C17—24no—
550C22×C17—24no—
551C22×C17—24no—
552C22×C17—24no—
553C22×C17—24no—
554C22×C17—42no—
555C22×C17—42no—
556C22×C17—42no—
557C22×C17—42no—
558C22×C17—42no—
559C22×C17—42no—
560C22×C17—42no—
561C22×C17—42no—
562C22×C17—42no—
563C22×C17—42no—
564C22×C17—42no—
565C22×C17—42no—
566C22×C17#38518yescomplemented
567C22×C17C22×C4⋊C411yescharacteristic
568C22×C17C2×C4×D411yescharacteristic
569C22×C17C2×C4×D411yescharacteristic
570C22×C17C2×C4×D411yescharacteristic
571C22×C17C4×#4111yescharacteristic
572C22×C17#51811yescharacteristic
573C22×C17#52011yescharacteristic
574C22×C17C2×#12011yescharacteristic
575C22×C17C2×#12111yescharacteristic
576C22×C17C2×C22⋊Q811yescharacteristic
577C22×C17C2×C22⋊Q811yescharacteristic
578C22×C17C2×#12311yescharacteristic
579C22×C17#52511yescharacteristic
580C22×C17#52911yescharacteristic
581C22×C17#53211yescharacteristic
582C22×C17#53411yescharacteristic
583C22×C17#53711yescharacteristic
584C22×C17#53811yescharacteristic
585C22×C17#53911yescharacteristic
586C22×C17D4211yescharacteristic
587C22×C17D4211yescharacteristic
588C22×C17#54611yescharacteristic
589C22×C17#54611yescharacteristic
590C22×C17#54611yescharacteristic
591C22×C17#54611yescharacteristic
592C22×C17#54611yescharacteristic
593C22×C17#54711yescharacteristic
594C22×C17#54711yescharacteristic
595C22×C17D4×Q811yescharacteristic
596C22×C17#55111yescharacteristic
597C22×C17#55111yescharacteristic
598C22×C17#55211yescharacteristic
599C22×C17#55411yescharacteristic
600C22×C17#55411yescharacteristic
601C22×C17#55411yescharacteristic
602C4×C17—24no—
603C4×C17—24no—
604C4×C17—42no—
605C4×C17—42no—
606C4×C17—42no—
607Dic17—24no—
608Dic17—42no—
609Dic17—42no—
610Dic17—42no—
611Dic17—42no—
612Dic17—42no—
613Dic17—81no—
614Dic17—81no—
615C23×D4C2×D1711yescharacteristic
616C24×C4—171no—
617C24×C4—171no—
618C24×C4—171no—
619C24×C4C2×D1711yescharacteristic
620C2×C4×D4—344no—
621C2×C4×D4—344no—
622C2×C4×D4—344no—
623C22×C4⋊C4—171no—
624C22×C4⋊C4—171no—
625C22×C4⋊C4—171no—
626C22×C4⋊C4—171no—
627C22×C4⋊C4—171no—
628C22×C22⋊C4—171no—
629C22×C22⋊C4—171no—
630C22×C22⋊C4—171no—
631C22×C22⋊C4—171no—
632C22×C22⋊C4—171no—
633C22×C22⋊C4C2×D1711yescharacteristic
634C22×C22⋊C4C2×D1711yescharacteristic
635C22×C22⋊C4C2×D1711yescharacteristic
636C22×C42—171no—
637#386—344no—
638#386Dic1718yescomplemented
639#385—344no—
640#385—344no—
641#380—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—171no—
654C2×#95—171no—
655C2×#95—171no—
656C2×#95—344no—
657C2×#95C2×D1711yescharacteristic
658C2×#95C2×D1711yescharacteristic
659C2×C17—28no—
660C2×C17—44no—
661C2×C17C2×#38511yescharacteristic
662C2×C17C4×#12111yescharacteristic
663C2×C17#232511yescharacteristic
664C2×C17D4×C4⋊C411yescharacteristic
665C2×C17#234911yescharacteristic
666C2×C17#235811yescharacteristic
667C2×C17#235911yescharacteristic
668C2×C17#241011yescharacteristic
669C2×C17#241711yescharacteristic
670C2×C17#241811yescharacteristic
671C2×C17#241911yescharacteristic
672C2×C17#243011yescharacteristic
673C2×C17#244911yescharacteristic
674C2×C17#245011yescharacteristic
675C2×C17#256411yescharacteristic
676C25C22×D1711yescharacteristic
677C25C22×D1711yescharacteristic
678C22×D4—22no—
679C22×D4—22no—
680C22×D4—22no—
681C22×D4—22no—
682C22×D4Dic3414yes—
683C22×D4D6814yes—
684C22×D4C2×Dic1714yes—
685C23×C4—22no—
686C23×C4—22no—
687C23×C4—22no—
688C23×C4—22no—
689C23×C4—41no—
690C23×C4—41no—
691C23×C4—171no—
692C23×C4—171no—
693C23×C4—171no—
694C23×C4—171no—
695C23×C4—171no—
696C23×C4—171no—
697C23×C4—174no—
698C23×C4—171no—
699C23×C4—171no—
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—342no—
712C23×C4—342no—
713C23×C4—342no—
714C23×C4—681no—
715C23×C4—681no—
716C23×C4—681no—
717C23×C4—681no—
718C23×C4—681no—
719C23×C4—681no—
720C23×C4C2×Dic1714yescomplemented
721C23×C4C22×D1711yescharacteristic
722C23×C4C22×D1711yescharacteristic
723C23×C4C22×D1711yescharacteristic
724C23×C4C22×D1711yescharacteristic
725C23×C4C22×D1711yescharacteristic
726C4×D4—3432no—
727C2×C4⋊C4—342no—
728C2×C4⋊C4—342no—
729C2×C4⋊C4—342no—
730C2×C4⋊C4—342no—
731C2×C4⋊C4—342no—
732C2×C4⋊C4—342no—
733C2×C4⋊C4—342no—
734C2×C4⋊C4—342no—
735C2×C4⋊C4—342no—
736C2×C4⋊C4—342no—
737C2×C4⋊C4—342no—
738C2×C4⋊C4—681no—
739C2×C4⋊C4—681no—
740C2×C4⋊C4—681no—
741C2×C4⋊C4—681no—
742C2×C22⋊C4—22no—
743C2×C22⋊C4—22no—
744C2×C22⋊C4—22no—
745C2×C22⋊C4—22no—
746C2×C22⋊C4—41no—
747C2×C22⋊C4—41no—
748C2×C22⋊C4—174no—
749C2×C22⋊C4—342no—
750C2×C22⋊C4—342no—
751C2×C22⋊C4—342no—
752C2×C22⋊C4—342no—
753C2×C22⋊C4—342no—
754C2×C22⋊C4—342no—
755C2×C22⋊C4—342no—
756C2×C22⋊C4—342no—
757C2×C22⋊C4—342no—
758C2×C22⋊C4—342no—
759C2×C22⋊C4—342no—
760C2×C22⋊C4—342no—
761C2×C22⋊C4—681no—
762C2×C22⋊C4—681no—
763C2×C22⋊C4C2×Dic1714yescomplemented
764C2×C22⋊C4C2×Dic1714yescomplemented
765C2×C22⋊C4C2×Dic1714yescomplemented
766C2×C42—342no—
767C2×C42—342no—
768C2×C42—342no—
769#95—174no—
770#95—342no—
771#95—342no—
772#95—342no—
773#95—342no—
774#95—342no—
775#95—342no—
776#95—342no—
777#95—342no—
778#95—342no—
779#95—342no—
780#95—342no—
781#95—681no—
782#95—681no—
783#95C2×Dic1714yescomplemented
784#95C2×Dic1714yescomplemented
785C17#1397511yescharacteristic, complemented, Sylow
786C24—21no—
787C24—21no—
788C24—21no—
789C24—21no—
790C24—21no—
791C24—21no—
792C24—21no—
793C24—21no—
794C24—21no—
795C24—21no—
796C24—21no—
797C24—21no—
798C24—21no—
799C24—21no—
800C24—21no—
801C24—21no—
802C24—21no—
803C24—21no—
804C24—21no—
805C24—21no—
806C24C2×Dic3412yes—
807C24C2×Dic3412yes—
808C24C2×D6812yes—
809C24C2×D6812yes—
810C24D4×D1712yes—
811C24D4×D1712yes—
812C24#6325412yes—
813C24#6325412yes—
814C24C22×Dic1712yes—
815C24C22×Dic1712yes—
816C24C23×D1711yescharacteristic
817C2×D4—28no—
818C2×D4—28no—
819C2×D4—28no—
820C2×D4—28no—
821C2×D4—28no—
822C2×D4—28no—
823C2×D4C4⋊Dic17116yescomplemented
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—28no—
851C22×C4—28no—
852C22×C4—44no—
853C22×C4—44no—
854C22×C4—44no—
855C22×C4—44no—
856C22×C4—44no—
857C22×C4—172no—
858C22×C4—172no—
859C22×C4—172no—
860C22×C4—172no—
861C22×C4—172no—
862C22×C4—172no—
863C22×C4—172no—
864C22×C4—172no—
865C22×C4—348no—
866C22×C4—341no—
867C22×C4—341no—
868C22×C4—341no—
869C22×C4—341no—
870C22×C4—348no—
871C22×C4—348no—
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—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—348no—
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—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×C4—684no—
931C22×C4—684no—
932C22×C4—684no—
933C22×C4—684no—
934C22×C4C2×Dic3412yes—
935C22×C4C2×D6812yes—
936C22×C4D4×D1712yes—
937C22×C4#6325412yes—
938C22×C4C22×Dic1712yes—
939C22×C4C22×Dic1712yes—
940C22×C4C22×Dic1712yes—
941C22×C4C22×Dic1712yes—
942C22×C4C22×Dic1712yes—
943C4⋊C4—348no—
944C4⋊C4—684no—
945C4⋊C4—684no—
946C4⋊C4—684no—
947C4⋊C4—684no—
948C22⋊C4—28no—
949C22⋊C4—28no—
950C22⋊C4—44no—
951C22⋊C4—348no—
952C22⋊C4—348no—
953C22⋊C4—684no—
954C22⋊C4—684no—
955C22⋊C4—684no—
956C42—348no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23#1058756414yes—
1020C23#1058756414yes—
1021C23#1058756814yes—
1022C23#1058757214yes—
1023C23C2×C4⋊Dic1714yes—
1024C23C2×C4⋊Dic1714yes—
1025C23D4×Dic1714yes—
1026C23D4×Dic1714yes—
1027C23C22×Dic3411yescharacteristic
1028C23C22×D6811yescharacteristic
1029C23C2×D4×D1711yescharacteristic
1030C23C2×D4×D1711yescharacteristic
1031C23C2×D4×D1711yescharacteristic
1032C23C2×#6325411yescharacteristic
1033C23C2×#6325411yescharacteristic
1034C23C2×#6325411yescharacteristic
1035C23#1058769111yescharacteristic
1036C23#1058769111yescharacteristic
1037C23#41×D1711yescharacteristic
1038C23#41×D1711yescharacteristic
1039C23#1058769611yescharacteristic
1040C23#1058769711yescharacteristic
1041C23C23×Dic1711yescharacteristic
1042D4—232no—
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—416no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—174no—
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—342no—
1090C2×C4—342no—
1091C2×C4—342no—
1092C2×C4—342no—
1093C2×C4—342no—
1094C2×C4—342no—
1095C2×C4—342no—
1096C2×C4—342no—
1097C2×C4—342no—
1098C2×C4—342no—
1099C2×C4—6816no—
1100C2×C4—6816no—
1101C2×C4—6816no—
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×C4—681no—
1115C2×C4—681no—
1116C2×C4—681no—
1117C2×C4—681no—
1118C2×C4—681no—
1119C2×C4—681no—
1120C2×C4—681no—
1121C2×C4—681no—
1122C2×C4—681no—
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×C4—681no—
1136C2×C4C2×C4⋊Dic1714yes—
1137C2×C4D4×Dic1714yescomplemented
1138C22—24no—
1139C22—24no—
1140C22—24no—
1141C22—24no—
1142C22—24no—
1143C22—24no—
1144C22—24no—
1145C22—24no—
1146C22—24no—
1147C22—24no—
1148C22—24no—
1149C22—24no—
1150C22—24no—
1151C22—24no—
1152C22—24no—
1153C22—24no—
1154C22—24no—
1155C22—42no—
1156C22—42no—
1157C22—42no—
1158C22—42no—
1159C22—42no—
1160C22—42no—
1161C22—42no—
1162C22—42no—
1163C22—42no—
1164C22—42no—
1165C22—42no—
1166C22—42no—
1167C22#1176268418yescomplemented
1168C22C22×C4⋊Dic1711yescharacteristic
1169C22C2×D4×Dic1711yescharacteristic
1170C22C2×D4×Dic1711yescharacteristic
1171C22C2×D4×Dic1711yescharacteristic
1172C22#41×Dic1711yescharacteristic
1173C22#1176328411yescharacteristic
1174C22#1176329211yescharacteristic
1175C22C2×#1058756811yescharacteristic
1176C22#121×D1711yescharacteristic
1177C22C2×#1058756411yescharacteristic
1178C22C2×#1058756411yescharacteristic
1179C22C2×#1058757211yescharacteristic
1180C22#1176331911yescharacteristic
1181C22#1176334011yescharacteristic
1182C22#1176335411yescharacteristic
1183C22#1176336711yescharacteristic
1184C22#1176338611yescharacteristic
1185C22#1176339611yescharacteristic
1186C22#1176340411yescharacteristic
1187C22#1176344111yescharacteristic
1188C22D4×D6811yescharacteristic
1189C22#1176344611yescharacteristic
1190C22#1176344611yescharacteristic
1191C22#1176345111yescharacteristic
1192C22#1176345411yescharacteristic
1193C22#1176345411yescharacteristic
1194C22#1176345711yescharacteristic
1195C22#1176346311yescharacteristic
1196C22D4×Dic3411yescharacteristic
1197C22#1176348211yescharacteristic
1198C22#1176349011yescharacteristic
1199C22#1176349611yescharacteristic
1200C22#1176351611yescharacteristic
1201C22#1176351811yescharacteristic
1202C22#1176351811yescharacteristic
1203C4—24no—
1204C4—24no—
1205C4—42no—
1206C4—42no—
1207C4—42no—
1208C4—344no—
1209C4—682no—
1210C4—682no—
1211C4—682no—
1212C4—682no—
1213C4—682no—
1214C4—1361no—
1215C4—1361no—
1216C2—28no—
1217C2—44no—
1218C2C2×#1176268411yescharacteristic
1219C2#121×Dic1711yescharacteristic
1220C2#1453148911yescharacteristic
1221C2D4×C4⋊Dic1711yescharacteristic
1222C2#1453169411yescharacteristic
1223C2#1453176811yescharacteristic
1224C2#1453178011yescharacteristic
1225C2#1453215711yescharacteristic
1226C2#1453223211yescharacteristic
1227C2#1453224411yescharacteristic
1228C2#1453225911yescharacteristic
1229C2#1453239211yescharacteristic
1230C2#1453259711yescharacteristic
1231C2#1453261211yescharacteristic
1232C2#1453396811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC2×C17×#386C2
socle, cosocleC24×C17C24
prime radicalC23×D4×C17C22
hypercenterC2×#386D17
hypocenterC17#13975
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
3. C2×#11762684C2semidirect
4. C2×#11762684C2semidirect
5. C2×#11762669C2semidirect
6. C22×#10587502C2semidirect
7. #14527049C2semidirect
8. #14527041C2semidirect
9. #14527029C2semidirect
10. #14527029C2semidirect
11. #14527018C2semidirect
12. #14527018C2semidirect
13. #14527006C2semidirect
14. #14527006C2semidirect
57. C17×#386C4semidirect
75. C23×C4×C17C2×C4semidirect
116. C2×C22⋊C4×C17C2×C4semidirect
117. C2×C22⋊C4×C17C2×C4semidirect
118. C2×C22⋊C4×C17C2×C4semidirect
153. C17×#95C2×C4semidirect
154. C17×#95C2×C4semidirect
168. #10587502D4semidirect
206. C2×D4×C17C4⋊C4semidirect
462. C2×C4×C17C4×D4semidirect
566. C22×C17#385semidirect
638. #386Dic17semidirect
720. C23×C4C2×Dic17semidirect
763. C2×C22⋊C4C2×Dic17semidirect
764. C2×C22⋊C4C2×Dic17semidirect
765. C2×C22⋊C4C2×Dic17semidirect
783. #95C2×Dic17semidirect
784. #95C2×Dic17semidirect
785. C17#13975semidirect
823. C2×D4C4⋊Dic17semidirect
1137. C2×C4D4×Dic17semidirect
1167. C22#11762684semidirect

Maximal subgroups

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

subgroupindex
C22×D4×Dic172
C2×#117626892
C2×#117626842
C2×#117626692
C22×#105875022
#145270492
#145270412
#145270292
#145270182
#145270062
C2×C17×#3862
#1397517