Finite Group Databasebeta

← #16957230

Subgroups — #16957230

Order 4352.

1962 conjugacy classes of subgroups.

The subgroup lattice has 1042 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762694C211yesmaximal, characteristic, complemented
2C2×#11762683C211yesmaximal, characteristic
3C2×#11762668C211yesmaximal, characteristic
4C2×#11762656C211yesmaximal, characteristic
5C2×#95×D17C211yesmaximal, characteristic
6#14527050C211yesmaximal, characteristic, complemented
7#14527042C211yesmaximal, characteristic, complemented
8#14527036C211yesmaximal, characteristic, complemented
9#14527015C211yesmaximal, characteristic, complemented
10#14527015C211yesmaximal, characteristic, complemented
11#14527009C211yesmaximal, characteristic, complemented
12#14527005C211yesmaximal, characteristic
13#14527005C211yesmaximal, characteristic
14#14527005C211yesmaximal, characteristic
15C17×#1443C211yesmaximal, characteristic, complemented
16C23×C4×D17C2211yescharacteristic
17C23×C4×D17C2211yescharacteristic
18C23×C4×D17C2211yescharacteristic
19C22×C4⋊Dic17C2211yescharacteristic
20C22×#63225C2211yescharacteristic
21C22×#63225C2211yescharacteristic
22C22×#63225C2211yescharacteristic
23C22×#63227C2211yescharacteristic
24C22×#63227C2211yescharacteristic
25C22×#63227C2211yescharacteristic
26C22×#63227C2211yescharacteristic
27C22×C4×Dic17C2211yescharacteristic
28C22×C4×Dic17C2211yescharacteristic
29#11762694—24no—
30#11762683C418yescomplemented
31#11762668—24no—
32#11762656—24no—
33C2×#10587502C2211yescharacteristic
34C2×#10587502C2211yescharacteristic
35C2×#10587502C2211yescharacteristic
36C2×#10587502C2211yescharacteristic
37C2×#10587502C2211yescharacteristic
38C2×#10587502C2211yescharacteristic
39C2×#10587502C2211yescharacteristic
40C2×#10587502C2211yescharacteristic
41C2×#10587502C2211yescharacteristic
42C2×#10587502C2211yescharacteristic
43C2×#10587502C2211yescharacteristic
44C2×#10587502C2211yescharacteristic
45C2×#10587502C2211yescharacteristic
46C2×#10587502C2211yescharacteristic
47C2×#10587502C2211yescharacteristic
48#95×D17—24no—
49C2×C17×#95C2211yescharacteristic
50C2×C17×#95C2211yescharacteristic
51C2×C17×#95C2211yescharacteristic
52C2×C17×#95C2211yescharacteristic
53C2×C17×#95C2211yescharacteristic
54C2×C17×#95C2211yescharacteristic
55C2×C17×#95C2211yescharacteristic
56C24×D17C2311yescharacteristic
57C23×C4×C17C2311yescharacteristic
58C23×C4×C17C2311yescharacteristic
59C23×C4×C17C2311yescharacteristic
60C23×C4×C17C2311yescharacteristic
61C23×C4×C17C2311yescharacteristic
62C23×C4×C17C2311yescharacteristic
63C23×C4×C17C2311yescharacteristic
64C23×Dic17C2311yescharacteristic
65C23×Dic17C2311yescharacteristic
66C23×Dic17C2311yescharacteristic
67C23×Dic17C2311yescharacteristic
68C23×Dic17C2311yescharacteristic
69C23×Dic17C2311yescharacteristic
70C23×Dic17C2311yescharacteristic
71C22×C4×D17—22no—
72C22×C4×D17—22no—
73C22×C4×D17—22no—
74C22×C4×D17—22no—
75C22×C4×D17—22no—
76C22×C4×D17—22no—
77C22×C4×D17—22no—
78C22×C4×D17—22no—
79C22×C4×D17—22no—
80C22×C4×D17—22no—
81C22×C4×D17—22no—
82C22×C4×D17—22no—
83C22×C4×D17—22no—
84C22×C4×D17—41no—
85C22×C4×D17—41no—
86C22×C4×D17—41no—
87C22×C4×D17—41no—
88C22×C4×D17—41no—
89C22×C4×D17—41no—
90C22×C4×D17C2×C414yes—
91C22×C4×D17Q814yes—
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—22no—
101C2×#63227C2×C414yes—
102C2×#63227C2×C414yes—
103C2×#63227D414yes—
104C2×C4⋊Dic17—22no—
105C2×C4⋊Dic17—22no—
106C2×C4⋊Dic17C2×C414yescomplemented
107C2×#63225—22no—
108C2×#63225—22no—
109C2×#63225—22no—
110C2×#63225—22no—
111C2×#63225—41no—
112C2×#63225—41no—
113C2×#63225—41no—
114C2×#63225—41no—
115C2×#63225C2×C414yescomplemented
116C2×C4×Dic17—22no—
117C2×C4×Dic17—22no—
118C2×C4×Dic17—22no—
119C2×C4×Dic17—22no—
120C2×C4×Dic17—41no—
121C2×C4×Dic17—41no—
122C17×#95—22no—
123C17×#95—22no—
124C17×#95—22no—
125C17×#95—22no—
126C17×#95—41no—
127C17×#95—41no—
128C17×#95C2×C414yescomplemented
129#10587502—22no—
130#10587502—22no—
131#10587502—22no—
132#10587502—22no—
133#10587502—22no—
134#10587502—22no—
135#10587502—22no—
136#10587502—22no—
137#10587502—22no—
138#10587502—41no—
139#10587502—41no—
140#10587502—41no—
141#10587502—41no—
142#10587502C2×C414yescomplemented
143#10587502D414yes—
144C24×C17C2411yescharacteristic
145C23×D17—21no—
146C23×D17—21no—
147C23×D17—21no—
148C23×D17—21no—
149C23×D17—21no—
150C23×D17—21no—
151C23×D17—21no—
152C23×D17—21no—
153C23×D17C22×C412yes—
154C23×D17C2×D412yes—
155C23×D17C2×Q812yes—
156C23×D17#4112yes—
157C23×D17#4112yes—
158C23×D17#4112yes—
159C23×D17#4112yes—
160C22×C4×C17—21no—
161C22×C4×C17—21no—
162C22×C4×C17—21no—
163C22×C4×C17—21no—
164C22×C4×C17—21no—
165C22×C4×C17—21no—
166C22×C4×C17—21no—
167C22×C4×C17—21no—
168C22×C4×C17—21no—
169C22×C4×C17—21no—
170C22×C4×C17—21no—
171C22×C4×C17—21no—
172C22×C4×C17—21no—
173C22×C4×C17—21no—
174C22×C4×C17—21no—
175C22×C4×C17—21no—
176C22×C4×C17—21no—
177C22×C4×C17—21no—
178C22×C4×C17—21no—
179C22×C4×C17—21no—
180C22×C4×C17—21no—
181C22×C4×C17—21no—
182C22×C4×C17—21no—
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×C17C22×C412yes—
204C22×C4×C17C22×C412yes—
205C22×C4×C17C22×C412yes—
206C22×C4×C17C2×D412yes—
207C22×C4×C17C2×D412yes—
208C22×C4×C17C2×Q812yes—
209C22×Dic17—21no—
210C22×Dic17—21no—
211C22×Dic17—21no—
212C22×Dic17—21no—
213C22×Dic17—21no—
214C22×Dic17—21no—
215C22×Dic17—21no—
216C22×Dic17—21no—
217C22×Dic17—21no—
218C22×Dic17—21no—
219C22×Dic17—21no—
220C22×Dic17—21no—
221C22×Dic17—21no—
222C22×Dic17—21no—
223C22×Dic17—21no—
224C22×Dic17—21no—
225C22×Dic17—21no—
226C22×Dic17—21no—
227C22×Dic17—21no—
228C22×Dic17—21no—
229C22×Dic17—21no—
230C22×Dic17—21no—
231C22×Dic17—21no—
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×Dic17C22×C412yes—
249C22×Dic17C22×C412yes—
250C22×Dic17C22×C412yes—
251C22×Dic17C2×D412yes—
252C22×Dic17C2×D412yes—
253C22×Dic17C2×D412yes—
254C22×Dic17C2×Q812yes—
255C22×Dic17#4112yes—
256C22×Dic17#4112yes—
257C22×Dic17#4112yes—
258C2×C4×D17—28no—
259C2×C4×D17—28no—
260C2×C4×D17—28no—
261C2×C4×D17—28no—
262C2×C4×D17—28no—
263C2×C4×D17—44no—
264C2×C4×D17—44no—
265C2×C4×D17—44no—
266C2×C4×D17—44no—
267C2×C4×D17—44no—
268C2×C4×D17—44no—
269C2×C4×D17—44no—
270C2×C4×D17—44no—
271C2×C4×D17—44no—
272C2×C4×D17—44no—
273C2×C4×D17—44no—
274C2×C4×D17—44no—
275C2×C4×D17—44no—
276C2×C4×D17—44no—
277C2×C4×D17—44no—
278C2×C4×D17—44no—
279#63227—28no—
280#63227—28no—
281#63227—28no—
282#63227—44no—
283C4⋊Dic17—28no—
284#63225—44no—
285#63225—44no—
286#63225—44no—
287C4×Dic17—44no—
288C4×Dic17—44no—
289#13980—171nomaximal, Sylow
290C23×C17C23×C411yescharacteristic
291C23×C17C22×D411yescharacteristic
292C23×C17C22×D411yescharacteristic
293C23×C17C22×Q811yescharacteristic
294C23×C17C2×#4111yescharacteristic
295C23×C17C2×#4111yescharacteristic
296C23×C17C2×#4111yescharacteristic
297C23×C17C2×#4111yescharacteristic
298C23×C17C2×#4111yescharacteristic
299C23×C17C2×#4111yescharacteristic
300C23×C17C2×#4111yescharacteristic
301C23×C17H(5,𝔽2)11yescharacteristic
302C23×C17H(5,𝔽2)11yescharacteristic
303C23×C17H(5,𝔽2)11yescharacteristic
304C23×C172−1+411yescharacteristic
305C22×D17—22no—
306C22×D17—22no—
307C22×D17—22no—
308C22×D17—22no—
309C22×D17—22no—
310C22×D17—22no—
311C22×D17—22no—
312C22×D17—22no—
313C22×D17—22no—
314C22×D17—22no—
315C22×D17—22no—
316C22×D17—22no—
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—22no—
332C22×D17—22no—
333C22×D17#11714yes—
334C22×D17C4×D414yes—
335C22×D17C4×Q814yes—
336C22×D17C22⋊Q814yes—
337C22×D17#12314yes—
338C22×D17#12514yes—
339C22×D17#12614yes—
340C2×C4×C17—22no—
341C2×C4×C17—22no—
342C2×C4×C17—22no—
343C2×C4×C17—22no—
344C2×C4×C17—22no—
345C2×C4×C17—22no—
346C2×C4×C17—22no—
347C2×C4×C17—22no—
348C2×C4×C17—22no—
349C2×C4×C17—22no—
350C2×C4×C17—22no—
351C2×C4×C17—22no—
352C2×C4×C17—22no—
353C2×C4×C17—22no—
354C2×C4×C17—22no—
355C2×C4×C17—22no—
356C2×C4×C17—22no—
357C2×C4×C17—22no—
358C2×C4×C17—41no—
359C2×C4×C17—41no—
360C2×C4×C17—41no—
361C2×C4×C17—41no—
362C2×C4×C17—41no—
363C2×C4×C17—41no—
364C2×C4×C17—41no—
365C2×C4×C17—41no—
366C2×C4×C17—41no—
367C2×C4×C17—41no—
368C2×C4×C17—41no—
369C2×C4×C17—41no—
370C2×C4×C17—41no—
371C2×C4×C17—41no—
372C2×C4×C17—41no—
373C2×C4×C17—41no—
374C2×C4×C17—41no—
375C2×C4×C17—41no—
376C2×C4×C17—41no—
377C2×C4×C17—41no—
378C2×C4×C17—41no—
379C2×C4×C17—41no—
380C2×C4×C17—41no—
381C2×C4×C17—41no—
382C2×C4×C17—41no—
383C2×C4×C17—41no—
384C2×C4×C17—41no—
385C2×C4×C17—41no—
386C2×C4×C17—41no—
387C2×C4×C17—41no—
388C2×C4×C17—41no—
389C2×Dic17—22no—
390C2×Dic17—22no—
391C2×Dic17—22no—
392C2×Dic17—22no—
393C2×Dic17—22no—
394C2×Dic17—22no—
395C2×Dic17—22no—
396C2×Dic17—22no—
397C2×Dic17—22no—
398C2×Dic17—22no—
399C2×Dic17—22no—
400C2×Dic17—22no—
401C2×Dic17—22no—
402C2×Dic17—22no—
403C2×Dic17—22no—
404C2×Dic17—22no—
405C2×Dic17—22no—
406C2×Dic17—22no—
407C2×Dic17—22no—
408C2×Dic17—22no—
409C2×Dic17—22no—
410C2×Dic17—22no—
411C2×Dic17—22no—
412C2×Dic17—22no—
413C2×Dic17—41no—
414C2×Dic17—41no—
415C2×Dic17—41no—
416C2×Dic17—41no—
417C2×Dic17—41no—
418C2×Dic17—41no—
419C2×Dic17—41no—
420C2×Dic17—41no—
421C2×Dic17—41no—
422C2×Dic17—41no—
423C2×Dic17—41no—
424C2×Dic17—41no—
425C2×Dic17—41no—
426C2×Dic17—41no—
427C2×Dic17—41no—
428C2×Dic17—41no—
429C2×Dic17—41no—
430C2×Dic17—41no—
431C2×Dic17—41no—
432C2×Dic17—41no—
433C2×Dic17—41no—
434C2×Dic17—41no—
435C2×Dic17—41no—
436C2×Dic17C4×D414yes—
437C2×Dic17C22⋊Q814yes—
438C4×D17—416no—
439C4×D17—416no—
440C4×D17—416no—
441C2×#387—171no—
442C2×#385—171no—
443C2×#380—171no—
444C2×C4×C22⋊C4—171no—
445C22×#95—171no—
446#1445—171no—
447#1443D1711yescharacteristic, complemented
448#1442—171no—
449#1441—171no—
450#1436—171no—
451#1436—171no—
452#1434—171no—
453C22⋊#95—171no—
454C22⋊#95—171no—
455C22⋊#95—171no—
456C22×C17C2×#11711yescharacteristic
457C22×C17C2×C4×D411yescharacteristic
458C22×C17C2×C4×D411yescharacteristic
459C22×C17C2×C4×Q811yescharacteristic
460C22×C17C4×#4111yescharacteristic
461C22×C17#51811yescharacteristic
462C22×C17#52011yescharacteristic
463C22×C17C2×C22⋊Q811yescharacteristic
464C22×C17C2×C22⋊Q811yescharacteristic
465C22×C17C2×#12311yescharacteristic
466C22×C17#52511yescharacteristic
467C22×C17C2×#12511yescharacteristic
468C22×C17C2×#12611yescharacteristic
469C22×C17#52911yescharacteristic
470C22×C17#53311yescharacteristic
471C22×C17#53811yescharacteristic
472C22×C17#53911yescharacteristic
473C22×C17#54311yescharacteristic
474C22×C17#54411yescharacteristic
475C22×C17D4211yescharacteristic
476C22×C17#54611yescharacteristic
477C22×C17#54611yescharacteristic
478C22×C17#54611yescharacteristic
479C22×C17#54611yescharacteristic
480C22×C17#54711yescharacteristic
481C22×C17#54811yescharacteristic
482C22×C17#55111yescharacteristic
483C22×C17#55111yescharacteristic
484C22×C17#55111yescharacteristic
485C22×C17#55111yescharacteristic
486C22×C17#55211yescharacteristic
487C22×C17#55211yescharacteristic
488C22×C17#55311yescharacteristic
489C22×C17#55311yescharacteristic
490C22×C17#55311yescharacteristic
491C2×D17—24no—
492C2×D17—24no—
493C2×D17—24no—
494C2×D17—24no—
495C2×D17—24no—
496C2×D17—24no—
497C2×D17—24no—
498C2×D17—24no—
499C2×D17—24no—
500C2×D17—24no—
501C2×D17—24no—
502C2×D17—24no—
503C2×D17—24no—
504C2×D17—24no—
505C2×D17#38718yescomplemented
506C4×C17—42no—
507C4×C17—42no—
508C4×C17—42no—
509C4×C17—42no—
510C4×C17—42no—
511C4×C17—42no—
512C4×C17—81no—
513Dic17—24no—
514Dic17—24no—
515Dic17—42no—
516Dic17—42no—
517Dic17—42no—
518Dic17—42no—
519Dic17—81no—
520C24×C4—171no—
521C24×C4—171no—
522C24×C4—171no—
523C22×C4⋊C4—171no—
524C22×C4⋊C4—171no—
525C22×C4⋊C4—171no—
526C22×C4⋊C4—171no—
527C22×C22⋊C4—171no—
528C22×C22⋊C4—171no—
529C22×C22⋊C4—171no—
530C22×C22⋊C4—171no—
531C22×C42—171no—
532C22×C42—171no—
533#387—344no—
534#385—178no—
535#380—344no—
536C4×C22⋊C4—344no—
537C2×#95—171no—
538C2×#95—171no—
539C2×#95—171no—
540C2×#95—171no—
541C2×#95—171no—
542C2×#95—171no—
543C2×#95—171no—
544C2×#95—171no—
545C2×#95—171no—
546C2×#95—171no—
547C2×#95—171no—
548C2×#95—171no—
549C2×#95—171no—
550C2×#95—171no—
551C2×#95—171no—
552C2×#95—344no—
553C2×#95C2×D1711yescharacteristic
554C2×#95C2×D1711yescharacteristic
555C2×#95C2×D1711yescharacteristic
556C2×#95C2×D1711yescharacteristic
557C2×#95C2×D1711yescharacteristic
558C2×#95C2×D1711yescharacteristic
559C2×#95C2×D1711yescharacteristic
560C2×C17C2×#38711yescharacteristic
561C2×C17C4×C22⋊Q811yescharacteristic
562C2×C17#232911yescharacteristic
563C2×C17#235211yescharacteristic
564C2×C17#235311yescharacteristic
565C2×C17#235811yescharacteristic
566C2×C17#235911yescharacteristic
567C2×C17#243711yescharacteristic
568C2×C17#243811yescharacteristic
569C2×C17#244211yescharacteristic
570C2×C17#244311yescharacteristic
571C2×C17#244411yescharacteristic
572C2×C17#248011yescharacteristic
573C2×C17#249311yescharacteristic
574C2×C17#256911yescharacteristic
575D17—28no—
576C25—171no—
577C23×C4—171no—
578C23×C4—171no—
579C23×C4—171no—
580C23×C4—171no—
581C23×C4—171no—
582C23×C4—171no—
583C23×C4—174no—
584C23×C4—174no—
585C23×C4—171no—
586C23×C4—342no—
587C23×C4—342no—
588C23×C4—342no—
589C23×C4—342no—
590C23×C4—342no—
591C23×C4—342no—
592C23×C4—342no—
593C23×C4—342no—
594C23×C4—342no—
595C23×C4—342no—
596C23×C4—342no—
597C23×C4—342no—
598C23×C4—342no—
599C23×C4—681no—
600C23×C4—681no—
601C23×C4—681no—
602C23×C4—681no—
603C23×C4—681no—
604C23×C4—681no—
605C23×C4C22×D1711yescharacteristic
606C23×C4C22×D1711yescharacteristic
607C23×C4C22×D1711yescharacteristic
608C23×C4C22×D1711yescharacteristic
609C23×C4C22×D1711yescharacteristic
610C23×C4C22×D1711yescharacteristic
611C23×C4C22×D1711yescharacteristic
612C2×C4⋊C4—174no—
613C2×C4⋊C4—174no—
614C2×C4⋊C4—342no—
615C2×C4⋊C4—342no—
616C2×C4⋊C4—342no—
617C2×C4⋊C4—342no—
618C2×C4⋊C4—342no—
619C2×C4⋊C4—342no—
620C2×C4⋊C4—681no—
621C2×C4⋊C4—681no—
622C2×C4⋊C4—681no—
623C2×C4⋊C4—681no—
624C2×C22⋊C4—174no—
625C2×C22⋊C4—174no—
626C2×C22⋊C4—174no—
627C2×C22⋊C4—342no—
628C2×C22⋊C4—342no—
629C2×C22⋊C4—342no—
630C2×C22⋊C4—342no—
631C2×C22⋊C4—342no—
632C2×C22⋊C4—342no—
633C2×C22⋊C4—342no—
634C2×C22⋊C4—342no—
635C2×C22⋊C4—342no—
636C2×C42—342no—
637C2×C42—342no—
638C2×C42—342no—
639C2×C42—342no—
640C2×C42—681no—
641C2×C42—681no—
642#95—22no—
643#95—22no—
644#95—22no—
645#95—22no—
646#95—41no—
647#95—41no—
648#95—174no—
649#95—174no—
650#95—342no—
651#95—342no—
652#95—342no—
653#95—342no—
654#95—342no—
655#95—342no—
656#95—342no—
657#95—342no—
658#95—342no—
659#95—681no—
660#95—681no—
661#95—681no—
662#95—681no—
663#95C4×D1714yescomplemented
664C17#1398011yescharacteristic, complemented, Sylow
665C24—172no—
666C24—172no—
667C24—172no—
668C24—172no—
669C24—172no—
670C24—172no—
671C24—172no—
672C24—341no—
673C24—341no—
674C24—341no—
675C24—341no—
676C24—341no—
677C24—341no—
678C24—341no—
679C24—341no—
680C24C23×D1711yescharacteristic
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—172no—
725C22×C4—172no—
726C22×C4—172no—
727C22×C4—172no—
728C22×C4—172no—
729C22×C4—172no—
730C22×C4—172no—
731C22×C4—172no—
732C22×C4—172no—
733C22×C4—172no—
734C22×C4—348no—
735C22×C4—348no—
736C22×C4—348no—
737C22×C4—348no—
738C22×C4—348no—
739C22×C4—341no—
740C22×C4—341no—
741C22×C4—341no—
742C22×C4—341no—
743C22×C4—341no—
744C22×C4—341no—
745C22×C4—341no—
746C22×C4—341no—
747C22×C4—341no—
748C22×C4—341no—
749C22×C4—341no—
750C22×C4—341no—
751C22×C4—341no—
752C22×C4—341no—
753C22×C4—341no—
754C22×C4—341no—
755C22×C4—341no—
756C22×C4—341no—
757C22×C4—341no—
758C22×C4—341no—
759C22×C4—341no—
760C22×C4—341no—
761C22×C4—341no—
762C22×C4—341no—
763C22×C4—341no—
764C22×C4—341no—
765C22×C4—341no—
766C22×C4—341no—
767C22×C4—341no—
768C22×C4—341no—
769C22×C4—341no—
770C22×C4—341no—
771C22×C4—341no—
772C22×C4—341no—
773C22×C4—341no—
774C22×C4—341no—
775C22×C4—341no—
776C22×C4—341no—
777C22×C4—341no—
778C22×C4—684no—
779C22×C4—684no—
780C22×C4—684no—
781C22×C4—684no—
782C22×C4—684no—
783C22×C4—684no—
784C22×C4—684no—
785C22×C4—684no—
786C22×C4—684no—
787C22×C4—684no—
788C22×C4—684no—
789C22×C4—684no—
790C22×C4—684no—
791C22×C4—684no—
792C22×C4—684no—
793C22×C4—684no—
794C22×C4C2×C4×D1712yes—
795C22×C4C2×C4×D1712yes—
796C22×C4C2×C4×D1712yes—
797C22×C4D4×D1712yes—
798C22×C4D4×D1712yes—
799C22×C4Q8×D1712yes—
800C4⋊C4—348no—
801C4⋊C4—684no—
802C4⋊C4—684no—
803C4⋊C4—684no—
804C22⋊C4—348no—
805C22⋊C4—348no—
806C22⋊C4—348no—
807C22⋊C4—684no—
808C42—684no—
809C42—684no—
810C23—174no—
811C23—174no—
812C23—174no—
813C23—174no—
814C23—174no—
815C23—174no—
816C23—174no—
817C23—342no—
818C23—342no—
819C23—342no—
820C23—342no—
821C23—342no—
822C23—342no—
823C23—342no—
824C23—342no—
825C23—342no—
826C23—342no—
827C23—342no—
828C23—342no—
829C23—342no—
830C23—342no—
831C23—342no—
832C23—342no—
833C23—342no—
834C23—342no—
835C23—342no—
836C23—342no—
837C23—342no—
838C23—342no—
839C23—342no—
840C23—342no—
841C23—342no—
842C23—342no—
843C23—342no—
844C23—342no—
845C23C22×C4×D1711yescharacteristic
846C23C2×D4×D1711yescharacteristic
847C23C2×D4×D1711yescharacteristic
848C23#1058769111yescharacteristic
849C23C2×Q8×D1711yescharacteristic
850C23#41×D1711yescharacteristic
851C23#41×D1711yescharacteristic
852C23#41×D1711yescharacteristic
853C23#41×D1711yescharacteristic
854C23#41×D1711yescharacteristic
855C23#41×D1711yescharacteristic
856C23#41×D1711yescharacteristic
857C23#1058769611yescharacteristic
858C23#1058769611yescharacteristic
859C23#1058769711yescharacteristic
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—174no—
910C2×C4—174no—
911C2×C4—342no—
912C2×C4—342no—
913C2×C4—342no—
914C2×C4—342no—
915C2×C4—342no—
916C2×C4—342no—
917C2×C4—342no—
918C2×C4—342no—
919C2×C4—342no—
920C2×C4—342no—
921C2×C4—342no—
922C2×C4—342no—
923C2×C4—342no—
924C2×C4—342no—
925C2×C4—342no—
926C2×C4—342no—
927C2×C4—342no—
928C2×C4—342no—
929C2×C4—342no—
930C2×C4—342no—
931C2×C4—342no—
932C2×C4—342no—
933C2×C4—342no—
934C2×C4—342no—
935C2×C4—6816no—
936C2×C4—6816no—
937C2×C4—6816no—
938C2×C4—681no—
939C2×C4—681no—
940C2×C4—681no—
941C2×C4—681no—
942C2×C4—681no—
943C2×C4—681no—
944C2×C4—681no—
945C2×C4—681no—
946C2×C4—681no—
947C2×C4—681no—
948C2×C4—681no—
949C2×C4—681no—
950C2×C4—681no—
951C2×C4—681no—
952C2×C4—681no—
953C2×C4—681no—
954C2×C4—681no—
955C2×C4—681no—
956C2×C4—681no—
957C2×C4—681no—
958C2×C4—681no—
959C2×C4—681no—
960C2×C4—681no—
961C22—178no—
962C22—344no—
963C22—344no—
964C22—344no—
965C22—344no—
966C22—344no—
967C22—344no—
968C22—344no—
969C22—344no—
970C22—344no—
971C22—344no—
972C22—344no—
973C22—344no—
974C22—344no—
975C22—344no—
976C22#117×D1711yescharacteristic
977C22C4×D4×D1711yescharacteristic
978C22C4×D4×D1711yescharacteristic
979C22C4×Q8×D1711yescharacteristic
980C22#1176327711yescharacteristic
981C22#1176328311yescharacteristic
982C22#1176328811yescharacteristic
983C22C22⋊Q8×D1711yescharacteristic
984C22C22⋊Q8×D1711yescharacteristic
985C22#123×D1711yescharacteristic
986C22#1176331711yescharacteristic
987C22#125×D1711yescharacteristic
988C22#126×D1711yescharacteristic
989C22#1176334211yescharacteristic
990C22#1176336511yescharacteristic
991C22#1176339511yescharacteristic
992C22#1176340011yescharacteristic
993C22#1176343411yescharacteristic
994C22#1176343911yescharacteristic
995C22#1176344311yescharacteristic
996C22#1176344811yescharacteristic
997C22#1176345111yescharacteristic
998C22#1176345211yescharacteristic
999C22#1176345611yescharacteristic
1000C22#1176345711yescharacteristic
1001C22#1176346711yescharacteristic
1002C22#1176348411yescharacteristic
1003C22#1176348411yescharacteristic
1004C22#1176348411yescharacteristic
1005C22#1176348911yescharacteristic
1006C22#1176349511yescharacteristic
1007C22#1176349511yescharacteristic
1008C22#1176350411yescharacteristic
1009C22#1176351011yescharacteristic
1010C22#1176351011yescharacteristic
1011C4—42no—
1012C4—42no—
1013C4—42no—
1014C4—42no—
1015C4—42no—
1016C4—42no—
1017C4—81no—
1018C4—344no—
1019C4—344no—
1020C4—682no—
1021C4—682no—
1022C4—682no—
1023C4—682no—
1024C4—1361no—
1025C2—348no—
1026C2D17×#38711yescharacteristic
1027C2#1453131811yescharacteristic
1028C2#1453151311yescharacteristic
1029C2#1453171211yescharacteristic
1030C2#1453171711yescharacteristic
1031C2#1453176211yescharacteristic
1032C2#1453177311yescharacteristic
1033C2#1453244611yescharacteristic
1034C2#1453246311yescharacteristic
1035C2#1453250111yescharacteristic
1036C2#1453251411yescharacteristic
1037C2#1453253711yescharacteristic
1038C2#1453302311yescharacteristic
1039C2#1453316411yescharacteristic
1040C2#1453400411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1443C2
socle, cosocleC24×C17C24
prime radicalC24×D17C23
hypercenter#1443D17
hypocenterC17#13980
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1443

Complements

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

NH ≅ G/Ntype
1. C2×#11762694C2semidirect
6. #14527050C2semidirect
7. #14527042C2semidirect
8. #14527036C2semidirect
9. #14527015C2semidirect
10. #14527015C2semidirect
11. #14527009C2semidirect
15. C17×#1443C2semidirect
30. #11762683C4semidirect
106. C2×C4⋊Dic17C2×C4semidirect
115. C2×#63225C2×C4semidirect
128. C17×#95C2×C4semidirect
142. #10587502C2×C4semidirect
447. #1443D17semidirect
505. C2×D17#387semidirect
663. #95C4×D17semidirect
664. C17#13980semidirect

Maximal subgroups

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

subgroupindex
C2×#117626942
C2×#117626832
C2×#117626682
C2×#117626562
C2×#95×D172
#145270502
#145270422
#145270362
#145270152
#145270092
#145270052
C17×#14432
#1398017