Finite Group Databasebeta

← #16960749

Subgroups — #16960749

Order 4352.

1926 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587558C211yesmaximal, characteristic
2C2×#11762705C211yesmaximal, characteristic, complemented
3C2×#11762666C211yesmaximal, characteristic
4C2×#11762666C211yesmaximal, characteristic
5#14527047C212yesmaximal, complemented
6#14527042C212yesmaximal, complemented
7#14527028C212yesmaximal
8#14527026C212yesmaximal
9#14527014C211yesmaximal, characteristic, complemented
10#14527013C211yesmaximal, characteristic, complemented
11C2×C17×#389C211yesmaximal, characteristic, complemented
12C23×C4×D17C2211yescharacteristic
13C2×#10587558—24no—
14C2×#10587558—24no—
15C2×#10587558—24no—
16C22×C4⋊Dic17C2211yescharacteristic
17C22×C4⋊Dic17C2211yescharacteristic
18C22×#63225C2211yescharacteristic
19C22×#63225C2211yescharacteristic
20C22×#63225C2212yes—
21C22×#63227C2211yescharacteristic
22C22×#63227C2211yescharacteristic
23C22×#63227C2212yes—
24C22×#63227C2212yes—
25C22×C4×Dic17C2211yescharacteristic
26#11762705—24no—
27#11762666—24no—
28#11762666C418yescomplemented
29C2×#10587502C2212yes—
30C2×#10587502C2212yes—
31C2×#10587502C2212yes—
32C2×#10587502C2212yes—
33C2×#10587502C2212yes—
34C2×#10587502C2212yes—
35C2×#10587502C2212yes—
36C22×C4⋊C4×C17C2211yescharacteristic
37C22×C4⋊C4×C17C2211yescharacteristic
38C22×C4⋊C4×C17C2212yes—
39C22×C42×C17C2211yescharacteristic
40C17×#389—24no—
41C2×C17×#95C2212yes—
42C24×D17C2311yescharacteristic
43C23×C4×C17C2312yes—
44C23×C4×C17C2312yes—
45C23×C4×C17C2311yescharacteristic
46C23×C4×C17C2311yescharacteristic
47C23×C4×C17C2311yescharacteristic
48C23×Dic17C2312yes—
49C23×Dic17C2312yes—
50C23×Dic17C2311yescharacteristic
51C23×Dic17C2311yescharacteristic
52C23×Dic17C2311yescharacteristic
53C22×C4×D17—22no—
54C22×C4×D17—22no—
55C22×C4×D17—22no—
56C22×C4×D17—22no—
57C22×C4×D17C2×C414yes—
58C22×C4×D17D414yes—
59C22×C4×D17Q814yes—
60C2×C4⋊C4×C17—22no—
61C2×C4⋊C4×C17—22no—
62C2×C4⋊C4×C17—22no—
63C2×C4⋊C4×C17—24no—
64C2×C4⋊C4×C17—22no—
65C2×C4⋊C4×C17—22no—
66C2×C4⋊C4×C17—42no—
67C2×C4⋊C4×C17—42no—
68C2×C4⋊C4×C17C2×C414yes—
69C2×C42×C17—22no—
70C2×C42×C17—22no—
71C2×C42×C17D414yes—
72C2×#63227—22no—
73C2×#63227—22no—
74C2×#63227—24no—
75C2×#63227—22no—
76C2×#63227—22no—
77C2×#63227—22no—
78C2×#63227—22no—
79C2×#63227—42no—
80C2×#63227—42no—
81C2×#63227—42no—
82C2×#63227—42no—
83C2×#63227C2×C418yes—
84C2×C4⋊Dic17—22no—
85C2×C4⋊Dic17—22no—
86C2×C4⋊Dic17—22no—
87C2×C4⋊Dic17—22no—
88C2×C4⋊Dic17—22no—
89C2×C4⋊Dic17C2×C414yes—
90C2×#63225—22no—
91C2×#63225—22no—
92C2×#63225—22no—
93C2×#63225—22no—
94C2×#63225—22no—
95C2×#63225—22no—
96C2×#63225—24no—
97C2×#63225—42no—
98C2×#63225—42no—
99C2×C4×Dic17—22no—
100C2×C4×Dic17—22no—
101C2×C4×Dic17D414yes—
102#10587558—232no—
103C17×#95—24no—
104#10587502—24no—
105#10587502—24no—
106#10587502—42no—
107#10587502—42no—
108#10587502—42no—
109#10587502—42no—
110#10587502C2×C418yes—
111C24×C17C2411yescharacteristic
112C23×D17—21no—
113C23×D17—21no—
114C23×D17—21no—
115C23×D17—21no—
116C23×D17—21no—
117C23×D17—21no—
118C23×D17—21no—
119C23×D17—21no—
120C23×D17—21no—
121C23×D17—21no—
122C23×D17—21no—
123C23×D17—21no—
124C23×D17C22×C412yes—
125C23×D17C2×D412yes—
126C23×D17C2×Q812yes—
127C22×C4×C17—22no—
128C22×C4×C17—21no—
129C22×C4×C17—21no—
130C22×C4×C17—21no—
131C22×C4×C17—21no—
132C22×C4×C17—22no—
133C22×C4×C17—21no—
134C22×C4×C17—21no—
135C22×C4×C17—22no—
136C22×C4×C17—22no—
137C22×C4×C17—22no—
138C22×C4×C17—21no—
139C22×C4×C17—21no—
140C22×C4×C17—21no—
141C22×C4×C17—21no—
142C22×C4×C17—22no—
143C22×C4×C17—21no—
144C22×C4×C17—21no—
145C22×C4×C17—22no—
146C22×C4×C17—22no—
147C22×C4×C17—22no—
148C22×C4×C17—22no—
149C22×C4×C17—22no—
150C22×C4×C17—22no—
151C22×C4×C17—22no—
152C22×C4×C17C22×C414yes—
153C22×C4×C17C22×C412yes—
154C22×C4×C17C2×D412yes—
155C22×C4×C17C2×D412yes—
156C22×C4×C17C2×D412yes—
157C22×C4×C17C2×D412yes—
158C22×C4×C17C2×D412yes—
159C22×C4×C17C2×Q812yes—
160C22×C4×C17#4112yes—
161C22×C4×C17#4112yes—
162C22×Dic17—21no—
163C22×Dic17—21no—
164C22×Dic17—21no—
165C22×Dic17—21no—
166C22×Dic17—22no—
167C22×Dic17—21no—
168C22×Dic17—21no—
169C22×Dic17—21no—
170C22×Dic17—21no—
171C22×Dic17—22no—
172C22×Dic17—21no—
173C22×Dic17—21no—
174C22×Dic17—22no—
175C22×Dic17—22no—
176C22×Dic17—21no—
177C22×Dic17—21no—
178C22×Dic17—22no—
179C22×Dic17—22no—
180C22×Dic17—21no—
181C22×Dic17—21no—
182C22×Dic17—21no—
183C22×Dic17—21no—
184C22×Dic17—22no—
185C22×Dic17—22no—
186C22×Dic17—22no—
187C22×Dic17—22no—
188C22×Dic17—22no—
189C22×Dic17—22no—
190C22×Dic17—22no—
191C22×Dic17C22×C414yes—
192C22×Dic17C22×C412yes—
193C22×Dic17C2×D412yes—
194C22×Dic17C2×D412yes—
195C22×Dic17C2×D412yes—
196C22×Dic17C2×Q812yes—
197C2×C4×D17—28no—
198C2×C4×D17—28no—
199C2×C4×D17—28no—
200C2×C4×D17—28no—
201C2×C4×D17—28no—
202C2×C4×D17—28no—
203C2×C4×D17C4⋊C4116yescomplemented
204C4⋊C4×C17—28no—
205C4⋊C4×C17—48no—
206C4⋊C4×C17—44no—
207C42×C17—28no—
208#63227—28no—
209#63227—28no—
210#63227—48no—
211#63227—48no—
212C4⋊Dic17—28no—
213C4⋊Dic17—44no—
214#63225—28no—
215#63225—28no—
216#63225—48no—
217C4×Dic17—28no—
218#14264—171nomaximal, Sylow
219C23×C17C23×C411yescharacteristic
220C23×C17C22×D411yescharacteristic
221C23×C17C22×D411yescharacteristic
222C23×C17C22×D411yescharacteristic
223C23×C17C22×Q811yescharacteristic
224C23×C17C2×#4111yescharacteristic
225C23×C17C2×#4111yescharacteristic
226C23×C17H(5,𝔽2)11yescharacteristic
227C23×C17H(5,𝔽2)11yescharacteristic
228C23×C17H(5,𝔽2)11yescharacteristic
229C23×C17H(5,𝔽2)11yescharacteristic
230C23×C172−1+411yescharacteristic
231C23×C172−1+411yescharacteristic
232C23×C172−1+411yescharacteristic
233C23×C172−1+411yescharacteristic
234C22×D17—22no—
235C22×D17—22no—
236C22×D17—22no—
237C22×D17—22no—
238C22×D17—22no—
239C22×D17—22no—
240C22×D17—22no—
241C22×D17—22no—
242C22×D17—22no—
243C22×D17—22no—
244C22×D17—22no—
245C22×D17—22no—
246C22×D17—22no—
247C22×D17—22no—
248C22×D17—22no—
249C22×D17—22no—
250C22×D17—22no—
251C22×D17—22no—
252C22×D17—41no—
253C22×D17—41no—
254C22×D17—41no—
255C22×D17—41no—
256C22×D17—41no—
257C22×D17—41no—
258C22×D17—41no—
259C22×D17—41no—
260C22×D17—41no—
261C22×D17—41no—
262C22×D17—41no—
263C22×D17—41no—
264C22×D17—41no—
265C22×D17—41no—
266C22×D17—41no—
267C22×D17—41no—
268C22×D17C2×C4⋊C414yes—
269C2×C4×C17—24no—
270C2×C4×C17—24no—
271C2×C4×C17—24no—
272C2×C4×C17—22no—
273C2×C4×C17—22no—
274C2×C4×C17—22no—
275C2×C4×C17—22no—
276C2×C4×C17—22no—
277C2×C4×C17—22no—
278C2×C4×C17—42no—
279C2×C4×C17—41no—
280C2×C4×C17—41no—
281C2×C4×C17—41no—
282C2×C4×C17—41no—
283C2×C4×C17—42no—
284C2×C4×C17—41no—
285C2×C4×C17—41no—
286C2×C4×C17—41no—
287C2×C4×C17—41no—
288C2×C4×C17—42no—
289C2×C4×C17—42no—
290C2×C4×C17—42no—
291C2×C4×C17—42no—
292C2×C4×C17—42no—
293C2×C4×C17—42no—
294C2×C4×C17—42no—
295C2×C4×C17—42no—
296C2×C4×C17—42no—
297C2×C4×C17C2×C4⋊C414yes—
298C2×C4×C17C4×D414yes—
299C2×C4×C17C4×D414yes—
300C2×C4×C17#12014yes—
301C2×C4×C17C22⋊Q814yes—
302C2×C4×C17C22⋊Q814yes—
303C2×C4×C17#12314yes—
304C2×Dic17—22no—
305C2×Dic17—22no—
306C2×Dic17—22no—
307C2×Dic17—22no—
308C2×Dic17—22no—
309C2×Dic17—22no—
310C2×Dic17—24no—
311C2×Dic17—24no—
312C2×Dic17—24no—
313C2×Dic17—22no—
314C2×Dic17—22no—
315C2×Dic17—22no—
316C2×Dic17—22no—
317C2×Dic17—22no—
318C2×Dic17—22no—
319C2×Dic17—41no—
320C2×Dic17—41no—
321C2×Dic17—42no—
322C2×Dic17—41no—
323C2×Dic17—41no—
324C2×Dic17—41no—
325C2×Dic17—41no—
326C2×Dic17—41no—
327C2×Dic17—42no—
328C2×Dic17—41no—
329C2×Dic17—42no—
330C2×Dic17—42no—
331C2×Dic17—42no—
332C2×Dic17—42no—
333C2×Dic17—42no—
334C2×Dic17—42no—
335C2×Dic17—42no—
336C2×Dic17—42no—
337C2×Dic17—42no—
338C2×Dic17C2×C4⋊C414yes—
339C4×D17—232no—
340C22×#117—171no—
341C2×#389—171no—
342C2×#389D1711yescharacteristic, complemented
343C2×#380—171no—
344C2×#380—171no—
345#1444—172no—
346#1442—172no—
347#1439—172no—
348#1439—172no—
349C4⋊#95—171no—
350C4⋊#95—171no—
351C22×C17C22×C4⋊C411yescharacteristic
352C22×C17C2×C4×D411yescharacteristic
353C22×C17C2×C4×D411yescharacteristic
354C22×C17#51811yescharacteristic
355C22×C17#51911yescharacteristic
356C22×C17#52011yescharacteristic
357C22×C17#52011yescharacteristic
358C22×C17C2×#12011yescharacteristic
359C22×C17C2×C22⋊Q811yescharacteristic
360C22×C17C2×C22⋊Q811yescharacteristic
361C22×C17C2×#12311yescharacteristic
362C22×C17#53511yescharacteristic
363C22×C17#53511yescharacteristic
364C22×C17#53511yescharacteristic
365C22×C17#53611yescharacteristic
366C22×C17#53611yescharacteristic
367C22×C17#53611yescharacteristic
368C22×C17#53711yescharacteristic
369C22×C17#53711yescharacteristic
370C22×C17#53711yescharacteristic
371C22×C17#53711yescharacteristic
372C22×C17#53711yescharacteristic
373C22×C17#53711yescharacteristic
374C22×C17#54011yescharacteristic
375C22×C17#54011yescharacteristic
376C22×C17#54111yescharacteristic
377C22×C17#54111yescharacteristic
378C22×C17#54211yescharacteristic
379C22×C17#54211yescharacteristic
380C22×C17#54211yescharacteristic
381C22×C17#54211yescharacteristic
382C22×C17#54411yescharacteristic
383C22×C17#54411yescharacteristic
384C22×C17#54411yescharacteristic
385C22×C17#54411yescharacteristic
386C2×D17—24no—
387C2×D17—24no—
388C2×D17—24no—
389C2×D17—42no—
390C2×D17—42no—
391C2×D17—42no—
392C2×D17—42no—
393C2×D17—42no—
394C2×D17—42no—
395C2×D17—42no—
396C2×D17—42no—
397C2×D17—42no—
398C2×D17—42no—
399C2×D17—42no—
400C2×D17—42no—
401C4×C17—44no—
402C4×C17—42no—
403C4×C17—42no—
404C4×C17—82no—
405C4×C17#38518yes—
406Dic17—24no—
407Dic17—44no—
408Dic17—42no—
409Dic17—42no—
410Dic17—82no—
411C24×C4—171no—
412C2×#117—344no—
413C2×#117—344no—
414C2×#117—344no—
415C22×C4⋊C4—171no—
416C22×C4⋊C4—171no—
417C22×C4⋊C4—171no—
418C22×C4⋊C4—171no—
419C22×C4⋊C4—172no—
420C22×C4⋊C4C2×D1711yescharacteristic
421C22×C4⋊C4C2×D1711yescharacteristic
422C22×C4⋊C4C2×D1712yes—
423C22×C22⋊C4—172no—
424C22×C22⋊C4—171no—
425C22×C22⋊C4—171no—
426C22×C22⋊C4—172no—
427C22×C42—171no—
428C22×C42C2×D1711yescharacteristic
429#389—24no—
430#389—344no—
431#380—178no—
432#380—344no—
433C2×#95—172no—
434C2×#95—172no—
435C2×#95—172no—
436C2×#95—172no—
437C2×#95—172no—
438C2×#95—172no—
439C2×#95—172no—
440C2×#95C2×D1712yes—
441C2×C17C2×#38511yescharacteristic
442C2×C17#231611yescharacteristic
443C2×C17#231711yescharacteristic
444C2×C17#232311yescharacteristic
445C2×C17#232311yescharacteristic
446C2×C17#232411yescharacteristic
447C2×C17#232411yescharacteristic
448C2×C17#261511yescharacteristic
449C2×C17#261611yescharacteristic
450C2×C17#262411yescharacteristic
451C2×C17#262511yescharacteristic
452C2×C17#262811yescharacteristic
453C2×C17#262811yescharacteristic
454C2×C17#262911yescharacteristic
455C2×C17#262911yescharacteristic
456D17—44no—
457C25—171no—
458C23×C4—171no—
459C23×C4—174no—
460C23×C4—174no—
461C23×C4—174no—
462C23×C4—171no—
463C23×C4—172no—
464C23×C4—171no—
465C23×C4—172no—
466C23×C4—342no—
467C23×C4—342no—
468C23×C4—342no—
469C23×C4—342no—
470C23×C4C22×D1712yes—
471C23×C4C22×D1712yes—
472C23×C4C22×D1711yescharacteristic
473C23×C4C22×D1711yescharacteristic
474C23×C4C22×D1711yescharacteristic
475#117—3432no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—22no—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—22no—
480C2×C4⋊C4—24no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—42no—
483C2×C4⋊C4—42no—
484C2×C4⋊C4—174no—
485C2×C4⋊C4—342no—
486C2×C4⋊C4—342no—
487C2×C4⋊C4—342no—
488C2×C4⋊C4—342no—
489C2×C4⋊C4—342no—
490C2×C4⋊C4—342no—
491C2×C4⋊C4—342no—
492C2×C4⋊C4—342no—
493C2×C4⋊C4—344no—
494C2×C4⋊C4—342no—
495C2×C4⋊C4—342no—
496C2×C4⋊C4—342no—
497C2×C4⋊C4—682no—
498C2×C4⋊C4—682no—
499C2×C4⋊C4C4×D1714yes—
500C2×C22⋊C4—178no—
501C2×C22⋊C4—342no—
502C2×C22⋊C4—342no—
503C2×C22⋊C4—342no—
504C2×C22⋊C4—342no—
505C2×C22⋊C4—342no—
506C2×C22⋊C4—342no—
507C2×C22⋊C4—344no—
508C2×C22⋊C4—682no—
509C2×C22⋊C4—682no—
510C2×C22⋊C4—682no—
511C2×C22⋊C4—682no—
512C2×C42—22no—
513C2×C42—22no—
514C2×C42—174no—
515C2×C42—342no—
516C2×C42—342no—
517C2×C42C22⋊D1714yes—
518#95—24no—
519#95—178no—
520#95—344no—
521#95—344no—
522#95—682no—
523#95—682no—
524#95—682no—
525#95—682no—
526C17#1426411yescharacteristic, complemented, Sylow
527C24—172no—
528C24—172no—
529C24—172no—
530C24—341no—
531C24—341no—
532C24—341no—
533C24—341no—
534C24—341no—
535C24—341no—
536C24—341no—
537C24—341no—
538C24—341no—
539C24—341no—
540C24—341no—
541C24—341no—
542C24C23×D1711yescharacteristic
543C22×C4—22no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—172no—
569C22×C4—172no—
570C22×C4—172no—
571C22×C4—1716no—
572C22×C4—174no—
573C22×C4—172no—
574C22×C4—172no—
575C22×C4—341no—
576C22×C4—341no—
577C22×C4—341no—
578C22×C4—341no—
579C22×C4—348no—
580C22×C4—348no—
581C22×C4—348no—
582C22×C4—348no—
583C22×C4—348no—
584C22×C4—348no—
585C22×C4—342no—
586C22×C4—341no—
587C22×C4—341no—
588C22×C4—341no—
589C22×C4—342no—
590C22×C4—341no—
591C22×C4—342no—
592C22×C4—342no—
593C22×C4—341no—
594C22×C4—341no—
595C22×C4—341no—
596C22×C4—342no—
597C22×C4—342no—
598C22×C4—341no—
599C22×C4—341no—
600C22×C4—341no—
601C22×C4—341no—
602C22×C4—341no—
603C22×C4—342no—
604C22×C4—342no—
605C22×C4—342no—
606C22×C4—342no—
607C22×C4—342no—
608C22×C4—342no—
609C22×C4—342no—
610C22×C4C2×C4×D1714yes—
611C22×C4C2×C4×D1712yes—
612C22×C4#6325212yes—
613C22×C4D4×D1712yes—
614C22×C4D4×D1712yes—
615C22×C4Q8×D1712yes—
616C22×C4#6325612yes—
617C22×C4C2×C22⋊D1712yes—
618C22×C4C2×C22⋊D1712yes—
619C22×C4C2×C22⋊D1712yes—
620C4⋊C4—28no—
621C4⋊C4—48no—
622C4⋊C4—44no—
623C4⋊C4—348no—
624C4⋊C4—348no—
625C4⋊C4—348no—
626C4⋊C4—688no—
627C4⋊C4—684no—
628C22⋊C4—348no—
629C22⋊C4—348no—
630C22⋊C4—688no—
631C22⋊C4—688no—
632C42—28no—
633C42—348no—
634C23—174no—
635C23—342no—
636C23—342no—
637C23—342no—
638C23—342no—
639C23—342no—
640C23—342no—
641C23—342no—
642C23—342no—
643C23—342no—
644C23—342no—
645C23—342no—
646C23—342no—
647C23—342no—
648C23—342no—
649C23—342no—
650C23—342no—
651C23—342no—
652C23—342no—
653C23—681no—
654C23—681no—
655C23—681no—
656C23—681no—
657C23—681no—
658C23—681no—
659C23—681no—
660C23—681no—
661C23—681no—
662C23—681no—
663C23—681no—
664C23—681no—
665C23—681no—
666C23—681no—
667C23—681no—
668C23—681no—
669C23C22×C4×D1711yescharacteristic
670C23C2×#6325211yescharacteristic
671C23C2×D4×D1711yescharacteristic
672C23C2×D4×D1711yescharacteristic
673C23#1058769111yescharacteristic
674C23#1058769111yescharacteristic
675C23C2×Q8×D1711yescharacteristic
676C23C2×#6325611yescharacteristic
677C23#1058769411yescharacteristic
678C23#1058769411yescharacteristic
679C23#1058769611yescharacteristic
680C23#1058769611yescharacteristic
681C23#1058769711yescharacteristic
682C23#1058769711yescharacteristic
683C23C22×C22⋊D1711yescharacteristic
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—42no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—42no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—174no—
713C2×C4—342no—
714C2×C4—342no—
715C2×C4—342no—
716C2×C4—342no—
717C2×C4—342no—
718C2×C4—342no—
719C2×C4—3432no—
720C2×C4—344no—
721C2×C4—344no—
722C2×C4—344no—
723C2×C4—342no—
724C2×C4—342no—
725C2×C4—342no—
726C2×C4—342no—
727C2×C4—342no—
728C2×C4—342no—
729C2×C4—682no—
730C2×C4—681no—
731C2×C4—681no—
732C2×C4—681no—
733C2×C4—681no—
734C2×C4—681no—
735C2×C4—681no—
736C2×C4—681no—
737C2×C4—681no—
738C2×C4—682no—
739C2×C4—682no—
740C2×C4—682no—
741C2×C4—682no—
742C2×C4—682no—
743C2×C4—682no—
744C2×C4—682no—
745C2×C4—682no—
746C2×C4—682no—
747C2×C4—682no—
748C2×C4C4⋊C4×D1714yes—
749C2×C4#1058757914yes—
750C2×C4#1058758014yes—
751C2×C4#1058758214yes—
752C2×C4C4×C22⋊D1714yes—
753C2×C4#1058762314yes—
754C2×C4#1058763214yes—
755C22—344no—
756C22—344no—
757C22—344no—
758C22—682no—
759C22—682no—
760C22—682no—
761C22—682no—
762C22—682no—
763C22—682no—
764C22—682no—
765C22—682no—
766C22—682no—
767C22—682no—
768C22—682no—
769C22—682no—
770C22C2×C4⋊C4×D1711yescharacteristic
771C22C2×C4×C22⋊D1711yescharacteristic
772C22C2×#1058757911yescharacteristic
773C22#1176328111yescharacteristic
774C22#1176328511yescharacteristic
775C22#1176328811yescharacteristic
776C22#1176329111yescharacteristic
777C22C2×#1058762311yescharacteristic
778C22C2×#1058763211yescharacteristic
779C22C2×#1058758211yescharacteristic
780C22C2×#1058758011yescharacteristic
781C22#1176337511yescharacteristic
782C22#1176337511yescharacteristic
783C22#1176337611yescharacteristic
784C22#1176338211yescharacteristic
785C22#1176338211yescharacteristic
786C22#1176338311yescharacteristic
787C22#1176338711yescharacteristic
788C22#1176338711yescharacteristic
789C22#1176338811yescharacteristic
790C22#1176338811yescharacteristic
791C22#1176338911yescharacteristic
792C22#1176338911yescharacteristic
793C22#1176341011yescharacteristic
794C22#1176341511yescharacteristic
795C22#1176341711yescharacteristic
796C22#1176342211yescharacteristic
797C22#1176342411yescharacteristic
798C22#1176343111yescharacteristic
799C22#1176343311yescharacteristic
800C22#1176343311yescharacteristic
801C22#1176343611yescharacteristic
802C22#1176343611yescharacteristic
803C22#1176343911yescharacteristic
804C22#1176343911yescharacteristic
805C4—42no—
806C4—42no—
807C4—44no—
808C4—82no—
809C4—344no—
810C4—682no—
811C4—682no—
812C4—684no—
813C4—1362no—
814C4#1176268018yes—
815C2—684no—
816C2C2×#1176268011yescharacteristic
817C2#1453139911yescharacteristic
818C2#1453140611yescharacteristic
819C2#1453146011yescharacteristic
820C2#1453146411yescharacteristic
821C2#1453147111yescharacteristic
822C2#1453147511yescharacteristic
823C2#1453450911yescharacteristic
824C2#1453451411yescharacteristic
825C2#1453457811yescharacteristic
826C2#1453458611yescharacteristic
827C2#1453460611yescharacteristic
828C2#1453461111yescharacteristic
829C2#1453461511yescharacteristic
830C2#1453461911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC2×C17×#389C2
socle, cosocleC24×C17C24
prime radicalC24×D17C23
hypercenterC2×#389D17
hypocenterC17#14264
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
2. C2×#11762705C2semidirect
5. #14527047C2semidirect
6. #14527042C2semidirect
9. #14527014C2semidirect
10. #14527013C2semidirect
11. C2×C17×#389C2semidirect
28. #11762666C4semidirect
203. C2×C4×D17C4⋊C4semidirect
342. C2×#389D17semidirect
526. C17#14264semidirect

Maximal subgroups

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

subgroupindex
C22×#105875582
C2×#117627052
C2×#117626662
#145270472
#145270422
#145270282
#145270262
#145270142
#145270132
C2×C17×#3892
#1426417