Finite Group Databasebeta

← #17061830

Subgroups — #17061830

Order 4352.

1650 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762852C211yesmaximal, characteristic, complemented
2C2×#11762810C211yesmaximal, characteristic, complemented
3C2×#11762810C211yesmaximal, characteristic, complemented
4C2×#11762773C211yesmaximal, characteristic, complemented
5C2×#11762669C211yesmaximal, characteristic, complemented
6#14529984C212yesmaximal, complemented
7#14529977C212yesmaximal, complemented
8#14529970C212yesmaximal, complemented
9#14529963C212yesmaximal, complemented
10#14528505C211yesmaximal, characteristic, complemented
11C2×C17×#525C211yesmaximal, characteristic
12C22×#63223C2211yescharacteristic
13C22×#63223C2211yescharacteristic
14C22×C4⋊Dic17C2211yescharacteristic
15C22×C4⋊Dic17C2211yescharacteristic
16C22×C22⋊Dic17—21no—
17#11762852—24no—
18C2×#10587478C2212yescomplemented
19C2×#10587479C2212yescomplemented
20#11762810—24no—
21#11762810—24no—
22C2×#10587506C2212yescomplemented
23C2×#10587506C2212yescomplemented
24C2×#10587503C2212yescomplemented
25C2×#10587503C2212yescomplemented
26#11762773—24no—
27C2×C22⋊#3622C2212yes—
28C2×C22⋊#3622C2212yes—
29#11762669—21no—
30#11762669—21no—
31#11762669C2212yes—
32#11762669C2212yes—
33C2×#10587502—21no—
34#11762571C2212yescomplemented
35#11762571C2212yescomplemented
36C22×#41×C17C2211yescharacteristic
37C24×C4×C17C2211yescharacteristic
38C17×#525—24no—
39C17×#525—24no—
40C2×C17×#123—21no—
41C2×C17×C22⋊Q8C2211yescharacteristic
42C2×C17×C22⋊Q8C2211yescharacteristic
43C2×C17×#121C2211yescharacteristic
44C2×C17×#121C2211yescharacteristic
45C2×C17×#120—21no—
46C2×C4×D4×C17—21no—
47C2×C4×D4×C17—21no—
48C2×C17×#117C2211yescharacteristic
49C25×C17D411yescharacteristic
50C2×#41×C17—22no—
51C2×#41×C17—22no—
52C2×#41×C17—22no—
53C2×#41×C17—22no—
54C2×#41×C17—22no—
55C2×#41×C17D414yes—
56C22×Q8×C17C2311yescharacteristic
57C22×D4×C17—21no—
58C22×D4×C17—21no—
59C22×D4×C17—21no—
60C22×D4×C17C2311yescharacteristic
61C23×C4×C17—21no—
62C23×C4×C17—22no—
63C23×C4×C17—22no—
64C23×C4×C17—22no—
65C23×C4×C17—22no—
66C23×C4×C17—22no—
67C23×C4×C17—22no—
68C23×C4×C17D411yescharacteristic
69C23×C4×C17D411yescharacteristic
70C23×C4×C17D411yescharacteristic
71C23×C4×C17C2311yescharacteristic
72C23×C4×C17C2311yescharacteristic
73C23×C4×C17C2311yescharacteristic
74C23×Dic17—21no—
75C23×Dic17—21no—
76C17×#123—28no—
77C17×C22⋊Q8—22no—
78C17×C22⋊Q8—22no—
79C17×C22⋊Q8—22no—
80C17×C22⋊Q8—22no—
81C17×#121—22no—
82C17×#121—22no—
83C17×#121—22no—
84C17×#121—22no—
85C17×#120—28no—
86C4×D4×C17—28no—
87C4×D4×C17—28no—
88C17×#117—22no—
89C17×#117D414yes—
90C2×C4⋊C4×C17—21no—
91C2×C4⋊C4×C17—21no—
92C2×C4⋊C4×C17C2311yescharacteristic
93C2×C4⋊C4×C17C2311yescharacteristic
94C2×C22⋊C4×C17—21no—
95C2×C22⋊C4×C17—21no—
96C2×C22⋊C4×C17—21no—
97C2×C22⋊C4×C17—21no—
98C2×C22⋊C4×C17—21no—
99C2×C42×C17—21no—
100C2×C22⋊Dic17—22no—
101C2×C22⋊Dic17—22no—
102C2×C22⋊Dic17—44no—
103C2×C4⋊Dic17—21no—
104C2×C4⋊Dic17—21no—
105C2×C4⋊Dic17—22no—
106C2×C4⋊Dic17—22no—
107C2×C4⋊Dic17—22no—
108C2×C4⋊Dic17—22no—
109C2×C4⋊Dic17C2312yes—
110C2×C4⋊Dic17C2312yes—
111C2×#63223—22no—
112C2×#63223—22no—
113C2×#63223—22no—
114C2×#63223—22no—
115C2×#63223—22no—
116C2×#63223D414yescomplemented
117C22×#3622C2312yes—
118C22×#3622C2312yes—
119#10587506—24no—
120#10587506—24no—
121#10587503—24no—
122#10587503—24no—
123#10587502—22no—
124#10587502—22no—
125C22⋊#3622—24no—
126C22⋊#3622—24no—
127#10587479—24no—
128#10587478—24no—
129C24×C17—22no—
130C24×C17—22no—
131C24×C17—22no—
132C24×C17—22no—
133C24×C17—22no—
134C24×C17—21no—
135C24×C17—41no—
136C24×C17—41no—
137C24×C17C2×D411yescharacteristic
138C24×C17C2×D411yescharacteristic
139C24×C17C2×D411yescharacteristic
140#41×C17—28no—
141#41×C17—28no—
142#41×C17—44no—
143#41×C17—44no—
144C2×Q8×C17—21no—
145C2×Q8×C17—21no—
146C2×Q8×C17—21no—
147C2×Q8×C17—21no—
148C2×Q8×C17—21no—
149C2×Q8×C17C2×D412yes—
150C2×D4×C17—24no—
151C2×D4×C17—24no—
152C2×D4×C17—24no—
153C2×D4×C17—21no—
154C2×D4×C17—21no—
155C2×D4×C17—21no—
156C2×D4×C17—21no—
157C2×D4×C17—21no—
158C2×D4×C17—42no—
159C2×D4×C17—42no—
160C2×D4×C17—42no—
161C2×D4×C17—42no—
162C2×D4×C17—42no—
163C2×D4×C17—42no—
164C2×D4×C17C2×D412yes—
165C22×C4×C17—22no—
166C22×C4×C17—22no—
167C22×C4×C17—22no—
168C22×C4×C17—21no—
169C22×C4×C17—21no—
170C22×C4×C17—21no—
171C22×C4×C17—22no—
172C22×C4×C17—22no—
173C22×C4×C17—24no—
174C22×C4×C17—22no—
175C22×C4×C17—22no—
176C22×C4×C17—22no—
177C22×C4×C17—22no—
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—44no—
191C22×C4×C17—44no—
192C22×C4×C17—42no—
193C22×C4×C17—44no—
194C22×C4×C17—42no—
195C22×C4×C17—44no—
196C22×C4×C17C2×D412yes—
197C22×C4×C17C2×D411yescharacteristic
198C22×C4×C17C2×D411yescharacteristic
199C22×C4×C17C2×D411yescharacteristic
200C22×C4×C17C2×D412yes—
201C22×C4×C17C2×D412yes—
202C22×C4×C17#4112yes—
203C22×C4×C17#4112yes—
204C22×C4×C17#4112yes—
205C22×C4×C17C2411yescharacteristic
206C22×Dic17—22no—
207C22×Dic17—22no—
208C22×Dic17—42no—
209C22×Dic17—42no—
210C22×Dic17—42no—
211C22×Dic17—42no—
212C22×Dic17—42no—
213C22×Dic17—42no—
214C4⋊C4×C17—24no—
215C4⋊C4×C17—24no—
216C4⋊C4×C17—21no—
217C4⋊C4×C17—21no—
218C4⋊C4×C17C2×D412yes—
219C4⋊C4×C17C2×D412yes—
220C22⋊C4×C17—24no—
221C22⋊C4×C17—24no—
222C22⋊C4×C17—24no—
223C22⋊C4×C17—24no—
224C22⋊C4×C17—24no—
225C42×C17—24no—
226C22⋊Dic17—44no—
227C22⋊Dic17—44no—
228C4⋊Dic17—22no—
229C4⋊Dic17—22no—
230C4⋊Dic17—22no—
231C4⋊Dic17—22no—
232C4⋊Dic17—42no—
233C4⋊Dic17—42no—
234#63223—28no—
235#63223—44no—
236C2×#3622—22no—
237C2×#3622—22no—
238C2×#3622—22no—
239C2×#3622—22no—
240C2×#3622—22no—
241C2×#3622C2×D414yes—
242#23482—171nomaximal, Sylow
243C23×C17—21no—
244C23×C17—21no—
245C23×C17—21no—
246C23×C17—21no—
247C23×C17—28no—
248C23×C17—21no—
249C23×C17—21no—
250C23×C17—21no—
251C23×C17—21no—
252C23×C17—21no—
253C23×C17—21no—
254C23×C17—21no—
255C23×C17—21no—
256C23×C17—21no—
257C23×C17—21no—
258C23×C17—21no—
259C23×C17—21no—
260C23×C17—22no—
261C23×C17—44no—
262C23×C17—44no—
263C23×C17—44no—
264C23×C17—44no—
265C23×C17—44no—
266C23×C17—44no—
267C23×C17—41no—
268C23×C17—41no—
269C23×C17—41no—
270C23×C17—41no—
271C23×C17—41no—
272C23×C17—41no—
273C23×C17#12012yes—
274C23×C17#12112yes—
275C23×C17#12312yes—
276C23×C17AGL(1,ℤ/8)12yes—
277C23×C17#13712yes—
278C23×C17C22×D411yescharacteristic
279Q8×C17—22no—
280Q8×C17—22no—
281Q8×C17—41no—
282Q8×C17—41no—
283D4×C17—22no—
284D4×C17—22no—
285D4×C17—48no—
286D4×C17—48no—
287D4×C17—48no—
288D4×C17—41no—
289D4×C17—41no—
290C2×C4×C17—22no—
291C2×C4×C17—22no—
292C2×C4×C17—21no—
293C2×C4×C17—21no—
294C2×C4×C17—22no—
295C2×C4×C17—21no—
296C2×C4×C17—21no—
297C2×C4×C17—21no—
298C2×C4×C17—21no—
299C2×C4×C17—41no—
300C2×C4×C17—41no—
301C2×C4×C17—41no—
302C2×C4×C17—41no—
303C2×C4×C17—41no—
304C2×C4×C17—41no—
305C2×C4×C17—44no—
306C2×C4×C17—41no—
307C2×C4×C17—41no—
308C2×C4×C17—41no—
309C2×C4×C17—41no—
310C2×C4×C17—41no—
311C2×C4×C17—41no—
312C2×C4×C17—41no—
313C2×C4×C17—41no—
314C2×C4×C17—44no—
315C2×C4×C17—44no—
316C2×C4×C17—48no—
317C2×C4×C17#12012yes—
318C2×C4×C17#12114yes—
319C2×C4×C17#12114yes—
320C2×C4×C17#12112yes—
321C2×C4×C17#12314yes—
322C2×C4×C17#12312yes—
323C2×C4×C17#12414yes—
324C2×C4×C17C22×D411yescharacteristic
325C2×C4×C17C22×D411yescharacteristic
326C2×C4×C17C22×D411yescharacteristic
327C2×C4×C17C2×#4111yescharacteristic
328C2×C4×C17C2×#4111yescharacteristic
329C2×C4×C17C2×#4111yescharacteristic
330C2×Dic17—42no—
331C2×Dic17—42no—
332C2×Dic17—42no—
333C2×Dic17—42no—
334C2×Dic17—42no—
335C2×Dic17—42no—
336C2×Dic17—84no—
337C2×Dic17—84no—
338#3622—24no—
339#3622—42no—
340C2×#525D1711yescharacteristic
341C2×#428—171no—
342C2×#417—171no—
343C2×#417—171no—
344C2×#407—171no—
345C2×#380—171no—
346#2036—172no—
347#2035—172no—
348#2034—172no—
349#2033—172no—
350#1736—171no—
351C22×C17—22no—
352C22×C17—22no—
353C22×C17—22no—
354C22×C17—22no—
355C22×C17—22no—
356C22×C17—22no—
357C22×C17—22no—
358C22×C17—22no—
359C22×C17—22no—
360C22×C17—22no—
361C22×C17—22no—
362C22×C17—22no—
363C22×C17—416no—
364C22×C17—41no—
365C22×C17—41no—
366C22×C17—41no—
367C22×C17—41no—
368C22×C17—41no—
369C22×C17—41no—
370C22×C17—41no—
371C22×C17—41no—
372C22×C17—42no—
373C22×C17—42no—
374C22×C17—42no—
375C22×C17—81no—
376C22×C17—81no—
377C22×C17—81no—
378C22×C17—81no—
379C22×C17#39414yes—
380C22×C17C2×#12011yescharacteristic
381C22×C17C2×#12111yescharacteristic
382C22×C17C2×#12311yescharacteristic
383C22×C17C2×AGL(1,ℤ/8)11yescharacteristic
384C22×C17C2×#13711yescharacteristic
385C22×C17#57511yescharacteristic
386C22×C17#57511yescharacteristic
387C4×C17—41no—
388C4×C17—41no—
389C4×C17—42no—
390C4×C17—42no—
391C4×C17—42no—
392C4×C17#39414yes—
393C4×C17C2×#12111yescharacteristic
394C4×C17C2×#12111yescharacteristic
395C4×C17C2×#12311yescharacteristic
396C4×C17C2×#12411yescharacteristic
397Dic17—82no—
398Dic17—82no—
399C22×#41C2×D1711yescharacteristic
400C24×C4C2×D1711yescharacteristic
401C22×M16—171no—
402C22×M16—171no—
403#525—24no—
404#525—24no—
405C2×#123—21no—
406C2×C22⋊Q8C2×D1711yescharacteristic
407C2×C22⋊Q8C2×D1711yescharacteristic
408C2×#121C2×D1711yescharacteristic
409C2×#121C2×D1711yescharacteristic
410C2×#120—21no—
411C2×C4×D4—21no—
412C2×C4×D4—21no—
413C2×#117C2×D1711yescharacteristic
414C22×C4⋊C4—171no—
415C22×C4⋊C4—171no—
416C22×C22⋊C4—341no—
417#428—344no—
418C2×#107—172no—
419C2×#106—172no—
420#417—344no—
421#417—344no—
422C2×#103—172no—
423C2×#103—172no—
424C2×#102—172no—
425C2×#102—172no—
426#407—344no—
427C2×C22⋊C8—172no—
428C2×C22⋊C8—172no—
429#380—172no—
430#380—172no—
431#380—341no—
432#380—341no—
433C2×#95—341no—
434#340—172no—
435#340—172no—
436C2×C17—24no—
437C2×C17—42no—
438C2×C17—42no—
439C2×C17—82no—
440C2×C17C2×#39411yescharacteristic
441C2×C17#300611yescharacteristic
442C2×C17#300711yescharacteristic
443C2×C17#305511yescharacteristic
444C2×C17#305611yescharacteristic
445C2×C17#309211yescharacteristic
446C2×C17#309311yescharacteristic
447C25C22⋊D1711yescharacteristic
448C2×#41—22no—
449C2×#41—22no—
450C2×#41—22no—
451C2×#41—22no—
452C2×#41—22no—
453C2×#41C22⋊D1714yes—
454C22×Q8C22×D1711yescharacteristic
455C22×D4—21no—
456C22×D4—21no—
457C22×D4—21no—
458C22×D4C22×D1711yescharacteristic
459C23×C4—22no—
460C23×C4—22no—
461C23×C4—22no—
462C23×C4—22no—
463C23×C4—21no—
464C23×C4—22no—
465C23×C4—22no—
466C23×C4—341no—
467C23×C4—341no—
468C23×C4C22⋊D1711yescharacteristic
469C23×C4C22⋊D1711yescharacteristic
470C23×C4C22⋊D1711yescharacteristic
471C23×C4C22×D1711yescharacteristic
472C23×C4C22×D1711yescharacteristic
473C23×C4C22×D1711yescharacteristic
474C2×M16—174no—
475C2×M16—342no—
476C2×M16—342no—
477C2×M16—342no—
478C2×M16—342no—
479C2×M16—342no—
480C22×C8—172no—
481C22×C8—172no—
482#123—28no—
483C22⋊Q8—22no—
484C22⋊Q8—22no—
485C22⋊Q8—22no—
486C22⋊Q8—22no—
487#121—22no—
488#121—22no—
489#121—22no—
490#121—22no—
491#120—28no—
492C4×D4—28no—
493C4×D4—28no—
494#117—22no—
495#117C22⋊D1714yes—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—172no—
499C2×C4⋊C4—172no—
500C2×C4⋊C4—342no—
501C2×C4⋊C4—342no—
502C2×C4⋊C4—342no—
503C2×C4⋊C4—342no—
504C2×C4⋊C4—341no—
505C2×C4⋊C4—341no—
506C2×C4⋊C4C22×D1711yescharacteristic
507C2×C4⋊C4C22×D1711yescharacteristic
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—342no—
514C2×C22⋊C4—342no—
515C2×C22⋊C4—684no—
516C2×C42—21no—
517#107—344no—
518#106—344no—
519#103—344no—
520#103—344no—
521#102—344no—
522#102—344no—
523C22⋊C8—344no—
524C22⋊C8—344no—
525#95—342no—
526#95—342no—
527C17#2348211yescharacteristic, complemented, Sylow
528C24—22no—
529C24—22no—
530C24—22no—
531C24—21no—
532C24—22no—
533C24—22no—
534C24—41no—
535C24—41no—
536C24C2×C22⋊D1711yescharacteristic
537C24C2×C22⋊D1711yescharacteristic
538C24C2×C22⋊D1711yescharacteristic
539#41—28no—
540#41—28no—
541#41—44no—
542#41—44no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8C2×C22⋊D1712yes—
549C2×D4—24no—
550C2×D4—24no—
551C2×D4—24no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4C2×C22⋊D1712yes—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—24no—
589C22×C4—44no—
590C22×C4—42no—
591C22×C4—44no—
592C22×C4—44no—
593C22×C4—44no—
594C22×C4—42no—
595C22×C4—342no—
596C22×C4—342no—
597C22×C4—682no—
598C22×C4—682no—
599C22×C4—682no—
600C22×C4—682no—
601C22×C4—682no—
602C22×C4—682no—
603C22×C4D4×D1712yes—
604C22×C4#6325412yes—
605C22×C4#6325412yes—
606C22×C4#6325412yes—
607C22×C4C2×C22⋊D1711yescharacteristic
608C22×C4C2×C22⋊D1711yescharacteristic
609C22×C4C2×C22⋊D1712yes—
610C22×C4C2×C22⋊D1712yes—
611C22×C4C2×C22⋊D1711yescharacteristic
612C22×C4C23×D1711yescharacteristic
613M16—348no—
614M16—684no—
615C2×C8—174no—
616C2×C8—342no—
617C2×C8—342no—
618C2×C8—342no—
619C2×C8—342no—
620C2×C8—342no—
621C4⋊C4—24no—
622C4⋊C4—24no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—342no—
626C4⋊C4—342no—
627C4⋊C4—342no—
628C4⋊C4—342no—
629C4⋊C4—682no—
630C4⋊C4—682no—
631C4⋊C4C2×C22⋊D1712yes—
632C4⋊C4C2×C22⋊D1712yes—
633C22⋊C4—24no—
634C22⋊C4—24no—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4—24no—
638C22⋊C4—684no—
639C22⋊C4—684no—
640C42—24no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—28no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—22no—
659C23—44no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—44no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23#1058762112yes—
672C23#1058762512yes—
673C23#1058763512yes—
674C23#1058763712yes—
675C23#1058763912yes—
676C23C22×C22⋊D1711yescharacteristic
677Q8—22no—
678Q8—22no—
679Q8—41no—
680Q8—41no—
681D4—22no—
682D4—22no—
683D4—48no—
684D4—48no—
685D4—48no—
686D4—41no—
687D4—41no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—22no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—44no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—44no—
705C2×C4—44no—
706C2×C4—48no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—682no—
716C2×C4—682no—
717C2×C4—682no—
718C2×C4—682no—
719C2×C4—682no—
720C2×C4—682no—
721C2×C4—1364no—
722C2×C4—1364no—
723C2×C4#1058762112yes—
724C2×C4#1058762114yes—
725C2×C4#1058762214yes—
726C2×C4#1058762414yes—
727C2×C4#1058762512yes—
728C2×C4#1058762514yes—
729C2×C4#1058763912yes—
730C2×C4C2×D4×D1711yescharacteristic
731C2×C4C2×#6325411yescharacteristic
732C2×C4C2×#6325411yescharacteristic
733C2×C4C2×#6325411yescharacteristic
734C2×C4C22×C22⋊D1711yescharacteristic
735C2×C4C22×C22⋊D1711yescharacteristic
736C8—344no—
737C8—682no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—416no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22#1176272314yes—
767C22C2×#1058763911yescharacteristic
768C22C2×#1058762511yescharacteristic
769C22C2×#1058762111yescharacteristic
770C22C2×#1058763511yescharacteristic
771C22C2×#1058763711yescharacteristic
772C22#1176360711yescharacteristic
773C22#1176360711yescharacteristic
774C4—42no—
775C4—42no—
776C4—41no—
777C4—41no—
778C4—42no—
779C4—1362no—
780C4—1362no—
781C4#1176272314yes—
782C4C2×#1058762411yescharacteristic
783C4C2×#1058762511yescharacteristic
784C4C2×#1058762111yescharacteristic
785C4C2×#1058762211yescharacteristic
786C2—24no—
787C2—42no—
788C2—42no—
789C2—82no—
790C2C2×#1176272311yescharacteristic
791C2#1453803611yescharacteristic
792C2#1453804411yescharacteristic
793C2#1453840511yescharacteristic
794C2#1453841611yescharacteristic
795C2#1453870411yescharacteristic
796C2#1453871311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutator, cosocleC22×C4×C17C24
FrattiniC22×C4C23×D17
Fitting, prime radicalC2×C17×#525C2
socleC23×C17C22×D4
hypercenterC2×#525D17
hypocenterC17#23482
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. C2×#11762852C2semidirect
2. C2×#11762810C2semidirect
3. C2×#11762810C2semidirect
4. C2×#11762773C2semidirect
5. C2×#11762669C2semidirect
6. #14529984C2semidirect
7. #14529977C2semidirect
8. #14529970C2semidirect
9. #14529963C2semidirect
10. #14528505C2semidirect
18. C2×#10587478C22semidirect
19. C2×#10587479C22semidirect
22. C2×#10587506C22semidirect
23. C2×#10587506C22semidirect
24. C2×#10587503C22semidirect
25. C2×#10587503C22semidirect
34. #11762571C22semidirect
35. #11762571C22semidirect
116. C2×#63223D4semidirect
527. C17#23482semidirect

Maximal subgroups

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

subgroupindex
C2×#117628522
C2×#117628102
C2×#117627732
C2×#117626692
#145299842
#145299772
#145299702
#145299632
#145285052
C2×C17×#5252
#2348217