Finite Group Databasebeta

← C4×#11763060 #17040964

Subgroups — C4×#11763060 #17040964

Order 4352.

1170 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763060C211yesmaximal, characteristic
2C2×C4×#63228C211yesmaximal, characteristic, complemented
3C2×C4×#63223C211yesmaximal, characteristic, complemented
4C4×#10587616C211yesmaximal, characteristic, complemented
5#14529659C211yesmaximal, characteristic, complemented
6#14529524C211yesmaximal, characteristic, complemented
7#14529484C211yesmaximal, characteristic, complemented
8#14529480C211yesmaximal, characteristic, complemented
9#14529223C211yesmaximal, characteristic, complemented
10#14529220C211yesmaximal, characteristic, complemented
11#14528815C211yesmaximal, characteristic, complemented
12C4×#10587479C211yesmaximal, characteristic, complemented
13C4×#10587480C211yesmaximal, characteristic, complemented
14C4×#10587503C211yesmaximal, characteristic, complemented
15C4×C17×#121C211yesmaximal, characteristic, complemented
16C22×#63228C2211yescharacteristic
17C22×#63223C2211yescharacteristic
18C22×#63223C2211yescharacteristic
19C2×#10587616C2211yescharacteristic
20C2×C4×D68C2211yescharacteristic
21C2×C4×C22⋊D17—21no—
22#11763060C418yesdirect product factor
23C4×#63228—24no—
24C2×#10587478C2211yescharacteristic
25C2×#10587479C2211yescharacteristic
26C2×#10587479C2211yescharacteristic
27C2×#10587503C2211yescharacteristic
28C2×#10587503C2211yescharacteristic
29C2×#10587503C2211yescharacteristic
30C2×#10587480C2211yescharacteristic
31C2×#10587480C2211yescharacteristic
32C2×#10587480C2211yescharacteristic
33C4×#63223—24no—
34C2×#10587474C2211yescharacteristic
35C2×#10587474C2211yescharacteristic
36C2×C4×#3622C2211yescharacteristic
37C2×C4×#3622C2211yescharacteristic
38#11762711C2211yescharacteristic
39#11762707C2211yescharacteristic
40#11762700—21no—
41#11762688—21no—
42#11762669C2211yescharacteristic
43C4×C4⋊Dic17C2211yescharacteristic
44C4×#63227—21no—
45#11762571C2211yescharacteristic
46#11762571C2211yescharacteristic
47#11762571C2211yescharacteristic
48#11762571C2211yescharacteristic
49#11762571C2211yescharacteristic
50#11762571C2211yescharacteristic
51C2×C17×#121C2211yescharacteristic
52C2×C4×D4×C17—21no—
53C2×C4×D4×C17C2211yescharacteristic
54C22×C42×C17C2211yescharacteristic
55C17×#390C2211yescharacteristic
56C17×#389C2211yescharacteristic
57C17×#388—21no—
58C17×#386—21no—
59C17×#380C2211yescharacteristic
60C4×C4⋊C4×C17C2211yescharacteristic
61C4×C22⋊C4×C17—21no—
62C22×D4×C17—21no—
63C22×D4×C17C2311yescharacteristic
64C23×C4×C17—21no—
65C23×C4×C17D411yescharacteristic
66C23×C4×C17D411yescharacteristic
67C23×C4×C17C2311yescharacteristic
68C22×C22⋊D17—21no—
69C22×D68C2311yescharacteristic
70C22×C4×D17—21no—
71C17×#121—22no—
72C17×#121C2×C414yescomplemented
73C4×D4×C17—22no—
74C4×D4×C17—22no—
75C4×D4×C17—44no—
76C2×C4⋊C4×C17—21no—
77C2×C4⋊C4×C17C2311yescharacteristic
78C2×C4⋊C4×C17C2311yescharacteristic
79C2×C4⋊C4×C17C2311yescharacteristic
80C2×C22⋊C4×C17—21no—
81C2×C22⋊C4×C17—21no—
82C2×C22⋊C4×C17—21no—
83C2×C22⋊C4×C17—21no—
84C2×C22⋊C4×C17—21no—
85C2×C42×C17—22no—
86C2×C42×C17—22no—
87C2×C42×C17—21no—
88C2×C42×C17D411yescharacteristic
89C2×C42×C17D411yescharacteristic
90C2×C42×C17C2311yescharacteristic
91C2×C42×C17C2311yescharacteristic
92C2×C22⋊Dic17—21no—
93C2×#63228—22no—
94C2×#63228—22no—
95C2×#63228C2×C414yescomplemented
96#10587616—22no—
97#10587616C2×C414yescomplemented
98C4×C22⋊D17—44no—
99C2×#63227—21no—
100C2×#63227—21no—
101C2×#63227—21no—
102C2×#63227—21no—
103C2×C4⋊Dic17C2311yescharacteristic
104C2×C4⋊Dic17C2311yescharacteristic
105C2×C4⋊Dic17C2311yescharacteristic
106C2×#63225—21no—
107C2×C4×Dic17—21no—
108C2×#63223—22no—
109C2×#63223—22no—
110C2×#63223—22no—
111C2×#63223—22no—
112C2×#63223—22no—
113C2×#63223C2×C414yescomplemented
114C22×#3622C2311yescharacteristic
115C22×#3622C2311yescharacteristic
116C22×#3622C2311yescharacteristic
117C22×#3622C2311yescharacteristic
118C4×D68—22no—
119C4×D68—22no—
120C17×#95—21no—
121C17×#95—21no—
122C17×#95—21no—
123#10587503—22no—
124#10587503—22no—
125#10587503C2×C414yescomplemented
126#10587502—21no—
127#10587502—21no—
128#10587502—21no—
129#10587480—22no—
130#10587480—22no—
131#10587480C2×C414yescomplemented
132#10587479—22no—
133#10587479C2×C414yescomplemented
134#10587478—22no—
135#10587474—22no—
136#10587474—22no—
137C4×#3622—22no—
138C4×#3622D414yescomplemented
139C24×C17—21no—
140C24×C17C2×D411yescharacteristic
141C23×D17—21no—
142C2×D4×C17—24no—
143C2×D4×C17—21no—
144C2×D4×C17—21no—
145C2×D4×C17—21no—
146C2×D4×C17—21no—
147C2×D4×C17—21no—
148C2×D4×C17—42no—
149C2×D4×C17—42no—
150C2×D4×C17C22×C412yes—
151C22×C4×C17—21no—
152C22×C4×C17—21no—
153C22×C4×C17—21no—
154C22×C4×C17—21no—
155C22×C4×C17—21no—
156C22×C4×C17—22no—
157C22×C4×C17—22no—
158C22×C4×C17—22no—
159C22×C4×C17—22no—
160C22×C4×C17—21no—
161C22×C4×C17—21no—
162C22×C4×C17—41no—
163C22×C4×C17—41no—
164C22×C4×C17—42no—
165C22×C4×C17—42no—
166C22×C4×C17—42no—
167C22×C4×C17C22×C412yes—
168C22×C4×C17C2×D411yescharacteristic
169C22×C4×C17C2×D411yescharacteristic
170C22×C4×C17C2×D411yescharacteristic
171C22×C4×C17C2×D411yescharacteristic
172C22×C4×C17C2×D411yescharacteristic
173C22×C4×C17#4112yes—
174C22×C4×C17C2411yescharacteristic
175C2×C22⋊D17—24no—
176C2×C22⋊D17—42no—
177C2×C22⋊D17—42no—
178C22×Dic17—21no—
179C22×Dic17—21no—
180C22×Dic17—21no—
181C2×D68—21no—
182C2×D68—21no—
183C2×D68—21no—
184C2×D68—21no—
185C2×D68—21no—
186C2×D68C22×C412yes—
187C2×C4×D17—42no—
188C2×C4×D17—42no—
189C2×C4×D17—42no—
190C4⋊C4×C17—21no—
191C4⋊C4×C17—21no—
192C4⋊C4×C17—21no—
193C4⋊C4×C17—21no—
194C4⋊C4×C17—21no—
195C4⋊C4×C17—42no—
196C4⋊C4×C17C22×C412yes—
197C22⋊C4×C17—24no—
198C22⋊C4×C17—42no—
199C22⋊C4×C17—42no—
200C22⋊C4×C17—42no—
201C22⋊C4×C17—42no—
202C42×C17—22no—
203C42×C17—22no—
204C42×C17—21no—
205C42×C17—21no—
206C42×C17—42no—
207C42×C17C2×D412yes—
208C42×C17#4112yes—
209C22⋊Dic17—42no—
210#63228—28no—
211#63227—24no—
212#63227—42no—
213#63227—42no—
214#63227—42no—
215C4⋊Dic17—21no—
216C4⋊Dic17—21no—
217C4⋊Dic17—21no—
218C4⋊Dic17—21no—
219C4⋊Dic17—21no—
220C4⋊Dic17C22×C412yes—
221#63225—42no—
222C4×Dic17—42no—
223#63223—28no—
224#63223—28no—
225C2×#3622—21no—
226C2×#3622—21no—
227C2×#3622—21no—
228C2×#3622—21no—
229C2×#3622—21no—
230C2×#3622—21no—
231C2×#3622C22×C412yes—
232C2×#3622C22×C412yes—
233C2×#3622C2×D412yes—
234C2×#3622C2×D412yes—
235C2×#3622#4112yes—
236C2×#3622#4112yes—
237C4×#469—171nomaximal, Sylow
238C23×C17—21no—
239C23×C17—21no—
240C23×C17—21no—
241C23×C17—21no—
242C23×C17—21no—
243C23×C17—21no—
244C23×C17—22no—
245C23×C17—41no—
246C23×C17—41no—
247C23×C17—41no—
248C23×C17—41no—
249C23×C17—41no—
250C23×C17—41no—
251C23×C17C4×D412yes—
252C23×C17C22×D411yescharacteristic
253C22×D17—22no—
254C22×D17—41no—
255C22×D17—41no—
256C22×D17—41no—
257C22×D17—41no—
258C22×D17—41no—
259C22×D17—41no—
260D4×C17—22no—
261D4×C17—22no—
262D4×C17—48no—
263D4×C17—41no—
264D4×C17—41no—
265C2×C4×C17—21no—
266C2×C4×C17—21no—
267C2×C4×C17—21no—
268C2×C4×C17—21no—
269C2×C4×C17—22no—
270C2×C4×C17—22no—
271C2×C4×C17—22no—
272C2×C4×C17—22no—
273C2×C4×C17—22no—
274C2×C4×C17—21no—
275C2×C4×C17—21no—
276C2×C4×C17—21no—
277C2×C4×C17—21no—
278C2×C4×C17—21no—
279C2×C4×C17—21no—
280C2×C4×C17—44no—
281C2×C4×C17—41no—
282C2×C4×C17—41no—
283C2×C4×C17—44no—
284C2×C4×C17—41no—
285C2×C4×C17—41no—
286C2×C4×C17—41no—
287C2×C4×C17—41no—
288C2×C4×C17—41no—
289C2×C4×C17—41no—
290C2×C4×C17—84no—
291C2×C4×C17C4×D412yes—
292C2×C4×C17#12112yes—
293C2×C4×C17#12112yes—
294C2×C4×C17AGL(1,ℤ/8)12yes—
295C2×C4×C17AGL(1,ℤ/8)12yes—
296C2×C4×C17C23×C411yescharacteristic
297C2×C4×C17C22×D411yescharacteristic
298C2×C4×C17C2×#4111yescharacteristic
299C2×C4×C17C2×#4111yescharacteristic
300C2×C4×C17C2×#4111yescharacteristic
301C2×C4×C17C2×#4111yescharacteristic
302C22⋊D17—48no—
303C2×Dic17—22no—
304C2×Dic17—41no—
305C2×Dic17—41no—
306C2×Dic17—41no—
307C2×Dic17—41no—
308C2×Dic17—41no—
309C2×Dic17—41no—
310C2×Dic17—41no—
311C2×Dic17—41no—
312D68—22no—
313D68—22no—
314D68—41no—
315D68—41no—
316C4×D17—84no—
317#3622—22no—
318#3622—22no—
319#3622—22no—
320#3622C4×D414yescomplemented
321C2×#469—171no—
322C2×C4×D8—171no—
323C2×C4×M16—171no—
324C4×#121—171no—
325C4×#121D1711yescharacteristic, complemented
326#1972—171no—
327#1944—171no—
328#1936—171no—
329#1936—171no—
330#1895—171no—
331#1895—171no—
332#1809—171no—
333C4×#106—171no—
334C4×#102—171no—
335C4×#102—171no—
336C22×C17—22no—
337C22×C17—22no—
338C22×C17—22no—
339C22×C17—41no—
340C22×C17—41no—
341C22×C17—41no—
342C22×C17—41no—
343C22×C17—42no—
344C22×C17—42no—
345C22×C17—42no—
346C22×C17—81no—
347C22×C17—81no—
348C22×C17—81no—
349C22×C17—81no—
350C22×C17C2×C4×D411yescharacteristic
351C22×C17C2×#12111yescharacteristic
352C22×C17#53211yescharacteristic
353C22×C17C2×AGL(1,ℤ/8)11yescharacteristic
354C22×C17C2×AGL(1,ℤ/8)11yescharacteristic
355C22×C17#57511yescharacteristic
356C22×C17#57511yescharacteristic
357C2×D17—42no—
358C2×D17—42no—
359C2×D17—42no—
360C2×D17—81no—
361C2×D17—81no—
362C2×D17—81no—
363C2×D17—81no—
364C4×C17—22no—
365C4×C17—22no—
366C4×C17—42no—
367C4×C17—41no—
368C4×C17—41no—
369C4×C17—81no—
370C4×C17—81no—
371C4×C17#46914yescomplemented
372C4×C17C2×C4×D411yescharacteristic
373C4×C17C4×#4111yescharacteristic
374C4×C17#52511yescharacteristic
375C4×C17#52911yescharacteristic
376Dic17—42no—
377Dic17—81no—
378Dic17—81no—
379C22×D8—171no—
380C22×M16—171no—
381C22×M16—171no—
382C2×#121—171no—
383C2×#121C2×D1711yescharacteristic
384C2×C4×D4—21no—
385C2×C4×D4—171no—
386C2×C4×D4—341no—
387C2×C4×D4C2×D1711yescharacteristic
388C22×C42C2×D1711yescharacteristic
389#469—178no—
390C4×D8—344no—
391C2×#107—171no—
392C2×#106—171no—
393C2×#106—171no—
394C2×#102—171no—
395C2×#102—171no—
396C2×#102—171no—
397C2×#102—171no—
398C2×#102—171no—
399C2×#102—171no—
400C4×M16—344no—
401C2×#97—171no—
402C2×#97—171no—
403C2×C4×C8—171no—
404C2×C4×C8—171no—
405#390—171no—
406#390C2×D1711yescharacteristic
407#389—171no—
408#389C2×D1711yescharacteristic
409#388—21no—
410#388—341no—
411#386—21no—
412#386—341no—
413#380—171no—
414#380C2×D1711yescharacteristic
415C4×C4⋊C4—171no—
416C4×C4⋊C4C2×D1711yescharacteristic
417C4×C22⋊C4—21no—
418C4×C22⋊C4—341no—
419#340—171no—
420#340—171no—
421#340—171no—
422#340—171no—
423#340—171no—
424#340—171no—
425C2×C17—42no—
426C2×C17—82no—
427C2×C17C4×#12111yescharacteristic
428C2×C17C4×AGL(1,ℤ/8)11yescharacteristic
429C2×C17C4×AGL(1,ℤ/8)11yescharacteristic
430C2×C17C2×#46911yescharacteristic
431C2×C17#305411yescharacteristic
432C2×C17#317111yescharacteristic
433C2×C17#317111yescharacteristic
434D17—82no—
435C22×D4—21no—
436C22×D4—171no—
437C22×D4—341no—
438C22×D4C22×D1711yescharacteristic
439C23×C4—21no—
440C23×C4—341no—
441C23×C4C22⋊D1711yescharacteristic
442C23×C4C22⋊D1711yescharacteristic
443C23×C4C22×D1711yescharacteristic
444C2×D8—174no—
445C2×D8—342no—
446C2×D8—342no—
447C2×M16—174no—
448C2×M16—342no—
449C2×M16—342no—
450C2×M16—342no—
451C2×M16—342no—
452C2×M16—342no—
453C22×C8—171no—
454C22×C8—171no—
455C22×C8—171no—
456C22×C8—171no—
457#121—22no—
458#121—174no—
459#121—342no—
460#121C4×D1714yescomplemented
461C4×D4—22no—
462C4×D4—22no—
463C4×D4—44no—
464C4×D4—342no—
465C4×D4—342no—
466C4×D4—684no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—171no—
469C2×C4⋊C4—171no—
470C2×C4⋊C4—171no—
471C2×C4⋊C4—341no—
472C2×C4⋊C4C22×D1711yescharacteristic
473C2×C4⋊C4C22×D1711yescharacteristic
474C2×C4⋊C4C22×D1711yescharacteristic
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—341no—
481C2×C22⋊C4—341no—
482C2×C22⋊C4—341no—
483C2×C22⋊C4—341no—
484C2×C22⋊C4—341no—
485C2×C42—22no—
486C2×C42—22no—
487C2×C42—21no—
488C2×C42—341no—
489C2×C42C22⋊D1711yescharacteristic
490C2×C42C22⋊D1711yescharacteristic
491C2×C42C22×D1711yescharacteristic
492C2×C42C22×D1711yescharacteristic
493#107—342no—
494#106—174no—
495#106—342no—
496#102—174no—
497#102—174no—
498#102—342no—
499#102—342no—
500#102—342no—
501#102—342no—
502#97—342no—
503#97—342no—
504C4×C8—174no—
505C4×C8—342no—
506#95—21no—
507#95—21no—
508#95—21no—
509#95—341no—
510#95—341no—
511#95—341no—
512C17C4×#46911yescharacteristic, complemented, Sylow
513C24—21no—
514C24—341no—
515C24C2×C22⋊D1711yescharacteristic
516C2×D4—24no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—42no—
523C2×D4—42no—
524C2×D4—172no—
525C2×D4—344no—
526C2×D4—341no—
527C2×D4—341no—
528C2×D4—341no—
529C2×D4—341no—
530C2×D4—341no—
531C2×D4—682no—
532C2×D4—682no—
533C2×D4C2×C4×D1712yes—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—41no—
546C22×C4—41no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—341no—
551C22×C4—341no—
552C22×C4—341no—
553C22×C4—682no—
554C22×C4—682no—
555C22×C4—682no—
556C22×C4C2×C4×D1712yes—
557C22×C4#6325212yes—
558C22×C4C2×C22⋊D1711yescharacteristic
559C22×C4C2×C22⋊D1711yescharacteristic
560C22×C4C2×C22⋊D1711yescharacteristic
561C22×C4C2×C22⋊D1711yescharacteristic
562C22×C4C2×C22⋊D1711yescharacteristic
563C22×C4C23×D1711yescharacteristic
564D8—348no—
565M16—348no—
566M16—348no—
567C2×C8—172no—
568C2×C8—172no—
569C2×C8—172no—
570C2×C8—172no—
571C2×C8—172no—
572C2×C8—172no—
573C2×C8—341no—
574C2×C8—341no—
575C2×C8—341no—
576C2×C8—341no—
577C2×C8—341no—
578C2×C8—341no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—42no—
585C4⋊C4—172no—
586C4⋊C4—341no—
587C4⋊C4—341no—
588C4⋊C4—341no—
589C4⋊C4—341no—
590C4⋊C4—341no—
591C4⋊C4—682no—
592C4⋊C4C2×C4×D1712yes—
593C22⋊C4—24no—
594C22⋊C4—42no—
595C22⋊C4—42no—
596C22⋊C4—42no—
597C22⋊C4—42no—
598C22⋊C4—344no—
599C22⋊C4—682no—
600C22⋊C4—682no—
601C22⋊C4—682no—
602C22⋊C4—682no—
603C42—21no—
604C42—21no—
605C42—22no—
606C42—22no—
607C42—42no—
608C42—682no—
609C42D4×D1712yes—
610C42#6325412yes—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—22no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—342no—
625C23—681no—
626C23—681no—
627C23—681no—
628C23—681no—
629C23—681no—
630C23—681no—
631C23C4×C22⋊D1712yes—
632C23C22×C22⋊D1711yescharacteristic
633D4—22no—
634D4—22no—
635D4—48no—
636D4—41no—
637D4—41no—
638D4—342no—
639D4—342no—
640D4—688no—
641D4—681no—
642D4—681no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—44no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—44no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—84no—
669C2×C4—342no—
670C2×C4—681no—
671C2×C4—681no—
672C2×C4—681no—
673C2×C4—681no—
674C2×C4—681no—
675C2×C4—681no—
676C2×C4—681no—
677C2×C4—681no—
678C2×C4—1364no—
679C2×C4C4×C22⋊D1712yes—
680C2×C4#1058761812yes—
681C2×C4#1058762512yes—
682C2×C4#1058762512yes—
683C2×C4#1058763512yes—
684C2×C4C22×C4×D1711yescharacteristic
685C2×C4C2×#6325211yescharacteristic
686C2×C4C2×D4×D1711yescharacteristic
687C2×C4C2×#6325411yescharacteristic
688C2×C4#41×D1711yescharacteristic
689C2×C4#41×D1711yescharacteristic
690C8—174no—
691C8—342no—
692C8—342no—
693C8—342no—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—42no—
702C22—42no—
703C22—42no—
704C22—81no—
705C22—81no—
706C22—81no—
707C22—81no—
708C22—682no—
709C22—682no—
710C22—682no—
711C22—1361no—
712C22—1361no—
713C22—1361no—
714C22—1361no—
715C22C2×C4×C22⋊D1711yescharacteristic
716C22C2×#1058762511yescharacteristic
717C22#1176335511yescharacteristic
718C22C2×#1058763511yescharacteristic
719C22C2×#1058761811yescharacteristic
720C22#1176360711yescharacteristic
721C22#1176360711yescharacteristic
722C4—22no—
723C4—22no—
724C4—42no—
725C4—41no—
726C4—41no—
727C4—81no—
728C4—81no—
729C4—682no—
730C4—1361no—
731C4—1361no—
732C4#1176306014yesdirect product factor
733C4C4×D4×D1711yescharacteristic
734C4C4×#6325411yescharacteristic
735C4#1176331811yescharacteristic
736C4#1176333911yescharacteristic
737C2—42no—
738C2—82no—
739C2—1362no—
740C2C4×#1058762511yescharacteristic
741C2C4×#1058763511yescharacteristic
742C2C4×#1058761811yescharacteristic
743C2C2×#1176306011yescharacteristic
744C2#1453839011yescharacteristic
745C2#1453937311yescharacteristic
746C2#1453938011yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC4×C17×#121C2
socleC23×C17C22×D4
prime radicalC2×#11763060C2
cosocleC22×C4×C17C24
hypercenterC4×#121D17
hypocenterC17C4×#469
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
2. C2×C4×#63228C2semidirect
3. C2×C4×#63223C2semidirect
4. C4×#10587616C2semidirect
5. #14529659C2semidirect
6. #14529524C2semidirect
7. #14529484C2semidirect
8. #14529480C2semidirect
9. #14529223C2semidirect
10. #14529220C2semidirect
11. #14528815C2semidirect
12. C4×#10587479C2semidirect
13. C4×#10587480C2semidirect
14. C4×#10587503C2semidirect
15. C4×C17×#121C2semidirect
22. #11763060C4direct (N × H)
72. C17×#121C2×C4semidirect
95. C2×#63228C2×C4semidirect
97. #10587616C2×C4semidirect
113. C2×#63223C2×C4semidirect
125. #10587503C2×C4semidirect
131. #10587480C2×C4semidirect
133. #10587479C2×C4semidirect
138. C4×#3622D4semidirect
320. #3622C4×D4semidirect
325. C4×#121D17semidirect
371. C4×C17#469semidirect
460. #121C4×D17semidirect
512. C17C4×#469semidirect
732. C4#11763060direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117630602
C2×C4×#632282
C2×C4×#632232
C4×#105876162
#145296592
#145295242
#145294842
#145294802
#145292232
#145292202
#145288152
C4×#105874792
C4×#105874802
C4×#105875032
C4×C17×#1212
C4×#46917