Finite Group Databasebeta

← C2×#14541163 #17912771

Subgroups — C2×#14541163 #17912771

Order 4352.

1930 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763505C211yesmaximal, characteristic
2#14541163C2116yesmaximal, direct product factor
3C2×#11763208C211yesmaximal, characteristic, complemented
4C2×#11763142C211yesmaximal, characteristic, complemented
5C2×#11763147C211yesmaximal, characteristic, complemented
6C2×#11763133C211yesmaximal, characteristic, complemented
7C2×#11763122C211yesmaximal, characteristic, complemented
8C2×#11763116C211yesmaximal, characteristic, complemented
9C2×#11763106C211yesmaximal, characteristic, complemented
10C2×#11763040C211yesmaximal, characteristic, complemented
11C2×#11763040C211yesmaximal, characteristic, complemented
12C2×C4×#63230C211yesmaximal, characteristic, complemented
13C2×D4×#3622C211yesmaximal, characteristic, complemented
14C2×#11762845C211yesmaximal, characteristic, complemented
15C22×#10587479C211yesmaximal, characteristic, complemented
16C2×C17×#552C211yesmaximal, characteristic, complemented
17C22×#63230C2211yescharacteristic
18C23×#3622C2211yescharacteristic
19C23×#3622C2211yescharacteristic
20#11763505—24no—
21#11763505C2218yes—
22C2×#10587584—21no—
23C2×#10587556C2211yescharacteristic
24C2×#10587569—21no—
25C2×#10587616C2211yescharacteristic
26C2×#10587616C2211yescharacteristic
27C2×#10587625—21no—
28C2×C4×D68C2211yescharacteristic
29C2×#10587567—21no—
30C2×#10587612C2211yescharacteristic
31C22×C4⋊Dic17C2211yescharacteristic
32#11763208C2218yescomplemented
33#11763147C2218yescomplemented
34#11763142C2218yescomplemented
35#11763133C2218yescomplemented
36#11763122C2218yescomplemented
37#11763116C2218yescomplemented
38#11763106C2218yescomplemented
39#11763040C2218yescomplemented
40#11763040C2218yescomplemented
41C4×#63230C2218yescomplemented
42D4×#3622C2218yescomplemented
43#11762845C2218yescomplemented
44C2×#10587478C2211yescharacteristic
45C2×#10587478C2211yescharacteristic
46C2×#10587478C2211yescharacteristic
47C2×#10587478C2211yescharacteristic
48C2×#10587479C2211yescharacteristic
49C2×#10587479C2211yescharacteristic
50C2×#10587479C2211yescharacteristic
51C2×#10587479C2211yescharacteristic
52C2×#10587479C2211yescharacteristic
53C2×#10587479C2218yescomplemented
54C2×C4⋊#3622C2211yescharacteristic
55C2×#10587506C2211yescharacteristic
56C2×#10587506C2211yescharacteristic
57C2×#10587506C2211yescharacteristic
58C2×#10587480C2211yescharacteristic
59C2×#10587480C2211yescharacteristic
60C2×#10587480C2211yescharacteristic
61C2×C22⋊#3622C2211yescharacteristic
62C2×C22⋊#3622C2211yescharacteristic
63C2×C4×#3622C2211yescharacteristic
64C17×#552—24no—
65C17×#552C2218yescomplemented
66C2×C17×#126—21no—
67C2×C17×#125—21no—
68C2×C17×#125C2211yescharacteristic
69C2×C17×#123—21no—
70C2×C17×C22⋊Q8C2211yescharacteristic
71C2×C17×C22⋊Q8C2211yescharacteristic
72C2×C4×Q8×C17C2211yescharacteristic
73C2×C4×D4×C17C2211yescharacteristic
74C2×C17×#117—21no—
75C2×C17×#117C2211yescharacteristic
76C22×C4⋊C4×C17C2211yescharacteristic
77C22×Q8×C17C2311yescharacteristic
78C22×D4×C17D411yescharacteristic
79C23×C4×C17—21no—
80C23×C4×C17C2311yescharacteristic
81C23×C4×C17C2311yescharacteristic
82C22×C22⋊D17—21no—
83C22×C22⋊D17—21no—
84C23×Dic17—21no—
85C22×D68C2311yescharacteristic
86C22×C4×D17—21no—
87C17×#126—28no—
88C17×#125—28no—
89C17×#125—22no—
90C17×#125C2314yes—
91C17×#123—28no—
92C17×C22⋊Q8—22no—
93C17×C22⋊Q8—22no—
94C17×C22⋊Q8C2314yes—
95C17×C22⋊Q8C2314yes—
96C4×Q8×C17—22no—
97C4×Q8×C17C2314yes—
98C4×D4×C17D414yes—
99C4×D4×C17C2314yes—
100C17×#117—22no—
101C17×#117—28no—
102C17×#117C2314yes—
103C2×C4⋊C4×C17—21no—
104C2×C4⋊C4×C17—22no—
105C2×C4⋊C4×C17—21no—
106C2×C4⋊C4×C17—21no—
107C2×C4⋊C4×C17—21no—
108C2×C4⋊C4×C17—21no—
109C2×C4⋊C4×C17—21no—
110C2×C4⋊C4×C17D411yescharacteristic
111C2×C4⋊C4×C17C2311yescharacteristic
112C2×C4⋊C4×C17C2311yescharacteristic
113C2×C4⋊C4×C17C2314yes—
114C2×C4⋊C4×C17C2311yescharacteristic
115C2×C22⋊C4×C17—21no—
116C2×C22⋊C4×C17—21no—
117C2×C22⋊C4×C17—21no—
118C2×C22⋊C4×C17D411yescharacteristic
119C2×C22⋊C4×C17D411yescharacteristic
120C2×C42×C17—21no—
121C2×C42×C17—21no—
122C2×C42×C17C2311yescharacteristic
123C2×C22⋊Dic17—21no—
124C2×#63230—24no—
125C2×#63230C2314yes—
126#10587625—28no—
127#10587616—22no—
128#10587616—22no—
129#10587616C2314yes—
130#10587616C2314yes—
131C2×#63227—21no—
132C2×#63227—21no—
133C2×#63227—21no—
134#10587612—22no—
135#10587612C2314yes—
136C2×C4⋊Dic17—22no—
137C2×C4⋊Dic17—21no—
138C2×C4⋊Dic17C2314yes—
139C2×C4⋊Dic17C2311yescharacteristic
140C2×C4⋊Dic17C2311yescharacteristic
141C2×C4⋊Dic17C2311yescharacteristic
142C2×#63225—21no—
143C2×#63225—21no—
144C2×C4×Dic17—21no—
145C22×#3622—24no—
146C22×#3622—24no—
147C22×#3622C2311yescharacteristic
148C22×#3622C2311yescharacteristic
149C22×#3622C2311yescharacteristic
150C22×#3622C2314yes—
151C22×#3622C2314yes—
152C22×#3622C2311yescharacteristic
153#10587584—28no—
154#10587569—28no—
155#10587567—28no—
156C4×D68—22no—
157C4×D68C2314yes—
158#10587556—22no—
159#10587556C2314yes—
160#10587506C2314yes—
161#10587506C2314yes—
162#10587506C2314yes—
163C22⋊#3622C2314yes—
164C22⋊#3622C2314yes—
165#10587480C2314yes—
166#10587480C2314yes—
167#10587480C2314yes—
168#10587479C2314yes—
169#10587479C2314yes—
170#10587479C2314yes—
171#10587479C2314yes—
172#10587479C2314yes—
173#10587478C2314yes—
174#10587478C2314yes—
175#10587478C2314yes—
176#10587478C2314yes—
177C4⋊#3622C2314yes—
178C4×#3622C2314yes—
179C24×C17C2×D411yescharacteristic
180C24×C17C2×D411yescharacteristic
181C23×D17—21no—
182C2×Q8×C17—21no—
183C2×Q8×C17—22no—
184C2×Q8×C17—22no—
185C2×Q8×C17C2412yes—
186C2×D4×C17—24no—
187C2×D4×C17C2×D414yes—
188C22×C4×C17—22no—
189C22×C4×C17—22no—
190C22×C4×C17—22no—
191C22×C4×C17—22no—
192C22×C4×C17—24no—
193C22×C4×C17—21no—
194C22×C4×C17—21no—
195C22×C4×C17—21no—
196C22×C4×C17—21no—
197C22×C4×C17—44no—
198C22×C4×C17C2×D412yes—
199C22×C4×C17C2×D412yes—
200C22×C4×C17C2×D411yescharacteristic
201C22×C4×C17C2×D411yescharacteristic
202C22×C4×C17C2×D411yescharacteristic
203C22×C4×C17C2×D411yescharacteristic
204C22×C4×C17C2412yes—
205C22×C4×C17C2412yes—
206C22×C4×C17C2411yescharacteristic
207C2×C22⋊D17—24no—
208C2×C22⋊D17—24no—
209C2×C22⋊D17—44no—
210C2×C22⋊D17—82no—
211C22×Dic17—21no—
212C22×Dic17—21no—
213C22×Dic17—21no—
214C22×Dic17—24no—
215C22×Dic17—82no—
216C2×D68—22no—
217C2×D68—22no—
218C2×D68—21no—
219C2×D68C2412yes—
220C2×C4×D17—24no—
221C2×C4×D17—82no—
222C4⋊C4×C17—21no—
223C4⋊C4×C17—21no—
224C4⋊C4×C17—24no—
225C4⋊C4×C17—24no—
226C4⋊C4×C17—24no—
227C4⋊C4×C17—24no—
228C4⋊C4×C17—24no—
229C4⋊C4×C17—24no—
230C4⋊C4×C17—21no—
231C4⋊C4×C17C2×D414yes—
232C4⋊C4×C17C2412yes—
233C4⋊C4×C17C2412yes—
234C4⋊C4×C17C2412yes—
235C22⋊C4×C17—24no—
236C22⋊C4×C17—24no—
237C22⋊C4×C17—24no—
238C22⋊C4×C17C2×D414yes—
239C22⋊C4×C17C2×D414yes—
240C42×C17—24no—
241C42×C17—24no—
242C42×C17C2×D412yes—
243C42×C17C2412yes—
244C22⋊Dic17—24no—
245#63230—28no—
246#63227—24no—
247#63227—24no—
248#63227—24no—
249C4⋊Dic17—21no—
250C4⋊Dic17—21no—
251C4⋊Dic17—21no—
252C4⋊Dic17—24no—
253C4⋊Dic17C2412yes—
254C4⋊Dic17C2412yes—
255C4⋊Dic17C2412yes—
256#63225—24no—
257#63225—24no—
258C4×Dic17—24no—
259C2×#3622—22no—
260C2×#3622—22no—
261C2×#3622—22no—
262C2×#3622—28no—
263C2×#3622—28no—
264C2×#3622#4114yes—
265C2×#3622C2412yes—
266C2×#3622C2412yes—
267C2×#3622C2412yes—
268C2×#3622C2412yes—
269C2×#3337—171nomaximal, Sylow
270C23×C17—22no—
271C23×C17—22no—
272C23×C17—22no—
273C23×C17—22no—
274C23×C17—22no—
275C23×C17#13514yes—
276C23×C17C22×D412yes—
277C23×C17C22×D412yes—
278C23×C17C22×D411yescharacteristic
279C22×D17—22no—
280C22×D17—42no—
281C22×D17—42no—
282C22×D17—42no—
283Q8×C17—22no—
284Q8×C17—22no—
285Q8×C17—42no—
286D4×C17—28no—
287C2×C4×C17—22no—
288C2×C4×C17—22no—
289C2×C4×C17—22no—
290C2×C4×C17—22no—
291C2×C4×C17—24no—
292C2×C4×C17—24no—
293C2×C4×C17—22no—
294C2×C4×C17—22no—
295C2×C4×C17—22no—
296C2×C4×C17—22no—
297C2×C4×C17—22no—
298C2×C4×C17—22no—
299C2×C4×C17—22no—
300C2×C4×C17—22no—
301C2×C4×C17—42no—
302C2×C4×C17—48no—
303C2×C4×C17—42no—
304C2×C4×C17—42no—
305C2×C4×C17—42no—
306C2×C4×C17C22×D412yes—
307C2×C4×C17C22×D412yes—
308C2×C4×C17C22×D412yes—
309C2×C4×C17C22×D412yes—
310C2×C4×C17C22×D411yescharacteristic
311C2×C4×C17C2×#4112yes—
312C2×C4×C172−1+412yes—
313C2×C4×C17C2511yescharacteristic
314C22⋊D17—48no—
315C22⋊D17—84no—
316C2×Dic17—22no—
317C2×Dic17—22no—
318C2×Dic17—22no—
319C2×Dic17—42no—
320C2×Dic17—42no—
321C2×Dic17—42no—
322C2×Dic17—84no—
323D68—22no—
324D68—22no—
325D68—42no—
326C4×D17—84no—
327#3622—22no—
328#3622—22no—
329#3622—22no—
330#3622C2×#4114yes—
331C2×#553—171no—
332C2×#552D1711yescharacteristic, complemented
333#3337—1716no—
334C2×#499—171no—
335C2×#484—171no—
336C2×#485—171no—
337C2×#482—171no—
338C2×#480—171no—
339C2×#479—171no—
340C2×#478—171no—
341C2×#465—171no—
342C2×#465—171no—
343C2×C4×SD16—171no—
344C2×C8×D4—171no—
345C2×#427—171no—
346C22×#106—171no—
347C22×C17—28no—
348C22×C17—22no—
349C22×C17—22no—
350C22×C17—22no—
351C22×C17—22no—
352C22×C17—22no—
353C22×C17—44no—
354C22×C17#54712yes—
355C22×C17C2×#13514yes—
356C22×C17C2×#13512yes—
357C22×C17#57712yes—
358C22×C17C23×D411yescharacteristic
359C2×D17—42no—
360C2×D17—42no—
361C2×D17—42no—
362C2×D17—84no—
363C4×C17—22no—
364C4×C17—22no—
365C4×C17—22no—
366C4×C17—22no—
367C4×C17—42no—
368C4×C17—42no—
369C4×C17—42no—
370C4×C17—42no—
371C4×C17#54712yes—
372C4×C17C22×#4111yescharacteristic
373C4×C17C2×2−1+411yescharacteristic
374Dic17—42no—
375Dic17—42no—
376Dic17—42no—
377C22×SD16—171no—
378C23×C8—171no—
379C23×C8—171no—
380#553—178no—
381#553—344no—
382#552—24no—
383#552C2×D1718yescomplemented
384C2×#126—21no—
385C2×#126—341no—
386C2×#125—21no—
387C2×#125—171no—
388C2×#125C2×D1711yescharacteristic
389C2×#123—21no—
390C2×#123—341no—
391C2×C22⋊Q8C2×D1711yescharacteristic
392C2×C22⋊Q8C2×D1711yescharacteristic
393C2×#121—171no—
394C2×#121—171no—
395C2×#121—341no—
396C2×C4×Q8C2×D1711yescharacteristic
397C2×C4×D4—171no—
398C2×C4×D4—341no—
399C2×C4×D4C2×D1711yescharacteristic
400C2×#117—21no—
401C2×#117—171no—
402C2×#117C2×D1711yescharacteristic
403C22×C4⋊C4—171no—
404C22×C4⋊C4C2×D1711yescharacteristic
405#499—178no—
406#485—178no—
407#484—178no—
408#482—178no—
409#480—178no—
410#479—178no—
411#478—178no—
412#465—178no—
413#465—178no—
414C4×SD16—178no—
415C8×D4—178no—
416#427—178no—
417C2×#107—171no—
418C2×#107—171no—
419C2×#107—171no—
420C2×#107—171no—
421C2×#106—171no—
422C2×#106—171no—
423C2×#106—178no—
424C2×#106—171no—
425C2×#106—171no—
426C2×#106—171no—
427C2×C4⋊C8—171no—
428C2×#103—171no—
429C2×#103—171no—
430C2×#103—171no—
431C2×#102—171no—
432C2×#102—171no—
433C2×#102—171no—
434C2×C22⋊C8—171no—
435C2×C22⋊C8—171no—
436C2×C4×C8—171no—
437C2×C17—24no—
438C2×C17—42no—
439C2×C17#333714yescomplemented
440C2×C17C2×#54711yescharacteristic
441C2×C17C22×#13511yescharacteristic
442C2×C17C2×#57711yescharacteristic
443D17—82no—
444C22×Q8C22×D1711yescharacteristic
445C22×D4—171no—
446C22×D4—341no—
447C22×D4—341no—
448C22×D4C22⋊D1711yescharacteristic
449C23×C4—21no—
450C23×C4—341no—
451C23×C4—341no—
452C23×C4C22×D1711yescharacteristic
453C23×C4C22×D1711yescharacteristic
454C2×SD16—174no—
455C2×SD16—344no—
456C22×C8—171no—
457C22×C8—171no—
458C22×C8—171no—
459C22×C8—174no—
460C22×C8—174no—
461C22×C8—171no—
462C22×C8—344no—
463C22×C8—344no—
464#126—28no—
465#126—348no—
466#125—28no—
467#125—22no—
468#125—174no—
469#125—342no—
470#125C22×D1714yes—
471#123—28no—
472#123—348no—
473C22⋊Q8—22no—
474C22⋊Q8—22no—
475C22⋊Q8C22×D1714yes—
476C22⋊Q8C22×D1714yes—
477#121—174no—
478#121—174no—
479#121—348no—
480#121—342no—
481#121—342no—
482C4×Q8—22no—
483C4×Q8C22×D1714yes—
484C4×D4—174no—
485C4×D4—348no—
486C4×D4—342no—
487C4×D4C22⋊D1714yes—
488C4×D4C22×D1714yes—
489#117—22no—
490#117—28no—
491#117—174no—
492#117—342no—
493#117C22×D1714yes—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—22no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—171no—
502C2×C4⋊C4—171no—
503C2×C4⋊C4—174no—
504C2×C4⋊C4—171no—
505C2×C4⋊C4—341no—
506C2×C4⋊C4—342no—
507C2×C4⋊C4—341no—
508C2×C4⋊C4—341no—
509C2×C4⋊C4C22⋊D1711yescharacteristic
510C2×C4⋊C4C22×D1711yescharacteristic
511C2×C4⋊C4C22×D1711yescharacteristic
512C2×C4⋊C4C22×D1714yes—
513C2×C4⋊C4C22×D1711yescharacteristic
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—341no—
518C2×C22⋊C4—341no—
519C2×C22⋊C4—341no—
520C2×C22⋊C4—341no—
521C2×C22⋊C4C22⋊D1711yescharacteristic
522C2×C22⋊C4C22⋊D1711yescharacteristic
523C2×C42—21no—
524C2×C42—21no—
525C2×C42—341no—
526C2×C42C22×D1711yescharacteristic
527#107—174no—
528#107—174no—
529#107—174no—
530#107—174no—
531#106—174no—
532#106—174no—
533#106—174no—
534#106—174no—
535#106—174no—
536C4⋊C8—174no—
537#103—174no—
538#103—174no—
539#103—174no—
540#102—174no—
541#102—174no—
542#102—174no—
543C22⋊C8—174no—
544C22⋊C8—174no—
545C4×C8—174no—
546C17C2×#333711yescharacteristic, complemented, Sylow
547C24—341no—
548C24C2×C22⋊D1711yescharacteristic
549C24C2×C22⋊D1711yescharacteristic
550C2×Q8—21no—
551C2×Q8—22no—
552C2×Q8—22no—
553C2×Q8C23×D1712yes—
554C2×D4—24no—
555C2×D4—172no—
556C2×D4—344no—
557C2×D4—344no—
558C2×D4—342no—
559C2×D4—342no—
560C2×D4—341no—
561C2×D4—684no—
562C2×D4—1362no—
563C2×D4C2×C22⋊D1714yes—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—24no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—44no—
574C22×C4—341no—
575C22×C4—341no—
576C22×C4—341no—
577C22×C4—344no—
578C22×C4—344no—
579C22×C4—1362no—
580C22×C4—1362no—
581C22×C4C2×C22⋊D1712yes—
582C22×C4C2×C22⋊D1712yes—
583C22×C4C2×C22⋊D1711yescharacteristic
584C22×C4C2×C22⋊D1711yescharacteristic
585C22×C4C2×C22⋊D1711yescharacteristic
586C22×C4C2×C22⋊D1711yescharacteristic
587C22×C4C23×D1712yes—
588C22×C4C23×D1712yes—
589C22×C4C23×D1711yescharacteristic
590SD16—348no—
591C2×C8—174no—
592C2×C8—172no—
593C2×C8—172no—
594C2×C8—172no—
595C2×C8—172no—
596C2×C8—348no—
597C2×C8—348no—
598C2×C8—342no—
599C2×C8—342no—
600C2×C8—342no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—24no—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—24no—
609C4⋊C4—21no—
610C4⋊C4—172no—
611C4⋊C4—172no—
612C4⋊C4—172no—
613C4⋊C4—341no—
614C4⋊C4—341no—
615C4⋊C4—344no—
616C4⋊C4—341no—
617C4⋊C4—344no—
618C4⋊C4—344no—
619C4⋊C4C2×C22⋊D1714yes—
620C4⋊C4C23×D1712yes—
621C4⋊C4C23×D1712yes—
622C4⋊C4C23×D1712yes—
623C22⋊C4—24no—
624C22⋊C4—24no—
625C22⋊C4—24no—
626C22⋊C4—344no—
627C22⋊C4—344no—
628C22⋊C4—344no—
629C22⋊C4—344no—
630C22⋊C4C2×C22⋊D1714yes—
631C22⋊C4C2×C22⋊D1714yes—
632C42—24no—
633C42—24no—
634C42—344no—
635C42C2×C22⋊D1712yes—
636C42C23×D1712yes—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—342no—
643C23—682no—
644C23—682no—
645C23—682no—
646C23#1058763614yes—
647C23C22×C22⋊D1712yes—
648C23C22×C22⋊D1712yes—
649C23C22×C22⋊D1711yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—42no—
653D4—28no—
654D4—342no—
655D4—342no—
656D4—688no—
657D4—682no—
658D4—1364no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—42no—
674C2×C4—48no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—342no—
679C2×C4—342no—
680C2×C4—342no—
681C2×C4—682no—
682C2×C4—682no—
683C2×C4—682no—
684C2×C4—1364no—
685C2×C4—1364no—
686C2×C4#41×D1712yes—
687C2×C4#1058769712yes—
688C2×C4C22×C22⋊D1712yes—
689C2×C4C22×C22⋊D1712yes—
690C2×C4C22×C22⋊D1712yes—
691C2×C4C22×C22⋊D1712yes—
692C2×C4C22×C22⋊D1711yescharacteristic
693C2×C4C24×D1711yescharacteristic
694C8—174no—
695C8—342no—
696C8—342no—
697C8—342no—
698C22—28no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—44no—
705C22—682no—
706C22—682no—
707C22—682no—
708C22—1364no—
709C22#1176345812yes—
710C22C2×#1058763614yes—
711C22C2×#1058763612yes—
712C22#1176361712yes—
713C22C23×C22⋊D1711yescharacteristic
714C4—22no—
715C4—22no—
716C4—22no—
717C4—22no—
718C4—42no—
719C4—42no—
720C4—42no—
721C4—42no—
722C4—682no—
723C4—682no—
724C4—682no—
725C4#1176345812yes—
726C4C2×#41×D1711yescharacteristic
727C4C2×#1058769711yescharacteristic
728C2—24no—
729C2—42no—
730C2—1362no—
731C2#1454116314yesdirect product factor
732C2C2×#1176345811yescharacteristic
733C2C22×#1058763611yescharacteristic
734C2C2×#1176361711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#552C2
socleC23×C17C22×D4
prime radicalC2×#11763505C2
hypercenterC2×#552D17
hypocenterC17C2×#3337
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
2. #14541163C2direct (N × H)
3. C2×#11763208C2semidirect
4. C2×#11763142C2semidirect
5. C2×#11763147C2semidirect
6. C2×#11763133C2semidirect
7. C2×#11763122C2semidirect
8. C2×#11763116C2semidirect
9. C2×#11763106C2semidirect
10. C2×#11763040C2semidirect
11. C2×#11763040C2semidirect
12. C2×C4×#63230C2semidirect
13. C2×D4×#3622C2semidirect
14. C2×#11762845C2semidirect
15. C22×#10587479C2semidirect
16. C2×C17×#552C2semidirect
32. #11763208C22semidirect
33. #11763147C22semidirect
34. #11763142C22semidirect
35. #11763133C22semidirect
36. #11763122C22semidirect
37. #11763116C22semidirect
38. #11763106C22semidirect
39. #11763040C22semidirect
40. #11763040C22semidirect
41. C4×#63230C22semidirect
42. D4×#3622C22semidirect
43. #11762845C22semidirect
53. C2×#10587479C22semidirect
65. C17×#552C22semidirect
332. C2×#552D17semidirect
383. #552C2×D17semidirect
439. C2×C17#3337semidirect
546. C17C2×#3337semidirect
731. C2#14541163direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117635052
#145411632
C2×#117632082
C2×#117631422
C2×#117631472
C2×#117631332
C2×#117631222
C2×#117631162
C2×#117631062
C2×#117630402
C2×C4×#632302
C2×D4×#36222
C2×#117628452
C22×#105874792
C2×C17×#5522
C2×#333717