Finite Group Databasebeta

← C2×#14537662 #17898482

Subgroups — C2×#14537662 #17898482

Order 4352.

2806 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
1C22×#10587602C211yesmaximal, characteristic
2C2×#11763291C211yesmaximal, characteristic, complemented
3C2×#11763288C211yesmaximal, characteristic, complemented
4#14537662C2116yesmaximal, direct product factor
5C2×#11762919C211yesmaximal, characteristic, complemented
6C2×#11762918C211yesmaximal, characteristic, complemented
7C2×#11762914C211yesmaximal, characteristic, complemented
8C2×#11762913C211yesmaximal, characteristic, complemented
9C2×C4×#63219C211yesmaximal, characteristic, complemented
10C2×SD16×Dic17C211yesmaximal, characteristic, complemented
11C2×#11762896C211yesmaximal, characteristic, complemented
12C2×#106×D17C211yesmaximal, characteristic, complemented
13C2×#11762809C211yesmaximal, characteristic, complemented
14C2×#11762807C211yesmaximal, characteristic, complemented
15C2×#11762763C211yesmaximal, characteristic, complemented
16C2×C4×SD16×C17C211yesmaximal, characteristic, complemented
17C22×#63256C2211yescharacteristic
18C22×#63254C2211yescharacteristic
19C2×#10587602C4116yescomplemented
20C2×#10587602C2218yes—
21C22×#63231C2211yescharacteristic
22C22×#63219C2211yescharacteristic
23C22×#63228C2211yescharacteristic
24C22×#63218C2211yescharacteristic
25C22×C8×D17C2211yescharacteristic
26#11763291—24no—
27#11763291C2218yescomplemented
28#11763288—24no—
29#11763288C2218yescomplemented
30C2×Q8×Dic17C2211yescharacteristic
31C2×C4×Dic34C2211yescharacteristic
32C2×#10587573C2211yescharacteristic
33C2×C4×D68—21no—
34C2×C4×D68C2211yescharacteristic
35C2×D4×Dic17C2211yescharacteristic
36C2×#10587579—21no—
37C2×#10587579C2211yescharacteristic
38C2×C4×C22⋊D17—21no—
39C2×#10587567—21no—
40C2×#10587558—21no—
41C2×#10587558C2211yescharacteristic
42C2×#10587563—21no—
43C22×#63225—21no—
44C2×C4⋊C4×D17—21no—
45C2×C4⋊C4×D17C2211yescharacteristic
46C2×C4⋊C4×D17C2211yescharacteristic
47#11762919C2218yescomplemented
48#11762918C2218yescomplemented
49#11762914C2218yescomplemented
50#11762913C2218yescomplemented
51C4×#63219C2218yescomplemented
52SD16×Dic17C2218yescomplemented
53#11762896C2218yescomplemented
54C2×#10587488C2211yescharacteristic
55C2×#10587479C2211yescharacteristic
56C2×#10587479C2211yescharacteristic
57#106×D17C2218yescomplemented
58#11762809C2218yescomplemented
59#11762807C2218yescomplemented
60C2×#10587487C2211yescharacteristic
61C2×#10587506C2211yescharacteristic
62C2×#10587481C2211yescharacteristic
63C2×#10587492C2211yescharacteristic
64C2×#10587503C2211yescharacteristic
65C2×#10587480C2211yescharacteristic
66#11762763C2218yescomplemented
67C2×#10587474C2211yescharacteristic
68C2×#10587486C2211yescharacteristic
69C2×C8×Dic17C2211yescharacteristic
70C22×SD16×C17C2211yescharacteristic
71C2×C4×Q8×C17C2211yescharacteristic
72C2×C4×D4×C17C2211yescharacteristic
73C4×SD16×C17C2218yescomplemented
74C2×C17×#106C2211yescharacteristic
75C2×C17×#103C2211yescharacteristic
76C2×C17×#102C2211yescharacteristic
77C2×C4×C8×C17C2211yescharacteristic
78C22×Q8×C17C2311yescharacteristic
79C22×D4×C17C2311yescharacteristic
80C23×C4×C17—21no—
81C22×C22⋊D17—21no—
82C23×Dic17—21no—
83C23×Dic17—21no—
84C2×#63256—22no—
85C2×#63256—24no—
86C2×#63256C2×C418yescomplemented
87C2×#63256C2314yes—
88C2×#63254—22no—
89C2×#63254—24no—
90C2×#63254C2×C418yescomplemented
91C2×#63254C2314yes—
92C22×D68—21no—
93C22×D68C2311yescharacteristic
94C22×C4×D17—21no—
95C22×C4×D17—21no—
96C22×C4×D17—21no—
97C22×C4×D17—21no—
98C22×C4×D17—21no—
99C22×C4×D17C2311yescharacteristic
100C22×Dic34C2311yescharacteristic
101C2×SD16×C17C2×C418yescomplemented
102C2×SD16×C17C2314yes—
103C22×C8×C17C2311yescharacteristic
104C22×C8×C17C2311yescharacteristic
105C4×Q8×C17—22no—
106C4×Q8×C17C2314yes—
107C4×D4×C17—22no—
108C4×D4×C17C2314yes—
109C2×C4⋊C4×C17—21no—
110C2×C4⋊C4×C17C2311yescharacteristic
111C2×C4⋊C4×C17C2311yescharacteristic
112C2×C22⋊C4×C17—21no—
113C2×C42×C17—21no—
114C2×C42×C17C2311yescharacteristic
115C2×C22⋊Dic17—21no—
116Q8×Dic17—22no—
117Q8×Dic17C2314yes—
118C2×#63231C2×C418yescomplemented
119C2×#63231C2314yes—
120D4×Dic17—22no—
121D4×Dic17C2314yes—
122C2×#63228C2×C418yescomplemented
123C2×#63228C2314yes—
124C4×C22⋊D17—28no—
125C2×#63227—21no—
126C2×#63227—21no—
127C2×#63227D411yescharacteristic
128C2×#63227D411yescharacteristic
129C2×C4⋊Dic17—21no—
130C2×C4⋊Dic17C2311yescharacteristic
131C2×C4⋊Dic17C2311yescharacteristic
132C2×#63225—28no—
133C2×#63225—21no—
134C2×#63225—21no—
135C2×#63225—21no—
136C2×#63225—21no—
137C2×#63225D411yescharacteristic
138C2×#63225D411yescharacteristic
139C2×C4×Dic17—21no—
140C2×C4×Dic17—21no—
141C2×C4×Dic17—21no—
142C2×C4×Dic17C2311yescharacteristic
143C22×#3622C2311yescharacteristic
144C22×#3622C2311yescharacteristic
145#10587602C2×C4164yescomplemented
146C2×#63219C2×C418yescomplemented
147C2×#63219C2314yes—
148C2×#63218—24no—
149C2×#63218C2314yes—
150C2×C8×D17C2×C418yescomplemented
151C2×C8×D17C2314yes—
152#10587579—28no—
153#10587579—22no—
154#10587579C2314yes—
155C4⋊C4×D17—28no—
156C4⋊C4×D17—22no—
157C4⋊C4×D17—22no—
158C4⋊C4×D17C2314yes—
159C4⋊C4×D17C2314yes—
160#10587573—22no—
161#10587573C2314yes—
162#10587567—28no—
163#10587563—28no—
164C4×D68—28no—
165C4×D68—22no—
166C4×D68C2314yes—
167#10587558—28no—
168#10587558D414yes—
169#10587558C2314yes—
170C4×Dic34—22no—
171C4×Dic34C2314yes—
172C17×#106C2314yes—
173C17×#103C2314yes—
174C17×#102C2314yes—
175C4×C8×C17C2314yes—
176#10587506C2314yes—
177#10587503C2314yes—
178#10587492C2314yes—
179#10587488C2314yes—
180#10587487C2314yes—
181#10587486C2314yes—
182C8×Dic17C2314yes—
183#10587481C2314yes—
184#10587480C2314yes—
185#10587479C2314yes—
186#10587479C2314yes—
187#10587474C2314yes—
188C24×C17—21no—
189C23×D17—21no—
190C23×D17C2×D411yescharacteristic
191C2×Q8×C17—21no—
192C2×Q8×C17—22no—
193C2×Q8×C17C22×C414yes—
194C2×Q8×C17C2412yes—
195C2×D4×C17—21no—
196C2×D4×C17—22no—
197C2×D4×C17C22×C414yes—
198C2×D4×C17C2412yes—
199C22×C4×C17—21no—
200C22×C4×C17—21no—
201C22×C4×C17—21no—
202C22×C4×C17—24no—
203C22×C4×C17—82no—
204C22×C4×C17C2×D411yescharacteristic
205C22×C4×C17C2×D411yescharacteristic
206C22×C4×C17C2411yescharacteristic
207C2×C22⋊D17—28no—
208C2×C22⋊D17—24no—
209C22×Dic17—21no—
210C22×Dic17—28no—
211C22×Dic17—24no—
212C22×Dic17—21no—
213C22×Dic17—21no—
214C22×Dic17—24no—
215C22×Dic17—82no—
216C22×Dic17C2×D411yescharacteristic
217C22×Dic17C2×D411yescharacteristic
218C22×Dic17C2×D411yescharacteristic
219#63256—216no—
220#63256—28no—
221#63256C22×C4116yescomplemented
222#63254—216no—
223#63254—28no—
224#63254C22×C4116yescomplemented
225C2×D68—28no—
226C2×D68—24no—
227C2×D68—21no—
228C2×D68—22no—
229C2×D68C22×C414yes—
230C2×D68C2412yes—
231C2×C4×D17—28no—
232C2×C4×D17—24no—
233C2×C4×D17—24no—
234C2×C4×D17—24no—
235C2×C4×D17—24no—
236C2×C4×D17—24no—
237C2×C4×D17—82no—
238C2×C4×D17—82no—
239C2×C4×D17—82no—
240C2×C4×D17—82no—
241C2×C4×D17C22×C414yes—
242C2×C4×D17C2×D412yes—
243C2×C4×D17#4114yes—
244C2×C4×D17C2412yes—
245C2×Dic34—21no—
246C2×Dic34—22no—
247C2×Dic34C22×C414yes—
248C2×Dic34C2412yes—
249SD16×C17C22×C4116yescomplemented
250C2×C8×C17—22no—
251C2×C8×C17C22×C414yes—
252C2×C8×C17C2412yes—
253C2×C8×C17C2412yes—
254C4⋊C4×C17—21no—
255C4⋊C4×C17—24no—
256C4⋊C4×C17—21no—
257C4⋊C4×C17C2412yes—
258C4⋊C4×C17C2412yes—
259C22⋊C4×C17—24no—
260C42×C17—24no—
261C42×C17C2×D412yes—
262C42×C17C2412yes—
263C22⋊Dic17—24no—
264#63231C22×C4116yescomplemented
265#63228C22×C4116yescomplemented
266#63227—24no—
267#63227—24no—
268#63227C2×D414yes—
269#63227C2×D414yes—
270C4⋊Dic17—21no—
271C4⋊Dic17—21no—
272C4⋊Dic17—24no—
273C4⋊Dic17C2412yes—
274C4⋊Dic17C2412yes—
275#63225—24no—
276#63225—24no—
277#63225—24no—
278#63225—24no—
279#63225C2×D414yes—
280#63225C2×D414yes—
281C4×Dic17—24no—
282C4×Dic17—24no—
283C4×Dic17—24no—
284C4×Dic17C2×D412yes—
285C4×Dic17C2412yes—
286C2×#3622—22no—
287C2×#3622C22×C414yes—
288C2×#3622C2412yes—
289C2×#3622C2412yes—
290#63219C22×C4116yescomplemented
291#63218—28no—
292C8×D17C22×C4116yescomplemented
293C2×#2952—171nomaximal, Sylow
294C23×C17—24no—
295C23×C17—22no—
296C23×C17—42no—
297C23×C17—42no—
298C23×C17C22×D411yescharacteristic
299C22×D17—22no—
300C22×D17—22no—
301C22×D17—24no—
302C22×D17—22no—
303C22×D17—42no—
304C22×D17—42no—
305C22×D17C4×D414yes—
306C22×D17C22×D412yes—
307Q8×C17—24no—
308Q8×C17—22no—
309Q8×C17C23×C414yes—
310D4×C17—24no—
311D4×C17—22no—
312D4×C17C23×C414yes—
313C2×C4×C17—24no—
314C2×C4×C17—22no—
315C2×C4×C17—22no—
316C2×C4×C17—22no—
317C2×C4×C17—22no—
318C2×C4×C17—22no—
319C2×C4×C17—42no—
320C2×C4×C17—42no—
321C2×C4×C17—84no—
322C2×C4×C17C23×C412yes—
323C2×C4×C17C22×D412yes—
324C2×C4×C17C22×D412yes—
325C2×C4×C17C22×D411yescharacteristic
326C2×C4×C17C2×#4112yes—
327C2×C4×C17C2511yescharacteristic
328C22⋊D17—216no—
329C2×Dic17—24no—
330C2×Dic17—22no—
331C2×Dic17—22no—
332C2×Dic17—22no—
333C2×Dic17—216no—
334C2×Dic17—22no—
335C2×Dic17—22no—
336C2×Dic17—42no—
337C2×Dic17—42no—
338C2×Dic17—84no—
339C2×Dic17C4×D414yes—
340C2×Dic17C22×D412yes—
341C2×Dic17C22×D412yes—
342C2×Dic17C22×D412yes—
343D68—216no—
344D68—24no—
345D68—22no—
346D68C23×C414yes—
347C4×D17—216no—
348C4×D17—84no—
349C4×D17—84no—
350C4×D17—84no—
351C4×D17—84no—
352C4×D17C4×D418yes—
353C4×D17C23×C414yes—
354C4×D17C2×#4114yes—
355Dic34—24no—
356Dic34—22no—
357Dic34C23×C414yes—
358C8×C17—22no—
359C8×C17C23×C414yes—
360#3622—22no—
361#3622C23×C414yes—
362C22×#135—171no—
363C2×#520—171no—
364C2×#520—171no—
365#2952—1716no—
366C2×#442—171no—
367C2×#442—171no—
368C2×#441—171no—
369C2×#441—171no—
370C2×C4×SD16—171no—
371C2×C4×SD16—171no—
372C2×C4×SD16—171no—
373C2×C4×SD16D1711yescharacteristic, complemented
374C22×#106—171no—
375C2×#417—171no—
376C2×#417—171no—
377C2×#405—171no—
378C22×C17—24no—
379C22×C17—48no—
380C22×C17—42no—
381C22×C17—42no—
382C22×C17C2×C4×D412yes—
383C22×C17#57712yes—
384C22×C17#57712yes—
385C22×C17C23×D411yescharacteristic
386C2×D17—28no—
387C2×D17—22no—
388C2×D17—22no—
389C2×D17—24no—
390C2×D17—48no—
391C2×D17—42no—
392C2×D17—42no—
393C2×D17C2×C4×D414yes—
394C4×C17—24no—
395C4×C17—22no—
396C4×C17—22no—
397C4×C17—42no—
398C4×C17—42no—
399C4×C17C2×C4×D412yes—
400C4×C17C24×C411yescharacteristic
401C4×C17C22×#4111yescharacteristic
402Dic17—24no—
403Dic17—22no—
404Dic17—22no—
405Dic17—42no—
406Dic17—42no—
407Dic17C2×C4×D414yes—
408C22×#41—171no—
409C22×#41—171no—
410C2×#135—1716no—
411C2×#135—178no—
412C22×Q16—171no—
413C22×SD16—171no—
414C22×SD16C2×D1711yescharacteristic
415C22×D8—171no—
416C22×M16—171no—
417C23×C8—171no—
418#520—178no—
419#520—178no—
420#520—344no—
421#520—344no—
422C2×C4×Q8—171no—
423C2×C4×Q8—171no—
424C2×C4×Q8—171no—
425C2×C4×Q8C2×D1711yescharacteristic
426C2×C4×D4—171no—
427C2×C4×D4—171no—
428C2×C4×D4—171no—
429C2×C4×D4—341no—
430C2×C4×D4—341no—
431C2×C4×D4—341no—
432C2×C4×D4—341no—
433C2×C4×D4C2×D1711yescharacteristic
434C2×#117—171no—
435C2×#117—341no—
436C2×#117—341no—
437C22×C4⋊C4—171no—
438C22×C4⋊C4—171no—
439C22×C4⋊C4—341no—
440C22×C4⋊C4—341no—
441#442—178no—
442#442—178no—
443#441—178no—
444#441—178no—
445C4×SD16—178no—
446C4×SD16—178no—
447C4×SD16—178no—
448C4×SD16C2×D1718yescomplemented
449C2×#106—171no—
450C2×#106—171no—
451C2×#106—171no—
452C2×#106—178no—
453C2×#106C2×D1711yescharacteristic
454#417—178no—
455#417—178no—
456C2×#103—171no—
457C2×#103—171no—
458C2×#103—171no—
459C2×#103C2×D1711yescharacteristic
460C2×#102—171no—
461C2×#102—171no—
462C2×#102—171no—
463C2×#102C2×D1711yescharacteristic
464#405—178no—
465C2×#97—171no—
466C2×#97—171no—
467C2×C4×C8—171no—
468C2×C4×C8C2×D1711yescharacteristic
469C2×C17—44no—
470C2×C17#295214yescomplemented
471C2×C17C22×C4×D411yescharacteristic
472C2×C17C2×#57711yescharacteristic
473C2×C17C2×#57711yescharacteristic
474D17—24no—
475D17—44no—
476C2×#41—178no—
477C2×#41—174no—
478C2×#41—178no—
479C2×#41—174no—
480C2×#41—342no—
481C2×#41—344no—
482C2×#41—342no—
483C2×#41—344no—
484C22×Q8—171no—
485C22×Q8C22×D1711yescharacteristic
486C22×D4—171no—
487C22×D4—341no—
488C22×D4—341no—
489C22×D4C22×D1711yescharacteristic
490C23×C4—21no—
491C23×C4—171no—
492C23×C4—341no—
493C23×C4—341no—
494C23×C4—341no—
495C23×C4—341no—
496C23×C4—341no—
497C23×C4—341no—
498C23×C4—341no—
499#135—1764no—
500C2×Q16—178no—
501C2×Q16—174no—
502C2×SD16—178no—
503C2×SD16—174no—
504C2×SD16C4×D1718yescomplemented
505C2×SD16C22×D1714yes—
506C2×D8—178no—
507C2×D8—174no—
508C2×M16—174no—
509C2×M16—344no—
510C22×C8—171no—
511C22×C8—178no—
512C22×C8—174no—
513C22×C8—171no—
514C22×C8C22×D1711yescharacteristic
515C22×C8C22×D1711yescharacteristic
516C4×Q8—22no—
517C4×Q8—174no—
518C4×Q8—174no—
519C4×Q8—174no—
520C4×Q8—342no—
521C4×Q8—342no—
522C4×Q8—342no—
523C4×Q8C22×D1714yes—
524C4×D4—22no—
525C4×D4—174no—
526C4×D4—174no—
527C4×D4—174no—
528C4×D4—348no—
529C4×D4—342no—
530C4×D4—342no—
531C4×D4—348no—
532C4×D4—348no—
533C4×D4—348no—
534C4×D4—342no—
535C4×D4C22×D1714yes—
536#117—174no—
537#117—174no—
538#117—348no—
539#117—348no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—171no—
542C2×C4⋊C4—171no—
543C2×C4⋊C4—171no—
544C2×C4⋊C4—171no—
545C2×C4⋊C4—174no—
546C2×C4⋊C4—174no—
547C2×C4⋊C4—348no—
548C2×C4⋊C4—342no—
549C2×C4⋊C4—342no—
550C2×C4⋊C4—348no—
551C2×C4⋊C4—341no—
552C2×C4⋊C4—341no—
553C2×C4⋊C4—341no—
554C2×C4⋊C4—341no—
555C2×C4⋊C4—341no—
556C2×C4⋊C4C22×D1711yescharacteristic
557C2×C4⋊C4C22×D1711yescharacteristic
558C2×C22⋊C4—21no—
559C2×C22⋊C4—171no—
560C2×C22⋊C4—171no—
561C2×C22⋊C4—341no—
562C2×C22⋊C4—341no—
563C2×C22⋊C4—341no—
564C2×C42—21no—
565C2×C42—171no—
566C2×C42—341no—
567C2×C42—341no—
568C2×C42—341no—
569C2×C42C22×D1711yescharacteristic
570#106—174no—
571#106—174no—
572#106—174no—
573#106C22×D1714yes—
574#103—174no—
575#103—174no—
576#103—174no—
577#103C22×D1714yes—
578#102—174no—
579#102—174no—
580#102—174no—
581#102C22×D1714yes—
582#97—174no—
583#97—174no—
584C4×C8—174no—
585C4×C8C22×D1714yes—
586C17C2×#295211yescharacteristic, complemented, Sylow
587C24—21no—
588C24—171no—
589C24—341no—
590#41—1716no—
591#41—1716no—
592#41—3416no—
593#41—348no—
594#41—3416no—
595#41—348no—
596C2×Q8—21no—
597C2×Q8—22no—
598C2×Q8—174no—
599C2×Q8—172no—
600C2×Q8—341no—
601C2×Q8—342no—
602C2×Q8C2×C4×D1714yes—
603C2×Q8C23×D1712yes—
604C2×D4—21no—
605C2×D4—22no—
606C2×D4—174no—
607C2×D4—172no—
608C2×D4—344no—
609C2×D4—348no—
610C2×D4—344no—
611C2×D4—348no—
612C2×D4—341no—
613C2×D4—342no—
614C2×D4C2×C4×D1714yes—
615C2×D4C23×D1712yes—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—24no—
620C22×C4—82no—
621C22×C4—171no—
622C22×C4—174no—
623C22×C4—172no—
624C22×C4—174no—
625C22×C4—172no—
626C22×C4—171no—
627C22×C4—171no—
628C22×C4—344no—
629C22×C4—348no—
630C22×C4—344no—
631C22×C4—344no—
632C22×C4—344no—
633C22×C4—344no—
634C22×C4—348no—
635C22×C4—344no—
636C22×C4—341no—
637C22×C4—341no—
638C22×C4—341no—
639C22×C4—344no—
640C22×C4—1362no—
641C22×C4—1362no—
642C22×C4—1362no—
643C22×C4—1362no—
644C22×C4—1362no—
645C22×C4D4×D1711yescharacteristic
646C22×C4D4×D1711yescharacteristic
647C22×C4C23×D1711yescharacteristic
648Q16—1716no—
649SD16—1716no—
650SD16C2×C4×D17116yescomplemented
651D8—1716no—
652M16—348no—
653C2×C8—22no—
654C2×C8—174no—
655C2×C8—172no—
656C2×C8—1716no—
657C2×C8—172no—
658C2×C8—342no—
659C2×C8C2×C4×D1714yes—
660C2×C8C23×D1712yes—
661C2×C8C23×D1712yes—
662C4⋊C4—24no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—174no—
666C4⋊C4—174no—
667C4⋊C4—172no—
668C4⋊C4—172no—
669C4⋊C4—344no—
670C4⋊C4—344no—
671C4⋊C4—344no—
672C4⋊C4—344no—
673C4⋊C4—341no—
674C4⋊C4—341no—
675C4⋊C4—344no—
676C4⋊C4C23×D1712yes—
677C4⋊C4C23×D1712yes—
678C22⋊C4—24no—
679C22⋊C4—174no—
680C22⋊C4—174no—
681C22⋊C4—344no—
682C22⋊C4—344no—
683C22⋊C4—344no—
684C42—24no—
685C42—172no—
686C42—172no—
687C42—344no—
688C42—344no—
689C42—344no—
690C42D4×D1712yes—
691C42C23×D1712yes—
692C23—24no—
693C23—22no—
694C23—42no—
695C23—42no—
696C23—174no—
697C23—172no—
698C23—342no—
699C23—342no—
700C23—344no—
701C23—342no—
702C23—682no—
703C23—682no—
704C23C2×D4×D1711yescharacteristic
705Q8—24no—
706Q8—22no—
707Q8—174no—
708Q8—344no—
709Q8—342no—
710Q8C22×C4×D1714yes—
711D4—24no—
712D4—22no—
713D4—174no—
714D4—3416no—
715D4—3416no—
716D4—344no—
717D4—342no—
718D4C22×C4×D1714yes—
719C2×C4—24no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—84no—
728C2×C4—174no—
729C2×C4—172no—
730C2×C4—178no—
731C2×C4—174no—
732C2×C4—174no—
733C2×C4—172no—
734C2×C4—172no—
735C2×C4—3416no—
736C2×C4—3416no—
737C2×C4—344no—
738C2×C4—342no—
739C2×C4—342no—
740C2×C4—342no—
741C2×C4—342no—
742C2×C4—342no—
743C2×C4—682no—
744C2×C4—682no—
745C2×C4—1364no—
746C2×C4—1364no—
747C2×C4—1364no—
748C2×C4—1364no—
749C2×C4—1364no—
750C2×C4C22×C4×D1712yes—
751C2×C4C2×D4×D1712yes—
752C2×C4C2×D4×D1712yes—
753C2×C4C2×D4×D1711yescharacteristic
754C2×C4#41×D1712yes—
755C2×C4C24×D1711yescharacteristic
756C8—22no—
757C8—174no—
758C8—342no—
759C8C22×C4×D1714yes—
760C22—24no—
761C22—42no—
762C22—42no—
763C22—48no—
764C22—174no—
765C22—342no—
766C22—342no—
767C22—348no—
768C22—344no—
769C22—682no—
770C22—682no—
771C22—688no—
772C22C4×D4×D1712yes—
773C22#1176361512yes—
774C22#1176361612yes—
775C22C22×D4×D1711yescharacteristic
776C4—24no—
777C4—22no—
778C4—22no—
779C4—42no—
780C4—42no—
781C4—174no—
782C4—344no—
783C4—342no—
784C4—342no—
785C4—682no—
786C4—682no—
787C4C4×D4×D1712yes—
788C4C23×C4×D1711yescharacteristic
789C4C2×#41×D1711yescharacteristic
790C2—44no—
791C2—344no—
792C2—684no—
793C2#1453766214yesdirect product factor
794C2C2×C4×D4×D1711yescharacteristic
795C2C2×#1176361511yescharacteristic
796C2C2×#1176361611yescharacteristic
subgroupG/H
centerC23C2×D4×D17
commutatorC4×C17C24×C4
FrattiniC2×C4C24×D17
FittingC2×C4×SD16×C17C2
socleC23×C17C22×D4
prime radicalC22×#10587602C2
cosocleC2×C4×C17C25
hypercenterC2×C4×SD16D17
hypocenterC17C2×#2952
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
2. C2×#11763291C2semidirect
3. C2×#11763288C2semidirect
4. #14537662C2direct (N × H)
5. C2×#11762919C2semidirect
6. C2×#11762918C2semidirect
7. C2×#11762914C2semidirect
8. C2×#11762913C2semidirect
9. C2×C4×#63219C2semidirect
10. C2×SD16×Dic17C2semidirect
11. C2×#11762896C2semidirect
12. C2×#106×D17C2semidirect
13. C2×#11762809C2semidirect
14. C2×#11762807C2semidirect
15. C2×#11762763C2semidirect
16. C2×C4×SD16×C17C2semidirect
19. C2×#10587602C4semidirect
27. #11763291C22semidirect
29. #11763288C22semidirect
47. #11762919C22semidirect
48. #11762918C22semidirect
49. #11762914C22semidirect
50. #11762913C22semidirect
51. C4×#63219C22semidirect
52. SD16×Dic17C22semidirect
53. #11762896C22semidirect
57. #106×D17C22semidirect
58. #11762809C22semidirect
59. #11762807C22semidirect
66. #11762763C22semidirect
73. C4×SD16×C17C22semidirect
86. C2×#63256C2×C4semidirect
90. C2×#63254C2×C4semidirect
101. C2×SD16×C17C2×C4semidirect
118. C2×#63231C2×C4semidirect
122. C2×#63228C2×C4semidirect
145. #10587602C2×C4semidirect
146. C2×#63219C2×C4semidirect
150. C2×C8×D17C2×C4semidirect
221. #63256C22×C4semidirect
224. #63254C22×C4semidirect
249. SD16×C17C22×C4semidirect
264. #63231C22×C4semidirect
265. #63228C22×C4semidirect
290. #63219C22×C4semidirect
292. C8×D17C22×C4semidirect
373. C2×C4×SD16D17semidirect
448. C4×SD16C2×D17semidirect
470. C2×C17#2952semidirect
504. C2×SD16C4×D17semidirect
586. C17C2×#2952semidirect
650. SD16C2×C4×D17semidirect
793. C2#14537662direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#105876022
C2×#117632912
C2×#117632882
#145376622
C2×#117629192
C2×#117629182
C2×#117629142
C2×#117629132
C2×C4×#632192
C2×SD16×Dic172
C2×#117628962
C2×#106×D172
C2×#117628092
C2×#117628072
C2×#117627632
C2×C4×SD16×C172
C2×#295217