Finite Group Databasebeta

← C2×#14537600 #17898395

Subgroups — C2×#14537600 #17898395

Order 4352.

2810 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587604C211yesmaximal, characteristic
2C2×C4×#63256C211yesmaximal, characteristic
3C2×C4×Q8×D17C211yesmaximal, characteristic, complemented
4#14537600C2116yesmaximal, direct product factor
5C2×#11762914C211yesmaximal, characteristic, complemented
6C2×#11762911C211yesmaximal, characteristic, complemented
7C2×#11762907C211yesmaximal, characteristic, complemented
8C2×Q16×Dic17C211yesmaximal, characteristic, complemented
9C2×#11762901C211yesmaximal, characteristic, complemented
10C2×#11762896C211yesmaximal, characteristic, complemented
11C2×#11762894C211yesmaximal, characteristic, complemented
12C2×#11762848C211yesmaximal, characteristic, complemented
13C2×#11762809C211yesmaximal, characteristic
14C2×#11762816C211yesmaximal, characteristic, complemented
15C2×#11762761C211yesmaximal, characteristic, complemented
16C2×C17×#441C211yesmaximal, characteristic, complemented
17C22×#63256C2211yescharacteristic
18C22×Q8×D17C2211yescharacteristic
19C2×#10587604C4116yescomplemented
20C2×#10587604C2218yes—
21C22×#63231C2211yescharacteristic
22C22×#63219C2211yescharacteristic
23C22×#63230C2211yescharacteristic
24C22×#63218C2211yescharacteristic
25C22×#63218C2211yescharacteristic
26C4×#63256—24no—
27C4×#63256C2218yes—
28C2×Q8×Dic17C2211yescharacteristic
29C2×Q8×Dic17C2211yescharacteristic
30C2×C4×Dic34—21no—
31C2×C4×Dic34C2211yescharacteristic
32C2×#10587573—21no—
33C2×#10587573C2211yescharacteristic
34C4×Q8×D17—24no—
35C4×Q8×D17C2218yescomplemented
36C2×C4×D68—21no—
37C2×C4×D68C2211yescharacteristic
38C2×#10587579—21no—
39C2×#10587579C2211yescharacteristic
40C2×#10587578—21no—
41C2×#10587578C2211yescharacteristic
42C2×C4⋊C4×D17—21no—
43C2×C4⋊C4×D17C2211yescharacteristic
44C2×C42×D17—21no—
45C2×C42×D17—21no—
46C2×C42×D17C2211yescharacteristic
47#11762914C2218yescomplemented
48#11762911C2218yescomplemented
49#11762907C2218yescomplemented
50Q16×Dic17C2218yescomplemented
51#11762901C2218yescomplemented
52#11762896C2218yescomplemented
53#11762894C2218yescomplemented
54#11762848C2218yescomplemented
55C2×#10587489C2211yescharacteristic
56C2×#10587478C2211yescharacteristic
57C2×#10587479C2211yescharacteristic
58#11762816C2218yescomplemented
59#11762809C2218yes—
60C2×#10587487C2211yescharacteristic
61C2×#10587506C2211yescharacteristic
62C2×#10587506C2211yescharacteristic
63C2×#10587481C2211yescharacteristic
64C2×#10587492C2211yescharacteristic
65C2×#10587480C2211yescharacteristic
66#11762761C2218yescomplemented
67C2×#10587474C2211yescharacteristic
68C2×C8×Dic17C2211yescharacteristic
69C2×C8×Dic17C2211yescharacteristic
70C22×Q16×C17C2211yescharacteristic
71C2×C4×Q8×C17C2211yescharacteristic
72C2×C4×Q8×C17C2211yescharacteristic
73C17×#441C2218yescomplemented
74C2×C17×#106C2211yescharacteristic
75C2×C17×#103C2211yescharacteristic
76C2×C17×#103C2211yescharacteristic
77C2×C17×#97C2211yescharacteristic
78C22×Q8×C17C2311yescharacteristic
79C22×Q8×C17C2311yescharacteristic
80C2×#63256—22no—
81C2×#63256—24no—
82C2×#63256C2×C418yes—
83C2×#63256C2314yes—
84C2×Q8×D17—22no—
85C2×Q8×D17—24no—
86C2×Q8×D17C2×C418yescomplemented
87C2×Q8×D17C2314yes—
88C22×D68—21no—
89C22×D68C2311yescharacteristic
90C22×C4×D17—21no—
91C22×C4×D17—21no—
92C22×C4×D17—21no—
93C22×C4×D17—21no—
94C22×C4×D17—21no—
95C22×C4×D17D411yescharacteristic
96C22×C4×D17D411yescharacteristic
97C22×C4×D17C2311yescharacteristic
98C22×Dic34—21no—
99C22×Dic34C2311yescharacteristic
100C2×Q16×C17C2×C418yescomplemented
101C2×Q16×C17C2314yes—
102C22×C8×C17C2311yescharacteristic
103C22×C8×C17C2311yescharacteristic
104C4×Q8×C17—22no—
105C4×Q8×C17—22no—
106C4×Q8×C17C2314yes—
107C4×Q8×C17C2314yes—
108C2×C4⋊C4×C17—21no—
109C2×C4⋊C4×C17—21no—
110C2×C4⋊C4×C17C2311yescharacteristic
111C2×C4⋊C4×C17C2311yescharacteristic
112C2×C42×C17—21no—
113C2×C42×C17—21no—
114C2×C42×C17C2311yescharacteristic
115Q8×Dic17—22no—
116Q8×Dic17—22no—
117Q8×Dic17C2314yes—
118Q8×Dic17C2314yes—
119C2×#63231C2×C418yescomplemented
120C2×#63231C2314yes—
121C2×#63230C2×C418yescomplemented
122C2×#63230C2314yes—
123C2×#63227—21no—
124C2×#63227—21no—
125C2×#63227—21no—
126C2×C4⋊Dic17—21no—
127C2×C4⋊Dic17—21no—
128C2×C4⋊Dic17C2311yescharacteristic
129C2×C4⋊Dic17C2311yescharacteristic
130C2×#63225—21no—
131C2×#63225—21no—
132C2×#63225—21no—
133C2×C4×Dic17—21no—
134C2×C4×Dic17—21no—
135C2×C4×Dic17—21no—
136C2×C4×Dic17—21no—
137C2×C4×Dic17—21no—
138C2×C4×Dic17D411yescharacteristic
139C2×C4×Dic17D411yescharacteristic
140C2×C4×Dic17C2311yescharacteristic
141C22×#3622C2311yescharacteristic
142C22×#3622C2311yescharacteristic
143#10587604C2×C4164yescomplemented
144C2×#63219C2×C418yescomplemented
145C2×#63219C2314yes—
146C2×#63218—24no—
147C2×#63218C2×C418yescomplemented
148C2×#63218C2314yes—
149C2×#63218C2314yes—
150#10587579—22no—
151#10587579—28no—
152#10587579C2314yes—
153#10587578—28no—
154#10587578—22no—
155#10587578C2314yes—
156C4⋊C4×D17—28no—
157C4⋊C4×D17—22no—
158C4⋊C4×D17C2314yes—
159#10587573—22no—
160#10587573—28no—
161#10587573C2314yes—
162C4×D68—28no—
163C4×D68—22no—
164C4×D68C2314yes—
165C42×D17—28no—
166C42×D17—28no—
167C42×D17D414yes—
168C42×D17C2314yes—
169C4×Dic34—28no—
170C4×Dic34—22no—
171C4×Dic34C2314yes—
172C17×#106C2314yes—
173C17×#103C2314yes—
174C17×#103C2314yes—
175C17×#97C2314yes—
176#10587506C2314yes—
177#10587506C2314yes—
178#10587492C2314yes—
179#10587489C2314yes—
180#10587487C2314yes—
181C8×Dic17C2314yes—
182C8×Dic17C2314yes—
183#10587481C2314yes—
184#10587480C2314yes—
185#10587479C2314yes—
186#10587478C2314yes—
187#10587474C2314yes—
188C23×D17—21no—
189C23×D17C2×D411yescharacteristic
190C2×Q8×C17—21no—
191C2×Q8×C17—21no—
192C2×Q8×C17—22no—
193C2×Q8×C17—22no—
194C2×Q8×C17C22×C414yes—
195C2×Q8×C17C22×C414yes—
196C2×Q8×C17C2412yes—
197C2×Q8×C17C2412yes—
198C22×C4×C17—21no—
199C22×C4×C17—21no—
200C22×C4×C17—21no—
201C22×C4×C17—21no—
202C22×C4×C17C2×D411yescharacteristic
203C22×C4×C17C2×D411yescharacteristic
204C22×C4×C17C2411yescharacteristic
205C22×Dic17—21no—
206C22×Dic17—21no—
207C22×Dic17—21no—
208C22×Dic17C2×D411yescharacteristic
209C22×Dic17C2×D411yescharacteristic
210C22×Dic17C2×D411yescharacteristic
211#63256—216no—
212#63256—28no—
213#63256C22×C4116yes—
214Q8×D17—216no—
215Q8×D17—28no—
216Q8×D17C22×C4116yescomplemented
217C2×D68—28no—
218C2×D68—24no—
219C2×D68—21no—
220C2×D68—22no—
221C2×D68C22×C414yes—
222C2×D68C2412yes—
223C2×C4×D17—28no—
224C2×C4×D17—24no—
225C2×C4×D17—28no—
226C2×C4×D17—24no—
227C2×C4×D17—24no—
228C2×C4×D17—24no—
229C2×C4×D17—24no—
230C2×C4×D17—24no—
231C2×C4×D17—42no—
232C2×C4×D17—44no—
233C2×C4×D17—44no—
234C2×C4×D17—44no—
235C2×C4×D17C22×C414yes—
236C2×C4×D17C2×D414yes—
237C2×C4×D17C2×D414yes—
238C2×C4×D17C2×D412yes—
239C2×C4×D17#4114yes—
240C2×C4×D17C2412yes—
241C2×Dic34—21no—
242C2×Dic34—22no—
243C2×Dic34—28no—
244C2×Dic34—24no—
245C2×Dic34C22×C414yes—
246C2×Dic34C2412yes—
247Q16×C17C22×C4116yescomplemented
248C2×C8×C17—22no—
249C2×C8×C17C22×C414yes—
250C2×C8×C17C2412yes—
251C2×C8×C17C2412yes—
252C4⋊C4×C17—24no—
253C4⋊C4×C17—21no—
254C4⋊C4×C17—24no—
255C4⋊C4×C17—21no—
256C4⋊C4×C17C2412yes—
257C4⋊C4×C17C2412yes—
258C42×C17—24no—
259C42×C17—24no—
260C42×C17C2×D412yes—
261C42×C17C2412yes—
262#63231C22×C4116yescomplemented
263#63230C22×C4116yescomplemented
264#63227—24no—
265#63227—24no—
266#63227—24no—
267C4⋊Dic17—21no—
268C4⋊Dic17—21no—
269C4⋊Dic17—24no—
270C4⋊Dic17—24no—
271C4⋊Dic17C2412yes—
272C4⋊Dic17C2412yes—
273#63225—24no—
274#63225—24no—
275#63225—24no—
276C4×Dic17—24no—
277C4×Dic17—24no—
278C4×Dic17—24no—
279C4×Dic17—24no—
280C4×Dic17—24no—
281C4×Dic17C2×D414yes—
282C4×Dic17C2×D414yes—
283C4×Dic17C2×D412yes—
284C4×Dic17C2412yes—
285C2×#3622—22no—
286C2×#3622C22×C414yes—
287C2×#3622C2412yes—
288C2×#3622C2412yes—
289#63219C22×C4116yescomplemented
290#63218—28no—
291#63218C22×C4116yescomplemented
292C2×C4×#137—171nomaximal, Sylow
293C23×C17C22×D411yescharacteristic
294C22×D17—22no—
295C22×D17—22no—
296C22×D17—24no—
297C22×D17—22no—
298C22×D17—42no—
299C22×D17—42no—
300C22×D17C4×D414yes—
301C22×D17C22×D412yes—
302Q8×C17—24no—
303Q8×C17—24no—
304Q8×C17—22no—
305Q8×C17—22no—
306Q8×C17C23×C414yes—
307Q8×C17C23×C414yes—
308C2×C4×C17—24no—
309C2×C4×C17—24no—
310C2×C4×C17—22no—
311C2×C4×C17—22no—
312C2×C4×C17—22no—
313C2×C4×C17—22no—
314C2×C4×C17—22no—
315C2×C4×C17—22no—
316C2×C4×C17—42no—
317C2×C4×C17—42no—
318C2×C4×C17C23×C412yes—
319C2×C4×C17C22×D412yes—
320C2×C4×C17C22×D412yes—
321C2×C4×C17C22×D411yescharacteristic
322C2×C4×C17C2×#4112yes—
323C2×C4×C17C2511yescharacteristic
324C2×Dic17—24no—
325C2×Dic17—22no—
326C2×Dic17—22no—
327C2×Dic17—22no—
328C2×Dic17—22no—
329C2×Dic17—42no—
330C2×Dic17—42no—
331C2×Dic17C4×D414yes—
332C2×Dic17#13714yescomplemented
333C2×Dic17C22×D412yes—
334C2×Dic17C22×D412yes—
335C2×Dic17C22×D412yes—
336D68—216no—
337D68—24no—
338D68—22no—
339D68C23×C414yes—
340C4×D17—216no—
341C4×D17—216no—
342C4×D17—28no—
343C4×D17—44no—
344C4×D17—48no—
345C4×D17—48no—
346C4×D17—48no—
347C4×D17C4×D418yes—
348C4×D17C23×C414yes—
349C4×D17C2×#4114yes—
350Dic34—24no—
351Dic34—22no—
352Dic34—216no—
353Dic34C23×C414yes—
354C8×C17—22no—
355C8×C17C23×C414yes—
356#3622—22no—
357#3622C23×C414yes—
358C22×#137—171no—
359C2×C4×#41—171no—
360C22×C4×Q8—171no—
361C4×#137—1716no—
362C2×#441—171no—
363C2×#441D1711yescharacteristic, complemented
364C2×#440—171no—
365C2×#440—171no—
366C2×C4×Q16—171no—
367C2×C4×Q16—171no—
368C2×C4×SD16—171no—
369C2×C4×SD16—171no—
370C2×#428—171no—
371C2×#417—171no—
372C2×#419—171no—
373C2×C4×M16—171no—
374C22×C17C2×C4×D412yes—
375C22×C17C2×#13712yes—
376C22×C17#57512yes—
377C22×C17C23×D411yescharacteristic
378C2×D17—28no—
379C2×D17—22no—
380C2×D17—22no—
381C2×D17—24no—
382C2×D17—48no—
383C2×D17—42no—
384C2×D17—42no—
385C2×D17C2×C4×D414yes—
386C4×C17—24no—
387C4×C17—24no—
388C4×C17—22no—
389C4×C17—22no—
390C4×C17—42no—
391C4×C17—42no—
392C4×C17C2×C4×D412yes—
393C4×C17C24×C411yescharacteristic
394C4×C17C22×#4111yescharacteristic
395Dic17—24no—
396Dic17—22no—
397Dic17—42no—
398Dic17—42no—
399Dic17C2×C4×D414yes—
400Dic17C2×#13714yescomplemented
401C22×#41—171no—
402C23×Q8—171no—
403C2×#137—1716no—
404C2×#137—178no—
405C22×Q16—171no—
406C22×Q16C2×D1711yescharacteristic
407C22×SD16—171no—
408C22×SD16—171no—
409C22×M16—171no—
410C22×M16—171no—
411C4×#41—178no—
412C4×#41—344no—
413C2×C4×Q8—171no—
414C2×C4×Q8—171no—
415C2×C4×Q8—178no—
416C2×C4×Q8—171no—
417C2×C4×Q8—171no—
418C2×C4×Q8—341no—
419C2×C4×Q8—341no—
420C2×C4×Q8—344no—
421C2×C4×Q8C2×D1711yescharacteristic
422C2×C4×Q8C2×D1711yescharacteristic
423C2×C4×D4—171no—
424C2×C4×D4—171no—
425C2×C4×D4—341no—
426C2×C4×D4—341no—
427C2×#117—171no—
428C2×#117—341no—
429C22×C4⋊C4—171no—
430C22×C4⋊C4—341no—
431C22×C42—171no—
432C22×C42—341no—
433C22×C42—341no—
434#441—178no—
435#441C2×D1718yescomplemented
436#440—178no—
437#440—178no—
438C4×Q16—178no—
439C4×Q16—178no—
440C4×SD16—178no—
441C4×SD16—178no—
442#428—178no—
443C2×#107—171no—
444C2×#107—171no—
445C2×#106—171no—
446C2×#106C2×D1711yescharacteristic
447#419—178no—
448#417—178no—
449C2×#103—171no—
450C2×#103—171no—
451C2×#103—171no—
452C2×#103—171no—
453C2×#103C2×D1711yescharacteristic
454C2×#103C2×D1711yescharacteristic
455C2×#102—171no—
456C2×#102—171no—
457C4×M16—178no—
458C2×#97—171no—
459C2×#97C2×D1711yescharacteristic
460C2×C4×C8—171no—
461C2×C4×C8—171no—
462C2×C17C4×#13714yescomplemented
463C2×C17C22×C4×D411yescharacteristic
464C2×C17C22×#13711yescharacteristic
465C2×C17C2×#57511yescharacteristic
466D17—24no—
467D17—44no—
468C2×#41—178no—
469C2×#41—174no—
470C2×#41—342no—
471C2×#41—344no—
472C22×Q8—178no—
473C22×Q8—174no—
474C22×Q8—171no—
475C22×Q8—341no—
476C22×Q8—342no—
477C22×Q8—344no—
478C22×Q8C22×D1711yescharacteristic
479C22×Q8C22×D1711yescharacteristic
480C22×D4—171no—
481C22×D4—341no—
482C23×C4—171no—
483C23×C4—171no—
484C23×C4—171no—
485C23×C4—341no—
486C23×C4—341no—
487C23×C4—341no—
488C23×C4—341no—
489C23×C4—341no—
490#137—1764no—
491C2×Q16—178no—
492C2×Q16—174no—
493C2×Q16C4×D1718yescomplemented
494C2×Q16C22×D1714yes—
495C2×SD16—178no—
496C2×SD16—174no—
497C2×SD16—178no—
498C2×SD16—174no—
499C2×M16—178no—
500C2×M16—174no—
501C2×M16—174no—
502C2×M16—344no—
503C22×C8—171no—
504C22×C8—171no—
505C22×C8C22×D1711yescharacteristic
506C22×C8C22×D1711yescharacteristic
507C4×Q8—22no—
508C4×Q8—22no—
509C4×Q8—174no—
510C4×Q8—174no—
511C4×Q8—174no—
512C4×Q8—174no—
513C4×Q8—348no—
514C4×Q8—348no—
515C4×Q8—342no—
516C4×Q8—342no—
517C4×Q8—342no—
518C4×Q8—342no—
519C4×Q8C22×D1714yes—
520C4×Q8C22×D1714yes—
521C4×D4—174no—
522C4×D4—174no—
523C4×D4—348no—
524C4×D4—342no—
525C4×D4—348no—
526C4×D4—342no—
527#117—174no—
528#117—348no—
529#117—342no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—171no—
533C2×C4⋊C4—171no—
534C2×C4⋊C4—174no—
535C2×C4⋊C4—342no—
536C2×C4⋊C4—348no—
537C2×C4⋊C4—341no—
538C2×C4⋊C4—341no—
539C2×C4⋊C4—341no—
540C2×C4⋊C4—341no—
541C2×C4⋊C4—341no—
542C2×C4⋊C4C22×D1711yescharacteristic
543C2×C4⋊C4C22×D1711yescharacteristic
544C2×C22⋊C4—341no—
545C2×C22⋊C4—341no—
546C2×C22⋊C4—341no—
547C2×C42—21no—
548C2×C42—21no—
549C2×C42—171no—
550C2×C42—171no—
551C2×C42—171no—
552C2×C42—174no—
553C2×C42—174no—
554C2×C42—348no—
555C2×C42—348no—
556C2×C42—341no—
557C2×C42—341no—
558C2×C42—341no—
559C2×C42—341no—
560C2×C42—341no—
561C2×C42C22×D1711yescharacteristic
562#107—174no—
563#107—174no—
564#106—174no—
565#106C22×D1714yes—
566#103—174no—
567#103—174no—
568#103—174no—
569#103—174no—
570#103C22×D1714yes—
571#103C22×D1714yes—
572#102—174no—
573#102—174no—
574#97—174no—
575#97C22×D1714yes—
576C4×C8—174no—
577C4×C8—174no—
578C17C2×C4×#13711yescharacteristic, complemented, Sylow
579C24—171no—
580C24—341no—
581#41—1716no—
582#41—3416no—
583#41—348no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—22no—
587C2×Q8—22no—
588C2×Q8—1716no—
589C2×Q8—174no—
590C2×Q8—172no—
591C2×Q8—344no—
592C2×Q8—348no—
593C2×Q8—3416no—
594C2×Q8—348no—
595C2×Q8—341no—
596C2×Q8—342no—
597C2×Q8C2×C4×D1714yes—
598C2×Q8C2×C4×D1714yes—
599C2×Q8C23×D1712yes—
600C2×Q8C23×D1712yes—
601C2×D4—174no—
602C2×D4—172no—
603C2×D4—344no—
604C2×D4—348no—
605C2×D4—341no—
606C2×D4—342no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—171no—
612C22×C4—171no—
613C22×C4—174no—
614C22×C4—172no—
615C22×C4—174no—
616C22×C4—172no—
617C22×C4—171no—
618C22×C4—174no—
619C22×C4—174no—
620C22×C4—344no—
621C22×C4—344no—
622C22×C4—348no—
623C22×C4—344no—
624C22×C4—344no—
625C22×C4—348no—
626C22×C4—344no—
627C22×C4—341no—
628C22×C4—341no—
629C22×C4—341no—
630C22×C4—344no—
631C22×C4—682no—
632C22×C4—684no—
633C22×C4—684no—
634C22×C4—684no—
635C22×C4D4×D1711yescharacteristic
636C22×C4D4×D1711yescharacteristic
637C22×C4C23×D1711yescharacteristic
638Q16—1716no—
639Q16C2×C4×D17116yescomplemented
640SD16—1716no—
641SD16—1716no—
642M16—1716no—
643M16—348no—
644C2×C8—22no—
645C2×C8—174no—
646C2×C8—172no—
647C2×C8—172no—
648C2×C8—342no—
649C2×C8C2×C4×D1714yes—
650C2×C8C23×D1712yes—
651C2×C8C23×D1712yes—
652C4⋊C4—24no—
653C4⋊C4—24no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—172no—
657C4⋊C4—172no—
658C4⋊C4—344no—
659C4⋊C4—344no—
660C4⋊C4—344no—
661C4⋊C4—344no—
662C4⋊C4—341no—
663C4⋊C4—341no—
664C4⋊C4—344no—
665C4⋊C4C23×D1712yes—
666C4⋊C4C23×D1712yes—
667C22⋊C4—344no—
668C22⋊C4—344no—
669C22⋊C4—344no—
670C42—24no—
671C42—24no—
672C42—174no—
673C42—174no—
674C42—172no—
675C42—172no—
676C42—344no—
677C42—344no—
678C42—344no—
679C42—344no—
680C42—344no—
681C42D4×D1712yes—
682C42C23×D1712yes—
683C23—174no—
684C23—172no—
685C23—342no—
686C23—342no—
687C23—344no—
688C23—342no—
689C23—682no—
690C23—682no—
691C23C2×D4×D1711yescharacteristic
692Q8—24no—
693Q8—24no—
694Q8—22no—
695Q8—22no—
696Q8—174no—
697Q8—3416no—
698Q8—344no—
699Q8—342no—
700Q8C22×C4×D1714yes—
701Q8C22×C4×D1714yes—
702D4—174no—
703D4—3416no—
704D4—344no—
705D4—342no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—174no—
717C2×C4—174no—
718C2×C4—172no—
719C2×C4—172no—
720C2×C4—178no—
721C2×C4—174no—
722C2×C4—174no—
723C2×C4—172no—
724C2×C4—348no—
725C2×C4—3416no—
726C2×C4—3416no—
727C2×C4—344no—
728C2×C4—342no—
729C2×C4—342no—
730C2×C4—342no—
731C2×C4—342no—
732C2×C4—684no—
733C2×C4—688no—
734C2×C4—688no—
735C2×C4—688no—
736C2×C4—682no—
737C2×C4—682no—
738C2×C4C22×C4×D1712yes—
739C2×C4C2×D4×D1712yes—
740C2×C4C2×D4×D1712yes—
741C2×C4C2×D4×D1711yescharacteristic
742C2×C4#41×D1712yes—
743C2×C4C24×D1711yescharacteristic
744C8—22no—
745C8—174no—
746C8—342no—
747C8C22×C4×D1714yes—
748C22—174no—
749C22—348no—
750C22—342no—
751C22—342no—
752C22—344no—
753C22—688no—
754C22—682no—
755C22—682no—
756C22C4×D4×D1712yes—
757C22#137×D1712yes—
758C22#1176360812yes—
759C22C22×D4×D1711yescharacteristic
760C4—24no—
761C4—24no—
762C4—22no—
763C4—22no—
764C4—42no—
765C4—42no—
766C4—174no—
767C4—174no—
768C4—344no—
769C4—342no—
770C4—682no—
771C4—682no—
772C4C4×D4×D1712yes—
773C4C23×C4×D1711yescharacteristic
774C4C2×#41×D1711yescharacteristic
775C2—344no—
776C2—684no—
777C2#1453760014yesdirect product factor
778C2C2×C4×D4×D1711yescharacteristic
779C2C2×#137×D1711yescharacteristic
780C2C2×#1176360811yescharacteristic
subgroupG/H
centerC23C2×D4×D17
commutatorC4×C17C24×C4
FrattiniC2×C4C24×D17
FittingC2×C17×#441C2
socleC23×C17C22×D4
prime radicalC22×#63256C22
cosocleC2×C4×C17C25
hypercenterC2×#441D17
hypocenterC17C2×C4×#137
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#441

Complements

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

NH ≅ G/Ntype
3. C2×C4×Q8×D17C2semidirect
4. #14537600C2direct (N × H)
5. C2×#11762914C2semidirect
6. C2×#11762911C2semidirect
7. C2×#11762907C2semidirect
8. C2×Q16×Dic17C2semidirect
9. C2×#11762901C2semidirect
10. C2×#11762896C2semidirect
11. C2×#11762894C2semidirect
12. C2×#11762848C2semidirect
14. C2×#11762816C2semidirect
15. C2×#11762761C2semidirect
16. C2×C17×#441C2semidirect
19. C2×#10587604C4semidirect
35. C4×Q8×D17C22semidirect
47. #11762914C22semidirect
48. #11762911C22semidirect
49. #11762907C22semidirect
50. Q16×Dic17C22semidirect
51. #11762901C22semidirect
52. #11762896C22semidirect
53. #11762894C22semidirect
54. #11762848C22semidirect
58. #11762816C22semidirect
66. #11762761C22semidirect
73. C17×#441C22semidirect
86. C2×Q8×D17C2×C4semidirect
100. C2×Q16×C17C2×C4semidirect
119. C2×#63231C2×C4semidirect
121. C2×#63230C2×C4semidirect
143. #10587604C2×C4semidirect
144. C2×#63219C2×C4semidirect
147. C2×#63218C2×C4semidirect
216. Q8×D17C22×C4semidirect
247. Q16×C17C22×C4semidirect
262. #63231C22×C4semidirect
263. #63230C22×C4semidirect
289. #63219C22×C4semidirect
291. #63218C22×C4semidirect
332. C2×Dic17#137semidirect
363. C2×#441D17semidirect
400. Dic17C2×#137semidirect
435. #441C2×D17semidirect
462. C2×C17C4×#137semidirect
493. C2×Q16C4×D17semidirect
578. C17C2×C4×#137semidirect
639. Q16C2×C4×D17semidirect
777. C2#14537600direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#105876042
C2×C4×#632562
C2×C4×Q8×D172
#145376002
C2×#117629142
C2×#117629112
C2×#117629072
C2×Q16×Dic172
C2×#117629012
C2×#117628962
C2×#117628942
C2×#117628482
C2×#117628092
C2×#117628162
C2×#117627612
C2×C17×#4412
C2×C4×#13717