Finite Group Databasebeta

← C2×#14541537 #17914073

Subgroups — C2×#14541537 #17914073

Order 4352.

1950 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×#11763544C211yesmaximal, characteristic, complemented
2#14541537C2116yesmaximal, direct product factor
3C2×#11763175C211yesmaximal, characteristic, complemented
4C2×#11763171C211yesmaximal, characteristic, complemented
5C2×#11763166C211yesmaximal, characteristic, complemented
6C2×#11763113C211yesmaximal, characteristic, complemented
7C2×#11763106C211yesmaximal, characteristic, complemented
8C2×#11763086C211yesmaximal, characteristic, complemented
9C2×#11763024C211yesmaximal, characteristic, complemented
10C2×#11763024C211yesmaximal, characteristic, complemented
11C2×#11763004C211yesmaximal, characteristic
12C2×#11762940C211yesmaximal, characteristic, complemented
13C2×#11762919C211yesmaximal, characteristic, complemented
14C2×#11762909C211yesmaximal, characteristic, complemented
15C2×C4×#63228C211yesmaximal, characteristic, complemented
16C2×C17×#554C211yesmaximal, characteristic, complemented
17C22×#63229C2211yescharacteristic
18C22×#63228C2211yescharacteristic
19C22×#63228C2211yescharacteristic
20#11763544—24no—
21#11763544C2218yescomplemented
22C2×#10587560C2211yescharacteristic
23C2×#10587633—21no—
24C2×#10587561C2211yescharacteristic
25C2×#10587561C2211yescharacteristic
26C2×#10587580—21no—
27C2×#10587580—21no—
28C2×C4×Dic34C2211yescharacteristic
29C2×C4×D68C2211yescharacteristic
30C2×C4×D68C2211yescharacteristic
31C2×#10587579—21no—
32#11763175C2218yescomplemented
33#11763171C2218yescomplemented
34#11763166C2218yescomplemented
35#11763113C2218yescomplemented
36#11763106C2218yescomplemented
37#11763086C2218yescomplemented
38#11763024C2218yescomplemented
39#11763024C2218yescomplemented
40#11763004C2218yes—
41#11762940C2218yescomplemented
42#11762919C2218yescomplemented
43#11762909C2218yescomplemented
44C4×#63228C2218yescomplemented
45C2×#10587478C2211yescharacteristic
46C2×#10587478C2211yescharacteristic
47C2×#10587479C2211yescharacteristic
48C2×C4⋊#3622C2211yescharacteristic
49C2×C4⋊#3622C2211yescharacteristic
50C2×C4⋊#3622C2211yescharacteristic
51C2×#10587481C2211yescharacteristic
52C2×#10587481C2211yescharacteristic
53C2×#10587481C2211yescharacteristic
54C2×#10587503C2211yescharacteristic
55C2×#10587480C2211yescharacteristic
56C2×#10587480C2211yescharacteristic
57C2×#10587480C2211yescharacteristic
58C2×#10587480C2211yescharacteristic
59C2×#10587480C2211yescharacteristic
60C2×#10587480C2211yescharacteristic
61C2×#10587474C2211yescharacteristic
62C2×#10587474C2211yescharacteristic
63C2×C4×#3622C2211yescharacteristic
64C17×#554—24no—
65C17×#554C2218yescomplemented
66C2×C17×C4⋊Q8C2211yescharacteristic
67C2×C17×#125C2211yescharacteristic
68C2×C17×#125C2211yescharacteristic
69C2×C17×C22⋊Q8—21no—
70C2×C17×C22⋊Q8—21no—
71C2×C17×C22⋊Q8—21no—
72C2×C4×Q8×C17C2211yescharacteristic
73C2×C4×D4×C17C2211yescharacteristic
74C2×C4×D4×C17C2211yescharacteristic
75C2×C4×D4×C17C2211yescharacteristic
76C22×C4⋊C4×C17—21no—
77C22×Q8×C17—21no—
78C22×Q8×C17D411yescharacteristic
79C22×D4×C17C2311yescharacteristic
80C23×C4×C17—21no—
81C23×C4×C17—21no—
82C23×C4×C17—21no—
83C22×D68—21no—
84C22×D68—21no—
85C22×D68C2311yescharacteristic
86C22×D68C2311yescharacteristic
87C22×C4×D17—21no—
88C22×C4×D17—21no—
89C22×Dic34C2311yescharacteristic
90C17×C4⋊Q8—22no—
91C17×C4⋊Q8C2314yes—
92C17×#125—22no—
93C17×#125—22no—
94C17×#125C2314yes—
95C17×#125C2314yes—
96C17×C22⋊Q8—28no—
97C17×C22⋊Q8—28no—
98C17×C22⋊Q8—28no—
99C4×Q8×C17D414yes—
100C4×Q8×C17C2314yes—
101C4×D4×C17—22no—
102C4×D4×C17—22no—
103C4×D4×C17—22no—
104C4×D4×C17C2314yes—
105C4×D4×C17C2314yes—
106C4×D4×C17C2314yes—
107C2×C4⋊C4×C17—21no—
108C2×C4⋊C4×C17—21no—
109C2×C4⋊C4×C17—21no—
110C2×C4⋊C4×C17—21no—
111C2×C4⋊C4×C17—21no—
112C2×C4⋊C4×C17—28no—
113C2×C4⋊C4×C17D411yescharacteristic
114C2×C4⋊C4×C17D411yescharacteristic
115C2×C4⋊C4×C17D411yescharacteristic
116C2×C4⋊C4×C17C2311yescharacteristic
117C2×C4⋊C4×C17C2311yescharacteristic
118C2×C4⋊C4×C17C2311yescharacteristic
119C2×C22⋊C4×C17—21no—
120C2×C22⋊C4×C17—21no—
121C2×C22⋊C4×C17—21no—
122C2×C42×C17C2311yescharacteristic
123C2×C42×C17C2311yescharacteristic
124C2×C42×C17C2311yescharacteristic
125#10587633—28no—
126C2×#63229—24no—
127C2×#63229C2314yes—
128C2×#63228—24no—
129C2×#63228—24no—
130C2×#63228C2314yes—
131C2×#63228C2314yes—
132C2×#63227—21no—
133C2×#63227—21no—
134C2×#63227—21no—
135C2×#63227—21no—
136C2×#63227—21no—
137C2×#63227—21no—
138C2×C4⋊Dic17C2311yescharacteristic
139C2×#63225—21no—
140C2×C4×Dic17—21no—
141C22×#3622C2311yescharacteristic
142C22×#3622C2311yescharacteristic
143C22×#3622C2311yescharacteristic
144C22×#3622C2311yescharacteristic
145#10587580—28no—
146#10587580—28no—
147#10587579—28no—
148#10587561—22no—
149#10587561—22no—
150#10587561C2314yes—
151#10587561C2314yes—
152#10587560—22no—
153#10587560C2314yes—
154C4×D68—22no—
155C4×D68—22no—
156C4×D68C2314yes—
157C4×D68C2314yes—
158C4×Dic34—22no—
159C4×Dic34C2314yes—
160#10587503C2314yes—
161#10587481C2314yes—
162#10587481C2314yes—
163#10587481C2314yes—
164#10587480C2314yes—
165#10587480C2314yes—
166#10587480C2314yes—
167#10587480C2314yes—
168#10587480C2314yes—
169#10587480C2314yes—
170#10587479C2314yes—
171#10587478C2314yes—
172#10587478C2314yes—
173C4⋊#3622C2314yes—
174C4⋊#3622C2314yes—
175C4⋊#3622C2314yes—
176#10587474C2314yes—
177#10587474C2314yes—
178C4×#3622C2314yes—
179C24×C17—21no—
180C23×D17—21no—
181C23×D17—21no—
182C2×Q8×C17—24no—
183C2×Q8×C17—42no—
184C2×Q8×C17—82no—
185C2×Q8×C17C2×D414yes—
186C2×D4×C17—21no—
187C2×D4×C17—22no—
188C2×D4×C17#4114yes—
189C2×D4×C17C2412yes—
190C22×C4×C17—21no—
191C22×C4×C17—21no—
192C22×C4×C17—21no—
193C22×C4×C17—24no—
194C22×C4×C17—24no—
195C22×C4×C17—24no—
196C22×C4×C17—44no—
197C22×C4×C17—82no—
198C22×C4×C17—82no—
199C22×C4×C17C2×D411yescharacteristic
200C22×C4×C17C2×D411yescharacteristic
201C22×C4×C17C2×D411yescharacteristic
202C22×C4×C17C2×D411yescharacteristic
203C22×C4×C17C2×D411yescharacteristic
204C22×C4×C17C2×D411yescharacteristic
205C22×C4×C17C2411yescharacteristic
206C22×Dic17—21no—
207C22×Dic17—21no—
208C2×D68—22no—
209C2×D68—22no—
210C2×D68—22no—
211C2×D68—22no—
212C2×D68—24no—
213C2×D68—21no—
214C2×D68—21no—
215C2×D68—24no—
216C2×D68—44no—
217C2×D68—82no—
218C2×D68C2412yes—
219C2×D68C2412yes—
220C2×C4×D17—24no—
221C2×C4×D17—24no—
222C2×C4×D17—82no—
223C2×C4×D17—82no—
224C2×Dic34—22no—
225C2×Dic34—22no—
226C2×Dic34—21no—
227C2×Dic34C2412yes—
228C4⋊C4×C17—24no—
229C4⋊C4×C17—24no—
230C4⋊C4×C17—24no—
231C4⋊C4×C17—24no—
232C4⋊C4×C17—24no—
233C4⋊C4×C17—21no—
234C4⋊C4×C17—21no—
235C4⋊C4×C17—21no—
236C4⋊C4×C17C2×D414yes—
237C4⋊C4×C17C2×D414yes—
238C4⋊C4×C17C2×D414yes—
239C4⋊C4×C17C2412yes—
240C4⋊C4×C17C2412yes—
241C4⋊C4×C17C2412yes—
242C22⋊C4×C17—24no—
243C22⋊C4×C17—24no—
244C22⋊C4×C17—24no—
245C42×C17C2×D412yes—
246C42×C17C2×D412yes—
247C42×C17C2×D412yes—
248C42×C17C2412yes—
249C42×C17C2412yes—
250C42×C17C2412yes—
251#63229—28no—
252#63228—28no—
253#63228—28no—
254#63227—24no—
255#63227—24no—
256#63227—24no—
257#63227—24no—
258#63227—24no—
259#63227—24no—
260C4⋊Dic17—21no—
261C4⋊Dic17C2412yes—
262#63225—24no—
263C4×Dic17—24no—
264C2×#3622—22no—
265C2×#3622—22no—
266C2×#3622—22no—
267C2×#3622—22no—
268C2×#3622C2412yes—
269C2×#3622C2412yes—
270C2×#3622C2412yes—
271C2×#3622C2412yes—
272C2×#3370—171nomaximal, Sylow
273C23×C17—24no—
274C23×C17—22no—
275C23×C17—42no—
276C23×C17—42no—
277C23×C17C22×D411yescharacteristic
278C22×D17—22no—
279C22×D17—22no—
280C22×D17—42no—
281C22×D17—42no—
282C22×D17—42no—
283C22×D17—42no—
284C22×D17—42no—
285C22×D17—42no—
286Q8×C17—44no—
287Q8×C17—84no—
288D4×C17—24no—
289D4×C17—22no—
290D4×C17C2×#4114yes—
291C2×C4×C17—22no—
292C2×C4×C17—22no—
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—48no—
301C2×C4×C17—42no—
302C2×C4×C17—42no—
303C2×C4×C17—42no—
304C2×C4×C17—84no—
305C2×C4×C17—84no—
306C2×C4×C17C22×D412yes—
307C2×C4×C17C22×D412yes—
308C2×C4×C17C22×D412yes—
309C2×C4×C17C22×D412yes—
310C2×C4×C17C22×D412yes—
311C2×C4×C17C22×D412yes—
312C2×C4×C17C22×D411yescharacteristic
313C2×C4×C17C2×#4112yes—
314C2×C4×C172−1+412yes—
315C2×C4×C17C2511yescharacteristic
316C2×Dic17—22no—
317C2×Dic17—22no—
318C2×Dic17—42no—
319C2×Dic17—42no—
320D68—22no—
321D68—22no—
322D68—22no—
323D68—22no—
324D68—48no—
325D68—42no—
326D68—42no—
327D68—84no—
328C4×D17—84no—
329C4×D17—84no—
330Dic34—22no—
331Dic34—22no—
332Dic34—42no—
333#3622—22no—
334#3622—22no—
335#3622—22no—
336#3622—22no—
337C2×#559—171no—
338C2×#554D1711yescharacteristic, complemented
339#3370—1716no—
340C2×#490—171no—
341C2×#489—171no—
342C2×#488—171no—
343C2×#479—171no—
344C2×#478—171no—
345C2×#474—171no—
346C2×#463—171no—
347C2×#463—171no—
348C2×#459—171no—
349C2×#446—171no—
350C2×#442—171no—
351C2×#440—171no—
352C2×C4×D8—171no—
353C22×C17—24no—
354C22×C17—48no—
355C22×C17—42no—
356C22×C17—42no—
357C22×C17#54812yes—
358C22×C17#57512yes—
359C22×C17#57612yes—
360C22×C17C23×D411yescharacteristic
361C2×D17—42no—
362C2×D17—42no—
363C2×D17—42no—
364C2×D17—42no—
365C2×D17—42no—
366C2×D17—42no—
367C2×D17—84no—
368C2×D17—84no—
369C4×C17—22no—
370C4×C17—22no—
371C4×C17—22no—
372C4×C17—22no—
373C4×C17—22no—
374C4×C17—22no—
375C4×C17—42no—
376C4×C17—42no—
377C4×C17—42no—
378C4×C17#54812yes—
379C4×C17C22×#4111yescharacteristic
380C4×C17C2×2−1+411yescharacteristic
381Dic17—42no—
382Dic17—42no—
383C22×SD16—171no—
384C22×D8—171no—
385C22×D8—171no—
386#559—178no—
387#559—344no—
388#554—24no—
389#554C2×D1718yescomplemented
390C2×C4⋊Q8C2×D1711yescharacteristic
391C2×#127—171no—
392C2×#125C2×D1711yescharacteristic
393C2×#125C2×D1711yescharacteristic
394C2×#124—171no—
395C2×#124—171no—
396C2×#124—341no—
397C2×#123—341no—
398C2×#123—341no—
399C2×C22⋊Q8—21no—
400C2×C22⋊Q8—21no—
401C2×C22⋊Q8—21no—
402C2×C4×Q8—171no—
403C2×C4×Q8C2×D1711yescharacteristic
404C2×C4×D4—171no—
405C2×C4×D4—171no—
406C2×C4×D4—341no—
407C2×C4×D4C2×D1711yescharacteristic
408C2×C4×D4C2×D1711yescharacteristic
409C2×C4×D4C2×D1711yescharacteristic
410C22×C4⋊C4—21no—
411#490—178no—
412#489—178no—
413#488—178no—
414#479—178no—
415#478—178no—
416#474—178no—
417#463—178no—
418#463—178no—
419#459—178no—
420#446—178no—
421#442—178no—
422#440—178no—
423C4×D8—178no—
424C2×#107—171no—
425C2×#107—171no—
426C2×#106—171no—
427C2×C4⋊C8—171no—
428C2×C4⋊C8—171no—
429C2×C4⋊C8—171no—
430C2×#103—171no—
431C2×#103—171no—
432C2×#103—171no—
433C2×#102—171no—
434C2×#102—171no—
435C2×#102—171no—
436C2×#102—171no—
437C2×#102—171no—
438C2×#102—171no—
439C2×#102—171no—
440C2×#97—171no—
441C2×#97—171no—
442C2×C4×C8—171no—
443C2×C17—44no—
444C2×C17#337014yescomplemented
445C2×C17C2×#54811yescharacteristic
446C2×C17C2×#57511yescharacteristic
447C2×C17C2×#57611yescharacteristic
448D17—82no—
449D17—82no—
450C22×Q8—21no—
451C22×Q8—171no—
452C22×Q8C22⋊D1711yescharacteristic
453C22×D4—171no—
454C22×D4—171no—
455C22×D4—341no—
456C22×D4—341no—
457C22×D4C22×D1711yescharacteristic
458C23×C4—21no—
459C23×C4—21no—
460C23×C4—21no—
461C23×C4—341no—
462C23×C4—341no—
463C2×SD16—174no—
464C2×SD16—344no—
465C2×D8—174no—
466C2×D8—174no—
467C2×D8—344no—
468C2×D8—344no—
469C22×C8—171no—
470C22×C8—171no—
471C22×C8—171no—
472C22×C8—171no—
473C4⋊Q8—22no—
474C4⋊Q8C22×D1714yes—
475#127—174no—
476#127—342no—
477#125—22no—
478#125—22no—
479#125C22×D1714yes—
480#125C22×D1714yes—
481#124—174no—
482#124—174no—
483#124—348no—
484#124—342no—
485#124—342no—
486#123—348no—
487#123—348no—
488C22⋊Q8—28no—
489C22⋊Q8—28no—
490C22⋊Q8—28no—
491C4×Q8—174no—
492C4×Q8—342no—
493C4×Q8C22⋊D1714yes—
494C4×Q8C22×D1714yes—
495C4×D4—22no—
496C4×D4—22no—
497C4×D4—22no—
498C4×D4—174no—
499C4×D4—174no—
500C4×D4—348no—
501C4×D4—342no—
502C4×D4—342no—
503C4×D4C22×D1714yes—
504C4×D4C22×D1714yes—
505C4×D4C22×D1714yes—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—28no—
512C2×C4⋊C4—171no—
513C2×C4⋊C4—341no—
514C2×C4⋊C4C22⋊D1711yescharacteristic
515C2×C4⋊C4C22⋊D1711yescharacteristic
516C2×C4⋊C4C22⋊D1711yescharacteristic
517C2×C4⋊C4C22×D1711yescharacteristic
518C2×C4⋊C4C22×D1711yescharacteristic
519C2×C4⋊C4C22×D1711yescharacteristic
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—341no—
524C2×C22⋊C4—341no—
525C2×C22⋊C4—341no—
526C2×C22⋊C4—341no—
527C2×C22⋊C4—341no—
528C2×C22⋊C4—341no—
529C2×C42—341no—
530C2×C42C22×D1711yescharacteristic
531C2×C42C22×D1711yescharacteristic
532C2×C42C22×D1711yescharacteristic
533#107—174no—
534#107—174no—
535#106—174no—
536C4⋊C8—174no—
537C4⋊C8—174no—
538C4⋊C8—174no—
539#103—174no—
540#103—174no—
541#103—174no—
542#102—174no—
543#102—174no—
544#102—174no—
545#102—174no—
546#102—174no—
547#102—174no—
548#102—174no—
549#97—174no—
550#97—174no—
551C4×C8—174no—
552C17C2×#337011yescharacteristic, complemented, Sylow
553C24—21no—
554C24—341no—
555C24—341no—
556C2×Q8—24no—
557C2×Q8—42no—
558C2×Q8—82no—
559C2×Q8—172no—
560C2×Q8—341no—
561C2×Q8—342no—
562C2×Q8—342no—
563C2×Q8C2×C22⋊D1714yes—
564C2×D4—22no—
565C2×D4—21no—
566C2×D4—172no—
567C2×D4—172no—
568C2×D4—342no—
569C2×D4—342no—
570C2×D4—342no—
571C2×D4—342no—
572C2×D4—344no—
573C2×D4—341no—
574C2×D4—341no—
575C2×D4—344no—
576C2×D4—684no—
577C2×D4—1362no—
578C2×D4#6325614yes—
579C2×D4C23×D1712yes—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—24no—
584C22×C4—24no—
585C22×C4—24no—
586C22×C4—44no—
587C22×C4—82no—
588C22×C4—82no—
589C22×C4—341no—
590C22×C4—341no—
591C22×C4—344no—
592C22×C4—344no—
593C22×C4—1362no—
594C22×C4—1362no—
595C22×C4C2×C22⋊D1711yescharacteristic
596C22×C4C2×C22⋊D1711yescharacteristic
597C22×C4C2×C22⋊D1711yescharacteristic
598C22×C4C2×C22⋊D1711yescharacteristic
599C22×C4C2×C22⋊D1711yescharacteristic
600C22×C4C2×C22⋊D1711yescharacteristic
601C22×C4C23×D1711yescharacteristic
602SD16—348no—
603D8—348no—
604D8—348no—
605C2×C8—172no—
606C2×C8—172no—
607C2×C8—172no—
608C2×C8—172no—
609C2×C8—342no—
610C2×C8—342no—
611C2×C8—342no—
612C2×C8—342no—
613C4⋊C4—24no—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—24no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—172no—
622C4⋊C4—341no—
623C4⋊C4—344no—
624C4⋊C4C2×C22⋊D1714yes—
625C4⋊C4C2×C22⋊D1714yes—
626C4⋊C4C2×C22⋊D1714yes—
627C4⋊C4C23×D1712yes—
628C4⋊C4C23×D1712yes—
629C4⋊C4C23×D1712yes—
630C22⋊C4—24no—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—344no—
634C22⋊C4—344no—
635C22⋊C4—344no—
636C22⋊C4—344no—
637C22⋊C4—344no—
638C22⋊C4—344no—
639C42—344no—
640C42C2×C22⋊D1712yes—
641C42C2×C22⋊D1712yes—
642C42C2×C22⋊D1712yes—
643C42C23×D1712yes—
644C42C23×D1712yes—
645C42C23×D1712yes—
646C23—24no—
647C23—22no—
648C23—42no—
649C23—42no—
650C23—342no—
651C23—342no—
652C23—682no—
653C23—682no—
654C23—682no—
655C23—682no—
656C23—682no—
657C23—682no—
658C23C22×C22⋊D1711yescharacteristic
659Q8—44no—
660Q8—84no—
661Q8—342no—
662Q8—342no—
663Q8—682no—
664D4—24no—
665D4—22no—
666D4—342no—
667D4—342no—
668D4—342no—
669D4—342no—
670D4—688no—
671D4—682no—
672D4—682no—
673D4—1364no—
674D4C2×#6325614yes—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—48no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—84no—
689C2×C4—84no—
690C2×C4—342no—
691C2×C4—342no—
692C2×C4—682no—
693C2×C4—682no—
694C2×C4—1364no—
695C2×C4—1364no—
696C2×C4C2×#6325612yes—
697C2×C4#1058769412yes—
698C2×C4C22×C22⋊D1712yes—
699C2×C4C22×C22⋊D1712yes—
700C2×C4C22×C22⋊D1712yes—
701C2×C4C22×C22⋊D1712yes—
702C2×C4C22×C22⋊D1712yes—
703C2×C4C22×C22⋊D1712yes—
704C2×C4C22×C22⋊D1711yescharacteristic
705C2×C4C24×D1711yescharacteristic
706C8—342no—
707C8—342no—
708C8—342no—
709C8—342no—
710C22—24no—
711C22—42no—
712C22—42no—
713C22—48no—
714C22—682no—
715C22—682no—
716C22—682no—
717C22—682no—
718C22—682no—
719C22—682no—
720C22—1364no—
721C22—1364no—
722C22#1176347012yes—
723C22#1176360712yes—
724C22#1176361212yes—
725C22C23×C22⋊D1711yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—22no—
731C4—22no—
732C4—42no—
733C4—42no—
734C4—42no—
735C4—682no—
736C4—682no—
737C4#1176347012yes—
738C4C22×#6325611yescharacteristic
739C4C2×#1058769411yescharacteristic
740C2—44no—
741C2—1362no—
742C2—1362no—
743C2#1454153714yesdirect product factor
744C2C2×#1176347011yescharacteristic
745C2C2×#1176360711yescharacteristic
746C2C2×#1176361211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#554C2
socleC23×C17C22×D4
prime radicalC2×#11763004C2
hypercenterC2×#554D17
hypocenterC17C2×#3370
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. C2×#11763544C2semidirect
2. #14541537C2direct (N × H)
3. C2×#11763175C2semidirect
4. C2×#11763171C2semidirect
5. C2×#11763166C2semidirect
6. C2×#11763113C2semidirect
7. C2×#11763106C2semidirect
8. C2×#11763086C2semidirect
9. C2×#11763024C2semidirect
10. C2×#11763024C2semidirect
12. C2×#11762940C2semidirect
13. C2×#11762919C2semidirect
14. C2×#11762909C2semidirect
15. C2×C4×#63228C2semidirect
16. C2×C17×#554C2semidirect
21. #11763544C22semidirect
32. #11763175C22semidirect
33. #11763171C22semidirect
34. #11763166C22semidirect
35. #11763113C22semidirect
36. #11763106C22semidirect
37. #11763086C22semidirect
38. #11763024C22semidirect
39. #11763024C22semidirect
41. #11762940C22semidirect
42. #11762919C22semidirect
43. #11762909C22semidirect
44. C4×#63228C22semidirect
65. C17×#554C22semidirect
338. C2×#554D17semidirect
389. #554C2×D17semidirect
444. C2×C17#3370semidirect
552. C17C2×#3370semidirect
743. C2#14541537direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117635442
#145415372
C2×#117631752
C2×#117631712
C2×#117631662
C2×#117631132
C2×#117631062
C2×#117630862
C2×#117630242
C2×#117630042
C2×#117629402
C2×#117629192
C2×#117629092
C2×C4×#632282
C2×C17×#5542
C2×#337017