Finite Group Databasebeta

← C2×#14541363 #17913023

Subgroups — C2×#14541363 #17913023

Order 4352.

2082 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×#11763530C211yesmaximal, characteristic, complemented
2C2×#11763459C211yesmaximal, characteristic
3#14541363C2116yesmaximal, direct product factor
4C2×#11763213C211yesmaximal, characteristic, complemented
5C2×#11763143C211yesmaximal, characteristic, complemented
6C2×#11763142C211yesmaximal, characteristic, complemented
7C2×#11763132C211yesmaximal, characteristic, complemented
8C2×#11763130C211yesmaximal, characteristic, complemented
9C2×#11763092C211yesmaximal, characteristic, complemented
10C2×#11763087C211yesmaximal, characteristic, complemented
11C2×#11763052C211yesmaximal, characteristic, complemented
12C2×SD16×Dic17C211yesmaximal, characteristic, complemented
13C2×#11762885C211yesmaximal, characteristic, complemented
14C2×#11762851C211yesmaximal, characteristic, complemented
15C2×#11762850C211yesmaximal, characteristic, complemented
16C2×C17×#468C211yesmaximal, characteristic, complemented
17C22×#63254—21no—
18C22×#63218C2211yescharacteristic
19#11763530—24no—
20#11763530C2218yescomplemented
21#11763459—24no—
22#11763459C2218yes—
23C2×#10587574C2211yescharacteristic
24C2×#10587574C2211yescharacteristic
25C2×#10587584—21no—
26C2×#10587565—21no—
27C2×#10587571—21no—
28C2×#10587569—21no—
29C2×#10587621—21no—
30C2×#10587564—21no—
31C2×#10587632C2211yescharacteristic
32C2×#10587624C2211yescharacteristic
33C2×Q8×Dic17C2211yescharacteristic
34C2×#10587573—21no—
35C2×D4×Dic17C2211yescharacteristic
36C2×C4×C22⋊D17C2211yescharacteristic
37C2×#10587612C2211yescharacteristic
38C2×#10587578C2211yescharacteristic
39C22×C4⋊Dic17C2211yescharacteristic
40C2×C4⋊C4×D17C2211yescharacteristic
41#11763213C2218yescomplemented
42#11763143C2218yescomplemented
43#11763142C2218yescomplemented
44#11763132C2218yescomplemented
45#11763130C2218yescomplemented
46#11763092C2218yescomplemented
47#11763087C2218yescomplemented
48#11763052C2218yescomplemented
49SD16×Dic17C2218yescomplemented
50#11762885C2218yescomplemented
51#11762851C2218yescomplemented
52#11762850C2218yescomplemented
53C2×#10587489C2211yescharacteristic
54C2×#10587489C2211yescharacteristic
55C2×#10587478C2211yescharacteristic
56C2×#10587478C2211yescharacteristic
57C2×#10587478C2211yescharacteristic
58C2×#10587488C2211yescharacteristic
59C2×#10587488C2211yescharacteristic
60C2×#10587479C2211yescharacteristic
61C2×#10587485C2211yescharacteristic
62C2×#10587506C2211yescharacteristic
63C2×#10587506C2211yescharacteristic
64C2×#10587503C2211yescharacteristic
65C2×#10587503C2211yescharacteristic
66C2×C22⋊#3622C2211yescharacteristic
67C2×#10587491C2211yescharacteristic
68C2×C8×Dic17C2211yescharacteristic
69C22×SD16×C17C2211yescharacteristic
70C22×M16×C17C2211yescharacteristic
71C2×C17×C22⋊Q8C2211yescharacteristic
72C2×C17×#121C2211yescharacteristic
73C17×#468C2218yescomplemented
74C2×C17×#107C2211yescharacteristic
75C2×C17×#103C2211yescharacteristic
76C2×C17×#102C2211yescharacteristic
77C22×Q8×C17C2311yescharacteristic
78C22×D4×C17—21no—
79C22×D4×C17C2311yescharacteristic
80C23×C4×C17C2311yescharacteristic
81C22×C22⋊D17—21no—
82C22×C22⋊D17D411yescharacteristic
83C23×Dic17—21no—
84C23×Dic17—21no—
85C2×#63254—28no—
86C2×#63254—48no—
87C22×C4×D17—21no—
88C22×C4×D17C2311yescharacteristic
89C22×Dic34—21no—
90C22×Dic34—21no—
91C2×SD16×C17—24no—
92C2×SD16×C17C2314yes—
93C2×M16×C17—24no—
94C2×M16×C17C2314yes—
95C22×C8×C17C2311yescharacteristic
96C22×C8×C17C2311yescharacteristic
97C17×C22⋊Q8—22no—
98C17×C22⋊Q8C2314yes—
99C17×#121—22no—
100C17×#121C2314yes—
101C2×C4⋊C4×C17—21no—
102C2×C4⋊C4×C17C2311yescharacteristic
103C2×C4⋊C4×C17C2311yescharacteristic
104C2×C22⋊C4×C17—21no—
105C2×C22⋊C4×C17—21no—
106C2×C22⋊Dic17—21no—
107C2×C22⋊Dic17—21no—
108C2×C22⋊Dic17—21no—
109C2×C22⋊Dic17D411yescharacteristic
110#10587632—22no—
111#10587632C2314yes—
112Q8×Dic17—22no—
113Q8×Dic17C2314yes—
114#10587624—22no—
115#10587624C2314yes—
116#10587621—28no—
117D4×Dic17—22no—
118D4×Dic17C2314yes—
119C4×C22⋊D17D414yes—
120C4×C22⋊D17C2314yes—
121C2×#63227—21no—
122C2×#63227—21no—
123C2×#63227D411yescharacteristic
124#10587612—22no—
125#10587612C2314yes—
126C2×C4⋊Dic17—22no—
127C2×C4⋊Dic17—21no—
128C2×C4⋊Dic17—21no—
129C2×C4⋊Dic17C2314yes—
130C2×C4⋊Dic17C2311yescharacteristic
131C2×C4⋊Dic17C2311yescharacteristic
132C2×C4⋊Dic17C2311yescharacteristic
133C2×C4⋊Dic17C2311yescharacteristic
134C2×#63225—21no—
135C2×#63225—21no—
136C2×#63225—21no—
137C2×#63225—21no—
138C2×#63225D411yescharacteristic
139C2×C4×Dic17—21no—
140C2×C4×Dic17—21no—
141C2×C4×Dic17—21no—
142C2×C4×Dic17C2311yescharacteristic
143C22×#3622C2311yescharacteristic
144C22×#3622C2311yescharacteristic
145C2×#63218—24no—
146C2×#63218C2314yes—
147#10587584—28no—
148#10587578—22no—
149#10587578C2314yes—
150C4⋊C4×D17—22no—
151C4⋊C4×D17C2314yes—
152#10587574—22no—
153#10587574—22no—
154#10587574C2314yes—
155#10587574C2314yes—
156#10587573—28no—
157#10587571—28no—
158#10587569—28no—
159#10587565—28no—
160#10587564—28no—
161C17×#107C2314yes—
162C17×#103C2314yes—
163C17×#102C2314yes—
164#10587506C2314yes—
165#10587506C2314yes—
166#10587503C2314yes—
167#10587503C2314yes—
168C22⋊#3622C2314yes—
169#10587491C2314yes—
170#10587489C2314yes—
171#10587489C2314yes—
172#10587488C2314yes—
173#10587488C2314yes—
174#10587485C2314yes—
175C8×Dic17C2314yes—
176#10587479C2314yes—
177#10587478C2314yes—
178#10587478C2314yes—
179#10587478C2314yes—
180C24×C17—21no—
181C24×C17C2×D411yescharacteristic
182C23×D17C2×D411yescharacteristic
183C2×Q8×C17—21no—
184C2×Q8×C17—22no—
185C2×Q8×C17—22no—
186C2×Q8×C17C2412yes—
187C2×D4×C17—24no—
188C2×D4×C17—21no—
189C2×D4×C17—22no—
190C2×D4×C17—22no—
191C2×D4×C17—44no—
192C2×D4×C17C2412yes—
193C22×C4×C17—22no—
194C22×C4×C17—22no—
195C22×C4×C17—21no—
196C22×C4×C17—21no—
197C22×C4×C17—21no—
198C22×C4×C17C2×D412yes—
199C22×C4×C17C2×D411yescharacteristic
200C22×C4×C17C2412yes—
201C22×C4×C17C2411yescharacteristic
202C2×C22⋊D17—24no—
203C2×C22⋊D17—24no—
204C2×C22⋊D17—44no—
205C2×C22⋊D17C2×D414yes—
206C22×Dic17—21no—
207C22×Dic17—21no—
208C22×Dic17—21no—
209C22×Dic17—24no—
210C22×Dic17—21no—
211C22×Dic17—24no—
212C22×Dic17—44no—
213C22×Dic17—44no—
214C22×Dic17C2×D411yescharacteristic
215C22×Dic17C2×D411yescharacteristic
216C22×Dic17C2×D411yescharacteristic
217#63254—432no—
218C2×C4×D17—22no—
219C2×C4×D17—22no—
220C2×C4×D17—24no—
221C2×C4×D17—44no—
222C2×C4×D17C2×D412yes—
223C2×C4×D17C2412yes—
224C2×Dic34—24no—
225C2×Dic34—24no—
226C2×Dic34—44no—
227C2×Dic34—44no—
228SD16×C17—28no—
229M16×C17—28no—
230C2×C8×C17—22no—
231C2×C8×C17#4114yescomplemented
232C2×C8×C17C2412yes—
233C2×C8×C17C2412yes—
234C4⋊C4×C17—21no—
235C4⋊C4×C17—24no—
236C4⋊C4×C17—21no—
237C4⋊C4×C17C2412yes—
238C4⋊C4×C17C2412yes—
239C22⋊C4×C17—24no—
240C22⋊C4×C17—24no—
241C22⋊Dic17—24no—
242C22⋊Dic17—24no—
243C22⋊Dic17—24no—
244C22⋊Dic17C2×D414yes—
245#63227—24no—
246#63227—24no—
247#63227C2×D414yes—
248C4⋊Dic17—24no—
249C4⋊Dic17—21no—
250C4⋊Dic17—21no—
251C4⋊Dic17—21no—
252C4⋊Dic17—21no—
253C4⋊Dic17—24no—
254C4⋊Dic17C2412yes—
255C4⋊Dic17C2412yes—
256C4⋊Dic17C2412yes—
257C4⋊Dic17C2412yes—
258#63225—24no—
259#63225—24no—
260#63225—24no—
261#63225—24no—
262#63225C2×D414yes—
263C4×Dic17—24no—
264C4×Dic17—24no—
265C4×Dic17—24no—
266C4×Dic17C2×D412yes—
267C4×Dic17C2412yes—
268C2×#3622—22no—
269C2×#3622—22no—
270C2×#3622C2412yes—
271C2×#3622C2412yes—
272#63218—28no—
273C2×#3353—171nomaximal, Sylow
274C23×C17—22no—
275C23×C17—22no—
276C23×C17—22no—
277C23×C17—22no—
278C23×C17—42no—
279C23×C17—42no—
280C23×C17—42no—
281C23×C17C22×D412yes—
282C23×C17C22×D411yescharacteristic
283C22×D17—22no—
284C22×D17—22no—
285C22×D17—22no—
286C22×D17C22×D412yes—
287Q8×C17—22no—
288Q8×C17—22no—
289Q8×C17—42no—
290D4×C17—22no—
291D4×C17—22no—
292D4×C17—48no—
293D4×C17—42no—
294C2×C4×C17—22no—
295C2×C4×C17—24no—
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—42no—
303C2×C4×C17—42no—
304C2×C4×C17C22×D412yes—
305C2×C4×C17C22×D411yescharacteristic
306C2×C4×C17C2×#4112yes—
307C2×C4×C172−1+412yes—
308C2×C4×C17C2511yescharacteristic
309C22⋊D17—28no—
310C22⋊D17—48no—
311C2×Dic17—22no—
312C2×Dic17—22no—
313C2×Dic17—22no—
314C2×Dic17—22no—
315C2×Dic17—22no—
316C2×Dic17—22no—
317C2×Dic17—48no—
318C2×Dic17—42no—
319C2×Dic17—42no—
320C2×Dic17—42no—
321C2×Dic17—42no—
322C2×Dic17—48no—
323C2×Dic17AGL(1,ℤ/8)14yes—
324C2×Dic17C22×D412yes—
325C2×Dic17C22×D412yes—
326C2×Dic17C22×D412yes—
327C4×D17—24no—
328C4×D17—22no—
329C4×D17—22no—
330C4×D17—48no—
331Dic34—48no—
332Dic34—48no—
333C8×C17—22no—
334C8×C17C2×#4114yescomplemented
335#3622—22no—
336#3622—22no—
337C2×#556—171no—
338C2×#547—171no—
339#3353—1716no—
340C2×#500—171no—
341C2×#484—171no—
342C2×#484—171no—
343C2×#482—171no—
344C2×#482—171no—
345C2×#475—171no—
346C2×#474—171no—
347C2×#468—171no—
348C2×#468D1711yescharacteristic, complemented
349C2×C4×SD16—171no—
350C2×#436—171no—
351C2×#428—171no—
352C2×#428—171no—
353C22×C17—22no—
354C22×C17—22no—
355C22×C17—22no—
356C22×C17—44no—
357C22×C17—42no—
358C22×C17—42no—
359C22×C17—42no—
360C22×C17—84no—
361C22×C17#54712yes—
362C22×C17C2×AGL(1,ℤ/8)12yes—
363C22×C17#57812yes—
364C22×C17C23×D411yescharacteristic
365C2×D17—22no—
366C2×D17—22no—
367C2×D17—22no—
368C2×D17—44no—
369C4×C17—22no—
370C4×C17—42no—
371C4×C17—42no—
372C4×C17—42no—
373C4×C17#54712yes—
374C4×C17C22×#4111yescharacteristic
375C4×C17C2×2−1+411yescharacteristic
376Dic17—22no—
377Dic17—22no—
378Dic17—42no—
379Dic17—42no—
380Dic17—42no—
381Dic17—42no—
382Dic17C2×AGL(1,ℤ/8)14yes—
383C22×#41—341no—
384C22×SD16C2×D1711yescharacteristic
385C22×M16—171no—
386C22×M16C2×D1711yescharacteristic
387#556—178no—
388#556—344no—
389#547—178no—
390#547—344no—
391C2×C4⋊Q8—171no—
392C2×C4⋊Q8—171no—
393C2×#126—341no—
394C2×#126—341no—
395C2×#124—341no—
396C2×#123—341no—
397C2×#123—341no—
398C2×C22⋊Q8—171no—
399C2×C22⋊Q8—341no—
400C2×C22⋊Q8C2×D1711yescharacteristic
401C2×#121—171no—
402C2×#121C2×D1711yescharacteristic
403C2×C4×Q8—171no—
404C2×C4×Q8—341no—
405C2×C4×D4—171no—
406C2×C4×D4—171no—
407C2×#117—171no—
408C2×#117—171no—
409C22×C4⋊C4—171no—
410C22×C4⋊C4—171no—
411#500—178no—
412#484—178no—
413#484—178no—
414#482—178no—
415#482—178no—
416#475—178no—
417#474—178no—
418#468—178no—
419#468C2×D1718yescomplemented
420C4×SD16—178no—
421#436—178no—
422#428—178no—
423#428—178no—
424C2×#107—171no—
425C2×#107—171no—
426C2×#107—171no—
427C2×#107—171no—
428C2×#107—171no—
429C2×#107C2×D1711yescharacteristic
430C2×#106—171no—
431C2×#106—171no—
432C2×#106—171no—
433C2×C4⋊C8—171no—
434C2×#103—171no—
435C2×#103—171no—
436C2×#103C2×D1711yescharacteristic
437C2×#102—171no—
438C2×#102—171no—
439C2×#102C2×D1711yescharacteristic
440C2×C22⋊C8—171no—
441C2×C22⋊C8—171no—
442C2×C4×C8—171no—
443C2×C17—42no—
444C2×C17—82no—
445C2×C17#335314yescomplemented
446C2×C17C2×#54711yescharacteristic
447C2×C17C22×AGL(1,ℤ/8)11yescharacteristic
448C2×C17C2×#57811yescharacteristic
449D17—42no—
450C2×#41—348no—
451C2×#41—688no—
452C22×Q8—341no—
453C22×Q8—341no—
454C22×Q8C22×D1711yescharacteristic
455C22×D4—21no—
456C22×D4—171no—
457C22×D4—341no—
458C22×D4C22×D1711yescharacteristic
459C23×C4—171no—
460C23×C4—341no—
461C23×C4—341no—
462C23×C4—341no—
463C23×C4C22×D1711yescharacteristic
464C2×SD16—24no—
465C2×SD16C22×D1714yes—
466C2×M16—24no—
467C2×M16—174no—
468C2×M16—344no—
469C2×M16C22×D1714yes—
470C22×C8—171no—
471C22×C8—171no—
472C22×C8C22×D1711yescharacteristic
473C22×C8C22×D1711yescharacteristic
474C4⋊Q8—174no—
475C4⋊Q8—174no—
476C4⋊Q8—342no—
477C4⋊Q8—342no—
478#126—348no—
479#126—348no—
480#124—348no—
481#123—348no—
482#123—348no—
483C22⋊Q8—22no—
484C22⋊Q8—174no—
485C22⋊Q8—348no—
486C22⋊Q8—342no—
487C22⋊Q8C22×D1714yes—
488#121—22no—
489#121—174no—
490#121—342no—
491#121C22×D1714yes—
492C4×Q8—174no—
493C4×Q8—342no—
494C4×Q8—348no—
495C4×D4—174no—
496C4×D4—174no—
497C4×D4—174no—
498C4×D4—342no—
499#117—174no—
500#117—174no—
501#117—342no—
502#117—342no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—171no—
505C2×C4⋊C4—171no—
506C2×C4⋊C4—171no—
507C2×C4⋊C4—174no—
508C2×C4⋊C4—171no—
509C2×C4⋊C4—171no—
510C2×C4⋊C4—174no—
511C2×C4⋊C4—342no—
512C2×C4⋊C4—341no—
513C2×C4⋊C4—341no—
514C2×C4⋊C4—341no—
515C2×C4⋊C4—341no—
516C2×C4⋊C4—341no—
517C2×C4⋊C4—341no—
518C2×C4⋊C4—342no—
519C2×C4⋊C4C22×D1711yescharacteristic
520C2×C4⋊C4C22×D1711yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—171no—
524C2×C22⋊C4—171no—
525C2×C22⋊C4—341no—
526C2×C22⋊C4—341no—
527C2×C22⋊C4—341no—
528C2×C22⋊C4—341no—
529C2×C22⋊C4—341no—
530C2×C42—171no—
531C2×C42—341no—
532C2×C42—341no—
533C2×C42—341no—
534#107—174no—
535#107—174no—
536#107—174no—
537#107—174no—
538#107—174no—
539#107C22×D1714yes—
540#106—174no—
541#106—174no—
542#106—174no—
543C4⋊C8—174no—
544#103—174no—
545#103—174no—
546#103C22×D1714yes—
547#102—174no—
548#102—174no—
549#102C22×D1714yes—
550C22⋊C8—174no—
551C22⋊C8—174no—
552C4×C8—174no—
553C17C2×#335311yescharacteristic, complemented, Sylow
554C24—21no—
555C24—171no—
556C24D4×D1711yescharacteristic
557#41—6832no—
558C2×Q8—21no—
559C2×Q8—22no—
560C2×Q8—22no—
561C2×Q8—344no—
562C2×Q8—344no—
563C2×Q8—684no—
564C2×Q8—684no—
565C2×Q8C23×D1712yes—
566C2×D4—24no—
567C2×D4—21no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—44no—
571C2×D4—174no—
572C2×D4—344no—
573C2×D4—344no—
574C2×D4—684no—
575C2×D4C23×D1712yes—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—171no—
582C22×C4—171no—
583C22×C4—171no—
584C22×C4—172no—
585C22×C4—172no—
586C22×C4—344no—
587C22×C4—344no—
588C22×C4—342no—
589C22×C4—342no—
590C22×C4—344no—
591C22×C4—341no—
592C22×C4—341no—
593C22×C4—341no—
594C22×C4—341no—
595C22×C4—684no—
596C22×C4—684no—
597C22×C4—684no—
598C22×C4D4×D1712yes—
599C22×C4D4×D1711yescharacteristic
600C22×C4C23×D1712yes—
601C22×C4C23×D1711yescharacteristic
602SD16—28no—
603M16—28no—
604M16—348no—
605C2×C8—22no—
606C2×C8—172no—
607C2×C8—172no—
608C2×C8—342no—
609C2×C8—342no—
610C2×C8#6325414yescomplemented
611C2×C8C23×D1712yes—
612C2×C8C23×D1712yes—
613C4⋊C4—24no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—174no—
617C4⋊C4—172no—
618C4⋊C4—172no—
619C4⋊C4—172no—
620C4⋊C4—172no—
621C4⋊C4—344no—
622C4⋊C4—344no—
623C4⋊C4—344no—
624C4⋊C4—344no—
625C4⋊C4—344no—
626C4⋊C4—341no—
627C4⋊C4—341no—
628C4⋊C4—344no—
629C4⋊C4—341no—
630C4⋊C4—341no—
631C4⋊C4C23×D1712yes—
632C4⋊C4C23×D1712yes—
633C22⋊C4—24no—
634C22⋊C4—24no—
635C22⋊C4—174no—
636C22⋊C4—174no—
637C22⋊C4—344no—
638C22⋊C4—344no—
639C22⋊C4—344no—
640C22⋊C4—344no—
641C22⋊C4—344no—
642C42—172no—
643C42—172no—
644C42—344no—
645C42—344no—
646C42—344no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—172no—
655C23—342no—
656C23—342no—
657C23—342no—
658C23C2×D4×D1712yes—
659C23C2×D4×D1711yescharacteristic
660Q8—22no—
661Q8—22no—
662Q8—42no—
663Q8—688no—
664Q8—688no—
665D4—22no—
666D4—22no—
667D4—48no—
668D4—42no—
669D4—348no—
670D4—688no—
671C2×C4—22no—
672C2×C4—24no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—174no—
682C2×C4—172no—
683C2×C4—172no—
684C2×C4—172no—
685C2×C4—342no—
686C2×C4—342no—
687C2×C4—344no—
688C2×C4—342no—
689C2×C4—342no—
690C2×C4—342no—
691C2×C4—342no—
692C2×C4—342no—
693C2×C4—342no—
694C2×C4—688no—
695C2×C4—688no—
696C2×C4—688no—
697C2×C4—682no—
698C2×C4—682no—
699C2×C4—682no—
700C2×C4—682no—
701C2×C4C2×D4×D1712yes—
702C2×C4C2×D4×D1711yescharacteristic
703C2×C4C2×#6325412yes—
704C2×C4#1058769712yes—
705C2×C4C24×D1711yescharacteristic
706C8—22no—
707C8—342no—
708C8—342no—
709C8C2×#6325414yescomplemented
710C22—22no—
711C22—22no—
712C22—22no—
713C22—44no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—84no—
718C22—342no—
719C22—342no—
720C22—342no—
721C22—684no—
722C22#1176345912yes—
723C22AGL(1,ℤ/8)×D1712yes—
724C22#1176362512yes—
725C22C22×D4×D1711yescharacteristic
726C4—22no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—174no—
731C4—342no—
732C4—342no—
733C4—682no—
734C4—682no—
735C4—682no—
736C4—682no—
737C4#1176345912yes—
738C4C22×#6325411yescharacteristic
739C4C2×#1058769711yescharacteristic
740C2—42no—
741C2—82no—
742C2—682no—
743C2#1454136314yesdirect product factor
744C2C2×#1176345911yescharacteristic
745C2C2×AGL(1,ℤ/8)×D1711yescharacteristic
746C2C2×#1176362511yescharacteristic
subgroupG/H
centerC23C2×D4×D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#468C2
socleC23×C17C22×D4
prime radicalC2×#11763459C2
hypercenterC2×#468D17
hypocenterC17C2×#3353
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
1. C2×#11763530C2semidirect
3. #14541363C2direct (N × H)
4. C2×#11763213C2semidirect
5. C2×#11763143C2semidirect
6. C2×#11763142C2semidirect
7. C2×#11763132C2semidirect
8. C2×#11763130C2semidirect
9. C2×#11763092C2semidirect
10. C2×#11763087C2semidirect
11. C2×#11763052C2semidirect
12. C2×SD16×Dic17C2semidirect
13. C2×#11762885C2semidirect
14. C2×#11762851C2semidirect
15. C2×#11762850C2semidirect
16. C2×C17×#468C2semidirect
20. #11763530C22semidirect
41. #11763213C22semidirect
42. #11763143C22semidirect
43. #11763142C22semidirect
44. #11763132C22semidirect
45. #11763130C22semidirect
46. #11763092C22semidirect
47. #11763087C22semidirect
48. #11763052C22semidirect
49. SD16×Dic17C22semidirect
50. #11762885C22semidirect
51. #11762851C22semidirect
52. #11762850C22semidirect
73. C17×#468C22semidirect
231. C2×C8×C17#41semidirect
334. C8×C17C2×#41semidirect
348. C2×#468D17semidirect
419. #468C2×D17semidirect
445. C2×C17#3353semidirect
553. C17C2×#3353semidirect
610. C2×C8#63254semidirect
709. C8C2×#63254semidirect
743. C2#14541363direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117635302
C2×#117634592
#145413632
C2×#117632132
C2×#117631432
C2×#117631422
C2×#117631322
C2×#117631302
C2×#117630922
C2×#117630872
C2×#117630522
C2×SD16×Dic172
C2×#117628852
C2×#117628512
C2×#117628502
C2×C17×#4682
C2×#335317