Finite Group Databasebeta

← C2×#14538612 #17901880

Subgroups — C2×#14538612 #17901880

Order 4352.

2234 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763439C211yesmaximal, characteristic, complemented
2C2×#11763281C211yesmaximal, characteristic
3#14538612C2116yesmaximal, direct product factor
4C2×#11763112C211yesmaximal, characteristic, complemented
5C2×#11763107C211yesmaximal, characteristic, complemented
6C2×#11763106C211yesmaximal, characteristic, complemented
7C2×#11763099C211yesmaximal, characteristic, complemented
8C2×#11763098C211yesmaximal, characteristic, complemented
9C2×#11763090C211yesmaximal, characteristic, complemented
10C2×#11763087C211yesmaximal, characteristic, complemented
11C2×#11762848C211yesmaximal, characteristic, complemented
12C2×#11762846C211yesmaximal, characteristic, complemented
13C2×#11762834C211yesmaximal, characteristic, complemented
14C2×#11762812C211yesmaximal, characteristic
15C2×#102×D17C211yesmaximal, characteristic
16C2×C17×#478C211yesmaximal, characteristic, complemented
17C22×D4×D17C2211yescharacteristic
18C22×#63218C2211yescharacteristic
19C22×C8×D17C2211yescharacteristic
20#11763439—24no—
21#11763439C2218yescomplemented
22C2×#10587555C2211yescharacteristic, complemented
23C2×#10587574—21no—
24C2×#10587574C2211yescharacteristic, complemented
25C2×#10587576C2211yescharacteristic, complemented
26C2×#10587575—21no—
27C2×#10587583—21no—
28C2×#10587582—21no—
29#11763281—24no—
30#11763281C2218yes—
31C2×C4×D68C2211yescharacteristic
32C2×D4×Dic17C2211yescharacteristic
33C2×#10587579C2211yescharacteristic
34C2×C4×C22⋊D17—21no—
35C2×#10587567—21no—
36C2×#10587578C2211yescharacteristic
37C2×#10587578C2211yescharacteristic
38C2×#10587558C2211yescharacteristic
39C2×C4⋊C4×D17C2211yescharacteristic
40C22×#63227—21no—
41C2×C22⋊C4×D17—21no—
42#11763112C2218yescomplemented
43#11763107C2218yescomplemented
44#11763106C2218yescomplemented
45#11763099C2218yescomplemented
46#11763098C2218yescomplemented
47#11763090C2218yescomplemented
48#11763087C2218yescomplemented
49#11762848C2218yescomplemented
50#11762846C2218yescomplemented
51C2×#10587489C2211yescharacteristic, complemented
52C2×#10587489C2211yescharacteristic, complemented
53C2×#10587478C2211yescharacteristic, complemented
54C2×#10587479C2211yescharacteristic, complemented
55C2×#10587479C2211yescharacteristic, complemented
56C2×#10587479C2211yescharacteristic, complemented
57#11762834C2218yescomplemented
58C2×C4⋊#3622C2211yescharacteristic, complemented
59C2×#10587485C2211yescharacteristic, complemented
60C2×#10587485C2211yescharacteristic, complemented
61#11762812C2218yes—
62C2×#10587492C2211yescharacteristic
63C2×#10587492C2211yescharacteristic
64C2×#10587503C2211yescharacteristic
65C2×#10587503C2211yescharacteristic
66C2×#10587480C2211yescharacteristic
67C2×#10587480C2211yescharacteristic
68#102×D17C2218yes—
69C2×C17×#125C2211yescharacteristic, complemented
70C2×C4×D4×C17C2211yescharacteristic
71C17×#478C2218yescomplemented
72C2×C17×#107C2211yescharacteristic, complemented
73C2×C17×#106C2211yescharacteristic, complemented
74C2×C17×C4⋊C8C2211yescharacteristic, complemented
75C2×C17×#102C2211yescharacteristic
76C2×C17×#102C2211yescharacteristic
77C24×D17—21no—
78C22×D4×C17C2311yescharacteristic
79C23×C4×C17—21no—
80C22×C22⋊D17—21no—
81C23×Dic17—21no—
82C2×D4×D17—22no—
83C2×D4×D17—24no—
84C2×D4×D17Q818yescomplemented
85C2×D4×D17C2314yes—
86C22×D68C2311yescharacteristic
87C22×C4×D17—21no—
88C22×C4×D17—21no—
89C22×C4×D17—21no—
90C22×C4×D17C2311yescharacteristic
91C22×Dic34—21no—
92C22×Dic34—21no—
93C22×C8×C17C2311yescharacteristic
94C22×C8×C17C2311yescharacteristic
95C17×#125—22no—
96C17×#125C2314yescomplemented
97C4×D4×C17—22no—
98C4×D4×C17C2314yes—
99C2×C4⋊C4×C17—21no—
100C2×C4⋊C4×C17—21no—
101C2×C4⋊C4×C17C2311yescharacteristic
102C2×C4⋊C4×C17C2311yescharacteristic
103C2×C4⋊C4×C17C2311yescharacteristic
104C2×C22⋊C4×C17—21no—
105C2×C42×C17C2311yescharacteristic
106C2×C22⋊Dic17—21no—
107D4×Dic17—22no—
108D4×Dic17C2314yes—
109C4×C22⋊D17—28no—
110C2×#63227—28no—
111C2×#63227—21no—
112C2×#63227—21no—
113C2×#63227—21no—
114C2×#63227—21no—
115C2×#63227D411yescharacteristic
116C2×#63227D411yescharacteristic
117C2×C4⋊Dic17—21no—
118C2×C4⋊Dic17—21no—
119C2×C4⋊Dic17C2311yescharacteristic
120C2×C4⋊Dic17C2311yescharacteristic
121C2×C4⋊Dic17C2311yescharacteristic
122C2×#63225—21no—
123C2×#63225—21no—
124C2×#63225—21no—
125C2×#63225D411yescharacteristic
126C2×#63225D411yescharacteristic
127C2×C4×Dic17—21no—
128C2×C4×Dic17—21no—
129C2×C4×Dic17C2311yescharacteristic
130C22×#3622C2311yescharacteristic
131C22×#3622C2311yescharacteristic
132C2×#63218—24no—
133C2×#63218C2314yes—
134C2×C8×D17—24no—
135C2×C8×D17C2314yes—
136#10587583—28no—
137#10587582—28no—
138#10587579—22no—
139#10587579C2314yes—
140#10587578—22no—
141#10587578—22no—
142#10587578C2314yes—
143#10587578C2314yes—
144C4⋊C4×D17—22no—
145C4⋊C4×D17C2314yes—
146#10587576—22no—
147#10587576C2314yescomplemented
148#10587575—28no—
149#10587574—28no—
150#10587574—22no—
151#10587574C2314yescomplemented
152#10587567—28no—
153C22⋊C4×D17—28no—
154C4×D68—22no—
155C4×D68C2314yes—
156#10587558D414yes—
157#10587558C2314yes—
158#10587555—22no—
159#10587555C2314yescomplemented
160C17×#107C2314yescomplemented
161C17×#106C2314yescomplemented
162C17×C4⋊C8C2314yescomplemented
163C17×#102C2314yes—
164C17×#102C2314yes—
165#10587503C2314yes—
166#10587503C2314yes—
167#10587492C2314yes—
168#10587492C2314yes—
169#10587489C2314yescomplemented
170#10587489C2314yescomplemented
171#10587485C2314yescomplemented
172#10587485C2314yescomplemented
173#10587480C2314yes—
174#10587480C2314yes—
175#10587479C2314yescomplemented
176#10587479C2314yescomplemented
177#10587479C2314yescomplemented
178#10587478C2314yescomplemented
179C4⋊#3622C2314yescomplemented
180C24×C17—21no—
181C23×D17—21no—
182C23×D17—28no—
183C23×D17—24no—
184C23×D17—82no—
185C23×D17—82no—
186C23×D17C2×D411yescharacteristic
187C2×D4×C17—21no—
188C2×D4×C17—22no—
189C2×D4×C17C2×Q814yes—
190C2×D4×C17C2412yes—
191C22×C4×C17—21no—
192C22×C4×C17—21no—
193C22×C4×C17—21no—
194C22×C4×C17—24no—
195C22×C4×C17—82no—
196C22×C4×C17C2×D411yescharacteristic
197C22×C4×C17C2×D411yescharacteristic
198C22×C4×C17C2411yescharacteristic
199C2×C22⋊D17—28no—
200C2×C22⋊D17—24no—
201C22×Dic17—21no—
202C22×Dic17—21no—
203C22×Dic17—21no—
204C22×Dic17—24no—
205C22×Dic17—82no—
206C22×Dic17C2×D411yescharacteristic
207C22×Dic17C2×D411yescharacteristic
208C22×Dic17C2×D411yescharacteristic
209D4×D17—216no—
210D4×D17—28no—
211D4×D17C2×Q8116yescomplemented
212C2×D68—21no—
213C2×D68—22no—
214C2×D68C2×Q814yes—
215C2×D68C2412yes—
216C2×C4×D17—24no—
217C2×C4×D17—24no—
218C2×C4×D17—24no—
219C2×C4×D17—82no—
220C2×C4×D17—82no—
221C2×C4×D17—82no—
222C2×C4×D17C2×D412yes—
223C2×C4×D17C2×Q814yes—
224C2×C4×D17#4114yes—
225C2×C4×D17C2412yes—
226C2×Dic34—24no—
227C2×Dic34—24no—
228C2×Dic34—82no—
229C2×Dic34—82no—
230C2×C8×C17—22no—
231C2×C8×C17—22no—
232C2×C8×C17C2412yes—
233C2×C8×C17C2412yes—
234C4⋊C4×C17—21no—
235C4⋊C4×C17—21no—
236C4⋊C4×C17—24no—
237C4⋊C4×C17—24no—
238C4⋊C4×C17—21no—
239C4⋊C4×C17C2412yes—
240C4⋊C4×C17C2412yes—
241C4⋊C4×C17C2412yes—
242C22⋊C4×C17—24no—
243C42×C17C2×D412yes—
244C42×C17C2412yes—
245C22⋊Dic17—24no—
246#63227—24no—
247#63227—24no—
248#63227—24no—
249#63227—24no—
250#63227C2×D414yes—
251#63227C2×D414yes—
252C4⋊Dic17—21no—
253C4⋊Dic17—21no—
254C4⋊Dic17—24no—
255C4⋊Dic17—21no—
256C4⋊Dic17—24no—
257C4⋊Dic17C2412yes—
258C4⋊Dic17C2412yes—
259C4⋊Dic17C2412yes—
260#63225—24no—
261#63225—24no—
262#63225—24no—
263#63225C2×D414yes—
264#63225C2×D414yes—
265C4×Dic17—24no—
266C4×Dic17—24no—
267C4×Dic17C2×D412yes—
268C4×Dic17C2412yes—
269C2×#3622—22no—
270C2×#3622—22no—
271C2×#3622C2412yes—
272C2×#3622C2412yes—
273#63218—28no—
274C8×D17—28no—
275C2×#3081—171nomaximal, Sylow
276C23×C17—24no—
277C23×C17—22no—
278C23×C17—42no—
279C23×C17—42no—
280C23×C17C22×D411yescharacteristic
281C22×D17—22no—
282C22×D17—22no—
283C22×D17—24no—
284C22×D17—22no—
285C22×D17—216no—
286C22×D17—42no—
287C22×D17—42no—
288C22×D17—816no—
289C22×D17—84no—
290C22×D17—84no—
291C22×D17C22⋊Q814yes—
292C22×D17C22×D412yes—
293D4×C17—24no—
294D4×C17—22no—
295D4×C17C22×Q814yes—
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×C17—84no—
305C2×C4×C17C22×D412yes—
306C2×C4×C17C22×D412yes—
307C2×C4×C17C22×D411yescharacteristic
308C2×C4×C17C22×Q812yes—
309C2×C4×C17C2×#4112yes—
310C2×C4×C17C2511yescharacteristic
311C22⋊D17—216no—
312C2×Dic17—22no—
313C2×Dic17—22no—
314C2×Dic17—22no—
315C2×Dic17—22no—
316C2×Dic17—22no—
317C2×Dic17—42no—
318C2×Dic17—42no—
319C2×Dic17—42no—
320C2×Dic17—84no—
321C2×Dic17C22⋊Q814yes—
322C2×Dic17C22×D412yes—
323C2×Dic17C22×D412yes—
324C2×Dic17C22×D412yes—
325D68—24no—
326D68—22no—
327D68C22×Q814yes—
328C4×D17—84no—
329C4×D17—84no—
330C4×D17—84no—
331C4×D17C22⋊Q818yes—
332C4×D17C22×Q814yes—
333C4×D17C2×#4114yes—
334Dic34—84no—
335Dic34—84no—
336C8×C17—22no—
337C8×C17—22no—
338#3622—22no—
339#3622—22no—
340C2×#544—171no—
341C2×#518—171no—
342#3081—1716no—
343C2×#478—171no—
344C2×#478—171no—
345C2×#478—171no—
346C2×#478D1711yescharacteristic, complemented
347C2×#476—171no—
348C2×#476—171no—
349C2×#474—171no—
350C2×#474—171no—
351C2×#428—171no—
352C2×#427—171no—
353C2×#424—171no—
354C2×#418—171no—
355C22×#102—171no—
356C22×C17—24no—
357C22×C17—48no—
358C22×C17—42no—
359C22×C17—42no—
360C22×C17C2×C22⋊Q812yes—
361C22×C17#57612yes—
362C22×C17#57712yes—
363C22×C17C23×D411yescharacteristic
364C2×D17—28no—
365C2×D17—22no—
366C2×D17—22no—
367C2×D17—24no—
368C2×D17—48no—
369C2×D17—42no—
370C2×D17—42no—
371C2×D17—816no—
372C2×D17C2×C22⋊Q814yes—
373C4×C17—22no—
374C4×C17—22no—
375C4×C17—42no—
376C4×C17—42no—
377C4×C17—42no—
378C4×C17C2×C22⋊Q812yes—
379C4×C17C23×Q811yescharacteristic
380C4×C17C22×#4111yescharacteristic
381Dic17—22no—
382Dic17—22no—
383Dic17—42no—
384Dic17—42no—
385Dic17—42no—
386Dic17C2×C22⋊Q814yes—
387C23×D4—171no—
388C22×M16—171no—
389C23×C8—171no—
390#544—178no—
391#544—344no—
392C2×C4⋊Q8—171no—
393C2×C4⋊Q8—171no—
394C2×C4⋊Q8—341no—
395C2×#125—171no—
396C2×#125—341no—
397C2×#125C2×D1711yescharacteristic, complemented
398C2×C22⋊Q8—341no—
399C2×C22⋊Q8—341no—
400#518—178no—
401#518—344no—
402C2×C4×D4—171no—
403C2×C4×D4—171no—
404C2×C4×D4—171no—
405C2×C4×D4—341no—
406C2×C4×D4—341no—
407C2×C4×D4C2×D1711yescharacteristic
408C2×#117—171no—
409C2×#117—171no—
410C2×#117—171no—
411C22×C4⋊C4—171no—
412C22×C22⋊C4—341no—
413C22×C22⋊C4—341no—
414#478—178no—
415#478—178no—
416#478—178no—
417#478C2×D1718yescomplemented
418#476—178no—
419#476—178no—
420#474—178no—
421#474—178no—
422#428—178no—
423#427—178no—
424C2×#107—171no—
425C2×#107—171no—
426C2×#107—171no—
427C2×#107C2×D1711yescharacteristic, complemented
428C2×#106—171no—
429C2×#106—171no—
430C2×#106—171no—
431C2×#106C2×D1711yescharacteristic, complemented
432#424—178no—
433C2×C4⋊C8—171no—
434C2×C4⋊C8—171no—
435C2×C4⋊C8—171no—
436C2×C4⋊C8C2×D1711yescharacteristic, complemented
437#418—178no—
438C2×#102—171no—
439C2×#102—171no—
440C2×#102—171no—
441C2×#102—171no—
442C2×#102—171no—
443C2×#102—171no—
444C2×#102—178no—
445C2×#102C2×D1711yescharacteristic
446C2×#102C2×D1711yescharacteristic
447C2×C17—44no—
448C2×C17#308114yescomplemented
449C2×C17C22×C22⋊Q811yescharacteristic
450C2×C17C2×#57611yescharacteristic
451C2×C17C2×#57711yescharacteristic
452D17—24no—
453D17—44no—
454C25—341no—
455C22×Q8—341no—
456C22×Q8—341no—
457C22×D4—178no—
458C22×D4—174no—
459C22×D4—171no—
460C22×D4—342no—
461C22×D4—344no—
462C22×D4—341no—
463C22×D4C22×D1711yescharacteristic
464C23×C4—21no—
465C23×C4—171no—
466C23×C4—341no—
467C23×C4—341no—
468C23×C4—341no—
469C23×C4—341no—
470C2×M16—174no—
471C2×M16—344no—
472C22×C8—171no—
473C22×C8—171no—
474C22×C8—174no—
475C22×C8—344no—
476C22×C8C22×D1711yescharacteristic
477C22×C8C22×D1711yescharacteristic
478C4⋊Q8—174no—
479C4⋊Q8—174no—
480C4⋊Q8—342no—
481C4⋊Q8—348no—
482C4⋊Q8—342no—
483#125—22no—
484#125—174no—
485#125—342no—
486#125—348no—
487#125C22×D1714yescomplemented
488C22⋊Q8—348no—
489C22⋊Q8—348no—
490C4×D4—22no—
491C4×D4—174no—
492C4×D4—174no—
493C4×D4—174no—
494C4×D4—342no—
495C4×D4—342no—
496C4×D4—348no—
497C4×D4—348no—
498C4×D4—342no—
499C4×D4C22×D1714yes—
500#117—174no—
501#117—174no—
502#117—174no—
503#117—174no—
504#117—342no—
505#117—342no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—171no—
509C2×C4⋊C4—171no—
510C2×C4⋊C4—171no—
511C2×C4⋊C4—171no—
512C2×C4⋊C4—171no—
513C2×C4⋊C4—174no—
514C2×C4⋊C4—342no—
515C2×C4⋊C4—341no—
516C2×C4⋊C4—341no—
517C2×C4⋊C4—341no—
518C2×C4⋊C4—341no—
519C2×C4⋊C4—341no—
520C2×C4⋊C4C22×D1711yescharacteristic
521C2×C4⋊C4C22×D1711yescharacteristic
522C2×C4⋊C4C22×D1711yescharacteristic
523C2×C22⋊C4—21no—
524C2×C22⋊C4—171no—
525C2×C22⋊C4—171no—
526C2×C22⋊C4—348no—
527C2×C22⋊C4—348no—
528C2×C22⋊C4—341no—
529C2×C22⋊C4—341no—
530C2×C22⋊C4—341no—
531C2×C22⋊C4—341no—
532C2×C22⋊C4—341no—
533C2×C42—171no—
534C2×C42—341no—
535C2×C42—341no—
536C2×C42C22×D1711yescharacteristic
537#107—174no—
538#107—174no—
539#107—174no—
540#107C22×D1714yescomplemented
541#106—174no—
542#106—174no—
543#106—174no—
544#106C22×D1714yescomplemented
545C4⋊C8—174no—
546C4⋊C8—174no—
547C4⋊C8—174no—
548C4⋊C8C22×D1714yescomplemented
549#102—174no—
550#102—174no—
551#102—174no—
552#102—174no—
553#102—174no—
554#102—174no—
555#102C22×D1714yes—
556#102C22×D1714yes—
557C17C2×#308111yescharacteristic, complemented, Sylow
558C24—21no—
559C24—171no—
560C24—344no—
561C24—348no—
562C24—341no—
563C24—1362no—
564C24—1362no—
565C2×Q8—344no—
566C2×Q8—344no—
567C2×Q8—1362no—
568C2×Q8—1362no—
569C2×D4—21no—
570C2×D4—22no—
571C2×D4—1716no—
572C2×D4—174no—
573C2×D4—172no—
574C2×D4—3416no—
575C2×D4—348no—
576C2×D4—344no—
577C2×D4—348no—
578C2×D4—341no—
579C2×D4—342no—
580C2×D4Q8×D1714yes—
581C2×D4C23×D1712yes—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—24no—
586C22×C4—82no—
587C22×C4—171no—
588C22×C4—172no—
589C22×C4—174no—
590C22×C4—174no—
591C22×C4—172no—
592C22×C4—171no—
593C22×C4—171no—
594C22×C4—344no—
595C22×C4—344no—
596C22×C4—344no—
597C22×C4—341no—
598C22×C4—341no—
599C22×C4—341no—
600C22×C4—344no—
601C22×C4—1362no—
602C22×C4—1362no—
603C22×C4—1362no—
604C22×C4—1362no—
605C22×C4D4×D1711yescharacteristic
606C22×C4D4×D1711yescharacteristic
607C22×C4C23×D1711yescharacteristic
608M16—348no—
609C2×C8—22no—
610C2×C8—22no—
611C2×C8—172no—
612C2×C8—172no—
613C2×C8—348no—
614C2×C8—342no—
615C2×C8—342no—
616C2×C8C23×D1712yes—
617C2×C8C23×D1712yes—
618C4⋊C4—24no—
619C4⋊C4—24no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—174no—
624C4⋊C4—174no—
625C4⋊C4—172no—
626C4⋊C4—172no—
627C4⋊C4—172no—
628C4⋊C4—344no—
629C4⋊C4—344no—
630C4⋊C4—344no—
631C4⋊C4—344no—
632C4⋊C4—341no—
633C4⋊C4—341no—
634C4⋊C4—341no—
635C4⋊C4—344no—
636C4⋊C4C23×D1712yes—
637C4⋊C4C23×D1712yes—
638C4⋊C4C23×D1712yes—
639C22⋊C4—24no—
640C22⋊C4—174no—
641C22⋊C4—174no—
642C22⋊C4—344no—
643C22⋊C4—344no—
644C22⋊C4—344no—
645C22⋊C4—344no—
646C22⋊C4—344no—
647C42—172no—
648C42—172no—
649C42—344no—
650C42—344no—
651C42D4×D1712yes—
652C42C23×D1712yes—
653C23—24no—
654C23—22no—
655C23—42no—
656C23—42no—
657C23—174no—
658C23—172no—
659C23—3416no—
660C23—342no—
661C23—342no—
662C23—344no—
663C23—342no—
664C23—682no—
665C23—682no—
666C23—13616no—
667C23—1364no—
668C23—1364no—
669C23C2×D4×D1711yescharacteristic
670Q8—1364no—
671Q8—1364no—
672D4—24no—
673D4—22no—
674D4—174no—
675D4—3416no—
676D4—344no—
677D4—342no—
678D4C2×Q8×D1714yes—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—84no—
688C2×C4—174no—
689C2×C4—172no—
690C2×C4—178no—
691C2×C4—174no—
692C2×C4—174no—
693C2×C4—172no—
694C2×C4—172no—
695C2×C4—342no—
696C2×C4—342no—
697C2×C4—342no—
698C2×C4—342no—
699C2×C4—342no—
700C2×C4—682no—
701C2×C4—682no—
702C2×C4—682no—
703C2×C4—1364no—
704C2×C4—1364no—
705C2×C4—1364no—
706C2×C4—1364no—
707C2×C4C2×D4×D1712yes—
708C2×C4C2×D4×D1712yes—
709C2×C4C2×D4×D1711yescharacteristic
710C2×C4C2×Q8×D1712yes—
711C2×C4#41×D1712yes—
712C2×C4C24×D1711yescharacteristic
713C8—22no—
714C8—22no—
715C8—342no—
716C8—342no—
717C22—24no—
718C22—48no—
719C22—42no—
720C22—42no—
721C22—174no—
722C22—348no—
723C22—342no—
724C22—342no—
725C22—344no—
726C22—688no—
727C22—682no—
728C22—682no—
729C22—13616no—
730C22C22⋊Q8×D1712yes—
731C22#1176361112yes—
732C22#1176361912yes—
733C22C22×D4×D1711yescharacteristic
734C4—22no—
735C4—22no—
736C4—42no—
737C4—42no—
738C4—42no—
739C4—174no—
740C4—342no—
741C4—342no—
742C4—682no—
743C4—682no—
744C4—682no—
745C4C22⋊Q8×D1712yes—
746C4C22×Q8×D1711yescharacteristic
747C4C2×#41×D1711yescharacteristic
748C2—44no—
749C2—344no—
750C2—684no—
751C2#1453861214yesdirect product factor
752C2C2×C22⋊Q8×D1711yescharacteristic
753C2C2×#1176361111yescharacteristic
754C2C2×#1176361911yescharacteristic
subgroupG/H
centerC23C2×D4×D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#478C2
socleC23×C17C22×D4
prime radicalC22×D4×D17C22
hypercenterC2×#478D17
hypocenterC17C2×#3081
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. C2×#11763439C2semidirect
3. #14538612C2direct (N × H)
4. C2×#11763112C2semidirect
5. C2×#11763107C2semidirect
6. C2×#11763106C2semidirect
7. C2×#11763099C2semidirect
8. C2×#11763098C2semidirect
9. C2×#11763090C2semidirect
10. C2×#11763087C2semidirect
11. C2×#11762848C2semidirect
12. C2×#11762846C2semidirect
13. C2×#11762834C2semidirect
16. C2×C17×#478C2semidirect
21. #11763439C22semidirect
22. C2×#10587555C22semidirect
24. C2×#10587574C22semidirect
25. C2×#10587576C22semidirect
42. #11763112C22semidirect
43. #11763107C22semidirect
44. #11763106C22semidirect
45. #11763099C22semidirect
46. #11763098C22semidirect
47. #11763090C22semidirect
48. #11763087C22semidirect
49. #11762848C22semidirect
50. #11762846C22semidirect
51. C2×#10587489C22semidirect
52. C2×#10587489C22semidirect
53. C2×#10587478C22semidirect
54. C2×#10587479C22semidirect
55. C2×#10587479C22semidirect
56. C2×#10587479C22semidirect
57. #11762834C22semidirect
58. C2×C4⋊#3622C22semidirect
59. C2×#10587485C22semidirect
60. C2×#10587485C22semidirect
69. C2×C17×#125C22semidirect
71. C17×#478C22semidirect
72. C2×C17×#107C22semidirect
73. C2×C17×#106C22semidirect
74. C2×C17×C4⋊C8C22semidirect
84. C2×D4×D17Q8semidirect
96. C17×#125C23semidirect
147. #10587576C23semidirect
151. #10587574C23semidirect
159. #10587555C23semidirect
160. C17×#107C23semidirect
161. C17×#106C23semidirect
162. C17×C4⋊C8C23semidirect
169. #10587489C23semidirect
170. #10587489C23semidirect
171. #10587485C23semidirect
172. #10587485C23semidirect
175. #10587479C23semidirect
176. #10587479C23semidirect
177. #10587479C23semidirect
178. #10587478C23semidirect
179. C4⋊#3622C23semidirect
211. D4×D17C2×Q8semidirect
346. C2×#478D17semidirect
397. C2×#125C2×D17semidirect
417. #478C2×D17semidirect
427. C2×#107C2×D17semidirect
431. C2×#106C2×D17semidirect
436. C2×C4⋊C8C2×D17semidirect
448. C2×C17#3081semidirect
487. #125C22×D17semidirect
540. #107C22×D17semidirect
544. #106C22×D17semidirect
548. C4⋊C8C22×D17semidirect
557. C17C2×#3081semidirect
751. C2#14538612direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117634392
C2×#117632812
#145386122
C2×#117631122
C2×#117631072
C2×#117631062
C2×#117630992
C2×#117630982
C2×#117630902
C2×#117630872
C2×#117628482
C2×#117628462
C2×#117628342
C2×#117628122
C2×#102×D172
C2×C17×#4782
C2×#308117