Finite Group Databasebeta

← C2×#14538636 #17901906

Subgroups — C2×#14538636 #17901906

Order 4352.

2094 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763439C211yesmaximal, characteristic, complemented
2C2×#11763288C211yesmaximal, characteristic
3#14538636C2116yesmaximal, direct product factor
4C2×#11763119C211yesmaximal, characteristic, complemented
5C2×#11763113C211yesmaximal, characteristic, complemented
6C2×#11763105C211yesmaximal, characteristic, complemented
7C2×#11763103C211yesmaximal, characteristic, complemented
8C2×#11763107C211yesmaximal, characteristic, complemented
9C2×#11763089C211yesmaximal, characteristic, complemented
10C2×#11763087C211yesmaximal, characteristic, complemented
11C2×#11762848C211yesmaximal, characteristic, complemented
12C2×#107×D17C211yesmaximal, characteristic, complemented
13C2×#11762834C211yesmaximal, characteristic, complemented
14C2×#11762807C211yesmaximal, characteristic
15C2×#11762802C211yesmaximal, characteristic
16C2×C17×#478C211yesmaximal, characteristic, complemented
17C22×#63254C2211yescharacteristic
18C22×#63218C2211yescharacteristic
19C22×C8×D17C2211yescharacteristic
20#11763439—24no—
21#11763439C2218yescomplemented
22C2×#10587555C2211yescharacteristic
23C2×#10587574—21no—
24C2×#10587574C2211yescharacteristic
25C2×#10587576C2211yescharacteristic
26C2×#10587575—21no—
27C2×#10587583—21no—
28C2×#10587582—21no—
29#11763288—24no—
30#11763288C2218yes—
31C2×C4×Dic34C2211yescharacteristic
32C2×#10587573C2211yescharacteristic
33C2×D4×Dic17C2211yescharacteristic
34C2×C4×C22⋊D17—21no—
35C2×#10587567—21no—
36C2×#10587578C2211yescharacteristic
37C2×#10587558C2211yescharacteristic
38C2×#10587563—21no—
39C22×#63225—21no—
40C2×C4⋊C4×D17C2211yescharacteristic
41C2×C4⋊C4×D17C2211yescharacteristic
42#11763119C2218yescomplemented
43#11763113C2218yescomplemented
44#11763107C2218yescomplemented
45#11763105C2218yescomplemented
46#11763103C2218yescomplemented
47#11763089C2218yescomplemented
48#11763087C2218yescomplemented
49#11762848C2218yescomplemented
50C2×#10587489C2211yescharacteristic
51C2×#10587489C2211yescharacteristic
52C2×#10587478C2211yescharacteristic
53C2×#10587478C2211yescharacteristic
54C2×#10587478C2211yescharacteristic
55#107×D17C2218yescomplemented
56C2×#10587479C2211yescharacteristic
57#11762834C2218yescomplemented
58C2×C4⋊#3622C2211yescharacteristic
59C2×#10587485C2211yescharacteristic
60C2×#10587485C2211yescharacteristic
61#11762807C2218yes—
62#11762802C2218yes—
63C2×#10587487C2211yescharacteristic
64C2×#10587487C2211yescharacteristic
65C2×#10587481C2211yescharacteristic
66C2×#10587481C2211yescharacteristic
67C2×#10587503C2211yescharacteristic
68C2×#10587503C2211yescharacteristic
69C2×C17×#125C2211yescharacteristic
70C2×C4×D4×C17C2211yescharacteristic
71C17×#478C2218yescomplemented
72C2×C17×#107C2211yescharacteristic
73C2×C17×#106C2211yescharacteristic
74C2×C17×C4⋊C8C2211yescharacteristic
75C2×C17×#102C2211yescharacteristic
76C2×C17×#102C2211yescharacteristic
77C22×D4×C17C2311yescharacteristic
78C23×C4×C17—21no—
79C22×C22⋊D17—21no—
80C23×Dic17—21no—
81C23×Dic17—21no—
82C2×#63254—22no—
83C2×#63254—24no—
84C2×#63254Q818yescomplemented
85C2×#63254C2314yes—
86C22×C4×D17—21no—
87C22×C4×D17—21no—
88C22×C4×D17C2311yescharacteristic
89C22×Dic34—21no—
90C22×Dic34—21no—
91C22×Dic34C2311yescharacteristic
92C22×C8×C17C2311yescharacteristic
93C22×C8×C17C2311yescharacteristic
94C17×#125—22no—
95C17×#125C2314yes—
96C4×D4×C17—22no—
97C4×D4×C17C2314yes—
98C2×C4⋊C4×C17—21no—
99C2×C4⋊C4×C17—21no—
100C2×C4⋊C4×C17C2311yescharacteristic
101C2×C4⋊C4×C17C2311yescharacteristic
102C2×C4⋊C4×C17C2311yescharacteristic
103C2×C22⋊C4×C17—21no—
104C2×C42×C17C2311yescharacteristic
105C2×C22⋊Dic17—21no—
106D4×Dic17—22no—
107D4×Dic17C2314yes—
108C4×C22⋊D17—28no—
109C2×#63227—21no—
110C2×#63227D411yescharacteristic
111C2×#63227D411yescharacteristic
112C2×C4⋊Dic17—21no—
113C2×C4⋊Dic17—21no—
114C2×C4⋊Dic17C2311yescharacteristic
115C2×C4⋊Dic17C2311yescharacteristic
116C2×C4⋊Dic17C2311yescharacteristic
117C2×#63225—28no—
118C2×#63225—21no—
119C2×#63225—21no—
120C2×#63225—21no—
121C2×#63225—21no—
122C2×#63225—21no—
123C2×#63225—21no—
124C2×#63225D411yescharacteristic
125C2×#63225D411yescharacteristic
126C2×C4×Dic17—21no—
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#10587578—22no—
139#10587578C2314yes—
140C4⋊C4×D17—22no—
141C4⋊C4×D17—22no—
142C4⋊C4×D17C2314yes—
143C4⋊C4×D17C2314yes—
144#10587576—22no—
145#10587576C2314yes—
146#10587575—28no—
147#10587574—28no—
148#10587574—22no—
149#10587574C2314yes—
150#10587573—22no—
151#10587573C2314yes—
152#10587567—28no—
153#10587563—28no—
154#10587558D414yes—
155#10587558C2314yes—
156#10587555—22no—
157#10587555C2314yes—
158C4×Dic34—22no—
159C4×Dic34C2314yes—
160C17×#107C2314yes—
161C17×#106C2314yes—
162C17×C4⋊C8C2314yes—
163C17×#102C2314yes—
164C17×#102C2314yes—
165#10587503C2314yes—
166#10587503C2314yes—
167#10587489C2314yes—
168#10587489C2314yes—
169#10587487C2314yes—
170#10587487C2314yes—
171#10587485C2314yes—
172#10587485C2314yes—
173#10587481C2314yes—
174#10587481C2314yes—
175#10587479C2314yes—
176#10587478C2314yes—
177#10587478C2314yes—
178#10587478C2314yes—
179C4⋊#3622C2314yes—
180C24×C17—21no—
181C23×D17C2×D411yescharacteristic
182C2×D4×C17—21no—
183C2×D4×C17—22no—
184C2×D4×C17C2×Q814yes—
185C2×D4×C17C2412yes—
186C22×C4×C17—21no—
187C22×C4×C17—21no—
188C22×C4×C17—21no—
189C22×C4×C17—24no—
190C22×C4×C17—82no—
191C22×C4×C17C2×D411yescharacteristic
192C22×C4×C17C2×D411yescharacteristic
193C22×C4×C17C2411yescharacteristic
194C2×C22⋊D17—28no—
195C2×C22⋊D17—24no—
196C22×Dic17—21no—
197C22×Dic17—28no—
198C22×Dic17—24no—
199C22×Dic17—21no—
200C22×Dic17—21no—
201C22×Dic17—21no—
202C22×Dic17—24no—
203C22×Dic17—82no—
204C22×Dic17C2×D411yescharacteristic
205C22×Dic17C2×D411yescharacteristic
206C22×Dic17C2×D411yescharacteristic
207#63254—216no—
208#63254—28no—
209#63254C2×Q8116yescomplemented
210C2×C4×D17—24no—
211C2×C4×D17—24no—
212C2×C4×D17—82no—
213C2×C4×D17—82no—
214C2×C4×D17C2×D412yes—
215C2×C4×D17C2×Q814yes—
216C2×C4×D17#4114yes—
217C2×C4×D17C2412yes—
218C2×Dic34—21no—
219C2×Dic34—22no—
220C2×Dic34—24no—
221C2×Dic34—24no—
222C2×Dic34—82no—
223C2×Dic34—82no—
224C2×Dic34C2×Q814yes—
225C2×Dic34C2412yes—
226C2×C8×C17—22no—
227C2×C8×C17—22no—
228C2×C8×C17C2412yes—
229C2×C8×C17C2412yes—
230C4⋊C4×C17—21no—
231C4⋊C4×C17—21no—
232C4⋊C4×C17—24no—
233C4⋊C4×C17—24no—
234C4⋊C4×C17—21no—
235C4⋊C4×C17C2412yes—
236C4⋊C4×C17C2412yes—
237C4⋊C4×C17C2412yes—
238C22⋊C4×C17—24no—
239C42×C17C2×D412yes—
240C42×C17C2412yes—
241C22⋊Dic17—24no—
242#63227—24no—
243#63227C2×D414yes—
244#63227C2×D414yes—
245C4⋊Dic17—21no—
246C4⋊Dic17—21no—
247C4⋊Dic17—21no—
248C4⋊Dic17—24no—
249C4⋊Dic17—24no—
250C4⋊Dic17C2412yes—
251C4⋊Dic17C2412yes—
252C4⋊Dic17C2412yes—
253#63225—24no—
254#63225—24no—
255#63225—24no—
256#63225—24no—
257#63225—24no—
258#63225—24no—
259#63225C2×D414yes—
260#63225C2×D414yes—
261C4×Dic17—24no—
262C4×Dic17—24no—
263C4×Dic17—24no—
264C4×Dic17C2×D412yes—
265C4×Dic17C2412yes—
266C2×#3622—22no—
267C2×#3622—22no—
268C2×#3622C2412yes—
269C2×#3622C2412yes—
270#63218—28no—
271C8×D17—28no—
272C2×#3083—171nomaximal, Sylow
273C23×C17—24no—
274C23×C17—22no—
275C23×C17—42no—
276C23×C17—42no—
277C23×C17C22×D411yescharacteristic
278C22×D17—22no—
279C22×D17—22no—
280C22×D17C22⋊Q814yes—
281C22×D17C22×D412yes—
282D4×C17—24no—
283D4×C17—22no—
284D4×C17C22×Q814yes—
285C2×C4×C17—22no—
286C2×C4×C17—22no—
287C2×C4×C17—22no—
288C2×C4×C17—22no—
289C2×C4×C17—22no—
290C2×C4×C17—42no—
291C2×C4×C17—42no—
292C2×C4×C17—42no—
293C2×C4×C17—84no—
294C2×C4×C17C22×D412yes—
295C2×C4×C17C22×D412yes—
296C2×C4×C17C22×D411yescharacteristic
297C2×C4×C17C22×Q812yes—
298C2×C4×C17C2×#4112yes—
299C2×C4×C17C2511yescharacteristic
300C22⋊D17—216no—
301C2×Dic17—24no—
302C2×Dic17—22no—
303C2×Dic17—22no—
304C2×Dic17—22no—
305C2×Dic17—216no—
306C2×Dic17—22no—
307C2×Dic17—22no—
308C2×Dic17—22no—
309C2×Dic17—42no—
310C2×Dic17—42no—
311C2×Dic17—42no—
312C2×Dic17—84no—
313C2×Dic17C22⋊Q814yes—
314C2×Dic17C22×D412yes—
315C2×Dic17C22×D412yes—
316C2×Dic17C22×D412yes—
317C4×D17—84no—
318C4×D17—84no—
319C4×D17C22⋊Q818yes—
320C4×D17C22×Q814yes—
321C4×D17C2×#4114yes—
322Dic34—24no—
323Dic34—22no—
324Dic34—84no—
325Dic34—84no—
326Dic34C22×Q814yes—
327C8×C17—22no—
328C8×C17—22no—
329#3622—22no—
330#3622—22no—
331C2×#544—171no—
332C2×#520—171no—
333#3083—1716no—
334C2×#479—171no—
335C2×#479—171no—
336C2×#477—171no—
337C2×#477—171no—
338C2×#478—171no—
339C2×#478D1711yescharacteristic, complemented
340C2×#474—171no—
341C2×#474—171no—
342C2×#428—171no—
343C22×#107—171no—
344C2×#424—171no—
345C2×#417—171no—
346C2×#416—171no—
347C22×C17—24no—
348C22×C17—48no—
349C22×C17—42no—
350C22×C17—42no—
351C22×C17C2×C22⋊Q812yes—
352C22×C17#57612yes—
353C22×C17#57812yes—
354C22×C17C23×D411yescharacteristic
355C2×D17—28no—
356C2×D17—22no—
357C2×D17—22no—
358C2×D17C2×C22⋊Q814yes—
359C4×C17—22no—
360C4×C17—22no—
361C4×C17—42no—
362C4×C17—42no—
363C4×C17—42no—
364C4×C17C2×C22⋊Q812yes—
365C4×C17C23×Q811yescharacteristic
366C4×C17C22×#4111yescharacteristic
367Dic17—24no—
368Dic17—22no—
369Dic17—22no—
370Dic17—42no—
371Dic17—42no—
372Dic17—42no—
373Dic17C2×C22⋊Q814yes—
374C22×#41—171no—
375C22×M16—171no—
376C23×C8—171no—
377#544—178no—
378#544—344no—
379C2×C4⋊Q8—171no—
380C2×C4⋊Q8—171no—
381C2×C4⋊Q8—341no—
382C2×#125—171no—
383C2×#125—341no—
384C2×#125C2×D1711yescharacteristic
385C2×C22⋊Q8—341no—
386C2×C22⋊Q8—341no—
387#520—178no—
388#520—344no—
389C2×C4×Q8—171no—
390C2×C4×Q8—171no—
391C2×C4×D4—171no—
392C2×C4×D4—341no—
393C2×C4×D4—341no—
394C2×C4×D4C2×D1711yescharacteristic
395C2×#117—171no—
396C2×#117—171no—
397C2×#117—341no—
398C22×C4⋊C4—171no—
399C22×C4⋊C4—171no—
400C22×C4⋊C4—341no—
401#479—178no—
402#479—178no—
403#478—178no—
404#478C2×D1718yescomplemented
405#477—178no—
406#477—178no—
407#474—178no—
408#474—178no—
409#428—178no—
410C2×#107—171no—
411C2×#107—171no—
412C2×#107—171no—
413C2×#107—171no—
414C2×#107—171no—
415C2×#107—178no—
416C2×#107C2×D1711yescharacteristic
417C2×#106—171no—
418C2×#106C2×D1711yescharacteristic
419#424—178no—
420C2×C4⋊C8—171no—
421C2×C4⋊C8—171no—
422C2×C4⋊C8—171no—
423C2×C4⋊C8C2×D1711yescharacteristic
424#417—178no—
425#416—178no—
426C2×#103—171no—
427C2×#103—171no—
428C2×#103—171no—
429C2×#103—171no—
430C2×#102—171no—
431C2×#102—171no—
432C2×#102C2×D1711yescharacteristic
433C2×#102C2×D1711yescharacteristic
434C2×C17—44no—
435C2×C17#308314yescomplemented
436C2×C17C22×C22⋊Q811yescharacteristic
437C2×C17C2×#57611yescharacteristic
438C2×C17C2×#57811yescharacteristic
439D17—24no—
440C2×#41—178no—
441C2×#41—174no—
442C2×#41—342no—
443C2×#41—344no—
444C22×Q8—171no—
445C22×Q8—341no—
446C22×Q8—341no—
447C22×D4—341no—
448C22×D4C22×D1711yescharacteristic
449C23×C4—21no—
450C23×C4—171no—
451C23×C4—341no—
452C23×C4—341no—
453C23×C4—341no—
454C23×C4—341no—
455C2×M16—174no—
456C2×M16—344no—
457C22×C8—171no—
458C22×C8—171no—
459C22×C8—174no—
460C22×C8—344no—
461C22×C8C22×D1711yescharacteristic
462C22×C8C22×D1711yescharacteristic
463C4⋊Q8—174no—
464C4⋊Q8—174no—
465C4⋊Q8—342no—
466C4⋊Q8—348no—
467C4⋊Q8—342no—
468#125—22no—
469#125—174no—
470#125—342no—
471#125—348no—
472#125C22×D1714yes—
473C22⋊Q8—348no—
474C22⋊Q8—348no—
475C4×Q8—174no—
476C4×Q8—174no—
477C4×Q8—342no—
478C4×Q8—342no—
479C4×D4—22no—
480C4×D4—174no—
481C4×D4—342no—
482C4×D4—348no—
483C4×D4—348no—
484C4×D4C22×D1714yes—
485#117—174no—
486#117—174no—
487#117—174no—
488#117—348no—
489#117—342no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—171no—
493C2×C4⋊C4—171no—
494C2×C4⋊C4—171no—
495C2×C4⋊C4—171no—
496C2×C4⋊C4—171no—
497C2×C4⋊C4—174no—
498C2×C4⋊C4—174no—
499C2×C4⋊C4—342no—
500C2×C4⋊C4—342no—
501C2×C4⋊C4—348no—
502C2×C4⋊C4—341no—
503C2×C4⋊C4—341no—
504C2×C4⋊C4—341no—
505C2×C4⋊C4—341no—
506C2×C4⋊C4—341no—
507C2×C4⋊C4—341no—
508C2×C4⋊C4—341no—
509C2×C4⋊C4—341no—
510C2×C4⋊C4C22×D1711yescharacteristic
511C2×C4⋊C4C22×D1711yescharacteristic
512C2×C4⋊C4C22×D1711yescharacteristic
513C2×C22⋊C4—21no—
514C2×C22⋊C4—171no—
515C2×C22⋊C4—171no—
516C2×C22⋊C4—341no—
517C2×C22⋊C4—341no—
518C2×C42—171no—
519C2×C42—341no—
520C2×C42—341no—
521C2×C42—341no—
522C2×C42C22×D1711yescharacteristic
523#107—174no—
524#107—174no—
525#107—174no—
526#107—174no—
527#107—174no—
528#107C22×D1714yes—
529#106—174no—
530#106C22×D1714yes—
531C4⋊C8—174no—
532C4⋊C8—174no—
533C4⋊C8—174no—
534C4⋊C8C22×D1714yes—
535#103—174no—
536#103—174no—
537#103—174no—
538#103—174no—
539#102—174no—
540#102—174no—
541#102C22×D1714yes—
542#102C22×D1714yes—
543C17C2×#308311yescharacteristic, complemented, Sylow
544C24—21no—
545C24—171no—
546#41—1716no—
547#41—3416no—
548#41—348no—
549C2×Q8—174no—
550C2×Q8—172no—
551C2×Q8—344no—
552C2×Q8—341no—
553C2×Q8—344no—
554C2×Q8—342no—
555C2×Q8—1362no—
556C2×Q8—1362no—
557C2×D4—21no—
558C2×D4—22no—
559C2×D4—344no—
560C2×D4—348no—
561C2×D4Q8×D1714yes—
562C2×D4C23×D1712yes—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—24no—
567C22×C4—82no—
568C22×C4—171no—
569C22×C4—172no—
570C22×C4—174no—
571C22×C4—174no—
572C22×C4—172no—
573C22×C4—171no—
574C22×C4—171no—
575C22×C4—344no—
576C22×C4—344no—
577C22×C4—344no—
578C22×C4—348no—
579C22×C4—344no—
580C22×C4—341no—
581C22×C4—341no—
582C22×C4—341no—
583C22×C4—341no—
584C22×C4—1362no—
585C22×C4—1362no—
586C22×C4—1362no—
587C22×C4D4×D1711yescharacteristic
588C22×C4D4×D1711yescharacteristic
589C22×C4C23×D1711yescharacteristic
590M16—348no—
591C2×C8—22no—
592C2×C8—22no—
593C2×C8—172no—
594C2×C8—172no—
595C2×C8—348no—
596C2×C8—342no—
597C2×C8—342no—
598C2×C8C23×D1712yes—
599C2×C8C23×D1712yes—
600C4⋊C4—24no—
601C4⋊C4—24no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—174no—
606C4⋊C4—174no—
607C4⋊C4—172no—
608C4⋊C4—172no—
609C4⋊C4—172no—
610C4⋊C4—344no—
611C4⋊C4—344no—
612C4⋊C4—344no—
613C4⋊C4—344no—
614C4⋊C4—344no—
615C4⋊C4—344no—
616C4⋊C4—341no—
617C4⋊C4—341no—
618C4⋊C4—341no—
619C4⋊C4—344no—
620C4⋊C4—344no—
621C4⋊C4C23×D1712yes—
622C4⋊C4C23×D1712yes—
623C4⋊C4C23×D1712yes—
624C22⋊C4—24no—
625C22⋊C4—174no—
626C22⋊C4—174no—
627C22⋊C4—344no—
628C22⋊C4—344no—
629C42—172no—
630C42—172no—
631C42—344no—
632C42—344no—
633C42—344no—
634C42D4×D1712yes—
635C42C23×D1712yes—
636C23—24no—
637C23—22no—
638C23—42no—
639C23—42no—
640C23—174no—
641C23—172no—
642C23—342no—
643C23—342no—
644C23C2×D4×D1711yescharacteristic
645Q8—174no—
646Q8—344no—
647Q8—342no—
648Q8—1364no—
649Q8—1364no—
650D4—24no—
651D4—22no—
652D4—3416no—
653D4C2×Q8×D1714yes—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—84no—
663C2×C4—174no—
664C2×C4—172no—
665C2×C4—178no—
666C2×C4—174no—
667C2×C4—174no—
668C2×C4—172no—
669C2×C4—172no—
670C2×C4—3416no—
671C2×C4—344no—
672C2×C4—342no—
673C2×C4—342no—
674C2×C4—342no—
675C2×C4—342no—
676C2×C4—342no—
677C2×C4—342no—
678C2×C4—682no—
679C2×C4—682no—
680C2×C4—682no—
681C2×C4—1364no—
682C2×C4—1364no—
683C2×C4—1364no—
684C2×C4C2×D4×D1712yes—
685C2×C4C2×D4×D1712yes—
686C2×C4C2×D4×D1711yescharacteristic
687C2×C4C2×Q8×D1712yes—
688C2×C4#41×D1712yes—
689C2×C4C24×D1711yescharacteristic
690C8—22no—
691C8—22no—
692C8—342no—
693C8—342no—
694C22—24no—
695C22—48no—
696C22—42no—
697C22—42no—
698C22—174no—
699C22—348no—
700C22—342no—
701C22—342no—
702C22C22⋊Q8×D1712yes—
703C22#1176361312yes—
704C22#1176362312yes—
705C22C22×D4×D1711yescharacteristic
706C4—22no—
707C4—22no—
708C4—42no—
709C4—42no—
710C4—42no—
711C4—174no—
712C4—342no—
713C4—344no—
714C4—342no—
715C4—682no—
716C4—682no—
717C4—682no—
718C4C22⋊Q8×D1712yes—
719C4C22×Q8×D1711yescharacteristic
720C4C2×#41×D1711yescharacteristic
721C2—44no—
722C2—344no—
723C2#1453863614yesdirect product factor
724C2C2×C22⋊Q8×D1711yescharacteristic
725C2C2×#1176361311yescharacteristic
726C2C2×#1176362311yescharacteristic
subgroupG/H
centerC23C2×D4×D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#478C2
socleC23×C17C22×D4
prime radicalC22×#63254C22
hypercenterC2×#478D17
hypocenterC17C2×#3083
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. #14538636C2direct (N × H)
4. C2×#11763119C2semidirect
5. C2×#11763113C2semidirect
6. C2×#11763105C2semidirect
7. C2×#11763103C2semidirect
8. C2×#11763107C2semidirect
9. C2×#11763089C2semidirect
10. C2×#11763087C2semidirect
11. C2×#11762848C2semidirect
12. C2×#107×D17C2semidirect
13. C2×#11762834C2semidirect
16. C2×C17×#478C2semidirect
21. #11763439C22semidirect
42. #11763119C22semidirect
43. #11763113C22semidirect
44. #11763107C22semidirect
45. #11763105C22semidirect
46. #11763103C22semidirect
47. #11763089C22semidirect
48. #11763087C22semidirect
49. #11762848C22semidirect
55. #107×D17C22semidirect
57. #11762834C22semidirect
71. C17×#478C22semidirect
84. C2×#63254Q8semidirect
209. #63254C2×Q8semidirect
339. C2×#478D17semidirect
404. #478C2×D17semidirect
435. C2×C17#3083semidirect
543. C17C2×#3083semidirect
723. C2#14538636direct (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×#117632882
#145386362
C2×#117631192
C2×#117631132
C2×#117631052
C2×#117631032
C2×#117631072
C2×#117630892
C2×#117630872
C2×#117628482
C2×#107×D172
C2×#117628342
C2×#117628072
C2×#117628022
C2×C17×#4782
C2×#308317