Finite Group Databasebeta

← C2×#14540082 #17906561

Subgroups — C2×#14540082 #17906561

Order 4352.

1742 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763430C211yesmaximal, characteristic
2#14540082C2116yesmaximal, direct product factor
3C2×#11763219C211yesmaximal, characteristic, complemented
4C2×#11763205C211yesmaximal, characteristic, complemented
5C2×#11763171C211yesmaximal, characteristic, complemented
6C2×#11763166C211yesmaximal, characteristic, complemented
7C2×#11763127C211yesmaximal, characteristic
8C2×#11763150C211yesmaximal, characteristic, complemented
9C2×#11763133C211yesmaximal, characteristic
10C2×#11763139C211yesmaximal, characteristic, complemented
11C2×#11763113C211yesmaximal, characteristic, complemented
12C2×#11763091C211yesmaximal, characteristic, complemented
13C2×#11763106C211yesmaximal, characteristic, complemented
14C2×#11763096C211yesmaximal, characteristic, complemented
15C2×#11762870C211yesmaximal, characteristic, complemented
16C2×C17×#544C211yesmaximal, characteristic, complemented
17#11763430—24no—
18#11763430C2218yes—
19C2×#10587555C2211yescharacteristic
20C2×#10587584—21no—
21C2×#10587561C2211yescharacteristic
22C2×#10587571—21no—
23C2×#10587569—21no—
24C2×#10587610C2211yescharacteristic
25C2×#10587582—21no—
26C2×#10587616C2211yescharacteristic
27C2×C4×Dic34C2211yescharacteristic
28C2×C4×D68C2211yescharacteristic
29#11763219C2218yescomplemented
30#11763205C2218yescomplemented
31#11763171C2218yescomplemented
32#11763166C2218yescomplemented
33#11763150C2218yescomplemented
34#11763139C2218yescomplemented
35#11763133C2218yes—
36#11763127C2218yes—
37#11763113C2218yescomplemented
38#11763106C2218yescomplemented
39#11763096C2218yescomplemented
40#11763091C2218yescomplemented
41#11762870C2218yescomplemented
42C2×#10587478C2211yescharacteristic
43C2×#10587478C2211yescharacteristic
44C2×#10587479C2211yescharacteristic
45C2×#10587479C2211yescharacteristic
46C2×#10587479C2211yescharacteristic
47C2×#10587479C2211yescharacteristic
48C2×#10587479C2211yescharacteristic
49C2×#10587479C2211yescharacteristic
50C2×C4⋊#3622C2211yescharacteristic
51C2×C4⋊#3622C2211yescharacteristic
52C2×#10587481C2211yescharacteristic
53C2×#10587481C2211yescharacteristic
54C2×#10587481C2211yescharacteristic
55C2×#10587481C2211yescharacteristic
56C2×#10587480C2211yescharacteristic
57C2×#10587480C2211yescharacteristic
58C2×#10587480C2211yescharacteristic
59C2×#10587480C2211yescharacteristic
60C2×C22⋊#3622C2211yescharacteristic
61C2×C22⋊#3622C2211yescharacteristic
62C2×#10587474C2211yescharacteristic
63C2×C4×#3622C2211yescharacteristic
64C17×#544—24no—
65C17×#544C2218yescomplemented
66C2×C17×C4⋊Q8—21no—
67C2×C17×C4⋊Q8C2211yescharacteristic
68C2×C17×C4⋊Q8C2211yescharacteristic
69C2×C17×#125—21no—
70C2×C17×#125C2211yescharacteristic
71C2×C17×#125C2211yescharacteristic
72C2×C17×C22⋊Q8—21no—
73C2×C17×C22⋊Q8—21no—
74C2×C17×#117C2211yescharacteristic
75C2×C17×#117C2211yescharacteristic
76C22×C4⋊C4×C17C2211yescharacteristic
77C22×Q8×C17—21no—
78C22×Q8×C17—21no—
79C23×C4×C17—21no—
80C23×C4×C17C2311yescharacteristic
81C22×C22⋊D17—21no—
82C22×D68C2311yescharacteristic
83C22×C4×D17—21no—
84C22×Dic34—21no—
85C22×Dic34C2311yescharacteristic
86C17×C4⋊Q8—28no—
87C17×C4⋊Q8—22no—
88C17×C4⋊Q8—22no—
89C17×C4⋊Q8C2314yes—
90C17×C4⋊Q8C2314yes—
91C17×#125—28no—
92C17×#125—22no—
93C17×#125—22no—
94C17×#125C2314yes—
95C17×#125C2314yes—
96C17×C22⋊Q8—28no—
97C17×C22⋊Q8—28no—
98C17×#117—22no—
99C17×#117D414yes—
100C17×#117C2314yes—
101C17×#117C2314yes—
102C2×C4⋊C4×C17—21no—
103C2×C4⋊C4×C17—22no—
104C2×C4⋊C4×C17—21no—
105C2×C4⋊C4×C17—21no—
106C2×C4⋊C4×C17—21no—
107C2×C4⋊C4×C17—21no—
108C2×C4⋊C4×C17—21no—
109C2×C4⋊C4×C17—21no—
110C2×C4⋊C4×C17D411yescharacteristic
111C2×C4⋊C4×C17D411yescharacteristic
112C2×C4⋊C4×C17C2311yescharacteristic
113C2×C4⋊C4×C17C2311yescharacteristic
114C2×C4⋊C4×C17C2314yes—
115C2×C4⋊C4×C17C2311yescharacteristic
116C2×C4⋊C4×C17C2311yescharacteristic
117C2×C22⋊C4×C17—21no—
118C2×C22⋊C4×C17D411yescharacteristic
119C2×C22⋊C4×C17D411yescharacteristic
120C2×C42×C17—21no—
121C2×C42×C17C2311yescharacteristic
122C2×C42×C17C2311yescharacteristic
123C2×C22⋊Dic17—21no—
124#10587616—22no—
125#10587616C2314yes—
126C2×#63227—21no—
127C2×#63227—21no—
128C2×#63227—21no—
129C2×#63227—21no—
130C2×C4⋊Dic17—21no—
131C2×C4⋊Dic17C2311yescharacteristic
132C2×C4⋊Dic17C2311yescharacteristic
133#10587610—22no—
134#10587610C2314yes—
135C2×#63225—21no—
136C2×#63225—21no—
137C2×C4×Dic17—21no—
138C22×#3622C2311yescharacteristic
139C22×#3622C2311yescharacteristic
140C22×#3622C2311yescharacteristic
141C22×#3622C2311yescharacteristic
142#10587584—28no—
143#10587582—28no—
144#10587571—28no—
145#10587569—28no—
146#10587561—22no—
147#10587561C2314yes—
148C4×D68—22no—
149C4×D68C2314yes—
150#10587555—22no—
151#10587555C2314yes—
152C4×Dic34—22no—
153C4×Dic34C2314yes—
154C22⋊#3622C2314yes—
155C22⋊#3622C2314yes—
156#10587481C2314yes—
157#10587481C2314yes—
158#10587481C2314yes—
159#10587481C2314yes—
160#10587480C2314yes—
161#10587480C2314yes—
162#10587480C2314yes—
163#10587480C2314yes—
164#10587479C2314yes—
165#10587479C2314yes—
166#10587479C2314yes—
167#10587479C2314yes—
168#10587479C2314yes—
169#10587479C2314yes—
170#10587478C2314yes—
171#10587478C2314yes—
172C4⋊#3622C2314yes—
173C4⋊#3622C2314yes—
174#10587474C2314yes—
175C4×#3622C2314yes—
176C24×C17C2×D411yescharacteristic
177C23×D17—21no—
178C2×Q8×C17—24no—
179C2×Q8×C17—24no—
180C2×Q8×C17—82no—
181C2×Q8×C17—82no—
182C22×C4×C17—22no—
183C22×C4×C17—22no—
184C22×C4×C17—21no—
185C22×C4×C17—21no—
186C22×C4×C17—21no—
187C22×C4×C17—21no—
188C22×C4×C17—24no—
189C22×C4×C17—82no—
190C22×C4×C17C2×D411yescharacteristic
191C22×C4×C17C2×D411yescharacteristic
192C22×C4×C17C2×D411yescharacteristic
193C22×C4×C17C2×D412yes—
194C22×C4×C17C2×D411yescharacteristic
195C22×C4×C17C2×D411yescharacteristic
196C22×C4×C17C2412yes—
197C22×C4×C17C2411yescharacteristic
198C2×C22⋊D17—24no—
199C2×C22⋊D17—82no—
200C22×Dic17—21no—
201C22×Dic17—21no—
202C22×Dic17—21no—
203C2×D68—22no—
204C2×D68—22no—
205C2×D68—21no—
206C2×D68C2412yes—
207C2×C4×D17—24no—
208C2×C4×D17—82no—
209C2×Dic34—22no—
210C2×Dic34—22no—
211C2×Dic34—21no—
212C2×Dic34—24no—
213C2×Dic34—82no—
214C2×Dic34C2412yes—
215C4⋊C4×C17—24no—
216C4⋊C4×C17—24no—
217C4⋊C4×C17—24no—
218C4⋊C4×C17—24no—
219C4⋊C4×C17—24no—
220C4⋊C4×C17—24no—
221C4⋊C4×C17—21no—
222C4⋊C4×C17—24no—
223C4⋊C4×C17—21no—
224C4⋊C4×C17—21no—
225C4⋊C4×C17—21no—
226C4⋊C4×C17C2×D414yes—
227C4⋊C4×C17C2×D414yes—
228C4⋊C4×C17C2412yes—
229C4⋊C4×C17C2412yes—
230C4⋊C4×C17C2412yes—
231C4⋊C4×C17C2412yes—
232C22⋊C4×C17—24no—
233C22⋊C4×C17C2×D414yes—
234C22⋊C4×C17C2×D414yes—
235C42×C17—24no—
236C42×C17C2×D412yes—
237C42×C17C2×D412yes—
238C42×C17C2412yes—
239C42×C17C2412yes—
240C22⋊Dic17—24no—
241#63227—24no—
242#63227—24no—
243#63227—24no—
244#63227—24no—
245C4⋊Dic17—21no—
246C4⋊Dic17—21no—
247C4⋊Dic17—24no—
248C4⋊Dic17C2412yes—
249C4⋊Dic17C2412yes—
250#63225—24no—
251#63225—24no—
252C4×Dic17—24no—
253C2×#3622—22no—
254C2×#3622—22no—
255C2×#3622—22no—
256C2×#3622—22no—
257C2×#3622C2412yes—
258C2×#3622C2412yes—
259C2×#3622C2412yes—
260C2×#3622C2412yes—
261C2×#3244—171nomaximal, Sylow
262C23×C17—22no—
263C23×C17—22no—
264C23×C17—22no—
265C23×C17C22×D412yes—
266C23×C17C22×D411yescharacteristic
267C22×D17—22no—
268C22×D17—42no—
269C22×D17—42no—
270C22×D17—42no—
271Q8×C17—84no—
272Q8×C17—84no—
273C2×C4×C17—22no—
274C2×C4×C17—22no—
275C2×C4×C17—22no—
276C2×C4×C17—22no—
277C2×C4×C17—22no—
278C2×C4×C17—24no—
279C2×C4×C17—22no—
280C2×C4×C17—22no—
281C2×C4×C17—22no—
282C2×C4×C17—22no—
283C2×C4×C17—22no—
284C2×C4×C17—22no—
285C2×C4×C17—42no—
286C2×C4×C17—42no—
287C2×C4×C17—42no—
288C2×C4×C17—42no—
289C2×C4×C17—84no—
290C2×C4×C17C22×D412yes—
291C2×C4×C17C22×D412yes—
292C2×C4×C17C22×D412yes—
293C2×C4×C17C22×D412yes—
294C2×C4×C17C22×D412yes—
295C2×C4×C17C22×D411yescharacteristic
296C2×C4×C172−1+412yes—
297C2×C4×C172−1+412yes—
298C2×C4×C17C2511yescharacteristic
299C22⋊D17—84no—
300C2×Dic17—22no—
301C2×Dic17—22no—
302C2×Dic17—22no—
303C2×Dic17—42no—
304C2×Dic17—42no—
305C2×Dic17—42no—
306D68—22no—
307D68—22no—
308D68—42no—
309C4×D17—84no—
310Dic34—22no—
311Dic34—22no—
312Dic34—42no—
313Dic34—84no—
314#3622—22no—
315#3622—22no—
316#3622—22no—
317#3622—22no—
318C2×#544D1711yescharacteristic, complemented
319C2×#542—171no—
320#3244—1716no—
321C2×#501—171no—
322C2×#498—171no—
323C2×#489—171no—
324C2×#488—171no—
325C2×#481—171no—
326C2×#485—171no—
327C2×#482—171no—
328C2×#483—171no—
329C2×#479—171no—
330C2×#475—171no—
331C2×#478—171no—
332C2×#476—171no—
333C2×#433—171no—
334C22×C17—22no—
335C22×C17—22no—
336C22×C17—22no—
337C22×C17—44no—
338C22×C17#53612yes—
339C22×C17#57712yes—
340C22×C17#57712yes—
341C22×C17C23×D411yescharacteristic
342C2×D17—42no—
343C2×D17—42no—
344C2×D17—42no—
345C2×D17—84no—
346C4×C17—22no—
347C4×C17—22no—
348C4×C17—22no—
349C4×C17—22no—
350C4×C17—22no—
351C4×C17—42no—
352C4×C17—42no—
353C4×C17—42no—
354C4×C17—42no—
355C4×C17#53612yes—
356C4×C17C2×2−1+411yescharacteristic
357C4×C17C2×2−1+411yescharacteristic
358Dic17—42no—
359Dic17—42no—
360Dic17—42no—
361#544—24no—
362#544C2×D1718yescomplemented
363#542—178no—
364#542—344no—
365C2×C4⋊Q8—21no—
366C2×C4⋊Q8—171no—
367C2×C4⋊Q8C2×D1711yescharacteristic
368C2×C4⋊Q8C2×D1711yescharacteristic
369C2×#126—341no—
370C2×#125—21no—
371C2×#125C2×D1711yescharacteristic
372C2×#125C2×D1711yescharacteristic
373C2×#124—171no—
374C2×#124—341no—
375C2×#123—341no—
376C2×C22⋊Q8—21no—
377C2×C22⋊Q8—21no—
378C2×C22⋊Q8—171no—
379C2×C22⋊Q8—341no—
380C2×#121—171no—
381C2×C4×Q8—171no—
382C2×C4×D4—171no—
383C2×#117C2×D1711yescharacteristic
384C2×#117C2×D1711yescharacteristic
385C22×C4⋊C4C2×D1711yescharacteristic
386#501—178no—
387#498—178no—
388#489—178no—
389#488—178no—
390#485—178no—
391#483—178no—
392#482—178no—
393#481—178no—
394#479—178no—
395#478—178no—
396#476—178no—
397#475—178no—
398#433—178no—
399C2×#107—171no—
400C2×#107—171no—
401C2×#106—171no—
402C2×#106—171no—
403C2×#106—171no—
404C2×#106—171no—
405C2×#106—171no—
406C2×#106—171no—
407C2×C4⋊C8—171no—
408C2×C4⋊C8—171no—
409C2×#103—171no—
410C2×#103—171no—
411C2×#103—171no—
412C2×#103—171no—
413C2×#102—171no—
414C2×#102—171no—
415C2×#102—171no—
416C2×#102—171no—
417C2×C22⋊C8—171no—
418C2×C22⋊C8—171no—
419C2×#97—171no—
420C2×C4×C8—171no—
421C2×C17—42no—
422C2×C17#324414yescomplemented
423C2×C17C2×#53611yescharacteristic
424C2×C17C2×#57711yescharacteristic
425C2×C17C2×#57711yescharacteristic
426D17—82no—
427C22×Q8—21no—
428C22×Q8—21no—
429C22×Q8—171no—
430C22×Q8—341no—
431C22×D4—171no—
432C22×D4—341no—
433C23×C4—21no—
434C23×C4—341no—
435C23×C4C22×D1711yescharacteristic
436C22×C8—171no—
437C22×C8—171no—
438C22×C8—171no—
439C22×C8—171no—
440C4⋊Q8—28no—
441C4⋊Q8—22no—
442C4⋊Q8—22no—
443C4⋊Q8—174no—
444C4⋊Q8—342no—
445C4⋊Q8C22×D1714yes—
446C4⋊Q8C22×D1714yes—
447#126—348no—
448#125—28no—
449#125—22no—
450#125—22no—
451#125C22×D1714yes—
452#125C22×D1714yes—
453#124—174no—
454#124—348no—
455#124—342no—
456#123—348no—
457C22⋊Q8—28no—
458C22⋊Q8—28no—
459C22⋊Q8—174no—
460C22⋊Q8—342no—
461C22⋊Q8—348no—
462#121—174no—
463#121—342no—
464C4×Q8—174no—
465C4×Q8—342no—
466C4×D4—174no—
467C4×D4—342no—
468#117—22no—
469#117C22⋊D1714yes—
470#117C22×D1714yes—
471#117C22×D1714yes—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—22no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—171no—
481C2×C4⋊C4—171no—
482C2×C4⋊C4—341no—
483C2×C4⋊C4—341no—
484C2×C4⋊C4—341no—
485C2×C4⋊C4C22⋊D1711yescharacteristic
486C2×C4⋊C4C22⋊D1711yescharacteristic
487C2×C4⋊C4C22×D1711yescharacteristic
488C2×C4⋊C4C22×D1711yescharacteristic
489C2×C4⋊C4C22×D1714yes—
490C2×C4⋊C4C22×D1711yescharacteristic
491C2×C4⋊C4C22×D1711yescharacteristic
492C2×C22⋊C4—21no—
493C2×C22⋊C4—341no—
494C2×C22⋊C4—341no—
495C2×C22⋊C4—341no—
496C2×C22⋊C4—341no—
497C2×C22⋊C4—341no—
498C2×C22⋊C4C22⋊D1711yescharacteristic
499C2×C22⋊C4C22⋊D1711yescharacteristic
500C2×C42—21no—
501C2×C42—341no—
502C2×C42C22×D1711yescharacteristic
503C2×C42C22×D1711yescharacteristic
504#107—174no—
505#107—174no—
506#106—174no—
507#106—174no—
508#106—174no—
509#106—174no—
510#106—174no—
511#106—174no—
512C4⋊C8—174no—
513C4⋊C8—174no—
514#103—174no—
515#103—174no—
516#103—174no—
517#103—174no—
518#102—174no—
519#102—174no—
520#102—174no—
521#102—174no—
522C22⋊C8—174no—
523C22⋊C8—174no—
524#97—174no—
525C4×C8—174no—
526C17C2×#324411yescharacteristic, complemented, Sylow
527C24—341no—
528C24C2×C22⋊D1711yescharacteristic
529C2×Q8—24no—
530C2×Q8—24no—
531C2×Q8—82no—
532C2×Q8—82no—
533C2×Q8—172no—
534C2×Q8—341no—
535C2×Q8—344no—
536C2×Q8—342no—
537C2×Q8—342no—
538C2×Q8—1362no—
539C2×D4—172no—
540C2×D4—344no—
541C2×D4—342no—
542C2×D4—342no—
543C2×D4—341no—
544C2×D4—1362no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—24no—
552C22×C4—82no—
553C22×C4—341no—
554C22×C4—341no—
555C22×C4—341no—
556C22×C4—344no—
557C22×C4—1362no—
558C22×C4C2×C22⋊D1712yes—
559C22×C4C2×C22⋊D1711yescharacteristic
560C22×C4C2×C22⋊D1711yescharacteristic
561C22×C4C2×C22⋊D1711yescharacteristic
562C22×C4C2×C22⋊D1711yescharacteristic
563C22×C4C2×C22⋊D1711yescharacteristic
564C22×C4C23×D1712yes—
565C22×C4C23×D1711yescharacteristic
566C2×C8—172no—
567C2×C8—172no—
568C2×C8—172no—
569C2×C8—172no—
570C2×C8—342no—
571C2×C8—342no—
572C2×C8—342no—
573C2×C8—342no—
574C4⋊C4—24no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—24no—
580C4⋊C4—24no—
581C4⋊C4—24no—
582C4⋊C4—24no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—172no—
586C4⋊C4—172no—
587C4⋊C4—341no—
588C4⋊C4—341no—
589C4⋊C4—344no—
590C4⋊C4—344no—
591C4⋊C4—344no—
592C4⋊C4C2×C22⋊D1714yes—
593C4⋊C4C2×C22⋊D1714yes—
594C4⋊C4C23×D1712yes—
595C4⋊C4C23×D1712yes—
596C4⋊C4C23×D1712yes—
597C4⋊C4C23×D1712yes—
598C22⋊C4—24no—
599C22⋊C4—344no—
600C22⋊C4—344no—
601C22⋊C4—344no—
602C22⋊C4—344no—
603C22⋊C4—344no—
604C22⋊C4C2×C22⋊D1714yes—
605C22⋊C4C2×C22⋊D1714yes—
606C42—24no—
607C42—344no—
608C42C2×C22⋊D1712yes—
609C42C2×C22⋊D1712yes—
610C42C23×D1712yes—
611C42C23×D1712yes—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—342no—
616C23—682no—
617C23—682no—
618C23—682no—
619C23C22×C22⋊D1712yes—
620C23C22×C22⋊D1711yescharacteristic
621Q8—84no—
622Q8—84no—
623Q8—342no—
624Q8—342no—
625Q8—682no—
626Q8—1364no—
627D4—342no—
628D4—342no—
629D4—682no—
630D4—1364no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—24no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—84no—
648C2×C4—342no—
649C2×C4—342no—
650C2×C4—342no—
651C2×C4—682no—
652C2×C4—682no—
653C2×C4—682no—
654C2×C4—1364no—
655C2×C4#1058769412yes—
656C2×C4#1058769412yes—
657C2×C4C22×C22⋊D1712yes—
658C2×C4C22×C22⋊D1712yes—
659C2×C4C22×C22⋊D1712yes—
660C2×C4C22×C22⋊D1712yes—
661C2×C4C22×C22⋊D1712yes—
662C2×C4C22×C22⋊D1711yescharacteristic
663C2×C4C24×D1711yescharacteristic
664C8—342no—
665C8—342no—
666C8—342no—
667C8—342no—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—44no—
672C22—682no—
673C22—682no—
674C22—682no—
675C22—1364no—
676C22#1176338312yes—
677C22#1176361712yes—
678C22#1176362012yes—
679C22C23×C22⋊D1711yescharacteristic
680C4—22no—
681C4—22no—
682C4—22no—
683C4—22no—
684C4—22no—
685C4—42no—
686C4—42no—
687C4—42no—
688C4—42no—
689C4—682no—
690C4—682no—
691C4—682no—
692C4#1176338312yes—
693C4C2×#1058769411yescharacteristic
694C4C2×#1058769411yescharacteristic
695C2—42no—
696C2—1362no—
697C2#1454008214yesdirect product factor
698C2C2×#1176338311yescharacteristic
699C2C2×#1176361711yescharacteristic
700C2C2×#1176362011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#544C2
socleC23×C17C22×D4
prime radicalC2×#10587616C22
hypercenterC2×#544D17
hypocenterC17C2×#3244
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
2. #14540082C2direct (N × H)
3. C2×#11763219C2semidirect
4. C2×#11763205C2semidirect
5. C2×#11763171C2semidirect
6. C2×#11763166C2semidirect
8. C2×#11763150C2semidirect
10. C2×#11763139C2semidirect
11. C2×#11763113C2semidirect
12. C2×#11763091C2semidirect
13. C2×#11763106C2semidirect
14. C2×#11763096C2semidirect
15. C2×#11762870C2semidirect
16. C2×C17×#544C2semidirect
29. #11763219C22semidirect
30. #11763205C22semidirect
31. #11763171C22semidirect
32. #11763166C22semidirect
33. #11763150C22semidirect
34. #11763139C22semidirect
37. #11763113C22semidirect
38. #11763106C22semidirect
39. #11763096C22semidirect
40. #11763091C22semidirect
41. #11762870C22semidirect
65. C17×#544C22semidirect
318. C2×#544D17semidirect
362. #544C2×D17semidirect
422. C2×C17#3244semidirect
526. C17C2×#3244semidirect
697. C2#14540082direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117634302
#145400822
C2×#117632192
C2×#117632052
C2×#117631712
C2×#117631662
C2×#117631272
C2×#117631502
C2×#117631332
C2×#117631392
C2×#117631132
C2×#117630912
C2×#117631062
C2×#117630962
C2×#117628702
C2×C17×#5442
C2×#324417