Finite Group Databasebeta

← C2×#14541234 #17912866

Subgroups — C2×#14541234 #17912866

Order 4352.

1878 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763517C211yesmaximal, characteristic
2C2×#11763493C211yesmaximal, characteristic
3#14541234C2116yesmaximal, direct product factor
4C2×#11763216C211yesmaximal, characteristic, complemented
5C2×#11763143C211yesmaximal, characteristic, complemented
6C2×#11763147C211yesmaximal, characteristic, complemented
7C2×#11763138C211yesmaximal, characteristic, complemented
8C2×#11763137C211yesmaximal, characteristic, complemented
9C2×#11763118C211yesmaximal, characteristic, complemented
10C2×#11763092C211yesmaximal, characteristic, complemented
11C2×#11763047C211yesmaximal, characteristic, complemented
12C2×#11762916C211yesmaximal, characteristic, complemented
13C2×#11762878C211yesmaximal, characteristic
14C2×#11762851C211yesmaximal, characteristic, complemented
15C2×#106×D17C211yesmaximal, characteristic, complemented
16C2×C17×#470C211yesmaximal, characteristic, complemented
17C22×C8×D17C2211yescharacteristic
18#11763517—24no—
19#11763517C2218yes—
20#11763493—24no—
21#11763493C2218yes—
22C2×#10587574C2211yescharacteristic
23C2×#10587565—21no—
24C2×#10587576C2211yescharacteristic
25C2×#10587575—21no—
26C2×#10587575—21no—
27C2×#10587569—21no—
28C2×#10587583—21no—
29C2×#10587564—21no—
30C2×#10587632C2211yescharacteristic
31C2×#10587632C2211yescharacteristic
32C2×Q8×Dic17C2211yescharacteristic
33C2×Q8×Dic17C2211yescharacteristic
34C2×C4×C22⋊D17C2211yescharacteristic
35C2×#10587567—21no—
36C2×#10587612C2211yescharacteristic
37C2×#10587578—21no—
38C22×C4⋊Dic17C2211yescharacteristic
39C2×C4⋊C4×D17C2211yescharacteristic
40C2×C4⋊C4×D17C2211yescharacteristic
41#11763216C2218yescomplemented
42#11763147C2218yescomplemented
43#11763143C2218yescomplemented
44#11763138C2218yescomplemented
45#11763137C2218yescomplemented
46#11763118C2218yescomplemented
47#11763092C2218yescomplemented
48#11763047C2218yescomplemented
49#11762916C2218yescomplemented
50#11762878C2218yes—
51#11762851C2218yescomplemented
52C2×#10587489C2211yescharacteristic
53C2×#10587489C2211yescharacteristic
54C2×#10587478C2211yescharacteristic
55C2×#10587488C2211yescharacteristic
56C2×#10587488C2211yescharacteristic
57C2×#10587479C2211yescharacteristic
58C2×#10587479C2211yescharacteristic
59C2×#10587479C2211yescharacteristic
60#106×D17C2218yescomplemented
61C2×#10587485C2211yescharacteristic
62C2×#10587506C2211yescharacteristic
63C2×#10587506C2211yescharacteristic
64C2×#10587506C2211yescharacteristic
65C2×#10587506C2211yescharacteristic
66C2×C22⋊#3622C2211yescharacteristic
67C2×#10587491C2211yescharacteristic
68C2×#10587486C2211yescharacteristic
69C22×Q16×C17C2211yescharacteristic
70C22×M16×C17C2211yescharacteristic
71C2×C17×C22⋊Q8C2211yescharacteristic
72C2×C17×C22⋊Q8C2211yescharacteristic
73C17×#470C2218yescomplemented
74C2×C17×#106C2211yescharacteristic
75C2×C17×#103C2211yescharacteristic
76C2×C17×#103C2211yescharacteristic
77C22×Q8×C17C2311yescharacteristic
78C22×Q8×C17C2311yescharacteristic
79C23×C4×C17C2311yescharacteristic
80C22×C22⋊D17D411yescharacteristic
81C23×Dic17—21no—
82C22×C4×D17—21no—
83C22×C4×D17—21no—
84C22×C4×D17C2311yescharacteristic
85C22×Dic34—21no—
86C2×Q16×C17—24no—
87C2×Q16×C17C2314yes—
88C2×M16×C17—24no—
89C2×M16×C17C2314yes—
90C22×C8×C17C2311yescharacteristic
91C22×C8×C17C2311yescharacteristic
92C17×C22⋊Q8—22no—
93C17×C22⋊Q8—22no—
94C17×C22⋊Q8C2314yes—
95C17×C22⋊Q8C2314yes—
96C2×C4⋊C4×C17—21no—
97C2×C4⋊C4×C17—21no—
98C2×C4⋊C4×C17C2311yescharacteristic
99C2×C4⋊C4×C17C2311yescharacteristic
100C2×C22⋊C4×C17—21no—
101C2×C22⋊C4×C17—21no—
102C2×C22⋊Dic17—21no—
103C2×C22⋊Dic17D411yescharacteristic
104#10587632—22no—
105#10587632—22no—
106#10587632C2314yes—
107#10587632C2314yes—
108Q8×Dic17—22no—
109Q8×Dic17—22no—
110Q8×Dic17C2314yes—
111Q8×Dic17C2314yes—
112C4×C22⋊D17D414yes—
113C4×C22⋊D17C2314yes—
114C2×#63227—21no—
115C2×#63227—21no—
116C2×#63227D411yescharacteristic
117#10587612—22no—
118#10587612C2314yes—
119C2×C4⋊Dic17—22no—
120C2×C4⋊Dic17—21no—
121C2×C4⋊Dic17—21no—
122C2×C4⋊Dic17—21no—
123C2×C4⋊Dic17—21no—
124C2×C4⋊Dic17C2311yescharacteristic
125C2×C4⋊Dic17C2311yescharacteristic
126C2×C4⋊Dic17C2314yes—
127C2×C4⋊Dic17C2311yescharacteristic
128C2×C4⋊Dic17C2311yescharacteristic
129C2×#63225—21no—
130C2×#63225—21no—
131C2×#63225—21no—
132C2×#63225—21no—
133C2×#63225—21no—
134C2×#63225—21no—
135C2×#63225D411yescharacteristic
136C2×C4×Dic17—21no—
137C2×C4×Dic17—21no—
138C2×C4×Dic17—21no—
139C2×C4×Dic17C2311yescharacteristic
140C22×#3622C2311yescharacteristic
141C22×#3622C2311yescharacteristic
142C2×C8×D17—24no—
143C2×C8×D17C2314yes—
144#10587583—28no—
145#10587578—28no—
146C4⋊C4×D17—22no—
147C4⋊C4×D17—22no—
148C4⋊C4×D17C2314yes—
149C4⋊C4×D17C2314yes—
150#10587576—22no—
151#10587576C2314yes—
152#10587575—28no—
153#10587575—28no—
154#10587574—22no—
155#10587574C2314yes—
156#10587569—28no—
157#10587567—28no—
158#10587565—28no—
159#10587564—28no—
160C17×#106C2314yes—
161C17×#103C2314yes—
162C17×#103C2314yes—
163#10587506C2314yes—
164#10587506C2314yes—
165#10587506C2314yes—
166#10587506C2314yes—
167C22⋊#3622C2314yes—
168#10587491C2314yes—
169#10587489C2314yes—
170#10587489C2314yes—
171#10587488C2314yes—
172#10587488C2314yes—
173#10587486C2314yes—
174#10587485C2314yes—
175#10587479C2314yes—
176#10587479C2314yes—
177#10587479C2314yes—
178#10587478C2314yes—
179C24×C17C2×D411yescharacteristic
180C23×D17C2×D411yescharacteristic
181C2×Q8×C17—21no—
182C2×Q8×C17—21no—
183C2×Q8×C17—22no—
184C2×Q8×C17—22no—
185C2×Q8×C17—22no—
186C2×Q8×C17—22no—
187C2×Q8×C17C2412yes—
188C2×Q8×C17C2412yes—
189C22×C4×C17—22no—
190C22×C4×C17—22no—
191C22×C4×C17—21no—
192C22×C4×C17—21no—
193C22×C4×C17—21no—
194C22×C4×C17—21no—
195C22×C4×C17C2×D412yes—
196C22×C4×C17C2×D411yescharacteristic
197C22×C4×C17C2412yes—
198C22×C4×C17C2411yescharacteristic
199C2×C22⋊D17—24no—
200C2×C22⋊D17C2×D414yes—
201C22×Dic17—21no—
202C22×Dic17—21no—
203C22×Dic17—21no—
204C22×Dic17—21no—
205C22×Dic17—24no—
206C22×Dic17—82no—
207C22×Dic17C2×D411yescharacteristic
208C22×Dic17C2×D411yescharacteristic
209C22×Dic17C2×D411yescharacteristic
210C2×C4×D17—22no—
211C2×C4×D17—22no—
212C2×C4×D17—24no—
213C2×C4×D17—24no—
214C2×C4×D17—44no—
215C2×C4×D17—82no—
216C2×C4×D17C2×D412yes—
217C2×C4×D17C2412yes—
218C2×Dic34—24no—
219C2×Dic34—82no—
220Q16×C17—28no—
221M16×C17—28no—
222C2×C8×C17—22no—
223C2×C8×C17#4114yes—
224C2×C8×C17C2412yes—
225C2×C8×C17C2412yes—
226C4⋊C4×C17—21no—
227C4⋊C4×C17—21no—
228C4⋊C4×C17—24no—
229C4⋊C4×C17—24no—
230C4⋊C4×C17C2412yes—
231C4⋊C4×C17C2412yes—
232C22⋊C4×C17—24no—
233C22⋊C4×C17—24no—
234C22⋊Dic17—24no—
235C22⋊Dic17C2×D414yes—
236#63227—24no—
237#63227—24no—
238#63227C2×D414yes—
239C4⋊Dic17—21no—
240C4⋊Dic17—24no—
241C4⋊Dic17—21no—
242C4⋊Dic17—21no—
243C4⋊Dic17—21no—
244C4⋊Dic17—24no—
245C4⋊Dic17—24no—
246C4⋊Dic17—24no—
247C4⋊Dic17C2412yes—
248C4⋊Dic17C2412yes—
249C4⋊Dic17C2412yes—
250C4⋊Dic17C2412yes—
251#63225—24no—
252#63225—24no—
253#63225—24no—
254#63225—24no—
255#63225—24no—
256#63225—24no—
257#63225C2×D414yes—
258C4×Dic17—24no—
259C4×Dic17—24no—
260C4×Dic17—24no—
261C4×Dic17C2×D412yes—
262C4×Dic17C2412yes—
263C2×#3622—22no—
264C2×#3622—22no—
265C2×#3622C2412yes—
266C2×#3622C2412yes—
267C8×D17—28no—
268C2×#3344—171nomaximal, Sylow
269C23×C17—22no—
270C23×C17—22no—
271C23×C17—22no—
272C23×C17C22×D412yes—
273C23×C17C22×D411yescharacteristic
274C22×D17—22no—
275C22×D17—22no—
276C22×D17#13714yes—
277C22×D17C22×D412yes—
278Q8×C17—22no—
279Q8×C17—22no—
280Q8×C17—22no—
281Q8×C17—22no—
282Q8×C17—42no—
283Q8×C17—42no—
284C2×C4×C17—22no—
285C2×C4×C17—24no—
286C2×C4×C17—22no—
287C2×C4×C17—22no—
288C2×C4×C17—22no—
289C2×C4×C17—22no—
290C2×C4×C17—22no—
291C2×C4×C17—22no—
292C2×C4×C17—42no—
293C2×C4×C17—42no—
294C2×C4×C17—42no—
295C2×C4×C17—42no—
296C2×C4×C17C22×D412yes—
297C2×C4×C17C22×D411yescharacteristic
298C2×C4×C17C2×#4112yes—
299C2×C4×C172−1+412yes—
300C2×C4×C17C2511yescharacteristic
301C22⋊D17—28no—
302C2×Dic17—22no—
303C2×Dic17—22no—
304C2×Dic17—22no—
305C2×Dic17—22no—
306C2×Dic17—22no—
307C2×Dic17—22no—
308C2×Dic17—22no—
309C2×Dic17—42no—
310C2×Dic17—42no—
311C2×Dic17—42no—
312C2×Dic17—42no—
313C2×Dic17—84no—
314C2×Dic17C22×D412yes—
315C2×Dic17C22×D412yes—
316C2×Dic17C22×D412yes—
317C4×D17—24no—
318C4×D17—22no—
319C4×D17—22no—
320C4×D17—48no—
321C4×D17—84no—
322Dic34—84no—
323C8×C17—22no—
324C8×C17C2×#4114yes—
325#3622—22no—
326#3622—22no—
327C2×#554—171no—
328C2×#552—171no—
329#3344—1716no—
330C2×#501—171no—
331C2×#484—171no—
332C2×#485—171no—
333C2×#483—171no—
334C2×#483—171no—
335C2×#479—171no—
336C2×#475—171no—
337C2×#470D1711yescharacteristic, complemented
338C2×#467—171no—
339C2×#441—171no—
340C2×#435—171no—
341C2×#428—171no—
342C22×#106—171no—
343C22×C17—22no—
344C22×C17—22no—
345C22×C17—22no—
346C22×C17—44no—
347C22×C17#54712yes—
348C22×C17C2×#13712yes—
349C22×C17#57712yes—
350C22×C17C23×D411yescharacteristic
351C2×D17—28no—
352C2×D17—22no—
353C2×D17—22no—
354C2×D17C2×#13714yes—
355C4×C17—22no—
356C4×C17—42no—
357C4×C17—42no—
358C4×C17—42no—
359C4×C17—42no—
360C4×C17#54712yes—
361C4×C17C22×#4111yescharacteristic
362C4×C17C2×2−1+411yescharacteristic
363Dic17—22no—
364Dic17—22no—
365Dic17—22no—
366Dic17—42no—
367Dic17—42no—
368Dic17—42no—
369Dic17—42no—
370C22×Q16C2×D1711yescharacteristic
371C22×M16C2×D1711yescharacteristic
372C23×C8—171no—
373#554—178no—
374#554—344no—
375#552—178no—
376#552—344no—
377C2×C4⋊Q8—171no—
378C2×#126—341no—
379C2×#125—171no—
380C2×#125—341no—
381C2×#125—341no—
382C2×#123—341no—
383C2×C22⋊Q8—171no—
384C2×C22⋊Q8—171no—
385C2×C22⋊Q8—341no—
386C2×C22⋊Q8—341no—
387C2×C22⋊Q8C2×D1711yescharacteristic
388C2×C22⋊Q8C2×D1711yescharacteristic
389C2×C4×Q8—171no—
390C2×C4×Q8—171no—
391C2×C4×D4—171no—
392C2×C4×D4—341no—
393C2×#117—171no—
394C2×#117—341no—
395C22×C4⋊C4—171no—
396C22×C4⋊C4—171no—
397C22×C4⋊C4—171no—
398#501—178no—
399#485—178no—
400#484—178no—
401#483—178no—
402#483—178no—
403#479—178no—
404#475—178no—
405#470C2×D1718yescomplemented
406#467—178no—
407#441—178no—
408#435—178no—
409#428—178no—
410C2×#107—171no—
411C2×#107—171no—
412C2×#107—171no—
413C2×#106—171no—
414C2×#106—171no—
415C2×#106—171no—
416C2×#106—171no—
417C2×#106—171no—
418C2×#106—178no—
419C2×#106C2×D1711yescharacteristic
420C2×C4⋊C8—171no—
421C2×#103—171no—
422C2×#103—171no—
423C2×#103—171no—
424C2×#103—171no—
425C2×#103C2×D1711yescharacteristic
426C2×#103C2×D1711yescharacteristic
427C2×C22⋊C8—171no—
428C2×C22⋊C8—171no—
429C2×#97—171no—
430C2×C17—42no—
431C2×C17#334414yescomplemented
432C2×C17C2×#54711yescharacteristic
433C2×C17C22×#13711yescharacteristic
434C2×C17C2×#57711yescharacteristic
435D17—24no—
436C22×Q8—341no—
437C22×Q8C22×D1711yescharacteristic
438C22×Q8C22×D1711yescharacteristic
439C22×D4—171no—
440C23×C4—171no—
441C23×C4—341no—
442C23×C4—341no—
443C23×C4—341no—
444C23×C4C22×D1711yescharacteristic
445C2×Q16—24no—
446C2×Q16C22×D1714yes—
447C2×M16—24no—
448C2×M16C22×D1714yes—
449C22×C8—171no—
450C22×C8—171no—
451C22×C8—174no—
452C22×C8—344no—
453C22×C8C22×D1711yescharacteristic
454C22×C8C22×D1711yescharacteristic
455C4⋊Q8—174no—
456C4⋊Q8—342no—
457#126—348no—
458#125—174no—
459#125—342no—
460#125—348no—
461#125—348no—
462#123—348no—
463C22⋊Q8—22no—
464C22⋊Q8—22no—
465C22⋊Q8—174no—
466C22⋊Q8—174no—
467C22⋊Q8—348no—
468C22⋊Q8—348no—
469C22⋊Q8—342no—
470C22⋊Q8—342no—
471C22⋊Q8C22×D1714yes—
472C22⋊Q8C22×D1714yes—
473C4×Q8—174no—
474C4×Q8—174no—
475C4×Q8—342no—
476C4×Q8—342no—
477C4×D4—174no—
478C4×D4—174no—
479C4×D4—348no—
480#117—174no—
481#117—348no—
482#117—342no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—171no—
486C2×C4⋊C4—171no—
487C2×C4⋊C4—171no—
488C2×C4⋊C4—171no—
489C2×C4⋊C4—174no—
490C2×C4⋊C4—171no—
491C2×C4⋊C4—174no—
492C2×C4⋊C4—174no—
493C2×C4⋊C4—342no—
494C2×C4⋊C4—342no—
495C2×C4⋊C4—341no—
496C2×C4⋊C4—341no—
497C2×C4⋊C4—341no—
498C2×C4⋊C4—341no—
499C2×C4⋊C4—341no—
500C2×C4⋊C4—341no—
501C2×C4⋊C4—341no—
502C2×C4⋊C4—341no—
503C2×C4⋊C4—341no—
504C2×C4⋊C4—341no—
505C2×C4⋊C4—342no—
506C2×C4⋊C4C22×D1711yescharacteristic
507C2×C4⋊C4C22×D1711yescharacteristic
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—171no—
511C2×C22⋊C4—171no—
512C2×C22⋊C4—341no—
513C2×C22⋊C4—341no—
514C2×C22⋊C4—341no—
515C2×C42—171no—
516C2×C42—341no—
517C2×C42—341no—
518C2×C42—341no—
519#107—174no—
520#107—174no—
521#107—174no—
522#106—174no—
523#106—174no—
524#106—174no—
525#106—174no—
526#106—174no—
527#106C22×D1714yes—
528C4⋊C8—174no—
529#103—174no—
530#103—174no—
531#103—174no—
532#103—174no—
533#103C22×D1714yes—
534#103C22×D1714yes—
535C22⋊C8—174no—
536C22⋊C8—174no—
537#97—174no—
538C17C2×#334411yescharacteristic, complemented, Sylow
539C24—171no—
540C24D4×D1711yescharacteristic
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—22no—
544C2×Q8—22no—
545C2×Q8—22no—
546C2×Q8—22no—
547C2×Q8—344no—
548C2×Q8—1362no—
549C2×Q8C23×D1712yes—
550C2×Q8C23×D1712yes—
551C2×D4—174no—
552C2×D4—344no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—171no—
560C22×C4—171no—
561C22×C4—171no—
562C22×C4—172no—
563C22×C4—172no—
564C22×C4—344no—
565C22×C4—344no—
566C22×C4—342no—
567C22×C4—342no—
568C22×C4—341no—
569C22×C4—341no—
570C22×C4—341no—
571C22×C4—341no—
572C22×C4—344no—
573C22×C4—684no—
574C22×C4—1362no—
575C22×C4—1362no—
576C22×C4D4×D1712yes—
577C22×C4D4×D1711yescharacteristic
578C22×C4C23×D1712yes—
579C22×C4C23×D1711yescharacteristic
580Q16—28no—
581M16—28no—
582C2×C8—22no—
583C2×C8—172no—
584C2×C8—172no—
585C2×C8—342no—
586C2×C8—342no—
587C2×C8—348no—
588C2×C8#6325414yes—
589C2×C8C23×D1712yes—
590C2×C8C23×D1712yes—
591C4⋊C4—24no—
592C4⋊C4—24no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—174no—
596C4⋊C4—172no—
597C4⋊C4—172no—
598C4⋊C4—172no—
599C4⋊C4—172no—
600C4⋊C4—344no—
601C4⋊C4—344no—
602C4⋊C4—344no—
603C4⋊C4—344no—
604C4⋊C4—344no—
605C4⋊C4—344no—
606C4⋊C4—344no—
607C4⋊C4—344no—
608C4⋊C4—344no—
609C4⋊C4—341no—
610C4⋊C4—341no—
611C4⋊C4—344no—
612C4⋊C4—341no—
613C4⋊C4—341no—
614C4⋊C4C23×D1712yes—
615C4⋊C4C23×D1712yes—
616C22⋊C4—24no—
617C22⋊C4—24no—
618C22⋊C4—174no—
619C22⋊C4—174no—
620C22⋊C4—344no—
621C22⋊C4—344no—
622C22⋊C4—344no—
623C42—172no—
624C42—172no—
625C42—344no—
626C42—344no—
627C42—344no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—174no—
632C23—172no—
633C23—342no—
634C23—342no—
635C23C2×D4×D1712yes—
636C23C2×D4×D1711yescharacteristic
637Q8—22no—
638Q8—22no—
639Q8—22no—
640Q8—22no—
641Q8—42no—
642Q8—42no—
643Q8—1364no—
644D4—348no—
645C2×C4—22no—
646C2×C4—24no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—172no—
658C2×C4—172no—
659C2×C4—172no—
660C2×C4—342no—
661C2×C4—342no—
662C2×C4—342no—
663C2×C4—344no—
664C2×C4—342no—
665C2×C4—342no—
666C2×C4—342no—
667C2×C4—342no—
668C2×C4—342no—
669C2×C4—342no—
670C2×C4—688no—
671C2×C4—682no—
672C2×C4—682no—
673C2×C4—682no—
674C2×C4—682no—
675C2×C4—1364no—
676C2×C4—1364no—
677C2×C4C2×D4×D1712yes—
678C2×C4C2×D4×D1711yescharacteristic
679C2×C4C2×#6325412yes—
680C2×C4#1058769712yes—
681C2×C4C24×D1711yescharacteristic
682C8—22no—
683C8—342no—
684C8—342no—
685C8C2×#6325414yes—
686C22—22no—
687C22—22no—
688C22—22no—
689C22—44no—
690C22—174no—
691C22—342no—
692C22—348no—
693C22—342no—
694C22#1176345912yes—
695C22#137×D1712yes—
696C22#1176361812yes—
697C22C22×D4×D1711yescharacteristic
698C4—22no—
699C4—42no—
700C4—42no—
701C4—42no—
702C4—42no—
703C4—342no—
704C4—342no—
705C4—342no—
706C4—682no—
707C4—682no—
708C4—682no—
709C4—682no—
710C4#1176345912yes—
711C4C22×#6325411yescharacteristic
712C4C2×#1058769711yescharacteristic
713C2—42no—
714C2—344no—
715C2#1454123414yesdirect product factor
716C2C2×#1176345911yescharacteristic
717C2C2×#137×D1711yescharacteristic
718C2C2×#1176361811yescharacteristic
subgroupG/H
centerC23C2×D4×D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#470C2
socleC23×C17C22×D4
prime radicalC22×C22⋊D17D4
hypercenterC2×#470D17
hypocenterC17C2×#3344
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#470

Complements

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

NH ≅ G/Ntype
3. #14541234C2direct (N × H)
4. C2×#11763216C2semidirect
5. C2×#11763143C2semidirect
6. C2×#11763147C2semidirect
7. C2×#11763138C2semidirect
8. C2×#11763137C2semidirect
9. C2×#11763118C2semidirect
10. C2×#11763092C2semidirect
11. C2×#11763047C2semidirect
12. C2×#11762916C2semidirect
14. C2×#11762851C2semidirect
15. C2×#106×D17C2semidirect
16. C2×C17×#470C2semidirect
41. #11763216C22semidirect
42. #11763147C22semidirect
43. #11763143C22semidirect
44. #11763138C22semidirect
45. #11763137C22semidirect
46. #11763118C22semidirect
47. #11763092C22semidirect
48. #11763047C22semidirect
49. #11762916C22semidirect
51. #11762851C22semidirect
60. #106×D17C22semidirect
73. C17×#470C22semidirect
337. C2×#470D17semidirect
405. #470C2×D17semidirect
431. C2×C17#3344semidirect
538. C17C2×#3344semidirect
715. C2#14541234direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117635172
C2×#117634932
#145412342
C2×#117632162
C2×#117631432
C2×#117631472
C2×#117631382
C2×#117631372
C2×#117631182
C2×#117630922
C2×#117630472
C2×#117629162
C2×#117628782
C2×#117628512
C2×#106×D172
C2×C17×#4702
C2×#334417