Finite Group Databasebeta

← C2×#14541241 #17912873

Subgroups — C2×#14541241 #17912873

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×#11763516C211yesmaximal, characteristic
2C2×#11763499C211yesmaximal, characteristic
3#14541241C2116yesmaximal, direct product factor
4C2×#11763218C211yesmaximal, characteristic, complemented
5C2×#11763145C211yesmaximal, characteristic, complemented
6C2×#11763151C211yesmaximal, characteristic, complemented
7C2×#11763140C211yesmaximal, characteristic, complemented
8C2×#11763140C211yesmaximal, characteristic, complemented
9C2×#11763117C211yesmaximal, characteristic, complemented
10C2×#11763095C211yesmaximal, characteristic, complemented
11C2×#11763067C211yesmaximal, characteristic, complemented
12C2×#11763050C211yesmaximal, characteristic, complemented
13C2×#11762917C211yesmaximal, characteristic, complemented
14C2×#11762851C211yesmaximal, characteristic, complemented
15C22×#10587488C211yesmaximal, characteristic, complemented
16C2×C17×#435C211yesmaximal, characteristic
17C22×Dic68C2211yescharacteristic
18#11763516—24no—
19#11763516C2218yes—
20#11763499—24no—
21#11763499C2218yes—
22C2×#10587555C2211yescharacteristic
23C2×#10587565—21no—
24C2×#10587556C2211yescharacteristic
25C2×#10587576—21no—
26C2×#10587575—21no—
27C2×#10587621—21no—
28C2×#10587610C2211yescharacteristic
29C2×#10587610C2211yescharacteristic
30C2×#10587610C2211yescharacteristic
31C2×#10587610C2211yescharacteristic
32C2×#10587564—21no—
33C2×#10587564—21no—
34C2×C4×Dic34C2211yescharacteristic
35C2×C4×Dic34C2211yescharacteristic
36C2×D4×Dic17—21no—
37C2×#10587612C2211yescharacteristic
38C2×#10587563—21no—
39C22×C4⋊Dic17C2211yescharacteristic
40C22×C4⋊Dic17C2211yescharacteristic
41C22×C4⋊Dic17C2211yescharacteristic
42#11763218C2218yescomplemented
43#11763151C2218yescomplemented
44#11763145C2218yescomplemented
45#11763140C2218yescomplemented
46#11763140C2218yescomplemented
47#11763117C2218yescomplemented
48#11763095C2218yescomplemented
49#11763067C2218yescomplemented
50#11763050C2218yescomplemented
51#11762917C2218yescomplemented
52#11762851C2218yescomplemented
53C2×#10587489C2211yescharacteristic
54C2×#10587489C2211yescharacteristic
55C2×#10587489C2211yescharacteristic
56C2×#10587488C2211yescharacteristic
57C2×#10587488C2211yescharacteristic
58C2×#10587488C2211yescharacteristic
59C2×#10587488C2211yescharacteristic
60C2×#10587488C2211yescharacteristic
61C2×#10587488C2211yescharacteristic
62C2×#10587488C2218yescomplemented
63C2×#10587487C2211yescharacteristic
64C2×#10587487C2211yescharacteristic
65C2×#10587487C2211yescharacteristic
66C2×#10587487C2211yescharacteristic
67C2×#10587487C2211yescharacteristic
68C2×#10587487C2211yescharacteristic
69C22×M16×C17C2211yescharacteristic
70C23×C8×C17C2211yescharacteristic
71C2×C4×D4×C17C2211yescharacteristic
72C17×#435C2218yes—
73C2×C17×C4⋊C8C2211yescharacteristic
74C2×C17×C22⋊C8C2211yescharacteristic
75C2×C17×C22⋊C8C2211yescharacteristic
76C2×C17×#97C2211yescharacteristic
77C22×D4×C17D411yescharacteristic
78C23×C4×C17C2311yescharacteristic
79C23×C4×C17C2311yescharacteristic
80C23×Dic17—21no—
81C23×Dic17—21no—
82C23×Dic17—21no—
83C22×Dic34—21no—
84C22×Dic34C2311yescharacteristic
85C22×Dic34C2311yescharacteristic
86C2×M16×C17—24no—
87C2×M16×C17C2314yes—
88C22×C8×C17—24no—
89C22×C8×C17C2314yes—
90C22×C8×C17C2311yescharacteristic
91C22×C8×C17C2311yescharacteristic
92C22×C8×C17C2311yescharacteristic
93C22×C8×C17C2311yescharacteristic
94C4×D4×C17D414yes—
95C4×D4×C17C2314yes—
96C2×C4⋊C4×C17D411yescharacteristic
97C2×C22⋊C4×C17D411yescharacteristic
98C2×C22⋊C4×C17D411yescharacteristic
99C2×C42×C17C2311yescharacteristic
100C2×C22⋊Dic17—21no—
101C2×C22⋊Dic17—21no—
102C2×C22⋊Dic17—21no—
103C2×C22⋊Dic17—21no—
104C2×C22⋊Dic17—21no—
105#10587621—28no—
106D4×Dic17—28no—
107#10587612—22no—
108#10587612C2314yes—
109C2×C4⋊Dic17—22no—
110C2×C4⋊Dic17—22no—
111C2×C4⋊Dic17—22no—
112C2×C4⋊Dic17—21no—
113C2×C4⋊Dic17—21no—
114C2×C4⋊Dic17—21no—
115C2×C4⋊Dic17—21no—
116C2×C4⋊Dic17C2314yes—
117C2×C4⋊Dic17C2311yescharacteristic
118C2×C4⋊Dic17C2314yes—
119C2×C4⋊Dic17C2314yes—
120C2×C4⋊Dic17C2311yescharacteristic
121C2×C4⋊Dic17C2311yescharacteristic
122C2×C4⋊Dic17C2311yescharacteristic
123C2×C4⋊Dic17C2311yescharacteristic
124C2×C4⋊Dic17C2311yescharacteristic
125#10587610—22no—
126#10587610—22no—
127#10587610—22no—
128#10587610—22no—
129#10587610C2314yes—
130#10587610C2314yes—
131#10587610C2314yes—
132#10587610C2314yes—
133C2×#63225—21no—
134C2×#63225—21no—
135C2×#63225—21no—
136C2×#63225—21no—
137C2×#63225—21no—
138C2×#63225—21no—
139C2×#63225—21no—
140C2×#63225—21no—
141C2×C4×Dic17—21no—
142C2×C4×Dic17—21no—
143C2×C4×Dic17—21no—
144C2×Dic68—24no—
145C2×Dic68C2314yes—
146#10587576—28no—
147#10587575—28no—
148#10587565—28no—
149#10587564—28no—
150#10587564—28no—
151#10587563—28no—
152#10587556—22no—
153#10587556C2314yes—
154#10587555—22no—
155#10587555C2314yes—
156C4×Dic34—22no—
157C4×Dic34—22no—
158C4×Dic34C2314yes—
159C4×Dic34C2314yes—
160C17×C4⋊C8C2314yes—
161C17×C22⋊C8C2314yes—
162C17×C22⋊C8C2314yes—
163C17×#97C2314yes—
164#10587489C2314yes—
165#10587489C2314yes—
166#10587489C2314yes—
167#10587488C2314yes—
168#10587488C2314yes—
169#10587488C2314yes—
170#10587488C2314yes—
171#10587488C2314yes—
172#10587488C2314yes—
173#10587487C2314yes—
174#10587487C2314yes—
175#10587487C2314yes—
176#10587487C2314yes—
177#10587487C2314yes—
178#10587487C2314yes—
179C24×C17C2×D411yescharacteristic
180C24×C17C2×D411yescharacteristic
181C2×D4×C17—24no—
182C2×D4×C17C2×D414yes—
183C22×C4×C17—22no—
184C22×C4×C17—22no—
185C22×C4×C17—22no—
186C22×C4×C17—22no—
187C22×C4×C17C2×D411yescharacteristic
188C22×C4×C17C2×D411yescharacteristic
189C22×C4×C17C2×D411yescharacteristic
190C22×C4×C17C2×D412yes—
191C22×C4×C17C2×D412yes—
192C22×C4×C17C2×D411yescharacteristic
193C22×C4×C17C2412yes—
194C22×C4×C17C2412yes—
195C22×C4×C17C2411yescharacteristic
196C22×Dic17—21no—
197C22×Dic17—21no—
198C22×Dic17—21no—
199C22×Dic17—21no—
200C22×Dic17—21no—
201C22×Dic17—24no—
202C22×Dic17—21no—
203C22×Dic17—21no—
204C22×Dic17—21no—
205C22×Dic17—24no—
206C22×Dic17—24no—
207C22×Dic17—44no—
208C22×Dic17—82no—
209C22×Dic17—82no—
210C2×Dic34—22no—
211C2×Dic34—22no—
212C2×Dic34—22no—
213C2×Dic34—22no—
214C2×Dic34—21no—
215C2×Dic34—21no—
216C2×Dic34—24no—
217C2×Dic34—82no—
218C2×Dic34C2412yes—
219C2×Dic34C2412yes—
220M16×C17—28no—
221C2×C8×C17—22no—
222C2×C8×C17—22no—
223C2×C8×C17—22no—
224C2×C8×C17—28no—
225C2×C8×C17#4114yes—
226C2×C8×C17C2412yes—
227C2×C8×C17C2412yes—
228C2×C8×C17C2412yes—
229C2×C8×C17C2412yes—
230C4⋊C4×C17C2×D414yes—
231C22⋊C4×C17C2×D414yes—
232C22⋊C4×C17C2×D414yes—
233C42×C17C2×D412yes—
234C42×C17C2412yes—
235C22⋊Dic17—24no—
236C22⋊Dic17—24no—
237C22⋊Dic17—24no—
238C22⋊Dic17—24no—
239C22⋊Dic17—24no—
240C4⋊Dic17—21no—
241C4⋊Dic17—21no—
242C4⋊Dic17—21no—
243C4⋊Dic17—21no—
244C4⋊Dic17—24no—
245C4⋊Dic17—21no—
246C4⋊Dic17—21no—
247C4⋊Dic17—24no—
248C4⋊Dic17—24no—
249C4⋊Dic17—24no—
250C4⋊Dic17C2412yes—
251C4⋊Dic17C2412yes—
252C4⋊Dic17C2412yes—
253C4⋊Dic17C2412yes—
254C4⋊Dic17C2412yes—
255C4⋊Dic17C2412yes—
256#63225—24no—
257#63225—24no—
258#63225—24no—
259#63225—24no—
260#63225—24no—
261#63225—24no—
262#63225—24no—
263#63225—24no—
264C4×Dic17—24no—
265C4×Dic17—24no—
266C4×Dic17—24no—
267Dic68—28no—
268C2×#3344—171nomaximal, Sylow
269C23×C17—22no—
270C23×C17—22no—
271C23×C17—22no—
272C23×C17—22no—
273C23×C17—22no—
274C23×C17#13714yes—
275C23×C17C22×D412yes—
276C23×C17C22×D412yes—
277C23×C17C22×D411yescharacteristic
278D4×C17—28no—
279C2×C4×C17—22no—
280C2×C4×C17—22no—
281C2×C4×C17—22no—
282C2×C4×C17—22no—
283C2×C4×C17—24no—
284C2×C4×C17—24no—
285C2×C4×C17—22no—
286C2×C4×C17—22no—
287C2×C4×C17—22no—
288C2×C4×C17—22no—
289C2×C4×C17C22×D412yes—
290C2×C4×C17C22×D412yes—
291C2×C4×C17C22×D412yes—
292C2×C4×C17C22×D412yes—
293C2×C4×C17C22×D411yescharacteristic
294C2×C4×C17C2×#4112yes—
295C2×C4×C172−1+412yes—
296C2×C4×C17C2511yescharacteristic
297C2×Dic17—22no—
298C2×Dic17—22no—
299C2×Dic17—22no—
300C2×Dic17—22no—
301C2×Dic17—22no—
302C2×Dic17—22no—
303C2×Dic17—22no—
304C2×Dic17—22no—
305C2×Dic17—42no—
306C2×Dic17—42no—
307C2×Dic17—48no—
308C2×Dic17—42no—
309C2×Dic17—42no—
310C2×Dic17—42no—
311C2×Dic17—42no—
312C2×Dic17—42no—
313C2×Dic17—42no—
314C2×Dic17—84no—
315C2×Dic17—84no—
316Dic34—22no—
317Dic34—22no—
318Dic34—22no—
319Dic34—22no—
320Dic34—42no—
321Dic34—42no—
322Dic34—84no—
323C8×C17—22no—
324C8×C17—22no—
325C8×C17—22no—
326C8×C17C2×#4114yes—
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×#470—171no—
338C2×#467—171no—
339C2×#441—171no—
340C2×#435D1711yescharacteristic
341C2×#428—171no—
342C22×#106—171no—
343C22×C17—28no—
344C22×C17—22no—
345C22×C17—22no—
346C22×C17—22no—
347C22×C17—22no—
348C22×C17—22no—
349C22×C17—44no—
350C22×C17#54712yes—
351C22×C17C2×#13714yes—
352C22×C17C2×#13712yes—
353C22×C17#57712yes—
354C22×C17C23×D411yescharacteristic
355C4×C17—22no—
356C4×C17—22no—
357C4×C17—22no—
358C4×C17—22no—
359C4×C17#54712yes—
360C4×C17C22×#4111yescharacteristic
361C4×C17C2×2−1+411yescharacteristic
362Dic17—42no—
363Dic17—42no—
364Dic17—42no—
365Dic17—42no—
366Dic17—42no—
367Dic17—42no—
368Dic17—42no—
369Dic17—42no—
370C22×Q16—171no—
371C22×M16C2×D1711yescharacteristic
372C23×C8C2×D1711yescharacteristic
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—171no—
386C2×C22⋊Q8—171no—
387C2×C22⋊Q8—341no—
388C2×C22⋊Q8—341no—
389C2×C4×Q8—171no—
390C2×C4×Q8—171no—
391C2×C4×D4—341no—
392C2×C4×D4C2×D1711yescharacteristic
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#470—178no—
406#467—178no—
407#441—178no—
408#435C2×D1718yes—
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—178no—
418C2×#106—171no—
419C2×#106—171no—
420C2×C4⋊C8C2×D1711yescharacteristic
421C2×#103—171no—
422C2×#103—171no—
423C2×#103—171no—
424C2×#103—171no—
425C2×#103—171no—
426C2×#103—171no—
427C2×C22⋊C8C2×D1711yescharacteristic
428C2×C22⋊C8C2×D1711yescharacteristic
429C2×#97C2×D1711yescharacteristic
430C2×C17—24no—
431C2×C17—42no—
432C2×C17#334414yescomplemented
433C2×C17C2×#54711yescharacteristic
434C2×C17C22×#13711yescharacteristic
435C2×C17C2×#57711yescharacteristic
436C22×Q8—171no—
437C22×Q8—171no—
438C22×Q8—341no—
439C22×D4D6811yescharacteristic
440C23×C4—341no—
441C23×C4—341no—
442C23×C4—341no—
443C23×C4C22×D1711yescharacteristic
444C23×C4C22×D1711yescharacteristic
445C2×Q16—174no—
446C2×Q16—344no—
447C2×M16—24no—
448C2×M16C22×D1714yes—
449C22×C8—24no—
450C22×C8C22×D1711yescharacteristic
451C22×C8C22×D1714yes—
452C22×C8C22×D1711yescharacteristic
453C22×C8C22×D1711yescharacteristic
454C22×C8C22×D1711yescharacteristic
455C4⋊Q8—174no—
456C4⋊Q8—342no—
457#126—348no—
458#125—174no—
459#125—348no—
460#125—348no—
461#125—342no—
462#123—348no—
463C22⋊Q8—174no—
464C22⋊Q8—174no—
465C22⋊Q8—174no—
466C22⋊Q8—174no—
467C22⋊Q8—342no—
468C22⋊Q8—342no—
469C22⋊Q8—342no—
470C22⋊Q8—342no—
471C22⋊Q8—348no—
472C22⋊Q8—348no—
473C4×Q8—174no—
474C4×Q8—174no—
475C4×Q8—342no—
476C4×Q8—342no—
477C4×D4—348no—
478C4×D4D6814yes—
479C4×D4C22×D1714yes—
480#117—174no—
481#117—342no—
482#117—348no—
483C2×C4⋊C4—171no—
484C2×C4⋊C4—171no—
485C2×C4⋊C4—171no—
486C2×C4⋊C4—171no—
487C2×C4⋊C4—171no—
488C2×C4⋊C4—174no—
489C2×C4⋊C4—174no—
490C2×C4⋊C4—174no—
491C2×C4⋊C4—171no—
492C2×C4⋊C4—341no—
493C2×C4⋊C4—341no—
494C2×C4⋊C4—341no—
495C2×C4⋊C4—342no—
496C2×C4⋊C4—342no—
497C2×C4⋊C4—342no—
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—341no—
506C2×C4⋊C4—341no—
507C2×C4⋊C4D6811yescharacteristic
508C2×C22⋊C4—341no—
509C2×C22⋊C4—341no—
510C2×C22⋊C4—341no—
511C2×C22⋊C4—341no—
512C2×C22⋊C4—341no—
513C2×C22⋊C4D6811yescharacteristic
514C2×C22⋊C4D6811yescharacteristic
515C2×C42—341no—
516C2×C42—341no—
517C2×C42—341no—
518C2×C42C22×D1711yescharacteristic
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#106—174no—
528C4⋊C8C22×D1714yes—
529#103—174no—
530#103—174no—
531#103—174no—
532#103—174no—
533#103—174no—
534#103—174no—
535C22⋊C8C22×D1714yes—
536C22⋊C8C22×D1714yes—
537#97C22×D1714yes—
538C17C2×#334411yescharacteristic, complemented, Sylow
539C24C2×D6811yescharacteristic
540C24C2×D6811yescharacteristic
541C2×Q8—172no—
542C2×Q8—172no—
543C2×Q8—341no—
544C2×Q8—341no—
545C2×Q8—344no—
546C2×Q8—342no—
547C2×Q8—342no—
548C2×Q8—342no—
549C2×Q8—342no—
550C2×Q8—1362no—
551C2×D4—24no—
552C2×D4C2×D6814yes—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—344no—
558C22×C4—341no—
559C22×C4—341no—
560C22×C4—341no—
561C22×C4—341no—
562C22×C4—341no—
563C22×C4—341no—
564C22×C4—341no—
565C22×C4—341no—
566C22×C4—344no—
567C22×C4—344no—
568C22×C4—684no—
569C22×C4—1362no—
570C22×C4—1362no—
571C22×C4C2×D6812yes—
572C22×C4C2×D6812yes—
573C22×C4C2×D6811yescharacteristic
574C22×C4C2×D6811yescharacteristic
575C22×C4C2×D6811yescharacteristic
576C22×C4C2×D6811yescharacteristic
577C22×C4C23×D1712yes—
578C22×C4C23×D1712yes—
579C22×C4C23×D1711yescharacteristic
580Q16—348no—
581M16—28no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—28no—
586C2×C8#6325414yes—
587C2×C8C23×D1712yes—
588C2×C8C23×D1712yes—
589C2×C8C23×D1712yes—
590C2×C8C23×D1712yes—
591C4⋊C4—172no—
592C4⋊C4—172no—
593C4⋊C4—172no—
594C4⋊C4—172no—
595C4⋊C4—172no—
596C4⋊C4—172no—
597C4⋊C4—341no—
598C4⋊C4—341no—
599C4⋊C4—344no—
600C4⋊C4—344no—
601C4⋊C4—341no—
602C4⋊C4—341no—
603C4⋊C4—341no—
604C4⋊C4—344no—
605C4⋊C4—341no—
606C4⋊C4—344no—
607C4⋊C4—344no—
608C4⋊C4—344no—
609C4⋊C4—344no—
610C4⋊C4—344no—
611C4⋊C4—344no—
612C4⋊C4—344no—
613C4⋊C4—344no—
614C4⋊C4—344no—
615C4⋊C4C2×D6814yes—
616C22⋊C4—344no—
617C22⋊C4—344no—
618C22⋊C4—344no—
619C22⋊C4—344no—
620C22⋊C4—344no—
621C22⋊C4C2×D6814yes—
622C22⋊C4C2×D6814yes—
623C42—344no—
624C42—344no—
625C42—344no—
626C42C2×D6812yes—
627C42C23×D1712yes—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23#1058759514yes—
634C23C22×D6812yes—
635C23C22×D6812yes—
636C23C22×D6811yescharacteristic
637Q8—342no—
638Q8—342no—
639Q8—342no—
640Q8—342no—
641Q8—682no—
642Q8—682no—
643Q8—1364no—
644D4—28no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—342no—
656C2×C4—342no—
657C2×C4—342no—
658C2×C4—342no—
659C2×C4—342no—
660C2×C4—342no—
661C2×C4—342no—
662C2×C4—342no—
663C2×C4—682no—
664C2×C4—682no—
665C2×C4—688no—
666C2×C4—682no—
667C2×C4—682no—
668C2×C4—682no—
669C2×C4—682no—
670C2×C4—682no—
671C2×C4—682no—
672C2×C4—1364no—
673C2×C4—1364no—
674C2×C4C22×D6812yes—
675C2×C4C22×D6812yes—
676C2×C4C22×D6812yes—
677C2×C4C22×D6812yes—
678C2×C4C22×D6811yescharacteristic
679C2×C4C2×#6325412yes—
680C2×C4#1058769712yes—
681C2×C4C24×D1711yescharacteristic
682C8—22no—
683C8—22no—
684C8—22no—
685C8C2×#6325414yes—
686C22—22no—
687C22—28no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—44no—
693C22#1176346312yes—
694C22C2×#1058759514yes—
695C22C2×#1058759512yes—
696C22#1176362112yes—
697C22C23×D6811yescharacteristic
698C4—22no—
699C4—22no—
700C4—22no—
701C4—22no—
702C4—682no—
703C4—682no—
704C4—682no—
705C4—682no—
706C4—682no—
707C4—682no—
708C4—682no—
709C4—682no—
710C4#1176346312yes—
711C4C22×#6325411yescharacteristic
712C4C2×#1058769711yescharacteristic
713C2—24no—
714C2—42no—
715C2#1454124114yesdirect product factor
716C2C2×#1176346311yescharacteristic
717C2C22×#1058759511yescharacteristic
718C2C2×#1176362111yescharacteristic
subgroupG/H
centerC23C22×D68
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#435C2
socleC23×C17C22×D4
prime radicalC22×D4×C17D4
hypercenterC2×#435D17
hypocenterC17C2×#3344
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
3. #14541241C2direct (N × H)
4. C2×#11763218C2semidirect
5. C2×#11763145C2semidirect
6. C2×#11763151C2semidirect
7. C2×#11763140C2semidirect
8. C2×#11763140C2semidirect
9. C2×#11763117C2semidirect
10. C2×#11763095C2semidirect
11. C2×#11763067C2semidirect
12. C2×#11763050C2semidirect
13. C2×#11762917C2semidirect
14. C2×#11762851C2semidirect
15. C22×#10587488C2semidirect
42. #11763218C22semidirect
43. #11763151C22semidirect
44. #11763145C22semidirect
45. #11763140C22semidirect
46. #11763140C22semidirect
47. #11763117C22semidirect
48. #11763095C22semidirect
49. #11763067C22semidirect
50. #11763050C22semidirect
51. #11762917C22semidirect
52. #11762851C22semidirect
62. C2×#10587488C22semidirect
432. C2×C17#3344semidirect
538. C17C2×#3344semidirect
715. C2#14541241direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117635162
C2×#117634992
#145412412
C2×#117632182
C2×#117631452
C2×#117631512
C2×#117631402
C2×#117631172
C2×#117630952
C2×#117630672
C2×#117630502
C2×#117629172
C2×#117628512
C22×#105874882
C2×C17×#4352
C2×#334417