Finite Group Databasebeta

← C2×#14541265 #17912899

Subgroups — C2×#14541265 #17912899

Order 4352.

1942 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763514C211yesmaximal, characteristic, complemented
2C2×#11763507C211yesmaximal, characteristic
3#14541265C2116yesmaximal, direct product factor
4C2×#11763217C211yesmaximal, characteristic, complemented
5C2×#11763144C211yesmaximal, characteristic, complemented
6C2×#11763127C211yesmaximal, characteristic, complemented
7C2×#11763152C211yesmaximal, characteristic, complemented
8C2×#11763124C211yesmaximal, characteristic, complemented
9C2×#11763115C211yesmaximal, characteristic, complemented
10C2×#11763088C211yesmaximal, characteristic, complemented
11C2×#11763056C211yesmaximal, characteristic, complemented
12C2×#11763038C211yesmaximal, characteristic, complemented
13C2×#11762908C211yesmaximal, characteristic, complemented
14C2×#11762880C211yesmaximal, characteristic, complemented
15C2×#11762850C211yesmaximal, characteristic, complemented
16C22×C17×#107C211yesmaximal, characteristic, complemented
17C22×#63219C2211yescharacteristic
18C22×#63218C2211yescharacteristic
19#11763514—24no—
20#11763514C2218yescomplemented
21#11763507—24no—
22#11763507C2218yes—
23C2×#10587574C2211yescharacteristic
24C2×#10587584—21no—
25C2×#10587576C2211yescharacteristic
26C2×#10587575—21no—
27C2×#10587580—21no—
28C2×#10587583C2211yescharacteristic
29C2×#10587610—21no—
30C2×#10587610C2211yescharacteristic
31C2×#10587582—21no—
32C2×#10587581C2211yescharacteristic
33C2×#10587616—21no—
34C2×#10587616C2211yescharacteristic
35C2×#10587573C2211yescharacteristic
36C2×#10587579C2211yescharacteristic
37C2×C4×C22⋊D17—21no—
38C2×C4×C22⋊D17—21no—
39C2×C4×C22⋊D17C2211yescharacteristic
40C2×#10587578C2211yescharacteristic
41C2×C4⋊C4×D17C2211yescharacteristic
42#11763217C2218yescomplemented
43#11763152C2218yescomplemented
44#11763144C2218yescomplemented
45#11763127C2218yescomplemented
46#11763124C2218yescomplemented
47#11763115C2218yescomplemented
48#11763088C2218yescomplemented
49#11763056C2218yescomplemented
50#11763038C2218yescomplemented
51#11762908C2218yescomplemented
52#11762880C2218yescomplemented
53#11762850C2218yescomplemented
54C2×#10587478C2211yescharacteristic
55C2×#10587478C2211yescharacteristic
56C2×#10587488C2211yescharacteristic
57C2×#10587479C2211yescharacteristic
58C2×#10587479C2211yescharacteristic
59C2×#10587485C2211yescharacteristic
60C2×#10587487C2211yescharacteristic
61C2×#10587481C2211yescharacteristic
62C2×#10587481C2211yescharacteristic
63C2×#10587492C2211yescharacteristic
64C2×#10587480C2211yescharacteristic
65C2×#10587480C2211yescharacteristic
66C2×C22⋊#3622C2211yescharacteristic
67C2×#10587491C2211yescharacteristic
68C2×#10587486C2211yescharacteristic
69C23×C8×C17C2211yescharacteristic
70C22×C4⋊C4×C17C2211yescharacteristic
71C22×C4⋊C4×C17C2211yescharacteristic
72C2×C17×#107C2211yescharacteristic
73C2×C17×#107C2211yescharacteristic
74C2×C17×#107C2211yescharacteristic
75C2×C17×#107C2211yescharacteristic
76C2×C17×#107C2218yescomplemented
77C23×C4×C17—21no—
78C23×C4×C17—21no—
79C23×C4×C17C2311yescharacteristic
80C22×C22⋊D17—21no—
81C22×C22⋊D17D411yescharacteristic
82C22×D68—21no—
83C22×D68C2311yescharacteristic
84C22×C4×D17—21no—
85C22×C4×D17—21no—
86C22×C4×D17C2311yescharacteristic
87C22×Dic34—21no—
88C22×Dic34C2311yescharacteristic
89C22×C8×C17—24no—
90C22×C8×C17C2311yescharacteristic
91C22×C8×C17C2314yes—
92C22×C8×C17C2311yescharacteristic
93C2×C4⋊C4×C17—22no—
94C2×C4⋊C4×C17—22no—
95C2×C4⋊C4×C17—21no—
96C2×C4⋊C4×C17—21no—
97C2×C4⋊C4×C17C2314yes—
98C2×C4⋊C4×C17C2311yescharacteristic
99C2×C4⋊C4×C17C2314yes—
100C2×C4⋊C4×C17C2311yescharacteristic
101C2×C4⋊C4×C17C2311yescharacteristic
102C2×C4⋊C4×C17C2311yescharacteristic
103C2×C22⋊Dic17—21no—
104C2×C22⋊Dic17D411yescharacteristic
105#10587616—22no—
106#10587616—28no—
107#10587616C2314yes—
108C4×C22⋊D17—28no—
109C4×C22⋊D17—28no—
110C4×C22⋊D17D414yes—
111C4×C22⋊D17C2314yes—
112C2×#63227—21no—
113C2×#63227—21no—
114C2×#63227—21no—
115C2×#63227—21no—
116C2×#63227—21no—
117C2×#63227D411yescharacteristic
118C2×C4⋊Dic17—21no—
119C2×C4⋊Dic17—21no—
120C2×C4⋊Dic17C2311yescharacteristic
121C2×C4⋊Dic17C2311yescharacteristic
122#10587610—22no—
123#10587610—28no—
124#10587610C2314yes—
125C2×#63225—21no—
126C2×#63225—21no—
127C2×#63225—21no—
128C2×#63225—21no—
129C2×#63225—21no—
130C2×#63225D411yescharacteristic
131C2×C4×Dic17—21no—
132C2×C4×Dic17—21no—
133C2×C4×Dic17C2311yescharacteristic
134C22×#3622C2311yescharacteristic
135C22×#3622C2311yescharacteristic
136C2×#63219—24no—
137C2×#63219C2314yes—
138C2×#63218—24no—
139C2×#63218C2314yes—
140#10587584—28no—
141#10587583—22no—
142#10587583C2314yes—
143#10587582—28no—
144#10587581—22no—
145#10587581C2314yes—
146#10587580—28no—
147#10587579—22no—
148#10587579C2314yes—
149#10587578—22no—
150#10587578C2314yes—
151C4⋊C4×D17—22no—
152C4⋊C4×D17C2314yes—
153#10587576—22no—
154#10587576C2314yes—
155#10587575—28no—
156#10587574—22no—
157#10587574C2314yes—
158#10587573—22no—
159#10587573C2314yes—
160C17×#107C2314yes—
161C17×#107C2314yes—
162C17×#107C2314yes—
163C17×#107C2314yes—
164C22⋊#3622C2314yes—
165#10587492C2314yes—
166#10587491C2314yes—
167#10587488C2314yes—
168#10587487C2314yes—
169#10587486C2314yes—
170#10587485C2314yes—
171#10587481C2314yes—
172#10587481C2314yes—
173#10587480C2314yes—
174#10587480C2314yes—
175#10587479C2314yes—
176#10587479C2314yes—
177#10587478C2314yes—
178#10587478C2314yes—
179C24×C17C2×D411yescharacteristic
180C23×D17—21no—
181C23×D17C2×D411yescharacteristic
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—24no—
190C22×C4×C17—82no—
191C22×C4×C17—82no—
192C22×C4×C17C2×D411yescharacteristic
193C22×C4×C17C2×D412yes—
194C22×C4×C17C2412yes—
195C22×C4×C17C2411yescharacteristic
196C2×C22⋊D17—24no—
197C2×C22⋊D17—24no—
198C2×C22⋊D17—44no—
199C2×C22⋊D17C2×D414yes—
200C22×Dic17—21no—
201C22×Dic17—21no—
202C22×Dic17—21no—
203C22×Dic17C2×D411yescharacteristic
204C22×Dic17C2×D411yescharacteristic
205C22×Dic17C2×D411yescharacteristic
206C2×D68—22no—
207C2×D68—22no—
208C2×D68—21no—
209C2×D68—24no—
210C2×D68—82no—
211C2×D68C2412yes—
212C2×C4×D17—22no—
213C2×C4×D17—22no—
214C2×C4×D17—24no—
215C2×C4×D17—24no—
216C2×C4×D17—82no—
217C2×C4×D17—82no—
218C2×C4×D17C2×D412yes—
219C2×C4×D17C2412yes—
220C2×Dic34—22no—
221C2×Dic34—22no—
222C2×Dic34—21no—
223C2×Dic34—24no—
224C2×Dic34—82no—
225C2×Dic34C2412yes—
226C2×C8×C17—22no—
227C2×C8×C17—28no—
228C2×C8×C17#4114yes—
229C2×C8×C17C2412yes—
230C2×C8×C17C2412yes—
231C4⋊C4×C17—21no—
232C4⋊C4×C17—21no—
233C4⋊C4×C17—24no—
234C4⋊C4×C17—21no—
235C4⋊C4×C17—21no—
236C4⋊C4×C17—24no—
237C4⋊C4×C17C2412yes—
238C4⋊C4×C17C2412yes—
239C4⋊C4×C17C2412yes—
240C4⋊C4×C17C2412yes—
241C22⋊Dic17—24no—
242C22⋊Dic17C2×D414yes—
243#63227—24no—
244#63227—24no—
245#63227—24no—
246#63227—24no—
247#63227—24no—
248#63227C2×D414yes—
249C4⋊Dic17—21no—
250C4⋊Dic17—21no—
251C4⋊Dic17—24no—
252C4⋊Dic17—24no—
253C4⋊Dic17C2412yes—
254C4⋊Dic17C2412yes—
255#63225—24no—
256#63225—24no—
257#63225—24no—
258#63225—24no—
259#63225—24no—
260#63225C2×D414yes—
261C4×Dic17—24no—
262C4×Dic17—24no—
263C4×Dic17C2×D412yes—
264C4×Dic17C2412yes—
265C2×#3622—22no—
266C2×#3622—22no—
267C2×#3622C2412yes—
268C2×#3622C2412yes—
269#63219—28no—
270#63218—28no—
271C2×#3346—171nomaximal, Sylow
272C23×C17—22no—
273C23×C17—22no—
274C23×C17#13714yes—
275C23×C17C22×D412yes—
276C23×C17C22×D411yescharacteristic
277C22×D17—22no—
278C22×D17—22no—
279C22×D17—22no—
280C22×D17—22no—
281C22×D17—42no—
282C22×D17—42no—
283C22×D17—42no—
284C22×D17C22×D412yes—
285C2×C4×C17—22no—
286C2×C4×C17—24no—
287C2×C4×C17—22no—
288C2×C4×C17—22no—
289C2×C4×C17—22no—
290C2×C4×C17—22no—
291C2×C4×C17—22no—
292C2×C4×C17—22no—
293C2×C4×C17—42no—
294C2×C4×C17—42no—
295C2×C4×C17—42no—
296C2×C4×C17—42no—
297C2×C4×C17—84no—
298C2×C4×C17—84no—
299C2×C4×C17C22×D412yes—
300C2×C4×C17C22×D411yescharacteristic
301C2×C4×C17C2×#4112yes—
302C2×C4×C172−1+412yes—
303C2×C4×C17C2511yescharacteristic
304C22⋊D17—28no—
305C22⋊D17—48no—
306C2×Dic17—22no—
307C2×Dic17—22no—
308C2×Dic17—22no—
309C2×Dic17—22no—
310C2×Dic17—22no—
311C2×Dic17—22no—
312C2×Dic17—42no—
313C2×Dic17—42no—
314C2×Dic17—42no—
315C2×Dic17C22×D412yes—
316C2×Dic17C22×D412yes—
317C2×Dic17C22×D412yes—
318D68—22no—
319D68—22no—
320D68—42no—
321D68—84no—
322C4×D17—24no—
323C4×D17—22no—
324C4×D17—22no—
325C4×D17—84no—
326C4×D17—84no—
327Dic34—22no—
328Dic34—22no—
329Dic34—42no—
330Dic34—84no—
331C8×C17—22no—
332C8×C17C2×#4114yes—
333#3622—22no—
334#3622—22no—
335C2×#554—171no—
336C2×#553—171no—
337#3346—1716no—
338C2×#501—171no—
339C2×#484—171no—
340C2×#481—171no—
341C2×#485—171no—
342C2×#480—171no—
343C2×#479—171no—
344C2×#474—171no—
345C2×#468—171no—
346C2×#465—171no—
347C2×#440—171no—
348C2×#435—171no—
349C2×#428—171no—
350C22×#107D1711yescharacteristic, complemented
351C22×C17—28no—
352C22×C17—22no—
353C22×C17—22no—
354C22×C17#54712yes—
355C22×C17C2×#13714yes—
356C22×C17C2×#13712yes—
357C22×C17#57612yes—
358C22×C17C23×D411yescharacteristic
359C2×D17—22no—
360C2×D17—22no—
361C2×D17—22no—
362C2×D17—44no—
363C2×D17—42no—
364C2×D17—42no—
365C2×D17—42no—
366C2×D17—84no—
367C4×C17—22no—
368C4×C17—42no—
369C4×C17—42no—
370C4×C17—42no—
371C4×C17—42no—
372C4×C17#54712yes—
373C4×C17C22×#4111yescharacteristic
374C4×C17C2×2−1+411yescharacteristic
375Dic17—22no—
376Dic17—22no—
377Dic17—22no—
378Dic17—42no—
379Dic17—42no—
380Dic17—42no—
381C22×SD16—171no—
382C22×M16—171no—
383C23×C8C2×D1711yescharacteristic
384#554—178no—
385#554—344no—
386#553—178no—
387#553—344no—
388C2×C4⋊Q8—171no—
389C2×#126—341no—
390C2×#125—171no—
391C2×#125—341no—
392C2×#123—341no—
393C2×C22⋊Q8—171no—
394C2×C22⋊Q8—171no—
395C2×C22⋊Q8—341no—
396C2×C22⋊Q8—341no—
397C2×#121—171no—
398C2×#121—171no—
399C2×#121—341no—
400C2×C4×Q8—171no—
401C2×C4×D4—171no—
402C2×C4×D4—171no—
403C2×C4×D4—341no—
404C2×C4×D4—341no—
405C2×#117—171no—
406C22×C4⋊C4—171no—
407C22×C4⋊C4C2×D1711yescharacteristic
408C22×C4⋊C4C2×D1711yescharacteristic
409#501—178no—
410#485—178no—
411#484—178no—
412#481—178no—
413#480—178no—
414#479—178no—
415#474—178no—
416#468—178no—
417#465—178no—
418#440—178no—
419#435—178no—
420#428—178no—
421C2×#107—171no—
422C2×#107—171no—
423C2×#107C2×D1711yescharacteristic
424C2×#107C2×D1711yescharacteristic
425C2×#107C2×D1711yescharacteristic
426C2×#107C2×D1711yescharacteristic
427C2×#107C2×D1718yescomplemented
428C2×#106—171no—
429C2×#106—171no—
430C2×#106—171no—
431C2×C4⋊C8—171no—
432C2×#103—171no—
433C2×#103—171no—
434C2×#103—171no—
435C2×#102—171no—
436C2×#102—171no—
437C2×#102—171no—
438C2×C22⋊C8—171no—
439C2×C22⋊C8—171no—
440C2×#97—171no—
441C2×C17—24no—
442C2×C17#334614yescomplemented
443C2×C17C2×#54711yescharacteristic
444C2×C17C22×#13711yescharacteristic
445C2×C17C2×#57611yescharacteristic
446D17—42no—
447D17—82no—
448C22×Q8—171no—
449C22×Q8—341no—
450C22×D4—171no—
451C22×D4—171no—
452C22×D4—341no—
453C22×D4—341no—
454C23×C4—21no—
455C23×C4—21no—
456C23×C4—171no—
457C23×C4—341no—
458C23×C4—341no—
459C23×C4C22×D1711yescharacteristic
460C2×SD16—174no—
461C2×SD16—344no—
462C2×M16—174no—
463C2×M16—344no—
464C22×C8—24no—
465C22×C8—171no—
466C22×C8—171no—
467C22×C8C22×D1711yescharacteristic
468C22×C8C22×D1714yes—
469C22×C8C22×D1711yescharacteristic
470C4⋊Q8—174no—
471C4⋊Q8—342no—
472#126—348no—
473#125—174no—
474#125—342no—
475#125—348no—
476#123—348no—
477C22⋊Q8—174no—
478C22⋊Q8—174no—
479C22⋊Q8—348no—
480C22⋊Q8—348no—
481C22⋊Q8—342no—
482C22⋊Q8—342no—
483#121—174no—
484#121—174no—
485#121—342no—
486#121—348no—
487#121—342no—
488C4×Q8—174no—
489C4×Q8—342no—
490C4×D4—174no—
491C4×D4—174no—
492C4×D4—174no—
493C4×D4—342no—
494C4×D4—348no—
495C4×D4—348no—
496#117—174no—
497#117—342no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—22no—
502C2×C4⋊C4—171no—
503C2×C4⋊C4—171no—
504C2×C4⋊C4—171no—
505C2×C4⋊C4—174no—
506C2×C4⋊C4—342no—
507C2×C4⋊C4—341no—
508C2×C4⋊C4—341no—
509C2×C4⋊C4—341no—
510C2×C4⋊C4—341no—
511C2×C4⋊C4—341no—
512C2×C4⋊C4—341no—
513C2×C4⋊C4—341no—
514C2×C4⋊C4C22×D1711yescharacteristic
515C2×C4⋊C4C22×D1711yescharacteristic
516C2×C4⋊C4C22×D1711yescharacteristic
517C2×C4⋊C4C22×D1711yescharacteristic
518C2×C4⋊C4C22×D1714yes—
519C2×C4⋊C4C22×D1714yes—
520C2×C22⋊C4—171no—
521C2×C22⋊C4—171no—
522C2×C22⋊C4—341no—
523C2×C22⋊C4—341no—
524C2×C22⋊C4—341no—
525C2×C22⋊C4—341no—
526C2×C22⋊C4—341no—
527C2×C22⋊C4—341no—
528C2×C42—171no—
529C2×C42—341no—
530C2×C42—341no—
531#107—174no—
532#107—174no—
533#107C22×D1714yes—
534#107C22×D1714yes—
535#107C22×D1714yes—
536#107C22×D1714yes—
537#106—174no—
538#106—174no—
539#106—174no—
540C4⋊C8—174no—
541#103—174no—
542#103—174no—
543#103—174no—
544#102—174no—
545#102—174no—
546#102—174no—
547C22⋊C8—174no—
548C22⋊C8—174no—
549#97—174no—
550C17C2×#334611yescharacteristic, complemented, Sylow
551C24—171no—
552C24—341no—
553C24D4×D1711yescharacteristic
554C2×Q8—172no—
555C2×Q8—344no—
556C2×Q8—341no—
557C2×Q8—342no—
558C2×Q8—342no—
559C2×Q8—1362no—
560C2×D4—174no—
561C2×D4—172no—
562C2×D4—344no—
563C2×D4—344no—
564C2×D4—344no—
565C2×D4—342no—
566C2×D4—341no—
567C2×D4—342no—
568C2×D4—684no—
569C2×D4—1362no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—24no—
577C22×C4—24no—
578C22×C4—82no—
579C22×C4—82no—
580C22×C4—171no—
581C22×C4—171no—
582C22×C4—171no—
583C22×C4—172no—
584C22×C4—172no—
585C22×C4—344no—
586C22×C4—344no—
587C22×C4—342no—
588C22×C4—342no—
589C22×C4—341no—
590C22×C4—341no—
591C22×C4—341no—
592C22×C4—1362no—
593C22×C4—1362no—
594C22×C4D4×D1712yes—
595C22×C4D4×D1711yescharacteristic
596C22×C4C23×D1712yes—
597C22×C4C23×D1711yescharacteristic
598SD16—348no—
599M16—348no—
600C2×C8—22no—
601C2×C8—28no—
602C2×C8—172no—
603C2×C8—172no—
604C2×C8—342no—
605C2×C8—342no—
606C2×C8#6325214yes—
607C2×C8C23×D1712yes—
608C2×C8C23×D1712yes—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—24no—
613C4⋊C4—21no—
614C4⋊C4—24no—
615C4⋊C4—174no—
616C4⋊C4—172no—
617C4⋊C4—172no—
618C4⋊C4—344no—
619C4⋊C4—344no—
620C4⋊C4—344no—
621C4⋊C4—344no—
622C4⋊C4—344no—
623C4⋊C4—344no—
624C4⋊C4—341no—
625C4⋊C4—341no—
626C4⋊C4—344no—
627C4⋊C4C23×D1712yes—
628C4⋊C4C23×D1712yes—
629C4⋊C4C23×D1712yes—
630C4⋊C4C23×D1712yes—
631C22⋊C4—174no—
632C22⋊C4—174no—
633C22⋊C4—344no—
634C22⋊C4—344no—
635C22⋊C4—344no—
636C22⋊C4—344no—
637C22⋊C4—344no—
638C22⋊C4—344no—
639C42—172no—
640C42—172no—
641C42—344no—
642C42—344no—
643C23—22no—
644C23—22no—
645C23—172no—
646C23—342no—
647C23—342no—
648C23—342no—
649C23—342no—
650C23—682no—
651C23—682no—
652C23—682no—
653C23#1058760414yes—
654C23C2×D4×D1712yes—
655C23C2×D4×D1711yescharacteristic
656Q8—342no—
657Q8—342no—
658Q8—682no—
659Q8—1364no—
660D4—348no—
661D4—342no—
662D4—342no—
663D4—688no—
664D4—682no—
665D4—1364no—
666C2×C4—22no—
667C2×C4—24no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—84no—
679C2×C4—84no—
680C2×C4—172no—
681C2×C4—172no—
682C2×C4—172no—
683C2×C4—342no—
684C2×C4—342no—
685C2×C4—342no—
686C2×C4—344no—
687C2×C4—342no—
688C2×C4—342no—
689C2×C4—342no—
690C2×C4—342no—
691C2×C4—342no—
692C2×C4—682no—
693C2×C4—682no—
694C2×C4—682no—
695C2×C4—1364no—
696C2×C4—1364no—
697C2×C4C2×#6325212yes—
698C2×C4C2×D4×D1712yes—
699C2×C4C2×D4×D1711yescharacteristic
700C2×C4#1058769412yes—
701C2×C4C24×D1711yescharacteristic
702C8—22no—
703C8—342no—
704C8—342no—
705C8C2×#6325214yes—
706C22—22no—
707C22—22no—
708C22—28no—
709C22—342no—
710C22—342no—
711C22—342no—
712C22—684no—
713C22—682no—
714C22—682no—
715C22—682no—
716C22—1364no—
717C22#1176346012yes—
718C22C2×#1058760414yes—
719C22C2×#1058760412yes—
720C22#1176361012yes—
721C22C22×D4×D1711yescharacteristic
722C4—22no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—42no—
727C4—342no—
728C4—342no—
729C4—342no—
730C4—682no—
731C4—682no—
732C4—682no—
733C4#1176346012yes—
734C4C22×#6325211yescharacteristic
735C4C2×#1058769411yescharacteristic
736C2—24no—
737C2—682no—
738C2—1362no—
739C2#1454126514yesdirect product factor
740C2C2×#1176346011yescharacteristic
741C2C22×#1058760411yescharacteristic
742C2C2×#1176361011yescharacteristic
subgroupG/H
centerC23C2×D4×D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC22×C17×#107C2
socleC23×C17C22×D4
prime radicalC2×#11763507C2
hypercenterC22×#107D17
hypocenterC17C2×#3346
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#107

Complements

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

NH ≅ G/Ntype
1. C2×#11763514C2semidirect
3. #14541265C2direct (N × H)
4. C2×#11763217C2semidirect
5. C2×#11763144C2semidirect
6. C2×#11763127C2semidirect
7. C2×#11763152C2semidirect
8. C2×#11763124C2semidirect
9. C2×#11763115C2semidirect
10. C2×#11763088C2semidirect
11. C2×#11763056C2semidirect
12. C2×#11763038C2semidirect
13. C2×#11762908C2semidirect
14. C2×#11762880C2semidirect
15. C2×#11762850C2semidirect
16. C22×C17×#107C2semidirect
20. #11763514C22semidirect
42. #11763217C22semidirect
43. #11763152C22semidirect
44. #11763144C22semidirect
45. #11763127C22semidirect
46. #11763124C22semidirect
47. #11763115C22semidirect
48. #11763088C22semidirect
49. #11763056C22semidirect
50. #11763038C22semidirect
51. #11762908C22semidirect
52. #11762880C22semidirect
53. #11762850C22semidirect
76. C2×C17×#107C22semidirect
350. C22×#107D17semidirect
427. C2×#107C2×D17semidirect
442. C2×C17#3346semidirect
550. C17C2×#3346semidirect
739. C2#14541265direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117635142
C2×#117635072
#145412652
C2×#117632172
C2×#117631442
C2×#117631272
C2×#117631522
C2×#117631242
C2×#117631152
C2×#117630882
C2×#117630562
C2×#117630382
C2×#117629082
C2×#117628802
C2×#117628502
C22×C17×#1072
C2×#334617