Finite Group Databasebeta

← C2×#14540204 #17907244

Subgroups — C2×#14540204 #17907244

Order 4352.

1818 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763430C211yesmaximal, characteristic
2#14540204C2116yesmaximal, direct product factor
3C2×#11763113C211yesmaximal, characteristic, complemented
4C2×#11763104C211yesmaximal, characteristic, complemented
5C2×#11763094C211yesmaximal, characteristic, complemented
6C2×#11763106C211yesmaximal, characteristic, complemented
7C2×#11763065C211yesmaximal, characteristic, complemented
8C2×#11763057C211yesmaximal, characteristic
9C2×#11763048C211yesmaximal, characteristic, complemented
10C2×#11763040C211yesmaximal, characteristic
11C2×#11763031C211yesmaximal, characteristic, complemented
12C2×#11763031C211yesmaximal, characteristic, complemented
13C2×#11763016C211yesmaximal, characteristic, complemented
14C2×#11763011C211yesmaximal, characteristic, complemented
15C2×#11762836C211yesmaximal, characteristic, complemented
16C2×C17×#541C211yesmaximal, characteristic, complemented
17C22×#63231C2211yescharacteristic
18C22×#63231C2211yescharacteristic
19C22×#63230C2211yescharacteristic
20C22×#63230C2211yescharacteristic
21C22×#63223C2211yescharacteristic
22C23×#3622C2211yescharacteristic
23#11763430—24no—
24#11763430C2218yes—
25C2×#10587555C2211yescharacteristic
26C2×#10587584—21no—
27C2×#10587561C2211yescharacteristic
28C2×#10587571—21no—
29C2×#10587569—21no—
30C2×#10587610C2211yescharacteristic
31C2×#10587582—21no—
32C2×#10587616C2211yescharacteristic
33C2×C4×Dic34C2211yescharacteristic
34C2×C4×D68C2211yescharacteristic
35#11763113C2218yescomplemented
36#11763106C2218yescomplemented
37#11763104C2218yescomplemented
38#11763094C2218yescomplemented
39#11763065C2218yescomplemented
40#11763057C2218yes—
41#11763048C2218yescomplemented
42#11763040C2218yes—
43#11763031C2218yescomplemented
44#11763031C2218yescomplemented
45#11763016C2218yescomplemented
46#11763011C2218yescomplemented
47C2×#10587478C2211yescharacteristic
48C2×#10587478C2211yescharacteristic
49C2×#10587479C2211yescharacteristic
50C2×#10587479C2211yescharacteristic
51#11762836C2218yescomplemented
52C2×C4⋊#3622C2211yescharacteristic
53C2×C4⋊#3622C2211yescharacteristic
54C2×C4⋊#3622C2211yescharacteristic
55C2×C4⋊#3622C2211yescharacteristic
56C2×#10587506C2211yescharacteristic
57C2×#10587506C2211yescharacteristic
58C2×#10587506C2211yescharacteristic
59C2×#10587506C2211yescharacteristic
60C2×#10587481C2211yescharacteristic
61C2×#10587481C2211yescharacteristic
62C2×#10587480C2211yescharacteristic
63C2×#10587480C2211yescharacteristic
64C17×#541—24no—
65C17×#541C2218yescomplemented
66C2×C17×C4⋊Q8C2211yescharacteristic
67C2×C17×#126—21no—
68C2×C17×#126—21no—
69C2×C17×#125—21no—
70C2×C17×#125—21no—
71C2×C17×#125C2211yescharacteristic
72C2×C17×C22⋊Q8C2211yescharacteristic
73C2×C17×C22⋊Q8C2211yescharacteristic
74C2×C4×Q8×C17C2211yescharacteristic
75C2×C4×Q8×C17C2211yescharacteristic
76C2×C17×#117C2211yescharacteristic
77C22×Q8×C17C2311yescharacteristic
78C22×Q8×C17C2311yescharacteristic
79C23×C4×C17C2311yescharacteristic
80C22×C22⋊D17—21no—
81C22×D68C2311yescharacteristic
82C22×C4×D17—21no—
83C22×Dic34—21no—
84C22×Dic34C2311yescharacteristic
85C17×C4⋊Q8—22no—
86C17×C4⋊Q8C2314yes—
87C17×#126—28no—
88C17×#126—28no—
89C17×#125—28no—
90C17×#125—28no—
91C17×#125—22no—
92C17×#125C2314yes—
93C17×C22⋊Q8—22no—
94C17×C22⋊Q8—22no—
95C17×C22⋊Q8C2314yes—
96C17×C22⋊Q8C2314yes—
97C4×Q8×C17—22no—
98C4×Q8×C17—22no—
99C4×Q8×C17C2314yes—
100C4×Q8×C17C2314yes—
101C17×#117D414yes—
102C17×#117C2314yes—
103C2×C4⋊C4×C17—21no—
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×C17—21no—
111C2×C4⋊C4×C17D411yescharacteristic
112C2×C4⋊C4×C17D411yescharacteristic
113C2×C4⋊C4×C17C2311yescharacteristic
114C2×C4⋊C4×C17C2311yescharacteristic
115C2×C22⋊C4×C17—21no—
116C2×C22⋊C4×C17—21no—
117C2×C22⋊C4×C17D411yescharacteristic
118C2×C22⋊C4×C17D411yescharacteristic
119C2×C42×C17—21no—
120C2×C42×C17—21no—
121C2×C42×C17C2311yescharacteristic
122C2×C42×C17C2311yescharacteristic
123C2×C22⋊Dic17—21no—
124C2×#63231—42no—
125C2×#63231—42no—
126C2×#63231C2314yes—
127C2×#63231C2314yes—
128C2×#63230—42no—
129C2×#63230—42no—
130C2×#63230C2314yes—
131C2×#63230C2314yes—
132#10587616—22no—
133#10587616C2314yes—
134C2×#63227—21no—
135C2×#63227—21no—
136C2×#63227—21no—
137C2×#63227—21no—
138C2×C4⋊Dic17—21no—
139C2×C4⋊Dic17C2311yescharacteristic
140C2×C4⋊Dic17C2311yescharacteristic
141#10587610—22no—
142#10587610C2314yes—
143C2×#63225—21no—
144C2×#63225—21no—
145C2×C4×Dic17—21no—
146C2×#63223—42no—
147C2×#63223C2314yes—
148C22×#3622—42no—
149C22×#3622C2311yescharacteristic
150C22×#3622C2311yescharacteristic
151C22×#3622C2311yescharacteristic
152C22×#3622C2311yescharacteristic
153C22×#3622C2314yes—
154#10587584—28no—
155#10587582—28no—
156#10587571—28no—
157#10587569—28no—
158#10587561—22no—
159#10587561C2314yes—
160C4×D68—22no—
161C4×D68C2314yes—
162#10587555—22no—
163#10587555C2314yes—
164C4×Dic34—22no—
165C4×Dic34C2314yes—
166#10587506C2314yes—
167#10587506C2314yes—
168#10587506C2314yes—
169#10587506C2314yes—
170#10587481C2314yes—
171#10587481C2314yes—
172#10587480C2314yes—
173#10587480C2314yes—
174#10587479C2314yes—
175#10587479C2314yes—
176#10587478C2314yes—
177#10587478C2314yes—
178C4⋊#3622C2314yes—
179C4⋊#3622C2314yes—
180C4⋊#3622C2314yes—
181C4⋊#3622C2314yes—
182C24×C17C2×D411yescharacteristic
183C23×D17—21no—
184C2×Q8×C17—21no—
185C2×Q8×C17—21no—
186C2×Q8×C17—22no—
187C2×Q8×C17—22no—
188C2×Q8×C17—22no—
189C2×Q8×C17—22no—
190C2×Q8×C17C2412yes—
191C2×Q8×C17C2412yes—
192C22×C4×C17—22no—
193C22×C4×C17—22no—
194C22×C4×C17—21no—
195C22×C4×C17—21no—
196C22×C4×C17—21no—
197C22×C4×C17—21no—
198C22×C4×C17C2×D412yes—
199C22×C4×C17C2×D411yescharacteristic
200C22×C4×C17C2×D411yescharacteristic
201C22×C4×C17C2×D411yescharacteristic
202C22×C4×C17C2×D411yescharacteristic
203C22×C4×C17C2×D411yescharacteristic
204C22×C4×C17C2412yes—
205C22×C4×C17C2411yescharacteristic
206C2×C22⋊D17—24no—
207C2×C22⋊D17—82no—
208C22×Dic17—21no—
209C22×Dic17—21no—
210C22×Dic17—21no—
211C2×D68—22no—
212C2×D68—22no—
213C2×D68—21no—
214C2×D68C2412yes—
215C2×C4×D17—24no—
216C2×C4×D17—82no—
217C2×Dic34—22no—
218C2×Dic34—22no—
219C2×Dic34—21no—
220C2×Dic34—24no—
221C2×Dic34—82no—
222C2×Dic34C2412yes—
223C4⋊C4×C17—21no—
224C4⋊C4×C17—21no—
225C4⋊C4×C17—24no—
226C4⋊C4×C17—24no—
227C4⋊C4×C17—24no—
228C4⋊C4×C17—24no—
229C4⋊C4×C17—24no—
230C4⋊C4×C17—24no—
231C4⋊C4×C17—24no—
232C4⋊C4×C17—24no—
233C4⋊C4×C17C2×D414yes—
234C4⋊C4×C17C2×D414yes—
235C4⋊C4×C17C2412yes—
236C4⋊C4×C17C2412yes—
237C22⋊C4×C17—24no—
238C22⋊C4×C17—24no—
239C22⋊C4×C17C2×D414yes—
240C22⋊C4×C17C2×D414yes—
241C42×C17—24no—
242C42×C17—24no—
243C42×C17C2×D412yes—
244C42×C17C2×D412yes—
245C42×C17C2412yes—
246C42×C17C2412yes—
247C22⋊Dic17—24no—
248#63231—44no—
249#63231—44no—
250#63230—44no—
251#63230—44no—
252#63227—24no—
253#63227—24no—
254#63227—24no—
255#63227—24no—
256C4⋊Dic17—21no—
257C4⋊Dic17—21no—
258C4⋊Dic17—24no—
259C4⋊Dic17C2412yes—
260C4⋊Dic17C2412yes—
261#63225—24no—
262#63225—24no—
263C4×Dic17—24no—
264#63223—44no—
265C2×#3622—22no—
266C2×#3622—22no—
267C2×#3622—22no—
268C2×#3622—22no—
269C2×#3622—44no—
270C2×#3622C2412yes—
271C2×#3622C2412yes—
272C2×#3622C2412yes—
273C2×#3622C2412yes—
274C2×#3258—171nomaximal, Sylow
275C23×C17—22no—
276C23×C17—22no—
277C23×C17—22no—
278C23×C17C22×D412yes—
279C23×C17C22×D411yescharacteristic
280C22×D17—22no—
281C22×D17—42no—
282C22×D17—42no—
283C22×D17—42no—
284Q8×C17—22no—
285Q8×C17—22no—
286Q8×C17—22no—
287Q8×C17—22no—
288Q8×C17—42no—
289Q8×C17—42no—
290C2×C4×C17—22no—
291C2×C4×C17—22no—
292C2×C4×C17—22no—
293C2×C4×C17—22no—
294C2×C4×C17—22no—
295C2×C4×C17—24no—
296C2×C4×C17—22no—
297C2×C4×C17—22no—
298C2×C4×C17—22no—
299C2×C4×C17—22no—
300C2×C4×C17—22no—
301C2×C4×C17—22no—
302C2×C4×C17—42no—
303C2×C4×C17—42no—
304C2×C4×C17—42no—
305C2×C4×C17—42no—
306C2×C4×C17C22×D412yes—
307C2×C4×C17C22×D412yes—
308C2×C4×C17C22×D412yes—
309C2×C4×C17C22×D412yes—
310C2×C4×C17C22×D412yes—
311C2×C4×C17C22×D411yescharacteristic
312C2×C4×C17H(5,𝔽2)12yes—
313C2×C4×C172−1+412yes—
314C2×C4×C17C2511yescharacteristic
315C22⋊D17—84no—
316C2×Dic17—22no—
317C2×Dic17—22no—
318C2×Dic17—22no—
319C2×Dic17—42no—
320C2×Dic17—42no—
321C2×Dic17—42no—
322D68—22no—
323D68—22no—
324D68—42no—
325C4×D17—84no—
326Dic34—22no—
327Dic34—22no—
328Dic34—42no—
329Dic34—84no—
330#3622—22no—
331#3622—22no—
332#3622—22no—
333#3622—22no—
334C2×#542—171no—
335C2×#541D1711yescharacteristic, complemented
336#3258—1716no—
337C2×#479—171no—
338C2×#477—171no—
339C2×#475—171no—
340C2×#478—171no—
341C2×#470—171no—
342C2×#468—171no—
343C2×#467—171no—
344C2×#465—171no—
345C2×#464—171no—
346C2×#464—171no—
347C2×#462—171no—
348C2×#461—171no—
349C2×#424—171no—
350C22×C17—22no—
351C22×C17—22no—
352C22×C17—22no—
353C22×C17—44no—
354C22×C17#53712yes—
355C22×C17#57712yes—
356C22×C17#57812yes—
357C22×C17C23×D411yescharacteristic
358C2×D17—42no—
359C2×D17—42no—
360C2×D17—42no—
361C2×D17—84no—
362C4×C17—22no—
363C4×C17—22no—
364C4×C17—22no—
365C4×C17—22no—
366C4×C17—22no—
367C4×C17—42no—
368C4×C17—42no—
369C4×C17—42no—
370C4×C17—42no—
371C4×C17#53712yes—
372C4×C17C2×H(5,𝔽2)11yescharacteristic
373C4×C17C2×2−1+411yescharacteristic
374Dic17—42no—
375Dic17—42no—
376Dic17—42no—
377C22×Q16—171no—
378C22×Q16—171no—
379C22×SD16—171no—
380C22×SD16—171no—
381C22×M16—171no—
382C23×C8—171no—
383#542—178no—
384#542—344no—
385#541—24no—
386#541C2×D1718yescomplemented
387C2×C4⋊Q8—171no—
388C2×C4⋊Q8C2×D1711yescharacteristic
389C2×#126—21no—
390C2×#126—21no—
391C2×#126—341no—
392C2×#125—21no—
393C2×#125—21no—
394C2×#125C2×D1711yescharacteristic
395C2×#124—171no—
396C2×#124—341no—
397C2×#123—341no—
398C2×C22⋊Q8—171no—
399C2×C22⋊Q8—341no—
400C2×C22⋊Q8C2×D1711yescharacteristic
401C2×C22⋊Q8C2×D1711yescharacteristic
402C2×#121—171no—
403C2×C4×Q8—171no—
404C2×C4×Q8C2×D1711yescharacteristic
405C2×C4×Q8C2×D1711yescharacteristic
406C2×C4×D4—171no—
407C2×#117C2×D1711yescharacteristic
408#479—178no—
409#478—178no—
410#477—178no—
411#475—178no—
412#470—178no—
413#468—178no—
414#467—178no—
415#465—178no—
416#464—178no—
417#464—178no—
418#462—178no—
419#461—178no—
420C2×#107—171no—
421C2×#107—171no—
422C2×#106—171no—
423C2×#106—171no—
424#424—178no—
425C2×C4⋊C8—171no—
426C2×C4⋊C8—171no—
427C2×C4⋊C8—171no—
428C2×C4⋊C8—171no—
429C2×#103—171no—
430C2×#103—171no—
431C2×#103—171no—
432C2×#103—171no—
433C2×#103—171no—
434C2×#103—171no—
435C2×#102—171no—
436C2×#102—171no—
437C2×C17—42no—
438C2×C17#325814yescomplemented
439C2×C17C2×#53711yescharacteristic
440C2×C17C2×#57711yescharacteristic
441C2×C17C2×#57811yescharacteristic
442D17—82no—
443C22×Q8—171no—
444C22×Q8—341no—
445C22×Q8C22×D1711yescharacteristic
446C22×Q8C22×D1711yescharacteristic
447C22×D4—171no—
448C22×D4—341no—
449C23×C4—341no—
450C23×C4C22×D1711yescharacteristic
451C2×Q16—174no—
452C2×Q16—174no—
453C2×Q16—682no—
454C2×Q16—682no—
455C2×SD16—174no—
456C2×SD16—174no—
457C2×SD16—682no—
458C2×SD16—682no—
459C2×M16—174no—
460C2×M16—682no—
461C22×C8—171no—
462C22×C8—171no—
463C22×C8—171no—
464C22×C8—171no—
465C22×C8—174no—
466C22×C8—682no—
467C4⋊Q8—22no—
468C4⋊Q8—174no—
469C4⋊Q8—342no—
470C4⋊Q8C22×D1714yes—
471#126—28no—
472#126—28no—
473#126—348no—
474#125—28no—
475#125—28no—
476#125—22no—
477#125C22×D1714yes—
478#124—174no—
479#124—348no—
480#124—342no—
481#123—348no—
482C22⋊Q8—22no—
483C22⋊Q8—22no—
484C22⋊Q8—174no—
485C22⋊Q8—342no—
486C22⋊Q8—348no—
487C22⋊Q8C22×D1714yes—
488C22⋊Q8C22×D1714yes—
489#121—174no—
490#121—342no—
491C4×Q8—22no—
492C4×Q8—22no—
493C4×Q8—174no—
494C4×Q8—342no—
495C4×Q8C22×D1714yes—
496C4×Q8C22×D1714yes—
497C4×D4—174no—
498C4×D4—342no—
499#117C22⋊D1714yes—
500#117C22×D1714yes—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—171no—
510C2×C4⋊C4—171no—
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×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—341no—
521C2×C22⋊C4—341no—
522C2×C22⋊C4—341no—
523C2×C22⋊C4—341no—
524C2×C22⋊C4—341no—
525C2×C22⋊C4C22⋊D1711yescharacteristic
526C2×C22⋊C4C22⋊D1711yescharacteristic
527C2×C42—21no—
528C2×C42—21no—
529C2×C42—341no—
530C2×C42C22×D1711yescharacteristic
531C2×C42C22×D1711yescharacteristic
532#107—174no—
533#107—174no—
534#106—174no—
535#106—174no—
536C4⋊C8—174no—
537C4⋊C8—174no—
538C4⋊C8—174no—
539C4⋊C8—174no—
540#103—174no—
541#103—174no—
542#103—174no—
543#103—174no—
544#103—174no—
545#103—174no—
546#102—174no—
547#102—174no—
548C17C2×#325811yescharacteristic, complemented, Sylow
549C24—341no—
550C24C2×C22⋊D1711yescharacteristic
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—22no—
554C2×Q8—22no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—172no—
558C2×Q8—341no—
559C2×Q8—344no—
560C2×Q8—342no—
561C2×Q8—342no—
562C2×Q8—1362no—
563C2×Q8C23×D1712yes—
564C2×Q8C23×D1712yes—
565C2×D4—172no—
566C2×D4—344no—
567C2×D4—342no—
568C2×D4—342no—
569C2×D4—341no—
570C2×D4—1362no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—341no—
578C22×C4—341no—
579C22×C4—341no—
580C22×C4—344no—
581C22×C4—1362no—
582C22×C4C2×C22⋊D1712yes—
583C22×C4C2×C22⋊D1711yescharacteristic
584C22×C4C2×C22⋊D1711yescharacteristic
585C22×C4C2×C22⋊D1711yescharacteristic
586C22×C4C2×C22⋊D1711yescharacteristic
587C22×C4C2×C22⋊D1711yescharacteristic
588C22×C4C23×D1712yes—
589C22×C4C23×D1711yescharacteristic
590Q16—684no—
591Q16—684no—
592SD16—684no—
593SD16—684no—
594M16—684no—
595C2×C8—172no—
596C2×C8—172no—
597C2×C8—172no—
598C2×C8—172no—
599C2×C8—342no—
600C2×C8—342no—
601C2×C8—342no—
602C2×C8—342no—
603C2×C8—684no—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—24no—
609C4⋊C4—24no—
610C4⋊C4—24no—
611C4⋊C4—24no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—172no—
615C4⋊C4—172no—
616C4⋊C4—341no—
617C4⋊C4—341no—
618C4⋊C4—344no—
619C4⋊C4—344no—
620C4⋊C4—344no—
621C4⋊C4C2×C22⋊D1714yes—
622C4⋊C4C2×C22⋊D1714yes—
623C4⋊C4C23×D1712yes—
624C4⋊C4C23×D1712yes—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—344no—
628C22⋊C4—344no—
629C22⋊C4—344no—
630C22⋊C4—344no—
631C22⋊C4—344no—
632C22⋊C4C2×C22⋊D1714yes—
633C22⋊C4C2×C22⋊D1714yes—
634C42—24no—
635C42—24no—
636C42—344no—
637C42C2×C22⋊D1712yes—
638C42C2×C22⋊D1712yes—
639C42C23×D1712yes—
640C42C23×D1712yes—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—342no—
645C23—682no—
646C23—682no—
647C23—682no—
648C23C22×C22⋊D1712yes—
649C23C22×C22⋊D1711yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—22no—
653Q8—22no—
654Q8—42no—
655Q8—42no—
656Q8—342no—
657Q8—342no—
658Q8—682no—
659Q8—1364no—
660D4—342no—
661D4—342no—
662D4—682no—
663D4—1364no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—342no—
681C2×C4—342no—
682C2×C4—342no—
683C2×C4—682no—
684C2×C4—682no—
685C2×C4—682no—
686C2×C4—1364no—
687C2×C4#1058769612yes—
688C2×C4#1058769712yes—
689C2×C4C22×C22⋊D1712yes—
690C2×C4C22×C22⋊D1712yes—
691C2×C4C22×C22⋊D1712yes—
692C2×C4C22×C22⋊D1712yes—
693C2×C4C22×C22⋊D1712yes—
694C2×C4C22×C22⋊D1711yescharacteristic
695C2×C4C24×D1711yescharacteristic
696C8—342no—
697C8—342no—
698C8—342no—
699C8—342no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—44no—
704C22—682no—
705C22—682no—
706C22—682no—
707C22—1364no—
708C22#1176338712yes—
709C22#1176361712yes—
710C22#1176362412yes—
711C22C23×C22⋊D1711yescharacteristic
712C4—22no—
713C4—22no—
714C4—22no—
715C4—22no—
716C4—22no—
717C4—42no—
718C4—42no—
719C4—42no—
720C4—42no—
721C4—682no—
722C4—682no—
723C4—682no—
724C4#1176338712yes—
725C4C2×#1058769611yescharacteristic
726C4C2×#1058769711yescharacteristic
727C2—42no—
728C2—1362no—
729C2#1454020414yesdirect product factor
730C2C2×#1176338711yescharacteristic
731C2C2×#1176361711yescharacteristic
732C2C2×#1176362411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#541C2
socleC23×C17C22×D4
prime radicalC2×#10587616C22
hypercenterC2×#541D17
hypocenterC17C2×#3258
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#541

Complements

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

NH ≅ G/Ntype
2. #14540204C2direct (N × H)
3. C2×#11763113C2semidirect
4. C2×#11763104C2semidirect
5. C2×#11763094C2semidirect
6. C2×#11763106C2semidirect
7. C2×#11763065C2semidirect
9. C2×#11763048C2semidirect
11. C2×#11763031C2semidirect
12. C2×#11763031C2semidirect
13. C2×#11763016C2semidirect
14. C2×#11763011C2semidirect
15. C2×#11762836C2semidirect
16. C2×C17×#541C2semidirect
35. #11763113C22semidirect
36. #11763106C22semidirect
37. #11763104C22semidirect
38. #11763094C22semidirect
39. #11763065C22semidirect
41. #11763048C22semidirect
43. #11763031C22semidirect
44. #11763031C22semidirect
45. #11763016C22semidirect
46. #11763011C22semidirect
51. #11762836C22semidirect
65. C17×#541C22semidirect
335. C2×#541D17semidirect
386. #541C2×D17semidirect
438. C2×C17#3258semidirect
548. C17C2×#3258semidirect
729. C2#14540204direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117634302
#145402042
C2×#117631132
C2×#117631042
C2×#117630942
C2×#117631062
C2×#117630652
C2×#117630572
C2×#117630482
C2×#117630402
C2×#117630312
C2×#117630162
C2×#117630112
C2×#117628362
C2×C17×#5412
C2×#325817