Finite Group Databasebeta

← C2×#14541850 #17915330

Subgroups — C2×#14541850 #17915330

Order 4352.

2002 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763544C211yesmaximal, characteristic, complemented
2#14541850C2116yesmaximal, direct product factor
3C2×#11763201C211yesmaximal, characteristic, complemented
4C2×#11763199C211yesmaximal, characteristic
5C2×#11763191C211yesmaximal, characteristic, complemented
6C2×#11763031C211yesmaximal, characteristic, complemented
7C2×#11763028C211yesmaximal, characteristic, complemented
8C2×#11763009C211yesmaximal, characteristic, complemented
9C2×#11763024C211yesmaximal, characteristic, complemented
10C2×#11763021C211yesmaximal, characteristic, complemented
11C2×#11763011C211yesmaximal, characteristic, complemented
12C2×#11762940C211yesmaximal, characteristic, complemented
13C2×#11762919C211yesmaximal, characteristic, complemented
14C2×#11762914C211yesmaximal, characteristic, complemented
15C2×C4×#63230C211yesmaximal, characteristic, complemented
16C2×C17×#556C211yesmaximal, characteristic, complemented
17C22×#63231C2211yescharacteristic
18C22×#63231C2211yescharacteristic
19C22×#63229C2211yescharacteristic
20C22×#63230C2211yescharacteristic
21C22×#63230C2211yescharacteristic
22C22×#63230C2211yescharacteristic
23C22×#63230C2211yescharacteristic
24C22×#63228C2211yescharacteristic
25C22×#63228C2211yescharacteristic
26#11763544—24no—
27#11763544C2218yescomplemented
28C2×#10587560C2211yescharacteristic
29C2×#10587633—21no—
30C2×#10587561C2211yescharacteristic
31C2×#10587561C2211yescharacteristic
32C2×#10587580—21no—
33C2×#10587580—21no—
34C2×C4×Dic34C2211yescharacteristic
35C2×C4×D68C2211yescharacteristic
36C2×C4×D68C2211yescharacteristic
37C2×#10587579—21no—
38#11763201C2218yescomplemented
39#11763199C2218yes—
40#11763191C2218yescomplemented
41#11763031C2218yescomplemented
42#11763028C2218yescomplemented
43#11763024C2218yescomplemented
44#11763021C2218yescomplemented
45#11763011C2218yescomplemented
46#11763009C2218yescomplemented
47#11762940C2218yescomplemented
48#11762919C2218yescomplemented
49#11762914C2218yescomplemented
50C4×#63230C2218yescomplemented
51C2×#10587479C2211yescharacteristic
52C2×C4⋊#3622C2211yescharacteristic
53C2×C4⋊#3622C2211yescharacteristic
54C2×C4⋊#3622C2211yescharacteristic
55C2×#10587506C2211yescharacteristic
56C2×#10587506C2211yescharacteristic
57C2×#10587481C2211yescharacteristic
58C2×#10587503C2211yescharacteristic
59C2×#10587480C2211yescharacteristic
60C2×#10587480C2211yescharacteristic
61C2×#10587474C2211yescharacteristic
62C2×#10587474C2211yescharacteristic
63C2×C4×#3622C2211yescharacteristic
64C17×#556—24no—
65C17×#556C2218yescomplemented
66C2×C17×C4⋊Q8C2211yescharacteristic
67C2×C17×#126—21no—
68C2×C17×#126—21no—
69C2×C17×#124C2211yescharacteristic
70C2×C17×#124C2211yescharacteristic
71C2×C17×C22⋊Q8—21no—
72C2×C4×Q8×C17C2211yescharacteristic
73C2×C4×Q8×C17C2211yescharacteristic
74C2×C4×Q8×C17C2211yescharacteristic
75C2×C4×D4×C17C2211yescharacteristic
76C2×C17×#117—21no—
77C22×Q8×C17D411yescharacteristic
78C22×Q8×C17C2311yescharacteristic
79C22×Q8×C17C2311yescharacteristic
80C22×D4×C17C2311yescharacteristic
81C23×C4×C17—21no—
82C22×D68—21no—
83C22×D68—21no—
84C22×D68C2311yescharacteristic
85C22×D68C2311yescharacteristic
86C22×C4×D17—21no—
87C22×C4×D17—21no—
88C22×Dic34C2311yescharacteristic
89C17×C4⋊Q8—22no—
90C17×C4⋊Q8C2314yes—
91C17×#126—28no—
92C17×#126—28no—
93C17×#124—22no—
94C17×#124—22no—
95C17×#124C2314yes—
96C17×#124C2314yes—
97C17×C22⋊Q8—28no—
98C4×Q8×C17—22no—
99C4×Q8×C17—22no—
100C4×Q8×C17D414yes—
101C4×Q8×C17C2314yes—
102C4×Q8×C17C2314yes—
103C4×Q8×C17C2314yes—
104C4×D4×C17—22no—
105C4×D4×C17C2314yes—
106C17×#117—28no—
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×C17D411yescharacteristic
114C2×C4⋊C4×C17C2311yescharacteristic
115C2×C22⋊C4×C17—21no—
116C2×C22⋊C4×C17—21no—
117C2×C22⋊C4×C17—21no—
118C2×C22⋊C4×C17—21no—
119C2×C22⋊C4×C17—21no—
120C2×C42×C17—21no—
121C2×C42×C17—21no—
122C2×C42×C17C2311yescharacteristic
123C2×C42×C17C2311yescharacteristic
124C2×C42×C17C2311yescharacteristic
125#10587633—28no—
126C2×#63231—24no—
127C2×#63231—42no—
128C2×#63231C2314yes—
129C2×#63231C2314yes—
130C2×#63230—24no—
131C2×#63230—42no—
132C2×#63230—42no—
133C2×#63230—42no—
134C2×#63230C2314yes—
135C2×#63230C2314yes—
136C2×#63230C2314yes—
137C2×#63230C2314yes—
138C2×#63229—42no—
139C2×#63229C2314yes—
140C2×#63228—24no—
141C2×#63228—42no—
142C2×#63228C2314yes—
143C2×#63228C2314yes—
144C2×#63227—21no—
145C2×#63227—21no—
146C2×#63227—21no—
147C2×#63227—21no—
148C2×#63227—21no—
149C2×#63227—21no—
150C2×C4⋊Dic17C2311yescharacteristic
151C2×#63225—21no—
152C2×C4×Dic17—21no—
153C22×#3622C2311yescharacteristic
154C22×#3622C2311yescharacteristic
155C22×#3622C2311yescharacteristic
156C22×#3622C2311yescharacteristic
157#10587580—28no—
158#10587580—28no—
159#10587579—28no—
160#10587561—22no—
161#10587561—22no—
162#10587561C2314yes—
163#10587561C2314yes—
164#10587560—22no—
165#10587560C2314yes—
166C4×D68—22no—
167C4×D68—22no—
168C4×D68C2314yes—
169C4×D68C2314yes—
170C4×Dic34—22no—
171C4×Dic34C2314yes—
172#10587506C2314yes—
173#10587506C2314yes—
174#10587503C2314yes—
175#10587481C2314yes—
176#10587480C2314yes—
177#10587480C2314yes—
178#10587479C2314yes—
179C4⋊#3622C2314yes—
180C4⋊#3622C2314yes—
181C4⋊#3622C2314yes—
182#10587474C2314yes—
183#10587474C2314yes—
184C4×#3622C2314yes—
185C24×C17—21no—
186C23×D17—21no—
187C23×D17—21no—
188C2×Q8×C17—21no—
189C2×Q8×C17—21no—
190C2×Q8×C17—22no—
191C2×Q8×C17—22no—
192C2×Q8×C17—22no—
193C2×Q8×C17—22no—
194C2×Q8×C17—42no—
195C2×Q8×C17C2×D414yes—
196C2×Q8×C17C2412yes—
197C2×Q8×C17C2412yes—
198C2×D4×C17—21no—
199C2×D4×C17—22no—
200C2×D4×C17—22no—
201C2×D4×C17C2412yes—
202C22×C4×C17—21no—
203C22×C4×C17—21no—
204C22×C4×C17—21no—
205C22×C4×C17—24no—
206C22×C4×C17—44no—
207C22×C4×C17C2×D411yescharacteristic
208C22×C4×C17C2×D411yescharacteristic
209C22×C4×C17C2×D411yescharacteristic
210C22×C4×C17C2×D411yescharacteristic
211C22×C4×C17C2×D411yescharacteristic
212C22×C4×C17C2×D411yescharacteristic
213C22×C4×C17C2411yescharacteristic
214C22×Dic17—21no—
215C22×Dic17—21no—
216C2×D68—22no—
217C2×D68—22no—
218C2×D68—22no—
219C2×D68—22no—
220C2×D68—24no—
221C2×D68—21no—
222C2×D68—21no—
223C2×D68—24no—
224C2×D68—44no—
225C2×D68—82no—
226C2×D68C2412yes—
227C2×D68C2412yes—
228C2×C4×D17—24no—
229C2×C4×D17—24no—
230C2×C4×D17—82no—
231C2×C4×D17—82no—
232C2×Dic34—22no—
233C2×Dic34—22no—
234C2×Dic34—21no—
235C2×Dic34C2412yes—
236C4⋊C4×C17—24no—
237C4⋊C4×C17—24no—
238C4⋊C4×C17—24no—
239C4⋊C4×C17—24no—
240C4⋊C4×C17—21no—
241C4⋊C4×C17C2×D414yes—
242C4⋊C4×C17C2×D414yes—
243C4⋊C4×C17C2×D414yes—
244C4⋊C4×C17C2412yes—
245C22⋊C4×C17—24no—
246C22⋊C4×C17—24no—
247C22⋊C4×C17—24no—
248C22⋊C4×C17—24no—
249C22⋊C4×C17—24no—
250C42×C17—24no—
251C42×C17—24no—
252C42×C17C2×D412yes—
253C42×C17C2×D412yes—
254C42×C17C2×D412yes—
255C42×C17C2412yes—
256C42×C17C2412yes—
257C42×C17C2412yes—
258#63231—28no—
259#63231—44no—
260#63230—28no—
261#63230—44no—
262#63230—44no—
263#63230—44no—
264#63229—44no—
265#63228—28no—
266#63228—44no—
267#63227—24no—
268#63227—24no—
269#63227—24no—
270#63227—24no—
271#63227—24no—
272#63227—24no—
273C4⋊Dic17—21no—
274C4⋊Dic17C2412yes—
275#63225—24no—
276C4×Dic17—24no—
277C2×#3622—22no—
278C2×#3622—22no—
279C2×#3622—22no—
280C2×#3622#4114yes—
281C2×#3622C2412yes—
282C2×#3622C2412yes—
283C2×#3622C2412yes—
284C2×#3622C2412yes—
285C2×#3401—171nomaximal, Sylow
286C23×C17—22no—
287C23×C17—42no—
288C23×C17—42no—
289C23×C17—42no—
290C23×C17C22×D411yescharacteristic
291C22×D17—22no—
292C22×D17—22no—
293C22×D17—42no—
294C22×D17—42no—
295C22×D17—42no—
296C22×D17—42no—
297C22×D17—42no—
298C22×D17—42no—
299Q8×C17—22no—
300Q8×C17—22no—
301Q8×C17—22no—
302Q8×C17—22no—
303Q8×C17—44no—
304Q8×C17—42no—
305Q8×C17—42no—
306D4×C17—22no—
307D4×C17—22no—
308D4×C17—42no—
309C2×C4×C17—22no—
310C2×C4×C17—22no—
311C2×C4×C17—22no—
312C2×C4×C17—22no—
313C2×C4×C17—22no—
314C2×C4×C17—22no—
315C2×C4×C17—22no—
316C2×C4×C17—22no—
317C2×C4×C17—22no—
318C2×C4×C17—48no—
319C2×C4×C17—42no—
320C2×C4×C17—42no—
321C2×C4×C17—42no—
322C2×C4×C17C22×D412yes—
323C2×C4×C17C22×D412yes—
324C2×C4×C17C22×D412yes—
325C2×C4×C17C22×D412yes—
326C2×C4×C17C22×D412yes—
327C2×C4×C17C22×D412yes—
328C2×C4×C17C22×D411yescharacteristic
329C2×C4×C17C2×#4112yes—
330C2×C4×C17H(5,𝔽2)12yes—
331C2×C4×C17C2511yescharacteristic
332C2×Dic17—22no—
333C2×Dic17—22no—
334C2×Dic17—42no—
335C2×Dic17—42no—
336D68—22no—
337D68—22no—
338D68—22no—
339D68—22no—
340D68—48no—
341D68—42no—
342D68—42no—
343D68—84no—
344C4×D17—84no—
345C4×D17—84no—
346Dic34—22no—
347Dic34—22no—
348Dic34—42no—
349#3622—22no—
350#3622—22no—
351#3622—22no—
352#3622C2×#4114yes—
353C2×#559—171no—
354C2×#556D1711yescharacteristic, complemented
355#3401—1716no—
356C2×#497—171no—
357C2×#496—171no—
358C2×#495—171no—
359C2×#464—171no—
360C2×#464—171no—
361C2×#460—171no—
362C2×#463—171no—
363C2×#463—171no—
364C2×#461—171no—
365C2×#446—171no—
366C2×#442—171no—
367C2×#441—171no—
368C2×C4×SD16—171no—
369C22×C17—42no—
370C22×C17—42no—
371C22×C17—42no—
372C22×C17—84no—
373C22×C17#55012yes—
374C22×C17#57512yes—
375C22×C17#57712yes—
376C22×C17C23×D411yescharacteristic
377C2×D17—42no—
378C2×D17—42no—
379C2×D17—42no—
380C2×D17—42no—
381C2×D17—42no—
382C2×D17—42no—
383C2×D17—84no—
384C2×D17—84no—
385C4×C17—22no—
386C4×C17—22no—
387C4×C17—22no—
388C4×C17—22no—
389C4×C17—22no—
390C4×C17—22no—
391C4×C17—42no—
392C4×C17—42no—
393C4×C17—42no—
394C4×C17#55012yes—
395C4×C17C22×#4111yescharacteristic
396C4×C17C2×H(5,𝔽2)11yescharacteristic
397Dic17—42no—
398Dic17—42no—
399C22×Q16—171no—
400C22×Q16—171no—
401C22×SD16—171no—
402C22×SD16—171no—
403C22×SD16—171no—
404C22×SD16—171no—
405C22×SD16—171no—
406C22×D8—171no—
407C22×D8—171no—
408#559—178no—
409#559—344no—
410#556—24no—
411#556C2×D1718yescomplemented
412C2×C4⋊Q8C2×D1711yescharacteristic
413C2×#127—171no—
414C2×#126—21no—
415C2×#126—21no—
416C2×#124—171no—
417C2×#124—171no—
418C2×#124—341no—
419C2×#124C2×D1711yescharacteristic
420C2×#124C2×D1711yescharacteristic
421C2×#123—341no—
422C2×#123—341no—
423C2×C22⋊Q8—21no—
424C2×C4×Q8—171no—
425C2×C4×Q8C2×D1711yescharacteristic
426C2×C4×Q8C2×D1711yescharacteristic
427C2×C4×Q8C2×D1711yescharacteristic
428C2×C4×D4—171no—
429C2×C4×D4—171no—
430C2×C4×D4—341no—
431C2×C4×D4C2×D1711yescharacteristic
432C2×#117—21no—
433#497—178no—
434#496—178no—
435#495—178no—
436#464—178no—
437#464—178no—
438#463—178no—
439#463—178no—
440#461—178no—
441#460—178no—
442#446—178no—
443#442—178no—
444#441—178no—
445C4×SD16—178no—
446C2×#106—171no—
447C2×C4⋊C8—171no—
448C2×C4⋊C8—171no—
449C2×C4⋊C8—171no—
450C2×#103—171no—
451C2×#103—171no—
452C2×#103—171no—
453C2×#102—171no—
454C2×#102—171no—
455C2×#102—171no—
456C2×#97—171no—
457C2×#97—171no—
458C2×C4×C8—171no—
459C2×C17—82no—
460C2×C17#340114yescomplemented
461C2×C17C2×#55011yescharacteristic
462C2×C17C2×#57511yescharacteristic
463C2×C17C2×#57711yescharacteristic
464D17—82no—
465D17—82no—
466C22×Q8—171no—
467C22×Q8C22⋊D1711yescharacteristic
468C22×Q8C22×D1711yescharacteristic
469C22×Q8C22×D1711yescharacteristic
470C22×D4—171no—
471C22×D4—171no—
472C22×D4—341no—
473C22×D4—341no—
474C22×D4C22×D1711yescharacteristic
475C23×C4—21no—
476C23×C4—341no—
477C23×C4—341no—
478C2×Q16—174no—
479C2×Q16—174no—
480C2×Q16—344no—
481C2×Q16—682no—
482C2×SD16—174no—
483C2×SD16—174no—
484C2×SD16—174no—
485C2×SD16—174no—
486C2×SD16—174no—
487C2×SD16—344no—
488C2×SD16—682no—
489C2×SD16—682no—
490C2×SD16—682no—
491C2×SD16—682no—
492C2×D8—174no—
493C2×D8—174no—
494C2×D8—344no—
495C2×D8—682no—
496C22×C8—171no—
497C22×C8—171no—
498C22×C8—171no—
499C22×C8—171no—
500C4⋊Q8—22no—
501C4⋊Q8C22×D1714yes—
502#127—174no—
503#127—342no—
504#126—28no—
505#126—28no—
506#124—22no—
507#124—22no—
508#124—174no—
509#124—174no—
510#124—348no—
511#124—342no—
512#124—342no—
513#124C22×D1714yes—
514#124C22×D1714yes—
515#123—348no—
516#123—348no—
517C22⋊Q8—28no—
518C4×Q8—22no—
519C4×Q8—22no—
520C4×Q8—174no—
521C4×Q8—342no—
522C4×Q8C22⋊D1714yes—
523C4×Q8C22×D1714yes—
524C4×Q8C22×D1714yes—
525C4×Q8C22×D1714yes—
526C4×D4—22no—
527C4×D4—174no—
528C4×D4—174no—
529C4×D4—348no—
530C4×D4—342no—
531C4×D4—342no—
532C4×D4C22×D1714yes—
533#117—28no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—171no—
539C2×C4⋊C4—341no—
540C2×C4⋊C4C22⋊D1711yescharacteristic
541C2×C4⋊C4C22⋊D1711yescharacteristic
542C2×C4⋊C4C22⋊D1711yescharacteristic
543C2×C4⋊C4C22×D1711yescharacteristic
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—341no—
550C2×C22⋊C4—341no—
551C2×C22⋊C4—341no—
552C2×C22⋊C4—341no—
553C2×C22⋊C4—341no—
554C2×C22⋊C4—341no—
555C2×C42—21no—
556C2×C42—21no—
557C2×C42—341no—
558C2×C42C22×D1711yescharacteristic
559C2×C42C22×D1711yescharacteristic
560C2×C42C22×D1711yescharacteristic
561#106—174no—
562C4⋊C8—174no—
563C4⋊C8—174no—
564C4⋊C8—174no—
565#103—174no—
566#103—174no—
567#103—174no—
568#102—174no—
569#102—174no—
570#102—174no—
571#97—174no—
572#97—174no—
573C4×C8—174no—
574C17C2×#340111yescharacteristic, complemented, Sylow
575C24—21no—
576C24—341no—
577C24—341no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—22no—
581C2×Q8—22no—
582C2×Q8—22no—
583C2×Q8—22no—
584C2×Q8—42no—
585C2×Q8—172no—
586C2×Q8—341no—
587C2×Q8—342no—
588C2×Q8—342no—
589C2×Q8C2×C22⋊D1714yes—
590C2×Q8C23×D1712yes—
591C2×Q8C23×D1712yes—
592C2×D4—22no—
593C2×D4—22no—
594C2×D4—21no—
595C2×D4—172no—
596C2×D4—172no—
597C2×D4—342no—
598C2×D4—342no—
599C2×D4—342no—
600C2×D4—342no—
601C2×D4—344no—
602C2×D4—341no—
603C2×D4—341no—
604C2×D4—344no—
605C2×D4—684no—
606C2×D4—1362no—
607C2×D4C23×D1712yes—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—24no—
612C22×C4—44no—
613C22×C4—341no—
614C22×C4—341no—
615C22×C4—344no—
616C22×C4—344no—
617C22×C4—1362no—
618C22×C4—1362no—
619C22×C4C2×C22⋊D1711yescharacteristic
620C22×C4C2×C22⋊D1711yescharacteristic
621C22×C4C2×C22⋊D1711yescharacteristic
622C22×C4C2×C22⋊D1711yescharacteristic
623C22×C4C2×C22⋊D1711yescharacteristic
624C22×C4C2×C22⋊D1711yescharacteristic
625C22×C4C23×D1711yescharacteristic
626Q16—348no—
627Q16—684no—
628SD16—348no—
629SD16—684no—
630SD16—684no—
631SD16—684no—
632SD16—684no—
633D8—348no—
634D8—684no—
635C2×C8—174no—
636C2×C8—172no—
637C2×C8—172no—
638C2×C8—172no—
639C2×C8—172no—
640C2×C8—342no—
641C2×C8—342no—
642C2×C8—342no—
643C4⋊C4—24no—
644C4⋊C4—24no—
645C4⋊C4—24no—
646C4⋊C4—24no—
647C4⋊C4—21no—
648C4⋊C4—172no—
649C4⋊C4—341no—
650C4⋊C4—344no—
651C4⋊C4C2×C22⋊D1714yes—
652C4⋊C4C2×C22⋊D1714yes—
653C4⋊C4C2×C22⋊D1714yes—
654C4⋊C4C23×D1712yes—
655C22⋊C4—24no—
656C22⋊C4—24no—
657C22⋊C4—24no—
658C22⋊C4—24no—
659C22⋊C4—24no—
660C22⋊C4—344no—
661C22⋊C4—344no—
662C22⋊C4—344no—
663C22⋊C4—344no—
664C22⋊C4—344no—
665C22⋊C4—344no—
666C42—24no—
667C42—24no—
668C42—344no—
669C42C2×C22⋊D1712yes—
670C42C2×C22⋊D1712yes—
671C42C2×C22⋊D1712yes—
672C42C23×D1712yes—
673C42C23×D1712yes—
674C42C23×D1712yes—
675C23—22no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—342no—
680C23—342no—
681C23—682no—
682C23—682no—
683C23—682no—
684C23—682no—
685C23—682no—
686C23—682no—
687C23C22×C22⋊D1711yescharacteristic
688Q8—22no—
689Q8—22no—
690Q8—22no—
691Q8—22no—
692Q8—44no—
693Q8—42no—
694Q8—42no—
695Q8—342no—
696Q8—342no—
697Q8—682no—
698D4—22no—
699D4—22no—
700D4—42no—
701D4—342no—
702D4—342no—
703D4—342no—
704D4—342no—
705D4—688no—
706D4—682no—
707D4—682no—
708D4—1364no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—48no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—342no—
723C2×C4—342no—
724C2×C4—682no—
725C2×C4—682no—
726C2×C4—1364no—
727C2×C4—1364no—
728C2×C4#41×D1712yes—
729C2×C4#1058769612yes—
730C2×C4C22×C22⋊D1712yes—
731C2×C4C22×C22⋊D1712yes—
732C2×C4C22×C22⋊D1712yes—
733C2×C4C22×C22⋊D1712yes—
734C2×C4C22×C22⋊D1712yes—
735C2×C4C22×C22⋊D1712yes—
736C2×C4C22×C22⋊D1711yescharacteristic
737C2×C4C24×D1711yescharacteristic
738C8—174no—
739C8—342no—
740C8—342no—
741C8—342no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—84no—
746C22—682no—
747C22—682no—
748C22—682no—
749C22—682no—
750C22—682no—
751C22—682no—
752C22—1364no—
753C22—1364no—
754C22#1176347812yes—
755C22#1176360712yes—
756C22#1176361712yes—
757C22C23×C22⋊D1711yescharacteristic
758C4—22no—
759C4—22no—
760C4—22no—
761C4—22no—
762C4—22no—
763C4—22no—
764C4—42no—
765C4—42no—
766C4—42no—
767C4—682no—
768C4—682no—
769C4#1176347812yes—
770C4C2×#41×D1711yescharacteristic
771C4C2×#1058769611yescharacteristic
772C2—82no—
773C2—1362no—
774C2—1362no—
775C2#1454185014yesdirect product factor
776C2C2×#1176347811yescharacteristic
777C2C2×#1176360711yescharacteristic
778C2C2×#1176361711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#556C2
socleC23×C17C22×D4
prime radicalC2×#11763199C2
hypercenterC2×#556D17
hypocenterC17C2×#3401
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. C2×#11763544C2semidirect
2. #14541850C2direct (N × H)
3. C2×#11763201C2semidirect
5. C2×#11763191C2semidirect
6. C2×#11763031C2semidirect
7. C2×#11763028C2semidirect
8. C2×#11763009C2semidirect
9. C2×#11763024C2semidirect
10. C2×#11763021C2semidirect
11. C2×#11763011C2semidirect
12. C2×#11762940C2semidirect
13. C2×#11762919C2semidirect
14. C2×#11762914C2semidirect
15. C2×C4×#63230C2semidirect
16. C2×C17×#556C2semidirect
27. #11763544C22semidirect
38. #11763201C22semidirect
40. #11763191C22semidirect
41. #11763031C22semidirect
42. #11763028C22semidirect
43. #11763024C22semidirect
44. #11763021C22semidirect
45. #11763011C22semidirect
46. #11763009C22semidirect
47. #11762940C22semidirect
48. #11762919C22semidirect
49. #11762914C22semidirect
50. C4×#63230C22semidirect
65. C17×#556C22semidirect
354. C2×#556D17semidirect
411. #556C2×D17semidirect
460. C2×C17#3401semidirect
574. C17C2×#3401semidirect
775. C2#14541850direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117635442
#145418502
C2×#117632012
C2×#117631992
C2×#117631912
C2×#117630312
C2×#117630282
C2×#117630092
C2×#117630242
C2×#117630212
C2×#117630112
C2×#117629402
C2×#117629192
C2×#117629142
C2×C4×#632302
C2×C17×#5562
C2×#340117