Finite Group Databasebeta

← C2×#14541263 #17912897

Subgroups — C2×#14541263 #17912897

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×#11763505C211yesmaximal, characteristic
2#14541263C2116yesmaximal, direct product factor
3C2×#11763215C211yesmaximal, characteristic, complemented
4C2×#11763142C211yesmaximal, characteristic, complemented
5C2×#11763127C211yesmaximal, characteristic, complemented
6C2×#11763147C211yesmaximal, characteristic, complemented
7C2×#11763122C211yesmaximal, characteristic, complemented
8C2×#11763116C211yesmaximal, characteristic, complemented
9C2×#11763086C211yesmaximal, characteristic, complemented
10C2×#11763057C211yesmaximal, characteristic, complemented
11C2×#11763040C211yesmaximal, characteristic, complemented
12C2×#11762907C211yesmaximal, characteristic, complemented
13C2×#11762881C211yesmaximal, characteristic, complemented
14C2×#11762849C211yesmaximal, characteristic, complemented
15C22×#10587478C211yesmaximal, characteristic, complemented
16C2×C17×#554C211yesmaximal, characteristic, complemented
17C22×#63230C2211yescharacteristic
18C22×#63223C2211yescharacteristic
19C23×#3622C2211yescharacteristic
20#11763505—24no—
21#11763505C2218yes—
22C2×#10587584—21no—
23C2×#10587556C2211yescharacteristic
24C2×#10587569—21no—
25C2×#10587616C2211yescharacteristic
26C2×#10587616C2211yescharacteristic
27C2×#10587625—21no—
28C2×C4×D68C2211yescharacteristic
29C2×#10587567—21no—
30C2×#10587612C2211yescharacteristic
31C22×C4⋊Dic17C2211yescharacteristic
32#11763215C2218yescomplemented
33#11763147C2218yescomplemented
34#11763142C2218yescomplemented
35#11763127C2218yescomplemented
36#11763122C2218yescomplemented
37#11763116C2218yescomplemented
38#11763086C2218yescomplemented
39#11763057C2218yescomplemented
40#11763040C2218yescomplemented
41#11762907C2218yescomplemented
42#11762881C2218yescomplemented
43#11762849C2218yescomplemented
44C2×#10587478C2211yescharacteristic
45C2×#10587478C2211yescharacteristic
46C2×#10587478C2211yescharacteristic
47C2×#10587478C2211yescharacteristic
48C2×#10587478C2211yescharacteristic
49C2×#10587478C2211yescharacteristic
50C2×#10587478C2218yescomplemented
51C2×#10587479C2211yescharacteristic
52C2×#10587479C2211yescharacteristic
53C2×#10587479C2211yescharacteristic
54C2×C4⋊#3622C2211yescharacteristic
55C2×#10587506C2211yescharacteristic
56C2×#10587506C2211yescharacteristic
57C2×#10587506C2211yescharacteristic
58C2×#10587480C2211yescharacteristic
59C2×#10587480C2211yescharacteristic
60C2×#10587480C2211yescharacteristic
61C2×C22⋊#3622C2211yescharacteristic
62C2×C22⋊#3622C2211yescharacteristic
63C2×#10587474C2211yescharacteristic
64C17×#554—24no—
65C17×#554C2218yescomplemented
66C2×C17×C4⋊Q8C2211yescharacteristic
67C2×C17×#125—21no—
68C2×C17×C22⋊Q8—21no—
69C2×C17×C22⋊Q8—21no—
70C2×C17×C22⋊Q8C2211yescharacteristic
71C2×C17×C22⋊Q8C2211yescharacteristic
72C2×C4×Q8×C17C2211yescharacteristic
73C2×C4×D4×C17—21no—
74C2×C4×D4×C17C2211yescharacteristic
75C22×C4⋊C4×C17C2211yescharacteristic
76C22×C4⋊C4×C17C2211yescharacteristic
77C22×Q8×C17—21no—
78C22×Q8×C17C2311yescharacteristic
79C22×D4×C17D411yescharacteristic
80C23×C4×C17—21no—
81C23×C4×C17—21no—
82C23×C4×C17C2311yescharacteristic
83C23×C4×C17C2311yescharacteristic
84C22×C22⋊D17—21no—
85C22×C22⋊D17—21no—
86C23×Dic17—21no—
87C22×D68C2311yescharacteristic
88C22×C4×D17—21no—
89C17×C4⋊Q8—22no—
90C17×C4⋊Q8C2314yes—
91C17×#125—28no—
92C17×C22⋊Q8—22no—
93C17×C22⋊Q8—22no—
94C17×C22⋊Q8—28no—
95C17×C22⋊Q8—28no—
96C17×C22⋊Q8C2314yes—
97C17×C22⋊Q8C2314yes—
98C4×Q8×C17—22no—
99C4×Q8×C17C2314yes—
100C4×D4×C17—28no—
101C4×D4×C17D414yes—
102C4×D4×C17C2314yes—
103C2×C4⋊C4×C17—21no—
104C2×C4⋊C4×C17—21no—
105C2×C4⋊C4×C17—22no—
106C2×C4⋊C4×C17—22no—
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×C17C2311yescharacteristic
113C2×C4⋊C4×C17C2311yescharacteristic
114C2×C4⋊C4×C17C2311yescharacteristic
115C2×C4⋊C4×C17C2314yes—
116C2×C4⋊C4×C17C2314yes—
117C2×C22⋊C4×C17—21no—
118C2×C22⋊C4×C17—21no—
119C2×C22⋊C4×C17D411yescharacteristic
120C2×C22⋊C4×C17D411yescharacteristic
121C2×C42×C17—21no—
122C2×C42×C17C2311yescharacteristic
123C2×C22⋊Dic17—21no—
124C2×#63230—24no—
125C2×#63230C2314yes—
126#10587625—28no—
127#10587616—22no—
128#10587616—22no—
129#10587616C2314yes—
130#10587616C2314yes—
131C2×#63227—21no—
132C2×#63227—21no—
133C2×#63227—21no—
134#10587612—22no—
135#10587612C2314yes—
136C2×C4⋊Dic17—22no—
137C2×C4⋊Dic17—21no—
138C2×C4⋊Dic17C2314yes—
139C2×C4⋊Dic17C2311yescharacteristic
140C2×C4⋊Dic17C2311yescharacteristic
141C2×C4⋊Dic17C2311yescharacteristic
142C2×#63225—21no—
143C2×#63225—21no—
144C2×C4×Dic17—21no—
145C2×#63223—24no—
146C2×#63223C2314yes—
147C22×#3622—24no—
148C22×#3622C2311yescharacteristic
149C22×#3622C2311yescharacteristic
150C22×#3622C2311yescharacteristic
151C22×#3622C2314yes—
152C22×#3622C2311yescharacteristic
153#10587584—28no—
154#10587569—28no—
155#10587567—28no—
156C4×D68—22no—
157C4×D68C2314yes—
158#10587556—22no—
159#10587556C2314yes—
160#10587506C2314yes—
161#10587506C2314yes—
162#10587506C2314yes—
163C22⋊#3622C2314yes—
164C22⋊#3622C2314yes—
165#10587480C2314yes—
166#10587480C2314yes—
167#10587480C2314yes—
168#10587479C2314yes—
169#10587479C2314yes—
170#10587479C2314yes—
171#10587478C2314yes—
172#10587478C2314yes—
173#10587478C2314yes—
174#10587478C2314yes—
175#10587478C2314yes—
176#10587478C2314yes—
177C4⋊#3622C2314yes—
178#10587474C2314yes—
179C24×C17C2×D411yescharacteristic
180C24×C17C2×D411yescharacteristic
181C23×D17—21no—
182C2×Q8×C17—21no—
183C2×Q8×C17—24no—
184C2×Q8×C17—22no—
185C2×Q8×C17—22no—
186C2×Q8×C17—82no—
187C2×Q8×C17C2412yes—
188C2×D4×C17—24no—
189C2×D4×C17C2×D414yes—
190C22×C4×C17—22no—
191C22×C4×C17—22no—
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×C17—24no—
199C22×C4×C17—24no—
200C22×C4×C17—82no—
201C22×C4×C17—82no—
202C22×C4×C17C2×D412yes—
203C22×C4×C17C2×D412yes—
204C22×C4×C17C2×D411yescharacteristic
205C22×C4×C17C2×D411yescharacteristic
206C22×C4×C17C2×D411yescharacteristic
207C22×C4×C17C2×D411yescharacteristic
208C22×C4×C17C2412yes—
209C22×C4×C17C2412yes—
210C22×C4×C17C2411yescharacteristic
211C2×C22⋊D17—24no—
212C2×C22⋊D17—24no—
213C2×C22⋊D17—44no—
214C2×C22⋊D17—82no—
215C22×Dic17—21no—
216C22×Dic17—21no—
217C22×Dic17—21no—
218C22×Dic17—24no—
219C22×Dic17—82no—
220C2×D68—22no—
221C2×D68—22no—
222C2×D68—21no—
223C2×D68C2412yes—
224C2×C4×D17—24no—
225C2×C4×D17—82no—
226C4⋊C4×C17—24no—
227C4⋊C4×C17—24no—
228C4⋊C4×C17—24no—
229C4⋊C4×C17—24no—
230C4⋊C4×C17—24no—
231C4⋊C4×C17—21no—
232C4⋊C4×C17—21no—
233C4⋊C4×C17—24no—
234C4⋊C4×C17—21no—
235C4⋊C4×C17C2×D414yes—
236C4⋊C4×C17C2412yes—
237C4⋊C4×C17C2412yes—
238C4⋊C4×C17C2412yes—
239C22⋊C4×C17—24no—
240C22⋊C4×C17—24no—
241C22⋊C4×C17C2×D414yes—
242C22⋊C4×C17C2×D414yes—
243C42×C17—24no—
244C42×C17C2×D412yes—
245C42×C17C2412yes—
246C22⋊Dic17—24no—
247#63230—28no—
248#63227—24no—
249#63227—24no—
250#63227—24no—
251C4⋊Dic17—21no—
252C4⋊Dic17—21no—
253C4⋊Dic17—21no—
254C4⋊Dic17—24no—
255C4⋊Dic17C2412yes—
256C4⋊Dic17C2412yes—
257C4⋊Dic17C2412yes—
258#63225—24no—
259#63225—24no—
260C4×Dic17—24no—
261#63223—28no—
262C2×#3622—22no—
263C2×#3622—22no—
264C2×#3622—22no—
265C2×#3622—28no—
266C2×#3622#4114yes—
267C2×#3622C2412yes—
268C2×#3622C2412yes—
269C2×#3622C2412yes—
270C2×#3622C2412yes—
271C2×#3346—171nomaximal, Sylow
272C23×C17—22no—
273C23×C17—22no—
274C23×C17—22no—
275C23×C17—22no—
276C23×C17—22no—
277C23×C17#13714yes—
278C23×C17C22×D412yes—
279C23×C17C22×D412yes—
280C23×C17C22×D411yescharacteristic
281C22×D17—22no—
282C22×D17—42no—
283C22×D17—42no—
284C22×D17—42no—
285Q8×C17—22no—
286Q8×C17—22no—
287Q8×C17—42no—
288Q8×C17—84no—
289D4×C17—28no—
290C2×C4×C17—22no—
291C2×C4×C17—22no—
292C2×C4×C17—22no—
293C2×C4×C17—22no—
294C2×C4×C17—24no—
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—22no—
303C2×C4×C17—22no—
304C2×C4×C17—42no—
305C2×C4×C17—42no—
306C2×C4×C17—42no—
307C2×C4×C17—42no—
308C2×C4×C17—84no—
309C2×C4×C17—84no—
310C2×C4×C17C22×D412yes—
311C2×C4×C17C22×D412yes—
312C2×C4×C17C22×D412yes—
313C2×C4×C17C22×D412yes—
314C2×C4×C17C22×D411yescharacteristic
315C2×C4×C17C2×#4112yes—
316C2×C4×C172−1+412yes—
317C2×C4×C17C2511yescharacteristic
318C22⋊D17—48no—
319C22⋊D17—84no—
320C2×Dic17—22no—
321C2×Dic17—22no—
322C2×Dic17—22no—
323C2×Dic17—42no—
324C2×Dic17—42no—
325C2×Dic17—42no—
326C2×Dic17—84no—
327D68—22no—
328D68—22no—
329D68—42no—
330C4×D17—84no—
331#3622—22no—
332#3622—22no—
333#3622—22no—
334#3622C2×#4114yes—
335C2×#554D1711yescharacteristic, complemented
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×#107—171no—
351C22×C17—28no—
352C22×C17—22no—
353C22×C17—22no—
354C22×C17—22no—
355C22×C17—22no—
356C22×C17—22no—
357C22×C17—44no—
358C22×C17#54712yes—
359C22×C17C2×#13714yes—
360C22×C17C2×#13712yes—
361C22×C17#57612yes—
362C22×C17C23×D411yescharacteristic
363C2×D17—42no—
364C2×D17—42no—
365C2×D17—42no—
366C2×D17—84no—
367C4×C17—22no—
368C4×C17—22no—
369C4×C17—22no—
370C4×C17—22no—
371C4×C17—42no—
372C4×C17—42no—
373C4×C17—42no—
374C4×C17—42no—
375C4×C17#54712yes—
376C4×C17C22×#4111yescharacteristic
377C4×C17C2×2−1+411yescharacteristic
378Dic17—42no—
379Dic17—42no—
380Dic17—42no—
381C22×SD16—171no—
382C22×M16—171no—
383C23×C8—171no—
384#554—24no—
385#554C2×D1718yescomplemented
386#553—178no—
387#553—344no—
388C2×C4⋊Q8C2×D1711yescharacteristic
389C2×#126—341no—
390C2×#125—21no—
391C2×#125—171no—
392C2×#123—341no—
393C2×C22⋊Q8—21no—
394C2×C22⋊Q8—21no—
395C2×C22⋊Q8C2×D1711yescharacteristic
396C2×C22⋊Q8C2×D1711yescharacteristic
397C2×#121—171no—
398C2×#121—171no—
399C2×#121—341no—
400C2×C4×Q8C2×D1711yescharacteristic
401C2×C4×D4—21no—
402C2×C4×D4—171no—
403C2×C4×D4—341no—
404C2×C4×D4C2×D1711yescharacteristic
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×#107—171no—
424C2×#107—171no—
425C2×#107—178no—
426C2×#107—171no—
427C2×#107—171no—
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—42no—
443C2×C17#334614yescomplemented
444C2×C17C2×#54711yescharacteristic
445C2×C17C22×#13711yescharacteristic
446C2×C17C2×#57611yescharacteristic
447D17—82no—
448C22×Q8—21no—
449C22×Q8C22×D1711yescharacteristic
450C22×D4—171no—
451C22×D4—341no—
452C22×D4—341no—
453C22×D4C22⋊D1711yescharacteristic
454C23×C4—21no—
455C23×C4—21no—
456C23×C4—341no—
457C23×C4—341no—
458C23×C4C22×D1711yescharacteristic
459C23×C4C22×D1711yescharacteristic
460C2×SD16—174no—
461C2×SD16—344no—
462C2×M16—174no—
463C2×M16—344no—
464C22×C8—171no—
465C22×C8—171no—
466C22×C8—174no—
467C22×C8—171no—
468C22×C8—171no—
469C22×C8—344no—
470C4⋊Q8—22no—
471C4⋊Q8C22×D1714yes—
472#126—348no—
473#125—28no—
474#125—174no—
475#125—342no—
476#123—348no—
477C22⋊Q8—22no—
478C22⋊Q8—22no—
479C22⋊Q8—28no—
480C22⋊Q8—28no—
481C22⋊Q8C22×D1714yes—
482C22⋊Q8C22×D1714yes—
483#121—174no—
484#121—174no—
485#121—348no—
486#121—342no—
487#121—342no—
488C4×Q8—22no—
489C4×Q8C22×D1714yes—
490C4×D4—28no—
491C4×D4—174no—
492C4×D4—348no—
493C4×D4—342no—
494C4×D4C22⋊D1714yes—
495C4×D4C22×D1714yes—
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—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—171no—
507C2×C4⋊C4—171no—
508C2×C4⋊C4—174no—
509C2×C4⋊C4—171no—
510C2×C4⋊C4—341no—
511C2×C4⋊C4—342no—
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—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—341no—
523C2×C22⋊C4—341no—
524C2×C22⋊C4—341no—
525C2×C22⋊C4—341no—
526C2×C22⋊C4C22⋊D1711yescharacteristic
527C2×C22⋊C4C22⋊D1711yescharacteristic
528C2×C42—21no—
529C2×C42—341no—
530C2×C42C22×D1711yescharacteristic
531#107—174no—
532#107—174no—
533#107—174no—
534#107—174no—
535#107—174no—
536#107—174no—
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—341no—
552C24C2×C22⋊D1711yescharacteristic
553C24C2×C22⋊D1711yescharacteristic
554C2×Q8—21no—
555C2×Q8—24no—
556C2×Q8—22no—
557C2×Q8—22no—
558C2×Q8—82no—
559C2×Q8C23×D1712yes—
560C2×D4—24no—
561C2×D4—172no—
562C2×D4—344no—
563C2×D4—344no—
564C2×D4—342no—
565C2×D4—342no—
566C2×D4—341no—
567C2×D4—684no—
568C2×D4—1362no—
569C2×D4C2×C22⋊D1714yes—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—82no—
581C22×C4—82no—
582C22×C4—341no—
583C22×C4—341no—
584C22×C4—341no—
585C22×C4—344no—
586C22×C4—344no—
587C22×C4—1362no—
588C22×C4—1362no—
589C22×C4C2×C22⋊D1712yes—
590C22×C4C2×C22⋊D1712yes—
591C22×C4C2×C22⋊D1711yescharacteristic
592C22×C4C2×C22⋊D1711yescharacteristic
593C22×C4C2×C22⋊D1711yescharacteristic
594C22×C4C2×C22⋊D1711yescharacteristic
595C22×C4C23×D1712yes—
596C22×C4C23×D1712yes—
597C22×C4C23×D1711yescharacteristic
598SD16—348no—
599M16—348no—
600C2×C8—174no—
601C2×C8—172no—
602C2×C8—172no—
603C2×C8—172no—
604C2×C8—172no—
605C2×C8—348no—
606C2×C8—342no—
607C2×C8—342no—
608C2×C8—342no—
609C4⋊C4—21no—
610C4⋊C4—24no—
611C4⋊C4—24no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—24no—
618C4⋊C4—172no—
619C4⋊C4—172no—
620C4⋊C4—172no—
621C4⋊C4—341no—
622C4⋊C4—341no—
623C4⋊C4—344no—
624C4⋊C4—341no—
625C4⋊C4—344no—
626C4⋊C4—344no—
627C4⋊C4C2×C22⋊D1714yes—
628C4⋊C4C23×D1712yes—
629C4⋊C4C23×D1712yes—
630C4⋊C4C23×D1712yes—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—344no—
634C22⋊C4—344no—
635C22⋊C4—344no—
636C22⋊C4—344no—
637C22⋊C4C2×C22⋊D1714yes—
638C22⋊C4C2×C22⋊D1714yes—
639C42—24no—
640C42—344no—
641C42C2×C22⋊D1712yes—
642C42C23×D1712yes—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—342no—
649C23—682no—
650C23—682no—
651C23—682no—
652C23#1058762814yes—
653C23C22×C22⋊D1712yes—
654C23C22×C22⋊D1712yes—
655C23C22×C22⋊D1711yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—42no—
659Q8—84no—
660D4—28no—
661D4—342no—
662D4—342no—
663D4—688no—
664D4—682no—
665D4—1364no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—84no—
685C2×C4—84no—
686C2×C4—342no—
687C2×C4—342no—
688C2×C4—342no—
689C2×C4—682no—
690C2×C4—682no—
691C2×C4—682no—
692C2×C4—1364no—
693C2×C4—1364no—
694C2×C4#41×D1712yes—
695C2×C4#1058769712yes—
696C2×C4C22×C22⋊D1712yes—
697C2×C4C22×C22⋊D1712yes—
698C2×C4C22×C22⋊D1712yes—
699C2×C4C22×C22⋊D1712yes—
700C2×C4C22×C22⋊D1711yescharacteristic
701C2×C4C24×D1711yescharacteristic
702C8—174no—
703C8—342no—
704C8—342no—
705C8—342no—
706C22—22no—
707C22—22no—
708C22—28no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—44no—
713C22—682no—
714C22—682no—
715C22—682no—
716C22—1364no—
717C22#1176345812yes—
718C22C2×#1058762814yes—
719C22C2×#1058762812yes—
720C22#1176361212yes—
721C22C23×C22⋊D1711yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—22no—
726C4—42no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—682no—
731C4—682no—
732C4—682no—
733C4#1176345812yes—
734C4C2×#41×D1711yescharacteristic
735C4C2×#1058769711yescharacteristic
736C2—24no—
737C2—42no—
738C2—1362no—
739C2#1454126314yesdirect product factor
740C2C2×#1176345811yescharacteristic
741C2C22×#1058762811yescharacteristic
742C2C2×#1176361211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#554C2
socleC23×C17C22×D4
prime radicalC2×#11763505C2
hypercenterC2×#554D17
hypocenterC17C2×#3346
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
2. #14541263C2direct (N × H)
3. C2×#11763215C2semidirect
4. C2×#11763142C2semidirect
5. C2×#11763127C2semidirect
6. C2×#11763147C2semidirect
7. C2×#11763122C2semidirect
8. C2×#11763116C2semidirect
9. C2×#11763086C2semidirect
10. C2×#11763057C2semidirect
11. C2×#11763040C2semidirect
12. C2×#11762907C2semidirect
13. C2×#11762881C2semidirect
14. C2×#11762849C2semidirect
15. C22×#10587478C2semidirect
16. C2×C17×#554C2semidirect
32. #11763215C22semidirect
33. #11763147C22semidirect
34. #11763142C22semidirect
35. #11763127C22semidirect
36. #11763122C22semidirect
37. #11763116C22semidirect
38. #11763086C22semidirect
39. #11763057C22semidirect
40. #11763040C22semidirect
41. #11762907C22semidirect
42. #11762881C22semidirect
43. #11762849C22semidirect
50. C2×#10587478C22semidirect
65. C17×#554C22semidirect
335. C2×#554D17semidirect
385. #554C2×D17semidirect
443. C2×C17#3346semidirect
550. C17C2×#3346semidirect
739. C2#14541263direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117635052
#145412632
C2×#117632152
C2×#117631422
C2×#117631272
C2×#117631472
C2×#117631222
C2×#117631162
C2×#117630862
C2×#117630572
C2×#117630402
C2×#117629072
C2×#117628812
C2×#117628492
C22×#105874782
C2×C17×#5542
C2×#334617