Finite Group Databasebeta

← #17050719

Subgroups — #17050719

Order 4352.

1186 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763505C211yesmaximal, characteristic
2#14531733C211yesmaximal, characteristic, complemented
3#14529753C211yesmaximal, characteristic, complemented
4#14529739C211yesmaximal, characteristic, complemented
5#14529222C211yesmaximal, characteristic, complemented
6#14529212C211yesmaximal, characteristic, complemented
7#14529104C211yesmaximal, characteristic, complemented
8#14529104C211yesmaximal, characteristic, complemented
9#14528880C211yesmaximal, characteristic, complemented
10#14528871C211yesmaximal, characteristic, complemented
11#14528785C211yesmaximal, characteristic, complemented
12#14528610C211yesmaximal, characteristic, complemented
13#14528504C211yesmaximal, characteristic, complemented
14#14528501C211yesmaximal, characteristic, complemented
15C2×C17×#435C211yesmaximal, characteristic, complemented
16#11763505—24no—
17#11763505C418yescomplemented
18C2×#10587584—21no—
19C2×#10587556C2211yescharacteristic
20C2×#10587569—21no—
21C2×#10587616C2211yescharacteristic
22C2×#10587616C2211yescharacteristic
23C2×#10587625—21no—
24C2×C4×D68C2211yescharacteristic
25C2×#10587567—21no—
26C2×#10587612C2211yescharacteristic
27C2×#10587612C2211yescharacteristic
28C2×#10587612C2211yescharacteristic
29C22×C4⋊Dic17C2211yescharacteristic
30C2×#10587492C2211yescharacteristic
31C2×#10587492C2211yescharacteristic
32C2×#10587492C2211yescharacteristic
33C2×#10587492C2211yescharacteristic
34#11762712—21no—
35#11762702—21no—
36#11762702—21no—
37#11762679C2211yescharacteristic
38#11762669C2211yescharacteristic
39#11762669C2211yescharacteristic
40C4⋊C4×Dic17—21no—
41C4×C4⋊Dic17C2211yescharacteristic
42#11762572C2211yescharacteristic
43#11762572C2211yescharacteristic
44#11762572C2211yescharacteristic
45#11762572C2211yescharacteristic
46#11762572C2211yescharacteristic
47#11762572C2211yescharacteristic
48#11762572C2211yescharacteristic
49#11762572C2211yescharacteristic
50#11762572C2211yescharacteristic
51#11762572C2211yescharacteristic
52#11762572C2211yescharacteristic
53#11762572C2211yescharacteristic
54C22×M16×C17C2211yescharacteristic
55C23×C8×C17C2211yescharacteristic
56C2×C4×D4×C17C2211yescharacteristic
57C17×#435—24no—
58C2×C17×C4⋊C8C2211yescharacteristic
59C2×C17×C22⋊C8C2211yescharacteristic
60C2×C17×C22⋊C8C2211yescharacteristic
61C2×C17×#97C2211yescharacteristic
62C22×D4×C17D411yescharacteristic
63C23×C4×C17C2311yescharacteristic
64C23×C4×C17C2311yescharacteristic
65C22×C22⋊D17—21no—
66C22×C22⋊D17—21no—
67C23×Dic17—21no—
68C22×D68C2311yescharacteristic
69C22×C4×D17—21no—
70C2×M16×C17—22no—
71C2×M16×C17—22no—
72C2×M16×C17—41no—
73C22×C8×C17—22no—
74C22×C8×C17—22no—
75C22×C8×C17—41no—
76C22×C8×C17C2311yescharacteristic
77C22×C8×C17C2311yescharacteristic
78C22×C8×C17C2311yescharacteristic
79C22×C8×C17C2311yescharacteristic
80C4×D4×C17C2×C414yes—
81C4×D4×C17D414yes—
82C2×C4⋊C4×C17D411yescharacteristic
83C2×C22⋊C4×C17D411yescharacteristic
84C2×C22⋊C4×C17D411yescharacteristic
85C2×C42×C17C2311yescharacteristic
86C2×C22⋊Dic17—21no—
87C2×C22⋊Dic17—21no—
88C2×C22⋊Dic17—21no—
89C2×C22⋊Dic17—21no—
90C2×C22⋊Dic17—21no—
91#10587625—28no—
92#10587616—22no—
93#10587616—22no—
94#10587616C2×C414yes—
95#10587616C2×C414yes—
96C2×#63227—21no—
97C2×#63227—21no—
98C2×#63227—21no—
99#10587612—22no—
100#10587612—22no—
101#10587612—22no—
102#10587612—41no—
103#10587612—41no—
104#10587612C2×C414yes—
105C2×C4⋊Dic17—22no—
106C2×C4⋊Dic17—21no—
107C2×C4⋊Dic17—21no—
108C2×C4⋊Dic17—21no—
109C2×C4⋊Dic17C2×C414yes—
110C2×C4⋊Dic17C2311yescharacteristic
111C2×C4⋊Dic17C2311yescharacteristic
112C2×C4⋊Dic17C2311yescharacteristic
113C2×C4⋊Dic17C2311yescharacteristic
114C2×C4⋊Dic17C2311yescharacteristic
115C2×C4⋊Dic17C2311yescharacteristic
116C2×C4⋊Dic17C2311yescharacteristic
117C2×#63225—21no—
118C2×#63225—21no—
119C2×C4×Dic17—21no—
120C2×C4×Dic17—21no—
121C2×C4×Dic17—21no—
122C2×C4×Dic17—21no—
123#10587584—28no—
124#10587569—28no—
125#10587567—28no—
126C4×D68—22no—
127C4×D68C2×C414yes—
128#10587556—22no—
129#10587556C2×C414yes—
130C17×C4⋊C8—22no—
131C17×C22⋊C8—22no—
132C17×C22⋊C8—22no—
133C17×#97—22no—
134#10587502—21no—
135#10587502—21no—
136#10587502—21no—
137#10587492—22no—
138#10587492—22no—
139#10587492—41no—
140#10587492—41no—
141C24×C17C2×D411yescharacteristic
142C24×C17C2×D411yescharacteristic
143C23×D17—21no—
144C2×D4×C17—41no—
145C2×D4×C17—41no—
146C2×D4×C17C22⋊C414yes—
147C22×C4×C17—21no—
148C22×C4×C17—21no—
149C22×C4×C17—21no—
150C22×C4×C17—21no—
151C22×C4×C17—21no—
152C22×C4×C17—21no—
153C22×C4×C17—21no—
154C22×C4×C17—21no—
155C22×C4×C17C22×C412yes—
156C22×C4×C17C22×C412yes—
157C22×C4×C17C2×D411yescharacteristic
158C22×C4×C17C2×D411yescharacteristic
159C22×C4×C17C2×D411yescharacteristic
160C22×C4×C17C2×D411yescharacteristic
161C22×C4×C17C2×D412yes—
162C22×C4×C17C2×D412yes—
163C22×C4×C17C2411yescharacteristic
164C2×C22⋊D17—24no—
165C2×C22⋊D17—24no—
166C2×C22⋊D17—42no—
167C2×C22⋊D17—42no—
168C2×C22⋊D17—81no—
169C2×C22⋊D17—81no—
170C22×Dic17—21no—
171C22×Dic17—21no—
172C22×Dic17—21no—
173C22×Dic17—21no—
174C22×Dic17—24no—
175C22×Dic17—21no—
176C22×Dic17—21no—
177C22×Dic17—21no—
178C22×Dic17—81no—
179C22×Dic17—81no—
180C2×D68—21no—
181C2×D68—21no—
182C2×D68—21no—
183C2×D68—21no—
184C2×D68—21no—
185C2×D68C22×C412yes—
186C2×C4×D17—24no—
187C2×C4×D17—81no—
188C2×C4×D17—81no—
189M16×C17—44no—
190C2×C8×C17—21no—
191C2×C8×C17—21no—
192C2×C8×C17—21no—
193C2×C8×C17—21no—
194C2×C8×C17—21no—
195C2×C8×C17—21no—
196C2×C8×C17—21no—
197C2×C8×C17—21no—
198C2×C8×C17—21no—
199C2×C8×C17—21no—
200C2×C8×C17—21no—
201C2×C8×C17—44no—
202C2×C8×C17#4112yes—
203C4⋊C4×C17C22⋊C414yes—
204C22⋊C4×C17C22⋊C414yes—
205C22⋊C4×C17C22⋊C414yes—
206C42×C17C22×C412yes—
207C42×C17C2×D412yes—
208C22⋊Dic17—24no—
209C22⋊Dic17—42no—
210C22⋊Dic17—42no—
211C22⋊Dic17—81no—
212C22⋊Dic17—81no—
213#63227—24no—
214#63227—24no—
215#63227—24no—
216C4⋊Dic17—24no—
217C4⋊Dic17—21no—
218C4⋊Dic17—21no—
219C4⋊Dic17—21no—
220C4⋊Dic17—21no—
221C4⋊Dic17—21no—
222C4⋊Dic17—21no—
223C4⋊Dic17—21no—
224C4⋊Dic17—21no—
225C4⋊Dic17—21no—
226C4⋊Dic17—21no—
227C4⋊Dic17—42no—
228C4⋊Dic17—81no—
229C4⋊Dic17C22×C412yes—
230C4⋊Dic17C22×C412yes—
231C4⋊Dic17C22×C412yes—
232C4⋊Dic17#4112yes—
233#63225—24no—
234#63225—24no—
235C4×Dic17—24no—
236C4×Dic17—42no—
237C4×Dic17—42no—
238C4×Dic17—42no—
239#22498—171nomaximal, Sylow
240C23×C17—21no—
241C23×C17—21no—
242C23×C17—21no—
243C23×C17—21no—
244C23×C17—21no—
245C23×C17—21no—
246C23×C17—21no—
247C23×C17—21no—
248C23×C17—21no—
249C23×C17—21no—
250C23×C17—21no—
251C23×C17—21no—
252C23×C17C2×C22⋊C412yes—
253C23×C17C2×C22⋊C412yes—
254C23×C17C22×D411yescharacteristic
255C22×D17—22no—
256C22×D17—41no—
257C22×D17—41no—
258C22×D17—41no—
259C22×D17—41no—
260C22×D17—41no—
261C22×D17—41no—
262D4×C17—44no—
263C2×C4×C17—21no—
264C2×C4×C17—21no—
265C2×C4×C17—21no—
266C2×C4×C17—21no—
267C2×C4×C17—21no—
268C2×C4×C17—21no—
269C2×C4×C17—21no—
270C2×C4×C17—21no—
271C2×C4×C17—22no—
272C2×C4×C17—22no—
273C2×C4×C17—22no—
274C2×C4×C17—22no—
275C2×C4×C17—22no—
276C2×C4×C17—22no—
277C2×C4×C17—22no—
278C2×C4×C17—22no—
279C2×C4×C17C2×C22⋊C412yes—
280C2×C4×C17C2×C22⋊C412yes—
281C2×C4×C17C2×C22⋊C412yes—
282C2×C4×C17C2×C22⋊C412yes—
283C2×C4×C17C23×C411yescharacteristic
284C2×C4×C17C22×D411yescharacteristic
285C2×C4×C17C2×#4111yescharacteristic
286C2×C4×C17C2×#4111yescharacteristic
287C2×C4×C17H(5,𝔽2)11yescharacteristic
288C2×C4×C172−1+411yescharacteristic
289C22⋊D17—48no—
290C22⋊D17—84no—
291C2×Dic17—22no—
292C2×Dic17—22no—
293C2×Dic17—22no—
294C2×Dic17—22no—
295C2×Dic17—41no—
296C2×Dic17—41no—
297C2×Dic17—41no—
298C2×Dic17—41no—
299C2×Dic17—41no—
300C2×Dic17—41no—
301C2×Dic17—41no—
302C2×Dic17—41no—
303C2×Dic17—41no—
304C2×Dic17—41no—
305C2×Dic17—41no—
306C2×Dic17—41no—
307C2×Dic17—41no—
308C2×Dic17—41no—
309C2×Dic17—41no—
310C2×Dic17—41no—
311C2×Dic17—41no—
312C2×Dic17—84no—
313D68—22no—
314D68—22no—
315D68—41no—
316D68—41no—
317C4×D17—84no—
318C8×C17—22no—
319C8×C17—41no—
320C8×C17—41no—
321C8×C17—41no—
322C2×#553—171no—
323C2×#435D1711yescharacteristic, complemented
324#2354—171no—
325#1992—171no—
326#1989—171no—
327#1895—171no—
328#1893—171no—
329#1875—171no—
330#1875—171no—
331#1825—171no—
332#1823—171no—
333#1802—171no—
334#1762—171no—
335#1736—171no—
336#1735—171no—
337C22×C17—22no—
338C22×C17—22no—
339C22×C17—22no—
340C22×C17—22no—
341C22×C17—22no—
342C22×C17—22no—
343C22×C17—41no—
344C22×C17—41no—
345C22×C17—41no—
346C22×C17—41no—
347C22×C17—41no—
348C22×C17—41no—
349C22×C17—41no—
350C22×C17—41no—
351C22×C17C22×C22⋊C411yescharacteristic
352C22×C17#54611yescharacteristic
353C22×C17#54711yescharacteristic
354C22×C17#57511yescharacteristic
355C22×C17#57511yescharacteristic
356C22×C17#57611yescharacteristic
357C22×C17#57711yescharacteristic
358C2×D17—42no—
359C2×D17—42no—
360C2×D17—42no—
361C2×D17—81no—
362C2×D17—81no—
363C2×D17—81no—
364C2×D17—81no—
365C4×C17—22no—
366C4×C17—22no—
367C4×C17—22no—
368C4×C17—22no—
369C4×C17C4×#4111yescharacteristic
370C4×C17#52011yescharacteristic
371C4×C17#54611yescharacteristic
372C4×C17#54711yescharacteristic
373Dic17—42no—
374Dic17—42no—
375Dic17—42no—
376Dic17—42no—
377Dic17—81no—
378Dic17—81no—
379Dic17—81no—
380C22×M16C2×D1711yescharacteristic
381C23×C8C2×D1711yescharacteristic
382#553—178no—
383#553—344no—
384C2×#126—341no—
385C2×#125—171no—
386C2×#123—341no—
387C2×#121—171no—
388C2×#121—171no—
389C2×#121—341no—
390C2×C4×D4—171no—
391C2×C4×D4—341no—
392C2×C4×D4C2×D1711yescharacteristic
393C2×#117—171no—
394C2×#117—171no—
395C2×#117—171no—
396C22×C4⋊C4—171no—
397#435—24no—
398C2×C4⋊C8C2×D1711yescharacteristic
399C2×#102—171no—
400C2×#102—171no—
401C2×#102—171no—
402C2×#102—171no—
403C2×C22⋊C8C2×D1711yescharacteristic
404C2×C22⋊C8C2×D1711yescharacteristic
405C2×#97C2×D1711yescharacteristic
406#390—341no—
407#388—341no—
408#388—341no—
409#384—171no—
410#380—171no—
411#380—171no—
412C4×C4⋊C4—171no—
413C4×C4⋊C4—341no—
414#340—171no—
415#340—171no—
416#340—171no—
417#340—171no—
418#340—171no—
419#340—171no—
420#340—171no—
421#340—171no—
422#340—171no—
423#340—171no—
424#340—171no—
425#340—171no—
426C2×C17—42no—
427C2×C17—42no—
428C2×C17#233911yescharacteristic
429C2×C17#289611yescharacteristic
430C2×C17#289711yescharacteristic
431C2×C17#330711yescharacteristic
432C2×C17#330911yescharacteristic
433C2×C17#334711yescharacteristic
434C2×C17#335011yescharacteristic
435D17—82no—
436C22×D4—171no—
437C22×D4—341no—
438C22×D4—341no—
439C22×D4D6811yescharacteristic
440C23×C4—341no—
441C23×C4—341no—
442C23×C4C22×D1711yescharacteristic
443C23×C4C22×D1711yescharacteristic
444C2×M16—22no—
445C2×M16—22no—
446C2×M16—41no—
447C22×C8—22no—
448C22×C8—22no—
449C22×C8—41no—
450C22×C8C22×D1711yescharacteristic
451C22×C8C22×D1711yescharacteristic
452C22×C8C22×D1711yescharacteristic
453C22×C8C22×D1711yescharacteristic
454#126—348no—
455#125—174no—
456#125—342no—
457#123—348no—
458#121—174no—
459#121—174no—
460#121—348no—
461#121—342no—
462#121—342no—
463C4×D4—174no—
464C4×D4—348no—
465C4×D4—342no—
466C4×D4C4×D1714yes—
467C4×D4C22⋊D1714yes—
468#117—174no—
469#117—342no—
470#117—342no—
471#117—342no—
472#117—681no—
473#117—681no—
474C2×C4⋊C4—174no—
475C2×C4⋊C4—171no—
476C2×C4⋊C4—171no—
477C2×C4⋊C4—171no—
478C2×C4⋊C4—171no—
479C2×C4⋊C4—171no—
480C2×C4⋊C4—171no—
481C2×C4⋊C4—171no—
482C2×C4⋊C4—341no—
483C2×C4⋊C4—341no—
484C2×C4⋊C4—341no—
485C2×C4⋊C4—342no—
486C2×C4⋊C4—341no—
487C2×C4⋊C4—341no—
488C2×C4⋊C4D6811yescharacteristic
489C2×C22⋊C4—341no—
490C2×C22⋊C4—341no—
491C2×C22⋊C4—341no—
492C2×C22⋊C4—341no—
493C2×C22⋊C4—341no—
494C2×C22⋊C4—341no—
495C2×C22⋊C4—341no—
496C2×C22⋊C4—341no—
497C2×C22⋊C4D6811yescharacteristic
498C2×C22⋊C4D6811yescharacteristic
499C2×C42—341no—
500C2×C42—341no—
501C2×C42—341no—
502C2×C42—341no—
503C2×C42C22×D1711yescharacteristic
504C4⋊C8—22no—
505#102—342no—
506#102—342no—
507#102—681no—
508#102—681no—
509C22⋊C8—22no—
510C22⋊C8—22no—
511#97—22no—
512#95—341no—
513#95—341no—
514#95—341no—
515C17#2249811yescharacteristic, complemented, Sylow
516C24—341no—
517C24C2×D6811yescharacteristic
518C24C2×D6811yescharacteristic
519C2×D4—41no—
520C2×D4—41no—
521C2×D4—172no—
522C2×D4—344no—
523C2×D4—344no—
524C2×D4—341no—
525C2×D4—341no—
526C2×D4—341no—
527C2×D4—341no—
528C2×D4—341no—
529C2×D4—682no—
530C2×D4—682no—
531C2×D4—1361no—
532C2×D4—1361no—
533C2×D4#6322714yes—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—341no—
543C22×C4—341no—
544C22×C4—341no—
545C22×C4—341no—
546C22×C4—344no—
547C22×C4—344no—
548C22×C4—341no—
549C22×C4—341no—
550C22×C4—341no—
551C22×C4—1361no—
552C22×C4—1361no—
553C22×C4—1361no—
554C22×C4—1361no—
555C22×C4C2×C4×D1712yes—
556C22×C4C2×C4×D1712yes—
557C22×C4C2×D6811yescharacteristic
558C22×C4C2×D6811yescharacteristic
559C22×C4C2×D6811yescharacteristic
560C22×C4C2×D6811yescharacteristic
561C22×C4C2×C22⋊D1712yes—
562C22×C4C2×C22⋊D1712yes—
563C22×C4C23×D1711yescharacteristic
564M16—44no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—44no—
577C2×C8#6325412yes—
578C4⋊C4—172no—
579C4⋊C4—172no—
580C4⋊C4—172no—
581C4⋊C4—172no—
582C4⋊C4—341no—
583C4⋊C4—341no—
584C4⋊C4—341no—
585C4⋊C4—341no—
586C4⋊C4—344no—
587C4⋊C4—344no—
588C4⋊C4—344no—
589C4⋊C4—341no—
590C4⋊C4—341no—
591C4⋊C4—341no—
592C4⋊C4—341no—
593C4⋊C4—341no—
594C4⋊C4—341no—
595C4⋊C4—682no—
596C4⋊C4—1361no—
597C4⋊C4#6322714yes—
598C22⋊C4—344no—
599C22⋊C4—344no—
600C22⋊C4—344no—
601C22⋊C4—344no—
602C22⋊C4—682no—
603C22⋊C4—682no—
604C22⋊C4—1361no—
605C22⋊C4—1361no—
606C22⋊C4#6322714yes—
607C22⋊C4#6322714yes—
608C42—344no—
609C42—682no—
610C42—682no—
611C42—682no—
612C42C2×C4×D1712yes—
613C42C2×C22⋊D1712yes—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—342no—
627C23—681no—
628C23—681no—
629C23—681no—
630C23—681no—
631C23—681no—
632C23—681no—
633C23C2×#6322712yes—
634C23C2×#6322712yes—
635C23C22×D6811yescharacteristic
636D4—44no—
637D4—342no—
638D4—342no—
639D4—688no—
640D4—681no—
641D4—681no—
642D4—1364no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—342no—
660C2×C4—342no—
661C2×C4—342no—
662C2×C4—342no—
663C2×C4—681no—
664C2×C4—681no—
665C2×C4—681no—
666C2×C4—681no—
667C2×C4—681no—
668C2×C4—681no—
669C2×C4—681no—
670C2×C4—681no—
671C2×C4—681no—
672C2×C4—681no—
673C2×C4—681no—
674C2×C4—681no—
675C2×C4—681no—
676C2×C4—681no—
677C2×C4—681no—
678C2×C4—681no—
679C2×C4—681no—
680C2×C4—1364no—
681C2×C4—1364no—
682C2×C4C2×#6322712yes—
683C2×C4C2×#6322712yes—
684C2×C4C2×#6322712yes—
685C2×C4C2×#6322712yes—
686C2×C4C22×C4×D1711yescharacteristic
687C2×C4C2×#6325411yescharacteristic
688C2×C4#1058769111yescharacteristic
689C2×C4#41×D1711yescharacteristic
690C2×C4#1058769711yescharacteristic
691C2×C4C22×C22⋊D1711yescharacteristic
692C8—22no—
693C8—41no—
694C8—41no—
695C8—41no—
696C22—22no—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—682no—
711C22—682no—
712C22—682no—
713C22—1361no—
714C22—1361no—
715C22—1361no—
716C22—1361no—
717C22C22×#6322711yescharacteristic
718C22#1176345411yescharacteristic
719C22#1176346311yescharacteristic
720C22#1176360911yescharacteristic
721C22#1176360911yescharacteristic
722C22#1176361411yescharacteristic
723C22#1176362111yescharacteristic
724C4—22no—
725C4—22no—
726C4—22no—
727C4—22no—
728C4—682no—
729C4—682no—
730C4—682no—
731C4—682no—
732C4—1361no—
733C4—1361no—
734C4—1361no—
735C4C4×#6325411yescharacteristic
736C4#1176328811yescharacteristic
737C4#1176345311yescharacteristic
738C4#1176345811yescharacteristic
739C2—42no—
740C2—42no—
741C2—1362no—
742C2#1453160911yescharacteristic
743C2#1453730411yescharacteristic
744C2#1453731111yescharacteristic
745C2#1454076211yescharacteristic
746C2#1454079211yescharacteristic
747C2#1454128611yescharacteristic
748C2#1454133111yescharacteristic
subgroupG/H
centerC23C22×D68
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC2×C17×#435C2
socleC23×C17C22×D4
prime radicalC2×#11763505C2
cosocleC22×C4×C17C24
hypercenterC2×#435D17
hypocenterC17#22498
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
2. #14531733C2semidirect
3. #14529753C2semidirect
4. #14529739C2semidirect
5. #14529222C2semidirect
6. #14529212C2semidirect
7. #14529104C2semidirect
8. #14529104C2semidirect
9. #14528880C2semidirect
10. #14528871C2semidirect
11. #14528785C2semidirect
12. #14528610C2semidirect
13. #14528504C2semidirect
14. #14528501C2semidirect
15. C2×C17×#435C2semidirect
17. #11763505C4semidirect
323. C2×#435D17semidirect
515. C17#22498semidirect

Maximal subgroups

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

subgroupindex
C2×#117635052
#145317332
#145297532
#145297392
#145292222
#145292122
#145291042
#145288802
#145288712
#145287852
#145286102
#145285042
#145285012
C2×C17×#4352
#2249817