Finite Group Databasebeta

← #17050704

Subgroups — #17050704

Order 4352.

1174 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763516C211yesmaximal, characteristic
2#14531713C211yesmaximal, characteristic
3#14529757C211yesmaximal, characteristic, complemented
4#14529735C211yesmaximal, characteristic, complemented
5#14529217C211yesmaximal, characteristic, complemented
6#14529207C211yesmaximal, characteristic, complemented
7#14529094C211yesmaximal, characteristic, complemented
8#14529089C211yesmaximal, characteristic, complemented
9#14528875C211yesmaximal, characteristic, complemented
10#14528871C211yesmaximal, characteristic, complemented
11#14528800C211yesmaximal, characteristic, complemented
12#14528615C211yesmaximal, characteristic, complemented
13#14528504C211yesmaximal, characteristic, complemented
14C2×#11762572C211yesmaximal, characteristic, complemented
15C2×C17×#435C211yesmaximal, characteristic
16#11763516—24no—
17#11763516C418yescomplemented
18C2×#10587555C2211yescharacteristic
19C2×#10587576—21no—
20C2×#10587610C2211yescharacteristic
21C2×#10587610C2211yescharacteristic
22C2×#10587564—21no—
23C2×#10587564—21no—
24C2×C4×Dic34C2211yescharacteristic
25C2×D4×Dic17—21no—
26C2×#10587612C2211yescharacteristic
27C22×C4⋊Dic17C2211yescharacteristic
28C22×C4⋊Dic17C2211yescharacteristic
29C22×C4⋊Dic17C2211yescharacteristic
30C2×#10587487C2211yescharacteristic
31C2×#10587487C2211yescharacteristic
32C2×#10587487C2211yescharacteristic
33C2×#10587487C2211yescharacteristic
34#11762702—21no—
35#11762695—21no—
36#11762689—21no—
37#11762675C2211yescharacteristic
38#11762669C2211yescharacteristic
39#11762669C2211yescharacteristic
40C4×C4⋊Dic17C2211yescharacteristic
41C22⋊C4×Dic17—21no—
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
65C23×Dic17—21no—
66C23×Dic17—21no—
67C23×Dic17—21no—
68C22×Dic34—21no—
69C22×Dic34C2311yescharacteristic
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—
91D4×Dic17—28no—
92#10587612—22no—
93#10587612—41no—
94C2×C4⋊Dic17—22no—
95C2×C4⋊Dic17—22no—
96C2×C4⋊Dic17—21no—
97C2×C4⋊Dic17—21no—
98C2×C4⋊Dic17—21no—
99C2×C4⋊Dic17—21no—
100C2×C4⋊Dic17—22no—
101C2×C4⋊Dic17—41no—
102C2×C4⋊Dic17C2×C414yes—
103C2×C4⋊Dic17C2×C414yescomplemented
104C2×C4⋊Dic17C2311yescharacteristic
105C2×C4⋊Dic17C2311yescharacteristic
106C2×C4⋊Dic17C2311yescharacteristic
107C2×C4⋊Dic17C2311yescharacteristic
108C2×C4⋊Dic17C2311yescharacteristic
109C2×C4⋊Dic17C2311yescharacteristic
110C2×C4⋊Dic17C2311yescharacteristic
111#10587610—22no—
112#10587610—22no—
113#10587610C2×C414yes—
114#10587610C2×C414yescomplemented
115C2×#63225—21no—
116C2×#63225—21no—
117C2×#63225—21no—
118C2×C4×Dic17—21no—
119C2×C4×Dic17—21no—
120C2×C4×Dic17—21no—
121#10587576—28no—
122#10587564—28no—
123#10587564—28no—
124#10587555—22no—
125#10587555C2×C414yescomplemented
126C4×Dic34—22no—
127C4×Dic34C2×C414yescomplemented
128C17×C4⋊C8—22no—
129C17×C22⋊C8—22no—
130C17×C22⋊C8—22no—
131C17×#97—22no—
132#10587502—21no—
133#10587502—21no—
134#10587502—21no—
135#10587502—21no—
136#10587502—21no—
137#10587487—22no—
138#10587487—22no—
139#10587487—41no—
140#10587487—41no—
141C24×C17C2×D411yescharacteristic
142C24×C17C2×D411yescharacteristic
143C2×D4×C17—22no—
144C2×D4×C17—22no—
145C2×D4×C17C22⋊C414yes—
146C22×C4×C17—21no—
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×C17C22×C412yes—
155C22×C4×C17C22×C412yes—
156C22×C4×C17C2×D411yescharacteristic
157C22×C4×C17C2×D411yescharacteristic
158C22×C4×C17C2×D411yescharacteristic
159C22×C4×C17C2×D411yescharacteristic
160C22×C4×C17C2×D412yes—
161C22×C4×C17C2×D412yes—
162C22×C4×C17C2411yescharacteristic
163C22×Dic17—21no—
164C22×Dic17—21no—
165C22×Dic17—21no—
166C22×Dic17—21no—
167C22×Dic17—21no—
168C22×Dic17—24no—
169C22×Dic17—24no—
170C22×Dic17—21no—
171C22×Dic17—21no—
172C22×Dic17—21no—
173C22×Dic17—42no—
174C22×Dic17—42no—
175C22×Dic17—81no—
176C22×Dic17—81no—
177C22×Dic17—81no—
178C22×Dic17—81no—
179C22×Dic17—81no—
180C2×Dic34—21no—
181C2×Dic34—21no—
182C2×Dic34—21no—
183C2×Dic34—21no—
184C2×Dic34—21no—
185C2×Dic34—24no—
186C2×Dic34—81no—
187C2×Dic34—81no—
188C2×Dic34C22×C412yes—
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—24no—
210C22⋊Dic17—42no—
211C22⋊Dic17—42no—
212C22⋊Dic17—81no—
213C4⋊Dic17—24no—
214C4⋊Dic17—24no—
215C4⋊Dic17—24no—
216C4⋊Dic17—21no—
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—42no—
227C4⋊Dic17C22×C412yes—
228C4⋊Dic17C22×C412yes—
229C4⋊Dic17C22×C412yes—
230C4⋊Dic17#4112yes—
231#63225—24no—
232#63225—24no—
233#63225—24no—
234C4×Dic17—24no—
235C4×Dic17—42no—
236C4×Dic17—81no—
237#22497—171nomaximal, Sylow
238C23×C17—21no—
239C23×C17—21no—
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×C17C2×C22⋊C412yes—
249C23×C17C2×C22⋊C412yes—
250C23×C17#13712yes—
251C23×C17#13712yes—
252C23×C17C22×D411yescharacteristic
253D4×C17—28no—
254C2×C4×C17—21no—
255C2×C4×C17—21no—
256C2×C4×C17—21no—
257C2×C4×C17—21no—
258C2×C4×C17—21no—
259C2×C4×C17—21no—
260C2×C4×C17—21no—
261C2×C4×C17—21no—
262C2×C4×C17—22no—
263C2×C4×C17—22no—
264C2×C4×C17—22no—
265C2×C4×C17—22no—
266C2×C4×C17—22no—
267C2×C4×C17—22no—
268C2×C4×C17—22no—
269C2×C4×C17—22no—
270C2×C4×C17C2×C22⋊C412yes—
271C2×C4×C17C2×C22⋊C412yes—
272C2×C4×C17C2×C22⋊C412yes—
273C2×C4×C17C2×C22⋊C412yes—
274C2×C4×C17C23×C411yescharacteristic
275C2×C4×C17C22×D411yescharacteristic
276C2×C4×C17C2×#4111yescharacteristic
277C2×C4×C17C2×#4111yescharacteristic
278C2×C4×C17H(5,𝔽2)11yescharacteristic
279C2×C4×C172−1+411yescharacteristic
280C2×Dic17—22no—
281C2×Dic17—22no—
282C2×Dic17—22no—
283C2×Dic17—22no—
284C2×Dic17—22no—
285C2×Dic17—41no—
286C2×Dic17—41no—
287C2×Dic17—41no—
288C2×Dic17—41no—
289C2×Dic17—41no—
290C2×Dic17—41no—
291C2×Dic17—41no—
292C2×Dic17—41no—
293C2×Dic17—41no—
294C2×Dic17—41no—
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—84no—
305C2×Dic17—84no—
306C2×Dic17—84no—
307Dic34—22no—
308Dic34—22no—
309Dic34—41no—
310Dic34—41no—
311Dic34—84no—
312C8×C17—22no—
313C8×C17—41no—
314C8×C17—41no—
315C8×C17—41no—
316C2×#554—171no—
317C2×#435D1711yescharacteristic
318#2352—171no—
319#1993—171no—
320#1988—171no—
321#1894—171no—
322#1892—171no—
323#1873—171no—
324#1872—171no—
325#1824—171no—
326#1823—171no—
327#1805—171no—
328#1763—171no—
329#1736—171no—
330C2×#340—171no—
331C22×C17—22no—
332C22×C17—22no—
333C22×C17—22no—
334C22×C17—22no—
335C22×C17—22no—
336C22×C17—22no—
337C22×C17—22no—
338C22×C17—22no—
339C22×C17—22no—
340C22×C17—41no—
341C22×C17—41no—
342C22×C17—41no—
343C22×C17—41no—
344C22×C17#41914yes—
345C22×C17C22×C22⋊C411yescharacteristic
346C22×C17#54611yescharacteristic
347C22×C17#54711yescharacteristic
348C22×C17C2×#13711yescharacteristic
349C22×C17C2×#13711yescharacteristic
350C22×C17#57611yescharacteristic
351C22×C17#57711yescharacteristic
352C4×C17—22no—
353C4×C17—22no—
354C4×C17—22no—
355C4×C17—22no—
356C4×C17C4×#4111yescharacteristic
357C4×C17#52011yescharacteristic
358C4×C17#54611yescharacteristic
359C4×C17#54711yescharacteristic
360Dic17—42no—
361Dic17—42no—
362Dic17—42no—
363Dic17—42no—
364Dic17—42no—
365Dic17—81no—
366Dic17—81no—
367Dic17—81no—
368C22×M16C2×D1711yescharacteristic
369C23×C8C2×D1711yescharacteristic
370#554—178no—
371#554—344no—
372C2×C4⋊Q8—171no—
373C2×#125—341no—
374C2×C22⋊Q8—171no—
375C2×C22⋊Q8—171no—
376C2×C22⋊Q8—341no—
377C2×C22⋊Q8—341no—
378C2×C4×Q8—171no—
379C2×C4×D4—341no—
380C2×C4×D4C2×D1711yescharacteristic
381C2×#117—171no—
382C22×C4⋊C4—171no—
383C22×C4⋊C4—171no—
384C22×C4⋊C4—171no—
385#435—24no—
386C2×C4⋊C8C2×D1711yescharacteristic
387C2×#103—171no—
388C2×#103—171no—
389C2×#103—171no—
390C2×#103—171no—
391C2×C22⋊C8C2×D1711yescharacteristic
392C2×C22⋊C8C2×D1711yescharacteristic
393C2×#97C2×D1711yescharacteristic
394#388—341no—
395#387—341no—
396#386—341no—
397#382—171no—
398#380—171no—
399#380—171no—
400C4×C4⋊C4—171no—
401C4×C22⋊C4—341no—
402#340—171no—
403#340—171no—
404#340—171no—
405#340—171no—
406#340—171no—
407#340—171no—
408#340—171no—
409#340—171no—
410#340—171no—
411#340—171no—
412#340—171no—
413#340—171no—
414C2×C17—24no—
415C2×C17—42no—
416C2×C17#233911yescharacteristic
417C2×C17C2×#41911yescharacteristic
418C2×C17#289711yescharacteristic
419C2×C17#331411yescharacteristic
420C2×C17#331611yescharacteristic
421C2×C17#334411yescharacteristic
422C2×C17#334611yescharacteristic
423C22×Q8—171no—
424C22×Q8—341no—
425C22×D4D6811yescharacteristic
426C23×C4—341no—
427C23×C4—341no—
428C23×C4—341no—
429C23×C4C22×D1711yescharacteristic
430C23×C4C22×D1711yescharacteristic
431C2×M16—22no—
432C2×M16—22no—
433C2×M16—41no—
434C22×C8—22no—
435C22×C8—22no—
436C22×C8—41no—
437C22×C8C22×D1711yescharacteristic
438C22×C8C22×D1711yescharacteristic
439C22×C8C22×D1711yescharacteristic
440C22×C8C22×D1711yescharacteristic
441C4⋊Q8—174no—
442C4⋊Q8—342no—
443#125—348no—
444C22⋊Q8—174no—
445C22⋊Q8—174no—
446C22⋊Q8—342no—
447C22⋊Q8—342no—
448C22⋊Q8—348no—
449C22⋊Q8—348no—
450C4×Q8—174no—
451C4×Q8—342no—
452C4×D4—348no—
453C4×D4C4×D1714yes—
454C4×D4C22⋊D1714yes—
455#117—342no—
456#117—681no—
457C2×C4⋊C4—174no—
458C2×C4⋊C4—174no—
459C2×C4⋊C4—171no—
460C2×C4⋊C4—171no—
461C2×C4⋊C4—171no—
462C2×C4⋊C4—171no—
463C2×C4⋊C4—171no—
464C2×C4⋊C4—171no—
465C2×C4⋊C4—171no—
466C2×C4⋊C4—342no—
467C2×C4⋊C4—341no—
468C2×C4⋊C4—341no—
469C2×C4⋊C4—341no—
470C2×C4⋊C4—341no—
471C2×C4⋊C4—341no—
472C2×C4⋊C4—341no—
473C2×C4⋊C4—342no—
474C2×C4⋊C4—342no—
475C2×C4⋊C4—341no—
476C2×C4⋊C4—681no—
477C2×C4⋊C4D6811yescharacteristic
478C2×C22⋊C4—341no—
479C2×C22⋊C4—341no—
480C2×C22⋊C4—341no—
481C2×C22⋊C4—341no—
482C2×C22⋊C4—341no—
483C2×C22⋊C4D6811yescharacteristic
484C2×C22⋊C4D6811yescharacteristic
485C2×C42—341no—
486C2×C42—341no—
487C2×C42—341no—
488C2×C42C22×D1711yescharacteristic
489C4⋊C8—22no—
490#103—342no—
491#103—342no—
492#103—681no—
493#103—681no—
494C22⋊C8—22no—
495C22⋊C8—22no—
496#97—22no—
497#95—341no—
498#95—341no—
499#95—341no—
500#95—341no—
501#95—341no—
502C17#2249711yescharacteristic, complemented, Sylow
503C24C2×D6811yescharacteristic
504C24C2×D6811yescharacteristic
505C2×Q8—172no—
506C2×Q8—341no—
507C2×Q8—344no—
508C2×Q8—341no—
509C2×Q8—341no—
510C2×Q8—341no—
511C2×Q8—341no—
512C2×Q8—1361no—
513C2×Q8—1361no—
514C2×D4—22no—
515C2×D4—22no—
516C2×D4#6322714yes—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—341no—
526C22×C4—341no—
527C22×C4—341no—
528C22×C4—341no—
529C22×C4—341no—
530C22×C4—344no—
531C22×C4—344no—
532C22×C4—341no—
533C22×C4—341no—
534C22×C4—341no—
535C22×C4—682no—
536C22×C4—682no—
537C22×C4—1361no—
538C22×C4—1361no—
539C22×C4—1361no—
540C22×C4—1361no—
541C22×C4—1361no—
542C22×C4C2×C4×D1712yes—
543C22×C4C2×C4×D1712yes—
544C22×C4C2×D6811yescharacteristic
545C22×C4C2×D6811yescharacteristic
546C22×C4C2×D6811yescharacteristic
547C22×C4C2×D6811yescharacteristic
548C22×C4C2×C22⋊D1712yes—
549C22×C4C2×C22⋊D1712yes—
550C22×C4C23×D1711yescharacteristic
551M16—44no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—44no—
564C2×C8#6325412yes—
565C4⋊C4—172no—
566C4⋊C4—172no—
567C4⋊C4—172no—
568C4⋊C4—172no—
569C4⋊C4—341no—
570C4⋊C4—341no—
571C4⋊C4—341no—
572C4⋊C4—341no—
573C4⋊C4—344no—
574C4⋊C4—344no—
575C4⋊C4—344no—
576C4⋊C4—344no—
577C4⋊C4—344no—
578C4⋊C4—344no—
579C4⋊C4—341no—
580C4⋊C4—341no—
581C4⋊C4—341no—
582C4⋊C4—341no—
583C4⋊C4—341no—
584C4⋊C4—341no—
585C4⋊C4—682no—
586C4⋊C4#6322714yes—
587C22⋊C4—344no—
588C22⋊C4—344no—
589C22⋊C4—682no—
590C22⋊C4—682no—
591C22⋊C4—1361no—
592C22⋊C4#6322714yes—
593C22⋊C4#6322714yes—
594C42—344no—
595C42—682no—
596C42—1361no—
597C42C2×C4×D1712yes—
598C42C2×C22⋊D1712yes—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23#1058759512yes—
610C23#1058759512yes—
611C23C2×#6322712yes—
612C23C2×#6322712yes—
613C23C22×D6811yescharacteristic
614Q8—342no—
615Q8—342no—
616Q8—681no—
617Q8—681no—
618Q8—1364no—
619D4—28no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—342no—
637C2×C4—342no—
638C2×C4—342no—
639C2×C4—342no—
640C2×C4—342no—
641C2×C4—681no—
642C2×C4—681no—
643C2×C4—681no—
644C2×C4—681no—
645C2×C4—681no—
646C2×C4—681no—
647C2×C4—681no—
648C2×C4—681no—
649C2×C4—681no—
650C2×C4—681no—
651C2×C4—681no—
652C2×C4—681no—
653C2×C4—681no—
654C2×C4—681no—
655C2×C4—681no—
656C2×C4—681no—
657C2×C4—681no—
658C2×C4—681no—
659C2×C4—681no—
660C2×C4—1364no—
661C2×C4—1364no—
662C2×C4—1364no—
663C2×C4C2×#6322712yes—
664C2×C4C2×#6322712yes—
665C2×C4C2×#6322712yes—
666C2×C4C2×#6322712yes—
667C2×C4C22×C4×D1711yescharacteristic
668C2×C4C2×#6325411yescharacteristic
669C2×C4#1058769111yescharacteristic
670C2×C4#41×D1711yescharacteristic
671C2×C4#1058769711yescharacteristic
672C2×C4C22×C22⋊D1711yescharacteristic
673C8—22no—
674C8—41no—
675C8—41no—
676C8—41no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—22no—
684C22—22no—
685C22—22no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22#1176281914yes—
691C22C22×#6322711yescharacteristic
692C22#1176345411yescharacteristic
693C22#1176346311yescharacteristic
694C22C2×#1058759511yescharacteristic
695C22C2×#1058759511yescharacteristic
696C22#1176361411yescharacteristic
697C22#1176362111yescharacteristic
698C4—22no—
699C4—22no—
700C4—22no—
701C4—22no—
702C4—682no—
703C4—682no—
704C4—682no—
705C4—682no—
706C4—682no—
707C4—1361no—
708C4—1361no—
709C4—1361no—
710C4C4×#6325411yescharacteristic
711C4#1176328811yescharacteristic
712C4#1176345311yescharacteristic
713C4#1176345811yescharacteristic
714C2—24no—
715C2—42no—
716C2#1453160911yescharacteristic
717C2C2×#1176281911yescharacteristic
718C2#1453731111yescharacteristic
719C2#1454086711yescharacteristic
720C2#1454089711yescharacteristic
721C2#1454124111yescharacteristic
722C2#1454127111yescharacteristic
subgroupG/H
centerC23C22×D68
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC2×C17×#435C2
socleC23×C17C22×D4
prime radicalC22×D4×C17D4
cosocleC22×C4×C17C24
hypercenterC2×#435D17
hypocenterC17#22497
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
3. #14529757C2semidirect
4. #14529735C2semidirect
5. #14529217C2semidirect
6. #14529207C2semidirect
7. #14529094C2semidirect
8. #14529089C2semidirect
9. #14528875C2semidirect
10. #14528871C2semidirect
11. #14528800C2semidirect
12. #14528615C2semidirect
13. #14528504C2semidirect
14. C2×#11762572C2semidirect
17. #11763516C4semidirect
103. C2×C4⋊Dic17C2×C4semidirect
114. #10587610C2×C4semidirect
125. #10587555C2×C4semidirect
127. C4×Dic34C2×C4semidirect
502. C17#22497semidirect

Maximal subgroups

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

subgroupindex
C2×#117635162
#145317132
#145297572
#145297352
#145292172
#145292072
#145290942
#145290892
#145288752
#145288712
#145288002
#145286152
#145285042
C2×#117625722
C2×C17×#4352
#2249717