Finite Group Databasebeta

← #17049895

Subgroups — #17049895

Order 4352.

1446 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×C22⋊D17C211yesmaximal, characteristic
2C2×#11762878C211yesmaximal, characteristic
3C2×#103×D17C211yesmaximal, characteristic, complemented
4#14531714C211yesmaximal, characteristic
5#14529705C211yesmaximal, characteristic, complemented
6#14529602C211yesmaximal, characteristic, complemented
7#14529217C211yesmaximal, characteristic, complemented
8#14529204C211yesmaximal, characteristic, complemented
9#14529096C211yesmaximal, characteristic, complemented
10#14529088C211yesmaximal, characteristic, complemented
11#14528797C211yesmaximal, characteristic, complemented
12#14528719C211yesmaximal, characteristic, complemented
13#14528717C211yesmaximal, characteristic, complemented
14#14528616C211yesmaximal, characteristic, complemented
15C2×C17×#419C211yesmaximal, characteristic, complemented
16C22×Q8×D17C2211yescharacteristic
17C22×C8×D17C2211yescharacteristic
18Q8×C22⋊D17—24no—
19Q8×C22⋊D17C418yescomplemented
20C2×#10587630—21no—
21C2×#10587630C2211yescharacteristic
22C2×#10587610—21no—
23C2×#10587610C2211yescharacteristic
24C2×#10587632—21no—
25C2×#10587632C2211yescharacteristic
26C2×Q8×Dic17C2211yescharacteristic
27C2×C4×C22⋊D17—21no—
28C2×C4×C22⋊D17C2211yescharacteristic
29C2×C4⋊C4×D17C2211yescharacteristic
30#11762878—24no—
31C2×#10587485C2211yescharacteristic
32C2×#10587487C2211yescharacteristic
33C2×#10587487C2211yescharacteristic
34C2×#10587506C2211yescharacteristic
35C2×#10587506C2211yescharacteristic
36C2×#10587506C2211yescharacteristic
37C2×#10587506C2211yescharacteristic
38C2×#10587481C2211yescharacteristic
39C2×#10587481C2211yescharacteristic
40#103×D17—24no—
41C2×C22⋊#3622C2211yescharacteristic
42C2×#10587491C2211yescharacteristic
43C2×#10587486C2211yescharacteristic
44#11762703—21no—
45#11762693—21no—
46#11762685—21no—
47#11762674C2211yescharacteristic
48#11762669C2211yescharacteristic
49#11762666C2211yescharacteristic
50C4⋊C4×Dic17C2211yescharacteristic
51C4×#63227—21no—
52#11762572C2211yescharacteristic
53#11762572C2211yescharacteristic
54#11762571C2211yescharacteristic
55#11762571C2211yescharacteristic
56C23×Q8×C17C2211yescharacteristic
57C22×M16×C17C2211yescharacteristic
58C2×C17×#117C2211yescharacteristic
59C17×#419—24no—
60C2×C17×#103C2211yescharacteristic
61C2×C17×#103C2211yescharacteristic
62C2×C17×#103C2211yescharacteristic
63C2×C17×#103C2211yescharacteristic
64C22×Q8×C17—22no—
65C22×Q8×C17—21no—
66C22×Q8×C17—22no—
67C22×Q8×C17—22no—
68C22×Q8×C17—41no—
69C22×Q8×C17—41no—
70C22×Q8×C17C2×C414yescomplemented
71C22×Q8×C17C2311yescharacteristic
72C22×Q8×C17C2311yescharacteristic
73C23×C4×C17—21no—
74C23×C4×C17C2311yescharacteristic
75C22×C22⋊D17D411yescharacteristic
76C2×Q8×D17—22no—
77C2×Q8×D17—22no—
78C2×Q8×D17—22no—
79C2×Q8×D17—41no—
80C2×Q8×D17—41no—
81C2×Q8×D17C2×C414yes—
82C22×C4×D17—21no—
83C22×C4×D17—21no—
84C22×C4×D17C2311yescharacteristic
85C22×Dic34—21no—
86C22×Dic34C2311yescharacteristic
87C2×M16×C17—22no—
88C2×M16×C17—22no—
89C2×M16×C17—41no—
90C22×C8×C17C2311yescharacteristic
91C22×C8×C17C2311yescharacteristic
92C17×#117—22no—
93C17×#117—41no—
94C2×C4⋊C4×C17C2311yescharacteristic
95C2×C4⋊C4×C17C2311yescharacteristic
96C2×C22⋊C4×C17—21no—
97C2×C42×C17—21no—
98C2×C22⋊Dic17—21no—
99C2×C22⋊Dic17—21no—
100C2×C22⋊Dic17D411yescharacteristic
101#10587632—28no—
102#10587632—22no—
103#10587632C2×C414yes—
104Q8×Dic17—22no—
105Q8×Dic17C2×C414yescomplemented
106#10587630—28no—
107#10587630—22no—
108#10587630C2×C414yescomplemented
109C4×C22⋊D17—28no—
110C4×C22⋊D17C2×C414yes—
111C4×C22⋊D17D414yes—
112C2×#63227—21no—
113C2×#63227—21no—
114C2×#63227D411yescharacteristic
115C2×C4⋊Dic17—21no—
116C2×C4⋊Dic17C2311yescharacteristic
117C2×C4⋊Dic17C2311yescharacteristic
118C2×C4⋊Dic17C2311yescharacteristic
119#10587610—22no—
120#10587610—28no—
121#10587610C2×C414yescomplemented
122C2×#63225—21no—
123C2×#63225—21no—
124C2×#63225—21no—
125C2×#63225—21no—
126C2×#63225—21no—
127C2×#63225D411yescharacteristic
128C2×C4×Dic17—21no—
129C2×C4×Dic17—21no—
130C2×C4×Dic17C2311yescharacteristic
131C22×#3622C2311yescharacteristic
132C22×#3622C2311yescharacteristic
133C2×C8×D17—22no—
134C2×C8×D17—22no—
135C2×C8×D17—41no—
136C4⋊C4×D17—22no—
137C4⋊C4×D17—41no—
138C17×#103—22no—
139C17×#103—22no—
140C17×#103—22no—
141C17×#103D414yescomplemented
142#10587506—22no—
143#10587506—22no—
144#10587506—41no—
145#10587506—41no—
146#10587502—21no—
147#10587502—21no—
148#10587502—21no—
149#10587502—21no—
150#10587502—21no—
151C22⋊#3622—22no—
152#10587491—22no—
153#10587487—22no—
154#10587487—41no—
155#10587486—22no—
156#10587485—22no—
157#10587481—22no—
158#10587481—41no—
159C24×C17C2×D411yescharacteristic
160C23×D17C2×D411yescharacteristic
161C2×Q8×C17—24no—
162C2×Q8×C17—21no—
163C2×Q8×C17—21no—
164C2×Q8×C17—21no—
165C2×Q8×C17—21no—
166C2×Q8×C17—28no—
167C2×Q8×C17—21no—
168C2×Q8×C17—21no—
169C2×Q8×C17—21no—
170C2×Q8×C17—21no—
171C2×Q8×C17—42no—
172C2×Q8×C17—42no—
173C2×Q8×C17—44no—
174C2×Q8×C17—44no—
175C2×Q8×C17—44no—
176C2×Q8×C17C22×C412yes—
177C2×Q8×C17C22×C412yes—
178C2×Q8×C17C2×D412yes—
179C2×Q8×C17#4112yes—
180C22×C4×C17—21no—
181C22×C4×C17—21no—
182C22×C4×C17—21no—
183C22×C4×C17—21no—
184C22×C4×C17—21no—
185C22×C4×C17—24no—
186C22×C4×C17—21no—
187C22×C4×C17—21no—
188C22×C4×C17—21no—
189C22×C4×C17—42no—
190C22×C4×C17—42no—
191C22×C4×C17C22×C412yes—
192C22×C4×C17C2×D411yescharacteristic
193C22×C4×C17C2×D412yes—
194C22×C4×C17C2411yescharacteristic
195C2×C22⋊D17—22no—
196C2×C22⋊D17—22no—
197C2×C22⋊D17C22⋊C414yes—
198C22×Dic17—21no—
199C22×Dic17—21no—
200C22×Dic17—21no—
201C22×Dic17—21no—
202C22×Dic17C2×D411yescharacteristic
203C22×Dic17C2×D411yescharacteristic
204C22×Dic17C2×D411yescharacteristic
205Q8×D17—28no—
206Q8×D17—44no—
207Q8×D17—44no—
208Q8×D17—44no—
209C2×C4×D17—21no—
210C2×C4×D17—21no—
211C2×C4×D17—21no—
212C2×C4×D17—21no—
213C2×C4×D17—24no—
214C2×C4×D17—42no—
215C2×C4×D17—42no—
216C2×C4×D17—42no—
217C2×C4×D17—42no—
218C2×C4×D17—81no—
219C2×C4×D17C22×C412yes—
220C2×C4×D17C2×D412yes—
221C2×Dic34—21no—
222C2×Dic34—21no—
223C2×Dic34—21no—
224C2×Dic34—21no—
225C2×Dic34—21no—
226C2×Dic34—24no—
227C2×Dic34—42no—
228C2×Dic34—42no—
229C2×Dic34C22×C412yes—
230M16×C17—44no—
231C2×C8×C17—21no—
232C2×C8×C17—21no—
233C2×C8×C17—21no—
234C2×C8×C17—21no—
235C2×C8×C17—21no—
236C2×C8×C17C2×D412yes—
237C4⋊C4×C17—21no—
238C4⋊C4×C17—21no—
239C4⋊C4×C17—21no—
240C4⋊C4×C17C2×D412yes—
241C22⋊C4×C17—42no—
242C42×C17—42no—
243C22⋊Dic17—24no—
244C22⋊Dic17—81no—
245C22⋊Dic17C22⋊C414yes—
246#63227—24no—
247#63227—42no—
248#63227C22⋊C414yes—
249C4⋊Dic17—21no—
250C4⋊Dic17—24no—
251C4⋊Dic17—21no—
252C4⋊Dic17—21no—
253C4⋊Dic17—21no—
254C4⋊Dic17—21no—
255C4⋊Dic17C22×C412yes—
256#63225—24no—
257#63225—24no—
258#63225—24no—
259#63225—24no—
260#63225—42no—
261#63225C22⋊C414yes—
262C4×Dic17—24no—
263C4×Dic17—81no—
264C4×Dic17C22×C412yes—
265C4×Dic17C2×D412yes—
266C2×#3622—21no—
267C2×#3622—21no—
268C2×#3622—21no—
269C2×#3622—21no—
270C2×#3622—21no—
271C2×#3622—21no—
272C8×D17—44no—
273#22425—171nomaximal, Sylow
274C23×C17—21no—
275C23×C17—21no—
276C23×C17—21no—
277C23×C17—21no—
278C23×C17—21no—
279C23×C17—21no—
280C23×C17C2×C22⋊C412yes—
281C23×C17C22×D411yescharacteristic
282C22×D17—21no—
283C22×D17—21no—
284C22×D17—21no—
285C22×D17—21no—
286C22×D17C2×C22⋊C412yes—
287C22×D17#13712yes—
288C22×D17#13712yes—
289Q8×C17—22no—
290Q8×C17—22no—
291Q8×C17—22no—
292Q8×C17—22no—
293Q8×C17—22no—
294Q8×C17—48no—
295Q8×C17—41no—
296Q8×C17—41no—
297Q8×C17C4×D414yes—
298C2×C4×C17—22no—
299C2×C4×C17—21no—
300C2×C4×C17—22no—
301C2×C4×C17—22no—
302C2×C4×C17—21no—
303C2×C4×C17—22no—
304C2×C4×C17—22no—
305C2×C4×C17—22no—
306C2×C4×C17—22no—
307C2×C4×C17—22no—
308C2×C4×C17—22no—
309C2×C4×C17—48no—
310C2×C4×C17—41no—
311C2×C4×C17—41no—
312C2×C4×C17—41no—
313C2×C4×C17—41no—
314C2×C4×C17—41no—
315C2×C4×C17—41no—
316C2×C4×C17—41no—
317C2×C4×C17C2×C22⋊C412yes—
318C2×C4×C17C23×C411yescharacteristic
319C2×C4×C17C22×D411yescharacteristic
320C2×C4×C17C22×D411yescharacteristic
321C2×C4×C17C2×#4111yescharacteristic
322C2×C4×C17H(5,𝔽2)11yescharacteristic
323C2×C4×C17H(5,𝔽2)11yescharacteristic
324C22⋊D17—28no—
325C2×Dic17—21no—
326C2×Dic17—21no—
327C2×Dic17—21no—
328C2×Dic17—21no—
329C2×Dic17—21no—
330C2×Dic17—21no—
331C2×Dic17—22no—
332C2×Dic17—22no—
333C2×Dic17—41no—
334C2×Dic17—41no—
335C2×Dic17—41no—
336C2×Dic17—41no—
337C2×Dic17—41no—
338C2×Dic17—41no—
339C2×Dic17—41no—
340C2×Dic17—41no—
341C2×Dic17—41no—
342C2×Dic17—41no—
343C2×Dic17C2×C22⋊C412yes—
344C2×Dic17C2×C22⋊C412yes—
345C2×Dic17C2×C22⋊C412yes—
346C4×D17—22no—
347C4×D17—22no—
348C4×D17—22no—
349C4×D17—22no—
350C4×D17—48no—
351C4×D17—84no—
352Dic34—22no—
353Dic34—22no—
354Dic34—48no—
355Dic34—41no—
356Dic34—41no—
357C8×C17—22no—
358C8×C17—41no—
359#3622—41no—
360#3622—41no—
361C2×D4×Q8—171no—
362C2×#435—171no—
363C2×#419D1711yescharacteristic, complemented
364C22×#103—171no—
365#2352—171no—
366#1981—171no—
367#1960—171no—
368#1894—171no—
369#1892—171no—
370#1873—171no—
371#1872—171no—
372#1805—171no—
373#1787—171no—
374#1787—171no—
375#1763—171no—
376C22×C17—22no—
377C22×C17—22no—
378C22×C17—22no—
379C22×C17—41no—
380C22×C17—41no—
381C22×C17—41no—
382C22×C17—41no—
383C22×C17C22×C22⋊C411yescharacteristic
384C22×C17D4211yescharacteristic
385C22×C17#54611yescharacteristic
386C22×C17C2×#13711yescharacteristic
387C22×C17C2×#13711yescharacteristic
388C22×C17#57711yescharacteristic
389C22×C17#57811yescharacteristic
390C2×D17—22no—
391C2×D17—22no—
392C2×D17—22no—
393C2×D17—22no—
394C2×D17—22no—
395C2×D17—22no—
396C2×D17#41914yescomplemented
397C4×C17—24no—
398C4×C17—22no—
399C4×C17—42no—
400C4×C17—42no—
401C4×C17—81no—
402C4×C17C2×C4×D411yescharacteristic
403C4×C17#51811yescharacteristic
404C4×C17D4211yescharacteristic
405C4×C17#54611yescharacteristic
406Dic17—22no—
407Dic17—22no—
408Dic17—22no—
409Dic17—42no—
410Dic17—42no—
411Dic17—81no—
412Dic17—81no—
413C23×Q8—171no—
414C23×Q8C2×D1711yescharacteristic
415C22×M16C2×D1711yescharacteristic
416C23×C8—171no—
417D4×Q8—178no—
418D4×Q8—344no—
419C2×C4⋊Q8—171no—
420C2×C4⋊Q8—341no—
421C2×C22⋊Q8—171no—
422C2×C22⋊Q8—171no—
423C2×C22⋊Q8—341no—
424C2×C22⋊Q8—341no—
425C2×C4×Q8—171no—
426C2×C4×D4—171no—
427C2×C4×D4—341no—
428C2×#117C2×D1711yescharacteristic
429C22×C4⋊C4—171no—
430#435—344no—
431C2×C4⋊C8—171no—
432#419—24no—
433C2×#103—171no—
434C2×#103—171no—
435C2×#103—171no—
436C2×#103—171no—
437C2×#103—171no—
438C2×#103—171no—
439C2×#103—171no—
440C2×#103—171no—
441C2×#103—344no—
442C2×#103C2×D1711yescharacteristic
443C2×#103C2×D1711yescharacteristic
444C2×#103C2×D1711yescharacteristic
445C2×#103C2×D1711yescharacteristic
446C2×C22⋊C8—171no—
447C2×C22⋊C8—171no—
448C2×#97—171no—
449#388—341no—
450#387—341no—
451#386—341no—
452#382—171no—
453#380—171no—
454#380—171no—
455C4×C4⋊C4—171no—
456C4×C22⋊C4—341no—
457#340—171no—
458#340—171no—
459#340—171no—
460#340—171no—
461C2×C17—42no—
462C2×C17D4×C22⋊C411yescharacteristic
463C2×C17C2×#41911yescharacteristic
464C2×C17#289811yescharacteristic
465C2×C17#326611yescharacteristic
466C2×C17#327011yescharacteristic
467C2×C17#331211yescharacteristic
468C2×C17#332011yescharacteristic
469D17—24no—
470C22×Q8—21no—
471C22×Q8—22no—
472C22×Q8—22no—
473C22×Q8—22no—
474C22×Q8—41no—
475C22×Q8—41no—
476C22×Q8—174no—
477C22×Q8—171no—
478C22×Q8—341no—
479C22×Q8—342no—
480C22×Q8—342no—
481C22×Q8—342no—
482C22×Q8—681no—
483C22×Q8—681no—
484C22×Q8C4×D1714yescomplemented
485C22×Q8C22×D1711yescharacteristic
486C22×Q8C22×D1711yescharacteristic
487C22×D4—171no—
488C23×C4—21no—
489C23×C4—171no—
490C23×C4—341no—
491C23×C4—341no—
492C23×C4C22×D1711yescharacteristic
493C2×M16—22no—
494C2×M16—22no—
495C2×M16—41no—
496C22×C8—171no—
497C22×C8—171no—
498C22×C8—342no—
499C22×C8—342no—
500C22×C8—681no—
501C22×C8C22×D1711yescharacteristic
502C22×C8C22×D1711yescharacteristic
503C4⋊Q8—174no—
504C4⋊Q8—342no—
505C4⋊Q8—348no—
506C22⋊Q8—174no—
507C22⋊Q8—174no—
508C22⋊Q8—348no—
509C22⋊Q8—348no—
510C22⋊Q8—342no—
511C22⋊Q8—342no—
512C4×Q8—174no—
513C4×Q8—342no—
514C4×D4—174no—
515C4×D4—174no—
516C4×D4—348no—
517#117—22no—
518#117—41no—
519C2×C4⋊C4—171no—
520C2×C4⋊C4—171no—
521C2×C4⋊C4—171no—
522C2×C4⋊C4—171no—
523C2×C4⋊C4—341no—
524C2×C4⋊C4—341no—
525C2×C4⋊C4—341no—
526C2×C4⋊C4—341no—
527C2×C4⋊C4—341no—
528C2×C4⋊C4—342no—
529C2×C4⋊C4—341no—
530C2×C4⋊C4—681no—
531C2×C4⋊C4C22×D1711yescharacteristic
532C2×C4⋊C4C22×D1711yescharacteristic
533C2×C22⋊C4—21no—
534C2×C22⋊C4—171no—
535C2×C22⋊C4—171no—
536C2×C22⋊C4—341no—
537C2×C22⋊C4—341no—
538C2×C22⋊C4—341no—
539C2×C22⋊C4—341no—
540C2×C42—21no—
541C2×C42—171no—
542C2×C42—341no—
543C2×C42—341no—
544C4⋊C8—342no—
545#103—22no—
546#103—22no—
547#103—22no—
548#103—342no—
549#103—342no—
550#103—342no—
551#103—342no—
552#103—681no—
553#103—681no—
554#103—681no—
555#103—681no—
556#103C22⋊D1714yescomplemented
557C22⋊C8—342no—
558C22⋊C8—342no—
559#97—342no—
560#95—341no—
561#95—341no—
562#95—341no—
563#95—341no—
564#95—341no—
565C17#2242511yescharacteristic, complemented, Sylow
566C24—171no—
567C24D4×D1711yescharacteristic
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—24no—
573C2×Q8—28no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—42no—
579C2×Q8—42no—
580C2×Q8—44no—
581C2×Q8—44no—
582C2×Q8—44no—
583C2×Q8—172no—
584C2×Q8—344no—
585C2×Q8—341no—
586C2×Q8—348no—
587C2×Q8—341no—
588C2×Q8—341no—
589C2×Q8—341no—
590C2×Q8—341no—
591C2×Q8—682no—
592C2×Q8—682no—
593C2×Q8—684no—
594C2×Q8—684no—
595C2×Q8—684no—
596C2×Q8C2×C4×D1712yes—
597C2×Q8C2×C4×D1712yes—
598C2×Q8#6325212yes—
599C2×Q8C2×C22⋊D1712yes—
600C2×D4—174no—
601C2×D4—342no—
602C2×D4—342no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—24no—
611C22×C4—21no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—171no—
615C22×C4—171no—
616C22×C4—171no—
617C22×C4—172no—
618C22×C4—172no—
619C22×C4—344no—
620C22×C4—341no—
621C22×C4—341no—
622C22×C4—341no—
623C22×C4—341no—
624C22×C4—341no—
625C22×C4—341no—
626C22×C4—341no—
627C22×C4—341no—
628C22×C4—682no—
629C22×C4—682no—
630C22×C4—682no—
631C22×C4—682no—
632C22×C4—1361no—
633C22×C4C2×C4×D1712yes—
634C22×C4D4×D1712yes—
635C22×C4D4×D1711yescharacteristic
636C22×C4C23×D1711yescharacteristic
637M16—44no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—341no—
644C2×C8—341no—
645C2×C8—341no—
646C2×C8—341no—
647C2×C8—341no—
648C2×C8—341no—
649C2×C8—684no—
650C2×C8C2×C22⋊D1712yes—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—174no—
655C4⋊C4—172no—
656C4⋊C4—344no—
657C4⋊C4—344no—
658C4⋊C4—344no—
659C4⋊C4—344no—
660C4⋊C4—341no—
661C4⋊C4—344no—
662C4⋊C4—341no—
663C4⋊C4—341no—
664C4⋊C4—341no—
665C4⋊C4—341no—
666C4⋊C4—682no—
667C4⋊C4C2×C22⋊D1712yes—
668C22⋊C4—42no—
669C22⋊C4—174no—
670C22⋊C4—174no—
671C22⋊C4—344no—
672C22⋊C4—344no—
673C22⋊C4—682no—
674C22⋊C4—1361no—
675C42—42no—
676C42—172no—
677C42—172no—
678C42—344no—
679C42—1361no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—172no—
687C23—172no—
688C23—172no—
689C23—341no—
690C23—341no—
691C23—341no—
692C23—341no—
693C23C22⋊C4×D1712yes—
694C23C2×D4×D1711yescharacteristic
695Q8—22no—
696Q8—22no—
697Q8—22no—
698Q8—22no—
699Q8—22no—
700Q8—48no—
701Q8—41no—
702Q8—41no—
703Q8—342no—
704Q8—342no—
705Q8—688no—
706Q8—681no—
707Q8—681no—
708Q8C4×C22⋊D1714yes—
709D4—348no—
710C2×C4—22no—
711C2×C4—21no—
712C2×C4—22no—
713C2×C4—21no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—48no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—172no—
730C2×C4—172no—
731C2×C4—172no—
732C2×C4—341no—
733C2×C4—341no—
734C2×C4—341no—
735C2×C4—341no—
736C2×C4—341no—
737C2×C4—341no—
738C2×C4—342no—
739C2×C4—342no—
740C2×C4—342no—
741C2×C4—342no—
742C2×C4—342no—
743C2×C4—342no—
744C2×C4—688no—
745C2×C4—681no—
746C2×C4—681no—
747C2×C4—681no—
748C2×C4—681no—
749C2×C4—681no—
750C2×C4—681no—
751C2×C4—681no—
752C2×C4—681no—
753C2×C4—681no—
754C2×C4—681no—
755C2×C4—1364no—
756C2×C4C22⋊C4×D1712yes—
757C2×C4C22×C4×D1711yescharacteristic
758C2×C4C2×#6325211yescharacteristic
759C2×C4C2×D4×D1711yescharacteristic
760C2×C4#1058769111yescharacteristic
761C2×C4#1058769111yescharacteristic
762C2×C4C22×C22⋊D1711yescharacteristic
763C8—22no—
764C8—41no—
765C8—681no—
766C8—681no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—174no—
775C22—342no—
776C22—342no—
777C22—342no—
778C22—342no—
779C22—342no—
780C22—342no—
781C22C2×C22⋊C4×D1711yescharacteristic
782C22D4×C22⋊D1711yescharacteristic
783C22#1176344911yescharacteristic
784C22#137×D1711yescharacteristic
785C22#137×D1711yescharacteristic
786C22#1176361811yescharacteristic
787C22#1176362511yescharacteristic
788C4—22no—
789C4—24no—
790C4—42no—
791C4—42no—
792C4—81no—
793C4—342no—
794C4—342no—
795C4—342no—
796C4—682no—
797C4—682no—
798C4—1361no—
799C4—1361no—
800C4C2×C4×C22⋊D1711yescharacteristic
801C4#1176328211yescharacteristic
802C4D4×C22⋊D1711yescharacteristic
803C4#1176344911yescharacteristic
804C2—42no—
805C2—344no—
806C2C22⋊C4×C22⋊D1711yescharacteristic
807C2D17×#41911yescharacteristic
808C2#1453731611yescharacteristic
809C2#1454028811yescharacteristic
810C2#1454034811yescharacteristic
811C2#1454083611yescharacteristic
812C2#1454095611yescharacteristic
subgroupG/H
centerC23C2×D4×D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC2×C17×#419C2
socleC23×C17C22×D4
prime radicalC22×C22⋊D17D4
cosocleC22×C4×C17C24
hypercenterC2×#419D17
hypocenterC17#22425
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#419

Complements

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

NH ≅ G/Ntype
3. C2×#103×D17C2semidirect
5. #14529705C2semidirect
6. #14529602C2semidirect
7. #14529217C2semidirect
8. #14529204C2semidirect
9. #14529096C2semidirect
10. #14529088C2semidirect
11. #14528797C2semidirect
12. #14528719C2semidirect
13. #14528717C2semidirect
14. #14528616C2semidirect
15. C2×C17×#419C2semidirect
19. Q8×C22⋊D17C4semidirect
70. C22×Q8×C17C2×C4semidirect
105. Q8×Dic17C2×C4semidirect
108. #10587630C2×C4semidirect
121. #10587610C2×C4semidirect
141. C17×#103D4semidirect
363. C2×#419D17semidirect
396. C2×D17#419semidirect
484. C22×Q8C4×D17semidirect
556. #103C22⋊D17semidirect
565. C17#22425semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×C22⋊D172
C2×#117628782
C2×#103×D172
#145317142
#145297052
#145296022
#145292172
#145292042
#145290962
#145290882
#145287972
#145287192
#145287172
#145286162
C2×C17×#4192
#2242517