Finite Group Databasebeta

← #17049819

Subgroups — #17049819

Order 4352.

1478 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762881C211yesmaximal, characteristic, complemented
2C2×#11762810C211yesmaximal, characteristic, complemented
3C2×#11762805C211yesmaximal, characteristic, complemented
4#14531713C211yesmaximal, characteristic, complemented
5#14529708C211yesmaximal, characteristic, complemented
6#14529605C211yesmaximal, characteristic, complemented
7#14529218C211yesmaximal, characteristic, complemented
8#14529208C211yesmaximal, characteristic, complemented
9#14529097C211yesmaximal, characteristic, complemented
10#14529092C211yesmaximal, characteristic, complemented
11#14528794C211yesmaximal, characteristic, complemented
12#14528724C211yesmaximal, characteristic, complemented
13#14528724C211yesmaximal, characteristic, complemented
14#14528609C211yesmaximal, characteristic, complemented
15C2×C17×#547C211yesmaximal, characteristic
16C22×#63223C2211yescharacteristic
17C23×#3622C2211yescharacteristic
18C2×#10587612C2211yescharacteristic
19C22×C4⋊Dic17C2211yescharacteristic
20#11762881—24no—
21C2×C4⋊#3622C2211yescharacteristic
22#11762810—24no—
23#11762805—24no—
24C2×#10587506C2211yescharacteristic
25C2×#10587506C2211yescharacteristic
26C2×#10587506C2211yescharacteristic
27C2×#10587506C2211yescharacteristic
28C2×#10587506C2211yescharacteristic
29C2×#10587506C2211yescharacteristic
30C2×#10587506C2211yescharacteristic
31C2×#10587506C2211yescharacteristic
32C2×#10587503C2211yescharacteristic
33C2×#10587503C2211yescharacteristic
34C2×#10587503C2211yescharacteristic
35C2×#10587503C2211yescharacteristic
36C2×C22⋊#3622C2211yescharacteristic
37C2×C22⋊#3622C2211yescharacteristic
38C2×#10587474C2211yescharacteristic
39#11762702—21no—
40#11762695—21no—
41#11762689—21no—
42#11762675C2211yescharacteristic
43#11762669C2211yescharacteristic
44#11762669C2211yescharacteristic
45C4×C4⋊Dic17C2211yescharacteristic
46C22⋊C4×Dic17—21no—
47#11762571C2211yescharacteristic
48#11762571C2211yescharacteristic
49#11762571C2211yescharacteristic
50#11762571C2211yescharacteristic
51C22×#41×C17C2211yescharacteristic
52C22×#41×C17C2211yescharacteristic
53C17×#547—24no—
54C17×#547C418yescomplemented
55C2×C17×C4⋊Q8C2211yescharacteristic
56C2×C17×#123—21no—
57C2×C17×#123—21no—
58C2×C17×C22⋊Q8C2211yescharacteristic
59C2×C17×C22⋊Q8C2211yescharacteristic
60C2×C17×#121—21no—
61C2×C4×D4×C17C2211yescharacteristic
62C2×C4×D4×C17C2211yescharacteristic
63C22×C4⋊C4×C17—21no—
64C2×#41×C17—22no—
65C2×#41×C17—22no—
66C2×#41×C17—22no—
67C2×#41×C17—22no—
68C2×#41×C17—22no—
69C2×#41×C17—22no—
70C2×#41×C17—41no—
71C2×#41×C17—41no—
72C2×#41×C17—41no—
73C2×#41×C17—41no—
74C2×#41×C17C2×C414yes—
75C2×#41×C17C2×C414yescomplemented
76C22×Q8×C17C2311yescharacteristic
77C22×Q8×C17C2311yescharacteristic
78C22×D4×C17—21no—
79C22×D4×C17—21no—
80C22×D4×C17D411yescharacteristic
81C22×D4×C17C2311yescharacteristic
82C23×C4×C17—21no—
83C23×C4×C17—21no—
84C23×C4×C17—21no—
85C23×C4×C17C2311yescharacteristic
86C23×C4×C17C2311yescharacteristic
87C23×Dic17—21no—
88C17×C4⋊Q8—22no—
89C17×C4⋊Q8C2×C414yescomplemented
90C17×#123—28no—
91C17×#123—28no—
92C17×C22⋊Q8—22no—
93C17×C22⋊Q8—22no—
94C17×C22⋊Q8C2×C414yes—
95C17×C22⋊Q8C2×C414yescomplemented
96C17×#121—28no—
97C4×D4×C17—22no—
98C4×D4×C17C2×C414yes—
99C4×D4×C17C2×C414yescomplemented
100C4×D4×C17D414yes—
101C2×C4⋊C4×C17—21no—
102C2×C4⋊C4×C17—21no—
103C2×C4⋊C4×C17—21no—
104C2×C4⋊C4×C17—21no—
105C2×C4⋊C4×C17—28no—
106C2×C4⋊C4×C17D411yescharacteristic
107C2×C4⋊C4×C17C2311yescharacteristic
108C2×C22⋊C4×C17—21no—
109C2×C22⋊C4×C17—21no—
110C2×C22⋊C4×C17—21no—
111C2×C22⋊C4×C17D411yescharacteristic
112C2×C22⋊C4×C17D411yescharacteristic
113C2×C42×C17C2311yescharacteristic
114C2×C22⋊Dic17—21no—
115C2×C22⋊Dic17—21no—
116C2×C22⋊Dic17—21no—
117#10587612—22no—
118#10587612—41no—
119C2×C4⋊Dic17—21no—
120C2×C4⋊Dic17—22no—
121C2×C4⋊Dic17—41no—
122C2×C4⋊Dic17C2311yescharacteristic
123C2×C4⋊Dic17C2311yescharacteristic
124C2×C4⋊Dic17C2311yescharacteristic
125C2×C4⋊Dic17C2311yescharacteristic
126C2×C4×Dic17—21no—
127C2×C4×Dic17—21no—
128C2×#63223—22no—
129C2×#63223—22no—
130C2×#63223—41no—
131C22×#3622—22no—
132C22×#3622—22no—
133C22×#3622—41no—
134C22×#3622C2311yescharacteristic
135C22×#3622C2311yescharacteristic
136C22×#3622C2311yescharacteristic
137C22×#3622C2311yescharacteristic
138#10587506—22no—
139#10587506—22no—
140#10587506—22no—
141#10587506—22no—
142#10587506—41no—
143#10587506—41no—
144#10587506—41no—
145#10587506—41no—
146#10587503—22no—
147#10587503—22no—
148#10587503—22no—
149#10587503D414yescomplemented
150#10587502—21no—
151#10587502—21no—
152#10587502—21no—
153#10587502—21no—
154#10587502—21no—
155C22⋊#3622—22no—
156C22⋊#3622—22no—
157C4⋊#3622—22no—
158#10587474—22no—
159C24×C17—21no—
160C24×C17C2×D411yescharacteristic
161C24×C17C2×D411yescharacteristic
162#41×C17—28no—
163#41×C17—28no—
164#41×C17—44no—
165#41×C17—44no—
166#41×C17—44no—
167#41×C17—44no—
168#41×C17—44no—
169#41×C17—44no—
170C2×Q8×C17—21no—
171C2×Q8×C17—21no—
172C2×Q8×C17—21no—
173C2×Q8×C17—21no—
174C2×Q8×C17—21no—
175C2×Q8×C17—21no—
176C2×Q8×C17—21no—
177C2×Q8×C17—21no—
178C2×Q8×C17—21no—
179C2×Q8×C17—21no—
180C2×Q8×C17C22×C412yes—
181C2×Q8×C17C22×C412yes—
182C2×D4×C17—24no—
183C2×D4×C17—24no—
184C2×D4×C17—21no—
185C2×D4×C17—21no—
186C2×D4×C17—21no—
187C2×D4×C17—41no—
188C2×D4×C17—41no—
189C2×D4×C17—42no—
190C2×D4×C17—42no—
191C2×D4×C17—42no—
192C2×D4×C17—42no—
193C2×D4×C17C22⋊C414yes—
194C2×D4×C17C22×C412yes—
195C2×D4×C17C2×D412yes—
196C2×D4×C17#4112yes—
197C22×C4×C17—21no—
198C22×C4×C17—21no—
199C22×C4×C17—21no—
200C22×C4×C17—21no—
201C22×C4×C17—21no—
202C22×C4×C17—21no—
203C22×C4×C17—21no—
204C22×C4×C17—21no—
205C22×C4×C17—21no—
206C22×C4×C17—21no—
207C22×C4×C17—21no—
208C22×C4×C17—24no—
209C22×C4×C17—24no—
210C22×C4×C17—24no—
211C22×C4×C17—42no—
212C22×C4×C17—42no—
213C22×C4×C17—42no—
214C22×C4×C17—42no—
215C22×C4×C17—42no—
216C22×C4×C17—42no—
217C22×C4×C17C22×C412yes—
218C22×C4×C17C22×C412yes—
219C22×C4×C17C2×D411yescharacteristic
220C22×C4×C17C2×D411yescharacteristic
221C22×C4×C17C2×D411yescharacteristic
222C22×C4×C17C2×D411yescharacteristic
223C22×C4×C17C2×D412yes—
224C22×C4×C17C2×D412yes—
225C22×C4×C17C2411yescharacteristic
226C22×Dic17—21no—
227C22×Dic17—21no—
228C22×Dic17—21no—
229C22×Dic17—21no—
230C22×Dic17—42no—
231C22×Dic17—42no—
232C22×Dic17—81no—
233C4⋊C4×C17—24no—
234C4⋊C4×C17—24no—
235C4⋊C4×C17—24no—
236C4⋊C4×C17—24no—
237C4⋊C4×C17—21no—
238C4⋊C4×C17C22⋊C414yes—
239C4⋊C4×C17C22×C412yes—
240C22⋊C4×C17—24no—
241C22⋊C4×C17—24no—
242C22⋊C4×C17—24no—
243C22⋊C4×C17C22⋊C414yes—
244C22⋊C4×C17C22⋊C414yes—
245C42×C17C22×C412yes—
246C42×C17C2×D412yes—
247C22⋊Dic17—42no—
248C22⋊Dic17—42no—
249C22⋊Dic17—81no—
250C4⋊Dic17—21no—
251C4⋊Dic17—21no—
252C4⋊Dic17—21no—
253C4⋊Dic17—21no—
254C4⋊Dic17—21no—
255C4⋊Dic17—21no—
256C4⋊Dic17—21no—
257C4⋊Dic17—42no—
258C4⋊Dic17C2×D412yes—
259C4×Dic17—42no—
260C4×Dic17—81no—
261#63223—44no—
262C2×#3622—21no—
263C2×#3622—21no—
264C2×#3622—21no—
265C2×#3622—21no—
266C2×#3622—21no—
267C2×#3622—21no—
268C2×#3622—21no—
269C2×#3622—21no—
270C2×#3622—21no—
271C2×#3622—21no—
272C2×#3622—21no—
273C2×#3622—44no—
274C2×#3622C2×D412yes—
275#22420—171nomaximal, Sylow
276C23×C17—22no—
277C23×C17—21no—
278C23×C17—21no—
279C23×C17—22no—
280C23×C17—21no—
281C23×C17—21no—
282C23×C17—22no—
283C23×C17—21no—
284C23×C17—21no—
285C23×C17—21no—
286C23×C17—21no—
287C23×C17—21no—
288C23×C17—21no—
289C23×C17—21no—
290C23×C17—21no—
291C23×C17—41no—
292C23×C17—41no—
293C23×C17—41no—
294C23×C17—41no—
295C23×C17C2×C22⋊C412yes—
296C23×C17C2×C22⋊C412yes—
297C23×C17C22×D411yescharacteristic
298Q8×C17—22no—
299Q8×C17—22no—
300Q8×C17—22no—
301Q8×C17—22no—
302Q8×C17—41no—
303Q8×C17—41no—
304Q8×C17—41no—
305Q8×C17—41no—
306D4×C17—22no—
307D4×C17—22no—
308D4×C17—22no—
309D4×C17—44no—
310D4×C17—48no—
311D4×C17—48no—
312D4×C17C4×D414yes—
313C2×C4×C17—21no—
314C2×C4×C17—21no—
315C2×C4×C17—21no—
316C2×C4×C17—21no—
317C2×C4×C17—21no—
318C2×C4×C17—21no—
319C2×C4×C17—21no—
320C2×C4×C17—21no—
321C2×C4×C17—22no—
322C2×C4×C17—22no—
323C2×C4×C17—22no—
324C2×C4×C17—22no—
325C2×C4×C17—22no—
326C2×C4×C17—22no—
327C2×C4×C17—22no—
328C2×C4×C17—22no—
329C2×C4×C17—22no—
330C2×C4×C17—22no—
331C2×C4×C17—22no—
332C2×C4×C17—48no—
333C2×C4×C17—48no—
334C2×C4×C17—48no—
335C2×C4×C17—41no—
336C2×C4×C17—41no—
337C2×C4×C17—41no—
338C2×C4×C17—41no—
339C2×C4×C17—41no—
340C2×C4×C17—41no—
341C2×C4×C17C2×C22⋊C412yes—
342C2×C4×C17C2×C22⋊C412yes—
343C2×C4×C17C2×C22⋊C412yes—
344C2×C4×C17C2×C22⋊C412yes—
345C2×C4×C17C23×C411yescharacteristic
346C2×C4×C17C22×D411yescharacteristic
347C2×C4×C17C22×D411yescharacteristic
348C2×C4×C17C2×#4111yescharacteristic
349C2×C4×C17H(5,𝔽2)11yescharacteristic
350C2×C4×C17H(5,𝔽2)11yescharacteristic
351C2×Dic17—22no—
352C2×Dic17—41no—
353C2×Dic17—41no—
354C2×Dic17—41no—
355C2×Dic17—41no—
356C2×Dic17—41no—
357C2×Dic17—41no—
358C2×Dic17—41no—
359C2×Dic17—41no—
360C2×Dic17—41no—
361C2×Dic17—41no—
362C2×Dic17—41no—
363C2×Dic17—84no—
364#3622—22no—
365#3622—41no—
366#3622—41no—
367#3622—41no—
368C2×#547D1711yescharacteristic
369C2×#435—171no—
370C2×#417—171no—
371C2×#416—171no—
372#2352—171no—
373#1981—171no—
374#1960—171no—
375#1894—171no—
376#1892—171no—
377#1873—171no—
378#1872—171no—
379#1804—171no—
380#1788—171no—
381#1788—171no—
382#1762—171no—
383C22×C17—22no—
384C22×C17—22no—
385C22×C17—24no—
386C22×C17—22no—
387C22×C17—22no—
388C22×C17—22no—
389C22×C17—22no—
390C22×C17—42no—
391C22×C17—42no—
392C22×C17—41no—
393C22×C17—41no—
394C22×C17—42no—
395C22×C17—41no—
396C22×C17—41no—
397C22×C17—42no—
398C22×C17—41no—
399C22×C17—41no—
400C22×C17—42no—
401C22×C17—41no—
402C22×C17—41no—
403C22×C17—42no—
404C22×C17C22×C22⋊C411yescharacteristic
405C22×C17D4211yescharacteristic
406C22×C17#54611yescharacteristic
407C22×C17#57511yescharacteristic
408C22×C17#57511yescharacteristic
409C22×C17#57711yescharacteristic
410C22×C17#57811yescharacteristic
411C4×C17—22no—
412C4×C17—22no—
413C4×C17—22no—
414C4×C17—22no—
415C4×C17—42no—
416C4×C17—42no—
417C4×C17—42no—
418C4×C17C2×C4×D411yescharacteristic
419C4×C17#51811yescharacteristic
420C4×C17D4211yescharacteristic
421C4×C17#54611yescharacteristic
422Dic17—42no—
423Dic17—81no—
424Dic17—81no—
425Dic17—81no—
426C22×#41C2×D1711yescharacteristic
427C22×#41C2×D1711yescharacteristic
428C22×M16—171no—
429C23×C8—171no—
430#547—24no—
431#547Dic1718yescomplemented
432C2×C4⋊Q8C2×D1711yescharacteristic
433C2×#123—21no—
434C2×#123—21no—
435C2×C22⋊Q8C2×D1711yescharacteristic
436C2×C22⋊Q8C2×D1711yescharacteristic
437C2×#121—21no—
438C2×C4×D4C2×D1711yescharacteristic
439C2×C4×D4C2×D1711yescharacteristic
440C2×#117—171no—
441C22×C4⋊C4—21no—
442C22×C4⋊C4—171no—
443#435—344no—
444C2×C4⋊C8—171no—
445#417—344no—
446#416—344no—
447C2×#103—171no—
448C2×#103—171no—
449C2×#103—171no—
450C2×#103—171no—
451C2×#103—171no—
452C2×#103—171no—
453C2×#103—171no—
454C2×#103—171no—
455C2×#102—171no—
456C2×#102—171no—
457C2×#102—171no—
458C2×#102—171no—
459C2×C22⋊C8—171no—
460C2×C22⋊C8—171no—
461C2×#97—171no—
462#388—341no—
463#387—341no—
464#386—341no—
465#382—171no—
466#380—171no—
467#380—171no—
468C4×C4⋊C4—171no—
469C4×C22⋊C4—341no—
470#340—171no—
471#340—171no—
472#340—171no—
473#340—171no—
474C2×C17—42no—
475C2×C17—42no—
476C2×C17—44no—
477C2×C17D4×C22⋊C411yescharacteristic
478C2×C17#289611yescharacteristic
479C2×C17#289811yescharacteristic
480C2×C17#326711yescharacteristic
481C2×C17#326911yescharacteristic
482C2×C17#330711yescharacteristic
483C2×C17#331511yescharacteristic
484C2×#41—22no—
485C2×#41—22no—
486C2×#41—22no—
487C2×#41—22no—
488C2×#41—22no—
489C2×#41—22no—
490C2×#41—41no—
491C2×#41—41no—
492C2×#41—41no—
493C2×#41—41no—
494C2×#41C2×Dic1714yes—
495C2×#41C2×Dic1714yescomplemented
496C22×Q8C22×D1711yescharacteristic
497C22×Q8C22×D1711yescharacteristic
498C22×D4—21no—
499C22×D4—21no—
500C22×D4C22⋊D1711yescharacteristic
501C22×D4C22×D1711yescharacteristic
502C23×C4—21no—
503C23×C4—21no—
504C23×C4—21no—
505C23×C4—341no—
506C23×C4C22×D1711yescharacteristic
507C23×C4C22×D1711yescharacteristic
508C2×M16—342no—
509C2×M16—342no—
510C2×M16—681no—
511C22×C8—171no—
512C22×C8—171no—
513C22×C8—171no—
514C22×C8—171no—
515C22×C8—342no—
516C22×C8—342no—
517C22×C8—681no—
518C4⋊Q8—22no—
519C4⋊Q8C2×Dic1714yescomplemented
520#123—28no—
521#123—28no—
522C22⋊Q8—22no—
523C22⋊Q8—22no—
524C22⋊Q8C2×Dic1714yes—
525C22⋊Q8C2×Dic1714yescomplemented
526#121—28no—
527C4×D4—22no—
528C4×D4C2×Dic1714yes—
529C4×D4C2×Dic1714yescomplemented
530C4×D4C22⋊D1714yes—
531#117—342no—
532#117—681no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—28no—
538C2×C4⋊C4—171no—
539C2×C4⋊C4—171no—
540C2×C4⋊C4—171no—
541C2×C4⋊C4—171no—
542C2×C4⋊C4—342no—
543C2×C4⋊C4—341no—
544C2×C4⋊C4—681no—
545C2×C4⋊C4C22⋊D1711yescharacteristic
546C2×C4⋊C4C22×D1711yescharacteristic
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—341no—
551C2×C22⋊C4—341no—
552C2×C22⋊C4—341no—
553C2×C22⋊C4C22⋊D1711yescharacteristic
554C2×C22⋊C4C22⋊D1711yescharacteristic
555C2×C42—341no—
556C2×C42—341no—
557C2×C42C22×D1711yescharacteristic
558C4⋊C8—342no—
559#103—342no—
560#103—342no—
561#103—342no—
562#103—342no—
563#103—681no—
564#103—681no—
565#103—681no—
566#103—681no—
567#102—174no—
568#102—342no—
569#102—342no—
570#102—342no—
571C22⋊C8—342no—
572C22⋊C8—342no—
573#97—342no—
574#95—341no—
575#95—341no—
576#95—341no—
577#95—341no—
578#95—341no—
579C17#2242011yescharacteristic, complemented, Sylow
580C24—21no—
581C24C2×C22⋊D1711yescharacteristic
582C24C2×C22⋊D1711yescharacteristic
583#41—28no—
584#41—28no—
585#41—44no—
586#41—44no—
587#41—44no—
588#41—44no—
589#41—44no—
590#41—44no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8C22×Dic1712yes—
602C2×Q8C22×Dic1712yes—
603C2×D4—24no—
604C2×D4—24no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—41no—
609C2×D4—41no—
610C2×D4—42no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4C22⋊Dic1714yes—
615C2×D4D4×D1712yes—
616C2×D4#6325412yes—
617C2×D4C22×Dic1712yes—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—24no—
630C22×C4—24no—
631C22×C4—24no—
632C22×C4—42no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—341no—
639C22×C4—341no—
640C22×C4—341no—
641C22×C4—341no—
642C22×C4—682no—
643C22×C4—682no—
644C22×C4—1361no—
645C22×C4C22×Dic1712yes—
646C22×C4C22×Dic1712yes—
647C22×C4C2×C22⋊D1712yes—
648C22×C4C2×C22⋊D1712yes—
649C22×C4C2×C22⋊D1711yescharacteristic
650C22×C4C2×C22⋊D1711yescharacteristic
651C22×C4C2×C22⋊D1711yescharacteristic
652C22×C4C2×C22⋊D1711yescharacteristic
653C22×C4C23×D1711yescharacteristic
654M16—684no—
655C2×C8—172no—
656C2×C8—341no—
657C2×C8—341no—
658C2×C8—341no—
659C2×C8—341no—
660C2×C8—341no—
661C2×C8—341no—
662C2×C8—341no—
663C2×C8—341no—
664C2×C8—341no—
665C2×C8—341no—
666C2×C8—341no—
667C2×C8—684no—
668C4⋊C4—21no—
669C4⋊C4—24no—
670C4⋊C4—24no—
671C4⋊C4—24no—
672C4⋊C4—24no—
673C4⋊C4—172no—
674C4⋊C4—341no—
675C4⋊C4—341no—
676C4⋊C4—341no—
677C4⋊C4—341no—
678C4⋊C4—341no—
679C4⋊C4—341no—
680C4⋊C4—341no—
681C4⋊C4—682no—
682C4⋊C4C22⋊Dic1714yes—
683C4⋊C4C22×Dic1712yes—
684C22⋊C4—24no—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—682no—
688C22⋊C4—682no—
689C22⋊C4—1361no—
690C22⋊C4C22⋊Dic1714yes—
691C22⋊C4C22⋊Dic1714yes—
692C42—682no—
693C42—1361no—
694C42C22×Dic1712yes—
695C42C2×C22⋊D1712yes—
696C23—22no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—22no—
708C23—21no—
709C23—21no—
710C23—22no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23C2×C22⋊Dic1712yes—
716C23C2×C22⋊Dic1712yes—
717C23C22×C22⋊D1711yescharacteristic
718Q8—22no—
719Q8—22no—
720Q8—22no—
721Q8—22no—
722Q8—41no—
723Q8—41no—
724Q8—41no—
725Q8—41no—
726D4—22no—
727D4—22no—
728D4—22no—
729D4—44no—
730D4—48no—
731D4—48no—
732D4D4×Dic1714yes—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—48no—
753C2×C4—48no—
754C2×C4—48no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—342no—
762C2×C4—681no—
763C2×C4—681no—
764C2×C4—681no—
765C2×C4—681no—
766C2×C4—681no—
767C2×C4—681no—
768C2×C4—681no—
769C2×C4—681no—
770C2×C4—681no—
771C2×C4—681no—
772C2×C4—681no—
773C2×C4—1364no—
774C2×C4C2×C22⋊Dic1712yes—
775C2×C4C2×C22⋊Dic1712yes—
776C2×C4C2×C22⋊Dic1712yes—
777C2×C4C2×C22⋊Dic1712yes—
778C2×C4C2×D4×D1711yescharacteristic
779C2×C4C2×#6325411yescharacteristic
780C2×C4#1058769111yescharacteristic
781C2×C4#1058769111yescharacteristic
782C2×C4C23×Dic1711yescharacteristic
783C2×C4C22×C22⋊D1711yescharacteristic
784C8—342no—
785C8—681no—
786C8—681no—
787C8—681no—
788C22—22no—
789C22—22no—
790C22—24no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—41no—
796C22—41no—
797C22—42no—
798C22—41no—
799C22—41no—
800C22—42no—
801C22—41no—
802C22—41no—
803C22—42no—
804C22—42no—
805C22—42no—
806C22—41no—
807C22—41no—
808C22—42no—
809C22C22×C22⋊Dic1711yescharacteristic
810C22D4×C22⋊D1711yescharacteristic
811C22#1176345311yescharacteristic
812C22#1176360711yescharacteristic
813C22#1176360711yescharacteristic
814C22#1176361711yescharacteristic
815C22#1176362411yescharacteristic
816C4—22no—
817C4—22no—
818C4—22no—
819C4—22no—
820C4—42no—
821C4—42no—
822C4—42no—
823C4—682no—
824C4—1361no—
825C4—1361no—
826C4—1361no—
827C4C2×D4×Dic1711yescharacteristic
828C4#1176328411yescharacteristic
829C4D4×C22⋊D1711yescharacteristic
830C4#1176345311yescharacteristic
831C2—42no—
832C2—42no—
833C2—44no—
834C2D4×C22⋊Dic1711yescharacteristic
835C2#1453730311yescharacteristic
836C2#1453731711yescharacteristic
837C2#1454031011yescharacteristic
838C2#1454033511yescharacteristic
839C2#1454076011yescharacteristic
840C2#1454088011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
Fitting, prime radicalC2×C17×#547C2
socleC23×C17C22×D4
cosocleC22×C4×C17C24
hypercenterC2×#547D17
hypocenterC17#22420
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×#11762881C2semidirect
2. C2×#11762810C2semidirect
3. C2×#11762805C2semidirect
4. #14531713C2semidirect
5. #14529708C2semidirect
6. #14529605C2semidirect
7. #14529218C2semidirect
8. #14529208C2semidirect
9. #14529097C2semidirect
10. #14529092C2semidirect
11. #14528794C2semidirect
12. #14528724C2semidirect
13. #14528724C2semidirect
14. #14528609C2semidirect
54. C17×#547C4semidirect
75. C2×#41×C17C2×C4semidirect
89. C17×C4⋊Q8C2×C4semidirect
95. C17×C22⋊Q8C2×C4semidirect
99. C4×D4×C17C2×C4semidirect
149. #10587503D4semidirect
431. #547Dic17semidirect
495. C2×#41C2×Dic17semidirect
519. C4⋊Q8C2×Dic17semidirect
525. C22⋊Q8C2×Dic17semidirect
529. C4×D4C2×Dic17semidirect
579. C17#22420semidirect

Maximal subgroups

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

subgroupindex
C2×#117628812
C2×#117628102
C2×#117628052
#145317132
#145297082
#145296052
#145292182
#145292082
#145290972
#145290922
#145287942
#145287242
#145286092
C2×C17×#5472
#2242017