Finite Group Databasebeta

← #17049849

Subgroups — #17049849

Order 4352.

1530 conjugacy classes of subgroups.

The subgroup lattice has 882 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#14529712C211yesmaximal, characteristic, complemented
6#14529609C211yesmaximal, characteristic, complemented
7#14529223C211yesmaximal, characteristic, complemented
8#14529213C211yesmaximal, characteristic, complemented
9#14529107C211yesmaximal, characteristic, complemented
10#14529102C211yesmaximal, characteristic, complemented
11#14528799C211yesmaximal, characteristic, complemented
12#14528724C211yesmaximal, characteristic, complemented
13#14528724C211yesmaximal, characteristic, complemented
14#14528614C211yesmaximal, characteristic, complemented
15C2×C17×#550C211yesmaximal, 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×#10587503C2211yescharacteristic
29C2×#10587503C2211yescharacteristic
30C2×#10587503C2211yescharacteristic
31C2×#10587503C2211yescharacteristic
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×#550—24no—
54C17×#550C418yescomplemented
55C2×C17×#127—21no—
56C2×C17×#127C2211yescharacteristic
57C2×C17×#121—21no—
58C2×C17×#121—21no—
59C2×C17×#121C2211yescharacteristic
60C2×C17×#121C2211yescharacteristic
61C2×C4×Q8×C17C2211yescharacteristic
62C2×C4×D4×C17—21no—
63C2×C4×D4×C17C2211yescharacteristic
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×D4×C17—21no—
78C22×D4×C17—21no—
79C22×D4×C17—21no—
80C22×D4×C17—21no—
81C22×D4×C17—21no—
82C22×D4×C17—21no—
83C22×D4×C17D411yescharacteristic
84C22×D4×C17C2311yescharacteristic
85C22×D4×C17C2311yescharacteristic
86C23×C4×C17—21no—
87C23×C4×C17—21no—
88C23×C4×C17C2311yescharacteristic
89C23×C4×C17C2311yescharacteristic
90C23×Dic17—21no—
91C17×#127—28no—
92C17×#127—22no—
93C17×#127C2×C414yescomplemented
94C17×#121—22no—
95C17×#121—22no—
96C17×#121—28no—
97C17×#121—28no—
98C17×#121C2×C414yes—
99C17×#121C2×C414yescomplemented
100C4×Q8×C17—22no—
101C4×Q8×C17C2×C414yescomplemented
102C4×D4×C17—28no—
103C4×D4×C17C2×C414yes—
104C4×D4×C17D414yes—
105C2×C4⋊C4×C17—21no—
106C2×C4⋊C4×C17D411yescharacteristic
107C2×C4⋊C4×C17C2311yescharacteristic
108C2×C22⋊C4×C17—21no—
109C2×C22⋊C4×C17—21no—
110C2×C22⋊C4×C17D411yescharacteristic
111C2×C22⋊C4×C17D411yescharacteristic
112C2×C42×C17—21no—
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#10587506D414yescomplemented
142#10587503—22no—
143#10587503—22no—
144#10587503—22no—
145#10587503—22no—
146#10587503—41no—
147#10587503—41no—
148#10587503—41no—
149#10587503—41no—
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×C17—21no—
161C24×C17C2×D411yescharacteristic
162C24×C17C2×D411yescharacteristic
163#41×C17—28no—
164#41×C17—28no—
165#41×C17—44no—
166#41×C17—44no—
167#41×C17—44no—
168#41×C17—44no—
169#41×C17—44no—
170#41×C17—44no—
171C2×Q8×C17—21no—
172C2×Q8×C17—21no—
173C2×Q8×C17—21no—
174C2×Q8×C17C22×C412yes—
175C2×Q8×C17C2×D412yes—
176C2×Q8×C17#4112yes—
177C2×D4×C17—24no—
178C2×D4×C17—24no—
179C2×D4×C17—24no—
180C2×D4×C17—24no—
181C2×D4×C17—24no—
182C2×D4×C17—24no—
183C2×D4×C17—21no—
184C2×D4×C17—21no—
185C2×D4×C17—21no—
186C2×D4×C17—21no—
187C2×D4×C17—21no—
188C2×D4×C17—21no—
189C2×D4×C17—21no—
190C2×D4×C17—21no—
191C2×D4×C17—21no—
192C2×D4×C17—21no—
193C2×D4×C17—41no—
194C2×D4×C17—41no—
195C2×D4×C17—42no—
196C2×D4×C17—42no—
197C2×D4×C17—42no—
198C2×D4×C17—42no—
199C2×D4×C17—42no—
200C2×D4×C17—42no—
201C2×D4×C17—81no—
202C2×D4×C17—81no—
203C2×D4×C17—81no—
204C2×D4×C17—81no—
205C2×D4×C17—81no—
206C2×D4×C17—81no—
207C2×D4×C17C22⋊C414yes—
208C2×D4×C17C22×C412yes—
209C2×D4×C17C22×C412yes—
210C22×C4×C17—21no—
211C22×C4×C17—21no—
212C22×C4×C17—21no—
213C22×C4×C17—21no—
214C22×C4×C17—21no—
215C22×C4×C17—21no—
216C22×C4×C17—21no—
217C22×C4×C17—21no—
218C22×C4×C17—21no—
219C22×C4×C17—21no—
220C22×C4×C17—24no—
221C22×C4×C17—24no—
222C22×C4×C17—42no—
223C22×C4×C17—42no—
224C22×C4×C17—42no—
225C22×C4×C17—42no—
226C22×C4×C17C22×C412yes—
227C22×C4×C17C22×C412yes—
228C22×C4×C17C2×D411yescharacteristic
229C22×C4×C17C2×D411yescharacteristic
230C22×C4×C17C2×D411yescharacteristic
231C22×C4×C17C2×D411yescharacteristic
232C22×C4×C17C2×D412yes—
233C22×C4×C17C2×D412yes—
234C22×C4×C17C2411yescharacteristic
235C22×Dic17—21no—
236C22×Dic17—21no—
237C22×Dic17—21no—
238C22×Dic17—21no—
239C22×Dic17—42no—
240C22×Dic17—42no—
241C22×Dic17—81no—
242C4⋊C4×C17—24no—
243C4⋊C4×C17—21no—
244C4⋊C4×C17C22⋊C414yes—
245C4⋊C4×C17C22×C412yes—
246C22⋊C4×C17—24no—
247C22⋊C4×C17—24no—
248C22⋊C4×C17C22⋊C414yes—
249C22⋊C4×C17C22⋊C414yes—
250C42×C17—24no—
251C42×C17C22×C412yes—
252C42×C17C2×D412yes—
253C22⋊Dic17—42no—
254C22⋊Dic17—42no—
255C22⋊Dic17—81no—
256C4⋊Dic17—21no—
257C4⋊Dic17—21no—
258C4⋊Dic17—21no—
259C4⋊Dic17—21no—
260C4⋊Dic17—21no—
261C4⋊Dic17—21no—
262C4⋊Dic17—21no—
263C4⋊Dic17—42no—
264C4⋊Dic17C2×D412yes—
265C4×Dic17—42no—
266C4×Dic17—81no—
267#63223—44no—
268C2×#3622—21no—
269C2×#3622—21no—
270C2×#3622—21no—
271C2×#3622—21no—
272C2×#3622—21no—
273C2×#3622—21no—
274C2×#3622—21no—
275C2×#3622—21no—
276C2×#3622—21no—
277C2×#3622—21no—
278C2×#3622—21no—
279C2×#3622—44no—
280C2×#3622C2×D412yes—
281#22422—171nomaximal, Sylow
282C23×C17—21no—
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—21no—
292C23×C17—21no—
293C23×C17—21no—
294C23×C17—22no—
295C23×C17—22no—
296C23×C17—41no—
297C23×C17—41no—
298C23×C17—41no—
299C23×C17—41no—
300C23×C17—41no—
301C23×C17—41no—
302C23×C17—41no—
303C23×C17—41no—
304C23×C17—41no—
305C23×C17—41no—
306C23×C17—41no—
307C23×C17—41no—
308C23×C17C2×C22⋊C412yes—
309C23×C17C2×C22⋊C412yes—
310C23×C17C22×D411yescharacteristic
311Q8×C17—22no—
312Q8×C17—22no—
313Q8×C17—22no—
314Q8×C17C4×D414yes—
315D4×C17—22no—
316D4×C17—22no—
317D4×C17—22no—
318D4×C17—22no—
319D4×C17—44no—
320D4×C17—48no—
321D4×C17—48no—
322D4×C17—48no—
323D4×C17—41no—
324D4×C17—41no—
325D4×C17—41no—
326D4×C17—41no—
327D4×C17—84no—
328D4×C17—84no—
329D4×C17—84no—
330C2×C4×C17—22no—
331C2×C4×C17—21no—
332C2×C4×C17—21no—
333C2×C4×C17—22no—
334C2×C4×C17—21no—
335C2×C4×C17—21no—
336C2×C4×C17—22no—
337C2×C4×C17—21no—
338C2×C4×C17—21no—
339C2×C4×C17—21no—
340C2×C4×C17—21no—
341C2×C4×C17—22no—
342C2×C4×C17—22no—
343C2×C4×C17—22no—
344C2×C4×C17—22no—
345C2×C4×C17—22no—
346C2×C4×C17—22no—
347C2×C4×C17—22no—
348C2×C4×C17—22no—
349C2×C4×C17—22no—
350C2×C4×C17—48no—
351C2×C4×C17—48no—
352C2×C4×C17—41no—
353C2×C4×C17—41no—
354C2×C4×C17C2×C22⋊C412yes—
355C2×C4×C17C2×C22⋊C412yes—
356C2×C4×C17C2×C22⋊C412yes—
357C2×C4×C17C2×C22⋊C412yes—
358C2×C4×C17C23×C411yescharacteristic
359C2×C4×C17C22×D411yescharacteristic
360C2×C4×C17C22×D411yescharacteristic
361C2×C4×C17C2×#4111yescharacteristic
362C2×C4×C17H(5,𝔽2)11yescharacteristic
363C2×C4×C17H(5,𝔽2)11yescharacteristic
364C2×Dic17—22no—
365C2×Dic17—41no—
366C2×Dic17—41no—
367C2×Dic17—41no—
368C2×Dic17—41no—
369C2×Dic17—41no—
370C2×Dic17—41no—
371C2×Dic17—41no—
372C2×Dic17—41no—
373C2×Dic17—41no—
374C2×Dic17—41no—
375C2×Dic17—41no—
376C2×Dic17—84no—
377#3622—22no—
378#3622—41no—
379#3622—41no—
380#3622—41no—
381C2×#550D1711yescharacteristic
382C2×#435—171no—
383C2×#417—171no—
384C2×#416—171no—
385#2352—171no—
386#1982—171no—
387#1961—171no—
388#1895—171no—
389#1893—171no—
390#1875—171no—
391#1874—171no—
392#1805—171no—
393#1788—171no—
394#1788—171no—
395#1763—171no—
396C22×C17—22no—
397C22×C17—22no—
398C22×C17—22no—
399C22×C17—22no—
400C22×C17—22no—
401C22×C17—22no—
402C22×C17—41no—
403C22×C17—41no—
404C22×C17—41no—
405C22×C17—41no—
406C22×C17—41no—
407C22×C17—41no—
408C22×C17—41no—
409C22×C17—41no—
410C22×C17—42no—
411C22×C17—42no—
412C22×C17—42no—
413C22×C17—42no—
414C22×C17—42no—
415C22×C17—42no—
416C22×C17—81no—
417C22×C17—81no—
418C22×C17—81no—
419C22×C17—81no—
420C22×C17—81no—
421C22×C17—81no—
422C22×C17—81no—
423C22×C17—81no—
424C22×C17C22×C22⋊C411yescharacteristic
425C22×C17D4211yescharacteristic
426C22×C17#54611yescharacteristic
427C22×C17#57511yescharacteristic
428C22×C17#57511yescharacteristic
429C22×C17#57611yescharacteristic
430C22×C17#57711yescharacteristic
431C4×C17—22no—
432C4×C17—22no—
433C4×C17—24no—
434C4×C17—22no—
435C4×C17—22no—
436C4×C17—42no—
437C4×C17C2×C4×D411yescharacteristic
438C4×C17#51811yescharacteristic
439C4×C17D4211yescharacteristic
440C4×C17#54611yescharacteristic
441Dic17—42no—
442Dic17—81no—
443Dic17—81no—
444Dic17—81no—
445C22×#41C2×D1711yescharacteristic
446C22×#41C2×D1711yescharacteristic
447C22×M16—171no—
448C23×C8—171no—
449#550—24no—
450#550Dic1718yescomplemented
451C2×#127—21no—
452C2×#127C2×D1711yescharacteristic
453C2×#121—21no—
454C2×#121—21no—
455C2×#121C2×D1711yescharacteristic
456C2×#121C2×D1711yescharacteristic
457C2×C4×Q8C2×D1711yescharacteristic
458C2×C4×D4—21no—
459C2×C4×D4C2×D1711yescharacteristic
460C2×#117—171no—
461C22×C4⋊C4—171no—
462#435—344no—
463C2×C4⋊C8—171no—
464#417—344no—
465#416—344no—
466C2×#103—171no—
467C2×#103—171no—
468C2×#103—171no—
469C2×#103—171no—
470C2×#102—171no—
471C2×#102—171no—
472C2×#102—171no—
473C2×#102—171no—
474C2×#102—171no—
475C2×#102—171no—
476C2×#102—171no—
477C2×#102—171no—
478C2×C22⋊C8—171no—
479C2×C22⋊C8—171no—
480C2×#97—171no—
481#388—341no—
482#387—341no—
483#386—341no—
484#382—171no—
485#380—171no—
486#380—171no—
487C4×C4⋊C4—171no—
488C4×C22⋊C4—341no—
489#340—171no—
490#340—171no—
491#340—171no—
492#340—171no—
493C2×C17—42no—
494C2×C17—42no—
495C2×C17—82no—
496C2×C17—82no—
497C2×C17D4×C22⋊C411yescharacteristic
498C2×C17#289611yescharacteristic
499C2×C17#289711yescharacteristic
500C2×C17#326811yescharacteristic
501C2×C17#327111yescharacteristic
502C2×C17#330911yescharacteristic
503C2×C17#331711yescharacteristic
504C2×#41—22no—
505C2×#41—22no—
506C2×#41—22no—
507C2×#41—22no—
508C2×#41—22no—
509C2×#41—22no—
510C2×#41—41no—
511C2×#41—41no—
512C2×#41—41no—
513C2×#41—41no—
514C2×#41C2×Dic1714yes—
515C2×#41C2×Dic1714yescomplemented
516C22×Q8C22×D1711yescharacteristic
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4C22⋊D1711yescharacteristic
524C22×D4C22×D1711yescharacteristic
525C22×D4C22×D1711yescharacteristic
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—341no—
529C23×C4C22×D1711yescharacteristic
530C23×C4C22×D1711yescharacteristic
531C2×M16—342no—
532C2×M16—342no—
533C2×M16—681no—
534C22×C8—171no—
535C22×C8—171no—
536C22×C8—171no—
537C22×C8—171no—
538C22×C8—342no—
539C22×C8—342no—
540C22×C8—681no—
541#127—28no—
542#127—22no—
543#127C2×Dic1714yescomplemented
544#121—22no—
545#121—22no—
546#121—28no—
547#121—28no—
548#121C2×Dic1714yes—
549#121C2×Dic1714yescomplemented
550C4×Q8—22no—
551C4×Q8C2×Dic1714yescomplemented
552C4×D4—28no—
553C4×D4C2×Dic1714yes—
554C4×D4C22⋊D1714yes—
555#117—342no—
556#117—681no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—171no—
559C2×C4⋊C4—171no—
560C2×C4⋊C4—171no—
561C2×C4⋊C4—171no—
562C2×C4⋊C4—342no—
563C2×C4⋊C4—341no—
564C2×C4⋊C4—681no—
565C2×C4⋊C4C22⋊D1711yescharacteristic
566C2×C4⋊C4C22×D1711yescharacteristic
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
569C2×C22⋊C4—341no—
570C2×C22⋊C4—341no—
571C2×C22⋊C4—341no—
572C2×C22⋊C4C22⋊D1711yescharacteristic
573C2×C22⋊C4C22⋊D1711yescharacteristic
574C2×C42—21no—
575C2×C42—341no—
576C2×C42—341no—
577C2×C42C22×D1711yescharacteristic
578C4⋊C8—342no—
579#103—174no—
580#103—342no—
581#103—342no—
582#103—342no—
583#102—342no—
584#102—342no—
585#102—342no—
586#102—342no—
587#102—681no—
588#102—681no—
589#102—681no—
590#102—681no—
591C22⋊C8—342no—
592C22⋊C8—342no—
593#97—342no—
594#95—341no—
595#95—341no—
596#95—341no—
597#95—341no—
598#95—341no—
599C17#2242211yescharacteristic, complemented, Sylow
600C24—21no—
601C24—21no—
602C24C2×C22⋊D1711yescharacteristic
603C24C2×C22⋊D1711yescharacteristic
604#41—28no—
605#41—28no—
606#41—44no—
607#41—44no—
608#41—44no—
609#41—44no—
610#41—44no—
611#41—44no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8—21no—
615C2×Q8D4×D1712yes—
616C2×Q8#6325412yes—
617C2×Q8C22×Dic1712yes—
618C2×D4—24no—
619C2×D4—24no—
620C2×D4—24no—
621C2×D4—24no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—24no—
633C2×D4—24no—
634C2×D4—41no—
635C2×D4—41no—
636C2×D4—42no—
637C2×D4—42no—
638C2×D4—42no—
639C2×D4—42no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—81no—
643C2×D4—81no—
644C2×D4—81no—
645C2×D4—81no—
646C2×D4—81no—
647C2×D4—81no—
648C2×D4C22⋊Dic1714yes—
649C2×D4C22×Dic1712yes—
650C2×D4C22×Dic1712yes—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—24no—
662C22×C4—24no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—341no—
668C22×C4—341no—
669C22×C4—341no—
670C22×C4—341no—
671C22×C4—682no—
672C22×C4—682no—
673C22×C4—1361no—
674C22×C4C22×Dic1712yes—
675C22×C4C22×Dic1712yes—
676C22×C4C2×C22⋊D1712yes—
677C22×C4C2×C22⋊D1712yes—
678C22×C4C2×C22⋊D1711yescharacteristic
679C22×C4C2×C22⋊D1711yescharacteristic
680C22×C4C2×C22⋊D1711yescharacteristic
681C22×C4C2×C22⋊D1711yescharacteristic
682C22×C4C23×D1711yescharacteristic
683M16—684no—
684C2×C8—172no—
685C2×C8—341no—
686C2×C8—341no—
687C2×C8—341no—
688C2×C8—341no—
689C2×C8—341no—
690C2×C8—341no—
691C2×C8—341no—
692C2×C8—341no—
693C2×C8—341no—
694C2×C8—341no—
695C2×C8—341no—
696C2×C8—684no—
697C4⋊C4—21no—
698C4⋊C4—24no—
699C4⋊C4—172no—
700C4⋊C4—341no—
701C4⋊C4—341no—
702C4⋊C4—341no—
703C4⋊C4—341no—
704C4⋊C4—341no—
705C4⋊C4—341no—
706C4⋊C4—341no—
707C4⋊C4—682no—
708C4⋊C4C22⋊Dic1714yes—
709C4⋊C4C22×Dic1712yes—
710C22⋊C4—24no—
711C22⋊C4—24no—
712C22⋊C4—682no—
713C22⋊C4—682no—
714C22⋊C4—1361no—
715C22⋊C4C22⋊Dic1714yes—
716C22⋊C4C22⋊Dic1714yes—
717C42—24no—
718C42—682no—
719C42—1361no—
720C42C22×Dic1712yes—
721C42C2×C22⋊D1712yes—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—22no—
735C23—22no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23C2×C22⋊Dic1712yes—
749C23C2×C22⋊Dic1712yes—
750C23C22×C22⋊D1711yescharacteristic
751Q8—22no—
752Q8—22no—
753Q8—22no—
754Q8D4×Dic1714yes—
755D4—22no—
756D4—22no—
757D4—22no—
758D4—22no—
759D4—44no—
760D4—48no—
761D4—48no—
762D4—48no—
763D4—41no—
764D4—41no—
765D4—41no—
766D4—41no—
767D4—84no—
768D4—84no—
769D4—84no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—48no—
791C2×C4—48no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—342no—
795C2×C4—681no—
796C2×C4—681no—
797C2×C4—681no—
798C2×C4—681no—
799C2×C4—681no—
800C2×C4—681no—
801C2×C4—681no—
802C2×C4—681no—
803C2×C4—681no—
804C2×C4—681no—
805C2×C4—681no—
806C2×C4—1364no—
807C2×C4C2×C22⋊Dic1712yes—
808C2×C4C2×C22⋊Dic1712yes—
809C2×C4C2×C22⋊Dic1712yes—
810C2×C4C2×C22⋊Dic1712yes—
811C2×C4C2×D4×D1711yescharacteristic
812C2×C4C2×#6325411yescharacteristic
813C2×C4#1058769111yescharacteristic
814C2×C4#1058769111yescharacteristic
815C2×C4C23×Dic1711yescharacteristic
816C2×C4C22×C22⋊D1711yescharacteristic
817C8—342no—
818C8—681no—
819C8—681no—
820C8—681no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—81no—
842C22—81no—
843C22—81no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22—81no—
848C22—81no—
849C22C22×C22⋊Dic1711yescharacteristic
850C22D4×C22⋊D1711yescharacteristic
851C22#1176345311yescharacteristic
852C22#1176360711yescharacteristic
853C22#1176360711yescharacteristic
854C22#1176361211yescharacteristic
855C22#1176362011yescharacteristic
856C4—22no—
857C4—22no—
858C4—24no—
859C4—22no—
860C4—22no—
861C4—42no—
862C4—682no—
863C4—1361no—
864C4—1361no—
865C4—1361no—
866C4C2×D4×Dic1711yescharacteristic
867C4#1176328411yescharacteristic
868C4D4×C22⋊D1711yescharacteristic
869C4#1176345311yescharacteristic
870C2—42no—
871C2—42no—
872C2—82no—
873C2—82no—
874C2D4×C22⋊Dic1711yescharacteristic
875C2#1453730311yescharacteristic
876C2#1453731011yescharacteristic
877C2#1454032511yescharacteristic
878C2#1454036511yescharacteristic
879C2#1454079011yescharacteristic
880C2#1454091011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
Fitting, prime radicalC2×C17×#550C2
socleC23×C17C22×D4
cosocleC22×C4×C17C24
hypercenterC2×#550D17
hypocenterC17#22422
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#550

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. #14529712C2semidirect
6. #14529609C2semidirect
7. #14529223C2semidirect
8. #14529213C2semidirect
9. #14529107C2semidirect
10. #14529102C2semidirect
11. #14528799C2semidirect
12. #14528724C2semidirect
13. #14528724C2semidirect
14. #14528614C2semidirect
54. C17×#550C4semidirect
75. C2×#41×C17C2×C4semidirect
93. C17×#127C2×C4semidirect
99. C17×#121C2×C4semidirect
101. C4×Q8×C17C2×C4semidirect
141. #10587506D4semidirect
450. #550Dic17semidirect
515. C2×#41C2×Dic17semidirect
543. #127C2×Dic17semidirect
549. #121C2×Dic17semidirect
551. C4×Q8C2×Dic17semidirect
599. C17#22422semidirect

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
#145297122
#145296092
#145292232
#145292132
#145291072
#145291022
#145287992
#145287242
#145286142
C2×C17×#5502
#2242217