Finite Group Databasebeta

← #17049924

Subgroups — #17049924

Order 4352.

1606 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762887C211yesmaximal, characteristic, complemented
2C2×#11762810C211yesmaximal, characteristic, complemented
3C2×#11762814C211yesmaximal, characteristic, complemented
4#14531713C211yesmaximal, characteristic, complemented
5#14529717C211yesmaximal, characteristic, complemented
6#14529596C211yesmaximal, characteristic, complemented
7#14529223C211yesmaximal, characteristic, complemented
8#14529218C211yesmaximal, characteristic, complemented
9#14529102C211yesmaximal, characteristic, complemented
10#14529097C211yesmaximal, characteristic, complemented
11#14528794C211yesmaximal, characteristic, complemented
12#14528724C211yesmaximal, characteristic, complemented
13#14528715C211yesmaximal, characteristic, complemented
14C4×#10587503C211yesmaximal, characteristic, complemented
15C2×C17×#546C211yesmaximal, characteristic
16C22×#63223C2211yescharacteristic
17C22×#63223C2211yescharacteristic, complemented
18C2×#10587612C2211yescharacteristic
19C22×C4⋊Dic17C2211yescharacteristic, complemented
20#11762887—24no—
21C2×C4⋊#3622C2211yescharacteristic, complemented
22#11762814—24no—
23#11762810—24no—
24C2×#10587506C2211yescharacteristic, complemented
25C2×#10587506C2211yescharacteristic, complemented
26C2×#10587506C2211yescharacteristic, complemented
27C2×#10587506C2211yescharacteristic, complemented
28C2×#10587503C2211yescharacteristic
29C2×#10587503C2211yescharacteristic
30C2×#10587503C2211yescharacteristic
31C2×#10587503C2211yescharacteristic
32C2×#10587503C2211yescharacteristic
33C2×#10587503C2211yescharacteristic
34C2×#10587503C2211yescharacteristic
35C2×#10587503C2211yescharacteristic
36C2×C22⋊#3622C2211yescharacteristic
37C2×C22⋊#3622C2211yescharacteristic, complemented
38C2×C4×#3622C2211yescharacteristic, complemented
39#11762702—21no—
40#11762695—21no—
41#11762689—21no—
42#11762675C2211yescharacteristic, complemented
43#11762669C2211yescharacteristic
44#11762669C2211yescharacteristic, complemented
45C4×C4⋊Dic17C2211yescharacteristic, complemented
46C22⋊C4×Dic17—21no—
47#11762571C2211yescharacteristic, complemented
48#11762571C2211yescharacteristic, complemented
49#11762571C2211yescharacteristic, complemented
50#11762571C2211yescharacteristic, complemented
51C22×#41×C17C2211yescharacteristic
52C23×D4×C17C2211yescharacteristic
53C17×#546—24no—
54C17×#546C418yescomplemented
55C2×C17×#124C2211yescharacteristic
56C2×C17×#123—21no—
57C2×C17×C22⋊Q8C2211yescharacteristic
58C2×C17×#121—21no—
59C2×C17×#121C2211yescharacteristic
60C2×C17×#120—21no—
61C2×C4×D4×C17C2211yescharacteristic
62C2×C4×D4×C17C2211yescharacteristic
63C22×C22⋊C4×C17—21no—
64C25×C17—21no—
65C2×#41×C17—22no—
66C2×#41×C17—22no—
67C2×#41×C17—22no—
68C2×#41×C17—41no—
69C2×#41×C17—41no—
70C2×#41×C17C2×C414yes—
71C22×Q8×C17C2311yescharacteristic
72C22×D4×C17—22no—
73C22×D4×C17—22no—
74C22×D4×C17—21no—
75C22×D4×C17—21no—
76C22×D4×C17—21no—
77C22×D4×C17—22no—
78C22×D4×C17—41no—
79C22×D4×C17—41no—
80C22×D4×C17C2×C414yescomplemented
81C22×D4×C17D411yescharacteristic
82C22×D4×C17C2311yescharacteristic
83C22×D4×C17C2311yescharacteristic
84C23×C4×C17—21no—
85C23×C4×C17—21no—
86C23×C4×C17C2311yescharacteristic
87C23×C4×C17C2311yescharacteristic
88C23×Dic17—21no—
89C17×#124—22no—
90C17×#124C2×C414yescomplemented
91C17×#123—28no—
92C17×C22⋊Q8—22no—
93C17×C22⋊Q8C2×C414yescomplemented
94C17×#121—22no—
95C17×#121—28no—
96C17×#121C2×C414yes—
97C17×#120—28no—
98C4×D4×C17—22no—
99C4×D4×C17C2×C414yes—
100C4×D4×C17C2×C414yescomplemented
101C4×D4×C17D414yes—
102C2×C4⋊C4×C17—21no—
103C2×C4⋊C4×C17D411yescharacteristic
104C2×C4⋊C4×C17C2311yescharacteristic
105C2×C22⋊C4×C17—21no—
106C2×C22⋊C4×C17—21no—
107C2×C22⋊C4×C17—21no—
108C2×C22⋊C4×C17—21no—
109C2×C22⋊C4×C17—21no—
110C2×C22⋊C4×C17—28no—
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—22no—
131C2×#63223—22no—
132C2×#63223—41no—
133C2×#63223—41no—
134C22×#3622C2311yescharacteristic
135C22×#3622C2311yescharacteristic
136C22×#3622C2311yescharacteristic
137C22×#3622C2311yescharacteristic
138#10587506—22no—
139#10587506—22no—
140#10587506—41no—
141#10587506—41no—
142#10587503—22no—
143#10587503—22no—
144#10587503—22no—
145#10587503—22no—
146#10587503—22no—
147#10587503—41no—
148#10587503—41no—
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—
158C4×#3622—22no—
159C24×C17—21no—
160C24×C17—21no—
161C24×C17—24no—
162C24×C17—42no—
163C24×C17—42no—
164C24×C17—42no—
165C24×C17—42no—
166C24×C17—81no—
167C24×C17—81no—
168C24×C17C2×D411yescharacteristic
169C24×C17C2×D411yescharacteristic
170#41×C17—28no—
171#41×C17—44no—
172#41×C17—44no—
173#41×C17—44no—
174C2×Q8×C17—21no—
175C2×Q8×C17—21no—
176C2×Q8×C17—21no—
177C2×Q8×C17—21no—
178C2×Q8×C17—21no—
179C2×Q8×C17C22×C412yes—
180C2×D4×C17—28no—
181C2×D4×C17—24no—
182C2×D4×C17—24no—
183C2×D4×C17—24no—
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—44no—
193C2×D4×C17—44no—
194C2×D4×C17—44no—
195C2×D4×C17—41no—
196C2×D4×C17—41no—
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×C17C22⋊C414yes—
204C2×D4×C17C22×C412yes—
205C2×D4×C17C22×C412yes—
206C2×D4×C17C2×D412yes—
207C2×D4×C17#4112yes—
208C22×C4×C17—21no—
209C22×C4×C17—21no—
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—24no—
219C22×C4×C17—24no—
220C22×C4×C17—42no—
221C22×C4×C17—42no—
222C22×C4×C17—81no—
223C22×C4×C17—81no—
224C22×C4×C17C22×C412yes—
225C22×C4×C17C22×C412yes—
226C22×C4×C17C2×D411yescharacteristic
227C22×C4×C17C2×D411yescharacteristic
228C22×C4×C17C2×D411yescharacteristic
229C22×C4×C17C2×D411yescharacteristic
230C22×C4×C17C2×D412yes—
231C22×C4×C17C2×D412yes—
232C22×C4×C17C2411yescharacteristic
233C22×Dic17—21no—
234C22×Dic17—21no—
235C22×Dic17—21no—
236C22×Dic17—21no—
237C22×Dic17—42no—
238C22×Dic17—42no—
239C22×Dic17—81no—
240C4⋊C4×C17—24no—
241C4⋊C4×C17—21no—
242C4⋊C4×C17C22⋊C414yes—
243C4⋊C4×C17C22×C412yes—
244C22⋊C4×C17—24no—
245C22⋊C4×C17—24no—
246C22⋊C4×C17—24no—
247C22⋊C4×C17—24no—
248C22⋊C4×C17—24no—
249C22⋊C4×C17C22⋊C414yes—
250C22⋊C4×C17C22⋊C414yes—
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—
268#63223—44no—
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—21no—
280C2×#3622C2×D412yes—
281#22427—171nomaximal, Sylow
282C23×C17—22no—
283C23×C17—21no—
284C23×C17—21no—
285C23×C17—22no—
286C23×C17—21no—
287C23×C17—21no—
288C23×C17—22no—
289C23×C17—21no—
290C23×C17—21no—
291C23×C17—21no—
292C23×C17—21no—
293C23×C17—21no—
294C23×C17—21no—
295C23×C17—21no—
296C23×C17—21no—
297C23×C17—22no—
298C23×C17—48no—
299C23×C17—48no—
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×C17—41no—
309C23×C17—41no—
310C23×C17—84no—
311C23×C17—84no—
312C23×C17—84no—
313C23×C17—84no—
314C23×C17—84no—
315C23×C17C2×C22⋊C412yes—
316C23×C17C2×C22⋊C412yes—
317C23×C17C22×D411yescharacteristic
318Q8×C17—22no—
319Q8×C17—22no—
320Q8×C17—41no—
321Q8×C17—41no—
322D4×C17—22no—
323D4×C17—22no—
324D4×C17—22no—
325D4×C17—22no—
326D4×C17—22no—
327D4×C17—44no—
328D4×C17—48no—
329D4×C17—48no—
330D4×C17—41no—
331D4×C17—41no—
332D4×C17—84no—
333D4×C17C4×D414yes—
334C2×C4×C17—21no—
335C2×C4×C17—21no—
336C2×C4×C17—21no—
337C2×C4×C17—21no—
338C2×C4×C17—21no—
339C2×C4×C17—21no—
340C2×C4×C17—21no—
341C2×C4×C17—21no—
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—22no—
351C2×C4×C17—22no—
352C2×C4×C17—48no—
353C2×C4×C17—41no—
354C2×C4×C17—41no—
355C2×C4×C17—41no—
356C2×C4×C17—41no—
357C2×C4×C17—84no—
358C2×C4×C17C2×C22⋊C412yes—
359C2×C4×C17C2×C22⋊C412yes—
360C2×C4×C17C2×C22⋊C412yes—
361C2×C4×C17C2×C22⋊C412yes—
362C2×C4×C17C23×C411yescharacteristic
363C2×C4×C17C22×D411yescharacteristic
364C2×C4×C17C22×D411yescharacteristic
365C2×C4×C17C2×#4111yescharacteristic
366C2×C4×C17H(5,𝔽2)11yescharacteristic
367C2×C4×C17H(5,𝔽2)11yescharacteristic
368C2×Dic17—22no—
369C2×Dic17—41no—
370C2×Dic17—41no—
371C2×Dic17—41no—
372C2×Dic17—41no—
373C2×Dic17—41no—
374C2×Dic17—41no—
375C2×Dic17—41no—
376C2×Dic17—41no—
377C2×Dic17—41no—
378C2×Dic17—41no—
379C2×Dic17—41no—
380C2×Dic17—84no—
381#3622—22no—
382#3622—41no—
383#3622—41no—
384#3622—41no—
385C2×#546D1711yescharacteristic
386C2×#436—171no—
387C2×#417—171no—
388C2×#418—171no—
389#2352—171no—
390#1983—171no—
391#1958—171no—
392#1895—171no—
393#1894—171no—
394#1874—171no—
395#1873—171no—
396#1804—171no—
397#1788—171no—
398#1786—171no—
399C4×#102—171no—
400C22×C17—22no—
401C22×C17—22no—
402C22×C17—24no—
403C22×C17—22no—
404C22×C17—22no—
405C22×C17—22no—
406C22×C17—22no—
407C22×C17—42no—
408C22×C17—42no—
409C22×C17—41no—
410C22×C17—41no—
411C22×C17—42no—
412C22×C17—41no—
413C22×C17—41no—
414C22×C17—42no—
415C22×C17—41no—
416C22×C17—41no—
417C22×C17—42no—
418C22×C17—41no—
419C22×C17—41no—
420C22×C17—42no—
421C22×C17—42no—
422C22×C17—42no—
423C22×C17—42no—
424C22×C17—816no—
425C22×C17—81no—
426C22×C17—81no—
427C22×C17—81no—
428C22×C17—81no—
429C22×C17C22×C22⋊C411yescharacteristic
430C22×C17D4211yescharacteristic
431C22×C17#54611yescharacteristic
432C22×C17#57511yescharacteristic
433C22×C17#57511yescharacteristic
434C22×C17#57611yescharacteristic
435C22×C17#57711yescharacteristic
436C4×C17—22no—
437C4×C17—22no—
438C4×C17—22no—
439C4×C17—22no—
440C4×C17—42no—
441C4×C17—42no—
442C4×C17C2×C4×D411yescharacteristic
443C4×C17#51811yescharacteristic
444C4×C17D4211yescharacteristic
445C4×C17#54611yescharacteristic
446Dic17—42no—
447Dic17—81no—
448Dic17—81no—
449Dic17—81no—
450C22×#41C2×D1711yescharacteristic
451C23×D4C2×D1711yescharacteristic
452C22×M16—171no—
453C22×M16—171no—
454#546—24no—
455#546Dic1718yescomplemented
456C2×#124C2×D1711yescharacteristic
457C2×#123—21no—
458C2×C22⋊Q8C2×D1711yescharacteristic
459C2×#121—21no—
460C2×#121C2×D1711yescharacteristic
461C2×#120—21no—
462C2×C4×D4C2×D1711yescharacteristic
463C2×C4×D4C2×D1711yescharacteristic
464C2×#117—171no—
465C22×C4⋊C4—171no—
466C22×C22⋊C4—21no—
467#436—344no—
468C2×C4⋊C8—171no—
469#418—344no—
470#417—344no—
471C2×#103—171no—
472C2×#103—171no—
473C2×#103—171no—
474C2×#103—171no—
475C2×#102—171no—
476C2×#102—171no—
477C2×#102—171no—
478C2×#102—171no—
479C2×#102—171no—
480C2×#102—171no—
481C2×#102—171no—
482C2×#102—171no—
483C2×C22⋊C8—171no—
484C2×C22⋊C8—171no—
485C2×C4×C8—171no—
486#388—341no—
487#387—341no—
488#386—341no—
489#382—171no—
490#380—171no—
491#380—171no—
492C4×C4⋊C4—171no—
493C4×C22⋊C4—341no—
494#340—171no—
495#340—171no—
496#340—171no—
497#340—171no—
498C2×C17—42no—
499C2×C17—42no—
500C2×C17—44no—
501C2×C17—82no—
502C2×C17D4×C22⋊C411yescharacteristic
503C2×C17#289611yescharacteristic
504C2×C17#289711yescharacteristic
505C2×C17#327311yescharacteristic
506C2×C17#327511yescharacteristic
507C2×C17#332211yescharacteristic
508C2×C17#332311yescharacteristic
509C25—21no—
510C2×#41—22no—
511C2×#41—22no—
512C2×#41—22no—
513C2×#41—41no—
514C2×#41—41no—
515C2×#41C2×Dic1714yes—
516C22×Q8C22×D1711yescharacteristic
517C22×D4—22no—
518C22×D4—22no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—22no—
523C22×D4—41no—
524C22×D4—41no—
525C22×D4C2×Dic1714yescomplemented
526C22×D4C22⋊D1711yescharacteristic
527C22×D4C22×D1711yescharacteristic
528C22×D4C22×D1711yescharacteristic
529C23×C4—21no—
530C23×C4—21no—
531C23×C4—341no—
532C23×C4C22×D1711yescharacteristic
533C23×C4C22×D1711yescharacteristic
534C2×M16—342no—
535C2×M16—342no—
536C2×M16—342no—
537C2×M16—342no—
538C2×M16—681no—
539C2×M16—681no—
540C22×C8—171no—
541C22×C8—171no—
542C22×C8—171no—
543C22×C8—171no—
544#124—22no—
545#124C2×Dic1714yescomplemented
546#123—28no—
547C22⋊Q8—22no—
548C22⋊Q8C2×Dic1714yescomplemented
549#121—22no—
550#121—28no—
551#121C2×Dic1714yes—
552#120—28no—
553C4×D4—22no—
554C4×D4C2×Dic1714yes—
555C4×D4C2×Dic1714yescomplemented
556C4×D4C22⋊D1714yes—
557#117—342no—
558#117—681no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—171no—
561C2×C4⋊C4—171no—
562C2×C4⋊C4—171no—
563C2×C4⋊C4—171no—
564C2×C4⋊C4—342no—
565C2×C4⋊C4—341no—
566C2×C4⋊C4—681no—
567C2×C4⋊C4C22⋊D1711yescharacteristic
568C2×C4⋊C4C22×D1711yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—28no—
575C2×C22⋊C4—341no—
576C2×C22⋊C4—341no—
577C2×C22⋊C4—341no—
578C2×C22⋊C4C22⋊D1711yescharacteristic
579C2×C22⋊C4C22⋊D1711yescharacteristic
580C2×C42—341no—
581C2×C42—341no—
582C2×C42C22×D1711yescharacteristic
583C4⋊C8—342no—
584#103—342no—
585#103—342no—
586#103—681no—
587#103—681no—
588#102—174no—
589#102—342no—
590#102—342no—
591#102—342no—
592#102—342no—
593#102—342no—
594#102—681no—
595#102—681no—
596C22⋊C8—342no—
597C22⋊C8—342no—
598C4×C8—342no—
599#95—341no—
600#95—341no—
601#95—341no—
602#95—341no—
603#95—341no—
604C17#2242711yescharacteristic, complemented, Sylow
605C24—21no—
606C24—21no—
607C24—24no—
608C24—42no—
609C24—42no—
610C24—42no—
611C24—42no—
612C24—81no—
613C24—81no—
614C24C2×C22⋊D1711yescharacteristic
615C24C2×C22⋊D1711yescharacteristic
616#41—28no—
617#41—44no—
618#41—44no—
619#41—44no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8—21no—
625C2×Q8C22×Dic1712yes—
626C2×D4—28no—
627C2×D4—24no—
628C2×D4—24no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—24no—
638C2×D4—44no—
639C2×D4—44no—
640C2×D4—44no—
641C2×D4—41no—
642C2×D4—41no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—42no—
647C2×D4—81no—
648C2×D4—81no—
649C2×D4C22⋊Dic1714yes—
650C2×D4D4×D1712yes—
651C2×D4#6325412yes—
652C2×D4C22×Dic1712yes—
653C2×D4C22×Dic1712yes—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—24no—
665C22×C4—24no—
666C22×C4—42no—
667C22×C4—42no—
668C22×C4—81no—
669C22×C4—81no—
670C22×C4—341no—
671C22×C4—341no—
672C22×C4—341no—
673C22×C4—341no—
674C22×C4—682no—
675C22×C4—682no—
676C22×C4—1361no—
677C22×C4C22×Dic1712yes—
678C22×C4C22×Dic1712yes—
679C22×C4C2×C22⋊D1712yes—
680C22×C4C2×C22⋊D1712yes—
681C22×C4C2×C22⋊D1711yescharacteristic
682C22×C4C2×C22⋊D1711yescharacteristic
683C22×C4C2×C22⋊D1711yescharacteristic
684C22×C4C2×C22⋊D1711yescharacteristic
685C22×C4C23×D1711yescharacteristic
686M16—684no—
687M16—684no—
688C2×C8—172no—
689C2×C8—341no—
690C2×C8—341no—
691C2×C8—341no—
692C2×C8—341no—
693C2×C8—341no—
694C2×C8—341no—
695C2×C8—341no—
696C2×C8—341no—
697C2×C8—341no—
698C2×C8—341no—
699C2×C8—341no—
700C4⋊C4—21no—
701C4⋊C4—24no—
702C4⋊C4—172no—
703C4⋊C4—341no—
704C4⋊C4—341no—
705C4⋊C4—341no—
706C4⋊C4—341no—
707C4⋊C4—341no—
708C4⋊C4—341no—
709C4⋊C4—341no—
710C4⋊C4—682no—
711C4⋊C4C22⋊Dic1714yes—
712C4⋊C4C22×Dic1712yes—
713C22⋊C4—24no—
714C22⋊C4—24no—
715C22⋊C4—24no—
716C22⋊C4—24no—
717C22⋊C4—24no—
718C22⋊C4—682no—
719C22⋊C4—682no—
720C22⋊C4—1361no—
721C22⋊C4C22⋊Dic1714yes—
722C22⋊C4C22⋊Dic1714yes—
723C42—682no—
724C42—1361no—
725C42C22×Dic1712yes—
726C42C2×C22⋊D1712yes—
727C23—22no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—22no—
739C23—21no—
740C23—21no—
741C23—22no—
742C23—22no—
743C23—48no—
744C23—48no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—84no—
756C23—84no—
757C23—84no—
758C23—84no—
759C23—84no—
760C23C2×C22⋊Dic1712yes—
761C23C2×C22⋊Dic1712yes—
762C23C22×C22⋊D1711yescharacteristic
763Q8—22no—
764Q8—22no—
765Q8—41no—
766Q8—41no—
767D4—22no—
768D4—22no—
769D4—22no—
770D4—22no—
771D4—22no—
772D4—44no—
773D4—48no—
774D4—48no—
775D4—41no—
776D4—41no—
777D4—84no—
778D4D4×Dic1714yes—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—48no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—84no—
803C2×C4—342no—
804C2×C4—681no—
805C2×C4—681no—
806C2×C4—681no—
807C2×C4—681no—
808C2×C4—681no—
809C2×C4—681no—
810C2×C4—681no—
811C2×C4—681no—
812C2×C4—681no—
813C2×C4—681no—
814C2×C4—681no—
815C2×C4—1364no—
816C2×C4C2×C22⋊Dic1712yes—
817C2×C4C2×C22⋊Dic1712yes—
818C2×C4C2×C22⋊Dic1712yes—
819C2×C4C2×C22⋊Dic1712yes—
820C2×C4C2×D4×D1711yescharacteristic
821C2×C4C2×#6325411yescharacteristic
822C2×C4#1058769111yescharacteristic
823C2×C4#1058769111yescharacteristic
824C2×C4C23×Dic1711yescharacteristic
825C2×C4C22×C22⋊D1711yescharacteristic
826C8—342no—
827C8—681no—
828C8—681no—
829C8—681no—
830C22—22no—
831C22—22no—
832C22—24no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—42no—
838C22—42no—
839C22—41no—
840C22—41no—
841C22—42no—
842C22—41no—
843C22—41no—
844C22—42no—
845C22—41no—
846C22—41no—
847C22—42no—
848C22—41no—
849C22—41no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—816no—
855C22—81no—
856C22—81no—
857C22—81no—
858C22—81no—
859C22C22×C22⋊Dic1711yescharacteristic
860C22D4×C22⋊D1711yescharacteristic
861C22#1176345311yescharacteristic
862C22#1176360711yescharacteristic
863C22#1176360711yescharacteristic
864C22#1176361211yescharacteristic
865C22#1176362011yescharacteristic
866C4—22no—
867C4—22no—
868C4—22no—
869C4—22no—
870C4—42no—
871C4—42no—
872C4—682no—
873C4—1361no—
874C4—1361no—
875C4—1361no—
876C4C2×D4×Dic1711yescharacteristic
877C4#1176328411yescharacteristic
878C4D4×C22⋊D1711yescharacteristic
879C4#1176345311yescharacteristic
880C2—42no—
881C2—42no—
882C2—44no—
883C2—82no—
884C2D4×C22⋊Dic1711yescharacteristic
885C2#1453730311yescharacteristic
886C2#1453731011yescharacteristic
887C2#1454039111yescharacteristic
888C2#1454041111yescharacteristic
889C2#1454098511yescharacteristic
890C2#1454100011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
Fitting, prime radicalC2×C17×#546C2
socleC23×C17C22×D4
cosocleC22×C4×C17C24
hypercenterC2×#546D17
hypocenterC17#22427
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#546

Complements

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

NH ≅ G/Ntype
1. C2×#11762887C2semidirect
2. C2×#11762810C2semidirect
3. C2×#11762814C2semidirect
4. #14531713C2semidirect
5. #14529717C2semidirect
6. #14529596C2semidirect
7. #14529223C2semidirect
8. #14529218C2semidirect
9. #14529102C2semidirect
10. #14529097C2semidirect
11. #14528794C2semidirect
12. #14528724C2semidirect
13. #14528715C2semidirect
14. C4×#10587503C2semidirect
17. C22×#63223C22semidirect
19. C22×C4⋊Dic17C22semidirect
21. C2×C4⋊#3622C22semidirect
24. C2×#10587506C22semidirect
25. C2×#10587506C22semidirect
26. C2×#10587506C22semidirect
27. C2×#10587506C22semidirect
37. C2×C22⋊#3622C22semidirect
38. C2×C4×#3622C22semidirect
42. #11762675C22semidirect
44. #11762669C22semidirect
45. C4×C4⋊Dic17C22semidirect
47. #11762571C22semidirect
48. #11762571C22semidirect
49. #11762571C22semidirect
50. #11762571C22semidirect
54. C17×#546C4semidirect
80. C22×D4×C17C2×C4semidirect
90. C17×#124C2×C4semidirect
93. C17×C22⋊Q8C2×C4semidirect
100. C4×D4×C17C2×C4semidirect
149. #10587503D4semidirect
455. #546Dic17semidirect
525. C22×D4C2×Dic17semidirect
545. #124C2×Dic17semidirect
548. C22⋊Q8C2×Dic17semidirect
555. C4×D4C2×Dic17semidirect
604. C17#22427semidirect

Maximal subgroups

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

subgroupindex
C2×#117628872
C2×#117628102
C2×#117628142
#145317132
#145297172
#145295962
#145292232
#145292182
#145291022
#145290972
#145287942
#145287242
#145287152
C4×#105875032
C2×C17×#5462
#2242717