Finite Group Databasebeta

← #17049879

Subgroups — #17049879

Order 4352.

1598 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762881C211yesmaximal, characteristic, complemented
2C2×#11762814C211yesmaximal, characteristic, complemented
3C2×#11762805C211yesmaximal, characteristic, complemented
4#14531733C211yesmaximal, characteristic, complemented
5#14529717C211yesmaximal, characteristic, complemented
6#14529601C211yesmaximal, characteristic, complemented
7#14529218C211yesmaximal, characteristic, complemented
8#14529213C211yesmaximal, characteristic, complemented
9#14529107C211yesmaximal, characteristic, complemented
10#14529097C211yesmaximal, characteristic, complemented
11#14528784C211yesmaximal, characteristic, complemented
12#14528724C211yesmaximal, characteristic, complemented
13#14528715C211yesmaximal, characteristic, complemented
14#14528609C211yesmaximal, characteristic, complemented
15C2×C17×#546C211yesmaximal, characteristic
16C22×#63223C2211yescharacteristic
17C23×#3622C2211yescharacteristic, complemented
18C2×#10587612C2211yescharacteristic
19C2×#10587612C2211yescharacteristic, complemented
20#11762881—24no—
21C2×C4⋊#3622C2211yescharacteristic, complemented
22#11762814—24no—
23#11762805—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×#10587474C2211yescharacteristic, complemented
39#11762712—21no—
40#11762702—21no—
41#11762702—21no—
42#11762679C2211yescharacteristic, complemented
43#11762669C2211yescharacteristic
44#11762669C2211yescharacteristic, complemented
45C4⋊C4×Dic17—21no—
46C4×C4⋊Dic17C2211yescharacteristic, complemented
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×C414yes—
81C22×D4×C17D411yescharacteristic
82C22×D4×C17C2311yescharacteristic
83C22×D4×C17C2311yescharacteristic
84C23×C4×C17—21no—
85C23×C4×C17—21no—
86C23×C4×C17C2311yescharacteristic
87C23×C4×C17C2311yescharacteristic
88C17×#124—22no—
89C17×#124C2×C414yes—
90C17×#123—28no—
91C17×C22⋊Q8—22no—
92C17×C22⋊Q8C2×C414yes—
93C17×#121—22no—
94C17×#121—28no—
95C17×#121C2×C414yes—
96C17×#120—28no—
97C4×D4×C17—22no—
98C4×D4×C17C2×C414yes—
99C4×D4×C17C2×C414yes—
100C4×D4×C17D414yes—
101C2×C4⋊C4×C17—21no—
102C2×C4⋊C4×C17D411yescharacteristic
103C2×C4⋊C4×C17C2311yescharacteristic
104C2×C22⋊C4×C17—21no—
105C2×C22⋊C4×C17—21no—
106C2×C22⋊C4×C17—21no—
107C2×C22⋊C4×C17—21no—
108C2×C22⋊C4×C17—21no—
109C2×C22⋊C4×C17—28no—
110C2×C22⋊C4×C17D411yescharacteristic
111C2×C22⋊C4×C17D411yescharacteristic
112C2×C42×C17C2311yescharacteristic
113C2×C22⋊Dic17—21no—
114C2×C22⋊Dic17—21no—
115C2×C22⋊Dic17—21no—
116C2×C22⋊Dic17—21no—
117#10587612—22no—
118#10587612—22no—
119#10587612—41no—
120#10587612—41no—
121C2×C4⋊Dic17—21no—
122C2×C4⋊Dic17—21no—
123C2×C4⋊Dic17C2311yescharacteristic
124C2×C4⋊Dic17C2311yescharacteristic
125C2×C4⋊Dic17C2311yescharacteristic
126C2×C4⋊Dic17C2311yescharacteristic
127C2×C4×Dic17—21no—
128C2×C4×Dic17—21no—
129C2×C4×Dic17—21no—
130C2×#63223—22no—
131C2×#63223—22no—
132C2×#63223—41no—
133C22×#3622—22no—
134C22×#3622—22no—
135C22×#3622—41no—
136C22×#3622C2311yescharacteristic
137C22×#3622C2311yescharacteristic
138C22×#3622C2311yescharacteristic
139C22×#3622C2311yescharacteristic
140#10587506—22no—
141#10587506—22no—
142#10587506—41no—
143#10587506—41no—
144#10587503—22no—
145#10587503—22no—
146#10587503—22no—
147#10587503—22no—
148#10587503—22no—
149#10587503—41no—
150#10587503—41no—
151#10587503D414yescomplemented
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×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—
237C4⋊C4×C17—24no—
238C4⋊C4×C17—21no—
239C4⋊C4×C17C22⋊C414yes—
240C4⋊C4×C17C22×C412yes—
241C22⋊C4×C17—24no—
242C22⋊C4×C17—24no—
243C22⋊C4×C17—24no—
244C22⋊C4×C17—24no—
245C22⋊C4×C17—24no—
246C22⋊C4×C17C22⋊C414yes—
247C22⋊C4×C17C22⋊C414yes—
248C42×C17C22×C412yes—
249C42×C17C2×D412yes—
250C22⋊Dic17—42no—
251C22⋊Dic17—42no—
252C22⋊Dic17—81no—
253C22⋊Dic17—81no—
254C4⋊Dic17—21no—
255C4⋊Dic17—21no—
256C4⋊Dic17—21no—
257C4⋊Dic17—21no—
258C4⋊Dic17—21no—
259C4⋊Dic17—21no—
260C4⋊Dic17—21no—
261C4⋊Dic17—42no—
262C4⋊Dic17—81no—
263C4⋊Dic17C2×D412yes—
264C4×Dic17—42no—
265C4×Dic17—42no—
266C4×Dic17—42no—
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#22424—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—
380#3622—22no—
381#3622—41no—
382#3622—41no—
383#3622—41no—
384C2×#546D1711yescharacteristic
385C2×#435—171no—
386C2×#418—171no—
387C2×#416—171no—
388#2354—171no—
389#1983—171no—
390#1959—171no—
391#1894—171no—
392#1893—171no—
393#1875—171no—
394#1873—171no—
395#1802—171no—
396#1788—171no—
397#1786—171no—
398#1762—171no—
399C22×C17—22no—
400C22×C17—22no—
401C22×C17—24no—
402C22×C17—22no—
403C22×C17—22no—
404C22×C17—22no—
405C22×C17—22no—
406C22×C17—42no—
407C22×C17—42no—
408C22×C17—41no—
409C22×C17—41no—
410C22×C17—42no—
411C22×C17—41no—
412C22×C17—41no—
413C22×C17—42no—
414C22×C17—41no—
415C22×C17—41no—
416C22×C17—42no—
417C22×C17—41no—
418C22×C17—41no—
419C22×C17—42no—
420C22×C17—42no—
421C22×C17—42no—
422C22×C17—42no—
423C22×C17—816no—
424C22×C17—81no—
425C22×C17—81no—
426C22×C17—81no—
427C22×C17—81no—
428C22×C17C22×C22⋊C411yescharacteristic
429C22×C17D4211yescharacteristic
430C22×C17#54611yescharacteristic
431C22×C17#57511yescharacteristic
432C22×C17#57511yescharacteristic
433C22×C17#57611yescharacteristic
434C22×C17#57711yescharacteristic
435C4×C17—22no—
436C4×C17—22no—
437C4×C17—22no—
438C4×C17—22no—
439C4×C17—42no—
440C4×C17—42no—
441C4×C17C2×C4×D411yescharacteristic
442C4×C17#51811yescharacteristic
443C4×C17D4211yescharacteristic
444C4×C17#54611yescharacteristic
445Dic17—42no—
446Dic17—81no—
447Dic17—81no—
448Dic17—81no—
449C22×#41C2×D1711yescharacteristic
450C23×D4C2×D1711yescharacteristic
451C22×M16—171no—
452C23×C8—171no—
453#546—24no—
454#546Dic1718yescomplemented
455C2×#124C2×D1711yescharacteristic
456C2×#123—21no—
457C2×C22⋊Q8C2×D1711yescharacteristic
458C2×#121—21no—
459C2×#121C2×D1711yescharacteristic
460C2×#120—21no—
461C2×C4×D4C2×D1711yescharacteristic
462C2×C4×D4C2×D1711yescharacteristic
463C2×#117—171no—
464C2×#117—171no—
465C22×C22⋊C4—21no—
466#435—344no—
467C2×C4⋊C8—171no—
468#418—344no—
469#416—344no—
470C2×#103—171no—
471C2×#103—171no—
472C2×#103—171no—
473C2×#103—171no—
474C2×#102—171no—
475C2×#102—171no—
476C2×#102—171no—
477C2×#102—171no—
478C2×#102—171no—
479C2×#102—171no—
480C2×#102—171no—
481C2×#102—171no—
482C2×C22⋊C8—171no—
483C2×C22⋊C8—171no—
484C2×#97—171no—
485#390—341no—
486#388—341no—
487#388—341no—
488#384—171no—
489#380—171no—
490#380—171no—
491C4×C4⋊C4—171no—
492C4×C4⋊C4—341no—
493#340—171no—
494#340—171no—
495#340—171no—
496#340—171no—
497C2×C17—42no—
498C2×C17—42no—
499C2×C17—44no—
500C2×C17—82no—
501C2×C17D4×C22⋊C411yescharacteristic
502C2×C17#289611yescharacteristic
503C2×C17#289711yescharacteristic
504C2×C17#326711yescharacteristic
505C2×C17#326811yescharacteristic
506C2×C17#331111yescharacteristic
507C2×C17#331911yescharacteristic
508C25—21no—
509C2×#41—22no—
510C2×#41—22no—
511C2×#41—22no—
512C2×#41—41no—
513C2×#41—41no—
514C2×#41C2×Dic1714yes—
515C22×Q8C22×D1711yescharacteristic
516C22×D4—22no—
517C22×D4—22no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—22no—
522C22×D4—41no—
523C22×D4—41no—
524C22×D4C2×Dic1714yes—
525C22×D4C22⋊D1711yescharacteristic
526C22×D4C22×D1711yescharacteristic
527C22×D4C22×D1711yescharacteristic
528C23×C4—21no—
529C23×C4—21no—
530C23×C4C22×D1711yescharacteristic
531C23×C4C22×D1711yescharacteristic
532C2×M16—342no—
533C2×M16—342no—
534C2×M16—681no—
535C22×C8—171no—
536C22×C8—171no—
537C22×C8—171no—
538C22×C8—171no—
539C22×C8—342no—
540C22×C8—342no—
541C22×C8—681no—
542#124—22no—
543#124C2×Dic1714yes—
544#123—28no—
545C22⋊Q8—22no—
546C22⋊Q8C2×Dic1714yes—
547#121—22no—
548#121—28no—
549#121C2×Dic1714yes—
550#120—28no—
551C4×D4—22no—
552C4×D4C2×Dic1714yes—
553C4×D4C2×Dic1714yes—
554C4×D4C22⋊D1714yes—
555#117—342no—
556#117—342no—
557#117—681no—
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—341no—
565C2×C4⋊C4—341no—
566C2×C4⋊C4C22⋊D1711yescharacteristic
567C2×C4⋊C4C22×D1711yescharacteristic
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—28no—
574C2×C22⋊C4—341no—
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×C42—341no—
583C2×C42C22×D1711yescharacteristic
584C4⋊C8—342no—
585#103—342no—
586#103—342no—
587#103—681no—
588#103—681no—
589#102—174no—
590#102—342no—
591#102—342no—
592#102—342no—
593#102—342no—
594#102—342no—
595#102—681no—
596#102—681no—
597C22⋊C8—342no—
598C22⋊C8—342no—
599#97—342no—
600#95—341no—
601#95—341no—
602#95—341no—
603C17#2242411yescharacteristic, complemented, Sylow
604C24—21no—
605C24—21no—
606C24—24no—
607C24—42no—
608C24—42no—
609C24—42no—
610C24—42no—
611C24—81no—
612C24—81no—
613C24C2×C22⋊D1711yescharacteristic
614C24C2×C22⋊D1711yescharacteristic
615#41—28no—
616#41—44no—
617#41—44no—
618#41—44no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8C22×Dic1712yes—
625C2×D4—28no—
626C2×D4—24no—
627C2×D4—24no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—24no—
637C2×D4—44no—
638C2×D4—44no—
639C2×D4—44no—
640C2×D4—41no—
641C2×D4—41no—
642C2×D4—42no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—81no—
647C2×D4—81no—
648C2×D4C22⋊Dic1714yes—
649C2×D4D4×D1712yes—
650C2×D4#6325412yes—
651C2×D4C22×Dic1712yes—
652C2×D4C22×Dic1712yes—
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—21no—
662C22×C4—21no—
663C22×C4—24no—
664C22×C4—24no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—81no—
668C22×C4—81no—
669C22×C4—341no—
670C22×C4—341no—
671C22×C4—341no—
672C22×C4—341no—
673C22×C4C22×Dic1712yes—
674C22×C4C22×Dic1712yes—
675C22×C4C2×C22⋊D1712yes—
676C22×C4C2×C22⋊D1712yes—
677C22×C4C2×C22⋊D1711yescharacteristic
678C22×C4C2×C22⋊D1711yescharacteristic
679C22×C4C2×C22⋊D1711yescharacteristic
680C22×C4C2×C22⋊D1711yescharacteristic
681C22×C4C23×D1711yescharacteristic
682M16—684no—
683C2×C8—172no—
684C2×C8—341no—
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—684no—
696C4⋊C4—21no—
697C4⋊C4—24no—
698C4⋊C4—172no—
699C4⋊C4—341no—
700C4⋊C4—341no—
701C4⋊C4—341no—
702C4⋊C4—341no—
703C4⋊C4—341no—
704C4⋊C4—341no—
705C4⋊C4—341no—
706C4⋊C4—682no—
707C4⋊C4—1361no—
708C4⋊C4C22⋊Dic1714yes—
709C4⋊C4C22×Dic1712yes—
710C22⋊C4—24no—
711C22⋊C4—24no—
712C22⋊C4—24no—
713C22⋊C4—24no—
714C22⋊C4—24no—
715C22⋊C4—682no—
716C22⋊C4—682no—
717C22⋊C4—1361no—
718C22⋊C4—1361no—
719C22⋊C4C22⋊Dic1714yes—
720C22⋊C4C22⋊Dic1714yes—
721C42—682no—
722C42—682no—
723C42—682no—
724C42C22×Dic1712yes—
725C42C2×C22⋊D1712yes—
726C23—22no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—22no—
738C23—21no—
739C23—21no—
740C23—22no—
741C23—22no—
742C23—48no—
743C23—48no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—84no—
755C23—84no—
756C23—84no—
757C23—84no—
758C23—84no—
759C23C2×C22⋊Dic1712yes—
760C23C2×C22⋊Dic1712yes—
761C23C22×C22⋊D1711yescharacteristic
762Q8—22no—
763Q8—22no—
764Q8—41no—
765Q8—41no—
766D4—22no—
767D4—22no—
768D4—22no—
769D4—22no—
770D4—22no—
771D4—44no—
772D4—48no—
773D4—48no—
774D4—41no—
775D4—41no—
776D4—84no—
777D4D4×Dic1714yes—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—22no—
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—48no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—84no—
802C2×C4—342no—
803C2×C4—681no—
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×C4C2×C22⋊Dic1712yes—
815C2×C4C2×C22⋊Dic1712yes—
816C2×C4C2×C22⋊Dic1712yes—
817C2×C4C2×C22⋊Dic1712yes—
818C2×C4C2×D4×D1711yescharacteristic
819C2×C4C2×#6325411yescharacteristic
820C2×C4#1058769111yescharacteristic
821C2×C4#1058769111yescharacteristic
822C2×C4C23×Dic1711yescharacteristic
823C2×C4C22×C22⋊D1711yescharacteristic
824C8—342no—
825C8—681no—
826C8—681no—
827C8—681no—
828C22—22no—
829C22—22no—
830C22—24no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—41no—
836C22—41no—
837C22—42no—
838C22—41no—
839C22—41no—
840C22—42no—
841C22—41no—
842C22—41no—
843C22—42no—
844C22—42no—
845C22—42no—
846C22—41no—
847C22—41no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—816no—
853C22—81no—
854C22—81no—
855C22—81no—
856C22—81no—
857C22C22×C22⋊Dic1711yescharacteristic
858C22D4×C22⋊D1711yescharacteristic
859C22#1176345311yescharacteristic
860C22#1176360711yescharacteristic
861C22#1176360711yescharacteristic
862C22#1176361211yescharacteristic
863C22#1176362011yescharacteristic
864C4—22no—
865C4—22no—
866C4—22no—
867C4—22no—
868C4—42no—
869C4—42no—
870C4—682no—
871C4—1361no—
872C4—1361no—
873C4—1361no—
874C4C2×D4×Dic1711yescharacteristic
875C4#1176328411yescharacteristic
876C4D4×C22⋊D1711yescharacteristic
877C4#1176345311yescharacteristic
878C2—42no—
879C2—42no—
880C2—44no—
881C2—82no—
882C2D4×C22⋊Dic1711yescharacteristic
883C2#1453730311yescharacteristic
884C2#1453731011yescharacteristic
885C2#1454030511yescharacteristic
886C2#1454032011yescharacteristic
887C2#1454082011yescharacteristic
888C2#1454094011yescharacteristic
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#22424
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×#11762881C2semidirect
2. C2×#11762814C2semidirect
3. C2×#11762805C2semidirect
4. #14531733C2semidirect
5. #14529717C2semidirect
6. #14529601C2semidirect
7. #14529218C2semidirect
8. #14529213C2semidirect
9. #14529107C2semidirect
10. #14529097C2semidirect
11. #14528784C2semidirect
12. #14528724C2semidirect
13. #14528715C2semidirect
14. #14528609C2semidirect
17. C23×#3622C22semidirect
19. C2×#10587612C22semidirect
21. C2×C4⋊#3622C22semidirect
24. C2×#10587506C22semidirect
25. C2×#10587506C22semidirect
26. C2×#10587506C22semidirect
27. C2×#10587506C22semidirect
37. C2×C22⋊#3622C22semidirect
38. C2×#10587474C22semidirect
42. #11762679C22semidirect
44. #11762669C22semidirect
46. C4×C4⋊Dic17C22semidirect
47. #11762571C22semidirect
48. #11762571C22semidirect
49. #11762571C22semidirect
50. #11762571C22semidirect
54. C17×#546C4semidirect
151. #10587503D4semidirect
454. #546Dic17semidirect
603. C17#22424semidirect

Maximal subgroups

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

subgroupindex
C2×#117628812
C2×#117628142
C2×#117628052
#145317332
#145297172
#145296012
#145292182
#145292132
#145291072
#145290972
#145287842
#145287242
#145287152
#145286092
C2×C17×#5462
#2242417