Finite Group Databasebeta

← #17039597

Subgroups — #17039597

Order 4352.

1134 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762765C211yesmaximal, characteristic, complemented
2#14531393C211yesmaximal, characteristic, complemented
3#14529758C211yesmaximal, characteristic, complemented
4#14529746C211yesmaximal, characteristic, complemented
5#14529601C211yesmaximal, characteristic, complemented
6#14529596C211yesmaximal, characteristic, complemented
7#14529223C211yesmaximal, characteristic
8#14529218C211yesmaximal, characteristic, complemented
9#14529213C211yesmaximal, characteristic
10#14529208C211yesmaximal, characteristic, complemented
11#14528614C211yesmaximal, characteristic, complemented
12#14528609C211yesmaximal, characteristic, complemented
13C4×#10587506C211yesmaximal, characteristic, complemented
14C4×#10587503C211yesmaximal, characteristic, complemented
15C2×C17×#542C211yesmaximal, characteristic
16C22×#63223C2211yescharacteristic
17C23×#3622C2211yescharacteristic
18C2×#10587506C2211yescharacteristic
19C2×#10587506C2211yescharacteristic
20C2×#10587506C2211yescharacteristic
21C2×#10587506C2211yescharacteristic
22C2×#10587503C2211yescharacteristic
23C2×#10587503C2211yescharacteristic
24C2×#10587503C2211yescharacteristic
25C2×#10587503C2211yescharacteristic
26#11762765—24no—
27C2×#10587474C2211yescharacteristic
28C2×#10587474C2211yescharacteristic
29C2×C4×#3622C2211yescharacteristic
30C2×C4×#3622C2211yescharacteristic
31#11762702—21no—
32#11762702—21no—
33#11762695—21no—
34#11762695—21no—
35#11762679C2211yescharacteristic
36#11762675C2211yescharacteristic
37#11762669C2211yescharacteristic
38#11762669C2211yescharacteristic
39C4×C4⋊Dic17C2211yescharacteristic
40C4×C4⋊Dic17C2211yescharacteristic
41#11762571C2211yescharacteristic
42#11762571C2211yescharacteristic
43#11762571C2211yescharacteristic
44#11762571C2211yescharacteristic
45#11762571C2211yescharacteristic
46#11762571C2211yescharacteristic
47#11762571C2211yescharacteristic
48#11762571C2211yescharacteristic
49C17×#542—24no—
50C17×#542C418yescomplemented
51C2×C17×C4⋊Q8C2211yescharacteristic
52C2×C17×#126—21no—
53C2×C17×#124—21no—
54C2×C17×#124C2211yescharacteristic
55C2×C17×#123—21no—
56C2×C17×C22⋊Q8—21no—
57C2×C17×C22⋊Q8C2211yescharacteristic
58C2×C17×#121C2211yescharacteristic
59C2×C4×Q8×C17C2211yescharacteristic
60C2×C4×D4×C17C2211yescharacteristic
61C2×C17×#117C2211yescharacteristic
62C22×Q8×C17—21no—
63C22×Q8×C17C2311yescharacteristic
64C22×D4×C17—21no—
65C22×D4×C17C2311yescharacteristic
66C23×C4×C17—21no—
67C23×C4×C17C2311yescharacteristic
68C17×C4⋊Q8—22no—
69C17×C4⋊Q8C2×C414yes—
70C17×#126—28no—
71C17×#124—28no—
72C17×#124—22no—
73C17×#124C2×C414yes—
74C17×#123—28no—
75C17×C22⋊Q8—22no—
76C17×C22⋊Q8—28no—
77C17×C22⋊Q8C2×C414yes—
78C17×#121—22no—
79C17×#121C2×C414yes—
80C4×Q8×C17—22no—
81C4×Q8×C17C2×C414yes—
82C4×D4×C17—22no—
83C4×D4×C17C2×C414yes—
84C17×#117C2×C414yes—
85C17×#117D414yes—
86C2×C4⋊C4×C17—21no—
87C2×C4⋊C4×C17—21no—
88C2×C4⋊C4×C17—21no—
89C2×C4⋊C4×C17D411yescharacteristic
90C2×C4⋊C4×C17D411yescharacteristic
91C2×C4⋊C4×C17C2311yescharacteristic
92C2×C4⋊C4×C17C2311yescharacteristic
93C2×C22⋊C4×C17—21no—
94C2×C22⋊C4×C17—21no—
95C2×C22⋊C4×C17—21no—
96C2×C22⋊C4×C17—21no—
97C2×C22⋊C4×C17—21no—
98C2×C22⋊C4×C17D411yescharacteristic
99C2×C22⋊C4×C17D411yescharacteristic
100C2×C42×C17—21no—
101C2×C42×C17C2311yescharacteristic
102C2×C42×C17C2311yescharacteristic
103C2×C22⋊Dic17—21no—
104C2×C22⋊Dic17—21no—
105C2×C4⋊Dic17—21no—
106C2×C4⋊Dic17—21no—
107C2×C4⋊Dic17C2311yescharacteristic
108C2×C4⋊Dic17C2311yescharacteristic
109C2×C4⋊Dic17C2311yescharacteristic
110C2×C4⋊Dic17C2311yescharacteristic
111C2×C4×Dic17—21no—
112C2×C4×Dic17—21no—
113C2×#63223—22no—
114C2×#63223—22no—
115C2×#63223—22no—
116C22×#3622—22no—
117C22×#3622—22no—
118C22×#3622—22no—
119C22×#3622C2311yescharacteristic
120C22×#3622C2311yescharacteristic
121C22×#3622C2311yescharacteristic
122C22×#3622C2311yescharacteristic
123#10587506—22no—
124#10587506—22no—
125#10587506—22no—
126#10587506—22no—
127#10587503—22no—
128#10587503—22no—
129#10587503—22no—
130#10587503—22no—
131#10587502—21no—
132#10587502—21no—
133#10587502—21no—
134#10587502—21no—
135#10587502—21no—
136#10587502—21no—
137#10587474—22no—
138#10587474—22no—
139C4×#3622—22no—
140C4×#3622—22no—
141C24×C17—21no—
142C24×C17C2×D411yescharacteristic
143C2×Q8×C17—24no—
144C2×Q8×C17—21no—
145C2×Q8×C17—21no—
146C2×Q8×C17—21no—
147C2×Q8×C17—21no—
148C2×Q8×C17—21no—
149C2×Q8×C17—81no—
150C2×Q8×C17—81no—
151C2×Q8×C17C22×C412yes—
152C2×D4×C17—24no—
153C2×D4×C17—21no—
154C2×D4×C17—21no—
155C2×D4×C17—21no—
156C2×D4×C17—21no—
157C2×D4×C17—21no—
158C2×D4×C17—81no—
159C2×D4×C17—81no—
160C2×D4×C17C22×C412yes—
161C22×C4×C17—21no—
162C22×C4×C17—21no—
163C22×C4×C17—21no—
164C22×C4×C17—21no—
165C22×C4×C17—21no—
166C22×C4×C17—21no—
167C22×C4×C17—21no—
168C22×C4×C17—24no—
169C22×C4×C17—81no—
170C22×C4×C17—81no—
171C22×C4×C17C22×C412yes—
172C22×C4×C17C2×D411yescharacteristic
173C22×C4×C17C2×D411yescharacteristic
174C22×C4×C17C2×D411yescharacteristic
175C22×C4×C17C2×D411yescharacteristic
176C22×C4×C17C2×D411yescharacteristic
177C22×C4×C17C2×D412yes—
178C22×C4×C17C2411yescharacteristic
179C22×Dic17—21no—
180C22×Dic17—21no—
181C22×Dic17—21no—
182C22×Dic17—21no—
183C4⋊C4×C17—24no—
184C4⋊C4×C17—24no—
185C4⋊C4×C17—24no—
186C4⋊C4×C17—21no—
187C4⋊C4×C17—21no—
188C4⋊C4×C17C22⋊C414yes—
189C4⋊C4×C17C22⋊C414yes—
190C4⋊C4×C17C22×C412yes—
191C4⋊C4×C17C22×C412yes—
192C22⋊C4×C17—24no—
193C22⋊C4×C17—24no—
194C22⋊C4×C17—24no—
195C22⋊C4×C17—24no—
196C22⋊C4×C17—24no—
197C22⋊C4×C17C22⋊C414yes—
198C22⋊C4×C17C22⋊C414yes—
199C42×C17—24no—
200C42×C17C22×C412yes—
201C42×C17C22×C412yes—
202C42×C17C2×D412yes—
203C42×C17C2×D412yes—
204C22⋊Dic17—81no—
205C22⋊Dic17—81no—
206C4⋊Dic17—21no—
207C4⋊Dic17—21no—
208C4⋊Dic17—21no—
209C4⋊Dic17—21no—
210C4⋊Dic17—21no—
211C4⋊Dic17—21no—
212C4⋊Dic17—21no—
213C4⋊Dic17—21no—
214C4⋊Dic17—81no—
215C4⋊Dic17—81no—
216C4×Dic17—81no—
217C4×Dic17—81no—
218#63223—28no—
219C2×#3622—28no—
220C2×#3622—21no—
221C2×#3622—21no—
222C2×#3622—21no—
223C2×#3622—21no—
224C2×#3622—21no—
225C2×#3622—21no—
226C2×#3622—21no—
227C2×#3622—21no—
228C2×#3622#4112yes—
229C2×#3622#4112yes—
230C2×#3622#4112yes—
231C2×#3622#4112yes—
232#21412—171nomaximal, Sylow
233C23×C17—21no—
234C23×C17—21no—
235C23×C17—21no—
236C23×C17—21no—
237C23×C17—21no—
238C23×C17—21no—
239C23×C17—22no—
240C23×C17—41no—
241C23×C17—41no—
242C23×C17—41no—
243C23×C17—41no—
244C23×C17—41no—
245C23×C17—41no—
246C23×C17C2×C22⋊C412yes—
247C23×C17C22×D411yescharacteristic
248Q8×C17—22no—
249Q8×C17—22no—
250Q8×C17—41no—
251Q8×C17—41no—
252Q8×C17—84no—
253D4×C17—22no—
254D4×C17—22no—
255D4×C17—41no—
256D4×C17—41no—
257D4×C17—84no—
258C2×C4×C17—21no—
259C2×C4×C17—21no—
260C2×C4×C17—21no—
261C2×C4×C17—21no—
262C2×C4×C17—21no—
263C2×C4×C17—21no—
264C2×C4×C17—21no—
265C2×C4×C17—21no—
266C2×C4×C17—21no—
267C2×C4×C17—21no—
268C2×C4×C17—22no—
269C2×C4×C17—22no—
270C2×C4×C17—22no—
271C2×C4×C17—22no—
272C2×C4×C17—22no—
273C2×C4×C17—22no—
274C2×C4×C17—22no—
275C2×C4×C17—41no—
276C2×C4×C17—41no—
277C2×C4×C17—41no—
278C2×C4×C17—41no—
279C2×C4×C17—41no—
280C2×C4×C17—41no—
281C2×C4×C17—84no—
282C2×C4×C17C2×C22⋊C412yes—
283C2×C4×C17C2×C22⋊C412yes—
284C2×C4×C17C2×C22⋊C412yes—
285C2×C4×C17C2×C22⋊C412yes—
286C2×C4×C17C2×C22⋊C412yes—
287C2×C4×C17C23×C411yescharacteristic
288C2×C4×C17C22×D411yescharacteristic
289C2×C4×C17C2×#4111yescharacteristic
290C2×C4×C17C2×#4111yescharacteristic
291C2×C4×C17C2×#4111yescharacteristic
292C2×C4×C17C2×#4111yescharacteristic
293C2×Dic17—41no—
294C2×Dic17—41no—
295C2×Dic17—41no—
296C2×Dic17—41no—
297C2×Dic17—41no—
298C2×Dic17—41no—
299C2×Dic17—41no—
300C2×Dic17—41no—
301C2×Dic17—41no—
302C2×Dic17—41no—
303C2×Dic17—41no—
304C2×Dic17—41no—
305#3622—22no—
306#3622—22no—
307#3622—22no—
308#3622—22no—
309C2×#542D1711yescharacteristic
310C2×#405—171no—
311#2314—171no—
312#1993—171no—
313#1990—171no—
314#1959—171no—
315#1958—171no—
316#1895—171no—
317#1894—171no—
318#1893—171no—
319#1892—171no—
320#1763—171no—
321#1762—171no—
322C4×#103—171no—
323C4×#102—171no—
324C22×C17—22no—
325C22×C17—22no—
326C22×C17—22no—
327C22×C17—41no—
328C22×C17—41no—
329C22×C17—41no—
330C22×C17—41no—
331C22×C17—42no—
332C22×C17—42no—
333C22×C17—42no—
334C22×C17—81no—
335C22×C17—81no—
336C22×C17—81no—
337C22×C17—81no—
338C22×C17C22×C22⋊C411yescharacteristic
339C22×C17#53211yescharacteristic
340C22×C17#53211yescharacteristic
341C22×C17#57611yescharacteristic
342C22×C17#57711yescharacteristic
343C22×C17#57711yescharacteristic
344C22×C17#57811yescharacteristic
345C4×C17—22no—
346C4×C17—22no—
347C4×C17—22no—
348C4×C17—22no—
349C4×C17—22no—
350C4×C17—42no—
351C4×C17—42no—
352C4×C17—42no—
353C4×C17C4×#4111yescharacteristic
354C4×C17C4×#4111yescharacteristic
355C4×C17#52511yescharacteristic
356C4×C17#52511yescharacteristic
357Dic17—81no—
358Dic17—81no—
359Dic17—81no—
360Dic17—81no—
361C22×M16—171no—
362C23×C8—171no—
363#542—24no—
364#542Dic1718yescomplemented
365C2×C4⋊Q8C2×D1711yescharacteristic
366C2×#126—21no—
367C2×#124—21no—
368C2×#124C2×D1711yescharacteristic
369C2×#123—21no—
370C2×C22⋊Q8—21no—
371C2×C22⋊Q8C2×D1711yescharacteristic
372C2×#121C2×D1711yescharacteristic
373C2×C4×Q8C2×D1711yescharacteristic
374C2×C4×D4C2×D1711yescharacteristic
375C2×#117C2×D1711yescharacteristic
376C2×#103—171no—
377C2×#103—171no—
378C2×#103—171no—
379C2×#103—171no—
380C2×#102—171no—
381C2×#102—171no—
382C2×#102—171no—
383C2×#102—171no—
384#405—344no—
385C2×#97—171no—
386C2×#97—171no—
387C2×C4×C8—171no—
388C2×C4×C8—171no—
389#388—341no—
390#388—341no—
391#387—341no—
392#387—341no—
393#384—171no—
394#382—171no—
395#380—171no—
396#380—171no—
397C4×C4⋊C4—171no—
398C4×C4⋊C4—171no—
399#340—171no—
400#340—171no—
401#340—171no—
402#340—171no—
403#340—171no—
404#340—171no—
405#340—171no—
406#340—171no—
407C2×C17—42no—
408C2×C17—82no—
409C2×C17#229711yescharacteristic
410C2×C17#289711yescharacteristic
411C2×C17#289811yescharacteristic
412C2×C17#317311yescharacteristic
413C2×C17#317511yescharacteristic
414C2×C17#317811yescharacteristic
415C2×C17#317911yescharacteristic
416C22×Q8—21no—
417C22×Q8C22×D1711yescharacteristic
418C22×D4—21no—
419C22×D4C22×D1711yescharacteristic
420C23×C4—21no—
421C23×C4C22×D1711yescharacteristic
422C2×M16—342no—
423C2×M16—342no—
424C2×M16—342no—
425C22×C8—171no—
426C22×C8—171no—
427C22×C8—171no—
428C22×C8—171no—
429C22×C8—342no—
430C22×C8—342no—
431C22×C8—342no—
432C4⋊Q8—22no—
433C4⋊Q8C2×Dic1714yes—
434#126—28no—
435#124—28no—
436#124—22no—
437#124C2×Dic1714yes—
438#123—28no—
439C22⋊Q8—22no—
440C22⋊Q8—28no—
441C22⋊Q8C2×Dic1714yes—
442#121—22no—
443#121C2×Dic1714yes—
444C4×Q8—22no—
445C4×Q8C2×Dic1714yes—
446C4×D4—22no—
447C4×D4C2×Dic1714yes—
448#117C2×Dic1714yes—
449#117C22⋊D1714yes—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—171no—
454C2×C4⋊C4—171no—
455C2×C4⋊C4—171no—
456C2×C4⋊C4—171no—
457C2×C4⋊C4—341no—
458C2×C4⋊C4—341no—
459C2×C4⋊C4C22⋊D1711yescharacteristic
460C2×C4⋊C4C22⋊D1711yescharacteristic
461C2×C4⋊C4C22×D1711yescharacteristic
462C2×C4⋊C4C22×D1711yescharacteristic
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—341no—
469C2×C22⋊C4—341no—
470C2×C22⋊C4C22⋊D1711yescharacteristic
471C2×C22⋊C4C22⋊D1711yescharacteristic
472C2×C42—21no—
473C2×C42—341no—
474C2×C42—341no—
475C2×C42C22×D1711yescharacteristic
476C2×C42C22×D1711yescharacteristic
477#103—342no—
478#103—342no—
479#103—342no—
480#103—342no—
481#102—342no—
482#102—342no—
483#102—342no—
484#102—342no—
485#97—342no—
486#97—342no—
487C4×C8—342no—
488C4×C8—342no—
489#95—341no—
490#95—341no—
491#95—341no—
492#95—341no—
493#95—341no—
494#95—341no—
495C17#2141211yescharacteristic, complemented, Sylow
496C24—21no—
497C24C2×C22⋊D1711yescharacteristic
498C2×Q8—21no—
499C2×Q8—24no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—81no—
505C2×Q8—81no—
506C2×Q8C22×Dic1712yes—
507C2×D4—24no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—81no—
514C2×D4—81no—
515C2×D4C22×Dic1712yes—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—24no—
524C22×C4—81no—
525C22×C4—81no—
526C22×C4—341no—
527C22×C4—341no—
528C22×C4—341no—
529C22×C4—341no—
530C22×C4C22×Dic1712yes—
531C22×C4C2×C22⋊D1712yes—
532C22×C4C2×C22⋊D1711yescharacteristic
533C22×C4C2×C22⋊D1711yescharacteristic
534C22×C4C2×C22⋊D1711yescharacteristic
535C22×C4C2×C22⋊D1711yescharacteristic
536C22×C4C2×C22⋊D1711yescharacteristic
537C22×C4C23×D1711yescharacteristic
538M16—348no—
539C2×C8—172no—
540C2×C8—172no—
541C2×C8—172no—
542C2×C8—172no—
543C2×C8—348no—
544C2×C8—341no—
545C2×C8—341no—
546C2×C8—341no—
547C2×C8—341no—
548C2×C8—341no—
549C2×C8—341no—
550C2×C8—341no—
551C2×C8—341no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—24no—
555C4⋊C4—24no—
556C4⋊C4—24no—
557C4⋊C4—341no—
558C4⋊C4—341no—
559C4⋊C4—341no—
560C4⋊C4—341no—
561C4⋊C4—341no—
562C4⋊C4—341no—
563C4⋊C4—341no—
564C4⋊C4—341no—
565C4⋊C4—1361no—
566C4⋊C4—1361no—
567C4⋊C4C22⋊Dic1714yes—
568C4⋊C4C22⋊Dic1714yes—
569C4⋊C4C22×Dic1712yes—
570C4⋊C4C22×Dic1712yes—
571C22⋊C4—24no—
572C22⋊C4—24no—
573C22⋊C4—24no—
574C22⋊C4—24no—
575C22⋊C4—24no—
576C22⋊C4—1361no—
577C22⋊C4—1361no—
578C22⋊C4C22⋊Dic1714yes—
579C22⋊C4C22⋊Dic1714yes—
580C42—24no—
581C42—1361no—
582C42—1361no—
583C42C22×Dic1712yes—
584C42C22×Dic1712yes—
585C42C2×C22⋊D1712yes—
586C42C2×C22⋊D1712yes—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—22no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23C2×C22⋊Dic1712yes—
601C23C22×C22⋊D1711yescharacteristic
602Q8—22no—
603Q8—22no—
604Q8—41no—
605Q8—41no—
606Q8—84no—
607D4—22no—
608D4—22no—
609D4—41no—
610D4—41no—
611D4—84no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—84no—
636C2×C4—681no—
637C2×C4—681no—
638C2×C4—681no—
639C2×C4—681no—
640C2×C4—681no—
641C2×C4—681no—
642C2×C4—681no—
643C2×C4—681no—
644C2×C4—681no—
645C2×C4—681no—
646C2×C4—681no—
647C2×C4—681no—
648C2×C4C2×C22⋊Dic1712yes—
649C2×C4C2×C22⋊Dic1712yes—
650C2×C4C2×C22⋊Dic1712yes—
651C2×C4C2×C22⋊Dic1712yes—
652C2×C4C2×C22⋊Dic1712yes—
653C2×C4#41×D1711yescharacteristic
654C2×C4#41×D1711yescharacteristic
655C2×C4#41×D1711yescharacteristic
656C2×C4#41×D1711yescharacteristic
657C2×C4C23×Dic1711yescharacteristic
658C2×C4C22×C22⋊D1711yescharacteristic
659C8—342no—
660C8—342no—
661C8—342no—
662C8—342no—
663C22—22no—
664C22—22no—
665C22—22no—
666C22—41no—
667C22—41no—
668C22—41no—
669C22—41no—
670C22—42no—
671C22—42no—
672C22—42no—
673C22—81no—
674C22—81no—
675C22—81no—
676C22—81no—
677C22C22×C22⋊Dic1711yescharacteristic
678C22#1176335511yescharacteristic
679C22#1176335511yescharacteristic
680C22#1176361211yescharacteristic
681C22#1176361711yescharacteristic
682C22#1176362011yescharacteristic
683C22#1176362411yescharacteristic
684C4—22no—
685C4—22no—
686C4—22no—
687C4—22no—
688C4—22no—
689C4—42no—
690C4—42no—
691C4—42no—
692C4—1361no—
693C4—1361no—
694C4—1361no—
695C4—1361no—
696C4#41×Dic1711yescharacteristic
697C4#41×Dic1711yescharacteristic
698C4#1176331611yescharacteristic
699C4#1176331611yescharacteristic
700C2—42no—
701C2—82no—
702C2#1453127511yescharacteristic
703C2#1453731011yescharacteristic
704C2#1453731711yescharacteristic
705C2#1453939511yescharacteristic
706C2#1453941711yescharacteristic
707C2#1453944611yescharacteristic
708C2#1453946111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC2×C17×#542C2
socleC23×C17C22×D4
prime radicalC2×C17×#121C22
cosocleC22×C4×C17C24
hypercenterC2×#542D17
hypocenterC17#21412
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#11762765C2semidirect
2. #14531393C2semidirect
3. #14529758C2semidirect
4. #14529746C2semidirect
5. #14529601C2semidirect
6. #14529596C2semidirect
8. #14529218C2semidirect
10. #14529208C2semidirect
11. #14528614C2semidirect
12. #14528609C2semidirect
13. C4×#10587506C2semidirect
14. C4×#10587503C2semidirect
50. C17×#542C4semidirect
364. #542Dic17semidirect
495. C17#21412semidirect

Maximal subgroups

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

subgroupindex
C2×#117627652
#145313932
#145297582
#145297462
#145296012
#145295962
#145292232
#145292182
#145292132
#145292082
#145286142
#145286092
C4×#105875062
C4×#105875032
C2×C17×#5422
#2141217