Finite Group Databasebeta

← #17050607

Subgroups — #17050607

Order 4352.

1194 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763493C211yesmaximal, characteristic
2C2×#11762878C211yesmaximal, characteristic
3#14531680C211yesmaximal, characteristic
4#14529751C211yesmaximal, characteristic, complemented
5#14529738C211yesmaximal, characteristic, complemented
6#14529204C211yesmaximal, characteristic, complemented
7#14529092C211yesmaximal, characteristic, complemented
8#14529088C211yesmaximal, characteristic, complemented
9#14528876C211yesmaximal, characteristic, complemented
10#14528869C211yesmaximal, characteristic, complemented
11#14528787C211yesmaximal, characteristic, complemented
12#14528616C211yesmaximal, characteristic, complemented
13#14528504C211yesmaximal, characteristic, complemented
14D17×#340C211yesmaximal, characteristic, complemented
15C17×#1894C211yesmaximal, characteristic, complemented
16C22×C8×D17C2211yescharacteristic
17#11763493—24no—
18#11763493C418yescomplemented
19C2×#10587565—21no—
20C2×#10587576C2211yescharacteristic
21C2×#10587575—21no—
22C2×#10587569—21no—
23C2×#10587632C2211yescharacteristic
24C2×Q8×Dic17C2211yescharacteristic
25C2×C4×C22⋊D17C2211yescharacteristic
26C2×#10587567—21no—
27C2×#10587612C2211yescharacteristic
28C2×#10587578—21no—
29C22×C4⋊Dic17C2211yescharacteristic
30C2×C4⋊C4×D17C2211yescharacteristic
31C2×C4⋊C4×D17C2211yescharacteristic
32#11762878—24no—
33C2×#10587485C2211yescharacteristic
34C2×#10587506C2211yescharacteristic
35C2×#10587506C2211yescharacteristic
36C2×C22⋊#3622C2211yescharacteristic
37C2×#10587491C2211yescharacteristic
38C2×#10587486C2211yescharacteristic
39#11762706—21no—
40#11762683—21no—
41#11762681—21no—
42#11762678C2211yescharacteristic
43#11762666C2211yescharacteristic
44C4⋊C4×Dic17C2211yescharacteristic
45#11762572C2211yescharacteristic
46#11762572C2211yescharacteristic
47#11762572C2211yescharacteristic
48#11762572C2211yescharacteristic
49#11762571C2211yescharacteristic
50#11762571C2211yescharacteristic
51#11762571C2211yescharacteristic
52#11762571C2211yescharacteristic
53#11762571C2211yescharacteristic
54#11762571C2211yescharacteristic
55C22×M16×C17C2211yescharacteristic
56C2×C17×C22⋊Q8C2211yescharacteristic
57C2×C17×#103C2211yescharacteristic
58C2×C17×#103C2211yescharacteristic
59C17×#380C2211yescharacteristic
60C17×#340C2211yescharacteristic
61C17×#340C2211yescharacteristic
62C22×Q8×C17C2311yescharacteristic
63C23×C4×C17C2311yescharacteristic
64C22×C22⋊D17D411yescharacteristic
65C23×Dic17—21no—
66C22×C4×D17—21no—
67C22×C4×D17—21no—
68C22×C4×D17C2311yescharacteristic
69C2×M16×C17—22no—
70C2×M16×C17—22no—
71C2×M16×C17—41no—
72C22×C8×C17C2311yescharacteristic
73C22×C8×C17C2311yescharacteristic
74C17×C22⋊Q8—22no—
75C17×C22⋊Q8C2×C414yescomplemented
76C2×C4⋊C4×C17—21no—
77C2×C4⋊C4×C17C2311yescharacteristic
78C2×C4⋊C4×C17C2311yescharacteristic
79C2×C4⋊C4×C17C2311yescharacteristic
80C2×C22⋊C4×C17—21no—
81C2×C22⋊C4×C17—21no—
82C2×C22⋊Dic17—21no—
83C2×C22⋊Dic17D411yescharacteristic
84#10587632—22no—
85#10587632C2×C414yescomplemented
86Q8×Dic17—22no—
87Q8×Dic17C2×C414yescomplemented
88C4×C22⋊D17C2×C414yes—
89C4×C22⋊D17D414yes—
90C2×#63227—21no—
91C2×#63227—21no—
92C2×#63227D411yescharacteristic
93#10587612—22no—
94#10587612C2×C414yescomplemented
95C2×C4⋊Dic17—21no—
96C2×C4⋊Dic17—21no—
97C2×C4⋊Dic17—21no—
98C2×C4⋊Dic17—22no—
99C2×C4⋊Dic17—41no—
100C2×C4⋊Dic17C2311yescharacteristic
101C2×C4⋊Dic17C2311yescharacteristic
102C2×C4⋊Dic17C2311yescharacteristic
103C2×C4⋊Dic17C2311yescharacteristic
104C2×#63225—21no—
105C2×#63225—21no—
106C2×#63225—21no—
107C2×#63225—21no—
108C2×#63225—21no—
109C2×#63225—21no—
110C2×#63225D411yescharacteristic
111C2×C4×Dic17—21no—
112C2×C4×Dic17—21no—
113C2×C4×Dic17—21no—
114C2×C4×Dic17C2311yescharacteristic
115C22×#3622C2311yescharacteristic
116C22×#3622C2311yescharacteristic
117C2×C8×D17—22no—
118C2×C8×D17—22no—
119C2×C8×D17—41no—
120#10587578—28no—
121C4⋊C4×D17—22no—
122C4⋊C4×D17—22no—
123C4⋊C4×D17—41no—
124C4⋊C4×D17C2×C414yescomplemented
125#10587576—22no—
126#10587576C2×C414yescomplemented
127#10587575—28no—
128#10587569—28no—
129#10587567—44no—
130#10587565—28no—
131C17×#103—22no—
132C17×#103—41no—
133C17×#95—21no—
134#10587506—22no—
135#10587506—41no—
136#10587502—21no—
137#10587502—21no—
138C22⋊#3622—22no—
139#10587491—22no—
140#10587486—22no—
141#10587485—22no—
142C24×C17C2×D411yescharacteristic
143C23×D17C2×D411yescharacteristic
144C2×Q8×C17—21no—
145C2×Q8×C17—21no—
146C2×Q8×C17—21no—
147C2×Q8×C17—21no—
148C2×Q8×C17—21no—
149C2×Q8×C17C22×C412yes—
150C22×C4×C17—21no—
151C22×C4×C17—21no—
152C22×C4×C17—21no—
153C22×C4×C17—21no—
154C22×C4×C17—21no—
155C22×C4×C17—21no—
156C22×C4×C17—21no—
157C22×C4×C17—21no—
158C22×C4×C17C22×C412yes—
159C22×C4×C17C2×D411yescharacteristic
160C22×C4×C17C2×D412yes—
161C22×C4×C17C2411yescharacteristic
162C2×C22⋊D17—22no—
163C2×C22⋊D17—22no—
164C2×C22⋊D17C22⋊C414yes—
165C22×Dic17—21no—
166C22×Dic17—21no—
167C22×Dic17—21no—
168C22×Dic17—21no—
169C22×Dic17—42no—
170C22×Dic17—42no—
171C22×Dic17—81no—
172C22×Dic17C2×D411yescharacteristic
173C22×Dic17C2×D411yescharacteristic
174C22×Dic17C2×D411yescharacteristic
175C2×C4×D17—21no—
176C2×C4×D17—21no—
177C2×C4×D17—21no—
178C2×C4×D17—21no—
179C2×C4×D17—24no—
180C2×C4×D17—42no—
181C2×C4×D17—42no—
182C2×C4×D17—42no—
183C2×C4×D17—42no—
184C2×C4×D17—81no—
185C2×C4×D17C22×C412yes—
186C2×C4×D17C2×D412yes—
187M16×C17—44no—
188C2×C8×C17—21no—
189C2×C8×C17—21no—
190C2×C8×C17—21no—
191C2×C8×C17—21no—
192C2×C8×C17—21no—
193C2×C8×C17#4112yes—
194C4⋊C4×C17—24no—
195C4⋊C4×C17—21no—
196C4⋊C4×C17—21no—
197C4⋊C4×C17—21no—
198C4⋊C4×C17—21no—
199C4⋊C4×C17—21no—
200C4⋊C4×C17C22×C412yes—
201C22⋊C4×C17—24no—
202C22⋊C4×C17—42no—
203C22⋊Dic17—24no—
204C22⋊Dic17C22⋊C414yes—
205#63227—24no—
206#63227—42no—
207#63227C22⋊C414yes—
208C4⋊Dic17—21no—
209C4⋊Dic17—21no—
210C4⋊Dic17—21no—
211C4⋊Dic17—24no—
212C4⋊Dic17—24no—
213C4⋊Dic17—21no—
214C4⋊Dic17—21no—
215C4⋊Dic17—42no—
216C4⋊Dic17C22×C412yes—
217C4⋊Dic17C22×C412yes—
218C4⋊Dic17#4112yes—
219#63225—24no—
220#63225—24no—
221#63225—24no—
222#63225—42no—
223#63225—42no—
224#63225—81no—
225#63225C22⋊C414yes—
226C4×Dic17—24no—
227C4×Dic17—24no—
228C4×Dic17—42no—
229C4×Dic17C22×C412yes—
230C4×Dic17C2×D412yes—
231C2×#3622—21no—
232C2×#3622—21no—
233C2×#3622—21no—
234C2×#3622—21no—
235C2×#3622—21no—
236C2×#3622—21no—
237C8×D17—44no—
238#22491—171nomaximal, Sylow
239C23×C17—21no—
240C23×C17—21no—
241C23×C17—21no—
242C23×C17—21no—
243C23×C17—21no—
244C23×C17—21no—
245C23×C17C2×C22⋊C412yes—
246C23×C17C22×D411yescharacteristic
247C22×D17—21no—
248C22×D17—21no—
249C22×D17—21no—
250C22×D17—21no—
251C22×D17C2×C22⋊C412yes—
252C22×D17AGL(1,ℤ/8)12yes—
253C22×D17#13712yes—
254Q8×C17—22no—
255Q8×C17—22no—
256Q8×C17—41no—
257Q8×C17—41no—
258C2×C4×C17—21no—
259C2×C4×C17—21no—
260C2×C4×C17—22no—
261C2×C4×C17—22no—
262C2×C4×C17—22no—
263C2×C4×C17—22no—
264C2×C4×C17—22no—
265C2×C4×C17—22no—
266C2×C4×C17—41no—
267C2×C4×C17—41no—
268C2×C4×C17—41no—
269C2×C4×C17—41no—
270C2×C4×C17—41no—
271C2×C4×C17—41no—
272C2×C4×C17—41no—
273C2×C4×C17—41no—
274C2×C4×C17—41no—
275C2×C4×C17—41no—
276C2×C4×C17C2×C22⋊C412yes—
277C2×C4×C17C23×C411yescharacteristic
278C2×C4×C17C22×D411yescharacteristic
279C2×C4×C17C2×#4111yescharacteristic
280C2×C4×C17C2×#4111yescharacteristic
281C2×C4×C17H(5,𝔽2)11yescharacteristic
282C2×C4×C172−1+411yescharacteristic
283C22⋊D17—28no—
284C2×Dic17—21no—
285C2×Dic17—21no—
286C2×Dic17—21no—
287C2×Dic17—21no—
288C2×Dic17—21no—
289C2×Dic17—21no—
290C2×Dic17—22no—
291C2×Dic17—22no—
292C2×Dic17—22no—
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—84no—
303C2×Dic17C2×C22⋊C412yes—
304C2×Dic17C2×C22⋊C412yes—
305C2×Dic17C2×C22⋊C412yes—
306C4×D17—22no—
307C4×D17—22no—
308C4×D17—22no—
309C4×D17—22no—
310C4×D17—48no—
311C4×D17—84no—
312C8×C17—22no—
313C8×C17—41no—
314#3622—41no—
315#3622—41no—
316C2×#552—171no—
317C2×#435—171no—
318D4×C4⋊C4—171no—
319#1992—171no—
320#1989—171no—
321#1894D1711yescharacteristic, complemented
322#1892—171no—
323#1872—171no—
324#1872—171no—
325#1825—171no—
326#1823—171no—
327#1803—171no—
328#1763—171no—
329#1736—171no—
330C2×#340—171no—
331C22×C17—22no—
332C22×C17—22no—
333C22×C17—22no—
334C22×C17—41no—
335C22×C17—41no—
336C22×C17—41no—
337C22×C17—41no—
338C22×C17C22×C22⋊C411yescharacteristic
339C22×C17#54611yescharacteristic
340C22×C17#54711yescharacteristic
341C22×C17C2×AGL(1,ℤ/8)11yescharacteristic
342C22×C17C2×#13711yescharacteristic
343C22×C17#57711yescharacteristic
344C22×C17#57811yescharacteristic
345C2×D17—22no—
346C2×D17—22no—
347C2×D17—22no—
348C2×D17—22no—
349C2×D17—22no—
350C2×D17—22no—
351C2×D17#41714yes—
352C4×C17—22no—
353C4×C17—42no—
354C4×C17—42no—
355C4×C17—81no—
356C4×C17—81no—
357C4×C17C4×#4111yescharacteristic
358C4×C17#52011yescharacteristic
359C4×C17#54611yescharacteristic
360C4×C17#54711yescharacteristic
361Dic17—22no—
362Dic17—22no—
363Dic17—22no—
364Dic17—42no—
365Dic17—42no—
366Dic17—42no—
367Dic17—81no—
368C22×M16C2×D1711yescharacteristic
369C23×C8—171no—
370#552—178no—
371#552—344no—
372C2×#126—341no—
373C2×#125—171no—
374C2×#125—341no—
375C2×#123—341no—
376C2×C22⋊Q8—171no—
377C2×C22⋊Q8C2×D1711yescharacteristic
378C2×C4×Q8—171no—
379C2×C4×D4—171no—
380C2×C4×D4—341no—
381C2×#117—171no—
382C2×#117—341no—
383C22×C4⋊C4—171no—
384C22×C4⋊C4—171no—
385C22×C4⋊C4—171no—
386#435—344no—
387C2×C4⋊C8—171no—
388C2×#103—171no—
389C2×#103—171no—
390C2×#103C2×D1711yescharacteristic
391C2×#103C2×D1711yescharacteristic
392C2×C22⋊C8—171no—
393C2×C22⋊C8—171no—
394C2×#97—171no—
395#389—341no—
396#385—341no—
397#385—341no—
398#384—171no—
399#380—171no—
400#380C2×D1711yescharacteristic
401C4×C4⋊C4—171no—
402#340—171no—
403#340—171no—
404#340—171no—
405#340—171no—
406#340—171no—
407#340—171no—
408#340—171no—
409#340—171no—
410#340—171no—
411#340—171no—
412#340C2×D1711yescharacteristic
413#340C2×D1711yescharacteristic
414C2×C17—42no—
415C2×C17#233911yescharacteristic
416C2×C17C2×#41711yescharacteristic
417C2×C17#289811yescharacteristic
418C2×C17#331011yescharacteristic
419C2×C17#331211yescharacteristic
420C2×C17#334311yescharacteristic
421C2×C17#334411yescharacteristic
422D17—24no—
423C22×Q8C22×D1711yescharacteristic
424C22×D4—171no—
425C23×C4—171no—
426C23×C4—341no—
427C23×C4—341no—
428C23×C4—341no—
429C23×C4C22×D1711yescharacteristic
430C2×M16—22no—
431C2×M16—22no—
432C2×M16—41no—
433C22×C8—171no—
434C22×C8—171no—
435C22×C8—342no—
436C22×C8—342no—
437C22×C8—681no—
438C22×C8C22×D1711yescharacteristic
439C22×C8C22×D1711yescharacteristic
440#126—348no—
441#125—174no—
442#125—342no—
443#125—348no—
444#123—348no—
445C22⋊Q8—22no—
446C22⋊Q8—174no—
447C22⋊Q8—342no—
448C22⋊Q8C4×D1714yescomplemented
449C4×Q8—174no—
450C4×Q8—342no—
451C4×D4—174no—
452C4×D4—174no—
453C4×D4—684no—
454#117—174no—
455#117—348no—
456#117—342no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—171no—
459C2×C4⋊C4—171no—
460C2×C4⋊C4—171no—
461C2×C4⋊C4—171no—
462C2×C4⋊C4—174no—
463C2×C4⋊C4—171no—
464C2×C4⋊C4—342no—
465C2×C4⋊C4—342no—
466C2×C4⋊C4—342no—
467C2×C4⋊C4—341no—
468C2×C4⋊C4—341no—
469C2×C4⋊C4—341no—
470C2×C4⋊C4—341no—
471C2×C4⋊C4—341no—
472C2×C4⋊C4—341no—
473C2×C4⋊C4—341no—
474C2×C4⋊C4—341no—
475C2×C4⋊C4—341no—
476C2×C4⋊C4—681no—
477C2×C4⋊C4—681no—
478C2×C4⋊C4C22×D1711yescharacteristic
479C2×C4⋊C4C22×D1711yescharacteristic
480C2×C4⋊C4C22×D1711yescharacteristic
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—171no—
484C2×C22⋊C4—171no—
485C2×C22⋊C4—341no—
486C2×C22⋊C4—341no—
487C2×C22⋊C4—341no—
488C2×C42—171no—
489C2×C42—341no—
490C2×C42—341no—
491C2×C42—341no—
492C4⋊C8—342no—
493#103—22no—
494#103—41no—
495#103—342no—
496#103—681no—
497C22⋊C8—342no—
498C22⋊C8—342no—
499#97—342no—
500#95—21no—
501#95—341no—
502#95—341no—
503C17#2249111yescharacteristic, complemented, Sylow
504C24—171no—
505C24D4×D1711yescharacteristic
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8C2×C4×D1712yes—
512C2×D4—174no—
513C2×D4—342no—
514C2×D4—342no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—171no—
524C22×C4—171no—
525C22×C4—171no—
526C22×C4—172no—
527C22×C4—172no—
528C22×C4—344no—
529C22×C4—341no—
530C22×C4—341no—
531C22×C4—341no—
532C22×C4—341no—
533C22×C4—341no—
534C22×C4—341no—
535C22×C4—341no—
536C22×C4—341no—
537C22×C4—682no—
538C22×C4—682no—
539C22×C4—682no—
540C22×C4—682no—
541C22×C4—682no—
542C22×C4—682no—
543C22×C4—1361no—
544C22×C4—1361no—
545C22×C4C2×C4×D1712yes—
546C22×C4D4×D1712yes—
547C22×C4D4×D1711yescharacteristic
548C22×C4C23×D1711yescharacteristic
549M16—44no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—341no—
556C2×C8—341no—
557C2×C8—341no—
558C2×C8—341no—
559C2×C8—341no—
560C2×C8—341no—
561C2×C8—684no—
562C2×C8#6325412yes—
563C4⋊C4—21no—
564C4⋊C4—24no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—174no—
570C4⋊C4—172no—
571C4⋊C4—172no—
572C4⋊C4—172no—
573C4⋊C4—344no—
574C4⋊C4—344no—
575C4⋊C4—344no—
576C4⋊C4—344no—
577C4⋊C4—344no—
578C4⋊C4—341no—
579C4⋊C4—341no—
580C4⋊C4—341no—
581C4⋊C4—341no—
582C4⋊C4—341no—
583C4⋊C4—682no—
584C4⋊C4—682no—
585C4⋊C4—682no—
586C4⋊C4—1361no—
587C4⋊C4C2×C4×D1712yes—
588C22⋊C4—24no—
589C22⋊C4—42no—
590C22⋊C4—174no—
591C22⋊C4—174no—
592C22⋊C4—344no—
593C22⋊C4—344no—
594C22⋊C4—682no—
595C42—172no—
596C42—172no—
597C42—344no—
598C42—344no—
599C42—682no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—172no—
607C23—172no—
608C23—172no—
609C23—341no—
610C23—341no—
611C23—341no—
612C23—341no—
613C23C22⋊C4×D1712yes—
614C23C2×D4×D1711yescharacteristic
615Q8—22no—
616Q8—22no—
617Q8—41no—
618Q8—41no—
619D4—348no—
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—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—172no—
639C2×C4—172no—
640C2×C4—172no—
641C2×C4—341no—
642C2×C4—341no—
643C2×C4—341no—
644C2×C4—341no—
645C2×C4—341no—
646C2×C4—341no—
647C2×C4—342no—
648C2×C4—342no—
649C2×C4—342no—
650C2×C4—342no—
651C2×C4—342no—
652C2×C4—342no—
653C2×C4—342no—
654C2×C4—688no—
655C2×C4—681no—
656C2×C4—681no—
657C2×C4—681no—
658C2×C4—681no—
659C2×C4—681no—
660C2×C4—681no—
661C2×C4—681no—
662C2×C4—681no—
663C2×C4—681no—
664C2×C4—1364no—
665C2×C4—1364no—
666C2×C4C22⋊C4×D1712yes—
667C2×C4C22×C4×D1711yescharacteristic
668C2×C4C2×D4×D1711yescharacteristic
669C2×C4C2×#6325411yescharacteristic
670C2×C4#1058769111yescharacteristic
671C2×C4#41×D1711yescharacteristic
672C2×C4#1058769711yescharacteristic
673C8—22no—
674C8—41no—
675C8—681no—
676C8—681no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—174no—
685C22—342no—
686C22—342no—
687C22—342no—
688C22—342no—
689C22—342no—
690C22—342no—
691C22C2×C22⋊C4×D1711yescharacteristic
692C22#1176344811yescharacteristic
693C22#1176345911yescharacteristic
694C22AGL(1,ℤ/8)×D1711yescharacteristic
695C22#137×D1711yescharacteristic
696C22#1176361811yescharacteristic
697C22#1176362511yescharacteristic
698C4—22no—
699C4—42no—
700C4—42no—
701C4—81no—
702C4—81no—
703C4—342no—
704C4—342no—
705C4—342no—
706C4—682no—
707C4—682no—
708C4—682no—
709C4—1361no—
710C4C4×#6325411yescharacteristic
711C4#1176328811yescharacteristic
712C4#1176344611yescharacteristic
713C4#1176345711yescharacteristic
714C2—42no—
715C2—344no—
716C2#1453161011yescharacteristic
717C2D17×#41711yescharacteristic
718C2#1453731611yescharacteristic
719C2#1454080011yescharacteristic
720C2#1454083011yescharacteristic
721C2#1454121911yescharacteristic
722C2#1454123411yescharacteristic
subgroupG/H
centerC23C2×D4×D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC17×#1894C2
socleC23×C17C22×D4
prime radicalC22×C22⋊D17D4
cosocleC22×C4×C17C24
hypercenter#1894D17
hypocenterC17#22491
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1894

Complements

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

NH ≅ G/Ntype
4. #14529751C2semidirect
5. #14529738C2semidirect
6. #14529204C2semidirect
7. #14529092C2semidirect
8. #14529088C2semidirect
9. #14528876C2semidirect
10. #14528869C2semidirect
11. #14528787C2semidirect
12. #14528616C2semidirect
13. #14528504C2semidirect
14. D17×#340C2semidirect
15. C17×#1894C2semidirect
18. #11763493C4semidirect
75. C17×C22⋊Q8C2×C4semidirect
85. #10587632C2×C4semidirect
87. Q8×Dic17C2×C4semidirect
94. #10587612C2×C4semidirect
124. C4⋊C4×D17C2×C4semidirect
126. #10587576C2×C4semidirect
321. #1894D17semidirect
448. C22⋊Q8C4×D17semidirect
503. C17#22491semidirect

Maximal subgroups

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

subgroupindex
C2×#117634932
C2×#117628782
#145316802
#145297512
#145297382
#145292042
#145290922
#145290882
#145288762
#145288692
#145287872
#145286162
#145285042
D17×#3402
C17×#18942
#2249117