Finite Group Databasebeta

← C2×#14532553 #17202353

Subgroups — C2×#14532553 #17202353

Order 4352.

2550 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587574C211yesmaximal, characteristic
2C22×#10587573C211yesmaximal, characteristic
3#14532553C2116yesmaximal, direct product factor
4C2×#11762750C211yesmaximal, characteristic
5C2×#11762747C211yesmaximal, characteristic
6C2×#11762742C211yesmaximal, characteristic
7C2×#11762713C211yesmaximal, characteristic
8C2×#11762713C211yesmaximal, characteristic
9C2×#11762713C211yesmaximal, characteristic
10C2×#11762704C211yesmaximal, characteristic
11C2×#11762695C211yesmaximal, characteristic
12C2×#11762694C211yesmaximal, characteristic
13C2×#11762692C211yesmaximal, characteristic
14C2×#11762690C211yesmaximal, characteristic
15C2×C4⋊C4×Dic17C211yesmaximal, characteristic
16C2×C17×#398C211yesmaximal, characteristic
17C23×Dic34C2211yescharacteristic
18C23×Dic34C2211yescharacteristic
19C2×#10587574—28no—
20C2×#10587574C2218yes—
21C2×#10587573—28no—
22C2×#10587573C2218yes—
23C22×C4⋊Dic17C2211yescharacteristic
24C22×C4⋊Dic17C2211yescharacteristic
25C22×#63225C2211yescharacteristic
26C22×#63225C2211yescharacteristic
27C22×#63225C2211yescharacteristic
28C22×#63225C2211yescharacteristic
29C22×#63225C2211yescharacteristic
30C22×#63225C2211yescharacteristic
31C22×C4×Dic17C2211yescharacteristic
32C22×C4×Dic17C2211yescharacteristic
33C22×C4×Dic17C2211yescharacteristic
34C22×C4×Dic17C2211yescharacteristic
35C22×C4×Dic17C2211yescharacteristic
36#11762750C2218yes—
37#11762747C2218yes—
38#11762742C2218yes—
39#11762713C2218yes—
40#11762713C2218yes—
41#11762713C2218yes—
42#11762704C2218yes—
43#11762695C2218yes—
44#11762694C2218yes—
45#11762692C2218yes—
46#11762690C2218yes—
47C4⋊C4×Dic17C2218yes—
48C2×#10587502C2211yescharacteristic
49C2×#10587502C2211yescharacteristic
50C2×#10587502C2211yescharacteristic
51C2×#10587502C2211yescharacteristic
52C2×#10587502C2211yescharacteristic
53C2×#10587502C2211yescharacteristic
54C2×#10587502C2211yescharacteristic
55C2×#10587502C2211yescharacteristic
56C2×#10587502C2211yescharacteristic
57C2×#10587502C2211yescharacteristic
58C2×#10587502C2211yescharacteristic
59C2×#10587502C2211yescharacteristic
60C2×#10587502C2211yescharacteristic
61C22×C4⋊C4×C17C2211yescharacteristic
62C22×C4⋊C4×C17C2211yescharacteristic
63C22×C4⋊C4×C17C2211yescharacteristic
64C22×C4⋊C4×C17C2211yescharacteristic
65C17×#398C2218yes—
66C2×C17×#95C2211yescharacteristic
67C2×C17×#95C2211yescharacteristic
68C2×C17×#95C2211yescharacteristic
69C23×C4×C17C2311yescharacteristic
70C23×C4×C17C2311yescharacteristic
71C23×C4×C17C2311yescharacteristic
72C23×C4×C17C2311yescharacteristic
73C23×C4×C17C2311yescharacteristic
74C23×C4×C17C2311yescharacteristic
75C23×C4×C17C2311yescharacteristic
76C23×Dic17C2311yescharacteristic
77C23×Dic17C2311yescharacteristic
78C23×Dic17C2311yescharacteristic
79C23×Dic17C2311yescharacteristic
80C23×Dic17C2311yescharacteristic
81C23×Dic17C2311yescharacteristic
82C23×Dic17C2311yescharacteristic
83C23×Dic17C2311yescharacteristic
84C22×Dic34—24no—
85C22×Dic34—24no—
86C22×Dic34—24no—
87C22×Dic34—24no—
88C22×Dic34—24no—
89C22×Dic34D418yes—
90C22×Dic34C2314yes—
91C22×Dic34C2314yes—
92C2×C4⋊C4×C17—24no—
93C2×C4⋊C4×C17—24no—
94C2×C4⋊C4×C17—24no—
95C2×C4⋊C4×C17—24no—
96C2×C4⋊C4×C17C2314yes—
97C2×C4⋊C4×C17C2314yes—
98C2×C4⋊C4×C17C2314yes—
99C2×C4⋊C4×C17C2314yes—
100C2×C4⋊Dic17—24no—
101C2×C4⋊Dic17Q818yescomplemented
102C2×C4⋊Dic17C2314yes—
103C2×C4⋊Dic17C2314yes—
104C2×#63225—24no—
105C2×#63225—24no—
106C2×#63225—24no—
107C2×#63225—24no—
108C2×#63225—24no—
109C2×#63225—24no—
110C2×#63225C2314yes—
111C2×#63225C2314yes—
112C2×#63225C2314yes—
113C2×#63225C2314yes—
114C2×#63225C2314yes—
115C2×#63225C2314yes—
116C2×C4×Dic17—24no—
117C2×C4×Dic17—24no—
118C2×C4×Dic17—24no—
119C2×C4×Dic17—24no—
120C2×C4×Dic17—24no—
121C2×C4×Dic17C2314yes—
122C2×C4×Dic17C2314yes—
123C2×C4×Dic17C2314yes—
124C2×C4×Dic17C2314yes—
125C2×C4×Dic17C2314yes—
126#10587574—232no—
127#10587573—232no—
128C17×#95C2314yes—
129C17×#95C2314yes—
130C17×#95C2314yes—
131#10587502C2314yes—
132#10587502C2314yes—
133#10587502C2314yes—
134#10587502C2314yes—
135#10587502C2314yes—
136#10587502C2314yes—
137#10587502C2314yes—
138#10587502C2314yes—
139#10587502C2314yes—
140#10587502C2314yes—
141#10587502C2314yes—
142#10587502C2314yes—
143#10587502C2314yes—
144C24×C17C2411yescharacteristic
145C22×C4×C17—22no—
146C22×C4×C17—22no—
147C22×C4×C17—22no—
148C22×C4×C17—22no—
149C22×C4×C17—22no—
150C22×C4×C17—22no—
151C22×C4×C17—22no—
152C22×C4×C17—22no—
153C22×C4×C17—22no—
154C22×C4×C17—22no—
155C22×C4×C17—22no—
156C22×C4×C17—22no—
157C22×C4×C17—22no—
158C22×C4×C17—22no—
159C22×C4×C17—22no—
160C22×C4×C17—22no—
161C22×C4×C17—22no—
162C22×C4×C17—22no—
163C22×C4×C17C2×D414yes—
164C22×C4×C17C2×Q814yes—
165C22×C4×C17#4114yes—
166C22×C4×C17C2412yes—
167C22×C4×C17C2412yes—
168C22×C4×C17C2412yes—
169C22×C4×C17C2412yes—
170C22×C4×C17C2412yes—
171C22×C4×C17C2412yes—
172C22×C4×C17C2412yes—
173C22×Dic17—22no—
174C22×Dic17—22no—
175C22×Dic17—22no—
176C22×Dic17—22no—
177C22×Dic17—22no—
178C22×Dic17—22no—
179C22×Dic17—22no—
180C22×Dic17—22no—
181C22×Dic17—22no—
182C22×Dic17—22no—
183C22×Dic17—22no—
184C22×Dic17—22no—
185C22×Dic17—22no—
186C22×Dic17—22no—
187C22×Dic17—22no—
188C22×Dic17—22no—
189C22×Dic17—22no—
190C22×Dic17—22no—
191C22×Dic17C2×D414yes—
192C22×Dic17C2×D414yes—
193C22×Dic17C2×Q814yes—
194C22×Dic17C2×Q814yes—
195C22×Dic17#4114yes—
196C22×Dic17#4114yes—
197C22×Dic17C2412yes—
198C22×Dic17C2412yes—
199C22×Dic17C2412yes—
200C22×Dic17C2412yes—
201C22×Dic17C2412yes—
202C22×Dic17C2412yes—
203C22×Dic17C2412yes—
204C22×Dic17C2412yes—
205C2×Dic34—232no—
206C2×Dic34—28no—
207C2×Dic34—28no—
208C2×Dic34—28no—
209C2×Dic34—28no—
210C2×Dic34—28no—
211C2×Dic34—416no—
212C2×Dic34C2×D4116yes—
213C4⋊C4×C17—28no—
214C4⋊C4×C17—28no—
215C4⋊C4×C17—28no—
216C4⋊C4×C17—28no—
217C4⋊Dic17—28no—
218C4⋊Dic17C2×Q8116yescomplemented
219#63225—28no—
220#63225—28no—
221#63225—28no—
222#63225—28no—
223#63225—28no—
224#63225—28no—
225C4×Dic17—28no—
226C4×Dic17—28no—
227C4×Dic17—28no—
228C4×Dic17—28no—
229C4×Dic17—28no—
230C2×#2446—171nomaximal, Sylow
231C23×C17C22×D412yes—
232C23×C17C22×Q812yes—
233C23×C17C2×#4112yes—
234C23×C17C2×#4112yes—
235C23×C17C2×#4112yes—
236C23×C172−1+412yes—
237C23×C172−1+412yes—
238C23×C17C2511yescharacteristic
239C2×C4×C17—28no—
240C2×C4×C17—28no—
241C2×C4×C17—28no—
242C2×C4×C17—22no—
243C2×C4×C17—22no—
244C2×C4×C17—22no—
245C2×C4×C17—22no—
246C2×C4×C17—22no—
247C2×C4×C17—22no—
248C2×C4×C17—22no—
249C2×C4×C17—22no—
250C2×C4×C17—22no—
251C2×C4×C17—22no—
252C2×C4×C17—22no—
253C2×C4×C17—22no—
254C2×C4×C17—22no—
255C2×C4×C17—22no—
256C2×C4×C17—22no—
257C2×C4×C17—22no—
258C2×C4×C17—22no—
259C2×C4×C17—22no—
260C2×C4×C17—44no—
261C2×C4×C17—44no—
262C2×C4×C17—44no—
263C2×C4×C17—44no—
264C2×C4×C17C22×D414yes—
265C2×C4×C17C22×Q814yes—
266C2×C4×C17C2×#4114yes—
267C2×Dic17—28no—
268C2×Dic17—28no—
269C2×Dic17—28no—
270C2×Dic17—22no—
271C2×Dic17—22no—
272C2×Dic17—22no—
273C2×Dic17—22no—
274C2×Dic17—22no—
275C2×Dic17—22no—
276C2×Dic17—22no—
277C2×Dic17—22no—
278C2×Dic17—22no—
279C2×Dic17—22no—
280C2×Dic17—22no—
281C2×Dic17—22no—
282C2×Dic17—22no—
283C2×Dic17—22no—
284C2×Dic17—22no—
285C2×Dic17—22no—
286C2×Dic17—22no—
287C2×Dic17—22no—
288C2×Dic17—44no—
289C2×Dic17—44no—
290C2×Dic17—44no—
291C2×Dic17—44no—
292C2×Dic17#123116yes—
293C2×Dic17C22×D414yes—
294C2×Dic17C22×D414yes—
295C2×Dic17C22×Q814yes—
296C2×Dic17C22×Q814yes—
297C2×Dic17C2×#4114yes—
298C2×Dic17C2×#4114yes—
299Dic34—232no—
300Dic34—416no—
301C22×C4⋊Q8—171no—
302C22×C4×Q8—171no—
303#2446—1716no—
304C2×#400—171no—
305C2×#400—171no—
306C2×#398—171no—
307C2×#398D1711yescharacteristic
308C2×#391—171no—
309C2×#391—171no—
310C2×#391—171no—
311C2×#389—171no—
312C2×#387—171no—
313C2×#387—171no—
314C2×#387—171no—
315C2×#387—171no—
316C2×C4×C4⋊C4—171no—
317C22×C17C2×#12314yes—
318C22×C17#53314yes—
319C22×C17#54114yes—
320C22×C17#54814yes—
321C22×C17D4×Q814yes—
322C22×C17#55614yes—
323C22×C17#55714yes—
324C22×C17C23×D411yescharacteristic
325C22×C17C23×Q811yescharacteristic
326C22×C17C22×#4111yescharacteristic
327C22×C17C22×#4111yescharacteristic
328C22×C17C22×#4111yescharacteristic
329C22×C17C2×2−1+411yescharacteristic
330C22×C17C2×2−1+411yescharacteristic
331C4×C17—24no—
332C4×C17—24no—
333C4×C17—24no—
334C4×C17—42no—
335C4×C17—42no—
336C4×C17—42no—
337C4×C17—42no—
338Dic17—24no—
339Dic17—24no—
340Dic17—24no—
341Dic17—42no—
342Dic17—42no—
343Dic17—42no—
344Dic17—42no—
345Dic17C2×#12318yes—
346C23×Q8—171no—
347C23×Q8—171no—
348C2×C4⋊Q8—178no—
349C2×C4⋊Q8—348no—
350C2×C4×Q8—178no—
351C2×C4×Q8—348no—
352C22×C4⋊C4—171no—
353C22×C4⋊C4—171no—
354C22×C4⋊C4—171no—
355C22×C4⋊C4—171no—
356C22×C4⋊C4—171no—
357C22×C4⋊C4—171no—
358C22×C4⋊C4—171no—
359C22×C4⋊C4—171no—
360C22×C4⋊C4C2×D1711yescharacteristic
361C22×C4⋊C4C2×D1711yescharacteristic
362C22×C4⋊C4C2×D1711yescharacteristic
363C22×C4⋊C4C2×D1711yescharacteristic
364C22×C42—171no—
365C22×C42—171no—
366C22×C42—171no—
367C22×C42—171no—
368C22×C42—171no—
369#400—178no—
370#400—178no—
371#398—178no—
372#398C2×D1718yes—
373#391—178no—
374#391—178no—
375#391—178no—
376#389—178no—
377#387—178no—
378#387—178no—
379#387—178no—
380#387—178no—
381C4×C4⋊C4—178no—
382C2×#95—171no—
383C2×#95—171no—
384C2×#95—171no—
385C2×#95—171no—
386C2×#95—171no—
387C2×#95—171no—
388C2×#95—171no—
389C2×#95—171no—
390C2×#95—171no—
391C2×#95—171no—
392C2×#95—171no—
393C2×#95—171no—
394C2×#95—171no—
395C2×#95C2×D1711yescharacteristic
396C2×#95C2×D1711yescharacteristic
397C2×#95C2×D1711yescharacteristic
398C2×C17#244618yescomplemented
399C2×C17C22×#12311yescharacteristic
400C2×C17C2×#53311yescharacteristic
401C2×C17C2×#54111yescharacteristic
402C2×C17C2×#54811yescharacteristic
403C2×C17C2×D4×Q811yescharacteristic
404C2×C17C2×#55611yescharacteristic
405C2×C17C2×#55711yescharacteristic
406C22×Q8—178no—
407C22×Q8—174no—
408C22×Q8—174no—
409C22×Q8—344no—
410C22×Q8—344no—
411C22×Q8—344no—
412C22×Q8—344no—
413C22×Q8—344no—
414C23×C4—171no—
415C23×C4—171no—
416C23×C4—171no—
417C23×C4—171no—
418C23×C4—171no—
419C23×C4—171no—
420C23×C4—171no—
421C23×C4—171no—
422C23×C4C22×D1711yescharacteristic
423C23×C4C22×D1711yescharacteristic
424C23×C4C22×D1711yescharacteristic
425C23×C4C22×D1711yescharacteristic
426C23×C4C22×D1711yescharacteristic
427C23×C4C22×D1711yescharacteristic
428C23×C4C22×D1711yescharacteristic
429C4⋊Q8—3432no—
430C4×Q8—3432no—
431C2×C4⋊C4—24no—
432C2×C4⋊C4—24no—
433C2×C4⋊C4—24no—
434C2×C4⋊C4—24no—
435C2×C4⋊C4—178no—
436C2×C4⋊C4—174no—
437C2×C4⋊C4—174no—
438C2×C4⋊C4—174no—
439C2×C4⋊C4—174no—
440C2×C4⋊C4—174no—
441C2×C4⋊C4—174no—
442C2×C4⋊C4—174no—
443C2×C4⋊C4—174no—
444C2×C4⋊C4—344no—
445C2×C4⋊C4—344no—
446C2×C4⋊C4—344no—
447C2×C4⋊C4—344no—
448C2×C4⋊C4—344no—
449C2×C4⋊C4—344no—
450C2×C4⋊C4—344no—
451C2×C4⋊C4C22×D1714yes—
452C2×C4⋊C4C22×D1714yes—
453C2×C4⋊C4C22×D1714yes—
454C2×C4⋊C4C22×D1714yes—
455C2×C42—174no—
456C2×C42—174no—
457C2×C42—174no—
458C2×C42—174no—
459C2×C42—174no—
460C2×C42—344no—
461C2×C42—344no—
462C2×C42—344no—
463C2×C42—344no—
464C2×C42—344no—
465#95—174no—
466#95—174no—
467#95—174no—
468#95—174no—
469#95—174no—
470#95—174no—
471#95—174no—
472#95—174no—
473#95—174no—
474#95—174no—
475#95—174no—
476#95—174no—
477#95—174no—
478#95C22×D1714yes—
479#95C22×D1714yes—
480#95C22×D1714yes—
481C17C2×#244611yescharacteristic, complemented, Sylow
482C24C23×D1711yescharacteristic
483C2×Q8—1716no—
484C2×Q8—3432no—
485C2×Q8—348no—
486C2×Q8—348no—
487C2×Q8—348no—
488C2×Q8—348no—
489C2×Q8—348no—
490C2×Q8—6816no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—174no—
510C22×C4—174no—
511C22×C4—174no—
512C22×C4—172no—
513C22×C4—174no—
514C22×C4—174no—
515C22×C4—174no—
516C22×C4—172no—
517C22×C4—172no—
518C22×C4—172no—
519C22×C4—172no—
520C22×C4—172no—
521C22×C4—172no—
522C22×C4—172no—
523C22×C4—342no—
524C22×C4—342no—
525C22×C4—342no—
526C22×C4—342no—
527C22×C4—342no—
528C22×C4—342no—
529C22×C4—342no—
530C22×C4—342no—
531C22×C4—342no—
532C22×C4—342no—
533C22×C4—342no—
534C22×C4—342no—
535C22×C4—342no—
536C22×C4—342no—
537C22×C4—342no—
538C22×C4—342no—
539C22×C4—342no—
540C22×C4—342no—
541C22×C4D4×D1714yes—
542C22×C4#6325414yes—
543C22×C4Q8×D1714yes—
544C22×C4C23×D1712yes—
545C22×C4C23×D1712yes—
546C22×C4C23×D1712yes—
547C22×C4C23×D1712yes—
548C22×C4C23×D1712yes—
549C22×C4C23×D1712yes—
550C22×C4C23×D1712yes—
551C4⋊C4—28no—
552C4⋊C4—28no—
553C4⋊C4—28no—
554C4⋊C4—28no—
555C4⋊C4—1716no—
556C4⋊C4—348no—
557C4⋊C4—348no—
558C4⋊C4—348no—
559C4⋊C4—348no—
560C4⋊C4—348no—
561C4⋊C4—348no—
562C4⋊C4—348no—
563C42—348no—
564C42—348no—
565C42—348no—
566C42—348no—
567C42—348no—
568C23C2×D4×D1712yes—
569C23C2×#6325412yes—
570C23C2×Q8×D1712yes—
571C23#1058769412yes—
572C23#41×D1712yes—
573C23#41×D1712yes—
574C23#1058769712yes—
575C23C24×D1711yescharacteristic
576Q8—3432no—
577Q8—6816no—
578C2×C4—28no—
579C2×C4—28no—
580C2×C4—28no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—44no—
600C2×C4—44no—
601C2×C4—44no—
602C2×C4—44no—
603C2×C4—1716no—
604C2×C4—174no—
605C2×C4—174no—
606C2×C4—174no—
607C2×C4—174no—
608C2×C4—174no—
609C2×C4—174no—
610C2×C4—348no—
611C2×C4—348no—
612C2×C4—348no—
613C2×C4—342no—
614C2×C4—342no—
615C2×C4—342no—
616C2×C4—342no—
617C2×C4—342no—
618C2×C4—342no—
619C2×C4—342no—
620C2×C4—342no—
621C2×C4—342no—
622C2×C4—342no—
623C2×C4—342no—
624C2×C4—342no—
625C2×C4—342no—
626C2×C4—342no—
627C2×C4—342no—
628C2×C4—342no—
629C2×C4—342no—
630C2×C4—342no—
631C2×C4—684no—
632C2×C4—684no—
633C2×C4—684no—
634C2×C4—684no—
635C2×C4C2×D4×D1714yes—
636C2×C4C2×#6325414yes—
637C2×C4C2×Q8×D1714yes—
638C22#123×D1714yes—
639C22#1176336114yes—
640C22#1176341814yes—
641C22#1176346514yes—
642C22#1176347414yes—
643C22#1176353014yes—
644C22#1176353614yes—
645C22C22×D4×D1711yescharacteristic
646C22C22×Q8×D1711yescharacteristic
647C22C2×#41×D1711yescharacteristic
648C22C2×#41×D1711yescharacteristic
649C22C22×#6325411yescharacteristic
650C22C2×#1058769711yescharacteristic
651C22C2×#1058769411yescharacteristic
652C4—24no—
653C4—24no—
654C4—24no—
655C4—42no—
656C4—42no—
657C4—42no—
658C4—42no—
659C4—178no—
660C4—344no—
661C4—344no—
662C4—344no—
663C4—682no—
664C4—682no—
665C4—682no—
666C4—682no—
667C2#1453255318yesdirect product factor
668C2C2×#123×D1711yescharacteristic
669C2C2×#1176336111yescharacteristic
670C2C2×#1176341811yescharacteristic
671C2C2×#1176346511yescharacteristic
672C2C2×#1176347411yescharacteristic
673C2C2×#1176353011yescharacteristic
674C2C2×#1176353611yescharacteristic
subgroupG/H
centerC24C23×D17
commutator, cosocleC23×C17C25
FrattiniC23C24×D17
FittingC2×C17×#398C2
socle, prime radicalC24×C17C24
hypercenterC2×#398D17
hypocenterC17C2×#2446
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
3. #14532553C2direct (N × H)
101. C2×C4⋊Dic17Q8semidirect
218. C4⋊Dic17C2×Q8semidirect
398. C2×C17#2446semidirect
481. C17C2×#2446semidirect
667. C2#14532553direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#105875742
C22×#105875732
#145325532
C2×#117627502
C2×#117627472
C2×#117627422
C2×#117627132
C2×#117627042
C2×#117626952
C2×#117626942
C2×#117626922
C2×#117626902
C2×C4⋊C4×Dic172
C2×C17×#3982
C2×#244617