Finite Group Databasebeta

← C2×#14530237 #17063245

Subgroups — C2×#14530237 #17063245

Order 4352.

906 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762837C211yesmaximal, characteristic, complemented
2C2×#11762826C211yesmaximal, characteristic
3C2×#11762805C211yesmaximal, characteristic
4#14530237C218yesmaximal, direct product factor
5C2×#11762581C211yesmaximal, characteristic, complemented
6C2×#11762573C211yesmaximal, characteristic, complemented
7C2×#11762566C211yesmaximal, characteristic, complemented
8C2×C17×#413C211yesmaximal, characteristic
9C22×#63223C2211yescharacteristic
10C23×#3622C2211yescharacteristic
11C2×#10587612C2211yescharacteristic
12C2×#10587612C2211yescharacteristic
13#11762837—22no—
14#11762837C2214yescomplemented
15C2×#10587485—22no—
16#11762826—22no—
17#11762826C2214yes—
18C2×#10587508—22no—
19#11762805—22no—
20#11762805C2214yes—
21C2×#10587506—21no—
22C2×#10587503—21no—
23#11762581C2214yescomplemented
24#11762573C2214yescomplemented
25#11762566C2214yescomplemented
26C22×#41×C17C2211yescharacteristic
27C22×M16×C17C2211yescharacteristic
28C22×M16×C17C2211yescharacteristic
29C17×#413—22no—
30C17×#413C2214yes—
31C2×C17×#101—21no—
32C2×C17×#100—21no—
33C2×#41×C17—21no—
34C2×#41×C17—21no—
35C2×#41×C17—21no—
36C2×#41×C17—21no—
37C2×#41×C17—21no—
38C2×#41×C17—21no—
39C2×#41×C17—21no—
40C2×#41×C17—21no—
41C2×#41×C17—21no—
42C2×#41×C17—21no—
43C2×#41×C17D412yes—
44C2×#41×C17C2312yes—
45C22×Q8×C17D411yescharacteristic
46C22×D4×C17—21no—
47C22×D4×C17D411yescharacteristic
48C23×C4×C17—21no—
49C23×C4×C17C2311yescharacteristic
50C2×M16×C17—21no—
51C2×M16×C17—21no—
52C2×M16×C17—21no—
53C2×M16×C17—21no—
54C2×M16×C17—21no—
55C2×M16×C17—21no—
56C2×M16×C17—21no—
57C2×M16×C17—21no—
58C2×M16×C17—21no—
59C2×M16×C17—21no—
60C2×M16×C17C2312yes—
61C2×M16×C17C2312yes—
62C22×C8×C17—21no—
63C22×C8×C17—21no—
64C2×C22⋊Dic17—21no—
65C2×C22⋊Dic17—21no—
66#10587612—21no—
67#10587612—21no—
68#10587612—21no—
69#10587612—21no—
70#10587612—21no—
71#10587612D412yes—
72#10587612C2312yes—
73#10587612C2312yes—
74C2×C4⋊Dic17—21no—
75C2×C4⋊Dic17—21no—
76C2×C4×Dic17—21no—
77C2×C4×Dic17D412yes—
78C2×#63223—21no—
79C2×#63223—21no—
80C2×#63223—21no—
81C2×#63223—21no—
82C2×#63223—21no—
83C2×#63223C2312yes—
84C22×#3622—21no—
85C22×#3622—21no—
86C22×#3622—21no—
87C22×#3622—21no—
88C22×#3622—21no—
89C22×#3622—21no—
90C22×#3622—21no—
91C22×#3622C2312yes—
92C17×#101—24no—
93C17×#100—24no—
94#10587508—28no—
95#10587506—24no—
96#10587503—24no—
97#10587485—28no—
98C24×C17—21no—
99C24×C17#4111yescharacteristic
100#41×C17—22no—
101#41×C17—22no—
102#41×C17—22no—
103#41×C17—22no—
104#41×C17—22no—
105#41×C17—22no—
106#41×C17—22no—
107#41×C17—22no—
108#41×C17—41no—
109#41×C17—41no—
110#41×C17—41no—
111#41×C17—41no—
112#41×C17—41no—
113#41×C17—41no—
114#41×C17—41no—
115#41×C17—41no—
116C2×Q8×C17—21no—
117C2×Q8×C17—21no—
118C2×Q8×C17—21no—
119C2×Q8×C17—21no—
120C2×Q8×C17—21no—
121C2×Q8×C17C2×D412yes—
122C2×D4×C17—22no—
123C2×D4×C17—22no—
124C2×D4×C17—21no—
125C2×D4×C17—21no—
126C2×D4×C17—21no—
127C2×D4×C17—21no—
128C2×D4×C17—21no—
129C2×D4×C17—41no—
130C2×D4×C17—41no—
131C2×D4×C17—41no—
132C2×D4×C17—41no—
133C2×D4×C17C2×D412yes—
134C22×C4×C17—21no—
135C22×C4×C17—22no—
136C22×C4×C17—22no—
137C22×C4×C17—41no—
138C22×C4×C17—41no—
139C22×C4×C17—41no—
140C22×C4×C17—41no—
141C22×C4×C17C2×D411yescharacteristic
142C22×C4×C17C2×D411yescharacteristic
143C22×C4×C17C2×D411yescharacteristic
144C22×C4×C17C2×D411yescharacteristic
145C22×C4×C17#4111yescharacteristic
146C22×C4×C17#4111yescharacteristic
147C22×C4×C17#4111yescharacteristic
148C22×C4×C17#4111yescharacteristic
149C22×C4×C17#4111yescharacteristic
150C22×C4×C17#4111yescharacteristic
151C22×C4×C17#4111yescharacteristic
152C22×C4×C17#4111yescharacteristic
153C22×C4×C17#4111yescharacteristic
154C22×C4×C17C2411yescharacteristic
155C22×Dic17—22no—
156C22×Dic17—41no—
157M16×C17—22no—
158M16×C17—22no—
159M16×C17—22no—
160M16×C17—22no—
161M16×C17—41no—
162M16×C17—41no—
163M16×C17—41no—
164M16×C17—41no—
165C2×C8×C17—22no—
166C2×C8×C17—22no—
167C2×C8×C17—41no—
168C2×C8×C17—41no—
169C2×C8×C17—41no—
170C2×C8×C17—41no—
171C22⋊Dic17—22no—
172C22⋊Dic17—22no—
173C22⋊Dic17—22no—
174C22⋊Dic17—41no—
175C4⋊Dic17—22no—
176C4⋊Dic17—22no—
177C4⋊Dic17—22no—
178C4⋊Dic17—41no—
179C4×Dic17—22no—
180C4×Dic17—22no—
181C4×Dic17—41no—
182C4×Dic17C2×D414yes—
183#63223—22no—
184#63223—22no—
185#63223—41no—
186#63223—41no—
187C2×#3622—22no—
188C2×#3622—22no—
189C2×#3622—22no—
190C2×#3622—22no—
191C2×#3622—41no—
192C2×#3622—41no—
193C2×#3622—41no—
194C2×#3622—41no—
195C2×#3622—41no—
196C2×#3622—41no—
197C2×#2080—171nomaximal, Sylow
198C23×C17—22no—
199C23×C17—42no—
200C23×C17—41no—
201C23×C17—41no—
202C23×C17—82no—
203C23×C17#12311yescharacteristic
204C23×C17#12311yescharacteristic
205C23×C17#12311yescharacteristic
206C23×C17#12311yescharacteristic
207C23×C17#12611yescharacteristic
208C23×C17#12611yescharacteristic
209C23×C17C2×#4111yescharacteristic
210Q8×C17—22no—
211Q8×C17—22no—
212Q8×C17—41no—
213Q8×C17—41no—
214D4×C17—22no—
215D4×C17—22no—
216D4×C17—42no—
217D4×C17—42no—
218D4×C17—42no—
219D4×C17—42no—
220D4×C17—41no—
221D4×C17—41no—
222C2×C4×C17—22no—
223C2×C4×C17—41no—
224C2×C4×C17—41no—
225C2×C4×C17—42no—
226C2×C4×C17—42no—
227C2×C4×C17—42no—
228C2×C4×C17—42no—
229C2×C4×C17#12111yescharacteristic
230C2×C4×C17#12111yescharacteristic
231C2×C4×C17#12111yescharacteristic
232C2×C4×C17#12111yescharacteristic
233C2×C4×C17#12311yescharacteristic
234C2×C4×C17#12311yescharacteristic
235C2×C4×C17#12311yescharacteristic
236C2×C4×C17#12311yescharacteristic
237C2×C4×C17#12311yescharacteristic
238C2×C4×C17#12311yescharacteristic
239C2×C4×C17#12311yescharacteristic
240C2×C4×C17#12311yescharacteristic
241C2×C4×C17#12411yescharacteristic
242C2×C4×C17#12411yescharacteristic
243C2×C4×C17#12411yescharacteristic
244C2×C4×C17#12411yescharacteristic
245C2×C4×C17#12611yescharacteristic
246C2×C4×C17#12611yescharacteristic
247C2×C4×C17#12611yescharacteristic
248C2×C4×C17#12611yescharacteristic
249C2×C4×C17#12611yescharacteristic
250C2×C4×C17#12611yescharacteristic
251C2×C4×C17C22×D411yescharacteristic
252C2×C4×C17C22×D411yescharacteristic
253C2×C4×C17C2×#4111yescharacteristic
254C2×C4×C17C2×#4111yescharacteristic
255C2×C4×C17C2×#4111yescharacteristic
256C2×C4×C17C2×#4111yescharacteristic
257C2×Dic17—24no—
258C2×Dic17—44no—
259C2×Dic17—42no—
260C2×Dic17—82no—
261C8×C17—42no—
262C8×C17—42no—
263#3622—42no—
264#3622—42no—
265C2×#424—171no—
266C2×#421—171no—
267C2×#416—171no—
268C2×#413D1711yescharacteristic
269#2080—178no—
270C2×#344—171no—
271C2×#341—171no—
272C2×H(3,ℤ/4)—171no—
273C22×C17—22no—
274C22×C17—22no—
275C22×C17—22no—
276C22×C17—41no—
277C22×C17—41no—
278C22×C17—41no—
279C22×C17—41no—
280C22×C17—42no—
281C22×C17—82no—
282C22×C17—82no—
283C22×C17—82no—
284C22×C17#39711yescharacteristic
285C22×C17#39711yescharacteristic
286C22×C17#39711yescharacteristic
287C22×C17#39711yescharacteristic
288C22×C17C2×#12311yescharacteristic
289C22×C17C2×#12311yescharacteristic
290C22×C17C2×#12611yescharacteristic
291C4×C17—42no—
292C4×C17#39711yescharacteristic
293C4×C17#39711yescharacteristic
294C4×C17#39711yescharacteristic
295C4×C17#39711yescharacteristic
296C4×C17C2×#12111yescharacteristic
297C4×C17C2×#12311yescharacteristic
298C4×C17C2×#12411yescharacteristic
299C4×C17C2×#12611yescharacteristic
300Dic17—44no—
301Dic17—82no—
302C22×#41C2×D1711yescharacteristic
303C22×M16—171no—
304C22×M16C2×D1711yescharacteristic
305C22×M16C2×D1711yescharacteristic
306C23×C8—171no—
307C2×#117—171no—
308C2×#117—171no—
309#424—174no—
310#424—342no—
311C2×C4⋊C8—342no—
312#421—174no—
313#421—342no—
314C2×#104—342no—
315#416—174no—
316#416—342no—
317C2×#103—341no—
318C2×#102—341no—
319#413—22no—
320#413C2×D1714yes—
321C2×#101—21no—
322C2×#100—21no—
323#344—174no—
324#341—174no—
325H(3,ℤ/4)—174no—
326C2×C17—21no—
327C2×C17—21no—
328C2×C17—21no—
329C2×C17—21no—
330C2×C17—21no—
331C2×C17—21no—
332C2×C17—82no—
333C2×C17#208012yescomplemented
334C2×C17C2×#39711yescharacteristic
335C2×#41—21no—
336C2×#41—21no—
337C2×#41—21no—
338C2×#41—21no—
339C2×#41—21no—
340C2×#41—21no—
341C2×#41—21no—
342C2×#41—21no—
343C2×#41—21no—
344C2×#41—21no—
345C2×#41C22⋊D1712yes—
346C2×#41C22×D1712yes—
347C22×Q8C22⋊D1711yescharacteristic
348C22×D4—21no—
349C22×D4C22⋊D1711yescharacteristic
350C23×C4—21no—
351C23×C4C22×D1711yescharacteristic
352C2×M16—21no—
353C2×M16—21no—
354C2×M16—21no—
355C2×M16—21no—
356C2×M16—21no—
357C2×M16—21no—
358C2×M16—21no—
359C2×M16—21no—
360C2×M16—21no—
361C2×M16—21no—
362C2×M16—172no—
363C2×M16—341no—
364C2×M16—341no—
365C2×M16—341no—
366C2×M16—341no—
367C2×M16—341no—
368C2×M16C22×D1712yes—
369C2×M16C22×D1712yes—
370C22×C8—21no—
371C22×C8—21no—
372C22×C8—172no—
373C22×C8—341no—
374C22×C8—341no—
375C22×C8—341no—
376C22×C8—341no—
377C22×C8—341no—
378C22×C8—341no—
379C22×C8—341no—
380#117—172no—
381#117—172no—
382#117—172no—
383#117—341no—
384#117—341no—
385#117—341no—
386#117—341no—
387#117—341no—
388C2×C4⋊C4—341no—
389C2×C4⋊C4—341no—
390C2×C22⋊C4—341no—
391C2×C22⋊C4—341no—
392C2×C42—172no—
393C2×C42—341no—
394C4⋊C8—348no—
395#104—348no—
396#103—344no—
397#102—344no—
398#101—24no—
399#100—24no—
400C17C2×#208011yescharacteristic, complemented, Sylow
401C24—21no—
402C24#6325211yescharacteristic
403#41—22no—
404#41—22no—
405#41—22no—
406#41—22no—
407#41—22no—
408#41—22no—
409#41—22no—
410#41—22no—
411#41—41no—
412#41—41no—
413#41—41no—
414#41—41no—
415#41—41no—
416#41—41no—
417#41—41no—
418#41—41no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8C2×C22⋊D1712yes—
425C2×D4—22no—
426C2×D4—22no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—41no—
433C2×D4—41no—
434C2×D4—41no—
435C2×D4—41no—
436C2×D4C2×C22⋊D1712yes—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—342no—
445C22×C4—681no—
446C22×C4#6325211yescharacteristic
447C22×C4#6325211yescharacteristic
448C22×C4#6325211yescharacteristic
449C22×C4D4×D1711yescharacteristic
450C22×C4D4×D1711yescharacteristic
451C22×C4#6325411yescharacteristic
452C22×C4#6325411yescharacteristic
453C22×C4#6325411yescharacteristic
454C22×C4#6325411yescharacteristic
455C22×C4#6325411yescharacteristic
456C22×C4#6325411yescharacteristic
457C22×C4C2×C22⋊D1711yescharacteristic
458C22×C4C2×C22⋊D1711yescharacteristic
459C22×C4C23×D1711yescharacteristic
460M16—22no—
461M16—22no—
462M16—22no—
463M16—22no—
464M16—41no—
465M16—41no—
466M16—41no—
467M16—41no—
468M16—342no—
469M16—342no—
470M16—681no—
471M16—681no—
472C2×C8—22no—
473C2×C8—22no—
474C2×C8—41no—
475C2×C8—41no—
476C2×C8—41no—
477C2×C8—41no—
478C2×C8—342no—
479C2×C8—342no—
480C2×C8—342no—
481C2×C8—342no—
482C2×C8—681no—
483C2×C8—681no—
484C2×C8—681no—
485C2×C8—681no—
486C2×C8—681no—
487C2×C8—681no—
488C4⋊C4—342no—
489C4⋊C4—342no—
490C4⋊C4—342no—
491C4⋊C4—681no—
492C22⋊C4—342no—
493C22⋊C4—342no—
494C22⋊C4—342no—
495C22⋊C4—681no—
496C42—174no—
497C42—342no—
498C42—342no—
499C42—681no—
500C23—22no—
501C23—42no—
502C23—41no—
503C23—41no—
504C23—82no—
505C23#1058756511yescharacteristic
506C23#1058756511yescharacteristic
507C23#1058756911yescharacteristic
508C23#1058756911yescharacteristic
509C23#1058761511yescharacteristic
510C23#1058761511yescharacteristic
511C23C2×#6325211yescharacteristic
512Q8—22no—
513Q8—22no—
514Q8—41no—
515Q8—41no—
516D4—22no—
517D4—22no—
518D4—42no—
519D4—42no—
520D4—42no—
521D4—42no—
522D4—41no—
523D4—41no—
524C2×C4—22no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—344no—
532C2×C4—684no—
533C2×C4—682no—
534C2×C4—1362no—
535C2×C4#1058756511yescharacteristic
536C2×C4#1058756511yescharacteristic
537C2×C4#1058756511yescharacteristic
538C2×C4#1058756511yescharacteristic
539C2×C4#1058756511yescharacteristic
540C2×C4#1058756511yescharacteristic
541C2×C4#1058756911yescharacteristic
542C2×C4#1058756911yescharacteristic
543C2×C4#1058757111yescharacteristic
544C2×C4#1058757111yescharacteristic
545C2×C4#1058757111yescharacteristic
546C2×C4#1058757111yescharacteristic
547C2×C4#1058761511yescharacteristic
548C2×C4#1058761511yescharacteristic
549C2×C4#1058762111yescharacteristic
550C2×C4#1058762111yescharacteristic
551C2×C4#1058762111yescharacteristic
552C2×C4#1058762111yescharacteristic
553C2×C4#1058762511yescharacteristic
554C2×C4#1058762511yescharacteristic
555C2×C4#1058762511yescharacteristic
556C2×C4#1058762511yescharacteristic
557C2×C4C2×#6325211yescharacteristic
558C2×C4C2×D4×D1711yescharacteristic
559C2×C4C2×#6325411yescharacteristic
560C2×C4C2×#6325411yescharacteristic
561C2×C4C2×#6325411yescharacteristic
562C2×C4C22×C22⋊D1711yescharacteristic
563C8—42no—
564C8—42no—
565C8—682no—
566C8—682no—
567C22—22no—
568C22—22no—
569C22—22no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—42no—
575C22—82no—
576C22—82no—
577C22—82no—
578C22#1176273711yescharacteristic
579C22#1176273711yescharacteristic
580C22#1176273711yescharacteristic
581C22#1176273711yescharacteristic
582C22C2×#1058756911yescharacteristic
583C22C2×#1058761511yescharacteristic
584C22C2×#1058756511yescharacteristic
585C4—42no—
586C4—684no—
587C4—1362no—
588C4#1176273711yescharacteristic
589C4#1176273711yescharacteristic
590C4#1176273711yescharacteristic
591C4#1176273711yescharacteristic
592C4C2×#1058762511yescharacteristic
593C4C2×#1058762111yescharacteristic
594C4C2×#1058757111yescharacteristic
595C4C2×#1058756511yescharacteristic
596C2—21no—
597C2—21no—
598C2—21no—
599C2—21no—
600C2—21no—
601C2—21no—
602C2—82no—
603C2#1453023712yesdirect product factor
604C2C2×#1176273711yescharacteristic
subgroupG/H
centerC2×C4#10587571
commutator, cosocleC22×C4×C17C24
FrattiniC22×C4C23×D17
FittingC2×C17×#413C2
socleC22×C17#397
prime radicalC22×#41×C17C22
hypercenterC2×#413D17
hypocenterC17C2×#2080
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#413

Complements

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

NH ≅ G/Ntype
1. C2×#11762837C2semidirect
4. #14530237C2direct (N × H)
5. C2×#11762581C2semidirect
6. C2×#11762573C2semidirect
7. C2×#11762566C2semidirect
14. #11762837C22semidirect
23. #11762581C22semidirect
24. #11762573C22semidirect
25. #11762566C22semidirect
333. C2×C17#2080semidirect
400. C17C2×#2080semidirect
603. C2#14530237direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117628372
C2×#117628262
C2×#117628052
#145302372
C2×#117625812
C2×#117625732
C2×#117625662
C2×C17×#4132
C2×#208017