Finite Group Databasebeta

← C2×#14528571 #17031969

Subgroups — C2×#14528571 #17031969

Order 4352.

2242 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587567C211yesmaximal, characteristic
2C22×#10587477C212yesmaximal
3C2×C22⋊C4×Dic17C212yesmaximal, complemented
4#14528571C218yesmaximal, direct product factor
5C2×#11762576C211yesmaximal, characteristic, complemented
6C2×C17×#342C211yesmaximal, characteristic, complemented
7C23×C22⋊D17C2211yescharacteristic
8C24×Dic17C2211yescharacteristic
9C23×C4×D17C411yescharacteristic, complemented
10C2×#10587567—22no—
11C2×#10587567—22no—
12C2×#10587567—24no—
13C2×#10587567C414yescomplemented
14C2×#10587567C2214yes—
15C22×#63225C411yescharacteristic, complemented
16C22×C22⋊Dic17C2212yes—
17C22×#63227C411yescharacteristic, complemented
18C22×C4×Dic17—22no—
19C22×C4×Dic17C411yescharacteristic, complemented
20C2×#10587477C4116yescomplemented
21C2×#10587477C2218yes—
22C22⋊C4×Dic17—24no—
23C22⋊C4×Dic17C2218yescomplemented
24C2×#10587502—22no—
25#11762576C2214yescomplemented
26C22×C22⋊C4×C17C2212yes—
27C22×C22⋊C4×C17C2211yescharacteristic
28C17×#342C2214yescomplemented
29C25×C17C2311yescharacteristic
30C24×D17C2×C411yescharacteristic
31C23×C4×C17—22no—
32C23×C4×C17C2×C411yescharacteristic
33C23×C4×C17C2×C411yescharacteristic
34C22×C22⋊D17—22no—
35C22×C22⋊D17—22no—
36C22×C22⋊D17—22no—
37C22×C22⋊D17—22no—
38C22×C22⋊D17C2×C418yes—
39C22×C22⋊D17C2×C412yes—
40C22×C22⋊D17C2312yes—
41C23×Dic17—22no—
42C23×Dic17—44no—
43C23×Dic17C2×C411yescharacteristic
44C23×Dic17C2×C411yescharacteristic
45C23×Dic17C2×C411yescharacteristic
46C23×Dic17C2×C412yes—
47C23×Dic17D412yes—
48C23×Dic17D412yes—
49C23×Dic17D414yes—
50C23×Dic17C2312yes—
51C22×C4×D17—21no—
52C22×C4×D17—22no—
53C22×C4×D17—21no—
54C22×C4×D17—44no—
55C22×C4×D17C2×C414yescomplemented
56C2×C22⋊C4×C17—22no—
57C2×C22⋊C4×C17—22no—
58C2×C22⋊C4×C17—22no—
59C2×C22⋊C4×C17—24no—
60C2×C22⋊C4×C17C2×C412yes—
61C2×C22⋊C4×C17C2×C418yescomplemented
62C2×C22⋊C4×C17C2312yes—
63C2×C22⋊C4×C17C2314yes—
64C2×C22⋊Dic17—22no—
65C2×C22⋊Dic17—24no—
66C2×C22⋊Dic17C2×C418yescomplemented
67C2×C22⋊Dic17C2314yes—
68C2×#63227—22no—
69C2×#63227—22no—
70C2×#63227C2×C414yescomplemented
71C2×#63225—22no—
72C2×#63225—22no—
73C2×#63225C2×C414yescomplemented
74C2×C4×Dic17—22no—
75C2×C4×Dic17—21no—
76C2×C4×Dic17—21no—
77C2×C4×Dic17—28no—
78C2×C4×Dic17—48no—
79C2×C4×Dic17C2×C414yescomplemented
80#10587567—28no—
81#10587567—28no—
82#10587567—28no—
83#10587567—28no—
84#10587502—28no—
85#10587477C2×C4132yescomplemented
86C24×C17—42no—
87C24×C17—42no—
88C24×C17C22×C411yescharacteristic
89C24×C17C22×C411yescharacteristic
90C24×C17C22×C414yes—
91C24×C17C2×D412yes—
92C24×C17C2×D412yes—
93C24×C17#4112yes—
94C24×C17#4112yes—
95C24×C17C2411yescharacteristic
96C23×D17—21no—
97C23×D17—21no—
98C23×D17—22no—
99C23×D17—42no—
100C23×D17—42no—
101C23×D17C4214yescomplemented
102C23×D17C22×C412yes—
103C22×C4×C17—21no—
104C22×C4×C17—21no—
105C22×C4×C17—21no—
106C22×C4×C17—21no—
107C22×C4×C17—28no—
108C22×C4×C17—24no—
109C22×C4×C17—44no—
110C22×C4×C17—44no—
111C22×C4×C17—42no—
112C22×C4×C17—42no—
113C22×C4×C17C22×C412yes—
114C22×C4×C17C22×C412yes—
115C2×C22⋊D17—24no—
116C2×C22⋊D17—24no—
117C2×C22⋊D17—28no—
118C2×C22⋊D17—28no—
119C2×C22⋊D17—28no—
120C2×C22⋊D17—28no—
121C2×C22⋊D17—24no—
122C2×C22⋊D17—22no—
123C2×C22⋊D17—22no—
124C2×C22⋊D17C4218yescomplemented
125C2×C22⋊D17C22×C418yes—
126C22×Dic17—21no—
127C22×Dic17—21no—
128C22×Dic17—22no—
129C22×Dic17—24no—
130C22×Dic17—28no—
131C22×Dic17—28no—
132C22×Dic17—24no—
133C22×Dic17—44no—
134C22×Dic17—48no—
135C22×Dic17—44no—
136C22×Dic17—42no—
137C22×Dic17—44no—
138C22×Dic17—44no—
139C22×Dic17—44no—
140C22×Dic17C4214yescomplemented
141C22×Dic17C22⋊C412yes—
142C22×Dic17C22⋊C411yescharacteristic
143C22×Dic17C22⋊C414yes—
144C22×Dic17C22⋊C412yes—
145C22×Dic17C22⋊C414yes—
146C22×Dic17C22⋊C412yes—
147C22×Dic17C22⋊C411yescharacteristic
148C22×Dic17C22×C412yes—
149C22×Dic17C22×C412yes—
150C22×Dic17C22×C412yes—
151C22×Dic17C2×D414yes—
152C22×Dic17C2×D414yes—
153C2×C4×D17—24no—
154C2×C4×D17—24no—
155C2×C4×D17—44no—
156C2×C4×D17—48no—
157C2×C4×D17—44no—
158C2×C4×D17—48no—
159C22⋊C4×C17—24no—
160C22⋊C4×C17—28no—
161C22⋊C4×C17—24no—
162C22⋊C4×C17—24no—
163C22⋊C4×C17C22×C418yescomplemented
164C22⋊Dic17—28no—
165C22⋊Dic17—24no—
166C22⋊Dic17C22×C418yescomplemented
167#63227—28no—
168#63225—28no—
169C4×Dic17—24no—
170C4×Dic17—24no—
171C4×Dic17—416no—
172C2×C4×#99—171nomaximal, Sylow
173C23×C17—24no—
174C23×C17—22no—
175C23×C17—24no—
176C23×C17—22no—
177C23×C17—41no—
178C23×C17—42no—
179C23×C17—41no—
180C23×C17—41no—
181C23×C17—48no—
182C23×C17—42no—
183C23×C17—44no—
184C23×C17—44no—
185C23×C17—41no—
186C23×C17C2×C4212yes—
187C23×C17C2×C4212yes—
188C23×C17C2×C22⋊C412yes—
189C23×C17C2×C22⋊C411yescharacteristic
190C23×C17C2×C22⋊C411yescharacteristic
191C23×C17#11712yes—
192C23×C17#11712yes—
193C23×C17C4×D414yes—
194C23×C17C4×D414yes—
195C23×C17C4×D414yes—
196C23×C17C4×D414yes—
197C23×C17C23×C411yescharacteristic
198C23×C17C23×C412yes—
199C23×C17C22×D412yes—
200C23×C17C2×#4111yescharacteristic
201C23×C17C2×#4111yescharacteristic
202C22×D17—22no—
203C22×D17—22no—
204C22×D17—24no—
205C22×D17—24no—
206C22×D17—42no—
207C22×D17—42no—
208C22×D17—48no—
209C22×D17—42no—
210C22×D17—42no—
211C22×D17—42no—
212C22×D17—48no—
213C22×D17—42no—
214C22×D17C2×C4214yescomplemented
215C2×C4×C17—22no—
216C2×C4×C17—22no—
217C2×C4×C17—28no—
218C2×C4×C17—42no—
219C2×C4×C17—44no—
220C2×C4×C17—416no—
221C2×C4×C17—42no—
222C2×C4×C17—44no—
223C2×C4×C17—42no—
224C2×C4×C17—42no—
225C2×C4×C17—42no—
226C2×C4×C17—42no—
227C22⋊D17—28no—
228C22⋊D17—28no—
229C22⋊D17—216no—
230C2×Dic17—22no—
231C2×Dic17—22no—
232C2×Dic17—24no—
233C2×Dic17—24no—
234C2×Dic17—22no—
235C2×Dic17—24no—
236C2×Dic17—24no—
237C2×Dic17—24no—
238C2×Dic17—28no—
239C2×Dic17—28no—
240C2×Dic17—28no—
241C2×Dic17—44no—
242C2×Dic17—42no—
243C2×Dic17—42no—
244C2×Dic17—44no—
245C2×Dic17—44no—
246C2×Dic17—416no—
247C2×Dic17—44no—
248C2×Dic17#9914yescomplemented
249C2×Dic17C2×C4214yescomplemented
250C2×Dic17C2×C22⋊C412yes—
251C2×Dic17C2×C22⋊C414yes—
252C2×Dic17C2×C22⋊C412yes—
253C4×D17—48no—
254C4×D17—48no—
255C22×C4×D4—171no—
256C22×#99—172no—
257C2×C4×C22⋊C4—172no—
258C4×#99—178no—
259C2×#342—171no—
260C2×#342D1711yescharacteristic, complemented
261C22×C17—22no—
262C22×C17—21no—
263C22×C17—21no—
264C22×C17—22no—
265C22×C17—22no—
266C22×C17—21no—
267C22×C17—21no—
268C22×C17—22no—
269C22×C17—28no—
270C22×C17—28no—
271C22×C17—24no—
272C22×C17—24no—
273C22×C17—42no—
274C22×C17—42no—
275C22×C17—44no—
276C22×C17—44no—
277C22×C17—42no—
278C22×C17—41no—
279C22×C17—41no—
280C22×C17C4×C22⋊C412yes—
281C22×C17C4×C22⋊C414yes—
282C22×C17C4×C22⋊C412yes—
283C22×C17C2×#9912yes—
284C22×C17#41012yes—
285C22×C17C22×C4211yescharacteristic
286C22×C17C22×C22⋊C411yescharacteristic
287C22×C17C2×#11711yescharacteristic
288C22×C17C2×C4×D412yes—
289C22×C17C2×C4×D412yes—
290C2×D17—24no—
291C2×D17—44no—
292C2×D17—48no—
293C2×D17—42no—
294C2×D17—42no—
295C2×D17—48no—
296C2×D17—44no—
297C4×C17—48no—
298C4×C17—42no—
299C4×C17—42no—
300Dic17—22no—
301Dic17—24no—
302Dic17—24no—
303Dic17—48no—
304Dic17C2×#9914yescomplemented
305C23×D4—171no—
306C24×C4—171no—
307C24×C4—171no—
308C2×C4×D4—174no—
309C2×C4×D4—174no—
310C2×C4×D4—342no—
311C2×C4×D4—342no—
312C2×C4×D4—344no—
313C22×C4⋊C4—171no—
314C22×C22⋊C4—172no—
315C22×C22⋊C4—171no—
316C22×C22⋊C4C2×D1711yescharacteristic
317C22×C22⋊C4C2×D1712yes—
318C22×C42—171no—
319C22×C42—342no—
320C2×#99—1716no—
321C2×#99—178no—
322C4×C22⋊C4—178no—
323C4×C22⋊C4—344no—
324C2×#95—342no—
325#342—174no—
326#342C2×D1714yescomplemented
327C2×C17—22no—
328C2×C17—22no—
329C2×C17—21no—
330C2×C17—22no—
331C2×C17—21no—
332C2×C17—24no—
333C2×C17C4×#9914yescomplemented
334C2×C17C2×C4×C22⋊C411yescharacteristic
335C2×C17C22×#9911yescharacteristic
336C2×C17C2×#41011yescharacteristic
337D17—44no—
338C25—171no—
339C25C22×D1711yescharacteristic
340C22×D4—172no—
341C22×D4—178no—
342C22×D4—172no—
343C22×D4—342no—
344C22×D4—342no—
345C22×D4—342no—
346C22×D4—342no—
347C23×C4—22no—
348C23×C4—171no—
349C23×C4—171no—
350C23×C4—172no—
351C23×C4—171no—
352C23×C4—172no—
353C23×C4—172no—
354C23×C4—174no—
355C23×C4—172no—
356C23×C4—174no—
357C23×C4—342no—
358C23×C4—341no—
359C23×C4—341no—
360C23×C4—342no—
361C23×C4—684no—
362C23×C4—684no—
363C23×C4C4×D1711yescharacteristic
364C23×C4C4×D1711yescharacteristic
365C4×D4—348no—
366C4×D4—348no—
367C4×D4—348no—
368C4×D4—348no—
369C2×C4⋊C4—174no—
370C2×C4⋊C4—342no—
371C2×C4⋊C4—342no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—178no—
377C2×C22⋊C4—174no—
378C2×C22⋊C4—174no—
379C2×C22⋊C4—342no—
380C2×C22⋊C4—342no—
381C2×C22⋊C4—342no—
382C2×C22⋊C4—344no—
383C2×C22⋊C4C4×D1712yes—
384C2×C22⋊C4C4×D1718yescomplemented
385C2×C22⋊C4C22×D1712yes—
386C2×C22⋊C4C22×D1714yes—
387C2×C42—174no—
388C2×C42—342no—
389C2×C42—341no—
390C2×C42—341no—
391C2×C42—348no—
392C2×C42—688no—
393#99—1732no—
394#95—348no—
395C17C2×C4×#9911yescharacteristic, complemented, Sylow
396C24—42no—
397C24—42no—
398C24—172no—
399C24—174no—
400C24—341no—
401C24—341no—
402C24—342no—
403C24—682no—
404C24—682no—
405C24C2×C4×D1711yescharacteristic
406C24C2×C4×D1711yescharacteristic
407C24C2×C4×D1714yes—
408C24D4×D1712yes—
409C24D4×D1712yes—
410C24#6325412yes—
411C24#6325612yes—
412C24C23×D1711yescharacteristic
413C2×D4—178no—
414C2×D4—178no—
415C2×D4—344no—
416C2×D4—342no—
417C2×D4—342no—
418C2×D4—344no—
419C2×D4—348no—
420C2×D4—348no—
421C2×D4—344no—
422C2×D4—348no—
423C2×D4—348no—
424C22×C4—24no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—28no—
430C22×C4—44no—
431C22×C4—44no—
432C22×C4—42no—
433C22×C4—42no—
434C22×C4—171no—
435C22×C4—172no—
436C22×C4—172no—
437C22×C4—174no—
438C22×C4—174no—
439C22×C4—172no—
440C22×C4—174no—
441C22×C4—171no—
442C22×C4—172no—
443C22×C4—172no—
444C22×C4—174no—
445C22×C4—172no—
446C22×C4—174no—
447C22×C4—344no—
448C22×C4—344no—
449C22×C4—348no—
450C22×C4—344no—
451C22×C4—341no—
452C22×C4—341no—
453C22×C4—342no—
454C22×C4—344no—
455C22×C4—348no—
456C22×C4—684no—
457C22×C4—688no—
458C22×C4—684no—
459C22×C4—688no—
460C22×C4—684no—
461C22×C4—688no—
462C22×C4—684no—
463C22×C4—684no—
464C22×C4—682no—
465C22×C4—684no—
466C22×C4—684no—
467C22×C4C2×C4×D1712yes—
468C22×C4C2×C4×D1712yes—
469C4⋊C4—348no—
470C22⋊C4—24no—
471C22⋊C4—24no—
472C22⋊C4—24no—
473C22⋊C4—28no—
474C22⋊C4—178no—
475C22⋊C4—348no—
476C22⋊C4—344no—
477C22⋊C4—348no—
478C22⋊C4C2×C4×D1718yescomplemented
479C42—344no—
480C42—344no—
481C42—6816no—
482C23—24no—
483C23—22no—
484C23—24no—
485C23—22no—
486C23—41no—
487C23—42no—
488C23—41no—
489C23—41no—
490C23—48no—
491C23—42no—
492C23—44no—
493C23—44no—
494C23—41no—
495C23—174no—
496C23—342no—
497C23—342no—
498C23—344no—
499C23—344no—
500C23—682no—
501C23—682no—
502C23—688no—
503C23—682no—
504C23—682no—
505C23—688no—
506C23—682no—
507C23—682no—
508C23C42×D1712yes—
509C23C42×D1712yes—
510C23C22⋊C4×D1712yes—
511C23C22⋊C4×D1711yescharacteristic
512C23C22⋊C4×D1711yescharacteristic
513C23#1058756714yes—
514C23#1058756714yes—
515C23#1058757812yes—
516C23#1058757812yes—
517C23#1058757914yes—
518C23#1058757914yes—
519C23C22×C4×D1711yescharacteristic
520C23C22×C4×D1712yes—
521C23C2×D4×D1712yes—
522C23C2×#6325411yescharacteristic
523C23C2×#6325611yescharacteristic
524D4—348no—
525D4—348no—
526D4—3416no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—28no—
530C2×C4—44no—
531C2×C4—42no—
532C2×C4—44no—
533C2×C4—416no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—172no—
540C2×C4—174no—
541C2×C4—174no—
542C2×C4—172no—
543C2×C4—174no—
544C2×C4—348no—
545C2×C4—344no—
546C2×C4—344no—
547C2×C4—348no—
548C2×C4—342no—
549C2×C4—342no—
550C2×C4—342no—
551C2×C4—344no—
552C2×C4—344no—
553C2×C4—344no—
554C2×C4—348no—
555C2×C4—688no—
556C2×C4—688no—
557C2×C4—684no—
558C2×C4—684no—
559C2×C4—682no—
560C2×C4—682no—
561C2×C4—684no—
562C2×C4—684no—
563C2×C4—6816no—
564C22—22no—
565C22—21no—
566C22—21no—
567C22—22no—
568C22—22no—
569C22—21no—
570C22—21no—
571C22—22no—
572C22—28no—
573C22—28no—
574C22—24no—
575C22—24no—
576C22—42no—
577C22—41no—
578C22—41no—
579C22—42no—
580C22—44no—
581C22—42no—
582C22—44no—
583C22—344no—
584C22—684no—
585C22—684no—
586C22—688no—
587C22—682no—
588C22—682no—
589C22—688no—
590C22#1176265612yes—
591C22#1176265614yes—
592C22#1176265612yes—
593C22#99×D1712yes—
594C22#1176278112yes—
595C22C2×C42×D1711yescharacteristic
596C22C2×C22⋊C4×D1711yescharacteristic
597C22C2×#1058757811yescharacteristic
598C22C2×#1058756712yes—
599C22C2×#1058757912yes—
600C4—48no—
601C4—42no—
602C4—42no—
603C4—174no—
604C4—342no—
605C4—344no—
606C4—344no—
607C4—688no—
608C2—22no—
609C2—22no—
610C2—21no—
611C2—21no—
612C2—22no—
613C2—24no—
614C2—684no—
615C2#1452857114yesdirect product factor
616C2C2×#1176265611yescharacteristic
617C2C2×#99×D1711yescharacteristic
618C2C2×#1176278111yescharacteristic
subgroupG/H
centerC23C22⋊C4×D17
commutatorC22×C17C22×C42
FrattiniC24C23×D17
FittingC2×C17×#342C2
socleC23×C17C2×C22⋊C4
prime radicalC23×C22⋊D17C22
cosocleC24×C17C24
hypercenterC2×#342D17
hypocenterC17C2×C4×#99
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C25 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
3. C2×C22⋊C4×Dic17C2semidirect
4. #14528571C2direct (N × H)
5. C2×#11762576C2semidirect
6. C2×C17×#342C2semidirect
9. C23×C4×D17C4semidirect
13. C2×#10587567C4semidirect
15. C22×#63225C4semidirect
17. C22×#63227C4semidirect
19. C22×C4×Dic17C4semidirect
20. C2×#10587477C4semidirect
23. C22⋊C4×Dic17C22semidirect
25. #11762576C22semidirect
28. C17×#342C22semidirect
55. C22×C4×D17C2×C4semidirect
61. C2×C22⋊C4×C17C2×C4semidirect
66. C2×C22⋊Dic17C2×C4semidirect
70. C2×#63227C2×C4semidirect
73. C2×#63225C2×C4semidirect
79. C2×C4×Dic17C2×C4semidirect
85. #10587477C2×C4semidirect
101. C23×D17C42semidirect
124. C2×C22⋊D17C42semidirect
140. C22×Dic17C42semidirect
163. C22⋊C4×C17C22×C4semidirect
166. C22⋊Dic17C22×C4semidirect
214. C22×D17C2×C42semidirect
248. C2×Dic17#99semidirect
249. C2×Dic17C2×C42semidirect
260. C2×#342D17semidirect
304. Dic17C2×#99semidirect
326. #342C2×D17semidirect
333. C2×C17C4×#99semidirect
384. C2×C22⋊C4C4×D17semidirect
395. C17C2×C4×#99semidirect
478. C22⋊C4C2×C4×D17semidirect
615. C2#14528571direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#105875672
C22×#105874772
C2×C22⋊C4×Dic172
#145285712
C2×#117625762
C2×C17×#3422
C2×C4×#9917