Finite Group Databasebeta

← C2×#14528771 #17033718

Subgroups — C2×#14528771 #17033718

Order 4352.

2066 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×#11762667C212yesmaximal, complemented
4#14528771C218yesmaximal, 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×#63225—22no—
16C22×#63225C411yescharacteristic, complemented
17C22×C22⋊Dic17C2212yes—
18C22×#63227C411yescharacteristic, complemented
19C22×C4×Dic17C411yescharacteristic, complemented
20C2×#10587477—28no—
21C2×#10587477C2218yes—
22#11762667—24no—
23#11762667C2218yescomplemented
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—24no—
37C22×C22⋊D17C2×C412yes—
38C22×C22⋊D17D414yes—
39C22×C22⋊D17Q814yes—
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—24no—
59C2×C22⋊C4×C17—24no—
60C2×C22⋊C4×C17—22no—
61C2×C22⋊C4×C17C2×C412yes—
62C2×C22⋊C4×C17C2314yes—
63C2×C22⋊C4×C17C2312yes—
64C2×C22⋊Dic17—24no—
65C2×C22⋊Dic17—24no—
66C2×C22⋊Dic17—22no—
67C2×C22⋊Dic17C2314yes—
68C2×#63227—22no—
69C2×#63227—22no—
70C2×#63227C2×C414yescomplemented
71C2×#63225—22no—
72C2×#63225—22no—
73C2×#63225—28no—
74C2×#63225—48no—
75C2×#63225C2×C414yescomplemented
76C2×C4×Dic17—22no—
77C2×C4×Dic17—21no—
78C2×C4×Dic17—21no—
79C2×C4×Dic17C2×C414yescomplemented
80#10587567—28no—
81#10587567—28no—
82#10587567—28no—
83#10587567—28no—
84#10587502—28no—
85#10587477—216no—
86C24×C17—42no—
87C24×C17—42no—
88C24×C17C22×C411yescharacteristic
89C24×C17C22×C411yescharacteristic
90C24×C17C2×D412yes—
91C24×C17C2×D412yes—
92C24×C17C2×D412yes—
93C24×C17C2×Q812yes—
94C24×C17#4114yes—
95C24×C17C2411yescharacteristic
96C23×D17—21no—
97C23×D17—21no—
98C23×D17—22no—
99C23×D17—42no—
100C23×D17—42no—
101C23×D17C4⋊C414yescomplemented
102C23×D17C22×C412yes—
103C22×C4×C17—21no—
104C22×C4×C17—21no—
105C22×C4×C17—21no—
106C22×C4×C17—21no—
107C22×C4×C17—24no—
108C22×C4×C17—42no—
109C22×C4×C17—42no—
110C22×C4×C17—44no—
111C22×C4×C17—44no—
112C22×C4×C17—44no—
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—24no—
123C2×C22⋊D17C4⋊C418yescomplemented
124C2×C22⋊D17C2×D414yes—
125C2×C22⋊D17C2×Q814yes—
126C22×Dic17—21no—
127C22×Dic17—21no—
128C22×Dic17—22no—
129C22×Dic17—24no—
130C22×Dic17—28no—
131C22×Dic17—24no—
132C22×Dic17—44no—
133C22×Dic17—48no—
134C22×Dic17—44no—
135C22×Dic17—42no—
136C22×Dic17—44no—
137C22×Dic17—44no—
138C22×Dic17—44no—
139C22×Dic17—44no—
140C22×Dic17C22⋊C412yes—
141C22×Dic17C22⋊C411yescharacteristic
142C22×Dic17C22⋊C414yes—
143C22×Dic17C22⋊C412yes—
144C22×Dic17C22⋊C414yes—
145C22×Dic17C22⋊C412yes—
146C22×Dic17C22⋊C411yescharacteristic
147C22×Dic17C4⋊C414yescomplemented
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—24no—
161C22⋊C4×C17—24no—
162C22⋊C4×C17—24no—
163C22⋊C4×C17—44no—
164C22⋊Dic17—24no—
165C22⋊Dic17—24no—
166C22⋊Dic17—44no—
167#63227—28no—
168#63225—28no—
169#63225—416no—
170C4×Dic17—24no—
171C4×Dic17—24no—
172C2×#1799—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—44no—
182C23×C17—42no—
183C23×C17—44no—
184C23×C17—48no—
185C23×C17—41no—
186C23×C17C2×C22⋊C412yes—
187C23×C17C2×C22⋊C411yescharacteristic
188C23×C17C2×C22⋊C411yescharacteristic
189C23×C17C2×C4⋊C412yes—
190C23×C17C2×C4⋊C412yes—
191C23×C17#11712yes—
192C23×C17#11712yes—
193C23×C17#12114yes—
194C23×C17#12114yes—
195C23×C17C22⋊Q814yes—
196C23×C17C22⋊Q814yes—
197C23×C17C23×C411yescharacteristic
198C23×C17C22×D412yes—
199C23×C17C22×D411yescharacteristic
200C23×C17C22×Q811yescharacteristic
201C23×C17C2×#4112yes—
202C22×D17—22no—
203C22×D17—22no—
204C22×D17—24no—
205C22×D17—24no—
206C22×D17—42no—
207C22×D17—48no—
208C22×D17—42no—
209C22×D17—42no—
210C22×D17—42no—
211C22×D17—42no—
212C22×D17—48no—
213C22×D17—42no—
214C22×D17C2×C4⋊C414yescomplemented
215C2×C4×C17—22no—
216C2×C4×C17—22no—
217C2×C4×C17—42no—
218C2×C4×C17—42no—
219C2×C4×C17—42no—
220C2×C4×C17—42no—
221C2×C4×C17—42no—
222C2×C4×C17—42no—
223C2×C4×C17—44no—
224C2×C4×C17—44no—
225C2×C4×C17—44no—
226C2×C4×C17—88no—
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—44no—
241C2×Dic17—42no—
242C2×Dic17—42no—
243C2×Dic17—44no—
244C2×Dic17—44no—
245C2×Dic17—44no—
246C2×Dic17—44no—
247C2×Dic17—88no—
248C2×Dic17#9914yescomplemented
249C2×Dic17C2×C22⋊C412yes—
250C2×Dic17C2×C22⋊C414yes—
251C2×Dic17C2×C22⋊C412yes—
252C2×Dic17C2×C4⋊C414yescomplemented
253C4×D17—48no—
254C4×D17—48no—
255C22×C4×D4—171no—
256C22×#99—172no—
257C2×#380—172no—
258#1799—178no—
259C2×#342—171no—
260C2×#342D1711yescharacteristic, complemented
261C22×C17—28no—
262C22×C17—24no—
263C22×C17—24no—
264C22×C17—28no—
265C22×C17—22no—
266C22×C17—21no—
267C22×C17—21no—
268C22×C17—22no—
269C22×C17—22no—
270C22×C17—21no—
271C22×C17—21no—
272C22×C17—22no—
273C22×C17—42no—
274C22×C17—42no—
275C22×C17—44no—
276C22×C17—44no—
277C22×C17—41no—
278C22×C17—41no—
279C22×C17—42no—
280C22×C17#38012yes—
281C22×C17#38014yes—
282C22×C17#38012yes—
283C22×C17C2×#9912yes—
284C22×C17#41012yes—
285C22×C17C22×C22⋊C411yescharacteristic
286C22×C17C22×C4⋊C411yescharacteristic
287C22×C17C2×#11711yescharacteristic
288C22×C17C2×#12112yes—
289C22×C17C2×C22⋊Q812yes—
290C2×D17—24no—
291C2×D17—44no—
292C2×D17—48no—
293C2×D17—48no—
294C2×D17—42no—
295C2×D17—42no—
296C2×D17—44no—
297C4×C17—42no—
298C4×C17—42no—
299C4×C17—84no—
300Dic17—22no—
301Dic17—24no—
302Dic17—24no—
303Dic17—84no—
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×C4⋊C4—342no—
315C22×C22⋊C4—171no—
316C22×C22⋊C4—172no—
317C22×C22⋊C4C2×D1712yes—
318C22×C22⋊C4C2×D1711yescharacteristic
319C22×C42—171no—
320C2×#99—178no—
321C2×#99—348no—
322#380—178no—
323#380—344no—
324C2×#95—342no—
325#342—174no—
326#342C2×D1714yescomplemented
327C2×C17—22no—
328C2×C17—21no—
329C2×C17—21no—
330C2×C17—22no—
331C2×C17—22no—
332C2×C17—24no—
333C2×C17#179914yescomplemented
334C2×C17C2×#38011yescharacteristic
335C2×C17C22×#9911yescharacteristic
336C2×C17C2×#41011yescharacteristic
337D17—44no—
338C25—171no—
339C25C22×D1711yescharacteristic
340C22×D4—172no—
341C22×D4—174no—
342C22×D4—174no—
343C22×D4—172no—
344C22×D4—344no—
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×C4⋊C4—348no—
373C2×C4⋊C4—688no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—174no—
380C2×C22⋊C4—174no—
381C2×C22⋊C4—342no—
382C2×C22⋊C4—342no—
383C2×C22⋊C4—344no—
384C2×C22⋊C4—344no—
385C2×C22⋊C4—342no—
386C2×C22⋊C4C4×D1712yes—
387C2×C22⋊C4C22×D1714yes—
388C2×C22⋊C4C22×D1712yes—
389C2×C42—174no—
390C2×C42—342no—
391C2×C42—341no—
392C2×C42—341no—
393#99—3416no—
394#95—348no—
395C17C2×#179911yescharacteristic, complemented, Sylow
396C24—42no—
397C24—42no—
398C24—172no—
399C24—174no—
400C24—342no—
401C24—341no—
402C24—341no—
403C24—682no—
404C24—682no—
405C24C2×C4×D1711yescharacteristic
406C24C2×C4×D1711yescharacteristic
407C24#6325214yes—
408C24D4×D1712yes—
409C24D4×D1712yes—
410C24D4×D1712yes—
411C24Q8×D1712yes—
412C24C23×D1711yescharacteristic
413C2×D4—174no—
414C2×D4—174no—
415C2×D4—178no—
416C2×D4—344no—
417C2×D4—344no—
418C2×D4—344no—
419C2×D4—344no—
420C2×D4—348no—
421C2×D4—348no—
422C2×D4—348no—
423C2×D4—348no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—24no—
429C22×C4—42no—
430C22×C4—42no—
431C22×C4—44no—
432C22×C4—44no—
433C22×C4—44no—
434C22×C4—171no—
435C22×C4—172no—
436C22×C4—172no—
437C22×C4—174no—
438C22×C4—172no—
439C22×C4—174no—
440C22×C4—171no—
441C22×C4—172no—
442C22×C4—174no—
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—342no—
452C22×C4—341no—
453C22×C4—341no—
454C22×C4—344no—
455C22×C4—684no—
456C22×C4—688no—
457C22×C4—684no—
458C22×C4—688no—
459C22×C4—684no—
460C22×C4—688no—
461C22×C4—684no—
462C22×C4—684no—
463C22×C4—682no—
464C22×C4—684no—
465C22×C4—684no—
466C22×C4—684no—
467C22×C4C2×C4×D1712yes—
468C22×C4C2×C4×D1712yes—
469C4⋊C4—348no—
470C4⋊C4—6816no—
471C22⋊C4—24no—
472C22⋊C4—24no—
473C22⋊C4—24no—
474C22⋊C4—24no—
475C22⋊C4—44no—
476C22⋊C4—348no—
477C22⋊C4—344no—
478C22⋊C4—344no—
479C22⋊C4—684no—
480C42—344no—
481C42—344no—
482C23—24no—
483C23—22no—
484C23—24no—
485C23—22no—
486C23—41no—
487C23—42no—
488C23—41no—
489C23—41no—
490C23—48no—
491C23—44no—
492C23—42no—
493C23—44no—
494C23—41no—
495C23—174no—
496C23—342no—
497C23—342no—
498C23—344no—
499C23—344no—
500C23—682no—
501C23—688no—
502C23—682no—
503C23—682no—
504C23—688no—
505C23—682no—
506C23—682no—
507C23—682no—
508C23#1058755812yes—
509C23#1058755812yes—
510C23C22⋊C4×D1712yes—
511C23C22⋊C4×D1711yescharacteristic
512C23C22⋊C4×D1711yescharacteristic
513C23#1058757014yes—
514C23#1058757014yes—
515C23C4⋊C4×D1712yes—
516C23C4⋊C4×D1712yes—
517C23#1058758214yes—
518C23#1058758214yes—
519C23C22×C4×D1711yescharacteristic
520C23C2×#6325212yes—
521C23C2×D4×D1712yes—
522C23C2×D4×D1711yescharacteristic
523C23C2×Q8×D1711yescharacteristic
524D4—348no—
525D4—348no—
526D4—3416no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—44no—
536C2×C4—44no—
537C2×C4—44no—
538C2×C4—88no—
539C2×C4—172no—
540C2×C4—174no—
541C2×C4—172no—
542C2×C4—174no—
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—688no—
555C2×C4—688no—
556C2×C4—684no—
557C2×C4—684no—
558C2×C4—682no—
559C2×C4—682no—
560C2×C4—684no—
561C2×C4—684no—
562C2×C4—684no—
563C2×C4—1368no—
564C22—28no—
565C22—24no—
566C22—24no—
567C22—28no—
568C22—22no—
569C22—21no—
570C22—21no—
571C22—22no—
572C22—22no—
573C22—21no—
574C22—21no—
575C22—22no—
576C22—42no—
577C22—41no—
578C22—41no—
579C22—42no—
580C22—44no—
581C22—42no—
582C22—44no—
583C22—344no—
584C22—684no—
585C22—684no—
586C22—688no—
587C22—688no—
588C22—682no—
589C22—682no—
590C22#1176266812yes—
591C22#1176266814yes—
592C22#1176266812yes—
593C22#99×D1712yes—
594C22#1176278112yes—
595C22C2×C22⋊C4×D1711yescharacteristic
596C22C2×C4⋊C4×D1711yescharacteristic
597C22C2×#1058755811yescharacteristic
598C22C2×#1058757012yes—
599C22C2×#1058758212yes—
600C4—42no—
601C4—42no—
602C4—84no—
603C4—174no—
604C4—342no—
605C4—344no—
606C4—344no—
607C4—1364no—
608C2—22no—
609C2—21no—
610C2—21no—
611C2—22no—
612C2—22no—
613C2—24no—
614C2—684no—
615C2#1452877114yesdirect product factor
616C2C2×#1176266811yescharacteristic
617C2C2×#99×D1711yescharacteristic
618C2C2×#1176278111yescharacteristic
subgroupG/H
centerC23C22⋊C4×D17
commutatorC23×C17C23×C4
FrattiniC24C23×D17
FittingC2×C17×#342C2
socleC23×C17C2×C22⋊C4
prime radicalC23×C22⋊D17C22
cosocleC24×C17C24
hypercenterC2×#342D17
hypocenterC17C2×#1799
LCSG ▷ C23×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×#11762667C2semidirect
4. #14528771C2direct (N × H)
5. C2×#11762576C2semidirect
6. C2×C17×#342C2semidirect
9. C23×C4×D17C4semidirect
13. C2×#10587567C4semidirect
16. C22×#63225C4semidirect
18. C22×#63227C4semidirect
19. C22×C4×Dic17C4semidirect
23. #11762667C22semidirect
25. #11762576C22semidirect
28. C17×#342C22semidirect
55. C22×C4×D17C2×C4semidirect
70. C2×#63227C2×C4semidirect
75. C2×#63225C2×C4semidirect
79. C2×C4×Dic17C2×C4semidirect
101. C23×D17C4⋊C4semidirect
123. C2×C22⋊D17C4⋊C4semidirect
147. C22×Dic17C4⋊C4semidirect
214. C22×D17C2×C4⋊C4semidirect
248. C2×Dic17#99semidirect
252. C2×Dic17C2×C4⋊C4semidirect
260. C2×#342D17semidirect
304. Dic17C2×#99semidirect
326. #342C2×D17semidirect
333. C2×C17#1799semidirect
395. C17C2×#1799semidirect
615. C2#14528771direct (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×#117626672
#145287712
C2×#117625762
C2×C17×#3422
C2×#179917