Finite Group Databasebeta

← C2×#14533081 #17203841

Subgroups — C2×#14533081 #17203841

Order 4352.

3070 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587612C211yesmaximal, characteristic, complemented
2#14533081C2116yesmaximal, direct product factor
3C2×#11762737C212yesmaximal, complemented
4C2×#11762723C212yesmaximal
5C2×#11762707C211yesmaximal, characteristic, complemented
6C2×#11762707C211yesmaximal, characteristic, complemented
7C2×#11762697C212yesmaximal, complemented
8C2×#11762690C212yesmaximal, complemented
9C2×#11762669C211yesmaximal, characteristic, complemented
10C2×#11762669C211yesmaximal, characteristic, complemented
11C2×#11762669C211yesmaximal, characteristic, complemented
12C22×C4×D4×C17C211yesmaximal, characteristic
13C2×#10587612—28no—
14C2×#10587612C2218yescomplemented
15C22×C4⋊Dic17C2211yescharacteristic
16C22×C4⋊Dic17C2211yescharacteristic
17C22×C4⋊Dic17C2211yescharacteristic
18C22×C4⋊Dic17C2211yescharacteristic
19C22×#63225C2212yes—
20C22×#63225C2212yes—
21C22×C22⋊Dic17C2212yes—
22C22×C22⋊Dic17C2212yes—
23C22×C22⋊Dic17C2212yes—
24C22×C22⋊Dic17C2212yes—
25C22×C4×Dic17C2212yes—
26#11762737C22116yescomplemented
27#11762723C22116yes—
28#11762707C2218yescomplemented
29#11762707C2218yescomplemented
30#11762697C22116yescomplemented
31#11762690C22116yescomplemented
32#11762669C2218yescomplemented
33#11762669C2218yescomplemented
34#11762669C2218yescomplemented
35C2×#10587502C2212yes—
36C2×#10587502C2212yes—
37C2×#10587502C2212yes—
38C2×#10587502C2212yes—
39C2×#10587502C2212yes—
40C23×D4×C17C2211yescharacteristic
41C24×C4×C17C2211yescharacteristic
42C24×C4×C17C2211yescharacteristic
43C2×C4×D4×C17—28no—
44C2×C4×D4×C17C2218yes—
45C22×C4⋊C4×C17C2211yescharacteristic
46C22×C22⋊C4×C17C2211yescharacteristic
47C22×C22⋊C4×C17C2211yescharacteristic
48C22×C42×C17C2211yescharacteristic
49C25×C17C2311yescharacteristic
50C25×C17C2311yescharacteristic
51C22×D4×C17—24no—
52C22×D4×C17—24no—
53C22×D4×C17—24no—
54C22×D4×C17C2314yes—
55C23×C4×C17—24no—
56C23×C4×C17—24no—
57C23×C4×C17—24no—
58C23×C4×C17—24no—
59C23×C4×C17—24no—
60C23×C4×C17D418yes—
61C23×C4×C17C2311yescharacteristic
62C23×C4×C17C2311yescharacteristic
63C23×C4×C17C2314yes—
64C23×C4×C17C2311yescharacteristic
65C23×C4×C17C2314yes—
66C23×C4×C17C2311yescharacteristic
67C23×C4×C17C2311yescharacteristic
68C23×Dic17C2312yes—
69C23×Dic17C2312yes—
70C23×Dic17C2312yes—
71C23×Dic17C2312yes—
72C4×D4×C17—232no—
73C2×C4⋊C4×C17—24no—
74C2×C4⋊C4×C17C2314yes—
75C2×C22⋊C4×C17—24no—
76C2×C22⋊C4×C17—24no—
77C2×C22⋊C4×C17C2314yes—
78C2×C22⋊C4×C17C2314yes—
79C2×C42×C17—24no—
80C2×C42×C17C2314yes—
81C2×C22⋊Dic17—28no—
82C2×C22⋊Dic17—28no—
83C2×C22⋊Dic17—44no—
84C2×C22⋊Dic17—44no—
85C2×C22⋊Dic17C2318yes—
86C2×C22⋊Dic17C2318yes—
87C2×C22⋊Dic17C2318yes—
88C2×C22⋊Dic17C2318yes—
89#10587612—232no—
90C2×C4⋊Dic17—24no—
91C2×C4⋊Dic17—24no—
92C2×C4⋊Dic17—24no—
93C2×C4⋊Dic17—24no—
94C2×C4⋊Dic17C2314yes—
95C2×C4⋊Dic17C2314yes—
96C2×C4⋊Dic17C2314yes—
97C2×C4⋊Dic17C2314yes—
98C2×#63225—28no—
99C2×#63225—44no—
100C2×#63225C2318yes—
101C2×#63225C2318yes—
102C2×C4×Dic17—28no—
103C2×C4×Dic17C2318yes—
104#10587502C2318yes—
105#10587502C2318yes—
106#10587502C2318yes—
107#10587502C2318yes—
108#10587502C2318yes—
109C24×C17—22no—
110C24×C17—22no—
111C24×C17—22no—
112C24×C17—22no—
113C24×C17—22no—
114C24×C17—22no—
115C24×C17—22no—
116C24×C17—22no—
117C24×C17—22no—
118C24×C17—22no—
119C24×C17—22no—
120C24×C17—22no—
121C24×C17C2×D414yes—
122C24×C17#4114yes—
123C24×C17C2412yes—
124C24×C17C2412yes—
125C24×C17C2411yescharacteristic
126C2×D4×C17—232no—
127C2×D4×C17—28no—
128C2×D4×C17—28no—
129C2×D4×C17—28no—
130C22×C4×C17—22no—
131C22×C4×C17—22no—
132C22×C4×C17—22no—
133C22×C4×C17—22no—
134C22×C4×C17—232no—
135C22×C4×C17—28no—
136C22×C4×C17—28no—
137C22×C4×C17—22no—
138C22×C4×C17—22no—
139C22×C4×C17—22no—
140C22×C4×C17—22no—
141C22×C4×C17—22no—
142C22×C4×C17—22no—
143C22×C4×C17—28no—
144C22×C4×C17—28no—
145C22×C4×C17—28no—
146C22×C4×C17—416no—
147C22×C4×C17C2×D414yes—
148C22×C4×C17C2×D4116yes—
149C22×C4×C17C2×D414yes—
150C22×C4×C17#4114yes—
151C22×C4×C17#4114yes—
152C22×C4×C17#4114yes—
153C22×C4×C17C2412yes—
154C22×C4×C17C2412yes—
155C22×C4×C17C2412yes—
156C22×C4×C17C2412yes—
157C22×C4×C17C2412yes—
158C22×Dic17—24no—
159C22×Dic17—24no—
160C22×Dic17—24no—
161C22×Dic17—24no—
162C22×Dic17—24no—
163C22×Dic17—24no—
164C22×Dic17—24no—
165C22×Dic17—24no—
166C22×Dic17—24no—
167C22×Dic17—24no—
168C22×Dic17—24no—
169C22×Dic17—24no—
170C22×Dic17C2414yes—
171C22×Dic17C2414yes—
172C22×Dic17C2414yes—
173C22×Dic17C2414yes—
174C4⋊C4×C17—28no—
175C22⋊C4×C17—28no—
176C22⋊C4×C17—28no—
177C42×C17—28no—
178C22⋊Dic17—216no—
179C22⋊Dic17—216no—
180C22⋊Dic17—48no—
181C22⋊Dic17—48no—
182C4⋊Dic17—28no—
183C4⋊Dic17—28no—
184C4⋊Dic17—28no—
185C4⋊Dic17—28no—
186#63225—216no—
187#63225—48no—
188C4×Dic17—216no—
189C2×#2485—171nomaximal, Sylow
190C23×C17—28no—
191C23×C17—28no—
192C23×C17—28no—
193C23×C17—28no—
194C23×C17—28no—
195C23×C17—28no—
196C23×C17—22no—
197C23×C17—22no—
198C23×C17—22no—
199C23×C17—22no—
200C23×C17—22no—
201C23×C17—22no—
202C23×C17—22no—
203C23×C17—22no—
204C23×C17—22no—
205C23×C17—22no—
206C23×C17—22no—
207C23×C17—22no—
208C23×C17—44no—
209C23×C17—44no—
210C23×C17—44no—
211C23×C17—44no—
212C23×C17—44no—
213C23×C17—44no—
214C23×C17—44no—
215C23×C17—44no—
216C23×C17C22×D414yes—
217C23×C17C22×D412yes—
218C23×C17C2×#4114yes—
219C23×C17C2×#4112yes—
220C23×C17C2×#4112yes—
221C23×C17C2×#4112yes—
222C23×C17C2×#4112yes—
223C23×C17H(5,𝔽2)12yes—
224C23×C172−1+412yes—
225C23×C17C2511yescharacteristic
226D4×C17—232no—
227C2×C4×C17—28no—
228C2×C4×C17—28no—
229C2×C4×C17—22no—
230C2×C4×C17—22no—
231C2×C4×C17—22no—
232C2×C4×C17—22no—
233C2×C4×C17—232no—
234C2×C4×C17—22no—
235C2×C4×C17—22no—
236C2×C4×C17—22no—
237C2×C4×C17—22no—
238C2×C4×C17—22no—
239C2×C4×C17—22no—
240C2×C4×C17—44no—
241C2×C4×C17—44no—
242C2×C4×C17—416no—
243C2×C4×C17#123116yes—
244C2×C4×C17C22×D414yes—
245C2×C4×C17C22×D414yes—
246C2×C4×C17C2×#4114yes—
247C2×C4×C17C2×#4114yes—
248C2×C4×C17C2×#4114yes—
249C2×Dic17—24no—
250C2×Dic17—24no—
251C2×Dic17—24no—
252C2×Dic17—24no—
253C2×Dic17—24no—
254C2×Dic17—24no—
255C2×Dic17—24no—
256C2×Dic17—24no—
257C2×Dic17—24no—
258C2×Dic17—24no—
259C2×Dic17—24no—
260C2×Dic17—24no—
261C2×Dic17—48no—
262C2×Dic17—48no—
263C2×Dic17—48no—
264C2×Dic17—48no—
265C22×C4×D4D1711yescharacteristic
266C22×#117—171no—
267#2485—1716no—
268C2×#397—172no—
269C2×#394—172no—
270C2×#389—171no—
271C2×#389—171no—
272C2×#388—172no—
273C2×#387—172no—
274C2×#380—171no—
275C2×#380—171no—
276C2×#380—171no—
277C22×C17—24no—
278C22×C17—24no—
279C22×C17—24no—
280C22×C17—24no—
281C22×C17—24no—
282C22×C17—24no—
283C22×C17—42no—
284C22×C17—42no—
285C22×C17—42no—
286C22×C17—42no—
287C22×C17—42no—
288C22×C17—42no—
289C22×C17—42no—
290C22×C17—42no—
291C22×C17—416no—
292C22×C17—416no—
293C22×C17C2×#12314yes—
294C22×C17#52514yes—
295C22×C17#53714yes—
296C22×C17#55214yes—
297C22×C17#55314yes—
298C22×C17#55514yes—
299C22×C17#55614yes—
300C22×C17C23×D411yescharacteristic
301C22×C17C22×#4111yescharacteristic
302C22×C17C22×#4111yescharacteristic
303C22×C17C22×#4111yescharacteristic
304C22×C17C22×#4111yescharacteristic
305C22×C17C2×H(5,𝔽2)11yescharacteristic
306C22×C17C2×2−1+411yescharacteristic
307C4×C17—24no—
308C4×C17—24no—
309C4×C17—42no—
310C4×C17—42no—
311C4×C17C2×#12318yes—
312Dic17—44no—
313Dic17—44no—
314Dic17—44no—
315Dic17—44no—
316C23×D4C2×D1711yescharacteristic
317C24×C4C2×D1711yescharacteristic
318C24×C4C2×D1711yescharacteristic
319C2×C4×D4—28no—
320C2×C4×D4C2×D1718yes—
321C2×#117—178no—
322C2×#117—348no—
323C22×C4⋊C4—172no—
324C22×C4⋊C4—171no—
325C22×C4⋊C4—171no—
326C22×C4⋊C4—171no—
327C22×C4⋊C4—171no—
328C22×C4⋊C4—172no—
329C22×C4⋊C4C2×D1711yescharacteristic
330C22×C22⋊C4—172no—
331C22×C22⋊C4—172no—
332C22×C22⋊C4—172no—
333C22×C22⋊C4—172no—
334C22×C22⋊C4C2×D1711yescharacteristic
335C22×C22⋊C4C2×D1711yescharacteristic
336C22×C42—172no—
337C22×C42C2×D1711yescharacteristic
338#397—1716no—
339#394—1716no—
340#389—178no—
341#389—178no—
342#388—1716no—
343#387—1716no—
344#380—178no—
345#380—178no—
346#380—178no—
347C2×#95—172no—
348C2×#95—172no—
349C2×#95—172no—
350C2×#95—172no—
351C2×#95—172no—
352C2×C17—44no—
353C2×C17—44no—
354C2×C17#248518yescomplemented
355C2×C17C22×#12311yescharacteristic
356C2×C17C2×#52511yescharacteristic
357C2×C17C2×#53711yescharacteristic
358C2×C17C2×#55211yescharacteristic
359C2×C17C2×#55311yescharacteristic
360C2×C17C2×#55511yescharacteristic
361C2×C17C2×#55611yescharacteristic
362C25C22×D1711yescharacteristic
363C25C22×D1711yescharacteristic
364C22×D4—24no—
365C22×D4—24no—
366C22×D4—24no—
367C22×D4C22×D1714yes—
368C23×C4—24no—
369C23×C4—24no—
370C23×C4—24no—
371C23×C4—24no—
372C23×C4—24no—
373C23×C4—172no—
374C23×C4—172no—
375C23×C4—172no—
376C23×C4—172no—
377C23×C4C22⋊D1718yes—
378C23×C4C22×D1714yes—
379C23×C4C22×D1711yescharacteristic
380C23×C4C22×D1711yescharacteristic
381C23×C4C22×D1711yescharacteristic
382C23×C4C22×D1714yes—
383C23×C4C22×D1711yescharacteristic
384C23×C4C22×D1711yescharacteristic
385C4×D4—232no—
386#117—3432no—
387C2×C4⋊C4—24no—
388C2×C4⋊C4—174no—
389C2×C4⋊C4—174no—
390C2×C4⋊C4—174no—
391C2×C4⋊C4—174no—
392C2×C4⋊C4—178no—
393C2×C4⋊C4—178no—
394C2×C4⋊C4—348no—
395C2×C4⋊C4—344no—
396C2×C4⋊C4—344no—
397C2×C4⋊C4—344no—
398C2×C4⋊C4—344no—
399C2×C4⋊C4—684no—
400C2×C4⋊C4C22×D1714yes—
401C2×C22⋊C4—24no—
402C2×C22⋊C4—24no—
403C2×C22⋊C4—178no—
404C2×C22⋊C4—178no—
405C2×C22⋊C4—178no—
406C2×C22⋊C4—178no—
407C2×C22⋊C4—348no—
408C2×C22⋊C4—348no—
409C2×C22⋊C4—684no—
410C2×C22⋊C4—684no—
411C2×C22⋊C4C22×D1714yes—
412C2×C22⋊C4C22×D1714yes—
413C2×C42—24no—
414C2×C42—178no—
415C2×C42—348no—
416C2×C42C22×D1714yes—
417#95—178no—
418#95—178no—
419#95—178no—
420#95—178no—
421#95—178no—
422C17C2×#248511yescharacteristic, complemented, Sylow
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24#6325214yes—
436C24C2×C22⋊D1714yes—
437C24C23×D1712yes—
438C24C23×D1712yes—
439C24C23×D1711yescharacteristic
440C2×D4—232no—
441C2×D4—28no—
442C2×D4—28no—
443C2×D4—28no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—28no—
449C22×C4—28no—
450C22×C4—232no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—28no—
458C22×C4—28no—
459C22×C4—28no—
460C22×C4—416no—
461C22×C4—174no—
462C22×C4—174no—
463C22×C4—174no—
464C22×C4—174no—
465C22×C4—344no—
466C22×C4—344no—
467C22×C4—344no—
468C22×C4—344no—
469C22×C4—344no—
470C22×C4—344no—
471C22×C4—344no—
472C22×C4—344no—
473C22×C4—344no—
474C22×C4—344no—
475C22×C4—344no—
476C22×C4—344no—
477C22×C4#6325214yes—
478C22×C4#6325414yes—
479C22×C4#6325414yes—
480C22×C4C2×C22⋊D1714yes—
481C22×C4C2×C22⋊D17116yes—
482C22×C4C2×C22⋊D1714yes—
483C22×C4C23×D1712yes—
484C22×C4C23×D1712yes—
485C22×C4C23×D1712yes—
486C22×C4C23×D1712yes—
487C22×C4C23×D1712yes—
488C4⋊C4—28no—
489C4⋊C4—3416no—
490C4⋊C4—348no—
491C4⋊C4—348no—
492C4⋊C4—348no—
493C4⋊C4—348no—
494C4⋊C4—688no—
495C22⋊C4—28no—
496C22⋊C4—28no—
497C22⋊C4—3416no—
498C22⋊C4—3416no—
499C22⋊C4—688no—
500C22⋊C4—688no—
501C42—28no—
502C42—3416no—
503C23—28no—
504C23—28no—
505C23—28no—
506C23—28no—
507C23—28no—
508C23—22no—
509C23—22no—
510C23—22no—
511C23—22no—
512C23—22no—
513C23—22no—
514C23—22no—
515C23—22no—
516C23—22no—
517C23—22no—
518C23—22no—
519C23—22no—
520C23—28no—
521C23—44no—
522C23—44no—
523C23—44no—
524C23—44no—
525C23—44no—
526C23—44no—
527C23—44no—
528C23—44no—
529C23C2×#6325214yes—
530C23C2×#6325212yes—
531C23C2×#6325212yes—
532C23C2×#6325412yes—
533C23C2×#6325412yes—
534C23#1058769612yes—
535C23#1058769712yes—
536C23C22×C22⋊D1714yes—
537C23C22×C22⋊D1712yes—
538C23C24×D1711yescharacteristic
539D4—232no—
540C2×C4—28no—
541C2×C4—28no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—232no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—44no—
554C2×C4—44no—
555C2×C4—416no—
556C2×C4—344no—
557C2×C4—344no—
558C2×C4—344no—
559C2×C4—344no—
560C2×C4—344no—
561C2×C4—344no—
562C2×C4—344no—
563C2×C4—344no—
564C2×C4—344no—
565C2×C4—344no—
566C2×C4—344no—
567C2×C4—344no—
568C2×C4—688no—
569C2×C4—688no—
570C2×C4—688no—
571C2×C4—688no—
572C2×C4#10587621116yes—
573C2×C4C2×#6325214yes—
574C2×C4C2×#6325414yes—
575C2×C4C2×#6325414yes—
576C2×C4C22×C22⋊D1714yes—
577C2×C4C22×C22⋊D1714yes—
578C22—24no—
579C22—24no—
580C22—24no—
581C22—24no—
582C22—24no—
583C22—24no—
584C22—42no—
585C22—42no—
586C22—42no—
587C22—416no—
588C22—416no—
589C22—42no—
590C22—42no—
591C22—42no—
592C22—42no—
593C22—42no—
594C22C2×#1058762114yes—
595C22#1176332014yes—
596C22#1176338714yes—
597C22#1176349914yes—
598C22#1176350514yes—
599C22#1176352414yes—
600C22#1176352914yes—
601C22C23×C22⋊D1711yescharacteristic
602C22C22×#6325411yescharacteristic
603C22C22×#6325411yescharacteristic
604C22C22×#6325211yescharacteristic
605C22C22×#6325211yescharacteristic
606C22C2×#1058769611yescharacteristic
607C22C2×#1058769711yescharacteristic
608C4—24no—
609C4—24no—
610C4—42no—
611C4—42no—
612C4—684no—
613C4—684no—
614C4—684no—
615C4—684no—
616C4C2×#1058762118yes—
617C2—44no—
618C2—44no—
619C2#1453308118yesdirect product factor
620C2C22×#1058762111yescharacteristic
621C2C2×#1176332011yescharacteristic
622C2C2×#1176338711yescharacteristic
623C2C2×#1176349911yescharacteristic
624C2C2×#1176350511yescharacteristic
625C2C2×#1176352411yescharacteristic
626C2C2×#1176352911yescharacteristic
subgroupG/H
centerC24C23×D17
commutator, cosocleC23×C17C25
FrattiniC23C24×D17
FittingC22×C4×D4×C17C2
socleC24×C17C24
prime radicalC23×D4×C17C22
hypercenterC22×C4×D4D17
hypocenterC17C2×#2485
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×#10587612C2semidirect
2. #14533081C2direct (N × H)
3. C2×#11762737C2semidirect
5. C2×#11762707C2semidirect
6. C2×#11762707C2semidirect
7. C2×#11762697C2semidirect
8. C2×#11762690C2semidirect
9. C2×#11762669C2semidirect
10. C2×#11762669C2semidirect
11. C2×#11762669C2semidirect
14. C2×#10587612C22semidirect
26. #11762737C22semidirect
28. #11762707C22semidirect
29. #11762707C22semidirect
30. #11762697C22semidirect
31. #11762690C22semidirect
32. #11762669C22semidirect
33. #11762669C22semidirect
34. #11762669C22semidirect
354. C2×C17#2485semidirect
422. C17C2×#2485semidirect
619. C2#14533081direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#105876122
#145330812
C2×#117627372
C2×#117627232
C2×#117627072
C2×#117626972
C2×#117626902
C2×#117626692
C22×C4×D4×C172
C2×#248517