Finite Group Databasebeta

← C2×#14533250 #17203380

Subgroups — C2×#14533250 #17203380

Order 4352.

4222 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×#10587580C212yesmaximal, complemented
2C22×#10587569C212yesmaximal, complemented
3C22×#10587570C211yesmaximal, characteristic
4C22×C4⋊C4×D17C211yesmaximal, characteristic, complemented
5#14533250C2116yesmaximal, direct product factor
6C2×#11762746C211yesmaximal, characteristic, complemented
7C2×#11762745C211yesmaximal, characteristic, complemented
8C2×#11762744C211yesmaximal, characteristic, complemented
9C2×#11762709C212yesmaximal, complemented
10C2×#11762678C212yesmaximal, complemented
11C2×#11762656C211yesmaximal, characteristic, complemented
12C2×C17×#399C211yesmaximal, characteristic, complemented
13C23×D68C2211yescharacteristic
14C23×C22⋊D17C2211yescharacteristic
15C23×C22⋊D17C2211yescharacteristic
16C23×C4×D17C2212yes—
17C23×C4×D17C2211yescharacteristic
18C2×#10587580—216no—
19C2×#10587580C22116yescomplemented
20C2×#10587569—216no—
21C2×#10587569C22116yescomplemented
22C2×#10587570—28no—
23C2×#10587570C2218yes—
24C22×C4⋊Dic17C2212yes—
25C22×C4⋊Dic17C2211yescharacteristic
26C22×#63225C2211yescharacteristic
27C22×#63225C2212yes—
28C22×#63225C2212yes—
29C22×#63225C2212yes—
30C2×C4⋊C4×D17—28no—
31C2×C4⋊C4×D17C2218yescomplemented
32C22×C22⋊Dic17C2212yes—
33C22×#63227C2212yes—
34C22×#63227C2212yes—
35C22×#63227C2211yescharacteristic
36C22×#63227C2212yes—
37C22×C4×Dic17C2212yes—
38#11762746C2218yescomplemented
39#11762745C2218yescomplemented
40#11762744C2218yescomplemented
41#11762709C22116yescomplemented
42#11762678C22116yescomplemented
43#11762656C2218yescomplemented
44C2×#10587502C2211yescharacteristic
45C22×C4⋊C4×C17C2212yes—
46C22×C4⋊C4×C17C2211yescharacteristic
47C22×C22⋊C4×C17C2212yes—
48C22×C22⋊C4×C17C2211yescharacteristic
49C17×#399C2218yescomplemented
50C2×C17×#95C2211yescharacteristic
51C25×C17C2311yescharacteristic
52C24×D17C2311yescharacteristic
53C24×D17C2311yescharacteristic
54C23×C4×C17C2312yes—
55C23×C4×C17C2311yescharacteristic
56C23×C4×C17C2312yes—
57C23×C4×C17C2311yescharacteristic
58C22×C22⋊D17—24no—
59C22×C22⋊D17—28no—
60C22×C22⋊D17—24no—
61C22×C22⋊D17—28no—
62C22×C22⋊D17C2314yes—
63C22×C22⋊D17C2314yes—
64C23×Dic17C2312yes—
65C23×Dic17C2311yescharacteristic
66C23×Dic17C2312yes—
67C23×Dic17C2311yescharacteristic
68C22×D68—24no—
69C22×D68—28no—
70C22×D68C2314yes—
71C22×C4×D17—28no—
72C22×C4×D17—28no—
73C22×C4×D17—28no—
74C22×C4×D17—28no—
75C22×C4×D17D418yes—
76C22×C4×D17C2318yes—
77C22×C4×D17C2314yes—
78C2×C4⋊C4×C17—24no—
79C2×C4⋊C4×C17—28no—
80C2×C4⋊C4×C17C2314yes—
81C2×C4⋊C4×C17C2318yes—
82C2×C22⋊C4×C17—24no—
83C2×C22⋊C4×C17—28no—
84C2×C22⋊C4×C17C2318yes—
85C2×C22⋊C4×C17C2314yes—
86C2×C22⋊Dic17—28no—
87C2×C22⋊Dic17C2318yes—
88C2×#63227—24no—
89C2×#63227—28no—
90C2×#63227—28no—
91C2×#63227D4116yescomplemented
92C2×#63227C2318yes—
93C2×#63227C2318yes—
94C2×#63227C2314yes—
95C2×#63227C2318yes—
96C2×C4⋊Dic17—24no—
97C2×C4⋊Dic17—28no—
98C2×C4⋊Dic17C2314yes—
99C2×C4⋊Dic17C2318yes—
100C2×#63225—28no—
101C2×#63225—24no—
102C2×#63225—28no—
103C2×#63225—28no—
104C2×#63225C2318yes—
105C2×#63225C2318yes—
106C2×#63225C2318yes—
107C2×#63225C2314yes—
108C2×C4×Dic17—28no—
109C2×C4×Dic17C2318yes—
110#10587580—264no—
111C4⋊C4×D17—232no—
112#10587570—232no—
113#10587569—264no—
114C17×#95C2314yes—
115#10587502C2314yes—
116C24×C17—22no—
117C24×C17—24no—
118C24×C17—24no—
119C24×C17—22no—
120C24×C17—22no—
121C24×C17C2412yes—
122C24×C17C2411yescharacteristic
123C23×D17—24no—
124C23×D17—22no—
125C23×D17—22no—
126C23×D17—22no—
127C23×D17—24no—
128C23×D17—24no—
129C23×D17—22no—
130C23×D17—22no—
131C23×D17C2×D414yes—
132C23×D17C2×D418yes—
133C23×D17C2412yes—
134C23×D17C2412yes—
135C22×C4×C17—24no—
136C22×C4×C17—24no—
137C22×C4×C17—24no—
138C22×C4×C17—24no—
139C22×C4×C17—24no—
140C22×C4×C17—24no—
141C22×C4×C17—22no—
142C22×C4×C17—24no—
143C22×C4×C17C2×D414yes—
144C22×C4×C17C2×D418yes—
145C22×C4×C17C2414yes—
146C22×C4×C17C2412yes—
147C22×C4×C17C2412yes—
148C22×C4×C17C2414yes—
149C2×C22⋊D17—216no—
150C2×C22⋊D17—28no—
151C2×C22⋊D17—28no—
152C2×C22⋊D17—216no—
153C2×C22⋊D17—416no—
154C2×C22⋊D17—416no—
155C22×Dic17—24no—
156C22×Dic17—24no—
157C22×Dic17—24no—
158C22×Dic17—24no—
159C22×Dic17—24no—
160C22×Dic17—24no—
161C22×Dic17—22no—
162C22×Dic17C2×D418yes—
163C22×Dic17C2×D414yes—
164C22×Dic17#4118yes—
165C22×Dic17C2414yes—
166C22×Dic17C2412yes—
167C22×Dic17C2414yes—
168C22×Dic17C2412yes—
169C2×D68—28no—
170C2×D68—216no—
171C2×D68—416no—
172C2×C4×D17—232no—
173C2×C4×D17—216no—
174C2×C4×D17—216no—
175C2×C4×D17—216no—
176C2×C4×D17—216no—
177C2×C4×D17—432no—
178C2×C4×D17C2×D4116yes—
179C4⋊C4×C17—28no—
180C4⋊C4×C17—216no—
181C22⋊C4×C17—216no—
182C22⋊C4×C17—28no—
183C22⋊Dic17—216no—
184#63227—28no—
185#63227—216no—
186#63227—216no—
187#63227C2×D4132yescomplemented
188C4⋊Dic17—216no—
189C4⋊Dic17—28no—
190#63225—216no—
191#63225—28no—
192#63225—216no—
193#63225—216no—
194C4×Dic17—216no—
195C2×#2501—171nomaximal, Sylow
196C23×C17—24no—
197C23×C17—22no—
198C23×C17—24no—
199C23×C17—22no—
200C23×C17—22no—
201C23×C17—44no—
202C23×C17—44no—
203C23×C17—44no—
204C23×C17—48no—
205C23×C17—48no—
206C23×C17C22×D412yes—
207C23×C17C22×D414yes—
208C23×C17C2×#4114yes—
209C23×C172−1+412yes—
210C23×C172−1+412yes—
211C23×C17C2511yescharacteristic
212C22×D17—28no—
213C22×D17—28no—
214C22×D17—216no—
215C22×D17—216no—
216C22×D17—24no—
217C22×D17—22no—
218C22×D17—22no—
219C22×D17—22no—
220C22×D17—24no—
221C22×D17—24no—
222C22×D17—22no—
223C22×D17—22no—
224C22×D17—44no—
225C22×D17—44no—
226C22×D17—44no—
227C22×D17—48no—
228C22×D17—48no—
229C22×D17#127116yes—
230C22×D17C22×D414yes—
231C22×D17C22×D418yes—
232C2×C4×C17—28no—
233C2×C4×C17—216no—
234C2×C4×C17—24no—
235C2×C4×C17—24no—
236C2×C4×C17—24no—
237C2×C4×C17—24no—
238C2×C4×C17—22no—
239C2×C4×C17—24no—
240C2×C4×C17—24no—
241C2×C4×C17—24no—
242C2×C4×C17—48no—
243C2×C4×C17—44no—
244C2×C4×C17C22×D414yes—
245C2×C4×C17C22×D418yes—
246C22⋊D17—416no—
247C22⋊D17—416no—
248C2×Dic17—216no—
249C2×Dic17—24no—
250C2×Dic17—24no—
251C2×Dic17—24no—
252C2×Dic17—24no—
253C2×Dic17—24no—
254C2×Dic17—24no—
255C2×Dic17—22no—
256C2×Dic17—48no—
257C2×Dic17—44no—
258C2×Dic17#123116yescomplemented
259C2×Dic17C22×D418yes—
260C2×Dic17C22×D414yes—
261C2×Dic17C2×#4118yes—
262D68—416no—
263C4×D17—232no—
264C4×D17—432no—
265C22×#123—172no—
266C22×#123—172no—
267C22×#121—171no—
268C23×C4⋊C4—171no—
269#2501—1716no—
270C2×#399—171no—
271C2×#399—171no—
272C2×#399—171no—
273C2×#399D1711yescharacteristic, complemented
274C2×#390—172no—
275C2×#384—172no—
276C2×C4×C22⋊C4—171no—
277C22×C17—42no—
278C22×C17—42no—
279C22×C17—42no—
280C22×C17—44no—
281C22×C17—44no—
282C22×C17—88no—
283C22×C17C2×#12314yes—
284C22×C17C2×#12714yes—
285C22×C17#53614yes—
286C22×C17#54718yes—
287C22×C17#54718yes—
288C22×C17C23×D411yescharacteristic
289C22×C17C23×D412yes—
290C22×C17C22×#4112yes—
291C22×C17C2×2−1+411yescharacteristic
292C22×C17C2×2−1+411yescharacteristic
293C2×D17—24no—
294C2×D17—24no—
295C2×D17—28no—
296C2×D17—28no—
297C2×D17—232no—
298C2×D17—42no—
299C2×D17—42no—
300C2×D17—42no—
301C2×D17—44no—
302C2×D17—44no—
303C2×D17—88no—
304C2×D17C2×#12718yes—
305C4×C17—24no—
306C4×C17—28no—
307C4×C17—44no—
308C4×C17—42no—
309Dic17—28no—
310Dic17—44no—
311Dic17—42no—
312Dic17C2×#12318yescomplemented
313C23×D4—171no—
314C23×D4—171no—
315C23×D4—171no—
316C24×C4—171no—
317C24×C4—172no—
318C2×#123—1716no—
319C2×#123—1716no—
320C2×#123—3416no—
321C2×#123—3416no—
322C2×#121—178no—
323C2×#121—348no—
324C22×C4⋊C4—172no—
325C22×C4⋊C4—172no—
326C22×C4⋊C4—172no—
327C22×C4⋊C4—171no—
328C22×C4⋊C4—171no—
329C22×C4⋊C4—172no—
330C22×C4⋊C4—178no—
331C22×C4⋊C4—348no—
332C22×C4⋊C4C2×D1711yescharacteristic
333C22×C4⋊C4C2×D1712yes—
334C22×C22⋊C4—172no—
335C22×C22⋊C4—172no—
336C22×C22⋊C4—171no—
337C22×C22⋊C4—172no—
338C22×C22⋊C4—172no—
339C22×C22⋊C4C2×D1711yescharacteristic
340C22×C22⋊C4C2×D1712yes—
341C22×C42—172no—
342#399—178no—
343#399—178no—
344#399—178no—
345#399C2×D1718yescomplemented
346#390—1716no—
347#384—1716no—
348C4×C22⋊C4—178no—
349C2×#95—171no—
350C2×#95C2×D1711yescharacteristic
351C2×C17—82no—
352C2×C17#250118yescomplemented
353C2×C17C22×#12311yescharacteristic
354C2×C17C22×#12711yescharacteristic
355C2×C17C2×#53611yescharacteristic
356C2×C17C2×#54712yes—
357C2×C17C2×#54712yes—
358D17—28no—
359D17—82no—
360C25—171no—
361C25—171no—
362C25C22×D1711yescharacteristic
363C22×D4—174no—
364C22×D4—174no—
365C22×D4—174no—
366C22×D4—344no—
367C22×D4—348no—
368C22×D4—344no—
369C22×D4—348no—
370C22×D4—344no—
371C22×D4—348no—
372C23×C4—171no—
373C23×C4—172no—
374C23×C4—178no—
375C23×C4—174no—
376C23×C4—172no—
377C23×C4—171no—
378C23×C4—178no—
379C23×C4—348no—
380C23×C4—348no—
381C23×C4—348no—
382C23×C4—348no—
383C23×C4C22×D1712yes—
384C23×C4C22×D1711yescharacteristic
385C23×C4C22×D1712yes—
386C23×C4C22×D1711yescharacteristic
387#123—3464no—
388#123—3464no—
389#121—3432no—
390C2×C4⋊C4—24no—
391C2×C4⋊C4—28no—
392C2×C4⋊C4—178no—
393C2×C4⋊C4—174no—
394C2×C4⋊C4—174no—
395C2×C4⋊C4—178no—
396C2×C4⋊C4—178no—
397C2×C4⋊C4—178no—
398C2×C4⋊C4—3432no—
399C2×C4⋊C4—348no—
400C2×C4⋊C4—344no—
401C2×C4⋊C4—348no—
402C2×C4⋊C4—348no—
403C2×C4⋊C4—344no—
404C2×C4⋊C4—348no—
405C2×C4⋊C4C22×D1714yes—
406C2×C4⋊C4C22×D1718yes—
407C2×C22⋊C4—24no—
408C2×C22⋊C4—28no—
409C2×C22⋊C4—1716no—
410C2×C22⋊C4—178no—
411C2×C22⋊C4—178no—
412C2×C22⋊C4—174no—
413C2×C22⋊C4—178no—
414C2×C22⋊C4—178no—
415C2×C22⋊C4—348no—
416C2×C22⋊C4—348no—
417C2×C22⋊C4—344no—
418C2×C22⋊C4—348no—
419C2×C22⋊C4C22×D1714yes—
420C2×C22⋊C4C22×D1718yes—
421C2×C42—178no—
422C2×C42—348no—
423#95—174no—
424#95C22×D1714yes—
425C17C2×#250111yescharacteristic, complemented, Sylow
426C24—24no—
427C24—22no—
428C24—22no—
429C24—24no—
430C24—22no—
431C24—178no—
432C24—174no—
433C24—172no—
434C24—172no—
435C24—342no—
436C24—344no—
437C24—342no—
438C24—344no—
439C24—342no—
440C24—342no—
441C24—344no—
442C24—342no—
443C24C23×D1712yes—
444C24C23×D1711yescharacteristic
445C2×D4—348no—
446C2×D4—3416no—
447C2×D4—348no—
448C2×D4—3416no—
449C2×D4—348no—
450C2×D4—3416no—
451C2×D4—6816no—
452C2×D4—6816no—
453C2×D4—6816no—
454C22×C4—24no—
455C22×C4—24no—
456C22×C4—24no—
457C22×C4—24no—
458C22×C4—22no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—24no—
462C22×C4—174no—
463C22×C4—178no—
464C22×C4—172no—
465C22×C4—178no—
466C22×C4—174no—
467C22×C4—1716no—
468C22×C4—174no—
469C22×C4—172no—
470C22×C4—3432no—
471C22×C4—3416no—
472C22×C4—3416no—
473C22×C4—3416no—
474C22×C4—3416no—
475C22×C4—344no—
476C22×C4—344no—
477C22×C4—344no—
478C22×C4—344no—
479C22×C4—342no—
480C22×C4—344no—
481C22×C4—344no—
482C22×C4—6832no—
483C22×C4D4×D1718yes—
484C22×C4D4×D1714yes—
485C22×C4C23×D1714yes—
486C22×C4C23×D1712yes—
487C22×C4C23×D1712yes—
488C22×C4C23×D1714yes—
489C4⋊C4—28no—
490C4⋊C4—216no—
491C4⋊C4—3416no—
492C4⋊C4—348no—
493C4⋊C4—3416no—
494C4⋊C4—3416no—
495C4⋊C4—348no—
496C4⋊C4—3416no—
497C22⋊C4—28no—
498C22⋊C4—216no—
499C22⋊C4—1732no—
500C22⋊C4—3416no—
501C22⋊C4—3416no—
502C22⋊C4—348no—
503C22⋊C4—3416no—
504C42—3416no—
505C23—24no—
506C23—22no—
507C23—24no—
508C23—22no—
509C23—22no—
510C23—48no—
511C23—48no—
512C23—44no—
513C23—44no—
514C23—44no—
515C23—1716no—
516C23—178no—
517C23—174no—
518C23—3416no—
519C23—3416no—
520C23—348no—
521C23—344no—
522C23—348no—
523C23—342no—
524C23—342no—
525C23—344no—
526C23—342no—
527C23—344no—
528C23—342no—
529C23—342no—
530C23—688no—
531C23—688no—
532C23—684no—
533C23—684no—
534C23—684no—
535C23C2×D4×D1714yes—
536C23C2×D4×D1712yes—
537C23#1058769412yes—
538C23#41×D1714yes—
539C23#1058769712yes—
540C23C24×D1711yescharacteristic
541D4—6816no—
542D4—6816no—
543D4—6816no—
544C2×C4—216no—
545C2×C4—28no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—24no—
550C2×C4—22no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—48no—
555C2×C4—44no—
556C2×C4—1716no—
557C2×C4—174no—
558C2×C4—178no—
559C2×C4—178no—
560C2×C4—3432no—
561C2×C4—3416no—
562C2×C4—344no—
563C2×C4—344no—
564C2×C4—344no—
565C2×C4—344no—
566C2×C4—342no—
567C2×C4—344no—
568C2×C4—344no—
569C2×C4—6832no—
570C2×C4—688no—
571C2×C4—684no—
572C2×C4C2×D4×D1718yes—
573C2×C4C2×D4×D1714yes—
574C22—42no—
575C22—44no—
576C22—44no—
577C22—42no—
578C22—42no—
579C22—88no—
580C22—178no—
581C22—344no—
582C22—3432no—
583C22—348no—
584C22—348no—
585C22—344no—
586C22—682no—
587C22—684no—
588C22—684no—
589C22—682no—
590C22—682no—
591C22—1368no—
592C22#123×D1714yes—
593C22#127×D1714yes—
594C22#1176338214yes—
595C22#1176345718yes—
596C22#1176346118yes—
597C22C22×D4×D1711yescharacteristic
598C22C22×D4×D1712yes—
599C22C2×#41×D1712yes—
600C22C2×#1058769711yescharacteristic
601C22C2×#1058769411yescharacteristic
602C4—28no—
603C4—24no—
604C4—44no—
605C4—42no—
606C4—178no—
607C4—348no—
608C4—684no—
609C4—682no—
610C2—82no—
611C2—348no—
612C2—1362no—
613C2#1453325018yesdirect product factor
614C2C2×#123×D1711yescharacteristic
615C2C2×#127×D1711yescharacteristic
616C2C2×#1176338211yescharacteristic
617C2C2×#1176345712yes—
618C2C2×#1176346112yes—
subgroupG/H
centerC24C23×D17
commutator, cosocleC23×C17C25
FrattiniC23C24×D17
FittingC2×C17×#399C2
socleC24×C17C24
prime radicalC22×#10587570C2
hypercenterC2×#399D17
hypocenterC17C2×#2501
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#399

Complements

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

NH ≅ G/Ntype
1. C22×#10587580C2semidirect
2. C22×#10587569C2semidirect
4. C22×C4⋊C4×D17C2semidirect
5. #14533250C2direct (N × H)
6. C2×#11762746C2semidirect
7. C2×#11762745C2semidirect
8. C2×#11762744C2semidirect
9. C2×#11762709C2semidirect
10. C2×#11762678C2semidirect
11. C2×#11762656C2semidirect
12. C2×C17×#399C2semidirect
19. C2×#10587580C22semidirect
21. C2×#10587569C22semidirect
31. C2×C4⋊C4×D17C22semidirect
38. #11762746C22semidirect
39. #11762745C22semidirect
40. #11762744C22semidirect
41. #11762709C22semidirect
42. #11762678C22semidirect
43. #11762656C22semidirect
49. C17×#399C22semidirect
91. C2×#63227D4semidirect
187. #63227C2×D4semidirect
258. C2×Dic17#123semidirect
273. C2×#399D17semidirect
312. Dic17C2×#123semidirect
345. #399C2×D17semidirect
352. C2×C17#2501semidirect
425. C17C2×#2501semidirect
613. C2#14533250direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#105875802
C22×#105875692
C22×#105875702
C22×C4⋊C4×D172
#145332502
C2×#117627462
C2×#117627452
C2×#117627442
C2×#117627092
C2×#117626782
C2×#117626562
C2×C17×#3992
C2×#250117