Finite Group Databasebeta

← C2×#14544471 #17968191

Subgroups — C2×#14544471 #17968191

Order 4352.

2574 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D17⋊M16C211yesmaximal, characteristic
2C22×#10587677C211yesmaximal, characteristic
3#14544471C218yesmaximal, direct product factor
4C2×#11763682C214yesmaximal, complemented
5C22×C4⋊C4×D17C211yesmaximal, characteristic
6C22×#63243—21no—
7C2×D17⋊M16—24no—
8C2×D17⋊M16—22no—
9C2×D17⋊M16C418yescomplemented
10C2×D17⋊M16C2214yes—
11C22×#63247—21no—
12C22×#63242C2212yes—
13C2×#10587677—24no—
14C2×#10587677—22no—
15C2×#10587677C418yescomplemented
16C2×#10587677C2214yes—
17C22×C4⋊#595C2212yes—
18C22×C22⋊#595—21no—
19C22×C4×#595—21no—
20#11763682C22116yescomplemented
21C23×C4×D17—21no—
22C23×C4×D17C2211yescharacteristic
23C22×C4⋊Dic17C411yescharacteristic, complemented
24C22×#63225—21no—
25C2×C4⋊C4×D17—22no—
26C2×C4⋊C4×D17—21no—
27C2×C4⋊C4×D17—21no—
28C2×C4⋊C4×D17—22no—
29C2×C4⋊C4×D17C414yescomplemented
30C2×C4⋊C4×D17C412yescomplemented
31C2×C4⋊C4×D17C2212yes—
32C2×C4⋊C4×D17C2214yes—
33C22×C4⋊C4×C17C411yescharacteristic, complemented
34C24×D17D411yescharacteristic
35C23×#595—22no—
36C23×C4×C17—21no—
37C23×C4×C17C2×C411yescharacteristic
38C23×Dic17—21no—
39C23×Dic17D411yescharacteristic
40C22×C4×D17—24no—
41C22×C4×D17—22no—
42C22×C4×D17—22no—
43C22×C4×D17—24no—
44C22×C4×D17—48no—
45C22×C4×D17C2×C412yes—
46C22×C4×D17C2×C411yescharacteristic
47C22×C4×D17C2×C414yes—
48C22×C4×D17C2×C414yes—
49C22×C4×D17D411yescharacteristic
50C22×C4×D17D412yes—
51C22×C4×D17D412yes—
52C22×C4×D17D411yescharacteristic
53C22×C4×D17D414yes—
54C22×C4×D17Q814yes—
55C22×C4×D17C2311yescharacteristic
56C22×C4×D17C2312yes—
57C2×C22⋊#595—28no—
58C2×C22⋊#595—24no—
59C2×#63247—28no—
60C2×#63247—24no—
61C22×#3624—22no—
62#10587677—216no—
63#10587677—28no—
64#10587677C2×C4116yescomplemented
65C2×C4⋊#595—22no—
66C2×C4⋊#595—24no—
67C2×C4⋊#595C2×C418yescomplemented
68C2×C4⋊#595C2314yes—
69C2×C4×#595—28no—
70C2×C4×#595—24no—
71D17⋊M16—216no—
72D17⋊M16—28no—
73D17⋊M16C2×C4116yescomplemented
74C2×#63243—28no—
75C2×#63243—24no—
76C2×#63242—22no—
77C2×#63242—24no—
78C2×#63242C2×C418yescomplemented
79C2×#63242C2314yes—
80C2×C4⋊C4×C17—22no—
81C2×C4⋊C4×C17—21no—
82C2×C4⋊C4×C17C2×C412yes—
83C2×C4⋊C4×C17C2×C414yescomplemented
84C2×C4⋊Dic17—21no—
85C2×C4⋊Dic17—22no—
86C2×C4⋊Dic17C2×C412yes—
87C2×C4⋊Dic17C2×C414yescomplemented
88C2×#63225—22no—
89C2×#63225—24no—
90C2×#63225—22no—
91C2×#63225—24no—
92C4⋊C4×D17—24no—
93C4⋊C4×D17—24no—
94C4⋊C4×D17—24no—
95C4⋊C4×D17—22no—
96C4⋊C4×D17—22no—
97C4⋊C4×D17—24no—
98C4⋊C4×D17—24no—
99C4⋊C4×D17C2×C414yes—
100C4⋊C4×D17C2×C418yescomplemented
101C4⋊C4×D17C2314yes—
102C24×C17C22⋊C411yescharacteristic
103C23×D17—24no—
104C23×D17—24no—
105C23×D17C22⋊C412yes—
106C23×D17C22⋊C411yescharacteristic
107C23×D17C22⋊C414yes—
108C23×D17C4⋊C414yes—
109C23×D17C2×D412yes—
110C23×D17C2×D411yescharacteristic
111C22×#595—28no—
112C22×#595—24no—
113C22×#595—44no—
114C22×#595—44no—
115C22×C4×C17—22no—
116C22×C4×C17—24no—
117C22×C4×C17—44no—
118C22×C4×C17C4214yes—
119C22×C4×C17C22⋊C412yes—
120C22×C4×C17C22⋊C411yescharacteristic
121C22×C4×C17C4⋊C414yes—
122C22×C4×C17C22×C411yescharacteristic
123C22×C4×C17C22×C412yes—
124C22×Dic17—22no—
125C22×Dic17—24no—
126C22×Dic17—44no—
127C22×Dic17C22⋊C412yes—
128C22×Dic17C22⋊C411yescharacteristic
129C22×Dic17C22⋊C414yes—
130C22×Dic17C4⋊C414yes—
131C22×Dic17C2×D411yescharacteristic
132C22×Dic17C2×D412yes—
133C2×C4×D17—24no—
134C2×C4×D17—28no—
135C2×C4×D17—24no—
136C2×C4×D17—48no—
137C2×C4×D17—416no—
138C2×C4×D17—416no—
139C2×C4×D17—48no—
140C2×C4×D17C4218yes—
141C2×C4×D17C4214yes—
142C2×C4×D17C22⋊C412yes—
143C2×C4×D17C22⋊C412yes—
144C2×C4×D17C22⋊C412yes—
145C2×C4×D17C22⋊C414yes—
146C2×C4×D17C22⋊C418yes—
147C2×C4×D17C22⋊C414yes—
148C2×C4×D17C22⋊C418yes—
149C2×C4×D17C4⋊C418yes—
150C2×C4×D17C4⋊C414yes—
151C2×C4×D17C4⋊C418yes—
152C2×C4×D17C4⋊C414yes—
153C2×C4×D17C4⋊C418yes—
154C2×C4×D17C4⋊C414yes—
155C2×C4×D17C22×C411yescharacteristic
156C2×C4×D17C22×C412yes—
157C2×C4×D17C22×C412yes—
158C2×C4×D17C22×C414yes—
159C2×C4×D17C22×C412yes—
160C2×C4×D17C22×C414yes—
161C2×C4×D17C2×D412yes—
162C2×C4×D17C2×D411yescharacteristic
163C2×C4×D17C2×D411yescharacteristic
164C2×C4×D17C2×D412yes—
165C2×C4×D17C2×D412yes—
166C2×C4×D17C2×D414yes—
167C2×C4×D17C2×Q814yes—
168C2×C4×D17C2×Q812yes—
169C2×C4×D17C2411yescharacteristic
170C22⋊#595—216no—
171#63247—216no—
172C2×#3624—28no—
173C2×#3624—24no—
174C4⋊#595—28no—
175C4⋊#595—24no—
176C4⋊#595C22×C418yescomplemented
177C4×#595—216no—
178#63243—216no—
179#63242—28no—
180#63242—24no—
181#63242C22×C418yescomplemented
182C4⋊C4×C17—22no—
183C4⋊C4×C17—24no—
184C4⋊C4×C17C22×C414yes—
185C4⋊Dic17—22no—
186C4⋊Dic17—24no—
187C4⋊Dic17C22×C414yes—
188#63225—24no—
189#63225—28no—
190#63225—24no—
191C2×#1736—171nomaximal, Sylow
192C23×C17—22no—
193C23×C17—22no—
194C23×C17#9514yes—
195C23×C17C2×C22⋊C412yes—
196C23×C17C2×C22⋊C411yescharacteristic
197C22×D17—22no—
198C22×D17—22no—
199C22×D17—24no—
200C22×D17—24no—
201C22×D17—216no—
202C22×D17—24no—
203C22×D17—24no—
204C22×D17—216no—
205C22×D17#9514yes—
206C22×D17#9518yes—
207C22×D17C2×C22⋊C414yes—
208C22×D17C2×C22⋊C412yes—
209C22×D17C2×C22⋊C412yes—
210C22×D17C2×C22⋊C411yescharacteristic
211C22×D17C2×C4⋊C414yes—
212C22×D17C2×C4⋊C412yes—
213C22×D17AGL(1,ℤ/8)14yes—
214C22×D17#13714yes—
215C22×D17C22×D411yescharacteristic
216C2×#595—28no—
217C2×#595—44no—
218C2×#595—44no—
219C2×#595—416no—
220C2×C4×C17—24no—
221C2×C4×C17—48no—
222C2×C4×C17—44no—
223C2×C4×C17#9518yes—
224C2×C4×C17#9514yes—
225C2×C4×C17C2×C4214yes—
226C2×C4×C17C2×C4212yes—
227C2×C4×C17C2×C22⋊C411yescharacteristic
228C2×C4×C17C2×C22⋊C412yes—
229C2×C4×C17C2×C4⋊C414yes—
230C2×C4×C17C2×C4⋊C412yes—
231C2×C4×C17C23×C411yescharacteristic
232C2×Dic17—24no—
233C2×Dic17—48no—
234C2×Dic17—44no—
235C2×Dic17#9518yes—
236C2×Dic17#9514yes—
237C2×Dic17C2×C22⋊C412yes—
238C2×Dic17C2×C22⋊C414yes—
239C2×Dic17C2×C22⋊C411yescharacteristic
240C2×Dic17C2×C22⋊C412yes—
241C2×Dic17C2×C4⋊C414yes—
242C2×Dic17C2×C4⋊C412yes—
243C2×Dic17C22×D411yescharacteristic
244C4×D17—416no—
245C4×D17—48no—
246C4×D17—48no—
247C4×D17#9518yes—
248C4×D17#9518yes—
249C4×D17#9518yes—
250C4×D17C2×C4214yes—
251C4×D17C2×C4212yes—
252C4×D17C2×C22⋊C412yes—
253C4×D17C2×C22⋊C414yes—
254C4×D17C2×C22⋊C414yes—
255C4×D17C2×C22⋊C412yes—
256C4×D17C2×C4⋊C414yes—
257C4×D17C2×C4⋊C412yes—
258C4×D17C2×C4⋊C414yes—
259C4×D17C2×C4⋊C412yes—
260C4×D17C2×C4⋊C412yes—
261C4×D17C2×C4⋊C414yes—
262C4×D17C23×C411yescharacteristic
263C4×D17C23×C411yescharacteristic
264C4×D17C22×D411yescharacteristic
265C4×D17C22×Q811yescharacteristic
266#3624—28no—
267C23×M16—171no—
268C22×#117—171no—
269C23×C4⋊C4—171no—
270#1736—178no—
271C2×#340—174no—
272C22×C17—22no—
273C22×C17—22no—
274C22×C17—28no—
275C22×C17C2×#9514yes—
276C22×C17C2×#9512yes—
277C22×C17#41812yes—
278C22×C17#41912yes—
279C22×C17C22×C22⋊C411yescharacteristic
280C2×D17—22no—
281C2×D17—22no—
282C2×D17—28no—
283C2×D17—28no—
284C2×D17—28no—
285C2×D17—216no—
286C2×D17C2×#9514yes—
287C2×D17C2×#9512yes—
288C2×D17#41718yes—
289C2×D17#41812yes—
290C2×D17#41912yes—
291C2×D17#42818yes—
292C2×D17C22×C22⋊C411yescharacteristic
293C2×D17C22×C4⋊C411yescharacteristic
294C2×D17C2×AGL(1,ℤ/8)12yes—
295C2×D17C2×#13712yes—
296#595—48no—
297C4×C17—44no—
298C4×C17C2×#9512yes—
299C4×C17C2×#9514yes—
300C4×C17C22×C4211yescharacteristic
301C4×C17C22×C4⋊C411yescharacteristic
302Dic17—44no—
303Dic17C2×#9514yes—
304Dic17C2×#9512yes—
305Dic17C22×C22⋊C411yescharacteristic
306Dic17C22×C4⋊C411yescharacteristic
307C24×C4—171no—
308C24×C4—341no—
309C22×M16—178no—
310C22×M16—174no—
311C22×M16—341no—
312C22×M16—344no—
313C22×M16—342no—
314C22×M16—341no—
315C23×C8—172no—
316C2×#117—178no—
317C2×#117—174no—
318C2×#117—344no—
319C2×#117—342no—
320C22×C4⋊C4—172no—
321C22×C4⋊C4—171no—
322C22×C4⋊C4—172no—
323C22×C4⋊C4—172no—
324C22×C4⋊C4—174no—
325C22×C4⋊C4—174no—
326C22×C4⋊C4—342no—
327C22×C4⋊C4—342no—
328C22×C4⋊C4—341no—
329C22×C4⋊C4—341no—
330C22×C4⋊C4—341no—
331C22×C4⋊C4#59511yescharacteristic, complemented
332C22×C22⋊C4—341no—
333C22×C42—341no—
334#340—1716no—
335C2×C17—24no—
336C2×C17#173614yescomplemented
337C2×C17C22×#9511yescharacteristic
338C2×C17C2×#41811yescharacteristic
339C2×C17C2×#41911yescharacteristic
340D17—24no—
341D17#173614yescomplemented
342D17C2×#41712yes—
343D17C2×#42812yes—
344C25—171no—
345C23×C4—21no—
346C23×C4—171no—
347C23×C4—174no—
348C23×C4—174no—
349C23×C4—174no—
350C23×C4—174no—
351C23×C4—172no—
352C23×C4—172no—
353C23×C4—171no—
354C23×C4—171no—
355C23×C4—171no—
356C23×C4—172no—
357C23×C4—172no—
358C23×C4—171no—
359C23×C4—344no—
360C23×C4—344no—
361C23×C4—342no—
362C23×C4—342no—
363C23×C4—342no—
364C23×C4—341no—
365C23×C4—688no—
366C23×C4C2×#59511yescharacteristic
367C2×M16—1716no—
368C2×M16—344no—
369C2×M16—348no—
370C2×M16—348no—
371C2×M16—3416no—
372C2×M16—344no—
373C2×M16—348no—
374C22×C8—178no—
375C22×C8—174no—
376C22×C8—344no—
377C22×C8—342no—
378C22×C8—342no—
379#117—1716no—
380#117—348no—
381#117—3416no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—178no—
385C2×C4⋊C4—174no—
386C2×C4⋊C4—172no—
387C2×C4⋊C4—174no—
388C2×C4⋊C4—174no—
389C2×C4⋊C4—174no—
390C2×C4⋊C4—178no—
391C2×C4⋊C4—344no—
392C2×C4⋊C4—342no—
393C2×C4⋊C4—342no—
394C2×C4⋊C4—344no—
395C2×C4⋊C4—344no—
396C2×C4⋊C4—344no—
397C2×C4⋊C4—344no—
398C2×C4⋊C4—344no—
399C2×C4⋊C4—344no—
400C2×C4⋊C4—342no—
401C2×C4⋊C4—342no—
402C2×C4⋊C4—344no—
403C2×C4⋊C4—342no—
404C2×C4⋊C4—342no—
405C2×C4⋊C4—341no—
406C2×C4⋊C4C2×#59512yes—
407C2×C4⋊C4C2×#59514yescomplemented
408C2×C22⋊C4—344no—
409C2×C22⋊C4—348no—
410C2×C42—344no—
411C2×C42—348no—
412C17C2×#173611yescharacteristic, complemented, Sylow
413C24—171no—
414C24—172no—
415C24—172no—
416C24—171no—
417C24—174no—
418C24—174no—
419C24—344no—
420C24—344no—
421C24C22⋊#59511yescharacteristic
422C22×C4—24no—
423C22×C4—22no—
424C22×C4—44no—
425C22×C4—172no—
426C22×C4—172no—
427C22×C4—171no—
428C22×C4—171no—
429C22×C4—174no—
430C22×C4—174no—
431C22×C4—178no—
432C22×C4—174no—
433C22×C4—172no—
434C22×C4—174no—
435C22×C4—172no—
436C22×C4—174no—
437C22×C4—178no—
438C22×C4—174no—
439C22×C4—172no—
440C22×C4—174no—
441C22×C4—172no—
442C22×C4—174no—
443C22×C4—172no—
444C22×C4—172no—
445C22×C4—172no—
446C22×C4—172no—
447C22×C4—171no—
448C22×C4—171no—
449C22×C4—172no—
450C22×C4—171no—
451C22×C4—172no—
452C22×C4—171no—
453C22×C4—174no—
454C22×C4—178no—
455C22×C4—174no—
456C22×C4—178no—
457C22×C4—174no—
458C22×C4—178no—
459C22×C4—178no—
460C22×C4—174no—
461C22×C4—344no—
462C22×C4—344no—
463C22×C4—348no—
464C22×C4—348no—
465C22×C4—344no—
466C22×C4—344no—
467C22×C4—342no—
468C22×C4—688no—
469C22×C4—6816no—
470C22×C4—6816no—
471C22×C4—688no—
472C22×C4—684no—
473C22×C4—684no—
474C22×C4—684no—
475C22×C4C4×#59514yes—
476C22×C4C4⋊#59514yes—
477C22×C4C22⋊#59512yes—
478C22×C4C22⋊#59511yescharacteristic
479C22×C4C22×#59512yes—
480C22×C4C22×#59511yescharacteristic
481M16—3416no—
482M16—3416no—
483C2×C8—178no—
484C2×C8—348no—
485C2×C8—344no—
486C2×C8—348no—
487C2×C8—344no—
488C4⋊C4—22no—
489C4⋊C4—24no—
490C4⋊C4—178no—
491C4⋊C4—174no—
492C4⋊C4—344no—
493C4⋊C4—344no—
494C4⋊C4—348no—
495C4⋊C4—348no—
496C4⋊C4—344no—
497C4⋊C4—342no—
498C4⋊C4—344no—
499C4⋊C4C22×#59514yes—
500C22⋊C4—3416no—
501C42—3416no—
502C23—22no—
503C23—22no—
504C23—172no—
505C23—172no—
506C23—174no—
507C23—174no—
508C23—171no—
509C23—171no—
510C23—174no—
511C23—178no—
512C23—174no—
513C23—174no—
514C23—172no—
515C23—344no—
516C23—344no—
517C23—3416no—
518C23—3416no—
519C23—344no—
520C23—344no—
521C23—342no—
522C23—342no—
523C23(C2×#595)⋊C414yes—
524C23C2×C22⋊#59512yes—
525C23C2×C22⋊#59511yescharacteristic
526C2×C4—24no—
527C2×C4—48no—
528C2×C4—44no—
529C2×C4—172no—
530C2×C4—174no—
531C2×C4—178no—
532C2×C4—174no—
533C2×C4—174no—
534C2×C4—172no—
535C2×C4—171no—
536C2×C4—171no—
537C2×C4—172no—
538C2×C4—174no—
539C2×C4—172no—
540C2×C4—172no—
541C2×C4—174no—
542C2×C4—178no—
543C2×C4—178no—
544C2×C4—178no—
545C2×C4—172no—
546C2×C4—174no—
547C2×C4—172no—
548C2×C4—174no—
549C2×C4—171no—
550C2×C4—171no—
551C2×C4—172no—
552C2×C4—174no—
553C2×C4—171no—
554C2×C4—172no—
555C2×C4—174no—
556C2×C4—171no—
557C2×C4—348no—
558C2×C4—344no—
559C2×C4—688no—
560C2×C4—688no—
561C2×C4—6816no—
562C2×C4—688no—
563C2×C4—6816no—
564C2×C4—684no—
565C2×C4—684no—
566C2×C4—684no—
567C2×C4(C2×#595)⋊C418yes—
568C2×C4(C2×#595)⋊C414yes—
569C2×C4C2×C4×#59514yes—
570C2×C4C2×C4×#59512yes—
571C2×C4C2×C4⋊#59514yes—
572C2×C4C2×C4⋊#59512yes—
573C2×C4C2×C22⋊#59511yescharacteristic
574C2×C4C2×C22⋊#59512yes—
575C2×C4C23×#59511yescharacteristic
576C8—348no—
577C22—28no—
578C22—22no—
579C22—22no—
580C22—171no—
581C22—171no—
582C22—172no—
583C22—178no—
584C22—178no—
585C22—172no—
586C22—172no—
587C22—172no—
588C22—172no—
589C22—174no—
590C22—348no—
591C22—348no—
592C22—3416no—
593C22—348no—
594C22—342no—
595C22—342no—
596C22C2×(C2×#595)⋊C414yes—
597C22C2×(C2×#595)⋊C412yes—
598C22#1176380112yes—
599C22#1176380212yes—
600C22C22×C22⋊#59511yescharacteristic
601C4—44no—
602C4—171no—
603C4—171no—
604C4—172no—
605C4—174no—
606C4—688no—
607C4—684no—
608C4C2×(C2×#595)⋊C414yes—
609C4C2×(C2×#595)⋊C412yes—
610C4C22×C4×#59511yescharacteristic
611C4C22×C4⋊#59511yescharacteristic
612C2—24no—
613C2—172no—
614C2—172no—
615C2—174no—
616C2—344no—
617C2#1454447114yesdirect product factor
618C2C22×(C2×#595)⋊C411yescharacteristic
619C2C2×#1176380111yescharacteristic
620C2C2×#1176380211yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC4×C17C22×C42
FrattiniC2×C4C23×#595
FittingC22×C4⋊C4×C17C4
socleC23×C17C2×C22⋊C4
prime radicalC24×D17D4
cosocleC2×C4×D17C24
hypercenterC22×C4⋊C4#595
hypocenterC17C2×#1736
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #14544471C2direct (N × H)
4. C2×#11763682C2semidirect
9. C2×D17⋊M16C4semidirect
15. C2×#10587677C4semidirect
20. #11763682C22semidirect
23. C22×C4⋊Dic17C4semidirect
29. C2×C4⋊C4×D17C4semidirect
30. C2×C4⋊C4×D17C4semidirect
33. C22×C4⋊C4×C17C4semidirect
64. #10587677C2×C4semidirect
67. C2×C4⋊#595C2×C4semidirect
73. D17⋊M16C2×C4semidirect
78. C2×#63242C2×C4semidirect
83. C2×C4⋊C4×C17C2×C4semidirect
87. C2×C4⋊Dic17C2×C4semidirect
100. C4⋊C4×D17C2×C4semidirect
176. C4⋊#595C22×C4semidirect
181. #63242C22×C4semidirect
331. C22×C4⋊C4#595semidirect
336. C2×C17#1736semidirect
341. D17#1736semidirect
407. C2×C4⋊C4C2×#595semidirect
412. C17C2×#1736semidirect
617. C2#14544471direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D17⋊M162
C22×#105876772
#145444712
C2×#117636822
C22×C4⋊C4×D172
C2×#173617