Finite Group Databasebeta

← #16940648

Subgroups — #16940648

Order 4352.

1066 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762773C211yesmaximal, characteristic
2#14537202C211yesmaximal, characteristic, complemented
3#14531167C211yesmaximal, characteristic
4C2×#11762581C211yesmaximal, characteristic, complemented
5C2×#11762580C211yesmaximal, characteristic, complemented
6#14528522C211yesmaximal, characteristic, complemented
7C2×C17×#407C211yesmaximal, characteristic
8C22×#63223C2211yescharacteristic
9C22×#63223C2211yescharacteristic
10C2×#10587612C2211yescharacteristic
11C2×#10587612C2211yescharacteristic
12#11762773—22no—
13#11762773C414yescomplemented
14C2×C22⋊#3622—22no—
15#11762767—22no—
16#11762764—22no—
17M16×Dic17—22no—
18#11762672C412yes—
19#11762669—22no—
20#11762665C412yes—
21C4×C22⋊Dic17—22no—
22#11762581—22no—
23#11762580—22no—
24#11762577—22no—
25C24×C4×C17C2211yescharacteristic
26C22×M16×C17C2211yescharacteristic
27C22×M16×C17C2211yescharacteristic
28C17×#407—22no—
29C17×#407C414yescomplemented
30C2×C17×C22⋊C8—22no—
31C25×C17C2×C411yescharacteristic
32C23×C4×C17—21no—
33C23×C4×C17—21no—
34C23×C4×C17—21no—
35C23×C4×C17—21no—
36C23×C4×C17—21no—
37C23×C4×C17—21no—
38C23×C4×C17—21no—
39C23×C4×C17—21no—
40C23×C4×C17—21no—
41C23×C4×C17—21no—
42C23×C4×C17—21no—
43C23×C4×C17—21no—
44C23×C4×C17C2×C411yescharacteristic
45C23×C4×C17C2×C412yes—
46C23×C4×C17C2×C412yes—
47C23×C4×C17C2311yescharacteristic
48C2×M16×C17—21no—
49C2×M16×C17—21no—
50C2×M16×C17—21no—
51C2×M16×C17—21no—
52C2×M16×C17—21no—
53C2×M16×C17—21no—
54C2×M16×C17—21no—
55C2×M16×C17—21no—
56C2×M16×C17—21no—
57C2×M16×C17C2×C412yes—
58C2×M16×C17C2×C412yes—
59C2×M16×C17D412yes—
60C22×C8×C17—21no—
61C22×C8×C17D412yes—
62C2×C22⋊Dic17—24no—
63C2×C22⋊Dic17C2×C412yes—
64C2×C22⋊Dic17C2×C412yes—
65#10587612—21no—
66#10587612—21no—
67#10587612—21no—
68#10587612—21no—
69#10587612—21no—
70#10587612—21no—
71#10587612—21no—
72#10587612—21no—
73C2×C4⋊Dic17—21no—
74C2×C4⋊Dic17D412yes—
75C2×C4×Dic17—21no—
76C2×C4×Dic17D412yes—
77C2×#63223—21no—
78C2×#63223—21no—
79C2×#63223—21no—
80C2×#63223—21no—
81C2×#63223—21no—
82C2×#63223—21no—
83C2×#63223—21no—
84C2×#63223—21no—
85C2×#63223—21no—
86C2×#63223C2×C412yes—
87C2×#63223C2×C412yes—
88C2×#63223D412yes—
89C22×#3622—21no—
90C22×#3622D412yes—
91C17×C22⋊C8—28no—
92#10587502—24no—
93C22⋊#3622—28no—
94#10587486—24no—
95C8×Dic17—24no—
96C24×C17—21no—
97C24×C17—21no—
98C24×C17—21no—
99C24×C17—21no—
100C24×C17—21no—
101C24×C17—21no—
102C24×C17—44no—
103C24×C17C4212yes—
104C24×C17C22×C411yescharacteristic
105C22×C4×C17—21no—
106C22×C4×C17—21no—
107C22×C4×C17—21no—
108C22×C4×C17—21no—
109C22×C4×C17—21no—
110C22×C4×C17—21no—
111C22×C4×C17—22no—
112C22×C4×C17—22no—
113C22×C4×C17—22no—
114C22×C4×C17—22no—
115C22×C4×C17—22no—
116C22×C4×C17—22no—
117C22×C4×C17—22no—
118C22×C4×C17—22no—
119C22×C4×C17—22no—
120C22×C4×C17—22no—
121C22×C4×C17—22no—
122C22×C4×C17—22no—
123C22×C4×C17—41no—
124C22×C4×C17—41no—
125C22×C4×C17—41no—
126C22×C4×C17—41no—
127C22×C4×C17—41no—
128C22×C4×C17—41no—
129C22×C4×C17—41no—
130C22×C4×C17—41no—
131C22×C4×C17—41no—
132C22×C4×C17—41no—
133C22×C4×C17—41no—
134C22×C4×C17—41no—
135C22×C4×C17—41no—
136C22×C4×C17—41no—
137C22×C4×C17—41no—
138C22×C4×C17—41no—
139C22×C4×C17C4212yes—
140C22×C4×C17C22×C411yescharacteristic
141C22×C4×C17C22×C411yescharacteristic
142C22×C4×C17C2×D411yescharacteristic
143C22×C4×C17C2×D411yescharacteristic
144C22×C4×C17C2×D411yescharacteristic
145C22×C4×C17C2×D411yescharacteristic
146C22×C4×C17C2×D411yescharacteristic
147C22×C4×C17C2×D411yescharacteristic
148C22×C4×C17#4111yescharacteristic
149C22×C4×C17#4111yescharacteristic
150C22×C4×C17#4111yescharacteristic
151C22×C4×C17#4111yescharacteristic
152C22×C4×C17#4111yescharacteristic
153C22×C4×C17#4111yescharacteristic
154C22×Dic17—22no—
155C22×Dic17C22⋊C414yes—
156M16×C17—22no—
157M16×C17—22no—
158M16×C17—22no—
159M16×C17—22no—
160M16×C17—22no—
161M16×C17—22no—
162M16×C17—41no—
163M16×C17—41no—
164C2×C8×C17—22no—
165C2×C8×C17—22no—
166C2×C8×C17—22no—
167C2×C8×C17—41no—
168C2×C8×C17—41no—
169C2×C8×C17C22⋊C414yescomplemented
170C22⋊Dic17—22no—
171C22⋊Dic17—22no—
172C22⋊Dic17—22no—
173C22⋊Dic17—22no—
174C22⋊Dic17—48no—
175C4⋊Dic17—22no—
176C4⋊Dic17—22no—
177C4⋊Dic17—41no—
178C4⋊Dic17—41no—
179C4×Dic17—22no—
180C4×Dic17—22no—
181C4×Dic17—41no—
182C4×Dic17—41no—
183#63223—22no—
184#63223—22no—
185#63223—22no—
186#63223—22no—
187#63223—22no—
188#63223—22no—
189#63223—41no—
190#63223—41no—
191C2×#3622—22no—
192C2×#3622—22no—
193C2×#3622—22no—
194C2×#3622—41no—
195C2×#3622—41no—
196C2×#3622C22⋊C414yescomplemented
197#10937—171nomaximal, Sylow
198C23×C17—24no—
199C23×C17—24no—
200C23×C17—24no—
201C23×C17—22no—
202C23×C17—22no—
203C23×C17—22no—
204C23×C17—44no—
205C23×C17—42no—
206C23×C17—42no—
207C23×C17—42no—
208C23×C17—42no—
209C23×C17—44no—
210C23×C17—44no—
211C23×C17—44no—
212C23×C17—41no—
213C23×C17—41no—
214C23×C17—41no—
215C23×C17—41no—
216C23×C17C2×C4211yescharacteristic
217C23×C17C2×C22⋊C411yescharacteristic
218C23×C17#11711yescharacteristic
219C23×C17C4×D411yescharacteristic
220C23×C17C4×D411yescharacteristic
221C23×C17C4×D411yescharacteristic
222C23×C17C4×D411yescharacteristic
223C2×C4×C17—22no—
224C2×C4×C17—22no—
225C2×C4×C17—22no—
226C2×C4×C17—41no—
227C2×C4×C17—41no—
228C2×C4×C17—41no—
229C2×C4×C17—41no—
230C2×C4×C17—42no—
231C2×C4×C17—42no—
232C2×C4×C17—42no—
233C2×C4×C17—42no—
234C2×C4×C17—42no—
235C2×C4×C17—42no—
236C2×C4×C17—42no—
237C2×C4×C17—42no—
238C2×C4×C17C2×C22⋊C411yescharacteristic
239C2×C4×C17C2×C22⋊C411yescharacteristic
240C2×C4×C17#11711yescharacteristic
241C2×C4×C17#11711yescharacteristic
242C2×C4×C17C4×D411yescharacteristic
243C2×C4×C17C4×D411yescharacteristic
244C2×C4×C17C4×D411yescharacteristic
245C2×C4×C17C4×D411yescharacteristic
246C2×C4×C17C4×D411yescharacteristic
247C2×C4×C17C4×D411yescharacteristic
248C2×C4×C17C4×D411yescharacteristic
249C2×C4×C17C4×D411yescharacteristic
250C2×C4×C17#12011yescharacteristic
251C2×C4×C17#12111yescharacteristic
252C2×C4×C17#12111yescharacteristic
253C2×C4×C17#12111yescharacteristic
254C2×C4×C17#12111yescharacteristic
255C2×C4×C17#12111yescharacteristic
256C2×C4×C17#12111yescharacteristic
257C2×C4×C17#12311yescharacteristic
258C2×C4×C17#12311yescharacteristic
259C2×C4×C17#12311yescharacteristic
260C2×C4×C17#12411yescharacteristic
261C2×C4×C17#12411yescharacteristic
262C2×C4×C17#12411yescharacteristic
263C2×C4×C17#12611yescharacteristic
264C2×C4×C17#12611yescharacteristic
265C2×C4×C17#12711yescharacteristic
266C2×Dic17—24no—
267C2×Dic17—44no—
268C2×Dic17—44no—
269C2×Dic17—42no—
270C8×C17—24no—
271C8×C17—42no—
272#3622—24no—
273#3622—42no—
274C2×#407—171no—
275C2×#407D1711yescharacteristic
276#2873—171no—
277#2280—171no—
278C2×#344—171no—
279C2×#344—171no—
280#1742—171no—
281C22×C17—22no—
282C22×C17—22no—
283C22×C17—22no—
284C22×C17—24no—
285C22×C17—24no—
286C22×C17—24no—
287C22×C17—41no—
288C22×C17—41no—
289C22×C17—41no—
290C22×C17—41no—
291C22×C17—44no—
292C22×C17—42no—
293C22×C17—42no—
294C22×C17—42no—
295C22×C17—44no—
296C22×C17—44no—
297C22×C17—44no—
298C22×C17—42no—
299C22×C17C4×C22⋊C411yescharacteristic
300C22×C17C4×C22⋊C411yescharacteristic
301C22×C17C4×C22⋊C411yescharacteristic
302C22×C17#38611yescharacteristic
303C22×C17#38811yescharacteristic
304C22×C17#38811yescharacteristic
305C22×C17#39011yescharacteristic
306C4×C17—42no—
307C4×C17#38611yescharacteristic
308C4×C17#38611yescharacteristic
309C4×C17#38811yescharacteristic
310C4×C17#38811yescharacteristic
311C4×C17#38811yescharacteristic
312C4×C17#38811yescharacteristic
313C4×C17#39011yescharacteristic
314C4×C17#39011yescharacteristic
315Dic17—44no—
316Dic17—82no—
317C24×C4C2×D1711yescharacteristic
318C22×M16—171no—
319C22×M16—171no—
320C22×M16C2×D1711yescharacteristic
321C22×M16C2×D1711yescharacteristic
322C2×#117—171no—
323C2×#117—171no—
324#407—22no—
325#407—174no—
326#407—342no—
327#407Dic1714yescomplemented
328C2×C22⋊C8—22no—
329C2×C22⋊C8—342no—
330#405—342no—
331#405—342no—
332C4×M16—342no—
333#381—172no—
334#380—342no—
335#379—172no—
336C4×C22⋊C4—342no—
337#344—342no—
338#344—342no—
339#343—342no—
340C2×C17—21no—
341C2×C17—21no—
342C2×C17—21no—
343C2×C17—21no—
344C2×C17—21no—
345C2×C17—21no—
346C2×C17—44no—
347C2×C17#143711yescharacteristic
348C2×C17#189112yes—
349C25C4×D1711yescharacteristic
350C23×C4—21no—
351C23×C4—21no—
352C23×C4—21no—
353C23×C4—21no—
354C23×C4—21no—
355C23×C4—21no—
356C23×C4—21no—
357C23×C4—21no—
358C23×C4—21no—
359C23×C4—21no—
360C23×C4—21no—
361C23×C4—21no—
362C23×C4C4×D1712yes—
363C23×C4C4×D1711yescharacteristic
364C23×C4C2×Dic1712yes—
365C23×C4C22×D1711yescharacteristic
366C2×M16—21no—
367C2×M16—21no—
368C2×M16—21no—
369C2×M16—21no—
370C2×M16—21no—
371C2×M16—21no—
372C2×M16—21no—
373C2×M16—21no—
374C2×M16—21no—
375C2×M16—172no—
376C2×M16—172no—
377C2×M16—172no—
378C2×M16—341no—
379C2×M16—341no—
380C2×M16—341no—
381C2×M16—341no—
382C2×M16—341no—
383C2×M16—341no—
384C2×M16—341no—
385C2×M16—341no—
386C2×M16—341no—
387C2×M16C2×Dic1712yes—
388C2×M16C2×Dic1712yes—
389C2×M16C22⋊D1712yes—
390C22×C8—21no—
391C22×C8—172no—
392C22×C8—341no—
393C22×C8C22⋊D1712yes—
394#117—341no—
395#117—341no—
396#117—341no—
397#117—341no—
398#117—341no—
399#117—341no—
400#117—341no—
401#117—341no—
402C2×C4⋊C4—172no—
403C2×C4⋊C4—341no—
404C2×C22⋊C4—172no—
405C2×C22⋊C4—172no—
406C2×C22⋊C4—344no—
407C2×C42—172no—
408C2×C42—341no—
409C22⋊C8—28no—
410C22⋊C8—348no—
411#97—344no—
412C4×C8—344no—
413#95—344no—
414C17#1093711yescharacteristic, complemented, Sylow
415C24—21no—
416C24—21no—
417C24—21no—
418C24—21no—
419C24—21no—
420C24—21no—
421C24—44no—
422C24C4×Dic1712yes—
423C24C2×C4×D1711yescharacteristic
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—174no—
459C22×C4—342no—
460C22×C4C4×Dic1712yes—
461C22×C4C2×C4×D1711yescharacteristic
462C22×C4#6325211yescharacteristic
463C22×C4#6325211yescharacteristic
464C22×C4D4×D1711yescharacteristic
465C22×C4D4×D1711yescharacteristic
466C22×C4D4×D1711yescharacteristic
467C22×C4D4×D1711yescharacteristic
468C22×C4#6325411yescharacteristic
469C22×C4#6325411yescharacteristic
470C22×C4#6325411yescharacteristic
471C22×C4#6325411yescharacteristic
472C22×C4C22×Dic1711yescharacteristic
473C22×C4C2×C22⋊D1711yescharacteristic
474C22×C4C2×C22⋊D1711yescharacteristic
475M16—22no—
476M16—22no—
477M16—22no—
478M16—22no—
479M16—22no—
480M16—22no—
481M16—41no—
482M16—41no—
483M16—342no—
484M16—342no—
485M16—342no—
486M16—342no—
487M16—342no—
488M16—342no—
489M16—681no—
490M16—681no—
491C2×C8—22no—
492C2×C8—22no—
493C2×C8—22no—
494C2×C8—41no—
495C2×C8—41no—
496C2×C8—174no—
497C2×C8—342no—
498C2×C8—342no—
499C2×C8—342no—
500C2×C8—681no—
501C2×C8—681no—
502C2×C8C22⋊Dic1714yescomplemented
503C4⋊C4—342no—
504C4⋊C4—342no—
505C4⋊C4—681no—
506C4⋊C4—681no—
507C22⋊C4—342no—
508C22⋊C4—342no—
509C22⋊C4—342no—
510C22⋊C4—342no—
511C22⋊C4—688no—
512C42—342no—
513C42—342no—
514C42—681no—
515C42—681no—
516C23—24no—
517C23—24no—
518C23—24no—
519C23—22no—
520C23—22no—
521C23—22no—
522C23—42no—
523C23—44no—
524C23—42no—
525C23—42no—
526C23—42no—
527C23—44no—
528C23—44no—
529C23—44no—
530C23—41no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23#1058756311yescharacteristic
535C23C22⋊C4×D1711yescharacteristic
536C23#1058756711yescharacteristic
537C23#1058756711yescharacteristic
538C23C2×C4×Dic1711yescharacteristic
539C23C4×C22⋊D1711yescharacteristic
540C23C4×C22⋊D1711yescharacteristic
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—344no—
557C2×C4—684no—
558C2×C4—684no—
559C2×C4—682no—
560C2×C4#1058756311yescharacteristic
561C2×C4#1058756511yescharacteristic
562C2×C4#1058756511yescharacteristic
563C2×C4C22⋊C4×D1711yescharacteristic
564C2×C4#1058756711yescharacteristic
565C2×C4#1058756711yescharacteristic
566C2×C4#1058756911yescharacteristic
567C2×C4#1058756911yescharacteristic
568C2×C4#1058757011yescharacteristic
569C2×C4#1058757011yescharacteristic
570C2×C4#1058757111yescharacteristic
571C2×C4#1058757111yescharacteristic
572C2×C4#1058761211yescharacteristic
573C2×C4C4×C22⋊D1711yescharacteristic
574C2×C4C4×C22⋊D1711yescharacteristic
575C2×C4D4×Dic1711yescharacteristic
576C2×C4D4×Dic1711yescharacteristic
577C2×C4D4×Dic1711yescharacteristic
578C2×C4D4×Dic1711yescharacteristic
579C2×C4#1058762111yescharacteristic
580C2×C4#1058762211yescharacteristic
581C2×C4#1058762311yescharacteristic
582C2×C4#1058762411yescharacteristic
583C2×C4#1058762411yescharacteristic
584C2×C4#1058762511yescharacteristic
585C2×C4#1058762511yescharacteristic
586C2×C4#1058762611yescharacteristic
587C2×C4C2×C22⋊Dic1711yescharacteristic
588C8—24no—
589C8—42no—
590C8—344no—
591C8—682no—
592C22—22no—
593C22—22no—
594C22—22no—
595C22—24no—
596C22—24no—
597C22—24no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—44no—
603C22—42no—
604C22—42no—
605C22—42no—
606C22—44no—
607C22—44no—
608C22—42no—
609C22—44no—
610C22C4×C22⋊Dic1711yescharacteristic
611C22C22⋊C4×Dic1711yescharacteristic
612C22C22⋊C4×Dic1711yescharacteristic
613C22#1176268511yescharacteristic
614C22#1176269711yescharacteristic
615C22#1176270311yescharacteristic
616C22#1176270911yescharacteristic
617C4—42no—
618C4—684no—
619C4—1362no—
620C4#1176268511yescharacteristic
621C4#1176268911yescharacteristic
622C4#1176269711yescharacteristic
623C4#1176270211yescharacteristic
624C4#1176270211yescharacteristic
625C4#1176270311yescharacteristic
626C4#1176270911yescharacteristic
627C4#1176271211yescharacteristic
628C2—21no—
629C2—21no—
630C2—21no—
631C2—21no—
632C2—21no—
633C2—21no—
634C2—44no—
635C2#1452702111yescharacteristic
636C2#1452919912yes—
subgroupG/H
centerC2×C4#10587623
commutatorC23×C17C2×C42
FrattiniC23×C4C22×D17
FittingC2×C17×#407C2
socleC22×C17#386
prime radicalC25×C17C2×C4
cosocleC23×C4×C17C23
hypercenterC2×#407D17
hypocenterC17#10937
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
2. #14537202C2semidirect
4. C2×#11762581C2semidirect
5. C2×#11762580C2semidirect
6. #14528522C2semidirect
13. #11762773C4semidirect
29. C17×#407C4semidirect
169. C2×C8×C17C22⋊C4semidirect
196. C2×#3622C22⋊C4semidirect
327. #407Dic17semidirect
414. C17#10937semidirect
502. C2×C8C22⋊Dic17semidirect

Maximal subgroups

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

subgroupindex
C2×#117627732
#145372022
#145311672
C2×#117625812
C2×#117625802
#145285222
C2×C17×#4072
#1093717