Finite Group Databasebeta

← #16940649

Subgroups — #16940649

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×#11762772C211yesmaximal, characteristic
2C2×#11762772C211yesmaximal, characteristic
3#14537202C211yesmaximal, characteristic, complemented
4#14531163C211yesmaximal, characteristic
5C2×#11762579C211yesmaximal, characteristic, complemented
6#14528522C211yesmaximal, characteristic, complemented
7C2×C17×#344C211yesmaximal, characteristic, complemented
8C23×C4×D17C2211yescharacteristic
9C22×#63223C2211yescharacteristic
10C22×#63223C2211yescharacteristic
11C2×#10587612C2211yescharacteristic
12#11762772—22no—
13#11762772—22no—
14#11762772C414yescomplemented
15#11762772C414yescomplemented
16C2×#10587491—22no—
17C2×#10587491—22no—
18#11762767—22no—
19#11762764—22no—
20M16×Dic17—22no—
21#11762670C412yes—
22#11762666—22no—
23#11762664C412yes—
24C4×#63227—22no—
25#11762579—22no—
26#11762577—22no—
27C22×M16×C17C2211yescharacteristic
28C22×M16×C17C2211yescharacteristic
29C2×C17×#117C2211yescharacteristic
30C17×#344—22no—
31C24×D17C2×C411yescharacteristic
32C23×C4×C17C2311yescharacteristic
33C23×Dic17C2×C411yescharacteristic
34C22×C4×D17—21no—
35C22×C4×D17—21no—
36C22×C4×D17—21no—
37C22×C4×D17—21no—
38C22×C4×D17—21no—
39C22×C4×D17—21no—
40C22×C4×D17—21no—
41C22×C4×D17—21no—
42C22×C4×D17—21no—
43C22×C4×D17—21no—
44C22×C4×D17—21no—
45C22×C4×D17—21no—
46C22×C4×D17C2×C412yes—
47C22×C4×D17C2×C412yes—
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—
62C17×#117—21no—
63C17×#117—21no—
64C17×#117—21no—
65C17×#117—21no—
66C2×C4⋊C4×C17—21no—
67C2×C22⋊C4×C17C2×C412yes—
68C2×C42×C17—21no—
69C2×C22⋊Dic17C2×C412yes—
70C2×#63227—24no—
71#10587612—21no—
72#10587612—21no—
73#10587612—21no—
74#10587612—21no—
75C2×C4⋊Dic17D412yes—
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—
91#10587502—24no—
92#10587491—28no—
93#10587491—28no—
94#10587486—24no—
95C8×Dic17—24no—
96C24×C17C22×C411yescharacteristic
97C23×D17—21no—
98C23×D17—21no—
99C23×D17—21no—
100C23×D17—21no—
101C23×D17—21no—
102C23×D17—21no—
103C23×D17—44no—
104C23×D17C4212yes—
105C22×C4×C17—22no—
106C22×C4×C17C22×C411yescharacteristic
107C22×C4×C17C22×C411yescharacteristic
108C22×C4×C17C2×D411yescharacteristic
109C22×C4×C17C2×D411yescharacteristic
110C22×C4×C17C2×D411yescharacteristic
111C22×C4×C17C2×D411yescharacteristic
112C22×C4×C17C2×D411yescharacteristic
113C22×C4×C17C2×D411yescharacteristic
114C22×C4×C17#4111yescharacteristic
115C22×C4×C17#4111yescharacteristic
116C22×C4×C17#4111yescharacteristic
117C22×C4×C17#4111yescharacteristic
118C22×C4×C17#4111yescharacteristic
119C22×C4×C17#4111yescharacteristic
120C22×Dic17—21no—
121C22×Dic17—21no—
122C22×Dic17—21no—
123C22×Dic17—21no—
124C22×Dic17—21no—
125C22×Dic17—21no—
126C22×Dic17C4212yes—
127C22×Dic17C22⋊C414yes—
128C2×C4×D17—22no—
129C2×C4×D17—22no—
130C2×C4×D17—22no—
131C2×C4×D17—22no—
132C2×C4×D17—22no—
133C2×C4×D17—22no—
134C2×C4×D17—22no—
135C2×C4×D17—22no—
136C2×C4×D17—22no—
137C2×C4×D17—22no—
138C2×C4×D17—22no—
139C2×C4×D17—22no—
140C2×C4×D17—41no—
141C2×C4×D17—41no—
142C2×C4×D17—41no—
143C2×C4×D17—41no—
144C2×C4×D17—41no—
145C2×C4×D17—41no—
146C2×C4×D17—41no—
147C2×C4×D17—41no—
148C2×C4×D17—41no—
149C2×C4×D17—41no—
150C2×C4×D17—41no—
151C2×C4×D17—41no—
152C2×C4×D17—41no—
153C2×C4×D17—41no—
154C2×C4×D17—41no—
155C2×C4×D17—41no—
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
170C4⋊C4×C17—41no—
171C4⋊C4×C17—41no—
172C22⋊C4×C17—22no—
173C22⋊C4×C17—22no—
174C42×C17—41no—
175C42×C17—41no—
176C22⋊Dic17—22no—
177C22⋊Dic17—22no—
178#63227—48no—
179C4⋊Dic17—22no—
180C4⋊Dic17—22no—
181C4×Dic17—22no—
182C4×Dic17—22no—
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—42no—
199C23×C17C2×C4211yescharacteristic
200C23×C17C2×C22⋊C411yescharacteristic
201C23×C17#11711yescharacteristic
202C23×C17C4×D411yescharacteristic
203C23×C17C4×D411yescharacteristic
204C23×C17C4×D411yescharacteristic
205C23×C17C4×D411yescharacteristic
206C22×D17—24no—
207C22×D17—24no—
208C22×D17—24no—
209C22×D17—22no—
210C22×D17—22no—
211C22×D17—22no—
212C22×D17—44no—
213C22×D17—44no—
214C22×D17—44no—
215C22×D17—44no—
216C22×D17—42no—
217C22×D17—42no—
218C22×D17—42no—
219C22×D17—41no—
220C22×D17—41no—
221C22×D17—41no—
222C22×D17—41no—
223C2×C4×C17—44no—
224C2×C4×C17—42no—
225C2×C4×C17C2×C22⋊C411yescharacteristic
226C2×C4×C17C2×C22⋊C411yescharacteristic
227C2×C4×C17#11711yescharacteristic
228C2×C4×C17#11711yescharacteristic
229C2×C4×C17C4×D411yescharacteristic
230C2×C4×C17C4×D411yescharacteristic
231C2×C4×C17C4×D411yescharacteristic
232C2×C4×C17C4×D411yescharacteristic
233C2×C4×C17C4×D411yescharacteristic
234C2×C4×C17C4×D411yescharacteristic
235C2×C4×C17C4×D411yescharacteristic
236C2×C4×C17C4×D411yescharacteristic
237C2×C4×C17#12011yescharacteristic
238C2×C4×C17#12111yescharacteristic
239C2×C4×C17#12111yescharacteristic
240C2×C4×C17#12111yescharacteristic
241C2×C4×C17#12111yescharacteristic
242C2×C4×C17#12111yescharacteristic
243C2×C4×C17#12111yescharacteristic
244C2×C4×C17#12311yescharacteristic
245C2×C4×C17#12311yescharacteristic
246C2×C4×C17#12311yescharacteristic
247C2×C4×C17#12411yescharacteristic
248C2×C4×C17#12411yescharacteristic
249C2×C4×C17#12411yescharacteristic
250C2×C4×C17#12611yescharacteristic
251C2×C4×C17#12611yescharacteristic
252C2×C4×C17#12711yescharacteristic
253C2×Dic17—22no—
254C2×Dic17—22no—
255C2×Dic17—22no—
256C2×Dic17—24no—
257C2×Dic17—41no—
258C2×Dic17—41no—
259C2×Dic17—41no—
260C2×Dic17—41no—
261C2×Dic17—44no—
262C4×D17—42no—
263C4×D17—42no—
264C4×D17—42no—
265C4×D17—42no—
266C4×D17—42no—
267C4×D17—42no—
268C4×D17—42no—
269C4×D17—42no—
270C8×C17—24no—
271C8×C17—42no—
272#3622—24no—
273#3622—42no—
274C2×#407—171no—
275C2×#407—171no—
276#2873—171no—
277#2280—171no—
278C2×#344—171no—
279C2×#344D1711yescharacteristic, complemented
280#1742—171no—
281C22×C17—22no—
282C22×C17—22no—
283C22×C17—22no—
284C22×C17—41no—
285C22×C17—41no—
286C22×C17—41no—
287C22×C17—41no—
288C22×C17C4×C22⋊C411yescharacteristic
289C22×C17C4×C22⋊C411yescharacteristic
290C22×C17C4×C22⋊C411yescharacteristic
291C22×C17#38611yescharacteristic
292C22×C17#38811yescharacteristic
293C22×C17#38811yescharacteristic
294C22×C17#39011yescharacteristic
295C2×D17—24no—
296C2×D17—24no—
297C2×D17—24no—
298C2×D17—44no—
299C2×D17—42no—
300C2×D17—42no—
301C2×D17—42no—
302C2×D17—44no—
303C2×D17—44no—
304C2×D17—44no—
305C2×D17—42no—
306C4×C17—82no—
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—42no—
317C24×C4—171no—
318C22×M16—171no—
319C22×M16—171no—
320C22×M16C2×D1711yescharacteristic
321C22×M16C2×D1711yescharacteristic
322C2×#117—171no—
323C2×#117C2×D1711yescharacteristic
324#407—174no—
325#407—174no—
326#407—342no—
327#407—342no—
328C2×C22⋊C8—342no—
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—22no—
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#143711yescharacteristic
347C2×C17#189112yes—
348D17—44no—
349C25—171no—
350C23×C4—171no—
351C23×C4—172no—
352C23×C4—172no—
353C23×C4—341no—
354C23×C4—341no—
355C23×C4—341no—
356C23×C4—341no—
357C23×C4—341no—
358C23×C4—341no—
359C23×C4—341no—
360C23×C4—341no—
361C23×C4—341no—
362C23×C4—341no—
363C23×C4—341no—
364C23×C4—341no—
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×M16C4×D1712yes—
388C2×M16C4×D1712yes—
389C2×M16C22⋊D1712yes—
390C22×C8—21no—
391C22×C8—172no—
392C22×C8—341no—
393C22×C8D6812yes—
394#117—21no—
395#117—21no—
396#117—21no—
397#117—21no—
398#117—341no—
399#117—341no—
400#117—341no—
401#117—341no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—172no—
404C2×C22⋊C4—172no—
405C2×C22⋊C4—344no—
406C2×C22⋊C4C4×D1712yes—
407C2×C42—21no—
408C2×C42—172no—
409C22⋊C8—348no—
410C22⋊C8—348no—
411#97—344no—
412C4×C8—344no—
413#95—344no—
414C17#1093711yescharacteristic, complemented, Sylow
415C24—172no—
416C24—341no—
417C24—341no—
418C24—341no—
419C24—341no—
420C24—341no—
421C24—341no—
422C24—684no—
423C24C2×C4×D1711yescharacteristic
424C22×C4—22no—
425C22×C4—172no—
426C22×C4—174no—
427C22×C4—341no—
428C22×C4—341no—
429C22×C4—341no—
430C22×C4—341no—
431C22×C4—341no—
432C22×C4—341no—
433C22×C4—342no—
434C22×C4—342no—
435C22×C4—342no—
436C22×C4—342no—
437C22×C4—342no—
438C22×C4—342no—
439C22×C4—342no—
440C22×C4—342no—
441C22×C4—342no—
442C22×C4—342no—
443C22×C4—342no—
444C22×C4—342no—
445C22×C4—681no—
446C22×C4—681no—
447C22×C4—681no—
448C22×C4—681no—
449C22×C4—681no—
450C22×C4—681no—
451C22×C4—681no—
452C22×C4—681no—
453C22×C4—681no—
454C22×C4—681no—
455C22×C4—681no—
456C22×C4—681no—
457C22×C4—681no—
458C22×C4—681no—
459C22×C4—681no—
460C22×C4—681no—
461C22×C4C2×C4×D1711yescharacteristic
462C22×C4C2×C4×D1711yescharacteristic
463C22×C4C2×D6811yescharacteristic
464C22×C4#6325211yescharacteristic
465C22×C4#6325211yescharacteristic
466C22×C4D4×D1711yescharacteristic
467C22×C4D4×D1711yescharacteristic
468C22×C4D4×D1711yescharacteristic
469C22×C4D4×D1711yescharacteristic
470C22×C4#6325411yescharacteristic
471C22×C4#6325411yescharacteristic
472C22×C4#6325611yescharacteristic
473C22×C4#6325611yescharacteristic
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×C8#6322714yescomplemented
503C4⋊C4—41no—
504C4⋊C4—41no—
505C4⋊C4—342no—
506C4⋊C4—342no—
507C22⋊C4—22no—
508C22⋊C4—22no—
509C22⋊C4—342no—
510C22⋊C4—342no—
511C22⋊C4—688no—
512C42—41no—
513C42—41no—
514C42—342no—
515C42—342no—
516C23—42no—
517C23—344no—
518C23—344no—
519C23—344no—
520C23—342no—
521C23—342no—
522C23—342no—
523C23—682no—
524C23—682no—
525C23—682no—
526C23—684no—
527C23—684no—
528C23—684no—
529C23—684no—
530C23—681no—
531C23—681no—
532C23—681no—
533C23—681no—
534C23C42×D1711yescharacteristic
535C23C4×D6811yescharacteristic
536C23C22⋊C4×D1711yescharacteristic
537C23#1058756711yescharacteristic
538C23#1058757811yescharacteristic
539C23#1058757911yescharacteristic
540C23C4×C22⋊D1711yescharacteristic
541C2×C4—44no—
542C2×C4—42no—
543C2×C4—342no—
544C2×C4—342no—
545C2×C4—342no—
546C2×C4—344no—
547C2×C4—681no—
548C2×C4—681no—
549C2×C4—681no—
550C2×C4—681no—
551C2×C4—682no—
552C2×C4—682no—
553C2×C4—682no—
554C2×C4—682no—
555C2×C4—682no—
556C2×C4—682no—
557C2×C4—682no—
558C2×C4—682no—
559C2×C4—684no—
560C2×C4#1058755811yescharacteristic
561C2×C4C4×D6811yescharacteristic
562C2×C4C22⋊C4×D1711yescharacteristic
563C2×C4#1058756711yescharacteristic
564C2×C4#1058756711yescharacteristic
565C2×C4#1058756711yescharacteristic
566C2×C4#1058756811yescharacteristic
567C2×C4#1058757011yescharacteristic
568C2×C4#1058757011yescharacteristic
569C2×C4#1058757111yescharacteristic
570C2×C4#1058757111yescharacteristic
571C2×C4#1058757211yescharacteristic
572C2×C4#1058757811yescharacteristic
573C2×C4#1058757911yescharacteristic
574C2×C4#1058757911yescharacteristic
575C2×C4#1058757911yescharacteristic
576C2×C4#1058758011yescharacteristic
577C2×C4#1058758011yescharacteristic
578C2×C4#1058758111yescharacteristic
579C2×C4#1058758111yescharacteristic
580C2×C4#1058758411yescharacteristic
581C2×C4#1058758411yescharacteristic
582C2×C4C2×#6322711yescharacteristic
583C2×C4C4×C22⋊D1711yescharacteristic
584C2×C4#1058762511yescharacteristic
585C2×C4#1058762511yescharacteristic
586C2×C4#1058762611yescharacteristic
587C2×C4#1058763311yescharacteristic
588C8—24no—
589C8—42no—
590C8—344no—
591C8—682no—
592C22—22no—
593C22—22no—
594C22—22no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—344no—
600C22—344no—
601C22—344no—
602C22—684no—
603C22—682no—
604C22—682no—
605C22—682no—
606C22—684no—
607C22—684no—
608C22—682no—
609C22—684no—
610C22#1176265611yescharacteristic
611C22#1176265611yescharacteristic
612C22C4×#6322711yescharacteristic
613C22#1176268711yescharacteristic
614C22#1176269911yescharacteristic
615C22#1176270111yescharacteristic
616C22#1176270911yescharacteristic
617C4—82no—
618C4—682no—
619C4—684no—
620C4#1176268611yescharacteristic
621C4#1176268711yescharacteristic
622C4#1176269811yescharacteristic
623C4#1176269811yescharacteristic
624C4#1176269911yescharacteristic
625C4#1176270111yescharacteristic
626C4#1176270911yescharacteristic
627C4#1176271011yescharacteristic
628C2—21no—
629C2—21no—
630C2—21no—
631C2—21no—
632C2—21no—
633C2—21no—
634C2—684no—
635C2#1452702011yescharacteristic
636C2#1452920112yes—
subgroupG/H
centerC2×C4#10587568
commutatorC23×C17C2×C42
FrattiniC23×C4C22×D17
FittingC2×C17×#344C2
socleC22×C17#386
prime radicalC24×D17C2×C4
cosocleC23×C4×C17C23
hypercenterC2×#344D17
hypocenterC17#10937
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#344

Complements

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

NH ≅ G/Ntype
3. #14537202C2semidirect
5. C2×#11762579C2semidirect
6. #14528522C2semidirect
7. C2×C17×#344C2semidirect
14. #11762772C4semidirect
15. #11762772C4semidirect
169. C2×C8×C17C22⋊C4semidirect
196. C2×#3622C22⋊C4semidirect
279. C2×#344D17semidirect
414. C17#10937semidirect
502. C2×C8#63227semidirect

Maximal subgroups

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

subgroupindex
C2×#117627722
#145372022
#145311632
C2×#117625792
#145285222
C2×C17×#3442
#1093717