Finite Group Databasebeta

← #17963024

Subgroups — #17963024

Order 4352.

2182 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763751C211yesmaximal, characteristic
2C2×C4⋊C4×#595C212yesmaximal, complemented
3C2×C4×C22⋊#595C211yesmaximal, characteristic
4#14543965C214yesmaximal
5#14543961C212yesmaximal, complemented
6#14543960C212yesmaximal, complemented
7C4×(C2×#595)⋊C4C212yesmaximal, complemented
8C2×#117×D17C211yesmaximal, characteristic
9C22×C4⋊#595C2212yes—
10C22×C22⋊#595C2212yes—
11C22×C22⋊#595C2212yes—
12C22×C4×#595C2214yes—
13C22×C4×#595C2212yes—
14#11763751C418yescomplemented
15C4⋊C4×#595—28no—
16C4×C22⋊#595C418yescomplemented
17C2×(C2×#595)⋊C4C2214yes—
18C2×(C2×#595)⋊C4C2214yes—
19C2×(C2×#595)⋊C4C2214yes—
20C2×(C2×#595)⋊C4C2211yescharacteristic
21C2×(C2×#595)⋊C4C2211yescharacteristic
22C2×(C2×#595)⋊C4C2212yes—
23C23×C4×D17C2211yescharacteristic
24C2×#10587612C411yescharacteristic, complemented
25C2×#10587578C411yescharacteristic, complemented
26C2×#10587578C411yescharacteristic, complemented
27C2×#10587558C412yescomplemented
28C2×#10587563C412yescomplemented
29#117×D17—28no—
30C2×C4⋊C4×D17C2211yescharacteristic
31C2×C4⋊C4×D17C2211yescharacteristic
32C2×C22⋊C4×D17C2212yes—
33C2×C42×D17C2212yes—
34C2×C17×#117C411yescharacteristic, complemented
35C24×D17C2311yescharacteristic
36C23×#595C2312yes—
37C23×#595C2314yes—
38C23×#595C2312yes—
39C23×C4×C17C2×C411yescharacteristic
40C23×Dic17C2×C411yescharacteristic
41C22×C4×D17—24no—
42C22×C4×D17—24no—
43C22×C4×D17C2×C411yescharacteristic
44C22×C4×D17C2×C411yescharacteristic
45C22×C4×D17C2×C414yes—
46C22×C4×D17C2×C414yes—
47C22×C4×D17C2312yes—
48C22×C4×D17C2311yescharacteristic
49C22×C4×D17C2312yes—
50C22×C4×D17C2311yescharacteristic
51C2×C22⋊#595—24no—
52C2×C22⋊#595—24no—
53C2×C22⋊#595—42no—
54C2×C22⋊#595—42no—
55C2×C22⋊#595C2×C418yes—
56C2×C22⋊#595C2×C418yes—
57C2×C4⋊#595—24no—
58C2×C4⋊#595—24no—
59C2×C4⋊#595C2×C418yes—
60C2×C4×#595—24no—
61C2×C4×#595—24no—
62C2×C4×#595—28no—
63C2×C4×#595—28no—
64C2×C4×#595—44no—
65C2×C4×#595C2×C418yes—
66C17×#117—24no—
67C2×C4⋊C4×C17C2×C411yescharacteristic
68C2×C4⋊C4×C17C2×C411yescharacteristic
69C2×C22⋊C4×C17C2×C412yes—
70C2×C42×C17C2×C412yes—
71C2×C22⋊Dic17C2×C412yes—
72C2×#63227C2×C412yes—
73C2×#63227C2×C412yes—
74#10587612—24no—
75C2×C4⋊Dic17C2×C411yescharacteristic
76C2×C4⋊Dic17C2×C411yescharacteristic
77C2×#63225C2×C412yes—
78C2×#63225C2×C412yes—
79C2×C4×Dic17C2×C412yes—
80C2×C4×Dic17C2×C412yes—
81C2×C4×Dic17C2×C412yes—
82#10587578—24no—
83#10587578—24no—
84C4⋊C4×D17—24no—
85C4⋊C4×D17D418yes—
86C22⋊C4×D17—28no—
87#10587563—28no—
88#10587558—28no—
89C42×D17—28no—
90(C2×#595)⋊C4—28no—
91(C2×#595)⋊C4—28no—
92(C2×#595)⋊C4—44no—
93(C2×#595)⋊C4C2×C414yes—
94(C2×#595)⋊C4C2×C414yes—
95(C2×#595)⋊C4C2×C418yes—
96C24×C17C22×C411yescharacteristic
97C23×D17—22no—
98C23×D17—22no—
99C23×D17—22no—
100C23×D17—22no—
101C23×D17—21no—
102C23×D17—21no—
103C23×D17—21no—
104C23×D17—21no—
105C23×D17C22×C411yescharacteristic
106C23×D17C22×C412yes—
107C23×D17C22×C412yes—
108C23×D17C2411yescharacteristic
109C22×#595—22no—
110C22×#595—22no—
111C22×#595—22no—
112C22×#595—22no—
113C22×#595—24no—
114C22×#595—22no—
115C22×#595—22no—
116C22×#595—24no—
117C22×#595—24no—
118C22×#595—22no—
119C22×#595—22no—
120C22×#595—24no—
121C22×#595—24no—
122C22×#595—24no—
123C22×#595—22no—
124C22×#595—22no—
125C22×#595C22×C414yes—
126C22×#595C22×C418yes—
127C22×#595C22×C414yes—
128C22×#595#4114yes—
129C22×#595#4114yes—
130C22×C4×C17—22no—
131C22×C4×C17—22no—
132C22×C4×C17C4214yescomplemented
133C22×C4×C17C22×C412yes—
134C22×C4×C17C22×C411yescharacteristic
135C22×C4×C17C22×C412yes—
136C22×C4×C17C22×C411yescharacteristic
137C22×Dic17—22no—
138C22×Dic17—22no—
139C22×Dic17C4214yescomplemented
140C22×Dic17C22×C412yes—
141C22×Dic17C22×C411yescharacteristic
142C22×Dic17C22×C412yes—
143C22×Dic17C22×C411yescharacteristic
144C2×C4×D17—22no—
145C2×C4×D17—24no—
146C2×C4×D17—22no—
147C2×C4×D17—22no—
148C2×C4×D17—22no—
149C2×C4×D17—22no—
150C2×C4×D17—22no—
151C2×C4×D17—22no—
152C2×C4×D17—22no—
153C2×C4×D17—216no—
154C2×C4×D17—216no—
155C2×C4×D17—24no—
156C2×C4×D17—24no—
157C2×C4×D17—22no—
158C2×C4×D17—22no—
159C2×C4×D17C4214yescomplemented
160C2×C4×D17C4214yescomplemented
161C2×C4×D17C22×C412yes—
162C2×C4×D17C22×C412yes—
163C2×C4×D17C22×C412yes—
164C2×C4×D17C22×C412yes—
165C2×C4×D17C2×D418yes—
166C2×C4×D17C2×D414yes—
167C2×C4×D17#4114yes—
168C22⋊#595—216no—
169C22⋊#595—48no—
170C4⋊#595—216no—
171C4×#595—216no—
172C4×#595—416no—
173C4⋊C4×C17—22no—
174C4⋊C4×C17C22⋊C414yescomplemented
175C22⋊C4×C17—24no—
176C42×C17—24no—
177C22⋊Dic17—24no—
178#63227—24no—
179#63227—24no—
180C4⋊Dic17—22no—
181C4⋊Dic17C22⋊C414yescomplemented
182#63225—24no—
183#63225C22⋊C418yescomplemented
184C4×Dic17—24no—
185C4×Dic17—24no—
186C4×Dic17—24no—
187#13801—171nomaximal, Sylow
188C23×C17—21no—
189C23×C17—21no—
190C23×C17—21no—
191C23×C17—21no—
192C23×C17—21no—
193C23×C17—21no—
194C23×C17C2×C4212yes—
195C23×C17C23×C411yescharacteristic
196C22×D17—21no—
197C22×D17—21no—
198C22×D17—21no—
199C22×D17—21no—
200C22×D17—21no—
201C22×D17—21no—
202C22×D17—24no—
203C22×D17—24no—
204C22×D17—24no—
205C22×D17—24no—
206C22×D17—22no—
207C22×D17—22no—
208C22×D17—22no—
209C22×D17—22no—
210C22×D17—42no—
211C22×D17—42no—
212C22×D17—42no—
213C22×D17—42no—
214C22×D17—42no—
215C22×D17—42no—
216C22×D17—42no—
217C22×D17—42no—
218C22×D17C2×C4212yes—
219C22×D17C23×C411yescharacteristic
220C22×D17C23×C411yescharacteristic
221C22×D17C22×D412yes—
222C22×D17C2×#4112yes—
223C22×D17C2×#4112yes—
224C22×D17C2×#4112yes—
225C22×D17H(5,𝔽2)11yescharacteristic
226C22×D17H(5,𝔽2)11yescharacteristic
227C22×D172−1+411yescharacteristic
228C22×D172−1+411yescharacteristic
229C2×#595—24no—
230C2×#595—24no—
231C2×#595—24no—
232C2×#595—24no—
233C2×#595—24no—
234C2×#595—24no—
235C2×#595—24no—
236C2×#595—24no—
237C2×#595—28no—
238C2×#595—28no—
239C2×#595—28no—
240C2×#595—24no—
241C2×#595—44no—
242C2×#595—42no—
243C2×#595—42no—
244C2×#595—44no—
245C2×#595—44no—
246C2×#595—42no—
247C2×#595—44no—
248C2×#595—42no—
249C2×#595#11718yescomplemented
250C2×C4×C17—21no—
251C2×C4×C17—21no—
252C2×C4×C17—22no—
253C2×C4×C17—22no—
254C2×C4×C17—28no—
255C2×C4×C17—22no—
256C2×C4×C17—22no—
257C2×C4×C17—22no—
258C2×C4×C17C2×C4212yes—
259C2×C4×C17C2×C4212yes—
260C2×C4×C17C2×C22⋊C414yes—
261C2×C4×C17C2×C22⋊C412yes—
262C2×C4×C17#11712yes—
263C2×Dic17—21no—
264C2×Dic17—21no—
265C2×Dic17—22no—
266C2×Dic17—22no—
267C2×Dic17—28no—
268C2×Dic17—22no—
269C2×Dic17—22no—
270C2×Dic17—22no—
271C2×Dic17C2×C4212yes—
272C2×Dic17C2×C4212yes—
273C2×Dic17C2×C22⋊C414yes—
274C2×Dic17C2×C22⋊C412yes—
275C2×Dic17#11712yes—
276C4×D17—24no—
277C4×D17—24no—
278C4×D17—28no—
279C4×D17—28no—
280C4×D17—28no—
281C4×D17—28no—
282C4×D17—44no—
283C4×D17—44no—
284C4×D17C4×D418yes—
285C4×D17C4×D418yes—
286C22×#117—171no—
287C2×#380—171no—
288C2×C4×C4⋊C4—172no—
289C2×C4×C22⋊C4—171no—
290#1437—174no—
291C4⋊#95—172no—
292#1434—172no—
293C4×#95—172no—
294C22×C17—22no—
295C22×C17—22no—
296C22×C17—22no—
297C22×C17—41no—
298C22×C17—41no—
299C22×C17—41no—
300C22×C17—41no—
301C22×C17C22×C4211yescharacteristic
302C22×C17C22×C22⋊C411yescharacteristic
303C22×C17C2×#11711yescharacteristic
304C22×C17C4×#4111yescharacteristic
305C22×C17C4×#4111yescharacteristic
306C22×C17#52011yescharacteristic
307C22×C17#52011yescharacteristic
308C2×D17—22no—
309C2×D17—22no—
310C2×D17—22no—
311C2×D17—41no—
312C2×D17—41no—
313C2×D17—41no—
314C2×D17—41no—
315C2×D17—44no—
316C2×D17—44no—
317C2×D17—44no—
318C2×D17—44no—
319C2×D17C2×#11712yes—
320C2×D17C2×C4×D412yes—
321C2×D17C2×C4×D412yes—
322C2×D17C4×#4112yes—
323C2×D17#51811yescharacteristic
324C2×D17#51911yescharacteristic
325C2×D17#52011yescharacteristic
326C2×D17#52011yescharacteristic
327C2×D17#54612yes—
328C2×D17#54712yes—
329C2×D17#54812yes—
330C2×D17#55012yes—
331C2×D17#55212yes—
332C2×D17#55312yes—
333C2×D17#55512yes—
334C2×D17#55612yes—
335#595—28no—
336#595—44no—
337#595—48no—
338C4×C17—24no—
339C4×C17—22no—
340C4×C17—42no—
341C4×C17C4×C22⋊C414yes—
342Dic17—24no—
343Dic17—22no—
344Dic17—42no—
345Dic17C4×C22⋊C414yes—
346C24×C4—171no—
347C2×#117—171no—
348C2×#117—171no—
349C2×#117—171no—
350C2×#117—172no—
351C2×#117—172no—
352C2×#117—348no—
353C2×#117#59511yescharacteristic, complemented
354C22×C4⋊C4—171no—
355C22×C4⋊C4—172no—
356C22×C4⋊C4—171no—
357C22×C22⋊C4—172no—
358C22×C22⋊C4—172no—
359C22×C22⋊C4—172no—
360C22×C42—172no—
361C22×C42—172no—
362C22×C42—174no—
363#380—178no—
364C4×C4⋊C4—348no—
365C4×C22⋊C4—178no—
366C2×#95—171no—
367C2×#95—172no—
368C2×#95—171no—
369C2×#95—174no—
370C2×#95—174no—
371C2×#95—174no—
372C2×C17—42no—
373C2×C17C2×C4×C22⋊C411yescharacteristic
374C2×C17C4×#11711yescharacteristic
375C2×C17#227411yescharacteristic
376C2×C17#233911yescharacteristic
377C2×C17#234111yescharacteristic
378C2×C17#234611yescharacteristic
379C2×C17#234711yescharacteristic
380D17—42no—
381D17#235212yes—
382D17#235412yes—
383D17#236212yes—
384D17#236312yes—
385C25—171no—
386C23×C4—171no—
387C23×C4—172no—
388C23×C4—171no—
389C23×C4—174no—
390C23×C4—174no—
391C23×C4—172no—
392C23×C4—171no—
393C23×C4—171no—
394C23×C4—171no—
395C23×C4—174no—
396C23×C4—172no—
397C23×C4—172no—
398C23×C4—344no—
399C23×C4—344no—
400C23×C4C2×#59511yescharacteristic
401#117—24no—
402#117—348no—
403#117—348no—
404#117—344no—
405#117—344no—
406#117—344no—
407C2×C4⋊C4—172no—
408C2×C4⋊C4—171no—
409C2×C4⋊C4—178no—
410C2×C4⋊C4—178no—
411C2×C4⋊C4—172no—
412C2×C4⋊C4—171no—
413C2×C4⋊C4—344no—
414C2×C4⋊C4—344no—
415C2×C4⋊C4—344no—
416C2×C4⋊C4C2×#59511yescharacteristic
417C2×C4⋊C4C2×#59511yescharacteristic
418C2×C22⋊C4—178no—
419C2×C22⋊C4—172no—
420C2×C22⋊C4—172no—
421C2×C22⋊C4—172no—
422C2×C22⋊C4—178no—
423C2×C22⋊C4—348no—
424C2×C22⋊C4—344no—
425C2×C22⋊C4—344no—
426C2×C22⋊C4—682no—
427C2×C22⋊C4—682no—
428C2×C22⋊C4C2×#59512yes—
429C2×C42—178no—
430C2×C42—172no—
431C2×C42—172no—
432C2×C42—172no—
433C2×C42—348no—
434C2×C42—344no—
435C2×C42—344no—
436C2×C42—348no—
437C2×C42—348no—
438C2×C42—684no—
439C2×C42C2×#59512yes—
440#95—174no—
441#95—174no—
442#95—178no—
443#95—348no—
444#95—348no—
445#95—684no—
446C17#1380111yescharacteristic, complemented, Sylow
447C24—171no—
448C24—172no—
449C24—172no—
450C24—171no—
451C24—342no—
452C24—342no—
453C24—342no—
454C24—341no—
455C24—341no—
456C24—342no—
457C24—341no—
458C24—341no—
459C24C22×#59511yescharacteristic
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—171no—
463C22×C4—172no—
464C22×C4—172no—
465C22×C4—174no—
466C22×C4—174no—
467C22×C4—174no—
468C22×C4—174no—
469C22×C4—174no—
470C22×C4—174no—
471C22×C4—171no—
472C22×C4—172no—
473C22×C4—174no—
474C22×C4—174no—
475C22×C4—172no—
476C22×C4—172no—
477C22×C4—178no—
478C22×C4—174no—
479C22×C4—178no—
480C22×C4—172no—
481C22×C4—342no—
482C22×C4—342no—
483C22×C4—3416no—
484C22×C4—3416no—
485C22×C4—342no—
486C22×C4—344no—
487C22×C4—342no—
488C22×C4—342no—
489C22×C4—342no—
490C22×C4—344no—
491C22×C4—342no—
492C22×C4—344no—
493C22×C4—342no—
494C22×C4—342no—
495C22×C4—342no—
496C22×C4—342no—
497C22×C4—342no—
498C22×C4—342no—
499C22×C4—342no—
500C22×C4—342no—
501C22×C4—342no—
502C22×C4—342no—
503C22×C4—344no—
504C22×C4—344no—
505C22×C4—342no—
506C22×C4—344no—
507C22×C4—342no—
508C22×C4—344no—
509C22×C4—344no—
510C22×C4—342no—
511C22×C4—342no—
512C22×C4—344no—
513C22×C4—342no—
514C22×C4C4×#59514yescomplemented
515C22×C4C22×#59512yes—
516C22×C4C22×#59511yescharacteristic
517C22×C4C22×#59512yes—
518C22×C4C22×#59511yescharacteristic
519C4⋊C4—22no—
520C4⋊C4—178no—
521C4⋊C4—174no—
522C4⋊C4—344no—
523C4⋊C4—3416no—
524C4⋊C4—342no—
525C4⋊C4C22⋊#59514yescomplemented
526C22⋊C4—24no—
527C22⋊C4—344no—
528C22⋊C4—344no—
529C22⋊C4—3416no—
530C22⋊C4—344no—
531C22⋊C4—688no—
532C42—24no—
533C42—344no—
534C42—344no—
535C42—3416no—
536C42—344no—
537C42—6816no—
538C23—21no—
539C23—21no—
540C23—21no—
541C23—21no—
542C23—21no—
543C23—21no—
544C23—171no—
545C23—171no—
546C23—172no—
547C23—172no—
548C23—172no—
549C23—172no—
550C23—171no—
551C23—171no—
552C23—171no—
553C23—171no—
554C23—172no—
555C23—344no—
556C23—342no—
557C23—344no—
558C23—344no—
559C23—344no—
560C23—342no—
561C23—342no—
562C23—342no—
563C23—341no—
564C23—341no—
565C23—341no—
566C23—341no—
567C23—341no—
568C23—341no—
569C23—682no—
570C23—682no—
571C23—682no—
572C23—682no—
573C23—682no—
574C23—682no—
575C23—682no—
576C23—682no—
577C23C2×C4×#59512yes—
578C23C23×#59511yescharacteristic
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—28no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—172no—
588C2×C4—172no—
589C2×C4—172no—
590C2×C4—178no—
591C2×C4—178no—
592C2×C4—178no—
593C2×C4—172no—
594C2×C4—174no—
595C2×C4—348no—
596C2×C4—348no—
597C2×C4—344no—
598C2×C4—344no—
599C2×C4—348no—
600C2×C4—348no—
601C2×C4—344no—
602C2×C4—344no—
603C2×C4—344no—
604C2×C4—344no—
605C2×C4—344no—
606C2×C4—344no—
607C2×C4—341no—
608C2×C4—341no—
609C2×C4—342no—
610C2×C4—342no—
611C2×C4—348no—
612C2×C4—344no—
613C2×C4—344no—
614C2×C4—348no—
615C2×C4—348no—
616C2×C4—348no—
617C2×C4—344no—
618C2×C4—342no—
619C2×C4—342no—
620C2×C4—342no—
621C2×C4—684no—
622C2×C4—684no—
623C2×C4—684no—
624C2×C4—682no—
625C2×C4—682no—
626C2×C4—684no—
627C2×C4—682no—
628C2×C4—684no—
629C2×C4—684no—
630C2×C4—682no—
631C2×C4C2×C4×#59512yes—
632C2×C4C2×C4×#59512yes—
633C2×C4#1058767712yes—
634C2×C4C2×C22⋊#59514yes—
635C2×C4C2×C22⋊#59512yes—
636C22—22no—
637C22—22no—
638C22—22no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22—172no—
644C22—172no—
645C22—172no—
646C22—172no—
647C22—171no—
648C22—171no—
649C22—171no—
650C22—171no—
651C22—172no—
652C22—172no—
653C22—172no—
654C22—172no—
655C22—172no—
656C22—172no—
657C22—172no—
658C22—172no—
659C22—342no—
660C22—342no—
661C22—342no—
662C22—684no—
663C22—684no—
664C22—684no—
665C22—684no—
666C22—681no—
667C22—681no—
668C22—681no—
669C22—681no—
670C22C22×C4×#59511yescharacteristic
671C22C22×C22⋊#59511yescharacteristic
672C22C2×#1058767711yescharacteristic
673C22#41×#59511yescharacteristic
674C22#41×#59511yescharacteristic
675C22#1176387811yescharacteristic
676C22#1176387811yescharacteristic
677C4—22no—
678C4—24no—
679C4—42no—
680C4—174no—
681C4—348no—
682C4—342no—
683C4—344no—
684C4—688no—
685C4—684no—
686C4—682no—
687C4C4×C22⋊#59514yes—
688C2—42no—
689C2—172no—
690C2—172no—
691C2—172no—
692C2—172no—
693C2—682no—
694C2C2×C4×C22⋊#59511yescharacteristic
695C2#117×#59511yescharacteristic
696C2#1454522111yescharacteristic
697C2#1454528711yescharacteristic
698C2#1454528911yescharacteristic
699C2#1454529411yescharacteristic
700C2#1454529511yescharacteristic
subgroupG/H
center, FrattiniC23C23×#595
commutatorC22×C17C22×C42
FittingC2×C17×#117C4
socleC23×C17C23×C4
prime radicalC24×D17C23
cosocleC23×D17C24
hypercenterC2×#117#595
hypocenterC17#13801
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×#595C2semidirect
5. #14543961C2semidirect
6. #14543960C2semidirect
7. C4×(C2×#595)⋊C4C2semidirect
14. #11763751C4semidirect
16. C4×C22⋊#595C4semidirect
24. C2×#10587612C4semidirect
25. C2×#10587578C4semidirect
26. C2×#10587578C4semidirect
27. C2×#10587558C4semidirect
28. C2×#10587563C4semidirect
34. C2×C17×#117C4semidirect
132. C22×C4×C17C42semidirect
139. C22×Dic17C42semidirect
159. C2×C4×D17C42semidirect
160. C2×C4×D17C42semidirect
174. C4⋊C4×C17C22⋊C4semidirect
181. C4⋊Dic17C22⋊C4semidirect
183. #63225C22⋊C4semidirect
249. C2×#595#117semidirect
353. C2×#117#595semidirect
446. C17#13801semidirect
514. C22×C4C4×#595semidirect
525. C4⋊C4C22⋊#595semidirect

Maximal subgroups

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

subgroupindex
C2×#117637512
C2×C4⋊C4×#5952
C2×C4×C22⋊#5952
#145439652
#145439612
#145439602
C4×(C2×#595)⋊C42
C2×#117×D172
#1380117