Finite Group Databasebeta

← #17969486

Subgroups — #17969486

Order 4352.

1378 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14545231C212yesmaximal, complemented
2#14544681C212yesmaximal, complemented
3#14544645C212yesmaximal, complemented
4#14544644C212yesmaximal, complemented
5#14544613C212yesmaximal
6C4×#10587539C212yesmaximal, complemented
7C4×#10587551C212yesmaximal, complemented
8C2×C4×#63252C211yesmaximal, characteristic
9C2×#10587539C2214yes—
10C2×#10587551C2214yes—
11#11763754—22no—
12#11763753—22no—
13#11763752C2214yes—
14#11763751C2214yes—
15C4×C4⋊#595—22no—
16C4×C22⋊#595C2214yes—
17#11763745—22no—
18#11763687C2214yes—
19#11763687C2214yes—
20C22×#63252C2211yescharacteristic
21C4×#63252—22no—
22C4×#63252—22no—
23C4×#63252—22no—
24C4×#63252—22no—
25C2×C4×Dic34C411yescharacteristic, complemented
26C2×C4×Dic34C411yescharacteristic, complemented
27C2×C4×D68C2211yescharacteristic
28C2×C4×D68C2211yescharacteristic
29C2×C4×C22⋊D17C411yescharacteristic, complemented
30C2×C4×C22⋊D17C411yescharacteristic, complemented
31C2×C4×C22⋊D17C2211yescharacteristic
32C2×C4×C22⋊D17C2211yescharacteristic
33C2×#10587612C411yescharacteristic, complemented
34C2×#10587558C411yescharacteristic, complemented
35C2×#10587558C2211yescharacteristic
36C2×C42×D17C411yescharacteristic, complemented
37C2×C42×D17C2211yescharacteristic
38C22×C42×C17C411yescharacteristic, complemented
39C23×C4×C17C2×C411yescharacteristic
40C23×C4×C17C2×C411yescharacteristic
41C23×C4×C17C2×C411yescharacteristic
42C22×C22⋊D17C2×C411yescharacteristic
43C22×C22⋊D17C2311yescharacteristic
44C2×#63252—24no—
45C2×#63252—24no—
46C2×#63252—22no—
47C2×#63252—22no—
48C22×D68C2311yescharacteristic
49C22×C4×D17C2×C411yescharacteristic
50C22×C4×D17C2×C411yescharacteristic
51C22×C4×D17C2×C411yescharacteristic
52C22×C4×D17C2311yescharacteristic
53C22×C4×D17C2311yescharacteristic
54C22×C4×D17C2311yescharacteristic
55C22×Dic34C2×C411yescharacteristic
56C2×C22⋊#595C2318yes—
57C2×C4⋊#595—24no—
58C2×C4×#595—24no—
59C2×C42×C17—21no—
60C2×C42×C17—21no—
61C2×C42×C17—21no—
62C2×C42×C17—21no—
63C2×C42×C17C2×C411yescharacteristic
64C2×C42×C17C2×C411yescharacteristic
65C2×C42×C17C2×C411yescharacteristic
66C2×C42×C17C2×C411yescharacteristic
67C2×C22⋊Dic17C2×C411yescharacteristic
68C2×C22⋊Dic17C2×C411yescharacteristic
69C4×C22⋊D17—22no—
70C4×C22⋊D17—22no—
71C4×C22⋊D17—22no—
72C4×C22⋊D17—22no—
73C4×C22⋊D17—22no—
74C4×C22⋊D17—22no—
75C4×C22⋊D17—22no—
76C4×C22⋊D17—22no—
77C2×#63227C2×C411yescharacteristic
78C2×#63227C2×C411yescharacteristic
79C2×#63227C2311yescharacteristic
80C2×#63227C2311yescharacteristic
81#10587612—22no—
82#10587612—22no—
83C2×C4⋊Dic17C2×C411yescharacteristic
84C2×C4⋊Dic17C2×C411yescharacteristic
85C2×#63225C2×C411yescharacteristic
86C2×#63225C2×C411yescharacteristic
87C2×#63225C2×C411yescharacteristic
88C2×#63225C2×C411yescharacteristic
89C2×C4×Dic17C2×C411yescharacteristic
90C2×C4×Dic17C2×C411yescharacteristic
91C2×C4×Dic17C2×C411yescharacteristic
92C2×C4×Dic17C2×C411yescharacteristic
93C2×C4×Dic17C2×C411yescharacteristic
94C2×C4×Dic17C2×C411yescharacteristic
95C4×D68—22no—
96C4×D68—22no—
97C4×D68—22no—
98C4×D68—22no—
99#10587558—22no—
100#10587558—22no—
101#10587558—22no—
102#10587558—22no—
103C42×D17—21no—
104C42×D17—21no—
105C42×D17—21no—
106C42×D17—21no—
107C42×D17D412yes—
108C42×D17D412yes—
109C42×D17D412yes—
110C42×D17D412yes—
111C4×Dic34—22no—
112C4×Dic34—22no—
113C4×Dic34—22no—
114C4×Dic34—22no—
115#10587551—28no—
116(C2×#595)⋊C4—24no—
117(C2×#595)⋊C4—24no—
118(C2×#595)⋊C4—24no—
119(C2×#595)⋊C4—24no—
120#10587539—28no—
121C24×C17C22×C411yescharacteristic
122C23×D17C22×C411yescharacteristic
123C23×D17C2411yescharacteristic
124C22×#595—28no—
125C22×C4×C17—22no—
126C22×C4×C17—21no—
127C22×C4×C17—21no—
128C22×C4×C17—22no—
129C22×C4×C17—21no—
130C22×C4×C17—21no—
131C22×C4×C17—21no—
132C22×C4×C17—21no—
133C22×C4×C17—42no—
134C22×C4×C17—42no—
135C22×C4×C17C22×C411yescharacteristic
136C22×C4×C17C22×C411yescharacteristic
137C22×C4×C17C22×C411yescharacteristic
138C22×C4×C17C22×C411yescharacteristic
139C22×C4×C17C22×C411yescharacteristic
140C22×C4×C17C22×C411yescharacteristic
141C2×C22⋊D17—22no—
142C2×C22⋊D17—22no—
143C2×C22⋊D17—22no—
144C2×C22⋊D17—22no—
145C2×C22⋊D17—22no—
146C2×C22⋊D17#4114yes—
147C22×Dic17C22×C411yescharacteristic
148C22×Dic17C22×C411yescharacteristic
149C22×Dic17C22×C411yescharacteristic
150C22×Dic17C22×C411yescharacteristic
151C22×Dic17C22×C411yescharacteristic
152C22×Dic17C22×C411yescharacteristic
153#63252—216no—
154#63252—216no—
155C2×D68—22no—
156C2×D68—22no—
157C2×D68#4114yes—
158C2×C4×D17—22no—
159C2×C4×D17—22no—
160C2×C4×D17—22no—
161C2×C4×D17—21no—
162C2×C4×D17—21no—
163C2×C4×D17—22no—
164C2×C4×D17—21no—
165C2×C4×D17—21no—
166C2×C4×D17—21no—
167C2×C4×D17—21no—
168C2×C4×D17—42no—
169C2×C4×D17—42no—
170C2×C4×D17—42no—
171C2×C4×D17—42no—
172C2×C4×D17C2×D412yes—
173C2×C4×D17C2×D412yes—
174C2×C4×D17C2×D412yes—
175C2×C4×D17C2×D412yes—
176C2×C4×D17C2×D412yes—
177C2×C4×D17C2×D412yes—
178C2×Dic34—22no—
179C2×Dic34—22no—
180C2×Dic34—22no—
181C22⋊#595—28no—
182C22⋊#595—28no—
183C4⋊#595—48no—
184C4×#595—48no—
185C42×C17—21no—
186C42×C17—21no—
187C42×C17—21no—
188C42×C17—21no—
189C42×C17—21no—
190C42×C17—21no—
191C42×C17C22⋊C411yescharacteristic
192C42×C17C22⋊C411yescharacteristic
193C42×C17C22⋊C411yescharacteristic
194C42×C17C22⋊C411yescharacteristic
195C22⋊Dic17—22no—
196C22⋊Dic17—22no—
197#63227—22no—
198#63227—22no—
199#63227—22no—
200#63227—22no—
201C4⋊Dic17—22no—
202C4⋊Dic17—22no—
203#63225—22no—
204#63225—22no—
205#63225—22no—
206#63225—22no—
207C4×Dic17—21no—
208C4×Dic17—21no—
209C4×Dic17—21no—
210C4×Dic17—21no—
211C4×Dic17—21no—
212C4×Dic17—21no—
213C4×Dic17C22⋊C412yes—
214C4×Dic17C22⋊C412yes—
215C4×Dic17C22⋊C412yes—
216C4×Dic17C22⋊C412yes—
217C4×Dic17C22⋊C412yes—
218C4×Dic17C22⋊C412yes—
219#20723—171nomaximal, Sylow
220C23×C17—21no—
221C23×C17—21no—
222C23×C17—41no—
223C23×C17—41no—
224C23×C17#11712yes—
225C23×C17C23×C411yescharacteristic
226C22×D17—21no—
227C22×D17—21no—
228C22×D17—41no—
229C22×D17—41no—
230C22×D17—41no—
231C22×D17—41no—
232C22×D17#11712yes—
233C22×D17C22×D412yes—
234C22×D17C2×#4112yes—
235C22×D17C2×#4112yes—
236C2×#595—48no—
237C2×#595—48no—
238C2×#595—48no—
239C2×C4×C17—24no—
240C2×C4×C17—24no—
241C2×C4×C17—21no—
242C2×C4×C17—21no—
243C2×C4×C17—21no—
244C2×C4×C17—21no—
245C2×C4×C17—22no—
246C2×C4×C17—22no—
247C2×C4×C17—21no—
248C2×C4×C17—21no—
249C2×C4×C17—42no—
250C2×C4×C17—42no—
251C2×C4×C17—42no—
252C2×C4×C17—42no—
253C2×C4×C17—41no—
254C2×C4×C17—41no—
255C2×C4×C17C2×C22⋊C411yescharacteristic
256C2×C4×C17C2×C22⋊C411yescharacteristic
257C2×C4×C17C2×C22⋊C411yescharacteristic
258C2×C4×C17C2×C22⋊C411yescharacteristic
259C2×C4×C17C2×C22⋊C411yescharacteristic
260C2×C4×C17C2×C22⋊C411yescharacteristic
261C2×C4×C17#11712yes—
262C22⋊D17—28no—
263C22⋊D17—28no—
264C2×Dic17—21no—
265C2×Dic17—21no—
266C2×Dic17—21no—
267C2×Dic17—21no—
268C2×Dic17—21no—
269C2×Dic17—21no—
270C2×Dic17—41no—
271C2×Dic17—41no—
272C2×Dic17—41no—
273C2×Dic17—41no—
274C2×Dic17C2×C22⋊C412yes—
275C2×Dic17C2×C22⋊C412yes—
276C2×Dic17C2×C22⋊C412yes—
277C2×Dic17#11712yes—
278D68—28no—
279C4×D17—24no—
280C4×D17—24no—
281C4×D17—24no—
282C4×D17—24no—
283C4×D17—24no—
284C4×D17—24no—
285C4×D17—42no—
286C4×D17—42no—
287C4×D17—42no—
288C4×D17—42no—
289C4×D17—42no—
290C4×D17—42no—
291Dic34—28no—
292C2×C4×#41—171no—
293#2283—172no—
294#1820—172no—
295#1799—172no—
296#1799—172no—
297#1782—172no—
298C4×#99—172no—
299C4×#99—172no—
300C22×C17—21no—
301C22×C17—21no—
302C22×C17—22no—
303C22×C17—42no—
304C22×C17—42no—
305C22×C17—41no—
306C22×C17—41no—
307C22×C17C22×C22⋊C411yescharacteristic
308C22×C17C2×#11711yescharacteristic
309C22×C17C2×#11711yescharacteristic
310C2×D17—22no—
311C2×D17—22no—
312C2×D17—22no—
313C2×D17—42no—
314C2×D17—42no—
315C2×D17—42no—
316C2×D17—41no—
317C2×D17—41no—
318C2×D17—42no—
319C2×D17#52514yes—
320#595—88no—
321C4×C17—21no—
322C4×C17—21no—
323C4×C17—22no—
324C4×C17—21no—
325C4×C17—21no—
326C4×C17—41no—
327C4×C17—41no—
328C4×C17#41012yes—
329C4×C17#41012yes—
330Dic17—22no—
331Dic17—22no—
332Dic17—22no—
333Dic17—22no—
334Dic17—41no—
335Dic17—41no—
336C22×#41—171no—
337C4×#41—342no—
338C4×#41—342no—
339C4×#41—342no—
340C4×#41—342no—
341C2×C4×Q8—171no—
342C2×C4×Q8—171no—
343C2×C4×D4—171no—
344C2×C4×D4—171no—
345C2×C4×D4—171no—
346C2×C4×D4—171no—
347C2×C4×D4—171no—
348C2×C4×D4—171no—
349C2×#117—171no—
350C2×#117—171no—
351C2×#117—171no—
352C22×C42—171no—
353C22×C42—171no—
354C22×C42#59511yescharacteristic, complemented
355C2×#99—174no—
356C2×#99—174no—
357#383—342no—
358#382—342no—
359#381—174no—
360#380—174no—
361C4×C4⋊C4—342no—
362C4×C22⋊C4—174no—
363#376—342no—
364#342—174no—
365#342—174no—
366C2×C17—21no—
367C2×C17—21no—
368C2×C17—42no—
369C2×C17#228011yescharacteristic
370C2×C17C2×#41011yescharacteristic
371C2×C17C2×#41011yescharacteristic
372D17—24no—
373D17—42no—
374C2×#41—342no—
375C2×#41—342no—
376C2×#41—344no—
377C2×#41—344no—
378C22×Q8—171no—
379C22×D4—171no—
380C22×D4—171no—
381C22×D4—171no—
382C23×C4—171no—
383C23×C4—171no—
384C23×C4—171no—
385C23×C4—171no—
386C23×C4—171no—
387C23×C4—171no—
388C23×C4C2×#59511yescharacteristic
389C23×C4C2×#59511yescharacteristic
390C23×C4C2×#59511yescharacteristic
391C4×Q8—342no—
392C4×Q8—342no—
393C4×Q8—342no—
394C4×Q8—342no—
395C4×D4—342no—
396C4×D4—342no—
397C4×D4—342no—
398C4×D4—342no—
399C4×D4—342no—
400C4×D4—342no—
401C4×D4—342no—
402C4×D4—342no—
403C4×D4—342no—
404C4×D4—342no—
405C4×D4—342no—
406C4×D4—342no—
407#117—342no—
408#117—342no—
409#117—342no—
410#117—342no—
411#117—342no—
412#117—342no—
413C2×C4⋊C4—171no—
414C2×C4⋊C4—171no—
415C2×C4⋊C4—171no—
416C2×C4⋊C4—171no—
417C2×C4⋊C4—171no—
418C2×C4⋊C4—171no—
419C2×C4⋊C4—344no—
420C2×C22⋊C4—171no—
421C2×C22⋊C4—171no—
422C2×C22⋊C4—171no—
423C2×C22⋊C4—171no—
424C2×C22⋊C4—171no—
425C2×C22⋊C4—171no—
426C2×C22⋊C4—178no—
427C2×C42—21no—
428C2×C42—21no—
429C2×C42—21no—
430C2×C42—21no—
431C2×C42—171no—
432C2×C42—171no—
433C2×C42—171no—
434C2×C42—172no—
435C2×C42—172no—
436C2×C42—172no—
437C2×C42—172no—
438C2×C42—171no—
439C2×C42—171no—
440C2×C42—171no—
441C2×C42—341no—
442C2×C42—341no—
443C2×C42—341no—
444C2×C42—341no—
445C2×C42—344no—
446C2×C42C2×#59511yescharacteristic
447C2×C42C2×#59511yescharacteristic
448C2×C42C2×#59511yescharacteristic
449C2×C42C2×#59511yescharacteristic
450#99—348no—
451#99—348no—
452#95—344no—
453#95—344no—
454#95—344no—
455#95—344no—
456C17#2072311yescharacteristic, complemented, Sylow
457C24—171no—
458C24—171no—
459C24C22×#59511yescharacteristic
460#41—3416no—
461#41—3416no—
462C2×Q8—342no—
463C2×Q8—342no—
464C2×Q8—342no—
465C2×D4—174no—
466C2×D4—174no—
467C2×D4—342no—
468C2×D4—342no—
469C2×D4—342no—
470C2×D4—342no—
471C2×D4—342no—
472C2×D4—342no—
473C2×D4—342no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—171no—
485C22×C4—171no—
486C22×C4—171no—
487C22×C4—171no—
488C22×C4—172no—
489C22×C4—172no—
490C22×C4—172no—
491C22×C4—172no—
492C22×C4—172no—
493C22×C4—172no—
494C22×C4—171no—
495C22×C4—171no—
496C22×C4—342no—
497C22×C4—342no—
498C22×C4—342no—
499C22×C4—342no—
500C22×C4—341no—
501C22×C4—341no—
502C22×C4—341no—
503C22×C4—341no—
504C22×C4—341no—
505C22×C4—341no—
506C22×C4—348no—
507C22×C4—682no—
508C22×C4—682no—
509C22×C4—682no—
510C22×C4—682no—
511C22×C4C22×#59511yescharacteristic
512C22×C4C22×#59511yescharacteristic
513C22×C4C22×#59511yescharacteristic
514C22×C4C22×#59511yescharacteristic
515C22×C4C22×#59511yescharacteristic
516C22×C4C22×#59511yescharacteristic
517C4⋊C4—342no—
518C4⋊C4—342no—
519C4⋊C4—342no—
520C4⋊C4—342no—
521C4⋊C4—342no—
522C4⋊C4—342no—
523C4⋊C4—688no—
524C22⋊C4—342no—
525C22⋊C4—342no—
526C22⋊C4—342no—
527C22⋊C4—342no—
528C22⋊C4—342no—
529C22⋊C4—342no—
530C22⋊C4—348no—
531C22⋊C4—348no—
532C42—21no—
533C42—21no—
534C42—21no—
535C42—21no—
536C42—21no—
537C42—21no—
538C42—172no—
539C42—172no—
540C42—172no—
541C42—172no—
542C42—172no—
543C42—172no—
544C42—341no—
545C42—341no—
546C42—341no—
547C42—341no—
548C42—341no—
549C42—341no—
550C42—688no—
551C42C22⋊#59511yescharacteristic
552C42C22⋊#59511yescharacteristic
553C42C22⋊#59511yescharacteristic
554C42C22⋊#59511yescharacteristic
555C23—21no—
556C23—21no—
557C23—41no—
558C23—41no—
559C23—172no—
560C23—172no—
561C23—172no—
562C23—172no—
563C23—341no—
564C23—341no—
565C23—681no—
566C23—681no—
567C23—681no—
568C23—681no—
569C23#1058767712yes—
570C23C23×#59511yescharacteristic
571Q8—348no—
572D4—348no—
573D4—348no—
574D4—348no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—172no—
592C2×C4—172no—
593C2×C4—172no—
594C2×C4—172no—
595C2×C4—344no—
596C2×C4—344no—
597C2×C4—344no—
598C2×C4—344no—
599C2×C4—341no—
600C2×C4—341no—
601C2×C4—341no—
602C2×C4—341no—
603C2×C4—344no—
604C2×C4—344no—
605C2×C4—341no—
606C2×C4—341no—
607C2×C4—682no—
608C2×C4—682no—
609C2×C4—682no—
610C2×C4—682no—
611C2×C4—681no—
612C2×C4—681no—
613C2×C4—682no—
614C2×C4—682no—
615C2×C4—681no—
616C2×C4—681no—
617C2×C4—688no—
618C2×C4—688no—
619C2×C4—688no—
620C2×C4#1058767712yes—
621C2×C4C2×C22⋊#59511yescharacteristic
622C2×C4C2×C22⋊#59511yescharacteristic
623C2×C4C2×C22⋊#59511yescharacteristic
624C2×C4C2×C22⋊#59511yescharacteristic
625C2×C4C2×C22⋊#59511yescharacteristic
626C2×C4C2×C22⋊#59511yescharacteristic
627C22—21no—
628C22—21no—
629C22—22no—
630C22—42no—
631C22—42no—
632C22—41no—
633C22—41no—
634C22—174no—
635C22—342no—
636C22—342no—
637C22—342no—
638C22—682no—
639C22—682no—
640C22—682no—
641C22—682no—
642C22—681no—
643C22—681no—
644C22C22×C22⋊#59511yescharacteristic
645C22C2×#1058767711yescharacteristic
646C22C2×#1058767711yescharacteristic
647C4—21no—
648C4—21no—
649C4—22no—
650C4—21no—
651C4—21no—
652C4—41no—
653C4—41no—
654C4—342no—
655C4—342no—
656C4—342no—
657C4—342no—
658C4—681no—
659C4—681no—
660C4—1368no—
661C4#1176378812yes—
662C4#1176378812yes—
663C2—21no—
664C2—21no—
665C2—42no—
666C2—344no—
667C2—682no—
668C2#1454522811yescharacteristic
669C2C2×#1176378811yescharacteristic
670C2C2×#1176378811yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#595
commutatorC23×C17C23×C4
FrattiniC23C23×#595
FittingC22×C42×C17C4
socleC22×C17C22×C22⋊C4
prime radicalC22×#63252C22
cosocleC23×D17C24
hypercenterC22×C42#595
hypocenterC17#20723
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
1. #14545231C2semidirect
2. #14544681C2semidirect
3. #14544645C2semidirect
4. #14544644C2semidirect
6. C4×#10587539C2semidirect
7. C4×#10587551C2semidirect
25. C2×C4×Dic34C4semidirect
26. C2×C4×Dic34C4semidirect
29. C2×C4×C22⋊D17C4semidirect
30. C2×C4×C22⋊D17C4semidirect
33. C2×#10587612C4semidirect
34. C2×#10587558C4semidirect
36. C2×C42×D17C4semidirect
38. C22×C42×C17C4semidirect
354. C22×C42#595semidirect
456. C17#20723semidirect

Maximal subgroups

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

subgroupindex
#145452312
#145446812
#145446452
#145446442
#145446132
C4×#105875392
C4×#105875512
C2×C4×#632522
#2072317