Finite Group Databasebeta

← #17046348

Subgroups — #17046348

Order 4352.

728 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762937C211yesmaximal, characteristic, complemented
2#14532052C211yesmaximal, characteristic
3#14529720C211yesmaximal, characteristic, complemented
4#14529504C211yesmaximal, characteristic, complemented
5#14529502C211yesmaximal, characteristic, complemented
6#14529499C211yesmaximal, characteristic, complemented
7#14529400C211yesmaximal, characteristic
8#14529394C211yesmaximal, characteristic
9#14529393C211yesmaximal, characteristic
10#14529387C211yesmaximal, characteristic
11#14529345C211yesmaximal, characteristic, complemented
12#14529338C211yesmaximal, characteristic, complemented
13#14528768C211yesmaximal, characteristic
14#14528656C211yesmaximal, characteristic, complemented
15C2×C17×#433C211yesmaximal, characteristic
16C2×C4×Dic34C2211yescharacteristic
17#11762937—24no—
18C2×C4⋊#3622C2211yescharacteristic
19C2×C4⋊#3622C2211yescharacteristic
20C2×#10587485C2211yescharacteristic
21C2×#10587485C2211yescharacteristic
22C2×#10587485C2211yescharacteristic
23C2×#10587485C2211yescharacteristic
24C2×C22⋊#3622C2211yescharacteristic
25C2×C22⋊#3622C2211yescharacteristic
26C2×#10587486C2211yescharacteristic
27C2×#10587486C2211yescharacteristic
28C2×C8×Dic17C2211yescharacteristic
29C2×C8×Dic17C2211yescharacteristic
30#11762748C411yescharacteristic
31#11762745C411yescharacteristic
32#11762742C411yescharacteristic
33#11762742C411yescharacteristic
34#11762732C411yescharacteristic
35#11762732C411yescharacteristic
36#11762729C411yescharacteristic
37#11762721C411yescharacteristic
38C4×#63225C2211yescharacteristic
39C4×#63225C2211yescharacteristic
40C4×C4⋊Dic17C2211yescharacteristic
41C4×C22⋊Dic17C2211yescharacteristic
42C4×C22⋊Dic17C2211yescharacteristic
43#11762564C2211yescharacteristic
44#11762564C2211yescharacteristic
45#11762563C2211yescharacteristic
46#11762563C2211yescharacteristic
47#11762563C2211yescharacteristic
48#11762563C2211yescharacteristic
49#11762563C2211yescharacteristic
50#11762563C2211yescharacteristic
51#11762563C2211yescharacteristic
52#11762563C2211yescharacteristic
53C2×C17×#117C2211yescharacteristic
54C17×#433—24no—
55C2×C17×C4⋊C8C2211yescharacteristic
56C2×C17×C4⋊C8C2211yescharacteristic
57C2×C17×C22⋊C8C2211yescharacteristic
58C2×C17×C22⋊C8C2211yescharacteristic
59C2×C17×#97C2211yescharacteristic
60C2×C4×C8×C17C2211yescharacteristic
61C23×C4×C17C2311yescharacteristic
62C22×Dic34C2×C411yescharacteristic
63C22×C8×C17C2311yescharacteristic
64C22×C8×C17C2311yescharacteristic
65C22×C8×C17C2311yescharacteristic
66C22×C8×C17C2311yescharacteristic
67C17×#117—22no—
68C17×#117—22no—
69C2×C4⋊C4×C17C2×C411yescharacteristic
70C2×C4⋊C4×C17C2×C411yescharacteristic
71C2×C22⋊C4×C17C2×C411yescharacteristic
72C2×C22⋊C4×C17C2×C411yescharacteristic
73C2×C42×C17C2311yescharacteristic
74C2×C42×C17C2311yescharacteristic
75C2×C22⋊Dic17C2×C411yescharacteristic
76C2×C22⋊Dic17C2×C411yescharacteristic
77C2×C22⋊Dic17C2×C411yescharacteristic
78C2×C22⋊Dic17C2×C411yescharacteristic
79C2×C4⋊Dic17C2×C411yescharacteristic
80C2×C4⋊Dic17C2×C411yescharacteristic
81C2×C4⋊Dic17C2×C411yescharacteristic
82C2×#63225C2×C411yescharacteristic
83C2×#63225C2×C411yescharacteristic
84C2×#63225C2×C411yescharacteristic
85C2×#63225C2×C411yescharacteristic
86C2×#63225C2×C411yescharacteristic
87C2×#63225C2×C411yescharacteristic
88C2×C4×Dic17C2311yescharacteristic
89C2×C4×Dic17C2311yescharacteristic
90C2×C4×Dic17C2311yescharacteristic
91C2×C4×Dic17C2311yescharacteristic
92C22×#3622C2311yescharacteristic
93C22×#3622C2311yescharacteristic
94C22×#3622C2311yescharacteristic
95C22×#3622C2311yescharacteristic
96C4×Dic34—22no—
97C4×Dic34—22no—
98C17×C4⋊C8—22no—
99C17×C4⋊C8—22no—
100C17×C22⋊C8—22no—
101C17×C22⋊C8—22no—
102C17×#97D414yes—
103C4×C8×C17—22no—
104#10587502C2×C411yescharacteristic
105#10587502C2×C411yescharacteristic
106#10587502C2×C411yescharacteristic
107#10587502C2×C411yescharacteristic
108#10587502C2×C411yescharacteristic
109#10587502C2×C411yescharacteristic
110#10587502C2×C411yescharacteristic
111#10587502C2×C411yescharacteristic
112#10587502C2×C411yescharacteristic
113#10587502C2×C411yescharacteristic
114C22⋊#3622—41no—
115C22⋊#3622—41no—
116#10587486—22no—
117#10587486—41no—
118#10587485—22no—
119#10587485—22no—
120#10587485—41no—
121#10587485—41no—
122C8×Dic17—22no—
123C8×Dic17—41no—
124C4⋊#3622—22no—
125C4⋊#3622—22no—
126C24×C17C22×C411yescharacteristic
127C22×C4×C17—21no—
128C22×C4×C17—21no—
129C22×C4×C17—21no—
130C22×C4×C17—21no—
131C22×C4×C17—21no—
132C22×C4×C17—21no—
133C22×C4×C17C22×C411yescharacteristic
134C22×C4×C17C22×C411yescharacteristic
135C22×C4×C17C22×C411yescharacteristic
136C22×C4×C17C22×C411yescharacteristic
137C22×C4×C17C22×C411yescharacteristic
138C22×C4×C17C2411yescharacteristic
139C22×Dic17C22×C411yescharacteristic
140C22×Dic17C22×C411yescharacteristic
141C22×Dic17C22×C411yescharacteristic
142C22×Dic17C22×C411yescharacteristic
143C22×Dic17C22×C411yescharacteristic
144C22×Dic17C22×C411yescharacteristic
145C22×Dic17C22×C411yescharacteristic
146C22×Dic17C22×C411yescharacteristic
147C2×Dic34—22no—
148C2×Dic34—22no—
149C2×Dic34—41no—
150C2×C8×C17—21no—
151C2×C8×C17—21no—
152C2×C8×C17—21no—
153C2×C8×C17—21no—
154C2×C8×C17—21no—
155C2×C8×C17—21no—
156C2×C8×C17—21no—
157C2×C8×C17—21no—
158C2×C8×C17—21no—
159C2×C8×C17—21no—
160C2×C8×C17C2×D412yes—
161C2×C8×C17C2×D412yes—
162C4⋊C4×C17—22no—
163C4⋊C4×C17—22no—
164C22⋊C4×C17—22no—
165C22⋊C4×C17—22no—
166C42×C17—21no—
167C42×C17—21no—
168C42×C17C2×D412yes—
169C42×C17#4112yes—
170C22⋊Dic17—22no—
171C22⋊Dic17—22no—
172C22⋊Dic17—41no—
173C22⋊Dic17—41no—
174C4⋊Dic17—22no—
175C4⋊Dic17—22no—
176C4⋊Dic17—41no—
177#63225—22no—
178#63225—22no—
179#63225—22no—
180#63225—22no—
181#63225—41no—
182#63225—41no—
183C4×Dic17—21no—
184C4×Dic17—21no—
185C4×Dic17—21no—
186C4×Dic17—21no—
187C4×Dic17—21no—
188C4×Dic17—21no—
189C4×Dic17—21no—
190C4×Dic17—21no—
191C2×#3622—21no—
192C2×#3622—21no—
193C2×#3622—21no—
194C2×#3622—21no—
195C2×#3622—21no—
196C2×#3622—21no—
197C2×#3622—21no—
198C2×#3622—21no—
199C2×#3622—21no—
200C2×#3622—21no—
201C2×#3622—21no—
202C2×#3622—21no—
203#22109—171nomaximal, Sylow
204C23×C17—21no—
205C23×C17—21no—
206C23×C17—21no—
207C23×C17—21no—
208C23×C17—21no—
209C23×C17—21no—
210C23×C17—21no—
211C23×C17C23×C411yescharacteristic
212C2×C4×C17—21no—
213C2×C4×C17—21no—
214C2×C4×C17—21no—
215C2×C4×C17—21no—
216C2×C4×C17—21no—
217C2×C4×C17—21no—
218C2×C4×C17—21no—
219C2×C4×C17—21no—
220C2×C4×C17—21no—
221C2×C4×C17—21no—
222C2×C4×C17—21no—
223C2×C4×C17—21no—
224C2×C4×C17—21no—
225C2×C4×C17—41no—
226C2×C4×C17—41no—
227C2×C4×C17—41no—
228C2×C4×C17—41no—
229C2×C4×C17C4×D412yes—
230C2×C4×C17C4×D412yes—
231C2×C4×C17C22×D411yescharacteristic
232C2×C4×C17C2×#4111yescharacteristic
233C2×C4×C17H(5,𝔽2)11yescharacteristic
234C2×C4×C172−1+411yescharacteristic
235C2×C4×C172−1+411yescharacteristic
236C2×C4×C172−1+411yescharacteristic
237C2×Dic17—21no—
238C2×Dic17—21no—
239C2×Dic17—21no—
240C2×Dic17—21no—
241C2×Dic17—21no—
242C2×Dic17—21no—
243C2×Dic17—21no—
244C2×Dic17—21no—
245C2×Dic17—21no—
246C2×Dic17—21no—
247C2×Dic17—21no—
248C2×Dic17—21no—
249C2×Dic17—21no—
250C2×Dic17—21no—
251C2×Dic17—21no—
252C2×Dic17—21no—
253C2×Dic17—21no—
254C2×Dic17—21no—
255C2×Dic17—21no—
256C2×Dic17—21no—
257C2×Dic17—21no—
258C2×Dic17—21no—
259C2×Dic17#13112yes—
260C2×Dic17#13112yes—
261Dic34—44no—
262C8×C17—22no—
263C8×C17—22no—
264C8×C17—41no—
265C8×C17—41no—
266#3622—41no—
267#3622—41no—
268#3622—41no—
269#3622—41no—
270C2×#446—171no—
271C2×#433D1711yescharacteristic
272#2396—171no—
273#1984—171no—
274#1940—171no—
275#1939—171no—
276#1939—171no—
277#1924—171no—
278#1924—171no—
279#1923—171no—
280#1923—171no—
281#1917—171no—
282#1916—171no—
283#1798—171no—
284#1771—171no—
285C22×C17—41no—
286C22×C17—41no—
287C22×C17—41no—
288C22×C17—41no—
289C22×C17—41no—
290C22×C17—41no—
291C22×C17—41no—
292C22×C17C2×C4×D411yescharacteristic
293C22×C17#51911yescharacteristic
294C22×C17#52011yescharacteristic
295C22×C17C2×#13111yescharacteristic
296C22×C17C2×#13111yescharacteristic
297C22×C17#56811yescharacteristic
298C22×C17#56811yescharacteristic
299C4×C17—22no—
300C4×C17—22no—
301C4×C17—41no—
302C4×C17—41no—
303C4×C17—41no—
304C4×C17#53611yescharacteristic
305C4×C17#53711yescharacteristic
306C4×C17#54111yescharacteristic
307C4×C17#54211yescharacteristic
308Dic17—22no—
309Dic17—22no—
310Dic17—41no—
311Dic17—41no—
312Dic17—41no—
313Dic17—41no—
314Dic17—41no—
315Dic17—41no—
316C2×C4×Q8—171no—
317C2×#117C2×D1711yescharacteristic
318#446—344no—
319#433—24no—
320C2×C4⋊C8—171no—
321C2×C4⋊C8—171no—
322C2×C4⋊C8—171no—
323C2×C4⋊C8—171no—
324C2×C4⋊C8—171no—
325C2×C4⋊C8—171no—
326C2×C4⋊C8C2×D1711yescharacteristic
327C2×C4⋊C8C2×D1711yescharacteristic
328C2×C22⋊C8—171no—
329C2×C22⋊C8—171no—
330C2×C22⋊C8C2×D1711yescharacteristic
331C2×C22⋊C8C2×D1711yescharacteristic
332C2×#97—171no—
333C2×#97—171no—
334C2×#97C2×D1711yescharacteristic
335C2×C4×C8—171no—
336C2×C4×C8—171no—
337C2×C4×C8C2×D1711yescharacteristic
338#400—171no—
339#399—171no—
340#398—171no—
341#398—171no—
342#396—171no—
343#396—171no—
344#395—171no—
345#393—171no—
346C4×C4⋊C4—171no—
347C4×C4⋊C4—171no—
348C4×C4⋊C4—171no—
349C4×C22⋊C4—171no—
350C4×C22⋊C4—171no—
351#336—171no—
352#336—171no—
353#336—171no—
354#336—171no—
355#336—171no—
356#336—171no—
357#336—171no—
358#336—171no—
359#336—171no—
360#336—171no—
361C2×C17—81no—
362C2×C17#232311yescharacteristic
363C2×C17#293311yescharacteristic
364C2×C17#293511yescharacteristic
365C2×C17#298611yescharacteristic
366C2×C17#298711yescharacteristic
367C2×C17#299211yescharacteristic
368C2×C17#299311yescharacteristic
369C22×Q8—171no—
370C23×C4C22×D1711yescharacteristic
371C22×C8—171no—
372C22×C8—171no—
373C22×C8—171no—
374C22×C8—171no—
375C22×C8C22×D1711yescharacteristic
376C22×C8C22×D1711yescharacteristic
377C22×C8C22×D1711yescharacteristic
378C22×C8C22×D1711yescharacteristic
379C4×Q8—342no—
380C4×Q8—342no—
381#117—22no—
382#117—22no—
383C2×C4⋊C4—171no—
384C2×C4⋊C4—171no—
385C2×C4⋊C4—171no—
386C2×C4⋊C4—171no—
387C2×C4⋊C4—171no—
388C2×C4⋊C4—171no—
389C2×C4⋊C4—171no—
390C2×C4⋊C4—171no—
391C2×C4⋊C4—171no—
392C2×C4⋊C4C4×D1711yescharacteristic
393C2×C4⋊C4C4×D1711yescharacteristic
394C2×C22⋊C4—171no—
395C2×C22⋊C4—171no—
396C2×C22⋊C4—171no—
397C2×C22⋊C4—171no—
398C2×C22⋊C4C4×D1711yescharacteristic
399C2×C22⋊C4C4×D1711yescharacteristic
400C2×C42—171no—
401C2×C42—171no—
402C2×C42—171no—
403C2×C42—171no—
404C2×C42C22×D1711yescharacteristic
405C2×C42C22×D1711yescharacteristic
406C4⋊C8—22no—
407C4⋊C8—22no—
408C4⋊C8—342no—
409C4⋊C8—342no—
410C4⋊C8—342no—
411C4⋊C8—342no—
412C4⋊C8—681no—
413C4⋊C8—681no—
414C22⋊C8—22no—
415C22⋊C8—22no—
416C22⋊C8—681no—
417C22⋊C8—681no—
418#97—342no—
419#97—681no—
420#97C22⋊D1714yes—
421C4×C8—22no—
422C4×C8—342no—
423C4×C8—681no—
424#95—171no—
425#95—171no—
426#95—171no—
427#95—171no—
428#95—171no—
429#95—171no—
430#95—171no—
431#95—171no—
432#95—171no—
433#95—171no—
434C17#2210911yescharacteristic, complemented, Sylow
435C24C2×C4×D1711yescharacteristic
436C2×Q8—342no—
437C2×Q8—342no—
438C2×Q8—681no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—171no—
446C22×C4—171no—
447C22×C4—171no—
448C22×C4—171no—
449C22×C4—171no—
450C22×C4—171no—
451C22×C4—171no—
452C22×C4—171no—
453C22×C4C2×C4×D1711yescharacteristic
454C22×C4C2×C4×D1711yescharacteristic
455C22×C4C2×C4×D1711yescharacteristic
456C22×C4C2×C4×D1711yescharacteristic
457C22×C4C2×C4×D1711yescharacteristic
458C22×C4C23×D1711yescharacteristic
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—341no—
470C2×C8—341no—
471C2×C8—341no—
472C2×C8—341no—
473C2×C8—341no—
474C2×C8—341no—
475C2×C8—341no—
476C2×C8—341no—
477C2×C8—341no—
478C2×C8—341no—
479C2×C8—341no—
480C2×C8—341no—
481C2×C8C2×C22⋊D1712yes—
482C2×C8C2×C22⋊D1712yes—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—342no—
486C4⋊C4—342no—
487C4⋊C4—342no—
488C4⋊C4—342no—
489C4⋊C4—342no—
490C4⋊C4—342no—
491C4⋊C4—681no—
492C4⋊C4—681no—
493C4⋊C4—681no—
494C22⋊C4—22no—
495C22⋊C4—22no—
496C22⋊C4—342no—
497C22⋊C4—342no—
498C22⋊C4—681no—
499C22⋊C4—681no—
500C42—21no—
501C42—21no—
502C42—341no—
503C42—341no—
504C42—341no—
505C42—341no—
506C42—341no—
507C42—341no—
508C42—341no—
509C42—341no—
510C42#6325212yes—
511C42C2×C22⋊D1712yes—
512C23—21no—
513C23—21no—
514C23—21no—
515C23—21no—
516C23—21no—
517C23—21no—
518C23—21no—
519C23C22×C4×D1711yescharacteristic
520Q8—684no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—172no—
539C2×C4—172no—
540C2×C4—341no—
541C2×C4—341no—
542C2×C4—341no—
543C2×C4—341no—
544C2×C4—341no—
545C2×C4—341no—
546C2×C4—341no—
547C2×C4—341no—
548C2×C4—341no—
549C2×C4—341no—
550C2×C4—341no—
551C2×C4—341no—
552C2×C4—341no—
553C2×C4—341no—
554C2×C4—341no—
555C2×C4—341no—
556C2×C4—341no—
557C2×C4—341no—
558C2×C4—341no—
559C2×C4—341no—
560C2×C4—341no—
561C2×C4—341no—
562C2×C4C4×C22⋊D1712yes—
563C2×C4C4×C22⋊D1712yes—
564C2×C4C2×#6325211yescharacteristic
565C2×C4#1058769611yescharacteristic
566C2×C4#1058769711yescharacteristic
567C2×C4#1058769711yescharacteristic
568C2×C4#1058769711yescharacteristic
569C2×C4C22×C22⋊D1711yescharacteristic
570C8—22no—
571C8—22no—
572C8—41no—
573C8—41no—
574C8—681no—
575C8—681no—
576C8—681no—
577C8—681no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22C2×C4×C22⋊D1711yescharacteristic
586C22#1176328611yescharacteristic
587C22#1176328911yescharacteristic
588C22#131×D1711yescharacteristic
589C22#131×D1711yescharacteristic
590C22#1176357411yescharacteristic
591C22#1176357411yescharacteristic
592C4—22no—
593C4—22no—
594C4—41no—
595C4—41no—
596C4—41no—
597C4—342no—
598C4—342no—
599C4—681no—
600C4—681no—
601C4—681no—
602C4—681no—
603C4—681no—
604C4—681no—
605C4#1176338011yescharacteristic
606C4#1176338711yescharacteristic
607C4#1176342111yescharacteristic
608C4#1176343011yescharacteristic
609C2—81no—
610C2#1453146611yescharacteristic
611C2#1453750611yescharacteristic
612C2#1453752611yescharacteristic
613C2#1453788311yescharacteristic
614C2#1453788811yescharacteristic
615C2#1453791811yescharacteristic
616C2#1453792711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D17
commutator, socleC23×C17C23×C4
FittingC2×C17×#433C2
prime radicalC24×C17C22×C4
cosocleC22×C4×C17C24
hypercenterC2×#433D17
hypocenterC17#22109
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
1. C2×#11762937C2semidirect
3. #14529720C2semidirect
4. #14529504C2semidirect
5. #14529502C2semidirect
6. #14529499C2semidirect
11. #14529345C2semidirect
12. #14529338C2semidirect
14. #14528656C2semidirect
434. C17#22109semidirect

Maximal subgroups

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

subgroupindex
C2×#117629372
#145320522
#145297202
#145295042
#145295022
#145294992
#145294002
#145293942
#145293932
#145293872
#145293452
#145293382
#145287682
#145286562
C2×C17×#4332
#2210917