Finite Group Databasebeta

← #17044983

Subgroups — #17044983

Order 4352.

800 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#14531225C211yesmaximal, characteristic
2#14529390C211yesmaximal, characteristic, complemented
3#14529388C211yesmaximal, characteristic, complemented
4#14529343C211yesmaximal, characteristic, complemented
5#14529075C211yesmaximal, characteristic
6#14529075C211yesmaximal, characteristic
7#14528963C211yesmaximal, characteristic, complemented
8#14528960C211yesmaximal, characteristic, complemented
9#14528928C211yesmaximal, characteristic, complemented
10#14528902C211yesmaximal, characteristic, complemented
11#14528854C211yesmaximal, characteristic, complemented
12#14528765C211yesmaximal, characteristic, complemented
13C4×#10587491C211yesmaximal, characteristic, complemented
14D17×#336C211yesmaximal, characteristic, complemented
15C17×#1916C211yesmaximal, characteristic, complemented
16C22×C8×D17C2211yescharacteristic
17C22×C8×D17C2211yescharacteristic
18C2×C4×D68C2211yescharacteristic
19C2×#10587558C2211yescharacteristic
20C2×C42×D17C2211yescharacteristic
21C2×C4⋊#3622C2211yescharacteristic
22C2×#10587485C2211yescharacteristic
23C2×#10587485C2211yescharacteristic
24C2×#10587491C2211yescharacteristic
25C2×#10587491C2211yescharacteristic
26C2×#10587491C2211yescharacteristic
27C2×#10587491C2211yescharacteristic
28C2×#10587491C2211yescharacteristic
29C2×#10587491C2211yescharacteristic
30C2×C4×#3622C2211yescharacteristic
31#11762699C411yescharacteristic
32#11762699C411yescharacteristic
33#11762692C411yescharacteristic
34#11762692C411yescharacteristic
35#11762687C411yescharacteristic
36#11762687C411yescharacteristic
37#11762680C411yescharacteristic
38#11762680C411yescharacteristic
39C4×#63227C2211yescharacteristic
40C4×#63227C2211yescharacteristic
41#11762655C2211yescharacteristic
42#11762564C2211yescharacteristic
43#11762564C2211yescharacteristic
44#11762564C2211yescharacteristic
45#11762564C2211yescharacteristic
46#11762563C2211yescharacteristic
47#11762563C2211yescharacteristic
48#11762563C2211yescharacteristic
49#11762563C2211yescharacteristic
50#11762563C2211yescharacteristic
51#11762563C2211yescharacteristic
52C2×C17×C4⋊C8C2211yescharacteristic
53C2×C4×C8×C17C2211yescharacteristic
54C4×C4⋊C4×C17C2211yescharacteristic
55C17×#336C2211yescharacteristic
56C17×#336C2211yescharacteristic
57C17×#336C2211yescharacteristic
58C17×#336C2211yescharacteristic
59C22×D68C2×C411yescharacteristic
60C22×C4×D17C2×C411yescharacteristic
61C22×C4×D17C2×C411yescharacteristic
62C22×C4×D17C2311yescharacteristic
63C22×C4×D17C2311yescharacteristic
64C22×C8×C17C2311yescharacteristic
65C22×C8×C17C2311yescharacteristic
66C22×C8×C17C2311yescharacteristic
67C22×C8×C17C2311yescharacteristic
68C2×C4⋊C4×C17C2×C411yescharacteristic
69C2×C4⋊C4×C17C2×C411yescharacteristic
70C2×C42×C17C2311yescharacteristic
71C2×C42×C17C2311yescharacteristic
72C2×C42×C17C2311yescharacteristic
73C2×#63227C2×C411yescharacteristic
74C2×#63227C2×C411yescharacteristic
75C2×#63227C2×C411yescharacteristic
76C2×#63227C2×C411yescharacteristic
77C2×#63227C2×C411yescharacteristic
78C2×#63227C2×C411yescharacteristic
79C2×#63227C2×C411yescharacteristic
80C2×#63227C2×C411yescharacteristic
81C2×C4⋊Dic17C2×C411yescharacteristic
82C2×#63225C2×C411yescharacteristic
83C2×#63225C2×C411yescharacteristic
84C2×C4×Dic17C2×C411yescharacteristic
85C2×C4×Dic17C2×C411yescharacteristic
86C2×C4×Dic17C2311yescharacteristic
87C2×C4×Dic17C2311yescharacteristic
88C22×#3622C2311yescharacteristic
89C22×#3622C2311yescharacteristic
90C22×#3622C2311yescharacteristic
91C22×#3622C2311yescharacteristic
92C2×C8×D17—22no—
93C2×C8×D17—22no—
94C2×C8×D17—41no—
95C2×C8×D17—41no—
96C2×C8×D17—41no—
97C2×C8×D17—41no—
98C4×D68—22no—
99C4×D68—22no—
100#10587558—41no—
101#10587558—41no—
102C42×D17—41no—
103C42×D17—41no—
104C17×C4⋊C8—41no—
105C4×C8×C17—41no—
106C17×#95C2×C411yescharacteristic
107C17×#95C2×C411yescharacteristic
108#10587502C2×C411yescharacteristic
109#10587502C2×C411yescharacteristic
110#10587502C2×C411yescharacteristic
111#10587502C2×C411yescharacteristic
112#10587502C2×C411yescharacteristic
113#10587502C2×C411yescharacteristic
114#10587502C2×C411yescharacteristic
115#10587502C2×C411yescharacteristic
116#10587491—22no—
117#10587491—22no—
118#10587491—41no—
119#10587491—41no—
120#10587491—41no—
121#10587491—41no—
122#10587485—41no—
123#10587485—41no—
124C4⋊#3622—41no—
125C4×#3622—41no—
126C23×D17C22×C411yescharacteristic
127C23×D17C22×C411yescharacteristic
128C22×C4×C17C22×C411yescharacteristic
129C22×C4×C17C22×C411yescharacteristic
130C22×C4×C17C22×C411yescharacteristic
131C22×C4×C17C22×C411yescharacteristic
132C22×C4×C17C22×C411yescharacteristic
133C22×C4×C17C22×C411yescharacteristic
134C22×C4×C17C2411yescharacteristic
135C22×Dic17C22×C411yescharacteristic
136C22×Dic17C22×C411yescharacteristic
137C22×Dic17C22×C411yescharacteristic
138C22×Dic17C22×C411yescharacteristic
139C22×Dic17C22×C411yescharacteristic
140C22×Dic17C22×C411yescharacteristic
141C2×D68—22no—
142C2×D68—22no—
143C2×D68—22no—
144C2×C4×D17—21no—
145C2×C4×D17—21no—
146C2×C4×D17—21no—
147C2×C4×D17—21no—
148C2×C4×D17—22no—
149C2×C4×D17—22no—
150C2×C4×D17—22no—
151C2×C4×D17—22no—
152C2×C4×D17—21no—
153C2×C4×D17—21no—
154C2×C4×D17—21no—
155C2×C4×D17—21no—
156C2×C4×D17—21no—
157C2×C4×D17—21no—
158C2×C4×D17—41no—
159C2×C4×D17—41no—
160C2×C4×D17#4112yes—
161C2×C4×D17#4112yes—
162C2×C8×C17—21no—
163C2×C8×C17—21no—
164C2×C8×C17—21no—
165C2×C8×C17—21no—
166C2×C8×C17—21no—
167C2×C8×C17—21no—
168C2×C8×C17—21no—
169C2×C8×C17—21no—
170C2×C8×C17—21no—
171C2×C8×C17—21no—
172C2×C8×C17—21no—
173C2×C8×C17—21no—
174C4⋊C4×C17—22no—
175C4⋊C4×C17—22no—
176C42×C17—21no—
177C42×C17—21no—
178C42×C17—21no—
179C42×C17—21no—
180C42×C17—21no—
181C42×C17—21no—
182#63227—22no—
183#63227—22no—
184#63227—22no—
185#63227—22no—
186#63227—22no—
187#63227—22no—
188#63227—41no—
189#63227—41no—
190C4⋊Dic17—22no—
191#63225—41no—
192#63225—41no—
193C4×Dic17—21no—
194C4×Dic17—21no—
195C4×Dic17—21no—
196C4×Dic17—21no—
197C4×Dic17—41no—
198C4×Dic17—41no—
199C2×#3622—21no—
200C2×#3622—21no—
201C2×#3622—21no—
202C2×#3622—21no—
203C2×#3622—21no—
204C2×#3622—21no—
205C2×#3622—21no—
206C2×#3622—21no—
207C2×#3622—21no—
208C2×#3622—21no—
209C2×#3622—21no—
210C2×#3622—21no—
211C8×D17—44no—
212C8×D17—44no—
213#21997—171nomaximal, Sylow
214C23×C17C23×C411yescharacteristic
215C22×D17—21no—
216C22×D17—21no—
217C22×D17—21no—
218C22×D17—21no—
219C22×D17—21no—
220C22×D17—21no—
221C22×D17—21no—
222C22×D17—21no—
223C22×D17—21no—
224C22×D17—21no—
225C22×D17—21no—
226C22×D17#11712yes—
227C22×D17#13112yes—
228C22×D17#13112yes—
229C2×C4×C17—21no—
230C2×C4×C17—21no—
231C2×C4×C17—21no—
232C2×C4×C17—21no—
233C2×C4×C17—21no—
234C2×C4×C17—21no—
235C2×C4×C17—21no—
236C2×C4×C17—21no—
237C2×C4×C17—21no—
238C2×C4×C17—21no—
239C2×C4×C17—21no—
240C2×C4×C17—21no—
241C2×C4×C17—21no—
242C2×C4×C17—21no—
243C2×C4×C17—21no—
244C2×C4×C17—21no—
245C2×C4×C17#13112yes—
246C2×C4×C17#13112yes—
247C2×C4×C17C2×#4111yescharacteristic
248C2×C4×C17C2×#4111yescharacteristic
249C2×C4×C17H(5,𝔽2)11yescharacteristic
250C2×C4×C17H(5,𝔽2)11yescharacteristic
251C2×C4×C17H(5,𝔽2)11yescharacteristic
252C2×C4×C172−1+411yescharacteristic
253C2×Dic17—21no—
254C2×Dic17—21no—
255C2×Dic17—21no—
256C2×Dic17—21no—
257C2×Dic17—21no—
258C2×Dic17—21no—
259C2×Dic17—21no—
260C2×Dic17—21no—
261C2×Dic17—21no—
262C2×Dic17—21no—
263C2×Dic17—21no—
264C2×Dic17—21no—
265C2×Dic17—21no—
266C2×Dic17—21no—
267C2×Dic17—21no—
268C2×Dic17—21no—
269C2×Dic17—21no—
270C2×Dic17#11712yes—
271D68—44no—
272C4×D17—22no—
273C4×D17—22no—
274C4×D17—22no—
275C4×D17—22no—
276C4×D17—44no—
277C4×D17—44no—
278C4×D17—41no—
279C4×D17—41no—
280C4×D17—41no—
281C4×D17—41no—
282C8×C17—41no—
283C8×C17—41no—
284C8×C17—41no—
285C8×C17—41no—
286#3622—41no—
287#3622—41no—
288#3622—41no—
289#3622—41no—
290#2290—171no—
291#1923—171no—
292#1923—171no—
293#1916—171no—
294#1916D1711yescharacteristic, complemented
295#1869—171no—
296#1869—171no—
297#1850—171no—
298#1850—171no—
299#1840—171no—
300#1832—171no—
301#1818—171no—
302#1798—171no—
303C4×C22⋊C8—171no—
304C2×#336—171no—
305C22×C17C2×#11711yescharacteristic
306C22×C17#51811yescharacteristic
307C22×C17#52011yescharacteristic
308C22×C17C2×#13111yescharacteristic
309C22×C17C2×#13111yescharacteristic
310C22×C17C2×#13111yescharacteristic
311C22×C17C2×#13111yescharacteristic
312C2×D17—22no—
313C2×D17—22no—
314C2×D17—22no—
315C2×D17—22no—
316C2×D17—22no—
317C2×D17—22no—
318C2×D17—41no—
319C2×D17—41no—
320C2×D17—41no—
321C2×D17—41no—
322C2×D17—41no—
323C2×D17—41no—
324C2×D17—41no—
325C2×D17#43314yes—
326C4×C17—22no—
327C4×C17—22no—
328C4×C17—41no—
329C4×C17—41no—
330C4×C17—41no—
331C4×C17—41no—
332C4×C17#53811yescharacteristic
333C4×C17#53811yescharacteristic
334C4×C17#53911yescharacteristic
335C4×C17#53911yescharacteristic
336Dic17—22no—
337Dic17—41no—
338Dic17—41no—
339Dic17—41no—
340Dic17—41no—
341Dic17—41no—
342C23×C8—171no—
343C23×C8—171no—
344C2×C4×D4—171no—
345C2×#117—171no—
346C22×C42—171no—
347C2×C4⋊C8—171no—
348C2×C4⋊C8—171no—
349C2×C4⋊C8—171no—
350C2×C4⋊C8C2×D1711yescharacteristic
351C2×C22⋊C8—171no—
352C2×C22⋊C8—171no—
353C2×C22⋊C8—171no—
354C2×C22⋊C8—171no—
355C2×C22⋊C8—171no—
356C2×C22⋊C8—171no—
357C2×C4×C8—171no—
358C2×C4×C8C2×D1711yescharacteristic
359#388—171no—
360#388—171no—
361#387—171no—
362#387—171no—
363#386—171no—
364#386—171no—
365#385—171no—
366#385—171no—
367C4×C4⋊C4C2×D1711yescharacteristic
368C4×C22⋊C4—171no—
369C4×C22⋊C4—171no—
370#376—171no—
371#336—171no—
372#336—171no—
373#336—171no—
374#336—171no—
375#336—171no—
376#336—171no—
377#336—171no—
378#336—171no—
379#336—171no—
380#336—171no—
381#336C2×D1711yescharacteristic
382#336C2×D1711yescharacteristic
383#336C2×D1711yescharacteristic
384#336C2×D1711yescharacteristic
385C2×C17#231811yescharacteristic
386C2×C17C2×#43311yescharacteristic
387C2×C17#292211yescharacteristic
388C2×C17#297711yescharacteristic
389C2×C17#297711yescharacteristic
390C2×C17#299411yescharacteristic
391C2×C17#299411yescharacteristic
392D17—24no—
393D17—81no—
394C22×D4—171no—
395C23×C4—171no—
396C23×C4—171no—
397C23×C4—171no—
398C23×C4—171no—
399C22×C8—171no—
400C22×C8—171no—
401C22×C8—171no—
402C22×C8—171no—
403C22×C8—342no—
404C22×C8—342no—
405C22×C8—681no—
406C22×C8—681no—
407C22×C8—681no—
408C22×C8—681no—
409C22×C8C22×D1711yescharacteristic
410C22×C8C22×D1711yescharacteristic
411C22×C8C22×D1711yescharacteristic
412C22×C8C22×D1711yescharacteristic
413C4×D4—342no—
414C4×D4—342no—
415#117—681no—
416#117—681no—
417C2×C4⋊C4—171no—
418C2×C4⋊C4—171no—
419C2×C4⋊C4—171no—
420C2×C4⋊C4C4×D1711yescharacteristic
421C2×C4⋊C4C4×D1711yescharacteristic
422C2×C22⋊C4—171no—
423C2×C22⋊C4—171no—
424C2×C22⋊C4—171no—
425C2×C22⋊C4—171no—
426C2×C22⋊C4—171no—
427C2×C22⋊C4—171no—
428C2×C22⋊C4—171no—
429C2×C22⋊C4—171no—
430C2×C42—171no—
431C2×C42—171no—
432C2×C42—171no—
433C2×C42—171no—
434C2×C42—681no—
435C2×C42—681no—
436C2×C42C22×D1711yescharacteristic
437C2×C42C22×D1711yescharacteristic
438C2×C42C22×D1711yescharacteristic
439C4⋊C8—41no—
440C4⋊C8—681no—
441C4⋊C8—681no—
442C4⋊C8—681no—
443C22⋊C8—342no—
444C22⋊C8—342no—
445C22⋊C8—681no—
446C22⋊C8—681no—
447C22⋊C8—681no—
448C22⋊C8—681no—
449C4×C8—41no—
450C4×C8—681no—
451#95—171no—
452#95—171no—
453#95—171no—
454#95—171no—
455#95—171no—
456#95—171no—
457#95—171no—
458#95—171no—
459#95C4×D1711yescharacteristic
460#95C4×D1711yescharacteristic
461C17#2199711yescharacteristic, complemented, Sylow
462C24—171no—
463C24—171no—
464C2×D4—342no—
465C2×D4—342no—
466C2×D4—342no—
467C22×C4—171no—
468C22×C4—172no—
469C22×C4—172no—
470C22×C4—171no—
471C22×C4—171no—
472C22×C4—171no—
473C22×C4—171no—
474C22×C4—171no—
475C22×C4—342no—
476C22×C4—342no—
477C22×C4—341no—
478C22×C4—341no—
479C22×C4—341no—
480C22×C4—341no—
481C22×C4—341no—
482C22×C4—341no—
483C22×C4—341no—
484C22×C4—341no—
485C22×C4—341no—
486C22×C4—341no—
487C22×C4—342no—
488C22×C4—342no—
489C22×C4—681no—
490C22×C4—681no—
491C22×C4C2×C4×D1711yescharacteristic
492C22×C4C2×C4×D1711yescharacteristic
493C22×C4C2×C4×D1711yescharacteristic
494C22×C4C2×C4×D1711yescharacteristic
495C22×C4C2×C4×D1711yescharacteristic
496C22×C4C2×C4×D1711yescharacteristic
497C22×C4C23×D1711yescharacteristic
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—341no—
511C2×C8—341no—
512C2×C8—341no—
513C2×C8—341no—
514C2×C8—341no—
515C2×C8—341no—
516C2×C8—341no—
517C2×C8—341no—
518C2×C8—341no—
519C2×C8—341no—
520C2×C8—341no—
521C2×C8—341no—
522C2×C8—684no—
523C2×C8—684no—
524C4⋊C4—22no—
525C4⋊C4—22no—
526C4⋊C4—342no—
527C4⋊C4—681no—
528C4⋊C4—681no—
529C22⋊C4—342no—
530C22⋊C4—342no—
531C22⋊C4—342no—
532C22⋊C4—342no—
533C22⋊C4—342no—
534C22⋊C4—342no—
535C22⋊C4—681no—
536C22⋊C4—681no—
537C42—21no—
538C42—21no—
539C42—21no—
540C42—21no—
541C42—21no—
542C42—21no—
543C42—341no—
544C42—341no—
545C42—341no—
546C42—341no—
547C42—681no—
548C42—681no—
549C23—172no—
550C23—172no—
551C23—172no—
552C23—341no—
553C23—341no—
554C23—341no—
555C23—341no—
556C23—341no—
557C23—341no—
558C23—341no—
559C23—341no—
560C23—341no—
561C23—341no—
562C23—341no—
563C23C22×C4×D1711yescharacteristic
564D4—684no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—172no—
582C2×C4—341no—
583C2×C4—341no—
584C2×C4—342no—
585C2×C4—342no—
586C2×C4—342no—
587C2×C4—342no—
588C2×C4—341no—
589C2×C4—341no—
590C2×C4—341no—
591C2×C4—341no—
592C2×C4—341no—
593C2×C4—341no—
594C2×C4—341no—
595C2×C4—341no—
596C2×C4—341no—
597C2×C4—341no—
598C2×C4—341no—
599C2×C4—341no—
600C2×C4—341no—
601C2×C4—341no—
602C2×C4—341no—
603C2×C4—684no—
604C2×C4—684no—
605C2×C4—681no—
606C2×C4—681no—
607C2×C4—681no—
608C2×C4—681no—
609C2×C4#1058758712yes—
610C2×C4#1058759312yes—
611C2×C4#1058769111yescharacteristic
612C2×C4#1058769411yescharacteristic
613C2×C4#41×D1711yescharacteristic
614C2×C4#41×D1711yescharacteristic
615C2×C4#1058769611yescharacteristic
616C2×C4#1058769611yescharacteristic
617C8—41no—
618C8—41no—
619C8—41no—
620C8—41no—
621C8—681no—
622C8—681no—
623C8—681no—
624C8—681no—
625C22—174no—
626C22—342no—
627C22—342no—
628C22—342no—
629C22—342no—
630C22—342no—
631C22—342no—
632C22—681no—
633C22—681no—
634C22—681no—
635C22—681no—
636C22—681no—
637C22—681no—
638C22—681no—
639C22#117×D1711yescharacteristic
640C22#1176328111yescharacteristic
641C22#1176329111yescharacteristic
642C22#131×D1711yescharacteristic
643C22#131×D1711yescharacteristic
644C22C2×#1058758711yescharacteristic
645C22C2×#1058759311yescharacteristic
646C4—22no—
647C4—22no—
648C4—41no—
649C4—41no—
650C4—41no—
651C4—41no—
652C4—342no—
653C4—681no—
654C4—681no—
655C4—681no—
656C4—681no—
657C4—681no—
658C4#1176339511yescharacteristic
659C4#1176339811yescharacteristic
660C4#1176340511yescharacteristic
661C4#1176340711yescharacteristic
662C2—344no—
663C2—1361no—
664C2#1453141611yescharacteristic
665C2D17×#43311yescharacteristic
666C2#1453742311yescharacteristic
667C2#1453783511yescharacteristic
668C2#1453783711yescharacteristic
669C2#1453794311yescharacteristic
670C2#1453794711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D17
commutator, socleC23×C17C23×C4
FittingC17×#1916C2
prime radicalC22×D68C2×C4
cosocleC22×C4×C17C24
hypercenter#1916D17
hypocenterC17#21997
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ #1916

Complements

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

NH ≅ G/Ntype
2. #14529390C2semidirect
3. #14529388C2semidirect
4. #14529343C2semidirect
7. #14528963C2semidirect
8. #14528960C2semidirect
9. #14528928C2semidirect
10. #14528902C2semidirect
11. #14528854C2semidirect
12. #14528765C2semidirect
13. C4×#10587491C2semidirect
14. D17×#336C2semidirect
15. C17×#1916C2semidirect
294. #1916D17semidirect
461. C17#21997semidirect

Maximal subgroups

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

subgroupindex
#145312252
#145293902
#145293882
#145293432
#145290752
#145289632
#145289602
#145289282
#145289022
#145288542
#145287652
C4×#105874912
D17×#3362
C17×#19162
#2199717