Finite Group Databasebeta

← #17045174

Subgroups — #17045174

Order 4352.

702 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14531247C211yesmaximal, characteristic
2#14529580C211yesmaximal, characteristic
3#14529580C211yesmaximal, characteristic
4#14529506C211yesmaximal, characteristic, complemented
5#14529504C211yesmaximal, characteristic, complemented
6#14529399C211yesmaximal, characteristic, complemented
7#14529397C211yesmaximal, characteristic, complemented
8#14529395C211yesmaximal, characteristic, complemented
9#14528854C211yesmaximal, characteristic, complemented
10#14528853C211yesmaximal, characteristic, complemented
11#14528766C211yesmaximal, characteristic, complemented
12#14528765C211yesmaximal, characteristic, complemented
13#14528638C211yesmaximal, characteristic, complemented
14#14528531C211yesmaximal, characteristic, complemented
15C17×#1924C211yesmaximal, characteristic, complemented
16C2×C4×C22⋊D17C2211yescharacteristic
17C2×#10587612C2211yescharacteristic
18C2×#10587558C2211yescharacteristic
19C2×C4⋊#3622C2211yescharacteristic
20C2×#10587485C2211yescharacteristic
21C2×#10587485C2211yescharacteristic
22C2×#10587485C2211yescharacteristic
23C2×#10587485C2211yescharacteristic
24C2×C22⋊#3622C2211yescharacteristic
25C2×C22⋊#3622C2211yescharacteristic
26C2×#10587491C2211yescharacteristic
27C2×#10587491C2211yescharacteristic
28C2×#10587491C2211yescharacteristic
29C2×#10587491C2211yescharacteristic
30C2×#10587474C2211yescharacteristic
31C2×#10587486C2211yescharacteristic
32C2×#10587486C2211yescharacteristic
33#11762709C411yescharacteristic
34#11762709C411yescharacteristic
35#11762706C411yescharacteristic
36#11762706C411yescharacteristic
37#11762701C411yescharacteristic
38#11762701C411yescharacteristic
39#11762697C411yescharacteristic
40#11762697C411yescharacteristic
41C4×#63225C2211yescharacteristic
42C4×#63227C2211yescharacteristic
43C42×Dic17C2211yescharacteristic
44#11762564C2211yescharacteristic
45#11762564C2211yescharacteristic
46#11762563C2211yescharacteristic
47#11762563C2211yescharacteristic
48#11762563C2211yescharacteristic
49#11762563C2211yescharacteristic
50#11762563C2211yescharacteristic
51#11762563C2211yescharacteristic
52C2×C17×C4⋊C8C2211yescharacteristic
53C2×C17×C22⋊C8C2211yescharacteristic
54C2×C17×C22⋊C8C2211yescharacteristic
55C2×C17×#97C2211yescharacteristic
56C4×C22⋊C4×C17C2211yescharacteristic
57C17×#336C2211yescharacteristic
58C17×#336C2211yescharacteristic
59C23×C4×C17C2311yescharacteristic
60C22×C22⋊D17C2×C411yescharacteristic
61C22×C4×D17C2311yescharacteristic
62C22×C8×C17C2311yescharacteristic
63C22×C8×C17C2311yescharacteristic
64C22×C8×C17C2311yescharacteristic
65C22×C8×C17C2311yescharacteristic
66C2×C22⋊C4×C17C2×C411yescharacteristic
67C2×C22⋊C4×C17C2×C411yescharacteristic
68C2×C42×C17C2311yescharacteristic
69C2×C42×C17C2311yescharacteristic
70C2×C22⋊Dic17C2×C411yescharacteristic
71C2×C22⋊Dic17C2×C411yescharacteristic
72C2×C22⋊Dic17C2×C411yescharacteristic
73C4×C22⋊D17—22no—
74C4×C22⋊D17—22no—
75C2×#63227C2×C411yescharacteristic
76C2×#63227C2×C411yescharacteristic
77C2×#63227C2×C411yescharacteristic
78C2×#63227C2×C411yescharacteristic
79C2×#63227C2×C411yescharacteristic
80#10587612—41no—
81#10587612—41no—
82C2×C4⋊Dic17C2×C411yescharacteristic
83C2×C4⋊Dic17C2×C411yescharacteristic
84C2×#63225C2×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×Dic17C2311yescharacteristic
94C2×C4×Dic17C2311yescharacteristic
95C2×C4×Dic17C2311yescharacteristic
96C22×#3622C2311yescharacteristic
97C22×#3622C2311yescharacteristic
98C22×#3622C2311yescharacteristic
99C22×#3622C2311yescharacteristic
100#10587558—41no—
101#10587558—41no—
102C17×C4⋊C8—41no—
103C17×C22⋊C8—41no—
104C17×C22⋊C8—41no—
105C17×#97—41no—
106C17×#95C2×C411yescharacteristic
107C17×#95C2×C411yescharacteristic
108#10587502C2×C411yescharacteristic
109#10587502C2×C411yescharacteristic
110#10587502C2×C411yescharacteristic
111#10587502C2×C411yescharacteristic
112C22⋊#3622—41no—
113C22⋊#3622—41no—
114#10587491—41no—
115#10587491—41no—
116#10587491—41no—
117#10587491—41no—
118#10587486—22no—
119#10587486—22no—
120#10587485—22no—
121#10587485—22no—
122#10587485—41no—
123#10587485—41no—
124C4⋊#3622—41no—
125#10587474—41no—
126C24×C17C22×C411yescharacteristic
127C23×D17C22×C411yescharacteristic
128C22×C4×C17—21no—
129C22×C4×C17—21no—
130C22×C4×C17—21no—
131C22×C4×C17—21no—
132C22×C4×C17—21no—
133C22×C4×C17—21no—
134C22×C4×C17C22×C411yescharacteristic
135C22×C4×C17C22×C411yescharacteristic
136C22×C4×C17C22×C411yescharacteristic
137C22×C4×C17C22×C411yescharacteristic
138C22×C4×C17C22×C411yescharacteristic
139C22×C4×C17C2411yescharacteristic
140C2×C22⋊D17—22no—
141C2×C22⋊D17—41no—
142C2×C22⋊D17—41no—
143C22×Dic17C22×C411yescharacteristic
144C22×Dic17C22×C411yescharacteristic
145C22×Dic17C22×C411yescharacteristic
146C22×Dic17C22×C411yescharacteristic
147C22×Dic17C22×C411yescharacteristic
148C22×Dic17C22×C411yescharacteristic
149C22×Dic17C22×C411yescharacteristic
150C2×C4×D17—21no—
151C2×C4×D17—21no—
152C2×C4×D17—21no—
153C2×C4×D17—21no—
154C2×C4×D17—21no—
155C2×C4×D17—21no—
156C2×C8×C17—21no—
157C2×C8×C17—21no—
158C2×C8×C17—21no—
159C2×C8×C17—21no—
160C2×C8×C17—21no—
161C2×C8×C17—21no—
162C2×C8×C17—21no—
163C2×C8×C17—21no—
164C2×C8×C17—21no—
165C2×C8×C17—21no—
166C2×C8×C17—21no—
167C2×C8×C17—21no—
168C22⋊C4×C17—41no—
169C22⋊C4×C17—41no—
170C42×C17—21no—
171C42×C17—21no—
172C42×C17—21no—
173C42×C17—21no—
174C22⋊Dic17—22no—
175C22⋊Dic17—41no—
176C22⋊Dic17—41no—
177#63227—22no—
178#63227—41no—
179#63227—41no—
180#63227—41no—
181#63227—41no—
182C4⋊Dic17—41no—
183C4⋊Dic17—41no—
184#63225—22no—
185#63225—41no—
186#63225—41no—
187#63225—41no—
188#63225—41no—
189C4×Dic17—21no—
190C4×Dic17—21no—
191C4×Dic17—21no—
192C4×Dic17—21no—
193C4×Dic17—41no—
194C4×Dic17—41no—
195C4×Dic17—41no—
196C4×Dic17—41no—
197C4×Dic17#4112yes—
198C4×Dic17#4112yes—
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—
211#22015—171nomaximal, Sylow
212C23×C17—21no—
213C23×C17—21no—
214C23×C17—21no—
215C23×C17—21no—
216C23×C17—21no—
217C23×C17—21no—
218C23×C17—21no—
219C23×C17C23×C411yescharacteristic
220C22×D17—21no—
221C22×D17—21no—
222C22×D17—21no—
223C22×D17—21no—
224C22×D17—21no—
225C22×D17—21no—
226C22×D17—21no—
227C2×C4×C17—21no—
228C2×C4×C17—21no—
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—41no—
243C2×C4×C17—41no—
244C2×C4×C17—41no—
245C2×C4×C17—41no—
246C2×C4×C17C2×#4111yescharacteristic
247C2×C4×C17C2×#4111yescharacteristic
248C2×C4×C17H(5,𝔽2)11yescharacteristic
249C2×C4×C17H(5,𝔽2)11yescharacteristic
250C2×C4×C17H(5,𝔽2)11yescharacteristic
251C2×C4×C172−1+411yescharacteristic
252C22⋊D17—44no—
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—21no—
271C2×Dic17—21no—
272C2×Dic17#11712yes—
273C2×Dic17#11712yes—
274C4×D17—41no—
275C4×D17—41no—
276C4×D17—41no—
277C4×D17—41no—
278C8×C17—41no—
279C8×C17—41no—
280C8×C17—41no—
281C8×C17—41no—
282#3622—41no—
283#3622—41no—
284#3622—41no—
285#3622—41no—
286#2293—171no—
287#1955—171no—
288#1955—171no—
289#1940—171no—
290#1940—171no—
291#1924—171no—
292#1924—171no—
293#1924—171no—
294#1924D1711yescharacteristic, complemented
295#1818—171no—
296#1818—171no—
297#1798—171no—
298#1798—171no—
299#1767—171no—
300#1745—171no—
301C22×C17—41no—
302C22×C17—41no—
303C22×C17—41no—
304C22×C17—41no—
305C22×C17—41no—
306C22×C17—41no—
307C22×C17—41no—
308C22×C17C2×#11711yescharacteristic
309C22×C17#51811yescharacteristic
310C22×C17#52011yescharacteristic
311C22×C17#56811yescharacteristic
312C22×C17#56811yescharacteristic
313C22×C17#56811yescharacteristic
314C22×C17#56811yescharacteristic
315C2×D17—41no—
316C2×D17—41no—
317C2×D17—41no—
318C2×D17—41no—
319C2×D17—41no—
320C2×D17—41no—
321C2×D17—41no—
322C4×C17—41no—
323C4×C17—41no—
324C4×C17—41no—
325C4×C17—41no—
326C4×C17—41no—
327C4×C17#54011yescharacteristic
328C4×C17#54011yescharacteristic
329C4×C17#54211yescharacteristic
330C4×C17#54211yescharacteristic
331Dic17—22no—
332Dic17—22no—
333Dic17—41no—
334Dic17—41no—
335Dic17—41no—
336Dic17—41no—
337Dic17—41no—
338C2×C4×D4—171no—
339C2×#117—171no—
340C2×#117—171no—
341C2×C4⋊C8—171no—
342C2×C4⋊C8—171no—
343C2×C4⋊C8—171no—
344C2×C4⋊C8—171no—
345C2×C4⋊C8—171no—
346C2×C4⋊C8C2×D1711yescharacteristic
347C2×C22⋊C8—171no—
348C2×C22⋊C8—171no—
349C2×C22⋊C8—171no—
350C2×C22⋊C8—171no—
351C2×C22⋊C8—171no—
352C2×C22⋊C8—171no—
353C2×C22⋊C8C2×D1711yescharacteristic
354C2×C22⋊C8C2×D1711yescharacteristic
355C2×#97—171no—
356C2×#97—171no—
357C2×#97—171no—
358C2×#97C2×D1711yescharacteristic
359#390—171no—
360#390—171no—
361#389—171no—
362#389—171no—
363#388—171no—
364#388—171no—
365#388—171no—
366#388—171no—
367C4×C4⋊C4—171no—
368C4×C22⋊C4—171no—
369C4×C22⋊C4C2×D1711yescharacteristic
370C43—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#336C2×D1711yescharacteristic
380#336C2×D1711yescharacteristic
381C2×C17—81no—
382C2×C17#231911yescharacteristic
383C2×C17#292111yescharacteristic
384C2×C17#292311yescharacteristic
385C2×C17#298011yescharacteristic
386C2×C17#298011yescharacteristic
387C2×C17#299511yescharacteristic
388C2×C17#299511yescharacteristic
389D17—81no—
390C22×D4—171no—
391C23×C4—171no—
392C23×C4C22×D1711yescharacteristic
393C22×C8—171no—
394C22×C8—171no—
395C22×C8—171no—
396C22×C8—171no—
397C22×C8C22×D1711yescharacteristic
398C22×C8C22×D1711yescharacteristic
399C22×C8C22×D1711yescharacteristic
400C22×C8C22×D1711yescharacteristic
401C4×D4—342no—
402C4×D4—342no—
403#117—681no—
404#117—681no—
405#117—681no—
406#117—681no—
407C2×C4⋊C4—171no—
408C2×C4⋊C4—171no—
409C2×C4⋊C4—171no—
410C2×C4⋊C4—171no—
411C2×C4⋊C4—171no—
412C2×C4⋊C4—171no—
413C2×C4⋊C4—171no—
414C2×C22⋊C4—171no—
415C2×C22⋊C4—171no—
416C2×C22⋊C4—171no—
417C2×C22⋊C4—171no—
418C2×C22⋊C4—171no—
419C2×C22⋊C4—171no—
420C2×C22⋊C4—171no—
421C2×C22⋊C4—171no—
422C2×C22⋊C4C4×D1711yescharacteristic
423C2×C22⋊C4C4×D1711yescharacteristic
424C2×C42—171no—
425C2×C42—171no—
426C2×C42—171no—
427C2×C42—171no—
428C2×C42—171no—
429C2×C42—171no—
430C2×C42—171no—
431C2×C42C22×D1711yescharacteristic
432C2×C42C22×D1711yescharacteristic
433C4⋊C8—41no—
434C4⋊C8—342no—
435C4⋊C8—342no—
436C4⋊C8—681no—
437C4⋊C8—681no—
438C4⋊C8—681no—
439C22⋊C8—41no—
440C22⋊C8—41no—
441C22⋊C8—681no—
442C22⋊C8—681no—
443C22⋊C8—681no—
444C22⋊C8—681no—
445C22⋊C8—681no—
446C22⋊C8—681no—
447#97—41no—
448#97—342no—
449#97—342no—
450#97—681no—
451#95—171no—
452#95—171no—
453#95—171no—
454#95—171no—
455#95C4×D1711yescharacteristic
456#95C4×D1711yescharacteristic
457C17#2201511yescharacteristic, complemented, Sylow
458C24—171no—
459C24C2×C4×D1711yescharacteristic
460C2×D4—342no—
461C2×D4—681no—
462C2×D4—681no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—171no—
470C22×C4—171no—
471C22×C4—171no—
472C22×C4—171no—
473C22×C4—171no—
474C22×C4—171no—
475C22×C4—171no—
476C22×C4—341no—
477C22×C4—341no—
478C22×C4—341no—
479C22×C4—341no—
480C22×C4—341no—
481C22×C4—341no—
482C22×C4C2×C4×D1711yescharacteristic
483C22×C4C2×C4×D1711yescharacteristic
484C22×C4C2×C4×D1711yescharacteristic
485C22×C4C2×C4×D1711yescharacteristic
486C22×C4C2×C4×D1711yescharacteristic
487C22×C4C23×D1711yescharacteristic
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—341no—
501C2×C8—341no—
502C2×C8—341no—
503C2×C8—341no—
504C2×C8—341no—
505C2×C8—341no—
506C2×C8—341no—
507C2×C8—341no—
508C2×C8—341no—
509C2×C8—341no—
510C2×C8—341no—
511C2×C8—341no—
512C4⋊C4—342no—
513C4⋊C4—681no—
514C4⋊C4—681no—
515C4⋊C4—681no—
516C4⋊C4—681no—
517C4⋊C4—681no—
518C4⋊C4—681no—
519C22⋊C4—41no—
520C22⋊C4—41no—
521C22⋊C4—342no—
522C22⋊C4—342no—
523C22⋊C4—681no—
524C22⋊C4—681no—
525C22⋊C4—681no—
526C22⋊C4—681no—
527C22⋊C4—681no—
528C22⋊C4—681no—
529C42—21no—
530C42—21no—
531C42—21no—
532C42—21no—
533C42—172no—
534C42—172no—
535C42—341no—
536C42—341no—
537C42—341no—
538C42—341no—
539C42—681no—
540C42—681no—
541C42—681no—
542C42—681no—
543C23—21no—
544C23—21no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—341no—
551C23—341no—
552C23—341no—
553C23—341no—
554C23—341no—
555C23—341no—
556C23—341no—
557C23C22×C4×D1711yescharacteristic
558D4—684no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
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—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—172no—
579C2×C4—172no—
580C2×C4—341no—
581C2×C4—341no—
582C2×C4—341no—
583C2×C4—341no—
584C2×C4—341no—
585C2×C4—341no—
586C2×C4—341no—
587C2×C4—341no—
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—681no—
600C2×C4—681no—
601C2×C4—681no—
602C2×C4—681no—
603C2×C4#1058769111yescharacteristic
604C2×C4#1058769111yescharacteristic
605C2×C4#41×D1711yescharacteristic
606C2×C4#41×D1711yescharacteristic
607C2×C4#1058769611yescharacteristic
608C2×C4#1058769711yescharacteristic
609C8—41no—
610C8—41no—
611C8—41no—
612C8—41no—
613C8—681no—
614C8—681no—
615C8—681no—
616C8—681no—
617C22—41no—
618C22—41no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—41no—
624C22—681no—
625C22—681no—
626C22—681no—
627C22—681no—
628C22—681no—
629C22—681no—
630C22—681no—
631C22#117×D1711yescharacteristic
632C22#1176328111yescharacteristic
633C22#1176328811yescharacteristic
634C22#1176357411yescharacteristic
635C22#1176357411yescharacteristic
636C22#1176357511yescharacteristic
637C22#1176357511yescharacteristic
638C4—41no—
639C4—41no—
640C4—41no—
641C4—41no—
642C4—41no—
643C4—342no—
644C4—342no—
645C4—681no—
646C4—681no—
647C4—681no—
648C4—681no—
649C4—681no—
650C4#1176340911yescharacteristic
651C4#1176341111yescharacteristic
652C4#1176342311yescharacteristic
653C4#1176342511yescharacteristic
654C2—81no—
655C2—1361no—
656C2#1453142511yescharacteristic
657C2#1453741811yescharacteristic
658C2#1453743011yescharacteristic
659C2#1453785211yescharacteristic
660C2#1453785211yescharacteristic
661C2#1453794811yescharacteristic
662C2#1453795511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D17
commutator, socleC23×C17C23×C4
FittingC17×#1924C2
prime radicalC22×C22⋊D17C2×C4
cosocleC22×C4×C17C24
hypercenter#1924D17
hypocenterC17#22015
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ #1924

Complements

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

NH ≅ G/Ntype
4. #14529506C2semidirect
5. #14529504C2semidirect
6. #14529399C2semidirect
7. #14529397C2semidirect
8. #14529395C2semidirect
9. #14528854C2semidirect
10. #14528853C2semidirect
11. #14528766C2semidirect
12. #14528765C2semidirect
13. #14528638C2semidirect
14. #14528531C2semidirect
15. C17×#1924C2semidirect
294. #1924D17semidirect
457. C17#22015semidirect

Maximal subgroups

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

subgroupindex
#145312472
#145295802
#145295062
#145295042
#145293992
#145293972
#145293952
#145288542
#145288532
#145287662
#145287652
#145286382
#145285312
C17×#19242
#2201517