Finite Group Databasebeta

← #17051936

Subgroups — #17051936

Order 4352.

686 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14537438C211yesmaximal, characteristic
2#14537373C211yesmaximal, characteristic
3#14529534C211yesmaximal, characteristic, complemented
4#14529529C211yesmaximal, characteristic, complemented
5#14529383C211yesmaximal, characteristic, complemented
6#14529383C211yesmaximal, characteristic, complemented
7#14529380C211yesmaximal, characteristic, complemented
8#14529380C211yesmaximal, characteristic, complemented
9#14528883C211yesmaximal, characteristic
10#14528881C211yesmaximal, characteristic
11#14528824C211yesmaximal, characteristic
12#14528669C211yesmaximal, characteristic, complemented
13#14528664C211yesmaximal, characteristic, complemented
14#14528570C211yesmaximal, characteristic
15C17×#2924C211yesmaximal, characteristic
16C22×#63223C2211yescharacteristic
17C2×#10587612C2211yescharacteristic
18#11762867—21no—
19#11762867—21no—
20#11762863—21no—
21#11762859—21no—
22C2×#10587493C2211yescharacteristic
23C2×#10587493C2211yescharacteristic
24#11762852C411yescharacteristic, complemented
25#11762852C411yescharacteristic, complemented
26#11762852C411yescharacteristic, complemented
27#11762852C411yescharacteristic, complemented
28#11762849C411yescharacteristic, complemented
29#11762849C411yescharacteristic, complemented
30#11762849C411yescharacteristic, complemented
31#11762849C411yescharacteristic, complemented
32#11762845C2211yescharacteristic
33#11762845C2211yescharacteristic
34#11762845C2211yescharacteristic
35#11762845C2211yescharacteristic
36#11762835C2211yescharacteristic
37#11762835C2211yescharacteristic
38#11762773C2211yescharacteristic
39#11762764C2211yescharacteristic
40#11762764C2211yescharacteristic
41C2×#10587486C2211yescharacteristic
42C2×C8×Dic17C2211yescharacteristic
43C4×C22⋊Dic17C2211yescharacteristic
44#11762573C2211yescharacteristic
45#11762573C2211yescharacteristic
46#11762570C2211yescharacteristic
47#11762570C2211yescharacteristic
48#11762570C2211yescharacteristic
49#11762570C2211yescharacteristic
50#11762568C2211yescharacteristic
51#11762568C2211yescharacteristic
52#11762568C2211yescharacteristic
53#11762568C2211yescharacteristic
54#11762563C2211yescharacteristic
55#11762563C2211yescharacteristic
56C2×C17×#117C2211yescharacteristic
57C17×#433—21no—
58C17×#433—21no—
59C17×#432—21no—
60C17×#431—21no—
61C17×#424C2211yescharacteristic
62C17×#424C2211yescharacteristic
63C17×#407C2211yescharacteristic
64C2×C17×C22⋊C8C2211yescharacteristic
65C17×#405C2211yescharacteristic
66C17×#405C2211yescharacteristic
67C23×C4×C17C2311yescharacteristic
68C2×M16×C17C2311yescharacteristic
69C2×M16×C17C2311yescharacteristic
70C22×C8×C17C2311yescharacteristic
71C22×C8×C17C2311yescharacteristic
72C17×#117—21no—
73C17×#117—21no—
74C17×#117C2×C411yescharacteristic
75C17×#117C2×C411yescharacteristic
76C17×#117C2311yescharacteristic
77C17×#117C2311yescharacteristic
78C2×C4⋊C4×C17C2×C411yescharacteristic
79C2×C4⋊C4×C17C2×C411yescharacteristic
80C2×C22⋊C4×C17—21no—
81C2×C42×C17—21no—
82C2×C22⋊Dic17—21no—
83C2×C22⋊Dic17—21no—
84#10587612—21no—
85#10587612—21no—
86#10587612C2×C411yescharacteristic
87#10587612C2×C411yescharacteristic
88#10587612C2311yescharacteristic
89#10587612C2311yescharacteristic
90C2×C4⋊Dic17C2×C411yescharacteristic
91C2×C4⋊Dic17C2×C411yescharacteristic
92C2×C4×Dic17—21no—
93C2×C4×Dic17C2311yescharacteristic
94C2×C4×Dic17C2311yescharacteristic
95C2×#63223—22no—
96C2×#63223—22no—
97C2×#63223C2×C411yescharacteristic
98C2×#63223C2×C411yescharacteristic
99C2×#63223C2×C411yescharacteristic
100C2×#63223C2×C411yescharacteristic
101C2×#63223C2311yescharacteristic
102C2×#63223C2311yescharacteristic
103C22×#3622C2311yescharacteristic
104C22×#3622C2311yescharacteristic
105C17×C4⋊C8—21no—
106C17×C4⋊C8—21no—
107C17×C4⋊C8—21no—
108C17×C4⋊C8—21no—
109C17×C22⋊C8—21no—
110C17×C22⋊C8—21no—
111C17×C22⋊C8D411yescharacteristic
112C17×C22⋊C8D411yescharacteristic
113C17×C22⋊C8D411yescharacteristic
114C17×C22⋊C8D411yescharacteristic
115C17×#97—21no—
116C17×#97—21no—
117C4×C8×C17—21no—
118C4×C8×C17—21no—
119#10587502—21no—
120C22⋊#3622—21no—
121C22⋊#3622—21no—
122#10587493—22no—
123#10587493—22no—
124#10587486—22no—
125#10587486—21no—
126#10587486—21no—
127#10587485—21no—
128#10587485—21no—
129#10587485—21no—
130#10587485—21no—
131C8×Dic17—22no—
132C8×Dic17—21no—
133C8×Dic17—21no—
134#10587479C2×C411yescharacteristic
135#10587479C2×C411yescharacteristic
136#10587479C2×C411yescharacteristic
137#10587479C2×C411yescharacteristic
138#10587479C2×C411yescharacteristic
139#10587479C2×C411yescharacteristic
140#10587479C2×C411yescharacteristic
141#10587479C2×C411yescharacteristic
142#10587478C2×C411yescharacteristic
143#10587478C2×C411yescharacteristic
144#10587478C2×C411yescharacteristic
145#10587478C2×C411yescharacteristic
146#10587478C2×C411yescharacteristic
147#10587478C2×C411yescharacteristic
148#10587478C2×C411yescharacteristic
149#10587478C2×C411yescharacteristic
150C24×C17#4111yescharacteristic
151C22×C4×C17—21no—
152C22×C4×C17—21no—
153C22×C4×C17—21no—
154C22×C4×C17—21no—
155C22×C4×C17—21no—
156C22×C4×C17—21no—
157C22×C4×C17C22×C411yescharacteristic
158C22×C4×C17C22×C411yescharacteristic
159C22×C4×C17C2×D411yescharacteristic
160C22×C4×C17C2×D411yescharacteristic
161C22×C4×C17#4111yescharacteristic
162C22×C4×C17C2411yescharacteristic
163C22×Dic17—21no—
164C22×Dic17—21no—
165C22×Dic17—21no—
166C22×Dic17—21no—
167M16×C17—21no—
168M16×C17—21no—
169M16×C17—21no—
170M16×C17—21no—
171C2×C8×C17—21no—
172C2×C8×C17—21no—
173C2×C8×C17—21no—
174C2×C8×C17—21no—
175C2×C8×C17—21no—
176C2×C8×C17—21no—
177C2×C8×C17C2×D411yescharacteristic
178C2×C8×C17C2×D411yescharacteristic
179C2×C8×C17C2×D411yescharacteristic
180C2×C8×C17C2×D411yescharacteristic
181C4⋊C4×C17—21no—
182C4⋊C4×C17—21no—
183C4⋊C4×C17C22×C411yescharacteristic
184C4⋊C4×C17C22×C411yescharacteristic
185C4⋊C4×C17C22×C411yescharacteristic
186C4⋊C4×C17C22×C411yescharacteristic
187C22⋊C4×C17—21no—
188C22⋊C4×C17—21no—
189C22⋊C4×C17—21no—
190C22⋊C4×C17—21no—
191C42×C17—21no—
192C42×C17—21no—
193C42×C17—21no—
194C42×C17—21no—
195C22⋊Dic17—21no—
196C22⋊Dic17—21no—
197C22⋊Dic17—21no—
198C22⋊Dic17—21no—
199C22⋊Dic17—42no—
200C4⋊Dic17—21no—
201C4⋊Dic17—21no—
202C4⋊Dic17C22×C411yescharacteristic
203C4⋊Dic17C22×C411yescharacteristic
204C4⋊Dic17C22×C411yescharacteristic
205C4⋊Dic17C22×C411yescharacteristic
206C4×Dic17—21no—
207C4×Dic17—21no—
208C4×Dic17—21no—
209C4×Dic17—21no—
210C4×Dic17—21no—
211C4×Dic17—21no—
212C4×Dic17—21no—
213C4×Dic17—21no—
214#63223—22no—
215#63223—22no—
216#63223—22no—
217#63223—22no—
218#63223—21no—
219#63223—21no—
220#63223—21no—
221#63223—21no—
222C2×#3622—21no—
223C2×#3622—21no—
224C2×#3622—21no—
225C2×#3622—21no—
226C2×#3622C22×C411yescharacteristic
227C2×#3622C22×C411yescharacteristic
228C2×#3622C22×C411yescharacteristic
229C2×#3622C22×C411yescharacteristic
230C2×#3622#4112yes—
231C2×#3622#4112yes—
232#22608—171nomaximal, Sylow
233C23×C17—21no—
234C23×C17—21no—
235C23×C17—41no—
236C23×C17—41no—
237C23×C17C4×D411yescharacteristic
238C23×C17C4×D411yescharacteristic
239C23×C17C2×#4111yescharacteristic
240C2×C4×C17—21no—
241C2×C4×C17—21no—
242C2×C4×C17—21no—
243C2×C4×C17—21no—
244C2×C4×C17—21no—
245C2×C4×C17—21no—
246C2×C4×C17—21no—
247C2×C4×C17—21no—
248C2×C4×C17—21no—
249C2×C4×C17—21no—
250C2×C4×C17—21no—
251C2×C4×C17—21no—
252C2×C4×C17—21no—
253C2×C4×C17—21no—
254C2×C4×C17—42no—
255C2×C4×C17—81no—
256C2×C4×C17C4×D411yescharacteristic
257C2×C4×C17C4×D411yescharacteristic
258C2×C4×C17C23×C411yescharacteristic
259C2×C4×C17C22×D411yescharacteristic
260C2×C4×C17C2×#4111yescharacteristic
261C2×C4×C17C2×#4111yescharacteristic
262C2×C4×C172−1+411yescharacteristic
263C2×C4×C172−1+411yescharacteristic
264C2×Dic17—22no—
265C2×Dic17—21no—
266C2×Dic17—21no—
267C2×Dic17—21no—
268C2×Dic17—21no—
269C2×Dic17—41no—
270C2×Dic17—42no—
271C2×Dic17—41no—
272C2×Dic17—41no—
273C2×Dic17—41no—
274C2×Dic17—41no—
275C2×Dic17—81no—
276C8×C17—21no—
277C8×C17—21no—
278C8×C17—21no—
279C8×C17—21no—
280C8×C17—41no—
281C8×C17—41no—
282#3622—21no—
283#3622—21no—
284#3622—41no—
285#3622—41no—
286#3622#11712yes—
287#3622#11712yes—
288#2924—171no—
289#2924D1711yescharacteristic
290#2911—171no—
291#1946—171no—
292#1945—171no—
293#1922—171no—
294#1922—171no—
295#1922—171no—
296#1922—171no—
297#1826—171no—
298#1826—171no—
299#1811—171no—
300#1773—171no—
301#1772—171no—
302#1753—171no—
303C22×C17—21no—
304C22×C17—21no—
305C22×C17—21no—
306C22×C17—21no—
307C22×C17—21no—
308C22×C17—21no—
309C22×C17—21no—
310C22×C17—21no—
311C22×C17—81no—
312C22×C17—81no—
313C22×C17C2×C4×D411yescharacteristic
314C22×C17#55211yescharacteristic
315C22×C17#55211yescharacteristic
316C4×C17—21no—
317C4×C17—21no—
318C4×C17—41no—
319C4×C17—41no—
320C4×C17—41no—
321C4×C17—41no—
322C4×C17C2×#11711yescharacteristic
323C4×C17#51911yescharacteristic
324C4×C17#54711yescharacteristic
325C4×C17#54711yescharacteristic
326Dic17—42no—
327Dic17—41no—
328Dic17—41no—
329Dic17—41no—
330Dic17—41no—
331Dic17—81no—
332C22×M16—171no—
333C2×#117—171no—
334C2×#117C2×D1711yescharacteristic
335#433—21no—
336#433—21no—
337#433—341no—
338#433—341no—
339#432—21no—
340#432—341no—
341#431—21no—
342#431—341no—
343C2×#108—171no—
344C2×#108—171no—
345#428—171no—
346#428—171no—
347#428—171no—
348#428—171no—
349#428—171no—
350#428—171no—
351#428—171no—
352#428—171no—
353#427—171no—
354#427—171no—
355#427—171no—
356#427—171no—
357#424—171no—
358#424—171no—
359#424C2×D1711yescharacteristic
360#424C2×D1711yescharacteristic
361#407—171no—
362#407C2×D1711yescharacteristic
363C2×C22⋊C8C2×D1711yescharacteristic
364#405—171no—
365#405—171no—
366#405C2×D1711yescharacteristic
367#405C2×D1711yescharacteristic
368C2×#97—171no—
369C2×C4×C8—171no—
370C4×C22⋊C4—171no—
371#341—171no—
372#341—171no—
373#339—171no—
374#339—171no—
375#339—171no—
376#339—171no—
377#339—171no—
378#339—171no—
379#339—171no—
380#339—171no—
381#336—171no—
382#336—171no—
383C2×C17—21no—
384C2×C17—21no—
385C2×C17—41no—
386C2×C17—41no—
387C2×C17#234411yescharacteristic
388C2×C17#295511yescharacteristic
389C2×C17#295611yescharacteristic
390C23×C4C22×D1711yescharacteristic
391C2×M16—171no—
392C2×M16—171no—
393C2×M16—171no—
394C2×M16—171no—
395C2×M16—171no—
396C2×M16—171no—
397C2×M16—342no—
398C2×M16—342no—
399C2×M16C22×D1711yescharacteristic
400C2×M16C22×D1711yescharacteristic
401C22×C8—171no—
402C22×C8—171no—
403C22×C8C22×D1711yescharacteristic
404C22×C8C22×D1711yescharacteristic
405#117—21no—
406#117—21no—
407#117—171no—
408#117—171no—
409#117—171no—
410#117—171no—
411#117—341no—
412#117—341no—
413#117C4×D1711yescharacteristic
414#117C4×D1711yescharacteristic
415#117C22×D1711yescharacteristic
416#117C22×D1711yescharacteristic
417C2×C4⋊C4—171no—
418C2×C4⋊C4—171no—
419C2×C4⋊C4C4×D1711yescharacteristic
420C2×C4⋊C4C4×D1711yescharacteristic
421C2×C22⋊C4—21no—
422C2×C22⋊C4—341no—
423C2×C22⋊C4—341no—
424C2×C42—21no—
425C2×C42—171no—
426C2×C42—171no—
427C2×C42—341no—
428#108—342no—
429#108—342no—
430#107—171no—
431#107—171no—
432#107—171no—
433#107—171no—
434#107—171no—
435#107—171no—
436#107—171no—
437#107—171no—
438#106—171no—
439#106—171no—
440#106—171no—
441#106—171no—
442#106—171no—
443#106—171no—
444#106—171no—
445#106—171no—
446C4⋊C8—21no—
447C4⋊C8—21no—
448C4⋊C8—21no—
449C4⋊C8—21no—
450C4⋊C8—341no—
451C4⋊C8—341no—
452C4⋊C8—341no—
453C4⋊C8—341no—
454C22⋊C8—21no—
455C22⋊C8—21no—
456C22⋊C8—341no—
457C22⋊C8—341no—
458C22⋊C8C22⋊D1711yescharacteristic
459C22⋊C8C22⋊D1711yescharacteristic
460C22⋊C8C22⋊D1711yescharacteristic
461C22⋊C8C22⋊D1711yescharacteristic
462#97—21no—
463#97—21no—
464#97—342no—
465#97—341no—
466#97—341no—
467C4×C8—21no—
468C4×C8—21no—
469C4×C8—342no—
470C4×C8—341no—
471C4×C8—341no—
472#95—341no—
473C17#2260811yescharacteristic, complemented, Sylow
474C24#6325211yescharacteristic
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—341no—
482C22×C4—341no—
483C22×C4—341no—
484C22×C4—341no—
485C22×C4C2×C4×D1711yescharacteristic
486C22×C4C2×C4×D1711yescharacteristic
487C22×C4#6325211yescharacteristic
488C22×C4C2×C22⋊D1711yescharacteristic
489C22×C4C2×C22⋊D1711yescharacteristic
490C22×C4C23×D1711yescharacteristic
491M16—21no—
492M16—21no—
493M16—21no—
494M16—21no—
495M16—342no—
496M16—342no—
497M16—342no—
498M16—342no—
499M16—341no—
500M16—341no—
501M16—341no—
502M16—341no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—171no—
510C2×C8—171no—
511C2×C8—172no—
512C2×C8—172no—
513C2×C8—171no—
514C2×C8—171no—
515C2×C8—341no—
516C2×C8—341no—
517C2×C8—341no—
518C2×C8—341no—
519C2×C8C2×C22⋊D1711yescharacteristic
520C2×C8C2×C22⋊D1711yescharacteristic
521C2×C8C2×C22⋊D1711yescharacteristic
522C2×C8C2×C22⋊D1711yescharacteristic
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—171no—
526C4⋊C4—171no—
527C4⋊C4—171no—
528C4⋊C4—171no—
529C4⋊C4—341no—
530C4⋊C4—341no—
531C4⋊C4C2×C4×D1711yescharacteristic
532C4⋊C4C2×C4×D1711yescharacteristic
533C4⋊C4C2×C4×D1711yescharacteristic
534C4⋊C4C2×C4×D1711yescharacteristic
535C22⋊C4—21no—
536C22⋊C4—21no—
537C22⋊C4—21no—
538C22⋊C4—21no—
539C22⋊C4—341no—
540C22⋊C4—341no—
541C22⋊C4—341no—
542C22⋊C4—341no—
543C22⋊C4—682no—
544C42—21no—
545C42—21no—
546C42—21no—
547C42—21no—
548C42—341no—
549C42—341no—
550C42—341no—
551C42—341no—
552C42—341no—
553C42—341no—
554C42—341no—
555C42—341no—
556C23—21no—
557C23—21no—
558C23—41no—
559C23—41no—
560C23C4×C22⋊D1711yescharacteristic
561C23C4×C22⋊D1711yescharacteristic
562C23C2×#6325211yescharacteristic
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—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—42no—
578C2×C4—81no—
579C2×C4—342no—
580C2×C4—341no—
581C2×C4—341no—
582C2×C4—341no—
583C2×C4—341no—
584C2×C4—681no—
585C2×C4—682no—
586C2×C4—681no—
587C2×C4—681no—
588C2×C4—681no—
589C2×C4—681no—
590C2×C4—1361no—
591C2×C4C4×C22⋊D1711yescharacteristic
592C2×C4C4×C22⋊D1711yescharacteristic
593C2×C4C22×C4×D1711yescharacteristic
594C2×C4#41×D1711yescharacteristic
595C2×C4#41×D1711yescharacteristic
596C2×C4#1058769711yescharacteristic
597C2×C4#1058769711yescharacteristic
598C2×C4C22×C22⋊D1711yescharacteristic
599C8—21no—
600C8—21no—
601C8—21no—
602C8—21no—
603C8—41no—
604C8—41no—
605C8—172no—
606C8—172no—
607C8—341no—
608C8—341no—
609C8—681no—
610C8—681no—
611C22—21no—
612C22—21no—
613C22—21no—
614C22—21no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—21no—
619C22—81no—
620C22—81no—
621C22C2×C4×C22⋊D1711yescharacteristic
622C22#1176349211yescharacteristic
623C22#1176349211yescharacteristic
624C4—21no—
625C4—21no—
626C4—41no—
627C4—41no—
628C4—41no—
629C4—41no—
630C4—682no—
631C4—681no—
632C4—681no—
633C4—681no—
634C4—681no—
635C4—1361no—
636C4#117×D1711yescharacteristic
637C4#1176328611yescharacteristic
638C4#1176345811yescharacteristic
639C4#1176345811yescharacteristic
640C2—21no—
641C2—21no—
642C2—41no—
643C2—41no—
644C2#1453165411yescharacteristic
645C2#1453768511yescharacteristic
646C2#1453769111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC17×#2924C2
socleC22×C17C2×C4×D4
prime radicalC24×C17#41
cosocleC22×C4×C17C24
hypercenter#2924D17
hypocenterC17#22608
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C22⋊C8 ◁ #2924

Complements

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

NH ≅ G/Ntype
3. #14529534C2semidirect
4. #14529529C2semidirect
5. #14529383C2semidirect
6. #14529383C2semidirect
7. #14529380C2semidirect
8. #14529380C2semidirect
12. #14528669C2semidirect
13. #14528664C2semidirect
24. #11762852C4semidirect
25. #11762852C4semidirect
26. #11762852C4semidirect
27. #11762852C4semidirect
28. #11762849C4semidirect
29. #11762849C4semidirect
30. #11762849C4semidirect
31. #11762849C4semidirect
473. C17#22608semidirect

Maximal subgroups

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

subgroupindex
#145374382
#145373732
#145295342
#145295292
#145293832
#145293802
#145288832
#145288812
#145288242
#145286692
#145286642
#145285702
C17×#29242
#2260817