Finite Group Databasebeta

← #17037421

Subgroups — #17037421

Order 4352.

938 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762919C211yesmaximal, characteristic
2#14531427C211yesmaximal, characteristic, complemented
3#14531144C211yesmaximal, characteristic, complemented
4#14529414C211yesmaximal, characteristic, complemented
5#14529407C211yesmaximal, characteristic, complemented
6#14529372C211yesmaximal, characteristic, complemented
7#14529365C211yesmaximal, characteristic, complemented
8#14529129C211yesmaximal, characteristic
9#14529129C211yesmaximal, characteristic
10#14529046C211yesmaximal, characteristic, complemented
11#14529032C211yesmaximal, characteristic, complemented
12#14528682C211yesmaximal, characteristic, complemented
13C4×#10587492C211yesmaximal, characteristic, complemented
14#14528535C211yesmaximal, characteristic, complemented
15C4×C17×#102C211yesmaximal, characteristic, complemented
16C22×#63228C2211yescharacteristic
17C2×C4×D68C2211yescharacteristic
18C2×#10587579C2211yescharacteristic
19C2×#10587579C2211yescharacteristic
20#11762919C418yescomplemented
21C2×#10587478C2211yescharacteristic
22C2×#10587479C2211yescharacteristic
23C2×#10587479C2211yescharacteristic
24C2×#10587492C2211yescharacteristic
25C2×#10587492C2211yescharacteristic
26C2×#10587503C2211yescharacteristic
27C2×#10587480C2211yescharacteristic
28C2×#10587474C2211yescharacteristic
29#11762712C2211yescharacteristic
30#11762712C2211yescharacteristic
31#11762708C2211yescharacteristic
32#11762708C2211yescharacteristic
33#11762702—21no—
34#11762702—21no—
35#11762672—21no—
36#11762669—21no—
37C4⋊C4×Dic17C2211yescharacteristic
38C4⋊C4×Dic17C2211yescharacteristic
39C4×C4⋊Dic17C2211yescharacteristic
40C4×#63227—21no—
41C4×#63227—21no—
42#11762656—21no—
43#11762655C2211yescharacteristic
44#95×D17—21no—
45#11762572C2211yescharacteristic
46#11762572C2211yescharacteristic
47#11762571C2211yescharacteristic
48#11762571C2211yescharacteristic
49#11762563C2211yescharacteristic
50#11762563C2211yescharacteristic
51#11762563C2211yescharacteristic
52#11762563C2211yescharacteristic
53C2×C4×D4×C17C2211yescharacteristic
54C2×C17×#102C2211yescharacteristic
55C2×C17×#102C2211yescharacteristic
56C2×C4×C8×C17C2211yescharacteristic
57C4×C4⋊C4×C17C2211yescharacteristic
58C17×#340C2211yescharacteristic
59C17×#340C2211yescharacteristic
60C22×D4×C17C2311yescharacteristic
61C23×C4×C17—21no—
62C22×D68C2311yescharacteristic
63C22×C4×D17—21no—
64C22×C4×D17—21no—
65C22×C4×D17—21no—
66C22×C8×C17C2311yescharacteristic
67C22×C8×C17C2311yescharacteristic
68C4×D4×C17—22no—
69C4×D4×C17C2×C414yescomplemented
70C2×C4⋊C4×C17C2311yescharacteristic
71C2×C4⋊C4×C17C2311yescharacteristic
72C2×C4⋊C4×C17C2311yescharacteristic
73C2×C22⋊C4×C17—21no—
74C2×C42×C17—21no—
75C2×C42×C17C2311yescharacteristic
76C2×C22⋊Dic17—21no—
77C2×C22⋊Dic17—21no—
78C2×C22⋊Dic17—21no—
79C2×C22⋊Dic17—21no—
80C2×#63228—22no—
81C2×#63228—22no—
82C2×#63228C2×C414yes—
83C2×#63227—21no—
84C2×#63227—21no—
85C2×#63227—21no—
86C2×C4⋊Dic17—21no—
87C2×C4⋊Dic17—21no—
88C2×C4⋊Dic17C2311yescharacteristic
89C2×C4⋊Dic17C2311yescharacteristic
90C2×C4⋊Dic17C2311yescharacteristic
91C2×C4×Dic17—21no—
92C2×C4×Dic17—21no—
93C2×C4×Dic17—21no—
94C2×C4×Dic17C2311yescharacteristic
95C2×C4×Dic17C2311yescharacteristic
96C22×#3622C2311yescharacteristic
97C22×#3622C2311yescharacteristic
98#10587579—22no—
99#10587579—22no—
100#10587579—22no—
101#10587579—22no—
102C4×D68—22no—
103C4×D68C2×C414yes—
104C17×#102—22no—
105C17×#102—22no—
106C4×C8×C17—22no—
107C17×#95—21no—
108#10587503C2×C414yescomplemented
109#10587502—21no—
110#10587502—21no—
111#10587502—21no—
112#10587502—21no—
113#10587502—21no—
114#10587502D411yescharacteristic
115#10587502D411yescharacteristic
116#10587502D411yescharacteristic
117#10587502D411yescharacteristic
118#10587492—22no—
119#10587492—22no—
120#10587480C2×C414yes—
121#10587479—22no—
122#10587479C2×C414yescomplemented
123#10587478—22no—
124#10587474C2×C414yescomplemented
125C24×C17—21no—
126C23×D17—21no—
127C2×D4×C17—21no—
128C2×D4×C17—21no—
129C2×D4×C17—21no—
130C2×D4×C17—21no—
131C2×D4×C17—21no—
132C2×D4×C17C22×C412yes—
133C22×C4×C17—21no—
134C22×C4×C17—21no—
135C22×C4×C17—21no—
136C22×C4×C17—24no—
137C22×C4×C17—81no—
138C22×C4×C17—81no—
139C22×C4×C17C2×D411yescharacteristic
140C22×C4×C17C2×D411yescharacteristic
141C22×C4×C17C2411yescharacteristic
142C22×Dic17—21no—
143C22×Dic17—21no—
144C22×Dic17—21no—
145C22×Dic17C2×D411yescharacteristic
146C22×Dic17C2×D411yescharacteristic
147C22×Dic17C2×D411yescharacteristic
148C22×Dic17C2×D411yescharacteristic
149C2×D68—21no—
150C2×D68—21no—
151C2×D68—21no—
152C2×D68C22×C412yes—
153C2×D68#4112yes—
154C2×D68#4112yes—
155C2×C4×D17—24no—
156C2×C4×D17—24no—
157C2×C4×D17—24no—
158C2×C4×D17—81no—
159C2×C4×D17—81no—
160C2×C4×D17—81no—
161C2×C4×D17—81no—
162C2×C4×D17—81no—
163C2×C4×D17—81no—
164C2×C8×C17—21no—
165C2×C8×C17—21no—
166C2×C8×C17—21no—
167C2×C8×C17—21no—
168C2×C8×C17—21no—
169C2×C8×C17—21no—
170C4⋊C4×C17—21no—
171C4⋊C4×C17—21no—
172C4⋊C4×C17—21no—
173C4⋊C4×C17C22×C412yes—
174C4⋊C4×C17#4112yes—
175C4⋊C4×C17#4112yes—
176C22⋊C4×C17—24no—
177C42×C17—81no—
178C42×C17C22×C412yes—
179C42×C17#4112yes—
180C22⋊Dic17—81no—
181C22⋊Dic17—81no—
182C22⋊Dic17—81no—
183C22⋊Dic17—81no—
184#63228—28no—
185#63227—24no—
186#63227—24no—
187#63227—24no—
188C4⋊Dic17—21no—
189C4⋊Dic17—21no—
190C4⋊Dic17—21no—
191C4⋊Dic17—21no—
192C4⋊Dic17—21no—
193C4⋊Dic17—81no—
194C4⋊Dic17—81no—
195C4⋊Dic17C22×C412yes—
196C4×Dic17—21no—
197C4×Dic17—21no—
198C4×Dic17—21no—
199C4×Dic17—21no—
200C4×Dic17—81no—
201C4×Dic17—81no—
202C4×Dic17—81no—
203C2×#3622—21no—
204C2×#3622—21no—
205C2×#3622—21no—
206C2×#3622—21no—
207C2×#3622C22×C412yes—
208C2×#3622C22×C412yes—
209#21126—171nomaximal, Sylow
210C23×C17—22no—
211C23×C17—41no—
212C23×C17—41no—
213C23×C17—41no—
214C23×C17—41no—
215C23×C17—41no—
216C23×C17—41no—
217C23×C17C22×D411yescharacteristic
218C22×D17—22no—
219C22×D17—22no—
220C22×D17—22no—
221C22×D17—41no—
222C22×D17—41no—
223C22×D17—41no—
224C22×D17—41no—
225D4×C17—22no—
226D4×C17—22no—
227D4×C17—41no—
228D4×C17—41no—
229C2×C4×C17—21no—
230C2×C4×C17—21no—
231C2×C4×C17—21no—
232C2×C4×C17—21no—
233C2×C4×C17—22no—
234C2×C4×C17—22no—
235C2×C4×C17—22no—
236C2×C4×C17—41no—
237C2×C4×C17—41no—
238C2×C4×C17—41no—
239C2×C4×C17—41no—
240C2×C4×C17—41no—
241C2×C4×C17—41no—
242C2×C4×C17—84no—
243C2×C4×C17C4×D412yes—
244C2×C4×C17C4×D412yes—
245C2×C4×C17C23×C411yescharacteristic
246C2×C4×C17C2×#4111yescharacteristic
247C2×C4×C17C2×#4111yescharacteristic
248C2×C4×C17C2×#4111yescharacteristic
249C2×C4×C17C2×#4111yescharacteristic
250C2×C4×C17C2×#4111yescharacteristic
251C2×Dic17—22no—
252C2×Dic17—21no—
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—41no—
265C2×Dic17—41no—
266C2×Dic17—41no—
267C2×Dic17—41no—
268C2×Dic17—41no—
269C2×Dic17—41no—
270C2×Dic17—41no—
271C2×Dic17—41no—
272D68—22no—
273D68—22no—
274D68—22no—
275D68#11714yes—
276C4×D17—84no—
277C4×D17—84no—
278C4×D17—84no—
279C8×C17—41no—
280C8×C17—41no—
281#3622—22no—
282#3622—22no—
283C2×#442—171no—
284#2319—171no—
285#2275—171no—
286#1926—171no—
287#1925—171no—
288#1920—171no—
289#1919—171no—
290#1879—171no—
291#1879—171no—
292#1864—171no—
293#1862—171no—
294#1776—171no—
295C4×#102—171no—
296C4×#102D1711yescharacteristic, complemented
297#1746—171no—
298C22×C17—42no—
299C22×C17—42no—
300C22×C17—42no—
301C22×C17—81no—
302C22×C17—81no—
303C22×C17—81no—
304C22×C17—81no—
305C22×C17C2×C4×D411yescharacteristic
306C22×C17#52511yescharacteristic
307C22×C17#52511yescharacteristic
308C22×C17#57611yescharacteristic
309C22×C17#57611yescharacteristic
310C22×C17#57711yescharacteristic
311C22×C17#57711yescharacteristic
312C2×D17—24no—
313C2×D17—42no—
314C2×D17—42no—
315C2×D17—42no—
316C2×D17—42no—
317C2×D17—42no—
318C2×D17—42no—
319C4×C17—22no—
320C4×C17—22no—
321C4×C17—42no—
322C4×C17—42no—
323C4×C17—42no—
324C4×C17C2×#11711yescharacteristic
325C4×C17C4×#4111yescharacteristic
326C4×C17#52911yescharacteristic
327C4×C17#52911yescharacteristic
328Dic17—41no—
329Dic17—41no—
330Dic17—41no—
331Dic17—41no—
332Dic17—42no—
333Dic17—81no—
334Dic17—81no—
335C22×D8—171no—
336C2×C4×D4—171no—
337C2×C4×D4—171no—
338C2×C4×D4—171no—
339C2×C4×D4C2×D1711yescharacteristic
340#442—178no—
341C2×#107—171no—
342C2×#106—171no—
343C2×#106—171no—
344C2×#102—171no—
345C2×#102—171no—
346C2×#102—171no—
347C2×#102—171no—
348C2×#102C2×D1711yescharacteristic
349C2×#102C2×D1711yescharacteristic
350C2×#97—171no—
351C2×C4×C8C2×D1711yescharacteristic
352#390—171no—
353#390—171no—
354#389—171no—
355#389—171no—
356#388—341no—
357#388—341no—
358#381—341no—
359#380—341no—
360C4×C4⋊C4—171no—
361C4×C4⋊C4—171no—
362C4×C4⋊C4—171no—
363C4×C4⋊C4C2×D1711yescharacteristic
364C4×C22⋊C4—341no—
365C4×C22⋊C4—341no—
366C4×C22⋊C4—341no—
367#376—171no—
368C2×#95—341no—
369#340—171no—
370#340—171no—
371#340—171no—
372#340—171no—
373#340C2×D1711yescharacteristic
374#340C2×D1711yescharacteristic
375#336—171no—
376#336—171no—
377#336—171no—
378#336—171no—
379C2×C17—82no—
380C2×C17#229011yescharacteristic
381C2×C17#294611yescharacteristic
382C2×C17#294611yescharacteristic
383C2×C17#311811yescharacteristic
384C2×C17#311911yescharacteristic
385C2×C17#312211yescharacteristic
386C2×C17#312511yescharacteristic
387D17—44no—
388C22×D4—171no—
389C22×D4C22×D1711yescharacteristic
390C23×C4—21no—
391C23×C4—341no—
392C23×C4—341no—
393C23×C4—341no—
394C2×D8—174no—
395C2×D8—342no—
396C2×D8—342no—
397C22×C8—171no—
398C22×C8—171no—
399C22×C8C22×D1711yescharacteristic
400C22×C8C22×D1711yescharacteristic
401C4×D4—22no—
402C4×D4—174no—
403C4×D4—342no—
404C4×D4—342no—
405C4×D4—342no—
406C4×D4—342no—
407C4×D4—342no—
408C4×D4C4×D1714yescomplemented
409C2×C4⋊C4—171no—
410C2×C4⋊C4—171no—
411C2×C4⋊C4—171no—
412C2×C4⋊C4—341no—
413C2×C4⋊C4—341no—
414C2×C4⋊C4C22×D1711yescharacteristic
415C2×C4⋊C4C22×D1711yescharacteristic
416C2×C4⋊C4C22×D1711yescharacteristic
417C2×C22⋊C4—21no—
418C2×C22⋊C4—341no—
419C2×C22⋊C4—341no—
420C2×C22⋊C4—341no—
421C2×C22⋊C4—341no—
422C2×C22⋊C4—341no—
423C2×C22⋊C4—341no—
424C2×C22⋊C4—341no—
425C2×C42—21no—
426C2×C42—171no—
427C2×C42—171no—
428C2×C42—341no—
429C2×C42—341no—
430C2×C42—341no—
431C2×C42C22×D1711yescharacteristic
432#107—342no—
433#106—174no—
434#106—342no—
435#102—22no—
436#102—22no—
437#102—174no—
438#102—174no—
439#102—342no—
440#102—342no—
441#97—174no—
442C4×C8—22no—
443#95—21no—
444#95—171no—
445#95—171no—
446#95—171no—
447#95—171no—
448#95—341no—
449#95—341no—
450#95—341no—
451#95—341no—
452#95—341no—
453C17#2112611yescharacteristic, complemented, Sylow
454C24—21no—
455C24—341no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—172no—
462C2×D4—172no—
463C2×D4—172no—
464C2×D4—341no—
465C2×D4—341no—
466C2×D4—341no—
467C2×D4C2×C4×D1712yes—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—24no—
472C22×C4—81no—
473C22×C4—81no—
474C22×C4—171no—
475C22×C4—171no—
476C22×C4—171no—
477C22×C4—171no—
478C22×C4—344no—
479C22×C4—344no—
480C22×C4—341no—
481C22×C4—344no—
482C22×C4—341no—
483C22×C4—341no—
484C22×C4—1361no—
485C22×C4—1361no—
486C22×C4—1361no—
487C22×C4—1361no—
488C22×C4—1361no—
489C22×C4—1361no—
490C22×C4D4×D1711yescharacteristic
491C22×C4D4×D1711yescharacteristic
492C22×C4C23×D1711yescharacteristic
493D8—348no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—172no—
501C2×C8—172no—
502C2×C8—341no—
503C2×C8—341no—
504C2×C8—341no—
505C2×C8—341no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—172no—
510C4⋊C4—341no—
511C4⋊C4—341no—
512C4⋊C4—341no—
513C4⋊C4—341no—
514C4⋊C4—341no—
515C4⋊C4—1361no—
516C4⋊C4—1361no—
517C4⋊C4C2×C4×D1712yes—
518C4⋊C4#6325212yes—
519C4⋊C4#6325212yes—
520C22⋊C4—24no—
521C22⋊C4—344no—
522C22⋊C4—344no—
523C22⋊C4—344no—
524C22⋊C4—1361no—
525C22⋊C4—1361no—
526C22⋊C4—1361no—
527C22⋊C4—1361no—
528C42—81no—
529C42—341no—
530C42—341no—
531C42—341no—
532C42—341no—
533C42—1361no—
534C42—1361no—
535C42—1361no—
536C42C2×C4×D1712yes—
537C42#6325412yes—
538C23—22no—
539C23—41no—
540C23—41no—
541C23—41no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23—342no—
546C23—342no—
547C23—342no—
548C23—681no—
549C23—681no—
550C23—681no—
551C23—681no—
552C23C2×D4×D1711yescharacteristic
553D4—22no—
554D4—22no—
555D4—41no—
556D4—41no—
557D4—174no—
558D4—342no—
559D4—342no—
560D4—342no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—84no—
575C2×C4—342no—
576C2×C4—341no—
577C2×C4—341no—
578C2×C4—341no—
579C2×C4—341no—
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—681no—
589C2×C4—681no—
590C2×C4—681no—
591C2×C4—681no—
592C2×C4—681no—
593C2×C4—681no—
594C2×C4—681no—
595C2×C4—681no—
596C2×C4—1364no—
597C2×C4—1364no—
598C2×C4—1364no—
599C2×C4#1058756712yes—
600C2×C4#1058756712yes—
601C2×C4C22×C4×D1711yescharacteristic
602C2×C4C2×#6325211yescharacteristic
603C2×C4C2×#6325211yescharacteristic
604C2×C4C2×#6325411yescharacteristic
605C2×C4#41×D1711yescharacteristic
606C2×C4#41×D1711yescharacteristic
607C8—41no—
608C8—41no—
609C8—342no—
610C8—342no—
611C22—42no—
612C22—42no—
613C22—42no—
614C22—81no—
615C22—81no—
616C22—81no—
617C22—81no—
618C22—344no—
619C22—682no—
620C22—682no—
621C22—682no—
622C22—682no—
623C22—682no—
624C22—682no—
625C22C2×#1058756711yescharacteristic
626C22#1176331811yescharacteristic
627C22#1176331811yescharacteristic
628C22#1176361011yescharacteristic
629C22#1176361111yescharacteristic
630C22#1176361511yescharacteristic
631C22#1176361611yescharacteristic
632C4—22no—
633C4—22no—
634C4—42no—
635C4—42no—
636C4—42no—
637C4—681no—
638C4—681no—
639C4—682no—
640C4—681no—
641C4—681no—
642C4—1361no—
643C4—1361no—
644C4#117×D1711yescharacteristic
645C4C4×#6325211yescharacteristic
646C4#1176334111yescharacteristic
647C4#1176334111yescharacteristic
648C2—82no—
649C2—684no—
650C2#1453123011yescharacteristic
651C2#1453761011yescharacteristic
652C2#1453761911yescharacteristic
653C2#1453896411yescharacteristic
654C2#1453898911yescharacteristic
655C2#1453902411yescharacteristic
656C2#1453906711yescharacteristic
subgroupG/H
centerC23C2×D4×D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC4×C17×#102C2
socleC23×C17C22×D4
prime radicalC22×#63228C22
cosocleC22×C4×C17C24
hypercenterC4×#102D17
hypocenterC17#21126
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
2. #14531427C2semidirect
3. #14531144C2semidirect
4. #14529414C2semidirect
5. #14529407C2semidirect
6. #14529372C2semidirect
7. #14529365C2semidirect
10. #14529046C2semidirect
11. #14529032C2semidirect
12. #14528682C2semidirect
13. C4×#10587492C2semidirect
14. #14528535C2semidirect
15. C4×C17×#102C2semidirect
20. #11762919C4semidirect
69. C4×D4×C17C2×C4semidirect
108. #10587503C2×C4semidirect
122. #10587479C2×C4semidirect
124. #10587474C2×C4semidirect
296. C4×#102D17semidirect
408. C4×D4C4×D17semidirect
453. C17#21126semidirect

Maximal subgroups

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

subgroupindex
C2×#117629192
#145314272
#145311442
#145294142
#145294072
#145293722
#145293652
#145291292
#145290462
#145290322
#145286822
C4×#105874922
#145285352
C4×C17×#1022
#2112617