Finite Group Databasebeta

← #17045193

Subgroups — #17045193

Order 4352.

744 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14531229C211yesmaximal, characteristic
2#14529583C211yesmaximal, characteristic
3#14529505C211yesmaximal, characteristic, complemented
4#14529502C211yesmaximal, characteristic, complemented
5#14529400C211yesmaximal, characteristic, complemented
6#14529394C211yesmaximal, characteristic, complemented
7#14529393C211yesmaximal, characteristic, complemented
8#14529387C211yesmaximal, characteristic, complemented
9#14528853C211yesmaximal, characteristic, complemented
10#14528850C211yesmaximal, characteristic, complemented
11#14528766C211yesmaximal, characteristic, complemented
12#14528762C211yesmaximal, characteristic, complemented
13#14528643C211yesmaximal, characteristic, complemented
14#14528535C211yesmaximal, characteristic, complemented
15C17×#1954C211yesmaximal, characteristic
16C2×#10587612C2211yescharacteristic
17C22×C4×Dic17C2211yescharacteristic
18C2×C4⋊#3622C2211yescharacteristic
19C2×#10587485C2211yescharacteristic
20C2×#10587485C2211yescharacteristic
21C2×#10587485C2211yescharacteristic
22C2×#10587485C2211yescharacteristic
23C2×C22⋊#3622C2211yescharacteristic
24C2×C22⋊#3622C2211yescharacteristic
25C2×C22⋊#3622C2211yescharacteristic
26C2×C22⋊#3622C2211yescharacteristic
27C2×#10587474C2211yescharacteristic
28C2×#10587486C2211yescharacteristic
29C2×C8×Dic17C2211yescharacteristic
30#11762702C411yescharacteristic
31#11762702C411yescharacteristic
32#11762695C411yescharacteristic
33#11762695C411yescharacteristic
34#11762689C411yescharacteristic
35#11762689C411yescharacteristic
36#11762684C411yescharacteristic
37#11762684C411yescharacteristic
38C4×C4⋊Dic17C2211yescharacteristic
39C4×C22⋊Dic17C2211yescharacteristic
40C4×C22⋊Dic17C2211yescharacteristic
41#11762655C2211yescharacteristic
42#11762563C2211yescharacteristic
43#11762563C2211yescharacteristic
44#11762563C2211yescharacteristic
45#11762563C2211yescharacteristic
46#11762563C2211yescharacteristic
47#11762563C2211yescharacteristic
48#11762563C2211yescharacteristic
49#11762563C2211yescharacteristic
50#11762563C2211yescharacteristic
51#11762563C2211yescharacteristic
52C2×C4×D4×C17C2211yescharacteristic
53C2×C17×C4⋊C8C2211yescharacteristic
54C2×C17×C22⋊C8C2211yescharacteristic
55C2×C17×C22⋊C8C2211yescharacteristic
56C2×C17×C22⋊C8C2211yescharacteristic
57C2×C17×C22⋊C8C2211yescharacteristic
58C2×C4×C8×C17C2211yescharacteristic
59C22×D4×C17C2×C411yescharacteristic
60C23×C4×C17C2311yescharacteristic
61C23×C4×C17C2311yescharacteristic
62C23×Dic17C2×C411yescharacteristic
63C23×Dic17C2×C411yescharacteristic
64C22×C8×C17C2311yescharacteristic
65C22×C8×C17C2311yescharacteristic
66C22×C8×C17C2311yescharacteristic
67C22×C8×C17C2311yescharacteristic
68C4×D4×C17—22no—
69C4×D4×C17—22no—
70C2×C4⋊C4×C17C2×C411yescharacteristic
71C2×C22⋊C4×C17C2×C411yescharacteristic
72C2×C22⋊C4×C17C2×C411yescharacteristic
73C2×C42×C17C2311yescharacteristic
74C2×C22⋊Dic17C2×C411yescharacteristic
75C2×C22⋊Dic17C2×C411yescharacteristic
76C2×C22⋊Dic17C2×C411yescharacteristic
77C2×C22⋊Dic17C2×C411yescharacteristic
78C2×C22⋊Dic17C2×C411yescharacteristic
79C2×C22⋊Dic17C2×C411yescharacteristic
80#10587612—41no—
81#10587612—41no—
82C2×C4⋊Dic17C2×C411yescharacteristic
83C2×C4⋊Dic17C2×C411yescharacteristic
84C2×C4⋊Dic17C2×C411yescharacteristic
85C2×C4⋊Dic17C2×C411yescharacteristic
86C2×C4×Dic17—41no—
87C2×C4×Dic17—41no—
88C2×C4×Dic17C2×C411yescharacteristic
89C2×C4×Dic17C2×C411yescharacteristic
90C2×C4×Dic17C2311yescharacteristic
91C2×C4×Dic17C2311yescharacteristic
92C2×C4×Dic17C2311yescharacteristic
93C2×C4×Dic17C2311yescharacteristic
94C22×#3622C2311yescharacteristic
95C22×#3622C2311yescharacteristic
96C22×#3622C2311yescharacteristic
97C22×#3622C2311yescharacteristic
98C17×C4⋊C8—22no—
99C17×C22⋊C8—41no—
100C17×C22⋊C8—41no—
101C17×C22⋊C8—41no—
102C17×C22⋊C8—41no—
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—
116C22⋊#3622—41no—
117C22⋊#3622—41no—
118#10587486—41no—
119#10587485—41no—
120#10587485—41no—
121#10587485—41no—
122#10587485—41no—
123C8×Dic17—41no—
124C4⋊#3622—22no—
125#10587474—22no—
126C24×C17C22×C411yescharacteristic
127C24×C17C22×C411yescharacteristic
128C2×D4×C17—22no—
129C2×D4×C17—22no—
130C2×D4×C17—41no—
131C22×C4×C17—21no—
132C22×C4×C17—21no—
133C22×C4×C17—21no—
134C22×C4×C17—21no—
135C22×C4×C17—21no—
136C22×C4×C17—21no—
137C22×C4×C17—21no—
138C22×C4×C17—21no—
139C22×C4×C17—21no—
140C22×C4×C17—21no—
141C22×C4×C17—21no—
142C22×C4×C17—21no—
143C22×C4×C17C22×C411yescharacteristic
144C22×C4×C17C22×C411yescharacteristic
145C22×C4×C17C22×C411yescharacteristic
146C22×C4×C17C22×C411yescharacteristic
147C22×C4×C17C2411yescharacteristic
148C22×Dic17—22no—
149C22×Dic17—22no—
150C22×Dic17—41no—
151C22×Dic17—41no—
152C22×Dic17—41no—
153C22×Dic17—41no—
154C22×Dic17C22×C411yescharacteristic
155C22×Dic17C22×C411yescharacteristic
156C22×Dic17C22×C411yescharacteristic
157C22×Dic17C22×C411yescharacteristic
158C22×Dic17C22×C411yescharacteristic
159C22×Dic17C22×C411yescharacteristic
160C22×Dic17C22×C411yescharacteristic
161C22×Dic17C22×C411yescharacteristic
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—
175C22⋊C4×C17—22no—
176C22⋊C4×C17—22no—
177C42×C17#4112yes—
178C42×C17#4112yes—
179C22⋊Dic17—22no—
180C22⋊Dic17—22no—
181C22⋊Dic17—41no—
182C22⋊Dic17—41no—
183C22⋊Dic17—41no—
184C22⋊Dic17—41no—
185C4⋊Dic17—22no—
186C4⋊Dic17—41no—
187C4⋊Dic17—41no—
188C4⋊Dic17—41no—
189C4×Dic17—21no—
190C4×Dic17—21no—
191C4×Dic17—21no—
192C4×Dic17—21no—
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—
211#22017—171nomaximal, Sylow
212C23×C17—21no—
213C23×C17—21no—
214C23×C17—21no—
215C23×C17—21no—
216C23×C17—21no—
217C23×C17—21no—
218C23×C17—21no—
219C23×C17—21no—
220C23×C17—21no—
221C23×C17—21no—
222C23×C17—21no—
223C23×C17—21no—
224C23×C17—21no—
225C23×C17#13112yes—
226C23×C17C23×C411yescharacteristic
227D4×C17—44no—
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—41no—
239C2×C4×C17—41no—
240C2×C4×C17—41no—
241C2×C4×C17—41no—
242C2×C4×C17—41no—
243C2×C4×C17—41no—
244C2×C4×C17—41no—
245C2×C4×C17—41no—
246C2×C4×C17#11712yes—
247C2×C4×C17#11712yes—
248C2×C4×C17C2×#4111yescharacteristic
249C2×C4×C17C2×#4111yescharacteristic
250C2×C4×C17H(5,𝔽2)11yescharacteristic
251C2×C4×C17H(5,𝔽2)11yescharacteristic
252C2×C4×C17H(5,𝔽2)11yescharacteristic
253C2×C4×C172−1+411yescharacteristic
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—21no—
273C2×Dic17—21no—
274C2×Dic17—21no—
275C2×Dic17—21no—
276C2×Dic17—21no—
277C2×Dic17—44no—
278C2×Dic17—44no—
279C2×Dic17#13112yes—
280C8×C17—41no—
281C8×C17—41no—
282C8×C17—41no—
283C8×C17—41no—
284#3622—41no—
285#3622—41no—
286#3622—41no—
287#3622—41no—
288#2290—171no—
289#1955—171no—
290#1954D1711yescharacteristic
291#1940—171no—
292#1939—171no—
293#1924—171no—
294#1924—171no—
295#1923—171no—
296#1923—171no—
297#1818—171no—
298#1817—171no—
299#1798—171no—
300#1797—171no—
301#1768—171no—
302#1746—171no—
303C22×C17—22no—
304C22×C17—22no—
305C22×C17—22no—
306C22×C17—41no—
307C22×C17—41no—
308C22×C17—41no—
309C22×C17—41no—
310C22×C17—41no—
311C22×C17—41no—
312C22×C17—41no—
313C22×C17—41no—
314C22×C17—41no—
315C22×C17—41no—
316C22×C17—41no—
317C22×C17C2×#11711yescharacteristic
318C22×C17#51811yescharacteristic
319C22×C17#52011yescharacteristic
320C22×C17C2×#13111yescharacteristic
321C22×C17C2×#13111yescharacteristic
322C22×C17#56811yescharacteristic
323C22×C17#56811yescharacteristic
324C4×C17—22no—
325C4×C17—22no—
326C4×C17—41no—
327C4×C17—41no—
328C4×C17#54011yescharacteristic
329C4×C17#54011yescharacteristic
330C4×C17#54211yescharacteristic
331C4×C17#54211yescharacteristic
332Dic17—22no—
333Dic17—41no—
334Dic17—41no—
335Dic17—41no—
336Dic17—41no—
337Dic17—41no—
338Dic17—41no—
339Dic17—41no—
340C2×C4×D4C2×D1711yescharacteristic
341C2×#117—171no—
342C22×C42—171no—
343C2×C4⋊C8—171no—
344C2×C4⋊C8—171no—
345C2×C4⋊C8—171no—
346C2×C4⋊C8—171no—
347C2×C4⋊C8—171no—
348C2×C4⋊C8C2×D1711yescharacteristic
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×C22⋊C8C2×D1711yescharacteristic
356C2×C22⋊C8C2×D1711yescharacteristic
357C2×#97—171no—
358C2×#97—171no—
359C2×C4×C8—171no—
360C2×C4×C8C2×D1711yescharacteristic
361#388—171no—
362#388—171no—
363#387—171no—
364#387—171no—
365#386—171no—
366#386—171no—
367#385—171no—
368#385—171no—
369C4×C4⋊C4—171no—
370C4×C22⋊C4—171no—
371C4×C22⋊C4—171no—
372#376—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#336—171no—
382#336—171no—
383C2×C17—42no—
384C2×C17—81no—
385C2×C17#231911yescharacteristic
386C2×C17#292411yescharacteristic
387C2×C17#292511yescharacteristic
388C2×C17#297711yescharacteristic
389C2×C17#297811yescharacteristic
390C2×C17#299211yescharacteristic
391C2×C17#299311yescharacteristic
392C22×D4C4×D1711yescharacteristic
393C23×C4—171no—
394C23×C4—171no—
395C23×C4C22×D1711yescharacteristic
396C23×C4C22×D1711yescharacteristic
397C22×C8—171no—
398C22×C8—171no—
399C22×C8—171no—
400C22×C8—171no—
401C22×C8C22×D1711yescharacteristic
402C22×C8C22×D1711yescharacteristic
403C22×C8C22×D1711yescharacteristic
404C22×C8C22×D1711yescharacteristic
405C4×D4—22no—
406C4×D4—22no—
407#117—681no—
408#117—681no—
409C2×C4⋊C4—171no—
410C2×C4⋊C4—171no—
411C2×C4⋊C4—171no—
412C2×C4⋊C4—171no—
413C2×C4⋊C4C4×D1711yescharacteristic
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⋊C4C4×D1711yescharacteristic
421C2×C22⋊C4C4×D1711yescharacteristic
422C2×C42—171no—
423C2×C42—171no—
424C2×C42—171no—
425C2×C42—171no—
426C2×C42—171no—
427C2×C42—171no—
428C2×C42—681no—
429C2×C42—681no—
430C2×C42C22×D1711yescharacteristic
431C4⋊C8—22no—
432C4⋊C8—342no—
433C4⋊C8—681no—
434C4⋊C8—681no—
435C4⋊C8—681no—
436C4⋊C8—681no—
437C22⋊C8—41no—
438C22⋊C8—41no—
439C22⋊C8—41no—
440C22⋊C8—41no—
441C22⋊C8—681no—
442C22⋊C8—681no—
443C22⋊C8—681no—
444C22⋊C8—681no—
445#97—342no—
446#97—681no—
447C4×C8—22no—
448C4×C8—681no—
449#95—171no—
450#95—171no—
451#95—171no—
452#95—171no—
453#95—171no—
454#95—171no—
455#95—171no—
456#95—171no—
457#95—171no—
458#95—171no—
459C17#2201711yescharacteristic, complemented, Sylow
460C24C2×C4×D1711yescharacteristic
461C24C2×C4×D1711yescharacteristic
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—41no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—171no—
478C22×C4—171no—
479C22×C4—171no—
480C22×C4—171no—
481C22×C4—171no—
482C22×C4—171no—
483C22×C4—171no—
484C22×C4—171no—
485C22×C4—342no—
486C22×C4—342no—
487C22×C4—681no—
488C22×C4—681no—
489C22×C4—681no—
490C22×C4—681no—
491C22×C4C2×C4×D1711yescharacteristic
492C22×C4C2×C4×D1711yescharacteristic
493C22×C4C2×C4×D1711yescharacteristic
494C22×C4C2×C4×D1711yescharacteristic
495C22×C4C23×D1711yescharacteristic
496C2×C8—21no—
497C2×C8—21no—
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—341no—
509C2×C8—341no—
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—
520C4⋊C4—22no—
521C4⋊C4—342no—
522C4⋊C4—681no—
523C4⋊C4—681no—
524C4⋊C4—681no—
525C22⋊C4—22no—
526C22⋊C4—22no—
527C22⋊C4—342no—
528C22⋊C4—342no—
529C22⋊C4—681no—
530C22⋊C4—681no—
531C22⋊C4—681no—
532C22⋊C4—681no—
533C42—341no—
534C42—341no—
535C42—341no—
536C42—341no—
537C42—341no—
538C42—341no—
539C42—341no—
540C42—341no—
541C42—681no—
542C42—681no—
543C42#6325412yes—
544C42#6325412yes—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23#1058758712yes—
559C23C22×C4×D1711yescharacteristic
560D4—44no—
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—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
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—341no—
600C2×C4—341no—
601C2×C4—341no—
602C2×C4—341no—
603C2×C4—684no—
604C2×C4—684no—
605C2×C4#1058756312yes—
606C2×C4#1058756312yes—
607C2×C4C2×#6325411yescharacteristic
608C2×C4C2×#6325411yescharacteristic
609C2×C4#1058769111yescharacteristic
610C2×C4#1058769111yescharacteristic
611C2×C4#1058769611yescharacteristic
612C2×C4#1058769711yescharacteristic
613C8—41no—
614C8—41no—
615C8—41no—
616C8—41no—
617C8—681no—
618C8—681no—
619C8—681no—
620C8—681no—
621C22—22no—
622C22—22no—
623C22—22no—
624C22—41no—
625C22—41no—
626C22—41no—
627C22—41no—
628C22—41no—
629C22—41no—
630C22—41no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22C2×#1058756311yescharacteristic
636C22#1176328111yescharacteristic
637C22#1176328811yescharacteristic
638C22#131×D1711yescharacteristic
639C22C2×#1058758711yescharacteristic
640C22#1176357411yescharacteristic
641C22#1176357511yescharacteristic
642C4—22no—
643C4—22no—
644C4—41no—
645C4—41no—
646C4—342no—
647C4—681no—
648C4—681no—
649C4—681no—
650C4—681no—
651C4—681no—
652C4—681no—
653C4—681no—
654C4#1176341211yescharacteristic
655C4#1176341311yescharacteristic
656C4#1176342611yescharacteristic
657C4#1176342811yescharacteristic
658C2—42no—
659C2—81no—
660C2#1453142111yescharacteristic
661C2#1453743811yescharacteristic
662C2#1453744611yescharacteristic
663C2#1453783711yescharacteristic
664C2#1453784111yescharacteristic
665C2#1453791711yescharacteristic
666C2#1453793011yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D17
commutator, socleC23×C17C23×C4
FittingC17×#1954C2
prime radicalC22×D4×C17C2×C4
cosocleC22×C4×C17C24
hypercenter#1954D17
hypocenterC17#22017
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ #1954

Complements

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

NH ≅ G/Ntype
3. #14529505C2semidirect
4. #14529502C2semidirect
5. #14529400C2semidirect
6. #14529394C2semidirect
7. #14529393C2semidirect
8. #14529387C2semidirect
9. #14528853C2semidirect
10. #14528850C2semidirect
11. #14528766C2semidirect
12. #14528762C2semidirect
13. #14528643C2semidirect
14. #14528535C2semidirect
459. C17#22017semidirect

Maximal subgroups

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

subgroupindex
#145312292
#145295832
#145295052
#145295022
#145294002
#145293942
#145293932
#145293872
#145288532
#145288502
#145287662
#145287622
#145286432
#145285352
C17×#19542
#2201717