Finite Group Databasebeta

← #17040717

Subgroups — #17040717

Order 4352.

1008 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763011C211yesmaximal, characteristic
2C2×#11762907C211yesmaximal, characteristic
3C2×C4×#63230C211yesmaximal, characteristic
4#14531146C211yesmaximal, characteristic
5#14529708C211yesmaximal, characteristic, complemented
6#14529550C211yesmaximal, characteristic, complemented
7#14529422C211yesmaximal, characteristic, complemented
8#14529415C211yesmaximal, characteristic, complemented
9#14529121C211yesmaximal, characteristic
10#14529121C211yesmaximal, characteristic
11#14528791C211yesmaximal, characteristic
12#14528641C211yesmaximal, characteristic, complemented
13#14528614C211yesmaximal, characteristic, complemented
14C4×#10587506C211yesmaximal, characteristic, complemented
15C17×#2327C211yesmaximal, characteristic, complemented
16C22×#63230C2211yescharacteristic
17C22×#63230C2211yescharacteristic
18C2×C4×D68C2211yescharacteristic
19C2×C4×D68C2211yescharacteristic
20C2×C4×D68C2211yescharacteristic
21#11763011C418yescomplemented
22#11762907—24no—
23C4×#63230—24no—
24C2×#10587478C2211yescharacteristic
25C2×#10587479C2211yescharacteristic
26C2×C4⋊#3622C2211yescharacteristic
27C2×C4⋊#3622C2211yescharacteristic
28C2×#10587506C2211yescharacteristic
29C2×#10587506C2211yescharacteristic
30C2×#10587506C2211yescharacteristic
31C2×#10587506C2211yescharacteristic
32C2×#10587506C2211yescharacteristic
33C2×#10587506C2211yescharacteristic
34C2×#10587480C2211yescharacteristic
35C2×#10587480C2211yescharacteristic
36C2×#10587474C2211yescharacteristic
37C2×C4×#3622C2211yescharacteristic
38C4×C4⋊Dic17C2211yescharacteristic
39C4×C4⋊Dic17C2211yescharacteristic
40C4×C4⋊Dic17C2211yescharacteristic
41#11762656—21no—
42#11762656—21no—
43#11762656—21no—
44#95×D17—21no—
45#11762571C2211yescharacteristic
46#11762571C2211yescharacteristic
47#11762571C2211yescharacteristic
48#11762571C2211yescharacteristic
49#11762564C2211yescharacteristic
50#11762564C2211yescharacteristic
51C2×C17×C4⋊Q8C2211yescharacteristic
52C2×C4×Q8×C17C2211yescharacteristic
53C2×C4×Q8×C17C2211yescharacteristic
54C17×#391C2211yescharacteristic
55C17×#391C2211yescharacteristic
56C17×#387—21no—
57C17×#387—21no—
58C17×#387—21no—
59C17×#387—21no—
60C17×#382C2211yescharacteristic
61C17×#376C2211yescharacteristic
62C22×Q8×C17C2311yescharacteristic
63C22×Q8×C17C2311yescharacteristic
64C22×D68C2311yescharacteristic
65C22×C4×D17—21no—
66C22×C4×D17—21no—
67C22×C4×D17—21no—
68C17×C4⋊Q8—22no—
69C17×C4⋊Q8C2×C414yescomplemented
70C4×Q8×C17—22no—
71C4×Q8×C17—22no—
72C4×Q8×C17—22no—
73C4×Q8×C17—22no—
74C2×C4⋊C4×C17—21no—
75C2×C4⋊C4×C17—21no—
76C2×C4⋊C4×C17—21no—
77C2×C4⋊C4×C17—21no—
78C2×C4⋊C4×C17C2311yescharacteristic
79C2×C4⋊C4×C17C2311yescharacteristic
80C2×C42×C17—21no—
81C2×C42×C17—21no—
82C2×C42×C17C2311yescharacteristic
83C2×C42×C17C2311yescharacteristic
84C2×C42×C17C2311yescharacteristic
85C2×#63230—22no—
86C2×#63230—22no—
87C2×#63230—22no—
88C2×#63230—22no—
89C2×#63230C2×C414yes—
90C2×#63230C2×C414yes—
91C2×#63227—21no—
92C2×#63227—21no—
93C2×#63227—21no—
94C2×C4⋊Dic17C2311yescharacteristic
95C2×C4⋊Dic17C2311yescharacteristic
96C2×C4⋊Dic17C2311yescharacteristic
97C2×C4×Dic17—21no—
98C2×C4×Dic17—21no—
99C2×C4×Dic17—21no—
100C22×#3622C2311yescharacteristic
101C22×#3622C2311yescharacteristic
102C22×#3622C2311yescharacteristic
103C22×#3622C2311yescharacteristic
104C4×D68—22no—
105C4×D68—22no—
106C4×D68—22no—
107C4×D68—22no—
108C4×D68C2×C414yes—
109C4×D68D414yes—
110C17×#95—21no—
111C17×#95—21no—
112C17×#95—21no—
113C17×#95—21no—
114C17×#95—21no—
115C17×#95—21no—
116C17×#95D411yescharacteristic
117C17×#95D411yescharacteristic
118C17×#95D411yescharacteristic
119C17×#95D411yescharacteristic
120#10587506—22no—
121#10587506—22no—
122#10587506—22no—
123#10587506—22no—
124#10587506C2×C414yescomplemented
125#10587506C2×C414yescomplemented
126#10587502—21no—
127#10587502—21no—
128#10587502—21no—
129#10587480—22no—
130#10587480—22no—
131#10587479—22no—
132#10587478—22no—
133C4⋊#3622—22no—
134C4⋊#3622C2×C414yescomplemented
135#10587474—22no—
136C4×#3622—22no—
137C23×D17—21no—
138C2×Q8×C17—21no—
139C2×Q8×C17—21no—
140C2×Q8×C17—21no—
141C2×Q8×C17—21no—
142C2×Q8×C17—21no—
143C2×Q8×C17—21no—
144C2×Q8×C17—21no—
145C2×Q8×C17—21no—
146C2×Q8×C17—21no—
147C2×Q8×C17—21no—
148C2×Q8×C17C22×C412yes—
149C2×Q8×C17C22×C412yes—
150C22×C4×C17—21no—
151C22×C4×C17—21no—
152C22×C4×C17—21no—
153C22×C4×C17—21no—
154C22×C4×C17C2×D411yescharacteristic
155C22×C4×C17C2×D411yescharacteristic
156C22×C4×C17C2×D411yescharacteristic
157C22×C4×C17C2×D411yescharacteristic
158C22×C4×C17C2×D411yescharacteristic
159C22×C4×C17C2×D411yescharacteristic
160C22×C4×C17C2411yescharacteristic
161C22×Dic17—21no—
162C22×Dic17—21no—
163C22×Dic17—21no—
164C2×D68—21no—
165C2×D68—21no—
166C2×D68—21no—
167C2×D68C22×C412yes—
168C2×D68C2×D412yes—
169C2×D68#4112yes—
170C2×C4×D17—24no—
171C2×C4×D17—24no—
172C2×C4×D17—24no—
173C2×C4×D17—81no—
174C2×C4×D17—81no—
175C2×C4×D17—81no—
176C2×C4×D17—81no—
177C2×C4×D17—81no—
178C2×C4×D17—81no—
179C4⋊C4×C17—24no—
180C4⋊C4×C17—24no—
181C4⋊C4×C17—21no—
182C4⋊C4×C17—21no—
183C4⋊C4×C17—21no—
184C4⋊C4×C17—21no—
185C4⋊C4×C17—42no—
186C4⋊C4×C17—42no—
187C42×C17—21no—
188C42×C17—21no—
189C42×C17—42no—
190C42×C17—42no—
191C42×C17C22×C412yes—
192C42×C17C2×D412yes—
193C42×C17#4112yes—
194C42×C17#4112yes—
195#63230—28no—
196#63230—28no—
197#63227—24no—
198#63227—24no—
199#63227—24no—
200C4⋊Dic17—21no—
201C4⋊Dic17—21no—
202C4⋊Dic17—21no—
203C4⋊Dic17C22×C412yes—
204C4⋊Dic17C2×D412yes—
205C4⋊Dic17#4112yes—
206C4×Dic17—81no—
207C4×Dic17—81no—
208C4×Dic17—81no—
209C2×#3622—21no—
210C2×#3622—21no—
211C2×#3622—21no—
212C2×#3622—21no—
213C2×#3622—21no—
214C2×#3622—21no—
215C2×#3622—21no—
216C2×#3622—21no—
217C2×#3622—21no—
218C2×#3622—21no—
219C2×#3622C22×C412yes—
220C2×#3622C22×C412yes—
221#21514—171nomaximal, Sylow
222C23×C17C22×D411yescharacteristic
223C22×D17—22no—
224C22×D17—22no—
225C22×D17—22no—
226C22×D17—41no—
227C22×D17—41no—
228C22×D17—41no—
229C22×D17—41no—
230Q8×C17—22no—
231Q8×C17—22no—
232Q8×C17—22no—
233Q8×C17—22no—
234Q8×C17—41no—
235Q8×C17—41no—
236Q8×C17—41no—
237Q8×C17—41no—
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—21no—
246C2×C4×C17—22no—
247C2×C4×C17—22no—
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—41no—
255C2×C4×C17—41no—
256C2×C4×C17—41no—
257C2×C4×C17—41no—
258C2×C4×C17—41no—
259C2×C4×C17—41no—
260C2×C4×C17—41no—
261C2×C4×C17—41no—
262C2×C4×C17—41no—
263C2×C4×C17—41no—
264C2×C4×C17C4×D412yes—
265C2×C4×C17C4×D412yes—
266C2×C4×C17#12112yes—
267C2×C4×C17#12112yes—
268C2×C4×C17C23×C411yescharacteristic
269C2×C4×C17C22×D411yescharacteristic
270C2×C4×C17C2×#4111yescharacteristic
271C2×C4×C17C2×#4111yescharacteristic
272C2×C4×C17C2×#4111yescharacteristic
273C2×C4×C17C2×#4111yescharacteristic
274C2×Dic17—22no—
275C2×Dic17—22no—
276C2×Dic17—22no—
277C2×Dic17—41no—
278C2×Dic17—41no—
279C2×Dic17—41no—
280C2×Dic17—41no—
281C2×Dic17—41no—
282C2×Dic17—41no—
283D68—22no—
284D68—22no—
285D68—22no—
286D68C4×D414yes—
287C4×D17—84no—
288C4×D17—84no—
289C4×D17—84no—
290#3622—22no—
291#3622—22no—
292#3622—41no—
293#3622—41no—
294C2×#461—171no—
295C2×#440—171no—
296C2×C4×SD16—171no—
297#2327D1711yescharacteristic, complemented
298#2275—171no—
299#1981—171no—
300#1949—171no—
301#1928—171no—
302#1927—171no—
303#1877—171no—
304#1877—171no—
305#1804—171no—
306#1768—171no—
307#1763—171no—
308C4×#103—171no—
309C22×C17C2×C4×D411yescharacteristic
310C22×C17C2×#12111yescharacteristic
311C22×C17#52511yescharacteristic
312C22×C17#57711yescharacteristic
313C22×C17#57711yescharacteristic
314C22×C17#57711yescharacteristic
315C22×C17#57811yescharacteristic
316C2×D17—24no—
317C2×D17—42no—
318C2×D17—42no—
319C2×D17—42no—
320C2×D17—42no—
321C2×D17—42no—
322C2×D17—42no—
323C4×C17—22no—
324C4×C17—22no—
325C4×C17—22no—
326C4×C17—22no—
327C4×C17—41no—
328C4×C17—41no—
329C4×C17—42no—
330C4×C17—42no—
331C4×C17—81no—
332C4×C17—81no—
333C4×C17C2×C4×D411yescharacteristic
334C4×C17C4×#4111yescharacteristic
335C4×C17#52911yescharacteristic
336C4×C17#53211yescharacteristic
337Dic17—42no—
338Dic17—42no—
339Dic17—42no—
340C22×SD16—171no—
341C22×SD16—171no—
342C2×C4⋊Q8C2×D1711yescharacteristic
343C2×C4×Q8C2×D1711yescharacteristic
344C2×C4×Q8C2×D1711yescharacteristic
345C2×C4×D4—171no—
346C2×C4×D4—171no—
347C2×C4×D4—171no—
348#461—178no—
349#440—344no—
350C4×SD16—344no—
351C2×#107—171no—
352C2×#106—171no—
353C2×C4⋊C8—171no—
354C2×C4⋊C8—171no—
355C2×#103—171no—
356C2×#103—171no—
357C2×#103—171no—
358C2×#103—171no—
359C2×#103—171no—
360C2×#103—171no—
361C2×#102—171no—
362C2×#102—171no—
363C2×#97—171no—
364C2×C4×C8—171no—
365#391C2×D1711yescharacteristic
366#391C2×D1711yescharacteristic
367#387—21no—
368#387—21no—
369#387—21no—
370#387—21no—
371#382C2×D1711yescharacteristic
372C4×C4⋊C4—171no—
373C4×C4⋊C4—171no—
374C4×C4⋊C4—171no—
375C4×C22⋊C4—341no—
376C4×C22⋊C4—341no—
377C4×C22⋊C4—341no—
378#376C2×D1711yescharacteristic
379C2×#95—341no—
380#340—171no—
381#340—171no—
382#340—171no—
383#340—171no—
384#336—171no—
385#336—171no—
386C2×C17C4×#12111yescharacteristic
387C2×C17#294711yescharacteristic
388C2×C17#294911yescharacteristic
389C2×C17#304211yescharacteristic
390C2×C17#304611yescharacteristic
391C2×C17#312011yescharacteristic
392C2×C17#312311yescharacteristic
393D17—44no—
394C22×Q8C22×D1711yescharacteristic
395C22×Q8C22×D1711yescharacteristic
396C22×D4—171no—
397C23×C4—341no—
398C23×C4—341no—
399C23×C4—341no—
400C2×SD16—174no—
401C2×SD16—174no—
402C2×SD16—342no—
403C2×SD16—342no—
404C2×SD16—342no—
405C2×SD16—342no—
406C22×C8—171no—
407C22×C8—171no—
408C22×C8—171no—
409C22×C8—171no—
410C4⋊Q8—22no—
411C4⋊Q8C4×D1714yescomplemented
412C4×Q8—22no—
413C4×Q8—22no—
414C4×Q8—22no—
415C4×Q8—22no—
416C4×D4—174no—
417C4×D4—174no—
418C4×D4—342no—
419C4×D4—342no—
420C4×D4—342no—
421C4×D4—342no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—171no—
427C2×C4⋊C4—171no—
428C2×C4⋊C4—171no—
429C2×C4⋊C4C22×D1711yescharacteristic
430C2×C4⋊C4C22×D1711yescharacteristic
431C2×C22⋊C4—341no—
432C2×C22⋊C4—341no—
433C2×C22⋊C4—341no—
434C2×C42—21no—
435C2×C42—21no—
436C2×C42—341no—
437C2×C42—341no—
438C2×C42—341no—
439C2×C42C22×D1711yescharacteristic
440C2×C42C22×D1711yescharacteristic
441C2×C42C22×D1711yescharacteristic
442#107—342no—
443#106—342no—
444C4⋊C8—174no—
445C4⋊C8—342no—
446#103—174no—
447#103—174no—
448#103—342no—
449#103—342no—
450#103—342no—
451#103—342no—
452#102—342no—
453#102—342no—
454#97—342no—
455C4×C8—342no—
456#95—21no—
457#95—21no—
458#95—21no—
459#95—21no—
460#95—21no—
461#95—21no—
462#95—341no—
463#95—341no—
464#95—341no—
465#95C22⋊D1711yescharacteristic
466#95C22⋊D1711yescharacteristic
467#95C22⋊D1711yescharacteristic
468#95C22⋊D1711yescharacteristic
469C17#2151411yescharacteristic, complemented, Sylow
470C24—341no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8C2×C4×D1712yes—
482C2×Q8C2×C4×D1712yes—
483C2×D4—172no—
484C2×D4—172no—
485C2×D4—172no—
486C2×D4—341no—
487C2×D4—341no—
488C2×D4—341no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—344no—
494C22×C4—341no—
495C22×C4—341no—
496C22×C4—341no—
497C22×C4—344no—
498C22×C4—344no—
499C22×C4—1361no—
500C22×C4—1361no—
501C22×C4—1361no—
502C22×C4—1361no—
503C22×C4—1361no—
504C22×C4—1361no—
505C22×C4C2×C22⋊D1711yescharacteristic
506C22×C4C2×C22⋊D1711yescharacteristic
507C22×C4C2×C22⋊D1711yescharacteristic
508C22×C4C2×C22⋊D1711yescharacteristic
509C22×C4C2×C22⋊D1711yescharacteristic
510C22×C4C2×C22⋊D1711yescharacteristic
511C22×C4C23×D1711yescharacteristic
512SD16—348no—
513SD16—348no—
514C2×C8—172no—
515C2×C8—172no—
516C2×C8—341no—
517C2×C8—341no—
518C2×C8—341no—
519C2×C8—341no—
520C2×C8—341no—
521C2×C8—341no—
522C2×C8—341no—
523C2×C8—341no—
524C2×C8—341no—
525C2×C8—341no—
526C4⋊C4—24no—
527C4⋊C4—24no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—42no—
533C4⋊C4—42no—
534C4⋊C4—172no—
535C4⋊C4—172no—
536C4⋊C4—172no—
537C4⋊C4—341no—
538C4⋊C4—341no—
539C4⋊C4—341no—
540C22⋊C4—344no—
541C22⋊C4—344no—
542C22⋊C4—344no—
543C42—21no—
544C42—21no—
545C42—42no—
546C42—42no—
547C42—1361no—
548C42—1361no—
549C42—1361no—
550C42C2×C4×D1712yes—
551C42#6325212yes—
552C42D4×D1712yes—
553C42#6325412yes—
554C23—342no—
555C23—342no—
556C23—342no—
557C23—681no—
558C23—681no—
559C23—681no—
560C23—681no—
561C23C22×C22⋊D1711yescharacteristic
562Q8—22no—
563Q8—22no—
564Q8—22no—
565Q8—22no—
566Q8—41no—
567Q8—41no—
568Q8—41no—
569Q8—41no—
570D4—174no—
571D4—342no—
572D4—342no—
573D4—342no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—342no—
601C2×C4—342no—
602C2×C4—342no—
603C2×C4—681no—
604C2×C4—681no—
605C2×C4—681no—
606C2×C4—681no—
607C2×C4—681no—
608C2×C4—681no—
609C2×C4—1364no—
610C2×C4—1364no—
611C2×C4—1364no—
612C2×C4C4×C22⋊D1712yes—
613C2×C4C4×C22⋊D1712yes—
614C2×C4#1058762412yes—
615C2×C4#1058762412yes—
616C2×C4C22×C4×D1711yescharacteristic
617C2×C4C2×#6325211yescharacteristic
618C2×C4C2×D4×D1711yescharacteristic
619C2×C4C2×#6325411yescharacteristic
620C2×C4#41×D1711yescharacteristic
621C2×C4#41×D1711yescharacteristic
622C8—342no—
623C8—342no—
624C8—681no—
625C8—681no—
626C22—344no—
627C22—682no—
628C22—682no—
629C22—682no—
630C22—682no—
631C22—682no—
632C22—682no—
633C22C2×C4×C22⋊D1711yescharacteristic
634C22C2×#1058762411yescharacteristic
635C22#1176331611yescharacteristic
636C22#1176361711yescharacteristic
637C22#1176361711yescharacteristic
638C22#1176361711yescharacteristic
639C22#1176362411yescharacteristic
640C4—22no—
641C4—22no—
642C4—22no—
643C4—22no—
644C4—41no—
645C4—42no—
646C4—42no—
647C4—41no—
648C4—81no—
649C4—81no—
650C4—682no—
651C4—682no—
652C4—682no—
653C4C4×D4×D1711yescharacteristic
654C4C4×#6325411yescharacteristic
655C4#1176334111yescharacteristic
656C4#1176335611yescharacteristic
657C2—684no—
658C2C4×#1058762411yescharacteristic
659C2#1453762711yescharacteristic
660C2#1453764311yescharacteristic
661C2#1453829211yescharacteristic
662C2#1453833011yescharacteristic
663C2#1453899211yescharacteristic
664C2#1453903111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC17×#2327C2
socleC23×C17C22×D4
prime radicalC22×D68C23
cosocleC22×C4×C17C24
hypercenter#2327D17
hypocenterC17#21514
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ #376 ◁ #2327

Complements

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

NH ≅ G/Ntype
5. #14529708C2semidirect
6. #14529550C2semidirect
7. #14529422C2semidirect
8. #14529415C2semidirect
12. #14528641C2semidirect
13. #14528614C2semidirect
14. C4×#10587506C2semidirect
15. C17×#2327C2semidirect
21. #11763011C4semidirect
69. C17×C4⋊Q8C2×C4semidirect
124. #10587506C2×C4semidirect
125. #10587506C2×C4semidirect
134. C4⋊#3622C2×C4semidirect
297. #2327D17semidirect
411. C4⋊Q8C4×D17semidirect
469. C17#21514semidirect

Maximal subgroups

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

subgroupindex
C2×#117630112
C2×#117629072
C2×C4×#632302
#145311462
#145297082
#145295502
#145294222
#145294152
#145291212
#145287912
#145286412
#145286142
C4×#105875062
C17×#23272
#2151417