Finite Group Databasebeta

← #16942181

Subgroups — #16942181

Order 4352.

962 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587476C211yesmaximal, characteristic
2C2×#11762808C211yesmaximal, characteristic
3#14531377C211yesmaximal, characteristic
4C2×#11762578C211yesmaximal, characteristic, complemented
5#14528503C211yesmaximal, characteristic, complemented
6C2×#11762569C211yesmaximal, characteristic, complemented
7C17×C4⋊#95C211yesmaximal, characteristic, complemented
8C22×#63252C2211yescharacteristic
9C22×#63223C2211yescharacteristic
10C22×#63223C2211yescharacteristic
11C2×#10587612C2211yescharacteristic
12C2×#10587476—22no—
13C2×#10587476—22no—
14C2×#10587476—22no—
15#11762808—22no—
16#11762808C414yescomplemented
17C2×#10587481—21no—
18C2×#10587480—21no—
19#11762714—21no—
20#11762710—21no—
21#11762688—22no—
22#11762666—21no—
23#11762666—21no—
24#11762578—22no—
25#11762571—21no—
26#11762571—21no—
27#11762569—22no—
28C22×C4⋊C4×C17C2211yescharacteristic
29C22×C4⋊C4×C17C2211yescharacteristic
30C22×C42×C17C2211yescharacteristic
31C2×C17×#95—22no—
32C23×C4×C17—21no—
33C23×C4×C17—21no—
34C23×C4×C17D412yes—
35C23×C4×C17C2311yescharacteristic
36C22×C22⋊D17—21no—
37C2×#63252—21no—
38C2×#63252—21no—
39C2×#63252—21no—
40C2×#63252—21no—
41C2×#63252—21no—
42C2×#63252—21no—
43C2×#63252—21no—
44C2×#63252—21no—
45C2×#63252—21no—
46C2×#63252—21no—
47C2×#63252C2×C412yes—
48C2×#63252D412yes—
49C22×D68D411yescharacteristic
50C22×C4×D17—21no—
51C22×Dic34D411yescharacteristic
52C2×C4⋊C4×C17—21no—
53C2×C4⋊C4×C17—21no—
54C2×C4⋊C4×C17—21no—
55C2×C4⋊C4×C17—21no—
56C2×C4⋊C4×C17—21no—
57C2×C4⋊C4×C17—21no—
58C2×C4⋊C4×C17—21no—
59C2×C4⋊C4×C17—21no—
60C2×C4⋊C4×C17—21no—
61C2×C4⋊C4×C17—21no—
62C2×C4⋊C4×C17—21no—
63C2×C4⋊C4×C17C2×C412yes—
64C2×C42×C17—21no—
65C2×C42×C17—21no—
66C2×C42×C17—21no—
67C2×C42×C17—21no—
68C2×C42×C17—21no—
69C2×C42×C17D412yes—
70C2×C22⋊Dic17—21no—
71C2×#63227—22no—
72C2×#63227—22no—
73#10587612—21no—
74#10587612—21no—
75#10587612—21no—
76#10587612—21no—
77C2×C4⋊Dic17D411yescharacteristic
78C2×C4⋊Dic17D411yescharacteristic
79C2×C4×Dic17—21no—
80C2×#63223—21no—
81C2×#63223—21no—
82C2×#63223—21no—
83C2×#63223—21no—
84C2×#63223—21no—
85C2×#63223—21no—
86C2×#63223—21no—
87C2×#63223—21no—
88C2×#63223—21no—
89C2×#63223—21no—
90C2×#63223C2×C412yes—
91C2×#63223D412yes—
92C22×#3622—21no—
93C22×#3622—21no—
94C17×#95—44no—
95#10587502—22no—
96#10587502—22no—
97#10587481—24no—
98#10587480—24no—
99#10587476—28no—
100C24×C17C2×D411yescharacteristic
101C23×D17—21no—
102C22×C4×C17—22no—
103C22×C4×C17—22no—
104C22×C4×C17—22no—
105C22×C4×C17—22no—
106C22×C4×C17—22no—
107C22×C4×C17—22no—
108C22×C4×C17—22no—
109C22×C4×C17—41no—
110C22×C4×C17—41no—
111C22×C4×C17—41no—
112C22×C4×C17—41no—
113C22×C4×C17—42no—
114C22×C4×C17—42no—
115C22×C4×C17—42no—
116C22×C4×C17—42no—
117C22×C4×C17—41no—
118C22×C4×C17—41no—
119C22×C4×C17C22×C411yescharacteristic
120C22×C4×C17C2×D411yescharacteristic
121C22×C4×C17C2×D411yescharacteristic
122C22×C4×C17C2×D411yescharacteristic
123C22×C4×C17C2×D411yescharacteristic
124C22×C4×C17C2×D411yescharacteristic
125C22×C4×C17#4111yescharacteristic
126C22×C4×C17#4111yescharacteristic
127C22×C4×C17#4111yescharacteristic
128C22×C4×C17#4111yescharacteristic
129C22×C4×C17#4111yescharacteristic
130C22×C4×C17#4111yescharacteristic
131C22×C4×C17#4111yescharacteristic
132C22×C4×C17#4111yescharacteristic
133C2×C22⋊D17—22no—
134C2×C22⋊D17—22no—
135C2×C22⋊D17—41no—
136C2×C22⋊D17—41no—
137C2×C22⋊D17—41no—
138C2×C22⋊D17—41no—
139C22×Dic17—21no—
140C22×Dic17—21no—
141C22×Dic17—21no—
142#63252—22no—
143#63252—22no—
144#63252—22no—
145#63252—22no—
146#63252—22no—
147#63252—22no—
148#63252—22no—
149#63252—22no—
150#63252—41no—
151#63252—41no—
152#63252—41no—
153#63252—41no—
154#63252—41no—
155#63252—41no—
156#63252—41no—
157#63252—41no—
158C2×D68—21no—
159C2×D68—21no—
160C2×D68—21no—
161C2×D68—21no—
162C2×D68—21no—
163C2×D68C22⋊C412yes—
164C2×C4×D17—22no—
165C2×C4×D17—22no—
166C2×C4×D17—41no—
167C2×C4×D17—41no—
168C2×C4×D17—41no—
169C2×C4×D17—41no—
170C2×Dic34—21no—
171C2×Dic34—21no—
172C2×Dic34—21no—
173C2×Dic34—21no—
174C2×Dic34—21no—
175C2×Dic34C22⋊C412yes—
176C4⋊C4×C17—22no—
177C4⋊C4×C17—22no—
178C4⋊C4×C17—41no—
179C4⋊C4×C17—41no—
180C4⋊C4×C17—41no—
181C4⋊C4×C17—41no—
182C4⋊C4×C17—41no—
183C4⋊C4×C17—41no—
184C42×C17—22no—
185C42×C17—22no—
186C42×C17—41no—
187C42×C17—41no—
188C22⋊Dic17—41no—
189C22⋊Dic17—41no—
190#63227—82no—
191#63227—82no—
192C4⋊Dic17—21no—
193C4⋊Dic17—21no—
194C4⋊Dic17—21no—
195C4⋊Dic17—21no—
196C4×Dic17—41no—
197C4×Dic17—41no—
198#63223—22no—
199#63223—22no—
200#63223—22no—
201#63223—22no—
202#63223—41no—
203#63223—41no—
204#63223—41no—
205#63223—41no—
206C2×#3622—22no—
207C2×#3622—22no—
208C2×#3622—41no—
209C2×#3622—41no—
210C2×#3622—41no—
211C2×#3622—41no—
212#11195—171nomaximal, Sylow
213C23×C17—21no—
214C23×C17—21no—
215C23×C17—21no—
216C23×C17—21no—
217C23×C17C4×D411yescharacteristic
218C23×C17#12011yescharacteristic
219C23×C17#12111yescharacteristic
220C23×C17#12111yescharacteristic
221C23×C17#12111yescharacteristic
222C23×C17#12311yescharacteristic
223C23×C17#12411yescharacteristic
224C22×D17—22no—
225C22×D17—41no—
226C22×D17—41no—
227C22×D17—41no—
228C22×D17—41no—
229C22×D17—41no—
230C22×D17—41no—
231C2×C4×C17—24no—
232C2×C4×C17—42no—
233C2×C4×C17—42no—
234C2×C4×C17—42no—
235C2×C4×C17—42no—
236C2×C4×C17—42no—
237C2×C4×C17—42no—
238C2×C4×C17—44no—
239C2×C4×C17—44no—
240C2×C4×C17—42no—
241C2×C4×C17—42no—
242C2×C4×C17—42no—
243C2×C4×C17—42no—
244C2×C4×C17—82no—
245C2×C4×C17—81no—
246C2×C4×C17—81no—
247C2×C4×C17—82no—
248C2×C4×C17C2×C22⋊C411yescharacteristic
249C2×C4×C17#11711yescharacteristic
250C2×C4×C17#11711yescharacteristic
251C2×C4×C17C4×D411yescharacteristic
252C2×C4×C17C4×D411yescharacteristic
253C2×C4×C17C4×D411yescharacteristic
254C2×C4×C17#12011yescharacteristic
255C2×C4×C17#12111yescharacteristic
256C2×C4×C17#12111yescharacteristic
257C2×C4×C17#12111yescharacteristic
258C2×C4×C17#12111yescharacteristic
259C2×C4×C17#12111yescharacteristic
260C2×C4×C17#12311yescharacteristic
261C2×C4×C17#12311yescharacteristic
262C2×C4×C17#12311yescharacteristic
263C2×C4×C17#12311yescharacteristic
264C2×C4×C17#12311yescharacteristic
265C2×C4×C17#12311yescharacteristic
266C2×C4×C17#12311yescharacteristic
267C2×C4×C17#12311yescharacteristic
268C2×C4×C17#12311yescharacteristic
269C2×C4×C17#12411yescharacteristic
270C2×C4×C17#12411yescharacteristic
271C2×C4×C17#12411yescharacteristic
272C2×C4×C17#12611yescharacteristic
273C2×C4×C17#12611yescharacteristic
274C2×C4×C17#12611yescharacteristic
275C2×C4×C17#12611yescharacteristic
276C22⋊D17—42no—
277C22⋊D17—42no—
278C22⋊D17—42no—
279C22⋊D17—42no—
280C2×Dic17—22no—
281C2×Dic17—41no—
282C2×Dic17—41no—
283C2×Dic17—41no—
284C2×Dic17—41no—
285C2×Dic17—41no—
286C2×Dic17—41no—
287C2×Dic17—41no—
288C2×Dic17—41no—
289D68—22no—
290D68—22no—
291D68—41no—
292D68—41no—
293C4×D17—42no—
294C4×D17—42no—
295C4×D17—42no—
296C4×D17—42no—
297Dic34—22no—
298Dic34—22no—
299Dic34—41no—
300Dic34—41no—
301#3622—42no—
302#3622—42no—
303C22×#104—171no—
304C2×#417—171no—
305#2311—171no—
306C2×#343—171no—
307#1736—171no—
308C2×#339—171no—
309C4⋊#95D1711yescharacteristic, complemented
310C22×C17—21no—
311C22×C17—21no—
312C22×C17—21no—
313C22×C17—21no—
314C22×C17—21no—
315C22×C17—21no—
316C22×C17—21no—
317C22×C17—21no—
318C22×C17—21no—
319C22×C17—21no—
320C22×C17—21no—
321C22×C17—21no—
322C22×C17#38611yescharacteristic
323C22×C17#38811yescharacteristic
324C22×C17#38811yescharacteristic
325C22×C17#39411yescharacteristic
326C22×C17#39411yescharacteristic
327C22×C17#39411yescharacteristic
328C22×C17#39711yescharacteristic
329C22×C17#45311yescharacteristic
330C22×C17#45411yescharacteristic
331C22×C17#45511yescharacteristic
332C22×C17#45611yescharacteristic
333C2×D17—42no—
334C2×D17—42no—
335C2×D17—42no—
336C2×D17—81no—
337C2×D17—81no—
338C2×D17—81no—
339C2×D17—81no—
340C4×C17—44no—
341C4×C17—82no—
342C4×C17—82no—
343C4×C17#38111yescharacteristic
344C4×C17#38611yescharacteristic
345C4×C17#38811yescharacteristic
346C4×C17#38811yescharacteristic
347C4×C17#39411yescharacteristic
348C4×C17#39711yescharacteristic
349C4×C17#39711yescharacteristic
350C4×C17#39711yescharacteristic
351Dic17—42no—
352Dic17—81no—
353Dic17—81no—
354C22×#41—171no—
355C22×M16—171no—
356C22×M16—171no—
357C2×#117—171no—
358C22×C4⋊C4C2×D1711yescharacteristic
359C22×C4⋊C4C2×D1711yescharacteristic
360C22×C42C2×D1711yescharacteristic
361C2×#104—342no—
362C2×#104—342no—
363C2×#104—342no—
364#417—174no—
365#417—342no—
366C2×#103—341no—
367C2×#102—341no—
368#391—341no—
369#390—341no—
370#386—342no—
371#380—341no—
372#380—341no—
373C2×#95—22no—
374#343—342no—
375#340—341no—
376#340—341no—
377#339—342no—
378C2×C17—21no—
379C2×C17—21no—
380C2×C17—21no—
381C2×C17—21no—
382C2×C17#144011yescharacteristic
383C2×C17#188211yescharacteristic
384C2×C17#188311yescharacteristic
385C2×C17#203711yescharacteristic
386C2×C17#203811yescharacteristic
387C2×C17#203911yescharacteristic
388C2×C17#204011yescharacteristic
389D17—82no—
390C2×#41—172no—
391C2×#41—172no—
392C2×#41—341no—
393C2×#41—341no—
394C2×#41—341no—
395C2×#41—341no—
396C2×#41—341no—
397C2×#41—341no—
398C2×#41—341no—
399C2×#41—341no—
400C2×#41—341no—
401C2×#41—341no—
402C22×Q8—171no—
403C22×D4—171no—
404C22×D4—341no—
405C23×C4—21no—
406C23×C4—21no—
407C23×C4—341no—
408C23×C4C22⋊D1712yes—
409C23×C4C22×D1711yescharacteristic
410C2×M16—172no—
411C2×M16—172no—
412C2×M16—341no—
413C2×M16—341no—
414C2×M16—341no—
415C2×M16—341no—
416C2×M16—341no—
417C2×M16—341no—
418C2×M16—341no—
419C2×M16—341no—
420C2×M16—341no—
421C2×M16—341no—
422C22×C8—341no—
423C22×C8—341no—
424#117—341no—
425#117—341no—
426#117—341no—
427#117—341no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—171no—
440C2×C4⋊C4—171no—
441C2×C4⋊C4C4×D1712yes—
442C2×C22⋊C4—341no—
443C2×C22⋊C4—342no—
444C2×C22⋊C4—342no—
445C2×C42—21no—
446C2×C42—21no—
447C2×C42—21no—
448C2×C42—21no—
449C2×C42—21no—
450C2×C42—341no—
451C2×C42D6812yes—
452#104—348no—
453#103—344no—
454#102—344no—
455#95—44no—
456#95—342no—
457#95—342no—
458C17#1119511yescharacteristic, complemented, Sylow
459C24—341no—
460C24C2×C22⋊D1711yescharacteristic
461#41—342no—
462#41—342no—
463#41—342no—
464#41—342no—
465#41—342no—
466#41—342no—
467#41—342no—
468#41—342no—
469#41—681no—
470#41—681no—
471#41—681no—
472#41—681no—
473#41—681no—
474#41—681no—
475#41—681no—
476#41—681no—
477C2×Q8—172no—
478C2×Q8—341no—
479C2×Q8—341no—
480C2×Q8—341no—
481C2×Q8—341no—
482C2×Q8—341no—
483C2×D4—172no—
484C2×D4—342no—
485C2×D4—342no—
486C2×D4—341no—
487C2×D4—341no—
488C2×D4—341no—
489C2×D4—341no—
490C2×D4—341no—
491C2×D4—681no—
492C2×D4—681no—
493C2×D4—681no—
494C2×D4—681no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—41no—
503C22×C4—41no—
504C22×C4—41no—
505C22×C4—41no—
506C22×C4—42no—
507C22×C4—42no—
508C22×C4—42no—
509C22×C4—42no—
510C22×C4—41no—
511C22×C4—41no—
512C22×C4—341no—
513C22×C4—342no—
514C22×C4—342no—
515C22×C4—341no—
516C22×C4—341no—
517C22×C4—681no—
518C22×C4—681no—
519C22×C4—681no—
520C22×C4—681no—
521C22×C4C2×C4×D1711yescharacteristic
522C22×C4C2×D6811yescharacteristic
523C22×C4#6325211yescharacteristic
524C22×C4#6325211yescharacteristic
525C22×C4#6325211yescharacteristic
526C22×C4#6325211yescharacteristic
527C22×C4D4×D1711yescharacteristic
528C22×C4D4×D1711yescharacteristic
529C22×C4D4×D1711yescharacteristic
530C22×C4D4×D1711yescharacteristic
531C22×C4#6325411yescharacteristic
532C22×C4#6325411yescharacteristic
533C22×C4#6325611yescharacteristic
534C22×C4#6325611yescharacteristic
535M16—342no—
536M16—342no—
537M16—342no—
538M16—342no—
539M16—681no—
540M16—681no—
541M16—681no—
542M16—681no—
543C2×C8—342no—
544C2×C8—342no—
545C2×C8—681no—
546C2×C8—681no—
547C2×C8—681no—
548C2×C8—681no—
549C4⋊C4—22no—
550C4⋊C4—22no—
551C4⋊C4—41no—
552C4⋊C4—41no—
553C4⋊C4—41no—
554C4⋊C4—41no—
555C4⋊C4—41no—
556C4⋊C4—41no—
557C4⋊C4—341no—
558C4⋊C4—341no—
559C4⋊C4—341no—
560C4⋊C4—341no—
561C22⋊C4—681no—
562C22⋊C4—681no—
563C22⋊C4—1362no—
564C22⋊C4—1362no—
565C42—22no—
566C42—22no—
567C42—41no—
568C42—41no—
569C42—681no—
570C42—681no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—342no—
576C23—681no—
577C23—681no—
578C23—681no—
579C23—681no—
580C23—681no—
581C23—681no—
582C23C4×C22⋊D1711yescharacteristic
583C23#1058761511yescharacteristic
584C23#1058761611yescharacteristic
585C23#1058762311yescharacteristic
586C23#1058762411yescharacteristic
587C23#1058762511yescharacteristic
588C23#1058763311yescharacteristic
589Q8—342no—
590Q8—342no—
591Q8—681no—
592Q8—681no—
593D4—342no—
594D4—342no—
595D4—682no—
596D4—682no—
597D4—682no—
598D4—682no—
599D4—681no—
600D4—681no—
601C2×C4—24no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—44no—
609C2×C4—44no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—82no—
615C2×C4—81no—
616C2×C4—81no—
617C2×C4—82no—
618C2×C4—342no—
619C2×C4—681no—
620C2×C4—681no—
621C2×C4—682no—
622C2×C4—682no—
623C2×C4—682no—
624C2×C4—682no—
625C2×C4—681no—
626C2×C4—681no—
627C2×C4—681no—
628C2×C4—681no—
629C2×C4—681no—
630C2×C4—681no—
631C2×C4#1058755811yescharacteristic
632C2×C4C4×D6811yescharacteristic
633C2×C4#1058756111yescharacteristic
634C2×C4#1058756211yescharacteristic
635C2×C4C22⋊C4×D1711yescharacteristic
636C2×C4#1058756711yescharacteristic
637C2×C4#1058756811yescharacteristic
638C2×C4#1058756911yescharacteristic
639C2×C4#1058756911yescharacteristic
640C2×C4#1058756911yescharacteristic
641C2×C4#1058757011yescharacteristic
642C2×C4#1058757011yescharacteristic
643C2×C4#1058757011yescharacteristic
644C2×C4#1058757111yescharacteristic
645C2×C4#1058757111yescharacteristic
646C2×C4#1058757211yescharacteristic
647C2×C4#1058757811yescharacteristic
648C2×C4#1058757911yescharacteristic
649C2×C4#1058758011yescharacteristic
650C2×C4#1058758011yescharacteristic
651C2×C4#1058758011yescharacteristic
652C2×C4#1058758011yescharacteristic
653C2×C4#1058758011yescharacteristic
654C2×C4#1058758111yescharacteristic
655C2×C4#1058758111yescharacteristic
656C2×C4#1058758411yescharacteristic
657C2×C4#1058758411yescharacteristic
658C2×C4#1058758411yescharacteristic
659C8—682no—
660C8—682no—
661C22—21no—
662C22—21no—
663C22—21no—
664C22—21no—
665C22—21no—
666C22—21no—
667C22—21no—
668C22—21no—
669C22—21no—
670C22—21no—
671C22—21no—
672C22—21no—
673C22—682no—
674C22—682no—
675C22—682no—
676C22—1361no—
677C22—1361no—
678C22—1361no—
679C22—1361no—
680C22#1176268511yescharacteristic
681C22#1176269911yescharacteristic
682C22#1176270011yescharacteristic
683C22#1176272411yescharacteristic
684C22#1176272511yescharacteristic
685C22#1176272611yescharacteristic
686C22#1176273511yescharacteristic
687C22#1176297611yescharacteristic
688C22#1176298111yescharacteristic
689C22#1176298611yescharacteristic
690C22#1176299111yescharacteristic
691C4—44no—
692C4—82no—
693C4—82no—
694C4—682no—
695C4—1361no—
696C4—1361no—
697C4#1176267111yescharacteristic
698C4#1176268711yescharacteristic
699C4#1176269811yescharacteristic
700C4#1176270111yescharacteristic
701C4#1176272711yescharacteristic
702C4#1176273611yescharacteristic
703C4#1176273811yescharacteristic
704C4#1176273811yescharacteristic
705C2—21no—
706C2—21no—
707C2—21no—
708C2—21no—
709C2—1362no—
710C2#1452703211yescharacteristic
711C2#1452915611yescharacteristic
712C2#1452916311yescharacteristic
713C2#1452999411yescharacteristic
714C2#1453000111yescharacteristic
715C2#1453000811yescharacteristic
716C2#1453001311yescharacteristic
subgroupG/H
centerC23#10587623
commutatorC22×C4×C17C22×C4
FrattiniC23×C4C22×D17
FittingC17×C4⋊#95C2
socleC23×C17#120
prime radicalC22×#63252C22
cosocleC23×C4×C17C23
hypercenterC4⋊#95D17
hypocenterC17#11195
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
4. C2×#11762578C2semidirect
5. #14528503C2semidirect
6. C2×#11762569C2semidirect
7. C17×C4⋊#95C2semidirect
16. #11762808C4semidirect
309. C4⋊#95D17semidirect
458. C17#11195semidirect

Maximal subgroups

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

subgroupindex
C22×#105874762
C2×#117628082
#145313772
C2×#117625782
#145285032
C2×#117625692
C17×C4⋊#952
#1119517