Finite Group Databasebeta

← #16942203

Subgroups — #16942203

Order 4352.

1146 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762772C211yesmaximal, characteristic
2#14531163C211yesmaximal, characteristic
3C2×C4×#63227C211yesmaximal, characteristic
4C2×#11762570C211yesmaximal, characteristic, complemented
5C2×#11762569C211yesmaximal, characteristic, complemented
6C2×#11762568C211yesmaximal, characteristic, complemented
7C2×C17×#339C211yesmaximal, characteristic, complemented
8C23×C4×D17C2211yescharacteristic
9C22×#63223C2211yescharacteristic
10C2×#10587612C2211yescharacteristic
11C22×#63227—21no—
12C22×C4×Dic17C2211yescharacteristic
13#11762772—22no—
14#11762772—22no—
15C2×#10587491—22no—
16#11762670—21no—
17#11762666C412yescomplemented
18#11762666C412yescomplemented
19#11762664—21no—
20C4×#63227—22no—
21C4×#63227—22no—
22C4×#63227—22no—
23C2×#10587502—21no—
24#11762570—22no—
25#11762569—22no—
26#11762568—22no—
27C22×M16×C17C2211yescharacteristic
28C2×C17×#117C2211yescharacteristic
29C22×C42×C17C2211yescharacteristic
30C17×#339—22no—
31C24×D17D411yescharacteristic
32C23×C4×C17—21no—
33C23×C4×C17C2311yescharacteristic
34C23×Dic17—21no—
35C23×Dic17D411yescharacteristic
36C22×C4×D17—21no—
37C22×C4×D17—21no—
38C22×C4×D17—21no—
39C22×C4×D17—21no—
40C22×C4×D17—21no—
41C22×C4×D17—21no—
42C22×C4×D17—21no—
43C22×C4×D17—21no—
44C22×C4×D17—21no—
45C22×C4×D17—21no—
46C22×C4×D17—21no—
47C22×C4×D17—21no—
48C22×C4×D17C2×C412yes—
49C22×C4×D17D412yes—
50C2×M16×C17—21no—
51C2×M16×C17—21no—
52C2×M16×C17—21no—
53C2×M16×C17—21no—
54C2×M16×C17—21no—
55C2×M16×C17D412yes—
56C22×C8×C17—21no—
57C17×#117—21no—
58C17×#117—21no—
59C17×#117—21no—
60C17×#117—21no—
61C2×C4⋊C4×C17C2×C411yescharacteristic
62C2×C4⋊C4×C17C2×C411yescharacteristic
63C2×C22⋊C4×C17—21no—
64C2×C42×C17—21no—
65C2×C42×C17—21no—
66C2×C42×C17—21no—
67C2×C42×C17—21no—
68C2×C42×C17—21no—
69C2×C42×C17—21no—
70C2×C42×C17D412yes—
71C2×C22⋊Dic17—21no—
72C2×#63227—28no—
73C2×#63227—24no—
74C2×#63227—22no—
75C2×#63227—22no—
76#10587612—21no—
77#10587612—21no—
78#10587612—21no—
79#10587612—21no—
80C2×C4⋊Dic17C2×C412yes—
81C2×C4×Dic17—21no—
82C2×C4×Dic17—21no—
83C2×C4×Dic17—21no—
84C2×C4×Dic17—21no—
85C2×C4×Dic17—21no—
86C2×C4×Dic17—21no—
87C2×C4×Dic17D412yes—
88C2×#63223—21no—
89C2×#63223—21no—
90C2×#63223—21no—
91C2×#63223—21no—
92C2×#63223—21no—
93C2×#63223D412yes—
94C22×#3622—21no—
95#10587502—24no—
96#10587502—22no—
97#10587502—22no—
98#10587491—28no—
99C24×C17C2×D411yescharacteristic
100C23×D17—21no—
101C23×D17—21no—
102C23×D17—24no—
103C23×D17—21no—
104C23×D17—21no—
105C23×D17—21no—
106C23×D17—21no—
107C23×D17—42no—
108C23×D17C22⋊C412yes—
109C22×C4×C17—24no—
110C22×C4×C17—22no—
111C22×C4×C17—21no—
112C22×C4×C17—21no—
113C22×C4×C17—42no—
114C22×C4×C17—41no—
115C22×C4×C17—41no—
116C22×C4×C17C22×C411yescharacteristic
117C22×C4×C17C2×D411yescharacteristic
118C22×C4×C17C2×D411yescharacteristic
119C22×C4×C17C2×D411yescharacteristic
120C22×C4×C17C2×D411yescharacteristic
121C22×C4×C17C2×D411yescharacteristic
122C22×C4×C17#4111yescharacteristic
123C22×C4×C17#4111yescharacteristic
124C22×C4×C17#4111yescharacteristic
125C22×C4×C17#4111yescharacteristic
126C22×C4×C17#4111yescharacteristic
127C22×C4×C17#4111yescharacteristic
128C22×C4×C17#4111yescharacteristic
129C22×C4×C17#4111yescharacteristic
130C22×Dic17—24no—
131C22×Dic17—21no—
132C22×Dic17—22no—
133C22×Dic17—21no—
134C22×Dic17—21no—
135C22×Dic17—21no—
136C22×Dic17—21no—
137C22×Dic17—21no—
138C22×Dic17—22no—
139C22×Dic17—42no—
140C22×Dic17—41no—
141C22×Dic17—41no—
142C22×Dic17C22⋊C412yes—
143C2×C4×D17—22no—
144C2×C4×D17—22no—
145C2×C4×D17—22no—
146C2×C4×D17—22no—
147C2×C4×D17—22no—
148C2×C4×D17—22no—
149C2×C4×D17—22no—
150C2×C4×D17—22no—
151C2×C4×D17—22no—
152C2×C4×D17—22no—
153C2×C4×D17—22no—
154C2×C4×D17—22no—
155C2×C4×D17—41no—
156C2×C4×D17—41no—
157C2×C4×D17—41no—
158C2×C4×D17—41no—
159C2×C4×D17—41no—
160C2×C4×D17—41no—
161C2×C4×D17—41no—
162C2×C4×D17—41no—
163C2×C4×D17—41no—
164C2×C4×D17—41no—
165C2×C4×D17—41no—
166C2×C4×D17—41no—
167C2×C4×D17—41no—
168C2×C4×D17—41no—
169C2×C4×D17—41no—
170C2×C4×D17—41no—
171M16×C17—22no—
172M16×C17—22no—
173M16×C17—41no—
174M16×C17—41no—
175C2×C8×C17—22no—
176C2×C8×C17—41no—
177C2×C8×C17—41no—
178C4⋊C4×C17—21no—
179C4⋊C4×C17—21no—
180C4⋊C4×C17—21no—
181C4⋊C4×C17—21no—
182C22⋊C4×C17—41no—
183C22⋊C4×C17—41no—
184C42×C17—22no—
185C42×C17—22no—
186C42×C17—41no—
187C42×C17—41no—
188C42×C17—41no—
189C42×C17—41no—
190C22⋊Dic17—41no—
191C22⋊Dic17—41no—
192#63227—216no—
193#63227—44no—
194#63227—44no—
195C4⋊Dic17—22no—
196C4⋊Dic17—22no—
197C4×Dic17—22no—
198C4×Dic17—22no—
199C4×Dic17—41no—
200C4×Dic17—41no—
201C4×Dic17—41no—
202C4×Dic17—41no—
203#63223—22no—
204#63223—22no—
205#63223—41no—
206#63223—41no—
207C2×#3622—22no—
208C2×#3622—41no—
209C2×#3622—41no—
210#11201—171nomaximal, Sylow
211C23×C17—22no—
212C23×C17—22no—
213C23×C17C2×C22⋊C411yescharacteristic
214C23×C17#12011yescharacteristic
215C23×C17#12111yescharacteristic
216C23×C17#12111yescharacteristic
217C23×C17#12311yescharacteristic
218C23×C17#12311yescharacteristic
219C23×C17#12311yescharacteristic
220C22×D17—24no—
221C22×D17—24no—
222C22×D17—22no—
223C22×D17—22no—
224C22×D17—22no—
225C22×D17—22no—
226C22×D17—22no—
227C22×D17—22no—
228C22×D17—44no—
229C22×D17—44no—
230C22×D17—44no—
231C22×D17—44no—
232C22×D17—42no—
233C22×D17—42no—
234C22×D17—41no—
235C22×D17—41no—
236C22×D17—41no—
237C22×D17—41no—
238C22×D17#10414yes—
239C2×C4×C17—24no—
240C2×C4×C17—44no—
241C2×C4×C17—44no—
242C2×C4×C17—42no—
243C2×C4×C17—42no—
244C2×C4×C17—41no—
245C2×C4×C17—41no—
246C2×C4×C17—42no—
247C2×C4×C17—42no—
248C2×C4×C17#11711yescharacteristic
249C2×C4×C17#11711yescharacteristic
250C2×C4×C17C4×D411yescharacteristic
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#12111yescharacteristic
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#12411yescharacteristic
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
276C2×Dic17—24no—
277C2×Dic17—22no—
278C2×Dic17—22no—
279C2×Dic17—22no—
280C2×Dic17—44no—
281C2×Dic17—44no—
282C2×Dic17—42no—
283C2×Dic17—41no—
284C2×Dic17—41no—
285C2×Dic17—42no—
286C2×Dic17—41no—
287C2×Dic17—41no—
288C2×Dic17—42no—
289C2×Dic17—42no—
290C2×Dic17—42no—
291C4×D17—42no—
292C4×D17—42no—
293C4×D17—42no—
294C4×D17—42no—
295C4×D17—42no—
296C4×D17—42no—
297C4×D17—42no—
298C4×D17—42no—
299C8×C17—42no—
300#3622—42no—
301C2×#407—171no—
302#2280—171no—
303C2×C4×C22⋊C4—171no—
304C2×#339—171no—
305C2×#339—171no—
306C2×#339—171no—
307C2×#339D1711yescharacteristic, complemented
308C22×C17—22no—
309C22×C17—22no—
310C22×C17—22no—
311C22×C17—22no—
312C22×C17—21no—
313C22×C17—21no—
314C22×C17—21no—
315C22×C17—21no—
316C22×C17#38111yescharacteristic
317C22×C17#38611yescharacteristic
318C22×C17#38611yescharacteristic
319C22×C17#39411yescharacteristic
320C22×C17#39411yescharacteristic
321C22×C17#39711yescharacteristic
322C22×C17#39711yescharacteristic
323C22×C17C2×#10412yes—
324C22×C17#42112yes—
325C2×D17—24no—
326C2×D17—24no—
327C2×D17—24no—
328C2×D17—44no—
329C2×D17—44no—
330C2×D17—44no—
331C2×D17—44no—
332C2×D17—42no—
333C2×D17—42no—
334C2×D17—42no—
335C2×D17—42no—
336C4×C17—44no—
337C4×C17—81no—
338C4×C17—81no—
339C4×C17#38811yescharacteristic
340C4×C17#38811yescharacteristic
341C4×C17#38811yescharacteristic
342C4×C17#38811yescharacteristic
343C4×C17#39411yescharacteristic
344C4×C17#39411yescharacteristic
345C4×C17#39711yescharacteristic
346C4×C17#39711yescharacteristic
347Dic17—44no—
348Dic17—42no—
349Dic17—82no—
350C24×C4—171no—
351C22×M16—171no—
352C22×M16C2×D1711yescharacteristic
353C2×#117—171no—
354C2×#117C2×D1711yescharacteristic
355C22×C22⋊C4—341no—
356C22×C42—171no—
357C22×C42C2×D1711yescharacteristic
358#407—342no—
359#407—342no—
360C2×C22⋊C8—342no—
361#381—341no—
362#380—172no—
363#380—172no—
364#379—341no—
365C4×C22⋊C4—342no—
366C4×C22⋊C4—342no—
367C4×C22⋊C4—342no—
368C2×#95—341no—
369#339—22no—
370#339—342no—
371#339—342no—
372#339—342no—
373C2×C17—21no—
374C2×C17—21no—
375C2×C17—21no—
376C2×C17—21no—
377C2×C17#144011yescharacteristic
378C2×C17#182612yes—
379C2×C17#187112yes—
380C2×C17#189611yescharacteristic
381C2×C17#189711yescharacteristic
382D17—44no—
383C25—171no—
384C23×C4—21no—
385C23×C4—171no—
386C23×C4—172no—
387C23×C4—172no—
388C23×C4—341no—
389C23×C4—341no—
390C23×C4—341no—
391C23×C4—341no—
392C23×C4—341no—
393C23×C4—341no—
394C23×C4—341no—
395C23×C4—341no—
396C23×C4—341no—
397C23×C4—341no—
398C23×C4—341no—
399C23×C4—341no—
400C23×C4—341no—
401C23×C4C22×D1711yescharacteristic
402C2×M16—21no—
403C2×M16—21no—
404C2×M16—21no—
405C2×M16—21no—
406C2×M16—21no—
407C2×M16—172no—
408C2×M16—341no—
409C2×M16—341no—
410C2×M16—341no—
411C2×M16—341no—
412C2×M16—341no—
413C2×M16D6812yes—
414C22×C8—21no—
415C22×C8—341no—
416#117—21no—
417#117—21no—
418#117—21no—
419#117—21no—
420#117—341no—
421#117—341no—
422#117—341no—
423#117—341no—
424C2×C4⋊C4—172no—
425C2×C4⋊C4C4×D1711yescharacteristic
426C2×C4⋊C4C4×D1711yescharacteristic
427C2×C22⋊C4—21no—
428C2×C22⋊C4—344no—
429C2×C22⋊C4—348no—
430C2×C22⋊C4—342no—
431C2×C22⋊C4—342no—
432C2×C22⋊C4—341no—
433C2×C42—21no—
434C2×C42—21no—
435C2×C42—21no—
436C2×C42—21no—
437C2×C42—21no—
438C2×C42—21no—
439C2×C42—172no—
440C2×C42—341no—
441C2×C42—341no—
442C2×C42—341no—
443C2×C42—341no—
444C2×C42—341no—
445C2×C42—341no—
446C2×C42C22⋊D1712yes—
447C22⋊C8—348no—
448#95—342no—
449#95—342no—
450#95—344no—
451C17#1120111yescharacteristic, complemented, Sylow
452C24—172no—
453C24—344no—
454C24—341no—
455C24—341no—
456C24—341no—
457C24—341no—
458C24—341no—
459C24—341no—
460C24—682no—
461C24D4×D1711yescharacteristic
462C22×C4—24no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—42no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4—172no—
470C22×C4—344no—
471C22×C4—341no—
472C22×C4—341no—
473C22×C4—341no—
474C22×C4—341no—
475C22×C4—341no—
476C22×C4—341no—
477C22×C4—342no—
478C22×C4—342no—
479C22×C4—342no—
480C22×C4—342no—
481C22×C4—342no—
482C22×C4—342no—
483C22×C4—342no—
484C22×C4—342no—
485C22×C4—342no—
486C22×C4—342no—
487C22×C4—342no—
488C22×C4—342no—
489C22×C4—342no—
490C22×C4—342no—
491C22×C4—682no—
492C22×C4—681no—
493C22×C4—681no—
494C22×C4—681no—
495C22×C4—681no—
496C22×C4—681no—
497C22×C4—681no—
498C22×C4—681no—
499C22×C4—681no—
500C22×C4—681no—
501C22×C4—681no—
502C22×C4—681no—
503C22×C4—681no—
504C22×C4—681no—
505C22×C4—681no—
506C22×C4—681no—
507C22×C4—681no—
508C22×C4—681no—
509C22×C4—681no—
510C22×C4C2×C4×D1711yescharacteristic
511C22×C4C2×D6811yescharacteristic
512C22×C4#6325211yescharacteristic
513C22×C4#6325211yescharacteristic
514C22×C4#6325211yescharacteristic
515C22×C4#6325211yescharacteristic
516C22×C4D4×D1711yescharacteristic
517C22×C4D4×D1711yescharacteristic
518C22×C4D4×D1711yescharacteristic
519C22×C4#6325411yescharacteristic
520C22×C4#6325411yescharacteristic
521C22×C4#6325611yescharacteristic
522C22×C4#6325611yescharacteristic
523C22×C4C2×C22⋊D1711yescharacteristic
524M16—22no—
525M16—22no—
526M16—41no—
527M16—41no—
528M16—342no—
529M16—342no—
530M16—681no—
531M16—681no—
532C2×C8—22no—
533C2×C8—41no—
534C2×C8—41no—
535C2×C8—342no—
536C2×C8—681no—
537C2×C8—681no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—342no—
543C4⋊C4—342no—
544C22⋊C4—41no—
545C22⋊C4—41no—
546C22⋊C4—3416no—
547C22⋊C4—684no—
548C22⋊C4—684no—
549C22⋊C4—681no—
550C22⋊C4—681no—
551C42—22no—
552C42—22no—
553C42—41no—
554C42—41no—
555C42—41no—
556C42—41no—
557C42—342no—
558C42—342no—
559C42—681no—
560C42—681no—
561C42—681no—
562C42—681no—
563C23—22no—
564C23—22no—
565C23—174no—
566C23—344no—
567C23—344no—
568C23—342no—
569C23—342no—
570C23—342no—
571C23—342no—
572C23—342no—
573C23—342no—
574C23—684no—
575C23—684no—
576C23—684no—
577C23—684no—
578C23—682no—
579C23—682no—
580C23—681no—
581C23—681no—
582C23—681no—
583C23—681no—
584C23C22⋊C4×D1711yescharacteristic
585C23#1058756911yescharacteristic
586C23#1058756911yescharacteristic
587C23#1058757011yescharacteristic
588C23#1058758011yescharacteristic
589C23#1058758111yescharacteristic
590C23#1058762311yescharacteristic
591C2×C4—24no—
592C2×C4—44no—
593C2×C4—44no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—344no—
601C2×C4—342no—
602C2×C4—342no—
603C2×C4—342no—
604C2×C4—684no—
605C2×C4—684no—
606C2×C4—682no—
607C2×C4—681no—
608C2×C4—682no—
609C2×C4—681no—
610C2×C4—681no—
611C2×C4—681no—
612C2×C4—682no—
613C2×C4—682no—
614C2×C4—682no—
615C2×C4—682no—
616C2×C4—682no—
617C2×C4—682no—
618C2×C4—682no—
619C2×C4—682no—
620C2×C4—682no—
621C2×C4—682no—
622C2×C4—682no—
623C2×C4#1058755811yescharacteristic
624C2×C4C4×D6811yescharacteristic
625C2×C4#1058756111yescharacteristic
626C2×C4#1058756211yescharacteristic
627C2×C4#1058756711yescharacteristic
628C2×C4#1058756811yescharacteristic
629C2×C4#1058756911yescharacteristic
630C2×C4#1058757011yescharacteristic
631C2×C4#1058757011yescharacteristic
632C2×C4#1058757111yescharacteristic
633C2×C4#1058757111yescharacteristic
634C2×C4#1058757211yescharacteristic
635C2×C4#1058757811yescharacteristic
636C2×C4#1058757911yescharacteristic
637C2×C4#1058758011yescharacteristic
638C2×C4#1058758011yescharacteristic
639C2×C4#1058758011yescharacteristic
640C2×C4#1058758011yescharacteristic
641C2×C4#1058758111yescharacteristic
642C2×C4#1058758411yescharacteristic
643C2×C4#1058758411yescharacteristic
644C2×C4#1058758411yescharacteristic
645C2×C4C4×C22⋊D1711yescharacteristic
646C2×C4#1058761511yescharacteristic
647C2×C4#1058761611yescharacteristic
648C2×C4#1058762411yescharacteristic
649C2×C4#1058762511yescharacteristic
650C2×C4#1058763311yescharacteristic
651C8—42no—
652C8—682no—
653C22—22no—
654C22—22no—
655C22—22no—
656C22—22no—
657C22—21no—
658C22—21no—
659C22—21no—
660C22—21no—
661C22—344no—
662C22—344no—
663C22—344no—
664C22—684no—
665C22—684no—
666C22—684no—
667C22—684no—
668C22—682no—
669C22—682no—
670C22—682no—
671C22—682no—
672C22#1176267111yescharacteristic
673C22#1176268511yescharacteristic
674C22#1176268711yescharacteristic
675C22#1176272411yescharacteristic
676C22#1176272611yescharacteristic
677C22#1176273611yescharacteristic
678C22#1176273811yescharacteristic
679C22#104×D1712yes—
680C22#1176282412yes—
681C4—44no—
682C4—81no—
683C4—81no—
684C4—684no—
685C4—682no—
686C4—1362no—
687C4#1176269811yescharacteristic
688C4#1176269911yescharacteristic
689C4#1176270011yescharacteristic
690C4#1176270111yescharacteristic
691C4#1176272511yescharacteristic
692C4#1176272711yescharacteristic
693C4#1176273511yescharacteristic
694C4#1176273811yescharacteristic
695C2—21no—
696C2—21no—
697C2—21no—
698C2—21no—
699C2—684no—
700C2#1452703211yescharacteristic
701C2#1452888212yes—
702C2#1452908512yes—
703C2#1452922411yescharacteristic
704C2#1452922911yescharacteristic
subgroupG/H
centerC22×C4D4×D17
commutatorC22×C4×C17C22×C4
FrattiniC23×C4C22×D17
FittingC2×C17×#339C2
socleC23×C17C2×C22⋊C4
prime radicalC24×D17D4
cosocleC23×C4×C17C23
hypercenterC2×#339D17
hypocenterC17#11201
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#339

Complements

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

NH ≅ G/Ntype
4. C2×#11762570C2semidirect
5. C2×#11762569C2semidirect
6. C2×#11762568C2semidirect
7. C2×C17×#339C2semidirect
17. #11762666C4semidirect
18. #11762666C4semidirect
307. C2×#339D17semidirect
451. C17#11201semidirect

Maximal subgroups

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

subgroupindex
C2×#117627722
#145311632
C2×C4×#632272
C2×#117625702
C2×#117625692
C2×#117625682
C2×C17×#3392
#1120117