Finite Group Databasebeta

← #16942186

Subgroups — #16942186

Order 4352.

1134 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762670C211yesmaximal, characteristic
2C2×#11762670C211yesmaximal, characteristic
3C2×#11762670C211yesmaximal, characteristic
4C2×#11762576C211yesmaximal, characteristic
5C2×#11762575C211yesmaximal, characteristic
6C2×#11762575C211yesmaximal, characteristic
7C2×C17×#342C211yesmaximal, characteristic
8C24×Dic17C2211yescharacteristic
9C22×C22⋊Dic17C2211yescharacteristic
10C22×C22⋊Dic17C2211yescharacteristic
11C22×C22⋊Dic17C2211yescharacteristic
12#11762670—22no—
13#11762670—22no—
14#11762670—22no—
15#11762670—22no—
16#11762670—22no—
17#11762670—22no—
18C2×#10587502—22no—
19C2×#10587502—22no—
20C2×#10587502C414yescomplemented
21#11762576—22no—
22#11762575—22no—
23#11762575—22no—
24C22×C22⋊C4×C17C2211yescharacteristic
25C22×C22⋊C4×C17C2211yescharacteristic
26C22×C22⋊C4×C17C2211yescharacteristic
27C17×#342—22no—
28C25×C17C2311yescharacteristic
29C23×C4×C17—21no—
30C23×C4×C17—21no—
31C23×C4×C17C2×C412yes—
32C23×Dic17—21no—
33C23×Dic17—21no—
34C23×Dic17—21no—
35C23×Dic17—21no—
36C23×Dic17—21no—
37C23×Dic17—21no—
38C23×Dic17—21no—
39C23×Dic17—21no—
40C23×Dic17—21no—
41C23×Dic17—21no—
42C23×Dic17—21no—
43C23×Dic17—21no—
44C23×Dic17—21no—
45C23×Dic17—21no—
46C23×Dic17C2×C412yes—
47C23×Dic17C2×C412yes—
48C23×Dic17D412yes—
49C23×Dic17D412yes—
50C2×C22⋊C4×C17—21no—
51C2×C22⋊C4×C17—21no—
52C2×C22⋊C4×C17—21no—
53C2×C22⋊C4×C17—21no—
54C2×C22⋊C4×C17—21no—
55C2×C22⋊C4×C17—21no—
56C2×C22⋊C4×C17—21no—
57C2×C22⋊C4×C17—21no—
58C2×C22⋊C4×C17—21no—
59C2×C22⋊C4×C17—21no—
60C2×C22⋊C4×C17—21no—
61C2×C22⋊C4×C17—21no—
62C2×C22⋊C4×C17—21no—
63C2×C22⋊C4×C17—21no—
64C2×C22⋊C4×C17—21no—
65C2×C22⋊C4×C17—21no—
66C2×C22⋊C4×C17D412yes—
67C2×C22⋊C4×C17D412yes—
68C2×C22⋊Dic17—21no—
69C2×C22⋊Dic17—21no—
70C2×C22⋊Dic17—21no—
71C2×C22⋊Dic17—21no—
72C2×C22⋊Dic17—21no—
73C2×C22⋊Dic17—21no—
74C2×C22⋊Dic17—21no—
75C2×C22⋊Dic17—21no—
76C2×C22⋊Dic17—21no—
77C2×C22⋊Dic17—21no—
78C2×C22⋊Dic17—21no—
79C2×C22⋊Dic17—21no—
80C2×C22⋊Dic17—21no—
81C2×C22⋊Dic17—21no—
82C2×C22⋊Dic17—21no—
83C2×C22⋊Dic17—21no—
84C2×C22⋊Dic17D412yes—
85C2×C22⋊Dic17D412yes—
86#10587502—28no—
87#10587502—28no—
88#10587502—28no—
89C24×C17—44no—
90C24×C17C22×C411yescharacteristic
91C24×C17C2×D411yescharacteristic
92C24×C17C2×D411yescharacteristic
93C24×C17C2×D411yescharacteristic
94C24×C17C2×D411yescharacteristic
95C24×C17C2×D411yescharacteristic
96C24×C17C2×D411yescharacteristic
97C24×C17#4111yescharacteristic
98C24×C17#4111yescharacteristic
99C24×C17#4111yescharacteristic
100C24×C17#4111yescharacteristic
101C24×C17#4111yescharacteristic
102C24×C17#4111yescharacteristic
103C24×C17#4111yescharacteristic
104C24×C17#4111yescharacteristic
105C22×C4×C17—22no—
106C22×C4×C17—22no—
107C22×C4×C17—22no—
108C22×C4×C17—22no—
109C22×C4×C17—22no—
110C22×C4×C17—44no—
111C22×C4×C17—44no—
112C22×C4×C17—41no—
113C22×C4×C17—41no—
114C22×C4×C17—41no—
115C22×C4×C17—41no—
116C22×C4×C17—44no—
117C22×Dic17—22no—
118C22×Dic17—22no—
119C22×Dic17—22no—
120C22×Dic17—22no—
121C22×Dic17—22no—
122C22×Dic17—22no—
123C22×Dic17—22no—
124C22×Dic17—22no—
125C22×Dic17—22no—
126C22×Dic17—22no—
127C22×Dic17—22no—
128C22×Dic17—22no—
129C22×Dic17—22no—
130C22×Dic17—22no—
131C22×Dic17—22no—
132C22×Dic17—22no—
133C22×Dic17—22no—
134C22×Dic17—22no—
135C22×Dic17—22no—
136C22×Dic17—22no—
137C22×Dic17—22no—
138C22×Dic17—22no—
139C22×Dic17—22no—
140C22×Dic17—41no—
141C22×Dic17—41no—
142C22×Dic17—41no—
143C22×Dic17—41no—
144C22×Dic17—41no—
145C22×Dic17—41no—
146C22×Dic17—41no—
147C22×Dic17—41no—
148C22×Dic17—41no—
149C22×Dic17—41no—
150C22×Dic17—41no—
151C22×Dic17—41no—
152C22×Dic17—41no—
153C22×Dic17—41no—
154C22×Dic17—41no—
155C22×Dic17—41no—
156C22×Dic17—44no—
157C22×Dic17—44no—
158C22×Dic17—41no—
159C22×Dic17—41no—
160C22×Dic17—41no—
161C22×Dic17—41no—
162C22×Dic17—44no—
163C22×Dic17C22⋊C414yes—
164C22⋊C4×C17—22no—
165C22⋊C4×C17—22no—
166C22⋊C4×C17—22no—
167C22⋊C4×C17—22no—
168C22⋊C4×C17—41no—
169C22⋊C4×C17—41no—
170C22⋊C4×C17—41no—
171C22⋊C4×C17—41no—
172C22⋊C4×C17—41no—
173C22⋊C4×C17—41no—
174C22⋊C4×C17—41no—
175C22⋊C4×C17—41no—
176C22⋊Dic17—22no—
177C22⋊Dic17—22no—
178C22⋊Dic17—22no—
179C22⋊Dic17—22no—
180C22⋊Dic17—41no—
181C22⋊Dic17—41no—
182C22⋊Dic17—41no—
183C22⋊Dic17—41no—
184C22⋊Dic17—41no—
185C22⋊Dic17—41no—
186C22⋊Dic17—41no—
187C22⋊Dic17—41no—
188#11197—171nomaximal, Sylow
189C23×C17—24no—
190C23×C17—24no—
191C23×C17—24no—
192C23×C17—42no—
193C23×C17—42no—
194C23×C17—42no—
195C23×C17—42no—
196C23×C17—42no—
197C23×C17—42no—
198C23×C17—42no—
199C23×C17—42no—
200C23×C17—42no—
201C23×C17—42no—
202C23×C17—42no—
203C23×C17—42no—
204C23×C17C2×C22⋊C411yescharacteristic
205C23×C17#11711yescharacteristic
206C23×C17#11711yescharacteristic
207C23×C17C4×D411yescharacteristic
208C23×C17C4×D411yescharacteristic
209C23×C17C4×D411yescharacteristic
210C23×C17C4×D411yescharacteristic
211C23×C17#12011yescharacteristic
212C23×C17#12011yescharacteristic
213C23×C17#12111yescharacteristic
214C23×C17#12111yescharacteristic
215C23×C17#12111yescharacteristic
216C23×C17#12111yescharacteristic
217C23×C17#12111yescharacteristic
218C23×C17#12111yescharacteristic
219C23×C17#12111yescharacteristic
220C23×C17#12111yescharacteristic
221C23×C17#12311yescharacteristic
222C23×C17#12311yescharacteristic
223C23×C17#12311yescharacteristic
224C23×C17#12311yescharacteristic
225C23×C17#12311yescharacteristic
226C23×C17#12311yescharacteristic
227C23×C17#12311yescharacteristic
228C23×C17#12311yescharacteristic
229C23×C17#12311yescharacteristic
230C23×C17#12311yescharacteristic
231C23×C17#12411yescharacteristic
232C23×C17#12411yescharacteristic
233C23×C17#12411yescharacteristic
234C23×C17#12411yescharacteristic
235C23×C17#12611yescharacteristic
236C23×C17#12611yescharacteristic
237C23×C17#12611yescharacteristic
238C23×C17#12611yescharacteristic
239C2×C4×C17—44no—
240C2×C4×C17—44no—
241C2×C4×C17—42no—
242C2×C4×C17—42no—
243C2×C4×C17—42no—
244C2×C4×C17—44no—
245C2×C4×C17—82no—
246C2×C4×C17—82no—
247C2×C4×C17—82no—
248C2×C4×C17—82no—
249C2×C4×C17—82no—
250C2×C4×C17—82no—
251C2×Dic17—24no—
252C2×Dic17—24no—
253C2×Dic17—24no—
254C2×Dic17—42no—
255C2×Dic17—42no—
256C2×Dic17—42no—
257C2×Dic17—42no—
258C2×Dic17—42no—
259C2×Dic17—42no—
260C2×Dic17—42no—
261C2×Dic17—42no—
262C2×Dic17—42no—
263C2×Dic17—42no—
264C2×Dic17—42no—
265C2×Dic17—42no—
266C2×Dic17—44no—
267C2×Dic17—44no—
268C2×Dic17—42no—
269C2×Dic17—42no—
270C2×Dic17—42no—
271C2×Dic17—44no—
272C2×Dic17—82no—
273C2×Dic17—82no—
274C2×Dic17—82no—
275C2×Dic17—82no—
276C2×Dic17—82no—
277C2×Dic17—82no—
278C2×#381—171no—
279C2×#381—171no—
280C2×#381—171no—
281C2×#342—171no—
282C2×#342—171no—
283C2×#342—171no—
284C2×#342D1711yescharacteristic
285C22×C17—22no—
286C22×C17—22no—
287C22×C17—22no—
288C22×C17—22no—
289C22×C17—22no—
290C22×C17—22no—
291C22×C17—22no—
292C22×C17—22no—
293C22×C17—22no—
294C22×C17—22no—
295C22×C17—22no—
296C22×C17—22no—
297C22×C17—22no—
298C22×C17—22no—
299C22×C17—22no—
300C22×C17—22no—
301C22×C17—22no—
302C22×C17—22no—
303C22×C17—41no—
304C22×C17—41no—
305C22×C17—41no—
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×C17—41no—
318C22×C17—41no—
319C22×C17#38111yescharacteristic
320C22×C17#38611yescharacteristic
321C22×C17#38611yescharacteristic
322C22×C17#38811yescharacteristic
323C22×C17#38811yescharacteristic
324C22×C17#38811yescharacteristic
325C22×C17#38811yescharacteristic
326C22×C17#39411yescharacteristic
327C22×C17#39411yescharacteristic
328C22×C17#39411yescharacteristic
329C22×C17#39411yescharacteristic
330C22×C17#39711yescharacteristic
331C22×C17#39711yescharacteristic
332C22×C17#39711yescharacteristic
333C22×C17#39711yescharacteristic
334C22×C17#41014yes—
335C4×C17—82no—
336C4×C17—82no—
337C4×C17—82no—
338Dic17—44no—
339Dic17—82no—
340Dic17—82no—
341Dic17—82no—
342C24×C4—171no—
343C22×C22⋊C4—171no—
344C22×C22⋊C4—171no—
345C22×C22⋊C4—171no—
346C22×C22⋊C4C2×D1711yescharacteristic
347C22×C22⋊C4C2×D1711yescharacteristic
348C22×C22⋊C4C2×D1711yescharacteristic
349#381—342no—
350#381—342no—
351#381—342no—
352#381—342no—
353#381—342no—
354#381—342no—
355C2×#95—174no—
356C2×#95—342no—
357C2×#95—342no—
358#342—22no—
359#342—342no—
360#342—342no—
361#342—342no—
362C2×C17—21no—
363C2×C17—21no—
364C2×C17—21no—
365C2×C17—21no—
366C2×C17—21no—
367C2×C17—21no—
368C2×C17—21no—
369C2×C17—21no—
370C2×C17—21no—
371C2×C17—21no—
372C2×C17—21no—
373C2×C17—21no—
374C2×C17#144011yescharacteristic
375C2×C17#182012yes—
376C2×C17#189912yes—
377C2×C17#189912yes—
378C25C22×D1711yescharacteristic
379C23×C4—21no—
380C23×C4—21no—
381C23×C4—172no—
382C23×C4—172no—
383C23×C4—172no—
384C23×C4—172no—
385C23×C4—341no—
386C23×C4—341no—
387C23×C4—341no—
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×C4C4×D1712yes—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—172no—
417C2×C22⋊C4—172no—
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×C22⋊C4—341no—
426C2×C22⋊C4—341no—
427C2×C22⋊C4—341no—
428C2×C22⋊C4—341no—
429C2×C22⋊C4—341no—
430C2×C22⋊C4—341no—
431C2×C22⋊C4—341no—
432C2×C22⋊C4—341no—
433C2×C22⋊C4—341no—
434C2×C22⋊C4D6812yes—
435C2×C22⋊C4C22⋊D1712yes—
436#95—348no—
437#95—348no—
438#95—348no—
439C17#1119711yescharacteristic, complemented, Sylow
440C24—44no—
441C24C2×C4×D1711yescharacteristic
442C24C2×D6811yescharacteristic
443C24#6325211yescharacteristic
444C24#6325211yescharacteristic
445C24#6325211yescharacteristic
446C24#6325211yescharacteristic
447C24D4×D1711yescharacteristic
448C24D4×D1711yescharacteristic
449C24D4×D1711yescharacteristic
450C24D4×D1711yescharacteristic
451C24#6325411yescharacteristic
452C24#6325411yescharacteristic
453C24#6325611yescharacteristic
454C24#6325611yescharacteristic
455C24C2×C22⋊D1711yescharacteristic
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—44no—
462C22×C4—44no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4—44no—
468C22×C4—174no—
469C22×C4—342no—
470C22×C4—342no—
471C22×C4—342no—
472C22×C4—342no—
473C22×C4—342no—
474C22×C4—342no—
475C22×C4—342no—
476C22×C4—342no—
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—342no—
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—684no—
509C22×C4—684no—
510C22×C4—681no—
511C22×C4—681no—
512C22×C4—681no—
513C22×C4—681no—
514C22×C4—684no—
515C22⋊C4—22no—
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—41no—
520C22⋊C4—41no—
521C22⋊C4—41no—
522C22⋊C4—41no—
523C22⋊C4—41no—
524C22⋊C4—41no—
525C22⋊C4—41no—
526C22⋊C4—41no—
527C22⋊C4—342no—
528C22⋊C4—342no—
529C22⋊C4—342no—
530C22⋊C4—342no—
531C22⋊C4—681no—
532C22⋊C4—681no—
533C22⋊C4—681no—
534C22⋊C4—681no—
535C22⋊C4—681no—
536C22⋊C4—681no—
537C22⋊C4—681no—
538C22⋊C4—681no—
539C23—24no—
540C23—24no—
541C23—24no—
542C23—42no—
543C23—42no—
544C23—42no—
545C23—42no—
546C23—42no—
547C23—42no—
548C23—42no—
549C23—42no—
550C23—42no—
551C23—42no—
552C23—42no—
553C23—42no—
554C23#1058755811yescharacteristic
555C23C4×D6811yescharacteristic
556C23#1058756111yescharacteristic
557C23#1058756211yescharacteristic
558C23C22⋊C4×D1711yescharacteristic
559C23#1058756711yescharacteristic
560C23#1058756811yescharacteristic
561C23#1058756911yescharacteristic
562C23#1058756911yescharacteristic
563C23#1058756911yescharacteristic
564C23#1058757011yescharacteristic
565C23#1058757011yescharacteristic
566C23#1058757011yescharacteristic
567C23#1058757111yescharacteristic
568C23#1058757111yescharacteristic
569C23#1058757211yescharacteristic
570C23#1058757811yescharacteristic
571C23#1058757911yescharacteristic
572C23#1058758011yescharacteristic
573C23#1058758011yescharacteristic
574C23#1058758011yescharacteristic
575C23#1058758011yescharacteristic
576C23#1058758011yescharacteristic
577C23#1058758111yescharacteristic
578C23#1058758111yescharacteristic
579C23#1058758411yescharacteristic
580C23#1058758411yescharacteristic
581C23#1058758411yescharacteristic
582C23C4×C22⋊D1711yescharacteristic
583C23#1058761511yescharacteristic
584C23#1058761611yescharacteristic
585C23#1058762311yescharacteristic
586C23#1058762411yescharacteristic
587C23#1058762511yescharacteristic
588C23#1058763311yescharacteristic
589C2×C4—44no—
590C2×C4—44no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—44no—
594C2×C4—42no—
595C2×C4—82no—
596C2×C4—82no—
597C2×C4—82no—
598C2×C4—82no—
599C2×C4—82no—
600C2×C4—82no—
601C2×C4—344no—
602C2×C4—344no—
603C2×C4—344no—
604C2×C4—682no—
605C2×C4—682no—
606C2×C4—682no—
607C2×C4—682no—
608C2×C4—682no—
609C2×C4—682no—
610C2×C4—682no—
611C2×C4—682no—
612C2×C4—682no—
613C2×C4—682no—
614C2×C4—682no—
615C2×C4—682no—
616C2×C4—684no—
617C2×C4—684no—
618C2×C4—682no—
619C2×C4—682no—
620C2×C4—684no—
621C2×C4—682no—
622C2×C4—1362no—
623C2×C4—1362no—
624C2×C4—1362no—
625C2×C4—1362no—
626C2×C4—1362no—
627C2×C4—1362no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—22no—
632C22—22no—
633C22—22no—
634C22—22no—
635C22—22no—
636C22—22no—
637C22—22no—
638C22—22no—
639C22—22no—
640C22—22no—
641C22—22no—
642C22—22no—
643C22—22no—
644C22—22no—
645C22—22no—
646C22—41no—
647C22—41no—
648C22—41no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22—41no—
653C22—41no—
654C22—41no—
655C22—41no—
656C22—41no—
657C22—41no—
658C22—41no—
659C22—41no—
660C22—41no—
661C22—41no—
662C22#1176267111yescharacteristic
663C22#1176268511yescharacteristic
664C22#1176268711yescharacteristic
665C22#1176269811yescharacteristic
666C22#1176269911yescharacteristic
667C22#1176270011yescharacteristic
668C22#1176270111yescharacteristic
669C22#1176272411yescharacteristic
670C22#1176272511yescharacteristic
671C22#1176272611yescharacteristic
672C22#1176272711yescharacteristic
673C22#1176273511yescharacteristic
674C22#1176273611yescharacteristic
675C22#1176273811yescharacteristic
676C22#1176273811yescharacteristic
677C22#1176278114yes—
678C4—82no—
679C4—82no—
680C4—82no—
681C4—684no—
682C4—1362no—
683C4—1362no—
684C4—1362no—
685C2—21no—
686C2—21no—
687C2—21no—
688C2—21no—
689C2—21no—
690C2—21no—
691C2—21no—
692C2—21no—
693C2—21no—
694C2—21no—
695C2—21no—
696C2—21no—
697C2#1452703211yescharacteristic
698C2#1452886012yes—
699C2#1452923912yes—
700C2#1452924112yes—
subgroupG/H
centerC23C22⋊C4×D17
commutatorC24×C17C22×C4
FrattiniC25C22×D17
FittingC2×C17×#342C2
socleC23×C17C2×C22⋊C4
prime radical, cosocleC25×C17C23
hypercenterC2×#342D17
hypocenterC17#11197
LCSG ▷ C24×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C25 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
20. C2×#10587502C4semidirect
439. C17#11197semidirect

Maximal subgroups

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

subgroupindex
C2×#117626702
C2×#117625762
C2×#117625752
C2×C17×#3422
#1119717