Finite Group Databasebeta

← #17956712

Subgroups — #17956712

Order 4352.

1822 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763777C211yesmaximal, characteristic
2C2×#11763751C211yesmaximal, characteristic
3C2×#11763682C214yesmaximal, complemented
4C22×C4⋊C4×D17C211yesmaximal, characteristic
5C22×#63242C2212yes—
6C22×C4⋊#595C2212yes—
7C22×C22⋊#595—21no—
8C2×#10587543—21no—
9#11763777—22no—
10#11763777C414yescomplemented
11C2×C22⋊#3624—21no—
12#11763751—22no—
13#11763751C414yescomplemented
14C2×(C2×#595)⋊C4—21no—
15#11763682—28no—
16C23×C4×D17—21no—
17C23×C4×D17C2211yescharacteristic
18C22×C4⋊Dic17C411yescharacteristic, complemented
19C22×#63225—21no—
20C2×C4⋊C4×D17—28no—
21C2×C4⋊C4×D17—21no—
22C2×C4⋊C4×D17—21no—
23C2×C4⋊C4×D17C412yescomplemented
24C2×C4⋊C4×D17C2212yes—
25C22×C4⋊C4×C17C411yescharacteristic, complemented
26C24×D17D411yescharacteristic
27C23×#595—22no—
28C23×C4×C17—21no—
29C23×C4×C17C2×C411yescharacteristic
30C23×Dic17—21no—
31C23×Dic17D411yescharacteristic
32C22×C4×D17—24no—
33C22×C4×D17—24no—
34C22×C4×D17—28no—
35C22×C4×D17—22no—
36C22×C4×D17—22no—
37C22×C4×D17—44no—
38C22×C4×D17—42no—
39C22×C4×D17—42no—
40C22×C4×D17C2×C411yescharacteristic
41C22×C4×D17C2×C412yes—
42C22×C4×D17C2×C412yes—
43C22×C4×D17D411yescharacteristic
44C22×C4×D17D411yescharacteristic
45C22×C4×D17D412yes—
46C22×C4×D17Q812yes—
47C22×C4×D17C2311yescharacteristic
48C2×C22⋊#595—24no—
49C2×C22⋊#595—42no—
50C2×C22⋊#595—42no—
51C22×#3624—22no—
52C2×C4⋊#595—24no—
53C2×C4⋊#595—24no—
54C2×C4⋊#595—22no—
55C2×C4⋊#595C2×C414yescomplemented
56C2×#63242—24no—
57C2×#63242—24no—
58C2×#63242—22no—
59C2×#63242C2×C414yescomplemented
60C2×C4⋊C4×C17—21no—
61C2×C4⋊C4×C17—24no—
62C2×C4⋊C4×C17C2×C412yes—
63C2×C4⋊Dic17—24no—
64C2×C4⋊Dic17—21no—
65C2×C4⋊Dic17C2×C412yes—
66C2×#63225—28no—
67C2×#63225—22no—
68C2×#63225—22no—
69C4⋊C4×D17—28no—
70C4⋊C4×D17—28no—
71C4⋊C4×D17—24no—
72C4⋊C4×D17—24no—
73C4⋊C4×D17—24no—
74C4⋊C4×D17D418yes—
75C22⋊#3624—24no—
76(C2×#595)⋊C4—24no—
77#10587543—24no—
78C24×C17C22⋊C411yescharacteristic
79C23×D17—22no—
80C23×D17—22no—
81C23×D17—22no—
82C23×D17—22no—
83C23×D17C22⋊C411yescharacteristic
84C23×D17C22⋊C412yes—
85C23×D17C4⋊C412yes—
86C23×D17D812yes—
87C23×D17SD1612yes—
88C23×D17SD1612yes—
89C23×D17Q1612yes—
90C23×D17C2×D411yescharacteristic
91C22×#595—24no—
92C22×#595—42no—
93C22×#595—42no—
94C22×#595—42no—
95C22×#595—42no—
96C22×#595—42no—
97C22×#595—42no—
98C22×C4×C17—22no—
99C22×C4×C17—22no—
100C22×C4×C17—24no—
101C22×C4×C17—22no—
102C22×C4×C17—42no—
103C22×C4×C17—42no—
104C22×C4×C17C4212yes—
105C22×C4×C17C22⋊C411yescharacteristic
106C22×C4×C17C4⋊C412yes—
107C22×C4×C17C22×C411yescharacteristic
108C22×Dic17—22no—
109C22×Dic17—22no—
110C22×Dic17—24no—
111C22×Dic17—22no—
112C22×Dic17—42no—
113C22×Dic17—42no—
114C22×Dic17C22⋊C411yescharacteristic
115C22×Dic17C22⋊C412yes—
116C22×Dic17C4⋊C412yes—
117C22×Dic17C2×D411yescharacteristic
118C2×C4×D17—22no—
119C2×C4×D17—22no—
120C2×C4×D17—22no—
121C2×C4×D17—22no—
122C2×C4×D17—22no—
123C2×C4×D17—22no—
124C2×C4×D17—28no—
125C2×C4×D17—28no—
126C2×C4×D17—28no—
127C2×C4×D17—28no—
128C2×C4×D17—28no—
129C2×C4×D17—28no—
130C2×C4×D17—44no—
131C2×C4×D17—416no—
132C2×C4×D17—416no—
133C2×C4×D17—44no—
134C2×C4×D17—42no—
135C2×C4×D17—42no—
136C2×C4×D17—44no—
137C2×C4×D17C4212yes—
138C2×C4×D17C22⋊C412yes—
139C2×C4×D17C22⋊C412yes—
140C2×C4×D17C4⋊C412yes—
141C2×C4×D17C4⋊C412yes—
142C2×C4×D17C4⋊C412yes—
143C2×C4×D17C22×C411yescharacteristic
144C2×C4×D17C22×C411yescharacteristic
145C2×C4×D17C2×D414yes—
146C2×C4×D17C2×D411yescharacteristic
147C2×C4×D17C2×Q811yescharacteristic
148C2×C4×D17#4114yes—
149C22⋊#595—48no—
150C2×#3624—24no—
151C2×#3624—42no—
152C2×#3624—42no—
153C4⋊#595—28no—
154C4⋊#595—44no—
155#63242—28no—
156#63242—44no—
157C4⋊C4×C17—24no—
158C4⋊C4×C17—22no—
159C4⋊C4×C17C22⋊C414yescomplemented
160C4⋊Dic17—24no—
161C4⋊Dic17—22no—
162C4⋊Dic17C22⋊C414yescomplemented
163#63225—28no—
164#63225—28no—
165#10730—171nomaximal, Sylow
166C23×C17—21no—
167C23×C17—21no—
168C23×C17—21no—
169C23×C17—21no—
170C23×C17#9512yes—
171C23×C17#10212yes—
172C23×C17#10312yes—
173C23×C17C2×C22⋊C411yescharacteristic
174C22×D17—21no—
175C22×D17—21no—
176C22×D17—21no—
177C22×D17—21no—
178C22×D17—24no—
179C22×D17—24no—
180C22×D17—24no—
181C22×D17—24no—
182C22×D17—24no—
183C22×D17—24no—
184C22×D17—24no—
185C22×D17—24no—
186C22×D17—24no—
187C22×D17—24no—
188C22×D17—24no—
189C22×D17—24no—
190C22×D17#9512yes—
191C22×D17#10212yes—
192C22×D17#10214yes—
193C22×D17#10312yes—
194C22×D17#10314yes—
195C22×D17#10614yes—
196C22×D17#10714yes—
197C22×D17C2×C22⋊C411yescharacteristic
198C22×D17C2×C4⋊C411yescharacteristic
199C22×D17#12012yes—
200C22×D17#12312yes—
201C22×D17C2×D811yescharacteristic
202C22×D17C2×SD1611yescharacteristic
203C22×D17C2×SD1611yescharacteristic
204C22×D17C2×Q1611yescharacteristic
205C22×D17AGL(1,ℤ/8)12yes—
206C22×D17#13712yes—
207C2×#595—44no—
208C2×#595—44no—
209C2×#595—44no—
210C2×#595—82no—
211C2×#595—82no—
212C2×#595—82no—
213C2×#595—82no—
214C2×C4×C17—21no—
215C2×C4×C17—21no—
216C2×C4×C17—24no—
217C2×C4×C17—24no—
218C2×C4×C17—24no—
219C2×C4×C17—48no—
220C2×C4×C17—42no—
221C2×C4×C17—42no—
222C2×C4×C17#9512yes—
223C2×C4×C17C2×C4211yescharacteristic
224C2×C4×C17C2×C22⋊C412yes—
225C2×C4×C17C2×C4⋊C411yescharacteristic
226C2×C4×C17#11712yes—
227C2×Dic17—21no—
228C2×Dic17—21no—
229C2×Dic17—24no—
230C2×Dic17—24no—
231C2×Dic17—24no—
232C2×Dic17—48no—
233C2×Dic17—42no—
234C2×Dic17—42no—
235C2×Dic17#9512yes—
236C2×Dic17C2×C22⋊C411yescharacteristic
237C2×Dic17C2×C4⋊C411yescharacteristic
238C2×Dic17#12012yes—
239C2×Dic17#12312yes—
240C4×D17—24no—
241C4×D17—24no—
242C4×D17—24no—
243C4×D17—24no—
244C4×D17—24no—
245C4×D17—24no—
246C4×D17—416no—
247C4×D17—48no—
248C4×D17—48no—
249C4×D17C4×D414yes—
250C4×D17C4×D414yes—
251C4×D17#12114yes—
252C4×D17C22⋊Q814yes—
253#3624—44no—
254C23×C4⋊C4—171no—
255C22×C22⋊C8—171no—
256C2×#380—171no—
257C2×#340—174no—
258C22×C17—22no—
259C22×C17—22no—
260C22×C17—22no—
261C22×C17—22no—
262C22×C17—22no—
263C22×C17—22no—
264C22×C17#34014yescomplemented
265C22×C17C2×#9511yescharacteristic
266C22×C17#37911yescharacteristic
267C22×C17#38111yescharacteristic
268C22×C17C2×#10211yescharacteristic
269C22×C17C2×#10311yescharacteristic
270C22×C17#41811yescharacteristic
271C22×C17#41911yescharacteristic
272C2×D17—22no—
273C2×D17—22no—
274C2×D17—22no—
275C2×D17—22no—
276C2×D17—22no—
277C2×D17—22no—
278C2×D17—28no—
279C2×D17—28no—
280C2×D17—28no—
281C2×D17—28no—
282C2×D17#34014yescomplemented
283C2×D17#38512yes—
284C2×D17#38612yes—
285C2×D17C2×#10211yescharacteristic
286C2×D17C2×#10311yescharacteristic
287C2×D17#41712yes—
288C2×D17C2×#10611yescharacteristic
289C2×D17C2×#10711yescharacteristic
290C2×D17#42812yes—
291C2×D17#44712yes—
292C2×D17#44812yes—
293C2×D17#45012yes—
294C2×D17#45112yes—
295C2×D17#48012yes—
296C2×D17#48112yes—
297C2×D17#48312yes—
298C2×D17#48412yes—
299#595—84no—
300C4×C17—22no—
301C4×C17—44no—
302C4×C17C4×C22⋊C412yes—
303C4×C17#38012yes—
304Dic17—22no—
305Dic17—44no—
306Dic17#38512yes—
307Dic17#38612yes—
308C24×C4—171no—
309C24×C4—341no—
310C23×C8—172no—
311C22×C4⋊C4—172no—
312C22×C4⋊C4—172no—
313C22×C4⋊C4—171no—
314C22×C4⋊C4—172no—
315C22×C4⋊C4—348no—
316C22×C4⋊C4—341no—
317C22×C4⋊C4—341no—
318C22×C4⋊C4—341no—
319C22×C4⋊C4#59511yescharacteristic, complemented
320C22×C22⋊C4—341no—
321C2×C22⋊C8—174no—
322C2×C22⋊C8—341no—
323C2×C22⋊C8—342no—
324C2×C22⋊C8—341no—
325#380—174no—
326#380—342no—
327C2×#95—341no—
328#340—348no—
329C2×C17—24no—
330C2×C17C22⋊#9511yescharacteristic
331C2×C17C2×#34011yescharacteristic
332C2×C17#173611yescharacteristic
333C2×C17#178611yescharacteristic
334C2×C17#178711yescharacteristic
335C2×C17#182311yescharacteristic
336C2×C17#182411yescharacteristic
337D17—24no—
338D17#185212yes—
339D17#185312yes—
340D17#187212yes—
341D17#187412yes—
342C25—171no—
343C23×C4—21no—
344C23×C4—171no—
345C23×C4—171no—
346C23×C4—172no—
347C23×C4—172no—
348C23×C4—172no—
349C23×C4—172no—
350C23×C4—171no—
351C23×C4—171no—
352C23×C4—171no—
353C23×C4—344no—
354C23×C4—344no—
355C23×C4—342no—
356C23×C4—342no—
357C23×C4—348no—
358C23×C4—341no—
359C23×C4—342no—
360C23×C4—682no—
361C23×C4—682no—
362C23×C4—684no—
363C23×C4C2×#59511yescharacteristic
364C22×C8—174no—
365C22×C8—344no—
366C22×C8—344no—
367C22×C8—342no—
368C22×C8—342no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—24no—
371C2×C4⋊C4—172no—
372C2×C4⋊C4—178no—
373C2×C4⋊C4—174no—
374C2×C4⋊C4—344no—
375C2×C4⋊C4—344no—
376C2×C4⋊C4—348no—
377C2×C4⋊C4—348no—
378C2×C4⋊C4—344no—
379C2×C4⋊C4—342no—
380C2×C4⋊C4—342no—
381C2×C4⋊C4—348no—
382C2×C4⋊C4—341no—
383C2×C4⋊C4—344no—
384C2×C4⋊C4—344no—
385C2×C4⋊C4—344no—
386C2×C4⋊C4—342no—
387C2×C4⋊C4C2×#59512yes—
388C2×C22⋊C4—344no—
389C2×C22⋊C4—682no—
390C2×C22⋊C4—682no—
391C22⋊C8—344no—
392C22⋊C8—344no—
393#95—344no—
394C17#1073011yescharacteristic, complemented, Sylow
395C24—171no—
396C24—171no—
397C24—172no—
398C24—172no—
399C24—172no—
400C24—172no—
401C24—172no—
402C24—172no—
403C24—342no—
404C24—342no—
405C24—342no—
406C24—342no—
407C24C22⋊#59511yescharacteristic
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—24no—
411C22×C4—22no—
412C22×C4—42no—
413C22×C4—42no—
414C22×C4—171no—
415C22×C4—171no—
416C22×C4—171no—
417C22×C4—171no—
418C22×C4—171no—
419C22×C4—174no—
420C22×C4—174no—
421C22×C4—171no—
422C22×C4—172no—
423C22×C4—172no—
424C22×C4—172no—
425C22×C4—172no—
426C22×C4—172no—
427C22×C4—172no—
428C22×C4—172no—
429C22×C4—172no—
430C22×C4—342no—
431C22×C4—342no—
432C22×C4—348no—
433C22×C4—348no—
434C22×C4—348no—
435C22×C4—348no—
436C22×C4—342no—
437C22×C4—342no—
438C22×C4—348no—
439C22×C4—348no—
440C22×C4—342no—
441C22×C4—342no—
442C22×C4—342no—
443C22×C4—342no—
444C22×C4—344no—
445C22×C4—342no—
446C22×C4—344no—
447C22×C4—682no—
448C22×C4—682no—
449C22×C4—684no—
450C22×C4—684no—
451C22×C4—6816no—
452C22×C4—6816no—
453C22×C4—684no—
454C22×C4—682no—
455C22×C4—682no—
456C22×C4—682no—
457C22×C4—682no—
458C22×C4—682no—
459C22×C4—682no—
460C22×C4—682no—
461C22×C4—682no—
462C22×C4C4×#59512yes—
463C22×C4C4⋊#59512yes—
464C22×C4C22⋊#59511yescharacteristic
465C22×C4C22×#59511yescharacteristic
466C2×C8—348no—
467C2×C8—344no—
468C2×C8—684no—
469C2×C8—682no—
470C2×C8—682no—
471C4⋊C4—24no—
472C4⋊C4—22no—
473C4⋊C4—174no—
474C4⋊C4—348no—
475C4⋊C4—348no—
476C4⋊C4—344no—
477C4⋊C4—348no—
478C4⋊C4—342no—
479C4⋊C4—684no—
480C4⋊C4C22⋊#59514yescomplemented
481C22⋊C4—688no—
482C23—21no—
483C23—21no—
484C23—21no—
485C23—21no—
486C23—171no—
487C23—171no—
488C23—172no—
489C23—172no—
490C23—171no—
491C23—171no—
492C23—171no—
493C23—171no—
494C23—172no—
495C23—172no—
496C23—172no—
497C23—172no—
498C23—172no—
499C23—174no—
500C23—174no—
501C23—174no—
502C23—174no—
503C23—344no—
504C23—344no—
505C23—344no—
506C23—344no—
507C23—344no—
508C23—344no—
509C23—344no—
510C23—344no—
511C23—344no—
512C23—344no—
513C23—344no—
514C23—344no—
515C23—341no—
516C23—341no—
517C23—341no—
518C23—341no—
519C23(C2×#595)⋊C412yes—
520C23#1058754712yes—
521C23#1058754912yes—
522C23C2×C22⋊#59511yescharacteristic
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—24no—
526C2×C4—24no—
527C2×C4—24no—
528C2×C4—48no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—171no—
532C2×C4—171no—
533C2×C4—172no—
534C2×C4—172no—
535C2×C4—174no—
536C2×C4—174no—
537C2×C4—174no—
538C2×C4—174no—
539C2×C4—172no—
540C2×C4—344no—
541C2×C4—344no—
542C2×C4—344no—
543C2×C4—344no—
544C2×C4—344no—
545C2×C4—344no—
546C2×C4—341no—
547C2×C4—341no—
548C2×C4—344no—
549C2×C4—344no—
550C2×C4—344no—
551C2×C4—688no—
552C2×C4—688no—
553C2×C4—6816no—
554C2×C4—688no—
555C2×C4—682no—
556C2×C4—682no—
557C2×C4—684no—
558C2×C4—684no—
559C2×C4—684no—
560C2×C4—1362no—
561C2×C4—1362no—
562C2×C4—1362no—
563C2×C4—1362no—
564C2×C4(C2×#595)⋊C412yes—
565C2×C4C2×C4×#59511yescharacteristic
566C2×C4C2×C4⋊#59511yescharacteristic
567C2×C4#1058767712yes—
568C2×C4C2×C22⋊#59512yes—
569C8—684no—
570C22—22no—
571C22—22no—
572C22—22no—
573C22—22no—
574C22—22no—
575C22—22no—
576C22—172no—
577C22—172no—
578C22—172no—
579C22—172no—
580C22—171no—
581C22—171no—
582C22—171no—
583C22—171no—
584C22—172no—
585C22—172no—
586C22—172no—
587C22—172no—
588C22—172no—
589C22—172no—
590C22—172no—
591C22—172no—
592C22—174no—
593C22—348no—
594C22—348no—
595C22—348no—
596C22—348no—
597C22—342no—
598C22—342no—
599C22—342no—
600C22—342no—
601C22—342no—
602C22—342no—
603C22#1176368214yescomplemented
604C22C2×(C2×#595)⋊C411yescharacteristic
605C22#1176375011yescharacteristic
606C22#1176375211yescharacteristic
607C22C2×#1058754711yescharacteristic
608C22C2×#1058754911yescharacteristic
609C22#1176380111yescharacteristic
610C22#1176380211yescharacteristic
611C4—22no—
612C4—44no—
613C4—172no—
614C4—172no—
615C4—342no—
616C4—684no—
617C4—1364no—
618C4C4×C22⋊#59512yes—
619C4#1176375112yes—
620C2—24no—
621C2—172no—
622C2—172no—
623C2—172no—
624C2—172no—
625C2—344no—
626C2#1454395811yescharacteristic
627C2C2×#1176368211yescharacteristic
628C2#1454447111yescharacteristic
629C2#1454462211yescharacteristic
630C2#1454462311yescharacteristic
631C2#1454468711yescharacteristic
632C2#1454468811yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC2×C4×C17C2×C42
FrattiniC22×C4C22×#595
FittingC22×C4⋊C4×C17C4
socleC23×C17C2×C22⋊C4
prime radicalC24×D17D4
cosocleC22×C4×D17C23
hypercenterC22×C4⋊C4#595
hypocenterC17#10730
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#11763682C2semidirect
10. #11763777C4semidirect
13. #11763751C4semidirect
18. C22×C4⋊Dic17C4semidirect
23. C2×C4⋊C4×D17C4semidirect
25. C22×C4⋊C4×C17C4semidirect
55. C2×C4⋊#595C2×C4semidirect
59. C2×#63242C2×C4semidirect
159. C4⋊C4×C17C22⋊C4semidirect
162. C4⋊Dic17C22⋊C4semidirect
264. C22×C17#340semidirect
282. C2×D17#340semidirect
319. C22×C4⋊C4#595semidirect
394. C17#10730semidirect
480. C4⋊C4C22⋊#595semidirect
603. C22#11763682semidirect

Maximal subgroups

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

subgroupindex
C2×#117637772
C2×#117637512
C2×#117636822
C22×C4⋊C4×D172
#1073017