Finite Group Databasebeta

← C4×#11763780 #17968292

Subgroups — C4×#11763780 #17968292

Order 4352.

2246 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×#11763780C212yesmaximal
2C2×C4×#63243C212yesmaximal, complemented
3#14544511C212yesmaximal, complemented
4#14544510C212yesmaximal, complemented
5C4×#10587543C212yesmaximal, complemented
6C4×C22⋊#3624C212yesmaximal, complemented
7#14544448C212yesmaximal, complemented
8C22×C42×D17C211yesmaximal, characteristic
9C22×#63243C2214yes—
10#11763780C4116yesdirect product factor
11C2×#10587543C2214yes—
12C2×C22⋊#3624C2214yes—
13C4×#63243—28no—
14C2×#10587542C2214yescomplemented
15C2×C4×#3624C2214yescomplemented
16#11763675C2214yescomplemented
17#11763675C2214yescomplemented
18C23×C4×D17C411yescharacteristic
19C23×C4×D17C411yescharacteristic
20C23×C4×D17C2211yescharacteristic
21C22×C4×Dic17C411yescharacteristic
22C22×C4×Dic17C2211yescharacteristic
23C22×C4×Dic17C2211yescharacteristic
24C2×C42×D17—28no—
25C2×C42×D17C411yescharacteristic
26C2×C42×D17C411yescharacteristic
27C2×C42×D17C411yescharacteristic
28C2×C42×D17C411yescharacteristic
29C2×C42×D17C2211yescharacteristic
30C2×C42×D17C2211yescharacteristic
31C2×C42×D17C2211yescharacteristic
32C2×C42×D17C2211yescharacteristic
33C22×C42×C17C411yescharacteristic
34C24×D17C2×C411yescharacteristic
35C23×C4×C17C2×C411yescharacteristic
36C23×C4×C17C2×C411yescharacteristic
37C23×C4×C17C2×C411yescharacteristic
38C23×Dic17C2×C411yescharacteristic
39C23×Dic17C2×C411yescharacteristic
40C23×Dic17C2311yescharacteristic
41C22×C4×D17—24no—
42C22×C4×D17—24no—
43C22×C4×D17—24no—
44C22×C4×D17—24no—
45C22×C4×D17—24no—
46C22×C4×D17—24no—
47C22×C4×D17—24no—
48C22×C4×D17—24no—
49C22×C4×D17C2×C411yescharacteristic
50C22×C4×D17C2×C411yescharacteristic
51C22×C4×D17C2×C411yescharacteristic
52C22×C4×D17C2×C411yescharacteristic
53C22×C4×D17C2×C411yescharacteristic
54C22×C4×D17C2×C411yescharacteristic
55C22×C4×D17C2×C418yes—
56C22×C4×D17C2×C411yescharacteristic
57C22×C4×D17C2×C411yescharacteristic
58C22×C4×D17C2×C411yescharacteristic
59C22×C4×D17C2×C411yescharacteristic
60C22×C4×D17C2311yescharacteristic
61C22×C4×D17C2311yescharacteristic
62C22×#3624C2318yes—
63C2×#63243—28no—
64C2×#63243—28no—
65C2×#63243C2×C4116yescomplemented
66C2×C42×C17—24no—
67C2×C42×C17C2×C411yescharacteristic
68C2×C42×C17C2×C411yescharacteristic
69C2×C42×C17C2×C411yescharacteristic
70C2×C42×C17C2×C411yescharacteristic
71C2×C4×Dic17—24no—
72C2×C4×Dic17—24no—
73C2×C4×Dic17—24no—
74C2×C4×Dic17C2×C411yescharacteristic
75C2×C4×Dic17C2×C411yescharacteristic
76C2×C4×Dic17C2×C411yescharacteristic
77C2×C4×Dic17C2×C411yescharacteristic
78C2×C4×Dic17C2×C411yescharacteristic
79C2×C4×Dic17C2×C411yescharacteristic
80C2×C4×Dic17C2×C411yescharacteristic
81C2×C4×Dic17C2×C411yescharacteristic
82C2×C4×Dic17C2311yescharacteristic
83C2×C4×Dic17C2311yescharacteristic
84C2×C4×Dic17C2311yescharacteristic
85C2×C4×Dic17C2311yescharacteristic
86C42×D17—24no—
87C42×D17—24no—
88C42×D17—24no—
89C42×D17—24no—
90C42×D17—24no—
91C42×D17—24no—
92C42×D17—24no—
93C42×D17D418yes—
94C22⋊#3624C2×C4116yescomplemented
95#10587543C2×C4116yescomplemented
96#10587542—28no—
97C4×#3624—28no—
98C24×C17C22×C411yescharacteristic
99C23×D17—22no—
100C23×D17—22no—
101C23×D17—22no—
102C23×D17—22no—
103C23×D17—22no—
104C23×D17—22no—
105C23×D17C4214yes—
106C23×D17C22×C411yescharacteristic
107C23×D17C22×C411yescharacteristic
108C22×C4×C17—22no—
109C22×C4×C17—22no—
110C22×C4×C17—22no—
111C22×C4×C17—22no—
112C22×C4×C17—22no—
113C22×C4×C17—22no—
114C22×C4×C17—22no—
115C22×C4×C17C4214yes—
116C22×C4×C17M1614yescomplemented
117C22×C4×C17C22×C411yescharacteristic
118C22×C4×C17C22×C411yescharacteristic
119C22×C4×C17C22×C411yescharacteristic
120C22×C4×C17C22×C411yescharacteristic
121C22×C4×C17C22×C411yescharacteristic
122C22×C4×C17C22×C411yescharacteristic
123C22×Dic17—22no—
124C22×Dic17—22no—
125C22×Dic17—22no—
126C22×Dic17—22no—
127C22×Dic17—22no—
128C22×Dic17—22no—
129C22×Dic17—22no—
130C22×Dic17M1614yescomplemented
131C22×Dic17C22×C411yescharacteristic
132C22×Dic17C22×C414yes—
133C22×Dic17C22×C411yescharacteristic
134C22×Dic17C22×C411yescharacteristic
135C22×Dic17C22×C411yescharacteristic
136C22×Dic17C22×C411yescharacteristic
137C22×Dic17C2411yescharacteristic
138C2×C4×D17—232no—
139C2×C4×D17—232no—
140C2×C4×D17—22no—
141C2×C4×D17—22no—
142C2×C4×D17—22no—
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—22no—
156C2×C4×D17—22no—
157C2×C4×D17—22no—
158C2×C4×D17—22no—
159C2×C4×D17—22no—
160C2×C4×D17—22no—
161C2×C4×D17—22no—
162C2×C4×D17—22no—
163C2×C4×D17—22no—
164C2×C4×D17—22no—
165C2×C4×D17—22no—
166C2×C4×D17—232no—
167C2×C4×D17C4214yes—
168C2×C4×D17C4214yes—
169C2×C4×D17C22⋊C414yes—
170C2×C4×D17C22⋊C414yes—
171C2×C4×D17M1614yescomplemented
172C2×C4×D17M1614yescomplemented
173C2×C4×D17C22×C414yes—
174C2×C4×D17C22×C414yes—
175C2×C4×D17C2×D414yes—
176C2×C4×D17#4114yes—
177C2×#3624—28no—
178C2×#3624—28no—
179C2×#3624C22×C4116yescomplemented
180#63243—232no—
181C42×C17—22no—
182C42×C17—22no—
183C42×C17—22no—
184C42×C17C22⋊C414yes—
185C4×Dic17—22no—
186C4×Dic17—22no—
187C4×Dic17—22no—
188C4×Dic17—22no—
189C4×Dic17—22no—
190C4×Dic17—22no—
191C4×Dic17—22no—
192C4×Dic17—22no—
193C4×Dic17—22no—
194C4×Dic17C22⋊C414yes—
195C4×Dic17C2×D414yes—
196C4×Dic17C2×D414yes—
197C4×#407—171nomaximal, Sylow
198C23×C17—21no—
199C23×C17—21no—
200C23×C17—21no—
201C23×C17—21no—
202C23×C17C2×C4212yes—
203C23×C17C2×M1612yes—
204C23×C17C2×M1612yes—
205C23×C17C23×C411yescharacteristic
206C22×D17—28no—
207C22×D17—28no—
208C22×D17—28no—
209C22×D17—28no—
210C22×D17—21no—
211C22×D17—21no—
212C22×D17—21no—
213C22×D17—21no—
214C22×D17—21no—
215C22×D17—21no—
216C22×D17—21no—
217C22×D17—21no—
218C22×D17—28no—
219C22×D17—28no—
220C22×D17—28no—
221C22×D17C2×C4212yes—
222C22×D17C2×C4212yes—
223C22×D17C2×C22⋊C412yes—
224C22×D17#11712yes—
225C22×D17C2×M1612yes—
226C22×D17C2×M1612yes—
227C2×C4×C17—28no—
228C2×C4×C17—21no—
229C2×C4×C17—21no—
230C2×C4×C17—21no—
231C2×C4×C17—21no—
232C2×C4×C17—21no—
233C2×C4×C17—21no—
234C2×C4×C17—21no—
235C2×C4×C17—21no—
236C2×C4×C17—28no—
237C2×C4×C17—28no—
238C2×C4×C17C2×C4212yes—
239C2×C4×C17C2×C4212yes—
240C2×C4×C17C2×C22⋊C412yes—
241C2×C4×C17C2×C22⋊C412yes—
242C2×C4×C17C2×C22⋊C412yes—
243C2×C4×C17#11712yes—
244C2×C4×C17C2×M1612yes—
245C2×C4×C17C2×M1612yes—
246C2×C4×C17C2×M1612yes—
247C2×C4×C17C2×M1612yes—
248C2×Dic17—28no—
249C2×Dic17—21no—
250C2×Dic17—21no—
251C2×Dic17—21no—
252C2×Dic17—21no—
253C2×Dic17—21no—
254C2×Dic17—21no—
255C2×Dic17—21no—
256C2×Dic17—21no—
257C2×Dic17—28no—
258C2×Dic17—28no—
259C2×Dic17C2×C4212yes—
260C2×Dic17C2×C22⋊C412yes—
261C2×Dic17C2×C22⋊C412yes—
262C2×Dic17C2×M1612yes—
263C2×Dic17C2×M1612yes—
264C2×Dic17C2×M1612yes—
265C2×Dic17C2×M1612yes—
266C2×Dic17C23×C412yes—
267C2×Dic17C22×D412yes—
268C2×Dic17C2×#4112yes—
269C4×D17—28no—
270C4×D17—28no—
271C4×D17—28no—
272C4×D17—28no—
273C4×D17—28no—
274C4×D17—28no—
275C4×D17—28no—
276C4×D17—28no—
277C4×D17—28no—
278C4×D17—28no—
279C4×D17—28no—
280C4×D17C4×D4116yes—
281#3624—216no—
282C23×C42—171no—
283C2×#407—172no—
284C2×C4×M16—172no—
285#1749—172no—
286#1749—172no—
287C4×C22⋊C8—172no—
288C4×C22⋊C8—172no—
289#1728—172no—
290C22×C17—22no—
291C22×C17—22no—
292C22×C17—22no—
293C22×C17—22no—
294C22×C17—22no—
295C22×C17—22no—
296C22×C17C4×M1614yescomplemented
297C22×C17C22×C4211yescharacteristic
298C22×C17C22×C22⋊C411yescharacteristic
299C22×C17C2×#11711yescharacteristic
300C22×C17C22×M1611yescharacteristic
301C22×C17C22×M1611yescharacteristic
302C22×C17C22×M1611yescharacteristic
303C22×C17C22×M1611yescharacteristic
304C2×D17—232no—
305C2×D17—22no—
306C2×D17—22no—
307C2×D17—22no—
308C2×D17—22no—
309C2×D17—22no—
310C2×D17—22no—
311C2×D17—22no—
312C2×D17—22no—
313C2×D17—22no—
314C2×D17—22no—
315C2×D17—22no—
316C2×D17—22no—
317C2×D17C4×C22⋊C414yes—
318C2×D17C4×M1614yescomplemented
319C4×C17—22no—
320C4×C17—22no—
321C4×C17—22no—
322C4×C17—22no—
323C4×C17C4×C22⋊C414yes—
324C4×C17#40714yescomplemented
325Dic17—22no—
326Dic17—22no—
327Dic17—22no—
328Dic17—22no—
329Dic17#40714yescomplemented
330Dic17C2×C4×D414yes—
331C24×C4—171no—
332C24×C4—171no—
333C24×C4—171no—
334C22×M16—174no—
335C22×C42—171no—
336C22×C42—171no—
337C22×C42—171no—
338C22×C42—171no—
339C22×C42—171no—
340C22×C42—171no—
341C22×C42—171no—
342C22×C42—171no—
343C22×C42—171no—
344C22×C42—171no—
345C22×C42—171no—
346C22×C42—348no—
347C22×C42#59511yescharacteristic
348#407—1716no—
349C2×C22⋊C8—174no—
350C2×C22⋊C8—174no—
351C4×M16—348no—
352C2×#97—174no—
353C2×C4×C8—174no—
354#336—174no—
355#336—174no—
356C2×C17—24no—
357C2×C17C2×C4×C22⋊C411yescharacteristic
358C2×C17C2×C4×M1611yescharacteristic
359C2×C17C2×C4×M1611yescharacteristic
360C2×C17C2×#40711yescharacteristic
361C2×C17C2×#40711yescharacteristic
362C2×C17#292011yescharacteristic
363C2×C17#292011yescharacteristic
364D17—24no—
365D17—24no—
366C25—171no—
367C23×C4—171no—
368C23×C4—171no—
369C23×C4—171no—
370C23×C4—178no—
371C23×C4—171no—
372C23×C4—171no—
373C23×C4—171no—
374C23×C4—171no—
375C23×C4—171no—
376C23×C4—171no—
377C23×C4—171no—
378C23×C4—171no—
379C23×C4—171no—
380C23×C4—171no—
381C23×C4—171no—
382C23×C4—171no—
383C23×C4—344no—
384C23×C4—344no—
385C23×C4—344no—
386C23×C4—344no—
387C23×C4—344no—
388C23×C4—344no—
389C23×C4—344no—
390C23×C4—344no—
391C23×C4C2×#59511yescharacteristic
392C23×C4C2×#59511yescharacteristic
393C23×C4C2×#59511yescharacteristic
394C2×M16—1716no—
395C2×M16—348no—
396C2×M16—348no—
397C22×C8—178no—
398C2×C42—24no—
399C2×C42—171no—
400C2×C42—171no—
401C2×C42—171no—
402C2×C42—178no—
403C2×C42—171no—
404C2×C42—171no—
405C2×C42—171no—
406C2×C42—171no—
407C2×C42—171no—
408C2×C42—171no—
409C2×C42—171no—
410C2×C42—171no—
411C2×C42—171no—
412C2×C42—344no—
413C2×C42—344no—
414C2×C42—344no—
415C2×C42—344no—
416C2×C42—344no—
417C2×C42—344no—
418C2×C42—344no—
419C2×C42—344no—
420C2×C42—344no—
421C2×C42—344no—
422C2×C42C2×#59511yescharacteristic
423C2×C42C2×#59511yescharacteristic
424C2×C42C2×#59511yescharacteristic
425C2×C42C2×#59511yescharacteristic
426C22⋊C8—1716no—
427C22⋊C8—1716no—
428#97—348no—
429C4×C8—348no—
430C17C4×#40711yescharacteristic, complemented, Sylow
431C24—171no—
432C24—171no—
433C24—174no—
434C24—342no—
435C24—342no—
436C24—342no—
437C24—342no—
438C24—342no—
439C24—342no—
440C24C22×#59511yescharacteristic
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—171no—
449C22×C4—171no—
450C22×C4—174no—
451C22×C4—174no—
452C22×C4—174no—
453C22×C4—174no—
454C22×C4—174no—
455C22×C4—171no—
456C22×C4—171no—
457C22×C4—171no—
458C22×C4—171no—
459C22×C4—174no—
460C22×C4—174no—
461C22×C4—174no—
462C22×C4—174no—
463C22×C4—174no—
464C22×C4—174no—
465C22×C4—174no—
466C22×C4—342no—
467C22×C4—342no—
468C22×C4—342no—
469C22×C4—342no—
470C22×C4—342no—
471C22×C4—342no—
472C22×C4—342no—
473C22×C4—342no—
474C22×C4—342no—
475C22×C4—342no—
476C22×C4—3432no—
477C22×C4—342no—
478C22×C4—342no—
479C22×C4—342no—
480C22×C4—342no—
481C22×C4—342no—
482C22×C4—342no—
483C22×C4—3432no—
484C22×C4—3432no—
485C22×C4—342no—
486C22×C4—342no—
487C22×C4—342no—
488C22×C4—342no—
489C22×C4—342no—
490C22×C4—342no—
491C22×C4—342no—
492C22×C4—342no—
493C22×C4—342no—
494C22×C4—342no—
495C22×C4—342no—
496C22×C4—342no—
497C22×C4—342no—
498C22×C4—342no—
499C22×C4—342no—
500C22×C4—342no—
501C22×C4—342no—
502C22×C4#6324314yescomplemented
503C22×C4C4×#59514yes—
504C22×C4C22×#59511yescharacteristic
505C22×C4C22×#59511yescharacteristic
506C22×C4C22×#59511yescharacteristic
507C22×C4C22×#59511yescharacteristic
508C22×C4C22×#59511yescharacteristic
509C22×C4C22×#59511yescharacteristic
510M16—3432no—
511C2×C8—1716no—
512C2×C8—348no—
513C2×C8—348no—
514C42—22no—
515C42—22no—
516C42—22no—
517C42—174no—
518C42—174no—
519C42—174no—
520C42—342no—
521C42—342no—
522C42—342no—
523C42—342no—
524C42—342no—
525C42—342no—
526C42—342no—
527C42—342no—
528C42—342no—
529C42C22⋊#59514yes—
530C23—21no—
531C23—21no—
532C23—21no—
533C23—21no—
534C23—172no—
535C23—172no—
536C23—172no—
537C23—172no—
538C23—172no—
539C23—172no—
540C23—348no—
541C23—348no—
542C23—348no—
543C23—348no—
544C23—348no—
545C23—348no—
546C23—348no—
547C23—341no—
548C23—341no—
549C23—341no—
550C23—341no—
551C23—341no—
552C23—341no—
553C23—341no—
554C23—341no—
555C23C2×#6324312yes—
556C23D17⋊M1612yes—
557C23C2×C4×#59512yes—
558C23C23×#59511yescharacteristic
559C2×C4—28no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—28no—
569C2×C4—28no—
570C2×C4—172no—
571C2×C4—172no—
572C2×C4—172no—
573C2×C4—172no—
574C2×C4—172no—
575C2×C4—172no—
576C2×C4—1716no—
577C2×C4—172no—
578C2×C4—172no—
579C2×C4—172no—
580C2×C4—172no—
581C2×C4—348no—
582C2×C4—348no—
583C2×C4—348no—
584C2×C4—348no—
585C2×C4—348no—
586C2×C4—348no—
587C2×C4—348no—
588C2×C4—348no—
589C2×C4—348no—
590C2×C4—348no—
591C2×C4—348no—
592C2×C4—341no—
593C2×C4—341no—
594C2×C4—341no—
595C2×C4—341no—
596C2×C4—341no—
597C2×C4—341no—
598C2×C4—341no—
599C2×C4—341no—
600C2×C4—348no—
601C2×C4—348no—
602C2×C4—348no—
603C2×C4C2×#6324312yes—
604C2×C4C2×#6324312yes—
605C2×C4D17⋊M1612yes—
606C2×C4D17⋊M1612yes—
607C2×C4C2×C4×#59512yes—
608C2×C4C2×C4×#59512yes—
609C2×C4#1058767712yes—
610C2×C4C2×C22⋊#59512yes—
611C2×C4C2×C22⋊#59512yes—
612C2×C4C2×C22⋊#59512yes—
613C8—3416no—
614C22—22no—
615C22—22no—
616C22—22no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—174no—
621C22—174no—
622C22—3432no—
623C22—342no—
624C22—342no—
625C22—342no—
626C22—342no—
627C22—342no—
628C22—342no—
629C22—342no—
630C22—342no—
631C22—342no—
632C22—342no—
633C22—342no—
634C22—342no—
635C22C4×#6324314yescomplemented
636C22C22×C4×#59511yescharacteristic
637C22C22×C22⋊#59511yescharacteristic
638C22C2×#1058767711yescharacteristic
639C22C2×D17⋊M1611yescharacteristic
640C22C2×D17⋊M1611yescharacteristic
641C22C2×D17⋊M1611yescharacteristic
642C22C22×#6324311yescharacteristic
643C4—22no—
644C4—22no—
645C4—22no—
646C4—22no—
647C4—174no—
648C4—174no—
649C4—342no—
650C4—342no—
651C4—342no—
652C4—342no—
653C4C4×C22⋊#59514yes—
654C4#1176378014yesdirect product factor
655C2—24no—
656C2—344no—
657C2—344no—
658C2C2×C4×C22⋊#59511yescharacteristic
659C2C4×D17⋊M1611yescharacteristic
660C2C2×C4×#6324311yescharacteristic
661C2D17⋊#40711yescharacteristic
662C2C2×#1176378011yescharacteristic
663C2#1454546111yescharacteristic
664C2#1454546311yescharacteristic
subgroupG/H
centerC22×C4C22×#595
commutatorC22×C17C22×C42
FrattiniC23C23×#595
FittingC22×C42×C17C4
socleC23×C17C23×C4
prime radicalC24×D17C2×C4
cosocleC22×Dic17C24
hypercenterC22×C42#595
hypocenterC17C4×#407
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
2. C2×C4×#63243C2semidirect
3. #14544511C2semidirect
4. #14544510C2semidirect
5. C4×#10587543C2semidirect
6. C4×C22⋊#3624C2semidirect
7. #14544448C2semidirect
10. #11763780C4direct (N × H)
14. C2×#10587542C22semidirect
15. C2×C4×#3624C22semidirect
16. #11763675C22semidirect
17. #11763675C22semidirect
65. C2×#63243C2×C4semidirect
94. C22⋊#3624C2×C4semidirect
95. #10587543C2×C4semidirect
116. C22×C4×C17M16semidirect
130. C22×Dic17M16semidirect
171. C2×C4×D17M16semidirect
172. C2×C4×D17M16semidirect
179. C2×#3624C22×C4semidirect
296. C22×C17C4×M16semidirect
318. C2×D17C4×M16semidirect
324. C4×C17#407semidirect
329. Dic17#407semidirect
430. C17C4×#407semidirect
502. C22×C4#63243semidirect
635. C22C4×#63243semidirect
654. C4#11763780direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117637802
C2×C4×#632432
#145445112
#145445102
C4×#105875432
C4×C22⋊#36242
#145444482
C22×C42×D172
C4×#40717