Finite Group Databasebeta

← C4×#11763030 #17040557

Subgroups — C4×#11763030 #17040557

Order 4352.

1016 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×#11763030C211yesmaximal, characteristic
2C2×C4×Dic68C211yesmaximal, characteristic, complemented
3C2×C4×#63229C211yesmaximal, characteristic
4C4×#10587622C211yesmaximal, characteristic
5C4×#10587573C211yesmaximal, characteristic, complemented
6#14529715C211yesmaximal, characteristic
7#14529555C211yesmaximal, characteristic, complemented
8#14529416C211yesmaximal, characteristic, complemented
9#14529406C211yesmaximal, characteristic
10#14529136C211yesmaximal, characteristic
11#14529126C211yesmaximal, characteristic, complemented
12#14528798C211yesmaximal, characteristic, complemented
13C4×#10587485C211yesmaximal, characteristic, complemented
14C4×#10587481C211yesmaximal, characteristic, complemented
15C4×C17×#102C211yesmaximal, characteristic
16C22×Dic68C2211yescharacteristic
17C22×#63229C2211yescharacteristic
18C2×#10587622C2211yescharacteristic
19C2×C4×Dic34C2211yescharacteristic
20C2×C4×Dic34C2211yescharacteristic
21C2×#10587573C2211yescharacteristic
22C2×#10587573C2211yescharacteristic
23#11763030C418yesdirect product factor
24C4×Dic68—24no—
25C4×#63229—24no—
26C2×#10587489C2211yescharacteristic
27C2×#10587479C2211yescharacteristic
28C2×#10587485C2211yescharacteristic
29C2×#10587485C2211yescharacteristic
30C2×#10587487C2211yescharacteristic
31C2×#10587487C2211yescharacteristic
32C2×#10587481C2211yescharacteristic
33C2×#10587481C2211yescharacteristic
34C2×#10587481C2211yescharacteristic
35C2×#10587503C2211yescharacteristic
36C2×C4×#3622C2211yescharacteristic
37#11762714C2211yescharacteristic
38#11762712C2211yescharacteristic
39#11762703—21no—
40#11762703—21no—
41#11762674C2211yescharacteristic
42C4⋊C4×Dic17C2211yescharacteristic
43C4⋊C4×Dic17C2211yescharacteristic
44C4×#63225—21no—
45#11762660—21no—
46#11762660—21no—
47C4×C22⋊Dic17—21no—
48C4×C22⋊Dic17—21no—
49C42×Dic17—21no—
50C42×Dic17C2211yescharacteristic
51#11762571C2211yescharacteristic
52#11762571C2211yescharacteristic
53#11762563C2211yescharacteristic
54#11762563C2211yescharacteristic
55C2×C4×D4×C17C2211yescharacteristic
56C2×C17×#102C2211yescharacteristic
57C2×C17×#102C2211yescharacteristic
58C2×C4×C8×C17C2211yescharacteristic
59C4×C4⋊C4×C17C2211yescharacteristic
60C17×#340C2211yescharacteristic
61C17×#340C2211yescharacteristic
62C22×D4×C17C2311yescharacteristic
63C23×C4×C17—21no—
64C22×Dic34C2311yescharacteristic
65C22×Dic34C2311yescharacteristic
66C22×C8×C17C2311yescharacteristic
67C22×C8×C17C2311yescharacteristic
68C4×D4×C17—22no—
69C4×D4×C17—22no—
70C2×C4⋊C4×C17C2311yescharacteristic
71C2×C4⋊C4×C17C2311yescharacteristic
72C2×C4⋊C4×C17C2311yescharacteristic
73C2×C22⋊C4×C17—21no—
74C2×C42×C17—21no—
75C2×C42×C17C2311yescharacteristic
76C2×C22⋊Dic17—21no—
77C2×C22⋊Dic17—21no—
78C2×C22⋊Dic17—21no—
79C2×C22⋊Dic17—21no—
80#10587622—22no—
81#10587622C2×C414yes—
82C2×#63229—22no—
83C2×#63229—22no—
84C2×#63229C2×C414yes—
85C2×C4⋊Dic17C2311yescharacteristic
86C2×C4⋊Dic17C2311yescharacteristic
87C2×#63225—21no—
88C2×#63225—21no—
89C2×#63225—21no—
90C2×#63225—21no—
91C2×C4×Dic17—21no—
92C2×C4×Dic17—21no—
93C2×C4×Dic17—21no—
94C2×C4×Dic17—21no—
95C2×C4×Dic17—21no—
96C2×C4×Dic17—21no—
97C2×C4×Dic17D411yescharacteristic
98C2×C4×Dic17D411yescharacteristic
99C2×C4×Dic17D411yescharacteristic
100C2×C4×Dic17D411yescharacteristic
101C2×C4×Dic17C2311yescharacteristic
102C2×C4×Dic17C2311yescharacteristic
103C22×#3622C2311yescharacteristic
104C22×#3622C2311yescharacteristic
105C2×Dic68—22no—
106C2×Dic68—22no—
107C2×Dic68C2×C414yescomplemented
108#10587573—22no—
109#10587573—22no—
110#10587573—22no—
111#10587573C2×C414yescomplemented
112C4×Dic34—22no—
113C4×Dic34—22no—
114C4×Dic34—22no—
115C4×Dic34D414yes—
116C17×#102—22no—
117C17×#102C2×C414yes—
118C4×C8×C17—22no—
119C17×#95—21no—
120#10587503—22no—
121#10587502—21no—
122#10587502—21no—
123#10587502—21no—
124#10587502—21no—
125#10587502—21no—
126#10587502—21no—
127#10587489—22no—
128#10587487—22no—
129#10587487—22no—
130#10587485—22no—
131#10587485C2×C414yescomplemented
132#10587481—22no—
133#10587481—22no—
134#10587481C2×C414yescomplemented
135#10587479—22no—
136C4×#3622—22no—
137C24×C17—21no—
138C2×D4×C17—21no—
139C2×D4×C17—21no—
140C2×D4×C17—21no—
141C2×D4×C17—21no—
142C2×D4×C17—21no—
143C2×D4×C17C22×C412yes—
144C22×C4×C17—21no—
145C22×C4×C17—21no—
146C22×C4×C17—21no—
147C22×C4×C17—42no—
148C22×C4×C17—42no—
149C22×C4×C17—42no—
150C22×C4×C17C2×D411yescharacteristic
151C22×C4×C17C2×D411yescharacteristic
152C22×C4×C17C2411yescharacteristic
153C22×Dic17—21no—
154C22×Dic17—21no—
155C22×Dic17—21no—
156C22×Dic17—21no—
157C22×Dic17C2×D411yescharacteristic
158C22×Dic17C2×D411yescharacteristic
159C22×Dic17C2×D411yescharacteristic
160C22×Dic17C2×D411yescharacteristic
161C2×Dic34—21no—
162C2×Dic34—21no—
163C2×Dic34—21no—
164C2×Dic34—21no—
165C2×Dic34—21no—
166C2×Dic34—21no—
167C2×Dic34—21no—
168C2×Dic34—21no—
169C2×Dic34C22×C412yes—
170C2×Dic34C22×C412yes—
171C2×Dic34C2×D412yes—
172C2×Dic34#4112yes—
173C2×C8×C17—21no—
174C2×C8×C17—21no—
175C2×C8×C17—21no—
176C2×C8×C17—21no—
177C2×C8×C17—21no—
178C2×C8×C17C22×C412yes—
179C4⋊C4×C17—21no—
180C4⋊C4×C17—21no—
181C4⋊C4×C17—21no—
182C4⋊C4×C17—21no—
183C4⋊C4×C17C22×C412yes—
184C4⋊C4×C17#4112yes—
185C22⋊C4×C17—42no—
186C42×C17—42no—
187C42×C17C2×D412yes—
188C42×C17#4112yes—
189C22⋊Dic17—24no—
190C22⋊Dic17—24no—
191C22⋊Dic17—42no—
192C22⋊Dic17—42no—
193#63229—28no—
194C4⋊Dic17—21no—
195C4⋊Dic17—21no—
196C4⋊Dic17—21no—
197C4⋊Dic17C2×D412yes—
198#63225—24no—
199#63225—24no—
200#63225—24no—
201#63225—42no—
202C4×Dic17—24no—
203C4×Dic17—24no—
204C4×Dic17—22no—
205C4×Dic17—22no—
206C4×Dic17—21no—
207C4×Dic17—21no—
208C4×Dic17—24no—
209C4×Dic17—22no—
210C4×Dic17—41no—
211C4×Dic17—42no—
212C4×Dic17—42no—
213C4×Dic17—42no—
214C4×Dic17C22×C412yes—
215C4×Dic17#4112yes—
216C2×#3622—21no—
217C2×#3622—21no—
218C2×#3622—21no—
219C2×#3622—21no—
220C2×#3622—21no—
221C2×#3622C22×C412yes—
222Dic68—28no—
223C4×#464—171nomaximal, Sylow
224C23×C17—22no—
225C23×C17—41no—
226C23×C17—41no—
227C23×C17—41no—
228C23×C17—41no—
229C23×C17—41no—
230C23×C17—41no—
231C23×C17C22×D411yescharacteristic
232D4×C17—22no—
233D4×C17—22no—
234D4×C17—41no—
235D4×C17—41no—
236C2×C4×C17—21no—
237C2×C4×C17—21no—
238C2×C4×C17—22no—
239C2×C4×C17—22no—
240C2×C4×C17—41no—
241C2×C4×C17—41no—
242C2×C4×C17—41no—
243C2×C4×C17—41no—
244C2×C4×C17—41no—
245C2×C4×C17—41no—
246C2×C4×C17—41no—
247C2×C4×C17—84no—
248C2×C4×C17#12112yes—
249C2×C4×C17#12112yes—
250C2×C4×C17#13512yes—
251C2×C4×C17#13712yes—
252C2×C4×C17C23×C411yescharacteristic
253C2×C4×C17C22×D411yescharacteristic
254C2×C4×C17C2×#4111yescharacteristic
255C2×C4×C17C2×#4111yescharacteristic
256C2×C4×C17C2×#4111yescharacteristic
257C2×C4×C17C2×#4111yescharacteristic
258C2×Dic17—22no—
259C2×Dic17—22no—
260C2×Dic17—22no—
261C2×Dic17—21no—
262C2×Dic17—21no—
263C2×Dic17—21no—
264C2×Dic17—21no—
265C2×Dic17—21no—
266C2×Dic17—21no—
267C2×Dic17—22no—
268C2×Dic17—22no—
269C2×Dic17—21no—
270C2×Dic17—21no—
271C2×Dic17—21no—
272C2×Dic17—41no—
273C2×Dic17—41no—
274C2×Dic17—41no—
275C2×Dic17—41no—
276C2×Dic17—41no—
277C2×Dic17—41no—
278C2×Dic17—41no—
279C2×Dic17C4×D412yes—
280C2×Dic17C4×D412yes—
281C2×Dic17#13512yes—
282Dic34—22no—
283Dic34—22no—
284Dic34—22no—
285Dic34—22no—
286Dic34—22no—
287Dic34—41no—
288Dic34—41no—
289Dic34C4×D414yes—
290C8×C17—22no—
291C8×C17—41no—
292#3622—22no—
293#3622—41no—
294C2×#464—171no—
295C2×C4×Q16—171no—
296C2×C4×SD16—171no—
297C4×#124—171no—
298C42×Q8—171no—
299#1983—171no—
300#1949—171no—
301#1927—171no—
302#1925—171no—
303#1880—171no—
304#1878—171no—
305#1805—171no—
306C4×C4⋊C8—171no—
307C4×#103—171no—
308C4×#102D1711yescharacteristic
309C22×C17—42no—
310C22×C17—42no—
311C22×C17—42no—
312C22×C17—81no—
313C22×C17—81no—
314C22×C17—81no—
315C22×C17—81no—
316C22×C17C2×C4×D411yescharacteristic
317C22×C17C2×#12111yescharacteristic
318C22×C17#52511yescharacteristic
319C22×C17C2×#13511yescharacteristic
320C22×C17C2×#13511yescharacteristic
321C22×C17C2×#13711yescharacteristic
322C22×C17#57511yescharacteristic
323C4×C17—22no—
324C4×C17—42no—
325C4×C17—42no—
326C4×C17—81no—
327C4×C17#46414yescomplemented
328C4×C17C2×C4×D411yescharacteristic
329C4×C17C4×#4111yescharacteristic
330C4×C17#52911yescharacteristic
331C4×C17#53211yescharacteristic
332Dic17—22no—
333Dic17—22no—
334Dic17—22no—
335Dic17—24no—
336Dic17—41no—
337Dic17—42no—
338Dic17—42no—
339Dic17—81no—
340C22×Q16—171no—
341C22×SD16—171no—
342C2×#124—171no—
343C2×C4×Q8—171no—
344C2×C4×Q8—171no—
345C2×C4×Q8—171no—
346C2×C4×Q8—171no—
347C2×C4×D4C2×D1711yescharacteristic
348#464—178no—
349C4×Q16—344no—
350C4×SD16—344no—
351C2×#107—171no—
352C2×#106—171no—
353C2×C4⋊C8—171no—
354C2×C4⋊C8—171no—
355C2×#103—171no—
356C2×#103—171no—
357C2×#103—171no—
358C2×#103—171no—
359C2×#103—171no—
360C2×#102—171no—
361C2×#102C2×D1711yescharacteristic
362C2×#102C2×D1711yescharacteristic
363C2×C4×C8—171no—
364C2×C4×C8C2×D1711yescharacteristic
365#391—171no—
366#390—171no—
367#388—341no—
368#388—341no—
369#382—171no—
370C4×C4⋊C4—171no—
371C4×C4⋊C4—171no—
372C4×C4⋊C4—341no—
373C4×C4⋊C4—341no—
374C4×C4⋊C4—341no—
375C4×C4⋊C4C2×D1711yescharacteristic
376C4×C22⋊C4—341no—
377C4×C22⋊C4—341no—
378C43—171no—
379C43—341no—
380#340—171no—
381#340—171no—
382#340C2×D1711yescharacteristic
383#340C2×D1711yescharacteristic
384#336—171no—
385#336—171no—
386C2×C17—82no—
387C2×C17C4×#12111yescharacteristic
388C2×C17C4×#13511yescharacteristic
389C2×C17C4×#13711yescharacteristic
390C2×C17C2×#46411yescharacteristic
391C2×C17#303511yescharacteristic
392C2×C17#310211yescharacteristic
393C2×C17#310811yescharacteristic
394C22×Q8—171no—
395C22×Q8—171no—
396C22×D4C22×D1711yescharacteristic
397C23×C4—21no—
398C2×Q16—174no—
399C2×Q16—342no—
400C2×Q16—342no—
401C2×SD16—174no—
402C2×SD16—342no—
403C2×SD16—342no—
404C22×C8—171no—
405C22×C8—171no—
406C22×C8C22×D1711yescharacteristic
407C22×C8C22×D1711yescharacteristic
408#124—174no—
409#124—342no—
410C4×Q8—174no—
411C4×Q8—174no—
412C4×Q8—342no—
413C4×Q8—342no—
414C4×Q8—342no—
415C4×Q8—342no—
416C4×Q8—342no—
417C4×Q8—342no—
418C4×D4—22no—
419C4×D4—22no—
420C2×C4⋊C4—171no—
421C2×C4⋊C4—171no—
422C2×C4⋊C4—341no—
423C2×C4⋊C4—341no—
424C2×C4⋊C4—341no—
425C2×C4⋊C4—341no—
426C2×C4⋊C4C22×D1711yescharacteristic
427C2×C4⋊C4C22×D1711yescharacteristic
428C2×C4⋊C4C22×D1711yescharacteristic
429C2×C22⋊C4—21no—
430C2×C22⋊C4—341no—
431C2×C22⋊C4—341no—
432C2×C22⋊C4—341no—
433C2×C22⋊C4—341no—
434C2×C42—21no—
435C2×C42—171no—
436C2×C42—171no—
437C2×C42—171no—
438C2×C42—171no—
439C2×C42—171no—
440C2×C42—171no—
441C2×C42—341no—
442C2×C42—341no—
443C2×C42—341no—
444C2×C42—341no—
445C2×C42—341no—
446C2×C42—341no—
447C2×C42C22×D1711yescharacteristic
448#107—342no—
449#106—342no—
450C4⋊C8—174no—
451C4⋊C8—342no—
452#103—174no—
453#103—342no—
454#103—342no—
455#103—342no—
456#103—342no—
457#102—22no—
458#102—342no—
459#102C4×D1714yes—
460C4×C8—22no—
461C4×C8—342no—
462#95—21no—
463#95—341no—
464#95—341no—
465#95—341no—
466#95—341no—
467#95—341no—
468#95—341no—
469C17C4×#46411yescharacteristic, complemented, Sylow
470C24—21no—
471C2×Q8—172no—
472C2×Q8—172no—
473C2×Q8—172no—
474C2×Q8—172no—
475C2×Q8—341no—
476C2×Q8—341no—
477C2×Q8—341no—
478C2×Q8—341no—
479C2×Q8—341no—
480C2×Q8—341no—
481C2×Q8—341no—
482C2×Q8—341no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4C2×C4×D1712yes—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—171no—
496C22×C4—171no—
497C22×C4—171no—
498C22×C4—171no—
499C22×C4—341no—
500C22×C4—341no—
501C22×C4—341no—
502C22×C4—341no—
503C22×C4D4×D1711yescharacteristic
504C22×C4D4×D1711yescharacteristic
505C22×C4C23×D1711yescharacteristic
506Q16—348no—
507SD16—348no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—172no—
514C2×C8—341no—
515C2×C8—341no—
516C2×C8—341no—
517C2×C8—341no—
518C2×C8—341no—
519C2×C8C2×C4×D1712yes—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—172no—
525C4⋊C4—344no—
526C4⋊C4—344no—
527C4⋊C4—341no—
528C4⋊C4—344no—
529C4⋊C4—341no—
530C4⋊C4—341no—
531C4⋊C4—682no—
532C4⋊C4C2×C4×D1712yes—
533C4⋊C4#6325212yes—
534C22⋊C4—42no—
535C22⋊C4—344no—
536C22⋊C4—344no—
537C22⋊C4—682no—
538C22⋊C4—682no—
539C42—42no—
540C42—172no—
541C42—172no—
542C42—342no—
543C42—344no—
544C42—344no—
545C42—341no—
546C42—341no—
547C42—344no—
548C42—342no—
549C42—342no—
550C42—681no—
551C42—682no—
552C42—682no—
553C42—682no—
554C42#6325212yes—
555C42D4×D1712yes—
556C23—22no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23C2×D4×D1711yescharacteristic
564Q8—174no—
565Q8—342no—
566Q8—342no—
567Q8—342no—
568Q8—342no—
569Q8—342no—
570Q8—681no—
571Q8—681no—
572D4—22no—
573D4—22no—
574D4—41no—
575D4—41no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—84no—
588C2×C4—172no—
589C2×C4—172no—
590C2×C4—172no—
591C2×C4—342no—
592C2×C4—342no—
593C2×C4—341no—
594C2×C4—342no—
595C2×C4—341no—
596C2×C4—341no—
597C2×C4—341no—
598C2×C4—341no—
599C2×C4—341no—
600C2×C4—342no—
601C2×C4—342no—
602C2×C4—341no—
603C2×C4—341no—
604C2×C4—341no—
605C2×C4—681no—
606C2×C4—681no—
607C2×C4—681no—
608C2×C4—681no—
609C2×C4—681no—
610C2×C4—681no—
611C2×C4—681no—
612C2×C4#1058757012yes—
613C2×C4#1058757012yes—
614C2×C4#1058759812yes—
615C2×C4#1058760112yes—
616C2×C4C22×C4×D1711yescharacteristic
617C2×C4C2×#6325211yescharacteristic
618C2×C4C2×#6325211yescharacteristic
619C2×C4C2×D4×D1711yescharacteristic
620C2×C4#41×D1711yescharacteristic
621C2×C4#41×D1711yescharacteristic
622C8—22no—
623C8—41no—
624C8—342no—
625C8—681no—
626C22—42no—
627C22—42no—
628C22—42no—
629C22—81no—
630C22—81no—
631C22—81no—
632C22—81no—
633C22C4×D4×D1711yescharacteristic
634C22C2×#1058757011yescharacteristic
635C22#1176331811yescharacteristic
636C22#135×D1711yescharacteristic
637C22C2×#1058759811yescharacteristic
638C22C2×#1058760111yescharacteristic
639C22#1176360611yescharacteristic
640C4—22no—
641C4—42no—
642C4—42no—
643C4—81no—
644C4—342no—
645C4—342no—
646C4—342no—
647C4—344no—
648C4—681no—
649C4—682no—
650C4—682no—
651C4—1361no—
652C4#1176303014yesdirect product factor
653C4C4×D4×D1711yescharacteristic
654C4C4×#6325211yescharacteristic
655C4#1176333711yescharacteristic
656C4#1176335611yescharacteristic
657C2—82no—
658C2C4×#1058757011yescharacteristic
659C2C4×#1058759811yescharacteristic
660C2C4×#1058760111yescharacteristic
661C2C2×#1176303011yescharacteristic
662C2#1453823711yescharacteristic
663C2#1453879811yescharacteristic
664C2#1453886211yescharacteristic
subgroupG/H
centerC22×C4D4×D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC4×C17×#102C2
socleC23×C17C22×D4
prime radicalC22×D4×C17C23
cosocleC22×C4×C17C24
hypercenterC4×#102D17
hypocenterC17C4×#464
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
2. C2×C4×Dic68C2semidirect
5. C4×#10587573C2semidirect
7. #14529555C2semidirect
8. #14529416C2semidirect
11. #14529126C2semidirect
12. #14528798C2semidirect
13. C4×#10587485C2semidirect
14. C4×#10587481C2semidirect
23. #11763030C4direct (N × H)
107. C2×Dic68C2×C4semidirect
111. #10587573C2×C4semidirect
131. #10587485C2×C4semidirect
134. #10587481C2×C4semidirect
327. C4×C17#464semidirect
469. C17C4×#464semidirect
652. C4#11763030direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117630302
C2×C4×Dic682
C2×C4×#632292
C4×#105876222
C4×#105875732
#145297152
#145295552
#145294162
#145294062
#145291362
#145291262
#145287982
C4×#105874852
C4×#105874812
C4×C17×#1022
C4×#46417