Finite Group Databasebeta

← C4×#19098892 #34295385

Subgroups — C4×#19098892 #34295385

Order 20224.

976 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19098892C211yesmaximal, characteristic
2C4×#14579137C211yesmaximal, characteristic
3C4×C4⋊C4×D79C211yesmaximal, characteristic
4#23764037C211yesmaximal, characteristic, complemented
5#23764036C211yesmaximal, characteristic, complemented
6#23763984C211yesmaximal, characteristic, complemented
7#23763983C211yesmaximal, characteristic, complemented
8#23763704C211yesmaximal, characteristic
9#23763594C211yesmaximal, characteristic
10#23763485C211yesmaximal, characteristic
11C4×#14579092C211yesmaximal, characteristic, complemented
12C4×#14579093C211yesmaximal, characteristic, complemented
13C4×#14579085C211yesmaximal, characteristic, complemented
14C4×(C2×D79)⋊C8C211yesmaximal, characteristic
15C4×#103×C79C211yesmaximal, characteristic, complemented
16C2×#14579137C2211yescharacteristic
17C2×C4⋊C4×D79C2211yescharacteristic
18C2×C4⋊C4×D79C2211yescharacteristic
19C2×C42×D79—21no—
20C2×C42×D79C2211yescharacteristic
21#19098892C418yesdirect product factor
22C2×#14579093C2211yescharacteristic
23C2×#14579093C2211yescharacteristic
24C2×#14579092C2211yescharacteristic
25C2×#14579092C2211yescharacteristic
26C2×#14579085C2211yescharacteristic
27C2×#14579085C2211yescharacteristic
28C2×(C2×D79)⋊C8C2211yescharacteristic
29C2×(C2×D79)⋊C8C2211yescharacteristic
30C2×C4×C79⋊C8C2211yescharacteristic
31#19098470C2211yescharacteristic
32#19098459C2211yescharacteristic
33#19098444—21no—
34#19098434—21no—
35#19098420C2211yescharacteristic
36C4⋊C4×Dic79C2211yescharacteristic
37C4⋊C4×Dic79C2211yescharacteristic
38C4×Dic79⋊C4—21no—
39C4×Dic79⋊C4—21no—
40C4×C4⋊Dic79C2211yescharacteristic
41C4×C4⋊Dic79C2211yescharacteristic
42#19098414—21no—
43C4×(C2×D79)⋊C4—21no—
44#95×D79—21no—
45#19098326C2211yescharacteristic
46#19098326C2211yescharacteristic
47#19098325C2211yescharacteristic
48#19098325C2211yescharacteristic
49#19098325C2211yescharacteristic
50#19098325C2211yescharacteristic
51#19098317C2211yescharacteristic
52#19098317C2211yescharacteristic
53C2×C4×Q8×C79C2211yescharacteristic
54C2×#103×C79C2211yescharacteristic
55C2×#103×C79C2211yescharacteristic
56C2×C4×C8×C79C2211yescharacteristic
57C4×C4⋊C4×C79C2211yescharacteristic
58#340×C79C2211yescharacteristic
59#340×C79C2211yescharacteristic
60C22×C4×D79—21no—
61C22×C4×D79—21no—
62C22×C4×D79D411yescharacteristic
63C22×C4×D79D411yescharacteristic
64C22×C4×D79C2311yescharacteristic
65C22×C79⋊C8C2311yescharacteristic
66C22×C79⋊C8C2311yescharacteristic
67#14579137—22no—
68#14579137C2×C414yes—
69C2×C4⋊Dic79C2311yescharacteristic
70C2×C4⋊Dic79C2311yescharacteristic
71C2×C4⋊Dic79C2311yescharacteristic
72C2×C4⋊Dic79C2311yescharacteristic
73C2×Dic79⋊C4—21no—
74C2×Dic79⋊C4—21no—
75C2×Dic79⋊C4—21no—
76C2×Dic79⋊C4—21no—
77C4⋊C4×D79—22no—
78C4⋊C4×D79—22no—
79C4⋊C4×D79—22no—
80C4⋊C4×D79C2×C414yes—
81C2×(C2×D79)⋊C4—21no—
82C2×(C2×D79)⋊C4—21no—
83C2×C4×Dic79—21no—
84C2×C4×Dic79—21no—
85C2×C4×Dic79—21no—
86C2×C4×Dic79—21no—
87C2×C4×Dic79D411yescharacteristic
88C2×C4×Dic79D411yescharacteristic
89C2×C4×Dic79C2311yescharacteristic
90C42×D79—22no—
91C42×D79—22no—
92C42×D79—44no—
93#14579093—22no—
94#14579093C2×C414yescomplemented
95#14579092—22no—
96#14579092C2×C414yescomplemented
97#14579085—22no—
98#14579085C2×C414yescomplemented
99(C2×D79)⋊C8—22no—
100(C2×D79)⋊C8C2×C414yes—
101C4×C79⋊C8—22no—
102C79⋊#95—21no—
103C79⋊#95—21no—
104C79⋊#95—21no—
105C79⋊#95—21no—
106C79⋊#95—21no—
107C79⋊#95—21no—
108C79⋊#95—21no—
109C79⋊#95—21no—
110C22×Q8×C79C2311yescharacteristic
111C22×C8×C79C2311yescharacteristic
112C22×C8×C79C2311yescharacteristic
113C4×Q8×C79—22no—
114C4×Q8×C79—22no—
115C2×C4⋊C4×C79—21no—
116C2×C4⋊C4×C79C2311yescharacteristic
117C2×C4⋊C4×C79C2311yescharacteristic
118C2×C4⋊C4×C79C2311yescharacteristic
119C2×C42×C79—21no—
120C2×C42×C79—21no—
121C2×C42×C79C2311yescharacteristic
122#103×C79—22no—
123#103×C79C2×C414yescomplemented
124C4×C8×C79—22no—
125#95×C79—21no—
126C23×D79C2×D411yescharacteristic
127C22×Dic79—21no—
128C22×Dic79—21no—
129C22×Dic79—21no—
130C22×Dic79—21no—
131C22×Dic79C2×D411yescharacteristic
132C22×Dic79C2×D411yescharacteristic
133C22×Dic79C2×D411yescharacteristic
134C2×C4×D79—24no—
135C2×C4×D79—24no—
136C2×C4×D79—22no—
137C2×C4×D79—22no—
138C2×C4×D79—22no—
139C2×C4×D79—22no—
140C2×C4×D79—21no—
141C2×C4×D79—21no—
142C2×C4×D79—21no—
143C2×C4×D79—21no—
144C2×C4×D79—41no—
145C2×C4×D79—42no—
146C2×C4×D79—42no—
147C2×C4×D79—42no—
148C2×C4×D79—42no—
149C2×C4×D79SD1614yes—
150C2×C4×D79C22×C412yes—
151C2×C4×D79#4112yes—
152C2×C79⋊C8—21no—
153C2×C79⋊C8—21no—
154C2×C79⋊C8—21no—
155C2×C79⋊C8—21no—
156C2×C79⋊C8—21no—
157C2×C79⋊C8C22×C412yes—
158C4⋊Dic79—21no—
159C4⋊Dic79—21no—
160C4⋊Dic79—21no—
161C4⋊Dic79—21no—
162C4⋊Dic79—21no—
163C4⋊Dic79C22×C412yes—
164C4⋊Dic79C22×C412yes—
165C4⋊Dic79#4112yes—
166Dic79⋊C4—24no—
167Dic79⋊C4—24no—
168Dic79⋊C4—24no—
169Dic79⋊C4—42no—
170(C2×D79)⋊C4—24no—
171(C2×D79)⋊C4—42no—
172C4×Dic79—22no—
173C4×Dic79—22no—
174C4×Dic79—21no—
175C4×Dic79—21no—
176C4×Dic79—42no—
177C4×Dic79—42no—
178C4×Dic79—42no—
179C4×Dic79—42no—
180C2×Q8×C79—21no—
181C2×Q8×C79—21no—
182C2×Q8×C79—21no—
183C2×Q8×C79—21no—
184C2×Q8×C79—21no—
185C2×Q8×C79C22×C412yes—
186C22×C4×C79—21no—
187C22×C4×C79—21no—
188C22×C4×C79—21no—
189C22×C4×C79—21no—
190C22×C4×C79C2×D411yescharacteristic
191C22×C4×C79C2×D411yescharacteristic
192C22×C4×C79C2411yescharacteristic
193C2×C8×C79—21no—
194C2×C8×C79—21no—
195C2×C8×C79—21no—
196C2×C8×C79—21no—
197C2×C8×C79—21no—
198C2×C8×C79C22×C412yes—
199C4⋊C4×C79—21no—
200C4⋊C4×C79—21no—
201C4⋊C4×C79—21no—
202C4⋊C4×C79—21no—
203C4⋊C4×C79—42no—
204C4⋊C4×C79C22×C412yes—
205C4⋊C4×C79#4112yes—
206C42×C79—42no—
207C42×C79—42no—
208C42×C79#4112yes—
209C42×C79#4112yes—
210C23×C79C22×D411yescharacteristic
211C22×D79—21no—
212C22×D79—21no—
213C22×D79—21no—
214C22×D79—21no—
215C22×D79C4×D412yes—
216C22×D79C2×SD1612yes—
217C22×D79#13512yes—
218Q8×C79—22no—
219Q8×C79—22no—
220Q8×C79—41no—
221Q8×C79—41no—
222C2×C4×C79—21no—
223C2×C4×C79—21no—
224C2×C4×C79—22no—
225C2×C4×C79—22no—
226C2×C4×C79—22no—
227C2×C4×C79—41no—
228C2×C4×C79—41no—
229C2×C4×C79—41no—
230C2×C4×C79—41no—
231C2×C4×C79—41no—
232C2×C4×C79—41no—
233C2×C4×C79—41no—
234C2×C4×C79—41no—
235C2×C4×C79—41no—
236C2×C4×C79#12312yes—
237C2×C4×C79#12312yes—
238C2×C4×C79C2×SD1612yes—
239C2×C4×C79#13712yes—
240C2×C4×C79C23×C411yescharacteristic
241C2×C4×C79C2×#4111yescharacteristic
242C2×C4×C79C2×#4111yescharacteristic
243C2×C4×C79C2×#4111yescharacteristic
244C2×C4×C79C2×#4111yescharacteristic
245C2×C4×C79C2×#4111yescharacteristic
246C2×Dic79—21no—
247C2×Dic79—21no—
248C2×Dic79—21no—
249C2×Dic79—21no—
250C2×Dic79—22no—
251C2×Dic79—22no—
252C2×Dic79—21no—
253C2×Dic79—22no—
254C2×Dic79—21no—
255C2×Dic79—21no—
256C2×Dic79—41no—
257C2×Dic79—41no—
258C2×Dic79—41no—
259C2×Dic79—41no—
260C2×Dic79—41no—
261C2×Dic79—41no—
262C2×Dic79—41no—
263C2×Dic79—41no—
264C2×Dic79—41no—
265C2×Dic79C4×D412yes—
266C2×Dic79C2×SD1612yes—
267C4×D79—22no—
268C4×D79—22no—
269C4×D79—22no—
270C4×D79—22no—
271C4×D79—28no—
272C4×D79—44no—
273C4×D79—48no—
274C4×D79—48no—
275C8×C79—22no—
276C8×C79—41no—
277C79⋊C8—22no—
278C79⋊C8—41no—
279C22×C79C2×C4×D411yescharacteristic
280C22×C79C2×#12311yescharacteristic
281C22×C79#52511yescharacteristic
282C22×C79C22×SD1611yescharacteristic
283C22×C79C2×#13511yescharacteristic
284C22×C79C2×#13711yescharacteristic
285C22×C79#57511yescharacteristic
286C2×D79—22no—
287C2×D79—22no—
288C2×D79—22no—
289C2×D79—22no—
290C2×D79—22no—
291C2×D79—22no—
292C2×D79C4×SD1614yes—
293C4×C79—22no—
294C4×C79—42no—
295C4×C79—42no—
296C4×C79—42no—
297C4×C79—81no—
298C4×C79#48314yescomplemented
299C4×C79C4×#4111yescharacteristic
300C4×C79C4×#4111yescharacteristic
301C4×C79#52911yescharacteristic
302C4×C79#52911yescharacteristic
303Dic79—22no—
304Dic79—22no—
305Dic79—41no—
306Dic79—42no—
307Dic79—42no—
308Dic79—42no—
309Dic79—81no—
310C4×#483—791nomaximal, Sylow
311C2×C79C4×#12311yescharacteristic
312C2×C79C2×C4×SD1611yescharacteristic
313C2×C79C4×#13711yescharacteristic
314C2×C79C2×#48311yescharacteristic
315C2×C79#309111yescharacteristic
316C2×C79#310111yescharacteristic
317C2×C79#310811yescharacteristic
318D79—24no—
319C2×#483—791no—
320C4×C22⋊Q8—791no—
321C2×C4×C4⋊C4—791no—
322#1927—791no—
323#1927—791no—
324#1920—791no—
325#1920—791no—
326#1872—791no—
327#1853—791no—
328#1823—791no—
329C4×#106—791no—
330C4×#106—791no—
331C4×#103—791no—
332C4×#103D7911yescharacteristic, complemented
333C4×C22⋊C8—791no—
334C79C4×#48311yescharacteristic, complemented, Sylow
335C2×C22⋊Q8—791no—
336C2×C4×Q8C2×D7911yescharacteristic
337C22×C4⋊C4—791no—
338C22×C4⋊C4—791no—
339C22×C42—791no—
340C22×C42—1581no—
341#483—798no—
342C2×#106—791no—
343C2×#106—791no—
344C2×#106—791no—
345C2×#106—791no—
346C2×#103—791no—
347C2×#103—791no—
348C2×#103C2×D7911yescharacteristic
349C2×#103C2×D7911yescharacteristic
350C2×C22⋊C8—791no—
351C2×C22⋊C8—791no—
352C2×C4×C8—791no—
353C2×C4×C8C2×D7911yescharacteristic
354#391—791no—
355#389—791no—
356#387—1581no—
357#385—1581no—
358#380—791no—
359C4×C4⋊C4—791no—
360C4×C4⋊C4—791no—
361C4×C4⋊C4—791no—
362C4×C4⋊C4—791no—
363C4×C4⋊C4—1581no—
364C4×C4⋊C4—1581no—
365C4×C4⋊C4—1581no—
366C4×C4⋊C4C2×D7911yescharacteristic
367C4×C22⋊C4—1581no—
368C2×#95—1581no—
369#340—791no—
370#340—791no—
371#340—791no—
372#340—791no—
373#340—791no—
374#340—791no—
375#340C2×D7911yescharacteristic
376#340C2×D7911yescharacteristic
377#336—791no—
378#336—791no—
379C22×Q8C22×D7911yescharacteristic
380C23×C4—791no—
381C23×C4—791no—
382C23×C4—791no—
383C23×C4—1581no—
384C23×C4—1581no—
385C22×C8—791no—
386C22×C8—791no—
387C22×C8C22×D7911yescharacteristic
388C22×C8C22×D7911yescharacteristic
389C22⋊Q8—794no—
390C22⋊Q8—1582no—
391C4×Q8—22no—
392C4×Q8—22no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—791no—
395C2×C4⋊C4—791no—
396C2×C4⋊C4—791no—
397C2×C4⋊C4—794no—
398C2×C4⋊C4—791no—
399C2×C4⋊C4—1582no—
400C2×C4⋊C4—1582no—
401C2×C4⋊C4—1581no—
402C2×C4⋊C4—1581no—
403C2×C4⋊C4—1581no—
404C2×C4⋊C4—1581no—
405C2×C4⋊C4—1582no—
406C2×C4⋊C4C22×D7911yescharacteristic
407C2×C4⋊C4C22×D7911yescharacteristic
408C2×C4⋊C4C22×D7911yescharacteristic
409C2×C22⋊C4—1581no—
410C2×C22⋊C4—1581no—
411C2×C42—21no—
412C2×C42—21no—
413C2×C42—3164no—
414C2×C42—791no—
415C2×C42—791no—
416C2×C42—791no—
417C2×C42—1581no—
418C2×C42—1581no—
419C2×C42—1581no—
420C2×C42—1581no—
421C2×C42—1582no—
422C2×C42—1582no—
423C2×C42C22×D7911yescharacteristic
424#106—794no—
425#106—794no—
426#106—1582no—
427#106—1582no—
428#103—22no—
429#103—794no—
430#103—1582no—
431#103C4×D7914yescomplemented
432C22⋊C8—794no—
433C22⋊C8—1582no—
434C4×C8—22no—
435C4×C8—1582no—
436#95—21no—
437#95—1581no—
438#95—1581no—
439#95—1581no—
440#95—1581no—
441#95—1581no—
442#95—1581no—
443#95—1581no—
444#95—1581no—
445C24—791no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8C2×C4×D7912yes—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—3161no—
457C22×C4—3162no—
458C22×C4—3162no—
459C22×C4—3162no—
460C22×C4—3162no—
461C22×C4—791no—
462C22×C4—791no—
463C22×C4—792no—
464C22×C4—794no—
465C22×C4—792no—
466C22×C4—791no—
467C22×C4—1584no—
468C22×C4—1582no—
469C22×C4—1584no—
470C22×C4—1581no—
471C22×C4—1581no—
472C22×C4—1581no—
473C22×C4—1581no—
474C22×C4—1582no—
475C22×C4—1581no—
476C22×C4—1581no—
477C22×C4—1581no—
478C22×C4—1581no—
479C22×C4—1582no—
480C22×C4—1582no—
481C22×C4D4×D7911yescharacteristic
482C22×C4D4×D7911yescharacteristic
483C22×C4C23×D7911yescharacteristic
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—792no—
490C2×C8—1581no—
491C2×C8—1581no—
492C2×C8—1581no—
493C2×C8—1581no—
494C2×C8—1581no—
495C2×C8C2×C4×D7912yes—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—42no—
501C4⋊C4—3162no—
502C4⋊C4—792no—
503C4⋊C4—792no—
504C4⋊C4—792no—
505C4⋊C4—1584no—
506C4⋊C4—1584no—
507C4⋊C4—1584no—
508C4⋊C4—1581no—
509C4⋊C4—1581no—
510C4⋊C4—1581no—
511C4⋊C4—1581no—
512C4⋊C4—1581no—
513C4⋊C4C2×C4×D7912yes—
514C4⋊C4#1192962412yes—
515C22⋊C4—3162no—
516C22⋊C4—1584no—
517C42—42no—
518C42—42no—
519C42—3162no—
520C42—3162no—
521C42—3162no—
522C42—3162no—
523C42—1581no—
524C42—1581no—
525C42—1582no—
526C42—1582no—
527C42#1192962312yes—
528C42#1192962412yes—
529C23—792no—
530C23—792no—
531C23—792no—
532C23—1581no—
533C23—1581no—
534C23—1581no—
535C23—1581no—
536C23C2×D4×D7911yescharacteristic
537Q8—22no—
538Q8—22no—
539Q8—41no—
540Q8—41no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—3164no—
556C2×C4—3168no—
557C2×C4—3168no—
558C2×C4—3161no—
559C2×C4—3161no—
560C2×C4—3161no—
561C2×C4—3161no—
562C2×C4—3161no—
563C2×C4—3161no—
564C2×C4—3161no—
565C2×C4—3161no—
566C2×C4—3161no—
567C2×C4—792no—
568C2×C4—792no—
569C2×C4—1582no—
570C2×C4—1582no—
571C2×C4—1581no—
572C2×C4—1582no—
573C2×C4—1581no—
574C2×C4—1581no—
575C2×C4—1581no—
576C2×C4—1581no—
577C2×C4—1581no—
578C2×C4—1581no—
579C2×C4—1588no—
580C2×C4—1582no—
581C2×C4—1582no—
582C2×C4—1582no—
583C2×C4—1582no—
584C2×C4#1457914312yes—
585C2×C4#1457914312yes—
586C2×C4SD16×D7912yes—
587C2×C4#1457919312yes—
588C2×C4C22×C4×D7911yescharacteristic
589C2×C4#41×D7911yescharacteristic
590C2×C4#41×D7911yescharacteristic
591C2×C4C2×#1192962311yescharacteristic
592C2×C4C2×#1192962411yescharacteristic
593C2×C4C2×#1192962411yescharacteristic
594C8—22no—
595C8—41no—
596C8—3161no—
597C8—1582no—
598C22—794no—
599C22—1582no—
600C22—1582no—
601C22—1582no—
602C22—1582no—
603C22—1582no—
604C22—1582no—
605C22C4×D4×D7911yescharacteristic
606C22C2×#1457914311yescharacteristic
607C22#1909907211yescharacteristic
608C22C2×SD16×D7911yescharacteristic
609C22#135×D7911yescharacteristic
610C22C2×#1457919311yescharacteristic
611C22#1909936011yescharacteristic
612C4—22no—
613C4—42no—
614C4—42no—
615C4—42no—
616C4—81no—
617C4—3162no—
618C4—3161no—
619C4—3162no—
620C4—3162no—
621C4—6321no—
622C4—1582no—
623C4—1582no—
624C4#1909889214yesdirect product factor
625C4C4×#1192962311yescharacteristic
626C4C4×#1192962411yescharacteristic
627C4#1909909111yescharacteristic
628C4#1909909511yescharacteristic
629C2—1584no—
630C2C4×#1457914311yescharacteristic
631C2C4×SD16×D7911yescharacteristic
632C2C4×#1457919311yescharacteristic
633C2C2×#1909889211yescharacteristic
634C2#2377331111yescharacteristic
635C2#2377340611yescharacteristic
636C2#2377348411yescharacteristic
subgroupG/H
centerC22×C4D4×D79
commutatorC2×C4×C79C23×C4
FrattiniC22×C4C23×D79
FittingC4×#103×C79C2
socleC23×C79C22×D4
prime radicalC23×D79C2×D4
cosocleC22×C4×C79C24
hypercenterC4×#103D79
hypocenterC79C4×#483
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×#103

Complements

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

NH ≅ G/Ntype
4. #23764037C2semidirect
5. #23764036C2semidirect
6. #23763984C2semidirect
7. #23763983C2semidirect
11. C4×#14579092C2semidirect
12. C4×#14579093C2semidirect
13. C4×#14579085C2semidirect
15. C4×#103×C79C2semidirect
21. #19098892C4direct (N × H)
94. #14579093C2×C4semidirect
96. #14579092C2×C4semidirect
98. #14579085C2×C4semidirect
123. #103×C79C2×C4semidirect
298. C4×C79#483semidirect
332. C4×#103D79semidirect
334. C79C4×#483semidirect
431. #103C4×D79semidirect
624. C4#19098892direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190988922
C4×#145791372
C4×C4⋊C4×D792
#237640372
#237640362
#237639842
#237639832
#237637042
#237635942
#237634852
C4×#145790922
C4×#145790932
C4×#145790852
C4×(C2×D79)⋊C82
C4×#103×C792
C4×#48379