Finite Group Databasebeta

← #1919×D79 #34290409

Subgroups — #1919×D79 #34290409

Order 20224.

1086 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×#106×D79C211yesmaximal, characteristic
2#389×D79C211yesmaximal, characteristic
3C4×C4⋊C4×D79C211yesmaximal, characteristic
4#23763981C211yesmaximal, characteristic, complemented
5#23763980C211yesmaximal, characteristic, complemented
6#23763979C211yesmaximal, characteristic, complemented
7#23763978C211yesmaximal, characteristic, complemented
8#23763977C211yesmaximal, characteristic, complemented
9#23763976C211yesmaximal, characteristic, complemented
10#23763975C211yesmaximal, characteristic, complemented
11#340×D79C211yesmaximal, characteristic
12#340×D79C211yesmaximal, characteristic
13#340×D79C211yesmaximal, characteristic
14#336×D79C211yesmaximal, characteristic
15C79×#1919C211yesmaximal, characteristic, complemented
16C22×C8×D79C2211yescharacteristic
17C22×C8×D79C2211yescharacteristic
18C2×C4⋊C4×D79—21no—
19C2×C4⋊C4×D79C2211yescharacteristic
20C2×C4⋊C4×D79C2211yescharacteristic
21C2×C4⋊C4×D79C2211yescharacteristic
22C2×C4⋊C4×D79C2211yescharacteristic
23C2×C42×D79—21no—
24C2×C42×D79C2211yescharacteristic
25C2×#14579093C2211yescharacteristic
26C2×#14579092C2211yescharacteristic
27C2×#14579092C2211yescharacteristic
28#106×D79C418yescomplemented
29#19098462C2211yescharacteristic
30#19098461C2211yescharacteristic
31#19098460—21no—
32#19098459C2211yescharacteristic
33#19098458—21no—
34C4⋊C4×Dic79C2211yescharacteristic
35C4⋊C4×Dic79C2211yescharacteristic
36C4×Dic79⋊C4—21no—
37C4×C4⋊Dic79C2211yescharacteristic
38#19098414—21no—
39#95×D79—21no—
40#95×D79—21no—
41#19098326C2211yescharacteristic
42#19098326C2211yescharacteristic
43#19098326C2211yescharacteristic
44#19098325C2211yescharacteristic
45#19098325C2211yescharacteristic
46#19098325C2211yescharacteristic
47#19098325C2211yescharacteristic
48#19098325C2211yescharacteristic
49#19098325C2211yescharacteristic
50#19098318C2211yescharacteristic
51#19098317C2211yescharacteristic
52#19098317C2211yescharacteristic
53C2×#106×C79C2211yescharacteristic
54#389×C79C2211yescharacteristic
55C4×C4⋊C4×C79C2211yescharacteristic
56#340×C79C2211yescharacteristic
57#340×C79C2211yescharacteristic
58#340×C79C2211yescharacteristic
59#336×C79C2211yescharacteristic
60C22×C4×D79—21no—
61C22×C4×D79—21no—
62C22×C4×D79—21no—
63C22×C4×D79—21no—
64C22×C4×D79D411yescharacteristic
65C22×C4×D79D411yescharacteristic
66C22×C4×D79C2311yescharacteristic
67C22×C79⋊C8C2311yescharacteristic
68C22×C79⋊C8C2311yescharacteristic
69C2×C8×D79—22no—
70C2×C8×D79—22no—
71C2×C8×D79—22no—
72C2×C8×D79—22no—
73C2×C8×D79—22no—
74C2×C8×D79C2×C414yes—
75C2×C4⋊Dic79—21no—
76C2×C4⋊Dic79C2311yescharacteristic
77C2×C4⋊Dic79C2311yescharacteristic
78C2×C4⋊Dic79C2311yescharacteristic
79C2×C4⋊Dic79C2311yescharacteristic
80C2×Dic79⋊C4—21no—
81C2×Dic79⋊C4—21no—
82C2×Dic79⋊C4—21no—
83C2×Dic79⋊C4—21no—
84C2×Dic79⋊C4—21no—
85C2×Dic79⋊C4—21no—
86C4⋊C4×D79—22no—
87C4⋊C4×D79—22no—
88C4⋊C4×D79—22no—
89C4⋊C4×D79—22no—
90C4⋊C4×D79—22no—
91C4⋊C4×D79—44no—
92C4⋊C4×D79C2×C414yes—
93C4⋊C4×D79C2×C414yes—
94C4⋊C4×D79Q814yes—
95C2×C4×Dic79—21no—
96C2×C4×Dic79—21no—
97C2×C4×Dic79—21no—
98C2×C4×Dic79D411yescharacteristic
99C2×C4×Dic79D411yescharacteristic
100C2×C4×Dic79C2311yescharacteristic
101C42×D79—22no—
102C42×D79—22no—
103C42×D79—44no—
104#14579093C2×C414yescomplemented
105#14579092C2×C414yescomplemented
106#14579092C2×C414yescomplemented
107C79⋊#95—21no—
108C79⋊#95—21no—
109C79⋊#95—21no—
110C79⋊#95—21no—
111C79⋊#95—21no—
112C79⋊#95—21no—
113C22×C8×C79C2311yescharacteristic
114C22×C8×C79C2311yescharacteristic
115C2×C4⋊C4×C79—21no—
116C2×C4⋊C4×C79C2311yescharacteristic
117C2×C4⋊C4×C79C2311yescharacteristic
118C2×C4⋊C4×C79C2311yescharacteristic
119C2×C4⋊C4×C79C2311yescharacteristic
120C2×C42×C79—21no—
121C2×C42×C79C2311yescharacteristic
122#106×C79C2×C414yescomplemented
123#95×C79—21no—
124#95×C79—21no—
125C23×D79C2×D411yescharacteristic
126C22×Dic79—21no—
127C22×Dic79—21no—
128C22×Dic79—21no—
129C22×Dic79—21no—
130C22×Dic79C2×D411yescharacteristic
131C22×Dic79C2×D411yescharacteristic
132C22×Dic79C2×D411yescharacteristic
133C2×C4×D79—24no—
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—22no—
141C2×C4×D79—42no—
142C2×C4×D79—42no—
143C2×C4×D79—42no—
144C2×C4×D79—42no—
145C2×C4×D79—42no—
146C2×C4×D79—42no—
147C2×C4×D79—42no—
148C2×C4×D79—42no—
149C2×C4×D79—42no—
150C2×C4×D79SD1614yes—
151C2×C4×D79C22×C412yes—
152C2×C4×D79C2×Q812yes—
153C2×C4×D79#4112yes—
154C2×C4×D79#4112yes—
155C2×C4×D79#4112yes—
156C2×C4×D79#4112yes—
157C2×C79⋊C8—21no—
158C2×C79⋊C8—21no—
159C2×C79⋊C8—21no—
160C2×C79⋊C8—21no—
161C2×C79⋊C8—21no—
162C2×C79⋊C8C22×C412yes—
163C8×D79—28no—
164C8×D79—44no—
165C4⋊Dic79—21no—
166C4⋊Dic79—21no—
167C4⋊Dic79—21no—
168C4⋊Dic79—21no—
169C4⋊Dic79—21no—
170C4⋊Dic79—42no—
171C4⋊Dic79C22×C412yes—
172C4⋊Dic79C22×C412yes—
173C4⋊Dic79C2×Q812yes—
174Dic79⋊C4—24no—
175Dic79⋊C4—24no—
176Dic79⋊C4—24no—
177Dic79⋊C4—42no—
178Dic79⋊C4—42no—
179Dic79⋊C4—42no—
180C4×Dic79—22no—
181C4×Dic79—22no—
182C4×Dic79—21no—
183C4×Dic79—21no—
184C4×Dic79—42no—
185C4×Dic79—42no—
186C4×Dic79—42no—
187C22×C4×C79—21no—
188C22×C4×C79—21no—
189C22×C4×C79—21no—
190C22×C4×C79—21no—
191C22×C4×C79C2×D411yescharacteristic
192C22×C4×C79C2×D411yescharacteristic
193C22×C4×C79C2411yescharacteristic
194C2×C8×C79—21no—
195C2×C8×C79—21no—
196C2×C8×C79—21no—
197C2×C8×C79—21no—
198C2×C8×C79—21no—
199C2×C8×C79C22×C412yes—
200C4⋊C4×C79—21no—
201C4⋊C4×C79—21no—
202C4⋊C4×C79—21no—
203C4⋊C4×C79—21no—
204C4⋊C4×C79—21no—
205C4⋊C4×C79—42no—
206C4⋊C4×C79C22×C412yes—
207C4⋊C4×C79C22×C412yes—
208C4⋊C4×C79C2×Q812yes—
209C42×C79—21no—
210C42×C79—21no—
211C42×C79—42no—
212C23×C79C22×D411yescharacteristic
213C22×D79C4×D412yes—
214C22×D79C22⋊Q812yes—
215C22×D79#12312yes—
216C22×D79C2×SD1612yes—
217C22×D79#13512yes—
218C22×D79AGL(1,ℤ/8)12yes—
219C22×D79#13712yes—
220C2×C4×C79—21no—
221C2×C4×C79—21no—
222C2×C4×C79—22no—
223C2×C4×C79—22no—
224C2×C4×C79—22no—
225C2×C4×C79—21no—
226C2×C4×C79—21no—
227C2×C4×C79—21no—
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—41no—
237C2×C4×C79C2×SD1612yes—
238C2×C4×C79C23×C411yescharacteristic
239C2×C4×C79C22×Q811yescharacteristic
240C2×C4×C79C2×#4111yescharacteristic
241C2×C4×C79C2×#4111yescharacteristic
242C2×C4×C79C2×#4111yescharacteristic
243C2×C4×C79C2×#4111yescharacteristic
244C2×Dic79—21no—
245C2×Dic79—21no—
246C2×Dic79—22no—
247C2×Dic79—22no—
248C2×Dic79—22no—
249C2×Dic79—21no—
250C2×Dic79—21no—
251C2×Dic79—21no—
252C2×Dic79—41no—
253C2×Dic79—41no—
254C2×Dic79—41no—
255C2×Dic79—41no—
256C2×Dic79—41no—
257C2×Dic79—41no—
258C2×Dic79—41no—
259C2×Dic79—41no—
260C2×Dic79—41no—
261C2×Dic79C4×D412yes—
262C2×Dic79C22⋊Q812yes—
263C2×Dic79#12312yes—
264C2×Dic79C2×SD1612yes—
265C4×D79—28no—
266C4×D79—48no—
267C4×D79—48no—
268C4×D79—48no—
269C4×D79—44no—
270C4×D79—84no—
271C4×D79#11714yes—
272C4×D79C4×Q814yes—
273C4×D79#12514yes—
274C4×D79#12614yes—
275C8×C79—22no—
276C8×C79—41no—
277C79⋊C8—22no—
278C79⋊C8—41no—
279C22×C79C2×C4×D411yescharacteristic
280C22×C79C2×C22⋊Q811yescharacteristic
281C22×C79C2×#12311yescharacteristic
282C22×C79C22×SD1611yescharacteristic
283C22×C79C2×#13511yescharacteristic
284C22×C79C2×AGL(1,ℤ/8)11yescharacteristic
285C22×C79C2×#13711yescharacteristic
286C2×D79#38714yes—
287C2×D79C4×SD1614yes—
288C2×D79#44014yes—
289C2×D79#47514yes—
290C2×D79#47814yes—
291C2×D79#48114yes—
292C2×D79#48514yes—
293C4×C79—22no—
294C4×C79—42no—
295C4×C79—41no—
296C4×C79—42no—
297C4×C79—42no—
298C4×C79—81no—
299C4×C79C2×#11711yescharacteristic
300C4×C79C2×C4×Q811yescharacteristic
301C4×C79C2×#12511yescharacteristic
302C4×C79C2×#12611yescharacteristic
303Dic79—22no—
304Dic79—42no—
305Dic79—41no—
306Dic79—42no—
307Dic79—42no—
308Dic79—81no—
309Dic79#38714yes—
310C2×#1919—791nomaximal, Sylow
311C2×C79C2×#38711yescharacteristic
312C2×C79C2×C4×SD1611yescharacteristic
313C2×C79C2×#44011yescharacteristic
314C2×C79C2×#47811yescharacteristic
315C2×C79C2×#47511yescharacteristic
316C2×C79C2×#48511yescharacteristic
317C2×C79C2×#48111yescharacteristic
318D79#191918yesdirect product factor
319C22×#106—791no—
320C2×#389—791no—
321C2×C4×C4⋊C4—791no—
322#1919—791no—
323#1919—791no—
324#1919—791no—
325#1919—791no—
326#1919—791no—
327#1919—791no—
328#1919—791no—
329#1919D7911yescharacteristic, direct product factor
330C2×#340—791no—
331C2×#340—791no—
332C2×#340—791no—
333C2×#336—791no—
334C79C2×#191911yescharacteristic, complemented, Sylow
335C23×C8—791no—
336C23×C8—791no—
337C22×C4⋊C4—791no—
338C22×C4⋊C4—791no—
339C22×C4⋊C4—791no—
340C22×C4⋊C4—791no—
341C22×C4⋊C4—1581no—
342C22×C42—791no—
343C22×C42—1581no—
344C2×#106—791no—
345C2×#106—791no—
346C2×#106—791no—
347C2×#106—798no—
348C2×#106C2×D7911yescharacteristic
349#389—791no—
350#389—791no—
351#389—791no—
352#389—1581no—
353#389—1581no—
354#389C2×D7911yescharacteristic
355C4×C4⋊C4—791no—
356C4×C4⋊C4—791no—
357C4×C4⋊C4—791no—
358C4×C4⋊C4—1581no—
359C4×C4⋊C4—1581no—
360C4×C4⋊C4C2×D7911yescharacteristic
361C2×#95—1581no—
362C2×#95—1581no—
363#340—791no—
364#340—791no—
365#340—791no—
366#340—791no—
367#340—791no—
368#340—791no—
369#340—791no—
370#340—791no—
371#340—791no—
372#340C2×D7911yescharacteristic
373#340C2×D7911yescharacteristic
374#340C2×D7911yescharacteristic
375#336—791no—
376#336—791no—
377#336—791no—
378#336C2×D7911yescharacteristic
379C23×C4—791no—
380C23×C4—791no—
381C23×C4—791no—
382C23×C4—1581no—
383C23×C4—1581no—
384C23×C4—1581no—
385C23×C4—1581no—
386C22×C8—791no—
387C22×C8—794no—
388C22×C8—791no—
389C22×C8—1582no—
390C22×C8—1582no—
391C22×C8—1582no—
392C22×C8—1582no—
393C22×C8—1582no—
394C22×C8C22×D7911yescharacteristic
395C22×C8C22×D7911yescharacteristic
396C2×C4⋊C4—21no—
397C2×C4⋊C4—3164no—
398C2×C4⋊C4—791no—
399C2×C4⋊C4—791no—
400C2×C4⋊C4—791no—
401C2×C4⋊C4—794no—
402C2×C4⋊C4—794no—
403C2×C4⋊C4—794no—
404C2×C4⋊C4—791no—
405C2×C4⋊C4—1582no—
406C2×C4⋊C4—1582no—
407C2×C4⋊C4—1582no—
408C2×C4⋊C4—1582no—
409C2×C4⋊C4—1582no—
410C2×C4⋊C4—1581no—
411C2×C4⋊C4—1581no—
412C2×C4⋊C4—1581no—
413C2×C4⋊C4—1581no—
414C2×C4⋊C4—1581no—
415C2×C4⋊C4—1581no—
416C2×C4⋊C4—1581no—
417C2×C4⋊C4C22×D7911yescharacteristic
418C2×C4⋊C4C22×D7911yescharacteristic
419C2×C4⋊C4C22×D7911yescharacteristic
420C2×C4⋊C4C22×D7911yescharacteristic
421C2×C42—21no—
422C2×C42—3164no—
423C2×C42—791no—
424C2×C42—791no—
425C2×C42—791no—
426C2×C42—1582no—
427C2×C42—1582no—
428C2×C42—1581no—
429C2×C42—1581no—
430C2×C42—1581no—
431C2×C42C22×D7911yescharacteristic
432#106—794no—
433#106—794no—
434#106—794no—
435#106C4×D7914yescomplemented
436#95—21no—
437#95—21no—
438#95—1581no—
439#95—1581no—
440#95—1581no—
441#95—1581no—
442#95—1581no—
443#95—1581no—
444C24—791no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—3162no—
450C22×C4—3162no—
451C22×C4—3162no—
452C22×C4—3162no—
453C22×C4—3162no—
454C22×C4—3162no—
455C22×C4—3162no—
456C22×C4—3162no—
457C22×C4—3162no—
458C22×C4—791no—
459C22×C4—792no—
460C22×C4—792no—
461C22×C4—792no—
462C22×C4—792no—
463C22×C4—792no—
464C22×C4—792no—
465C22×C4—791no—
466C22×C4—794no—
467C22×C4—791no—
468C22×C4—1582no—
469C22×C4—1584no—
470C22×C4—1584no—
471C22×C4—1584no—
472C22×C4—1582no—
473C22×C4—1582no—
474C22×C4—1582no—
475C22×C4—1582no—
476C22×C4—1581no—
477C22×C4—1581no—
478C22×C4—1581no—
479C22×C4—1581no—
480C22×C4D4×D7911yescharacteristic
481C22×C4D4×D7911yescharacteristic
482C22×C4C23×D7911yescharacteristic
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—3164no—
489C2×C8—792no—
490C2×C8—1588no—
491C2×C8—1581no—
492C2×C8—1581no—
493C2×C8—1581no—
494C2×C8—1581no—
495C2×C8—1581no—
496C2×C8C2×C4×D7912yes—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—42no—
503C4⋊C4—3162no—
504C4⋊C4—3162no—
505C4⋊C4—3162no—
506C4⋊C4—3162no—
507C4⋊C4—792no—
508C4⋊C4—792no—
509C4⋊C4—792no—
510C4⋊C4—1584no—
511C4⋊C4—1584no—
512C4⋊C4—1584no—
513C4⋊C4—1581no—
514C4⋊C4—1581no—
515C4⋊C4—1581no—
516C4⋊C4—1581no—
517C4⋊C4—1581no—
518C4⋊C4C2×C4×D7912yes—
519C4⋊C4C2×C4×D7912yes—
520C4⋊C4Q8×D7912yes—
521C42—21no—
522C42—21no—
523C42—42no—
524C42—3162no—
525C42—3162no—
526C42—3162no—
527C42—1582no—
528C42—1582no—
529C42—1581no—
530C42—1581no—
531C23—792no—
532C23—792no—
533C23—792no—
534C23—792no—
535C23—792no—
536C23—792no—
537C23—792no—
538C23C2×D4×D7911yescharacteristic
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
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—41no—
556C2×C4—3168no—
557C2×C4—3168no—
558C2×C4—3168no—
559C2×C4—3164no—
560C2×C4—3161no—
561C2×C4—3161no—
562C2×C4—3161no—
563C2×C4—3161no—
564C2×C4—3161no—
565C2×C4—3161no—
566C2×C4—3161no—
567C2×C4—3161no—
568C2×C4—3161no—
569C2×C4—792no—
570C2×C4—792no—
571C2×C4—792no—
572C2×C4—794no—
573C2×C4—794no—
574C2×C4—794no—
575C2×C4—794no—
576C2×C4—792no—
577C2×C4—6324no—
578C2×C4—1588no—
579C2×C4—1582no—
580C2×C4—1582no—
581C2×C4—1582no—
582C2×C4—1581no—
583C2×C4—1581no—
584C2×C4—1581no—
585C2×C4—1581no—
586C2×C4—1581no—
587C2×C4SD16×D7912yes—
588C2×C4C22×C4×D7911yescharacteristic
589C2×C4C2×Q8×D7911yescharacteristic
590C2×C4#41×D7911yescharacteristic
591C2×C4#41×D7911yescharacteristic
592C2×C4#41×D7911yescharacteristic
593C2×C4#41×D7911yescharacteristic
594C8—22no—
595C8—41no—
596C8—3161no—
597C8—1582no—
598C22—794no—
599C22—794no—
600C22—794no—
601C22—794no—
602C22—794no—
603C22—794no—
604C22—794no—
605C22C4×D4×D7911yescharacteristic
606C22C22⋊Q8×D7911yescharacteristic
607C22#123×D7911yescharacteristic
608C22C2×SD16×D7911yescharacteristic
609C22#135×D7911yescharacteristic
610C22AGL(1,ℤ/8)×D7911yescharacteristic
611C22#137×D7911yescharacteristic
612C4—22no—
613C4—42no—
614C4—41no—
615C4—42no—
616C4—42no—
617C4—81no—
618C4—3162no—
619C4—3161no—
620C4—3162no—
621C4—3162no—
622C4—794no—
623C4—6321no—
624C4—1582no—
625C4#117×D7911yescharacteristic
626C4C4×Q8×D7911yescharacteristic
627C4#125×D7911yescharacteristic
628C4#126×D7911yescharacteristic
629C2—798no—
630C2#387×D7911yescharacteristic
631C2C4×SD16×D7911yescharacteristic
632C2#440×D7911yescharacteristic
633C2#478×D7911yescharacteristic
634C2#475×D7911yescharacteristic
635C2#485×D7911yescharacteristic
636C2#481×D7911yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutatorC2×C4×C79C23×C4
FrattiniC22×C4C23×D79
FittingC79×#1919C2
socleC23×C79C22×D4
prime radicalC23×D79C2×D4
cosocleC22×C4×C79C24
hypercenter#1919D79
hypocenterC79C2×#1919
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1919

Complements

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

NH ≅ G/Ntype
4. #23763981C2semidirect
5. #23763980C2semidirect
6. #23763979C2semidirect
7. #23763978C2semidirect
8. #23763977C2semidirect
9. #23763976C2semidirect
10. #23763975C2semidirect
15. C79×#1919C2semidirect
28. #106×D79C4semidirect
104. #14579093C2×C4semidirect
105. #14579092C2×C4semidirect
106. #14579092C2×C4semidirect
122. #106×C79C2×C4semidirect
318. D79#1919direct (N × H)
329. #1919D79direct (N × H)
334. C79C2×#1919semidirect
435. #106C4×D79semidirect

Maximal subgroups

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

subgroupindex
C2×#106×D792
#389×D792
C4×C4⋊C4×D792
#237639812
#237639802
#237639792
#237639782
#237639772
#237639762
#237639752
#340×D792
#336×D792
C79×#19192
C2×#191979