Finite Group Databasebeta

← #2088×D79 #34317311

Subgroups — #2088×D79 #34317311

Order 20224.

1054 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#106×D79C211yesmaximal, characteristic
2C2×C4⋊C8×D79C211yesmaximal, characteristic
3#389×D79C211yesmaximal, characteristic
4#389×D79C211yesmaximal, characteristic
5#23764904C211yesmaximal, characteristic, complemented
6#23764903C211yesmaximal, characteristic, complemented
7#23764902C211yesmaximal, characteristic, complemented
8#23764901C211yesmaximal, characteristic, complemented
9#23764900C211yesmaximal, characteristic, complemented
10#23764899C211yesmaximal, characteristic, complemented
11#23764898C211yesmaximal, characteristic, complemented
12#340×D79C211yesmaximal, characteristic
13#340×D79C211yesmaximal, characteristic
14#340×D79C211yesmaximal, characteristic
15C79×#2088C211yesmaximal, characteristic, complemented
16C22×C8×D79C2211yescharacteristic
17C22×C8×D79C2211yescharacteristic
18C2×C4⋊C4×D79—21no—
19C2×C4⋊C4×D79—21no—
20C2×C4⋊C4×D79C2211yescharacteristic
21C2×C4⋊C4×D79C2211yescharacteristic
22C2×C4⋊C4×D79C2211yescharacteristic
23C2×C4⋊C4×D79C2211yescharacteristic
24C2×C42×D79C2211yescharacteristic
25C2×#14579093C2211yescharacteristic
26C2×#14579092C2211yescharacteristic
27C2×#14579092C2211yescharacteristic
28#106×D79—24no—
29C2×C4⋊(C79⋊C8)C2211yescharacteristic
30C2×Dic79⋊C8C2211yescharacteristic
31C2×Dic79⋊C8C2211yescharacteristic
32C4⋊C8×D79—24no—
33#19098462C2211yescharacteristic
34#19098462C2211yescharacteristic
35#19098461C2211yescharacteristic
36#19098461C2211yescharacteristic
37#19098460—21no—
38#19098460—21no—
39#19098459C2211yescharacteristic
40#19098459C2211yescharacteristic
41#19098458—21no—
42#19098458—21no—
43#95×D79—21no—
44#95×D79—21no—
45#19098326C2211yescharacteristic
46#19098326C2211yescharacteristic
47#19098326C2211yescharacteristic
48#19098325C2211yescharacteristic
49#19098325C2211yescharacteristic
50#19098325C2211yescharacteristic
51#19098325C2211yescharacteristic
52#19098325C2211yescharacteristic
53#19098325C2211yescharacteristic
54C2×#106×C79C2211yescharacteristic
55C2×C4⋊C8×C79C2211yescharacteristic
56#389×C79C2211yescharacteristic
57#389×C79C2211yescharacteristic
58#340×C79C2211yescharacteristic
59#340×C79C2211yescharacteristic
60#340×C79C2211yescharacteristic
61C22×C4×D79—21no—
62C22×C4×D79—21no—
63C22×C4×D79—21no—
64C22×C4×D79—21no—
65C22×C4×D79D411yescharacteristic
66C22×C4×D79D411yescharacteristic
67C22×C4×D79C2311yescharacteristic
68C22×C79⋊C8C2311yescharacteristic
69C22×C79⋊C8C2311yescharacteristic
70C2×C8×D79—22no—
71C2×C8×D79—22no—
72C2×C8×D79—22no—
73C2×C8×D79—22no—
74C2×C8×D79—22no—
75C2×C8×D79D414yes—
76C2×C4⋊Dic79—21no—
77C2×C4⋊Dic79—21no—
78C2×C4⋊Dic79C2311yescharacteristic
79C2×C4⋊Dic79C2311yescharacteristic
80C2×C4⋊Dic79C2311yescharacteristic
81C2×C4⋊Dic79C2311yescharacteristic
82C2×Dic79⋊C4—21no—
83C2×Dic79⋊C4—21no—
84C2×Dic79⋊C4—21no—
85C2×Dic79⋊C4—21no—
86C2×Dic79⋊C4—21no—
87C2×Dic79⋊C4—21no—
88C2×Dic79⋊C4—21no—
89C2×Dic79⋊C4—21no—
90C4⋊C4×D79—22no—
91C4⋊C4×D79—22no—
92C4⋊C4×D79—22no—
93C4⋊C4×D79—22no—
94C4⋊C4×D79—22no—
95C4⋊C4×D79—22no—
96C4⋊C4×D79—44no—
97C4⋊C4×D79—44no—
98C4⋊C4×D79Q814yes—
99C4⋊C4×D79Q814yes—
100C2×C4×Dic79D411yescharacteristic
101C2×C4×Dic79D411yescharacteristic
102C2×C4×Dic79C2311yescharacteristic
103C42×D79—22no—
104C42×D79—22no—
105#14579093—22no—
106#14579092—22no—
107#14579092—22no—
108C4⋊(C79⋊C8)—22no—
109Dic79⋊C8—22no—
110Dic79⋊C8—22no—
111C79⋊#95—21no—
112C79⋊#95—21no—
113C79⋊#95—21no—
114C79⋊#95—21no—
115C79⋊#95—21no—
116C79⋊#95—21no—
117C22×C8×C79C2311yescharacteristic
118C22×C8×C79C2311yescharacteristic
119C2×C4⋊C4×C79—21no—
120C2×C4⋊C4×C79—21no—
121C2×C4⋊C4×C79C2311yescharacteristic
122C2×C4⋊C4×C79C2311yescharacteristic
123C2×C4⋊C4×C79C2311yescharacteristic
124C2×C4⋊C4×C79C2311yescharacteristic
125C2×C42×C79C2311yescharacteristic
126#106×C79—22no—
127C4⋊C8×C79—22no—
128#95×C79—21no—
129#95×C79—21no—
130C23×D79C2×D411yescharacteristic
131C22×Dic79—21no—
132C22×Dic79—21no—
133C22×Dic79—21no—
134C22×Dic79—21no—
135C22×Dic79C2×D411yescharacteristic
136C22×Dic79C2×D411yescharacteristic
137C22×Dic79C2×D411yescharacteristic
138C2×C4×D79—22no—
139C2×C4×D79—22no—
140C2×C4×D79—24no—
141C2×C4×D79—24no—
142C2×C4×D79—22no—
143C2×C4×D79—22no—
144C2×C4×D79—22no—
145C2×C4×D79—42no—
146C2×C4×D79—42no—
147C2×C4×D79—42no—
148C2×C4×D79—42no—
149C2×C4×D79—42no—
150C2×C4×D79—42no—
151C2×C4×D79—42no—
152C2×C4×D79—42no—
153C2×C4×D79—42no—
154C2×C4×D79—42no—
155C2×C4×D79SD1614yes—
156C2×C4×D79C2×D412yes—
157C2×C4×D79C2×Q812yes—
158C2×C4×D79C2×Q812yes—
159C2×C4×D79#4112yes—
160C2×C4×D79#4112yes—
161C2×C4×D79#4112yes—
162C2×C79⋊C8—21no—
163C2×C79⋊C8—21no—
164C2×C79⋊C8—21no—
165C2×C79⋊C8—21no—
166C2×C79⋊C8—21no—
167C2×C79⋊C8C2×D412yes—
168C8×D79—28no—
169C8×D79—44no—
170C4⋊Dic79—21no—
171C4⋊Dic79—21no—
172C4⋊Dic79—21no—
173C4⋊Dic79—21no—
174C4⋊Dic79—21no—
175C4⋊Dic79—21no—
176C4⋊Dic79—42no—
177C4⋊Dic79—42no—
178C4⋊Dic79C2×Q812yes—
179C4⋊Dic79C2×Q812yes—
180Dic79⋊C4—24no—
181Dic79⋊C4—24no—
182Dic79⋊C4—42no—
183Dic79⋊C4—42no—
184Dic79⋊C4—42no—
185Dic79⋊C4—42no—
186Dic79⋊C4—42no—
187Dic79⋊C4—42no—
188C4×Dic79—22no—
189C4×Dic79—22no—
190C4×Dic79—21no—
191C4×Dic79—21no—
192C22×C4×C79—21no—
193C22×C4×C79—21no—
194C22×C4×C79—21no—
195C22×C4×C79—21no—
196C22×C4×C79C2×D411yescharacteristic
197C22×C4×C79C2×D411yescharacteristic
198C22×C4×C79C2411yescharacteristic
199C2×C8×C79—21no—
200C2×C8×C79—21no—
201C2×C8×C79—21no—
202C2×C8×C79—21no—
203C2×C8×C79—21no—
204C2×C8×C79C2×D412yes—
205C4⋊C4×C79—21no—
206C4⋊C4×C79—21no—
207C4⋊C4×C79—21no—
208C4⋊C4×C79—21no—
209C4⋊C4×C79—21no—
210C4⋊C4×C79—21no—
211C4⋊C4×C79—42no—
212C4⋊C4×C79—42no—
213C4⋊C4×C79C2×Q812yes—
214C4⋊C4×C79C2×Q812yes—
215C42×C79—21no—
216C42×C79—21no—
217C23×C79C22×D411yescharacteristic
218C22×D79#12112yes—
219C22×D79C22⋊Q812yes—
220C22×D79C22⋊Q812yes—
221C22×D79C2×SD1612yes—
222C22×D79#13512yes—
223C22×D79AGL(1,ℤ/8)12yes—
224C22×D79#13712yes—
225C2×C4×C79—21no—
226C2×C4×C79—21no—
227C2×C4×C79—21no—
228C2×C4×C79—22no—
229C2×C4×C79—22no—
230C2×C4×C79—21no—
231C2×C4×C79—21no—
232C2×C4×C79—41no—
233C2×C4×C79—41no—
234C2×C4×C79—41no—
235C2×C4×C79—41no—
236C2×C4×C79—41no—
237C2×C4×C79—41no—
238C2×C4×C79—41no—
239C2×C4×C79—41no—
240C2×C4×C79—41no—
241C2×C4×C79—41no—
242C2×C4×C79C2×SD1612yes—
243C2×C4×C79C22×D411yescharacteristic
244C2×C4×C79C22×Q811yescharacteristic
245C2×C4×C79C22×Q811yescharacteristic
246C2×C4×C79C2×#4111yescharacteristic
247C2×C4×C79C2×#4111yescharacteristic
248C2×C4×C79C2×#4111yescharacteristic
249C2×Dic79—21no—
250C2×Dic79—21no—
251C2×Dic79—21no—
252C2×Dic79—22no—
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×Dic79—41no—
266C2×Dic79#12112yes—
267C2×Dic79C22⋊Q812yes—
268C2×Dic79C22⋊Q812yes—
269C2×Dic79C2×SD1612yes—
270C4×D79—28no—
271C4×D79—44no—
272C4×D79—48no—
273C4×D79—48no—
274C4×D79—84no—
275C4×D79—84no—
276C4×D79#12314yes—
277C4×D79#12514yes—
278C4×D79#12514yes—
279C4×D79C4⋊Q814yes—
280C8×C79—22no—
281C8×C79—41no—
282C79⋊C8—22no—
283C79⋊C8—41no—
284C22×C79C2×#12111yescharacteristic
285C22×C79C2×C22⋊Q811yescharacteristic
286C22×C79C2×C22⋊Q811yescharacteristic
287C22×C79C22×SD1611yescharacteristic
288C22×C79C2×#13511yescharacteristic
289C22×C79C2×AGL(1,ℤ/8)11yescharacteristic
290C22×C79C2×#13711yescharacteristic
291C2×D79#39814yes—
292C2×D79#46514yes—
293C2×D79#46814yes—
294C2×D79#47514yes—
295C2×D79#47614yes—
296C2×D79#47814yes—
297C2×D79#47914yes—
298C4×C79—22no—
299C4×C79—42no—
300C4×C79—41no—
301C4×C79—42no—
302C4×C79—81no—
303C4×C79—81no—
304C4×C79C2×#12311yescharacteristic
305C4×C79C2×#12511yescharacteristic
306C4×C79C2×#12511yescharacteristic
307C4×C79C2×C4⋊Q811yescharacteristic
308Dic79—22no—
309Dic79—42no—
310Dic79—41no—
311Dic79—42no—
312Dic79—81no—
313Dic79—81no—
314Dic79#39814yes—
315C2×#2088—791nomaximal, Sylow
316C2×C79C2×#39811yescharacteristic
317C2×C79C2×#46511yescharacteristic
318C2×C79C2×#46811yescharacteristic
319C2×C79C2×#47611yescharacteristic
320C2×C79C2×#47811yescharacteristic
321C2×C79C2×#47511yescharacteristic
322C2×C79C2×#47911yescharacteristic
323D79#208818yesdirect product factor
324C22×#106—791no—
325C22×C4⋊C8—791no—
326C2×#389—791no—
327C2×#389—791no—
328#2088—791no—
329#2088—791no—
330#2088—791no—
331#2088—791no—
332#2088—791no—
333#2088—791no—
334#2088—791no—
335#2088D7911yescharacteristic, direct product factor
336C2×#340—791no—
337C2×#340—791no—
338C2×#340—791no—
339C79C2×#208811yescharacteristic, complemented, Sylow
340C23×C8—791no—
341C23×C8—791no—
342C22×C4⋊C4—791no—
343C22×C4⋊C4—791no—
344C22×C4⋊C4—791no—
345C22×C4⋊C4—791no—
346C22×C4⋊C4—1581no—
347C22×C4⋊C4—1581no—
348C22×C42—791no—
349C2×#106—791no—
350C2×#106—791no—
351C2×#106—791no—
352C2×#106—1584no—
353C2×#106C2×D7911yescharacteristic
354C2×C4⋊C8—791no—
355C2×C4⋊C8—791no—
356C2×C4⋊C8—791no—
357C2×C4⋊C8—1584no—
358C2×C4⋊C8C2×D7911yescharacteristic
359#389—791no—
360#389—791no—
361#389—791no—
362#389—791no—
363#389—791no—
364#389—791no—
365#389—1581no—
366#389—1581no—
367#389—1581no—
368#389—1581no—
369#389C2×D7911yescharacteristic
370#389C2×D7911yescharacteristic
371C2×#95—1581no—
372C2×#95—1581no—
373#340—791no—
374#340—791no—
375#340—791no—
376#340—791no—
377#340—791no—
378#340—791no—
379#340—791no—
380#340—791no—
381#340—791no—
382#340C2×D7911yescharacteristic
383#340C2×D7911yescharacteristic
384#340C2×D7911yescharacteristic
385C23×C4—791no—
386C23×C4—791no—
387C23×C4—791no—
388C23×C4—1581no—
389C23×C4—1581no—
390C23×C4—1581no—
391C23×C4—1581no—
392C22×C8—791no—
393C22×C8—794no—
394C22×C8—791no—
395C22×C8—1582no—
396C22×C8—1582no—
397C22×C8—1582no—
398C22×C8—1582no—
399C22×C8—1582no—
400C22×C8C22×D7911yescharacteristic
401C22×C8C22×D7911yescharacteristic
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—3164no—
405C2×C4⋊C4—3164no—
406C2×C4⋊C4—791no—
407C2×C4⋊C4—791no—
408C2×C4⋊C4—794no—
409C2×C4⋊C4—794no—
410C2×C4⋊C4—791no—
411C2×C4⋊C4—791no—
412C2×C4⋊C4—1582no—
413C2×C4⋊C4—1582no—
414C2×C4⋊C4—1582no—
415C2×C4⋊C4—1582no—
416C2×C4⋊C4—1582no—
417C2×C4⋊C4—1582no—
418C2×C4⋊C4—1581no—
419C2×C4⋊C4—1581no—
420C2×C4⋊C4—1581no—
421C2×C4⋊C4—1581no—
422C2×C4⋊C4—1581no—
423C2×C4⋊C4—1581no—
424C2×C4⋊C4—1581no—
425C2×C4⋊C4—1581no—
426C2×C4⋊C4—1581no—
427C2×C4⋊C4—1581no—
428C2×C4⋊C4C22×D7911yescharacteristic
429C2×C4⋊C4C22×D7911yescharacteristic
430C2×C4⋊C4C22×D7911yescharacteristic
431C2×C4⋊C4C22×D7911yescharacteristic
432C2×C42—791no—
433C2×C42—791no—
434C2×C42—791no—
435C2×C42—1582no—
436C2×C42—1582no—
437C2×C42C22×D7911yescharacteristic
438#106—22no—
439#106—1582no—
440#106—1582no—
441#106—1582no—
442C4⋊C8—22no—
443C4⋊C8—1582no—
444C4⋊C8—1582no—
445C4⋊C8—1582no—
446#95—21no—
447#95—21no—
448#95—1581no—
449#95—1581no—
450#95—1581no—
451#95—1581no—
452#95—1581no—
453#95—1581no—
454C24—791no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—3162no—
460C22×C4—3162no—
461C22×C4—3162no—
462C22×C4—3162no—
463C22×C4—3162no—
464C22×C4—3162no—
465C22×C4—3162no—
466C22×C4—3162no—
467C22×C4—3162no—
468C22×C4—3162no—
469C22×C4—791no—
470C22×C4—792no—
471C22×C4—792no—
472C22×C4—792no—
473C22×C4—792no—
474C22×C4—792no—
475C22×C4—792no—
476C22×C4—791no—
477C22×C4—794no—
478C22×C4—791no—
479C22×C4—1582no—
480C22×C4—1582no—
481C22×C4—1584no—
482C22×C4—1584no—
483C22×C4—1582no—
484C22×C4—1582no—
485C22×C4—1582no—
486C22×C4—1581no—
487C22×C4—1581no—
488C22×C4—1581no—
489C22×C4—1581no—
490C22×C4D4×D7911yescharacteristic
491C22×C4D4×D7911yescharacteristic
492C22×C4C23×D7911yescharacteristic
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—3164no—
499C2×C8—792no—
500C2×C8—1588no—
501C2×C8—1581no—
502C2×C8—1581no—
503C2×C8—1581no—
504C2×C8—1581no—
505C2×C8—1581no—
506C2×C8D4×D7912yes—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—42no—
514C4⋊C4—42no—
515C4⋊C4—3162no—
516C4⋊C4—3162no—
517C4⋊C4—3162no—
518C4⋊C4—3162no—
519C4⋊C4—3162no—
520C4⋊C4—3162no—
521C4⋊C4—3162no—
522C4⋊C4—3162no—
523C4⋊C4—792no—
524C4⋊C4—792no—
525C4⋊C4—1584no—
526C4⋊C4—1584no—
527C4⋊C4—1581no—
528C4⋊C4—1581no—
529C4⋊C4—1581no—
530C4⋊C4—1581no—
531C4⋊C4—1581no—
532C4⋊C4—1581no—
533C4⋊C4Q8×D7912yes—
534C4⋊C4Q8×D7912yes—
535C42—21no—
536C42—21no—
537C42—1582no—
538C42—1582no—
539C42—1581no—
540C42—1581no—
541C23—792no—
542C23—792no—
543C23—792no—
544C23—792no—
545C23—792no—
546C23—792no—
547C23—792no—
548C23C2×D4×D7911yescharacteristic
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—3168no—
567C2×C4—3168no—
568C2×C4—3164no—
569C2×C4—3161no—
570C2×C4—3161no—
571C2×C4—3161no—
572C2×C4—3161no—
573C2×C4—3161no—
574C2×C4—3161no—
575C2×C4—3161no—
576C2×C4—3161no—
577C2×C4—3161no—
578C2×C4—3161no—
579C2×C4—792no—
580C2×C4—792no—
581C2×C4—792no—
582C2×C4—794no—
583C2×C4—794no—
584C2×C4—794no—
585C2×C4—794no—
586C2×C4—792no—
587C2×C4—6324no—
588C2×C4—6324no—
589C2×C4—1588no—
590C2×C4—1581no—
591C2×C4—1582no—
592C2×C4—1582no—
593C2×C4—1581no—
594C2×C4—1581no—
595C2×C4—1581no—
596C2×C4—1581no—
597C2×C4SD16×D7912yes—
598C2×C4C2×D4×D7911yescharacteristic
599C2×C4C2×Q8×D7911yescharacteristic
600C2×C4C2×Q8×D7911yescharacteristic
601C2×C4#41×D7911yescharacteristic
602C2×C4#41×D7911yescharacteristic
603C2×C4#41×D7911yescharacteristic
604C8—22no—
605C8—41no—
606C8—3161no—
607C8—1582no—
608C22—794no—
609C22—794no—
610C22—794no—
611C22—794no—
612C22—794no—
613C22—794no—
614C22—794no—
615C22#121×D7911yescharacteristic
616C22C22⋊Q8×D7911yescharacteristic
617C22C22⋊Q8×D7911yescharacteristic
618C22C2×SD16×D7911yescharacteristic
619C22#135×D7911yescharacteristic
620C22AGL(1,ℤ/8)×D7911yescharacteristic
621C22#137×D7911yescharacteristic
622C4—22no—
623C4—41no—
624C4—42no—
625C4—42no—
626C4—81no—
627C4—81no—
628C4—3161no—
629C4—3162no—
630C4—3162no—
631C4—794no—
632C4—6321no—
633C4—6321no—
634C4—1582no—
635C4#123×D7911yescharacteristic
636C4#125×D7911yescharacteristic
637C4#125×D7911yescharacteristic
638C4C4⋊Q8×D7911yescharacteristic
639C2—798no—
640C2#398×D7911yescharacteristic
641C2#465×D7911yescharacteristic
642C2#468×D7911yescharacteristic
643C2#476×D7911yescharacteristic
644C2#478×D7911yescharacteristic
645C2#475×D7911yescharacteristic
646C2#479×D7911yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC22×C4×C79C24
FrattiniC22×C4C23×D79
FittingC79×#2088C2
socleC23×C79C22×D4
prime radicalC23×D79C2×D4
hypercenter#2088D79
hypocenterC79C2×#2088
LCSG ▷ C22×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2088

Complements

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

NH ≅ G/Ntype
5. #23764904C2semidirect
6. #23764903C2semidirect
7. #23764902C2semidirect
8. #23764901C2semidirect
9. #23764900C2semidirect
10. #23764899C2semidirect
11. #23764898C2semidirect
15. C79×#2088C2semidirect
323. D79#2088direct (N × H)
335. #2088D79direct (N × H)
339. C79C2×#2088semidirect

Maximal subgroups

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

subgroupindex
C2×#106×D792
C2×C4⋊C8×D792
#389×D792
#237649042
#237649032
#237649022
#237649012
#237649002
#237648992
#237648982
#340×D792
C79×#20882
C2×#208879