Finite Group Databasebeta

← #2085×D79 #34317233

Subgroups — #2085×D79 #34317233

Order 20224.

998 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×#107×D79C211yesmaximal, characteristic
2C2×#106×D79C211yesmaximal, characteristic
3#389×D79C211yesmaximal, characteristic
4#382×D79C211yesmaximal, characteristic
5#23764887C211yesmaximal, characteristic, complemented
6#23764886C211yesmaximal, characteristic, complemented
7#23764885C211yesmaximal, characteristic, complemented
8#23764884C211yesmaximal, characteristic, complemented
9#23764883C211yesmaximal, characteristic, complemented
10#23764882C211yesmaximal, characteristic, complemented
11#23764881C211yesmaximal, characteristic, complemented
12#340×D79C211yesmaximal, characteristic
13#340×D79C211yesmaximal, characteristic
14#336×D79C211yesmaximal, characteristic
15C79×#2085C211yesmaximal, 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×D79C2211yescharacteristic
24C2×#14579095C2211yescharacteristic
25C2×#14579094C2211yescharacteristic
26C2×#14579094C2211yescharacteristic
27#107×D79—24no—
28C2×#14579093C2211yescharacteristic
29C2×#14579092C2211yescharacteristic
30C2×#14579092C2211yescharacteristic
31#106×D79—24no—
32#19098462C2211yescharacteristic
33#19098461C2211yescharacteristic
34#19098460—21no—
35#19098459C2211yescharacteristic
36#19098458—21no—
37#19098429C2211yescharacteristic
38#19098428C2211yescharacteristic
39#19098428C2211yescharacteristic
40#19098427—21no—
41#19098427—21no—
42#95×D79—21no—
43#95×D79—21no—
44#95×D79—21no—
45#19098326C2211yescharacteristic
46#19098326C2211yescharacteristic
47#19098325C2211yescharacteristic
48#19098325C2211yescharacteristic
49#19098325C2211yescharacteristic
50#19098325C2211yescharacteristic
51#19098318C2211yescharacteristic
52#19098317C2211yescharacteristic
53#19098317C2211yescharacteristic
54C2×#107×C79C2211yescharacteristic
55C2×#106×C79C2211yescharacteristic
56#389×C79C2211yescharacteristic
57#382×C79C2211yescharacteristic
58#340×C79C2211yescharacteristic
59#340×C79C2211yescharacteristic
60#336×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×D79Q814yes—
75C2×C8×D79Q814yes—
76C2×C4⋊Dic79—21no—
77C2×C4⋊Dic79C2311yescharacteristic
78C2×C4⋊Dic79C2311yescharacteristic
79C2×C4⋊Dic79C2311yescharacteristic
80C2×C4⋊Dic79C2311yescharacteristic
81C2×Dic79⋊C4—21no—
82C2×Dic79⋊C4—21no—
83C2×Dic79⋊C4—21no—
84C2×Dic79⋊C4—21no—
85C2×Dic79⋊C4—21no—
86C2×Dic79⋊C4—21no—
87C4⋊C4×D79—22no—
88C4⋊C4×D79—22no—
89C4⋊C4×D79—22no—
90C4⋊C4×D79—22no—
91C4⋊C4×D79—22no—
92C4⋊C4×D79—22no—
93C4⋊C4×D79—22no—
94C4⋊C4×D79—44no—
95C4⋊C4×D79D414yes—
96C2×C4×Dic79D411yescharacteristic
97C2×C4×Dic79D411yescharacteristic
98C2×C4×Dic79C2311yescharacteristic
99C42×D79—22no—
100C42×D79—22no—
101#14579095—22no—
102#14579094—22no—
103#14579094—22no—
104#14579093—22no—
105#14579092—22no—
106#14579092—22no—
107C79⋊#95—21no—
108C79⋊#95—21no—
109C79⋊#95—21no—
110C79⋊#95—21no—
111C79⋊#95—21no—
112C79⋊#95—21no—
113C79⋊#95—21no—
114C79⋊#95—21no—
115C79⋊#95—21no—
116C22×C8×C79C2311yescharacteristic
117C22×C8×C79C2311yescharacteristic
118C2×C4⋊C4×C79—21no—
119C2×C4⋊C4×C79C2311yescharacteristic
120C2×C4⋊C4×C79C2311yescharacteristic
121C2×C4⋊C4×C79C2311yescharacteristic
122C2×C4⋊C4×C79C2311yescharacteristic
123C2×C42×C79C2311yescharacteristic
124#107×C79—22no—
125#106×C79—22no—
126#95×C79—21no—
127#95×C79—21no—
128#95×C79—21no—
129C23×D79C2×D411yescharacteristic
130C22×Dic79—21no—
131C22×Dic79—21no—
132C22×Dic79—21no—
133C22×Dic79—21no—
134C22×Dic79C2×D411yescharacteristic
135C22×Dic79C2×D411yescharacteristic
136C22×Dic79C2×D411yescharacteristic
137C2×C4×D79—24no—
138C2×C4×D79—22no—
139C2×C4×D79—22no—
140C2×C4×D79—22no—
141C2×C4×D79—22no—
142C2×C4×D79—22no—
143C2×C4×D79—22no—
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×D79—42no—
151C2×C4×D79—42no—
152C2×C4×D79—42no—
153C2×C4×D79—42no—
154C2×C4×D79—42no—
155C2×C4×D79C2×D412yes—
156C2×C4×D79C2×Q812yes—
157C2×C4×D79C2×Q812yes—
158C2×C4×D79#4112yes—
159C2×C4×D79#4112yes—
160C2×C4×D79#4112yes—
161C2×C79⋊C8—21no—
162C2×C79⋊C8—21no—
163C2×C79⋊C8—21no—
164C2×C79⋊C8—21no—
165C2×C79⋊C8C2×Q812yes—
166C2×C79⋊C8C2×Q812yes—
167C8×D79—28no—
168C8×D79—28no—
169C4⋊Dic79—21no—
170C4⋊Dic79—21no—
171C4⋊Dic79—21no—
172C4⋊Dic79—21no—
173C4⋊Dic79—21no—
174C4⋊Dic79—21no—
175C4⋊Dic79—21no—
176C4⋊Dic79—42no—
177C4⋊Dic79C2×D412yes—
178Dic79⋊C4—24no—
179Dic79⋊C4—42no—
180Dic79⋊C4—42no—
181Dic79⋊C4—42no—
182Dic79⋊C4—42no—
183Dic79⋊C4—42no—
184C4×Dic79—22no—
185C4×Dic79—22no—
186C4×Dic79—21no—
187C4×Dic79—21no—
188C22×C4×C79—21no—
189C22×C4×C79—21no—
190C22×C4×C79—21no—
191C22×C4×C79—21no—
192C22×C4×C79C2×D411yescharacteristic
193C22×C4×C79C2×D411yescharacteristic
194C22×C4×C79C2411yescharacteristic
195C2×C8×C79—21no—
196C2×C8×C79—21no—
197C2×C8×C79—21no—
198C2×C8×C79—21no—
199C2×C8×C79C2×Q812yes—
200C2×C8×C79C2×Q812yes—
201C4⋊C4×C79—21no—
202C4⋊C4×C79—21no—
203C4⋊C4×C79—21no—
204C4⋊C4×C79—21no—
205C4⋊C4×C79—21no—
206C4⋊C4×C79—21no—
207C4⋊C4×C79—21no—
208C4⋊C4×C79—42no—
209C4⋊C4×C79C2×D412yes—
210C42×C79—21no—
211C42×C79—21no—
212C23×C79C22×D411yescharacteristic
213C22×D79#12112yes—
214C22×D79#12312yes—
215C22×D79C4⋊Q812yes—
216C22×D79#13512yes—
217C22×D79#13512yes—
218C22×D79AGL(1,ℤ/8)12yes—
219C22×D79#13712yes—
220C2×C4×C79—22no—
221C2×C4×C79—21no—
222C2×C4×C79—21no—
223C2×C4×C79—21no—
224C2×C4×C79—21no—
225C2×C4×C79—21no—
226C2×C4×C79—21no—
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—41no—
237C2×C4×C79—41no—
238C2×C4×C79C22×D411yescharacteristic
239C2×C4×C79C22×Q811yescharacteristic
240C2×C4×C79C22×Q811yescharacteristic
241C2×C4×C79C2×#4111yescharacteristic
242C2×C4×C79C2×#4111yescharacteristic
243C2×C4×C79C2×#4111yescharacteristic
244C2×Dic79—22no—
245C2×Dic79—21no—
246C2×Dic79—21no—
247C2×Dic79—21no—
248C2×Dic79—21no—
249C2×Dic79—21no—
250C2×Dic79—21no—
251C2×Dic79—41no—
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×Dic79—41no—
262C2×Dic79#12112yes—
263C2×Dic79#12312yes—
264C2×Dic79C4⋊Q812yes—
265C4×D79—48no—
266C4×D79—44no—
267C4×D79—44no—
268C4×D79—84no—
269C4×D79—84no—
270C4×D79—84no—
271C4×D79C22⋊Q814yes—
272C4×D79C22⋊Q814yes—
273C4×D79#12514yes—
274C4×D79#12514yes—
275C8×C79—22no—
276C8×C79—22no—
277C79⋊C8—22no—
278C79⋊C8—22no—
279C22×C79C2×#12111yescharacteristic
280C22×C79C2×#12311yescharacteristic
281C22×C79C2×C4⋊Q811yescharacteristic
282C22×C79C2×#13511yescharacteristic
283C22×C79C2×#13511yescharacteristic
284C22×C79C2×AGL(1,ℤ/8)11yescharacteristic
285C22×C79C2×#13711yescharacteristic
286C2×D79#39814yes—
287C2×D79#46314yes—
288C2×D79#46414yes—
289C2×D79#48214yes—
290C2×D79#48514yes—
291C2×D79#49914yes—
292C2×D79#50114yes—
293C4×C79—41no—
294C4×C79—41no—
295C4×C79—42no—
296C4×C79—81no—
297C4×C79—81no—
298C4×C79—81no—
299C4×C79C2×C22⋊Q811yescharacteristic
300C4×C79C2×C22⋊Q811yescharacteristic
301C4×C79C2×#12511yescharacteristic
302C4×C79C2×#12511yescharacteristic
303Dic79—41no—
304Dic79—41no—
305Dic79—42no—
306Dic79—81no—
307Dic79—81no—
308Dic79—81no—
309Dic79#39814yes—
310C2×#2085—791nomaximal, Sylow
311C2×C79C2×#39811yescharacteristic
312C2×C79C2×#46311yescharacteristic
313C2×C79C2×#46411yescharacteristic
314C2×C79C2×#48211yescharacteristic
315C2×C79C2×#48511yescharacteristic
316C2×C79C2×#49911yescharacteristic
317C2×C79C2×#50111yescharacteristic
318D79#208518yesdirect product factor
319C22×#107—791no—
320C22×#106—791no—
321C2×#389—791no—
322C2×#382—791no—
323#2085—791no—
324#2085—791no—
325#2085—791no—
326#2085—791no—
327#2085—791no—
328#2085—791no—
329#2085—791no—
330#2085D7911yescharacteristic, direct product factor
331C2×#340—791no—
332C2×#340—791no—
333C2×#336—791no—
334C79C2×#208511yescharacteristic, 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—
343C2×#107—791no—
344C2×#107—791no—
345C2×#107—791no—
346C2×#107—1584no—
347C2×#107C2×D7911yescharacteristic
348C2×#106—791no—
349C2×#106—791no—
350C2×#106—791no—
351C2×#106—1584no—
352C2×#106C2×D7911yescharacteristic
353#389—791no—
354#389—791no—
355#389—791no—
356#389—1581no—
357#389—1581no—
358#389C2×D7911yescharacteristic
359#382—791no—
360#382—791no—
361#382—791no—
362#382—1581no—
363#382—1581no—
364#382C2×D7911yescharacteristic
365C2×#95—1581no—
366C2×#95—1581no—
367C2×#95—1581no—
368#340—791no—
369#340—791no—
370#340—791no—
371#340—791no—
372#340—791no—
373#340—791no—
374#340C2×D7911yescharacteristic
375#340C2×D7911yescharacteristic
376#336—791no—
377#336—791no—
378#336—791no—
379#336C2×D7911yescharacteristic
380C23×C4—791no—
381C23×C4—791no—
382C23×C4—791no—
383C23×C4—1581no—
384C23×C4—1581no—
385C23×C4—1581no—
386C23×C4—1581no—
387C22×C8—791no—
388C22×C8—791no—
389C22×C8—794no—
390C22×C8—794no—
391C22×C8—1582no—
392C22×C8—1582no—
393C22×C8—1582no—
394C22×C8—1582no—
395C22×C8C22×D7911yescharacteristic
396C22×C8C22×D7911yescharacteristic
397C2×C4⋊C4—21no—
398C2×C4⋊C4—3164no—
399C2×C4⋊C4—791no—
400C2×C4⋊C4—794no—
401C2×C4⋊C4—791no—
402C2×C4⋊C4—791no—
403C2×C4⋊C4—791no—
404C2×C4⋊C4—1582no—
405C2×C4⋊C4—1582no—
406C2×C4⋊C4—1582no—
407C2×C4⋊C4—1582no—
408C2×C4⋊C4—1582no—
409C2×C4⋊C4—1582no—
410C2×C4⋊C4—1582no—
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⋊C4—1581no—
418C2×C4⋊C4C22×D7911yescharacteristic
419C2×C4⋊C4C22×D7911yescharacteristic
420C2×C4⋊C4C22×D7911yescharacteristic
421C2×C4⋊C4C22×D7911yescharacteristic
422C2×C42—791no—
423C2×C42—791no—
424C2×C42—791no—
425C2×C42—1582no—
426C2×C42—1582no—
427C2×C42C22×D7911yescharacteristic
428#107—22no—
429#107—1582no—
430#107—1582no—
431#107—1582no—
432#106—22no—
433#106—1582no—
434#106—1582no—
435#106—1582no—
436#95—21no—
437#95—21no—
438#95—21no—
439#95—1581no—
440#95—1581no—
441#95—1581no—
442#95—1581no—
443#95—1581no—
444#95—1581no—
445#95—1581no—
446#95—1581no—
447#95—1581no—
448C24—791no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—3162no—
454C22×C4—3162no—
455C22×C4—3162no—
456C22×C4—3162no—
457C22×C4—3162no—
458C22×C4—3162no—
459C22×C4—3162no—
460C22×C4—3162no—
461C22×C4—3162no—
462C22×C4—3162no—
463C22×C4—3162no—
464C22×C4—791no—
465C22×C4—792no—
466C22×C4—792no—
467C22×C4—792no—
468C22×C4—792no—
469C22×C4—792no—
470C22×C4—792no—
471C22×C4—791no—
472C22×C4—791no—
473C22×C4—1582no—
474C22×C4—1582no—
475C22×C4—1582no—
476C22×C4—1584no—
477C22×C4—1582no—
478C22×C4—1582no—
479C22×C4—1582no—
480C22×C4—1581no—
481C22×C4—1581no—
482C22×C4—1581no—
483C22×C4—1581no—
484C22×C4D4×D7911yescharacteristic
485C22×C4D4×D7911yescharacteristic
486C22×C4C23×D7911yescharacteristic
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—792no—
492C2×C8—792no—
493C2×C8—1588no—
494C2×C8—1588no—
495C2×C8—1581no—
496C2×C8—1581no—
497C2×C8—1581no—
498C2×C8—1581no—
499C2×C8Q8×D7912yes—
500C2×C8Q8×D7912yes—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—42no—
509C4⋊C4—3162no—
510C4⋊C4—3162no—
511C4⋊C4—3162no—
512C4⋊C4—3162no—
513C4⋊C4—3162no—
514C4⋊C4—3162no—
515C4⋊C4—792no—
516C4⋊C4—1584no—
517C4⋊C4—1581no—
518C4⋊C4—1581no—
519C4⋊C4—1581no—
520C4⋊C4—1581no—
521C4⋊C4—1581no—
522C4⋊C4—1581no—
523C4⋊C4—1581no—
524C4⋊C4D4×D7912yes—
525C42—21no—
526C42—21no—
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—22no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
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—41no—
556C2×C4—41no—
557C2×C4—3168no—
558C2×C4—3164no—
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—3161no—
570C2×C4—3161no—
571C2×C4—792no—
572C2×C4—792no—
573C2×C4—792no—
574C2×C4—794no—
575C2×C4—794no—
576C2×C4—794no—
577C2×C4—794no—
578C2×C4—6324no—
579C2×C4—6324no—
580C2×C4—6324no—
581C2×C4—1582no—
582C2×C4—1581no—
583C2×C4—1581no—
584C2×C4—1581no—
585C2×C4—1581no—
586C2×C4—1581no—
587C2×C4—1581no—
588C2×C4C2×D4×D7911yescharacteristic
589C2×C4C2×Q8×D7911yescharacteristic
590C2×C4C2×Q8×D7911yescharacteristic
591C2×C4#41×D7911yescharacteristic
592C2×C4#41×D7911yescharacteristic
593C2×C4#41×D7911yescharacteristic
594C8—22no—
595C8—22no—
596C8—1582no—
597C8—1582no—
598C22—794no—
599C22—794no—
600C22—794no—
601C22—794no—
602C22—794no—
603C22—794no—
604C22—794no—
605C22#121×D7911yescharacteristic
606C22#123×D7911yescharacteristic
607C22C4⋊Q8×D7911yescharacteristic
608C22#135×D7911yescharacteristic
609C22#135×D7911yescharacteristic
610C22AGL(1,ℤ/8)×D7911yescharacteristic
611C22#137×D7911yescharacteristic
612C4—41no—
613C4—41no—
614C4—42no—
615C4—81no—
616C4—81no—
617C4—81no—
618C4—3161no—
619C4—3161no—
620C4—3162no—
621C4—794no—
622C4—6321no—
623C4—6321no—
624C4—6321no—
625C4C22⋊Q8×D7911yescharacteristic
626C4C22⋊Q8×D7911yescharacteristic
627C4#125×D7911yescharacteristic
628C4#125×D7911yescharacteristic
629C2—798no—
630C2#398×D7911yescharacteristic
631C2#463×D7911yescharacteristic
632C2#464×D7911yescharacteristic
633C2#482×D7911yescharacteristic
634C2#485×D7911yescharacteristic
635C2#499×D7911yescharacteristic
636C2#501×D7911yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC22×C4×C79C24
FrattiniC22×C4C23×D79
FittingC79×#2085C2
socleC23×C79C22×D4
prime radicalC23×D79C2×D4
hypercenter#2085D79
hypocenterC79C2×#2085
LCSG ▷ C22×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2085

Complements

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

NH ≅ G/Ntype
5. #23764887C2semidirect
6. #23764886C2semidirect
7. #23764885C2semidirect
8. #23764884C2semidirect
9. #23764883C2semidirect
10. #23764882C2semidirect
11. #23764881C2semidirect
15. C79×#2085C2semidirect
318. D79#2085direct (N × H)
330. #2085D79direct (N × H)
334. C79C2×#2085semidirect

Maximal subgroups

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

subgroupindex
C2×#107×D792
C2×#106×D792
#389×D792
#382×D792
#237648872
#237648862
#237648852
#237648842
#237648832
#237648822
#237648812
#340×D792
#336×D792
C79×#20852
C2×#208579