Finite Group Databasebeta

← #34296266

Subgroups — #34296266

Order 20224.

818 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19098920C211yesmaximal, characteristic
2#23766142C211yesmaximal, characteristic, complemented
3#23766108C211yesmaximal, characteristic
4#23764216C211yesmaximal, characteristic
5#23764098C211yesmaximal, characteristic
6#23764091C211yesmaximal, characteristic, complemented
7#23764084C211yesmaximal, characteristic
8#23764077C211yesmaximal, characteristic, complemented
9#23763527C211yesmaximal, characteristic, complemented
10#23763229C211yesmaximal, characteristic, complemented
11#23763224C211yesmaximal, characteristic
12#23763219C211yesmaximal, characteristic, complemented
13#23763214C211yesmaximal, characteristic
14#23763088C211yesmaximal, characteristic, complemented
15C79×#1992C211yesmaximal, characteristic, complemented
16C2×#14579149C2211yescharacteristic
17C2×#14579126C2211yescharacteristic
18C2×#14579123C2211yescharacteristic
19#19098920C418yescomplemented
20C2×#14579086C2211yescharacteristic
21C2×#14579086C2211yescharacteristic
22C2×#14579084C2211yescharacteristic
23C2×#14579084C2211yescharacteristic
24C2×#14579083C2211yescharacteristic
25C2×#14579083C2211yescharacteristic
26C2×#14579081C2211yescharacteristic
27C2×#14579081C2211yescharacteristic
28C2×#14579071C2211yescharacteristic
29C2×#14579071C2211yescharacteristic
30C2×C4×C79⋊C8C2211yescharacteristic
31C2×C8×Dic79C2211yescharacteristic
32C2×C8×Dic79C2211yescharacteristic
33#19098468C2211yescharacteristic
34#19098464C2211yescharacteristic
35#19098462—21no—
36#19098462—21no—
37#19098462C2211yescharacteristic
38#19098462C2211yescharacteristic
39#19098453—21no—
40#19098453—21no—
41#19098449—21no—
42#19098449—21no—
43#19098434—21no—
44#19098434—21no—
45#19098433C2211yescharacteristic
46C4⋊C4×Dic79C2211yescharacteristic
47C4⋊C4×Dic79C2211yescharacteristic
48#19098409C2211yescharacteristic
49#19098325C2211yescharacteristic
50#19098325C2211yescharacteristic
51#19098325C2211yescharacteristic
52#19098325C2211yescharacteristic
53C2×#125×C79C2211yescharacteristic
54C2×#97×C79C2211yescharacteristic
55#384×C79C2211yescharacteristic
56#340×C79C2211yescharacteristic
57#340×C79C2211yescharacteristic
58#340×C79C2211yescharacteristic
59#340×C79C2211yescharacteristic
60C22×Dic158C2311yescharacteristic
61C22×D316C2311yescharacteristic
62C22×C4×D79—21no—
63C22×C79⋊C8C2311yescharacteristic
64C22×C79⋊C8C2311yescharacteristic
65#14579149—22no—
66#14579149C2×C414yes—
67#14579126—22no—
68#14579126—22no—
69#14579123—22no—
70#14579123—22no—
71C2×C4⋊Dic79—21no—
72C2×C4⋊Dic79—21no—
73C2×C4⋊Dic79—21no—
74C2×C4⋊Dic79—21no—
75C2×C4⋊Dic79C2311yescharacteristic
76C2×C4⋊Dic79C2311yescharacteristic
77C2×Dic79⋊C4—21no—
78C2×(C2×D79)⋊C4—21no—
79C2×(C2×D79)⋊C4—21no—
80C2×(C2×D79)⋊C4—21no—
81C2×(C2×D79)⋊C4—21no—
82C2×(C2×D79)⋊C4—21no—
83C2×C4×Dic79—21no—
84C2×C4×Dic79—21no—
85C2×C4×Dic79—21no—
86C2×C4×Dic79C2311yescharacteristic
87C2×C4×Dic79C2311yescharacteristic
88#14579086—22no—
89#14579086—22no—
90#14579084C2×C414yescomplemented
91#14579084C2×C414yescomplemented
92#14579083—22no—
93#14579083—22no—
94#14579081C2×C414yes—
95#14579081C2×C414yes—
96#14579071—22no—
97#14579071—22no—
98C4×C79⋊C8C2×C414yescomplemented
99C8×Dic79—22no—
100C8×Dic79—22no—
101C79⋊#95—21no—
102C79⋊#95—21no—
103C79⋊#95—21no—
104C79⋊#95—21no—
105C79⋊#95—21no—
106C79⋊#95—21no—
107C79⋊#95D411yescharacteristic
108C79⋊#95D411yescharacteristic
109C79⋊#95D411yescharacteristic
110C79⋊#95D411yescharacteristic
111C22×C8×C79C2311yescharacteristic
112C22×C8×C79C2311yescharacteristic
113#125×C79—22no—
114#125×C79C2×C414yescomplemented
115C2×C4⋊C4×C79—21no—
116C2×C4⋊C4×C79—21no—
117C2×C4⋊C4×C79—21no—
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#97×C79—22no—
125C23×D79—21no—
126C2×Dic158—21no—
127C2×Dic158—21no—
128C2×Dic158—21no—
129C2×Dic158—21no—
130C2×Dic158—21no—
131C2×Dic158C22×C412yes—
132C2×D316—21no—
133C2×D316—21no—
134C2×D316—21no—
135C2×D316—21no—
136C2×D316—21no—
137C2×D316C22×C412yes—
138C22×Dic79—21no—
139C22×Dic79—21no—
140C22×Dic79—21no—
141C22×Dic79C2×D411yescharacteristic
142C22×Dic79C2×D411yescharacteristic
143C22×Dic79C2×D411yescharacteristic
144C22×Dic79C2×D411yescharacteristic
145C2×C4×D79—42no—
146C2×C4×D79—81no—
147C2×C4×D79—81no—
148C2×C79⋊C8—21no—
149C2×C79⋊C8—21no—
150C2×C79⋊C8—21no—
151C2×C79⋊C8—21no—
152C2×C79⋊C8C22×C412yes—
153C2×C79⋊C8C22×C412yes—
154C4⋊Dic79—21no—
155C4⋊Dic79—21no—
156C4⋊Dic79—21no—
157C4⋊Dic79—21no—
158C4⋊Dic79—81no—
159C4⋊Dic79—81no—
160C4⋊Dic79—81no—
161C4⋊Dic79—81no—
162Dic79⋊C4—42no—
163(C2×D79)⋊C4—24no—
164(C2×D79)⋊C4—24no—
165(C2×D79)⋊C4—42no—
166(C2×D79)⋊C4—81no—
167(C2×D79)⋊C4—81no—
168C4×Dic79—21no—
169C4×Dic79—21no—
170C4×Dic79—42no—
171C4×Dic79—81no—
172C4×Dic79—81no—
173C4×Dic79#4112yes—
174C4×Dic79#4112yes—
175C22×C4×C79—21no—
176C22×C4×C79—21no—
177C22×C4×C79—21no—
178C22×C4×C79—21no—
179C22×C4×C79C2×D411yescharacteristic
180C22×C4×C79C2×D411yescharacteristic
181C22×C4×C79C2411yescharacteristic
182C2×C8×C79—21no—
183C2×C8×C79—21no—
184C2×C8×C79—21no—
185C2×C8×C79—21no—
186C2×C8×C79#4112yes—
187C2×C8×C79#4112yes—
188C4⋊C4×C79—24no—
189C4⋊C4×C79—24no—
190C4⋊C4×C79—21no—
191C4⋊C4×C79—21no—
192C4⋊C4×C79—21no—
193C4⋊C4×C79—21no—
194C4⋊C4×C79—21no—
195C4⋊C4×C79—21no—
196C4⋊C4×C79—81no—
197C4⋊C4×C79—81no—
198C4⋊C4×C79C22×C412yes—
199C4⋊C4×C79C22×C412yes—
200C42×C79C22×C412yes—
201C42×C79#4112yes—
202C23×C79C22×D411yescharacteristic
203C22×D79—22no—
204C22×D79—41no—
205C22×D79—41no—
206C22×D79—41no—
207C22×D79—41no—
208C22×D79—41no—
209C22×D79—41no—
210C2×C4×C79—21no—
211C2×C4×C79—21no—
212C2×C4×C79—21no—
213C2×C4×C79—21no—
214C2×C4×C79—22no—
215C2×C4×C79—22no—
216C2×C4×C79—41no—
217C2×C4×C79—41no—
218C2×C4×C79—41no—
219C2×C4×C79—41no—
220C2×C4×C79—41no—
221C2×C4×C79—41no—
222C2×C4×C79—41no—
223C2×C4×C79—41no—
224C2×C4×C79—41no—
225C2×C4×C79—41no—
226C2×C4×C79C4×D412yes—
227C2×C4×C79C4×D412yes—
228C2×C4×C79C23×C411yescharacteristic
229C2×C4×C79C2×#4111yescharacteristic
230C2×C4×C79C2×#4111yescharacteristic
231C2×C4×C79C2×#4111yescharacteristic
232C2×C4×C79C2×#4111yescharacteristic
233C2×C4×C79C2×#4111yescharacteristic
234C2×Dic79—21no—
235C2×Dic79—21no—
236C2×Dic79—21no—
237C2×Dic79—21no—
238C2×Dic79—22no—
239C2×Dic79—21no—
240C2×Dic79—21no—
241C2×Dic79—21no—
242C2×Dic79—21no—
243C2×Dic79—21no—
244C2×Dic79—21no—
245C2×Dic79—41no—
246C2×Dic79—41no—
247C2×Dic79—41no—
248C2×Dic79—41no—
249C2×Dic79—41no—
250C2×Dic79—41no—
251C2×Dic79—41no—
252C2×Dic79—41no—
253C2×Dic79#12412yes—
254C2×Dic79#12412yes—
255D316—22no—
256D316—22no—
257D316—41no—
258D316—41no—
259C4×D79—84no—
260Dic158—22no—
261Dic158—22no—
262Dic158—41no—
263Dic158—41no—
264C8×C79—22no—
265C8×C79—22no—
266C79⋊C8—22no—
267C79⋊C8—22no—
268C22×C79C2×C4×D411yescharacteristic
269C22×C79C2×#12411yescharacteristic
270C22×C79#53211yescharacteristic
271C22×C79#57611yescharacteristic
272C22×C79#57711yescharacteristic
273C22×C79#57711yescharacteristic
274C22×C79#57811yescharacteristic
275C2×D79—42no—
276C2×D79—42no—
277C2×D79—42no—
278C2×D79—81no—
279C2×D79—81no—
280C2×D79—81no—
281C2×D79—81no—
282C4×C79—22no—
283C4×C79—22no—
284C4×C79—42no—
285C4×C79—42no—
286C4×C79—81no—
287C4×C79—81no—
288C4×C79C4×#4111yescharacteristic
289C4×C79C4×#4111yescharacteristic
290C4×C79#52911yescharacteristic
291C4×C79#52911yescharacteristic
292Dic79—22no—
293Dic79—22no—
294Dic79—41no—
295Dic79—41no—
296Dic79—42no—
297Dic79—81no—
298Dic79—81no—
299#21643—791nomaximal, Sylow
300C2×C79C4×#12411yescharacteristic
301C2×C79#295111yescharacteristic
302C2×C79#295211yescharacteristic
303C2×C79#313611yescharacteristic
304C2×C79#313711yescharacteristic
305C2×C79#317811yescharacteristic
306C2×C79#317911yescharacteristic
307D79—82no—
308C2×#488—791no—
309#2330—791no—
310#2326—791no—
311#1992D7911yescharacteristic, complemented
312#1959—791no—
313#1936—791no—
314#1935—791no—
315#1934—791no—
316#1933—791no—
317#1834—791no—
318#1763—791no—
319#1762—791no—
320C4×#103—791no—
321C4×#102—791no—
322#1726—791no—
323C79#2164311yescharacteristic, complemented, Sylow
324C2×#125C2×D7911yescharacteristic
325C2×#124—791no—
326C2×C4×Q8—791no—
327C2×C4×D4—791no—
328#488—798no—
329C2×#103—791no—
330C2×#103—791no—
331C2×#103—791no—
332C2×#103—791no—
333C2×#102—791no—
334C2×#102—791no—
335C2×#102—791no—
336C2×#102—791no—
337C2×#97—791no—
338C2×#97—791no—
339C2×#97C2×D7911yescharacteristic
340C2×C4×C8—791no—
341C2×C4×C8—791no—
342C2×C4×C8—791no—
343#391—791no—
344#390—791no—
345#389—791no—
346#389—791no—
347#389—1581no—
348#389—1581no—
349#388—1581no—
350#388—1581no—
351#387—1581no—
352#387—1581no—
353#385—1581no—
354#385—1581no—
355#384—791no—
356#384C2×D7911yescharacteristic
357C4×C4⋊C4—791no—
358C4×C4⋊C4—791no—
359#376—791no—
360#340—791no—
361#340—791no—
362#340—791no—
363#340—791no—
364#340C2×D7911yescharacteristic
365#340C2×D7911yescharacteristic
366#340C2×D7911yescharacteristic
367#340C2×D7911yescharacteristic
368C22×Q8—791no—
369C22×D4—791no—
370C23×C4—1581no—
371C22×C8—791no—
372C22×C8—791no—
373C22×C8C22×D7911yescharacteristic
374C22×C8C22×D7911yescharacteristic
375#125—22no—
376#125C4×D7914yescomplemented
377#124—794no—
378#124—1582no—
379C4×Q8—1582no—
380C4×Q8—1582no—
381C4×D4—1582no—
382C4×D4—1582no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—791no—
388C2×C4⋊C4—791no—
389C2×C4⋊C4—1581no—
390C2×C4⋊C4—1581no—
391C2×C4⋊C4—1581no—
392C2×C4⋊C4—1581no—
393C2×C4⋊C4—1581no—
394C2×C4⋊C4C22×D7911yescharacteristic
395C2×C4⋊C4C22×D7911yescharacteristic
396C2×C4⋊C4C22×D7911yescharacteristic
397C2×C4⋊C4C22×D7911yescharacteristic
398C2×C22⋊C4—1581no—
399C2×C22⋊C4—1581no—
400C2×C22⋊C4—1581no—
401C2×C22⋊C4—1581no—
402C2×C22⋊C4—1581no—
403C2×C42—791no—
404C2×C42—791no—
405C2×C42—1581no—
406C2×C42—1581no—
407C2×C42—1581no—
408C2×C42C22×D7911yescharacteristic
409#103—794no—
410#103—794no—
411#103—1582no—
412#103—1582no—
413#102—794no—
414#102—794no—
415#102—1582no—
416#102—1582no—
417#97—22no—
418#97—1582no—
419#97—1582no—
420C4×C8—794no—
421C4×C8—1582no—
422C4×C8—1582no—
423#95—791no—
424#95—791no—
425#95—791no—
426#95—791no—
427#95—1581no—
428#95—1581no—
429#95—1581no—
430#95—1581no—
431#95—1581no—
432#95—1581no—
433C24—1581no—
434C2×Q8—792no—
435C2×Q8—1581no—
436C2×Q8—1581no—
437C2×Q8—1581no—
438C2×Q8—1581no—
439C2×Q8—1581no—
440C2×D4—792no—
441C2×D4—1581no—
442C2×D4—1581no—
443C2×D4—1581no—
444C2×D4—1581no—
445C2×D4—1581no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—3162no—
451C22×C4—791no—
452C22×C4—791no—
453C22×C4—791no—
454C22×C4—791no—
455C22×C4—6321no—
456C22×C4—6321no—
457C22×C4—1581no—
458C22×C4—1581no—
459C22×C4—1581no—
460C22×C4D4×D7911yescharacteristic
461C22×C4D4×D7911yescharacteristic
462C22×C4C23×D7911yescharacteristic
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—792no—
468C2×C8—792no—
469C2×C8—1581no—
470C2×C8—1581no—
471C2×C8—1581no—
472C2×C8—1581no—
473C2×C8#1192962512yes—
474C2×C8#1192962512yes—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—24no—
478C4⋊C4—24no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—81no—
484C4⋊C4—81no—
485C4⋊C4—3162no—
486C4⋊C4—6321no—
487C4⋊C4—6321no—
488C4⋊C4—6321no—
489C4⋊C4—6321no—
490C4⋊C4—1581no—
491C4⋊C4—1581no—
492C4⋊C4—1581no—
493C4⋊C4—1581no—
494C4⋊C4C2×C4×D7912yes—
495C4⋊C4C2×C4×D7912yes—
496C22⋊C4—3162no—
497C22⋊C4—6321no—
498C22⋊C4—6321no—
499C22⋊C4—1584no—
500C22⋊C4—1584no—
501C42—3162no—
502C42—792no—
503C42—792no—
504C42—6321no—
505C42—6321no—
506C42—1581no—
507C42—1581no—
508C42C2×C4×D7912yes—
509C42#1192962312yes—
510C23—3161no—
511C23—3161no—
512C23—3161no—
513C23—3161no—
514C23—3161no—
515C23—3161no—
516C23—1582no—
517C23C2×D4×D7911yescharacteristic
518Q8—3161no—
519Q8—3161no—
520Q8—1582no—
521Q8—1582no—
522D4—3161no—
523D4—3161no—
524D4—1582no—
525D4—1582no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—3161no—
543C2×C4—3161no—
544C2×C4—3161no—
545C2×C4—3161no—
546C2×C4—3161no—
547C2×C4—3161no—
548C2×C4—3161no—
549C2×C4—3161no—
550C2×C4—792no—
551C2×C4—792no—
552C2×C4—6324no—
553C2×C4—1582no—
554C2×C4—1581no—
555C2×C4—1581no—
556C2×C4—1581no—
557C2×C4—1581no—
558C2×C4—1581no—
559C2×C4—1581no—
560C2×C4—1581no—
561C2×C4—1581no—
562C2×C4—1581no—
563C2×C4—1581no—
564C2×C4(C22⋊D79)⋊C412yes—
565C2×C4(C22⋊D79)⋊C412yes—
566C2×C4C22×C4×D7911yescharacteristic
567C2×C4#41×D7911yescharacteristic
568C2×C4#41×D7911yescharacteristic
569C2×C4C2×#1192962311yescharacteristic
570C2×C4C2×#1192962511yescharacteristic
571C2×C4C2×#1192962511yescharacteristic
572C8—22no—
573C8—22no—
574C8—1582no—
575C8—1582no—
576C22—3162no—
577C22—3162no—
578C22—3162no—
579C22—6321no—
580C22—6321no—
581C22—6321no—
582C22—6321no—
583C22C2×(C22⋊D79)⋊C411yescharacteristic
584C22#124×D7911yescharacteristic
585C22#1909911411yescharacteristic
586C22#1909936711yescharacteristic
587C22#1909937211yescharacteristic
588C22#1909937311yescharacteristic
589C22#1909937911yescharacteristic
590C4—22no—
591C4—22no—
592C4—42no—
593C4—42no—
594C4—81no—
595C4—81no—
596C4—3161no—
597C4—3161no—
598C4—3162no—
599C4—6321no—
600C4—6321no—
601C4—1582no—
602C4—1582no—
603C4C4×#1192962511yescharacteristic
604C4C4×#1192962511yescharacteristic
605C4#1909909911yescharacteristic
606C4#1909909911yescharacteristic
607C2—6322no—
608C2#2376594311yescharacteristic
609C2#2377227111yescharacteristic
610C2#2377227911yescharacteristic
611C2#2377375511yescharacteristic
612C2#2377376611yescharacteristic
613C2#2377407311yescharacteristic
614C2#2377408811yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutatorC2×C4×C79C23×C4
FrattiniC22×C4C23×D79
FittingC79×#1992C2
socleC23×C79C22×D4
prime radicalC22×D316C23
cosocleC22×C4×C79C24
hypercenter#1992D79
hypocenterC79#21643
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1992

Complements

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

NH ≅ G/Ntype
2. #23766142C2semidirect
6. #23764091C2semidirect
8. #23764077C2semidirect
9. #23763527C2semidirect
10. #23763229C2semidirect
12. #23763219C2semidirect
14. #23763088C2semidirect
15. C79×#1992C2semidirect
19. #19098920C4semidirect
90. #14579084C2×C4semidirect
91. #14579084C2×C4semidirect
98. C4×C79⋊C8C2×C4semidirect
114. #125×C79C2×C4semidirect
311. #1992D79semidirect
323. C79#21643semidirect
376. #125C4×D79semidirect

Maximal subgroups

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

subgroupindex
C2×#190989202
#237661422
#237661082
#237642162
#237640982
#237640912
#237640842
#237640772
#237635272
#237632292
#237632242
#237632192
#237632142
#237630882
C79×#19922
#2164379