Finite Group Databasebeta

← #34360982

Subgroups — #34360982

Order 20224.

728 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23766403C211yesmaximal, characteristic
2#23764809C211yesmaximal, characteristic, complemented
3#23764778C211yesmaximal, characteristic, complemented
4#23764596C211yesmaximal, characteristic
5#23764596C211yesmaximal, characteristic
6#23764161C211yesmaximal, characteristic, complemented
7#23764125C211yesmaximal, characteristic, complemented
8#23764008C211yesmaximal, characteristic
9#23763985C211yesmaximal, characteristic, complemented
10#23763975C211yesmaximal, characteristic, complemented
11#23763667C211yesmaximal, characteristic, complemented
12#23763592C211yesmaximal, characteristic
13#23763488C211yesmaximal, characteristic
14C4×#14579084C211yesmaximal, characteristic, complemented
15C79×#2496C211yesmaximal, characteristic
16C2×#14579140C2211yescharacteristic
17C2×C4×Dic158C2211yescharacteristic
18C22×C4⋊Dic79C2211yescharacteristic
19C2×#14579092C2211yescharacteristic
20C2×#14579092C2211yescharacteristic
21C2×#14579092C2211yescharacteristic
22C2×#14579092C2211yescharacteristic
23C2×C4⋊(C79⋊C8)C2211yescharacteristic
24C2×#14579084C2211yescharacteristic
25C2×#14579084C2211yescharacteristic
26C2×#14579084C2211yescharacteristic
27C2×#14579084C2211yescharacteristic
28C2×C22⋊(C79⋊C8)C2211yescharacteristic
29C2×C22⋊(C79⋊C8)C2211yescharacteristic
30C2×C4×C79⋊C8C2211yescharacteristic
31#19098469C2211yescharacteristic
32#19098461C2211yescharacteristic
33#19098460—21no—
34#19098450—21no—
35#19098435—21no—
36C4×C4⋊Dic79C2211yescharacteristic
37C22⋊C4×Dic79—21no—
38#19098325C2211yescharacteristic
39#19098325C2211yescharacteristic
40#19098325C2211yescharacteristic
41#19098325C2211yescharacteristic
42#19098325C2211yescharacteristic
43#19098325C2211yescharacteristic
44#19098325C2211yescharacteristic
45#19098325C2211yescharacteristic
46#19098318C2211yescharacteristic
47#19098318C2211yescharacteristic
48C2×#126×C79—21no—
49#400×C79—21no—
50#397×C79—21no—
51#389×C79C2211yescharacteristic
52#389×C79C2211yescharacteristic
53#387×C79—21no—
54#384×C79C2211yescharacteristic
55#380×C79C2211yescharacteristic
56#380×C79C2211yescharacteristic
57C4×C4⋊C4×C79C2211yescharacteristic
58C4×C22⋊C4×C79C2211yescharacteristic
59C22×Dic158C2311yescharacteristic
60C23×Dic79—21no—
61C22×C79⋊C8C2311yescharacteristic
62C22×C79⋊C8C2311yescharacteristic
63C22×C79⋊C8C2311yescharacteristic
64C22×C79⋊C8C2311yescharacteristic
65#14579140—22no—
66#14579140—22no—
67C4×Dic158—22no—
68C4×Dic158—41no—
69C2×C4⋊Dic79—22no—
70C2×C4⋊Dic79—21no—
71C2×C4⋊Dic79—41no—
72C2×C4⋊Dic79C2311yescharacteristic
73C2×C4⋊Dic79C2311yescharacteristic
74C2×C4⋊Dic79C2311yescharacteristic
75C2×Dic79⋊C4—21no—
76C2×Dic79⋊C4—21no—
77C2×Dic79⋊C4—21no—
78C2×C22⋊Dic79—21no—
79C2×C4×Dic79—21no—
80C2×C4×Dic79—21no—
81#14579092—22no—
82#14579092—22no—
83#14579092—22no—
84#14579092—41no—
85C4⋊(C79⋊C8)—22no—
86#14579084—22no—
87#14579084—22no—
88#14579084—22no—
89#14579084—41no—
90C22⋊(C79⋊C8)—22no—
91C22⋊(C79⋊C8)—41no—
92C4×C79⋊C8—41no—
93C79⋊#95—21no—
94C79⋊#95—21no—
95C79⋊#95—21no—
96C79⋊#95—21no—
97C23×C4×C79C2311yescharacteristic
98#126×C79—44no—
99C2×C4⋊C4×C79—21no—
100C2×C4⋊C4×C79—21no—
101C2×C4⋊C4×C79—21no—
102C2×C4⋊C4×C79—21no—
103C2×C4⋊C4×C79C2311yescharacteristic
104C2×C4⋊C4×C79C2311yescharacteristic
105C2×C4⋊C4×C79C2311yescharacteristic
106C2×C4⋊C4×C79C2311yescharacteristic
107C2×C22⋊C4×C79—21no—
108C2×C22⋊C4×C79—21no—
109C2×C22⋊C4×C79D411yescharacteristic
110C2×C22⋊C4×C79D411yescharacteristic
111C2×C42×C79—21no—
112C2×C42×C79C2311yescharacteristic
113C2×C42×C79C2311yescharacteristic
114#95×C79—21no—
115#95×C79—21no—
116#95×C79—21no—
117#95×C79—21no—
118#95×C79—21no—
119#95×C79D411yescharacteristic
120#95×C79D411yescharacteristic
121C2×Dic158—21no—
122C2×Dic158—21no—
123C2×Dic158—21no—
124C2×Dic158—21no—
125C2×Dic158—21no—
126C2×Dic158#4112yes—
127C22×Dic79—21no—
128C22×Dic79—21no—
129C22×Dic79—21no—
130C22×Dic79—21no—
131C22×Dic79—42no—
132C22×Dic79—42no—
133C22×Dic79—81no—
134C2×C79⋊C8—21no—
135C2×C79⋊C8—21no—
136C2×C79⋊C8—21no—
137C2×C79⋊C8—21no—
138C2×C79⋊C8—21no—
139C2×C79⋊C8—21no—
140C2×C79⋊C8—21no—
141C2×C79⋊C8—21no—
142C2×C79⋊C8—21no—
143C2×C79⋊C8—21no—
144C2×C79⋊C8—21no—
145C2×C79⋊C8#4112yes—
146C4⋊Dic79—21no—
147C4⋊Dic79—21no—
148C4⋊Dic79—21no—
149C4⋊Dic79—21no—
150C4⋊Dic79—42no—
151C4⋊Dic79#4112yes—
152C4⋊Dic79#4112yes—
153Dic79⋊C4—24no—
154Dic79⋊C4—42no—
155Dic79⋊C4—81no—
156C22⋊Dic79—24no—
157C4×Dic79—42no—
158C4×Dic79—81no—
159C24×C79C2×D411yescharacteristic
160C22×C4×C79—21no—
161C22×C4×C79—21no—
162C22×C4×C79—21no—
163C22×C4×C79—21no—
164C22×C4×C79—21no—
165C22×C4×C79—21no—
166C22×C4×C79—21no—
167C22×C4×C79—21no—
168C22×C4×C79—21no—
169C22×C4×C79—21no—
170C22×C4×C79C2×D411yescharacteristic
171C22×C4×C79C2×D411yescharacteristic
172C22×C4×C79C2×D411yescharacteristic
173C22×C4×C79C2×D411yescharacteristic
174C22×C4×C79C2×D411yescharacteristic
175C22×C4×C79C2411yescharacteristic
176C4⋊C4×C79—21no—
177C4⋊C4×C79—21no—
178C4⋊C4×C79—21no—
179C4⋊C4×C79—21no—
180C4⋊C4×C79—21no—
181C4⋊C4×C79—21no—
182C4⋊C4×C79—21no—
183C4⋊C4×C79—21no—
184C4⋊C4×C79—42no—
185C4⋊C4×C79—42no—
186C4⋊C4×C79—42no—
187C4⋊C4×C79—42no—
188C22⋊C4×C79—41no—
189C22⋊C4×C79—42no—
190C22⋊C4×C79—42no—
191C22⋊C4×C79SD1614yes—
192C42×C79—21no—
193C42×C79—21no—
194C42×C79—21no—
195C42×C79—21no—
196C42×C79—42no—
197C23×C79—21no—
198C23×C79—21no—
199C23×C79—21no—
200C23×C79—21no—
201C23×C79—21no—
202C23×C79—21no—
203C23×C79C2×SD1612yes—
204C23×C79C22×D411yescharacteristic
205C2×C4×C79—21no—
206C2×C4×C79—21no—
207C2×C4×C79—21no—
208C2×C4×C79—21no—
209C2×C4×C79—21no—
210C2×C4×C79—21no—
211C2×C4×C79—21no—
212C2×C4×C79—21no—
213C2×C4×C79—21no—
214C2×C4×C79—21no—
215C2×C4×C79—21no—
216C2×C4×C79—21no—
217C2×C4×C79—21no—
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×C79—41no—
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×C79C2×SD1612yes—
235C2×C4×C79C2×SD1612yes—
236C2×C4×C79C2×#4111yescharacteristic
237C2×C4×C79C2×#4111yescharacteristic
238C2×C4×C79C2×#4111yescharacteristic
239C2×C4×C79C2×#4111yescharacteristic
240C2×C4×C79H(5,𝔽2)11yescharacteristic
241C2×C4×C792−1+411yescharacteristic
242C2×Dic79—22no—
243C2×Dic79—22no—
244C2×Dic79—22no—
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—41no—
254C2×Dic79—84no—
255Dic158—22no—
256Dic158—22no—
257Dic158—41no—
258Dic158—41no—
259C79⋊C8—22no—
260C79⋊C8—41no—
261C79⋊C8—41no—
262C79⋊C8—41no—
263C22×C79—22no—
264C22×C79—22no—
265C22×C79—22no—
266C22×C79—41no—
267C22×C79—41no—
268C22×C79—41no—
269C22×C79—41no—
270C22×C79#52511yescharacteristic
271C22×C79#54611yescharacteristic
272C22×C79#54711yescharacteristic
273C22×C79C22×SD1611yescharacteristic
274C22×C79#57511yescharacteristic
275C22×C79#57711yescharacteristic
276C22×C79#57811yescharacteristic
277C4×C79—22no—
278C4×C79—22no—
279C4×C79—41no—
280C4×C79—41no—
281C4×C79—41no—
282C4×C79—81no—
283C4×C79—81no—
284C4×C79—81no—
285C4×C79—81no—
286C4×C79#52911yescharacteristic
287C4×C79#53911yescharacteristic
288C4×C79#55311yescharacteristic
289C4×C79#55611yescharacteristic
290Dic79—42no—
291Dic79—42no—
292Dic79—42no—
293Dic79—81no—
294#27034—791nomaximal, Sylow
295C2×C79—42no—
296C2×C79#246611yescharacteristic
297C2×C79#310311yescharacteristic
298C2×C79#312011yescharacteristic
299C2×C79#329811yescharacteristic
300C2×C79#331111yescharacteristic
301C2×C79#333511yescharacteristic
302C2×C79#335211yescharacteristic
303#2496D7911yescharacteristic
304#2360—791no—
305#2072—791no—
306#2066—791no—
307#2035—791no—
308#2035—791no—
309#1948—791no—
310#1941—791no—
311#1923—791no—
312#1920—791no—
313#1919—791no—
314#1865—791no—
315#1853—791no—
316#1824—791no—
317C4×#103—791no—
318C79#2703411yescharacteristic, complemented, Sylow
319C2×#126—21no—
320C2×C22⋊Q8—791no—
321C2×C4×Q8—791no—
322C22×C4⋊C4—791no—
323C2×#106—791no—
324C2×#106—791no—
325C2×#106—791no—
326C2×#106—791no—
327C2×C4⋊C8—791no—
328C2×#103—791no—
329C2×#103—791no—
330C2×#103—791no—
331C2×#103—791no—
332C2×C22⋊C8—791no—
333C2×C22⋊C8—791no—
334C2×C4×C8—791no—
335#400—21no—
336#397—21no—
337#391—791no—
338#389—791no—
339#389—1581no—
340#389C2×D7911yescharacteristic
341#389C2×D7911yescharacteristic
342#387—21no—
343#387—1581no—
344#385—1581no—
345#384C2×D7911yescharacteristic
346#380C2×D7911yescharacteristic
347#380C2×D7911yescharacteristic
348C4×C4⋊C4—791no—
349C4×C4⋊C4C2×D7911yescharacteristic
350C4×C22⋊C4—1581no—
351C4×C22⋊C4C2×D7911yescharacteristic
352#340—791no—
353#340—791no—
354#340—791no—
355#340—791no—
356#340—791no—
357#340—791no—
358#340—791no—
359#340—791no—
360#336—791no—
361#336—791no—
362C22×Q8—791no—
363C23×C4—1581no—
364C23×C4C22×D7911yescharacteristic
365C22×C8—791no—
366C22×C8—791no—
367C22×C8—791no—
368C22×C8—791no—
369#126—44no—
370C22⋊Q8—1582no—
371C22⋊Q8—1582no—
372C4×Q8—3161no—
373C4×Q8—1582no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—3161no—
379C2×C4⋊C4—791no—
380C2×C4⋊C4—791no—
381C2×C4⋊C4—791no—
382C2×C4⋊C4—1581no—
383C2×C4⋊C4—1581no—
384C2×C4⋊C4—1582no—
385C2×C4⋊C4—1581no—
386C2×C4⋊C4—1581no—
387C2×C4⋊C4C22×D7911yescharacteristic
388C2×C4⋊C4C22×D7911yescharacteristic
389C2×C4⋊C4C22×D7911yescharacteristic
390C2×C4⋊C4C22×D7911yescharacteristic
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—1581no—
394C2×C22⋊C4C22⋊D7911yescharacteristic
395C2×C22⋊C4C22⋊D7911yescharacteristic
396C2×C42—21no—
397C2×C42—1581no—
398C2×C42—1581no—
399C2×C42C22×D7911yescharacteristic
400C2×C42C22×D7911yescharacteristic
401#106—3161no—
402#106—1582no—
403#106—1582no—
404#106—1582no—
405C4⋊C8—1582no—
406#103—3161no—
407#103—1582no—
408#103—1582no—
409#103—1582no—
410C22⋊C8—3161no—
411C22⋊C8—1582no—
412C4×C8—3161no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—1581no—
419#95—1581no—
420#95—1581no—
421#95—1581no—
422#95C22⋊D7911yescharacteristic
423#95C22⋊D7911yescharacteristic
424C24C2×C22⋊D7911yescharacteristic
425C2×Q8—792no—
426C2×Q8—1581no—
427C2×Q8—1581no—
428C2×Q8—1581no—
429C2×Q8—1581no—
430C2×Q8—1581no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—3162no—
442C22×C4—3162no—
443C22×C4—6321no—
444C22×C4—1581no—
445C22×C4—1581no—
446C22×C4—1581no—
447C22×C4—1581no—
448C22×C4C2×C22⋊D7911yescharacteristic
449C22×C4C2×C22⋊D7911yescharacteristic
450C22×C4C2×C22⋊D7911yescharacteristic
451C22×C4C2×C22⋊D7911yescharacteristic
452C22×C4C2×C22⋊D7911yescharacteristic
453C22×C4C23×D7911yescharacteristic
454C2×C8—792no—
455C2×C8—1581no—
456C2×C8—1581no—
457C2×C8—1581no—
458C2×C8—1581no—
459C2×C8—1581no—
460C2×C8—1581no—
461C2×C8—1581no—
462C2×C8—1581no—
463C2×C8—1581no—
464C2×C8—1581no—
465C2×C8—1581no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—42no—
475C4⋊C4—42no—
476C4⋊C4—42no—
477C4⋊C4—42no—
478C4⋊C4—3162no—
479C4⋊C4—3162no—
480C4⋊C4—792no—
481C4⋊C4—792no—
482C4⋊C4—6321no—
483C4⋊C4—1584no—
484C4⋊C4—1581no—
485C4⋊C4—1581no—
486C4⋊C4—1581no—
487C4⋊C4—1581no—
488C22⋊C4—41no—
489C22⋊C4—42no—
490C22⋊C4—42no—
491C22⋊C4—1584no—
492C22⋊C4#1192961214yes—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—21no—
497C42—42no—
498C42—3162no—
499C42—6321no—
500C23—21no—
501C23—21no—
502C23—21no—
503C23—21no—
504C23—21no—
505C23—21no—
506C23C2×#1192961212yes—
507C23C22×C22⋊D7911yescharacteristic
508Q8—3161no—
509Q8—3161no—
510Q8—1582no—
511Q8—1582no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
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—3161no—
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—6324no—
551C2×C4—1582no—
552C2×C4—1582no—
553C2×C4—1582no—
554C2×C4C2×#1192961212yes—
555C2×C4C2×#1192961212yes—
556C2×C4#41×D7911yescharacteristic
557C2×C4#41×D7911yescharacteristic
558C2×C4#41×D7911yescharacteristic
559C2×C4#41×D7911yescharacteristic
560C2×C4#1457920711yescharacteristic
561C2×C4#1457920811yescharacteristic
562C8—3161no—
563C8—3161no—
564C8—3161no—
565C8—1582no—
566C22—22no—
567C22—22no—
568C22—22no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22#1909907011yescharacteristic
574C22#1909920111yescharacteristic
575C22#1909921211yescharacteristic
576C22C22×#1192961211yescharacteristic
577C22#1909936111yescharacteristic
578C22#1909937111yescharacteristic
579C22#1909937811yescharacteristic
580C4—22no—
581C4—22no—
582C4—41no—
583C4—41no—
584C4—41no—
585C4—81no—
586C4—81no—
587C4—81no—
588C4—81no—
589C4—3162no—
590C4—3162no—
591C4—3162no—
592C4—6321no—
593C4#1909909611yescharacteristic
594C4#1909915411yescharacteristic
595C4#1909926411yescharacteristic
596C4#1909928011yescharacteristic
597C2—42no—
598C2#2376743211yescharacteristic
599C2#2377342711yescharacteristic
600C2#2377360811yescharacteristic
601C2#2377525911yescharacteristic
602C2#2377543011yescharacteristic
603C2#2377575711yescharacteristic
604C2#2377596911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D79
commutator, cosocleC22×C4×C79C24
FrattiniC22×C4C23×D79
FittingC79×#2496C2
socleC23×C79C22×D4
prime radicalC24×C79C2×D4
hypercenter#2496D79
hypocenterC79#27034
LCSG ▷ C22×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2496

Complements

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

NH ≅ G/Ntype
2. #23764809C2semidirect
3. #23764778C2semidirect
6. #23764161C2semidirect
7. #23764125C2semidirect
9. #23763985C2semidirect
10. #23763975C2semidirect
11. #23763667C2semidirect
14. C4×#14579084C2semidirect
318. C79#27034semidirect

Maximal subgroups

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

subgroupindex
#237664032
#237648092
#237647782
#237645962
#237641612
#237641252
#237640082
#237639852
#237639752
#237636672
#237635922
#237634882
C4×#145790842
C79×#24962
#2703479