Finite Group Databasebeta

← #34361042

Subgroups — #34361042

Order 20224.

734 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23766436C211yesmaximal, characteristic
2#23764814C211yesmaximal, characteristic, complemented
3#23764785C211yesmaximal, characteristic, complemented
4#23764589C211yesmaximal, characteristic
5#23764582C211yesmaximal, characteristic
6#23764166C211yesmaximal, characteristic, complemented
7#23764130C211yesmaximal, characteristic, complemented
8#23764008C211yesmaximal, characteristic, complemented
9#23763985C211yesmaximal, characteristic, complemented
10#23763982C211yesmaximal, characteristic, complemented
11#23763660C211yesmaximal, characteristic, complemented
12#23763597C211yesmaximal, characteristic, complemented
13#23763492C211yesmaximal, characteristic, complemented
14C4×#14579081C211yesmaximal, characteristic, complemented
15C79×#2495C211yesmaximal, characteristic, complemented
16C2×#14579135C2211yescharacteristic
17C2×C4×D316C2211yescharacteristic
18C2×#14579120C2211yescharacteristic
19C2×#14579094C2211yescharacteristic
20C2×#14579094C2211yescharacteristic
21C2×#14579092C2211yescharacteristic
22C2×#14579092C2211yescharacteristic
23C2×C4⋊(C79⋊C8)C2211yescharacteristic
24C2×#14579081C2211yescharacteristic
25C2×#14579081C2211yescharacteristic
26C2×#14579081C2211yescharacteristic
27C2×#14579081C2211yescharacteristic
28C2×C22⋊(C79⋊C8)C2211yescharacteristic
29C2×C22⋊(C79⋊C8)C2211yescharacteristic
30C2×C4×C79⋊C8C2211yescharacteristic
31#19098465C2211yescharacteristic
32#19098463—21no—
33#19098461C2211yescharacteristic
34#19098452—21no—
35#19098439—21no—
36C4×C4⋊Dic79C2211yescharacteristic
37#19098410—21no—
38#19098325C2211yescharacteristic
39#19098325C2211yescharacteristic
40#19098325C2211yescharacteristic
41#19098325C2211yescharacteristic
42#19098325C2211yescharacteristic
43#19098325C2211yescharacteristic
44#19098325C2211yescharacteristic
45#19098325C2211yescharacteristic
46#19098318C2211yescharacteristic
47#19098318C2211yescharacteristic
48#400×C79—21no—
49#397×C79—21no—
50#389×C79C2211yescharacteristic
51#389×C79C2211yescharacteristic
52#388×C79—21no—
53#383×C79—21no—
54#382×C79C2211yescharacteristic
55#380×C79C2211yescharacteristic
56#380×C79C2211yescharacteristic
57C4×C4⋊C4×C79C2211yescharacteristic
58C4×C22⋊C4×C79C2211yescharacteristic
59C22×D316C2311yescharacteristic
60C22×C22⋊D79—21no—
61C22×C4×D79—21no—
62C22×C79⋊C8C2311yescharacteristic
63C22×C79⋊C8C2311yescharacteristic
64C22×C79⋊C8C2311yescharacteristic
65C22×C79⋊C8C2311yescharacteristic
66#14579135—22no—
67#14579135—22no—
68C4×D316—22no—
69C4×D316—41no—
70#14579120—22no—
71#14579120—41no—
72C2×C4⋊Dic79C2311yescharacteristic
73C2×C4⋊Dic79C2311yescharacteristic
74C2×C4⋊Dic79C2311yescharacteristic
75C2×Dic79⋊C4—21no—
76C2×C22⋊Dic79—21no—
77C2×(C2×D79)⋊C4—21no—
78C2×(C2×D79)⋊C4—21no—
79C2×(C2×D79)⋊C4—21no—
80C2×(C2×D79)⋊C4—21no—
81C2×C4×Dic79—21no—
82C2×C4×Dic79—21no—
83#14579094—22no—
84#14579094—41no—
85#14579092—22no—
86#14579092—22no—
87C4⋊(C79⋊C8)—22no—
88#14579081—22no—
89#14579081—22no—
90#14579081—22no—
91#14579081—41no—
92C22⋊(C79⋊C8)—22no—
93C22⋊(C79⋊C8)—41no—
94C4×C79⋊C8—41no—
95C79⋊#95—21no—
96C79⋊#95—21no—
97C23×C4×C79C2311yescharacteristic
98C2×C4⋊C4×C79—21no—
99C2×C4⋊C4×C79—21no—
100C2×C4⋊C4×C79C2311yescharacteristic
101C2×C4⋊C4×C79C2311yescharacteristic
102C2×C4⋊C4×C79C2311yescharacteristic
103C2×C4⋊C4×C79C2311yescharacteristic
104C2×C22⋊C4×C79—21no—
105C2×C22⋊C4×C79—21no—
106C2×C22⋊C4×C79D411yescharacteristic
107C2×C22⋊C4×C79D411yescharacteristic
108C2×C42×C79—21no—
109C2×C42×C79C2311yescharacteristic
110C2×C42×C79C2311yescharacteristic
111#95×C79—21no—
112#95×C79—21no—
113#95×C79—21no—
114#95×C79—21no—
115#95×C79—21no—
116#95×C79—21no—
117#95×C79—21no—
118#95×C79D411yescharacteristic
119#95×C79D411yescharacteristic
120C23×D79—21no—
121C2×D316—21no—
122C2×D316—21no—
123C2×D316—21no—
124C2×D316—21no—
125C2×D316—21no—
126C2×D316#4112yes—
127C2×C22⋊D79—24no—
128C2×C22⋊D79—81no—
129C2×C22⋊D79—81no—
130C22×Dic79—21no—
131C22×Dic79—21no—
132C22×Dic79—21no—
133C2×C4×D79—42no—
134C2×C4×D79—42no—
135C2×C4×D79—81no—
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—21no—
146C2×C79⋊C8—21no—
147C2×C79⋊C8#4112yes—
148C4⋊Dic79—21no—
149C4⋊Dic79—21no—
150C4⋊Dic79—21no—
151C4⋊Dic79—21no—
152C4⋊Dic79#4112yes—
153C4⋊Dic79#4112yes—
154Dic79⋊C4—81no—
155C22⋊Dic79—42no—
156(C2×D79)⋊C4—24no—
157(C2×D79)⋊C4—42no—
158(C2×D79)⋊C4—42no—
159(C2×D79)⋊C4—81no—
160C4×Dic79—42no—
161C4×Dic79—81no—
162C24×C79C2×D411yescharacteristic
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×C79—21no—
171C22×C4×C79—21no—
172C22×C4×C79—21no—
173C22×C4×C79C2×D411yescharacteristic
174C22×C4×C79C2×D411yescharacteristic
175C22×C4×C79C2×D411yescharacteristic
176C22×C4×C79C2×D411yescharacteristic
177C22×C4×C79C2×D411yescharacteristic
178C22×C4×C79C2411yescharacteristic
179C4⋊C4×C79—21no—
180C4⋊C4×C79—21no—
181C4⋊C4×C79—21no—
182C4⋊C4×C79—21no—
183C4⋊C4×C79—21no—
184C4⋊C4×C79—21no—
185C4⋊C4×C79—21no—
186C4⋊C4×C79—21no—
187C4⋊C4×C79—81no—
188C4⋊C4×C79—81no—
189C22⋊C4×C79—22no—
190C22⋊C4×C79—41no—
191C22⋊C4×C79—42no—
192C22⋊C4×C79—81no—
193C42×C79—21no—
194C42×C79—21no—
195C42×C79—21no—
196C42×C79—21no—
197C42×C79—42no—
198C23×C79—21no—
199C23×C79—21no—
200C23×C79—21no—
201C23×C79—21no—
202C23×C79—21no—
203C23×C79—21no—
204C23×C79—21no—
205C23×C79C22×D411yescharacteristic
206C22×D79—22no—
207C22×D79—41no—
208C22×D79—41no—
209C22×D79—41no—
210C22×D79—41no—
211C22×D79—41no—
212C22×D79—41no—
213C2×C4×C79—21no—
214C2×C4×C79—21no—
215C2×C4×C79—21no—
216C2×C4×C79—21no—
217C2×C4×C79—21no—
218C2×C4×C79—21no—
219C2×C4×C79—21no—
220C2×C4×C79—21no—
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×C79—41no—
239C2×C4×C79—41no—
240C2×C4×C79—41no—
241C2×C4×C79—41no—
242C2×C4×C79—41no—
243C2×C4×C79#13512yes—
244C2×C4×C79C2×#4111yescharacteristic
245C2×C4×C79C2×#4111yescharacteristic
246C2×C4×C79C2×#4111yescharacteristic
247C2×C4×C79C2×#4111yescharacteristic
248C2×C4×C79H(5,𝔽2)11yescharacteristic
249C2×C4×C792−1+411yescharacteristic
250C22⋊D79—84no—
251C2×Dic79—22no—
252C2×Dic79—22no—
253C2×Dic79—41no—
254C2×Dic79—41no—
255C2×Dic79—41no—
256C2×Dic79—41no—
257C2×Dic79—41no—
258C2×Dic79—41no—
259C2×Dic79—41no—
260D316—22no—
261D316—22no—
262D316—41no—
263D316—41no—
264C4×D79—84no—
265C79⋊C8—22no—
266C79⋊C8—41no—
267C79⋊C8—41no—
268C79⋊C8—41no—
269C22×C79—41no—
270C22×C79—41no—
271C22×C79—41no—
272C22×C79—41no—
273C22×C79—41no—
274C22×C79—41no—
275C22×C79—41no—
276C22×C79#52511yescharacteristic
277C22×C79#54611yescharacteristic
278C22×C79#54711yescharacteristic
279C22×C79C2×#13511yescharacteristic
280C22×C79#57511yescharacteristic
281C22×C79#57611yescharacteristic
282C22×C79#57711yescharacteristic
283C2×D79—42no—
284C2×D79—42no—
285C2×D79—42no—
286C2×D79—81no—
287C2×D79—81no—
288C2×D79—81no—
289C2×D79—81no—
290C4×C79—22no—
291C4×C79—41no—
292C4×C79—41no—
293C4×C79—41no—
294C4×C79—41no—
295C4×C79—81no—
296C4×C79—81no—
297C4×C79—81no—
298C4×C79—81no—
299C4×C79#52911yescharacteristic
300C4×C79#53911yescharacteristic
301C4×C79#55311yescharacteristic
302C4×C79#55611yescharacteristic
303Dic79—42no—
304Dic79—42no—
305Dic79—81no—
306#27038—791nomaximal, Sylow
307C2×C79—81no—
308C2×C79#246611yescharacteristic
309C2×C79#310211yescharacteristic
310C2×C79#311811yescharacteristic
311C2×C79#329611yescharacteristic
312C2×C79#330911yescharacteristic
313C2×C79#334111yescharacteristic
314C2×C79#335111yescharacteristic
315D79—82no—
316#2495D7911yescharacteristic, complemented
317#2363—791no—
318#2073—791no—
319#2067—791no—
320#2034—791no—
321#2033—791no—
322#1949—791no—
323#1942—791no—
324#1923—791no—
325#1920—791no—
326#1920—791no—
327#1864—791no—
328#1854—791no—
329#1825—791no—
330C4×#102—791no—
331C79#2703811yescharacteristic, complemented, Sylow
332C2×#121—791no—
333C2×C4×D4—791no—
334C2×#117—791no—
335C2×#107—791no—
336C2×#107—791no—
337C2×#106—791no—
338C2×#106—791no—
339C2×C4⋊C8—791no—
340C2×#102—791no—
341C2×#102—791no—
342C2×#102—791no—
343C2×#102—791no—
344C2×C22⋊C8—791no—
345C2×C22⋊C8—791no—
346C2×C4×C8—791no—
347#400—21no—
348#397—21no—
349#390—791no—
350#390—1581no—
351#389—791no—
352#389C2×D7911yescharacteristic
353#389C2×D7911yescharacteristic
354#388—21no—
355#388—1581no—
356#386—1581no—
357#383—21no—
358#382C2×D7911yescharacteristic
359#380C2×D7911yescharacteristic
360#380C2×D7911yescharacteristic
361C4×C4⋊C4—791no—
362C4×C4⋊C4C2×D7911yescharacteristic
363C4×C22⋊C4—1581no—
364C4×C22⋊C4C2×D7911yescharacteristic
365#340—791no—
366#340—791no—
367#340—791no—
368#340—791no—
369#340—791no—
370#340—791no—
371#340—791no—
372#340—791no—
373#336—791no—
374#336—791no—
375C22×D4—791no—
376C22×D4—1581no—
377C23×C4—1581no—
378C23×C4C22×D7911yescharacteristic
379C22×C8—791no—
380C22×C8—791no—
381C22×C8—791no—
382C22×C8—791no—
383#121—1582no—
384#121—1582no—
385C4×D4—3161no—
386C4×D4—1582no—
387#117—3161no—
388#117—1582no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—791no—
392C2×C4⋊C4—791no—
393C2×C4⋊C4—791no—
394C2×C4⋊C4—1581no—
395C2×C4⋊C4C22×D7911yescharacteristic
396C2×C4⋊C4C22×D7911yescharacteristic
397C2×C4⋊C4C22×D7911yescharacteristic
398C2×C4⋊C4C22×D7911yescharacteristic
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—1581no—
402C2×C22⋊C4—1581no—
403C2×C22⋊C4—1581no—
404C2×C22⋊C4—1581no—
405C2×C22⋊C4—1581no—
406C2×C22⋊C4C22⋊D7911yescharacteristic
407C2×C22⋊C4C22⋊D7911yescharacteristic
408C2×C42—21no—
409C2×C42—1581no—
410C2×C42—1581no—
411C2×C42C22×D7911yescharacteristic
412C2×C42C22×D7911yescharacteristic
413#107—3161no—
414#107—1582no—
415#106—1582no—
416#106—1582no—
417C4⋊C8—1582no—
418#102—3161no—
419#102—1582no—
420#102—1582no—
421#102—1582no—
422C22⋊C8—3161no—
423C22⋊C8—1582no—
424C4×C8—3161no—
425#95—21no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95—1581no—
433#95—1581no—
434#95C22⋊D7911yescharacteristic
435#95C22⋊D7911yescharacteristic
436C24—1581no—
437C24C2×C22⋊D7911yescharacteristic
438C2×D4—792no—
439C2×D4—6321no—
440C2×D4—6321no—
441C2×D4—1584no—
442C2×D4—1581no—
443C2×D4—1581no—
444C2×D4—1581no—
445C2×D4—1581no—
446C2×D4—1581no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—3162no—
458C22×C4—3162no—
459C22×C4—6321no—
460C22×C4—1581no—
461C22×C4—1581no—
462C22×C4—1581no—
463C22×C4C2×C22⋊D7911yescharacteristic
464C22×C4C2×C22⋊D7911yescharacteristic
465C22×C4C2×C22⋊D7911yescharacteristic
466C22×C4C2×C22⋊D7911yescharacteristic
467C22×C4C2×C22⋊D7911yescharacteristic
468C22×C4C23×D7911yescharacteristic
469C2×C8—792no—
470C2×C8—1581no—
471C2×C8—1581no—
472C2×C8—1581no—
473C2×C8—1581no—
474C2×C8—1581no—
475C2×C8—1581no—
476C2×C8—1581no—
477C2×C8—1581no—
478C2×C8—1581no—
479C2×C8—1581no—
480C2×C8—1581no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—81no—
490C4⋊C4—81no—
491C4⋊C4—792no—
492C4⋊C4—792no—
493C4⋊C4—6321no—
494C4⋊C4—1581no—
495C4⋊C4—1581no—
496C4⋊C4—1581no—
497C4⋊C4—1581no—
498C22⋊C4—22no—
499C22⋊C4—41no—
500C22⋊C4—42no—
501C22⋊C4—81no—
502C22⋊C4—3162no—
503C22⋊C4—3162no—
504C22⋊C4—3162no—
505C22⋊C4—6321no—
506C22⋊C4—1584no—
507C42—21no—
508C42—21no—
509C42—21no—
510C42—21no—
511C42—42no—
512C42—3162no—
513C42—6321no—
514C23—21no—
515C23—21no—
516C23—21no—
517C23—21no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23—3161no—
522C23—3161no—
523C23—3161no—
524C23—3161no—
525C23—3161no—
526C23—3161no—
527C23—1582no—
528C23C22×C22⋊D7911yescharacteristic
529D4—3161no—
530D4—3161no—
531D4—6324no—
532D4—1582no—
533D4—1582no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
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—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—3161no—
565C2×C4—3161no—
566C2×C4—3161no—
567C2×C4—3161no—
568C2×C4—3161no—
569C2×C4—3161no—
570C2×C4—3161no—
571C2×C4—6324no—
572C2×C4—1582no—
573C2×C4—1582no—
574C2×C4#1457918112yes—
575C2×C4#41×D7911yescharacteristic
576C2×C4#41×D7911yescharacteristic
577C2×C4#41×D7911yescharacteristic
578C2×C4#41×D7911yescharacteristic
579C2×C4#1457920711yescharacteristic
580C2×C4#1457920811yescharacteristic
581C8—3161no—
582C8—3161no—
583C8—3161no—
584C8—1582no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—3162no—
593C22—3162no—
594C22—3162no—
595C22—6321no—
596C22—6321no—
597C22—6321no—
598C22—6321no—
599C22#1909907011yescharacteristic
600C22#1909920111yescharacteristic
601C22#1909921211yescharacteristic
602C22C2×#1457918111yescharacteristic
603C22#1909936111yescharacteristic
604C22#1909936611yescharacteristic
605C22#1909937111yescharacteristic
606C4—22no—
607C4—41no—
608C4—41no—
609C4—41no—
610C4—41no—
611C4—81no—
612C4—81no—
613C4—81no—
614C4—81no—
615C4—3162no—
616C4—3162no—
617C4—6321no—
618C4#1909909611yescharacteristic
619C4#1909915411yescharacteristic
620C4#1909926411yescharacteristic
621C4#1909928011yescharacteristic
622C2—81no—
623C2—6322no—
624C2#2376743211yescharacteristic
625C2#2377341211yescharacteristic
626C2#2377357811yescharacteristic
627C2#2377522911yescharacteristic
628C2#2377540011yescharacteristic
629C2#2377581811yescharacteristic
630C2#2377596011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D79
commutator, cosocleC22×C4×C79C24
FrattiniC22×C4C23×D79
FittingC79×#2495C2
socleC23×C79C22×D4
prime radicalC2×#14579135C22
hypercenter#2495D79
hypocenterC79#27038
LCSG ▷ C22×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2495

Complements

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

NH ≅ G/Ntype
2. #23764814C2semidirect
3. #23764785C2semidirect
6. #23764166C2semidirect
7. #23764130C2semidirect
8. #23764008C2semidirect
9. #23763985C2semidirect
10. #23763982C2semidirect
11. #23763660C2semidirect
12. #23763597C2semidirect
13. #23763492C2semidirect
14. C4×#14579081C2semidirect
15. C79×#2495C2semidirect
316. #2495D79semidirect
331. C79#27038semidirect

Maximal subgroups

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

subgroupindex
#237664362
#237648142
#237647852
#237645892
#237645822
#237641662
#237641302
#237640082
#237639852
#237639822
#237636602
#237635972
#237634922
C4×#145790812
C79×#24952
#2703879