Finite Group Databasebeta

← #34181020

Subgroups — #34181020

Order 20224.

742 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#121×Dic79C211yesmaximal, characteristic
2#23763378C211yesmaximal, characteristic, complemented
3C2×#19098297C211yesmaximal, characteristic
4Dic79⋊#95C211yesmaximal, characteristic, complemented
5#23761280C211yesmaximal, characteristic, complemented
6#23761279C211yesmaximal, characteristic, complemented
7C2×#327×C79C211yesmaximal, characteristic
8C2×D4×Dic79—21no—
9C2×D4×Dic79C411yescharacteristic, complemented
10C22×Dic79⋊C4—21no—
11C22×C4×Dic79C2211yescharacteristic
12C2×Dic79⋊C8—21no—
13C2×C22⋊(C79⋊C8)C2211yescharacteristic
14#19098466C411yescharacteristic, complemented
15#19098462C411yescharacteristic, complemented
16#19098456—21no—
17#19098443—21no—
18#19098423C2211yescharacteristic
19C4⋊C4×Dic79C411yescharacteristic, complemented
20C22⋊C4×Dic79—21no—
21C2×C79⋊#95—21no—
22C2×C79⋊#95C2211yescharacteristic
23#19098317—21no—
24#19098297—22no—
25C2×#121×C79C2211yescharacteristic
26C2×C22⋊C8×C79C2211yescharacteristic
27C2×#95×C79C2211yescharacteristic
28#327×C79—22no—
29C23×Dic79—21no—
30C23×Dic79—21no—
31C23×Dic79D411yescharacteristic
32C23×Dic79D411yescharacteristic
33C22×C79⋊C8—21no—
34D4×Dic79—42no—
35D4×Dic79—42no—
36D4×Dic79—42no—
37C2×C4⋊Dic79—21no—
38C2×C4⋊Dic79C2×C411yescharacteristic
39C2×C4⋊Dic79C2×C411yescharacteristic
40C2×Dic79⋊C4—24no—
41C2×Dic79⋊C4—42no—
42C2×Dic79⋊C4—42no—
43C2×C22⋊Dic79—21no—
44C2×C22⋊Dic79—21no—
45C2×C22⋊Dic79—21no—
46C2×C22⋊Dic79—21no—
47C2×C4×Dic79—21no—
48C2×C4×Dic79—42no—
49C2×C4×Dic79C2×C411yescharacteristic
50C2×C4×Dic79C2×C411yescharacteristic
51C2×C4×Dic79D411yescharacteristic
52C2×C4×Dic79D411yescharacteristic
53Dic79⋊C8—42no—
54C22⋊(C79⋊C8)—21no—
55C22⋊(C79⋊C8)—21no—
56C79⋊#95—21no—
57C79⋊#95—21no—
58C79⋊#95—21no—
59C79⋊#95—21no—
60C79⋊#95—21no—
61C79⋊#95—42no—
62C22×D4×C79—21no—
63C22×D4×C79C2×C411yescharacteristic
64C23×C4×C79—21no—
65C23×C4×C79C2311yescharacteristic
66C22×C8×C79—21no—
67#121×C79—21no—
68#121×C79—21no—
69#121×C79D412yes—
70#121×C79Q812yes—
71C2×C4⋊C4×C79C2×C411yescharacteristic
72C2×C22⋊C4×C79—21no—
73C22⋊C8×C79—21no—
74C22⋊C8×C79—21no—
75#95×C79—21no—
76#95×C79—21no—
77C22×Dic79—22no—
78C22×Dic79—22no—
79C22×Dic79—22no—
80C22×Dic79—21no—
81C22×Dic79—21no—
82C22×Dic79—21no—
83C22×Dic79—21no—
84C22×Dic79—41no—
85C22×Dic79—41no—
86C22×Dic79—41no—
87C22×Dic79—41no—
88C22×Dic79—41no—
89C22×Dic79—42no—
90C22×Dic79—42no—
91C22×Dic79—42no—
92C22×Dic79—41no—
93C22×Dic79—41no—
94C22×Dic79—41no—
95C22×Dic79C22⋊C411yescharacteristic
96C22×Dic79C22⋊C411yescharacteristic
97C22×Dic79C22⋊C411yescharacteristic
98C22×Dic79C22⋊C411yescharacteristic
99C22×Dic79D812yes—
100C22×Dic79SD1612yes—
101C2×C79⋊C8—41no—
102C2×C79⋊C8—41no—
103C2×C79⋊C8—41no—
104C4⋊Dic79—41no—
105C4⋊Dic79—41no—
106C4⋊Dic79—42no—
107Dic79⋊C4—48no—
108C22⋊Dic79—42no—
109C22⋊Dic79—42no—
110C22⋊Dic79—42no—
111C22⋊Dic79—41no—
112C22⋊Dic79—41no—
113C4×Dic79—22no—
114C4×Dic79—22no—
115C4×Dic79—41no—
116C4×Dic79—41no—
117C4×Dic79—42no—
118C24×C79—21no—
119C24×C79C2×D411yescharacteristic
120C2×D4×C79—22no—
121C2×D4×C79—22no—
122C2×D4×C79—21no—
123C2×D4×C79—41no—
124C2×D4×C79—41no—
125C2×D4×C79—41no—
126C2×D4×C79—41no—
127C2×D4×C79—41no—
128C2×D4×C79—41no—
129C2×D4×C79C4⋊C412yescomplemented
130C22×C4×C79—21no—
131C22×C4×C79—22no—
132C22×C4×C79—41no—
133C22×C4×C79—41no—
134C22×C4×C79—41no—
135C22×C4×C79—41no—
136C22×C4×C79—41no—
137C22×C4×C79—41no—
138C22×C4×C79—41no—
139C22×C4×C79—41no—
140C22×C4×C79C22×C411yescharacteristic
141C22×C4×C79C2×D411yescharacteristic
142C22×C4×C79C2×D411yescharacteristic
143C22×C4×C79C2×Q811yescharacteristic
144C22×C4×C79#4111yescharacteristic
145C22×C4×C79#4111yescharacteristic
146C2×C8×C79—41no—
147C2×C8×C79—41no—
148C2×C8×C79—41no—
149C4⋊C4×C79—21no—
150C4⋊C4×C79C4⋊C412yescomplemented
151C22⋊C4×C79—22no—
152C22⋊C4×C79—22no—
153C23×C79—21no—
154C23×C79—21no—
155C23×C79—21no—
156C23×C79—21no—
157C23×C79—22no—
158C23×C79—41no—
159C23×C79—41no—
160C23×C79—41no—
161C23×C79—41no—
162C23×C79—41no—
163C23×C79—41no—
164C23×C79C2×C22⋊C411yescharacteristic
165C23×C79#12111yescharacteristic
166C23×C79C22⋊Q811yescharacteristic
167C23×C79C2×D811yescharacteristic
168C23×C79C2×SD1611yescharacteristic
169C23×C79AGL(1,ℤ/8)11yescharacteristic
170C23×C79#13711yescharacteristic
171D4×C79—42no—
172D4×C79—42no—
173D4×C79—42no—
174D4×C79—42no—
175D4×C79—42no—
176D4×C79—42no—
177C2×C4×C79—21no—
178C2×C4×C79—21no—
179C2×C4×C79—21no—
180C2×C4×C79—21no—
181C2×C4×C79—22no—
182C2×C4×C79—41no—
183C2×C4×C79—41no—
184C2×C4×C79—41no—
185C2×C4×C79—41no—
186C2×C4×C79—41no—
187C2×C4×C79—41no—
188C2×C4×C79—42no—
189C2×C4×C79—42no—
190C2×C4×C79—42no—
191C2×C4×C79—81no—
192C2×C4×C79—81no—
193C2×C4×C79—81no—
194C2×C4×C79—81no—
195C2×C4×C79C2×C4⋊C411yescharacteristic
196C2×C4×C79#11711yescharacteristic
197C2×C4×C79#12111yescharacteristic
198C2×C4×C79C22⋊Q811yescharacteristic
199C2×Dic79—24no—
200C2×Dic79—24no—
201C2×Dic79—21no—
202C2×Dic79—21no—
203C2×Dic79—21no—
204C2×Dic79—21no—
205C2×Dic79—21no—
206C2×Dic79—21no—
207C2×Dic79—21no—
208C2×Dic79—21no—
209C2×Dic79—42no—
210C2×Dic79—42no—
211C2×Dic79—42no—
212C2×Dic79—42no—
213C2×Dic79—42no—
214C2×Dic79—41no—
215C2×Dic79—41no—
216C2×Dic79—41no—
217C2×Dic79—41no—
218C2×Dic79—41no—
219C2×Dic79—41no—
220C2×Dic79—84no—
221C2×Dic79—81no—
222C2×Dic79—81no—
223C2×Dic79—81no—
224C2×Dic79—81no—
225C2×Dic79#9912yes—
226C2×Dic79#10212yes—
227C2×Dic79#10212yes—
228C2×Dic79#10412yes—
229C8×C79—81no—
230C79⋊C8—81no—
231C22×C79—21no—
232C22×C79—21no—
233C22×C79—21no—
234C22×C79—21no—
235C22×C79—21no—
236C22×C79—21no—
237C22×C79—21no—
238C22×C79—21no—
239C22×C79—21no—
240C22×C79—21no—
241C22×C79—21no—
242C22×C79—21no—
243C22×C79—42no—
244C22×C79—42no—
245C22×C79—42no—
246C22×C79—81no—
247C22×C79—81no—
248C22×C79—81no—
249C22×C79—81no—
250C22×C79#38011yescharacteristic
251C22×C79C2×#9911yescharacteristic
252C22×C79#41011yescharacteristic
253C22×C79C2×#10211yescharacteristic
254C22×C79#41711yescharacteristic
255C22×C79C2×#10411yescharacteristic
256C22×C79#42111yescharacteristic
257C22×C79#45911yescharacteristic
258C22×C79#46111yescharacteristic
259C22×C79#47411yescharacteristic
260C22×C79#47611yescharacteristic
261C4×C79—21no—
262C4×C79—21no—
263C4×C79—21no—
264C4×C79—21no—
265C4×C79—42no—
266C4×C79—82no—
267Dic79—22no—
268Dic79—22no—
269Dic79—22no—
270Dic79—22no—
271Dic79—82no—
272Dic79—81no—
273Dic79—81no—
274#8577—791nomaximal, Sylow
275C2×C79—21no—
276C2×C79—21no—
277C2×C79—21no—
278C2×C79—21no—
279C2×C79—82no—
280C2×C79#150211yescharacteristic
281C2×C79#150411yescharacteristic
282C2×C79#151211yescharacteristic
283C2×C79#151911yescharacteristic
284C2×C79#179911yescharacteristic
285C2×C79#180211yescharacteristic
286C2×C79#180611yescharacteristic
287C4×#121—791no—
288#1797—791no—
289C2×#327—791no—
290C2×#327D7911yescharacteristic
291C4⋊#95—791no—
292#1294—791no—
293#1294—791no—
294C79#857711yescharacteristic, complemented, Sylow
295C2×#121C2×D7911yescharacteristic
296C2×C4×D4—791no—
297C2×C4×D4—1581no—
298C22×C4⋊C4—1581no—
299C22×C42—791no—
300C2×C4⋊C8—1581no—
301C2×C22⋊C8—791no—
302C2×C22⋊C8C2×D7911yescharacteristic
303#390—791no—
304#389—791no—
305#388—1581no—
306#386—1581no—
307#380—791no—
308C4×C4⋊C4—791no—
309C4×C22⋊C4—1581no—
310C2×#95—791no—
311C2×#95—1581no—
312C2×#95C2×D7911yescharacteristic
313#336—1581no—
314#327—22no—
315#327—1582no—
316C22×D4—21no—
317C22×D4C4×D7911yescharacteristic
318C23×C4—21no—
319C23×C4—791no—
320C23×C4—791no—
321C23×C4—1581no—
322C23×C4—1581no—
323C23×C4C22×D7911yescharacteristic
324C22×C8—21no—
325C22×C8—1581no—
326#121—21no—
327#121—21no—
328#121Dic15812yes—
329#121C22⋊D7912yes—
330C4×D4—3162no—
331C4×D4—3162no—
332C4×D4—3162no—
333C2×C4⋊C4—3162no—
334C2×C4⋊C4—3162no—
335C2×C4⋊C4—791no—
336C2×C4⋊C4—791no—
337C2×C4⋊C4—1581no—
338C2×C4⋊C4—1584no—
339C2×C4⋊C4C4×D7911yescharacteristic
340C2×C22⋊C4—21no—
341C2×C22⋊C4—1581no—
342C2×C22⋊C4—1581no—
343C2×C22⋊C4—1581no—
344C2×C22⋊C4—1581no—
345C2×C42—3162no—
346C2×C42—791no—
347C2×C42—791no—
348C2×C42—791no—
349C2×C42—791no—
350C2×C42—1581no—
351C4⋊C8—3162no—
352C22⋊C8—21no—
353C22⋊C8—21no—
354C22⋊C8—1581no—
355C22⋊C8—1581no—
356#95—21no—
357#95—21no—
358#95—3162no—
359#95—1581no—
360#95—1581no—
361#95—1581no—
362#95—1581no—
363#95—1581no—
364C24—21no—
365C24D4×D7911yescharacteristic
366C2×D4—22no—
367C2×D4—22no—
368C2×D4—21no—
369C2×D4—41no—
370C2×D4—41no—
371C2×D4—41no—
372C2×D4—41no—
373C2×D4—41no—
374C2×D4—41no—
375C2×D4Dic79⋊C412yescomplemented
376C22×C4—21no—
377C22×C4—22no—
378C22×C4—41no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—41no—
384C22×C4—41no—
385C22×C4—41no—
386C22×C4—3161no—
387C22×C4—3161no—
388C22×C4—3161no—
389C22×C4—3161no—
390C22×C4—3161no—
391C22×C4—3161no—
392C22×C4—3161no—
393C22×C4—3161no—
394C22×C4—3162no—
395C22×C4—3162no—
396C22×C4—3162no—
397C22×C4—792no—
398C22×C4—792no—
399C22×C4—791no—
400C22×C4—791no—
401C22×C4—791no—
402C22×C4—791no—
403C22×C4—1582no—
404C22×C4—1581no—
405C22×C4—1581no—
406C22×C4—1582no—
407C22×C4—1582no—
408C22×C4—1581no—
409C22×C4—1581no—
410C22×C4C2×C4×D7911yescharacteristic
411C22×C4D4×D7911yescharacteristic
412C22×C4C2×C22⋊D7911yescharacteristic
413C22×C4C2×Dic15811yescharacteristic
414C22×C4#1192962311yescharacteristic
415C22×C4#1192962311yescharacteristic
416C2×C8—41no—
417C2×C8—41no—
418C2×C8—41no—
419C2×C8—3161no—
420C2×C8—3161no—
421C2×C8—3161no—
422C4⋊C4—21no—
423C4⋊C4—3161no—
424C4⋊C4—3161no—
425C4⋊C4—3162no—
426C4⋊C4—3168no—
427C4⋊C4Dic79⋊C412yescomplemented
428C22⋊C4—22no—
429C22⋊C4—22no—
430C22⋊C4—3161no—
431C22⋊C4—3161no—
432C22⋊C4—3162no—
433C22⋊C4—3162no—
434C22⋊C4—3162no—
435C42—3161no—
436C42—3161no—
437C42—3162no—
438C42—1582no—
439C42—1582no—
440C23—21no—
441C23—21no—
442C23—21no—
443C23—21no—
444C23—22no—
445C23—41no—
446C23—41no—
447C23—41no—
448C23—41no—
449C23—41no—
450C23—41no—
451C23C22⋊C4×D7911yescharacteristic
452C23#1457913311yescharacteristic
453C23#1457913811yescharacteristic
454C23D8×D7911yescharacteristic
455C23SD16×D7911yescharacteristic
456C23#1457918511yescharacteristic
457C23#1457919011yescharacteristic
458D4—42no—
459D4—42no—
460D4—42no—
461D4—42no—
462D4—42no—
463D4—42no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—22no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—81no—
479C2×C4—81no—
480C2×C4—81no—
481C2×C4—81no—
482C2×C4—3162no—
483C2×C4—3162no—
484C2×C4—3162no—
485C2×C4—3161no—
486C2×C4—3161no—
487C2×C4—3161no—
488C2×C4—3161no—
489C2×C4—3161no—
490C2×C4—3161no—
491C2×C4—3162no—
492C2×C4—3162no—
493C2×C4—792no—
494C2×C4—792no—
495C2×C4—792no—
496C2×C4—792no—
497C2×C4—6321no—
498C2×C4—6321no—
499C2×C4—6321no—
500C2×C4—6321no—
501C2×C4—6324no—
502C2×C4—1584no—
503C2×C4—1584no—
504C2×C4—1581no—
505C2×C4—1581no—
506C2×C4—1581no—
507C2×C4—1581no—
508C2×C4—1581no—
509C2×C4—1581no—
510C2×C4—1581no—
511C2×C4—1581no—
512C2×C4C2×Dic79⋊C411yescharacteristic
513C2×C4#1457911711yescharacteristic
514C2×C4#1457913311yescharacteristic
515C2×C4#1457913811yescharacteristic
516C8—81no—
517C8—6321no—
518C22—21no—
519C22—21no—
520C22—21no—
521C22—21no—
522C22—21no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22—21no—
527C22—21no—
528C22—21no—
529C22—21no—
530C22—42no—
531C22—42no—
532C22—42no—
533C22—81no—
534C22—81no—
535C22—81no—
536C22—81no—
537C22#1909842111yescharacteristic
538C22#99×D7911yescharacteristic
539C22#1909853511yescharacteristic
540C22#102×D7911yescharacteristic
541C22#1909856111yescharacteristic
542C22#104×D7911yescharacteristic
543C22#1909857811yescharacteristic
544C22#1909875611yescharacteristic
545C22#1909876611yescharacteristic
546C22#1909884111yescharacteristic
547C22#1909885111yescharacteristic
548C4—21no—
549C4—21no—
550C4—21no—
551C4—21no—
552C4—42no—
553C4—82no—
554C4—6322no—
555C4—6321no—
556C4—6321no—
557C4—1582no—
558C4—1582no—
559C4—1582no—
560C4—1582no—
561C2—21no—
562C2—21no—
563C2—21no—
564C2—21no—
565C2—82no—
566C2#2376189311yescharacteristic
567C2#2376190111yescharacteristic
568C2#2376193511yescharacteristic
569C2#2376196611yescharacteristic
570C2#2376338611yescharacteristic
571C2#2376339811yescharacteristic
572C2#2376341811yescharacteristic
subgroupG/H
centerC23C22⋊C4×D79
commutatorC22×C4×C79C22×C4
FrattiniC23×C4C22×D79
FittingC2×#327×C79C2
socleC23×C79C2×C22⋊C4
prime radicalC2×#121×C79C22
cosocleC23×C4×C79C23
hypercenterC2×#327D79
hypocenterC79#8577
LCSG ▷ C22×C4×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#327

Complements

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

NH ≅ G/Ntype
2. #23763378C2semidirect
4. Dic79⋊#95C2semidirect
5. #23761280C2semidirect
6. #23761279C2semidirect
9. C2×D4×Dic79C4semidirect
14. #19098466C4semidirect
15. #19098462C4semidirect
19. C4⋊C4×Dic79C4semidirect
129. C2×D4×C79C4⋊C4semidirect
150. C4⋊C4×C79C4⋊C4semidirect
294. C79#8577semidirect
375. C2×D4Dic79⋊C4semidirect
427. C4⋊C4Dic79⋊C4semidirect

Maximal subgroups

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

subgroupindex
#121×Dic792
#237633782
C2×#190982972
Dic79⋊#952
#237612802
#237612792
C2×#327×C792
#857779