Finite Group Databasebeta

← #34258348

Subgroups — #34258348

Order 20224.

596 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23773482C211yesmaximal, characteristic
2#23772551C211yesmaximal, characteristic
3#23772480C211yesmaximal, characteristic, complemented
4#23762280C211yesmaximal, characteristic, complemented
5#23762273C211yesmaximal, characteristic, complemented
6#23762252C211yesmaximal, characteristic, complemented
7#23762245C211yesmaximal, characteristic, complemented
8#23762220C211yesmaximal, characteristic, complemented
9#23762214C211yesmaximal, characteristic, complemented
10C8×Dic316C211yesmaximal, characteristic, complemented
11C8×#11929613C211yesmaximal, characteristic, complemented
12#23762189C211yesmaximal, characteristic, complemented
13#23761830C211yesmaximal, characteristic, complemented
14#23761809C211yesmaximal, characteristic
15C79×#1454C211yesmaximal, characteristic, complemented
16#19099097C2211yescharacteristic
17C2×C4×Dic158C2211yescharacteristic
18#19098894C411yescharacteristic
19#19098877C411yescharacteristic
20#19098871C411yescharacteristic
21#19098871C411yescharacteristic
22#19098786C411yescharacteristic
23#19098786C411yescharacteristic
24#19098721C411yescharacteristic
25#19098704C411yescharacteristic
26#19098693C2211yescharacteristic
27C8×Dic158C2211yescharacteristic
28C8×Dic158C2211yescharacteristic
29C8×Dic158C2211yescharacteristic
30C8×Dic158C2211yescharacteristic
31C8×Dic158C2211yescharacteristic
32#19098687—21no—
33#19098687—21no—
34C4×Dic316C2211yescharacteristic
35C4×Dic316C2211yescharacteristic
36C4×#11929613C2211yescharacteristic
37C4×#11929613C2211yescharacteristic
38#19098642C2211yescharacteristic
39#19098638—21no—
40#19098637—21no—
41C8×D316C2211yescharacteristic
42#19098623—21no—
43#19098616C2211yescharacteristic
44#19098613—21no—
45#19098613—21no—
46#19098588—21no—
47#19098587C2211yescharacteristic
48#19098316C2211yescharacteristic
49#19098316C2211yescharacteristic
50#19098314C2211yescharacteristic
51#19098314C2211yescharacteristic
52#19098295C2211yescharacteristic
53#19098295C2211yescharacteristic
54#19098295C2211yescharacteristic
55#19098295C2211yescharacteristic
56#19098295C2211yescharacteristic
57#19098295C2211yescharacteristic
58#19098292C2211yescharacteristic
59#19098292C2211yescharacteristic
60#431×C79C2211yescharacteristic
61#431×C79C2211yescharacteristic
62#431×C79C2211yescharacteristic
63#322×C79C2211yescharacteristic
64#322×C79C2211yescharacteristic
65#322×C79C2211yescharacteristic
66C82×C79C2211yescharacteristic
67C22×Dic158C2×C411yescharacteristic
68C2×Dic316C2×C411yescharacteristic
69C2×Dic316C2×C411yescharacteristic
70C2×#11929613C2×C411yescharacteristic
71C2×#11929613C2×C411yescharacteristic
72C2×#11929608—21no—
73C2×#11929607—21no—
74C2×C8×D79—21no—
75#14579155—21no—
76#14579153C2×C411yescharacteristic
77#14579149C2×C411yescharacteristic
78#14579144—21no—
79#14579140C2×C411yescharacteristic
80#14579135C2×C411yescharacteristic
81C4×Dic158—21no—
82C4×Dic158—21no—
83C4×Dic158C2×C411yescharacteristic
84C4×Dic158C2×C411yescharacteristic
85C4×Dic158C2311yescharacteristic
86C4×Dic158C2311yescharacteristic
87C4×Dic158C2311yescharacteristic
88C4×D316C2311yescharacteristic
89C4×C22⋊D79—21no—
90#14579118—21no—
91C2×C4⋊Dic79C2×C411yescharacteristic
92C2×Dic79⋊C4—21no—
93C2×C4×Dic79—21no—
94#14579095C2×C411yescharacteristic
95#14579095C2×C411yescharacteristic
96#14579093C2×C411yescharacteristic
97#14579093C2×C411yescharacteristic
98C4⋊(C79⋊C8)—21no—
99C4⋊(C79⋊C8)C2311yescharacteristic
100C4⋊(C79⋊C8)C2311yescharacteristic
101C4⋊(C79⋊C8)C2311yescharacteristic
102C4⋊(C79⋊C8)C2311yescharacteristic
103Dic79⋊C8—21no—
104Dic79⋊C8—21no—
105Dic79⋊C8—21no—
106Dic79⋊C8—21no—
107Dic79⋊C8—21no—
108Dic79⋊C8—21no—
109#14579086C2×C411yescharacteristic
110#14579086C2×C411yescharacteristic
111#14579086C2×C411yescharacteristic
112#14579086C2×C411yescharacteristic
113#14579086C2×C411yescharacteristic
114#14579086C2×C411yescharacteristic
115#14579083C2×C411yescharacteristic
116#14579083C2×C411yescharacteristic
117C22⋊(C79⋊C8)—21no—
118(C2×D79)⋊C8—21no—
119(C2×D79)⋊C8—21no—
120#14579071—21no—
121C4×C79⋊C8—21no—
122C8×Dic79—21no—
123C8×Dic79—21no—
124C8×Dic79—21no—
125C8×Dic79—21no—
126C8×Dic79—21no—
127C2×C42×C79C2311yescharacteristic
128C4⋊C8×C79—21no—
129C4⋊C8×C79C2×C411yescharacteristic
130C4⋊C8×C79C2×C411yescharacteristic
131C4⋊C8×C79D411yescharacteristic
132C4⋊C8×C79D411yescharacteristic
133C22⋊C8×C79—21no—
134C22⋊C8×C79C2×C411yescharacteristic
135C22⋊C8×C79C2×C411yescharacteristic
136C22⋊C8×C79D411yescharacteristic
137C22⋊C8×C79D411yescharacteristic
138C4×C8×C79C2311yescharacteristic
139C4×C8×C79C2311yescharacteristic
140C4×C8×C79C2311yescharacteristic
141C4×C8×C79C2311yescharacteristic
142C4×C8×C79C2311yescharacteristic
143C4×C8×C79C2311yescharacteristic
144C2×Dic158—22no—
145C2×Dic158—22no—
146C2×Dic158—21no—
147C2×Dic158C22×C411yescharacteristic
148C2×Dic158C22×C411yescharacteristic
149C2×Dic158C22×C411yescharacteristic
150C2×D316C22×C411yescharacteristic
151C2×C22⋊D79—21no—
152C22×Dic79—21no—
153C22×Dic79—21no—
154C2×C4×D79—21no—
155Dic316—22no—
156Dic316—22no—
157#11929613—22no—
158#11929613—22no—
159#11929608—81no—
160#11929607—81no—
161C2×C79⋊C8—21no—
162C2×C79⋊C8—21no—
163C2×C79⋊C8—21no—
164C2×C79⋊C8—21no—
165C8×D79—81no—
166C4⋊Dic79—21no—
167C4⋊Dic79C22×C411yescharacteristic
168C4⋊Dic79C22×C411yescharacteristic
169C4⋊Dic79C22×C411yescharacteristic
170C4⋊Dic79C22×C411yescharacteristic
171Dic79⋊C4—21no—
172Dic79⋊C4—21no—
173Dic79⋊C4—21no—
174Dic79⋊C4—21no—
175Dic79⋊C4—21no—
176Dic79⋊C4—21no—
177Dic79⋊C4—21no—
178Dic79⋊C4—21no—
179C22⋊Dic79—21no—
180(C2×D79)⋊C4—21no—
181(C2×D79)⋊C4—21no—
182(C2×D79)⋊C4—21no—
183(C2×D79)⋊C4—21no—
184C4×Dic79—21no—
185C4×Dic79—21no—
186C4×Dic79—21no—
187C4×Dic79—21no—
188C4×Dic79—21no—
189C22×C4×C79C22×C411yescharacteristic
190C22×C4×C79C2×D411yescharacteristic
191C22×C4×C79#4111yescharacteristic
192C2×C8×C79—21no—
193C2×C8×C79—21no—
194C2×C8×C79C22×C411yescharacteristic
195C2×C8×C79C22×C411yescharacteristic
196C2×C8×C79C22×C411yescharacteristic
197C2×C8×C79C22×C411yescharacteristic
198C2×C8×C79C2×D411yescharacteristic
199C2×C8×C79C2×D411yescharacteristic
200C2×C8×C79C2×D411yescharacteristic
201C2×C8×C79C2×D411yescharacteristic
202C42×C79C22×C411yescharacteristic
203C42×C79C2×D411yescharacteristic
204C42×C79#4111yescharacteristic
205C42×C79C2411yescharacteristic
206C23×C79C4×D411yescharacteristic
207C22×D79—21no—
208C2×C4×C79—21no—
209C2×C4×C79—21no—
210C2×C4×C79—21no—
211C2×C4×C79—21no—
212C2×C4×C79—41no—
213C2×C4×C79C4×D411yescharacteristic
214C2×C4×C79C4×D411yescharacteristic
215C2×C4×C79C4×D411yescharacteristic
216C2×C4×C79C23×C411yescharacteristic
217C2×C4×C79C22×D411yescharacteristic
218C2×C4×C79C2×#4111yescharacteristic
219C22⋊D79—81no—
220C2×Dic79—24no—
221C2×Dic79—21no—
222C2×Dic79—21no—
223C2×Dic79—21no—
224C2×Dic79—21no—
225C2×Dic79—21no—
226C2×Dic79—21no—
227C2×Dic79—21no—
228C2×Dic79—81no—
229D316—21no—
230D316—21no—
231C4×D79—41no—
232C4×D79—41no—
233Dic158—24no—
234Dic158—21no—
235Dic158—21no—
236Dic158—21no—
237Dic158—21no—
238Dic158#13112yes—
239Dic158#13112yes—
240C8×C79—21no—
241C8×C79—21no—
242C8×C79—21no—
243C8×C79—21no—
244C8×C79—21no—
245C8×C79—21no—
246C8×C79—21no—
247C8×C79—21no—
248C8×C79—41no—
249C8×C79—41no—
250C79⋊C8—41no—
251C79⋊C8—41no—
252C79⋊C8—41no—
253C79⋊C8—41no—
254C22×C79—21no—
255C22×C79—21no—
256C22×C79—21no—
257C22×C79C2×C4×D411yescharacteristic
258C2×D79—41no—
259C2×D79—41no—
260C2×D79—41no—
261C4×C79—21no—
262C4×C79—21no—
263C4×C79—21no—
264C4×C79—21no—
265C4×C79C2×#13111yescharacteristic
266C4×C79C2×#13111yescharacteristic
267C4×C79#57711yescharacteristic
268C4×C79#57811yescharacteristic
269Dic79—22no—
270Dic79—22no—
271Dic79—41no—
272Dic79—41no—
273Dic79—41no—
274Dic79—41no—
275Dic79—41no—
276#17919—791nomaximal, Sylow
277C2×C79—41no—
278C2×C79#292911yescharacteristic
279C2×C79#294711yescharacteristic
280C2×C79#295711yescharacteristic
281D79—81no—
282#3108—791no—
283#2993—791no—
284#2982—791no—
285#1588—791no—
286#1587—791no—
287#1584—791no—
288#1583—791no—
289#1579—791no—
290SD16⋊C8—791no—
291C8×Q16—791no—
292C8×SD16—791no—
293#1574—791no—
294#1487—791no—
295#1482—791no—
296#1454D7911yescharacteristic, complemented
297C79#1791911yescharacteristic, complemented, Sylow
298#529—791no—
299C2×C4×Q8—791no—
300#483—791no—
301#480—791no—
302#479—791no—
303#479—791no—
304#464—791no—
305#464—791no—
306#451—791no—
307#448—791no—
308#446—791no—
309C8×Q8—791no—
310C8×Q8—791no—
311C8×Q8—791no—
312C8×Q8—791no—
313C8×Q8—791no—
314C8×Q8—1581no—
315C8×Q8—1581no—
316C4×Q16—791no—
317C4×Q16—791no—
318C4×SD16—791no—
319C4×SD16—791no—
320#436—791no—
321#436—1581no—
322#435—1581no—
323C8×D4—791no—
324#433—1581no—
325#431—791no—
326#431—1581no—
327#431—1581no—
328#431C2×D7911yescharacteristic
329#431C2×D7911yescharacteristic
330#431C2×D7911yescharacteristic
331#424—1581no—
332#423—791no—
333#335—791no—
334#335—791no—
335#334—791no—
336#334—791no—
337Q8⋊C8—791no—
338Q8⋊C8—791no—
339Q8⋊C8—791no—
340Q8⋊C8—791no—
341Q8⋊C8—791no—
342Q8⋊C8—791no—
343D4⋊C8—791no—
344D4⋊C8—791no—
345#322C2×D7911yescharacteristic
346#322C2×D7911yescharacteristic
347#322C2×D7911yescharacteristic
348C82C2×D7911yescharacteristic
349C22×Q8—791no—
350C2×Q16—791no—
351C2×Q16—791no—
352C2×SD16—791no—
353C2×SD16—791no—
354C2×M16—1581no—
355C2×M16—1581no—
356C22×C8—1581no—
357#126—1581no—
358#125—791no—
359#124—791no—
360#123—1581no—
361C22⋊Q8—791no—
362#121—791no—
363C4×Q8—791no—
364C4×Q8—791no—
365C4×Q8—791no—
366C4×Q8—791no—
367C4×Q8—791no—
368C4×Q8—1581no—
369C4×Q8—1581no—
370C4×D4—791no—
371C4×D4—1581no—
372#117—1581no—
373C2×C4⋊C4—791no—
374C2×C4⋊C4—1581no—
375C2×C42—1581no—
376C2×C42C22×D7911yescharacteristic
377#107—791no—
378#107—791no—
379#106—791no—
380#106—791no—
381C4⋊C8—21no—
382C4⋊C8—791no—
383C4⋊C8—791no—
384C4⋊C8—791no—
385C4⋊C8—791no—
386C4⋊C8—1581no—
387C4⋊C8—1581no—
388C4⋊C8—1581no—
389C4⋊C8—1581no—
390C4⋊C8—1581no—
391C4⋊C8—1581no—
392C4⋊C8—1581no—
393C4⋊C8C4×D7911yescharacteristic
394C4⋊C8C4×D7911yescharacteristic
395C4⋊C8D31611yescharacteristic
396C4⋊C8D31611yescharacteristic
397#103—791no—
398#103—791no—
399#103—791no—
400#103—791no—
401#103—791no—
402#103—791no—
403#102—791no—
404#102—791no—
405C22⋊C8—21no—
406C22⋊C8—1581no—
407C22⋊C8—1581no—
408C22⋊C8—1581no—
409C22⋊C8C4×D7911yescharacteristic
410C22⋊C8C4×D7911yescharacteristic
411C22⋊C8D31611yescharacteristic
412C22⋊C8D31611yescharacteristic
413#97—1581no—
414C4×C8—1581no—
415C4×C8—1581no—
416C4×C8—1581no—
417C4×C8—1581no—
418C4×C8—1581no—
419C4×C8—1581no—
420C4×C8C22×D7911yescharacteristic
421C4×C8C22×D7911yescharacteristic
422C4×C8C22×D7911yescharacteristic
423C4×C8C22×D7911yescharacteristic
424C4×C8C22×D7911yescharacteristic
425C4×C8C22×D7911yescharacteristic
426C2×Q8—791no—
427C2×Q8—791no—
428C2×Q8—791no—
429C2×Q8—1582no—
430C2×Q8—1582no—
431C2×Q8—1581no—
432C2×D4—791no—
433C2×D4—1581no—
434C22×C4—1581no—
435C22×C4—1581no—
436C22×C4—1581no—
437C22×C4C2×C4×D7911yescharacteristic
438C22×C4C2×D31611yescharacteristic
439C22×C4#1192962411yescharacteristic
440Q16—1582no—
441Q16—1582no—
442SD16—1582no—
443SD16—1582no—
444M16—6321no—
445M16—6321no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—6321no—
449C2×C8—1581no—
450C2×C8—1581no—
451C2×C8—1581no—
452C2×C8—1581no—
453C2×C8C2×C4×D7911yescharacteristic
454C2×C8C2×C4×D7911yescharacteristic
455C2×C8C2×C4×D7911yescharacteristic
456C2×C8C2×C4×D7911yescharacteristic
457C2×C8C2×D31611yescharacteristic
458C2×C8C2×D31611yescharacteristic
459C2×C8C2×D31611yescharacteristic
460C2×C8C2×D31611yescharacteristic
461C4⋊C4—791no—
462C4⋊C4—791no—
463C4⋊C4—791no—
464C4⋊C4—791no—
465C4⋊C4—1581no—
466C4⋊C4—1581no—
467C4⋊C4—1581no—
468C4⋊C4—1581no—
469C4⋊C4—1581no—
470C4⋊C4—1581no—
471C4⋊C4—1581no—
472C4⋊C4—1581no—
473C4⋊C4—1581no—
474C22⋊C4—1581no—
475C22⋊C4—1581no—
476C22⋊C4—1581no—
477C22⋊C4—1581no—
478C22⋊C4—1581no—
479C42—1581no—
480C42—1581no—
481C42—1581no—
482C42—1581no—
483C42—1581no—
484C42C2×C4×D7911yescharacteristic
485C42C2×D31611yescharacteristic
486C42#1192962411yescharacteristic
487C42C23×D7911yescharacteristic
488C23—1581no—
489C23C4×D31611yescharacteristic
490Q8—792no—
491Q8—792no—
492Q8—1584no—
493Q8—1581no—
494Q8—1581no—
495Q8—1581no—
496Q8—1581no—
497D4—6321no—
498D4—1581no—
499D4—1581no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—41no—
505C2×C4—3161no—
506C2×C4—3161no—
507C2×C4—6321no—
508C2×C4—1581no—
509C2×C4—1581no—
510C2×C4—1581no—
511C2×C4—1581no—
512C2×C4—1581no—
513C2×C4—1584no—
514C2×C4—1581no—
515C2×C4—1581no—
516C2×C4C4×D31611yescharacteristic
517C2×C4C4×D31611yescharacteristic
518C2×C4C4×D31611yescharacteristic
519C2×C4C22×C4×D7911yescharacteristic
520C2×C4C22×D31611yescharacteristic
521C2×C4C2×#1192962411yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—21no—
527C8—21no—
528C8—21no—
529C8—21no—
530C8—41no—
531C8—41no—
532C8—3161no—
533C8—3161no—
534C8—3161no—
535C8—3161no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—3161no—
540C22—3161no—
541C22—3161no—
542C22C2×C4×D31611yescharacteristic
543C4—21no—
544C4—21no—
545C4—21no—
546C4—21no—
547C4—3161no—
548C4—3161no—
549C4—3161no—
550C4—3161no—
551C4—3161no—
552C4—1582no—
553C4—1582no—
554C4#131×D7911yescharacteristic
555C4#131×D7911yescharacteristic
556C4#1909937511yescharacteristic
557C4#1909938011yescharacteristic
558C2—41no—
559C2—6321no—
560C2#2377209611yescharacteristic
561C2#2377224511yescharacteristic
562C2#2377231811yescharacteristic
subgroupG/H
centerC2×C4C22×D316
commutatorC2×C4×C79C23×C4
FrattiniC42C23×D79
FittingC79×#1454C2
socleC22×C79C2×C4×D4
prime radical#14579135C2×C4
cosocleC42×C79C24
hypercenter#1454D79
hypocenterC79#17919
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ #431 ◁ #1454

Complements

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

NH ≅ G/Ntype
3. #23772480C2semidirect
4. #23762280C2semidirect
5. #23762273C2semidirect
6. #23762252C2semidirect
7. #23762245C2semidirect
8. #23762220C2semidirect
9. #23762214C2semidirect
10. C8×Dic316C2semidirect
11. C8×#11929613C2semidirect
12. #23762189C2semidirect
13. #23761830C2semidirect
15. C79×#1454C2semidirect
296. #1454D79semidirect
297. C79#17919semidirect

Maximal subgroups

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

subgroupindex
#237734822
#237725512
#237724802
#237622802
#237622732
#237622522
#237622452
#237622202
#237622142
C8×Dic3162
C8×#119296132
#237621892
#237618302
#237618092
C79×#14542
#1791979