Finite Group Databasebeta

← #34259290

Subgroups — #34259290

Order 20224.

608 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23773418C211yesmaximal, characteristic
2#23772404C211yesmaximal, characteristic, complemented
3#23762312C211yesmaximal, characteristic, complemented
4#23762302C211yesmaximal, characteristic, complemented
5#23762278C211yesmaximal, characteristic, complemented
6#23762276C211yesmaximal, characteristic, complemented
7#23762271C211yesmaximal, characteristic, complemented
8#23762262C211yesmaximal, characteristic, complemented
9#23762217C211yesmaximal, characteristic, complemented
10#23762210C211yesmaximal, characteristic, complemented
11#23762181C211yesmaximal, characteristic, complemented
12#23761858C211yesmaximal, characteristic, complemented
13#23761782C211yesmaximal, characteristic, complemented
14#23761687C211yesmaximal, characteristic, complemented
15C79×#2971C211yesmaximal, characteristic, complemented
16#19099097C2211yescharacteristic
17#19098904C411yescharacteristic
18#19098887C411yescharacteristic
19#19098870C411yescharacteristic
20#19098863C411yescharacteristic
21#19098785C411yescharacteristic
22#19098778C411yescharacteristic
23#19098725C411yescharacteristic
24#19098708C411yescharacteristic
25#19098693C2211yescharacteristic
26C8×Dic158C2211yescharacteristic
27C4×#11929614C2211yescharacteristic
28C4×#11929611C2211yescharacteristic
29C4×#11929612C2211yescharacteristic
30C4×#11929609C2211yescharacteristic
31#19098642C2211yescharacteristic
32#19098639—21no—
33#19098632—21no—
34C8×D316C2211yescharacteristic
35#19098625—21no—
36#19098616C2211yescharacteristic
37#19098616C2211yescharacteristic
38#19098520—21no—
39C2×C4×C79⋊C8C2211yescharacteristic
40#19098315C2211yescharacteristic
41#19098315C2211yescharacteristic
42#19098313C2211yescharacteristic
43#19098313C2211yescharacteristic
44Q8⋊(C79⋊C8)C2211yescharacteristic
45Q8⋊(C79⋊C8)C2211yescharacteristic
46#19098293C2211yescharacteristic
47#19098293C2211yescharacteristic
48D4⋊(C79⋊C8)C2211yescharacteristic
49D4⋊(C79⋊C8)C2211yescharacteristic
50#19098290C2211yescharacteristic
51#19098290C2211yescharacteristic
52#19098285C2211yescharacteristic
53#19098285C2211yescharacteristic
54#19098285C2211yescharacteristic
55#19098285C2211yescharacteristic
56C4×#41×C79C2211yescharacteristic
57C8×Q8×C79C2211yescharacteristic
58C8×Q8×C79C2211yescharacteristic
59#436×C79—21no—
60#436×C79—21no—
61#436×C79C2211yescharacteristic
62#436×C79C2211yescharacteristic
63#432×C79—21no—
64#432×C79C2211yescharacteristic
65C4×M16×C79—21no—
66C4×M16×C79C2211yescharacteristic
67C2×#11929614C2×C411yescharacteristic
68C2×#11929612C2×C411yescharacteristic
69C2×#11929611C2×C411yescharacteristic
70C2×#11929609C2×C411yescharacteristic
71C2×#11929607—21no—
72C22×C79⋊C8—21no—
73C2×C8×D79—21no—
74#14579155—21no—
75#14579153C2×C411yescharacteristic
76#14579149C2×C411yescharacteristic
77#14579144—21no—
78#14579140C2×C411yescharacteristic
79#14579135C2×C411yescharacteristic
80C4×Dic158C2311yescharacteristic
81C4×D316C2311yescharacteristic
82C4×C22⋊D79—21no—
83#14579118—21no—
84#14579094C2×C411yescharacteristic
85#14579094C2×C411yescharacteristic
86#14579092C2×C411yescharacteristic
87#14579092C2×C411yescharacteristic
88C4⋊(C79⋊C8)C2×C411yescharacteristic
89C4⋊(C79⋊C8)C2×C411yescharacteristic
90C4⋊(C79⋊C8)C2311yescharacteristic
91C4⋊(C79⋊C8)C2311yescharacteristic
92Dic79⋊C8—21no—
93Dic79⋊C8—21no—
94#14579085C2×C411yescharacteristic
95#14579085C2×C411yescharacteristic
96#14579084C2×C411yescharacteristic
97#14579084C2×C411yescharacteristic
98#14579082C2×C411yescharacteristic
99#14579082C2×C411yescharacteristic
100#14579081C2×C411yescharacteristic
101#14579081C2×C411yescharacteristic
102C22⋊(C79⋊C8)—21no—
103C22⋊(C79⋊C8)C2×C411yescharacteristic
104C22⋊(C79⋊C8)C2×C411yescharacteristic
105(C2×D79)⋊C8—21no—
106(C2×D79)⋊C8—21no—
107#14579071—21no—
108C4×C79⋊C8—21no—
109C4×C79⋊C8—21no—
110C4×C79⋊C8C2311yescharacteristic
111C4×C79⋊C8C2311yescharacteristic
112C4×C79⋊C8C2311yescharacteristic
113C4×C79⋊C8C2311yescharacteristic
114C8×Dic79—21no—
115C2×#41×C79C2×C411yescharacteristic
116C2×M16×C79—21no—
117C2×M16×C79—21no—
118C2×M16×C79D411yescharacteristic
119C2×M16×C79D411yescharacteristic
120C4×Q8×C79C2×C411yescharacteristic
121C4×Q8×C79C2311yescharacteristic
122C4×D4×C79—21no—
123C4×D4×C79—21no—
124C4×D4×C79C2×C411yescharacteristic
125C4×D4×C79C2311yescharacteristic
126#117×C79—21no—
127#117×C79C2×C411yescharacteristic
128C2×C42×C79—21no—
129C2×C42×C79C2311yescharacteristic
130C4⋊C8×C79—21no—
131C4⋊C8×C79—21no—
132C4⋊C8×C79C2311yescharacteristic
133C4⋊C8×C79C2311yescharacteristic
134C22⋊C8×C79—21no—
135C22⋊C8×C79—21no—
136C22⋊C8×C79—21no—
137#97×C79—21no—
138#97×C79D411yescharacteristic
139#97×C79D411yescharacteristic
140C4×C8×C79—21no—
141C4×C8×C79—21no—
142C4×C8×C79C2311yescharacteristic
143C4×C8×C79C2311yescharacteristic
144C2×Dic158C22×C411yescharacteristic
145C2×D316C22×C411yescharacteristic
146C2×C22⋊D79—21no—
147C2×C4×D79—21no—
148#11929614—22no—
149#11929612—41no—
150#11929611—22no—
151#11929609—41no—
152#11929607—42no—
153C2×C79⋊C8—21no—
154C2×C79⋊C8—21no—
155C2×C79⋊C8—21no—
156C2×C79⋊C8—21no—
157C2×C79⋊C8—42no—
158C2×C79⋊C8C22×C411yescharacteristic
159C2×C79⋊C8C22×C411yescharacteristic
160C2×C79⋊C8C22×C411yescharacteristic
161C2×C79⋊C8C22×C411yescharacteristic
162C8×D79—42no—
163C4⋊Dic79C22×C411yescharacteristic
164C4⋊Dic79C22×C411yescharacteristic
165Dic79⋊C4—21no—
166Dic79⋊C4—21no—
167Dic79⋊C4—21no—
168Dic79⋊C4—21no—
169C22⋊Dic79—21no—
170(C2×D79)⋊C4—21no—
171(C2×D79)⋊C4—21no—
172(C2×D79)⋊C4—21no—
173(C2×D79)⋊C4—21no—
174C4×Dic79—21no—
175#41×C79—22no—
176#41×C79—41no—
177C2×Q8×C79C22×C411yescharacteristic
178C2×D4×C79—21no—
179C2×D4×C79C22×C411yescharacteristic
180C22×C4×C79—21no—
181C22×C4×C79—21no—
182C22×C4×C79—21no—
183C22×C4×C79C22×C411yescharacteristic
184C22×C4×C79C2×D411yescharacteristic
185C22×C4×C79#4111yescharacteristic
186M16×C79—41no—
187M16×C79—41no—
188M16×C79—42no—
189M16×C79—42no—
190C2×C8×C79—21no—
191C2×C8×C79—21no—
192C2×C8×C79C2×D411yescharacteristic
193C2×C8×C79C2×D411yescharacteristic
194C2×C8×C79C2×D411yescharacteristic
195C2×C8×C79C2×D411yescharacteristic
196C4⋊C4×C79—21no—
197C4⋊C4×C79—21no—
198C4⋊C4×C79C22×C411yescharacteristic
199C4⋊C4×C79C22×C411yescharacteristic
200C22⋊C4×C79—21no—
201C22⋊C4×C79—21no—
202C22⋊C4×C79—21no—
203C42×C79—21no—
204C42×C79—21no—
205C42×C79—21no—
206C42×C79C22×C411yescharacteristic
207C42×C79C2×D411yescharacteristic
208C42×C79#4111yescharacteristic
209C42×C79C2411yescharacteristic
210C23×C79—21no—
211C23×C79C4×D411yescharacteristic
212C22×D79—21no—
213Q8×C79—21no—
214Q8×C79#13112yes—
215D4×C79—21no—
216D4×C79—21no—
217D4×C79—42no—
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—41no—
226C2×C4×C79—42no—
227C2×C4×C79—41no—
228C2×C4×C79—41no—
229C2×C4×C79—81no—
230C2×C4×C79C4×D411yescharacteristic
231C2×C4×C79C4×D411yescharacteristic
232C2×C4×C79C4×D411yescharacteristic
233C2×C4×C79C23×C411yescharacteristic
234C2×C4×C79C22×D411yescharacteristic
235C2×C4×C79C2×#4111yescharacteristic
236C22⋊D79—81no—
237C2×Dic79—21no—
238C2×Dic79—21no—
239C2×Dic79—21no—
240D316—21no—
241D316—21no—
242C4×D79—41no—
243C4×D79—41no—
244Dic158—21no—
245Dic158—21no—
246C8×C79—21no—
247C8×C79—21no—
248C8×C79—21no—
249C8×C79—21no—
250C8×C79—41no—
251C8×C79—41no—
252C79⋊C8—22no—
253C79⋊C8—21no—
254C79⋊C8—21no—
255C79⋊C8—21no—
256C79⋊C8—21no—
257C79⋊C8—41no—
258C79⋊C8—41no—
259C79⋊C8—41no—
260C22×C79—21no—
261C22×C79—21no—
262C22×C79—21no—
263C22×C79—41no—
264C22×C79—41no—
265C22×C79—41no—
266C22×C79C2×C4×D411yescharacteristic
267C2×D79—41no—
268C2×D79—41no—
269C2×D79—41no—
270C4×C79—21no—
271C4×C79—22no—
272C4×C79—21no—
273C4×C79—21no—
274C4×C79—21no—
275C4×C79—41no—
276C4×C79—41no—
277C4×C79C2×#13111yescharacteristic
278C4×C79#56811yescharacteristic
279C4×C79#57511yescharacteristic
280C4×C79#57511yescharacteristic
281Dic79—41no—
282Dic79—41no—
283Dic79—41no—
284#18005—791nomaximal, Sylow
285C2×C79—41no—
286C2×C79—81no—
287C2×C79#293311yescharacteristic
288C2×C79#294311yescharacteristic
289C2×C79#295611yescharacteristic
290D79—81no—
291#3102—791no—
292#2971D7911yescharacteristic, complemented
293#2969—791no—
294#1594—791no—
295#1592—791no—
296#1588—791no—
297#1588—791no—
298#1587—791no—
299#1586—791no—
300#1579—791no—
301SD16⋊C8—791no—
302#1572—791no—
303#1494—791no—
304#1476—791no—
305#1451—791no—
306C79#1800511yescharacteristic, complemented, Sylow
307#529—791no—
308C4×#41C2×D7911yescharacteristic
309#485—791no—
310#482—791no—
311#479—791no—
312#478—791no—
313#464—791no—
314#463—791no—
315#452—791no—
316#449—791no—
317#446—791no—
318C8×Q8—791no—
319C8×Q8C2×D7911yescharacteristic
320C8×Q8C2×D7911yescharacteristic
321C4×Q16—791no—
322C4×SD16—791no—
323C4×SD16—791no—
324C4×D8—791no—
325#436—21no—
326#436—21no—
327#436—791no—
328#436—1581no—
329#436C2×D7911yescharacteristic
330#436C2×D7911yescharacteristic
331#435—1581no—
332C8×D4—791no—
333#433—1581no—
334#432—21no—
335#432C2×D7911yescharacteristic
336#431—791no—
337#431—791no—
338#405—1581no—
339C4×M16—21no—
340C4×M16C2×D7911yescharacteristic
341C2×C4×C8—791no—
342#335—791no—
343#335—791no—
344#334—791no—
345#334—791no—
346Q8⋊C8—791no—
347Q8⋊C8—791no—
348Q8⋊C8—791no—
349Q8⋊C8—791no—
350D4⋊C8—791no—
351D4⋊C8—791no—
352D4⋊C8—791no—
353D4⋊C8—791no—
354#322—791no—
355#322—791no—
356#322—791no—
357#322—791no—
358C2×#41C4×D7911yescharacteristic
359C2×Q16—791no—
360C2×SD16—791no—
361C2×SD16—791no—
362C2×D8—791no—
363C2×M16—21no—
364C2×M16—21no—
365C2×M16—1581no—
366C2×M16C22⋊D7911yescharacteristic
367C2×M16C22⋊D7911yescharacteristic
368C22×C8—1581no—
369C22×C8—1581no—
370#126—1581no—
371#125—791no—
372#124—791no—
373#123—1581no—
374C22⋊Q8—791no—
375#121—791no—
376C4×Q8—791no—
377C4×Q8C4×D7911yescharacteristic
378C4×Q8C22×D7911yescharacteristic
379C4×D4—21no—
380C4×D4—21no—
381C4×D4—791no—
382C4×D4—1581no—
383C4×D4C4×D7911yescharacteristic
384C4×D4C22×D7911yescharacteristic
385#117—21no—
386#117—1581no—
387#117C4×D7911yescharacteristic
388C2×C42—21no—
389C2×C42C22×D7911yescharacteristic
390#107—791no—
391#107—791no—
392#106—791no—
393#106—791no—
394C4⋊C8—21no—
395C4⋊C8—21no—
396C4⋊C8—791no—
397C4⋊C8—791no—
398C4⋊C8—791no—
399C4⋊C8—791no—
400C4⋊C8—1581no—
401C4⋊C8—1581no—
402C4⋊C8C22×D7911yescharacteristic
403C4⋊C8C22×D7911yescharacteristic
404#103—791no—
405#103—791no—
406#103—791no—
407#103—791no—
408#102—791no—
409#102—791no—
410#102—791no—
411#102—791no—
412C22⋊C8—21no—
413C22⋊C8—21no—
414C22⋊C8—21no—
415C22⋊C8—791no—
416C22⋊C8—791no—
417C22⋊C8—1581no—
418C22⋊C8—1581no—
419C22⋊C8—1581no—
420#97—21no—
421#97—1581no—
422#97C22⋊D7911yescharacteristic
423#97C22⋊D7911yescharacteristic
424C4×C8—21no—
425C4×C8—21no—
426C4×C8—791no—
427C4×C8—791no—
428C4×C8—791no—
429C4×C8—791no—
430C4×C8—1581no—
431C4×C8—1581no—
432C4×C8—1581no—
433C4×C8C22×D7911yescharacteristic
434C4×C8C22×D7911yescharacteristic
435#41—22no—
436#41—41no—
437C2×Q8—791no—
438C2×Q8C2×C4×D7911yescharacteristic
439C2×D4—21no—
440C2×D4—791no—
441C2×D4—1581no—
442C2×D4C2×C4×D7911yescharacteristic
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—1581no—
447C22×C4C2×C4×D7911yescharacteristic
448C22×C4C2×C22⋊D7911yescharacteristic
449C22×C4#1192962411yescharacteristic
450Q16—1582no—
451SD16—3161no—
452SD16—1582no—
453D8—3161no—
454M16—41no—
455M16—41no—
456M16—42no—
457M16—42no—
458M16—3162no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—3162no—
462C2×C8—3162no—
463C2×C8—791no—
464C2×C8—791no—
465C2×C8—791no—
466C2×C8—791no—
467C2×C8—1581no—
468C2×C8—1581no—
469C2×C8—1581no—
470C2×C8—1581no—
471C2×C8C2×C22⋊D7911yescharacteristic
472C2×C8C2×C22⋊D7911yescharacteristic
473C2×C8C2×C22⋊D7911yescharacteristic
474C2×C8C2×C22⋊D7911yescharacteristic
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—791no—
478C4⋊C4—791no—
479C4⋊C4—1581no—
480C4⋊C4—1581no—
481C4⋊C4—1581no—
482C4⋊C4—1581no—
483C4⋊C4C2×C4×D7911yescharacteristic
484C4⋊C4C2×C4×D7911yescharacteristic
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—1581no—
489C22⋊C4—1581no—
490C22⋊C4—1581no—
491C22⋊C4—1581no—
492C22⋊C4—1581no—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—1581no—
497C42C2×C4×D7911yescharacteristic
498C42C2×C22⋊D7911yescharacteristic
499C42#1192962411yescharacteristic
500C42C23×D7911yescharacteristic
501C23—21no—
502C23—1581no—
503C23C4×C22⋊D7911yescharacteristic
504Q8—21no—
505Q8—1581no—
506Q8—1581no—
507Q8#1457916912yes—
508D4—21no—
509D4—21no—
510D4—42no—
511D4—6321no—
512D4—1581no—
513D4—1581no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—41no—
522C2×C4—42no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—81no—
526C2×C4—3161no—
527C2×C4—3161no—
528C2×C4—1581no—
529C2×C4—1581no—
530C2×C4—1581no—
531C2×C4C4×C22⋊D7911yescharacteristic
532C2×C4C4×C22⋊D7911yescharacteristic
533C2×C4C4×C22⋊D7911yescharacteristic
534C2×C4C22×C4×D7911yescharacteristic
535C2×C4C22×C22⋊D7911yescharacteristic
536C2×C4C2×#1192962411yescharacteristic
537C8—21no—
538C8—21no—
539C8—21no—
540C8—21no—
541C8—41no—
542C8—41no—
543C8—3161no—
544C8—3161no—
545C8—3161no—
546C8—1582no—
547C8—1581no—
548C8—1581no—
549C8—1581no—
550C8—1581no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—3161no—
558C22—3161no—
559C22—3161no—
560C22C2×C4×C22⋊D7911yescharacteristic
561C4—21no—
562C4—21no—
563C4—21no—
564C4—21no—
565C4—22no—
566C4—41no—
567C4—41no—
568C4—3161no—
569C4—3161no—
570C4—3161no—
571C4C2×#1457916911yescharacteristic
572C4#1909932911yescharacteristic
573C4#1909936111yescharacteristic
574C4#1909936111yescharacteristic
575C2—41no—
576C2—81no—
577C2—6321no—
578C2#2377212511yescharacteristic
579C2#2377219811yescharacteristic
580C2#2377230711yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D79
commutatorC2×C4×C79C23×C4
FrattiniC42C23×D79
FittingC79×#2971C2
socleC22×C79C2×C4×D4
prime radical#19098708C4
cosocleC42×C79C24
hypercenter#2971D79
hypocenterC79#18005
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ #2971

Complements

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

NH ≅ G/Ntype
2. #23772404C2semidirect
3. #23762312C2semidirect
4. #23762302C2semidirect
5. #23762278C2semidirect
6. #23762276C2semidirect
7. #23762271C2semidirect
8. #23762262C2semidirect
9. #23762217C2semidirect
10. #23762210C2semidirect
11. #23762181C2semidirect
12. #23761858C2semidirect
13. #23761782C2semidirect
14. #23761687C2semidirect
15. C79×#2971C2semidirect
292. #2971D79semidirect
306. C79#18005semidirect

Maximal subgroups

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

subgroupindex
#237734182
#237724042
#237623122
#237623022
#237622782
#237622762
#237622712
#237622622
#237622172
#237622102
#237621812
#237618582
#237617822
#237616872
C79×#29712
#1800579