Finite Group Databasebeta

← #34258499

Subgroups — #34258499

Order 20224.

604 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23773418C211yesmaximal, characteristic
2#23772375C211yesmaximal, characteristic, complemented
3#23762295C211yesmaximal, characteristic, complemented
4#23762290C211yesmaximal, characteristic, complemented
5#23762288C211yesmaximal, characteristic, complemented
6#23762283C211yesmaximal, characteristic, complemented
7#23762248C211yesmaximal, characteristic, complemented
8#23762241C211yesmaximal, characteristic, complemented
9#23762234C211yesmaximal, characteristic, complemented
10#23762227C211yesmaximal, characteristic, complemented
11#23762178C211yesmaximal, characteristic, complemented
12#23761834C211yesmaximal, characteristic, complemented
13#23761806C211yesmaximal, characteristic, complemented
14#23761683C211yesmaximal, characteristic, complemented
15C79×#2965C211yesmaximal, 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#19098634—21no—
33C8×D316C2211yescharacteristic
34C8×C22⋊D79—21no—
35#19098622—21no—
36#19098620C2211yescharacteristic
37#19098616C2211yescharacteristic
38#19098616C2211yescharacteristic
39#19098517—21no—
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#19098284C2211yescharacteristic
53#19098284C2211yescharacteristic
54C8×C79⋊C8C2211yescharacteristic
55C8×C79⋊C8C2211yescharacteristic
56C4×#41×C79C2211yescharacteristic
57#446×C79C2211yescharacteristic
58#446×C79C2211yescharacteristic
59#436×C79C2211yescharacteristic
60#436×C79C2211yescharacteristic
61#435×C79—21no—
62#435×C79—21no—
63#431×C79—21no—
64#431×C79C2211yescharacteristic
65C4×M16×C79—21no—
66C2×C4×C8×C79C2211yescharacteristic
67C2×#11929614C2×C411yescharacteristic
68C2×#11929612C2×C411yescharacteristic
69C2×#11929611C2×C411yescharacteristic
70C2×#11929609C2×C411yescharacteristic
71C2×#11929607—21no—
72C2×C8×D79—21no—
73#14579155—21no—
74#14579153C2×C411yescharacteristic
75#14579149C2×C411yescharacteristic
76#14579144—21no—
77#14579140C2×C411yescharacteristic
78#14579135C2×C411yescharacteristic
79C4×Dic158C2311yescharacteristic
80C4×D316C2311yescharacteristic
81C4×C22⋊D79—21no—
82#14579118—21no—
83#14579094C2×C411yescharacteristic
84#14579094C2×C411yescharacteristic
85#14579092C2×C411yescharacteristic
86#14579092C2×C411yescharacteristic
87C4⋊(C79⋊C8)—21no—
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)—21no—
104C22⋊(C79⋊C8)C2×C411yescharacteristic
105C22⋊(C79⋊C8)C2×C411yescharacteristic
106(C2×D79)⋊C8—21no—
107(C2×D79)⋊C8—21no—
108#14579072—21no—
109#14579071—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—
118C22×C8×C79D411yescharacteristic
119C22×C8×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×C79—21no—
139C4×C8×C79—21no—
140C4×C8×C79D411yescharacteristic
141C4×C8×C79D411yescharacteristic
142C4×C8×C79C2311yescharacteristic
143C4×C8×C79C2311yescharacteristic
144C2×Dic158C22×C411yescharacteristic
145C2×D316C22×C411yescharacteristic
146C2×C22⋊D79—21no—
147C2×C4×D79—21no—
148#11929614—41no—
149#11929612—41no—
150#11929611—41no—
151#11929609—41no—
152#11929607—42no—
153C2×C79⋊C8—21no—
154C2×C79⋊C8—21no—
155C2×C79⋊C8—21no—
156C2×C79⋊C8—21no—
157C2×C79⋊C8C22×C411yescharacteristic
158C2×C79⋊C8C22×C411yescharacteristic
159C2×C79⋊C8C22×C411yescharacteristic
160C2×C79⋊C8C22×C411yescharacteristic
161C8×D79—42no—
162C4⋊Dic79C22×C411yescharacteristic
163C4⋊Dic79C22×C411yescharacteristic
164Dic79⋊C4—21no—
165Dic79⋊C4—21no—
166Dic79⋊C4—21no—
167Dic79⋊C4—21no—
168C22⋊Dic79—21no—
169(C2×D79)⋊C4—21no—
170(C2×D79)⋊C4—21no—
171(C2×D79)⋊C4—21no—
172(C2×D79)⋊C4—21no—
173C4×Dic79—21no—
174#41×C79—41no—
175#41×C79—41no—
176C2×Q8×C79C22×C411yescharacteristic
177C2×D4×C79—21no—
178C2×D4×C79C22×C411yescharacteristic
179C22×C4×C79—21no—
180C22×C4×C79—21no—
181C22×C4×C79—21no—
182C22×C4×C79C22×C411yescharacteristic
183C22×C4×C79C2×D411yescharacteristic
184C22×C4×C79#4111yescharacteristic
185M16×C79—42no—
186M16×C79—42no—
187C2×C8×C79—22no—
188C2×C8×C79—22no—
189C2×C8×C79—21no—
190C2×C8×C79—21no—
191C2×C8×C79C2×D411yescharacteristic
192C2×C8×C79C2×D411yescharacteristic
193C2×C8×C79C2×D411yescharacteristic
194C2×C8×C79C2×D411yescharacteristic
195C4⋊C4×C79—21no—
196C4⋊C4×C79—21no—
197C4⋊C4×C79C22×C411yescharacteristic
198C4⋊C4×C79C22×C411yescharacteristic
199C22⋊C4×C79—21no—
200C22⋊C4×C79—21no—
201C22⋊C4×C79—21no—
202C42×C79—21no—
203C42×C79—21no—
204C42×C79—21no—
205C42×C79C22×C411yescharacteristic
206C42×C79C2×D411yescharacteristic
207C42×C79#4111yescharacteristic
208C42×C79C2411yescharacteristic
209C23×C79—21no—
210C23×C79C4×D411yescharacteristic
211C22×D79—21no—
212Q8×C79—21no—
213Q8×C79—21no—
214D4×C79—21no—
215D4×C79—21no—
216D4×C79—42no—
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—41no—
225C2×C4×C79—42no—
226C2×C4×C79—42no—
227C2×C4×C79—41no—
228C2×C4×C79—41no—
229C2×C4×C79C4×D411yescharacteristic
230C2×C4×C79C4×D411yescharacteristic
231C2×C4×C79C4×D411yescharacteristic
232C2×C4×C79C23×C411yescharacteristic
233C2×C4×C79C22×D411yescharacteristic
234C2×C4×C79C2×#4111yescharacteristic
235C22⋊D79—42no—
236C2×Dic79—21no—
237C2×Dic79—21no—
238C2×Dic79—21no—
239D316—21no—
240D316—21no—
241C4×D79—41no—
242C4×D79—41no—
243Dic158—21no—
244Dic158—21no—
245C8×C79—21no—
246C8×C79—21no—
247C8×C79—41no—
248C8×C79—41no—
249C8×C79#13512yes—
250C8×C79#13512yes—
251C79⋊C8—21no—
252C79⋊C8—21no—
253C79⋊C8—21no—
254C79⋊C8—21no—
255C79⋊C8—41no—
256C79⋊C8—41no—
257C79⋊C8—41no—
258C79⋊C8—41no—
259C22×C79—21no—
260C22×C79—21no—
261C22×C79—21no—
262C22×C79—41no—
263C22×C79—41no—
264C22×C79—41no—
265C22×C79C2×C4×D411yescharacteristic
266C2×D79—41no—
267C2×D79—41no—
268C2×D79—41no—
269C4×C79—21no—
270C4×C79—21no—
271C4×C79—21no—
272C4×C79—21no—
273C4×C79—41no—
274C4×C79—41no—
275C4×C79—41no—
276C4×C79#56811yescharacteristic
277C4×C79#56811yescharacteristic
278C4×C79C2×#13511yescharacteristic
279C4×C79C2×#13511yescharacteristic
280Dic79—41no—
281Dic79—41no—
282Dic79—41no—
283#17932—791nomaximal, Sylow
284C2×C79—41no—
285C2×C79—81no—
286C2×C79#293011yescharacteristic
287C2×C79C4×#13511yescharacteristic
288C2×C79#295511yescharacteristic
289D79—81no—
290#3102—791no—
291#2966—791no—
292#2965D7911yescharacteristic, complemented
293#1591—791no—
294#1590—791no—
295#1590—791no—
296#1589—791no—
297#1584—791no—
298#1583—791no—
299#1582—791no—
300#1581—791no—
301#1572—791no—
302#1488—791no—
303#1482—791no—
304#1450—791no—
305C79#1793211yescharacteristic, complemented, Sylow
306#529—791no—
307C4×#41C2×D7911yescharacteristic
308#485—791no—
309#482—791no—
310#479—791no—
311#478—791no—
312#464—791no—
313#463—791no—
314#452—791no—
315#449—791no—
316#446—791no—
317#446C2×D7911yescharacteristic
318#446C2×D7911yescharacteristic
319C8×Q8—791no—
320C4×Q16—791no—
321C4×SD16—791no—
322C4×SD16—791no—
323C4×D8—791no—
324#436—791no—
325#436C2×D7911yescharacteristic
326#436C2×D7911yescharacteristic
327#435—21no—
328#435—21no—
329#435—1581no—
330C8×D4—791no—
331C8×D4—1581no—
332#433—1581no—
333#432—791no—
334#431—21no—
335#431—791no—
336#431—791no—
337#431C2×D7911yescharacteristic
338#405—1581no—
339C4×M16—21no—
340C2×C4×C8C2×D7911yescharacteristic
341#335—791no—
342#335—791no—
343#334—791no—
344#334—791no—
345Q8⋊C8—791no—
346Q8⋊C8—791no—
347Q8⋊C8—791no—
348Q8⋊C8—791no—
349D4⋊C8—791no—
350D4⋊C8—791no—
351D4⋊C8—791no—
352D4⋊C8—791no—
353#322—791no—
354#322—791no—
355C82—791no—
356C82—791no—
357C2×#41C4×D7911yescharacteristic
358C2×Q16—791no—
359C2×SD16—791no—
360C2×SD16—791no—
361C2×D8—791no—
362C2×M16—21no—
363C2×M16—21no—
364C2×M16—1581no—
365C22×C8—1581no—
366C22×C8C22⋊D7911yescharacteristic
367C22×C8C22⋊D7911yescharacteristic
368#126—1581no—
369#125—791no—
370#124—791no—
371#123—1581no—
372C22⋊Q8—791no—
373#121—791no—
374C4×Q8—791no—
375C4×Q8C4×D7911yescharacteristic
376C4×Q8C22×D7911yescharacteristic
377C4×D4—21no—
378C4×D4—21no—
379C4×D4—791no—
380C4×D4—1581no—
381C4×D4C4×D7911yescharacteristic
382C4×D4C22×D7911yescharacteristic
383#117—21no—
384#117—1581no—
385#117C4×D7911yescharacteristic
386C2×C42—21no—
387C2×C42C22×D7911yescharacteristic
388#107—791no—
389#107—791no—
390#106—791no—
391#106—791no—
392C4⋊C8—21no—
393C4⋊C8—21no—
394C4⋊C8—791no—
395C4⋊C8—791no—
396C4⋊C8—791no—
397C4⋊C8—791no—
398C4⋊C8—1581no—
399C4⋊C8—1581no—
400C4⋊C8—1581no—
401C4⋊C8C22×D7911yescharacteristic
402C4⋊C8C22×D7911yescharacteristic
403#103—791no—
404#103—791no—
405#103—791no—
406#103—791no—
407#102—791no—
408#102—791no—
409#102—791no—
410#102—791no—
411C22⋊C8—21no—
412C22⋊C8—21no—
413C22⋊C8—21no—
414C22⋊C8—791no—
415C22⋊C8—791no—
416C22⋊C8—1581no—
417C22⋊C8—1581no—
418C22⋊C8—1581no—
419C22⋊C8—1581no—
420#97—21no—
421#97—21no—
422#97—1581no—
423#97—1581no—
424C4×C8—21no—
425C4×C8—791no—
426C4×C8—791no—
427C4×C8—791no—
428C4×C8—791no—
429C4×C8—1581no—
430C4×C8C22⋊D7911yescharacteristic
431C4×C8C22⋊D7911yescharacteristic
432C4×C8C22×D7911yescharacteristic
433C4×C8C22×D7911yescharacteristic
434#41—41no—
435#41—41no—
436C2×Q8—791no—
437C2×Q8C2×C4×D7911yescharacteristic
438C2×D4—21no—
439C2×D4—791no—
440C2×D4—1581no—
441C2×D4C2×C4×D7911yescharacteristic
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—1581no—
446C22×C4C2×C4×D7911yescharacteristic
447C22×C4C2×C22⋊D7911yescharacteristic
448C22×C4#1192962411yescharacteristic
449Q16—3161no—
450SD16—3161no—
451SD16—3161no—
452D8—3161no—
453M16—42no—
454M16—42no—
455M16—3162no—
456C2×C8—22no—
457C2×C8—22no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—3162no—
461C2×C8—791no—
462C2×C8—791no—
463C2×C8—791no—
464C2×C8—791no—
465C2×C8—1581no—
466C2×C8—1581no—
467C2×C8—1581no—
468C2×C8—1581no—
469C2×C8C2×C22⋊D7911yescharacteristic
470C2×C8C2×C22⋊D7911yescharacteristic
471C2×C8C2×C22⋊D7911yescharacteristic
472C2×C8C2×C22⋊D7911yescharacteristic
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—791no—
476C4⋊C4—791no—
477C4⋊C4—1581no—
478C4⋊C4—1581no—
479C4⋊C4—1581no—
480C4⋊C4—1581no—
481C4⋊C4C2×C4×D7911yescharacteristic
482C4⋊C4C2×C4×D7911yescharacteristic
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—1581no—
487C22⋊C4—1581no—
488C22⋊C4—1581no—
489C22⋊C4—1581no—
490C22⋊C4—1581no—
491C42—21no—
492C42—21no—
493C42—21no—
494C42—1581no—
495C42C2×C4×D7911yescharacteristic
496C42C2×C22⋊D7911yescharacteristic
497C42#1192962411yescharacteristic
498C42C23×D7911yescharacteristic
499C23—21no—
500C23—1581no—
501C23C4×C22⋊D7911yescharacteristic
502Q8—21no—
503Q8—21no—
504Q8—1581no—
505Q8—1581no—
506D4—21no—
507D4—21no—
508D4—42no—
509D4—3162no—
510D4—1581no—
511D4—1581no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—41no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—3161no—
525C2×C4—3161no—
526C2×C4—1581no—
527C2×C4—1581no—
528C2×C4—1581no—
529C2×C4C4×C22⋊D7911yescharacteristic
530C2×C4C4×C22⋊D7911yescharacteristic
531C2×C4C4×C22⋊D7911yescharacteristic
532C2×C4C22×C4×D7911yescharacteristic
533C2×C4C22×C22⋊D7911yescharacteristic
534C2×C4C2×#1192962411yescharacteristic
535C8—21no—
536C8—21no—
537C8—41no—
538C8—41no—
539C8—3161no—
540C8—3161no—
541C8—3161no—
542C8—3161no—
543C8—1581no—
544C8—1581no—
545C8—1581no—
546C8—1581no—
547C8#1457918112yes—
548C8#1457918112yes—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—3161no—
556C22—3161no—
557C22—3161no—
558C22C2×C4×C22⋊D7911yescharacteristic
559C4—21no—
560C4—21no—
561C4—21no—
562C4—21no—
563C4—41no—
564C4—41no—
565C4—41no—
566C4—3161no—
567C4—3161no—
568C4—3161no—
569C4#1909932911yescharacteristic
570C4#1909932911yescharacteristic
571C4C2×#1457918111yescharacteristic
572C4C2×#1457918111yescharacteristic
573C2—41no—
574C2—81no—
575C2—6321no—
576C2#2377210311yescharacteristic
577C2C4×#1457918111yescharacteristic
578C2#2377230111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D79
commutatorC2×C4×C79C23×C4
FrattiniC42C23×D79
FittingC79×#2965C2
socleC22×C79C2×C4×D4
prime radical#19098708C4
cosocleC42×C79C24
hypercenter#2965D79
hypocenterC79#17932
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C2×C4×C8 ◁ #2965

Complements

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

NH ≅ G/Ntype
2. #23772375C2semidirect
3. #23762295C2semidirect
4. #23762290C2semidirect
5. #23762288C2semidirect
6. #23762283C2semidirect
7. #23762248C2semidirect
8. #23762241C2semidirect
9. #23762234C2semidirect
10. #23762227C2semidirect
11. #23762178C2semidirect
12. #23761834C2semidirect
13. #23761806C2semidirect
14. #23761683C2semidirect
15. C79×#2965C2semidirect
292. #2965D79semidirect
305. C79#17932semidirect

Maximal subgroups

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

subgroupindex
#237734182
#237723752
#237622952
#237622902
#237622882
#237622832
#237622482
#237622412
#237622342
#237622272
#237621782
#237618342
#237618062
#237616832
C79×#29652
#1793279