Finite Group Databasebeta

← #34329274

Subgroups — #34329274

Order 20224.

778 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19098863C211yesmaximal, characteristic
2C2×C4×#11929612C211yesmaximal, characteristic
3#23768591C211yesmaximal, characteristic, complemented
4#23764813C211yesmaximal, characteristic
5#23764803C211yesmaximal, characteristic
6#23764717C211yesmaximal, characteristic
7#23764717C211yesmaximal, characteristic
8#23764364C211yesmaximal, characteristic, complemented
9#23764168C211yesmaximal, characteristic, complemented
10#23764163C211yesmaximal, characteristic, complemented
11#23764119C211yesmaximal, characteristic, complemented
12#23764041C211yesmaximal, characteristic, complemented
13#23764034C211yesmaximal, characteristic, complemented
14#23763412C211yesmaximal, characteristic, complemented
15C79×#2357C211yesmaximal, characteristic
16C22×#11929612C2211yescharacteristic
17C2×#14579153C2211yescharacteristic
18C2×C4×Dic158C2211yescharacteristic
19#19098863—24no—
20C4×#11929612—24no—
21C2×#14579094C2211yescharacteristic
22C2×#14579092C2211yescharacteristic
23C2×#14579092C2211yescharacteristic
24C2×C4⋊(C79⋊C8)C2211yescharacteristic
25C2×C4⋊(C79⋊C8)C2211yescharacteristic
26C2×C4⋊(C79⋊C8)C2211yescharacteristic
27C2×#14579084C2211yescharacteristic
28C2×#14579084C2211yescharacteristic
29C2×#14579084C2211yescharacteristic
30C2×#14579082C2211yescharacteristic
31C2×#14579082C2211yescharacteristic
32C2×#14579082C2211yescharacteristic
33C2×C4×C79⋊C8C2211yescharacteristic
34#19098493—21no—
35#19098493—21no—
36#19098469C2211yescharacteristic
37#19098469C2211yescharacteristic
38#19098448—21no—
39#19098448—21no—
40#19098433C2211yescharacteristic
41#19098429C2211yescharacteristic
42#19098325C2211yescharacteristic
43#19098325C2211yescharacteristic
44#19098325C2211yescharacteristic
45#19098325C2211yescharacteristic
46#19098325C2211yescharacteristic
47#19098325C2211yescharacteristic
48#19098318C2211yescharacteristic
49#19098318C2211yescharacteristic
50C2×C4×D4×C79C2211yescharacteristic
51#390×C79C2211yescharacteristic
52#390×C79C2211yescharacteristic
53#388×C79—21no—
54#388×C79—21no—
55#382×C79C2211yescharacteristic
56#381×C79—21no—
57C4×C4⋊C4×C79C2211yescharacteristic
58C4×C4⋊C4×C79C2211yescharacteristic
59C4×C4⋊C4×C79C2211yescharacteristic
60C4×C22⋊C4×C79—21no—
61C22×Dic158C2311yescharacteristic
62C2×#11929612—22no—
63C2×#11929612—22no—
64C2×#11929612—22no—
65C22×C79⋊C8C2311yescharacteristic
66C22×C79⋊C8C2311yescharacteristic
67C22×C79⋊C8C2311yescharacteristic
68C22×C79⋊C8C2311yescharacteristic
69#14579153—22no—
70#14579153—22no—
71C4×Dic158—22no—
72C4×Dic158—22no—
73C2×C4⋊Dic79—21no—
74C2×C4⋊Dic79—21no—
75C2×C4⋊Dic79C2311yescharacteristic
76C2×C4⋊Dic79C2311yescharacteristic
77C2×C4⋊Dic79C2311yescharacteristic
78C2×Dic79⋊C4—21no—
79C2×Dic79⋊C4—21no—
80C2×Dic79⋊C4—21no—
81C2×C4×Dic79—21no—
82#14579094—22no—
83#14579092—22no—
84#14579092—22no—
85C4⋊(C79⋊C8)—22no—
86C4⋊(C79⋊C8)—22no—
87C4⋊(C79⋊C8)—22no—
88#14579084—22no—
89#14579084—22no—
90#14579084—22no—
91#14579082—22no—
92#14579082—22no—
93#14579082—22no—
94C4×C79⋊C8—22no—
95C79⋊#95—21no—
96C79⋊#95—21no—
97C79⋊#95—21no—
98C79⋊#95—21no—
99C79⋊#95—21no—
100C79⋊#95—21no—
101C22×D4×C79C2311yescharacteristic
102C23×C4×C79—21no—
103C4×D4×C79—22no—
104C4×D4×C79D414yes—
105C2×C4⋊C4×C79D411yescharacteristic
106C2×C4⋊C4×C79D411yescharacteristic
107C2×C4⋊C4×C79C2311yescharacteristic
108C2×C4⋊C4×C79C2311yescharacteristic
109C2×C4⋊C4×C79C2311yescharacteristic
110C2×C22⋊C4×C79—21no—
111C2×C22⋊C4×C79—21no—
112C2×C22⋊C4×C79—21no—
113C2×C22⋊C4×C79—21no—
114C2×C22⋊C4×C79—21no—
115C2×C42×C79—21no—
116C2×C42×C79—21no—
117C2×C42×C79C2311yescharacteristic
118C2×C42×C79C2311yescharacteristic
119C2×C42×C79C2311yescharacteristic
120#95×C79—21no—
121#95×C79—21no—
122#95×C79—21no—
123#95×C79—21no—
124#95×C79D411yescharacteristic
125#95×C79D411yescharacteristic
126C2×Dic158—21no—
127C2×Dic158—21no—
128C2×Dic158—21no—
129C2×Dic158—21no—
130C2×Dic158—21no—
131C2×Dic158#4112yes—
132C22×Dic79—21no—
133C22×Dic79—21no—
134C22×Dic79—21no—
135C22×Dic79—21no—
136#11929612—28no—
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—21no—
148C2×C79⋊C8#4112yes—
149C4⋊Dic79—21no—
150C4⋊Dic79—21no—
151C4⋊Dic79—21no—
152C4⋊Dic79—21no—
153C4⋊Dic79—21no—
154C4⋊Dic79—21no—
155C4⋊Dic79—42no—
156C4⋊Dic79—42no—
157Dic79⋊C4—42no—
158Dic79⋊C4—42no—
159Dic79⋊C4—42no—
160C4×Dic79—42no—
161C24×C79—21no—
162C2×D4×C79—21no—
163C2×D4×C79—21no—
164C2×D4×C79—21no—
165C2×D4×C79—21no—
166C2×D4×C79—21no—
167C2×D4×C79C2×D412yes—
168C22×C4×C79—21no—
169C22×C4×C79—24no—
170C22×C4×C79—21no—
171C22×C4×C79—21no—
172C22×C4×C79—81no—
173C22×C4×C79—81no—
174C22×C4×C79C2×D411yescharacteristic
175C22×C4×C79C2×D411yescharacteristic
176C22×C4×C79C2×D411yescharacteristic
177C22×C4×C79C2×D411yescharacteristic
178C22×C4×C79C2×D411yescharacteristic
179C22×C4×C79C2×D411yescharacteristic
180C22×C4×C79C2411yescharacteristic
181C4⋊C4×C79—22no—
182C4⋊C4×C79—21no—
183C4⋊C4×C79—21no—
184C4⋊C4×C79—21no—
185C4⋊C4×C79—21no—
186C4⋊C4×C79—21no—
187C4⋊C4×C79—41no—
188C4⋊C4×C79C2×D412yes—
189C22⋊C4×C79—24no—
190C22⋊C4×C79—42no—
191C22⋊C4×C79—42no—
192C22⋊C4×C79—81no—
193C22⋊C4×C79—81no—
194C42×C79—21no—
195C42×C79—21no—
196C42×C79—21no—
197C42×C79—21no—
198C42×C79—81no—
199C42×C79—81no—
200C42×C79C2×D412yes—
201C42×C79#4112yes—
202C23×C79—22no—
203C23×C79—41no—
204C23×C79—41no—
205C23×C79—41no—
206C23×C79—41no—
207C23×C79—41no—
208C23×C79—41no—
209C23×C79C22×D411yescharacteristic
210D4×C79—22no—
211D4×C79—22no—
212D4×C79—41no—
213D4×C79—41no—
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—22no—
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—21no—
228C2×C4×C79—21no—
229C2×C4×C79—21no—
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—84no—
239C2×C4×C79#12112yes—
240C2×C4×C79#12112yes—
241C2×C4×C79#13512yes—
242C2×C4×C79C22×D411yescharacteristic
243C2×C4×C79C2×#4111yescharacteristic
244C2×C4×C79C2×#4111yescharacteristic
245C2×C4×C79C2×#4111yescharacteristic
246C2×C4×C792−1+411yescharacteristic
247C2×C4×C792−1+411yescharacteristic
248C2×Dic79—22no—
249C2×Dic79—41no—
250C2×Dic79—41no—
251C2×Dic79—41no—
252C2×Dic79—41no—
253C2×Dic79—41no—
254C2×Dic79—41no—
255C2×Dic79—41no—
256C2×Dic79—41no—
257C2×Dic79—41no—
258C2×Dic79—41no—
259C2×Dic79—41no—
260Dic158—22no—
261Dic158—22no—
262Dic158—41no—
263Dic158—41no—
264C79⋊C8—22no—
265C79⋊C8—41no—
266C79⋊C8—41no—
267C79⋊C8—41no—
268C22×C79—42no—
269C22×C79—42no—
270C22×C79—42no—
271C22×C79—81no—
272C22×C79—81no—
273C22×C79—81no—
274C22×C79—81no—
275C22×C79C2×#12111yescharacteristic
276C22×C79#54711yescharacteristic
277C22×C79#54811yescharacteristic
278C22×C79C2×#13511yescharacteristic
279C22×C79#57511yescharacteristic
280C22×C79#57711yescharacteristic
281C22×C79#57711yescharacteristic
282C4×C79—22no—
283C4×C79—22no—
284C4×C79—22no—
285C4×C79—41no—
286C4×C79—41no—
287C4×C79—41no—
288C4×C79—42no—
289C4×C79—81no—
290C4×C79—81no—
291C4×C79#52511yescharacteristic
292C4×C79#53611yescharacteristic
293C4×C79#55211yescharacteristic
294C4×C79#55611yescharacteristic
295Dic79—42no—
296Dic79—81no—
297Dic79—81no—
298Dic79—81no—
299#24686—791nomaximal, Sylow
300C2×C79—82no—
301C2×C79#241511yescharacteristic
302C2×C79#303511yescharacteristic
303C2×C79#304211yescharacteristic
304C2×C79#333711yescharacteristic
305C2×C79#335111yescharacteristic
306C2×C79#336511yescharacteristic
307C2×C79#337111yescharacteristic
308C2×#478—791no—
309C2×C4×SD16—791no—
310#2565—791no—
311#2357D7911yescharacteristic
312#2073—791no—
313#2071—791no—
314#2055—791no—
315#2055—791no—
316#1991—791no—
317#1949—791no—
318#1948—791no—
319#1939—791no—
320#1928—791no—
321#1927—791no—
322#1805—791no—
323C79#2468611yescharacteristic, complemented, Sylow
324C22×SD16—791no—
325C2×#125—791no—
326C2×C4×Q8—791no—
327C2×C4×D4C2×D7911yescharacteristic
328#478—1584no—
329C4×SD16—1584no—
330C2×#107—791no—
331C2×#106—791no—
332C2×#106—791no—
333C2×C4⋊C8—791no—
334C2×C4⋊C8—791no—
335C2×C4⋊C8—791no—
336C2×#103—791no—
337C2×#103—791no—
338C2×#103—791no—
339C2×#102—791no—
340C2×#102—791no—
341C2×#102—791no—
342C2×C4×C8—791no—
343#398—1581no—
344#398—1581no—
345#391—791no—
346#391—791no—
347#390C2×D7911yescharacteristic
348#390C2×D7911yescharacteristic
349#388—21no—
350#388—21no—
351#387—1581no—
352#387—1581no—
353#384—791no—
354#382—791no—
355#382C2×D7911yescharacteristic
356#381—21no—
357C4×C4⋊C4C2×D7911yescharacteristic
358C4×C4⋊C4C2×D7911yescharacteristic
359C4×C4⋊C4C2×D7911yescharacteristic
360C4×C22⋊C4—21no—
361#340—791no—
362#340—791no—
363#340—791no—
364#340—791no—
365#340—791no—
366#340—791no—
367#336—791no—
368#336—791no—
369C22×Q8—791no—
370C22×D4C22×D7911yescharacteristic
371C23×C4—21no—
372C2×SD16—1582no—
373C2×SD16—1582no—
374C2×SD16—1582no—
375C22×C8—791no—
376C22×C8—791no—
377C22×C8—791no—
378C22×C8—791no—
379#125—1582no—
380#125—1582no—
381C4×Q8—1582no—
382C4×Q8—1582no—
383C4×D4—22no—
384C4×D4D31614yes—
385C2×C4⋊C4—791no—
386C2×C4⋊C4—791no—
387C2×C4⋊C4—791no—
388C2×C4⋊C4—1581no—
389C2×C4⋊C4—1581no—
390C2×C4⋊C4—1581no—
391C2×C4⋊C4—1581no—
392C2×C4⋊C4—1581no—
393C2×C4⋊C4C22⋊D7911yescharacteristic
394C2×C4⋊C4C22⋊D7911yescharacteristic
395C2×C4⋊C4C22×D7911yescharacteristic
396C2×C4⋊C4C22×D7911yescharacteristic
397C2×C4⋊C4C22×D7911yescharacteristic
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C42—21no—
404C2×C42—21no—
405C2×C42—1581no—
406C2×C42C22×D7911yescharacteristic
407C2×C42C22×D7911yescharacteristic
408C2×C42C22×D7911yescharacteristic
409#107—1582no—
410#106—1582no—
411#106—1582no—
412C4⋊C8—1582no—
413C4⋊C8—1582no—
414C4⋊C8—1582no—
415#103—1582no—
416#103—1582no—
417#103—1582no—
418#102—1582no—
419#102—1582no—
420#102—1582no—
421C4×C8—1582no—
422#95—21no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—1581no—
427#95—1581no—
428#95—1581no—
429#95—1581no—
430#95—1581no—
431#95—1581no—
432#95C22⋊D7911yescharacteristic
433#95C22⋊D7911yescharacteristic
434C24—21no—
435C2×Q8—792no—
436C2×Q8—1581no—
437C2×Q8—1581no—
438C2×Q8—1581no—
439C2×Q8—1581no—
440C2×Q8—1581no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4C2×D31612yes—
447C22×C4—21no—
448C22×C4—24no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—81no—
452C22×C4—81no—
453C22×C4—1581no—
454C22×C4—1581no—
455C22×C4—1581no—
456C22×C4—1581no—
457C22×C4C2×C22⋊D7911yescharacteristic
458C22×C4C2×C22⋊D7911yescharacteristic
459C22×C4C2×C22⋊D7911yescharacteristic
460C22×C4C2×C22⋊D7911yescharacteristic
461C22×C4C2×C22⋊D7911yescharacteristic
462C22×C4C2×C22⋊D7911yescharacteristic
463C22×C4C23×D7911yescharacteristic
464SD16—1588no—
465C2×C8—792no—
466C2×C8—1581no—
467C2×C8—1581no—
468C2×C8—1581no—
469C2×C8—1581no—
470C2×C8—1581no—
471C2×C8—1581no—
472C2×C8—1581no—
473C2×C8—1581no—
474C2×C8—1581no—
475C2×C8—1581no—
476C2×C8—1581no—
477C4⋊C4—21no—
478C4⋊C4—22no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—41no—
484C4⋊C4—3162no—
485C4⋊C4—3162no—
486C4⋊C4—3162no—
487C4⋊C4—3162no—
488C4⋊C4—3162no—
489C4⋊C4—1581no—
490C4⋊C4—1581no—
491C4⋊C4—1581no—
492C4⋊C4—1581no—
493C4⋊C4—1581no—
494C4⋊C4—1581no—
495C4⋊C4C2×D31612yes—
496C22⋊C4—24no—
497C22⋊C4—42no—
498C22⋊C4—42no—
499C22⋊C4—81no—
500C22⋊C4—81no—
501C42—21no—
502C42—21no—
503C42—21no—
504C42—21no—
505C42—81no—
506C42—81no—
507C42—3162no—
508C42C2×D31612yes—
509C42#1192962412yes—
510C23—22no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23—41no—
516C23—41no—
517C23C22×C22⋊D7911yescharacteristic
518Q8—3161no—
519Q8—3161no—
520Q8—1582no—
521Q8—1582no—
522D4—22no—
523D4—22no—
524D4—41no—
525D4—41no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—22no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—84no—
551C2×C4—3161no—
552C2×C4—3161no—
553C2×C4—3161no—
554C2×C4—3161no—
555C2×C4—3161no—
556C2×C4—3161no—
557C2×C4—3161no—
558C2×C4—3161no—
559C2×C4—3161no—
560C2×C4—3161no—
561C2×C4—3161no—
562C2×C4—1582no—
563C2×C4#1457913512yes—
564C2×C4#1457913512yes—
565C2×C4#1457918112yes—
566C2×C4C22×D31611yescharacteristic
567C2×C4#41×D7911yescharacteristic
568C2×C4#41×D7911yescharacteristic
569C2×C4C2×#1192962411yescharacteristic
570C2×C4#1457920811yescharacteristic
571C2×C4#1457920811yescharacteristic
572C8—3161no—
573C8—3161no—
574C8—3161no—
575C8—1582no—
576C22—42no—
577C22—42no—
578C22—42no—
579C22—81no—
580C22—81no—
581C22—81no—
582C22—81no—
583C22C2×#1457913511yescharacteristic
584C22#1909921211yescharacteristic
585C22#1909922011yescharacteristic
586C22C2×#1457918111yescharacteristic
587C22#1909936111yescharacteristic
588C22#1909937411yescharacteristic
589C22#1909937411yescharacteristic
590C4—22no—
591C4—22no—
592C4—22no—
593C4—41no—
594C4—41no—
595C4—41no—
596C4—42no—
597C4—81no—
598C4—81no—
599C4—3162no—
600C4—6321no—
601C4—6321no—
602C4—6321no—
603C4#1909907511yescharacteristic
604C4#1909913911yescharacteristic
605C4#1909925211yescharacteristic
606C4#1909928111yescharacteristic
607C2—82no—
608C2#2376682311yescharacteristic
609C2#2377285511yescharacteristic
610C2#2377291211yescharacteristic
611C2#2377577311yescharacteristic
612C2#2377595411yescharacteristic
613C2#2377609211yescharacteristic
614C2#2377616211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D79
commutator, cosocleC22×C4×C79C24
FrattiniC22×C4C23×D79
FittingC79×#2357C2
socleC23×C79C22×D4
prime radicalC22×D4×C79C23
hypercenter#2357D79
hypocenterC79#24686
LCSG ▷ C22×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2357

Complements

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

NH ≅ G/Ntype
3. #23768591C2semidirect
8. #23764364C2semidirect
9. #23764168C2semidirect
10. #23764163C2semidirect
11. #23764119C2semidirect
12. #23764041C2semidirect
13. #23764034C2semidirect
14. #23763412C2semidirect
323. C79#24686semidirect

Maximal subgroups

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

subgroupindex
C2×#190988632
C2×C4×#119296122
#237685912
#237648132
#237648032
#237647172
#237643642
#237641682
#237641632
#237641192
#237640412
#237640342
#237634122
C79×#23572
#2468679