Finite Group Databasebeta

← #34292647

Subgroups — #34292647

Order 20224.

814 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19098663C211yesmaximal, characteristic
2#23766052C211yesmaximal, characteristic, complemented
3#23764280C211yesmaximal, characteristic
4#23764253C211yesmaximal, characteristic
5#23764135C211yesmaximal, characteristic, complemented
6#23764130C211yesmaximal, characteristic, complemented
7#23764100C211yesmaximal, characteristic
8#23764089C211yesmaximal, characteristic, complemented
9#23764086C211yesmaximal, characteristic
10#23764075C211yesmaximal, characteristic, complemented
11#23763298C211yesmaximal, characteristic, complemented
12C4×#14579084C211yesmaximal, characteristic, complemented
13C4×#14579082C211yesmaximal, characteristic
14#23763087C211yesmaximal, characteristic, complemented
15C79×#2319C211yesmaximal, characteristic
16C22×#11929612C2211yescharacteristic
17C2×C4×Dic158C2211yescharacteristic
18#19098663C418yescomplemented
19C2×#14579094C2211yescharacteristic
20C2×#14579094C2211yescharacteristic
21C2×#14579092C2211yescharacteristic
22C2×#14579084C2211yescharacteristic
23C2×#14579084C2211yescharacteristic
24C2×#14579084C2211yescharacteristic
25C2×#14579082C2211yescharacteristic
26C2×#14579082C2211yescharacteristic
27C2×#14579082C2211yescharacteristic
28C2×#14579072C2211yescharacteristic
29C2×#14579072C2211yescharacteristic
30C2×#14579072C2211yescharacteristic
31C2×C4×C79⋊C8C2211yescharacteristic
32C2×C4×C79⋊C8C2211yescharacteristic
33C2×C4×C79⋊C8C2211yescharacteristic
34#19098469C2211yescharacteristic
35#19098469C2211yescharacteristic
36#19098461C2211yescharacteristic
37#19098461C2211yescharacteristic
38#19098445—21no—
39#19098445—21no—
40#19098430—21no—
41#19098427—21no—
42C4×C4⋊Dic79C2211yescharacteristic
43#19098325C2211yescharacteristic
44#19098325C2211yescharacteristic
45#19098325C2211yescharacteristic
46#19098325C2211yescharacteristic
47#19098325C2211yescharacteristic
48#19098325C2211yescharacteristic
49C2×C4×D4×C79C2211yescharacteristic
50#390×C79C2211yescharacteristic
51#390×C79C2211yescharacteristic
52#389×C79C2211yescharacteristic
53#389×C79C2211yescharacteristic
54#388×C79—21no—
55#388×C79—21no—
56#381×C79—21no—
57#380×C79—21no—
58C4×C4⋊C4×C79C2211yescharacteristic
59#376×C79C2211yescharacteristic
60C22×Dic158C2311yescharacteristic
61C2×#11929612—22no—
62C2×#11929612—22no—
63C2×#11929612C2×C414yes—
64C22×C79⋊C8C2311yescharacteristic
65C22×C79⋊C8C2311yescharacteristic
66C22×C79⋊C8C2311yescharacteristic
67C22×C79⋊C8C2311yescharacteristic
68C4×Dic158—22no—
69C4×Dic158C2×C414yes—
70C2×C4⋊Dic79C2311yescharacteristic
71C2×C4⋊Dic79C2311yescharacteristic
72C2×C4⋊Dic79C2311yescharacteristic
73C2×Dic79⋊C4—21no—
74C2×Dic79⋊C4—21no—
75C2×Dic79⋊C4—21no—
76C2×C4×Dic79—21no—
77C2×C4×Dic79—21no—
78#14579094—22no—
79#14579094C2×C414yes—
80#14579092—22no—
81#14579084—22no—
82#14579084—22no—
83#14579084C2×C414yes—
84#14579082—22no—
85#14579082—22no—
86#14579082C2×C414yes—
87#14579072—22no—
88#14579072—22no—
89#14579072C2×C414yes—
90C4×C79⋊C8—22no—
91C4×C79⋊C8—22no—
92C4×C79⋊C8—22no—
93C79⋊#95—21no—
94C79⋊#95—21no—
95C79⋊#95—21no—
96C79⋊#95—21no—
97C79⋊#95—21no—
98C79⋊#95—21no—
99C79⋊#95—21no—
100C22×D4×C79C2311yescharacteristic
101C23×C4×C79—21no—
102C4×D4×C79—22no—
103C4×D4×C79C2×C414yes—
104C2×C4⋊C4×C79—21no—
105C2×C4⋊C4×C79—21no—
106C2×C4⋊C4×C79C2311yescharacteristic
107C2×C4⋊C4×C79C2311yescharacteristic
108C2×C4⋊C4×C79C2311yescharacteristic
109C2×C22⋊C4×C79—21no—
110C2×C22⋊C4×C79—21no—
111C2×C22⋊C4×C79—21no—
112C2×C22⋊C4×C79—21no—
113C2×C22⋊C4×C79—21no—
114C2×C42×C79—21no—
115C2×C42×C79C2311yescharacteristic
116C2×C42×C79C2311yescharacteristic
117C2×C42×C79C2311yescharacteristic
118#95×C79—21no—
119#95×C79—21no—
120#95×C79—21no—
121#95×C79D411yescharacteristic
122#95×C79D411yescharacteristic
123#95×C79D411yescharacteristic
124#95×C79D411yescharacteristic
125C2×Dic158—21no—
126C2×Dic158—21no—
127C2×Dic158—21no—
128C2×Dic158—21no—
129C2×Dic158—21no—
130C2×Dic158C22×C412yes—
131C22×Dic79—21no—
132C22×Dic79—21no—
133C22×Dic79—21no—
134C22×Dic79—21no—
135#11929612—28no—
136C2×C79⋊C8—21no—
137C2×C79⋊C8—21no—
138C2×C79⋊C8—21no—
139C2×C79⋊C8—21no—
140C2×C79⋊C8—21no—
141C2×C79⋊C8—21no—
142C2×C79⋊C8C22×C412yes—
143C2×C79⋊C8C22×C412yes—
144C2×C79⋊C8#4112yes—
145C2×C79⋊C8#4112yes—
146C2×C79⋊C8#4112yes—
147C2×C79⋊C8#4112yes—
148C4⋊Dic79—21no—
149C4⋊Dic79—21no—
150C4⋊Dic79—21no—
151C4⋊Dic79—21no—
152C4⋊Dic79—21no—
153C4⋊Dic79C22×C412yes—
154Dic79⋊C4—24no—
155Dic79⋊C4—81no—
156Dic79⋊C4—81no—
157C4×Dic79—24no—
158C4×Dic79—81no—
159C24×C79—21no—
160C2×D4×C79—21no—
161C2×D4×C79—21no—
162C2×D4×C79—21no—
163C2×D4×C79—21no—
164C2×D4×C79—21no—
165C2×D4×C79C22×C412yes—
166C22×C4×C79—21no—
167C22×C4×C79—24no—
168C22×C4×C79—21no—
169C22×C4×C79—21no—
170C22×C4×C79—81no—
171C22×C4×C79—81no—
172C22×C4×C79C2×D411yescharacteristic
173C22×C4×C79C2×D411yescharacteristic
174C22×C4×C79C2×D411yescharacteristic
175C22×C4×C79C2×D411yescharacteristic
176C22×C4×C79C2×D411yescharacteristic
177C22×C4×C79C2×D411yescharacteristic
178C22×C4×C79C2411yescharacteristic
179C4⋊C4×C79—21no—
180C4⋊C4×C79—21no—
181C4⋊C4×C79—21no—
182C4⋊C4×C79—21no—
183C4⋊C4×C79—21no—
184C4⋊C4×C79—81no—
185C4⋊C4×C79—81no—
186C4⋊C4×C79C22×C412yes—
187C22⋊C4×C79—24no—
188C22⋊C4×C79—81no—
189C22⋊C4×C79—81no—
190C22⋊C4×C79—81no—
191C22⋊C4×C79—81no—
192C42×C79—21no—
193C42×C79—21no—
194C42×C79—21no—
195C42×C79—21no—
196C42×C79—81no—
197C42×C79C22×C412yes—
198C42×C79#4112yes—
199C23×C79—22no—
200C23×C79—41no—
201C23×C79—41no—
202C23×C79—41no—
203C23×C79—41no—
204C23×C79—41no—
205C23×C79—41no—
206C23×C79C22×D411yescharacteristic
207D4×C79—22no—
208D4×C79—22no—
209D4×C79—41no—
210D4×C79—41no—
211C2×C4×C79—21no—
212C2×C4×C79—21no—
213C2×C4×C79—21no—
214C2×C4×C79—21no—
215C2×C4×C79—22no—
216C2×C4×C79—21no—
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—21no—
225C2×C4×C79—21no—
226C2×C4×C79—21no—
227C2×C4×C79—21no—
228C2×C4×C79—41no—
229C2×C4×C79—41no—
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—84no—
237C2×C4×C79C4×D412yes—
238C2×C4×C79C4×D412yes—
239C2×C4×C79C23×C411yescharacteristic
240C2×C4×C79C2×#4111yescharacteristic
241C2×C4×C79C2×#4111yescharacteristic
242C2×C4×C79C2×#4111yescharacteristic
243C2×C4×C79C2×#4111yescharacteristic
244C2×C4×C79C2×#4111yescharacteristic
245C2×Dic79—22no—
246C2×Dic79—22no—
247C2×Dic79—41no—
248C2×Dic79—41no—
249C2×Dic79—41no—
250C2×Dic79—41no—
251C2×Dic79—41no—
252C2×Dic79—41no—
253C2×Dic79—41no—
254C2×Dic79—41no—
255C2×Dic79—41no—
256C2×Dic79—41no—
257Dic158—22no—
258Dic158—22no—
259Dic158—41no—
260Dic158—41no—
261C79⋊C8—22no—
262C79⋊C8—22no—
263C79⋊C8—22no—
264C79⋊C8#11714yes—
265C22×C79—42no—
266C22×C79—42no—
267C22×C79—42no—
268C22×C79—81no—
269C22×C79—81no—
270C22×C79—81no—
271C22×C79—81no—
272C22×C79C2×C4×D411yescharacteristic
273C22×C79#53211yescharacteristic
274C22×C79#53211yescharacteristic
275C22×C79#57611yescharacteristic
276C22×C79#57711yescharacteristic
277C22×C79#57711yescharacteristic
278C22×C79#57811yescharacteristic
279C4×C79—22no—
280C4×C79—22no—
281C4×C79—41no—
282C4×C79—41no—
283C4×C79—41no—
284C4×C79—41no—
285C4×C79—42no—
286C4×C79—81no—
287C4×C79—81no—
288C4×C79C2×#11711yescharacteristic
289C4×C79C4×#4111yescharacteristic
290C4×C79#52911yescharacteristic
291C4×C79#52911yescharacteristic
292Dic79—42no—
293Dic79—42no—
294Dic79—81no—
295Dic79—81no—
296#21291—791nomaximal, Sylow
297C2×C79—82no—
298C2×C79#229311yescharacteristic
299C2×C79#294611yescharacteristic
300C2×C79#294711yescharacteristic
301C2×C79#317411yescharacteristic
302C2×C79#317511yescharacteristic
303C2×C79#317811yescharacteristic
304C2×C79#317911yescharacteristic
305C2×#440—791no—
306#2320—791no—
307#2319D7911yescharacteristic
308#1973—791no—
309#1968—791no—
310#1943—791no—
311#1942—791no—
312#1936—791no—
313#1935—791no—
314#1934—791no—
315#1933—791no—
316#1776—791no—
317C4×#103—791no—
318C4×#102—791no—
319#1726—791no—
320C79#2129111yescharacteristic, complemented, Sylow
321C22×SD16—791no—
322C2×C4×Q8—791no—
323C2×C4×D4C2×D7911yescharacteristic
324#440—798no—
325C2×#107—791no—
326C2×#107—791no—
327C2×#106—791no—
328C2×#103—791no—
329C2×#103—791no—
330C2×#103—791no—
331C2×#102—791no—
332C2×#102—791no—
333C2×#102—791no—
334C2×#97—791no—
335C2×#97—791no—
336C2×#97—791no—
337C2×C4×C8—791no—
338C2×C4×C8—791no—
339C2×C4×C8—791no—
340#391—791no—
341#391—791no—
342#390C2×D7911yescharacteristic
343#390C2×D7911yescharacteristic
344#389—791no—
345#389—791no—
346#389C2×D7911yescharacteristic
347#389C2×D7911yescharacteristic
348#388—21no—
349#388—21no—
350#387—1581no—
351#387—1581no—
352#383—1581no—
353#382—1581no—
354#381—21no—
355#380—21no—
356C4×C4⋊C4—791no—
357C4×C4⋊C4C2×D7911yescharacteristic
358#376C2×D7911yescharacteristic
359#340—791no—
360#340—791no—
361#340—791no—
362#340—791no—
363#340—791no—
364#340—791no—
365C22×Q8—791no—
366C22×D4C22×D7911yescharacteristic
367C23×C4—21no—
368C2×SD16—794no—
369C2×SD16—1582no—
370C2×SD16—1582no—
371C22×C8—791no—
372C22×C8—791no—
373C22×C8—791no—
374C22×C8—791no—
375C4×Q8—794no—
376C4×Q8—1582no—
377C4×D4—22no—
378C4×D4C4×D7914yes—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—791no—
382C2×C4⋊C4—791no—
383C2×C4⋊C4—791no—
384C2×C4⋊C4—1581no—
385C2×C4⋊C4—1581no—
386C2×C4⋊C4—1581no—
387C2×C4⋊C4C22×D7911yescharacteristic
388C2×C4⋊C4C22×D7911yescharacteristic
389C2×C4⋊C4C22×D7911yescharacteristic
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C42—21no—
396C2×C42—1581no—
397C2×C42—1581no—
398C2×C42C22×D7911yescharacteristic
399C2×C42C22×D7911yescharacteristic
400C2×C42C22×D7911yescharacteristic
401#107—794no—
402#107—1582no—
403#106—1582no—
404#103—794no—
405#103—1582no—
406#103—1582no—
407#102—794no—
408#102—1582no—
409#102—1582no—
410#97—794no—
411#97—1582no—
412#97—1582no—
413C4×C8—1582no—
414C4×C8—1582no—
415C4×C8—1582no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—1581no—
420#95—1581no—
421#95—1581no—
422#95—1581no—
423#95—1581no—
424#95—1581no—
425#95—1581no—
426#95C22⋊D7911yescharacteristic
427#95C22⋊D7911yescharacteristic
428#95C22⋊D7911yescharacteristic
429#95C22⋊D7911yescharacteristic
430C24—21no—
431C2×Q8—792no—
432C2×Q8—1581no—
433C2×Q8—1581no—
434C2×Q8—1581no—
435C2×Q8—1581no—
436C2×Q8—1581no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4C2×C4×D7912yes—
443C22×C4—21no—
444C22×C4—24no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—81no—
448C22×C4—81no—
449C22×C4—1581no—
450C22×C4—1581no—
451C22×C4—1581no—
452C22×C4—1581no—
453C22×C4C2×C22⋊D7911yescharacteristic
454C22×C4C2×C22⋊D7911yescharacteristic
455C22×C4C2×C22⋊D7911yescharacteristic
456C22×C4C2×C22⋊D7911yescharacteristic
457C22×C4C2×C22⋊D7911yescharacteristic
458C22×C4C2×C22⋊D7911yescharacteristic
459C22×C4C23×D7911yescharacteristic
460SD16—1588no—
461C2×C8—792no—
462C2×C8—792no—
463C2×C8—792no—
464C2×C8—792no—
465C2×C8—792no—
466C2×C8—792no—
467C2×C8—1581no—
468C2×C8—1581no—
469C2×C8—1581no—
470C2×C8—1581no—
471C2×C8—1581no—
472C2×C8—1581no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—81no—
479C4⋊C4—81no—
480C4⋊C4—792no—
481C4⋊C4—6321no—
482C4⋊C4—6321no—
483C4⋊C4—1581no—
484C4⋊C4—1581no—
485C4⋊C4—1581no—
486C4⋊C4—1581no—
487C4⋊C4—1581no—
488C4⋊C4—1584no—
489C4⋊C4C2×C4×D7912yes—
490C22⋊C4—24no—
491C22⋊C4—81no—
492C22⋊C4—81no—
493C22⋊C4—81no—
494C22⋊C4—81no—
495C42—21no—
496C42—21no—
497C42—21no—
498C42—21no—
499C42—81no—
500C42—6321no—
501C42—1584no—
502C42C2×C4×D7912yes—
503C42#1192962412yes—
504C23—22no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23C22×C22⋊D7911yescharacteristic
512Q8—3161no—
513Q8—3161no—
514Q8—1582no—
515Q8—1582no—
516D4—22no—
517D4—22no—
518D4—41no—
519D4—41no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—22no—
525C2×C4—21no—
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—21no—
536C2×C4—21no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—84no—
546C2×C4—3161no—
547C2×C4—3161no—
548C2×C4—3161no—
549C2×C4—3161no—
550C2×C4—3161no—
551C2×C4—3161no—
552C2×C4—3161no—
553C2×C4—3161no—
554C2×C4—3161no—
555C2×C4—3161no—
556C2×C4—1582no—
557C2×C4—1582no—
558C2×C4C4×C22⋊D7912yes—
559C2×C4C4×C22⋊D7912yes—
560C2×C4C22×C4×D7911yescharacteristic
561C2×C4#41×D7911yescharacteristic
562C2×C4#41×D7911yescharacteristic
563C2×C4#41×D7911yescharacteristic
564C2×C4#41×D7911yescharacteristic
565C2×C4C2×#1192962411yescharacteristic
566C8—794no—
567C8—1582no—
568C8—1582no—
569C8—1582no—
570C22—42no—
571C22—42no—
572C22—42no—
573C22—81no—
574C22—81no—
575C22—81no—
576C22—81no—
577C22C2×C4×C22⋊D7911yescharacteristic
578C22#1909910911yescharacteristic
579C22#1909910911yescharacteristic
580C22#1909936611yescharacteristic
581C22#1909937411yescharacteristic
582C22#1909937411yescharacteristic
583C22#1909937811yescharacteristic
584C4—22no—
585C4—22no—
586C4—41no—
587C4—42no—
588C4—41no—
589C4—41no—
590C4—41no—
591C4—81no—
592C4—81no—
593C4—3162no—
594C4—3162no—
595C4—6321no—
596C4—6321no—
597C4#117×D7911yescharacteristic
598C4#1909903111yescharacteristic
599C4#1909909111yescharacteristic
600C4#1909909111yescharacteristic
601C2—82no—
602C2#2376585911yescharacteristic
603C2#2377223211yescharacteristic
604C2#2377223911yescharacteristic
605C2#2377402211yescharacteristic
606C2#2377403311yescharacteristic
607C2#2377406211yescharacteristic
608C2#2377408511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D79
commutatorC2×C4×C79C23×C4
FrattiniC22×C4C23×D79
FittingC79×#2319C2
socleC23×C79C22×D4
prime radicalC22×D4×C79C23
cosocleC22×C4×C79C24
hypercenter#2319D79
hypocenterC79#21291
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ #376 ◁ #2319

Complements

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

NH ≅ G/Ntype
2. #23766052C2semidirect
5. #23764135C2semidirect
6. #23764130C2semidirect
8. #23764089C2semidirect
10. #23764075C2semidirect
11. #23763298C2semidirect
12. C4×#14579084C2semidirect
14. #23763087C2semidirect
18. #19098663C4semidirect
320. C79#21291semidirect

Maximal subgroups

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

subgroupindex
C2×#190986632
#237660522
#237642802
#237642532
#237641352
#237641302
#237641002
#237640892
#237640862
#237640752
#237632982
C4×#145790842
C4×#145790822
#237630872
C79×#23192
#2129179