Finite Group Databasebeta

← #34329259

Subgroups — #34329259

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×#19098870C211yesmaximal, characteristic, complemented
2C2×C4×#11929611C211yesmaximal, characteristic
3#23768600C211yesmaximal, characteristic
4#23764818C211yesmaximal, characteristic, complemented
5#23764808C211yesmaximal, characteristic, complemented
6#23764715C211yesmaximal, characteristic
7#23764715C211yesmaximal, characteristic
8#23764364C211yesmaximal, characteristic, complemented
9#23764168C211yesmaximal, characteristic, complemented
10#23764163C211yesmaximal, characteristic, complemented
11#23764119C211yesmaximal, characteristic, complemented
12#23764027C211yesmaximal, characteristic
13#23764020C211yesmaximal, characteristic
14#23763407C211yesmaximal, characteristic
15C79×#2356C211yesmaximal, characteristic, complemented
16C22×#11929611C2211yescharacteristic
17C2×#14579153C2211yescharacteristic
18C2×C4×D316C2211yescharacteristic
19#19098870—24no—
20C4×#11929611—24no—
21C2×#14579094C2211yescharacteristic
22C2×#14579092C2211yescharacteristic
23C2×#14579092C2211yescharacteristic
24C2×C4⋊(C79⋊C8)C2211yescharacteristic
25C2×C4⋊(C79⋊C8)C2211yescharacteristic
26C2×C4⋊(C79⋊C8)C2211yescharacteristic
27C2×#14579085C2211yescharacteristic
28C2×#14579085C2211yescharacteristic
29C2×#14579085C2211yescharacteristic
30C2×#14579081C2211yescharacteristic
31C2×#14579081C2211yescharacteristic
32C2×#14579081C2211yescharacteristic
33C2×C4×C79⋊C8C2211yescharacteristic
34#19098485—21no—
35#19098485—21no—
36#19098465C2211yescharacteristic
37#19098465C2211yescharacteristic
38#19098437—21no—
39#19098437—21no—
40#19098433C2211yescharacteristic
41#19098429C2211yescharacteristic
42#19098325C2211yescharacteristic
43#19098325C2211yescharacteristic
44#19098325C2211yescharacteristic
45#19098325C2211yescharacteristic
46#19098325C2211yescharacteristic
47#19098325C2211yescharacteristic
48#19098318C2211yescharacteristic
49#19098318C2211yescharacteristic
50C2×C4×Q8×C79C2211yescharacteristic
51#391×C79C2211yescharacteristic
52#391×C79C2211yescharacteristic
53#387×C79—21no—
54#387×C79—21no—
55#383×C79—21no—
56#382×C79C2211yescharacteristic
57C4×C4⋊C4×C79C2211yescharacteristic
58C4×C4⋊C4×C79C2211yescharacteristic
59C4×C4⋊C4×C79C2211yescharacteristic
60#376×C79—21no—
61C22×D316C2311yescharacteristic
62C22×C4×D79—21no—
63C2×#11929611—22no—
64C2×#11929611—22no—
65C2×#11929611—22no—
66C22×C79⋊C8C2311yescharacteristic
67C22×C79⋊C8C2311yescharacteristic
68C22×C79⋊C8C2311yescharacteristic
69C22×C79⋊C8C2311yescharacteristic
70#14579153—22no—
71#14579153—22no—
72C4×D316—22no—
73C4×D316—22no—
74C2×C4⋊Dic79—21no—
75C2×C4⋊Dic79—21no—
76C2×C4⋊Dic79C2311yescharacteristic
77C2×C4⋊Dic79C2311yescharacteristic
78C2×C4⋊Dic79C2311yescharacteristic
79C2×Dic79⋊C4—21no—
80C2×Dic79⋊C4—21no—
81C2×(C2×D79)⋊C4—21no—
82C2×(C2×D79)⋊C4—21no—
83C2×(C2×D79)⋊C4—21no—
84C2×(C2×D79)⋊C4—21no—
85C2×(C2×D79)⋊C4—21no—
86#14579094—22no—
87#14579092—22no—
88#14579092—22no—
89C4⋊(C79⋊C8)—22no—
90C4⋊(C79⋊C8)—22no—
91C4⋊(C79⋊C8)—22no—
92#14579085—22no—
93#14579085—22no—
94#14579085—22no—
95#14579081—22no—
96#14579081—22no—
97#14579081—22no—
98C4×C79⋊C8—22no—
99C79⋊#95—21no—
100C79⋊#95—21no—
101C22×Q8×C79C2311yescharacteristic
102C4×Q8×C79—22no—
103C4×Q8×C79D414yes—
104C2×C4⋊C4×C79—21no—
105C2×C4⋊C4×C79D411yescharacteristic
106C2×C4⋊C4×C79D411yescharacteristic
107C2×C4⋊C4×C79C2311yescharacteristic
108C2×C4⋊C4×C79C2311yescharacteristic
109C2×C4⋊C4×C79C2311yescharacteristic
110C2×C42×C79—21no—
111C2×C42×C79—21no—
112C2×C42×C79—21no—
113C2×C42×C79C2311yescharacteristic
114C2×C42×C79C2311yescharacteristic
115C2×C42×C79C2311yescharacteristic
116#95×C79—21no—
117#95×C79—21no—
118#95×C79—21no—
119#95×C79—21no—
120#95×C79—21no—
121#95×C79—21no—
122#95×C79—21no—
123#95×C79—21no—
124#95×C79D411yescharacteristic
125#95×C79D411yescharacteristic
126C23×D79—21no—
127C2×D316—21no—
128C2×D316—21no—
129C2×D316—21no—
130C2×D316—21no—
131C2×D316—21no—
132C2×D316#4112yes—
133C22×Dic79—21no—
134C22×Dic79—21no—
135C22×Dic79—21no—
136C2×C4×D79—42no—
137C2×C4×D79—81no—
138C2×C4×D79—81no—
139#11929611—28no—
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—21no—
149C2×C79⋊C8—21no—
150C2×C79⋊C8—21no—
151C2×C79⋊C8#4112yes—
152C4⋊Dic79—21no—
153C4⋊Dic79—21no—
154C4⋊Dic79—21no—
155C4⋊Dic79—21no—
156C4⋊Dic79—21no—
157C4⋊Dic79—21no—
158C4⋊Dic79—81no—
159C4⋊Dic79—81no—
160Dic79⋊C4—42no—
161Dic79⋊C4—42no—
162(C2×D79)⋊C4—42no—
163(C2×D79)⋊C4—42no—
164(C2×D79)⋊C4—42no—
165(C2×D79)⋊C4—81no—
166(C2×D79)⋊C4—81no—
167C2×Q8×C79—21no—
168C2×Q8×C79—21no—
169C2×Q8×C79—21no—
170C2×Q8×C79—21no—
171C2×Q8×C79—21no—
172C2×Q8×C79C2×D412yes—
173C22×C4×C79—21no—
174C22×C4×C79—21no—
175C22×C4×C79—21no—
176C22×C4×C79—21no—
177C22×C4×C79C2×D411yescharacteristic
178C22×C4×C79C2×D411yescharacteristic
179C22×C4×C79C2×D411yescharacteristic
180C22×C4×C79C2×D411yescharacteristic
181C22×C4×C79C2×D411yescharacteristic
182C22×C4×C79C2×D411yescharacteristic
183C22×C4×C79C2411yescharacteristic
184C4⋊C4×C79—24no—
185C4⋊C4×C79—22no—
186C4⋊C4×C79—21no—
187C4⋊C4×C79—21no—
188C4⋊C4×C79—21no—
189C4⋊C4×C79—21no—
190C4⋊C4×C79—21no—
191C4⋊C4×C79—41no—
192C4⋊C4×C79C2×D412yes—
193C42×C79—24no—
194C42×C79—21no—
195C42×C79—21no—
196C42×C79—21no—
197C42×C79—21no—
198C42×C79—42no—
199C42×C79—42no—
200C42×C79C2×D412yes—
201C42×C79#4112yes—
202C23×C79C22×D411yescharacteristic
203C22×D79—22no—
204C22×D79—41no—
205C22×D79—41no—
206C22×D79—41no—
207C22×D79—41no—
208C22×D79—41no—
209C22×D79—41no—
210Q8×C79—22no—
211Q8×C79—22no—
212Q8×C79—41no—
213Q8×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—22no—
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—21no—
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—41no—
239C2×C4×C79—41no—
240C2×C4×C79—41no—
241C2×C4×C79#12112yes—
242C2×C4×C79#12112yes—
243C2×C4×C79#13512yes—
244C2×C4×C79C22×D411yescharacteristic
245C2×C4×C79C2×#4111yescharacteristic
246C2×C4×C79C2×#4111yescharacteristic
247C2×C4×C79C2×#4111yescharacteristic
248C2×C4×C792−1+411yescharacteristic
249C2×C4×C792−1+411yescharacteristic
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—
259D316—22no—
260D316—22no—
261D316—41no—
262D316—41no—
263C4×D79—84no—
264C79⋊C8—22no—
265C79⋊C8—41no—
266C79⋊C8—41no—
267C79⋊C8—41no—
268C22×C79C2×#12111yescharacteristic
269C22×C79#54711yescharacteristic
270C22×C79#54811yescharacteristic
271C22×C79C2×#13511yescharacteristic
272C22×C79#57511yescharacteristic
273C22×C79#57711yescharacteristic
274C22×C79#57711yescharacteristic
275C2×D79—42no—
276C2×D79—42no—
277C2×D79—42no—
278C2×D79—81no—
279C2×D79—81no—
280C2×D79—81no—
281C2×D79—81no—
282C4×C79—22no—
283C4×C79—22no—
284C4×C79—22no—
285C4×C79—41no—
286C4×C79—41no—
287C4×C79—41no—
288C4×C79—42no—
289C4×C79—42no—
290C4×C79—81no—
291C4×C79—81no—
292C4×C79#52511yescharacteristic
293C4×C79#53611yescharacteristic
294C4×C79#55211yescharacteristic
295C4×C79#55611yescharacteristic
296Dic79—81no—
297Dic79—81no—
298Dic79—81no—
299#24685—791nomaximal, Sylow
300C2×C79#241511yescharacteristic
301C2×C79#303511yescharacteristic
302C2×C79#304311yescharacteristic
303C2×C79#333711yescharacteristic
304C2×C79#335111yescharacteristic
305C2×C79#336011yescharacteristic
306C2×C79#337611yescharacteristic
307D79—82no—
308C2×#479—791no—
309C2×C4×SD16—791no—
310#2566—791no—
311#2356D7911yescharacteristic, complemented
312#2074—791no—
313#2072—791no—
314#2055—791no—
315#2055—791no—
316#1991—791no—
317#1949—791no—
318#1948—791no—
319#1939—791no—
320#1926—791no—
321#1925—791no—
322#1804—791no—
323C79#2468511yescharacteristic, complemented, Sylow
324C22×SD16—791no—
325C2×#125—791no—
326C2×C4×Q8C2×D7911yescharacteristic
327C2×C4×D4—791no—
328#479—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#396—1581no—
344#396—1581no—
345#391C2×D7911yescharacteristic
346#391C2×D7911yescharacteristic
347#390—791no—
348#390—791no—
349#387—21no—
350#387—21no—
351#385—1581no—
352#385—1581no—
353#384—791no—
354#383—21no—
355#382—791no—
356#382C2×D7911yescharacteristic
357C4×C4⋊C4C2×D7911yescharacteristic
358C4×C4⋊C4C2×D7911yescharacteristic
359C4×C4⋊C4C2×D7911yescharacteristic
360#376—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×Q8C22×D7911yescharacteristic
370C22×D4—791no—
371C23×C4—1581no—
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—22no—
382C4×Q8D31614yes—
383C4×D4—1582no—
384C4×D4—1582no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—791no—
387C2×C4⋊C4—791no—
388C2×C4⋊C4—791no—
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—1581no—
399C2×C22⋊C4—1581no—
400C2×C22⋊C4—1581no—
401C2×C22⋊C4—1581no—
402C2×C22⋊C4—1581no—
403C2×C42—21no—
404C2×C42—21no—
405C2×C42—21no—
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—21no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95—1581no—
431#95—1581no—
432#95C22⋊D7911yescharacteristic
433#95C22⋊D7911yescharacteristic
434C24—1581no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8C2×D31612yes—
441C2×D4—792no—
442C2×D4—1581no—
443C2×D4—1581no—
444C2×D4—1581no—
445C2×D4—1581no—
446C2×D4—1581no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—3162no—
452C22×C4—6321no—
453C22×C4—6321no—
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—24no—
479C4⋊C4—22no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—41no—
485C4⋊C4—3162no—
486C4⋊C4—3162no—
487C4⋊C4—6321no—
488C4⋊C4—6321no—
489C4⋊C4—1581no—
490C4⋊C4—1581no—
491C4⋊C4—1581no—
492C4⋊C4—1581no—
493C4⋊C4—1581no—
494C4⋊C4—1581no—
495C4⋊C4C2×D31612yes—
496C22⋊C4—3162no—
497C22⋊C4—3162no—
498C22⋊C4—3162no—
499C22⋊C4—6321no—
500C22⋊C4—6321no—
501C42—21no—
502C42—21no—
503C42—21no—
504C42—21no—
505C42—24no—
506C42—42no—
507C42—42no—
508C42C2×D31612yes—
509C42#1192962412yes—
510C23—3161no—
511C23—3161no—
512C23—3161no—
513C23—3161no—
514C23—3161no—
515C23—3161no—
516C23—1582no—
517C23C22×C22⋊D7911yescharacteristic
518Q8—22no—
519Q8—22no—
520Q8—41no—
521Q8—41no—
522D4—3161no—
523D4—3161no—
524D4—1582no—
525D4—1582no—
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—22no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
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—6324no—
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—3162no—
577C22—3162no—
578C22—3162no—
579C22—6321no—
580C22—6321no—
581C22—6321no—
582C22—6321no—
583C22C2×#1457913511yescharacteristic
584C22#1909921211yescharacteristic
585C22#1909922011yescharacteristic
586C22C2×#1457918111yescharacteristic
587C22#1909936111yescharacteristic
588C22#1909937111yescharacteristic
589C22#1909937111yescharacteristic
590C4—22no—
591C4—22no—
592C4—22no—
593C4—41no—
594C4—42no—
595C4—42no—
596C4—41no—
597C4—41no—
598C4—81no—
599C4—81no—
600C4—6321no—
601C4—6321no—
602C4—6321no—
603C4#1909907511yescharacteristic
604C4#1909913911yescharacteristic
605C4#1909925211yescharacteristic
606C4#1909928111yescharacteristic
607C2—6322no—
608C2#2376682311yescharacteristic
609C2#2377285511yescharacteristic
610C2#2377292111yescharacteristic
611C2#2377577911yescharacteristic
612C2#2377596011yescharacteristic
613C2#2377604511yescharacteristic
614C2#2377622111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D79
commutator, cosocleC22×C4×C79C24
FrattiniC22×C4C23×D79
FittingC79×#2356C2
socleC23×C79C22×D4
prime radicalC22×D316C23
hypercenter#2356D79
hypocenterC79#24685
LCSG ▷ C22×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2356

Complements

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

NH ≅ G/Ntype
1. C2×#19098870C2semidirect
4. #23764818C2semidirect
5. #23764808C2semidirect
8. #23764364C2semidirect
9. #23764168C2semidirect
10. #23764163C2semidirect
11. #23764119C2semidirect
15. C79×#2356C2semidirect
311. #2356D79semidirect
323. C79#24685semidirect

Maximal subgroups

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

subgroupindex
C2×#190988702
C2×C4×#119296112
#237686002
#237648182
#237648082
#237647152
#237643642
#237641682
#237641632
#237641192
#237640272
#237640202
#237634072
C79×#23562
#2468579