Finite Group Databasebeta

← #34258335

Subgroups — #34258335

Order 20224.

648 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23773443C211yesmaximal, characteristic
2#23772549C211yesmaximal, characteristic, complemented
3#23772423C211yesmaximal, characteristic, complemented
4#23762267C211yesmaximal, characteristic, complemented
5#23762260C211yesmaximal, characteristic, complemented
6#23762239C211yesmaximal, characteristic, complemented
7#23762232C211yesmaximal, characteristic, complemented
8#23762221C211yesmaximal, characteristic, complemented
9#23762215C211yesmaximal, characteristic, complemented
10#23762197C211yesmaximal, characteristic, complemented
11#23762192C211yesmaximal, characteristic, complemented
12#23762188C211yesmaximal, characteristic, complemented
13#23761826C211yesmaximal, characteristic, complemented
14#23761700C211yesmaximal, characteristic, complemented
15C79×#1482C211yesmaximal, characteristic, complemented
16C2×C4×D316C2211yescharacteristic
17#19098896C411yescharacteristic
18#19098879C411yescharacteristic
19#19098860C411yescharacteristic
20#19098860C411yescharacteristic
21#19098775C411yescharacteristic
22#19098775C411yescharacteristic
23#19098713C411yescharacteristic
24#19098696C411yescharacteristic
25#19098694C2211yescharacteristic, complemented
26Q8×C79⋊C8C2211yescharacteristic, complemented
27C4×#11929611C2211yescharacteristic
28C4×#11929611C2211yescharacteristic
29C4×#11929609C2211yescharacteristic
30C4×#11929609C2211yescharacteristic
31#19098641—21no—
32#19098641C2211yescharacteristic, complemented
33#19098635—21no—
34C8×D316—21no—
35C8×D316—21no—
36D4×C79⋊C8C2211yescharacteristic, complemented
37#19098628C2211yescharacteristic
38#19098628C2211yescharacteristic
39#19098628C2211yescharacteristic
40#19098628C2211yescharacteristic
41#19098624—21no—
42#19098616C2211yescharacteristic
43#19098616C2211yescharacteristic
44#19098590—21no—
45#19098587C2211yescharacteristic
46C22⋊C8×D79—21no—
47C22⋊C8×D79—21no—
48#19098315C2211yescharacteristic, complemented
49#19098315C2211yescharacteristic, complemented
50#19098313C2211yescharacteristic, complemented
51#19098313C2211yescharacteristic, complemented
52#19098292C2211yescharacteristic
53#19098292C2211yescharacteristic
54#19098292C2211yescharacteristic
55#19098292C2211yescharacteristic
56#19098285C2211yescharacteristic, complemented
57#19098285C2211yescharacteristic, complemented
58#19098284C2211yescharacteristic, complemented
59C8×C79⋊C8C2211yescharacteristic, complemented
60#529×C79C2211yescharacteristic
61#431×C79C2211yescharacteristic
62#431×C79C2211yescharacteristic
63Q8⋊C8×C79C2211yescharacteristic, complemented
64Q8⋊C8×C79C2211yescharacteristic, complemented
65D4⋊C8×C79C2211yescharacteristic, complemented
66D4⋊C8×C79C2211yescharacteristic, complemented
67C22×D316C2×C411yescharacteristic
68C22×C4×D79—21no—
69C2×#11929611C2×C411yescharacteristic
70C2×#11929611C2×C411yescharacteristic
71C2×#11929609C2×C411yescharacteristic
72C2×#11929609C2×C411yescharacteristic
73C2×#11929608—21no—
74C2×#11929608—21no—
75C22×C79⋊C8—21no—
76C2×C8×D79—21no—
77C2×C8×D79—21no—
78C2×C8×D79—21no—
79C2×C8×D79—21no—
80C4×D316—21no—
81C4×D316—21no—
82C4×D316C2×C411yescharacteristic
83C4×D316C2×C411yescharacteristic
84C4×D316C2311yescharacteristic
85C4×D316C2311yescharacteristic
86C2×C4⋊Dic79C2×C411yescharacteristic
87C2×(C2×D79)⋊C4—21no—
88#14579094C2×C411yescharacteristic
89#14579094C2×C411yescharacteristic
90#14579092C2×C411yescharacteristic
91#14579092C2×C411yescharacteristic
92C4⋊(C79⋊C8)—21no—
93C4⋊(C79⋊C8)—21no—
94C4⋊(C79⋊C8)—21no—
95C4⋊(C79⋊C8)C2×C411yescharacteristic
96C4⋊(C79⋊C8)C2×C411yescharacteristic
97C4⋊(C79⋊C8)D411yescharacteristic
98C4⋊(C79⋊C8)D411yescharacteristic
99C4⋊(C79⋊C8)C2311yescharacteristic
100C4⋊(C79⋊C8)C2311yescharacteristic
101#14579085C2×C411yescharacteristic
102#14579085C2×C411yescharacteristic
103#14579082C2×C411yescharacteristic
104#14579082C2×C411yescharacteristic
105#14579081C2×C411yescharacteristic
106#14579081C2×C411yescharacteristic
107#14579081C2×C411yescharacteristic
108#14579081C2×C411yescharacteristic
109C22⋊(C79⋊C8)—21no—
110C22⋊(C79⋊C8)—21no—
111C22⋊(C79⋊C8)C2×C411yescharacteristic
112C22⋊(C79⋊C8)C2×C411yescharacteristic
113C22⋊(C79⋊C8)D411yescharacteristic
114C22⋊(C79⋊C8)D411yescharacteristic
115(C2×D79)⋊C8—21no—
116(C2×D79)⋊C8—21no—
117(C2×D79)⋊C8—21no—
118(C2×D79)⋊C8—21no—
119#14579072—21no—
120C4×C79⋊C8—21no—
121C4×C79⋊C8C2311yescharacteristic
122C4×C79⋊C8C2311yescharacteristic
123C4×C79⋊C8C2311yescharacteristic
124C4×C79⋊C8C2311yescharacteristic
125#126×C79—21no—
126#125×C79C2×C411yescharacteristic
127#124×C79C2×C411yescharacteristic
128#123×C79—21no—
129C22⋊Q8×C79C2×C411yescharacteristic
130#121×C79C2×C411yescharacteristic
131C4×Q8×C79C2311yescharacteristic
132C4×D4×C79—21no—
133C4×D4×C79C2311yescharacteristic
134#117×C79—21no—
135C2×C42×C79C2311yescharacteristic
136C4⋊C8×C79—21no—
137C4⋊C8×C79C2311yescharacteristic
138C4⋊C8×C79C2311yescharacteristic
139C22⋊C8×C79—21no—
140C22⋊C8×C79—21no—
141C4×C8×C79—21no—
142C4×C8×C79C2311yescharacteristic
143C4×C8×C79C2311yescharacteristic
144C23×D79—21no—
145C2×D316—22no—
146C2×D316—22no—
147C2×D316—21no—
148C2×D316C22×C411yescharacteristic
149C2×D316C22×C411yescharacteristic
150C22×Dic79—21no—
151C2×C4×D79—21no—
152C2×C4×D79—21no—
153C2×C4×D79—21no—
154C2×C4×D79—21no—
155C2×C4×D79—81no—
156C2×C4×D79—81no—
157#11929611—22no—
158#11929611—22no—
159#11929609—22no—
160#11929609—22no—
161#11929608—81no—
162#11929608—81no—
163C2×C79⋊C8—21no—
164C2×C79⋊C8—21no—
165C2×C79⋊C8—81no—
166C2×C79⋊C8C22×C411yescharacteristic
167C2×C79⋊C8C22×C411yescharacteristic
168C2×C79⋊C8C22×C411yescharacteristic
169C2×C79⋊C8C22×C411yescharacteristic
170C2×C79⋊C8C2×D411yescharacteristic
171C2×C79⋊C8C2×D411yescharacteristic
172C2×C79⋊C8C2×D411yescharacteristic
173C2×C79⋊C8C2×D411yescharacteristic
174C8×D79—81no—
175C8×D79—81no—
176C8×D79—81no—
177C8×D79—81no—
178C4⋊Dic79—21no—
179C4⋊Dic79C22×C411yescharacteristic
180C4⋊Dic79C22×C411yescharacteristic
181(C2×D79)⋊C4—21no—
182(C2×D79)⋊C4—21no—
183(C2×D79)⋊C4—21no—
184(C2×D79)⋊C4—21no—
185C2×Q8×C79C22×C411yescharacteristic
186C2×D4×C79—21no—
187C2×D4×C79C22×C411yescharacteristic
188C22×C4×C79—21no—
189C22×C4×C79C22×C411yescharacteristic
190C22×C4×C79C2×D411yescharacteristic
191C22×C4×C79#4111yescharacteristic
192C2×C8×C79—21no—
193C2×C8×C79—21no—
194C2×C8×C79—21no—
195C2×C8×C79—21no—
196C4⋊C4×C79—21no—
197C4⋊C4×C79—21no—
198C4⋊C4×C79—21no—
199C4⋊C4×C79—21no—
200C4⋊C4×C79C22×C411yescharacteristic
201C4⋊C4×C79C22×C411yescharacteristic
202C22⋊C4×C79—21no—
203C22⋊C4×C79—21no—
204C22⋊C4×C79—21no—
205C22⋊C4×C79—21no—
206C22⋊C4×C79—21no—
207C42×C79—21no—
208C42×C79C22×C411yescharacteristic
209C42×C79C2×D411yescharacteristic
210C42×C79#4111yescharacteristic
211C42×C79C2411yescharacteristic
212C23×C79—21no—
213C23×C79C4×D411yescharacteristic
214C22×D79—21no—
215C22×D79—21no—
216C22×D79—24no—
217C22×D79—81no—
218C22×D79—81no—
219Q8×C79—21no—
220Q8×C79—21no—
221D4×C79—21no—
222D4×C79—21no—
223D4×C79—81no—
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×C79C4×D411yescharacteristic
235C2×C4×C79C4×D411yescharacteristic
236C2×C4×C79C4×D411yescharacteristic
237C2×C4×C79C23×C411yescharacteristic
238C2×C4×C79C22×D411yescharacteristic
239C2×C4×C79C2×#4111yescharacteristic
240C2×Dic79—21no—
241C2×Dic79—21no—
242C2×Dic79—81no—
243D316—24no—
244D316—21no—
245D316—21no—
246D316#13112yes—
247D316#13112yes—
248C4×D79—41no—
249C4×D79—41no—
250C4×D79—41no—
251C4×D79—41no—
252C4×D79—81no—
253C4×D79—81no—
254C8×C79—41no—
255C8×C79—41no—
256C8×C79—41no—
257C8×C79—41no—
258C79⋊C8—21no—
259C79⋊C8—21no—
260C79⋊C8—21no—
261C79⋊C8—21no—
262C79⋊C8—21no—
263C79⋊C8—21no—
264C79⋊C8—21no—
265C79⋊C8—21no—
266C79⋊C8—41no—
267C79⋊C8—41no—
268C22×C79—21no—
269C22×C79—21no—
270C22×C79—21no—
271C22×C79—41no—
272C22×C79—41no—
273C22×C79—41no—
274C22×C79C2×C4×D411yescharacteristic
275C2×D79—22no—
276C2×D79—22no—
277C2×D79—41no—
278C2×D79—41no—
279C2×D79—41no—
280C2×D79—41no—
281C2×D79—84no—
282C4×C79—21no—
283C4×C79—21no—
284C4×C79—21no—
285C4×C79—21no—
286C4×C79—41no—
287C4×C79—41no—
288C4×C79—41no—
289C4×C79C2×#13111yescharacteristic
290C4×C79C2×#13111yescharacteristic
291C4×C79#57611yescharacteristic
292C4×C79#57711yescharacteristic
293Dic79—41no—
294Dic79—41no—
295#17918—791nomaximal, Sylow
296C2×C79—41no—
297C2×C79—81no—
298C2×C79#292911yescharacteristic
299C2×C79#294611yescharacteristic
300C2×C79#295711yescharacteristic
301D79—42no—
302D79—42no—
303#3105—791no—
304#2993—791no—
305#2972—791no—
306#1586—791no—
307#1585—791no—
308#1582—791no—
309#1581—791no—
310#1580—791no—
311SD16⋊C8—791no—
312C8×SD16—791no—
313C8×D8—791no—
314#1574—791no—
315#1486—791no—
316#1482D7911yescharacteristic, complemented
317#1454—791no—
318C79#1791811yescharacteristic, complemented, Sylow
319#529C2×D7911yescharacteristic
320C2×C4×D4—791no—
321#484—791no—
322#481—791no—
323#478—791no—
324#478—791no—
325#463—791no—
326#463—791no—
327#450—791no—
328#447—791no—
329#446—791no—
330C8×Q8—791no—
331C4×SD16—791no—
332C4×SD16—791no—
333C4×D8—791no—
334C4×D8—791no—
335#436—791no—
336#436—1581no—
337#435—1581no—
338C8×D4—791no—
339C8×D4—791no—
340C8×D4—791no—
341C8×D4—791no—
342C8×D4—791no—
343C8×D4—1581no—
344C8×D4—1581no—
345#433—1581no—
346#431—791no—
347#431—791no—
348#431C2×D7911yescharacteristic
349#431C2×D7911yescharacteristic
350#424—1581no—
351#423—791no—
352C2×C22⋊C8—1581no—
353C2×C22⋊C8—1581no—
354#335—791no—
355#335—791no—
356#334—791no—
357#334—791no—
358Q8⋊C8C2×D7911yescharacteristic, complemented
359Q8⋊C8C2×D7911yescharacteristic, complemented
360D4⋊C8—791no—
361D4⋊C8—791no—
362D4⋊C8—791no—
363D4⋊C8—791no—
364D4⋊C8C2×D7911yescharacteristic, complemented
365D4⋊C8C2×D7911yescharacteristic, complemented
366#322—791no—
367#322—791no—
368#322—791no—
369C82—791no—
370C22×D4—791no—
371C23×C4—1581no—
372C2×SD16—791no—
373C2×SD16—791no—
374C2×D8—791no—
375C2×D8—791no—
376C2×M16—1581no—
377C2×M16—1581no—
378C22×C8—1581no—
379C22×C8—1581no—
380C22×C8—1581no—
381C22×C8—1581no—
382C22×C8—1581no—
383#126—21no—
384#125C4×D7911yescharacteristic
385#124C4×D7911yescharacteristic
386#123—21no—
387C22⋊Q8C4×D7911yescharacteristic
388#121C4×D7911yescharacteristic
389C4×Q8C22×D7911yescharacteristic
390C4×D4—21no—
391C4×D4—791no—
392C4×D4—791no—
393C4×D4—791no—
394C4×D4—791no—
395C4×D4—1581no—
396C4×D4—1581no—
397C4×D4C22×D7911yescharacteristic
398#117—21no—
399C2×C4⋊C4—791no—
400C2×C22⋊C4—1581no—
401C2×C42C22×D7911yescharacteristic
402#107—791no—
403#107—791no—
404#106—791no—
405#106—791no—
406C4⋊C8—21no—
407C4⋊C8—791no—
408C4⋊C8—791no—
409C4⋊C8—791no—
410C4⋊C8—791no—
411C4⋊C8—791no—
412C4⋊C8—791no—
413C4⋊C8—1581no—
414C4⋊C8—1581no—
415C4⋊C8—1581no—
416C4⋊C8C22×D7911yescharacteristic
417C4⋊C8C22×D7911yescharacteristic
418#103—791no—
419#103—791no—
420#102—791no—
421#102—791no—
422#102—791no—
423#102—791no—
424#102—791no—
425#102—791no—
426C22⋊C8—21no—
427C22⋊C8—21no—
428C22⋊C8—791no—
429C22⋊C8—791no—
430C22⋊C8—791no—
431C22⋊C8—791no—
432C22⋊C8—1581no—
433C22⋊C8—1581no—
434C22⋊C8—1581no—
435C22⋊C8—1581no—
436C22⋊C8—1581no—
437C22⋊C8—1581no—
438#97—1581no—
439C4×C8—21no—
440C4×C8—791no—
441C4×C8—791no—
442C4×C8—791no—
443C4×C8—791no—
444C4×C8—1581no—
445C4×C8C22×D7911yescharacteristic
446C4×C8C22×D7911yescharacteristic
447C24—1581no—
448C2×Q8C2×C4×D7911yescharacteristic
449C2×D4—21no—
450C2×D4—791no—
451C2×D4—791no—
452C2×D4—1582no—
453C2×D4—1582no—
454C2×D4—1581no—
455C2×D4C2×C4×D7911yescharacteristic
456C22×C4—21no—
457C22×C4—6321no—
458C22×C4—6321no—
459C22×C4—1581no—
460C22×C4—1581no—
461C22×C4—1581no—
462C22×C4—1581no—
463C22×C4—1581no—
464C22×C4C2×C4×D7911yescharacteristic
465C22×C4D4×D7911yescharacteristic
466C22×C4#1192962311yescharacteristic
467SD16—1582no—
468SD16—1582no—
469D8—1582no—
470D8—1582no—
471M16—6321no—
472M16—6321no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—791no—
478C2×C8—791no—
479C2×C8—791no—
480C2×C8—791no—
481C2×C8—791no—
482C2×C8—791no—
483C2×C8—791no—
484C2×C8—791no—
485C2×C8—6321no—
486C2×C8—6321no—
487C2×C8—6321no—
488C2×C8—6321no—
489C2×C8—6321no—
490C2×C8—1581no—
491C2×C8—1581no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—791no—
497C4⋊C4—791no—
498C4⋊C4—1581no—
499C4⋊C4C2×C4×D7911yescharacteristic
500C4⋊C4C2×C4×D7911yescharacteristic
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—21no—
506C22⋊C4—1581no—
507C22⋊C4—1581no—
508C22⋊C4—1581no—
509C22⋊C4—1581no—
510C42—21no—
511C42C2×C4×D7911yescharacteristic
512C42D4×D7911yescharacteristic
513C42#1192962311yescharacteristic
514C42C23×D7911yescharacteristic
515C23—21no—
516C23—6321no—
517C23—6321no—
518C23—1584no—
519C23—1581no—
520C23—1581no—
521C23(C22⋊D79)⋊C411yescharacteristic
522Q8—21no—
523Q8—21no—
524D4—21no—
525D4—21no—
526D4—81no—
527D4—792no—
528D4—792no—
529D4—1584no—
530D4—1581no—
531D4—1581no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—3161no—
543C2×C4—3161no—
544C2×C4—3161no—
545C2×C4—3161no—
546C2×C4—6321no—
547C2×C4—6321no—
548C2×C4—6321no—
549C2×C4—1581no—
550C2×C4—1581no—
551C2×C4(C22⋊D79)⋊C411yescharacteristic
552C2×C4(C22⋊D79)⋊C411yescharacteristic
553C2×C4(C22⋊D79)⋊C411yescharacteristic
554C2×C4C22×C4×D7911yescharacteristic
555C2×C4C2×D4×D7911yescharacteristic
556C2×C4C2×#1192962311yescharacteristic
557C8—41no—
558C8—41no—
559C8—41no—
560C8—41no—
561C8—3161no—
562C8—3161no—
563C8—1581no—
564C8—1581no—
565C8—1581no—
566C8—1581no—
567C8—1581no—
568C8—1581no—
569C8—1581no—
570C8—1581no—
571C22—21no—
572C22—21no—
573C22—21no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—3161no—
578C22—3161no—
579C22—3161no—
580C22—3161no—
581C22—6324no—
582C22—1582no—
583C22—1582no—
584C22C2×(C22⋊D79)⋊C411yescharacteristic
585C4—21no—
586C4—21no—
587C4—21no—
588C4—21no—
589C4—41no—
590C4—41no—
591C4—41no—
592C4—3161no—
593C4—3161no—
594C4#131×D7911yescharacteristic
595C4#131×D7911yescharacteristic
596C4#1909936511yescharacteristic
597C4#1909937011yescharacteristic
598C2—41no—
599C2—81no—
600C2—3162no—
601C2—3162no—
602C2#2377209711yescharacteristic
603C2#2377223511yescharacteristic
604C2#2377231311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D79
commutatorC2×C4×C79C23×C4
FrattiniC42C23×D79
FittingC79×#1482C2
socleC22×C79C2×C4×D4
prime radical#19098696C4
cosocleC42×C79C24
hypercenter#1482D79
hypocenterC79#17918
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1482

Complements

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

NH ≅ G/Ntype
2. #23772549C2semidirect
3. #23772423C2semidirect
4. #23762267C2semidirect
5. #23762260C2semidirect
6. #23762239C2semidirect
7. #23762232C2semidirect
8. #23762221C2semidirect
9. #23762215C2semidirect
10. #23762197C2semidirect
11. #23762192C2semidirect
12. #23762188C2semidirect
13. #23761826C2semidirect
14. #23761700C2semidirect
15. C79×#1482C2semidirect
25. #19098694C22semidirect
26. Q8×C79⋊C8C22semidirect
32. #19098641C22semidirect
36. D4×C79⋊C8C22semidirect
48. #19098315C22semidirect
49. #19098315C22semidirect
50. #19098313C22semidirect
51. #19098313C22semidirect
56. #19098285C22semidirect
57. #19098285C22semidirect
58. #19098284C22semidirect
59. C8×C79⋊C8C22semidirect
63. Q8⋊C8×C79C22semidirect
64. Q8⋊C8×C79C22semidirect
65. D4⋊C8×C79C22semidirect
66. D4⋊C8×C79C22semidirect
316. #1482D79semidirect
318. C79#17918semidirect
358. Q8⋊C8C2×D79semidirect
359. Q8⋊C8C2×D79semidirect
364. D4⋊C8C2×D79semidirect
365. D4⋊C8C2×D79semidirect

Maximal subgroups

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

subgroupindex
#237734432
#237725492
#237724232
#237622672
#237622602
#237622392
#237622322
#237622212
#237622152
#237621972
#237621922
#237621882
#237618262
#237617002
C79×#14822
#1791879