Finite Group Databasebeta

← #34259627

Subgroups — #34259627

Order 20224.

606 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23773431C211yesmaximal, characteristic
2#23772489C211yesmaximal, characteristic, complemented
3#23772466C211yesmaximal, characteristic
4#23762305C211yesmaximal, characteristic, complemented
5#23762287C211yesmaximal, characteristic, complemented
6#23762275C211yesmaximal, characteristic, complemented
7#23762260C211yesmaximal, characteristic, complemented
8#23762240C211yesmaximal, characteristic, complemented
9#23762239C211yesmaximal, characteristic, complemented
10#23762215C211yesmaximal, characteristic, complemented
11#23762197C211yesmaximal, characteristic, complemented
12#23762178C211yesmaximal, characteristic, complemented
13#23761870C211yesmaximal, characteristic
14#23761700C211yesmaximal, characteristic, complemented
15C79×#1479C211yesmaximal, characteristic, complemented
16#19099113C2211yescharacteristic
17#19098881C411yescharacteristic
18#19098881C411yescharacteristic
19#19098848C411yescharacteristic
20#19098848C411yescharacteristic
21#19098763C411yescharacteristic
22#19098763C411yescharacteristic
23#19098702C411yescharacteristic
24#19098702C411yescharacteristic
25#19098694—21no—
26#19098694—21no—
27#19098694C2211yescharacteristic
28#19098694C2211yescharacteristic
29Q8×C79⋊C8C2211yescharacteristic
30Q8×C79⋊C8C2211yescharacteristic
31C4×#11929611C2211yescharacteristic
32C4×#11929611C2211yescharacteristic
33C4×#11929611C2211yescharacteristic
34C4×#11929611C2211yescharacteristic
35#19098642—21no—
36#19098640C2211yescharacteristic
37#19098640C2211yescharacteristic
38C8×D316—21no—
39#19098628C2211yescharacteristic
40#19098628C2211yescharacteristic
41#19098620—21no—
42#19098620C2211yescharacteristic
43#19098616—21no—
44#19098616C2211yescharacteristic
45#19098616C2211yescharacteristic
46#19098528—21no—
47#19098528—21no—
48#19098315C2211yescharacteristic
49#19098315C2211yescharacteristic
50#19098313C2211yescharacteristic
51#19098313C2211yescharacteristic
52#19098292C2211yescharacteristic
53#19098292C2211yescharacteristic
54#19098292C2211yescharacteristic
55#19098292C2211yescharacteristic
56#19098285C2211yescharacteristic
57#19098285C2211yescharacteristic
58#19098284C2211yescharacteristic
59C8×C79⋊C8C2211yescharacteristic
60C2×C4×Q8×C79C2211yescharacteristic
61#431×C79C2211yescharacteristic
62#431×C79C2211yescharacteristic
63Q8⋊C8×C79C2211yescharacteristic
64Q8⋊C8×C79C2211yescharacteristic
65Q8⋊C8×C79C2211yescharacteristic
66Q8⋊C8×C79C2211yescharacteristic
67C2×#11929624—21no—
68C2×#11929611C2×C411yescharacteristic
69C2×#11929611C2×C411yescharacteristic
70C2×#11929611C2×C411yescharacteristic
71C2×#11929611C2×C411yescharacteristic
72C2×#11929607—21no—
73C2×#11929607—21no—
74C2×C8×D79—21no—
75C2×C8×D79—21no—
76#14579161C2×C411yescharacteristic
77#14579158C2×C411yescharacteristic
78#14579149—21no—
79#14579135—21no—
80#14579135C2×C411yescharacteristic
81#14579135C2×C411yescharacteristic
82C4×D316—21no—
83C4×D316C2311yescharacteristic
84C4×D316C2311yescharacteristic
85#14579092C2×C411yescharacteristic
86#14579092C2×C411yescharacteristic
87#14579092C2×C411yescharacteristic
88#14579092C2×C411yescharacteristic
89C4⋊(C79⋊C8)—21no—
90C4⋊(C79⋊C8)—21no—
91C4⋊(C79⋊C8)—21no—
92C4⋊(C79⋊C8)—21no—
93C4⋊(C79⋊C8)C2×C411yescharacteristic
94C4⋊(C79⋊C8)C2×C411yescharacteristic
95C4⋊(C79⋊C8)D411yescharacteristic
96C4⋊(C79⋊C8)D411yescharacteristic
97C4⋊(C79⋊C8)C2311yescharacteristic
98C4⋊(C79⋊C8)C2311yescharacteristic
99#14579085C2×C411yescharacteristic
100#14579085C2×C411yescharacteristic
101#14579085C2×C411yescharacteristic
102#14579085C2×C411yescharacteristic
103#14579081C2×C411yescharacteristic
104#14579081C2×C411yescharacteristic
105#14579081C2×C411yescharacteristic
106#14579081C2×C411yescharacteristic
107C22⋊(C79⋊C8)—21no—
108C22⋊(C79⋊C8)C2×C411yescharacteristic
109C22⋊(C79⋊C8)C2×C411yescharacteristic
110C22⋊(C79⋊C8)D411yescharacteristic
111C22⋊(C79⋊C8)D411yescharacteristic
112(C2×D79)⋊C8—21no—
113(C2×D79)⋊C8—21no—
114(C2×D79)⋊C8—21no—
115(C2×D79)⋊C8—21no—
116#14579072—21no—
117#14579072—21no—
118#14579072—21no—
119C4×C79⋊C8—21no—
120C4×C79⋊C8—21no—
121C4×C79⋊C8C2311yescharacteristic
122C4×C79⋊C8C2311yescharacteristic
123C4×C79⋊C8C2311yescharacteristic
124C4×C79⋊C8C2311yescharacteristic
125C22×Q8×C79C2×C411yescharacteristic
126C4×Q8×C79—21no—
127C4×Q8×C79—21no—
128C4×Q8×C79C2×C411yescharacteristic
129C4×Q8×C79C2×C411yescharacteristic
130C4×Q8×C79C2311yescharacteristic
131C4×Q8×C79C2311yescharacteristic
132C2×C4⋊C4×C79—21no—
133C2×C4⋊C4×C79C2×C411yescharacteristic
134C2×C42×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
144#11929624—81no—
145#11929624—81no—
146C2×Dic158—21no—
147C2×D316—21no—
148C2×D316—21no—
149C2×D316C22×C411yescharacteristic
150C2×D316C22×C411yescharacteristic
151C2×C22⋊D79—21no—
152C2×C22⋊D79—21no—
153C2×C4×D79—21no—
154C2×C4×D79—21no—
155#11929611—22no—
156#11929611—22no—
157#11929611—41no—
158#11929611—41no—
159#11929607—81no—
160#11929607—81no—
161C2×C79⋊C8—21no—
162C2×C79⋊C8—21no—
163C2×C79⋊C8C22×C411yescharacteristic
164C2×C79⋊C8C22×C411yescharacteristic
165C2×C79⋊C8C22×C411yescharacteristic
166C2×C79⋊C8C22×C411yescharacteristic
167C2×C79⋊C8C2×D411yescharacteristic
168C2×C79⋊C8C2×D411yescharacteristic
169C2×C79⋊C8C2×D411yescharacteristic
170C2×C79⋊C8C2×D411yescharacteristic
171C8×D79—81no—
172C8×D79—81no—
173C4⋊Dic79—21no—
174C4⋊Dic79C22×C411yescharacteristic
175C4⋊Dic79C22×C411yescharacteristic
176(C2×D79)⋊C4—21no—
177(C2×D79)⋊C4—21no—
178(C2×D79)⋊C4—21no—
179(C2×D79)⋊C4—21no—
180C2×Q8×C79—21no—
181C2×Q8×C79—22no—
182C2×Q8×C79—41no—
183C2×Q8×C79C22×C411yescharacteristic
184C2×Q8×C79C22×C411yescharacteristic
185C22×C4×C79—21no—
186C22×C4×C79—21no—
187C22×C4×C79C22×C411yescharacteristic
188C22×C4×C79C2×D411yescharacteristic
189C22×C4×C79#4111yescharacteristic
190C2×C8×C79—21no—
191C2×C8×C79—21no—
192C2×C8×C79—21no—
193C2×C8×C79—21no—
194C4⋊C4×C79—21no—
195C4⋊C4×C79—21no—
196C4⋊C4×C79—21no—
197C4⋊C4×C79—21no—
198C4⋊C4×C79—21no—
199C4⋊C4×C79C22×C411yescharacteristic
200C4⋊C4×C79C22×C411yescharacteristic
201C42×C79—21no—
202C42×C79—21no—
203C42×C79—21no—
204C42×C79—21no—
205C42×C79C22×C411yescharacteristic
206C42×C79C2×D411yescharacteristic
207C42×C79#4111yescharacteristic
208C42×C79C2411yescharacteristic
209C23×C79C4×D411yescharacteristic
210C22×D79—21no—
211C22×D79—21no—
212Q8×C79—21no—
213Q8×C79—21no—
214Q8×C79—21no—
215Q8×C79—42no—
216Q8×C79#13112yes—
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—41no—
226C2×C4×C79—42no—
227C2×C4×C79—42no—
228C2×C4×C79C4×D411yescharacteristic
229C2×C4×C79C4×D411yescharacteristic
230C2×C4×C79C4×D411yescharacteristic
231C2×C4×C79C23×C411yescharacteristic
232C2×C4×C79C22×D411yescharacteristic
233C2×C4×C79C2×#4111yescharacteristic
234C22⋊D79—81no—
235C22⋊D79—81no—
236C2×Dic79—21no—
237C2×Dic79—21no—
238D316—21no—
239D316—21no—
240D316—21no—
241D316—21no—
242D316—42no—
243D316—81no—
244C4×D79—41no—
245C4×D79—41no—
246C4×D79—41no—
247C4×D79—41no—
248Dic158—81no—
249C8×C79—41no—
250C8×C79—41no—
251C8×C79—41no—
252C8×C79—41no—
253C79⋊C8—21no—
254C79⋊C8—21no—
255C79⋊C8—21no—
256C79⋊C8—21no—
257C79⋊C8—21no—
258C79⋊C8—21no—
259C79⋊C8—21no—
260C79⋊C8—21no—
261C79⋊C8—41no—
262C79⋊C8—41no—
263C22×C79—21no—
264C22×C79—21no—
265C22×C79—21no—
266C22×C79C2×C4×D411yescharacteristic
267C2×D79—41no—
268C2×D79—41no—
269C2×D79—41no—
270C2×D79—41no—
271C2×D79—41no—
272C2×D79—41no—
273C4×C79—21no—
274C4×C79—22no—
275C4×C79—21no—
276C4×C79—21no—
277C4×C79—21no—
278C4×C79—41no—
279C4×C79—41no—
280C4×C79—41no—
281C4×C79C2×#13111yescharacteristic
282C4×C79#56811yescharacteristic
283C4×C79#57711yescharacteristic
284C4×C79#57711yescharacteristic
285Dic79—41no—
286Dic79—41no—
287#18030—791nomaximal, Sylow
288C2×C79—41no—
289C2×C79#293311yescharacteristic
290C2×C79#294911yescharacteristic
291C2×C79#295511yescharacteristic
292D79—81no—
293D79—81no—
294#3103—791no—
295#2984—791no—
296#2979—791no—
297#1592—791no—
298#1590—791no—
299#1588—791no—
300#1585—791no—
301#1583—791no—
302#1582—791no—
303SD16⋊C8—791no—
304C8×SD16—791no—
305#1572—791no—
306#1496—791no—
307#1479D7911yescharacteristic, complemented
308#1454—791no—
309C79#1803011yescharacteristic, complemented, Sylow
310#532—791no—
311C2×C4×Q8C2×D7911yescharacteristic
312#481—791no—
313#481—791no—
314#475—791no—
315#475—791no—
316#460—791no—
317#460—791no—
318#448—791no—
319#448—791no—
320#446—791no—
321#446—791no—
322#446—1581no—
323#446—1581no—
324C8×Q8—791no—
325C8×Q8—791no—
326C4×SD16—791no—
327C4×SD16—791no—
328C4×SD16—791no—
329C4×SD16—791no—
330#436—791no—
331#436—791no—
332#436—1581no—
333C8×D4—791no—
334C8×D4—791no—
335C8×D4—1581no—
336#432—791no—
337#432—1581no—
338#431—791no—
339#431—791no—
340#431—1581no—
341#431C2×D7911yescharacteristic
342#431C2×D7911yescharacteristic
343#408—1581no—
344#408—1581no—
345#335—791no—
346#335—791no—
347#334—791no—
348#334—791no—
349Q8⋊C8C2×D7911yescharacteristic
350Q8⋊C8C2×D7911yescharacteristic
351Q8⋊C8C2×D7911yescharacteristic
352Q8⋊C8C2×D7911yescharacteristic
353D4⋊C8—791no—
354D4⋊C8—791no—
355D4⋊C8—791no—
356D4⋊C8—791no—
357#322—791no—
358#322—791no—
359#322—791no—
360C82—791no—
361C2×#41—1581no—
362C22×Q8C4×D7911yescharacteristic
363C2×SD16—791no—
364C2×SD16—791no—
365C2×SD16—791no—
366C2×SD16—791no—
367C2×M16—1581no—
368C2×M16—1581no—
369C22×C8—1581no—
370C22×C8—1581no—
371C4⋊Q8—791no—
372#127—791no—
373#124—1581no—
374#121—791no—
375#121—791no—
376#121—1581no—
377C4×Q8—21no—
378C4×Q8—21no—
379C4×Q8C4×D7911yescharacteristic
380C4×Q8C4×D7911yescharacteristic
381C4×Q8C22×D7911yescharacteristic
382C4×Q8C22×D7911yescharacteristic
383C4×D4—791no—
384C4×D4—791no—
385C4×D4—1581no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4C4×D7911yescharacteristic
388C2×C42—21no—
389C2×C42C22×D7911yescharacteristic
390#106—791no—
391#106—791no—
392#106—791no—
393#106—791no—
394C4⋊C8—21no—
395C4⋊C8—791no—
396C4⋊C8—791no—
397C4⋊C8—791no—
398C4⋊C8—791no—
399C4⋊C8—791no—
400C4⋊C8—791no—
401C4⋊C8—1581no—
402C4⋊C8—1581no—
403C4⋊C8—1581no—
404C4⋊C8—1581no—
405C4⋊C8C22×D7911yescharacteristic
406C4⋊C8C22×D7911yescharacteristic
407#103—791no—
408#103—791no—
409#103—791no—
410#103—791no—
411#102—791no—
412#102—791no—
413#102—791no—
414#102—791no—
415C22⋊C8—21no—
416C22⋊C8—21no—
417C22⋊C8—791no—
418C22⋊C8—791no—
419C22⋊C8—791no—
420C22⋊C8—791no—
421C22⋊C8—1581no—
422C22⋊C8—1581no—
423C22⋊C8—1581no—
424C22⋊C8—1581no—
425C22⋊C8—1581no—
426#97—1581no—
427#97—1581no—
428#97—1581no—
429C4×C8—21no—
430C4×C8—791no—
431C4×C8—791no—
432C4×C8—791no—
433C4×C8—791no—
434C4×C8—1581no—
435C4×C8—1581no—
436C4×C8C22×D7911yescharacteristic
437C4×C8C22×D7911yescharacteristic
438#41—6321no—
439#41—6321no—
440C2×Q8—21no—
441C2×Q8—22no—
442C2×Q8—41no—
443C2×Q8—1581no—
444C2×Q8C2×C4×D7911yescharacteristic
445C2×Q8C2×C4×D7911yescharacteristic
446C2×D4—791no—
447C2×D4—791no—
448C2×D4—1581no—
449C2×D4—1581no—
450C2×D4—1581no—
451C2×D4—1581no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—1581no—
455C22×C4—1581no—
456C22×C4C2×C4×D7911yescharacteristic
457C22×C4D4×D7911yescharacteristic
458C22×C4#1192962311yescharacteristic
459SD16—3161no—
460SD16—3161no—
461SD16—1582no—
462SD16—1582no—
463M16—6321no—
464M16—6321no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—791no—
470C2×C8—791no—
471C2×C8—791no—
472C2×C8—791no—
473C2×C8—791no—
474C2×C8—791no—
475C2×C8—791no—
476C2×C8—791no—
477C2×C8—6321no—
478C2×C8—6321no—
479C2×C8—1581no—
480C2×C8—1581no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—791no—
487C4⋊C4—791no—
488C4⋊C4—1581no—
489C4⋊C4C2×C4×D7911yescharacteristic
490C4⋊C4C2×C4×D7911yescharacteristic
491C22⋊C4—1581no—
492C22⋊C4—1581no—
493C22⋊C4—1581no—
494C22⋊C4—1581no—
495C42—21no—
496C42—21no—
497C42—21no—
498C42—21no—
499C42C2×C4×D7911yescharacteristic
500C42D4×D7911yescharacteristic
501C42#1192962311yescharacteristic
502C42C23×D7911yescharacteristic
503C23—1581no—
504C23—1581no—
505C23(C22⋊D79)⋊C411yescharacteristic
506Q8—21no—
507Q8—21no—
508Q8—21no—
509Q8—42no—
510Q8—6321no—
511Q8#1457916712yes—
512D4—3162no—
513D4—6321no—
514D4—6321no—
515D4—6321no—
516D4—1581no—
517D4—1581no—
518D4—1581no—
519D4—1581no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—41no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—3161no—
532C2×C4—3161no—
533C2×C4—3161no—
534C2×C4—3161no—
535C2×C4—1581no—
536C2×C4—1581no—
537C2×C4(C22⋊D79)⋊C411yescharacteristic
538C2×C4(C22⋊D79)⋊C411yescharacteristic
539C2×C4(C22⋊D79)⋊C411yescharacteristic
540C2×C4C22×C4×D7911yescharacteristic
541C2×C4C2×D4×D7911yescharacteristic
542C2×C4C2×#1192962311yescharacteristic
543C8—41no—
544C8—41no—
545C8—41no—
546C8—41no—
547C8—3161no—
548C8—3161no—
549C8—1581no—
550C8—1581no—
551C8—1581no—
552C8—1581no—
553C8—1581no—
554C8—1581no—
555C8—1581no—
556C8—1581no—
557C22—21no—
558C22—21no—
559C22—21no—
560C22—3161no—
561C22—3161no—
562C22—3161no—
563C22—3161no—
564C22—3161no—
565C22—3161no—
566C22C2×(C22⋊D79)⋊C411yescharacteristic
567C4—21no—
568C4—21no—
569C4—21no—
570C4—21no—
571C4—22no—
572C4—41no—
573C4—41no—
574C4—41no—
575C4—3161no—
576C4—3161no—
577C4C2×#1457916711yescharacteristic
578C4#1909932911yescharacteristic
579C4#1909937211yescharacteristic
580C4#1909937211yescharacteristic
581C2—41no—
582C2—6321no—
583C2—6321no—
584C2#2377212111yescharacteristic
585C2#2377225511yescharacteristic
586C2#2377229911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D79
commutatorC2×C4×C79C23×C4
FrattiniC42C23×D79
FittingC79×#1479C2
socleC22×C79C2×C4×D4
prime radical#19099113C22
cosocleC42×C79C24
hypercenter#1479D79
hypocenterC79#18030
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1479

Complements

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

NH ≅ G/Ntype
2. #23772489C2semidirect
4. #23762305C2semidirect
5. #23762287C2semidirect
6. #23762275C2semidirect
7. #23762260C2semidirect
8. #23762240C2semidirect
9. #23762239C2semidirect
10. #23762215C2semidirect
11. #23762197C2semidirect
12. #23762178C2semidirect
14. #23761700C2semidirect
15. C79×#1479C2semidirect
307. #1479D79semidirect
309. C79#18030semidirect

Maximal subgroups

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

subgroupindex
#237734312
#237724892
#237724662
#237623052
#237622872
#237622752
#237622602
#237622402
#237622392
#237622152
#237621972
#237621782
#237618702
#237617002
C79×#14792
#1803079