Finite Group Databasebeta

← #34190584

Subgroups — #34190584

Order 20224.

728 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19098843C211yesmaximal, characteristic, complemented
2C2×#19098768C211yesmaximal, characteristic, complemented
3#23764360C211yesmaximal, characteristic, complemented
4C2×D4⋊(C79⋊C8)C211yesmaximal, characteristic, complemented
5C2×D4⋊(C79⋊C8)C211yesmaximal, characteristic, complemented
6#23761283C211yesmaximal, characteristic, complemented
7C79×#2537C211yesmaximal, characteristic
8C22×#11929612—21no—
9C2×#14579161C2211yescharacteristic
10#19098843—22no—
11#19098843—22no—
12#19098768—22no—
13#19098768—22no—
14C2×#14579094—21no—
15C2×C4⋊(C79⋊C8)C2211yescharacteristic
16C2×C4⋊(C79⋊C8)C2211yescharacteristic
17C2×#14579084—21no—
18C2×#14579082—21no—
19C2×C4×C79⋊C8C2211yescharacteristic
20#19098325—22no—
21D4⋊(C79⋊C8)—22no—
22D4⋊(C79⋊C8)—22no—
23C2×#121×C79—21no—
24C2×#121×C79—21no—
25C2×C4×D4×C79C2211yescharacteristic
26C2×C4×D4×C79C2211yescharacteristic
27#394×C79—22no—
28#384×C79C2211yescharacteristic
29#380×C79—21no—
30#380×C79—21no—
31C22×Dic158—21no—
32C2×#11929612—24no—
33C2×#11929612—42no—
34C2×#11929612—42no—
35C22×C79⋊C8—21no—
36C22×C79⋊C8—21no—
37C22×C79⋊C8—21no—
38#14579161—21no—
39#14579161—21no—
40#14579161—21no—
41#14579161D412yescomplemented
42C2×C4⋊Dic79—21no—
43C2×C4⋊Dic79—21no—
44#14579094—24no—
45C4⋊(C79⋊C8)—21no—
46C4⋊(C79⋊C8)—21no—
47C4⋊(C79⋊C8)D412yescomplemented
48C4⋊(C79⋊C8)D412yescomplemented
49#14579084—24no—
50#14579082—24no—
51C4×C79⋊C8—21no—
52C4×C79⋊C8—21no—
53C22×D4×C79—22no—
54C22×D4×C79D411yescharacteristic
55C22×D4×C79D411yescharacteristic
56C23×C4×C79—21no—
57C23×C4×C79—21no—
58#121×C79—42no—
59#121×C79—42no—
60#121×C79—42no—
61#121×C79—42no—
62C4×D4×C79—21no—
63C4×D4×C79—21no—
64C4×D4×C79—21no—
65C4×D4×C79—21no—
66C4×D4×C79—21no—
67C4×D4×C79—21no—
68C4×D4×C79—21no—
69C4×D4×C79—21no—
70C2×C4⋊C4×C79—21no—
71C2×C4⋊C4×C79—21no—
72C2×C4⋊C4×C79D411yescharacteristic
73C2×C4⋊C4×C79D411yescharacteristic
74C2×C4⋊C4×C79D412yes—
75C2×C22⋊C4×C79—22no—
76C2×C22⋊C4×C79—22no—
77C2×C22⋊C4×C79—21no—
78C2×C22⋊C4×C79—21no—
79C2×C42×C79C2311yescharacteristic
80#95×C79—22no—
81C2×Dic158—22no—
82C2×Dic158—41no—
83C2×Dic158—41no—
84C2×Dic158—41no—
85C2×Dic158—41no—
86C2×Dic158—41no—
87C22×Dic79—41no—
88#11929612—48no—
89C2×C79⋊C8—22no—
90C2×C79⋊C8—22no—
91C2×C79⋊C8—22no—
92C2×C79⋊C8—41no—
93C2×C79⋊C8—41no—
94C2×C79⋊C8—41no—
95C2×C79⋊C8—41no—
96C2×C79⋊C8—41no—
97C2×C79⋊C8—41no—
98C4⋊Dic79—22no—
99C4⋊Dic79—22no—
100C4⋊Dic79—41no—
101C4⋊Dic79—41no—
102C24×C79—21no—
103C24×C79—21no—
104C2×D4×C79—21no—
105C2×D4×C79—21no—
106C2×D4×C79—21no—
107C2×D4×C79—21no—
108C2×D4×C79—21no—
109C2×D4×C79—21no—
110C2×D4×C79—21no—
111C2×D4×C79—21no—
112C2×D4×C79—21no—
113C2×D4×C79—21no—
114C2×D4×C79—44no—
115C2×D4×C79—44no—
116C2×D4×C79—82no—
117C2×D4×C79D812yes—
118C2×D4×C79SD1612yescomplemented
119C22×C4×C79—21no—
120C22×C4×C79—21no—
121C22×C4×C79—22no—
122C22×C4×C79—41no—
123C22×C4×C79—41no—
124C22×C4×C79—41no—
125C22×C4×C79—41no—
126C22×C4×C79—41no—
127C22×C4×C79—41no—
128C22×C4×C79—41no—
129C22×C4×C79—41no—
130C22×C4×C79—41no—
131C22×C4×C79—41no—
132C22×C4×C79—41no—
133C22×C4×C79—41no—
134C22×C4×C79C2×D411yescharacteristic
135C22×C4×C79C2×D411yescharacteristic
136C22×C4×C79C2×D411yescharacteristic
137C4⋊C4×C79—21no—
138C4⋊C4×C79—21no—
139C4⋊C4×C79—21no—
140C4⋊C4×C79—21no—
141C4⋊C4×C79—42no—
142C4⋊C4×C79—41no—
143C4⋊C4×C79—41no—
144C4⋊C4×C79—41no—
145C4⋊C4×C79—41no—
146C22⋊C4×C79—44no—
147C22⋊C4×C79—44no—
148C22⋊C4×C79—41no—
149C22⋊C4×C79—41no—
150C22⋊C4×C79—41no—
151C22⋊C4×C79—41no—
152C42×C79C2×D411yescharacteristic
153C42×C79C2×D411yescharacteristic
154C42×C79C2×D411yescharacteristic
155C42×C79#4111yescharacteristic
156C23×C79—22no—
157C23×C79—22no—
158C23×C79—41no—
159C23×C79—41no—
160C23×C79—41no—
161C23×C79—41no—
162C23×C79—41no—
163C23×C79—41no—
164C23×C79—41no—
165C23×C79—41no—
166C23×C79—41no—
167C23×C79—41no—
168C23×C79—41no—
169C23×C79—41no—
170C23×C79#12011yescharacteristic
171D4×C79—22no—
172D4×C79—22no—
173D4×C79—22no—
174D4×C79—22no—
175D4×C79—41no—
176D4×C79—41no—
177D4×C79—41no—
178D4×C79—41no—
179D4×C79—88no—
180C2×C4×C79—21no—
181C2×C4×C79—21no—
182C2×C4×C79—41no—
183C2×C4×C79—41no—
184C2×C4×C79—41no—
185C2×C4×C79—42no—
186C2×C4×C79—41no—
187C2×C4×C79—41no—
188C2×C4×C79—42no—
189C2×C4×C79—41no—
190C2×C4×C79—42no—
191C2×C4×C79—81no—
192C2×C4×C79—81no—
193C2×C4×C79—81no—
194C2×C4×C79—81no—
195C2×C4×C79—81no—
196C2×C4×C79—81no—
197C2×C4×C79—81no—
198C2×C4×C79—81no—
199C2×C4×C79#12011yescharacteristic
200C2×C4×C79#12011yescharacteristic
201C2×C4×C79#12111yescharacteristic
202C2×C4×C79#12111yescharacteristic
203C2×C4×C79#12111yescharacteristic
204C2×C4×C79#12711yescharacteristic
205C2×C4×C79C2×D811yescharacteristic
206C2×C4×C79C2×SD1611yescharacteristic
207C2×C4×C79#13511yescharacteristic
208C2×C4×C79#13511yescharacteristic
209C2×C4×C79AGL(1,ℤ/8)11yescharacteristic
210C2×C4×C79AGL(1,ℤ/8)11yescharacteristic
211C2×C4×C79AGL(1,ℤ/8)11yescharacteristic
212C2×C4×C79#13711yescharacteristic
213C2×Dic79—42no—
214C2×Dic79—81no—
215C2×Dic79—81no—
216Dic158—42no—
217Dic158—42no—
218Dic158—81no—
219Dic158—81no—
220C79⋊C8—42no—
221C79⋊C8—42no—
222C79⋊C8—42no—
223C22×C79—42no—
224C22×C79—42no—
225C22×C79—42no—
226C22×C79—42no—
227C22×C79—42no—
228C22×C79—42no—
229C22×C79—81no—
230C22×C79—81no—
231C22×C79—81no—
232C22×C79—81no—
233C22×C79—81no—
234C22×C79—81no—
235C22×C79—81no—
236C22×C79—81no—
237C22×C79#39211yescharacteristic
238C22×C79#44711yescharacteristic
239C22×C79#44911yescharacteristic
240C22×C79#45011yescharacteristic
241C22×C79#45211yescharacteristic
242C22×C79#45511yescharacteristic
243C22×C79#45611yescharacteristic
244C4×C79—21no—
245C4×C79—21no—
246C4×C79—82no—
247C4×C79—81no—
248C4×C79—81no—
249C4×C79#44711yescharacteristic
250C4×C79#44811yescharacteristic
251C4×C79#44911yescharacteristic
252C4×C79#44911yescharacteristic
253C4×C79#46511yescharacteristic
254C4×C79#46611yescharacteristic
255C4×C79#46811yescharacteristic
256C4×C79#46911yescharacteristic
257Dic79—82no—
258#10231—791nomaximal, Sylow
259C2×C79—82no—
260C2×C79—82no—
261C2×C79#163911yescharacteristic
262C2×C79#164611yescharacteristic
263C2×C79#164711yescharacteristic
264C2×C79#165411yescharacteristic
265C2×C79#199911yescharacteristic
266C2×C79#200011yescharacteristic
267C2×C79#200711yescharacteristic
268C2×#474—791no—
269C2×#461—791no—
270#2537D7911yescharacteristic
271#1990—791no—
272C2×D4⋊C8—791no—
273C2×D4⋊C8—791no—
274#1296—791no—
275C79#1023111yescharacteristic, complemented, Sylow
276C22×SD16—1581no—
277C2×C4⋊Q8—791no—
278C2×#121—21no—
279C2×#121—21no—
280C2×C4×D4C2×D7911yescharacteristic
281C2×C4×D4C2×D7911yescharacteristic
282#474—1582no—
283#474—1582no—
284#461—1582no—
285#461—1582no—
286C2×#107—1581no—
287C2×C4⋊C8—791no—
288C2×C4⋊C8—791no—
289C2×#103—1581no—
290C2×#102—1581no—
291C2×C4×C8—791no—
292#394—22no—
293#384C2×D7911yescharacteristic
294#380—21no—
295#380—21no—
296#340—1582no—
297D4⋊C8—1582no—
298D4⋊C8—1582no—
299C22×Q8—1581no—
300C22×D4—22no—
301C22×D4C22⋊D7911yescharacteristic
302C22×D4C22⋊D7911yescharacteristic
303C23×C4—21no—
304C23×C4—21no—
305C2×SD16—3162no—
306C2×SD16—3162no—
307C2×SD16—1584no—
308C22×C8—1581no—
309C22×C8—1581no—
310C22×C8—1581no—
311C4⋊Q8—792no—
312C4⋊Q8—1581no—
313C4⋊Q8—1581no—
314C4⋊Q8—1581no—
315#121—42no—
316#121—42no—
317#121—42no—
318#121—42no—
319C4×D4—21no—
320C4×D4—21no—
321C4×D4—21no—
322C4×D4—21no—
323C4×D4—21no—
324C4×D4—21no—
325C4×D4—21no—
326C4×D4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—1581no—
330C2×C4⋊C4—1581no—
331C2×C4⋊C4C22⋊D7911yescharacteristic
332C2×C4⋊C4C22⋊D7911yescharacteristic
333C2×C4⋊C4C22⋊D7912yes—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—22no—
336C2×C22⋊C4—21no—
337C2×C22⋊C4—21no—
338C2×C42C22×D7911yescharacteristic
339#107—1584no—
340C4⋊C8—792no—
341C4⋊C8—792no—
342C4⋊C8—1581no—
343C4⋊C8—1581no—
344#103—1584no—
345#102—1584no—
346C4×C8—1581no—
347C4×C8—1581no—
348#95—22no—
349C24—21no—
350C24—21no—
351C2×Q8—3161no—
352C2×Q8—3161no—
353C2×Q8—3161no—
354C2×Q8—3161no—
355C2×Q8—3161no—
356C2×Q8—1582no—
357C2×D4—21no—
358C2×D4—21no—
359C2×D4—21no—
360C2×D4—21no—
361C2×D4—21no—
362C2×D4—21no—
363C2×D4—21no—
364C2×D4—21no—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4—44no—
368C2×D4—44no—
369C2×D4—82no—
370C2×D4#1192960912yes—
371C2×D4#1192961212yescomplemented
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—22no—
375C22×C4—41no—
376C22×C4—41no—
377C22×C4—41no—
378C22×C4—41no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—41no—
384C22×C4—41no—
385C22×C4—41no—
386C22×C4—41no—
387C22×C4—3161no—
388C22×C4C2×C22⋊D7911yescharacteristic
389C22×C4C2×C22⋊D7911yescharacteristic
390C22×C4C2×C22⋊D7911yescharacteristic
391SD16—3168no—
392C2×C8—3161no—
393C2×C8—3161no—
394C2×C8—3161no—
395C2×C8—3161no—
396C2×C8—3161no—
397C2×C8—3161no—
398C2×C8—1582no—
399C2×C8—1582no—
400C2×C8—1582no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—42no—
406C4⋊C4—41no—
407C4⋊C4—41no—
408C4⋊C4—41no—
409C4⋊C4—41no—
410C4⋊C4—3161no—
411C4⋊C4—3161no—
412C4⋊C4—1582no—
413C4⋊C4—1582no—
414C22⋊C4—44no—
415C22⋊C4—44no—
416C22⋊C4—41no—
417C22⋊C4—41no—
418C22⋊C4—41no—
419C22⋊C4—41no—
420C42D4×D7911yescharacteristic
421C42D4×D7911yescharacteristic
422C42D4×D7911yescharacteristic
423C42#1192962311yescharacteristic
424C23—22no—
425C23—22no—
426C23—41no—
427C23—41no—
428C23—41no—
429C23—41no—
430C23—41no—
431C23—41no—
432C23—41no—
433C23—41no—
434C23—41no—
435C23—41no—
436C23—41no—
437C23—41no—
438C23#1457913011yescharacteristic
439Q8—3162no—
440Q8—3162no—
441Q8—6321no—
442Q8—6321no—
443D4—22no—
444D4—22no—
445D4—22no—
446D4—22no—
447D4—41no—
448D4—41no—
449D4—41no—
450D4—41no—
451D4—88no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—41no—
455C2×C4—42no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—42no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—42no—
463C2×C4—81no—
464C2×C4—81no—
465C2×C4—81no—
466C2×C4—81no—
467C2×C4—81no—
468C2×C4—81no—
469C2×C4—81no—
470C2×C4—81no—
471C2×C4—3162no—
472C2×C4—6321no—
473C2×C4—6321no—
474C2×C4#1457912911yescharacteristic
475C2×C4#1457912911yescharacteristic
476C2×C4#1457913211yescharacteristic
477C2×C4#1457913311yescharacteristic
478C2×C4#1457913311yescharacteristic
479C2×C4#1457915711yescharacteristic
480C2×C4C2×#1192960911yescharacteristic
481C2×C4C2×#1192961211yescharacteristic
482C2×C4#1457918111yescharacteristic
483C2×C4#1457918111yescharacteristic
484C2×C4#1457918611yescharacteristic
485C2×C4#1457918711yescharacteristic
486C2×C4#1457918711yescharacteristic
487C2×C4#1457919111yescharacteristic
488C8—3162no—
489C8—3162no—
490C8—3162no—
491C22—42no—
492C22—42no—
493C22—42no—
494C22—42no—
495C22—42no—
496C22—42no—
497C22—81no—
498C22—81no—
499C22—81no—
500C22—81no—
501C22—81no—
502C22—81no—
503C22—81no—
504C22—81no—
505C22#1909847111yescharacteristic
506C22#1909869711yescharacteristic
507C22#1909870811yescharacteristic
508C22#1909871411yescharacteristic
509C22#1909872511yescharacteristic
510C22#1909874111yescharacteristic
511C22#1909874611yescharacteristic
512C4—21no—
513C4—21no—
514C4—82no—
515C4—81no—
516C4—81no—
517C4—6322no—
518C4#1909869611yescharacteristic
519C4#1909870111yescharacteristic
520C4#1909870611yescharacteristic
521C4#1909870611yescharacteristic
522C4#1909879011yescharacteristic
523C4#1909879711yescharacteristic
524C4#1909880711yescharacteristic
525C4#1909881411yescharacteristic
526C2—82no—
527C2—82no—
528C2#2376257911yescharacteristic
529C2#2376262811yescharacteristic
530C2#2376263511yescharacteristic
531C2#2376268411yescharacteristic
532C2#2376439611yescharacteristic
533C2#2376440311yescharacteristic
534C2#2376444711yescharacteristic
subgroupG/H
centerC23#14579130
commutator, cosocleC2×C42×C79C23
FrattiniC2×C42C22×D79
Fitting, prime radicalC79×#2537C2
socleC23×C79#120
hypercenter#2537D79
hypocenterC79#10231
LCSG ▷ C2×C42×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2537

Complements

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

NH ≅ G/Ntype
1. C2×#19098843C2semidirect
2. C2×#19098768C2semidirect
3. #23764360C2semidirect
4. C2×D4⋊(C79⋊C8)C2semidirect
5. C2×D4⋊(C79⋊C8)C2semidirect
6. #23761283C2semidirect
41. #14579161D4semidirect
47. C4⋊(C79⋊C8)D4semidirect
48. C4⋊(C79⋊C8)D4semidirect
118. C2×D4×C79SD16semidirect
275. C79#10231semidirect
371. C2×D4#11929612semidirect

Maximal subgroups

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

subgroupindex
C2×#190988432
C2×#190987682
#237643602
C2×D4⋊(C79⋊C8)2
#237612832
C79×#25372
#1023179