Finite Group Databasebeta

← C2×#23775816 #35166756

Subgroups — C2×#23775816 #35166756

Order 20224.

1918 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099286C211yesmaximal, characteristic, complemented
2C2×#19099279C211yesmaximal, characteristic
3#23775816C2116yesmaximal, direct product factor
4C2×#19098959C211yesmaximal, characteristic, complemented
5C2×#19098903C212yesmaximal, complemented
6C2×#19098890C212yesmaximal, complemented
7C2×#19098844C211yesmaximal, characteristic, complemented
8C2×#19098795C212yesmaximal, complemented
9C2×C4×#11929611C211yesmaximal, characteristic, complemented
10C2×#19098628C211yesmaximal, characteristic, complemented
11C2×#19098600C212yesmaximal, complemented
12C2×#477×C79C211yesmaximal, characteristic, complemented
13C22×#11929611C2211yescharacteristic
14C22×C8×D79C2212yes—
15#19099286—24no—
16#19099286C2218yescomplemented
17#19099279—24no—
18#19099279C2218yes—
19C2×#14579161C2211yescharacteristic
20C2×#14579156—22no—
21C2×#14579150—22no—
22C2×#14579149—21no—
23C2×#14579137C2212yes—
24C2×#14579136—21no—
25C2×#14579136C2212yes—
26C2×C4×Dic158—21no—
27C2×C4×D316C2211yescharacteristic
28C2×C4×D316C2211yescharacteristic
29C2×#14579119—21no—
30C2×#14579119C2212yes—
31C2×#14579119C2212yes—
32#19098959C2218yescomplemented
33#19098903C22116yescomplemented
34#19098890C22116yescomplemented
35#19098844C2218yescomplemented
36#19098795C22116yescomplemented
37C4×#11929611C2218yescomplemented
38#19098628C2218yescomplemented
39#19098600C22116yescomplemented
40C2×#14579095C2212yes—
41C2×#14579092C2212yes—
42C2×#14579092C2211yescharacteristic
43C2×#14579092C2212yes—
44C2×#14579085C2211yescharacteristic
45C2×#14579083C2212yes—
46C2×#14579081C2211yescharacteristic
47C2×(C2×D79)⋊C8C2212yes—
48C2×C4×C79⋊C8C2211yescharacteristic
49C2×C4⋊Q8×C79C2211yescharacteristic
50C2×C4×Q8×C79C2211yescharacteristic
51#477×C79C2218yescomplemented
52C2×#107×C79C2212yes—
53C2×C4⋊C8×C79C2211yescharacteristic
54C2×#103×C79C2212yes—
55C22×Dic158—21no—
56C22×D316—22no—
57C22×D316D411yescharacteristic
58C22×D316C2311yescharacteristic
59C22×C4×D79—21no—
60C22×C4×D79C2312yes—
61C2×#11929611—24no—
62C2×#11929611C2314yes—
63C22×C79⋊C8C2311yescharacteristic
64C22×C79⋊C8C2311yescharacteristic
65C2×C8×D79—28no—
66C2×C8×D79C2318yes—
67#14579161—22no—
68#14579161C2314yes—
69#14579156—216no—
70#14579150—216no—
71#14579149—28no—
72#14579137—24no—
73#14579137C2318yes—
74#14579136—28no—
75#14579136—24no—
76#14579136C2318yes—
77C4×Dic158—28no—
78C4×D316—22no—
79C4×D316D414yes—
80C4×D316C2314yes—
81C4×D316C2314yes—
82#14579119—24no—
83#14579119—24no—
84#14579119—28no—
85#14579119C2318yes—
86#14579119C2318yes—
87C2×C4⋊Dic79—21no—
88C2×C4⋊Dic79D411yescharacteristic
89C2×C4⋊Dic79C2311yescharacteristic
90C2×C4⋊Dic79C2312yes—
91C2×Dic79⋊C4—22no—
92C2×(C2×D79)⋊C4—21no—
93C2×(C2×D79)⋊C4—22no—
94C2×(C2×D79)⋊C4—22no—
95C2×(C2×D79)⋊C4—22no—
96C2×(C2×D79)⋊C4—22no—
97C2×(C2×D79)⋊C4D412yes—
98C2×C4×Dic79—22no—
99C2×C4×Dic79—22no—
100#14579095C2318yes—
101#14579092C2318yes—
102#14579092C2314yes—
103#14579092C2318yes—
104#14579085C2314yes—
105#14579083C2318yes—
106#14579081C2314yes—
107(C2×D79)⋊C8C2318yes—
108C4×C79⋊C8C2314yes—
109C22×Q8×C79—21no—
110C22×Q8×C79C2311yescharacteristic
111C22×C8×C79C2312yes—
112C4⋊Q8×C79—22no—
113C4⋊Q8×C79C2314yes—
114C4×Q8×C79—22no—
115C4×Q8×C79C2314yes—
116C2×C4⋊C4×C79—21no—
117C2×C4⋊C4×C79—21no—
118C2×C4⋊C4×C79C2311yescharacteristic
119C2×C4⋊C4×C79C2312yes—
120C2×C42×C79—21no—
121C2×C42×C79C2311yescharacteristic
122#107×C79C2318yes—
123C4⋊C8×C79C2314yes—
124#103×C79C2318yes—
125C23×D79—21no—
126C23×D79C2×D412yes—
127C2×Dic158—24no—
128C2×Dic158—44no—
129C2×D316—28no—
130C2×D316—24no—
131C2×D316—21no—
132C2×D316—22no—
133C2×D316—22no—
134C2×D316—84no—
135C2×D316C2×D414yes—
136C2×D316C2412yes—
137C22×Dic79—22no—
138C22×Dic79—21no—
139C22×Dic79C2×D412yes—
140C2×C4×D79—24no—
141C2×C4×D79—24no—
142C2×C4×D79—24no—
143C2×C4×D79—44no—
144C2×C4×D79C2×D414yes—
145C2×C4×D79C2414yes—
146#11929611—28no—
147C2×C79⋊C8—22no—
148C2×C79⋊C8#4114yes—
149C2×C79⋊C8C2412yes—
150C2×C79⋊C8C2412yes—
151C8×D79—216no—
152C4⋊Dic79—24no—
153C4⋊Dic79—21no—
154C4⋊Dic79—22no—
155C4⋊Dic79C2×D414yes—
156C4⋊Dic79C2414yes—
157C4⋊Dic79C2412yes—
158Dic79⋊C4—28no—
159(C2×D79)⋊C4—28no—
160(C2×D79)⋊C4—28no—
161(C2×D79)⋊C4—28no—
162(C2×D79)⋊C4—28no—
163(C2×D79)⋊C4—24no—
164(C2×D79)⋊C4C2×D418yes—
165C4×Dic79—28no—
166C4×Dic79—28no—
167C2×Q8×C79—21no—
168C2×Q8×C79—24no—
169C2×Q8×C79—22no—
170C2×Q8×C79—22no—
171C2×Q8×C79—82no—
172C2×Q8×C79C2412yes—
173C22×C4×C79—21no—
174C22×C4×C79—21no—
175C22×C4×C79—22no—
176C22×C4×C79C2×D411yescharacteristic
177C22×C4×C79C2×D411yescharacteristic
178C22×C4×C79C2411yescharacteristic
179C2×C8×C79—24no—
180C2×C8×C79C2414yes—
181C4⋊C4×C79—24no—
182C4⋊C4×C79—24no—
183C4⋊C4×C79—21no—
184C4⋊C4×C79—22no—
185C4⋊C4×C79C2414yes—
186C4⋊C4×C79C2412yes—
187C42×C79—24no—
188C42×C79C2×D412yes—
189C42×C79C2412yes—
190C23×C79C22×D411yescharacteristic
191C22×D79—24no—
192C22×D79—24no—
193C22×D79—24no—
194C22×D79—22no—
195C22×D79—42no—
196C22×D79—42no—
197C22×D79—42no—
198C22×D79C22×D414yes—
199Q8×C79—22no—
200Q8×C79—22no—
201Q8×C79—42no—
202Q8×C79—84no—
203C2×C4×C79—22no—
204C2×C4×C79—22no—
205C2×C4×C79—24no—
206C2×C4×C79—22no—
207C2×C4×C79—42no—
208C2×C4×C79—44no—
209C2×C4×C79—42no—
210C2×C4×C79#13514yes—
211C2×C4×C79C22×D412yes—
212C2×C4×C79C22×D411yescharacteristic
213C2×C4×C79C22×D412yes—
214C2×C4×C79C2×#4112yes—
215C2×C4×C792−1+412yes—
216C2×C4×C79C2511yescharacteristic
217C2×Dic79—24no—
218C2×Dic79—22no—
219C2×Dic79—24no—
220C2×Dic79—42no—
221C2×Dic79—44no—
222C2×Dic79C22×D414yes—
223D316—28no—
224D316—22no—
225D316—22no—
226D316—42no—
227D316—88no—
228C4×D79—28no—
229C4×D79—24no—
230C4×D79—24no—
231C4×D79—48no—
232Dic158—48no—
233C8×C79—24no—
234C79⋊C8—22no—
235C79⋊C8C2×#4114yes—
236C22×C79#54712yes—
237C22×C79C2×#13512yes—
238C22×C79#57712yes—
239C22×C79C23×D411yescharacteristic
240C2×D79—24no—
241C2×D79—24no—
242C2×D79—24no—
243C2×D79—48no—
244C2×D79—42no—
245C2×D79—42no—
246C2×D79—42no—
247C2×D79—84no—
248C4×C79—22no—
249C4×C79—42no—
250C4×C79—42no—
251C4×C79—44no—
252C4×C79#54712yes—
253C4×C79C2×#13514yes—
254C4×C79C22×#4111yescharacteristic
255C4×C79C2×2−1+411yescharacteristic
256Dic79—24no—
257Dic79—44no—
258Dic79—42no—
259C2×#3340—791nomaximal, Sylow
260C2×C79#334014yescomplemented
261C2×C79C2×#54711yescharacteristic
262C2×C79C22×#13511yescharacteristic
263C2×C79C2×#57711yescharacteristic
264D79—44no—
265D79—82no—
266C2×#556—791no—
267C2×#555—791no—
268#3340—7916no—
269C2×#498—791no—
270C2×#485—792no—
271C2×#482—792no—
272C2×#477D7911yescharacteristic, complemented
273C2×#474—791no—
274C2×#465—792no—
275C2×C4×SD16—791no—
276C2×C8×D4—791no—
277C2×#427—792no—
278C79C2×#334011yescharacteristic, complemented, Sylow
279C22×SD16—791no—
280C23×C8—792no—
281#556—798no—
282#556—1584no—
283#555—798no—
284#555—1584no—
285C2×C4⋊Q8—791no—
286C2×C4⋊Q8C2×D7911yescharacteristic
287C2×#126—1582no—
288C2×#124—1581no—
289C2×#124—1582no—
290C2×C22⋊Q8—792no—
291C2×#121—792no—
292C2×#121—1581no—
293C2×C4×Q8—1581no—
294C2×C4×Q8C2×D7911yescharacteristic
295C2×C4×D4—791no—
296C2×C4×D4—791no—
297C2×#117—792no—
298C2×#117—792no—
299C2×#117—1581no—
300#498—798no—
301#485—7916no—
302#482—7916no—
303#477C2×D7918yescomplemented
304#474—798no—
305#465—7916no—
306C4×SD16—798no—
307C8×D4—798no—
308#427—7916no—
309C2×#107—792no—
310C2×#107C2×D7912yes—
311C2×#106—792no—
312C2×#106—792no—
313C2×#106—791no—
314C2×C4⋊C8C2×D7911yescharacteristic
315C2×#103—791no—
316C2×#103C2×D7912yes—
317C2×#102—792no—
318C2×#102—791no—
319C2×C22⋊C8—792no—
320C2×C4×C8—791no—
321C22×Q8—21no—
322C22×Q8—1581no—
323C22×Q8C22×D7911yescharacteristic
324C22×D4—791no—
325C22×D4—791no—
326C22×D4—1582no—
327C23×C4—792no—
328C23×C4—1581no—
329C2×SD16—794no—
330C2×SD16—1584no—
331C22×C8—791no—
332C22×C8—791no—
333C22×C8—798no—
334C22×C8—1588no—
335C22×C8C22×D7912yes—
336C4⋊Q8—22no—
337C4⋊Q8—794no—
338C4⋊Q8—1582no—
339C4⋊Q8C22×D7914yes—
340#126—15816no—
341#124—1588no—
342#124—15816no—
343C22⋊Q8—798no—
344C22⋊Q8—1584no—
345#121—798no—
346#121—1584no—
347#121—1588no—
348C4×Q8—22no—
349C4×Q8—1588no—
350C4×Q8C22×D7914yes—
351C4×D4—794no—
352C4×D4—794no—
353C4×D4—794no—
354C4×D4—1582no—
355#117—798no—
356#117—798no—
357#117—1588no—
358#117—1584no—
359#117—1584no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—791no—
363C2×C4⋊C4—791no—
364C2×C4⋊C4—792no—
365C2×C4⋊C4—1582no—
366C2×C4⋊C4—1581no—
367C2×C4⋊C4C22×D7911yescharacteristic
368C2×C4⋊C4C22×D7912yes—
369C2×C22⋊C4—792no—
370C2×C22⋊C4—1582no—
371C2×C22⋊C4—1582no—
372C2×C22⋊C4—1582no—
373C2×C22⋊C4—1582no—
374C2×C22⋊C4—1581no—
375C2×C42—21no—
376C2×C42—1582no—
377C2×C42—1582no—
378C2×C42C22×D7911yescharacteristic
379#107—798no—
380#107C22×D7918yes—
381#106—794no—
382#106—798no—
383#106—798no—
384C4⋊C8C22×D7914yes—
385#103—794no—
386#103C22×D7918yes—
387#102—798no—
388#102—794no—
389C22⋊C8—798no—
390C4×C8—794no—
391C24—792no—
392C24—1581no—
393C2×Q8—21no—
394C2×Q8—24no—
395C2×Q8—22no—
396C2×Q8—22no—
397C2×Q8—82no—
398C2×Q8—3164no—
399C2×Q8—1584no—
400C2×Q8C23×D7912yes—
401C2×D4—792no—
402C2×D4—794no—
403C2×D4—6324no—
404C2×D4—1588no—
405C2×D4—1582no—
406C2×D4—1582no—
407C2×D4—1584no—
408C2×D4—1581no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—22no—
412C22×C4—3164no—
413C22×C4—792no—
414C22×C4—794no—
415C22×C4—794no—
416C22×C4—1581no—
417C22×C4—1582no—
418C22×C4—1584no—
419C22×C4—1584no—
420C22×C4—1584no—
421C22×C4D4×D7911yescharacteristic
422C22×C4D4×D7911yescharacteristic
423C22×C4C23×D7911yescharacteristic
424SD16—1588no—
425C2×C8—24no—
426C2×C8—794no—
427C2×C8—792no—
428C2×C8—792no—
429C2×C8—15816no—
430C2×C8—1582no—
431C2×C8C23×D7914yes—
432C4⋊C4—24no—
433C4⋊C4—24no—
434C4⋊C4—21no—
435C4⋊C4—22no—
436C4⋊C4—794no—
437C4⋊C4—794no—
438C4⋊C4—792no—
439C4⋊C4—1588no—
440C4⋊C4—1581no—
441C4⋊C4—1582no—
442C4⋊C4—1584no—
443C4⋊C4C23×D7912yes—
444C4⋊C4C23×D7914yes—
445C22⋊C4—798no—
446C22⋊C4—1588no—
447C22⋊C4—1588no—
448C22⋊C4—1588no—
449C22⋊C4—1588no—
450C22⋊C4—1584no—
451C42—24no—
452C42—1588no—
453C42—1588no—
454C42D4×D7912yes—
455C42C23×D7912yes—
456C23—3162no—
457C23—3162no—
458C23—3162no—
459C23—794no—
460C23—1582no—
461C23—1584no—
462C23—1584no—
463C23—1584no—
464C23C2×D4×D7911yescharacteristic
465Q8—22no—
466Q8—22no—
467Q8—42no—
468Q8—84no—
469Q8—3168no—
470D4—3162no—
471D4—6328no—
472D4—1582no—
473D4—1588no—
474D4—1582no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—24no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—44no—
482C2×C4—3162no—
483C2×C4—3164no—
484C2×C4—3168no—
485C2×C4—794no—
486C2×C4—1582no—
487C2×C4—1584no—
488C2×C4—1584no—
489C2×C4—1584no—
490C2×C4—1588no—
491C2×C4—1584no—
492C2×C4#1457918414yes—
493C2×C4C2×D4×D7912yes—
494C2×C4C2×D4×D7911yescharacteristic
495C2×C4C2×D4×D7912yes—
496C2×C4#41×D7912yes—
497C2×C4#1457920912yes—
498C2×C4C24×D7911yescharacteristic
499C8—24no—
500C8—794no—
501C8—1582no—
502C22—3168no—
503C22—3162no—
504C22—3162no—
505C22—3162no—
506C22—6324no—
507C22—1584no—
508C22—1584no—
509C22—1584no—
510C22#1909921512yes—
511C22C2×#1457918412yes—
512C22#1909937312yes—
513C22C22×D4×D7911yescharacteristic
514C4—22no—
515C4—42no—
516C4—44no—
517C4—42no—
518C4—3162no—
519C4—3164no—
520C4—1584no—
521C4#1909921512yes—
522C4C2×#1457918414yes—
523C4C2×#41×D7911yescharacteristic
524C4C2×#1457920911yescharacteristic
525C2—3164no—
526C2—6322no—
527C2#2377581614yesdirect product factor
528C2C2×#1909921511yescharacteristic
529C2C22×#1457918411yescharacteristic
530C2C2×#1909937311yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#477×C79C2
socleC23×C79C22×D4
prime radicalC2×#19099279C2
hypercenterC2×#477D79
hypocenterC79C2×#3340
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
1. C2×#19099286C2semidirect
3. #23775816C2direct (N × H)
4. C2×#19098959C2semidirect
5. C2×#19098903C2semidirect
6. C2×#19098890C2semidirect
7. C2×#19098844C2semidirect
8. C2×#19098795C2semidirect
9. C2×C4×#11929611C2semidirect
10. C2×#19098628C2semidirect
11. C2×#19098600C2semidirect
12. C2×#477×C79C2semidirect
16. #19099286C22semidirect
32. #19098959C22semidirect
33. #19098903C22semidirect
34. #19098890C22semidirect
35. #19098844C22semidirect
36. #19098795C22semidirect
37. C4×#11929611C22semidirect
38. #19098628C22semidirect
39. #19098600C22semidirect
51. #477×C79C22semidirect
260. C2×C79#3340semidirect
272. C2×#477D79semidirect
278. C79C2×#3340semidirect
303. #477C2×D79semidirect
527. C2#23775816direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190992862
C2×#190992792
#237758162
C2×#190989592
C2×#190989032
C2×#190988902
C2×#190988442
C2×#190987952
C2×C4×#119296112
C2×#190986282
C2×#190986002
C2×#477×C792
C2×#334079